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The main camping area from the ferris wheel at the Bonnaroo Music and Arts Festival in Manchester, Tenn., on Thursday, June 7, 2018. (Photo: Shelley Mays / Tennessean.com) MANCHESTER, Tenn. - A Bonnaroo attendee was found dead Friday morning on the venue's grounds marking the 13th death at the music and arts festival in its 17-year history, officials said. The Coffee County Sheriff's Office identified the man as Michael Donivan Craddock, Jr., 32 of Mount Juliet, Tenn. Sheriff's office spokesman Lucky Knott said about 10:30 a.m., the sheriff's office responded to the festival's campground for a medical call. When deputies and investigators arrived at the scene, they found Craddock dead inside a vehicle. Sheriff Steve Graves said foul play is not suspected in the death. Graves said Craddock’s body has been sent to the medical examiner office in Nashville, for an autopsy to determine the exact cause of death. His death is the only known fatality so far at the festival, authorities said. Bonnaroo 2018 started Thursday and is scheduled to run through Sunday. Festival headliners include Eminem, the Killers, and Muse. Bonnaroo 2018 day 1: Here's what we saw in the fest’s first hours So far this year, Knott said dozens of people have been either treated or transported by ambulance to local hospitals to be treated for heat-related issues at the festival. First responders reminded festival attendees to hydrate and wear hats if possible. "The temperature is 90 with a heat index of 99," Knott said Friday afternoon. "We can't stress it enough that concert goers to drink a lot of water. Staying hydrated will save your life." Although he did not give an exact number, Bonnaroo medical director Carl Monzo said transports are "lower than the same time last year." A high of 94 topped Manchester on Friday and highs in the upper 80s and low 90s are expected during the next three days of the festival. More: Bonnaroo will now wash your clothes - for free The last death at Bonnaroo took place in June 2015 after a 47-year-old man died after collapsing in the event's main area — known as Centeroo. His death stemmed from a pre-existing cardiac issue, authorities at the time said. A year later, on June 11, 2016, festival attendee Casey J. Young, 22, of Louisville, was struck and killed by multiple vehicles outside the festival grounds on Interstate 24. According to a Davidson County autopsy report, his manner of death was accidental and his cause of death was from multiple blunt force injuries. No drugs or alcohol were found in his system at the time of his death, a toxicology report found. Arrests, citations and fire calls Law enforcement overseeing Bonnaroo have cited about 60 people and arrested about 19 people, records as of late afternoon Friday showed. A majority were for public intoxication, disorderly conduct and illegal possession of a controlled substance, Knott said. Bonnaroo fire authorities said no major fire calls had been reported. Glen Aussicker, a firefighter shift leader, said most of the calls stemmed from carbon monoxide alarms triggering in RVs so far this week. Most of the alarms sounded off during the evening hours, he said. If an RV alarm sounds, firefighters say residents should immediately open all windows to allow the poisonous air to escape, leave the camper and dial 911. They are also reminding campers carbon monoxide doesn't just affect people inside RVs. Firefighters are asking festival attendees to remember not to pitch tents next to an RV's exhausts or even car exhausts — especially if someone is in the car cooling off with the AC or charging their phone. Another safety tip: Crack RV windows when no one is inside. Read or Share this story: https://usat.ly/2sNt9CQ

– A person has died while attending the Bonnaroo Music and Arts Festival in Tennessee, reports the AP. Coffee County Sheriff Steve Graves confirmed a body was found Friday morning at a festival campground. The sheriff's office has identified the man as 32-year-old Michael Donivan Craddock, of Mount Juliet, Tenn. Coffee County sheriff's spokesman Lucky Knott says officials are investigating the cause of death but foul play is not suspected. Craddock was found dead inside a vehicle, reports USA Today. Graves said dozens of people have been treated for heat-related issues at the festival, which began Thursday in Manchester and runs through Sunday. This is the 13th death at the music and arts festival in its 17-year history, officials said. Festival headliners include Eminem, Muse, and the Killers.

clinically , osteoarthritis ( oa ) , or degenerative joint disease , is a painful and debilitating condition characterized by a progressive loss of articular cartilage , mild inflammation of the tissues in and around the joints , and sometimes formation of osteophytes and bone cysts . patients with oa report persistent pain and display increased sensitivity to pressure and noxious stimuli in the arthritic joint . at present , there is no cure for oa with available therapeutic approaches and analgesics are prescribed to alleviate the pain associated with this condition , with some degree of success . however , oa pain remains a clinical issue and animal models of oa are being developed to improve our understanding of oa - related pain mechanisms and disclose novel targets for therapy . however , they involve skillful surgical intervention and are primarily performed in the rat , while destabilization of medial meniscus ( dmm ) is used in the mouse . spontaneous development of oa occurs in guinea pig and spontaneous joint degeneration has been reported in c57 black mice from 3 to 16 months of age . spontaneous oa models do not involve any intervention to induce the condition , but they have inherent variability , and as such , incur greater numbers and cost . chemically induced models , on the other hand , require much less invasive procedures than surgical models , and as such , are easier to implement and permit the study of oa lesions at different stages . these models include single injections in the knee of inflammatory agents , immunotoxins , collagenase , papain , or monoiodoacetate , which can be toxic if they escape the joint space . of all chemical models of oa , mia is the one most often used , particularly to test the efficacy of pharmacologic agents to treat pain , as this model generates a reproducible , robust , and rapid pain - like phenotype that can be graded by altering mia dosage . intra - articular injection of mia in rodents reproduces oa - like lesions and functional impairment that can be analyzed and quantified . mia is an inhibitor of glyceraldehyde-3-phosphatase , disrupting cellular glycolysis and eventually resulting in cell death . intra - articular injection of mia causes chondrocyte cell death , leading to cartilage degeneration and subsequent subchondral bone alterations such as appearance of bone osteophytes . as the utility of mia in the rat has been described before , in this paper we focus on the methodology of mia - induced oa in mice as this model is being increasingly used with the availability of knock - out mice . we describe a procedure for the injection of very small volumes into the knee and methods for measuring sensitivity to noxious and non - noxious stimuli in the hind limbs . the breakdown of the methodology will help to reduce variability , and as such , refine the model and reduce the number of animals needed for study . procedures involving animal subjects have been approved by the ethical committee at king 's college london and are in accordance with uk home office regulations ( animals scientific procedures act 1986 ) . house 8 - 10 week - old mice in groups of 5 under a 12 hr light / dark cycle ( lights on at 7:00 am ) with food and water ad libitum . use body weights as parameters for randomization . on the day of injection , freshly prepare the solution of monoiodoacetate in sterile saline ( 0.9% nacl ) at the desired concentrations . use sterile saline for injections in a separate group of control mice . therefore , it is recommended that gloves and mask are worn when handling the powder and preparing the solution . anesthetize mice using an anesthetic trolley by first placing them in a chamber delivering 2% isoflurane in o2 mixture ( flow rate 1.5 l / min ) and then transfer mice to the nose cone section , which also delivers the 2% isoflurane - o2 mixture , and as such , maintains anesthesia during injection . place vet ointment on the eyes to avoid their drying out while under anesthesia . confirm anesthesia by checking the animal 's lack of response to a pinch stimulus on the hind paws . the patellar tendon ( white line bellow the patella ) will become visible . in order to stabilize the injection site , keep the knee still , in a bent position , by placing the index finger beneath the knee joint and the thumb above the anterior surface of the ankle joint . joint preference is not required . to find the precise site of injection , run a 26 g needle attached to a syringe horizontally along the knee ( so as not to pierce the skin with the tip ) until it finds the gap beneath the patella . apply gentle pressure to mark the area and then lift the needle and syringe vertically for the injection . insert the needle in the marked area , through the patellar tendon , perpendicular to the tibia . after injection , massage the knee to ensure even distribution of the solution . discard the needle immediately in the sharps bin.place mice back into a clean home cage on a heated mat and allow them to recover . keep constant vigilance on the animals until they regain suitable consciousness , which is measured by them regaining sternal recumbency . note : it is suggested for best practice and training purposes that a dye is used and immediate post - mortem dissection performed to confirm correct localization of injection . after injection , massage the knee to ensure even distribution of the solution . discard the needle immediately in the sharps bin . place mice back into a clean home cage on a heated mat and allow them to recover . keep constant vigilance on the animals until they regain suitable consciousness , which is measured by them regaining sternal recumbency . note : it is suggested for best practice and training purposes that a dye is used and immediate post - mortem dissection performed to confirm correct localization of injection . note : static mechanical withdrawal thresholds are assessed by applying von frey hairs to the plantar surface of the hind paw . bring mice to the behavioral room and let unrestrained animals acclimatize in acrylic cubicles ( 8 cm x 5 cm x 10 cm ) atop a wire mesh grid . train mice by handling and 2 hr habituation to the cubicles for two days prior to von frey hair application in order to limit stress and ambulation during application of von frey hairs . on test days , habituate animals to the cubicles for up to 60 min prior to testing . train mice by handling and 2 hr habituation to the cubicles for two days prior to von frey hair application in order to limit stress and ambulation during application of von frey hairs . on test days , habituate animals apply calibrated von frey hairs ( flexible nylon fibers of increasing diameter that exert defined levels of force as calibrated by the manufacturing company and expressed as grams ( g ) ) to the plantar surface of the hind paw until the fiber bends . use 0.008 , 0.02 , 0.04 , 0.07 , 0.16 , 0.4 , 0.6 , and 1.0 g fibers during testing . hold each hair in place for 3 sec or until the paw is withdrawn , the latter defining a positive response . starting with a stimulus strength of 0.07 g , apply hairs according to the " up - down method " : mark as x a withdrawal response and o an absence of response . apply in ascending order of force , up to 1 g ( cut - off force ) , until a response is detected.re-test the paw by repeating step 2.2.1 , starting with the filament that exerts a force below the one that produced a withdrawal.then , apply the remaining filaments sequentially , by descending force , until no withdrawal occurs . continue until a sequence of six responses is obtained ( e.g. , oxoxox ) , in order to obtain the ' k ' value by referring to tabular values .express use the formula ( 10)/10,000 where xr = value of last von frey filament used in the sequence ( in log units ) , k = tabular value , and = mean difference in forces between fibers . where no response is detected , use the maximal response of 1 g . hold each hair in place for 3 sec or until the paw is withdrawn , the latter defining a positive response . starting with a stimulus strength of 0.07 g , apply hairs according to the " up - down method " : mark as x a withdrawal response and o an absence of response . apply in ascending order of force , up to 1 g ( cut - off force ) , until a response is detected . re - test the paw by repeating step 2.2.1 , starting with the filament that exerts a force below the one that produced a withdrawal . then , apply the remaining filaments sequentially , by descending force , until no withdrawal occurs . continue until a sequence of six responses is obtained ( e.g. , oxoxox ) , in order to obtain the ' k ' value by referring to tabular values . use the formula ( 10)/10,000 where xr = value of last von frey filament used in the sequence ( in log units ) , k = tabular value , and = mean difference in forces between fibers . where no response is detected , use the maximal response of 1 g . following the procedure described above ( 2.2.1 - 2.2.4 ) , assess mechanical thresholds of both hind paws before mia injection as baseline values . after injection , assess thresholds of the ipsilateral and contralateral paws at regular day intervals for several weeks after mia to ascertain the development of mechanical allodynia . note : for example , we report thresholds measured 0 , 3 , 5 , 7 , 10 , 14 , 21 , and 28 days after mia injection . train each mouse to walk into a plexiglass chamber on the apparatus and sit in the holding box . place the mouse in front of the holding box , lift the entrance up 45 , and allow the mouse to walk in and close the box . this training takes at least two days and guarantees that the animal is still and not leaning on either side of the chamber . calibrate the instrument before use with a 100 g check weight ( or according to equipment instruction ) . the duration of each measurement takes 1 sec , as per the manufacturer 's instructions . the duration of each measurement takes 1 sec , as per the manufacturer 's instructions . collect three measurements of the weight borne on each hind paw from the recording pad for each recording session and use the mean value to calculate the difference in weight borne by ipsilateral and contralateral paws . then , repeat assessments at regular intervals over several weeks to ascertain the development of gate changes . for example , we report thresholds measured on 0 , 3 , 5 , 7 , 10 , 14 , 21 , and 28 days after mia injection . note : a normal weight bearing value of 50% represents an equal weight distribution across ipsilateral and contralateral hindlimb . measurements of mechanical thresholds and weight bearing deficits can be performed in the same mice , as neither end point affects the other . for pharmacological assessment , each group of animals should be tested at set times after dosing in line with the pharmacokinetic profile of the compound used . house 8 - 10 week - old mice in groups of 5 under a 12 hr light / dark cycle ( lights on at 7:00 am ) with food and water ad libitum . use body weights as parameters for randomization . on the day of injection , freshly prepare the solution of monoiodoacetate in sterile saline ( 0.9% nacl ) at the desired concentrations . use sterile saline for injections in a separate group of control mice . the highest recommend dose of mia is 1 mg in 10 l . caution : monoiodoacetate is very toxic . therefore , it is recommended that gloves and mask are worn when handling the powder and preparing the solution . anesthetize mice using an anesthetic trolley by first placing them in a chamber delivering 2% isoflurane in o2 mixture ( flow rate 1.5 l / min ) and then transfer mice to the nose cone section , which also delivers the 2% isoflurane - o2 mixture , and as such , maintains anesthesia during injection . place vet ointment on the eyes to avoid their drying out while under anesthesia . confirm anesthesia by checking the animal 's lack of response to a pinch stimulus on the hind paws . the patellar tendon ( white line bellow the patella ) will become visible . in order to stabilize the injection site , keep the knee still , in a bent position , by placing the index finger beneath the knee joint and the thumb above the anterior surface of the ankle joint . joint preference is not required . to find the precise site of injection , run a 26 g needle attached to a syringe horizontally along the knee ( so as not to pierce the skin with the tip ) until it finds the gap beneath the patella . apply gentle pressure to mark the area and then lift the needle and syringe vertically for the injection . insert the needle in the marked area , through the patellar tendon , perpendicular to the tibia . after injection , massage the knee to ensure even distribution of the solution . discard the needle immediately in the sharps bin.place mice back into a clean home cage on a heated mat and allow them to recover . keep constant vigilance on the animals until they regain suitable consciousness , which is measured by them regaining sternal recumbency . note : it is suggested for best practice and training purposes that a dye is used and immediate post - mortem dissection performed to confirm correct localization of injection . after injection , massage the knee to ensure even distribution of the solution . discard the needle immediately in the sharps bin . place mice back into a clean home cage on a heated mat and allow them to recover . keep constant vigilance on the animals until they regain suitable consciousness , which is measured by them regaining sternal recumbency . note : it is suggested for best practice and training purposes that a dye is used and immediate post - mortem dissection performed to confirm correct localization of injection . note : static mechanical withdrawal thresholds are assessed by applying von frey hairs to the plantar surface of the hind paw . bring mice to the behavioral room and let unrestrained animals acclimatize in acrylic cubicles ( 8 cm x 5 cm x 10 cm ) atop a wire mesh grid . train mice by handling and 2 hr habituation to the cubicles for two days prior to von frey hair application in order to limit stress and ambulation during application of von frey hairs . on test days , train mice by handling and 2 hr habituation to the cubicles for two days prior to von frey hair application in order to limit stress and ambulation during application of von frey hairs . on test days , habituate animals to the cubicles for up to 60 apply calibrated von frey hairs ( flexible nylon fibers of increasing diameter that exert defined levels of force as calibrated by the manufacturing company and expressed as grams ( g ) ) to the plantar surface of the hind paw until the fiber bends . use 0.008 , 0.02 , 0.04 , 0.07 , 0.16 , 0.4 , 0.6 , and 1.0 g fibers during testing . hold each hair in place for 3 sec or until the paw is withdrawn , the latter defining a positive response . starting with a stimulus strength of 0.07 g , apply hairs according to the " up - down method " : mark as x a withdrawal response and o an absence of response . apply in ascending order of force , up to 1 g ( cut - off force ) , until a response is detected.re-test the paw by repeating step 2.2.1 , starting with the filament that exerts a force below the one that produced a withdrawal.then , apply the remaining filaments sequentially , by descending force , until no withdrawal occurs . continue until a sequence of six responses is obtained ( e.g. , oxoxox ) , in order to obtain the ' k ' value by referring to tabular values .express use the formula ( 10)/10,000 where xr = value of last von frey filament used in the sequence ( in log units ) , k = tabular value , and = mean difference in forces between fibers . hold each hair in place for 3 sec or until the paw is withdrawn , the latter defining a positive response . starting with a stimulus strength of 0.07 g , apply hairs according to the " up - down method " : mark as x a withdrawal response and o an absence of response . apply in ascending order of force , up to 1 g ( cut - off force ) , until a response is detected . re - test the paw by repeating step 2.2.1 , starting with the filament that exerts a force below the one that produced a withdrawal . then , apply the remaining filaments sequentially , by descending force , until no withdrawal occurs . continue until a sequence of six responses is obtained ( e.g. , oxoxox ) , in order to obtain the ' k ' value by referring to tabular values . use the formula ( 10)/10,000 where xr = value of last von frey filament used in the sequence ( in log units ) , k = tabular value , and = mean difference in forces between fibers . where no response is detected , use the maximal response of 1 g . following the procedure described above ( 2.2.1 - 2.2.4 ) , after injection , assess thresholds of the ipsilateral and contralateral paws at regular day intervals for several weeks after mia to ascertain the development of mechanical allodynia . note : for example , we report thresholds measured 0 , 3 , 5 , 7 , 10 , 14 , 21 , and 28 days after mia injection . train each mouse to walk into a plexiglass chamber on the apparatus and sit in the holding box . place the mouse in front of the holding box , lift the entrance up 45 , and allow the mouse to walk in and close the box . this training takes at least two days and guarantees that the animal is still and not leaning on either side of the chamber . calibrate the instrument before use with a 100 g check weight ( or according to equipment instruction ) . the duration of each measurement takes 1 sec , as per the manufacturer 's instructions . the duration of each measurement takes 1 sec , as per the manufacturer 's instructions . collect three measurements of the weight borne on each hind paw from the recording pad for each recording session and use the mean value to calculate the difference in weight borne by ipsilateral and contralateral paws . then , repeat assessments at regular intervals over several weeks to ascertain the development of gate changes . for example , we report thresholds measured on 0 , 3 , 5 , 7 , 10 , 14 , 21 , and 28 days after mia injection . note : a normal weight bearing value of 50% represents an equal weight distribution across ipsilateral and contralateral hindlimb . . measurements of mechanical thresholds and weight bearing deficits can be performed in the same mice , as neither end point affects the other . for pharmacological assessment , each group of animals should be tested at set times after dosing in line with the pharmacokinetic profile of the compound used . we have recently reported that the injection of 0.5 - 1 mg mia in the mouse knee joint induces referred mechanical hypersensitivity ( allodynia ) in the ipsilateral hind paw and weight bearing deficits for up to 4 weeks , although onsets are dose - dependent . the data reported in figure 1 constitute an example of the time course of mia - induced mechanical hypersensitivity in the ipsilateral hind paws following a range of doses injected in the knee . specifically , the lowest dose of mia ( 0.5 mg / mouse ) induced a 50% decrease of thresholds compared to the injection of saline on day 10 , and thresholds decreased to 70% of those of saline controls by day 28 after injection . the intermediate dose of 0.75 mg of mia resulted in a gradual decrease in thresholds that were 80% lower than saline control thresholds on day 10 and remained low up to day 28 . the highest dose of 1 mg mia was associated with a significant drop in threshold on day 5 and a further decrease on day 10 , which was sustained up to day 28 . the data reported in figure 2 provide examples of weight bearing changes that are associated with mia injection in the knee joints . in this set of experiments , while the 0.5 mg mia dose did not induce significant changes in weight bearing throughout the 28 day duration of the study , the 0.75 mg mia dose resulted in a significant reduction in the weight borne by the ipsilateral paw from day 10 onwards . notably , weight bearing asymmetry associated with 0.75 mg of mia may produce variable and inconsistent results between studies . instead , the dose of 1 mg mia generally induces reproducible weight bearing asymmetry and the data in figure 2 demonstrate significant reduction of weight borne on the ipsilateral hind paw from day 3 until the end of the observation period . as expected , saline - treated animals showed no weight bearing changes . paw withdrawal thresholds of the ipsilateral and contralateral hind paws were assessed before and after injection of mia ( 0.5 , 0.75 , and 1mg / mouse ) and saline ( 0.9% nacl ) , n = 8 - 10 mice / group . * p<0.05 , * * p<0.01 , * * * p<0.001 versus saline - treated group ; two - way repeated measurements anova followed by student newman - keuls post hoc test . changes in body weight distribution between the two hind limbs were calculated as [ ( weight borne on ipsilateral paw / sum of the weight borne on the ipsilateral and contralateral paws)*100 ] were assessed before and after injection of mia ( 0.5 , 0.75 , and 1 mg / mouse ) and saline ( 0.9% nacl ) , n = 8 - 10 mice / group . * p<0.05 , * * p<0.01 , * * * p<0.001 versus saline - treated group . two - way repeated measurements anova followed by student newman - keuls post hoc test . with this methodology , we describe a preferred method for inducing oa - like pain in the mouse by an intra - articular injection of mia in a knee joint and assessment of sensitivity to non - noxious and noxious stimuli in the hind limbs . mia injection is associated with persistent pain behavior , namely altered hind limb weight bearing and development of referred mechanical hypersensitivity ( allodynia ) . such static measurements can be complemented by gait analysis on a treadmill or by catwalk analysis in freely moving animals . mia models are responsive to conventional pain - relieving therapies , indicating that they may be useful for discerning therapeutic approaches . while the injection of mia is not technically difficult , the joint capsule can be pierced during the injection , resulting in leakage of mia outside the capsule , and subsequent failure to induce toxicity of chondrocytes . indeed , systemic injection of mia can be fatal in rodents and possible effects of mia on tissues and cells other than chondrocytes may confound results , besides being undesirable . as such , it must be stressed that great care needs to be given to the injection of the mia , as it is a critical component of the model , and confidence needs to be given that the injection occurs into the articular space . this protocol helps to achieve that . the protocols described here aim to ensure the animals provide consistent pain - like responses throughout the test period . also , they allow adjustment of disease severity by altering the dose of mia used to induce the pathology . the rapid induction of both disease state and pain - like behavior allow timely evaluation of pain - modifying compounds . this is advantageous over existing surgical and spontaneously developing models of oa , which can take a longer period of time to develop hypersensitivity . also , particularly for the spontaneous models , the disease pathology does not manifest in all animals ( approximately 20 - 80% ) , whereas the mia model is associated with significant incidence of responders . furthermore , spontaneous models are not suitable for measurements of changes in weight bearing , as oa develops in both knees . when considering behavioral measurements , the animals need to be kept calm and relaxed during the assessments . this is achieved , as detailed in the protocol , by early training before recording measurements and by repetitive handling , which allows animals to become familiar with the experimenter . a key point to reduce stress is to use the same experimenter for the behavioral test throughout , as constant changing will induce the issues previously mentioned . like any model , the mia model of oa bears limitations , such as the rapidity of joint disruption , which does not resemble the slow development of oa pathology in patients . one way to overcome this issue would be to complement this model with a surgical model of oa . the use of the mia chemical model in compound development allows for the use of preventative and therapeutic protocols over the development and maintenance of oa - like pain . finally , the mia model would complement studies of phenotypical traits of knock - out mice , helping to further understand the oa disease .

a major symptom of patients with osteoarthritis ( oa ) is pain that is triggered by peripheral as well as central changes within the pain pathways . the current treatments for oa pain such as nsaids or opiates are neither sufficiently effective nor devoid of detrimental side effects . animal models of oa are being developed to improve our understanding of oa - related pain mechanisms and define novel pharmacological targets for therapy . currently available models of oa in rodents include surgical and chemical interventions into one knee joint . the monoiodoacetate ( mia ) model has become a standard for modelling joint disruption in oa in both rats and mice . the model , which is easier to perform in the rat , involves injection of mia into a knee joint that induces rapid pain - like responses in the ipsilateral limb , the level of which can be controlled by injection of different doses . intra - articular injection of mia disrupts chondrocyte glycolysis by inhibiting glyceraldehyde-3-phosphatase dehydrogenase and results in chondrocyte death , neovascularization , subchondral bone necrosis and collapse , as well as inflammation . the morphological changes of the articular cartilage and bone disruption are reflective of some aspects of patient pathology . along with joint damage , mia injection induces referred mechanical sensitivity in the ipsilateral hind paw and weight bearing deficits that are measurable and quantifiable . these behavioral changes resemble some of the symptoms reported by the patient population , thereby validating the mia injection in the knee as a useful and relevant pre - clinical model of oa pain.the aim of this article is to describe the methodology of intra - articular injections of mia and the behavioral recordings of the associated development of hypersensitivity with a mind to highlight the necessary steps to give consistent and reliable recordings .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Independent and Effective Federal Defenders Act of 2016''. SEC. 2. REVISION OF SYSTEM TO ENSURE ADEQUATE REPRESENTATION OF FEDERAL DEFENDANTS. Section 3006A of title 18, United States Code, is amended to read as follows: ``Sec. 3006A. Adequate representation of defendants ``(a) Federal Defender Commission.-- ``(1) In general.--There is established, as an independent agency within the executive branch, the Federal Defender Commission (hereinafter in this section referred to as the `Commission'). ``(2) Composition and appointment by president.--The Commission shall consist of 12 members, appointed by the President. ``(3) Director.--The President shall appoint a Director to serve on the Commission. The Director shall have all of the qualifications described in paragraph (5) and none of the disqualifications described in paragraph (6). The term of the Director shall be 6 years, but a Director may serve after the expiration of that term until a successor takes office. ``(4) Considerations in appointment.--In appointing members of the Commission, the President shall ensure that-- ``(A) each of the 12 members of the Commission has primary experience in criminal defense in a circuit in which no other member of the Commission has such experience at the time of the appointment; and ``(B) at least a majority of the members of the Commission are individuals who are former Federal defenders. ``(5) Qualifications of members.--To be a member of the Commission, an individual must-- ``(A) be a member of the bar of the highest court of a State; and ``(B) have significant experience in the legal defense of criminal cases or demonstrated a commitment to indigent defense representation or juvenile defense representation. ``(6) Disqualifications of members.--An individual shall not serve on the Commission who is-- ``(A) employed as a Federal defender; ``(B) employed as a prosecutor or law enforcement official; or ``(C) serving as an active judicial officer of the United States. ``(7) Term.-- ``(A) Except as otherwise provided in this paragraph, the term of a member of the Commission shall be 6 years. ``(B) A member may serve after the expiration of that member's term until a successor takes office. ``(C) Of the 12 members first appointed to the Commission, 6 shall be initially appointed for 2-year terms, so that the terms of members of the commission are staggered. ``(8) Duties of commission.--The Commission shall-- ``(A) consult with each United States district court on a plan operating throughout the district for furnishing representation to any person financially unable to obtain representation; ``(B) appoint, taking into consideration the recommendations of the relevant bar or bars of the State, law schools in the State, and other organizations and individuals, a Federal Public Defender, having the same qualifications for service as this subsection requires for a member of the Commission and not having any of the disqualifications described in this subsection, other than that described in paragraph (6)(A), for such service, for each district to carry out the plan for that district; and ``(C) develop for Federal Public Defender offices-- ``(i) national guidelines on quality of representation; ``(ii) program evaluation systems; ``(iii) attorney and staff evaluation systems to ensure effective management and representation; ``(iv) training, publications, and seminars; ``(v) specialty resource centers; ``(vi) research and development pilot projects; ``(vii) statistical studies; and ``(viii) committees, projects, or working groups. ``(9) Plan may combine districts.--The plan may include a combination of districts if such a combined office would be cost effective, based on the number of appointments each year, and where the interests of justice of effective representation require the establishment of such an office. The Commission shall determine the need for a Federal Public Defender office and geographic boundaries it serves. However, the Commission shall ensure that each Federal judicial district has within it a Federal Public Defender office providing representation. ``(10) Staff.--The Commission may appoint additional employees as it deems appropriate, to assist the Commission in carrying out its duties. ``(11) Compensation of members and employees.--Members of the Commission and employees of the Commission shall be compensated at rates determined by the Commission, but not in excess of the rate of level V of the Executive Schedule specified in section 5316 of title 5. ``(12) Professional responsibility.--The Commission shall not-- ``(A) interfere with any attorney providing representation under this section in carrying out such attorney's professional responsibilities to such attorney's client; or ``(B) abrogate as to attorneys in providing representation under this section the authority of a State or other jurisdiction to enforce standards of professional responsibility generally applicable to attorneys in such jurisdiction. ``(b) Requirements for Plan.--Each plan for representation under this section shall include the following: ``(1) Representation provided in all cases.--Representation shall be provided for any financially eligible person who-- ``(A) is charged with a criminal offense; ``(B) is a juvenile alleged to have committed an act of juvenile delinquency as defined in section 5031; ``(C) is charged with a violation of probation; ``(D) is under arrest, when such representation is required by law; ``(E) is charged with a violation of supervised release or faces modification, reduction, or enlargement of a condition, or extension or revocation of a term of supervised release; ``(F) is subject to a mental condition hearing under chapter 313; ``(G) is in custody as a material witness; ``(H) is entitled to appointment of counsel under the sixth amendment to the Constitution; ``(I) faces loss of liberty in a case, and Federal law requires the appointment of counsel; ``(J) is entitled to the appointment of counsel under section 4109; ``(K) is involved in a proceeding in which a criminal adjudication may result; ``(L) is being considered for, or seeks to obtain, under subsection (c)(1) or (c)(2) of section 3582, a modification of a term of imprisonment; or ``(M) is involved in proceedings seeking clemency or a pardon. ``(2) Representation provided in some cases.--Whenever the United States magistrate judge or the court determines that the interests of justice so require, representation may be provided for any financially eligible person who seeks relief under section 2241, 2254, or 2255 of title 28. ``(3) Appointment of private attorneys.--Each District shall develop a panel of private attorneys. A private attorney shall provide representation under this section when the nature of the case or ethical considerations so require. Cases shall be randomly assigned to private panel attorneys on a rotating basis. The Federal Public Defender in the district shall not be involved in the selection of private panel attorneys for individual cases. The panel of private attorneys shall divide themselves into areas of criminal proceeding expertise. ``(4) Qualifications of private attorneys.--To be a private attorney on the panel, an individual must have significant experience in the legal defense of criminal cases. ``(5) Ongoing training and certification of private attorneys.--Each District shall develop and provide ongoing, mandatory training programs for private attorneys on the panel. All attorneys participating on a panel shall have their performance in representing defendants regularly peer reviewed by and certified by distinguished members of the local criminal defense community. ``(6) Use of private attorneys.--Each plan shall provide that private attorneys be appointed to represent defendants in a substantial proportion of cases. ``(7) Use of other attorneys.--Each plan may include, in addition to the provisions for private attorneys, for the use of attorneys furnished by a bar association or legal aid society. ``(c) Budget Analyst.--Each District shall have a budget analyst. The budget analyst shall be hired by the Commission. The budget analyst shall be operationally independent of the Federal Public Defender and the judicial branch in such circuit. The budget analyst shall have significant experience in criminal defense practice. The budget analyst shall engage in timely, objective, and independent analysis of reimbursement for costs submitted by the private attorneys. The budget analyst may mediate any claims for reimbursement payments submitted by private attorneys. The budget analyst will oversee and approve the use of investigators and experts for cases. ``(d) Federal Public Defender.-- ``(1) Duties and powers.--The Federal Public Defender in each district shall carry out the plan for representation in that district. In order to do so, the Federal Public Defender may appoint such staff, establish salaries for the staff, and make such contracts as are necessary to carry out the functions of the office. The salary structure in each office shall be commensurate with that provided for the lawyers and staff of the United States Attorney for the relevant district. ``(2) Term.--The term of a Federal Public Defender is 4 years, but a Federal Public Defender may serve after the expiration of that term until a successor takes office. The Federal Public Defender may be appointed for more than one term. ``(3) Removal.--The Commission may, with the concurrence of three quarters of the members serving at the time of the removal, remove a Federal Public Defender for cause. ``(4) Vacancy.--The Commission may fill a vacancy of the office of Federal Public Defender for the remainder of the term, in the same manner as the original appointment was made. ``(e) Alternative Means of Representation in a District.-- ``(1) Generally.--The Commission may create a Community Defender Organization to carry out the plan for representation in the District. A Community Defender Organization shall be a nonprofit defense counsel service established and administered by any group authorized by the plan to provide representation. The organization shall be eligible to furnish attorneys and receive payments from the Commission if its bylaws are set forth in the plan of the district or districts in which it will serve. ``(2) Annual report.--Each organization shall submit to the Commission an annual report setting forth its activities and financial position and the anticipated caseload and expenses for the next fiscal year. ``(3) Grants.--Upon application an organization may, to the extent approved by the Commission-- ``(A) receive an initial grant for expenses necessary to establish the organization; and ``(B) receive periodic sustaining grants to provide representation and other expenses pursuant to this section. ``(f) Change of Structure Between That of Federal Public Defender and That of Community Defender Organization.--Either a Community Defender Organization or a Federal Public Defender may apply to the Commission to change its structure to that of the other. The Commission may allow that change if the Commission determines such a change would better serve the purposes of this section. ``(g) Duration and Substitution of Appointments.--A person for whom counsel is appointed shall be represented at every stage of the proceedings from before being interviewed by pretrial services or a probation officer through appeal, including ancillary matters appropriate to the proceedings. If at any time after the appointment of counsel the United States magistrate judge or the court finds that the person is financially able to obtain counsel or to make partial payment for the representation, it may terminate the appointment of counsel or authorize payment as provided in subsection (f), as the interests of justice may dictate. If at any stage of the proceedings, including an appeal, the United States magistrate judge or the court finds that the person is financially unable to pay counsel whom he had retained, it may appoint counsel under this section, as the interests of justice may dictate. The United States magistrate judge or the court may, in the interests of justice, substitute one appointed counsel for another at any stage of the proceedings. ``(h) Nonapplicability to Local Courts of the District of Columbia.--This section does not apply to representation in the Superior Court of the District of Columbia or the District of Columbia Court of Appeals. ``(i) Definitions.--In this section the following definitions apply: ``(1) Circuit.--The term `circuit' means one of the circuits for which there is a United States court of appeals. ``(2) District court.--The term `district court' means each district court of the United States created by chapter 5 of title 28, the District Court of the Virgin Islands, the District Court for the Northern Mariana Islands, and the District Court of Guam. ``(3) Representation.--The term `representation' means representation by legal counsel and also includes investigative, expert, and other services necessary for adequate representation. ``(4) State.--The term `State' includes any State or other similar entity in which a district court is established.''. SEC. 3. CONTINUATION OF ORGANIZATIONS ESTABLISHED BEFORE ENACTMENT. A Federal Defender organization established before enactment of this Act shall continue in operation, and the Federal Public Defender then in office shall continue to serve the Federal Public Defender's term in that capacity. A Community Defender Organization, committee, project, or working group established before enactment of this Act shall continue in operation. SEC. 4. GENERAL ACCOUNTABILITY OFFICE STUDY. Not later than 4 years after the date of the enactment of this Act, the Comptroller General shall complete a study and report to Congress on the provision and cost of Federal Defense services.

Independent and Effective Federal Defenders Act of 2016 This bill amends the federal criminal code to revise requirements related to the provision of&nbsp;adequate representation&nbsp;for defendants in federal criminal cases. Under current law, each U.S. district court must operate a plan, in accordance with specified requirements,&nbsp;for furnishing representation to any eligible person who is financially unable to obtain adequate representation. The bill&nbsp;revises these requirements and&nbsp;establishes the Federal Defender Commission as an independent agency tasked with ensuring the provision of adequate representation.

in this paper , we give further consideration to the 1-d continuum model for adhesion / diffusion of biological cells developed by anguige and schmeiser in @xcite , which took the form of the nonlinear diffusion equation = ( d ( ) ) , [ cont_rho]with quadratic diffusivity d()= 3(-)^2 + 1- , [ d]for the scaled cell density @xmath0 $ ] , and the adhesion coefficient @xmath1 $ ] , the boundary condition being just @xmath2 at @xmath3 . these equations were obtained as the formal continuum limit of the fundamental biased - random - walk model = ^+_i-1_i-1+^-_i+1_i+1-(^+_i+^-_i)_i , [ walk ] with transitional probabilities ^_i = ( 1-_i1)(1-_i1)/h^2 , [ ti ] on a lattice of points @xmath4 , by taking taylor expansions about @xmath5 , and letting @xmath6 . in the derivation of this equation , @xmath7 was interpreted as a ( microscopic ) measure of cell size . we recall from @xcite that ( [ cont_rho])-([d ] ) is globally well posed if @xmath8 . if , on the other hand , @xmath9 then ( [ cont_rho])-([d ] ) is ill - posed iff the initial density profile protrudes into the ` unstable ' interval i_= ( ^ ( ) , ^()):= ( , ) , [ rhointerval ] since in that case @xmath10 is positive iff @xmath11 , and positivity is preserved by the maximum principle . for completeness , note that in the borderline case @xmath12 , equation ( [ cont_rho ] ) is just the porous - medium equation with quadratic diffusivity and possible change of sign about @xmath13 . for initial data which stays away from @xmath13 ( either above or below ) , ( [ cont_rho ] ) is uniformly parabolic , and global existence of a smooth solution follows as for @xmath8 , while for degenerate initial data one is merely guaranteed a ( unique ) globally existing weak solution @xcite . the ill - posedness of ( [ cont_rho ] ) for @xmath9 is related to the presence of fine ( wavelength @xmath14 ) spatial oscillations , as well as plateau formation , in solutions of the discrete system ( [ walk ] ) , and the absence of a straightforward existence theory for ( [ cont_rho ] ) leads one to ask just what model should be taken as a reasonable continuum limit of ( [ walk ] ) in the high - adhesion regime . one approach , and the one we shall adopt in this paper , is to circumvent the problem of ill - posedness by simply declaring that @xmath15-values in @xmath16 are forbidden , and considering solutions to ( [ cont_rho])-([d ] ) which may jump across @xmath16 ( possibly multiple times ) , but which are otherwise smooth . mathematically , one is then dealing with a kind of ( multi - phase ) stefan problem for the density @xmath17 and the jump locations @xmath18 , such that the @xmath19 are dynamically determined by local conservation of mass , or , in other words , by the rankine - hugoniot condition . in @xcite , the analysis of ( [ walk ] ) was aided by considering higher - order modifications of the leading - order equation ( [ cont_rho ] ) . one such @xmath20-modification takes the form of the fourth - order pde [ mod - equ ] = ( k ( ) + h^2((-1 ) - ( ) ^2 + ) ) , where the cubic @xmath21 is a primitive for @xmath10 . this equation is rather similar to the viscous cahn - hilliard equation @xcite , and is a regularisation of ( [ cont_rho ] ) in the sense that it is ( at least locally ) well - posed on @xmath22 , for each fixed value of the microscopic parameter @xmath7 , and for all @xmath23 . presumably , solutions continue to exist globally , as for cahn - hilliard , but a proof is currently lacking . the steady - state equation for ( [ mod - equ ] ) can , after a change of variables , be written as a hamiltonian dynamical system , and amongst the solutions there is , for each @xmath24 , a unique heteroclinic cycle . these heteroclinic cycles correspond to ( two - level ) plateau solutions of ( [ mod - equ ] ) , are close ( for small @xmath7 ) to square - wave weak solutions of ( [ cont_rho ] ) , and their critical points , denoted by @xmath25 and @xmath26 , such that @xmath27 and @xmath28 , match very well the numerically - observed long - time plateau values in solutions of ( [ walk ] ) ( see @xcite ) . for these reasons , we demand in our stefan - problem framework that any jumps across @xmath29 should connect @xmath25 to @xmath26 . furthermore , in order to avoid the degeneracies at @xmath30 , we require that the initial data satisfy @xmath31 in low - density phases , and @xmath32 in high - density ones . we emphasise that @xmath33 and @xmath34 are determined by the particular choice of microscopic model ( [ walk])-([ti ] ) ; other model choices are possible , and these will result in different @xmath15-values . the paper is organised as follows . in section 2 , we develop a partial existence theory and perform a steady - state analysis for the simplest stefan problem , namely , that for which there is only a single discontinuity in the density ; solution behaviour is further clarified with the aid of several numerical simulations . in section 3 , we extend the analysis to the general multi - phase case , which , in particular , allows for the annihilation of phases via coalescence events . finally , in the appendices , we collect a number of results from classical parabolic theory which are used throughout the paper . we begin the analysis by considering the simplest possible case , in which there are just two phases , connected by a single jump from @xmath33 to @xmath34 ; this situation is depicted in figure 1 . for definiteness , we will assume that the low - density phase lies to the left , and the high - density phase to the right , of the discontinuity ; the converse arrangement can , of course , also be treated . let the location of the jump discontinuity be denoted by @xmath35 . the stefan problem for a given @xmath9 then consists of looking for a function @xmath17 on @xmath36\times[0,t]$ ] which satisfies = ( d ( ) ) ; 0<x < s(t),[lphase]g subject to ( 0,t ) = 0,(s^-(t),t ) = _ 1 ( ) , and = ( d ( ) ) ; s(t)<x<1 , subject to ( 1,t ) = 0,(s^+(t),t ) = _ 2().[rphase ] the evolution of @xmath35 is determined by the rankine - hugoniot jump condition = , [ rh ] where the fluxes are given by @xmath37 , this equation being obtained by differentiating the statement of conservation of mass _ 0^s(t ) ( x , t ) dx + _ s(t)^1 ( x , t ) dx = m,[mass ] and using ( [ lphase])-([rphase ] ) . the initial datum for @xmath15 , satisfying the boundary and jump conditions , is chosen to be smooth away from the initial discontinuity , with @xmath31 in the low - density phase and @xmath32 in the high - density phase . by construction , @xmath10 is then initially positive on each phase , and , by virtue of the maximum principle , we can reasonably expect the stefan problem to be well posed . in the sequel , we will refer to the coupled system ( [ lphase])-([rh ] ) as @xmath38 ; analogous problems @xmath39 , with @xmath40 jumps , will be treated in section 3 . finally , note that we allow for the possibility that @xmath35 may hit the domain boundary at @xmath41 or @xmath42 in finite time . in this case , provided the gradient remains bounded as the boundary is approached , the solution can be continued via the ordinary neumann problem for ( [ cont_rho ] ) , which we will call @xmath43 . as a convention , a solution continued in this way will still be referred to globally as a solution of @xmath38 . if the total mass @xmath44 satisfies @xmath45 then there is precisely one discontinuous steady - state solution of @xmath38 , given by the step function ^(x ) & = & \ { ccc _ 1 & : & x . + s^ & = & , [ s_star ] while if @xmath46 or @xmath47 then no such discontinuous solution exists . moreover , @xmath38 clearly has the uniform steady - state solution ( x)=m , 0x1 if and only if @xmath48 or @xmath49 . for the two possible kinds of steady state we have the following stability results : suppose we have a global smooth solution pair , ( @xmath50 ) , for @xmath38 , with initial data @xmath51 , such that @xmath52 . then + + ( i ) if @xmath53 , @xmath17 converges exponentially to @xmath54 in @xmath55-norm , and @xmath35 converges exponentially to @xmath56 , as @xmath57 , + + ( ii ) if @xmath58 ( resp . @xmath59 ) , and @xmath60 in the low ( high ) phase , the solution is attracted towards @xmath61 as in ( i ) , + + ( iii ) if @xmath62 ( resp . @xmath63 ) , then @xmath35 hits @xmath64 in finite time , and the continued solution converges to the uniform steady state @xmath65 , exponentially in @xmath55 . + + ( iv ) if @xmath66 ( resp . @xmath67 ) , then @xmath68 @xmath69 as @xmath70 , some @xmath71 , with the possibility that @xmath72 , and @xmath17 approaches @xmath33 ( @xmath34 ) exponentially in @xmath55 in the low ( high ) phase as @xmath70 . if @xmath71 is finite , the continued solution of np converges to the uniform steady state @xmath65 , exponentially in @xmath55 . _ to prove ( i ) , first note that , by ( [ mass ] ) and the fact that @xmath15 can not enter @xmath73 , 0<s_mins(t)s_max<1 , t , where s_min(m ) & = & ( ^-m)/^ , + s_max(m ) & = & ( 1-m)/(1-^ ) . next note that , on the subinterval @xmath74 , we have ( -_1 ) = ( d()(-_1 ) ) . hence , multiplying through by @xmath75 , integrating by parts , and using the mixed boundary conditions gives _ 0^s(t)(-_1)^2 dx = -_0^s(t)d()(_x(-_1))^2 dx , which implies -_1 ^ 2_l^2(0,s ) -_x(-_1)^2_l^2(0,s),[l2 ] where @xmath76 . since @xmath77 at @xmath78 , we also have the poincar inequality -_1_l^2(0,s)s_x(-_1)_l^2(0,s ) , and hence ( [ l2 ] ) implies -_1 ^ 2_l^2(0,s)(t)-_1 ^ 2_l^2(0,s)(0)e^-t / s^2_max . an analogous inequality on the subinterval @xmath79 is obtained in exactly the same way . next , from ( [ mass ] ) we have _ 0^s(t ) ( ( x , t)-_1 ) dx + _ 1s(t ) + _ s(t)^1 ( ( x , t)-_2 ) dx + _ 2(1-s(t ) ) = m , and hence , rearranging and using the @xmath55-decay just shown , substituting the definition of @xmath56 from ( [ s_star ] ) into ( [ s_est1 ] ) gives us to prove ( ii ) , note , for example , that if @xmath58 and @xmath80 for @xmath81 then @xmath65 is a supersolution in the low phase . from this , it follows once again that @xmath35 remains bounded away from @xmath82 and @xmath42 , by conservation of mass . convergence to @xmath61 is proved as before . the same argument goes through for @xmath59 and @xmath83 , @xmath84 . for ( iii ) , if @xmath62 ( resp . @xmath63 ) then the only candidate for a steady - state solution is given by @xmath65 and @xmath85 , and , by @xmath55-decay in the low ( high ) phase and conservation of mass , @xmath35 is forced to hit the boundary in finite time ; @xmath55-convergence for the subsequent @xmath43 is proved via the usual energy estimate finally , if @xmath66 ( resp . @xmath34 ) , then the only possible steady state is @xmath77 @xmath86 for @xmath87 . clearly , @xmath35 remains bounded away from @xmath82 ( @xmath42 ) and therefore @xmath88 decays to @xmath33 ( @xmath34 ) , exponentially in @xmath55 on @xmath89 ( @xmath90 ) , as we have already seen . the @xmath55-decay implies that @xmath68 ( @xmath82 ) as @xmath91 increases , but the convergence may take infinitely long in this exceptional case ; if the convergence takes place in finite time then the subsequent @xmath43 is as in ( iii ) . this proves part ( iv ) @xmath92 + + we conclude this discussion by noting that , for the cases not covered by theorem 2.1 , namely 1 . @xmath93 for some @xmath94 , 2 . @xmath95 for some @xmath96 , we have not been able to find a clean analytical criterion for determining which of the two possible steady states will be approached at large times , for given initial data . however , in the next subsection we show that the discontinuous steady state ( [ s_star ] ) is always linearly stable in a certain sense , whenever it exists , and , moreover , we report on numerical simulations which suggest that @xmath35 can hit the domain boundary in finite time , provided condition 1 or 2 ( directly above ) is satisifed , and the initial density profile is sufficiently far from ( [ s_star ] ) ; in other words , @xmath38 appears to be bistable for some values of the total mass . we can make a connection between our moving - boundary problem @xmath38 and the traditional two - phase stefan problem for the melting of ice in water by identifying @xmath15 as the specific latent heat , and @xmath97 as the temperature . in the traditional formulation , our low - density phase is thought of as the solid , and our high - density phase as the liquid phase . given this , one imposes the physically reasonable condition _ 0_1 _ 0_2 , [ class_data ] and then one can write down a favourable weak formulation of the problem , which can be shown to have a unique solution for bounded data ( see appendix c ) . furthermore , this weak solution turns out to be a global - in - time smooth solution of the original problem ( see , e.g. , @xcite ) . for @xmath38 , however , the restriction on the initial data is just _ 0<^ _ 0>^ , [ sp_1_data ] which is weaker than ( [ class_data ] ) . in particular , this entails that @xmath21 can no longer be assumed monotonically increasing , and , consequently , that there is no nice weak formulation of the problem . we note that , in the literature , uniqueness of solutions , given ( [ class_data ] ) , is usually proved using the weak formulation @xcite . moreover , in the basic proof of local existence of smooth solutions as presented in @xcite , for example , it is not so easy to discern whether the restriction ( [ class_data ] ) can be relaxed to ( [ sp_1_data ] ) . for these reasons , we now present a concise , reasonably self - contained , classical existence - and - uniqueness theory for @xmath38 , with data subject merely to ( [ sp_1_data ] ) , which employs the standard hlder and sobolev estimates of linear parabolic theory . in order to solve the moving - boundary problem @xmath38 , we employ , in each phase , the standard trick of rescaling the spatial variable ( see , for example , @xcite ) , such that ( [ lphase ] ) and ( [ rphase ] ) become a pair of fixed - boundary problems , coupled by the ( rescaled ) rankine - hugoniot condition . specifically , for @xmath98 we introduce the coordinate transformation ( x , t ) ( , ) : = , = t , while for @xmath99 we take ( x , t ) ( , ) : = , = t . in terms of these new coordinates , and writing @xmath100 for @xmath98 , @xmath101 for @xmath99 , equations ( [ lphase ] ) and ( [ rphase ] ) become , upon dropping hats , = ( d(v ) ) + x,[v ] for @xmath102 , subject to @xmath103 , and , respectively , = ( d(w ) ) + , [ w ] for @xmath102 , subject to @xmath104 , while the jump condition ( [ rh ] ) assumes the form = - ( - ) ( _ 2-_1)^-1,[rescaled_rh ] and we also have the rescaled conservation - of - mass equation s(t ) = .[resc_com ] finally , for the application of classical parabolic theory , the initial data and the dirichlet condition at @xmath105 must satisfy a certain first - order compatibility condition , which is obtained by setting @xmath106 and @xmath107 equal to zero in ( [ v ] ) and ( [ w ] ) , and substituting the initial data , evaluated at the phase boundary , into the right - hand sides of ( [ v ] ) , ( [ w ] ) , and ( [ rescaled_rh ] ) . the most compact way of writing this compatibility condition is to go back to the original coordinates and introduce the dependent ( temperature ) variable @xmath108 , in terms of which the relevant equations are simply -_x^+(_x^+ - _ x^- ) & = & d(_1)_xx^+ , + -_x^-(_x^+ - _ x^- ) & = & d(_2)_xx^- , where , for example , @xmath109 . we are able to prove the following : given initial data @xmath110 , such that @xmath111 , @xmath112 , @xmath52 , @xmath113 , @xmath114 , and such that the first - order compatibility condition is satisfied , the system of equations ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) ( and hence problem @xmath38 ) has a unique classical solution on some small time interval @xmath115 $ ] . _ the proof proceeds via an iterative scheme of successive approximations , and to get the required strong - convergence properties , we work in the setting of ` parabolic ' hlder spaces . first of all , we set @xmath116\times[0,t]$ ] , and , as in @xcite , @xcite , for example , let @xmath117 , @xmath112 non - integer , denote the banach space of functions @xmath118 with continuous derivatives @xmath119 , for @xmath120 , equipped with the norm d^r_td^s_xu^(l-[l])_x , q_t + _ 0<l-2r - s<2d_t^rd_x^su^(l-2r - s)/2_t , q_t , where , for @xmath121 , v^()_x , q_t & = & _ ( x , t),(x,t)q_t\{|v(x , t)-v(x,t)||x - x|^- } , + v^()_t , q_t & = & _ ( x , t),(x , t)q_t\{|v(x , t)-v(x , t)||t - t|^-}. now we describe our iterative scheme for obtaining new approximate solutions of ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) from old ones . suppose we have smooth @xmath122th iterates @xmath123 , with positive diffusivities on @xmath124 , which satisfy the initial and boundary conditions , and suppose that \{|v^i|^(l+1)_q_t , |w^i|^(l+1)_q_t}c,[vw_c_bound ] for some @xmath125 . next , determine the approximant @xmath126 by solving the nonlinear ode = - ( - ) ( _ 2-_1)^-1,[iterated_rh ] which , for the given datum @xmath127 , has a unique smooth solution on @xmath115 $ ] , provided @xmath128 is chosen small enough ( picard s theorem ) . clearly , the ordinary hlder norm of @xmath129 is bounded according to ^i_c^l/2([0,t])f(c),[sdot_bound ] for some function @xmath130 . the functions @xmath131 are now inserted into the right - hand sides of the linearised field equations = ( d(v^i ) ) + x,[newv ] for @xmath102 , subject to @xmath132 , and = ( d(w^i ) ) + ^i,[neww ] for @xmath102 , subject to @xmath133 . these equations are parabolic , by the choice of @xmath123 , and therefore have unique smooth solutions @xmath134 on @xmath124 , by lemma a.1 ( see appendix a ) , which is a convenient summary of relevant results from classical parabolic theory @xcite ; the updated approximants also have corresponding positive diffusivities , by the maximum principle . the coefficients of ( [ newv ] ) , ( [ neww ] ) , when expanded into the standard form ( [ linear_para ] ) , are such terms as @xmath135 , @xmath136 , @xmath137 , and analogues for @xmath138 , and are therefore dominated in @xmath139 by @xmath140 and @xmath141 . thus , by lemma a.1 , @xmath130 is some positive function , @xmath142 , and @xmath143 is the ordinary hlder norm . next , applying lemma b.1 to ( [ vnew_est1 ] ) and ( [ wnew_est1 ] ) results in and |w^i+1|^(l+1)_q_t - k()w_0_c^2 k()t^f(c)(|w_0|^(l+2)_+_2),[wnew_est2 ] where @xmath144 thus , if we choose @xmath145 , and @xmath146 is taken sufficiently small , then ( |v^i+1|^(l+1)_q_t , |w^i+1|^(l+1)_q_t)c . iteratively , we therefore have that ( [ vw_c_bound ] ) , ( [ sdot_bound ] ) , ( [ vnew_est1 ] ) , and ( [ wnew_est1 ] ) hold uniformly for all @xmath122 . next , taking the difference of ( [ newv ] ) and the corresponding equation for @xmath147 gives an equation of the form ( v^i+1-v^i ) & = & d_i(x , t)(v^i+1-v^i ) + a_i(x , t)(v^i+1-v^i ) + b_i(x , t)(v^i - v^i-1 ) + & + & c_i(x , t)(v^i - v^i-1 ) + d_i(x , t)(s^i - s^i-1 ) + e_i(x , t)(^i-^i-1),[v_diff_i ] where @xmath148 for all @xmath122 , some @xmath149 , and all the coefficients are bounded in @xmath150 , uniformly in @xmath122 , by the results just obtained . for the difference @xmath151 , we get , from ( [ rescaled_rh ] ) , ( s^i - s^i-1 ) = p_i(t)(s^i - s^i-1 ) + q_i(t)(v^i_x - v^i-1_x)(1,t ) + r_i(t)(w^i_x - w^i-1_x)(0,t ) , [ sdiff ] where @xmath152 are bounded in @xmath153 , uniformly in @xmath122 , and from this it is easy to deduce that thus , applying ( [ sdiff2 ] ) and lemma a.1 to ( [ v_diff_i ] ) , we get of course , there is also an analogous estimate for @xmath154 , which , together with ( [ vdiff2 ] ) , implies + |w^i - w^i-1|^(l+1)_q_t ) . finally , an application of lemma b.1 to the right - hand side of this inequality gives , since all iterates have the same initial data , c_1t^(|v^i - v^i-1|^(l+2)_q_t + |w^i - w^i-1|^(l+2)_q_t ) . ( note that @xmath155 stands for various constants in the above ) . if @xmath71 is chosen so small that @xmath156 , it is easy to see that @xmath147 and @xmath138 are cauchy sequences with respect to @xmath157-norm . moreover , it follows from ( [ sdiff2 ] ) that @xmath129 is cauchy in @xmath158-norm . by the strong convergence of these sequences , their limits @xmath159 satisfy ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) pointwise , and thus constitute a classical solution of @xmath38 . turning to the question of uniqueness , suppose we have two smooth solution triples @xmath160 , @xmath161 , satisfying ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) , and having the same initial data . subtracting the equation satisfied by @xmath162 from that satisfied by @xmath163 then gives an equation of the form _ t(v-|v ) = d(x , t)_x^2(v-|v ) + a(x , t)_x(v-|v ) + b(x , t)(v-|v ) + c(x , t)(s-|s ) + d(x , t)(-),[v - vbar ] where the coefficients are smooth , and @xmath164 , some @xmath149 . an analogous equation is obtained for @xmath165 in the same way . thus , by lemma a.1 , @xmath166 can be bounded by the inhomogeneity in ( [ v - vbar ] ) , according to & & c(|s-|s|^(l)_q_t + |-|^(l)_q_t ) + & & c(|v_x-|v_x|^(l)_q_t + |w_x-|w_x|^(l)_q_t ) + & & c(|v-|v|^(l+1)_q_t + |w-|w|^(l+1)_q_t),[inequality4 ] for various constants @xmath167 , where we used the rankine - hugoniot condition ( [ rescaled_rh ] ) to get the third line . adding the analogous inequality for @xmath165 therefore results in |v-|v|^(l+2)_q_t + |w-|w|^(l+2)_q_t c(|v-|v|^(l+1)_q_t + @xmath168 , as required @xmath92 we will prove a global - existence theorem for @xmath38 by showing that , for a local classical solution @xmath169 , the gradient , @xmath170 , and hence also @xmath171 , are _ a priori _ bounded , provided that the one - sided limits @xmath172 satisfy a sign condition . the proof is rather different from , and somewhat shorter than , that presented in @xcite . first , with the change of dependent variable @xmath108 , which is smooth and invertible in each phase , the governing pde becomes _ t = ( ) _ xx,[global_sigma ] where @xmath173 , the boundary conditions become _ x(0)=_x(1)=0,(s^-)=k(_1):=_1,(s^+)=k(_2):=_2 , and the rankine - hugoniot condition takes the form = -.[rh_sigma_0 ] next , note that integration by parts gives , for any smooth @xmath174 , and @xmath175 , _ t(_x)^2 m dx = -_0^s(t ) 2m(m-1)_x^2m-2_xx_t dx + _ 0^s(t)[int_by_parts ] . assuming now that @xmath176 solves @xmath38 , we have @xmath177 , and hence , by differentiation,@xmath178 at @xmath179 , which , with the aid of ( [ int_by_parts ] ) , leads to ( _ x)^m^2_l^2(0,s ) & = & -_0^s 2m(2m-1)(_x)^2m-2_xx_t dx + ( 1 - 2m)(_x)^2m.|_x = s^- + & & ( 1 - 2m)(t)(_x)^2m|_x = s^-,[sig_left ] where we used ( [ global_sigma ] ) to discard the integral term . by a similar calculation , there also follows ( _ x)^m^2_l^2(s,1 ) -(1 - 2m)(t)(_x)^2m|_x = s^+.[sig_right ] if we regard @xmath180 as a function in @xmath181 , then adding ( [ sig_left ] ) and ( [ sig_right ] ) , and using ( [ rh_sigma_0 ] ) , results in ( _ x)^m_2 ^ 2 ( 1 - 2m)((_x)^2m(s^+)-(_x)^2m(s^-)).[sig_decay ] now , if @xmath182 then , inductively , there is a _ positive _ multinomial @xmath183 such that ( a - b)(a^2^n - b^2^n ) = f_n(a , b)(a+b),a , b.[f_n ] using ( [ f_n ] ) in the right - hand side of ( [ sig_decay ] ) with @xmath184 shows that @xmath185 is decreasing for @xmath186 , provided _ x(s^+ ) + _ x(s^-)0t.[grad_sign ] this condition can be guaranteed , for example , by choosing data @xmath187 for @xmath38 satisfying the traditional condition ( [ class_data ] ) , and by appealing to the maximum principle in each phase . thus , assuming ( [ grad_sign ] ) holds , we have _ x_l^2^n(t ) _ x_l^2^n(0 ) _ x_(0 ) , for @xmath188 , and therefore , by theorem 2.8 of @xcite , _ x_(t)_x_(0 ) . in 1-d , such an _ a priori _ bound on @xmath189 , which of course also gives a pointwise bound on the corresponding @xmath190 and on @xmath171 , is actually enough to continue the local solution of @xmath38 obtained in sect.2.3 , by standard theory . indeed , if @xmath163 and @xmath191 are as in ( [ v])-([w ] ) , then combining the estimates of appendix a gives , for @xmath192 , and a constant @xmath167 which is controlled by @xmath193 , |v|^(2-)_q_tc(v_c^2((0,1))+_1 ) , and an analogous estimate for @xmath191 . thus , for some @xmath194 , the @xmath195-norm of @xmath163 and @xmath191 is controlled by @xmath193 and the @xmath196-norm of the initial data . given this , lemma a.1 implies in turn that the @xmath197-norm of @xmath163 and @xmath191 is controlled by @xmath193 and the @xmath198-norm of the initial data . thus , the local classical solution can always be extended onto to a larger time interval , provided , of course , @xmath35 stays away from the domain boundary . we have already seen ( theorem 2.1 ) that if the total mass @xmath44 lies outside the interval @xmath199 , it can not be ruled out that @xmath35 will hit the domain boundary in finite time ; should this occur , the solution can be continued via the neumann problem on @xmath200 , as mentioned above . note that , on a disappearing phase , the solution ( in terms of the original variable @xmath15 ) merely approaches @xmath33 or @xmath34 , as appropriate , by the boundedness of the gradient . since we have already extended our definition of @xmath38 to cover such eventualities , we have therefore proved given phase - wise smooth initial data @xmath51 satisfying ( [ class_data ] ) and the first - order compatibility condition , problem @xmath38 has a unique smooth , global - in - time solution @xmath169 , such that the corresponding @xmath201 is monotonically decreasing for all @xmath91 . in general , it is not clear whether a corresponding global - existence result can be obtained in the situation where ( [ class_data ] ) is not satisfied . an exception to this is the special case of 1-phase problems , to which we now turn our attention . if the initial density is constant for either @xmath94 or @xmath96 , then we refer to the corresponding evolution problem @xmath38 as a one - phase problem . as a consequence of the neumann condition at the domain boundary , it then turns out that there is a change of the spatial variable , different from a simple rescaling , which transforms the one - phase @xmath38 into a regular quasilinear parabolic problem on a fixed domain . this allows us to prove a global - existence theorem , using standard parabolic theory , regardless of the direction of the gradient at the phase boundary . without loss of generality , let us assume that @xmath15 is constant ( @xmath202 ) in the high - density phase , and variable in the low - density phase , and let us again make the change of dependent variable @xmath108 on @xmath98 . since we are assuming @xmath31 in the low - density phase , this change of variable is invertible there , with inverse denoted by @xmath203 . in terms of @xmath174 , the governing equation ( [ cont_rho ] ) becomes = , [ b_sigma ] subject to @xmath204 at @xmath41 , and @xmath205 at @xmath206 , while the rankine - hugoniot condition takes the form = ( s^-)/(_2-_1 ) . next , we transform ( [ b_sigma ] ) by introducing so - called mass lagrange coordinates @xcite , @xmath207 , which are defined by = t , y=_x^s(t ) d. since , by construction , @xmath208 , this coordinate change is good , and , introducing @xmath209 , ( [ b_sigma ] ) now takes the form = , [ b_v ] which is a regular quasilinear parabolic equation for @xmath163 . clearly , the moving boundary @xmath206 gets mapped to @xmath210 , and , as a consequence of conservation of mass , the domain boundary @xmath41 gets mapped to y_0:=_0^s(0 ) dx=. thus , ( [ b_v ] ) is to be solved on a fixed spatial domain subject to the boundary conditions @xmath211 at @xmath212 , and @xmath213 at @xmath210 . it is well known that this problem has a unique , global classical solution @xmath214 , given @xmath215 initial data compatible with the dirichlet condition at @xmath210 @xcite . the corresponding jump location @xmath35 , which can be reconstructed from @xmath214 by integrating , for each @xmath216 , the equation = b(v(y , ) ) from the point @xmath217 until @xmath218 hits zero , could conceivably hit @xmath219 in finite time ( see the numerics in the next subsection ) . if this occurs , the solution of ( [ b_v ] ) should be stopped , and then continued for all time via np for ( [ cont_rho ] ) on @xmath142 . we thus arrive at given smooth , one - phase initial data which satisfies the first - order compatibility condition , problem @xmath38 has a unique smooth , global - in - time solution @xmath169 . the use of rescaled coordinates , as introduced early on in this subsection , allows us to investigate linear stability of the unique discontinuous steady state ( [ s_star ] ) of @xmath38 , which exists as long as @xmath45 . linearising ( [ v ] ) and ( [ w ] ) around @xmath220 and @xmath221 , respectively , and using hats to denote differentials , we get the pair of heat equations _ t & = & d(_1)_xx , + _ t & = & d(_2)_xx , which are to be solved subject to @xmath222 , @xmath223 , @xmath224 , @xmath225 , while linearising ( [ resc_com ] ) around @xmath226 gives = ( _ 1-_2)^-2\{-(_1-_2)_0 ^ 1 dx + ( _ 2-m)_0 ^ 1(- ) dx}. for a solution @xmath227 of the linearisation , it is therefore clear that , say , @xmath228 and @xmath229 as @xmath57 , and also that @xmath230 as @xmath57 . in this sense , then , the unique discontinuous steady state of @xmath38 is always linearly stable , whenever it exists . as well as facilitating mathematical analysis , the rescaled , fixed - boundary representation of @xmath38 , ( [ v ] ) , ( [ w ] ) , ( [ rescaled_rh ] ) , also comes in useful for numerical simulations . specifically , we use a method - of - lines approach in which the diffusion terms in ( [ v ] ) and ( [ w ] ) are discretised using the random - walk model ( [ walk ] ) , while the advection terms are discretised by means of a standard , explicit upwinding scheme . a simulation in which the global - existence criterion ( [ class_data ] ) is satisfied is shown in figure 2 , and one in which it is violated is shown in figure 3 . in each case , the solution approaches the appropriate discontinuous steady state at large times . several other simulations have been carried out in the case where ( [ class_data ] ) is violated , and no singularities have been observed to develop . turning to the question of bistability for cetain values of the mass @xmath44 , we next show in figure 4 a close - up of a solution with @xmath231 and @xmath232 , for which the phase boundary hits the domain boundary in finite time . this should be compared with the simulation shown in figure 5 , in which the solution has the same mass and adhesion coefficient , but this time evolves to the unique discontinuous steady state as @xmath57 . it is perhaps worth noting that such bistability can not occur if the traditional restriction ( [ class_data ] ) is imposed on the initial data , by theorem 2.1 . we now consider the general case of our stefan - problem set - up , in which the initial density profile jumps @xmath40 times across the the unstable region @xmath16 . this initial / boundary - value problem will be denoted by @xmath39 . the problem @xmath39 consists of looking for a piecewise - smooth @xmath15 which satisfies the diffusion equation ( [ cont_rho ] ) away from @xmath40 discontinuities @xmath18 , with @xmath233 , such that @xmath15 always jumps between @xmath33 and @xmath34 at the @xmath19 , which evolve according to the rankine - hugoniot condition = , [ rh_i ] where @xmath234 , and @xmath235=(\rho(s_i^+,t)-\rho(s_i^-,t))$ ] ( @xmath236 ) , and the neumann condition is again imposed at the domain boundary @xmath237 ; a schematic for @xmath39 is given in figure 6 . we also allow for the possibility that @xmath238 or @xmath239 may hit the domain boundary in finite time , or that neighbouring discontinuities could collide , leading to the annihilation of a phase . should any of these events occur , the solution can be continued via @xmath240 or @xmath241 , as appropriate , and so on . a solution continued in this way will still be referred to globally as a solution of @xmath39 . the steady - state picture for @xmath39 , given @xmath242 is more complicated than that for @xmath38 . first of all , for a given mass @xmath44 satisfying @xmath45 , there is a continuum of two - valued , @xmath40-jump steady states , each of which is given by a choice of the @xmath19 which merely has to be compatible with @xmath44 . moreover , discontinuous steady states with fewer than @xmath40 jumps can also be considered permissible - these could be approached dynamically by ( multiple ) coalescence events , and/or by ( successive ) collisions of phase boundaries with the domain boundary . each steady state with more than one discontinuity is expected to be merely neutrally stable , since the total mass is invariant under small translations of an internal phase ( i.e. , one which does _ not _ touch the domain boundary ) . if the stronger condition @xmath53 holds , then there is no possible continuous steady state , and thus , for a global solution of @xmath39 , at least one discontinuity must remain as @xmath57 . if , instead , @xmath58 or @xmath59 , then the uniform steady state exists alongside the discontinuous family already discussed . in this regard , note that figures 4 and 5 could be considered as simulations of one half of a reflection - symmetric @xmath243 , with @xmath244 , in which the central high - density phase is either annihilated in finite time ( figure 4 ) or preserved as @xmath57 ( figure 5 ) , depending on the proximity of the initial data to the ( unique ) discontinuous , symmetric steady state . in general , it is difficult to say anything analytical about the stability of steady states of @xmath39 , although in each phase the solution will still decay to @xmath33 or @xmath34 , as appropriate , exponentially in @xmath55 , by essentially the same calculation as in section 2.2 , as long as the relevant phase boundaries stay away from the domain boundary . finally , note that if @xmath47 or @xmath46 , then there is only one possible steady state , namely the uniform one , and , by @xmath55-decay , phase boundaries for a global solution must disappear in finite time ( or possibly infinite time in the exceptional cases @xmath245 ) via coalescence events , or by merging with the domain boundary . for the subsequent @xmath43 , exponential @xmath55-convergence to the uniform steady state @xmath65 follows as before . the multi - phase problem , @xmath39 , is solved , locally in time , in the same way as @xmath38 ; in each phase the spatial variable is rescaled in order to fix the moving boundary ( or boundaries ) , and the same estimates go through as before . to be explicit , on the interval @xmath246 $ ] we make the coordinate transformation ( x , t ) ( , ) : = , = t , such that , writing @xmath247 , the governing pde ( [ cont_rho ] ) becomes , upon dropping hats = ( s_i+1-s_i)^-2(d(v_i ) ) + , [ v_i ] on @xmath36\times[0,t]$ ] , for @xmath248 , where we adopt the conventions @xmath249 and @xmath250 . on an internal phase , this equation is to be solved subject to the appropriate dirichlet conditions at @xmath237 , while on an extremal phase the mixed neumann / dirichlet conditions are used , as in the two - phase case ( see figure 6 ) . the rescaled family of rankine - hugoniot conditions takes the form = -(-)(_2-_1)^-1,[rescaled_rh_i ] for @xmath251 . equations ( [ v_i ] ) , ( [ rescaled_rh_i ] ) are solved by the same kind of iteration employed for @xmath38 ; the required hlder estimates are obtained via linear parabolic theory and picard s theorem for systems of odes . the upshot of all this is given initial data @xmath252 , @xmath251 , for which the @xmath253 and @xmath254 belong to the hlder space @xmath255 , @xmath112 , and such that the first - order compatibility conditions are satisfied , the system of equations ( [ v_i ] ) , ( [ rescaled_rh_i ] ) , and hence problem @xmath39 , has a unique classical solution on some small time interval @xmath115 $ ] . with the same notation as in sect . 2.4 , and by a similar calculation , it is straightforward to see that the gradient of a local solution of @xmath39 satisfies , for @xmath175 , the _ a priori _ estimate ( _ x)^m^2_l^2((0,1))()_i[]_i(_x(s_i^+)-_x(s_i^-))(_x^2m(s_i^+)-_x^2m(s_i^- ) ) . thus , @xmath201 , and hence also the @xmath256 and @xmath257 , are bounded for all time , provided [ ] _ i(_x(s_i^+)+_x(s_i^-))0,i . this condition holds if , for example , _ 0_1,_0_2,[grad_cond2 ] which is the multi - phase analogue of ( [ class_data ] ) . inequalities ( [ grad_cond2 ] ) therefore guarantee global existence of the corresponding solution to @xmath39 , modulo coalescence events , and the possibility that an extremal discontinuity might hit the boundary in finite time . in order to continue a solution of @xmath39 after the coalescence of two phases , it is necessary to extend our existence theory ( which has thus far required the initial data to lie in @xmath255 ) to the case where the initial density profile may have a ` corner ' in one of the phases . this can be seen by considering the situation illustrated in figure 7 , in which two high - density phases coalesce , thus annihilating a low - density phase . if we make the assumption that condition ( [ grad_cond2 ] ) holds , then , in fact , the required extension for such phase - wise @xmath215 data follows from theorem 14 , sect.v of @xcite , and hence , putting together the results of this section , we therefore arrive at given @xmath40 initial jump locations @xmath258 , and a phase - wise smooth initial density profile @xmath259 satisfying the first - order compatibility conditions at phase boundaries , along with the gradient condition ( [ grad_cond2 ] ) , the multi - phase stefan problem @xmath39 has a unique , global classical solution , on the understanding that phases may in time be annihilated via coalescence events , or that an extremal discontinuity may hit the domain boundary in finite time . moreover , @xmath201 is monotonically decreasing for all time . we end by noting that it is not clear whether even a local existence theorem for @xmath39 can be proved for merely @xmath215-data if ( [ grad_cond2 ] ) is not satisfied ; one can , for example , proceed by approximating @xmath215 data with smooth data , but it seems that the _ a priori _ bound on @xmath180 implied by ( [ grad_cond2 ] ) is required to get the necessary convergence . the results of this paper can be interpreted as saying that cell - cell adhesion is enough to stabilise sharp - edged aggregations of diffusing cells if there is enough mass present in the biological domain , and that diffusion homogenises the cell density in each given high- or low - density phase . for low masses , however , narrow high - density regions can become annihilated even if the adhesion is very strong - that is to say , diffusion in the low - density regions wins , leading to a globally uniform cell density at large times . in the case of intermediate masses , bistability becomes possible - either adhesion or diffusion can win out , depending on the profile of the initial data . next , while being motivated by the adhesion - diffusion equations ( [ cont_rho ] ) and ( [ mod - equ ] ) , it should be clear that the analysis carried out in this paper does not require that the diffusivity @xmath10 have the special form ( [ d ] ) ; indeed , all arguments go through for _ any _ equation of the form @xmath260 , provided the @xmath196 function @xmath261 is increasing outside an unstable interval of @xmath15 values , and provided @xmath262_i=0 $ ] at jump locations @xmath19 . finally , one rather obvious biologically - relevant extension of the work described here would be to carry out a similar analysis with a chemotactic term factored into the right - hand side of ( [ cont_rho ] ) . in that situation , one could imagine beginning with a low - density initial datum , evolving the solution until , through chemotactic aggregation , @xmath15 hits the unstable region @xmath16 at some point @xmath263 , and then continuing the solution via a stefan problem with an initial spike at @xmath263 which jumps from @xmath33 to @xmath34 . the transition from well - posed neumann problem to stefan problem is somewhat singular in that case , and is the subject of ongoing analytical investigation . the author wishes to thank christian schmeiser for suggesting this problem , and for several helpful discussions along the way . first of all , we have * lemma a.1 * _ the equation _ = d(x , t ) + a(x , t ) + b(x , t)u + f(x , t),[linear_para ] d(x,0 ) + a(x,0 ) + b(x,0)u_0 + f(x,0 ) = 0 , + for the proof , see @xcite , ch.4 , thms . 5.2 - 5.4 . next , let @xmath264 denote the usual second - order @xmath55-type sobolev space on the unit interval , let @xmath265 , @xmath266 , be the sobolev space with norm u_1,q = u_l^q((0,1 ) ) + u_x_l^q((0,1 ) ) , and let @xmath267 denote the fractional - order sobolev space with norm u_2-,q = u_1,q + \ { _ _ dxdy}^,[frac_norm ] where @xmath142 , @xmath268 . then it is elementary to prove + + * lemma a.2 * @xmath269 , _ for @xmath270_. + + finally , let @xmath271 be the @xmath272-type parabolic sobolev space with norm u^(2)_q , q_t = u_q(q_t)+u_x_q(q_t)+u_xx_q(q_t)+u_t_q(q_t ) . then , by the fractional - order case of @xcite , ch . iv , thm . 9.1 , we have + + * lemma a.3 * if @xmath118 is the solution of the mixed dirichlet / neumann problem for ( [ linear_para ] ) , and if @xmath273 is _ a priori _ bounded , then we have u^(2)_q , q_tc(u(,0)_2-,q ( ) + |u_1|).[w(2)_q_est ] finally , by @xcite , ch . iv , top of p.343 , we have + + * lemma a.4 * for @xmath274 , and @xmath275 , there holds the imbedding inequality |u|^(2-)_q_tc u^(2)_q , q_t . * lemma b.1 * _ for a function @xmath276 , @xmath277 , such that @xmath278 $ ] , @xmath279 , we have _ _ proof . _ the parabolic hlder norms in question are , when written out in full , & + & u^(l+1)/2_t,_t + u_x^l/2_t,_t , + & & + & + & u_x^l_x,_t + u_xx^l_x,_t + u_t^l_x,_t + & + & u_t^l/2_t,_t + u_x^(l+1)/2_t,_t + u_xx^l/2_t,_t . we proceed to estimate each of the terms appearing in @xmath280 . first , u_c(_t)tu_t_c(_t ) + u(,0)_c ( ) . second , u_x_c(_t ) & & _ x , t|u_x(x , t)-u_x(x,0)| + _ x|u_x(x,0)| + & & t^(l+1)/2u_x^(l+1)/2_t,_t + u_x(,0)_c(_t ) . third , u_x^l_x,_t & = & _ x , x,t + & = & _ x , x,t + & & _ x , x|x - x|^1-lu_xx_c(_t ) + & = & c(,l)u_xx_c(_t ) + & & c_x , t(|u_xx(x , t)-u_xx(x,0)| + |u_xx(x,0)| ) + & & ct^l/2u_xx^l/2_t,_t + u_xx(,0)_c ( ) . fourth , u^(l+1)/2_t,_t & = & _ x , t , t + & & u_t_c(_t)t^(1-l)/2 . fifth , u_x^l/2_t,_t & = & _ x , t , t + & & t^u_x^(l+1)/2_t , . putting these estimates together gives the desired result @xmath92 subject to a restriction on the initial data , a weak formulation of @xmath39 can be written down in such a way that the rankine - hugoniot condition becomes ` hidden ' , thus aiding mathematical analysis . essentially the same kind of formulation was written down many years ago by ladyenskaya _ @xcite , and , for example , their uniqueness proof goes through without change . to obtain the correct weak formulation on @xmath286\times[0,t]$ ] , first note that for a smooth test function @xmath287 such that @xmath288 , we have , for classical solutions of @xmath39 , and with @xmath289 , _ 0^t_0 ^ 1 dxdt = _ 0^t_0 ^ 1 dxdt - _ 0^t_i=1^n(s_i , t)[_x]_i dt - _ 0^t_i=1^n _ x(s_i , t)[]_i dt . thus , using ( [ rh_sigma ] ) , and noting that @xmath174 is continuous at @xmath19 by construction , we arrive at _ 0^t_0 ^ 1 ( b()_t+ ) dxdt + _ 0 ^ 1 b()|_t=0 dx = 0[weak ] for all smooth @xmath287 such that @xmath288 , as the weak formulation of @xmath39 . this is identical to the problem considered in chapter v.9 of @xcite , and existence and uniqueness of solutions follows by exactly the same argument used there , since one merely requires that @xmath291 be piecewise smooth and monotonically increasing . we record this result as + + * lemma c.1 * _ for a given bounded , continuous initial datum @xmath292 , equation ( [ weak ] ) has a unique bounded solution @xmath293 . _ 100 adams , r. : sobolev spaces . academic press ( 1975 ) . amann , h. : dynamic theory of quasilinear parabolic systems . iii . global existence . math . z. * 202 * , 219 - 250 ( 1989 ) . anguige , k. , schmeiser , c. : a one - dimensional model of cell diffusion and aggregation , incorporating volume - filling and cell - to - cell adhesion . j. math . , online first . ladyenskaya , o. , solonnikov , v. , uralceva , n. : linear and quasilinear equations of parabolic type . ams translations of mathematical monographs , vol.23 ( 1968 ) . meirmanov , a. : the stefan problem . de gruyter expositions in mathematics ( 1992 ) . sun , x. , ward , m. : the dynamics and coarsening of interfaces for the viscous cahn - hilliard equation in one spatial dimension . stud . appl . math . * 105 * , 203 - 234 ( 2000 ) . taylor , m. : partial differential equations iii . springer ( 1996 ) . vazquez , j. l. : the porous - medium equation : mathematical theory . oxford science publications ( 2007 ) .

we consider a family of multi - phase stefan problems for a certain 1-d model of cell - to - cell adhesion and diffusion , which takes the form of a nonlinear forward - backward parabolic equation . in each material phase the cell density stays either high or low , and phases are connected by jumps across an ` unstable ' interval . we develop an existence theory for such problems which allows for the annihilation of phases and the subsequent continuation of solutions . stability results for the long - time behaviour of solutions are also obtained , and , where necessary , the analysis is complemented by numerical simulations .

a pseudoaneurysm is an extra - luminal collection of blood with turbulent flow that communicates with the parent vessel through a defect in the arterial wall . the development of an arterial pseudoaneurysm is a rare but reported complication of pelvic surgery , vascular trauma during c - section or after uterine curettage . after hematoma formation , there is central liquefaction that leaves a cavity with turbulent blood flow , as a result of persistent communication between the parent artery and the hematoma . the absence of a 3-layer arterial wall lining the pseudoaneurysm differentiates it from a true aneurysm , which is less common than a pseudoaneurysm . pseudoaneurysm of the uterine artery is an uncommon cause of delayed postpartum hemorrhage following caesarean or vaginal delivery and is potentially life threatening . typically , the lesions are discovered because the patients have symptoms related to delayed rupture of the pseudoaneurysm , causing hemorrhage . a pseudoaneurysm may be asymptomatic , may thrombose , or may lead to distal painful embolization . transcatheter uterine artery embolization ( uae ) has emerged as a highly effective technique for controlling obstetric and gynaecologic hemorrhage , including that from pseudoaneurysms . we report a case of uterine artery pseudoaneurysm presenting with secondary postpartum hemorrhage 3 weeks after c - section delivery and managed successfully with coil embolization . a 28-year - old gravida 2 , para 1 was transferred to our institution 19 days post operation with symptoms of excessive bleeding per vaginum . she later developed excessive bleeding per vaginum , high grade fever , and was readmitted . on abdominal examination , the c - section scar was found to be healthy and no abnormality was detected . she was stabilized with crystalloids , five units packed red blood cells , and started on broad spectrum antibiotics . there was no evidence of residual placental tissue in the uterine cavity and endometrial thickness was 7 mm . a hypoechoic lesion measuring 2 cm 1.5 cm [ figure 1a ] was detected in the isthmic region of uterus and power doppler revealed blood flow within it [ figure 1b ] . color flow doppler sonography showed yin and yang blood flow pattern within the body of pseudoaneurysm . ( a ) gray - scale ultrasound of the pelvis shows a hypoechoic lesion in the anterior wall of uterus . ( b ) power doppler evaluation of the uterus demonstrates blood flow within this hypoechoic lesion . computed tomography angiogram was done with non - ionic contrast showed early contrast filling of the lesion within the uterus [ figure 2a , b ] . maximum intensity projection ( mip ) and volume rendered ( vr ) images nicely demonstrated the pseudoaneurysm in relation to the uterine artery [ figure 2c , d ] . ( a ) axial and ( b ) sagittal mpr ct angiogram images show contrast filling the pseudoaneurysm ( arrow ) within the uterus . ( c ) mip and ( d ) vr images show a pseudoaneurysm in relation to the left uterine artery . to preserve the fertility in this young patient , a transcatheter arterial embolization of this pseudoaneurysm was planned . arteriography revealed a pseudoaneurysm from the terminal part of the left uterine artery , in addition the left uterine artery was tortuous and was hypertrophied [ figure 3a , b ] . left uterine artery was selectively embolized with mixture of gelfoam and contrast media followed by 2 stainless steel coils 4 mm in diameter [ figure 4a ] . the right uterine artery was also tortuous and hypertrophied and was embolized with gel foam . a post embolization angiographic study was performed to ensure the complete occlusion of the vessels [ figure 4b ] . follow - up color doppler us showed aneurysmal cavity filled with echogenic content with no evidence of blood flow [ figure 4c ] , except for pain in the abdomen that was managed with analgesics . selective left internal iliac angiogram : ( a ) early and ( b ) late phase shows the pseudoaneurysm ( arrows ) , arising from the left uterine artery ( arrowhead ) in addition the hypertrophy of the left uterine artery can also be appreciated . ( b ) selective left internal iliac angiogram ( postembolization ) using gelfoam and embolization coils show complete obliteration of the pseudoaneurysm . ( c ) follow up color doppler sonography shows no evidence of blood flow within the pseudoaneurysm . secondary postpartum hemorrhage is defined as excessive bleeding starting any time from 24 hours after delivery up to 6 weeks postpartum and most commonly occurring between 8 and 14 days postpartum . common causes include retained products of conception , subinvolution of the placental bed , and endometritis . rare causes include pseudoaneurysm of uterine artery , arteriovenous malformations , and choriocarcinoma . when the more common causes have been excluded , pelvic angiography may be performed . brown et al . , reported the first case of selective arterial embolization used successfully to treat an extrauterine pelvic hematoma after three failed surgical attempts to control the bleeding . since then , arterial embolization has been used successfully to control postpartum bleeding from uterine atony , placenta accreta , and vulvar and vaginal hematomas . the efficacy and safety of selective arterial embolization of uterine arteries was evaluated by pelage et al . , in women with delayed secondary postpartum hemorrhage . in their series of 14 women , pseudoaneurysms of the uterine artery were found in 2 women . immediate resolution of external bleeding was observed after embolization . in this series , a true aneurysm has all three layers of arterial wall , whereas pseudoaneurysm does not have all the three layers of arterial wall . the differential diagnosis of pseudoaneurysm includes acquired arteriovenous malformations ( avms ) , arteriovenous fistulas , and direct vessel rupture . avms are characterized by multiple communications of varying sizes between arteries and veins , which can be congenital or acquired . congenital uterine avms are due to abnormality in the embryologic development of primitive vascular structures , whereas acquired avm 's consist of multiple small arteriovenous fistulas between intramural arterial branches and the myometrial venous plexus . acquired avm 's occur more commonly following d and c , uterine surgery , or trauma to the uterus . color flow doppler demonstrates to - and - fro sign in the neck of the pseudoaneurysm and yin - yang sign in the body of the pseudoaneurysm . avm 's are characterized by marked aliasing on color flow doppler and arterialized venous flow on spectral doppler evaluation . in a small series of women , who underwent embolotherapy for obstetric hemorrhage , all 3 women who attempted conception after embolization were successful . treatment was by angiographic embolization of uterine arteries with gelfoam and embolization coils . in a series of women , rosenthal et al . , observed angiographic arterial embolization was shown to be the most useful clinical tool in the management of post operative vaginal hemorrhage . angiographic embolization has the advantages of decreased morbidity , ability to localize the bleeding site and provide a more distal occlusion than surgical ligation , and preservation of future fertility compared to hysterectomy . burchell demonstrated that bilateral internal iliac artery ligation was more effective in reducing the pulse pressure than unilateral ligation . it is possible that the redistribution and redirection of blood or hypoxia - induced neovascularization allows bleeding to occur from the contralateral side after unilateral embolization . inadequate embolization of a pseudoaneurysm due to extrauterine feeding arteries , such as the internal pudendal artery , ovarian artery , inferior epigastric artery , or contralateral uterine artery leading to embolization failure can occur . we conclude that in a woman with unexplained vaginal bleeding after c - section delivery , pseudoaneurysm is a potentially life - threatening complication and should be considered in the differential diagnosis of secondary postpartum hemorrhage . although data are scant , bilateral uterine artery embolization for obstetric hemorrhage appears to have no increased deleterious effect on future fertility and is more effective when compared to unilateral embolization .

uterine artery pseudoaneurysm is a rare cause of secondary postpartum hemorrhage but is potentially life - threatening and can occur after caesarean section ( c - section ) or a hysterectomy . a 28-year - old woman who developed secondary postpartum hemorrhage after c - section was diagnosed to have pseudoaneurysm from the left uterine artery on ultrasound ( us ) and computed tomography ( ct ) scan . she was treated with coiling of the pseudoaneurysm with stainless steel coil via selective catheterization of the uterine artery . the procedure was uneventful and the pseudoaneurysm was successfully obliterated . angiographic embolization is a safe and effective method for treating postpartum hemorrhage due to pseudoaneurysm in hemodynamically stable patients . therefore , it should be considered as a treatment option before resorting to surgery , in appropriately selected cases .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Boosting Equity for the American Middle Class Act of 2016'' or as the ``BEAM Act of 2016''. SEC. 2. REFUNDABLE CREDIT FOR EARLY PRINCIPAL PAYMENTS ON CERTAIN HOME MORTGAGES. (a) In General.--Subpart C of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 is amended by inserting after section 36B the following new section: ``SEC. 36C. EARLY PRINCIPAL PAYMENTS ON CERTAIN HOME MORTGAGES. ``(a) In General.--In the case of an individual, there shall be allowed as a credit against the tax imposed by this subtitle for the taxable year an amount equal to 50 percent of the excess home mortgage principal payments made by the taxpayer during such taxable year. ``(b) Annual Dollar Limitation.--The credit allowed under subsection (a) with respect to any taxpayer for any taxable year shall not exceed $500. ``(c) Lifetime Limitation.--No credit shall be allowed under subsection (a) to any taxpayer for any taxable year if credit was allowed under subsection (a) to such taxpayer for any 10 preceding taxable years. ``(d) Limitation Based on Modified Adjusted Gross Income.-- ``(1) In general.--The amount which would (but for this paragraph and after the application of subsection (b)) be allowable as a credit under subsection (a) shall be reduced (but not below zero) by the amount which bears the same ratio to the amount which would be so allowable as-- ``(A) the excess of-- ``(i) the taxpayer's modified adjusted gross income for the taxable year, over ``(ii) $125,000 (twice such amount in the case of a joint return), bears to ``(B) $10,000 (twice such amount in the case of a joint return). ``(2) Modified adjusted gross income.--The term `modified adjusted gross income' means adjusted gross income increased by any amount excluded from gross income under section 911, 931, or 933. ``(e) Excess Home Mortgage Principal Payments.--For purposes of this subsection-- ``(1) In general.--The term `excess home mortgage principal payments' means, with respect to qualified home mortgage indebtedness for any taxable year, the excess of-- ``(A) the aggregate amount of principal paid by the taxpayer with respect to such indebtedness during such taxable year, over ``(B) the aggregate amount of principal which would have been paid by the taxpayer with respect to such indebtedness during such taxable year if the taxpayer had timely made each required payment under the terms of the indebtedness during such taxable year (and no other payments). ``(2) Qualified home mortgage indebtedness.-- ``(A) In general.--The term `qualified home mortgage indebtedness' means any acquisition indebtedness (as defined in section 163(h)(3)(B)) if-- ``(i) the residence with respect to such acquisition indebtedness is the primary residence (within the meaning of section 121) of the taxpayer, and ``(ii) such indebtedness constitutes a traditional mortgage. ``(B) Traditional mortgage.--For purposes of this paragraph, the term `traditional mortgage' means indebtedness-- ``(i) the term of which is not less than 15 years and not more than 30 years, and ``(ii) the required payments under which are each the same amount and made in equal intervals during the term of the indebtedness (or if any payment is required at a different interval, the amount of such payment is adjusted in the same proportion as the change in interval). ``(f) Rules Related to Joint Returns.-- ``(1) No credit for married individuals filing separately.--In the case of a married individual, no credit shall be allowed under this section for any taxable year unless such individual files a joint return with such individual's spouse for such taxable year. ``(2) Application of lifetime limitation with respect to joint returns.--If the credit under subsection (a) is allowed with respect to a joint return for any taxable year, such credit shall be treated for purposes of applying subsection (c) as allowed to both spouses for such taxable year. For purposes of applying subsection (c) with respect to a joint return for any taxable year, the taxpayer shall be treated as having been allowed the credit under subsection (a) for 10 or more preceding taxable years only if both spouses have been so allowed such credits.''. (b) Reporting of Excess Home Mortgage Principal Payments.--Section 6050H(b)(2) of such Code is amended by striking ``and'' at the end of subparagraph (C), by redesignating subparagraph (D) as subparagraph (E), and by inserting after subparagraph (C) the following new subparagraph: ``(D) the amount of excess home mortgage principal payments (as defined in section 36C(e)) received with respect to such mortgage during the calendar year, and''. (c) Conforming Amendments.-- (1) Section 6211(b)(4)(A) of such Code is amended by inserting ``36C,'' after ``36B,''. (2) Section 1324(b)(2) of title 31, United States Code, is amended by inserting ``36C,'' after ``36B,''. (3) The table of sections for subpart C of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 is amended by inserting after the item relating to section 36B the following new item: ``Sec. 36C. Early principal payments on certain home mortgages.''. (d) Effective Date.--The amendments made by this section shall apply to taxable years ending after the date of the enactment of this Act.

Boosting Equity for the American Middle Class Act of 2016 or the BEAM Act of 2016 This bill amends the Internal Revenue Code to allow a refundable tax credit equal to 50% of the excess home mortgage principal payments made by a taxpayer during the year. The credit is limited to $500 per year and to taxpayers who have not received the credit for any of the 10 preceding years. The bill reduces the amount of the credit for taxpayers with modified adjusted gross incomes above specified levels. An &quot;excess home mortgage principal payment&quot; is the excess of: (1) the amount of principal paid by the taxpayer with respect to a mortgage during the year, over (2) the amount of principal the taxpayer would have paid by making each required payment on a timely basis under the terms of the mortgage (and no other payments). The mortgage must: (1) be for a primary residence, (2) for a term between 15 and 30 years, and (3) require payments that are each the same amount and made in equal intervals during the term of the mortgage (or if any payment is required at a different interval, the amount of the payment is adjusted in the same proportion as the change in interval). Married individuals must file a joint tax return to claim the credit. Persons engaged in a trade or business (e.g., lenders, mortgage companies, or banks) who are required to report mortgage interest payments from individuals of $600 or more must also report the amount of excess home mortgage principal payments received during the year.

in recent years a lot of effort has been undertaken in order to prepare and investigate ordered structures of -conjugated organic molecules on nanoscopic and mesoscopic scales . the interest of both fundamental and applied science was mainly driven by the goal to understand and improve the properties of materials used for organic electronics ( e.g. , light emitting diodes , field effect transistors and solar cells ) and to establish novel systems for optical applications ( e.g. , waveguiding and lasing ) . frequently small rodlike molecules like oligothiophenes , oligoacenes and oligophenylenes have been selected as model systems . in the group of oligothiophenes sexithiophene ( 6 t ) has shown interesting high quality properties like a charge carrier mobility of up to 0.1 cm/(v s ) . consequently there has been an interest in understanding the growth mechanism of such molecules on well - defined model substrates like single crystalline cu , sheet silicates or patterned sio2 . the study in this paper aims at providing a conclusive picture of the formation of 6 t nanostructures by an in - depth analysis of the growth on an alkali - halide single crystal , namely potassium chloride ( kcl ) . kcl exhibits a face centered cubic crystal structure with a lattice constant of 6.36 . the unit cell of the ( 100 ) surface can be described by the 2d - space group p4 mm as shown in figure 1 . importantly , this high symmetry surface exhibits rotation centers of order 2 and 4 as well as mirror and gliding planes . it is expected that the symmetry of the substrate will be reflected in the multiplicity of epitaxial alignments of the deposited molecules . ( a ) the ( 100 ) surface of the kcl crystal , with the white rectangle illustrating the surface unit cell . ( b ) the p4 mm symmetry of the surface unit cell including the respective symmetry elements . the hot wall epitaxy ( hwe ) technique was applied for the deposition of the organic material , which allows the growth process to be performed close to thermodynamic equilibrium , and in further consequence relatively high vapor pressure of the organic deposit in the substrate region can be achieved . therefore the requirements concerning vacuum conditions are reduced as compared to , e.g. , molecular beam epitaxy . the source material 6 t was purified twice by thermal sublimation before filling it into the quartz tube of the hwe reactor . kcl substrates were transferred into the deposition chamber via a load lock and subsequently preheated at the deposition temperature ( 60135 c ) for 30 min to clean the surface from adsorbed species and to ensure a stable temperature during the whole deposition process . the deposition was performed thereafter under a base pressure of 9 10 mbar at a nominal deposition rate of 0.4 nm / min . x - ray diffraction ( xrd ) measurements were carried out on a philips xpert x - ray diffractometer using cr k radiation ( = 2.29 ) and a secondary graphite monochromator . brentano configuration by varying the z - component of the scattering vector q. consequently it is possible to detect lattice planes which are parallel to the sample surface . pole figures are acquired by measuring at a constant length of q and only varying its direction . based on both the observed bragg peaks of the specular scan and the direction of the poles ( net - plane normals ) within the pole figures , the involved crystallographic phases as well as the azimuthal alignment of the crystallites with respect to the substrate can be identified . optical microscope images have been acquired by a nikon labophot 2a microscope in combination with a nikon type 115 digital camera . scanning force microscopy ( sfm ) studies of the deposited organic films were performed using a digital instruments dimension 3100 in the tapping mode . the images have been acquired at scan speeds of 46 m / s using sic tips exhibiting a cone angle of 40. nominal values for resonance frequency and tip radius are 325 khz and 10 nm respectively . in this paper we reported on epitaxial growth of 6 t on kcl ( 100 ) , which was examined by crystallographic and morphological investigations . by means of sfm analysis different morphologies furthermore , it was found that the area covered by islands is declining with increasing substrate temperature , whereas the sample area covered by needles is constant over the investigated temperature range ( 60135 c ) . consequently we can draw the conclusion that needle - like structures are energetically more stable as compared to flat islands formed of standing 6 t molecules on kcl ( 100 ) . additionally , different activation energies for the growth of nanoneedles in height and width have been deduced from sfm analysis , namely , 0.26 0.02 ev and 0.15 0.04 ev , respectively . by means of xrd specular scans it was possible to determine the contact planes of the structures on the surface . needles with { 010 } and { 411 } and islands with the { 100 } facet parallel to the substrate surface have been detected . utilizing xrd pole figures and fft analysis of optical microscope images we observed that there is a well - defined azimuthal alignment of the structures on the surface in addition to the stacking in growth direction . notably structures with { 100 } and { 411 } contact planes are in perfect azimuthal alignment to each other , which is explained by ledge directed epitaxy of the islands on the sidewalls of already existing needles . the orientation of the crystallographic structures which are present on the substrate surface fulfills the growth model for rodlike molecules on sheet silicate substrates developed by simbrunner et al . therein it is explained that the adsorption of a single molecule dominates in a first step and the nucleation of organic crystallites which follows thereafter only leads to a slight reorientation of the lmas . in particular rotational and mirror symmetries have to be reflected by the formed needle orientations . the latter considerations are substantiated by the results presented in this paper . the 4-fold rotational symmetry and the mirror symmetry of the kcl ( 100 ) substrate surface leads to eight distinct growth directions of each crystal type . moreover two different crystal contact planes , namely , { 010 } and { 411 } , are characterized by an analogous lma orientation as similarly observed for p - hexaphenyl on kcl ( 100 ) . this hints that the adsorption geometry of single molecules seems to be decisive for the organic crystal nucleation as expected by the growth model . the fact that one adsorption geometry can lead to different crystal contact planes may be explained by polymorphs of the first monolayer , that are both based on the same azimuthal orientation of the lma on the substrate surface . the argument is supported by the fact that monolayer polymorphs of 6 t have already been reported on ag ( 001 ) and ag ( 110 ) . concluding the latter discussion it can be stated that the azimuthal alignment of the organic crystals and molecules is basically determined by a two step process . the initial phase is dominated by the adsorption of single molecules in their energetically preferred adsorption geometry on the substrate surface . this adsorption process is mainly determined by an interplay between substrate geometry , molecular geometry and importantly symmetry properties . in the second step , where the organic crystal nucleation takes place , only a slight azimuthal realignment of the molecules can be caused in order to optimize the lattice match at the interface .

the morphology and structure of sexithiophene deposited on kcl ( 100 ) substrates was investigated by scanning force microscopy and specular x - ray diffraction measurements . two different needle - like structures with { 010 } and { 411 } contact planes have been observed as well as islands of almost upright standing sexithiophene molecules with a { 100 } contact plane . furthermore an azimuthal alignment of all three crystal orientations was observed by x - ray diffraction pole figure measurements , and the growth directions reflect the 4-fold rotational symmetry of the substrate surface . in addition the analysis of crystals with { 411 } and { 100 } contact planes unveiled that they share a common crystallographic direction which is explained by ledge directed epitaxy .

ly@xmath0 nebulae , or `` blobs , '' are extended sources at @xmath9 @xmath6 26 with typical ly@xmath0 sizes of @xmath105 ( @xmath1050kpc ) and line luminosities of @xmath11 ergs@xmath4 . their number density and its large variance suggests that blobs lie in massive ( @xmath12 @xmath6 @xmath13@xmath14 ) dark matter halos , which will evolve into those typical of rich clusters today @xcite . galaxies embedded within blobs are likely to become brightest cluster galaxies . therefore , blobs are important sites for studying the early interaction of galaxies with the surrounding intergalactic medium ( igm ) . this interaction is probably tied on some scale to the source of the blobs extended ly@xmath0 emission , but the mechanism is poorly understood . for example , the blob may represent emission from galactic - scale outflows generated by star formation , intense radiative feedback from agns , or even cooling radiation from accreting gas . there are generally two ways to unravel the nature of the blobs . the first approach is to study what powers the ly@xmath0 emitting gas , counting all ionizing sources within or around the extended ly@xmath0 emission and comparing that energy budget with the observed ly@xmath0 luminosity . sometimes , one can identify possible energy sources , e.g. , powerful agns detected in x - rays @xcite . some potential sources may even lie outside a blob @xcite . if no such source is found , the remaining ly@xmath0 luminosity may be attributable to cooling radiation . an alternative path is to observe spectroscopically the kinematics of the extended ly@xmath0-emitting gas . even addressing whether the gas is falling into an embedded galaxy or outflowing into the igm would be a significant step forward , providing evidence for either gas accretion by forming galaxies or for agn / starburst - driven galactic winds , respectively . combining the two approaches by considering the blob s energetics and kinematics simultaneously is ideal , a test of whether the bulk motions of the gas are in fact coupled to the source of its illumination . for example , gas infall is possible even in the presence of an agn ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . cases in which blob gas is both outflowing on small scales due to galactic processes and infalling on larger scales from the extended igm are not unlikely . unfortunately , the kinematic approach has been stymied by the limitations of the ly@xmath0 line , which , although bright compared with other lines , is hard to interpret . the ambiguity arises because ly@xmath0 is a resonant line and typically optically thick in the surrounding intergalactic medium . as a result , studies even of the same blob s kinematics can disagree . on one hand , @xcite argue that ifu spectra from a certain blob are consistent with a simple model where the ly@xmath0 emission is absorbed by a foreground slab of neutral gas swept out by a galactic scale outflow . on the other , @xcite claim that the same data can be explained by the infall of the surrounding intergalactic medium . worse , @xcite comment that the same ly@xmath0 profiles are most consistent with static surrounding gas . to distinguish among such possibilities requires a comparison of the ly@xmath0 line center with the center of an optically - thin line like h@xmath0@xmath16563 ( see also * ? ? ? h@xmath0 is a better measure of the blob s systemic velocity , i.e. , of the precise redshift , because it is not seriously altered by radiative transfer effects and is more concentrated about the galaxies in the blob s core . despite the complexity of various blob models , infall models predict that the peak of the optically thick ly@xmath0 emission line must be blueshifted with respect to h@xmath0 , whereas outflows will redshift the ly@xmath0line @xcite . this diagnostic has been applied both to local starburst galaxies @xcite and to lyman break galaxies ( lbgs ) at @xmath9 = 1.52.5 @xcite and has provided evidence for outflows driven by strong stellar winds . an analysis in a similar spirit , but using the 21 cm absorption line to mark the systemic redshift of a high-@xmath9 radio galaxy , finds that the ly@xmath0line is blueshifted and thus that extended gas is inflowing to the agn @xcite . previous spectroscopic observations of ly@xmath0 blobs ( e.g. , at @xmath15 ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) include only ly@xmath0 , precluding a direct comparison with a cleaner line s center and muddling the interpretation of the kinematics . to overcome this challenge , @xcite conduct blind surveys for ly@xmath0 blobs at @xmath2 , a redshift at which important rest - frame optical diagnostic lines ( e.g. , [ ] @xmath13727 , [ ] @xmath15007 , h@xmath16@xmath14868 , h@xmath0@xmath16563 ) fall in nir windows and avoid bright oh sky lines ( or atmospheric absorption ) . in this paper , we present optical and nir spectroscopy of the two brightest blobs , cdfs - lab01 and cdfs - lab02 , of the 25 in the @xcite sample . for each , we compare the ly@xmath0line profile with the center of the h@xmath0 line and use existing radiative transfer models @xcite to test whether the detected gas is infalling or outflowing . in addition to the blob s systemic velocity , nir spectroscopy can constrain ( 1 ) the velocity dispersion and any ordered motion like disk rotation of the brightest embedded galaxies , ( 2 ) the presence of agns with rest - frame optical nebular line diagnostics ( e.g. , [ ] /h@xmath0 ) , ( 3 ) the gas - phase metallicity , and ( 4 ) the star formation rate ( sfr ) directly from the h@xmath0 flux , allowing a comparison with that derived from the rest - frame uv . before now , none of these measurements has been available for ly@xmath0 blobs . in this paper , we focus on the kinematics of the gas in the blob and in the embedded galaxies , deferring discussions of the agn line diagnostics , gas - phase metallicity , and sfrs to a future paper ( y. yang et al . 2011 , in preparation ) . in [ sec : observation ] , we review how we selected blobs from our narrowband imaging surveys @xcite and then describe the optical / nir spectroscopy of the first two blobs . in [ sec : result ] , we present the first results from the spectroscopic campaign . we confirm spectroscopically the blob redshift and discover multiple h@xmath0 sources within each blob ( [ sec : confirmation ] ) . we compare the ly@xmath0 profiles with the h@xmath0 line centers to discriminate between simple infall and outflow scenarios ( [ sec : shift ] ) . in [ sec : absorption ] , we describe the interstellar absorption lines detected in lab02 and compare the low ionization lines with h@xmath0 . we estimate the velocity dispersions of three of the embedded galaxies in [ sec : dynamical_mass ] . in [ sec : discussion ] , we compare the ly@xmath0 profiles and ly@xmath0@xmath17h@xmath0 offsets with existing radiative transfer models . we also discuss our results in the context of the clumpy circum - galactic gas model proposed by @xcite . [ sec : conclusion ] summarizes our conclusions . throughout this paper , we adopt cosmological parameters : @xmath18 = 70@xmath19 , @xmath20 , and @xmath21 . we observe the two brightest ly@xmath0 blobs from the @xcite sample , which consists of 25 blobs discovered in four different survey fields . these two blobs lie in the extended chandra deep field south ( e - cdfs ) and were found via deep imaging with the ctio-4 m mosaic ii camera and a custom narrowband filter ( _ nb_403 ) . this filter has a central wavelength of @xmath22 , designed for selecting ly@xmath0-emitting sources at @xmath23 , and a band - width of @xmath24 , providing a line of sight ( hereafter los ) depth of @xmath25 that corresponds to 46.8 comoving mpc . the blob selection criteria are : ew@xmath26 @xmath27 100 and isophotal area @xmath28 @xmath27 10 above the surface brightness threshold of 5.5 @xmath29 10@xmath30 ergs@xmath4@xmath31arcsec@xmath32 . we show the images of the two blobs ( cdfs - lab01 and cdfs - lab02 ) in figure [ fig : image ] . we refer readers to @xcite for details of the sample selection . we obtained high resolution optical spectra of the two ly@xmath0 blobs using the magellan echellette spectrograph ( mage ; * ? ? ? * ) on the magellan clay 6.5 m telescope . mage provides a spectral resolution of @xmath33 @xmath6 4100 for a 1 slit over a wide wavelength range of 3000 10000 . while the slit length is small ( 10 ) compared to typical longslits , the excellent blue sensitivity around 4000 is ideal for obtaining the ly@xmath0 line profile . observations were carried out on ut 2008 july 26 and october 1 , and 2009 february 17 . for lab01 , we first acquired a low resolution spectrum in 2008 july 26 to spectroscopically confirm the redshift prior to the nir spectroscopic run . later , we obtained the @xmath34 spectrum with a slit orientation of p.a.=42 as shown in figure [ fig : image ] ( ly@xmath0 panel ) . for lab02 , we used a 2 slit and a p.a.=0 to obtain a @xmath33 @xmath6 2000 spectrum . the sky condition was clear , and the seeing ranged from 0.9 to 1.3 . the individual exposure times varied from 20 to 40min , depending on the variability of the seeing . total exposure times were 2.5 and 2.0 hrs for lab01 and lab02 , respectively . for accurate wavelength calibration , we took thar lamp frames right before and after the science exposures and at the same telescope pointing to eliminate systematic errors introduced by instrument flexure . we reduce the mage data using the daniel kelson s carnegie - python package @xcite . the frames are overscan - corrected , bias - subtracted , and flat - fielded with xenon - flash and quartz ( incandescent ) lamps . using night sky lines and thar lamp spectra , we estimate the uncertainties in the wavelength solution to be @xmath60.03(0.1 pixel ) . the sky background is then subtracted in 2d using the method described in @xcite , and the frames are corrected for spatial distortions . we combine the rectified 2d spectra and extract the 1d spectra using idl routines . we also re - reduce the data with the mage spectral extractor package ( mase ; * ? ? ? * ) and confirm that the results are consistent . the spectra are flux - calibrated with 23 standard stars each night . due to the limited spatial coverage of the slit and the relatively short exposure times , our spectra are dominated by the brightest spots within the blobs , which coincide with the galaxies detected in the _ hst _ rest - frame uv images . future ifu observations should be helpful in constraining how the ly@xmath0 profiles vary over the blobs . we carried out nir integral field unit ( ifu ) spectroscopy of the two ly@xmath0blobs using sinfoni @xcite on the vlt ut4 telescope in visitor mode between ut 2009 january 30 and february 4 . to measure the redshifted h@xmath0 ( @xmath35 @xmath6 2.175 ) line , we used the _ k_-band grating , which covers 1.95 2.45 with a spectral resolution of @xmath33 @xmath36 4000 ( @xmath5 @xmath36 75kms@xmath4 ) and dispersion of 2.5pixel@xmath4 . because the blobs are spatially extended over 510 and include multiple sources , we employed the seeing - limited mode ( i.e. , no adaptive optics ) , which provided the largest fov ( 8@xmath298 ) and a plate scale of 025pixel@xmath4 for the spatial resolution elements ( spaxels ) . in each observing block , we observed reference stars , which we used to blind offset to the blobs as well as to monitor the telescope pointing accuracy and the seeing variations . the _ k_-band seeing ranged from 03 to 12 , and the sky condition was clear . to maximize the on - source integration time , we adopted an `` on - source dithering '' strategy in which the science targets were always kept within the fov but at different detector positions . for lab01 , we used a three - point dithering scheme that moves among the pointings by @xmath64 to south or west , providing a usable fov of two 4@xmath294 squares ( see the sinfoni panel in figure [ fig : image ] ) . for lab02 , we employed a two - point dither pattern in the north - south direction , resulting in a 8@xmath294 effective fov ( dot - dashed line in figure [ fig : image ] ) . the total integration times for lab01 and lab02 are 6 hrs and 0.5 hrs , respectively , which consist of 5 or 10 min individual exposures depending on the sky condition . for the telluric correction and flux calibration , we observed four b or g stars every night before or after the science targets with wide range of airmass . we reduce the sinfoni data using the eso pipeline . dark current and sky background are removed from each science frame by subtracting the pseudo - sky frame , which is constructed from the average of the two science frames bracketing each science frame . then , we flat - field the data and correct for bad pixels . because we will compare the velocity centers of the ly@xmath0 and h@xmath0 lines , accurate wavelength calibration is critical . we compare the wavelength solution obtained from the oh sky lines in the science frames to that from the daytime arc lamps . the arc lamp wavelength calibration error arising from instrument flexure can be as large as 1.5 , depending on the airmass ( which ranges up to @xmath62.0 ) . therefore , we adopt the oh sky line wavelength calibration , whose error is typically @xmath6 0.1(0.04 pixel ) for each science frame . using this wavelength solution , we constructed 3d data cubes from the 2d spectra after correcting spatial distortion . because it is not possible to identify / centroid the sources in individual exposures , we align them according to the dither offsets within each observing block ( ob ) . the spatial offsets between obs are calculated from the psf calibration frames and are typically small ( @xmath6 01 ) . when combining the data cubes , we adopt an iterative @xmath37-clipping algorithm to reject possible outliers and produce the `` sigma cubes '' that represent the standard deviation of the adopted pixels . because no stellar continuum is detected , we subtract the median sky values from each wavelength plane to avoid the strong variation of global sky background . finally , we flux - calibrate the cubes using the broad - band magnitudes of standard stars . atmospheric absorption is minimal at h@xmath0 due to our choice of survey redshift , so we do not apply a telluric correction . we spectroscopically confirm the redshifts ( @xmath9 @xmath36 2.31 2.32 ) of the two ly@xmath0 blobs using both the ly@xmath0 and h@xmath0 emission lines . figure [ fig : image ] shows the two ly@xmath0 blobs at various wavelengths : _ u _ , continuum - subtracted ly@xmath0 line , _ b _ , _ k _ , _ spitzer _ irac 3.6 , and _ hst _ f606w images overlain with the ly@xmath0contours ( left six panels ) . the archival ground - based images ( _ u , b _ , and _ k _ ) , the _ spitzer _ irac images , and the _ hst _ images are obtained from the multiwavelength survey by yale - chile ( musyc ; * ? ? ? * ) , the spitzer irac / musyc public legacy in e - cdfs survey ( simple ; * ? ? ? * ) , and the galaxy evolution from morphology and seds ( gems ; * ? ? ? * ) survey , respectively . in the right panels , we show the enlarged _ hst _ images and sinfoni h@xmath0 intensity maps that are collapsed in the wavelength direction centered at @xmath1 @xmath36 2.1746 ( @xmath38 @xmath36 66 ) and 2.1788 ( @xmath38 @xmath36 42 ) for the two blobs , respectively . for the sinfoni image of lab01 , we show only data taken in the best seeing ( @xmath6 03 ) to be comparable with the _ hst _ resolution . interestingly , in the _ hst _ rest - frame _ uv _ images , both ly@xmath0blobs include multiple galaxies and/or fragments , some of which appear to be interacting ( see also * ? ? ? a few are also detected in h@xmath0 , indicating that they lie at the same redshift . in @xcite , we found that the number density and the field - to - field variance of ly@xmath0 blobs are consistent with their occupying massive dark matter halos ( @xmath6 @xmath13@xmath14 ) that probably evolve into those of typical galaxy clusters today . thus , while some clumps / fragments could be part of a one large galaxy ( e.g. , * ? ? ? * ; * ? ? ? * ) , we speculate that others may merge and evolve into present - day brightest cluster galaxies . figure [ fig : spec1d ] shows the 1d ly@xmath0 spectra extracted from 1@xmath2924 and 2@xmath2924 mage slits for lab01 and lab02 , respectively . in addition to strong ly@xmath0 emission , lab01 also has @xmath11549 and @xmath11640 emission lines , implying the presence of hard ionizing sources ( e.g , * ? ? ? * ; * ? ? ? * ) . we defer analysis of these lines and their relative strengths to a future paper ( y. yang et al . 2011 , in preparation ) , which focuses on the multi - wavelength properties of the full blob survey and the implications for the sources of blob emission . lab02 has several interstellar absorption lines that we use in [ sec : absorption ] to help constrain the kinematics of gas around the embedded galaxies . in contrast to the optically thick and spatially extended ly@xmath0 emission , we can use the optically thin , more spatially concentrated h@xmath0 emission to make an independent determination of the blob redshift from the galaxies embedded in the centers of the blobs . we extract the h@xmath0 spectra from a 2@xmath292 aperture in the sinfoni cubes . figure [ fig : linefit ] shows the resulting spatially integrated h@xmath0 profiles within the blobs . the lab01 h@xmath0 spectrum includes all 6hr exposures combined to obtain higher s / n and total flux . note that whenever we show individual ly@xmath0 or h@xmath0 spectra ( figures [ fig : spec1d ] and [ fig : linefit ] ) , we adopt different aperture sizes that maximize the s / n . on the other hand , we use the same aperture when comparing the ly@xmath0 and h@xmath0 lines directly ( [ sec : shift ] ) . for lab01 , we focus on the brighter sw component of the blob . the excellent seeing of our sinfoni observation ( @xmath6 0.3 ) allows us to spatially resolve two embedded galaxies ( a and b ) in the sw part of the blob ( hereafter lab01a and lab01b ; fig . [ fig : image])5kpc and the velocity offset is @xmath6440kms@xmath4 . ] . these two galaxies are also kinematically separated as shown in the sinfoni h@xmath0 channel map ( figure [ fig : channel ] ) , a series of h@xmath0 intensity maps constructed by stepping through the 3d sinfoni data cubes in increments of 70kms@xmath4 . galaxy b shows an apparent velocity shear of @xmath6 250 kms@xmath4 , suggesting disk rotation , while galaxy a has no obvious velocity structure . in their spatially integrated h@xmath0 spectra , these two galaxies have the nearly same redshift , @xmath39 = 2.31421 @xmath40 0.0001 and @xmath41 = 2.30928 @xmath40 0.0001 , a separation of @xmath42 = 0.0049 or @xmath5(a b ) = 440kms@xmath4 . this relative velocity is a poor estimate of the velocity dispersion @xmath37 of the halo in which these galaxies are embedded . nevertheless , it is consistent with the @xmath37 expected for a massive , @xmath6@xmath13@xmath14 halo . lab02 also contains several continuum sources in the _ hst _ uv images ( labeled as a at least one of the brightest sources ( lab02a ) is detected in the sinfoni h@xmath0 image . with sinfoni , we marginally detect the two sources ( b+c ) blended in the _ hst _ image . it is also possible that galaxy d is blended with the much brighter galaxy a in the ifu data . we are not able to reliably extract h@xmath0 profiles from galaxies ( b+c ) and d because of the shallow exposure ( 30 min ) and insufficient spatial resolution . the integrated spectrum of lab02 is dominated by the brightest galaxy a , for which we measure the @xmath43 = 2.31928 @xmath40 0.0001 . we summarize the properties of h@xmath0 lines in table [ tab : line_properties ] . while it is possible that the h@xmath0 detections include some extended gas , the centers of the emission coincide with the galaxies resolved in the _ hst _ image and are likely to originate there . therefore , in the following section , we compare the ly@xmath0 and h@xmath0 profiles along the los toward these embedded galaxies . there are small astrometry offsets ( @xmath60.2 ) between _ hst _ uv images and sinfoni h@xmath0 maps ( right panels in figure [ fig : image ] ) . while it is likely that this mismatch arises from the astrometric calibrations of sinfoni , which rely entirely on blind offsets , we extract the ly@xmath0 and h@xmath0 spectra from the same aperture , accepting the current astrometric solution . changing the relative position of extraction aperture ( green boxes ) for ly@xmath0and h@xmath0 does not affect any of the conclusions in this paper . we show the selected extraction apertures ( small green boxes ) in figure [ fig : image ] . in lab01 , we extract the spectra along the los toward galaxy a , because the peak of ly@xmath0 map coincides with galaxy a. while galaxies a and b are well - resolved in the h@xmath0 image , the spectrum extracted from the sight - line to lab01a ( green box in fig . [ fig : image ] ) is slightly contaminated with light from galaxy b. therefore , we simultaneously fit the profile with a total of six components ( three for each galaxy ) and remove the galaxy b components when comparing the h@xmath0 and ly@xmath0 line centers in the following section . the ly@xmath0 profile emerging from the blob should be complicated , a mixture of the bulk motions of the gas and geometry . for the details of ly@xmath0 radiative transfer , we refer readers to the literature ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? in this section , we compare the ly@xmath0 and h@xmath0 lines to constrain the gas kinematics within the blobs . more specifically , we measure the velocity shift of the ly@xmath0 line relative to the h@xmath0 line center to distinguish between any infall and outflow of the igm relative to the blob s systemic velocity . once we measure this first - order kinematic diagnostic ( i.e. , any blueshift or redshift of the ly@xmath0 line ) , we discuss the detailed ly@xmath0 and h@xmath0 profiles in [ sec : discussion ] , comparing them with radiative transfer calculations to determine the velocity of the dominant bulk motion . to illustrate what we expect from this experiment , we first consider the simplest geometric case : a galaxy surrounded by a spherically symmetric gas cloud that is static , collapsing , or expanding @xcite . here we assume that the h@xmath0 line arises from the embedded galaxy , as we do not detect extended h@xmath0 emission , and that the ly@xmath0 line originates either in the same region of the galaxy before eventually escaping the surrounding cloud or in the cloud itself . thus this blob will be observed as a point source in h@xmath0 , but as an extended source in ly@xmath0 . note that the ly@xmath0 and h@xmath0 spectroscopy is along the los toward the central galaxy . while h@xmath0 from the galaxy can escape the surrounding gas without suffering absorption , ly@xmath0photons from the galaxy and from gas along the los will be resonantly scattered many times until their frequencies are right for escaping the cloud , a condition dependent on the bulk motions of gas along the los . because the cloud is optically thick to the ly@xmath0 line , ly@xmath0 photons on the doppler wings should escape the cloud through random scatterings in the frequency domain . if the surrounding gas is static , the ly@xmath0line will have a double - peaked profile , while the optically thin h@xmath0 photons will escape without any radiative transfer effects . if the cloud is collapsing , ly@xmath0 photons within the cloud on the red side of double - peaked profile will see higher optical depth due to the los infalling gas , and the red peak will be depressed . if the gas is outflowing , the blue side of the profile will be more diminished . therefore , if there is gas infall , the ly@xmath0 profile will be asymmetric and blueshifted against the h@xmath0 line due to radiative transfer in the optically thick medium , but the corresponding h@xmath0 line profile should be symmetric . for outflowing gas , the ly@xmath0 will be redshifted against the symmetric h@xmath0 line . the amount of shift depends on various parameters such as infall / outflow velocity and optical depth . note that one can not determine whether the ly@xmath0 line is redshifted or blueshifted against the background velocity field unless there is a optically thin reference line , i.e. , h@xmath0 . the actual geometry of the system is likely to be more complicated ( [ sec : discussion ] ) . yet the blue- or redshift of the ly@xmath0photons relative to the systemic velocity will occur as they make their way out of the system , as long as they encounter optically - thick gas that is infalling or outflowing along the los @xcite . in other words , we are studying the bulk motion of gas along the pencil beam toward the embedded galaxies when we compare the ly@xmath0 and h@xmath0 profiles extracted from this sight - line . in principle , it is even possible to compare the velocity offsets between extended ly@xmath0 and _ extended _ h@xmath0 lines in two dimensions ( i.e. , h@xmath0 and ly@xmath0 screens ) with much deeper h@xmath0 spectroscopy and optical ifu data . in summary , the basic assumptions for our simple test using the velocity offset between the ly@xmath0 and h@xmath0 lines are : 1 . ly@xmath0 should go through an optically thick column of gas ( either infalling or outflowing ) to escape . 2 . h@xmath0 represents the systemic velocity of the entire system , and gas is moving ( infalling or outflowing ) relative to this center . with these assumptions in mind , we now consider the ly@xmath0 and h@xmath0 line profiles for our two ly@xmath0 blobs . we then examine these assumptions further and discuss how to overcome their limitations in [ sec : discussion ] . we show the ly@xmath0 and h@xmath0 profiles for the two ly@xmath0 blobs in figure [ fig : line_comparison ] . we shift each blob s ly@xmath0 profile into its h@xmath0 frame using @xmath44 = @xmath45 @xmath29 @xmath46 . we place both blobs in the same velocity frame using the redshifts obtained from h@xmath0 . note that all the optical and nir wavelengths are converted to vacuum wavelengths and corrected to the heliocentric frame . in both blobs , the ly@xmath0 line is broader than the h@xmath0 line and has a more complicated structure ( i.e. , an asymmetric profile or multiple peaks ) , implying that the ly@xmath0 lines do experience resonant scattering . lab01 has a ly@xmath0 line width of @xmath47 = 520@xmath4040kms@xmath4 whose peak coincides with that of the h@xmath0 line . while the blue side of the ly@xmath0 profile ( @xmath48kms@xmath4 ) agrees well with that of the h@xmath0 line , it has an extended red wing up to at least @xmath49 @xmath6 + 600kms@xmath4 . it is not clear whether this red wing arises from the several poorly - resolved red peaks . lab02 shows a double peaked ly@xmath0 profile with a stronger red peak , which is often observed in high-@xmath9 ly@xmath0 galaxies @xcite . lab02 s ly@xmath0 profile is broad , extending from @xmath6@xmath50kms@xmath4 to @xmath6@xmath511000kms@xmath4 . the stronger red peak itself has a line width of @xmath47 @xmath6 420kms@xmath4 . lab02 s ly@xmath0 profile also has a sharp absorption feature ( or lack of emission ) at @xmath52kms@xmath4that coincides with its h@xmath0 line center . to quantitatively measure the velocity offset between the ly@xmath0 and h@xmath0 lines , we must first determine each line s center . for the asymmetric ly@xmath0 line , we measure the wavelength at the peak flux , which is consistent with the methodology of @xcite . because the ly@xmath0 profile is noisy , we smooth the spectrum with a boxcar filter of 3 spectral pixels ( @xmath5 @xmath36 40kms@xmath4 ) and measure the wavelength of the brightest flux . for the symmetric h@xmath0 profiles in both blobs , we fit the spectrum with a gaussian profile including the neighboring [ ] lines . we fit three gaussian components with the same velocity width , but different intensities , centered at 6563 ( h@xmath0 ) , 6549 , and 6583 ( [ ] ) . as mentioned earlier , due to the slight contamination of lab01a s spectrum with light from lab01b , we simultaneously fit the observed h@xmath0 profile for both galaxies and show only the spectrum of galaxy a in figure [ fig : line_comparison ] . ccccccc cdfs - lab01 & a & 2.31421 @xmath40 0.0001 & 1.16 @xmath40 0.06 & 184 @xmath40 9&@xmath510 @xmath40 20 + & b & 2.30928 @xmath40 0.0001 & 0.78 @xmath40 0.05 & 134 @xmath40 8 & ... + cdfs - lab02 & a & 2.31928 @xmath40 0.0001 & 2.42 @xmath40 0.11 & 152 @xmath40 5 & @xmath51230 @xmath40 30 [ tab : line_properties ] the velocity offset , @xmath7 is defined as the difference between the h@xmath0 line center and the ly@xmath0 peak wavelength . we find a negligible offset between ly@xmath0 and h@xmath0 ( @xmath7 @xmath36 @xmath53@xmath4020kms@xmath4 ) for lab01a , and an offset , @xmath7 @xmath36 @xmath54@xmath4030kms@xmath4 , for lab02a . these @xmath7 are smaller than those of lbgs , which range from + 150kms@xmath4 up to + 900kms@xmath4 with an average of + 450kms@xmath4@xcite . among this lbg sample , only 12% of galaxies have @xmath7 smaller than 225kms@xmath4 , thus the probability of finding @xmath7@xmath55 230kms@xmath4 for two ly@xmath0 blobs by chance is rather small ( @xmath61.5% ) if our ly@xmath0h@xmath0 offsets are drawn from the same @xmath7 distribution in @xcite is representative of all lbgs given its sharp break around 300kms@xmath4 . ] . for our two blobs , @xmath7 is either consistent with zero ( lab01 ) or somewhat redshifted ( lab02 ) . therefore , according to the simplest picture , we find no evidence for a blueshift and thus for gas infall in either blob . the absence of a redshifted @xmath7 in lab01 does not necessarily exclude an outflow , because lab01a s ly@xmath0 profile has an extended red wing and/or multiple red peaks , which can be outflow signatures . if we interpret the observed @xmath7 as a proxy for outflow velocity , then , at face value , any outflows in lab01 and lab02 are weaker than those typical of lbgs . in [ sec : discussion ] , we further consider the implications of our @xmath7 results using radiative transfer calculations . in addition to the ly@xmath0 emission line , the optical spectrum of lab02 shows several absorption lines ( figure [ fig : spec1d ] ) . these absorption lines provide an opportunity to constrain the kinematics of cold gas on the near side of the galaxy , i.e. , between the galaxy and observer , and thus to verify the detection of the modest @xmath7 outflow signature in the previous section . note that the systemic velocity from h@xmath0 spectroscopy is again critical . because the s / n of the continuum in the lab02 spectrum is very low , we first re - bin the spectrum by four spectral pixels , which worsens the resolution of the final velocity bins to @xmath690 kms@xmath4 . figure [ fig : absorption ] shows the velocity profiles of six absorption lines whose peaks were detected at the @xmath10 3@xmath37 level in the rebinned spectrum . we show the absorption profiles of three low - ionization interstellar lines ( @xmath11260.42 , @xmath11334.53 , and @xmath11526.72 ) and three high - ionization lines ( @xmath561393.76 , 1402.77 and @xmath11548.20 ) . for comparison , we also plot the composite lbg spectrum ( @xmath57 ) from @xcite and the individual spectrum of ms1512-cb58 ( @xmath58 ) which is one of the apparently brightest lbg whose light is amplified due to the gravitational lensing @xcite . although the s / n is low , the velocity ranges spanned by lab02 s absorption lines roughly agree with these two templates . we find that all interstellar absorption lines are blueshifted against the systemic velocity , indicating that the intervening gas is outflowing , which is consistent with the observed @xmath7 outflow signature discussed in the last section . to estimate the velocity of the outflowing material , we measure how much the centroids of these velocity profiles are offset from the h@xmath0 line : @xmath59 . while the high - ionization lines ( @xmath561393 , 1402 and @xmath11548 ) have the highest s / n , they are known to be contaminated with broader absorption features arising from stellar winds from massive stars @xcite . therefore , we measure the centroid velocities ( @xmath59 ) using the three low - ionization lines . two low - ionization lines ( @xmath11334 and @xmath11526 ) have @xmath59 @xmath6 @xmath17100kms@xmath4 to @xmath17200kms@xmath4 . ( it is difficult to reliably measure the centroid of the @xmath11260 line . ) the absorption profile of @xmath11334 might extend up to @xmath60 @xmath6 600kms@xmath4 blueward , although its low s / n precludes a reliable measurement . if we adopt its centroid velocity as an outflow velocity , then it is similar to that of lbgs , which average @xmath61 = @xmath62kms@xmath4 , but can be as large as @xmath17500kms@xmath4 @xcite . by fitting gaussian profiles to the integrated h@xmath0 profiles ( figure [ fig : linefit ] ) , we obtain the velocity dispersions , @xmath63 = 184@xmath409kms@xmath4 and 134@xmath408kms@xmath4 for the lab01a and lab01b , respectively . for lab02a , @xmath64 = 152@xmath405kms@xmath4 . these velocity dispersions are corrected for the instrumental resolution ( @xmath65 @xmath6 32kms@xmath4 ) . the internal velocity dispersions of the embedded galaxies ( @xmath66 = 130 190kms@xmath4 ) are high compared to those of star - forming galaxies at @xmath67 . @xcite find that lbgs at @xmath67 have an average of @xmath68 = 108kms@xmath4 with a standard deviation of 41kms@xmath4 , excluding galaxies with agns . our lowest @xmath69kms@xmath4 corresponds to the upper @xmath630% percentile of their distribution . in particular , there is only one galaxy in the @xcite sample that has higher @xmath37 than lab01a does ( @xmath64 = 190kms@xmath4 ) . in this section , we compare the observed ly@xmath0 profiles and their offsets from the h@xmath0 lines with the predictions of ly@xmath0radiative transfer ( rt ) calculations ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * hereafter d06 , v06 and v08 , respectively ) . to test the scenario in which gas in the surrounding cloud cools and flows toward the blob center , we compare our data with the spherical collapse model in d06 . for the picture in which gas outflows from the embedded galaxies in the blob s core , we employ the expanding shell model investigated by v06 . note that these rt calculations assume that infall and outflow occur in spherical symmetry , in a collapsing sphere for the inflow model and in an expanding shell for the outflow model . as we argued previously , even such simple models should reproduce the general behavior of the ly@xmath0profile as long as the basic assumptions listed in [ sec : shift ] are valid . in [ sec : future ] , we examine those assumptions in detail and discuss the future work required to overcome these limitations . in [ sec : shift ] , we found that the ly@xmath0 lines of the two blobs are not blueshifted relative to the h@xmath0 line centers within the measurement uncertainties . the absence of a blueshift rules out the simplest infall model where a spherical gas cloud is collapsing onto a central ly@xmath0 source or where the collapsing cloud itself is emitting ly@xmath0 photons . in this model , @xcite and @xcite study ly@xmath0radiative transfer , which depends on various parameters such as the location of the ly@xmath0 source , the infall velocity field , the column density of neutral hydrogen ( @xmath70 ) , and the doppler parameter @xmath71 representing the thermal and turbulent motion of the gas ( see fig . 4 and 7 in d06 or fig . 57 in v06 ) . the key prediction of these rt calculations is that the ly@xmath0 spectrum is double peaked with an enhanced blue peak , producing an effective blueshift of the ly@xmath0 profile . while the blue peak might be suppressed by the intervening igm after the ly@xmath0 photons escape the collapsing cloud @xcite , this effect is unlikely to be significant here because the mean transmission blueward of ly@xmath0 should be relatively high at @xmath2 : @xmath72 @xmath6 0.8 @xcite , where @xmath73 represents ly@xmath0 optical depth . the blueshift of ly@xmath0 photons against the systemic velocity should arise as long as 1 ) there are infall motions along the los and 2 ) ly@xmath0photons on their way out of the system encounter optically thick gas with a velocity opposite to their propagation direction @xcite . one possible way to hide a blueshift in this simple infall model would be if the infalling gas is made optically thin by an ionizing source or has low enough column density so that the ly@xmath0 photons do not suffer resonant scattering ( see fig . 11 in d06 or fig . 6 in v06 ) . in this case , we should still see nearly symmetric ly@xmath0 profiles or extended blue wings , neither of which is observed in our ly@xmath0 profiles . therefore , we rule out this simple gas infall scenario for our two ly@xmath0 blobs . in contrast to this simple model , the actual situation is likely to be more complex and the bulk motion of gas may not be spherically symmetric . for example , the h@xmath0 detections suggest that the galaxies embedded in the blobs are forming stars , which could generate mechanical feedback into the surrounding gas cloud . there is also ample evidence for galactic scale outflows in star - forming galaxies at @xmath9 = 23 ( e.g. , * ? ? ? thus , one could imagine that even if gas infall takes place over larger radii ( up to @xmath650 kpc ) , the innermost part of the gas cloud , close to the galaxies , could be strongly affected by outflows similar to those observed in other star - forming galaxies at @xmath74 . in this case , the emerging ly@xmath0 profile will be more sensitive to the core of the blob , presumably the densest part of the igm , than to the gas infall . as a result , it might be difficult to detect the infalling gas by measuring the ly@xmath0 line shift . more simulations are required to test whether generic galactic scale outflows could affect gas infall and whether infall and outflows can coexist . this kind of more realistic model has not been considered yet in rt calculations , so its spectral signatures ( if any ) are unknown . the other caveat is that the inflow might occur along filamentary streams @xcite and their covering factor could be small such that we might completely miss the infall signatures in a particular los . we will further discuss this caveat in [ sec : misalignment ] . in [ sec : shift ] , we found that the offset of the ly@xmath0 line relative to h@xmath0 was either consistent with zero ( lab01 ) or redshifted ( lab02 ) . the existence of a modest outflow in lab02 was further supported by the low - ionization absorption line shifts discussed in section [ sec : absorption ] . the absence of a redshifted @xmath7 in lab01 does not necessarily exclude an outflow because of its extended ly@xmath0 profile toward the red . here we compare the ly@xmath0 profiles of our blobs with the rt outflow models of @xcite to interpret the velocity offset @xmath7 in a more sophisticated manner . in these radiative transfer calculations , the ly@xmath0h@xmath0 velocity offset is modulated entirely by the radiative transfer of ly@xmath0 photons through a continuous medium within the shell . another possibility , which we discuss in section [ sec : clumpycgm ] , is that the gas around the galaxy is clumpy and that the bulk motions of these clumps primarily modulate the emerging ly@xmath0 profile @xcite . in the following section , we constrain the outflow velocity or `` wind velocity '' from the embedded galaxies using the rt calculations . it is then possible to ask whether such an outflow is energetic enough ( i.e. , the expansion velocity @xmath75 is large ) to expel / launch gas out to larger radii , thus creating the extended ly@xmath0 emission observed as a blob with a typical size of @xmath10 50kpc . to connect @xmath7 with an outflow velocity , we compare each blob s ly@xmath0profile with a model with an expanding shell geometry . such a geometry would arise in the simple `` superwind '' or `` hyperwind '' model for ly@xmath0blobs proposed by and @xcite . in this scenario , supernova explosions or stellar winds following an intense starburst in galaxies develop into a so - called superbubble . if the kinetic energy deposited into the surrounding gas overcomes the gravitational potential energy of the galaxy , the gas clouds are blown out into intergalactic space as a superwind ( e.g. , heckman et al . the gas blown out from the galaxies forms a shell , and the ly@xmath0photons are scattered from this expanding shell ( with @xmath75 ) , escaping preferentially by the scattering from the backside . in contrast , the h@xmath0 lines provide the systemic velocity of the star forming region . v06 and v08 demonstrate that the radiative transfer of ly@xmath0 in this simple shell geometry is able to explain a wide range of observed ly@xmath0profiles . v08 classified ly@xmath0 profiles into three categories : ( 1 ) single - peaked asymmetric profile with an extended red wing , ( 2 ) profile with double peaks separated by sharp absorption at @xmath52kms@xmath4 , and ( 3 ) asymmetric profile with bluer bump(s ) . thanks to the h@xmath0 line , which provides the velocity center , we can determine that lab01 and lab02 correspond to ( 1 ) and ( 2 ) without ambiguity . we start with lab01 , which has an asymmetric ly@xmath0 profile without any obvious blue peaks , but with an extended red wing and/or multiple red peaks ( i.e. , category 1 above ) . v06 show that a blue peak ( @xmath49 @xmath76 0kms@xmath4 ) is strongly suppressed with increasing ( @xmath77 ) ratio , i.e. , when the bulk outflow motion becomes more important than the thermal and turbulent motion of the shell gas . the resonant scattering in the expanding shell produces mainly two red peaks depending on the paths of the emergent photons : one peak near the line center ( @xmath49 @xmath6 0kms@xmath4 ) and another at @xmath78 , corresponding to photons that experience zero or one back - scattering from the receding shell , respectively . here , the back - scattering of a photon means that it travels across the empty interior before re - entering the shell at a different location . thus the location of the second red peak is a useful diagnostic for the outflow velocity . because of the degeneracy between many model parameters ( @xmath75 , @xmath71 , @xmath70 , @xmath79 ) , constraining the outflow velocity well requires fitting the spectra directly to the rt calculations . we do not have the means to do that here , so we estimate @xmath75 for lab01 from how much its red ly@xmath0 peaks are redshifted against its h@xmath0 line center . if @xmath70 is sufficiently large ( @xmath70@xmath10 @xmath80cm@xmath4 ) , the second red peak becomes larger and merges with the first red peak , so that the stronger red peak measures 2@xmath75 ( see fig . 1 of v08 ) . if this case applies here , our @xmath7@xmath6 0kms@xmath4 implies @xmath75@xmath6 0kms@xmath4 , i.e. , that the shell is static . on the other hand , decreasing @xmath70 , increasing dust extinction ( @xmath82 ) , and decreasing @xmath77 tends to strengthen the first red peak , so that the brighter peak is located at 0 @xmath83 @xmath75 and does not carry any @xmath75 information . in this case , the location of the weaker second peak provides an estimate of @xmath75 . as discussed in [ sec : confirmation ] , the lab01 profile s extended red wing could be interpreted as multiple components ( see figure [ fig : line_comparison ] ) . if we adopt the small bump at @xmath49 @xmath6 300kms@xmath4 as the second peak , the expansion velocity of the shell is @xmath75 @xmath6 150kms@xmath4 . considering both cases , the outflow velocity in lab01 could range from 0kms@xmath4 to @xmath6150kms@xmath4 . the ly@xmath0 profile of lab02 is most consistent with the double - peaked profile ( i.e , category 2 above ) of @xcite , who claim that such profiles arise when the shell is almost static ( @xmath75 @xmath6 0kms@xmath4 ) . due to the h@xmath0 measurement , there is no ambiguity about the location of the velocity center . even if we consider only the red side of the profile and classify it as a single asymmetric profile like lab01 , we would obtain an outflow velocity only as high as @xmath6 @xmath7/2 = 115kms@xmath4 . the blueshifted centroids of the low - ionization absorption lines in lab02 are also consistent with this inferred outflow velocity . therefore , if the expanding shell geometry is applicable to our two ly@xmath0 blobs , we conclude that any outflows from the embedded galaxies are not strong ( @xmath75 @xmath55 150kms@xmath4 ) compared to the values required by the extreme `` superwind '' or `` hyperwind '' scenarios to explain the large size ( @xmath84kpc ) and broad ly@xmath0 linewidth ( fwhm @xmath6 1000kms@xmath4 ) of blobs . the simple shell geometry assumed here has some physical motivation and has been explored by extensive rt calculations ( e.g. , v06 and v08 ) . however , this model implies that the outflows are intermittent with a small duty cycle , contrary to the observation that outflows are seen in most star forming galaxies at high redshift . we note that if there is a continuous stream of outflowing material , it might lead to a different interpretation of kinematic signatures discussed above . one other claim of an outflow in a blob was reported by @xcite using ifu observations of the ly@xmath0 line in steidel s blob 2 . using an expanding shell model , they found that the central wavelength , i.e. , velocity , of absorption systems on top of the underlying broad ly@xmath0 profiles is coherent across the whole blob with a blueshift of @xmath6250 kms@xmath4 . because the systemic velocity of the blob gas is unknown in their case , there are other possible interpretations of their data , even including an inflow @xcite . @xcite and @xcite found that steidel s blob 1 has an extremely complicated velocity structure , including velocity shears around the embedded galaxies that can be interpreted as either outflow or rotation . it is interesting that all investigations of blob kinematics to date ( in our cdfs - lab01 and cdfs - lab02 , steidel s blobs 1 and 2 ) suggest relatively small outflow velocities . therefore , the large wind speeds required by super / hyper - wind models to explain the extended ly@xmath0emission are excluded . one way to reconcile the small outflows with the `` superwind '' model is to assume that the outflow was once more energetic and that the expanding shell has been broken up or slowed by contact with the surrounding igm @xcite . clearly , constraining the kinematics of more ly@xmath0 blobs is needed to address whether these small outflows are representative . we conclude that the gas motion around the galaxies embedded in these ly@xmath0 blobs is not consistent with models like the simple superwind picture that assume a spherical shell geometry and a shell velocity exceeding @xmath6500 kms@xmath4 . yet galactic scale outflows from star - forming galaxies at @xmath74 appear to be common . the outflow properties have been extensively studied by comparing the ly@xmath0 velocity center with those of optically - thin nebular lines and/or interstellar absorption lines ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? recently , @xcite show that ly@xmath0 lines from lbgs are redshifted against h@xmath0 lines up to several hundreds kms@xmath4 with an average of @xmath85 = + 445kms@xmath4 , while the interstellar absorption lines are blueshifted against the nebular lines by @xmath86 = @xmath62kms@xmath4 . while these @xmath7 and @xmath59 offsets are interpreted as an outflow signature , it is not clear how the absorbing material is distributed around galaxies . _ were the gas blown out in a spherical shell _ , as in the superwind picture discussed above , we could directly compare the observed @xmath7of blobs and lbgs as a proxy for @xmath75 . the velocity offsets of our two ly@xmath0 blobs , @xmath7 @xmath6 0kms@xmath4 and 230kms@xmath4 , are small in relation to lbgs @xcite ; of 41 lbgs at @xmath9 = 2 2.6 with both ly@xmath0and h@xmath0 spectroscopy , @xmath688% have @xmath7 @xmath27 225kms@xmath4 . therefore , any wind arising from galactic star formation has a lower expansion velocity in these two labs than is typical of lbgs . we have adopted two basic assumptions in our analysis : that there is inflowing or outflowing gas in the los to the blob and that the h@xmath0 line marks the kinematic center of the blob gas . here we examine how these assumptions may affect our conclusions and comment on the recent model suggested by @xcite to explain the circum - galactic kinematics of lbgs . we have assumed that there is gas inflowing or outflowing along the los to the embedded galaxies that lie in our spectroscopic slit . in this case , the observed ly@xmath0 photons resonantly scatter in this optically thick infalling / outflowing material until escaping into the los of the observer . however , we do not know how the blob gas is distributed around the embedded galaxies nor whether it is clumpy or smooth . for example , the gas flow may not be isotropic . as in bipolar outflows , a galactic - scale outflow may occur in the direction of minimum ism pressure , which is typically perpendicular to the stellar disk . or , the covering factor of the outflow material , the fraction of emission intercepted by the absorbers , could be rather high , at least 0.5 or up to unity as observed in nearby agns @xcite . if gas accretion is taking place instead @xcite , numerical simulations suggest that the infall may occur preferentially along filamentary streams @xcite . if the bulk motion of gas ( either infalling or outflowing ) happens to be mis - aligned with our los , we may underestimate or even fail to detect the relative velocity shifts . therefore , it is critical to expand the ly@xmath0h@xmath0 comparison to a larger sample to average over any geometric effects and obtain better constraints on the incidence , direction , speed , and isotropy of bulk gas motions in blobs . if no large values of @xmath75 are measured , even for a larger sample , outflows are unlikely to push the blob gas to larger radii , where it can be illuminated . on the other hand , an absence of blueshifted ly@xmath0 lines would argue that infall is not dominant , at least not near the galaxies . recent cosmological simulations including radiative transfer are now able to examine the statistics of blobs whose extended ly@xmath0 emission arises from cooling radiation . these models can predict the range of gas accretion covering factors , surface brightness profiles and ratio of blue - to - redshifted ly@xmath0 lines for blobs . a larger sample of blobs with measured ly@xmath0 and h@xmath0 kinematics would provide a new test of these blob emission models . our second key assumption is that the h@xmath0 line marks the kinematic center of the surrounding gas , i.e. , the terminus of any infall or the origin of any outflow . for an outflow , this assumption is reasonable because all possible causes of the outflow ( e.g. , stellar winds , sne , or agns ) lie in or about galaxies , as does the h@xmath0 line itself . for similar reasons , this assumption is likely to be valid for gas accretion ( infall ) into an embedded galaxy . however , it is possible that the accreting gas responds to the overall dm potential rather than to individual galaxies . thus one could expect that detecting gas infall is more difficult than finding outflows using the technique presented in this paper . to overcome this issue , it is critical to increase the sample size and measure how each blob s ly@xmath0 profile varies spatially . this experiment should be conducted along multiple sightlines using using different h@xmath0 sources found in the same blob . in principle , it is possible to compare the offsets between the extended ly@xmath0 and and the _ extended _ h@xmath0 lines in two dimensions , i.e. , between the h@xmath0 and ly@xmath0 screens . unfortunately , the h@xmath0 surface brightness is expected to be @xmath63% 10% of ly@xmath0 depending on the energy source . thus , it will be challenging to obtain 2d h@xmath0 ifu measurements in the near future . currently , our ly@xmath0h@xmath0 comparison includes only a handful of ly@xmath0blobs because of the limited redshift range where nir spectroscopy of the optically - thin nebular lines ( e.g. , h@xmath0 and the [ ] @xmath15007 line ) is allowed . however , future co observations with alma will also provide the systemic velocity of the embedded galaxies , permitting this test to be expanded to a larger sample of ly@xmath0 blobs . as we were writing this paper , @xcite proposed a model for lbgs in which cool gas is distributed around the galaxy and accelerates radially outward with increasing galactocentric distance . they suggest that this blown - out material extends to @xmath680kpc , comparable to the typical size of ly@xmath0 blobs , and that all lbgs would be classified as blobs if narrowband images were sensitive to surface brightness thresholds 10 times lower than typical of blob / emitter surveys ( i.e. , @xmath6@xmath87ergs@xmath4@xmath31arcsec@xmath32 ) . is this `` clumpy circum - galactic medium ( cgm ) model '' consistent with the properties of our ly@xmath0 blobs ? unlike in the rt models that we considered earlier , the gas in this model is composed of small clumps . a critical part of the @xcite analysis involves stacking spectra of apparent galaxy - galaxy pairs at @xmath88 to obtain a high s / n interstellar absorption profile arising from the gas surrounding the foreground galaxies . sightlines to the background galaxies provide information on the spatial distribution of circum - galactic gas as a function of the galactocentric distances . there are no background galaxies behind our two blobs , and even constraining the absorption profile in lab02a was challenging . we do not detect a stellar continuum in lab01a or lab01b . as a result , we are unable to test whether the @xcite lbg model could explain the kinematics of either of our ly@xmath0 blobs . nevertheless , we add a few qualitative comments here . in the @xcite model , ly@xmath0 photons from the central galaxy are scattered off the _ surface _ of these discrete clumps ; thus photons acquire a doppler shift corresponding to the velocity of each clump . ly@xmath0 photons can escape the system when they achieve velocity offsets large enough to take the photons off - resonance for any material between the last scattering clump and the observer . therefore , the ly@xmath0 line shift is due to bulk motions of the clumpy material rather than to radiative transfer effects where ly@xmath0 photons experience numerous resonant scatterings before escaping the cloud ( section [ sec : outflow ] ) . the profiles of ly@xmath0 and the low - ionization interstellar absorption lines are determined by the velocity field and covering fraction of these gas clumps . the apparent peak of ly@xmath0 emission is modulated primarily by the clumps with @xmath52 : ly@xmath0 emission is more redshifted and weaker for a wider velocity range spanned by the interstellar absorption . the velocity of the clumpy medium continually increases outward , unlike in the radiative transfer models discussed earlier , where the outflowing shell had one velocity . in the @xcite model , the velocity range spanned by the absorption lines reflects that of the surrounding gas distribution , and the ly@xmath0h@xmath0 offset does _ not _ represent the outflow velocity . if this clumpy cgm model is applicable to blobs , then our observations of a small ly@xmath0h@xmath0 offset could indicate an absence of neutral gas at @xmath52 rather than the weak gas outflow suggested by the rt models . one test would be to constrain the interstellar absorption line profile , which should extend to larger blueward velocities , but lack a component around @xmath89kms@xmath4 , if the clumpy model is accurate . clearly , higher s / n spectra to reliably measure these weak absorption lines are required . the most notable outcome of the large spatial extent of a clumpy cgm around star - forming galaxies is diffuse ly@xmath0-emitting halos . extended ly@xmath0 emission has been detected in stacked narrowband images of lbgs by @xcite . more recently , by stacking deeper narrowband ly@xmath0 images of lbgs , @xcite show that all classes of star - forming galaxies exhibit diffuse ly@xmath0 halos out to projected radii of @xmath680kpc , regardless of their spectroscopic properties ( i.e. , either absorption or emission in ly@xmath0 within a spectroscopic slit ) , although these halos are 10@xmath29 lower surface brightness than typical blobs . the ly@xmath0surface brightness profiles of the stacked images are similar among lbg subclasses , with only different intensity scalings . thus , ly@xmath0 blobs may represent the most extreme example of galaxies with diffuse ly@xmath0 halos . the key difference of the clumpy cgm model is that the diffuse ly@xmath0 halo originates from ly@xmath0 photons scattered from the galaxy s region(s ) rather than from external mechanisms such as photoionization by agn , photoionzation by metagalactic uv background radiation , or via cooling radiation . at this time , the applicability of the clumpy model to ly@xmath0 blobs is unclear . any comprehensive model must explain the differences between our blobs and lbgs : 1 ) a comparison of their number density and clustering properties suggests that blobs could occupy higher density environments ( e.g. , * ? ? ? * ) , 2 ) the extended emission of blobs is typically 10 times brighter , 3 ) the ly@xmath0h@xmath0 offset of our blobs is lower . the first and second differences could arise if the blobs host more massive galaxies and higher star formation rates than typical of star - forming galaxies at high-@xmath9 . it remains to be tested whether star formation in the galaxies embedded in blobs can produce enough ly@xmath0 photons to explain the higher luminosity and surface brightness of ly@xmath0 halos . the ly@xmath0h@xmath0 offset is clearly tied in some way to the extended ly@xmath0 emission of our blobs , as it is unusually low for both blobs compared to the offset distribution for lbgs ( see also * ? ? ? * for compact ly@xmath0 emitters ) . it would interesting to check whether the lbg subclasses in @xcite with brighter extended emission have smaller ly@xmath0h@xmath0 offsets and weaker is absorption at @xmath89kms@xmath4 than the others . for now , we note that the rt outflow model discussed in section [ sec : discussion ] adequately explains the sense and magnitude of both the ly@xmath0h@xmath0 and the h@xmath0-interstellar absorption line offsets in lab02 , whereas the @xcite model would require this agreement of the offsets to be a coincidence . of course , we are only able to perform this test using one blob at present . as stressed earlier , a larger sample of ly@xmath0h@xmath0 offsets is required to test whether smaller ly@xmath0h@xmath0 offsets are generic properties of ly@xmath0 blobs . determining the source of ly@xmath0 emission in extended nebulae at high redshift requires that we measure their gas kinematics with an optically - thin line such as h@xmath0 @xmath16563 , which , unlike the optically - thick ly@xmath0 emission , is not much altered by radiative transfer effects and is more concentrated about the blob s core . the comparison of the ly@xmath0and h@xmath0 line centers then constrains any infall or outflow of the ly@xmath0-emitting gas relative to the systemic velocity of the blob defined by h@xmath0 . we obtain optical and nir spectra of the two brightest ly@xmath0 blobs ( cdfs - lab01 and cdfs - lab02 ) from the @xcite sample using the magellan / mage optical and vlt / sinfoni nir spectrographs . both the ly@xmath0 and h@xmath0 lines confirm that these blobs lie at the survey redshift , @xmath90 ( @xmath22 ) . the blobs contain several h@xmath0 sources , which roughly coincide with galaxies in _ hst _ rest - frame uv images . the h@xmath0 detections of these embedded galaxies reveal large internal velocity dispersions ( @xmath3kms@xmath4 ) . furthermore , in the one system ( lab01 ) where we can reliably extract profiles for two different h@xmath0 sources , their velocity difference is @xmath5 @xmath6 440kms@xmath4 . the presence of multiple galaxies within the blobs , and those galaxies large velocity dispersions and large relative motion , supports the result of @xcite that ly@xmath0 blobs inhabit massive dark matter halos that will evolve into rich clusters today . the embedded galaxies may represent the precursors of brightest cluster galaxies . to determine whether the gas near the embedded galaxies is predominantly infalling or outflowing , we compare the ly@xmath0 and h@xmath0 line centers . ly@xmath0 is not offset ( @xmath7 = + 0kms@xmath4 ) in lab01 and redshifted by only + 230kms@xmath4 in lab02 . these offsets are small compared to those of lyman break galaxies , which average + 450kms@xmath4 and extend to about + 700kms@xmath4 @xcite . by comparing the observed ly@xmath0 profiles with simple radiative transfer models , we constrain the outflow velocity from the embedded galaxies to be @xmath60 150kms@xmath4 in the two blobs . in lab02 , we detect low - ionization , interstellar absorption lines , including @xmath11334 and @xmath11526 , whose blueward shifts of @xmath8kms@xmath4 are consistent with the small outflow implied by the redward shift of ly@xmath0 . models with simple infall geometries or that require outflow velocities exceeding @xmath6500kms@xmath4 are ruled out . because of the unknown geometry of the gas distribution and the possibility of multiple sources of ly@xmath0 emission embedded in the blobs , a larger sample and more sophisticated models are required to test other infall and outflow scenarios . we thank anonymous referee for his / her helpful comments . we thank christy tremonti , dusan kere and mark dijkstra for useful discussions . we also thank max pettini for providing the spectrum of ms1512-cb58 . thanks the max - planck - institut fr astronomie and the center for cosmology and particle physics at new york university for their hospitality and support during her stays there . y.y . and a.i.z.acknowledge support from the nsf astronomy and astrophysics research program through grant ast-0908280 and from the nasa astrophysics data analysis program through grant nnx10ad47 g . is supported through the emmy noether programme of the german science foundation ( dfg ) . adams , j. j. , hill , g. j. , & macqueen , p. j. 2009 , , 694 , 314 adelberger , k. l. , steidel , c. c. , shapley , a. e. , & pettini , m. 2003 , , 584 , 45 ahn , s .- h . , lee , h .- w . , & lee , h. m. 2001 , , 554 , 604 ahn , s .- h . , lee , h .- w . , & lee , h. m. 2002 , , 567 , 922 bland , j. , & tully , b. 1988 , , 334 , 43 bochanski , j. j. , et al . 2009 , , 121 , 1409 bonnet , h. , et al . 2004 , the messenger , 117 , 17 bower , r. g. , et al . 2004 , , 351 , 63 colbert , j. w. , teplitz , h. , francis , p. , palunas , p. , williger , g. m. , & woodgate , b. 2006 , , 637 , l89 crenshaw , d. m. , kraemer , s. b. , & george , i. m. 2003 , , 41 , 117 damen , m. , et al . 2010 , arxiv:1011.2764 dekel , a. , et al . 2009 , , 457 , 451 dey , a. , et al . 2005 , , 629 , 654 dijkstra , m. , & loeb , a. 2009 , , 400 , 1109 dijkstra , m. , haiman , z. , & spaans , m. 2006 , , 649 , 14 dijkstra , m. , haiman , z. , & spaans , m. 2006 , , 649 , 37 eisenhauer , f. , et al . 2003 , , 4841 , 1548 elmegreen , d. m. , elmegreen , b. g. , marcus , m. t. , shahinyan , k. , yau , a. , & petersen , m. 2009 , , 701 , 306 erb , d. k. , steidel , c. c. , shapley , a. e. , pettini , m. , reddy , n. a. , & adelberger , k. l. 2006 , , 646 , 107 fardal , m. a. , katz , n. , gardner , j. p. , hernquist , l. , weinberg , d. h. , & dav ' e , r. 2001 , , 562 , 605 faucher - 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exploring the origin of ly@xmath0 nebulae ( blobs " ) at high redshift requires measurements of their gas kinematics that are impossible with only the resonant , optically - thick ly@xmath0 line . to define gas motions relative to the systemic velocity of the blob , the ly@xmath0 line must be compared with an optically - thin line like h@xmath0 @xmath16563 , which is not much altered by radiative transfer effects and is more concentrated about the galaxies embedded in the nebula s core . we obtain optical and near - infrared ( nir ) spectra of the two brightest ly@xmath0 blobs ( cdfs - lab01 and cdfs - lab02 ) from the @xcite sample using the magellan / mage optical and vlt / sinfoni nir spectrographs . both the ly@xmath0 and h@xmath0 lines confirm that these blobs lie at the survey redshift , @xmath2 . within each blob , we detect several h@xmath0 sources , which roughly correspond to galaxies seen in _ hst _ rest - frame uv images . the h@xmath0 detections show that these galaxies have large internal velocity dispersions ( @xmath3kms@xmath4 ) and that , in the one system ( lab01 ) , where we can reliably extract profiles for two h@xmath0 sources , their velocity difference is @xmath5 @xmath6 440kms@xmath4 . the presence of multiple galaxies within the blobs , and those galaxies large velocity dispersions and large relative motion , is consistent with our previous finding that ly@xmath0 blobs inhabit massive dark matter halos that will evolve into those typical of rich clusters today and that the embedded galaxies may eventually become brightest cluster galaxies @xcite . to determine whether the gas near the embedded galaxies is predominantly infalling or outflowing , we compare the ly@xmath0 and h@xmath0 line centers , finding that ly@xmath0 is not offset ( @xmath7 = + 0kms@xmath4 ) in lab01 and redshifted by only + 230kms@xmath4 in lab02 . these offsets are small compared to those of lyman break galaxies , which average + 450kms@xmath4and extend to about + 700kms@xmath4 . in lab02 , we detect @xmath11334 and @xmath11526 absorption lines , whose blueward shifts of @xmath8kms@xmath4 are consistent with the small outflow implied by the redward shift of ly@xmath0 . we test and rule out the simplest infall models and those outflow models with super / hyper - winds , which require large outflow velocities . because of the unknown geometry of the gas distribution and the possibility of multiple sources of ly@xmath0emission embedded in the blobs , a larger sample and more sophisticated models are required to test more complex or a wider range of infall and outflow scenarios .

Facts & Summary of Findings · Arkansas produces 11% of the nation’s broiler chickens. · Northwest Arkansas, the locus of poultry production, has much larger populations of people who are foreign-born, Hispanic or Latino, and Asian or Pacific Islander than Arkansas as a whole (see Figure 4). These demographics are represented in disparity and discrimination that workers reported on their surveys. · NWAWJC surveyed 500 Arkansas poultry workers about their experiences working in the industry. Wages and Hours Workers in Arkansas poultry processing plants often do not earn enough to support their families. On top of low pay, workers report experiencing wage and hour violations including having wages “disappear.” · Arkansas poultry workers make, on average, approximately $13.84 per hour ($28,792 per year). Even in a household with 2 adults making this wage ($57,584 total), this is well below living wage for a family of 4 ($71,000 is considered a living wage in nonmetro South). · 62% of surveyed workers report experiencing some sort of wage and hour violation. Example: non-payment of wages; cost of protective gear deducted from pay. · 21% of foreign-born workers reported being paid with payroll cards. These cards can have advantages, as they can be used like debit cards, but there are disadvantages because fees and payments can be difficult to track. 38% of those who are paid via payroll card reported having money “disappear.” And in 74% of those cases, the money was never recovered. Benefits Poultry workers in Arkansas report having limited access to health benefits such as earned sick leave and affordable comprehensive health insurance. In addition, workers report being punished or even fired for being sick and injured on the job. · Most poultry workers report having health insurance but only 22% said they were “always” able to afford medical care they needed. 62% reported that they could only pay “sometimes” or “never.” · Only 9% of surveyed workers report that they have earned sick leave. Another 38% reported having unpaid sick leave, often on a points system that discourages workers from taking time off. A full 32% report that they have no sick leave at all. · 62% reported that they had gone to work while sick. When asked why, 77% responded that they needed the money and had no earned sick leave. 54% reported that they worked because they were afraid of disciplinary action if they missed work. 44% reported that they had been directly threatened with discipline if they missed work. · 22% of surveyed workers reported being fired because they missed work due to sickness. Discrimination and Harassment The worker survey reveals widespread experiences of discrimination and harassment. Workers reported discrimination based on race, ethnicity, and gender. · Women, in particular, cite gender discrimination in the way bathroom breaks are withheld by male supervisors. Some have urinated on themselves because they were not granted breaks when needed. · 51% of surveyed workers report being discriminated against at work. · 44% report being verbally or sexually harassed. · Of those who reported being harassed, Black and Latino workers reported high rates of being harassed by a supervisor or lead (Black-71%, Latino-63%). White and API workers were more likely to report harassment by a coworker or combination of the 2. Lack of Mobility Among surveyed workers, tenure, mobility, and access to raises vary widely based on race and nationality. Foreign-born workers report being stuck in lower wage positions for longer periods of time, with fewer advancement opportunities. · Only 22% of surveyed workers reported being offered a promotion to a more comfortable or higher-paid role. · Foreign-born workers reported working on average twice as long at their U.S. counterparts (foreign-born-64 months, U.S.born-31 months). · Foreign-born and Latino workers reported both the longest average tenure as poultry workers AND the lowest rates of being offered promotions (Latino workers: 94% not offered a promotion; foreign-born 92% not offered a promotion). Health and Safety Health and safety conditions in poultry processing plants can pose a threat to both workers and consumers. Unhygienic environments combined with fast line speeds can result in injury and illness for workers and contamination of meat. · 31% of workers reported seeing contamination in the meat. There was a strong correlation between workers who did not have sick leave and those who saw contamination. Workers who come to work sick because they cannot take time off can infect other workers, perpetuate illness, and contaminate meat. · Over half of surveyed workers reported that they had had a work-related sickness or illness. But for those with earned sick days, that number was only 49%, while for those with no sick days, it was 71%. · 32% reported that they or someone they knew was punished for reporting health and safety or other issues to a supervisor. · Workers reported that a lack of proper training was a major cause of work related injury. · Those who reported being injured on the job also reported the fastest line speeds, in some cases almost double the piece/pound per minute rate of those who had not been injured. Recommendations · Policymakers should increase enforcement of wage and hour laws, including increasing penalties for violations and increased enforcement resources. · Line speeds should be regulated and reduced, to reduce injury and contamination. · Paid sick leave should be guaranteed for all workers. · Policymakers and companies should work to reduce discrimination and harassment in the workplace, including enforcing anti-discrimination laws and creating strategies to ensure equitable mobility for workers of color and foreign-born workers. · Companies and policymakers should ensure equitable access to bathroom breaks to protect worker health and dignity. · Workers should be encouraged to organize collectively to work for better conditions. To read the full report Wages and Working Conditions in Arkansas Poultry Plants: Click Here ||||| Jessica Rinaldi/Reuters This article was reported in partnership with the Investigative Fund at the Nation Institute. On the debone line, the birds come at you fast. That was Lisandro Vega’s first lesson. The former prison guard in Puerto Rico had moved to the town of Huntsville, Arkansas, in 2013, following relatives who found work at a Butterball turkey plant. There, he was given a knife and gloves and told to stand at a station, where 47 dead and defeathered turkeys rushed past each minute. He was responsible for every second bird. Sometimes he cut out the hip joints; other times the breasts and livers. The pace was relentless: 1,410 birds an hour, more than 11,000 a shift. Advertisement And sometimes they come at you faster. Beginning in October, Butterball requires plant employees to work approximately 50 days straight to meet the Thanksgiving rush. In Huntsville, people call this period “fresh”—in Spanish, la fresca—because that’s when birds are sold fresh, not frozen. During this time, the line speed increases; Vega recalls it reaching, according to his supervisor, 51 birds a minute. (Butterball declined to comment on its line speed.) A debone worker like Vega can slice up more than half a million turkeys before receiving a single day off. Gabriel Thompson “In training, they tell you that if you can’t get to the turkey, just let it go by, because you can injure yourself with the knife,” he says. “But once you are in debone, if you miss a turkey, you’re going to immediately hear: ‘What happened? You can’t let them go by!’ ” It is early evening, and we are standing in front of Lolo’s Mexican Grill in Huntsville, about a mile south of the plant. Vega, 46, is short and trim, with a shaved head that reflects the glow of a gorgeous October moon. It wasn’t that Vega harbored illusions about turkey plant work. His son-in-law had quit shortly before he arrived, after a supervisor refused to allow him to take a bathroom break—a frequent complaint among poultry workers. The man had peed himself right there on the line. “His pants were wet, yet he finished his shift. Then he walked out and didn’t come back,” Vega says. But the pain in Vega’s hands took some getting used to. He began submerging them in a container of hot bleached water, perched nearby to disinfect dropped knives. During brief moments between birds, he’d stretch out his fingers, which tended to harden, clawlike, around his knife. And though he knew that many of his co-workers went to the nurse’s station to ice their hands and others had surgery for carpal tunnel syndrome, he found his own ways to cope. In Puerto Rico, he had dealt with inmate uprisings. He was accustomed to soldiering through. “Once you are in debone, if you miss a turkey, you’re going to immediately hear: ‘What happened? You can’t let them go by!’ ” Advertisement During his third “fresh” in October 2015, the ache in Vega’s hands was superseded by shooting pains in his back. While moving a heavy container of turkey carcasses with a pallet jack, he slipped and fell, throwing out his back. He struggled to get up and hobbled over to the nurse’s station. For several days, he returned to the station during breaks, where his back was iced and rubbed down with Icy Hot by a nurse. (Butterball would not comment on whether its plant nurses are highly trained RNs or minimally trained LPNs; the federal Occupational Safety and Health Administration has no requirements as long as the nurses only operate within their scope of practice.) Within a week, the pain had become tolerable, though he still walked tentatively. Then, in February, while moving another carton of turkey, he slipped on ice in the plant’s freezer, landing hard on his tender back. He returned to the nurse’s station for more ice and pain-relieving cream. Soon he was a regular, visiting twice a day for treatments. Yet he wasn’t getting better. Vega asked about seeing a doctor but says that his supervisor told him that if he did, he would be suspended. One day, while signing in at the nurse’s station, he noticed a posting on the wall. It listed an impressive number of hours that workers had gone without suffering injuries causing them to miss shifts. According to Butterball, the plant was one of the safest worksites in the country; in 2013, the company announced that Huntsville employees had worked 8 million hours without what is called a lost-time injury. That’s a remarkable figure—the equivalent of a single person working full-time for 3,835 consecutive years. Vega looked around the nurse’s station. He saw three people whose swollen hands were being iced. Another man had his shoulder wrapped in ice. On the walk over from the debone line, sharp pains had shot through Vega’s back with each step. If none of us are hurt, he asked himself, then what are we all doing in the nurse’s station? Advertisement * * * The Butterball plant is set back on a quiet road that meanders through rolling hills, just inside the limits of Huntsville (population: 2,346), whose motto is “Crossroads of the Ozarks.” The sprawling white structure, whose doors opened in 1974, is surrounded by a barbed-wire fence and employs more than 650 people. Each year, leading up to Thanksgiving, it cranks out 45,000 turkeys a day. On a cloudy day, a few minutes after 5 o’clock, employees are emerging through a vertical metal turnstile to walk slowly to their cars. It is day 13 of “fresh.” I take a seat on a bench near the turnstile and talk to a Latina woman who looks to be in her 40s as she waits for her ride. She wears a purple sweater and is gingerly opening and closing her hands. “Of course they hurt,” she tells me. “But I can handle it.” She suggests, however, that I probably shouldn’t apply for a job inside, then declines to say more after I identify myself as a journalist. Gabriel Thompson Advertisement As in most poultry plants in Northwest Arkansas, the workforce is a mix of whites, blacks, Latino immigrants, and Marshallese—immigrants from the Marshall Islands, in the South Pacific, attracted to the region by poultry work. (The Marshallese have special permission to work in this country, a result of U.S. nuclear testing in the 1940s and ’50s that rendered many of their islands uninhabitable.) Turkey is big business in Arkansas. Last year, the state produced 561 million pounds of turkey meat, fifth in the nation behind North Carolina, Minnesota, Indiana, and Missouri. Butterball, the nation’s largest turkey company, has two other plants in the state. Thirty miles east of Huntsville is the city of Springdale, which the Arkansas state legislature recently declared the “poultry capital of the world.” It’s hard to argue with the title. The city is home to another hulking turkey plant, this one owned by Cargill, and is the corporate headquarters of Tyson Foods. On the short drive from my Springdale motel to the Cargill plant, I pass three chicken plants, two hatcheries, and a dead turkey on the side of the road.* In the middle of all these plants is a one-story brick complex that contains the offices of the Northwest Arkansas Workers’ Justice Center. With a staff of four, the group has launched a campaign to improve the working conditions and wages of the nearly 28,000 poultry processing workers in Arkansas. Earlier this year, they marched on the Tyson headquarters, holding signs that read “WE ARE NOT MACHINES, WE ARE HUMANS.” The group is underfunded, understaffed, and feisty. Gabriel Thompson I meet Nelson Escobar in the parking lot. Originally from El Salvador, he worked briefly at a poultry plant in Springdale but balked at what he felt were inhumane working conditions. “Out here, if you get hurt, they fire you,” he tells me. “If you complain, they fire you. I didn’t like any of that.” He started volunteering at the center several years ago and is now the group’s director of organizing. Advertisement Escobar ushers me into a room where a woman with brown hair is seated at a long table. Vilma Asencio began working at the Cargill turkey plant in 2001; her first job involved pushing around racks of turkeys, which she says can weigh up to 2,000 pounds. At one point, she was moved to the shackle line, where she spent her shifts lifting dead birds up onto hooks. “These were big turkeys,” she says. In 1960, according to the U.S. Department of Agriculture, the average turkey weighed less than 17 pounds. Today the average weight is more than 30 pounds, with some of the largest males reaching more than twice that. Such sizes make natural breeding impossible, which is why there is an occupation called an artificial turkey inseminator. Last year, Arkansas produced 561 million pounds of turkey meat. After a year on the shackle line, Asencio says her right hand began to feel like it was permanently asleep. “I had lost all my strength,” she says. “Even a water bottle was too hard to open.” She went to the company nurse, who offered her little more than ice. Asencio says she had a private insurance plan with Blue Cross Blue Shield, for which she paid $89 a week. “I knew that the company only wanted to put Band-Aids on everything. I didn’t trust them.” As the weakness in her hand worsened and the nurse continued to refuse to refer her for an outside exam, Asencio scheduled her own appointment with a doctor. He ordered a nerve conduction study, which confirmed carpal tunnel syndrome, and scheduled a surgery. Asencio took the report back to the plant nurse and filed a workers’ compensation claim. The company’s insurer denied the claim, she recalls, determining that the carpal tunnel was unrelated to the repetitive motions she made on the job. “I didn’t even try to fight it,” she says, lifting up her arm to reveal a scar on her wrist. “I just wanted the strength in my hand to return.” After the surgery, she was out of work for three months. Cargill spokesman Mike Martin said by email that although the company does not discuss individual cases, Cargill complies with all regulations related to workplace health and safety and considers the safety of its workers “paramount.” “It’s crazy,” says Evelyn Brooks, an attorney in Arkansas who specializes in workers’ compensation cases and estimates that half her caseload involves poultry companies. “A worker like Asencio did the same fast production line work since 2001. But then insurance companies will ask questions like, ‘Do you whittle in your spare time?’ They’ll try to blame the injury on anything else. It’s the insurance company that makes the decision, but a place like Cargill—which is like a workers’ comp machine—is heavily involved.” A company with a high number of workers’ compensation cases, she notes, will end up paying more for its premiums. Advertisement In 2014 Asencio had a second surgery to resolve what her doctor originally believed was tendinitis in her right shoulder, also caused by the repetitive lifting of turkeys. This time, the insurance company didn’t question that her pain was work-related. But three weeks before her surgery, Asencio was called into the plant’s office. Her mother had recently died, and a manager handed her a condolence card. Then she fired her. According to Asencio, she said she had been late too many times, a charge she disputes. (Martin declined to comment on the alleged firing but said Cargill “complies with all employment laws.”) When she had the surgery, doctors discovered that her tendon was not simply inflamed; it had actually snapped. Two years later, her shoulder still causes significant pain, but her doctor has not recommended further treatment. Brooks is now representing Asencio in a case in front of the Arkansas Workers’ Compensation Commission; she has requested that Asencio be assigned a new doctor. “I just want some of the pain to go away,” says Asencio, who is studying counseling at the University of Phoenix. Her hope is to someday land a job where she doesn’t need to use her arms or hands. * * * This February, the Northwest Arkansas Workers’ Justice Center published a lengthy report about poultry workers in Arkansas, which included data drawn from surveys of 500 turkey and chicken plant workers. About 60 percent of these workers reported having suffered an injury or illness on the job. One of the chief complaints was the dizzying line speed. Several workers reported that the lines go so fast that they often don’t even realize they have cut themselves until later. Gabriel Thompson During my interviews with a dozen turkey plant workers in Arkansas, line speed was identified as the major concern. The speed is regulated not by the Department of Labor but by the Department of Agriculture, whose sole criterion in setting maximum speeds is food safety. In 2012, under a proposed new poultry inspection system, the agency sought to increase the maximum line speed of turkeys from 51 to 55 birds per minutes and from 140 to 175 birds for chickens. The speed-up was supported by the National Turkey Federation, whose members include Butterball and Cargill; in its formal comments on the proposed regulation, the NTF cited the poultry industry’s “constantly improving” injury rates. (The NTF also heralded the proposed system as a step forward for food safety. But Food and Water Watch, an advocacy group, obtained 2011 inspection reports for three turkey plants that, as part of a USDA pilot project, were already running their lines at the higher speed. The group found inspection error rates—the rate at which employees missed items like bits of beak, bile, or fecal matter on turkey carcasses—of between 87 and 100 percent.) After an outcry among worker safety advocates and unions, along with food safety groups, the USDA backed off the increase in chicken speeds but let the turkey increase go through as planned. Vega told me that he couldn’t imagine working on a line going any faster than 51 birds a minute—the top speed he’d faced during “fresh”—but now workers might have to. “I think because there are fewer turkey plants, they got less focus,” says Deborah Berkowitz of the National Employment Law Project. “But the hazards are the exact same. The only difference is that turkeys are bigger, so you’ll see more cumulative trauma disorders, because it takes more effort to cut through the meat.” Berkowitz, a former chief of staff for OSHA under the Obama administration, first stepped inside a Virginia turkey plant in 1982, when she was with the AFL-CIO. The shock has stayed with her. “I had never seen people work so hard in my life,” she recalls. “And they were getting something called carpal tunnel syndrome. That’s where we really saw it first, in the turkeys. We brought someone in who told the company they could change the knife that workers used, and they wouldn’t get hurt as much. The company said F-you. I’ve been at war with the industry ever since.” The National Institute for Occupational Safety and Health, an arm of the federal Centers for Disease Control and Prevention, researches workplace injuries and ways to prevent them. The last time NIOSH looked at repetitive cutting motions in turkey plants was 1987, nearly 30 years ago. The agency visited a plant in Colorado, where it videotaped workers on the job and reviewed company paperwork. Its team, which included several doctors and an industrial engineer, discovered that employees performed up to 28,800 cuts in a single shift. The investigation also revealed what it called “considerable underreporting of injuries.” The company, it found, kept two books. The first tracked injuries for the plant’s medical log; the other listed injuries reported to OSHA. In one month, 160 injuries were noted in the medical log. Only six were reported to the government. Failing to record injuries is one strategy to create the illusion of a safe workplace. Another is to fail to refer workers to doctors for proper tests and diagnoses. Each time an injury causes an employee to miss a day of work or to receive medical treatment beyond first aid, the company is required to record it in an OSHA log book. This data is reported each year to the Department of Labor and is used to identify industries with high injury rates—whose facilities will then face increased inspections. An industry that reports low injury rates is less likely to receive scrutiny from OSHA’s overstretched investigators. In the summer of 2014, executives of the nation’s largest poultry companies—including Cargill and Butterball—gathered at the Hilton Sandestin Beach Golf Resort, a 2,400-acre retreat on the Florida coast. They were in town for an industry-sponsored safety conference that focused on “ergonomics and reducing cumulative trauma disorders.” The conference concluded with an awards ceremony, honoring poultry plants with better-than-average injury rates for three consecutive years. Wayne Farms, a Georgia-based company, took home 13 awards, including an “Award of Honor” for its processing plant in the unincorporated community of Jack, Alabama. A low injury rate may simply mean that companies have found new ways of discouraging workers from receiving needed medical treatment or taking time off. Several weeks earlier, OSHA had concluded an inspection of the same Jack plant. Inspectors found that Wayne Farms had a “standard practice of returning injured workers to regular duty.” One employee was seen by the nurse 94 times before finally being referred to a physician. “Perhaps more than any other industry, the poultry industry has focused its energies on the prevention of workplace injuries,” read a joint press release put out earlier this year, on behalf of the National Turkey Federation, the National Chicken Council, and the U.S. Poultry and Egg Association. It is true that the official injury rate for poultry workers has decreased: From 2004 to 2013, it dropped by 42 percent, from 9.8 to 5.7 injuries per 100 full-time workers. Yet as the Wayne Farms plant demonstrates, a low injury rate may simply mean that companies have found new ways of discouraging workers from receiving needed medical treatment or taking time off. It’s difficult to know the true injury rates among poultry workers—though they certainly are much greater than official figures suggest. Part of the problem is that OSHA is a severely underfunded agency. OSHA inspectors, according to the Wall Street Journal, only have the capacity to visit each U.S. workplace once every 99 years. Inspectors haven’t set foot inside Huntsville’s Butterball plant since 1995, back when Bill Clinton was in his first term. Many workers, after being injured, simply quit. In the Northwest Arkansas Workers’ Justice Center study, more than 1 in 5 injured workers reported that they were subsequently fired. There have been two recent investigations by NIOSH of repetitive stress injuries at chicken plants that give a more reliable indication of injury rates. In March of 2014, NIOSH found that 42 percent of workers at a chicken plant in South Carolina showed evidence of carpal tunnel syndrome. A year later, it published another study, this time of a Maryland chicken plant; 34 percent of the workers exhibited evidence of carpal tunnel. In Maryland, NIOSH also reviewed the company’s OSHA injury logs. Over a period of four years, from 2010 to 2013, it found only four entries for workers who had suffered work-related carpal tunnel syndrome. * * * For Lisandro Vega, the former prison guard from Puerto Rico, the breaking point came in late April, two months after his second fall. He had been visiting the plant nurse to have his back iced and rubbed down with cream during each break throughout late February, the entire month of March, and into April. Twice a day, every workday, he shuffled back and forth from the debone line to the plant nurse. He started visiting a massage therapist once a week in Springdale, on his own dime, but didn’t tell the company, not wanting to get in trouble. The therapist told Vega that his lower column was deviated, he recalls, and that the massages would only temporarily alleviate his pain. Standing upright and slicing through thousands of turkeys a day wasn’t giving his back a chance to recover. Several times, he woke up and tried to get out of bed, only to have his back seize on him. “I would just lie there, unable to move, staring at the ceiling,” he says. On those days, he didn’t make it in to work. Up to the end, he continued to get twice-a-day treatment at the nurse’s station. It had started to become second nature to walk leaning to one side, which slightly relieved the pain in his lower back. Yet he worried that he might do permanent damage to his body, and even the grizzled prison guard knew that it wasn’t worth taking the risk. Not knowing what else to do, in mid-April, he quit. Butterball’s injury-free streak remained intact. The Grind is a yearlong series looking at the unsavory—and often hidden—working conditions behind some of our cherished annual traditions. It is a collaboration with the Investigative Fund at the Nation Institute, a nonprofit journalism center.

– No one's more thankful for Thanksgiving than the workers who toil away in turkey plants in the days before, where it can be weeks before time off is earned, bathroom breaks are frowned upon, and employees' "deboning" quota can surpass 11,000 turkeys per shift, per an exposé on Slate, co-reported with the Nation Institute. The deep dive starts with the story of Lisandro Vega, an ex-worker in an Arkansas Butterball plant, and through him and others, tidbits are noted about the "relentless" pace and how workers in the state—Cargill and Tyson Foods also have an Arkansas presence—suffer constant injuries. Workers ice their hands, for example, or even resort to carpal tunnel surgery after their hands harden from "clawlike" grips on deboning knives or from pushing around heavy turkey racks. The beginning of the end for Vega: when he saw a notice at his Huntsville plant in which Butterball bragged about how workers in that facility had put in more than 8 million hours without a "lost-time injury." Not buying that: the Northwest Arkansas Workers’ Justice Center, an advocacy group pushing for better working conditions and pay for the 28,000 workers in Arkansas' poultry industry. The NAWJC estimates 60% of Arkansas poultry workers have suffered an illness or injury at work. "If you get hurt, they fire you. If you complain, they fire you," the group's organizing director says. Slate also explores how injuries at the plants are underreported to the feds and how insurance companies give workers a hard time on their claims. Meanwhile, a joint statement from the National Turkey Federation, the National Chicken Council, and the US Poultry and Egg Association earlier this year stated: "Perhaps more than any other industry, the poultry industry has focused its energies on the prevention of workplace injuries." As for Vega, he eventually quit because a back injury he'd suffered at work became too painful. Entire article here. (Denial of bathroom breaks is a serious industry issue.)

superconductivity is one of the most well studied phenomena in condensed matter physics . superconductivity in bulk samples , thin films , cylinders and hollow cylinders have been extensively studied and can even be found in text books @xcite . with the advent of nano - fabrication technologies , there is revived interest in superconductivity in mesoscopic samples [ 2 - 10 ] and to investigate the effect of the geometry and the size of the sample in the superconducting state . mesoscopic samples are defined as samples whose size is comparable to the coherence length . et al _ @xcite measured the superconducting - normal phase diagram of a mesoscopic superconducting square and rectangular ring . they used resistivity measurements which does not allow for probing deep inside the superconducting state . furthermore , the presence of conduction probes may influence the superconducting state of the studied sample . in order to circumvent these limitations one needs a contactless experiment which is provided by a magnetization measurement . @xcite performed magnetization measurements on an ensemble of @xmath2 disks with large separation between them in order to make the dipolar interaction between the disks negligible . recently geim _ et al _ @xcite used sub - micron hall probes to detect the magnetization of _ single _ superconducting @xmath3 disks with size down to 0.1 @xmath4 . these experimental works are the main motivation behind our present and previous theoretical work . already a substantial amount of theoretical work has been done on mesoscopic samples using the ginzburg - landau ( gl ) theory . some of these works neglect the non - linear term in the first gl eqn @xcite . but all these works neglect the de - magnetization effect which arises due to the finite thickness of the disk @xcite . the latter is very important in case there is a substantial meissner effect and is the reason for the discrepancies between the experimental observations and the existing theories . for example , buisson _ et al _ @xcite observed an oscillatory behavior ( or jumps ) in the magnetization which occurs above a certain applied magnetic field . linearized ginzburg - landau ( lgl ) theory could explain the origin of the oscillatory behavior , but is not able to explain : @xmath5 ) the magnetic field above which the oscillations occur , @xmath6 ) its amplitude , and @xmath7 ) the periodicity of these oscillations . hence they questioned the validity of the gl theory in dealing with the magnetization of mesoscopic samples . such oscillatory behavior has also been obtained in the single disk measurement of geim _ et al_. @xcite , provided the disk is large enough to accommodate many flux quanta . @xcite showed that the very nature of the normal to superconductor transition can change from a first order phase transition to a second order as the dimensions of the disk is varied . notice that bulk @xmath3 has @xmath8 , @xmath9=.016@xmath4 and consequently the gl parameter is @xmath10=0.01 which tells us that @xmath3 is a type i sample and consequently the superconducting to normal transition is first order in that case . we showed recently that the gl theory can explain the magnetic field at which the oscillations start , the amplitude of the oscillations and the periodicity of the oscillations , provided the non - linear term and the de - magnetization effect are included in the theoretical description @xcite . the gl theory does not have a firm mathematical derivation except in a narrow range of magnetic field close to the phase boundary of type ii bulk materials @xcite . however because of its simplicity , it enables us to make quantitative calculations for most of the experimentally observed quantities , which makes it a popular theory . from experience it is known that it gives sensible results even beyond this limited regime . for example it was found to work for type i thin films @xcite . the reason is that thin films are governed by an effective penetration length @xmath11= @xmath12 which results in an effective gl penetration length larger than @xmath13 . surface superconductivity or the giant vortex state could be quantitatively understood from the gl theory for samples with boundaries @xcite . the phase boundary of mesoscopic type i samples could be quantitatively explained from the gl theory @xcite . @xcite applied the gl theory to study the magnetization of mesoscopic disks deep inside the phase boundary and there was remarkable quantitative agreement with the experimental observations . in the present work the gl approach to disks is reviewed and the non - linear meissner effect is analyzed in detail . we show that the detector size greatly influences the measured magnetization . in smaller disks it only influences the magnitude whereas in larger disks it can influence both the magnitude as well as the line shape . thus we find that one has to be careful to translate the measured hall voltage directly into the sample magnetization . also the hysteresis behavior of the magnetization will be analyzed in detail . we consider superconducting disks with radius @xmath0 and thickness @xmath1 immersed in an insulating medium . as a first approximation , neglecting the non - local effects , we solve the system of two coupled gl eqns . @xmath14 @xmath15 where the density of superconducting current @xmath16 is given by @xmath17 here @xmath18 is a temperature dependent parameter : @xmath19 while @xmath20 is regular at @xmath21 , where @xmath21 is the critical temperature . on the disk surface we require that the normal component of the current density is zero @xmath22 the boundary condition for the vector potential is such that far away from the superconducting disk the field equals the applied field @xmath23 , i.e. , @xmath24 . here @xmath25 denotes the azimuthal direction and @xmath26 is the radial distance from the disk center . using the london gauge @xmath27 , we rewrite the system of eqns . ( 1 - 3 ) into the following form @xmath28 @xmath29 , the order parameter in @xmath30 , the vector potential in @xmath31 , @xmath32 is the gl parameter , and @xmath33 is the bulk penetration length . we measure the magnetic field in @xmath34 , where @xmath35 is the bulk critical field . notice that the parameters @xmath18 and @xmath20 are scaled out of the gl equations and consequently they only determine the energy and length scales . the difference of the gibbs free energy @xmath36 between the superconducting and the normal state , measured in @xmath37 , can be expressed through the integral @xmath38 over the disk volume @xmath39 , where @xmath40 is the external vector potential , and @xmath41 which is a direct measure of the expelled magnetic field from the surface area @xmath42 of the disk . we used the gauss - seidel method to solve eqn . 1 and the fast fourier transform to solve eqn 2 . the order parameter of the previous magnetic field is taken as the initial order parameter for a particular magnetic field . a large number of iterations are then made to arrive at a self consistent solution . in previous work we found that the assumption that the order parameter is uniform in the z - direction is a very good approximation for the thin disks considered here @xcite . consequently , as far as the order parameter is concerned the disk is reduced to a 2d disk . but the 3d nature of the field distribution is completely retained . hence eqs . 1 and 2 becomes @xmath43 @xmath44 @xmath45 with the boundary condition @xmath46 it is known that for superconducting cylinders , the sample can only exhibit the abrikosov vortex state when the gl parameter @xmath47 . this is no longer so for thin disks , because they have an _ effective _ @xmath10 which is much different from that of cylinders . outside the abrikosov vortex state region , both the meissner state and the giant vortex state have azimuthal symmetry . hence for a disk that does not exhibit the multi - vortex state @xcite , we can assume axially symmetric solutions with a general angular momentum : @xmath48 . this will reduce the dimensions of eqs . 1 and 2 and thus it greatly improves the computation time and the accuracy . for simplicity we will refer to the first method as 3d solution and the second method with fixed @xmath49 as 2d solution . as a typical case let us consider a disk of radius @xmath0=0.8@xmath50 , thickness @xmath1=0.134 @xmath4 , coherence length @xmath51=0.183 @xmath4 and penetration length @xmath9=0.07@xmath4 ( resulting in @xmath52 ) which are comparable to those of one of the @xmath3 disks considered in the experiment of geim _ et al _ @xcite . in the case of the 2d solution we solve for a particular @xmath49 state . the transition between the different @xmath49 states is obtained from a comparison of the free energies from which we obtain the ground state . the free energy g as a function of increasing applied magnetic field is shown by the thin solid curves in fig . 1(a ) for different @xmath49 states . the corresponding magnetization are shown in fig . 1(b ) by the thin solid curves . hence from fig . 1(a ) , it can be seen that up to a magnetic field of 42.6 gauss , the @xmath49=0 state is the ground state . beyond this field the @xmath49=1 state becomes the ground state . as we increase the field , higher @xmath49 states become the lowest energy states . this continues as long as the free energy g is negative . a positive g means that the normal state has a lower free energy than the superconducting state . hence the free energy of the ground state of the system is given by the thick solid curve in fig . the corresponding magnetization along this ground state is given by the thick solid curve in fig . notice that each @xmath49 state has a metastable region where the sample can be paramagnetic . the 3d approach does not have the restriction of fixed @xmath49 and consequently many solutions can be found for given magnetic field which are not necessarily the lowest energy state . our approach is to start at zero magnetic field , find the ground state , and then increase the magnetic field in small steps in which we use the order parameter of the previous magnetic field as the initial state in the iteration of the coupled set of differential equations . the magnetization as given by the 3d solution in increasing magnetic field is given by the thick dotted curve in fig . the corresponding free energy is given by the thick dotted curve in fig . as compared to the 2d solution we find that ( within errors arising due to the assumption that the order parameter is uniform in the disk in the z - direction in case of the 3d solution ) , the 3d solution in increasing magnetic field , takes the system along a state that conserves @xmath49 . this persists up to the point where the @xmath49=0 state is no longer metastable , i.e. it no longer has a local minimum . then the system jumps to the @xmath49=1 state and starts evolving along the @xmath49=1 state until it is no longer stable . following the 2d solution along a path of conserving @xmath49 we notice that the line shape of the magnetization and the number and position of jumps in the magnetization are similar to those of the 3d solution . the little difference in magnitude arises due to the fact that the 3d solution uses the extra approximation of constant order parameter in the z - direction while the order parameter should be reduced near the upper and lower surfaces of the disk . hence an important conclusion that can be made from the comparison of the 2d solution and the 3d solution is that the 2d solution can be used to study the magnetization of this sample . comparing the thick dotted curve in fig . 1(a ) ( 3d solution ) with the thick solid curve in fig . 1(a ) ( the ground state obtained from 2d solution ) we find that the 3d solution in increasing magnetic field makes the system evolve along metastable states . in the 3d solution the metastability is due to energy barriers which do not allow the sample to switch between different angular momentum states . in the ginzburg - landau theory there are two such energy barriers . one of them is a surface barrier known as the bean - livingston barrier @xcite that has been well studied in the case of cylinders . the other barrier is a volume barrier and it appears only when the sample makes a first order transition to the normal state . this appears because close to the first order transition the free energy has two minima corresponding to two different values of the order parameter and there is a barrier separating the two minima . these two barriers make the system evolve along metastable paths . therefore , the question arises : what makes the system evolve along the ground state in increasing magnetic fields ? the volume barriers in these disks are negligibly small for transitions between different @xmath49 states of the disk considered in fig . 1 because in such a case the order parameter on the average changes by a small amount or the local minima are very close to each other . and as is known for cylinders , the surface barrier in increasing fields ( but not in decreasing fields ) can be destroyed by small surface defects . the disks used in the experiment of ref @xcite have a rough boundary and therefore in increasing field the sample evolves along the ground state . the situation is different in decreasing field . the surface barrier does not disappear due to surface defects and so in decreasing field the sample will evolve along metastable states , thus resulting in hysteresis . in our model the barriers are present but what is not present are the thermal fluctuations in the system . to a first approximation we can neglect these effects because of the extreme low temperature at which the experiments are done and study hysteresis effects arising due to metastability alone . the result in decreasing field using our 3d solution is given by the thick dashed curves in fig the magnetometry used in the experimental work of ref . @xcite is explained in detail in refs . @xcite . the superconducting sample is mounted on top of a small hall cross . from the hall resistance one can estimate how much field is expelled from the hall cross , which is due to the expulsion of the field by the superconductor . the hall cross has a larger area than the sample and it measures the magnetization of this area rather than the sample . in ref . @xcite it was shown that the hall voltage of a hall bar , in the ballistic regime , is determined by the average magnetic field piercing through the hall cross region . due to the depletion of the two dimensional electron gas near the edges of the leads of the hall cross the effective area of the hall cross is not exactly known and may be smaller than the optical size . since the field distribution in case of thin disks is extremely non - uniform inside as well as outside the disks ( this is essentially different for cylinders where the magnetic field outside the sample always equals the applied field ) the detector size will have an effect on the measured magnitude of the magnetization . since the field just outside the disk is larger than the applied field , a larger detector will underestimate the magnetization , the nature and extent will depend on the field profile outside the disk . to understand these effects we calculate the magnetization of an area larger than that of the sample by integrating the field expelled from this area . we take a disk of radius 0.44 @xmath4 , thickness = 0.15 @xmath4 , coherence length @xmath51 = 0.275 @xmath50 and penetration length @xmath9 = 0.07 @xmath4 at t=0.4k . in fig . 2 we plot the calculated flux expulsion from the sample ( solid curve ) , and from a square area larger ( width 1.75 @xmath4 , dashed curve ) and smaller ( width .067 @xmath4 , dotted curve ) than the sample size . the detector area is taken immediately under the sample . when the detector width is larger than the diameter of the sample , increase of the detector width simply scales down the magnetization . when the detector width is smaller than the diameter of the sample there is a small change in the line shape . the dashed curve when multiplied by 15.83 practically coincides with the solid curve , whereas the dotted curve when scaled by 0.5291 goes over to the dash - dotted curve . in fig . 3 we show how the scale factor ( defined as peak value of magnetization for a certain detector width divided by the peak value of the sample magnetization ) scales with the width @xmath53 of the detector . the magnetic field profile ( applied field + field due to the magnetization of the sample ) for a disk of radius @xmath54 is shown in the lower inset . from this profile it is clear that increasing the detector size @xmath53 will result in an average magnetic field closer to the applied field and consequently a smaller measured field expulsion and consequently a smaller magnetization . the scale factor shown in fig . 3 could be fitted to a gaussian curve with center at 0.18 , width of 0.93 , height of 1.83 and offset of 0.055 . since the magnetic field is also non - uniform in the z - direction , the magnetization measurement will also be affected by the distance of the detector from the sample . we take a square detector whose width is equal to the diameter of the sample and place it at different distances below the sample . in this case there is no change in line shape and the different curves can be made to coincide with each other by appropriate scaling . in the upper inset of fig . 3 we show how the scale factor varies with the vertical distance from the middle of the sample . this curve could be fitted to the function @xmath55 $ ] where @xmath56=0.6 , @xmath57=0.07 and @xmath58=0.28 . in section v we will show that for samples with @xmath59 the line shape of the magnetization curve can also change with the size and position of the detector but the peak value scales in a similar manner as found in this section . we shall also show that in decreasing fields the conclusions can be very different because magnetization can change sign as a function of @xmath53 . if the upper critical field ( @xmath60 ) of a disk is such that @xmath61 , then we call it a fractional fluxoid disk , where @xmath62 is a single flux quantum . physically it means that the disk is not large enough to accommodate even a single vortex when in the superconducting state . in such a small disk the @xmath49=1 state can not nucleate and the superconducting state always corresponds to the @xmath49=0 state . in this regime the 2d solution is always valid . as an example , we fix the radius of the disk to be 0.3 @xmath4 , temperature t=0.4k , coherence length @xmath51=0.25 @xmath4 and penetration length @xmath9=0.07 @xmath4 which results in @xmath10=0.28 . we plot in fig . 4 the magnetization versus decreasing applied magnetic field for 5 different thicknesses @xmath1 . the values of @xmath63 are shown in the figure where @xmath64=0.31 for @xmath65=0.4k . it can be seen that for @xmath660.3 the disk shows a second order phase transition to the normal state , whereas for @xmath670.5 , we find a first order phase transition to the normal state . the magnetization ( multiplied by 0.5 ) from the lgl theory is shown by the dashed curve for the same radius and coherence length . the magnetization for a cylinder in decreasing magnetic field for the same radius and material parameters is shown by the dash - dotted curve . notice that for very small thickness @xmath58 the sample shows a second order transition between the normal - superconducting state but as the thickness increases , beyond a critical thickness of t=0.33 , this becomes a first order transition . the magnitude of the jump of the magnetization @xmath68 versus @xmath58 at the superconducting - normal transition point is shown in fig . this result can be fitted , ( solid curve ) to the function @xmath69 , where @xmath70 , @xmath71 and @xmath72 . in the inset we plot the peak position of the magnetization curve versus @xmath58 which we could fit to the function @xmath73 where @xmath74 , @xmath75 and @xmath76 . it is generally believed that the upper critical field is given accurately by the lgl theory which we find to be true in decreasing magnetic fields . the same results in increasing magnetic field is given in fig . 6 where curve conventions are the same as in fig . 4 . in increasing magnetic field the lgl theory gives the correct upper critical field as long as the sample shows a second order transition to the normal state . in this case the upper critical field is independent of the thickness . as the sample starts showing a first order transition the upper critical field starts increasing with increasing thickness . the reason behind this qualitative difference with the lgl theory in increasing and decreasing field arises due to the fact that in the lgl theory there is only one minimum in the free energy whereas in the gl theory , when the sample shows a second order transition , there is one minimum but when it shows a first order transition , there are two minima in the free energy ( the first minimum is at zero order parameter and the second minimum is at a finite order parameter ) . one of them is however metastable and we shall soon find that the experimental system can exist in such a metastable state . in this case @xmath68 versus @xmath58 is shown in fig . 7 . it fits to a function @xmath77 where @xmath78 , @xmath79=0.33 and @xmath80=0.58 . from figs . 4 and 6 we can understand why a disk can show a first order or a second order phase transition to the normal state as is found in the experiment . it also explains why a fractional fluxoid disk in case of a first order transition shows a different behavior in increasing and decreasing magnetic fields and as a result a remarkable hysteresis as seen in the experiment . in fig . 8 , we show that a disk of radius @xmath0=0.44 @xmath4 , thickness @xmath1=0.15 @xmath4 , coherence length @xmath51=0.275 @xmath4 and penetration length @xmath9=0.07 @xmath4 at t=0.4k can exhibit a magnetization like that of a disk whose magnetization was measured in the experiment and whose radius was reported as 0.5 @xmath4 , thickness between 0.07 @xmath4 and 0.15 @xmath4 , coherence length of 0.25 @xmath4 and penetration length of 0.07 @xmath4 . note that we decrease the coherence length by 10 @xmath81 and the radius by 12 @xmath81 to reproduce the experimental result which are well within the errors of experimental estimates . the increasing field behavior as seen in the experiment is given by the open squares and the decreasing field behavior is given by the open circles . our numerical calculation of the magnetization in increasing and decreasing magnetic field for a detector area of 2.5 @xmath4 placed 0.15 @xmath4 below the sample is shown by the solid and dotted curves , respectively . the inclusion of the detector size and position results in a magnetization which is a factor 50.44 smaller than the pure sample magnetization . the inset shows the dimensionless free energy as a function of the magnetic field . the dashed line in fig . 8 is the behavior expected in the case of a linear meissner effect and is drawn tangential to the small field magnetization curve . notice that even in the intermediate magnetic field region the magnetization is substantially non - linear . note that in decreasing field the position of the jump does not agree with the experiment . in case of a first order transition the free energy has two minima separated by a barrier and when the system tries to switch from one minima to the other it has to overcome this barrier . the position of the jump given here corresponds to the situation when this barrier disappears . but due to fluctuations in the system the jump can be at lower fields . the field distribution along a radial line starting from the center of the disk is shown in fig . the center of the disk is at the origin of the coordinates . notice that the field is minimum at the center of the disk . it increases drastically with distance from the center and becomes maximum at 0.44 @xmath50 which is precisely the radius of the disk . this implies that the field is strongly expelled from the center of the disk . the 11th curve ( applied field=70.86 gauss ) corresponds to the critical field at which superconductivity has disappeared . magnetization measurement on bulk samples and large radius cylinders shows that in the pure meissner state " , the sample behaves as a perfect diamagnet which means magnetization is proportional to the applied field with a susceptibility ( @xmath82=4@xmath83/h ) of -1 . this experimental observation led to the well known london theory . it can already be seen from the magnetization measurement ( see the experimental data in fig . 8) that london theory is not valid for the present disks because of the non - linear magnetization versus the applied field . even in the small field region the susceptibility is much smaller than -1 because of large field penetration in a finite size sample as can be seen from fig . 9(a ) . in the usual london approach the field penetration is determined by the field value at the boundary of the sample . in fig . 9(b ) we show the normalized field distribution , i.e. , the field is divided by its maximum value which is found at the edge of the disk . this helps us to compare the field penetration at different applied fields . for small applied fields ( say less than 25 g ) the curves fall on top of each other as expected from london theory . but for larger applied fields the field penetration is no longer only determined by the field at the boundary of the disk and becomes substantially larger . in the inset of fig . 9(b ) we plot the magnetic field normalized to the applied field . when a disk is large enough to accommodate one or more fluxoids we call it a few fluxoid disk " . unlike for fractional fluxoid disk " , for the few fluxoid disk " case the lgl and gl theories give qualitatively similar result . the upper critical field and the number of jumps in the magnetization is the same in both theories . but in order to explain the position and the magnitude of the jumps it is necessary to consider the full gl eqns . to explain the increasing field behavior we assume that the system remains in the ground state , which can be determined from the 2d solution as explained in section iii . 10(a ) shows the magnetization of a few fluxoid disk : the open circles are the experimental data ( at t=0.4 k ) plotted according to the scale on the left axis . the experimental estimates of radius is 0.75 @xmath4 , thickness is between 0.07 @xmath4 to 0.15 @xmath4 , coherence length is 0.25 @xmath4 and penetration length is 0.07 @xmath4 . sample magnetization along the ground state calculated from our 2d solution is shown by the dashed curve and it is plotted according to the scale on the right . parameter values used for the radius is 0.8 @xmath4 , thickness is 0.134 @xmath4 , temperature is 0.4 k , coherence length is 0.183 @xmath4 and penetration length is 0.07 @xmath4 . there is a factor of 25 difference in the magnitude of magnetization . however when we use a detector of width 3 @xmath50 placed 0.15 @xmath4 below the sample , the ground state magnetization , as defined by the flux expulsion from the detector square , is given by the solid curve plotted according to the scale on the left . notice that the inclusion of the detector effect explains the magnitude of magnetization and it also changes slightly the slope of the curve for fields larger than 40 g. namely the magnetization decreases faster with magnetic field . also the magnetization in decreasing magnetic field is shown in fig . 10(b ) where the curve conventions are the same as for the field sweep up . it is needless to say that the agreement with the experimental data is remarkable except for the last jump at low field . in fig . 11 we show how the minimum magnetization at 55.795 gauss scales with the size of the detector in case of the field down sweep . for detector size smaller than the sample the magnetization is strongly paramagnetic due to the pinned fluxoid in the sample . also when the detector size slightly exceeds the sample size the magnetization can be paramagnetic which decrease as the detector size is made larger . next in fig . 12 we consider an even larger disk which is able to contain 19 flux quanta before it becomes normal . the experimental data of magnetization versus increasing magnetic fields at t=0.4 k is shown by the open circles according to the scale on the left . the experimental estimate of the parameters are radius=1.2 @xmath4 , thickness is between 0.07 @xmath4 and 0.15 @xmath4 . our 2d solution for the ground state magnetization of the sample is shown by the dashed curve according to the scale on the right . parameter values used for radius is 1.25 @xmath4 , thickness is 0.136 @xmath4 , coherence length is 0.195 @xmath4 and penetration length is 0.07 @xmath4 . when we use a detector of width 4 @xmath4 placed 0.15 @xmath4 below the sample the ground state magnetization is given by the solid curve . note that the size of the detector used here appears to be a bit larger than expected experimentally . using a detector of smaller width does not appreciably change the line shape as long as it is slightly larger than the disk diameter . also the convex shape of the curve for field larger than 25 g is recovered although it is less than that found experimentally . note that the position of the first jump , the upper critical field and the total number of jumps is the same as that found experimentally . the jumps observed in figs . 10 and 12 reminds us of the little parks oscillations seen in ring shaped superconductors and other multiply connected geometries @xcite . in such geometries it occurs due to flux quantization in superconductors and hence these jumps occur at extremely regular intervals ( provided the sample is clean ) . it is to be noted that in figs . 10 and 12 the interval between jumps is slowly decreasing in the experimental data as well as in the theoretical curve . in fig . 13(a ) we plot the magnetic field interval between two successive jumps , @xmath84 , versus the angular momentum @xmath49 for the ground state ( open circles ) which are compared with the experimental data ( solid squares ) . we find that the experimental @xmath84 is extremely irregular , which suggests that entry of fluxoids into the sample is hindered by disorder and pinning centers . another reason may be the experimental accuracy and fluctuations in the applied field which are expected to lead to an error of about 10 @xmath81 in these quantities . the overall behavior : of a large @xmath84 for small @xmath49 and a smaller but constant @xmath84 for larger @xmath49 is clearly visible in the experimental result . the open squares in fig . 13(a ) are obtained from the recent theoretical result of ref . he used a variational approach to solve the gl equation with the approximation of an uniform magnetic field distribution . his calculation was done for @xmath85 and @xmath86 . the origin of this drastic decrease in @xmath84 arises due to strong flux expulsion and the demagnetization effects at low fields because of which the flux inside the sample increases at a very slow rate as compared to the applied field . so the external field has to be increased by more than a flux quantum to give rise to one flux quantum inside the disk . such strong flux expulsion becomes weaker as field is increased and becomes zero at the critical field . so at higher fields @xmath68 versus @xmath49 becomes flat and corresponds to the flux quantization condition : @xmath87 . in fig . 13(b ) the magnitude of the jumps in the magnetization ( @xmath68 ) is shown and compared with the experimental data and the theoretical result of ref . the theory gives a substantial larger magnitude of the jumps than seen experimentally except for the smaller radius sample ( see inset ) when @xmath88 . apart from explaining quantitatively and qualitatively the recent experiments of geim _ et al _ we can make some general conclusions . the gl theory captures all the features of mesoscopic superconductors provided the non - linear term and the field distribution is properly accounted for . hence it is necessary to review the calculation of various quantities in mesoscopic superconductors made so far which did not account for these effects . we can also conclude that in increasing magnetic fields the sample evolves along the free energy minimum and the bean - livingston barrier plays no role . surface defects destroy the bean - livingston barrier in increasing fields in the case of cylinders . this also seems to be true for disks . we also find that the magnitude of magnetization is drastically affected by the detector size . the nature of the measured magnetization curves are sensitive to small changes in parameters . this work is supported by the flemish science foundation(fwo - vl ) grant no : g.0232.96 , the belgian inter - university attraction poles ( iuap - vi ) . one of us ( psd ) is supported by a post doctoral scholarship from the fwo - vl and fmp is a research director with the fwo - vl . it is a pleasure to acknowledge stimulating discussions with a. geim . 99 electronic mail : [email protected] electronic mail : [email protected] permanent address : institute of theoretical and applied mechanics , russian academy of sciences , novosibirsk 630090 , russia . p. g. de gennes , _ superconductivity of metals and alloys _ , ( addison wesley , new york , 1989 ) . a. i. buzdin and j. p. brison , phys . a * 196 * , 267 ( 1994 ) . r. kato , y. enomoto , and s. maekawa , phys . b * 47 * , 8016 ( 1993 ) . c. bolech , g. c. buscaglia , and a. lpez 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. rev . lett . * 79 * , 4653 ( 1997 ) . p. singha deo , v. a. schweigert , and f. m. peeters , cond - mat/9804174 . v. l. ginzburg and l. d. landau , zh . * 20 * , 1064 ( 1950 ) ; l. p. gorkov , zh . fiz . * 36 * , 1918 ( 1959 ) [ soviet phys . - jetp * 9 * , 1364 ( 1959 ) . g. dolan , j. low temp . phys . * 15 * , 133 ( 1974 ) . d. saint - james and p. g. de gennes , phys . * 7 * , 306 ( 1963 ) . v. a. schweigert , f. m. peeters , and p. singha deo , phys . * 81 * , 2783 ( 1998 ) . c. p. bean and j. d. livingston , phys . * 12 * , 14 ( 1964 ) . a. k. geim , s. v. dubonos , i. v. grigorieva , j. g. s. lok and j. c. maan , appl . . lett . * 72 * , 572 ( 1998 ) . f. m. peeters and x. q. li , appl . * 72 * , 572 ( 1998 ) . 1 . free energy versus increasing magnetic field for different angular momentum ( @xmath49 ) states are shown by thin solid curves . thick solid curve is the free energy versus increasing magnetic field for the ground state of the sample , the thick dotted curve is the result from the 3d solution and the thick dashed curve shows the same for decreasing magnetic fields . here @xmath89= @xmath90 . ( b ) the corresponding magnetization for the curves in ( a ) with the same convention for the different curves . the scale factor for the magnetization as function of the width of the detector . the upper inset shows how this scale factor varies with the distance of the detector . the lower inset shows how the magnetic field varies along a line from the center of the disk for the particular disk considered in this figure . @xmath68 is the magnitude of the jumps in the magnetization seen in fig . the solid circles give @xmath91 for the corresponding value of @xmath58 . the solid curve is a @xmath92-fit to it . the inset shows how the peak position of the curves in fig . 4 vary with @xmath58 along with a @xmath92-fit . the solid circles give @xmath68 for the corresponding value of @xmath58 . the solid curve is @xmath92 fit to it . the inset shows how the transition field vary with @xmath58 along with a @xmath92 fit . comparison between experimentally observed magnetization in increasing ( open squares ) and decreasing fields ( open circles ) and our numerically calculated magnetization in increasing ( solid curve ) and decreasing ( dotted curve ) magnetic field . the dashed curve is a tangent to the experimental data at the origin . the inset shows the dimensionless free energy for the system . fig . 9 . ( a ) magnetic field change from the center of the disk considered in fig . 8 for different applied fields mentioned in the figure . ( b ) magnetic field curves of fig . 9(a ) when scaled by the maximum field for each curve . the inset shows the magnetic field when scaled by the applied field . fig . 10 . ( a ) comparison between experimentally observed magnetization in increasing ( open circles ) fields according to the scale on the left y - axis and our numerically calculated magnetization in increasing ( dashed curve ) magnetic field according to the scale on the right y - axis . the solid curve is according to the left y - axis and is obtained when the detector size is taken into account . ( b ) the same for decreasing magnetic fields . fig . 12 . comparison between experimentally observed magnetization in increasing ( open circles ) fields according to the scale on the left y - axis and our numerically calculated magnetization in increasing ( dashed curve ) magnetic field according to the scale on the right y - axis . the solid curve is according to the left y - axis and is obtained when the detector size is taken into account . fig ( a ) comparison of experimentally observed and numerically obtained @xmath84 ( magnetic field change due to penetration of one extra fluxoid ) versus @xmath49 for the disk considered in fig . the solid squares give the experimental data , the open circles are our numerically obtained values and the open squares correspond to the results of ref . the curves are guides to the eye . the inset shows the same for the case of fig . ( b ) comparison of experimentally observed and numerically obtained @xmath68 ( jumps in the magnetization ) versus @xmath49 for the disk considered in fig . 12 . the symbol conventions are the same as in fig . the inset shows the same for the case of fig .

using the non - linear ginzburg - landau ( gl ) eqs . type i superconducting disks of finite radius ( @xmath0 ) and thickness ( @xmath1 ) are studied in a perpendicular magnetic field . depending on @xmath0 and @xmath1 , first or second order phase transitions are found for the normal to superconducting state . for sufficiently large @xmath0 several transitions in the superconducting phase are found corresponding to different angular momentum giant vortex states . in increasing magnetic field the superconductor is in its ground state , while in field down sweep it is possible to drive the system into metastable states . we also present a quantitative analysis of the relation between the detector output and the sample magnetization . the latter , and the incorporation of the finite thickness of the disks , are essential in order to obtain quantitative agreement with experiment .

turbulence remains one of the unsolved problems of classical physics . turbulence generates strong nonlinear interactions among the large number of modes of the system , which makes theoretical analysis of such flows highly intractable . using kolmogorov s theory of fluid turbulence , it can be shown that the degrees of freedom of a turbulent flow with reynolds number @xmath2 is @xmath3 @xcite . consequently , a numerical simulation of a turbulent flow with a moderate reynolds number of @xmath4 requires @xmath5 trillion grid points , which is impossible even on the most sophisticated supercomputer of today . a low - dimensional model called _ shell model of turbulence _ @xcite is reasonably successful in explaining certain features of turbulence , e.g. , it reproduces the kolmogorov s theory of fluid turbulence , as well as the experimentally observed intermittency corrections @xcite . in a shell model , a single shell represents all the modes of a logarithmically - binned shell , hence the number of modes in a shell model is much smaller than @xmath3 . consequently , a large reynolds number can be easily achieved in a shell model with 40 or more shells . a large body of work exists on the shell model of fluid turbulence . however , till date , there is no shell model for the stably stratified turbulence , and there is no convergence on the shell model for the convective turbulence . brandenburg @xcite and mingshun and shida @xcite , have constructed shell models for convective turbulence , namely rayleigh bnard convection , but their results are divergent ( to be discussed later ; also see @xcite ) . in this paper , we introduce a shell model that describes both stably stratified and convective turbulence ; we can go from one to the other with a change of sign in the density or temperature gradient . our shell model reproduces the numerical results of kumar _ et al . _ @xcite , according to which stably stratified turbulence exhibits bolgiano - obukhov scaling @xcite , and convective turbulence shows kolmogorov scaling . we also observe the dual spectrum predicted by bolgiano @xcite and obukhov @xcite . buoyancy - induced turbulence @xcite , often encountered in geophysics , astrophysics , atmospheric and solar physics , engineering , come in two categories : ( a ) stably stratified flows in which a lighter fluid is above a heavier fluid . these flows are stable because of their stable density stratification ; ( b ) convective flows in which a heavier ( or colder ) fluid is above a lighter ( or hotter ) fluid . such flow configurations are unstable , hence , the heavier fluid elements come down , and the lighter ones go up . the linear regimes of the above flow are easy to solve , and they yield gravity waves and convective instabilities respectively . however , the turbulent aspects of such flows are active areas of research . for stably stratified turbulence , bolgiano @xcite and obukhov @xcite first proposed a phenomenology , according to which for @xmath6 ( @xmath7 is wavenumber , and @xmath8 is bolgiano wavenumber @xcite ) , the kinetic energy ( ke ) spectrum @xmath9 , entropy spectrum @xmath10 , ke energy flux @xmath11 , and entropy flux @xmath12 are @xmath13 here @xmath14 and @xmath15 are the velocity and temperature fluctuations respectively , @xmath16 is the thermal expansion coefficient , @xmath17 is the acceleration due to gravity , @xmath18 and @xmath19 are the ke and entropy dissipation rates respectively , and @xmath20 s are constants . the ke flux @xmath11 is forward , and it decreases with @xmath7 due to a conversion of kinetic energy to potential energy . this decrease @xmath11 causes a steepening in the kinetic energy spectrum to @xmath0 , compared to kolmogorov s classical @xmath1 spectrum . note that the stably stratified flows is also described in terms of density fluctuation @xmath21 , which leads to an equivalent description since @xmath22 . in convective turbulence , @xmath23 is referred to as the entropy , but in stably stratified turbulence , @xmath24 is called the potential energy . bolgiano @xcite also showed that the buoyancy effects become somewhat insignificant in the wavenumber band @xmath25 , where @xmath26 is the dissipation wavenumber . therefore , @xmath27 , @xmath28 , and @xmath29 . the aforementioned scaling , @xmath0 for @xmath6 , and @xmath1 for @xmath25 , is referred to as bolgiano - obukhov ( bo ) phenomenology . for convective turbulence , in particular for the idealised version called rayleigh bnard convection ( rbc ) , procaccia and zeitak @xcite , lvov @xcite , lvov and falkovich @xcite , and rubinstein @xcite argued in favour of bo scaling . the numerical and experimental findings however are inconclusive @xcite . in a recent numerical simulation , kumar _ et al . _ @xcite analysed the above phenomenologies in a great detail . they showed that stably stratified turbulence under strong buoyancy exhibits @xmath0 energy spectrum , as predicted by bolgiano @xcite and obukhov @xcite . they observed that @xmath30 , thus corroborating the net conversion of kinetic energy to potential energy . for rbc , et al . _ @xcite showed that @xmath31 , which is interpreted as a conversion of potential energy to kinetic energy , opposite to that in stably stratified turbulence . as a result , for rbc , the ke flux @xmath11 increases marginally with @xmath7 , and ke exhibits an approximate kolmogorov spectrum @xmath1 , contrary to the earlier predictions @xcite . the numerical results of kumar _ _ @xcite are consistent with those of borue and orszag @xcite . the powerlaw regimes in kumar _ @xcite simulations are somewhat narrow . also , they could not observe the dual spectrum of bo phenomenology , which may require much higher numerical resolution than @xmath32 . in this paper , we present a unified shell model of stably stratified and convective turbulence that overcomes some of the aforementioned limitations of the numerical simulations . for the unified shell model for the buoyancy driven flows , we assume that the fluid is subjected to a mean temperature gradient , @xmath33 , which is positive for a stably stratified flow ( cold below and hot above ) , and is negative for a convective flow ( hot below and cold above ) . here @xmath34 is computed by averaging the temperature over the horizontal plane whose height is at @xmath35 . the outline of the paper is as follows . in sec . [ sec : model ] , we introduce unified shell model , which can solve both stably stratified and convective turbulence ; we discuss the construction of nonlinear terms , the required constraints , and the method for computing the energy spectrum and flux . numerical results of the shell models for the stably stratified turbulence and the convective turbulence are discussed in sec . [ sec : sst ] and [ sec : ct ] respectively . we conclude in sec . [ sec : conclusions ] . our shell model for the buoyancy - driven turbulence is @xmath36 + \alpha g \theta_{n } - \nu k_{n}^{2}u_{n } + f_n , \label{eq : u_shell}\\ \frac{d\theta_{n}}{dt } & = & n_n[u,\theta ] - \frac{d \bar{t}}{dz } u_{n } - \kappa k_{n}^{2}\theta_{n } \label{eq : t_shell},\end{aligned}\ ] ] where @xmath37 and @xmath38 are the shell variables for the velocity and temperature fluctuations respectively , @xmath39 represents the external force field , @xmath40 is the wavenumber of the @xmath41-th shell , and @xmath42 and @xmath43 are the kinematic viscosity and thermal diffusivity , respectively , of the fluid . we choose @xmath44 , the golden mean @xcite . the nonlinear terms @xmath45 $ ] and @xmath46 $ ] are constructed keeping in mind the conservation of kinetic energy @xmath47 , kinetic helicity @xmath48 , and entropy @xmath49 in the absence of diffusive and forcing terms . for the shell model , the corresponding qualities are @xmath50 , @xmath51 , and @xmath52 respectively . the nonlinear term @xmath45 $ ] has been constructed earlier by invoking the conservation of kinetic energy and kinetic helicity as [ see e.g , @xcite ] @xmath53 & = & -i(a_{1}k_{n}u_{n+1}^{*}u_{n+2}+a_{2}k_{n-1}u_{n-1}^{*}u_{n+1 } \nonumber \\ & & -a_{3}k_{n-2}u_{n-1}u_{n-2}).\end{aligned}\ ] ] with constraints @xmath54 and @xmath55 . for our computation , we choose @xmath56 , @xmath57 , and @xmath58 @xcite . for the construction of the nonlinear term @xmath46 $ ] , we use the fact that the nonlinear term of the temperature equation is a bilinear product of the temperature fluctuation and the velocity fluctuation . also , the conservation of entropy yields a condition @xmath59 \right)= 0.\ ] ] a combination of the above yields @xmath60 & = & -i[k_{n}(d_{1}u_{n+1}^{*}\theta_{n+2}+d_{3}\theta_{n+1}^{*}u_{n+2 } ) \nonumber \\ & & + k_{n-1}(d_{2}u_{n-1}^{*}\theta_{n+1}-d_{3}\theta_{n-1}^{*}u_{n+1 } ) \nonumber\\ & & -k_{n-2}(-d_{1}u_{n-1}\theta_{n-2}-d_{2}\theta_{n-1}u_{n-2 } ) ] \label{eq : nlin_t } \end{aligned}\ ] ] with arbitrary @xmath61 , and @xmath62 . for our shell model , we choose @xmath63 , @xmath64 , and @xmath65 . for consistency , we choose the boundary conditions @xmath66 and @xmath67 , where @xmath68 is the total number of shells . also note that we use sabra model @xcite that yields less fluctuations for the spectrum compared to the goy model @xcite . the second term in the rhs of eq . ( [ eq : u_shell ] ) , @xmath69 , is the buoyancy term , while @xmath70 is the temperature stratification ( or equivalently density stratification ) term . clearly , @xmath71 for a stably stratified flow , and @xmath72 for the convective turbulence . the shell model for rbc does not require forcing to maintain a steady state however , the shell model for the stably stratified turbulence requires a forcing for the same ; we force a set of small wavenumber shells ( large length - scale modes ) randomly so as to feed a constant energy supply rate @xmath73 to the system . we assume that the forcing shells receive equal amount of energy . if @xmath74 shells are forced , then the above conditions yield the force at the @xmath41-th shell as @xmath75 where @xmath76 is the random phase of the @xmath41-th shell chosen from the uniform distribution in @xmath77 $ ] . in our simulation we force the shells @xmath78 and 4 , hence @xmath79 . it is convenient to work with the nondimensionalized equations , which is achieved by using box height or the characteristic length @xmath80 as the length scale , @xmath81 as the velocity scale , and @xmath82 as the temperature scale . therefore , @xmath83 , @xmath84 , @xmath85 , and @xmath86 . in terms of nondimensonalized variables , the equations are @xmath87 + \theta^{\prime}_{n } - \sqrt { \frac{\mathrm{pr}}{\mathrm{ra } } } { k^{\prime 2}_{n}}u^{\prime}_{n } + f^{\prime}_n , \label{eq : non_u_shell}\\ \frac{d\theta^{\prime}_{n}}{dt^{\prime } } & = & n^{\prime}_n[u^{\prime},\theta^{\prime } ] - s u^{\prime}_{n } - \frac{1}{\sqrt{\mathrm{ra}\mathrm{pr}}}k^{\prime 2}_{n}\theta^{\prime}_{n } \label{eq : non_t_shell},\end{aligned}\ ] ] where @xmath88 for positive @xmath89 , and @xmath90 for negative @xmath89 . we remark that ours is the first shell model for the stably stratified turbulence . for rbc , brandenburg @xcite , and mingshun and shida @xcite had constructed shell models . our shell model differs quite significantly from that of brandenburg . the shell model 2 " of mingshun and shida @xcite is applicable to neutral stratification , and it is a subset of our shell model . the shell model of ching and cheng @xcite is same as that of brandenburg @xcite . the important parameters for the buoyancy - driven turbulence are : the prandtl number @xmath91 , the reynolds number is @xmath92 , and @xmath93 where @xmath94 is the rms velocity of flow , and @xmath80 is the characteristic length scale . note that the brunt visl frequency is the frequency of the gravity wave , the froude number is the ratio of the characteristic fluid velocity and the gravitational wave velocity , and the richardson number is the ratio of the buoyancy and the nonlinearity @xmath95 . for convenience , the primes from the variables are dropped in our subsequent discussion . note that for rbc , the critical rayleigh number @xmath96 , after which the flow becomes unstable . due to the lower critical rayleigh number in the shell model , turbulence appears at a lower rayleigh number compared to that observed in direct numerical simulations . we compute energy spectrum [ @xmath9 ] and the entropy spectrum [ @xmath98 , defined as @xmath99 using the steady state data . we also compute the energy and entropy fluxes . in fluid turbulence , the energy flux @xmath100 is defined @xcite as the rate of energy transfer from modes inside a sphere of radius @xmath7 to the modes outside the sphere . for the shell model , the energy flux @xmath100 is the rate of energy transfer from the shells within the sphere of radius @xmath7 , i.e. @xmath101 $ ] , to the shells outside the sphere , i.e. @xmath102 $ ] @xcite : @xmath103 similarly , the entropy flux @xmath12 is defined as the rate of entropy transfer from the shells within the sphere of radius @xmath7 to the shells outside the sphere , i.e. , @xmath104 we simulate the aforementioned shell model [ eqs . ( [ eq : non_u_shell ] , [ eq : non_t_shell ] ) ] for stably - stratified and convective turbulence and compute the above spectra and fluxes . we take @xmath105 shells for the stably stratified turbulence simulations sst1 and sst2 , and @xmath106 shells for sst3 and the convective turbulence simulation ( ct ) . for time stepping , we use the fourth - order runge - kutta ( rk4 ) method . for stably stratified turbulence , we apply random force on shells @xmath78 and @xmath107 . the parameters of the simulations are listed in table [ table : simulation_details ] . c c c c c c c c c c + flow type & @xmath68 & @xmath108 & @xmath73 & @xmath2 & @xmath109 & @xmath110 & @xmath111 & @xmath19 & @xmath8 + + sst1 & @xmath105 & @xmath112 & @xmath113 & @xmath114 & @xmath115 & @xmath116 & @xmath117 & @xmath118 & @xmath119 + sst2 & @xmath105 & @xmath120 & @xmath121 & @xmath122 & @xmath123 & @xmath124 & @xmath125 & @xmath126 & @xmath127 + sst3 & @xmath106 & @xmath112 & @xmath120 & @xmath128 & @xmath129 & @xmath130 & @xmath131 & @xmath132 & @xmath133 + ct & @xmath106 & @xmath134 & na & @xmath135 & @xmath136 & na & @xmath137 & @xmath138 & na + [ table : simulation_details ] we compute the spectra and fluxes of ke and entropy , and average over many snapshots ( @xmath139 ) of the steady - state flow ( of a single run ) ; these values are further averaged over @xmath140 simulations with independent random initial conditions @xcite . the error bars reported in the paper for the spectral exponents and fluxes are the standard deviations of the aforementioned 100 independent data sets @xcite . this is the statistical error of our data . the spectral exponents of the energy and entropy spectra along with the errors for the sets of parameters are summarized in table [ table : spectral_exponent ] . the data also has some systematic error , for example the dip in energy spectrum near @xmath141 ( the fifth shell ) . the origin of the dip is not understood clearly at present , and it will be presented in future . to test the validity of bo scaling in the stably stratified turbulence , we simulate the shell model for the three sets of parameters , sst1 , sst2 , and sst3 , which are listed in table [ table : simulation_details ] . in fig . [ fig : spectrum_flux_ra_1e5](a ) we plot the ke spectrum @xmath9 and entropy spectrum @xmath142 for @xmath143 and @xmath144 . green shadow regions in all the figures of the paper are the forcing bands . the figure indicates that @xmath145 and @xmath146 for more than a decade , a result consistent with the bo scaling . we also compute the ke and potential energy fluxes , which are plotted in fig . [ fig : spectrum_flux_ra_1e5](b ) . in the inertial range , the entropy flux @xmath147 is constant , and the ke flux @xmath11 decreases with @xmath7 , but somewhat different from @xmath148 . these results are in general agreement with the bo scaling for the stably stratified turbulence . we also compute energy supply rate by buoyancy , @xmath149 , which is negative , as shown in fig . [ fig : force_spectrum ] . thus , we show a conversion of kinetic energy to potential energy by buoyancy , a result consistent with that of kumar _ et al . _ @xcite . c c c + flow type & @xmath150 & @xmath151 + + sst1 & @xmath152 & @xmath153 + & @xmath154 ; & @xmath155 ; + & @xmath156 & @xmath157 + sst3 & @xmath158 & @xmath159 + ct & @xmath160 & @xmath161 + [ table : spectral_exponent ] for the above case , the bolgiano wavenumber @xmath162 , which lies in the dissipation range , thus making the @xmath1 ke spectrum inaccessible . the bolgiano wavenumber @xmath8 is calculated by comparing eq . ( [ eq : eu ] ) and the kolmogorov s ke energy spectrum @xcite . to obtain the dual spectrum predicted in bo scaling , we increase the rayleigh number to @xmath120 , which yields @xmath163 , @xmath164 , and @xmath165 ( sst2 of table [ table : simulation_details ] ) . for these parameters , we observe an approximate dual spectrum , as shown in fig . [ fig : spectrum_ke_ra_1e10 ] . the ke spectrum can be approximately described by @xmath166 for @xmath167 , and @xmath168 and @xmath169 respectively , with bolgiano wavenumber @xmath170 . thus our simulations confirm the presence of dual scaling in stably stratified turbulence , as predicated by bolgiano @xcite and obukhov @xcite . we observe that a further increase of @xmath108 shrinks the @xmath171 regime and makes it invisible . for the parameters of sst3 , the nonlinearity is stronger than the buoyancy term , which is evident from the fact the richardson number @xmath172 . hence , we observe kolmogorov scaling , i.e. @xmath168 and @xmath173 for these parameters shown in fig . [ fig : spectrum_flux_ra_1e5_low_ri](a ) . the fluxes of ke and potential energy are constant in @xmath7 , as shown in fig . [ fig : spectrum_flux_ra_1e5_low_ri](b ) . in the next section we will discuss the results of convective turbulence . in convective turbulence , buoyancy feeds energy to the kinetic energy , hence the ke flux increases marginally at lower wavenumbers @xcite . in the intermediate range of wavenumbers , where the dissipation rate @xmath174 approximately balances the energy supplied by buoyancy @xmath175 , we expect kolmogorov s spectrum for the velocity field @xcite . we performed a shell model calculation to verify the above conjecture using the parameters @xmath176 and @xmath177 ( ct of table [ table : simulation_details ] ) . note that no external forcing is required to obtain a steady state in convective turbulence . in fig . [ fig : spectra_flux_rb](a ) we plot the ke and entropy spectra that indicates kolmogorov ( ko ) scaling , i.e. @xmath178 and @xmath179 , for convective turbulence . our spectrum results are consistent with the ke and entropy fluxes computations , which are plotted in fig . [ fig : spectra_flux_rb](b ) . the ke flux @xmath180 and entropy flux @xmath12 are constant in the inertial range , @xmath181 . we also compute energy supply rate @xmath182 and plot it in figs . [ fig : force_spectrum ] and [ fig : force_spectrum_ct ] . we observe that @xmath183 indicating a positive energy transfer from buoyancy to the kinetic energy . in fig . [ fig : force_spectrum_ct ] , we also plot the dissipation rate @xmath184 and @xmath185 . in inertial range , @xmath175 and @xmath186 cancel each other approximately , and hence yield a constant ke flux @xmath11 . thus , we show that in convective turbulence , the ke exhibits kolmogorov s spectrum , not bo spectrum , as envisaged in some of the earlier work @xcite . it is important to contrast our shell model with earlier ones . ours is the first shell model for stably stratified turbulence , and it yields results consistent with the bo scaling predicted by bolgiano @xcite and obukhov @xcite . we also observe an approximate dual spectrum ( @xmath0 and @xmath1 ) for the kinetic energy for a limited set of parameters . by switching the sign of the density gradient , our shell model transforms from stably stratified flows to convective turbulence . for convective turbulence , our shell model exhibits kolmogorov s spectrum in the intermediate range of wavenumbers . earlier , brandenburg @xcite and mingshun and shida @xcite had constructed shell models for rbc . brandenburg s @xcite shell model is quite different from ours ; he added several new terms in the goy shell model that leads to both forward and inverse ke fluxes . he observes @xmath168 for the forward cascade regime , consistent with our model . however , an inverse cascade of ke flux yields @xmath166 , which is consistent with the flux arguments of kumar _ et al . _ @xcite . when @xmath187 and @xmath183 , eq . ( 26 ) of kumar _ et al . _ @xcite would yield @xmath188 that could possibly yield @xmath189 ( bo scaling ) . these arguments need a clearcut validation from numerical simulations . ching and cheng @xcite used brandenburg s shell model and studied multiscaling exponents . the shell model 2 " of mingshun and shida @xcite is applicable to neutral stratification , and it is a subset of our shell model . mingshun and shida @xcite reported kolmogorov s spectrum for the model 2 , hence our model is consistent with the shell model of mingshun and shida @xcite . we also remark that the shell models are applicable to three - dimensional isotropic turbulence . the numerical work of kumar _ et al . _ @xcite focusses on froude number of the order of unity that yields somewhat isotropic flow . this is the reason why our shell model is consistent with the numerical results of kumar _ et al . _ however , our present shell model is not expected to work for anisotropic stably stratified flows studied earlier for which the froude number is quite low @xcite . a modification of our shell model to two - dimensional flows may work for the aforementioned quasi two - dimensional systems . in summary , we constructed a unified shell model for the buoyancy driven turbulence that yields bo scaling for stably stratified flows , but kolmogorov s spectrum for convective turbulence . such low dimensional models have strong utility since they can be used to explore highly non - linear regimes which are inaccessible to numerical simulations and experiments . we thank sagar chakraborty for valuable suggestions , and pankaj mishra for performing initial set of numerical simulations . our numerical simulations were performed at _ hpc2013 _ and _ chaos _ clusters of iit kanpur . this work was supported by a research grant ( grant no . serb / f/3279 ) from science and engineering research board , india .

in this paper we present a unified shell model for stably stratified and convective turbulence . numerical simulation of this model for stably stratified flow shows bolgiano - obukhbov scaling in which the kinetic energy spectrum varies as @xmath0 . we also observe a dual scaling ( @xmath0 and @xmath1 ) for a limited range of parameters . the shell model of convective turbulence yields kolmogorov s spectrum . these results are consistent with the energy flux and energy feed due to buoyancy , and are in good agreement with direct numerical simulations of kumar _ et al . _ [ phys . rev . e * 90 * , 023016 ( 2014 ) ] .

in recent years , we have been interested in studying joint polarization correlations of fundamental processes in qed and in the electro - weak theory@xcite for initially _ polarized _ and _ unpolarized _ particles . our main conclusion , based on explicit computations in quantum field theory , is that the mere fact that particles emerging from a process have non - zero speeds to reach detectors implies , in general , that their spin polarizations correlations probabilities _ depend on speed _ @xcite and _ may also depend on the underlying couplings _ @xcite . the explicit expressions of polarization correlations , follow from these _ dynamical _ computations and are non - speculative involving no arbitrary input assumptions , and are seen to depend on speed , and may depend on the couplings as well . these are unlike nave considerations of simply combining the spins of the particles in question which are of kinematical nature , in general , not applicable to relativistic particles , and formal arguments based on combining spins only , as is often done , completely fail . in the limit of low energies , our earlier expressions @xcite for the polarization correlations were shown to be reduced to the nave ones just mentioned by simply combining spins . in our earlier investigation @xcite in the electro - weak theory in a process for the creation of a @xmath1 pair , from @xmath0 scattering , for example it was noted that due to the threshold needed to create such a pair the zero energy limit may not be taken and the study of polarization correlations by simply combining spins , without recourse to quantum field theory , has no meaning . our interest in this paper is the derivation of the _ explicit _ polarization correlation probabilities in elastic @xmath0 scattering in qed for initially _ polarized _ as well as _ unpolarized _ particles , with emphasis put on the _ energy _ available in the process so that a detailed study can be carried out in the relativistic regime as well . the reasons for our present investigation are two fold . first several experiments on @xmath2 have been carried out over the years @xcite , and it is expected that our explicit new expression for the polarization correlations obtained , depending on speeds , may lead to new experiments on polarization correlations which monitor the speed of the underlying particles . second , such a study may be relevant to experiments in the light of bell s theorem ( monitoring speed ) as discussed below . the relevant quantity of interest here in testing bell s inequality @xcite is , in a standard notation , @xmath3 & \quad -\frac{p_{12}(a'_{1},\infty)}{p_{12}(\infty,\infty ) } -\frac{p_{12}(\infty , a_{2})}{p_{12}(\infty,\infty ) } \label{eq01}\end{aligned}\ ] ] as is _ computed from _ qed . here @xmath4 , @xmath5 @xmath6 specify directions along which the polarizations of two particles are measured , with @xmath7 denoting the joint probability , and @xmath8,@xmath9 denoting the probabilities when the polarization of only one of the particles is measured . [ @xmath10 is normalization factor . ] the corresponding probabilities as computed from qed will be denoted by @xmath11 $ ] , @xmath12 $ ] , @xmath13 $ ] with @xmath14 , @xmath15 denoting angles specifying directions along which spin measurements are carried out with respect to certain axes spelled out in the bulk of the paper . to show that the qed process is in violation with bell s inequality of lhv , it is sufficient to find one set of angles @xmath14 , @xmath15 , @xmath16 , @xmath17 , such that @xmath18 , as computed in qed , leads to a value of @xmath18 outside the interval @xmath19 $ ] . in this work , it is implicitly assumed that the polarization parameters in the particle states are directly observable and may be used for bell - type measurements as discussed . we show a clear violating of bell s inequality for _ all _ speeds in support of quantum theory in the relativistic regime , i.e. , of quantum field theory . scattering , with the electron and positron initially moving the @xmath20-axis , while the emerging electron and positron moving along the @xmath21-axis . the angle @xmath14 , measured relative to the @xmath22-axis , denotes the orientation of spin of the emerging electron may made.,scaledwidth=50.0% ] we consider the process @xmath2 in the center of mass frame ( see fig . [ fig_1 ] ) , with initially polarized electron - positron with one spin up , along @xmath21-axis , and one spin down . with @xmath23 denoting the momenta of initial electron and positron , respectively , @xmath24 , we consider momenta of emerging electron and positron with @xmath25 for four - spinors of the initial electron and positron , respectively , we have @xmath26 \rho&=\frac{\gamma\beta}{\gamma+1}=\frac{\beta}{1+\sqrt{1-\beta^{2 } } } \label{eq04}\end{aligned}\ ] ] where @xmath27 is a spin up , @xmath28 is a spin down , @xmath29 is a transpose matrix of spin up and @xmath30 is a transpose matrix of spin down , and for four - spinor of emerging electron and positron , respectively , we have @xmath31 \rho&=\frac{\gamma\beta}{\gamma+1}=\frac{\beta}{1+\sqrt{1-\beta^{2 } } } \label{eq06}\end{aligned}\ ] ] where the two - spinors @xmath32 , @xmath33 will be specified later . the expression for the amplitude of the process is well known @xcite @xmath34 & -\overline{u}(k_{1})\gamma^{\mu}u(p_{1})\overline{v}(p_{2 } ) \gamma_{\mu}v(k_{2})\frac{1}{(p_{1}-k_{1})^{2 } } \label{eq07}\end{aligned}\ ] ] given that such as the amplitude of the process above , we compute the conditional joint probability of spins measurements of @xmath35 , @xmath36 along directions specified by the angles @xmath14 , @xmath15 as shown in fig . [ fig_1 ] . we then have two - spinors as @xmath37 here we have considered only the single state cf . @xcite . by using the four - spinors of initial and emerging @xmath35 , @xmath36 , and two - spinors in term of the angles @xmath14 , @xmath15 to calculate the invariant amplitude of the process in fig . [ fig_1 ] leads to @xmath38\nonumber\\[0.5\baselineskip ] & + \mathrm{i}\left[c(\beta)\sin\left(\frac{\chi_{1}+\chi_{2}}{2}\right ) + d(\beta)\cos\left(\frac{\chi_{1}-\chi_{2}}{2}\right)\right ] \label{eq09}\end{aligned}\ ] ] where @xmath39 b(\beta)&=\rho(1+\rho)+8\beta^{2}\rho^{2 } \\[0.5\baselineskip ] c(\beta)&=1+\rho^{2}(1-\rho)+2\beta(1-\rho^{4 } ) \\[0.5\baselineskip ] d(\beta)&= \rho(1+\rho)\end{aligned}\ ] ] using the notation @xmath40 $ ] for the absolute value square of the right - hand side of ( [ eq09 ] ) , the conditional joint probability distribution of spin measurements along the directions specified by angle @xmath14 , @xmath15 is given by @xmath41=\frac{f[\chi_{1},\chi_{2}]}{n(\beta ) } \label{eq10}\ ] ] the normalization factor @xmath42 is obtained by summing over all the polarizations of the emerging particles . this is equivalent to summing of @xmath40 $ ] over the pairs of angles @xmath43 leads to @xmath44+f[\chi_{1}+\pi,\chi_{2}]\nonumber\\[0.5\baselineskip ] & + f[\chi_{1},\chi_{2}+\pi]+p[\chi_{1}+\pi,\chi_{2}+\pi]\nonumber\\[0.5\baselineskip ] & = 2[a^{2}(\beta)+b^{2}(\beta)+c^{2}(\beta)+d^{2}(\beta ) ] \label{eq12}\end{aligned}\ ] ] giving @xmath45&=\frac{\left[a(\beta)\cos\left(\frac{\chi_{1}+\chi_{2}}{2}\right ) + b(\beta)\sin\left(\frac{\chi_{1}-\chi_{2}}{2}\right)\right]^{2}}{2[a^{2}(\beta)+b^{2}(\beta)+c^{2}(\beta)+d^{2}(\beta)]}\nonumber\\[0.5\baselineskip ] & + \frac{\left[c(\beta)\sin\left(\frac{\chi_{1}+\chi_{2}}{2}\right ) + d(\beta)\cos\left(\frac{\chi_{1}-\chi_{2}}{2}\right)\right]^{2}}{2[a^{2}(\beta)+b^{2}(\beta)+c^{2}(\beta)+d^{2}(\beta ) ] } \label{eq13}\end{aligned}\ ] ] if only one of the spins is measured , say , corresponding to @xmath14 , we then have the probability as @xmath46&=p[\chi_{1},\chi_{2}]+p[\chi_{1},\chi_{2}+\pi]\nonumber\\[0.5\baselineskip ] & = \frac{1}{2}+\frac{2[a(\beta)b(\beta)+c(\beta)d(\beta)]\sin\chi_{1}}{2[a^{2}(\beta)+b^{2}(\beta)+c^{2}(\beta)+d^{2}(\beta ) ] } \label{eq14}\end{aligned}\ ] ] similarly , the only one of the spins is measured corresponding to @xmath15 , we then have the probability as @xmath47&=p[\chi_{1},\chi_{2}]+p[\chi_{1}+\pi,\chi_{2}]\nonumber\\[0.5\baselineskip ] & = \frac{1}{2}+\frac{2[c(\beta)d(\beta)-a(\beta)b(\beta)]\sin\chi_{2}}{2[a^{2}(\beta)+b^{2}(\beta)+c^{2}(\beta)+d^{2}(\beta ) ] } \label{eq15}\end{aligned}\ ] ] for all @xmath48 , angles @xmath14 , @xmath15 , @xmath16 , @xmath17 are readily found leading to a violation of bell s inequality of lhv theories . for example , for @xmath49 , @xmath50 , @xmath51 , @xmath52 , @xmath53 , @xmath54 violating the inequality from below . for the process @xmath2 , in the center of mass ( c.m . ) , with initially unpolarized spins , with momenta @xmath23 , the figure depicts @xmath0 scattering , with @xmath35 , @xmath36 moving along the @xmath20-axis , and the emerging electron and positron moving along the @xmath22-axis . the angle @xmath14 , measured relative to the @xmath21-axis , denotes the orientation of spin of the emerging electron may made.,scaledwidth=60.0% ] we take for the final electron and positron @xmath55 and for the four - spinors @xmath56 v(k_{2})&=\left(\frac{k^{0}+m}{2m}\right)^{\!\!1/2}\!\!\left ( \begin{array}{c } \frac{{\ensuremath{\boldsymbol{\mathrm{k}}}}_{2}\cdot{\ensuremath{\boldsymbol{\mathrm{\sigma}}}}}{k^{0}+m}\xi_{2 } \\ { } \xi_{2 } \end{array } \right),\ ; \xi_{2}=\left ( \begin{array}{c } -\mathrm{i}\cos\chi_{2}/2\\ \sin\chi_{2}/2 \end{array } \right)\label{eq18}\end{aligned}\ ] ] the absolute value square of the right - hand side of ( [ eq09 ] ) with initially unpolarized electrons and positron leads to @xmath57 \overline{u}(k_{1})\gamma_{\mu}v(k_{2})\overline{v}(k_{2})\gamma_{\sigma}u(k_{1})}{(p_{1}+p_{2})^{4}}\nonumber\\[0.5\baselineskip ] & -\frac{\tr\left[(\gamma{}p_{2}+m)\gamma^{\mu}(-\gamma{}p_{1}+m)\gamma^{\sigma}\right ] \overline{v}(k_{2})\gamma_{\sigma}u(k_{1})\overline{u}(k_{1})\gamma_{\mu}v(k_{2})}{(p_{1}+p_{2})^{2}(p_{1}-k_{1})^{2}}\nonumber\\[0.5\baselineskip ] & -\frac{\tr\left[\gamma^{\mu}(-\gamma{}p_{1}+m)\gamma^{\sigma}(\gamma{}p_{2}+m)\right ] \overline{u}(k_{1})\gamma_{\mu}v(k_{2})\overline{v}(k_{2})\gamma_{\sigma}u(k_{1})}{(p_{1}+p_{2})^{2}(p_{1}-k_{1})^{2}}\nonumber\\[0.5\baselineskip ] & + \frac{\overline{u}(k_{1})\gamma^{\mu}(-\gamma{}p_{1}+m)\gamma^{\sigma}u(k_{1 } ) \overline{v}(k_{2})\gamma_{\sigma}(\gamma{}p_{2}+m)\gamma_{\mu}v(k_{2})}{(p_{1}-k_{1})^{4}}\label{eq19}\end{aligned}\ ] ] which after simplification and of collecting terms reduces to @xmath58\sin^2\left(\case{\chi_1-\chi_2}{2}\right ) \nonumber\\[0.5\baselineskip ] & \quad+(1+\beta^{2}+2\beta^{4})\cos^2\left(\case{\chi_1+\chi_2}{2}\right)+5(1-\beta^{2})\nonumber\\[0.5\baselineskip ] & \equiv f[\chi_1,\chi_2 ] \label{eq20}\end{aligned}\ ] ] where we have used the expressions for the spinors in ( [ eq17 ] ) , ( [ eq18 ] ) . given that the process has occurred , the conditional probability that the spins of the emerging electron and positron make angles @xmath59 , @xmath60 , respectively , with the @xmath21-axis , is directly obtained from ( [ eq20 ] ) to be @xmath61=\frac{f[\chi_1,\chi_2]}{c } \label{eq21}\end{aligned}\ ] ] the normalization constant @xmath62 is obtained by summing over the polarizations of the emerging electrons . this is equivalent to summing of @xmath63 $ ] over the pairs of angles in ( [ eq11 ] ) for any arbitrarily chosen fixed @xmath59 , @xmath60 , corresponding to the orthonormal spinors @xmath64 providing a complete set , for each @xmath65 , in reference to ( [ eq17 ] ) , ( [ eq18]).this is , @xmath66+f[\chi_1+\pi,\chi_2]\nonumber\\[0.5\baselineskip ] & \quad+f[\chi_1,\chi_2+\pi]+f[\chi_1+\pi,\chi_2+\pi ] \nonumber\\[0.5\baselineskip ] & = 8[2 - 3\beta^{2}+\beta^{4}+\beta^{6 } ] \label{eq23}\end{aligned}\ ] ] which as expected is independent of @xmath59 , @xmath60 , giving @xmath61&=\frac{[2\beta^{4}(1 + 2\beta^{2})-3(1+\beta^{2})]\sin^2\left(\frac{\chi_1-\chi_2}{2}\right)}{8[2 - 3\beta^{2}+\beta^{4}+\beta^{6 } ] } \nonumber\\[0.5\baselineskip ] & \quad+\frac{[1+\beta^{2}+2\beta^{4}]\cos^2\left(\frac{\chi_1+\chi_2}{2}\right)+5(1-\beta^{2})}{8[2 - 3\beta^{2}+\beta^{4}+\beta^{6}]}\label{eq24}\end{aligned}\ ] ] by summing over @xmath67 for any arbitrarily fixed @xmath60 , we obtain @xmath68=\frac{1}{2 } \label{eq26}\end{aligned}\ ] ] and similarly , @xmath69=\frac{1}{2 } \label{eq27}\end{aligned}\ ] ] for the probabilities when only one of the photons polarizations is measured . a clear violation of bell s inequality of lhv theories was obtained for all @xmath48 . for example , for @xmath70 , with @xmath71 , @xmath72 , @xmath73 , @xmath74 give @xmath75 violating the inequality from below . violates lhv theories . a critical study of polarization correlations probabilities in elastic @xmath0 scattering was carried out , for initially _ polarized _ as well as _ unpolarized _ particles , emphasizing their dependence on speed and an explicit expression for them obtained in qed . the necessity of such a study within the realm of quantum field theory can not be overemphasized as estimates of such correlations obtained by simply combining spins , as is often done , have no meaning as they do not involve dynamical considerations . the relevant dynamics is , of course , dictated directly from quantum field theory . the explicit expression for the polarization correlation obtained is interesting in its own right but may also lead to experiments which investigate such correlations by monitoring speed not only for initially polarized particles but also for unpolarized ones . our results may be also relevant in the realm of bell s inequality with emphasis put on relativistic aspects of quantum theory , that is of quantum field theory . our expressions have shown clear violations of bell s inequality of lhv theories in support of quantum theory in the relativistic regime . several experiments have been already performed in recent years ( cf . @xcite ) on particles polarizations correlations . and , it is expected that the novel properties recorded here by explicit calculations following directly from field theory , which is based on the principle of relativity and quantum theory , will lead to new experiments on polarization correlations monitoring speed in the light of bell s theorem . we hope that theses computations , in general setting of quantum field theory , will be also useful in such areas of physics as quantum teleportation and quantum information in general . i would like to thank prof . dr . e. b. manoukian for discussions , guidance and for carefully reading the manuscript . i also would like to thank suppiya siranan and dr . burin gumjudpai for discussions and comments . finally , i would like to acknowledge with thanks for the award of a research grant by the trf - new researcher grant of the thailand research fund ( mrg5080288 ) and my gratitude to the faculty of science , naresuan university . 10 yongram n and manoukian e b 2003 _ int . phys . _ * 42 * 1775

spin correlations are carefully investigated in elastic @xmath0 scattering in qed , for initially _ polarized _ as well as _ unpolarized _ particles , with emphasis placed on energy or speed of the underlying particles involved in the process . an explicit expression is derived for the corresponding transition probabilities in closed form to the leading order . these expressions are unlike the ones obtained from simply combining spins of the relevant particles which are of kinematic nature . it is remarkable that these explicit results obtained from quantum field theory show a clear violation of bell s inequality at _ all _ energies in support of quantum theory in the relativistic regime . we hope that our explicit expression obtained will lead to experiments in the manner described in the bulk of this paper by monitoring speed .

in a previous paper , forshaw , kerley and shaw ( fks ) @xcite reported on a successful attempt to extract the cross - section for scattering colour dipoles of fixed transverse size off protons using both electroproduction and photoproduction @xmath3 total cross - section data , together with the constraint provided by the measured ratio of the diffraction dissociation cross - section to the total cross - section for real photons . subsequently , the same model has been applied to `` diffractive deep inelastic scatterring '' ( ddis ) @xmath4 @xcite and also to deeply virtual compton scattering ( dvcs ) @xmath5 @xcite . in both cases , the model was shown to yield predictions in agreement with the data @xcite with no adjustable parameters . the model can also be extended to diffractive vector meson production : @xmath6 where the squared centre of mass energy @xmath7 . in these processes the choice of vector meson , as well as of different photon virtualities , allows one to explore contributions from dipoles of different transverse sizes . the process also has the advantage that there is a wide range of available data . it ought also to provide important information on the poorly known light - cone wavefunctions of the the vector mesons . the aim of this paper is to confront the predictions of the dipole model with the hera data on @xmath8 and @xmath9 electroproduction . the predictions for @xmath10 production are best considered in conjunction with an analysis of open charm production , and will be discussed elsewhere . we shall focus on the fks model @xcite , but we also compare with the predictions of two other models : the golec - biernat - wsthoff ( gw ) saturation model @xcite ; and the recent `` colour glass condensate '' ( cgc ) model of iancu , itakura and munier @xcite . for the meson light - cone wavefunction , we shall consider three different anstze : the dosch , gousset , kulzinger and pirner ( dgkp ) @xcite model ; the nemchik , nikolaev , predazzi and zakharov ( nnpz ) @xcite model ; and a simple `` boosted gaussian '' wavefunction , which can be considered as a special case of the latter . the paper is laid out as follows . in the first two sections we summarise the dipole models used and discuss the forms chosen for the vector meson wavefunctions . we then compare their predictions with experiment before drawing our conclusions . in the colour dipole model @xcite , the eigenstates of the scattering ( diffraction ) operator are `` colour dipoles '' , i.e. quark - antiquark pairs of transverse size @xmath11 in which the quark carries a fraction @xmath12 of the photon s light - cone momentum in the convention where @xmath13 . here @xmath14 where the momentum @xmath15 of the quark is @xmath16 . ] . in the proton s rest frame , the formation of the dipole occurs on a timescale far longer than that of its interaction with the target proton . because of this , the forward imaginary amplitude for singly diffractive photoprocesses @xmath17 is assumed to factorise into a product of light - cone wavefunctions associated with the initial and final state particles @xmath18 and @xmath19 and a universal dipole cross - section @xmath20 , which contains all the dynamics of the interaction of the @xmath21 dipole with the target proton . in particular for reaction ( [ vmp ] ) one obtains @xmath22 where @xmath23 and @xmath24 are the light - cone wavefunctions of the photon and vector meson respectively . the quark and antiquark helicities are labelled by @xmath25 and @xmath26 and we have suppressed reference to the meson and photon helicities . the dipole cross - section is usually assumed to be flavour independent since some flavour dependence enters indirectly at small @xmath27 through the definitions of @xmath28 ( see below ) . ] and , as implied by our notation , `` geometric '' , i.e. for a given @xmath29 , it is assumed to depend on the transverse dipole size , but not the light - cone momentum fraction @xmath12 . the light - cone wavefunctions do depend on the quark flavour , via their charges and masses . finally , the corresponding real part of the amplitude ( [ amplitude ] ) is either neglected or , as here , is estimated using analyticity . while the photon light - cone wavefunction can be calculated within perturbation theory , at least for small dipole sizes , the vector meson light - cone wavefunctions are not reliably known , and must be obtained from models . this will be discussed in the following section . the rest of this section is devoted to the dipole cross - section , for which we shall consider three different models . since full details are given in the original papers , our treatment will be brief . the fks model @xcite is a two - component model @xmath30 in which each term has a regge type energy dependence on the dimensionless energy variable @xmath31 : @xmath32 @xmath33 this parametric form is chosen so that the hard term dominates at small @xmath11 and goes to zero like @xmath34 as @xmath35 in accordance with ideas of colour transparency , while the soft term dominates at larger @xmath36 fm , with a hadron - like soft pomeron behaviour . in addition , to allow for possible confinement effects in the photon wavefunction at large @xmath11 , fks modified the perturbative wavefunctions @xmath37 by multiplying them by an adjustable gaussian enhancement factor : @xmath38 where @xmath39 this behaviour is qualitatively suggested by an analysis @xcite of the scattering eigenstates in a generalised vector dominance model @xcite which provides a good description of the soft pomeron contribution to the nucleon structure function @xmath40 on both protons and nuclei @xcite . the free parameters in both the dipole cross - section and the photon wavefunction were then determined by a fit to structure function and real photoabsorption data . the resulting values are given in table 1 . having been obtained in this way , they were then used to predict successfully the cross - sections for other processes which depend solely on the dipole cross - section and the photon wavefunction , namely diffractive deep inelastic scattering ( ddis ) @xcite and deeply virtual compton scattering ( dvcs ) @xcite . the resulting dipole cross - section is shown fig . [ fig : fksdipole ] . as can be seen , as @xmath29 increases the dipole cross - section grows most rapidly for small @xmath11 , where the hard term dominates , eventually exceeding the typically hadronic cross - section found for dipoles of large @xmath36 fm . this rise could well be tamed by unitarity or saturation effects @xcite . however , the authors have argued @xcite that such saturation effects are unlikely to be important until the top of the hera range and beyond , and they are not included in the fks model in its present form . * table 1 * @xmath41 gev.,width=377 ] gev for @xmath42 and @xmath43 . the @xmath27-independent fks dipole cross - section at the same energy is shown for comparison.,title="fig:",width=302 ] gev for @xmath42 and @xmath43 . the @xmath27-independent fks dipole cross - section at the same energy is shown for comparison.,title="fig:",width=302 ] this well - known model @xcite combines the approximate behaviour @xmath44 at small @xmath11 together with a phenomenological saturation effect by adopting the attractively simple parametric form : @xmath45\right ) \;. \label{gbw - dipole}\ ] ] here @xmath28 is a modified bjorken variable , @xmath46 where @xmath47 is the quark mass and @xmath48 gev . the @xmath49 free parameters @xmath50 , @xmath51 and @xmath52 were successfully fitted to @xmath53 data . the four - flavour fit which we shall use in this paper yielded @xmath54 , @xmath55 and @xmath56 . the quark masses are chosen to be @xmath57 gev for the light quarks and @xmath58 gev for the charm quark . the model is also able to describe @xmath59 data @xcite . a recent refinement of the model takes into account corrections due to dglap evolution at large @xmath60 @xcite , but these are rather small corrections and are not included here . finally , all these results are obtained with a purely perturbative photon wavefunction , which is somewhat enhanced at large @xmath11-values by the use of a lighter quark mass than that used in the fks model . the resulting behaviour of the dipole cross - section is illustrated and compared to that of the fks model in figure [ gw_cgc_dipole.eps ] . the dipole model of iancu , itakura and munier @xcite can be thought of as a development of the golec - biernat wsthoff saturation model . though still largely a phenomenological parameterisation , the authors do claim that it contains the main features of the `` color glass condensate '' regime , where the gluon densities are high and non - linear effects become important . in particular , they take @xmath61 } \hspace*{1 cm } \mathrm{for } \hspace*{1 cm } rq_s \le 2 \nonumber \\ & = & 2 \pi r^2 \{1 - \exp[-a \ln^2(brq_s)]\ } \hspace*{1 cm } \mathrm{for } \hspace*{1 cm } rq_s > 2~ , \label{cgc - dipole } \end{aligned}\ ] ] where the saturation scale @xmath62 gev . the coefficients @xmath63 and @xmath64 are uniquely determined by ensuring continuity of the cross - section and its first derivative at @xmath65 . the leading order bfkl equation fixes @xmath66 and @xmath67 . the coefficient @xmath68 is strongly correlated to the definition of the saturation scale and the authors find that the quality of fit to @xmath53 data is only weakly dependent upon its value . for a fixed value of @xmath68 , there are therefore three parameters which need to be fixed by a fit to the data , i.e. @xmath69 , @xmath52 and @xmath70 . in this paper , we take @xmath71 and a light quark mass of @xmath72 mev , for which the fit values are @xmath73 , @xmath74 and @xmath75 fm . as for the gw dipole , we compare to the fks dipole at two values of @xmath27 in figure [ gw_cgc_dipole.eps ] . the light - cone wavefunctions @xmath76 in the mixed representation @xmath77 used in the dipole model are obtained from a two dimensional fourier transform @xmath78 of the momentum space light - cone wavefunctions @xmath79 , where the quark and antiquark are in states of definite helicity , @xmath25 and @xmath26 respectively . for transversely ( @xmath80 ) or longitudinally ( @xmath81 ) polarised photons , the momentum space light - cone wave functions themselves are calculated perturbatively @xcite ( per fermion of charge @xmath82 ) : @xmath83 hereafter , @xmath52 denotes the polarization state @xmath81 or @xmath80 . @xmath84 are the polarisation vectors and the `` scalar '' part of the photon light - cone wavefunction , @xmath85 , is given by @xmath86 for the vector mesons , the simplest approach is to assume the same vector current as in the photon case , with an additional ( unknown ) vertex factor @xmath87 : @xmath88 where the scalar part of the meson light - cone wavefunction is given by @xmath89 different models are defined by specifying these scalar wavefunctions . in practice , it is common to choose the same functional form for @xmath90 and @xmath91 ; perhaps allowing the numerical parameters to differ . it is instructive to consider the longitudinal wavefunctions more explicitly . using the polarisation vectors @xmath92 and the rules of light - cone perturbation theory given in @xcite , it follows that the longitudinal photon light - cone wavefunction is @xmath93 and that of the vector meson is @xmath94 on substituting ( [ photonwf - l ] ) in ( [ fourier ] ) the second term of ( [ photonwf - l ] ) leads to a dipole of vanishing size , which does not contribute to the cross - section . this is in accord with gauge invariance . the same argument can not be used to justify the omission of the second term in the meson wavefunction ( [ mesonwf - l ] ) , since the latter has a @xmath15 dependence . in practice , this term is omitted in the dgkp model @xcite , but retained in the nnpz model @xcite . a discussion of the gauge invariance issues surrounding this point can be found in @xcite . before discussing these models more fully , we give the explicit forms for the photon wavefunctions in @xmath11-space . the normalised photon light - cone wavefunctions are @xcite : @xmath95 and @xmath96\frac{k_{0}(\epsilon r)}{2\pi}\ ; , \label{photonwft}\ ] ] where @xmath97 since the modified bessel function @xmath98 decreases exponentially at large @xmath99 , these equations imply that at high @xmath60 , the wavefunctions are suppressed for large @xmath11 unless @xmath12 is close to its end - points values @xmath100 or @xmath101 . as can be seen from equations ( [ photonwfl])([photonwft ] ) , these end - points are suppressed for the longitudinal but not the transverse case . this is the origin of the statement that transverse meson production is more inherently non - perturbative than for longitudinal meson production . for small @xmath11 , the perturbative expressions given above are reliable . for large @xmath11-values , however , confinement corrections are likely to modify the perturbation theory result . these larger @xmath11-values contribute significantly at low @xmath60 , where the wavefunctions are sensitive to the non - zero quark masses @xmath47 , which prevent the modified bessel function from diverging in the photoproduction limit . for these reasons , the photon light - cone wavefunctions at large @xmath11 are clearly model - dependent . we now turn back to the meson wavefunctions . these are subject to two constraints . the first is the normalisation condition @xcite @xmath102 which embodies the assumption that the meson is composed solely of @xmath21 pairs . note that this normalisation is consistent with equation ( [ amplitude ] ) and differs by a factor @xmath103 relative to the conventional light - cone normalisation . the second constraint comes from the electronic decay width @xcite : @xmath104 where the coupling @xmath105 of the meson to electromagnetic current can be determined from the experimentally measured leptonic width @xmath106 since @xmath107 . we shall prefer to implement the constraint directly in terms of the @xmath11-space wavefunctions . for our purposes , we can write the meson wavefunctions in @xmath11-space as @xmath108 \phi_l(r , z ) \label{nnpz_l}\ ] ] where @xmath109 , and @xmath110 \phi_t(r , z ) . \label{nnpz_t}\ ] ] note the second term in square brackets which occurs in the longitudinal meson case . this is a direct consequence of keeping the second term in ( [ mesonwf - l ] ) . for the dgkp wavefunctions this term is absent , i.e. @xmath111 , whilst nnpz keep this term , i.e. @xmath112 . in terms of these wavefunctions , ( [ leptonic ] ) becomes ( assuming that @xmath113 at @xmath114 and @xmath115 ) @xmath116 \phi_l(r , z ) \right|_{r=0 } \label{longdecay}\ ] ] and @xmath117 ^ 2 } \left . \left [ ( z^2+(1-z)^2 ) \nabla_r^2 - m_f^2 \right ] \phi_t(r , z ) \right|_{r=0 } \label{trandecay } .\ ] ] in computing @xmath118 and all other observables involving the @xmath9 meson we in all cases take the quark mass to be equal to the light quark mass plus 150 mev . in the dgkp approach @xcite , the @xmath11 and @xmath12 dependence of the wavefunction are assumed to factorise . however , since the latter are suppressed in the dgkp wavefunction , this has no practical consequence . ] . specifically , the scalar wavefunction is given by in the scalar wavefunction . this is because they define the scalar wavefunction to be the r.h.s of ( [ scalar - meson ] ) divided by @xmath119 . ] @xmath120 a gaussian dependence on @xmath11 is assumed , that is @xmath121 and @xmath122 is given by the bauer - stech - wirbel model @xcite : @xmath123 setting @xmath124 ( recall that this is equivalent to neglecting the second term in ( [ mesonwf - l ] ) ) in ( [ nnpz_l ] ) results in @xmath125 for the dgkp longitudinal meson light - cone wavefunction . @xmath126 is the effective charge arising from the sum over quark flavours in the meson : @xmath127 and @xmath128 for the @xmath129 and @xmath10 respectively . similarly , the dgkp transverse meson light - cone wavefunctions can be written as @xmath130 + \frac{m_{f}}{m_{v}}\delta_{h\pm,\bar{h}\pm } \right ) \nonumber \\ & & \hspace*{5 cm } \times \frac{\sqrt{\pi } f_v}{\sqrt{2 n_{c } } \hat{e}_{f}}f_{t}(z)e^{-\omega_{t}^{2}r^{2}/2 } \;. \label{dgkp_t}\end{aligned}\ ] ] the normalisation condition ( [ normalisation ] ) on the dgkp wavefunction leads to the relations , @xmath131 with @xmath132 and @xmath133\omega_{t}^{2 } + m_{f}^{2}}{m_{v}^{2 } } f_{t}^{2}(z ) \;,\ ] ] the leptonic decay width constraints ( [ longdecay ] ) and ( [ trandecay ] ) on the dgkp wavefunction yield @xmath134\omega_{t}^{2 } + m_{f}^{2}}{2m_{v}^{2}z(1-z)}f_{t}(z ) \;. \label{dgkp - leptonic}\ ] ] the values of @xmath135 and @xmath136 are found by solving ( [ dgkp - normalisation ] ) and ( [ dgkp - leptonic ] ) simultaneously , and are given in table [ tab : dgkp - parameters ] . the values of the decay constants used are the central experimental values @xcite : @xmath137 gev , and @xmath138 gev . * table 2 * @xmath139 the resulting behaviour of the @xmath8 wavefunctions is shown for the case of the fks quark masses in figures [ fig : dgkprho ] . as is clear from equations ( [ dgkp1])([dgkp_t ] ) , the wavefunctions peak at @xmath140 and @xmath141 , and go rapidly to zero as @xmath142 and @xmath143 , so that large dipoles are suppressed . from the figures , we see that the transverse wavefunction has a broader distribution than the longitudinal wavefunction . the @xmath9 wavefunctions are qualitatively similar to , but slightly more sharply peaked than , the @xmath8 wavefunctions . -wavefunctions @xmath144 ( left ) and @xmath145 ( right ) in the dgkp model with the quark mass used in the fks dipole model . note the different scales for the ordinate.,title="fig:",width=234 ] -wavefunctions @xmath144 ( left ) and @xmath145 ( right ) in the dgkp model with the quark mass used in the fks dipole model . note the different scales for the ordinate.,title="fig:",width=234 ] the gw model uses a much smaller value for the light quark masses than the fks model , as we saw in section 2.3 . we might expect this to have a striking effect on the transverse wavefunction of the @xmath8 , since the transverse wavefunction ( [ dgkp_t ] ) vanishes at @xmath114 for zero quark masses , while the longitudinal wavefunction ( [ dgkp_l ] ) does not . the transverse dgkp wavefunction with the light quark mass used in the gw dipole model is shown in figure [ fig : dgkp - gw ] for the @xmath8 . as can be seen , the smaller quark mass decreases the wavefunction at the origin and shifts the peak to slightly larger @xmath11 . -wavefunction @xmath145 in the dgkp model with the quark mass used in the gw dipole model . , width=234 ] in this approach , the scalar part of the wavefunction is obtained by taking a given wavefunction in the meson rest frame . this is then `` boosted '' into a light - cone wavefunction using the brodsky - huang - lepage prescription , in which the expressions for the off - shellness in the centre - of - mass and light - cone frames are equated @xcite ( or equivalently , the expressions for the invariant mass of the @xmath146 pair in the centre - of - mass and light - cone frames are equated @xcite ) . the simplest version of this approach assumes a simple gaussian wavefunction in the meson rest frame . alternatively nnpz @xcite have supplemented this by adding a hard `` coulomb '' contribution in the hope of improving the description of the rest frame wavefunction at small @xmath11 . we refer to @xcite for details of this procedure . here we simply state the result , which is that the nnpz meson light - cone wavefunctions are given by equations ( [ nnpz_l ] , [ nnpz_t ] ) with @xmath147 , where the scalar wavefunctions @xmath148 are taken to be a sum of a soft ( gaussian in the rest frame ) part and a hard ( coulomb ) part : @xmath149 here @xmath150 @xmath151 and @xmath152 is a running bohr radius . the strong coupling @xmath153 is chosen to run according to the prescription @xcite : @xmath154 where @xmath155 fm , @xmath156 , @xmath157 and @xmath158 . apart from the normalisation constants @xmath159 , these wavefunctions depend on two free parameters which are independent of the meson helicity : a `` radius '' parameter @xmath70 and a parameter @xmath160 , introduced to control the transition between the hard coulomb - like interaction and the soft confining interaction in the rest - frame wavefunction . the case of a simple gaussian wavefunction in the rest - frame , which we will refer to as a `` boosted gaussian wavefunction '' can be obtained by simply setting @xmath161 ( we still choose @xmath147 when considering this wavefunction ) . at this point we comment on two issues associated with the behaviour of the coulomb part of the scalar wavefunction for small @xmath11 . the first is that ( [ nnpz - lc - wf ] ) diverges logarithmically as @xmath35 at @xmath140 . this divergence is however regulated in observables . for example , while the resulting squared wavefunctions @xmath162 exhibit a narrow , singular peak at @xmath163 , the quantity @xmath164 which enters the normalisation condition ( [ normalisation ] ) is zero in this limit . nevertheless , this singular behaviour does have a ( finite ) effect when computing the meson decay constant which depends upon the behaviour of the wavefunction at @xmath114 . the second issue is that when the scalar wavefunction ( [ nnpz - lc - wf ] ) is substituted into equations ( [ nnpz_l ] ) ( [ trandecay ] ) , the derivatives in @xmath11 give rise to inverse power divergences at @xmath114 when acting upon the running coupling ( [ running - alphas ] ) . however , these divergences occur solely in terms which are strictly higher order in @xmath153 . henceforth we discard these higher order terms , which is equivalent to omitting all derivatives of @xmath165 with respect to @xmath11 when differentiating the scalar wavefunction ( [ nnpz - lc - wf ] ) . we stress that none of these issues arise when using the boosted gaussian wavefunction . it remains to determine the various constants . nnpz @xcite determined both @xmath70 and @xmath160 by using a standard variational procedure for the initial centre - of - mass wavefunction using a non - relativistic potential . they then checked that the resulting predictions ( [ leptonic ] ) were in reasonable accord with the observed leptonic decay widths)([nnpz_t ] ) give slightly different predictions for the decay constant for the case of transverse and longitudinal meson helicities , because nnpz use helicity independent values of @xmath166 . ] . here we follow a slightly modified procedure , since we want to be able to easily adjust the quark masses to those assumed in the various dipole models . specifically , we fixed @xmath160 at the value chosen by nnpz and vary the value of @xmath70 to give approximate agreement with the decay width constraints ( [ leptonic ] ) . in practice , we found it adequate to use the same @xmath70-value for both the fks and gw mass choices . the resulting values of @xmath70 and @xmath160 , with the associated values of the normalisation constants , are shown in table [ tab : nnpz - parameters ] , and are not very different from the original parameters of nnpz . in addition we show the results for the boosted gaussian case ( @xmath161 ) in table [ tab : gaussian - parameters ] . * table 3 * @xmath167 * table 4 * @xmath168 the behaviour of the resulting @xmath8 wavefunctions is shown in figures [ fig : nnpzrho ] with the fks choice of quark masses . the divergence at @xmath169 is not visible since we do not plot down to @xmath114 . like the dgkp wavefunctions , they peak at @xmath140 and @xmath141 , and go rapidly to zero as @xmath142 and @xmath143 . however , on comparing these figures with each other , and with figures [ fig : dgkprho ] , two clear differences emerge . firstly , the peak in @xmath12 is less sharp in the boosted gaussian case than in the dgkp and nnpz cases . secondly , the large difference between the longitudinal and transverse wavefunctions found in the dgkp case is much less marked in the nnpz and boosted gaussian wavefunctions . in both cases , the peak in the transverse wavefunction is still broader than that in the longitudinal wavefuction , but it is a small effect in comparison with the dgkp case . this presumably reflects the fact that in the nnpz and boosted gaussian wavefunctions , the parameter @xmath70 has the same value for both helicities , since both wavefunctions are generated from the same non - relativistic wavefunction by the brodsky - huang - lepage procedure . figures [ fig : gaussrho ] show the wavefunctions in the case of the boosted gaussian wavefunction . -wavefunctions @xmath144 ( left ) and @xmath145 ( right ) in the nnpz model with the quark mass used in the fks dipole model.,title="fig:",width=234 ] -wavefunctions @xmath144 ( left ) and @xmath145 ( right ) in the nnpz model with the quark mass used in the fks dipole model.,title="fig:",width=234 ] -wavefunctions @xmath144 ( left ) and @xmath145 ( right ) in the boosted gaussian model with the quark mass used in the fks dipole model.,title="fig:",width=234 ] -wavefunctions @xmath144 ( left ) and @xmath145 ( right ) in the boosted gaussian model with the quark mass used in the fks dipole model.,title="fig:",width=234 ] we now have all the ingredients required to calculate the absorptive parts ( [ amplitude ] ) of the forward amplitudes for vector meson production . for the case of the nnpz wavefunctions , we substitute the photon wavefunctions ) . ] ( [ photonwfl ] ) , ( [ photonwft ] ) and the vector meson wavefunctions ( [ nnpz_l ] ) , ( [ nnpz_t ] ) with @xmath147 into ( [ amplitude ] ) . summing over the quark / antiquark helicities and averaging over the transverse polarisation states of the photon , we obtain ) , we integrate the second term by parts assuming an @xmath11-independent dipole cross - section . ] : @xmath170k_{0}(\epsilon r ) \phi_{l}(r , z ) - k_{0}(\epsilon r ) \nabla_{r}^{2 } ) \phi_{l}(r , z ) \right\ } \label{amp - nnpz - l}\end{aligned}\ ] ] @xmath171 \ ; , \label{amp - nnpz - t}\end{aligned}\ ] ] where @xmath172 are given by ( [ nnpz - lc - wf ] ) . similarly , using the dgkp wavefunctions ( [ dgkp_l ] ) and ( [ dgkp_t ] ) , we obtain @xcite @xmath173 @xmath174 k_{1}(\epsilon r ) + \frac{m_{f}^{2}}{m_{v}}k_{0}(\epsilon r ) \right ) \;. \label{amp - dgkp - t}\end{aligned}\ ] ] so far , we have focussed on the imaginary amplitude . taking into account the real part contribution , the differential cross - section is given by @xmath175 where @xmath176 is the ratio of real to imaginary parts of the amplitude . it is most straightforward to reconstruct the real part of the amplitude in the fks dipole model , where the dipole cross - section ( [ gammatot ] ) , and hence the amplitude ( [ amplitude ] ) , is given as the sum of hard and soft regge pole terms . in this case , the real part is given by @xmath177 where @xmath178 and @xmath179 and @xmath180 are the contributions from the soft and hard pomeron pieces of fks dipole cross - section ( [ gammatot ] ) respectively . it follows from ( [ ratio ] ) that , in the fks model , @xmath176 lies between 0.09 and 0.83 , corresponding to pure soft and hard pomeron dominance respectively ; within this range , the value of @xmath176 reflects directly the relative importance of the hard pomeron . other things being equal , @xmath176 will therefore increase with increasing energy , because the hard term in the dipole cross - section increases more rapidly with energy than the soft term . it will also increase with @xmath27 , because the hard term is dominant for small dipoles , which are increasingly explored as @xmath27 increases . these features are illustrated in figure [ fig : rp_beta_dgkp_q2 ] , which shows the values of @xmath176 obtained as functions of @xmath181 and @xmath27 obtained using the dgkp wavefunctions . here we also see that @xmath176 is larger for the longitudinal than for the transverse case , reflecting sharper peaking of the longitudinal vector meson wavefunctions . similar results for the real parts are obtained using the nnpz wavefunctions . -dependence of the ratio @xmath176 of the real to imaginary part of the forward amplitude in the fks model , using the dgkp wavefunctions , for @xmath182 gev@xmath183 . _ right _ : @xmath60-dependence of @xmath176 in the fks model , using the dgkp wavefunctions , for @xmath184 gev.,title="fig:",width=302,height=302]-dependence of the ratio @xmath176 of the real to imaginary part of the forward amplitude in the fks model , using the dgkp wavefunctions , for @xmath182 gev@xmath183 . _ right _ : @xmath60-dependence of @xmath176 in the fks model , using the dgkp wavefunctions , for @xmath184 gev.,title="fig:",width=302,height=302 ] from the above figures , we see that while the corrections from the real parts in the cross - section formulae ( [ dcs ] ) are clearly significant in some kinematic ranges , they are nowhere dominant . because of this and because the ratio @xmath176 is expected to be similar in the different models , we shall use the estimates ( [ ratio ] ) of the ratio @xmath176 obtained in the fks model in both dipole models . assuming the usual exponential ansatz for the @xmath185 dependence , the total cross - sections are given by @xmath186 unfortunately , the values of the slope parameter @xmath187 are not very accurately measured . here we use a parametrisation @xmath188 obtained from a fit to experimental data by mellado @xcite , and used in their analysis of the predictions of the gw dipole model by caldwell and soares @xcite . the resulting values for @xmath187 are shown in figure [ fig : slope ] , where we also show the results of an alternative parameterisation of kreisel @xcite to illustrate the range of values that can be obtained from different fits to the data . when comparing the predictions of ( [ sigmatot ] ) for the vector meson cross - sections with data , it is important to bear in mind that this uncertainty in the input value of the slope parameter can easily introduce errors up to of order 30@xmath189 or so and that , within this range , this error may be @xmath27 dependent . by mellado @xcite for the @xmath8 and @xmath9 . _ right _ : parametrisation of the slope @xmath187 by kreisel @xcite for the @xmath8 and @xmath9.,title="fig:",width=302 ] by mellado @xcite for the @xmath8 and @xmath9 . _ right _ : parametrisation of the slope @xmath187 by kreisel @xcite for the @xmath8 and @xmath9.,title="fig:",width=302 ] finally , on comparing with experimental data , we show @xmath190 with @xmath191 in all our plots , although the hera data range from 0.96 to 1.00 . in this section we will compare the predictions of the three dipole models with the experimental data for our three choices of vector meson wavefunction , without any adjustment of parameters . before doing so , however , we emphasize again that the uncertainty in the slope parameter can give rise to @xmath27-dependent errors of up to 30@xmath189 in the cross - section , which should be borne in mind when comparing with experiment . this effect should , hopefully , be much smaller in the ratio @xmath70 . however , it ought not to be completely negligible since the longitudinal and transverse cross - sections will presumably have slightly different slope parameters , as to some degree they explore dipoles of different sizes . the predictions of the fks model for the @xmath27 dependence of the cross - section and for the longitudinal to transverse ratio @xmath70 are shown in figure [ fks_rho_q2_r.eps ] for the three different wavefunctions considered . the equivalent plots for the gw and cgc model are in figures [ gw_rho_q2_r.eps ] and [ cgc_rho_q2_r.eps ] respectively . the zeus total cross - section data are at the following centre - of - mass energies : 0.27 gev@xmath192 0.69 gev@xmath183 , @xmath193 gev , otherwise @xmath184 gev . the h1 data on the longitudinal to transverse ratio are , for @xmath194 gev@xmath183 , in the range 40 gev @xmath195 140 gev , otherwise they are at @xmath196 gev . similarly the zeus data are , for @xmath197 gev@xmath183 , at @xmath198 gev or for @xmath199 gev@xmath183 at @xmath200 gev . for the theory curves we always take @xmath184 gev . for all three dipole models , the data favour the boosted gaussian wavefunction , whilst the dgkp wavefunction produces reasonable agreement for fks and is rather less satisfactory for the gw and cgc models . the nnpz wavefunction is well below the total cross - section data for all three models and , for the gw and cgc models , in disagreement with the data on the longitudinal to transverse ratio . however , as noted in section 3.2 , although the spurious singularity in this wavefunction does not contribute directly to the predicted cross - sections , it influences them indirectly because it influences the value of the radial parameter @xmath70 deduced from the decay width . in what follows , we will therefore focus on the dgkp and boosted gaussian wavefunctions . figures [ w_rho_fks.eps ] , [ w_rho_gw.eps ] and [ w_rho_cgc.eps ] show the @xmath181 dependence at fixed values of @xmath27 for the @xmath8 meson . apart from the normalisation , the @xmath181-dependence is good in all cases . the normalisation is best described by the boosted gaussian wavefunction . with this wavefunction , the fks model is in reasonably good agreement with the data , except for the zeus data at very low @xmath27 ; while the gw and cgc models give reasonable agreement everywhere . this last comment contrasts somewhat with the work of caldwell and soares @xcite , who have already presented predictions for the gw model using a boosted gaussian wavefunction . these authors also found good agreement with the data on the longitudinal to transverse ratio and with the @xmath181 dependence at fixed @xmath27 apart from the normalisation . however their results for the normalisation , and hence , implicitly , for the @xmath27-dependence of the production cross - section , were relatively poor . however , these authors did not implement the leptonic decay width constraint but fixed the radial parameter @xmath70 in the boosted gaussian by requiring that the exponential in @xmath70 of the wavefunction gives a value of @xmath201 when the @xmath21 invariant mass is equal to the meson s mass . this yielded @xmath202 for @xmath8 and @xmath203 for @xmath9 compared to our values shown in table 4 . in addition , they neglected real parts , which can result in a 20@xmath189 reduction in the cross - section for large @xmath27 . dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath8 production at @xmath196 gev in the fks model using the three different meson wavefunctions . data from _ left _ @xcite and _ right _ @xcite.,title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath8 production at @xmath196 gev in the fks model using the three different meson wavefunctions . data from _ left _ @xcite and _ right _ @xcite.,title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath8 production at @xmath196 gev in the gw model using the three different meson wavefunctions . data from _ left _ @xcite and _ right _ @xcite.,title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath8 production at @xmath196 gev in the gw model using the three different meson wavefunctions . data from _ left _ @xcite and _ right _ @xcite.,title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath8 production at @xmath196 gev in the cgc model using the three different meson wavefunctions . data from _ left _ @xcite and _ right _ @xcite.,title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath8 production at @xmath196 gev in the cgc model using the three different meson wavefunctions . data from _ left _ @xcite and _ right _ @xcite.,title="fig:",width=302,height=302 ] dependence of the total cross - section for @xmath8 production at various values of @xmath27 . we use the fks dipole model and compare the boosted gaussian and dgkp wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] dependence of the total cross - section for @xmath8 production at various values of @xmath27 . we use the fks dipole model and compare the boosted gaussian and dgkp wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] dependence of the total cross - section for @xmath8 production at various values of @xmath27 . we use the gw dipole model and compare the boosted gaussian and dgkp wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] dependence of the total cross - section for @xmath8 production at various values of @xmath27 . we use the gw dipole model and compare the boosted gaussian and dgkp wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] dependence of the total cross - section for @xmath8 production at various values of @xmath27 . we use the cgc dipole model and compare the boosted gaussian and dgkp wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] dependence of the total cross - section for @xmath8 production at various values of @xmath27 . we use the cgc dipole model and compare the boosted gaussian and dgkp wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] the corresponding plots to those in the previous section are repeated for the @xmath9 meson in figures [ fks_phi_q2_r.eps ] , [ gw_phi_q2_r.eps ] and [ cgc_phi_q2_r.eps ] . the h1 total cross - section data are at the following centre - of - mass energies : for @xmath204 gev@xmath183 , @xmath205 gev , otherwise @xmath196 gev . similarly for the zeus data , for @xmath206 gev@xmath183 , @xmath207 gev respectively . the h1 data on the longitudinal to transverse ratio are in the range 40 gev @xmath195 130 gev . similarly the zeus data are in the range 25 gev @xmath208 gev . for the theory curves we always take @xmath209 gev . the situation is rather similar , as one might expect , to that of the @xmath8 , i.e. all three dipole models tend to do rather well with either of the dgkp or boosted gaussian wavefunctions , while the nnpz wavefunction is less satisfactory . dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath9 production at @xmath209 gev in the fks model using the three different meson wavefunctions . data from _ left _ @xcite and _ right _ @xcite.,title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath9 production at @xmath209 gev in the fks model using the three different meson wavefunctions . data from _ left _ @xcite and _ right _ @xcite.,title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath9 production at @xmath209 gev in the gw model using the three different wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath9 production at @xmath209 gev in the gw model using the three different wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath9 production at @xmath209 gev in the cgc model using the three different wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , title="fig:",width=302,height=302 ] dependence of _ left _ the total cross - section and _ right _ the longitudinal to transverse cross - section ratio for @xmath9 production at @xmath209 gev in the cgc model using the three different wavefunctions . data from _ left _ @xcite and _ right _ @xcite . , we have performed a detailed study , comparing the predictions on @xmath8 and @xmath9 meson electroproduction arising from three different models of the meson wavefunction in combination with three different models for the fundamental dipole cross - section . our results are broadly encouraging and support the use of the dipole approach . the data can be explained rather well using the dipole model of forshaw , kerley and shaw , or those of golec - biernat and wsthoff and of iancu , itakura and munier , in conjunction with either the boosted gaussian or dgkp meson wavefunction . certainly , we anticipate that excellent agreement could be obtained if one decided to tune the meson wavefunctions . note that agreement extends to the ratio of longitudinal to transverse meson production . the nnpz wavefunction , which has , as noted , an unphysical singularity at @xmath140 , @xmath141 , is not so successful . for the future , it is clear that one could use the high quality data from hera to constrain the meson wavefunctions provided the dipole cross - section is sufficiently constrained . this research was supported in part by the uk particle physics and astronomy research council . r.s . was partly funded by a university of manchester research scholarship . we should like to thank s. munier , m. soares and a. stasto for useful discussions . we also thank m. v. t. machado for useful comments on the text .

we present a detailed comparison of a variety of predictions for diffractive light vector meson production with the data collected at the hera collider . all our calculations are performed within a dipole model framework and make use of different models for the meson light - cone wavefunction . there are no free parameters in any of the scenarios we consider . generally we find good agreement with the data using rather simple gaussian motivated wavefunctions in conjunction with dipole cross - sections which have been fitted to other data . + + j.r . forshaw@xmath0 , r. sandapen@xmath1 and g. shaw@xmath0 @xmath0department of physics and astronomy , + university of manchester , + manchester . m13 9pl . england . @xmath2department of physics , engineering physics and optics + laval university , + quebec . g1k 7p4 . canada .

while the large regular moons of the giant planets follow almost circular , low inclination , prograde orbits , the aptly named irregular moons tend to do the opposite : i.e. , they often have highly eccentric , high inclination orbits which may be retrograde _ or _ prograde . these moons , therefore , provide actual observational examples of the complexities of three - body dynamics . irregular moons are thought to have been captured during the early stages of the solar system but the detailed mechanism has not been fully elucidated . based on a study of the circular restricted three - body problem we have recently proposed that chaos played a key role in the initial stages of capture @xcite ; in this mechanism called chaos assisted capture ( cac ) particles may initially become entangled in chaotic layers which separate directly scattering from regular ( bound ) regions of phase space . this temporary trapping serves to extend the lifetimes of particles within the hill sphere thereby providing the breathing space necessary for relatively weak dissipative forces ( e.g. , gas - drag ) to effect permanent capture . while this basic scenario may be responsible for the _ initial _ formation of families of irregular moons , other factors may affect their subsequent long term evolution including collisions ; gravitational perturbations from other planets ; and deviations from circularity of the planet s orbit . here we investigate the effect of orbital ellipticity of the planet on the capture mechanism using monte carlo simulations and phase space visualisations based on the fast lyapunov indicator . two representative star - planet binaries are considered : the actual sun - jupiter system and a hypothetical extrasolar cousin of higher orbital eccentricity . we find that the chaos - assisted capture mechanism is robust to moderate ellipticities . recent discoveries of numerous irregular moons at giant planets @xcite have spurred the development of theories of their origin , which is generally thought to involve capture ( @xcite ; @xcite ; @xcite ) . these moons are considered to be primordial pieces of the solar system captured in the amber of time . while there is , as yet , no consensus on the detailed capture mechanism of these minor bodies a number of recent studies have , nevertheless , attemped to simulate their post - capture evolution in order to explain salient aspects of their orbits . for example , several attempts have recently been made to explain the observed clustering of irregular satellites as being the result either of the breakup of a larger parent body or from catastrophic collisions between planetesimals @xcite . these hypotheses are supported empirically by photometric surveys @xcite which indicate that members of the clusters have similar surface colours suggesting that they may have had common progenitors . however , whatever post - capture orbital evolution occurs _ within _ the hill sphere there has to have been an initial capture mechanism efficient enough to populate the hill sphere with moonlets in the first place . we have recently proposed one such mechanism chaos - assisted capture @xcite in which long - term , but temporary , trapping occurs in the ` sticky ' chaotic layers lying close to kolmogorov - arnold - moser ( kam , * ? ? ? * ) tori embedded within the planet s hill sphere . if a particle gets entangled in one of these layers then even a moderate level of dissipation ( or , alternatively , slow planetary growth , @xcite ) may be sufficient to make capture permanent . it is likely that comet - shoemaker - levy 9 was a recent example of an object trapped in such a chaotic zone for the best part of the last century @xcite . however , the absence of a large gas cloud at jupiter makes contemporary permanent capture of such objects by gas - drag unfeasible . qualitatively , in the cac model the capture probability of a planet is largely determined by the volume of phase space ( at a given energy ) taken up by chaotic zones within the hill sphere . simulations in the circular restricted three - body problem ( crtbp ) show that capture becomes less probable at higher energies because most of the phase space is directly scattering and relatively few kam tori survive ; those that do are surrounded by relatively thin chaotic layers which are less effective at trapping intruders @xcite . factors that are not included in the crtbp may also affect the capture mechanism , e.g. , the eccentricity of the parent planet s orbit . a more realistic extension of cac beyond the crtbp is , therefore , needed . as a first step we extend the model to the _ elliptic restricted three - body problem _ ( ertbp , @xcite ; @xcite ; @xcite ; @xcite ) which allows us to model perturbations induced by deviations of the planet s orbit from circularity . while orbital eccentricities are relatively small , although not negligible , for the giant planets of the solar system they may be appreciable for extrasolar planets ( @xcite ; @xcite ; @xcite ) . for example , compare jupiter s mean orbital eccentricity @xmath1 to typical extrasolar planet eccentricities which lie in the range @xmath2 @xcite . up to now there have been more than 100 extrasolar planetary systems detected and an intriguing question is whether these massive planets might harbour moons @xcite which might be habitable @xcite . as an exemplary extrasolar captor , we study a system similar in mass ratio to the idealized sun - jupiter binary but which follows a highly elliptic orbit . this provides a comparative estimate for the probability of capture and also suggests the ranges of energy and orbital inclination over which extrasolar irregular moons might be expected to exist . the paper is organized as follows : section 2 introduces the hamiltonian for the ertbp which , in the limit of zero ellipticity , reduces to the crtbp . we work in a coordinate system whose origin coincides with the planet and , in actual integrations , regularise the dynamics to deal with two - body collisions @xcite . because the ertbp is explicitly time dependent it is not possible to compute conventional poincar surfaces of section ( sos , * ? ? ? * ) even in the planar limit so as to visualise the structure of phase space . therefore we use the notion of a fast lyapunov indicator ( fli , * ? ? ? * ) to visualise the structure of phase space . section 3 briefly discusses the cac mechanism as applied to the crtbp in order to facilitate comparison with the ertbp . in particular , fli on the surfaces of section are computed which can be compared directly with sos in the crtbp . this is done in sec . 4 where monte carlo simulations of capture are performed . unlike in @xcite in these simulations we do not include dissipation and , instead , focus on the distributions of particles that can be temporarily trapped in chaotic zones for very long time periods . this avoids complications associated with the best choice of dissipative force ( see , e.g. , * ? ? ? finally , conclusions are contained in sec . the crtbp describes the dynamics of a test particle having infinitesimal mass and moving in the gravitational field of two massive bodies ( the ` primaries ' e.g. , a planet and a star ) which revolve around their center of mass on a circular orbit . the equations of motion are , therefore , most naturally presented in a non - inertial coordinate system that rotates with the mean motion of the primaries @xcite . in the rotating coordinate system the positions of the primaries are fixed . when the planet s orbit is elliptic rather than circular a nonuniformly rotating - pulsating coordinate system is commonly used . these new coordinates have the felicitous property that , again , the positions of the primaries are fixed ; however the hamiltonian is explicitly time - dependent @xcite . for our purposes it is most convenient to locate the origin at the planet ( fig . [ zvs ] ) because angular momentum will be measured with respect to the planet . then , following @xcite and @xcite , we obtain the planetocentric ertbp hamiltonian @xmath3 after introducing an isotropically pulsating length scale @xmath4 @xmath5 @xmath6 the semimajor axis of the orbit of the primaries @xmath7 has been scaled to unity and @xmath8 is the eccentricity of the planet s orbit ; @xmath9 , where @xmath10 and @xmath11 are the reduced mass and masses of the planet and star , respectively ( @xmath12 for sun - jupiter ) . the true anomaly @xmath13 , i.e. the planet s angular position measured from the pericenter , is related to the physical time @xmath14 through @xcite @xmath15 the ( planet - centered ) crtbp hamiltonian @xcite @xmath16 @xmath17 @xmath18 is recovered when @xmath19 . in both cases ( [ ertbp ] ) and ( [ crtbp ] ) , @xmath20 is the @xmath21-component of angular momentum @xmath22 with respect to the planet . note that the orbital inclination @xmath23 is invariant under isotropic pulsating rescaling from crtbp to ertbp . the orbit is said prograde if @xmath24 ( @xmath25 ) and retrograde otherwise . the hamiltonian of the elliptic problem ( [ ertbp ] ) is a periodic function of the true anomaly @xmath13 ( which plays the role of time ) and , hence , generates a non - autonomous dynamical system . unlike the circular problem , the ertbp does not possess an energy integral and , evidently , no such useful guiding concept as a static zero - velocity surface @xcite can be introduced . furthermore , due to the extra dimension associated with the explicit time dependence , construction of the sos and , indeed , any visual analysis of phase space seems impossible even in the planar limit . level curves of the zero velocity surface at high ( a ) and low ( b ) energies in the planetocentric planar crtbp along with the five lagrange equillibrium points ( labelled @xmath26 @xmath27 ) . the circle shaded grey is the hill sphere centered on the planet ( p ) . the star ( s ) is at @xmath28.,width=226 ] we have performed numerical integrations in which fluxes of particles are simulated as having passed from heliocentric orbits into the region surrounding the planet as defined by the hill sphere . this region roughly corresponds to the region between the points labelled @xmath26 and @xmath29 in fig . [ zvs ] . in practice it is convenient to go to extended phase space by introducing an additional pair of conjugate variables ` coordinate ' @xmath13 and ` momentum ' @xmath30 @xcite for which the new hamiltonian becomes conservative . in our numerical simulations we have used this method in combination with levi - civita ( in 2d ) and kustaanheimo - stiefel ( in 3d ) regularising techniques @xcite to avoid problems associated with two - body collisions @xcite . numerical integrations were done using a bulirsch - stoer adaptive integrator @xcite . one approach to visualising phase space structures in systems with greater than 2 degrees - of - freedom relies on computations of short - time lyapunov exponents ( le ) over sets of initial conditions of interest ( for recent developments and relevant applications see , e.g. , @xcite ; @xcite ; @xcite ; @xcite and references therein , although the idea of using finite - time le itself dates back at least to @xcite ) . as was demonstrated by @xcite various dynamical regimes ( including resonances ) can be distinguished by monitoring time profiles of a quantity called the fast lyapunov indicator . given an @xmath31-dimensional continuous - time dynamical system , @xmath32 the fast lyapunov indicator is defined as @xcite @xmath33 where * v*(t ) is a solution of the system of variational equations @xcite @xmath34 the complementary system ( [ variation ] ) contains spatial derivatives which only aggravate the singularities in the restricted three body problem ( rtbp ) and so the use of regularisation becomes even more important . for this reason , all calculations of fli reported herein were made using regularised versions of ( [ eom ] ) and ( [ variation ] ) . as distinct from the largest lyapunov characteristic exponent @xcite @xmath35 which just tends to zero for any regular orbit , the more sensitive fli can help discriminate between resonant and non - resonant regular orbits @xcite . although , in practice , detection of resonances may be tricky , since real differences in fli for quasiperiodic and periodic orbits of the same island are not always huge . in this section we briefly summarize the cac mechanism described in @xcite as applied to the crtbp . even though the basic mechanism applies in three - dimensions , it is simpler here to outline the general scheme in terms of the planar version of the crtbp . [ zvs ] shows the relevant zero velocity surface ( zvs , * ? ? ? * ) together with the five lagrange equilibrium points . a paradigmatic escaping ` sticky ' trajectory ( a ) in the planar sun - jupiter crtbp ; its multiple returns ( b ) to the hill sphere ( shaded grey , @xmath36 ) after heliocentric excursions ; its radial distance from the planet @xmath37 ( c ) and time profile of the fast lyapunov indicator ( d ) . the dotted vertical line indicates the first crossing of the hill sphere ( escape).,width=264 ] level curves of the zvs , similar to a potential energy surface ( pes ) , serve to limit the motion in the rotating frame and so define an energetically accessible region that may intersect the hill sphere . however , unlike a pes , because the zvs is defined in a rotating frame , it is possible for energy maxima to be stable as is , in fact , the case for @xmath38 and @xmath27 at which points jupiter s trojan asteroids are situated @xcite . the hill sphere ( see fig . [ zvs ] ) roughly occupies the region between the saddle points @xmath26 and @xmath29 which we term the ` capture zone ' with its radius being given by @xmath39 where @xmath7 is the planet s semimajor axis @xcite . in the case of ertbp the zvs pulsates , which defines periodically time - dependent capture regions @xcite . the two lagrange saddle points @xmath26 and @xmath29 act as gateways between the hill sphere and heliocentric orbits . a key finding of @xcite is that at energies close to ( but above ) the lagrange points only prograde orbits can enter ( or exit ) the capture zone . at higher capture energies the distribution shifts to include both senses of @xmath40 until , finally , retrograde capture becomes more likely . the statistics of inclination distributions will , therefore , be expected to depend strongly on energy , i.e. , how the curves of zero - velocity intersect the hill sphere . fig . [ sos ] portrays the structure of phase space in the planar limit ( @xmath41 ) in a series of poincar surfaces of section at four energies . at the lowest energy shown in fig . [ sos](a ) many of the prograde orbits are chaotic whereas all the retrograde orbits are regular . because incoming orbits can not penetrate the regular kam tori , prograde orbits must remain prograde while retrograde orbits can not be captured nor can already bound retrograde orbits escape . after @xmath29 has opened in fig . [ sos](b ) the chaotic sea of prograde orbits quickly ` evaporates ' except for a ` sticky ' layer of chaos which clings to the kam tori . with increasing energy this front evolves from prograde to retrograde motion . chaotic orbits close to the remaining tori can become trapped in almost regular orbits for very long times . in the presence of dissipation these chaotic orbits can be smoothly switched into the nearby kam region and almost always preserve the sign of angular momentum . thus , at low ( high ) energy permanent capture is almost always into prograde ( retrograde ) orbits . in this section we describe the results of our simulations in the planar ertbp using the fli and our monte carlo simulations in the spatial ertbp . we are primarily interested here in obtaining a qualitative picture of the volume and structure of phase space occupied by the chaotic layer in the ertbp as compared to the crtbp . for this we find a good diagnostic to be @xmath42 whose increase for chaotic orbits can usually be detected before , or no later than , a test particle finally escapes from the capture zone ( fig . [ escape ] ) . these measurements , when made over the capture region ( which contains permanently bound regular trajectories _ even at energies well above @xmath26 and @xmath29 _ ) , provide an estimate of the number of orbits that could be captured as illustrated in fig . [ fract ] . the number of chaotic orbits inside the capture zone , detected by computing fli , decreases with increasing ellipticity for moderate eccentricities ( fig . [ fract](a ) ) signifying that the chaotic layers get weaker and , therefore , capture is expected to become less probable than it is at @xmath19 . ideally the problem of separating the fractions of temporarily trapped and almost immediately escaping trajectories could be better quantified by partitioning the phase space into disjoint ( e.g. ` inner ' , hill sphere , and ` outer ' , heliocentric space ) regions and computing the fluxes across the barriers between them . but , given the current state of phase space transport theory , this has not yet been shown possible in practice for essentially 3d problems such as the spatial crtbp and ertbp hamiltonians . interestingly enough , despite strong theoretical grounds @xcite , and exhausting attempts , efforts to describe quantitatively spatial three - body dynamics by constructing global invariant manifolds @xcite , that would presumably contain all possible incoming and outgoing chaotic trajectories through @xmath26 and @xmath29 saddle points , have been not quite successful in approaching the 3d problem so far . part of the reason is that multiple escapes and recurrences of high energy trajectories to the hill sphere ( see example on fig . [ escape]a , b ) make local manifolds near multidimensional saddles extremely difficult to use as rigorous surfaces of no return . this is even more pronounced for chaotic ionization of atomic rydberg electrons ( @xcite ; @xcite ) which is closely related to rtbp dynamics . recent progress in pursuit of manifolds for the spatial three - body problem is reported by @xcite ; @xcite . fraction of chaotic orbits within the hill sphere that have @xmath43 at the cut - off time @xmath44 years in the planar sun - jupiter ertbp as a function of eccentricity . the phase space was sampled randomly with initial energies , true anomalies and eccentricities taken also at random . for reference , shown in parentheses are the mean eccentricities of jupiter , saturn , neptune , uranus , pluto , some extrasolar planetary systems ( hd 209452 , hd 169830 , hd 73526 , hd 108147 , hd 74156b ) , and binary trans - neptunian objects on elliptic orbits ( @xmath45,@xmath46 , @xmath47 , @xmath48 , @xmath49 , @xmath50).,width=264 ] to analyse the structure of phase space in ertbp , we first computed fli in the planar ( 2d ) circular case ( @xmath51 ) , where direct comparison with surfaces of section ( in the hill limit , @xmath52 , @xcite ) can be made . figs . [ fli](a c ) confirm that phase space visualisation via computing short - time fli ( [ fli ] ) works well in the planar crtbp , reproducing correctly all the relevant features visible in the sos shown in fig . in particular , the chaotic layer , and its evolution with increasing energy , can be easily identified by high values of fli ( shown in yellow ) . note also that fli measurements make sense even for relatively short time integrations , and are more economical than constructing the corresponding sos ( compare cut - off times given in the fig . [ fli ] and fig . [ sos ] captions ) . as for the sensitivity , it is not clear how reliable the numerical distinctions ( red - purple - blue ) between the fli for quasiperiodic and resonant orbits are , but this is irrelevant for our current purposes . in the planar limit , initial conditions were generated randomly within the hill radius on the surface of section ( see fig . [ fli ] caption ) and assuming that , initially , @xmath53 in which case the ertbp initial conditions reduce to those of crtbp . this guaranties that all ertbp initial conditions are generated with identical initial energies @xmath54 , and these are , in fact , true crtbp energies @xmath55 . the setting , thereby , allows for a direct comparison between the sos of fig . [ sos ] and results obtained using the fli . due to the dimensionality of the ertbp , relaxation of the above constraint , e.g. choosing the initial true anomalies at random , produced fli maps with no distinct structure . on the contrary , consistency in initial conditions at fixed @xmath53 helps track the smooth changes from crtbp to ertbp . as the planet s orbital eccentricity is increased to reach its actual value for jupiter , fli maps reveal a reduction of the density of orbits within the chaotic layers ( yellow paterns ) visible on fig . [ fli](d - f ) at each of the corresponding energies shown . however , at this moderate eccentricity , the phase space structures responsible for cac ( ` sticky ' kam tori surrounded by the chaotic layers ) generally survive any deviations introduced by ellipticity . this suggests robustness of the cac mechanism with respect to actual ellipticities of the giant planets orbits which lie well below @xmath56 ( see fig . [ fract ] ) . we further confirm this by direct monte carlo simulations of capture probability ( sec . 4.2 ) which reveal that cac indeed survives weak ellipticity in the rtbp . an important implication for future studies can be drawn by noticing that the heliocentric orbits of pluto ( with charon ) as well as of some recently discovered binary trans - neptunian objects are quite eccentric ( see examples on fig . [ fract ] ) , but not to the extent characteristic of extrasolars ( although the relative orbit of the binary partners as distinct from the heliocentric orbit of the combine can be very eccentric ) . these binary objects can be viewed in the framework of the hill approximation too , so the weakly elliptic chaos - assisted mutual capture , probably stabilized by the fast exchange of energy and angular momentum with a fourth body , may have been involved in early stages of their formation ( @xcite ; @xcite ; @xcite ) . the picture at much higher eccentricities evolves towards significant distorsions of the phase space stuctures as visualised by fli . in fig . [ fli](g i ) the kam tori ( red blue islands ) shrink , giving way to regions of scattering and chaotic orbits with short ( 200 years in this example ) residence times inside the hill sphere . these short - lived trajectories are the main contributions to the rapidly increasing number of chaotic orbits observed in fig . [ fract ] for @xmath57 . this does not mean , however , that capture will necessarily be enhanced , because a high density of strongly chaotic orbits does not correlate with the number of very long - lived trajectories trapped close to kam tori . on the other hand , lyapunov exponents computed for individual trajectories can not serve as a predictor of global stability , i.e. as an indicator of whether an orbit will stay long enough in a bound region , or if it escapes quickly . this aspect in computing lyapunov exponents for escaping ( captured ) trajectories concerns the notion of ` stable chaos ' @xcite . this term was coined to refer to chaotic motions that are locally hyperbolic , but demonstrate macroscopic long - term stability , so that the lyapunov time @xmath58 ( the inverse of the largest lyapunov exponent ( [ lyap ] ) ) is substantially less than the event time @xmath59 , e.g. the time for a trajectory to leave a certain region . however , there are indications of a possible simple linear correlation between @xmath59 and @xmath58 as shown in @xcite , which suggests that knowledge of the lyapunov time could allow one to predict an event time . concerning the residence ( escape ) time near the planet , simulations in the planar crtbp , however , show that such a correlation with the lyapunov time does not exist ( fig . [ l_times ] , see also discussion by @xcite and @xcite ) . among the randomly chosen escaping chaotic trajectories originating in the hill sphere , there are many very long - lived examples that have diverse , even quite small , lyapunov times . this means that local ( microscopic ) instabilities in the chaotic layer alone can not explain the distributions of survival probability . rather , as was pointed out by @xcite , long - term trapping with short @xmath58 near ` sticky ' kam structures can be attributed to the existence of phase space quasi - barriers and approximate integrals of motion . in the case of rtbp , these are the phase space structures around the saddle points at @xmath26 and @xmath29 and the @xmath21-component of angular momentum with respect to the planet , respectively . in 3d , the latter is approximately conserved @xcite for long - lived chaotic orbits which explains the unexpected strong correlation between initial and final inclinations of captured particles ( inclination memory we simulated capture statistics in the spatial ( three - dimensional ) ertbp by integrating isotropic fluxes of test particles that bombard the capture zone producing equal probabilities of initial conditions . initial conditions were generated as follows : the particle s position vector was chosen uniformly and randomly on the surface of the hill sphere . velocities were also chosen uniformly and randomly in accordance with the value of the crtbp energy @xmath55 . in turn , the starting energy ( jacobi constant @xmath60 ) was chosen uniformly random between its minimum possible value ( as defined by the energy of @xmath26 when @xmath53 ) and its highest value ( determined empirically such that above it the capture probability was essentially zero . ) then , by randomizing the initial true anomaly @xmath13 we model equal chances for a test particle to have any phase with respect to the mutual revolution of the primaries . the trajectories were integrated until one of the following occurred : the particle exited the hill sphere ; it penetrated a sphere , centred on the planet , of a given radius ( see fig . [ prob ] caption ) ; it survived for a predetermined cut - off time . escape time _ versus _ lyapunov time for 2d crtbp chaotic trajectories with initial conditions chosen randomly inside the hill sphere . escape was defined as the first crossing of the hill sphere.,width=302 ] choosing particles on the hill sphere , where the motion is chaotic or scattering , minimizes ( although does not eliminate ) the risk of accidentally starting orbits inside impenetrable kam regions @xcite . although permanently bound , these orbits could never actually have been captured because kam regions can not be penetrated at all in 2d and only exponentially slowly in 3d . it is only in the chaotic layer between scattering and stability that capture can happen . an initial swarm of incoming particles produces broad distribution of survivors with different residence times inside the hill sphere . we monitored its dynamics up to certain cut - off times ( of the order of several thousand years ) to find those long - lived chaotic orbits that may have been vulnerable to capture by a relatively weak dissipative force such as gas drag . only these orbits , in the cac model , could be the precursors to the currently observed distributions of irregular satellites . in a statistical sense , any short - time flybys are unlikely to have contributed to the primordial population of potential moons . also , since the sun - jupiter system was chosen as an example , we eliminated test particles that penetrated the inner region of the hill sphere occupied by jupiter s most influencial regular moon callisto . the massive regular moons may have acted as a source of strong perturbation removing some temporarily captured moonlets following prograde orbits . this provides a possible reason for the observed prograde - poor distribution of jovian irregulars @xcite . [ prob ] shows the results of these simulations . the capture probability density is plotted on the plane of initial and final inclinations . unlike other properties , e.g. , energy , inclination can be defined consistently in both the crtbp and the ertbp ( @xmath19 and @xmath61 in isotropically pulsating coordinates ) . as the distributions in fig.[prob ] confirm , inclination is approximately conserved during temporary capture in the ertbp , so that the rtbp energy / inclination dependent cac mechanism survives additional perturbations caused by deviations of the planet s orbit from circularity . this is clearly seen upon comparing fig.[prob ] ( a ) and ( b ) . the latter shows the capture probability for the sun - jupiter system with its actual eccentricity being used . we also verified by similar monte carlo runs that the basic energy inclination correlation discussed in sec . 3 remains valid in the 3d ertbp . we note , however , that since the energy is not a conserved quantity in the elliptic problem , a better representation of results is given in terms of inclinations . the most prominent effect observed in the ertpb compared to the circular case is the overall decrease of capture probability as eccentricity increases . simulations indicate that , given the same time scale , the actual ellipticity of jupiter s orbit accounts for approximately an order of magnitude lower capture probability than predicted by the circular model , while the relative number of progrades _ versus _ retrogrades remains unaffected . capture by typical extrasolar planets will be expected to become even more suppressed due to the wildly eccentric nature of these , essentially ertbp , star planet systems . to test this we used an eccentricity @xmath62 which is ten times greater than that of jupiter s orbit but quite similar to what has been estimated , for instance , for several already detected extrasolars ( the values of @xmath8 are given in parentheses ) : hd 108147 ( 0.498 ) , hd 168443b ( 0.53 ) , hd 82943c ( 0.54 ) , hd 142415 ( 0.5 ) , hd 4203 ( 0.46 ) , hd 210277 ( 0.46 ) , hd 147513 ( 0.52 ) , hd 190228 ( 0.5 ) , hd 50554 ( 0.5 ) , hd 33636 ( 0.53 ) . for consistency , we left unchanged all of the other parameters and environmental factors ( including callisto whose hypothetical extrasolar analogs may well exist around exo - jupiters ) exactly as they were used in the simulations for sun - jupiter . fig.[prob](c ) indicates that , due to the ellipticity of the orbits and assuming similar time scales and other conditions , capture by extrasolar planets may be as much as aproximately ten times less efficient than it could be by the giant planets of our system . the relatively low capture probability , predicted in ertbp , adds to other destructive mechanisms possibly operating on as yet undiscovered irregular satellites of extrasolar planets . the loss of satellites through yarkovsky @xcite or tidal @xcite effects may also diminish the possibility for highly elliptic extrasolar captors to marshal large populations of irregular moons . on the other hand , exo - planets with masses from one - half to four times jupiter s mass on low eccentricity orbits ( @xmath63 ) may be considered candidates for having irregular satellites . these may include , e.g. , already known extrasolars such as hd 179949 , 55 cnc b , hd 169830c , hd 187123 , tau boo , hd 75289 , 51 peg , ups and b , hd 195019 . capture probability ( the density of survivors normalized by the number of trajectories in the incoming fluxes ) as a function of initial and final inclinations in spatial circular ( a ) , elliptic sun - jupiter ( b ) and exemplary elliptic extrasolar ( c ) rtbp systems . the values of eccentricity @xmath8 are shown . chaotic trajectories with random energies ( @xmath64 $ ] ) , true anomalies ( @xmath65 $ ] ) , velocities and coordinates ( on the hill sphere with the radius @xmath36 ) were integrated until they either escaped from the sphere or crossed callisto s orbit at @xmath66 ( jupiter s orbital semimajor axis @xmath67 ) . each of the distrubutions was drawn from orbital elements of @xmath68 long - lived chaotic orbits that entered and survived within the hill sphere for @xmath69 years . incoming fluxes consisted of @xmath70 ( a ) , @xmath71 ( b ) , @xmath72 ( c ) particles.,width=302 ] the complexity of many - body systems evidently goes far beyond that of the simplest non - trivial case , the three - body problem . however , when considered on a hierarchical level , interactions between gravitional centers can often be decomposed to relatively low degree - of - freedom subsystems for which analysis from a dynamical systems point of view becomes possible . in the problem described here , the existence of sticky volumes of phase space where regular regions are surrounded by chaotic layers explains why several bodies may become temporarily ( but for rather long time periods ) trapped by mutual chaos - assisted capture . these quasi - stable configurations can subsequently be stabilised ( or destroyed ) on much longer time scales by various forces ( dissipative or not ) . here we have considered the effect introduced by a slow ( compared to time - scales of motion in the chaotic layer ) periodic parametric time dependence in the three - body problem . our simulations show that chaos - assisted capture applies and is , in fact , only slightly perturbed in cases when the primaries move on an elliptic orbit . it is expected to be of significant interest ( e.g. in applications to essentially many - particle systems such as star clusters and the asteroid belt ) to consider chaos - assisted capture at the next hierarchical level , i.e. when the primary two - body configuration is not restricted to a regular orbit , which may be the case in three - body encounters of comparably sized objects . this work was supported by grants from the us national science foundation through grant 0202185 and the petroleum research fund administered by the american chemical society . all opinions expressed in this article are those of the authors and do not necessarily reflect those of the national science foundation . s. a. a. also acknowledges support from forschungszentrum jlich , where part of this work was done .

several families of irregular moons orbit the giant planets . these moons are thought to have been captured into planetocentric orbits after straying into a region in which the planet s gravitation dominates solar perturbations ( the hill sphere ) . this mechanism requires a source of dissipation , such as gas - drag , in order to make capture permanent . however , capture by gas - drag requires that particles remain inside the hill sphere long enough for dissipation to be effective . recently we have proposed that in the circular restricted three - body problem particles may become caught up in ` sticky ' chaotic layers which tends to prolong their sojourn within the planet s hill sphere thereby assisting capture . here we show that this mechanism survives perturbations due to the ellipticity of the planet s orbit . however , monte carlo simulations indicate that the planet s ability to capture moons decreases with increasing orbital eccentricity . at the actual jupiter s orbital eccentricity , this effects in approximately an order of magnitude lower capture probability than estimated in the circular model . eccentricities of planetary orbits in the solar system are moderate but this is not necessarily the case for extrasolar planets which typically have rather eccentric orbits . therefore , our findings suggest that these extrasolar planets are unlikely to have substantial populations of irregular moons . celestial mechanics methods : @xmath0-body simulations planets and satellites : formation planetary systems : formation

transplantation assays , which involve the introduction of cells and tissues into specific body sites in mice , represent an essential approach for studies of tissue regeneration and carcinogenesis . orthotopic transplantations of cells , that is , their placement into a native milieu , are particularly important for characterization of adult stem cells . the existence of mammary stem cells was first suggested by the transplantation of epithelial mammary gland fragments into gland - free mammary fat pads of mice . engraftment assays to humanized mouse fat pad were used to recapitulate the regenerative potential and normal development of human primary breast epithelial cells . moreover , serial and limiting dilution transplantations of phenotypically distinct cell types into the cleared mammary fat pad were crucial to test the self - renewal capacity and multilineage differentiation of mammary stem cells . transplantation assays in combination with genetic lineage tracing provided evidence of the cell of origin in mammary carcinogenesis . orthotopic transplantation of normal and neoplastic mouse and human pancreatic organoids revealed genes and pathways altered in cancer progression . the importance of the native environment has also been supported by the demonstration of diverse regeneration after engraftments of sweat glands into different locations , such as mammary fat pads , shoulder fat pads , and back skin . the peritoneal cavity and the ovarian bursa are usually used as places for orthotopic transplantation of epithelial cells of the female reproductive tract . intraperitoneal injection of cells leads to their implantations in different areas of peritoneal cavity , thereby complicating monitoring cellular growth . furthermore , variations in the microenvironment , such as the extent of vascularization , innervation and immune cell representation , may be quite significant in different areas of the peritoneal cavity . the ovarian bursa has a very limited volume , allowing injection of no more than 10 l of liquid . furthermore , injections into the ovarian bursa can be quite technically challenging and the procedure requires a significant amount of time . to address these limitations , we have taken advantage of the ovarian fat pad properties . the mouse ovarian fat pad has a large size , is adjacent to the ovary and the uterine tube , and is easily accessible by surgery . it has been reported that equine trophoblast can be transplanted into the mouse ovarian fat pad . it was also not reported if this method can be applied to adult cells and tissues . here , we describe a reliable approach for the transplantation of mouse and human cells of the female reproductive tract and show that this method is also applicable to long - term organ transplantation . all the in vivo work described is approved by the cornell university institutional animal care and use committee . isolation and culture of primary tubal epithelium ( te ) cells euthanize donor 6- to 8-week - old virgin -actin - enhanced green fluorescent protein ( efgp ) or -actin - discosoma red fluorescent protein ( dsred ) mice by co2 administration followed by cervical dislocation . verify successful euthanasia by a toe pinch.place an individual mouse on an absorbent drape , ventral side up , and then wipe the abdomen with 70% ethanol . open the skin by making a lateral incision at the body midline and with fingertips pull the skin above and below the incision toward the head and tail of the mouse.hold the peritoneum using blunt forceps and make a cut with fine scissors to open the body cavity . gently push the coil of the intestine aside and locate the reproductive organs.with fine forceps pick up one uterine horn and cut 0.5 cm above the point where the uterine horns separate . while holding the uterine horn , dissect away connective tissue attached to the uterine horn , uterine tube , ovary and ovarian fat pad . place dissected reproductive tract in a dish with 6 ml sterile phosphate buffered saline ( pbs ) . proceed with the second reproductive tract.transfer the dish to a biosafety cabinet and wash the tissues 3 times in 6 ml sterile pbs . grab the uterine horn with fine tweezers and disconnect the uterine horn from the uterine tube by severing at the utero - tubal junction . note : after the ovarian bursa has been removed , the dissection is complete and the individual uterine tube remains in the pbs solution.transfer a single uterine tube in a 50 l drop of pbs to a 3.5 cm dish and mince into 0.1 mm pieces using 28 gauge needles . transfer to 200 l digestion buffer 1 ( dulbecco 's modified eagle 's medium ( dmem ) f12 ( ham 's ) medium supplemented with 300 units ml collagenase and 100 units ml hyaluronidase ) and incubate for 1 hr at 37 c in a 5% co2 incubator.after the incubation , add 1 ml 0.25% trypsin - ethylenediaminetetraacetic acid ( edta ) and suspend the solution with the help of a 1 ml pipette tip ( aka blue tip ) 20 times for 3 minutes . add 5 ml + 4 c dmem / f12 ( ham 's ) medium containing 2% fetal bovine serum.collect tissues by centrifugation ( 600 rcf , 5 min , room temperature ( rt ) ) , and add 1 ml digestion buffer 2 ( dmem f12 ( ham 's ) medium supplemented with 7 mg ml dispase ii and 10 g ml deoxyribonuclease i ( dnase i ) ) . suspend tissue pellet 20 times with help of a 1 ml pipette tip.add 5 ml serum free complete mouse tubal epithelium growth medium ( m - te - gm , table 1).collect cells by centrifugation ( 600 rcf , 5 min , rt ) . add 1 ml m - te - gm , suspend and count cells by hemocytometer . seed 1 x 10 cells in 1 ml per well in a 24-well low attachment plate and incubate in m - te - gm at 37c in a 5% co2 incubator for 4 days.change the medium every day.prepare single cell suspensions of cultured primary suspension te cells from -actin - egfp or -actin - dsred mice . centrifuge ( 600 rcf , 5 min , rt ) , and suspend cell pellets with 1 ml 0.25% trypsin - edta . incubate for 10 min at 37c in a 5% co2 incubator.stop trypsin activity by adding 5 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt ) . wash cell pellets twice with 4 ml of cold pbs ( 4c ) , add 1 ml pbs per cell pellet , and suspend . count cells by hemocytometer and transfer to 1.7 ml centrifugation tubes . working on ice , add 1 x 10 cells to 10 l pbs , then add 10 l basement membrane matrix . suspend and transport on ice to the animal room . note : perform all dissection and tissue culture work in a biosafety cabinet under sterile conditions . euthanize donor 6- to 8-week - old virgin -actin - enhanced green fluorescent protein ( efgp ) or -actin - discosoma red fluorescent protein ( dsred ) mice by co2 administration followed by cervical dislocation . place an individual mouse on an absorbent drape , ventral side up , and then wipe the abdomen with 70% ethanol . open the skin by making a lateral incision at the body midline and with fingertips pull the skin above and below the incision toward the head and tail of the mouse . hold the peritoneum using blunt forceps and make a cut with fine scissors to open the body cavity . gently push the coil of the intestine aside and locate the reproductive organs . with fine forceps pick up one uterine horn and cut 0.5 cm above the point where the uterine horns separate . while holding the uterine horn , dissect away connective tissue attached to the uterine horn , uterine tube , ovary and ovarian fat pad . place dissected reproductive tract in a dish with 6 ml sterile phosphate buffered saline ( pbs ) . transfer the dish to a biosafety cabinet and wash the tissues 3 times in 6 ml sterile pbs . continue the work under a dissection microscope located in the biosafety cabinet . grab the uterine horn with fine tweezers and disconnect the uterine horn from the uterine tube by severing at the utero - tubal junction . note : after the ovarian bursa has been removed , the dissection is complete and the individual uterine tube remains in the pbs solution . transfer a single uterine tube in a 50 l drop of pbs to a 3.5 cm dish and mince into 0.1 mm pieces using 28 gauge needles . transfer to 200 l digestion buffer 1 ( dulbecco 's modified eagle 's medium ( dmem ) f12 ( ham 's ) medium supplemented with 300 units ml collagenase and 100 units ml hyaluronidase ) and incubate for 1 hr at 37 c in a 5% co2 incubator . after the incubation , add 1 ml 0.25% trypsin - ethylenediaminetetraacetic acid ( edta ) and suspend the solution with the help of a 1 ml pipette tip ( aka blue tip ) 20 times for 3 minutes . add 5 ml + 4 c dmem / f12 ( ham 's ) medium containing 2% fetal bovine serum . collect tissues by centrifugation ( 600 rcf , 5 min , room temperature ( rt ) ) , and add 1 ml digestion buffer 2 ( dmem f12 ( ham 's ) medium supplemented with 7 mg ml dispase ii and 10 g ml deoxyribonuclease i ( dnase i ) ) . suspend tissue pellet 20 times with help of a 1 ml pipette tip . add 5 ml serum free complete mouse tubal epithelium growth medium ( m - te - gm , table 1 ) . add 1 ml m - te - gm , suspend and count cells by hemocytometer . seed 1 x 10 cells in 1 ml per well in a 24-well low attachment plate and incubate in m - te - gm at 37c in a 5% co2 incubator for 4 days . prepare single cell suspensions of cultured primary suspension te cells from -actin - egfp or -actin - dsred mice . centrifuge ( 600 rcf , 5 min , rt ) , and suspend cell pellets with 1 ml 0.25% trypsin - edta . incubate for 10 min at 37c in a 5% co2 incubator.stop trypsin activity by adding 5 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt ) . centrifuge ( 600 rcf , 5 min , rt ) , and suspend cell pellets with 1 ml 0.25% trypsin - edta . stop trypsin activity by adding 5 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . wash cell pellets twice with 4 ml of cold pbs ( 4c ) , add 1 ml pbs per cell pellet , and suspend . count cells by hemocytometer and transfer to 1.7 ml centrifugation tubes . working on ice , add 1 x 10 cells to 10 l pbs , then add 10 l basement membrane matrix . suspend and transport on ice to the animal room . note : perform all dissection and tissue culture work in a biosafety cabinet under sterile conditions . preparation of immortalized human cell line separately grow lentivirus - egfp and -mcherry labeled human immortalized ovarian surface epithelium cell linehio118 until 80 - 90% confluency on 10 cm dishes at 37c in a 5% co2 incubator.wash dishes twice with 10 ml pbs , add 1 ml 0.25% trypsin - edta per dish and incubate for 10 min at 37c in a 5% co2 incubator . stop the reaction by adding 10 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt).wash cell pellets twice with 10 ml of cold pbs ( 4c ) , add 1 ml pbs per cell pellet , and suspend . count cells by hemocytometer and transfer to 1.7 ml centrifugation tubes.working on ice , add 1.0 x 10 lenti - mcherry labeled cells + 1.0 x 10lenti - egfp labeled cells to 10 l pbs . separately grow lentivirus - egfp and -mcherry labeled human immortalized ovarian surface epithelium cell linehio118 until 80 - 90% confluency on 10 cm dishes at 37c in a 5% co2 incubator . wash dishes twice with 10 ml pbs , add 1 ml 0.25% trypsin - edta per dish and incubate for 10 min at 37c in a 5% co2 incubator . stop the reaction by adding 10 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt ) . wash cell pellets twice with 10 ml of cold pbs ( 4c ) , add 1 ml pbs per cell pellet , and suspend . count cells by hemocytometer and transfer to 1.7 ml centrifugation tubes . working on ice , add 1.0 x 10 lenti - mcherry labeled cells + 1.0 x 10lenti - egfp labeled cells to 10 l pbs . preparation of the uterine tube dissect individual uterine tubes from 6- to 8-week old virgin -actin - dsred mice in pbs as described in steps 1.1.1 - 1.1.5 . transfer single uterine tubes into a 200 l drop of pbs under a dissection microscope . gently uncoil uterine tubes with the help of tweezers and 28 gauge needles by removing the mesosalpinx , a portion of the broad ligament which supports the segments of the uterine tube . place single uncoiled uterine tubes in a drop of 200 l ice - cold pbs until the recipient 's ovarian fat pad is exposed and prepared to receive the transplant . dissect individual uterine tubes from 6- to 8-week old virgin -actin - dsred mice in pbs as described in steps 1.1.1 - 1.1.5 . transfer single uterine tubes into a 200 l drop of pbs under a dissection microscope . gently uncoil uterine tubes with the help of tweezers and 28 gauge needles by removing the mesosalpinx , a portion of the broad ligament which supports the segments of the uterine tube . place single uncoiled uterine tubes in a drop of 200 l ice - cold pbs until the recipient 's ovarian fat pad is exposed and prepared to receive the transplant . dorsal transplantations to the right ovarian fat pad are preferential as this avoids the spleen . use syngeneic mice or severe combined immunodeficiency ( scid / ncr ) mice as recipients of primary cells . for human cells , such as hio118 cells , use nod / scid / gamma ( nsg ) mice or scid mice . anesthetize recipient mouse with a single intra - peritoneal injection of 2,2,2-tribromoethanol at a dosage of 0.15 ml/10 g body weight . place the animal on a heating pad , in the animal hood and confirm proper anesthetization by loss of pedal reflex ( toe pinch ) . apply vet ointment on eyes to prevent dryness while the animal is under anesthesia . inject the animal subcutaneously with the analgesic ketoprofen at a dosage of 4 mg/ g body weight to treat for post - surgical pain . place the animal in the induction chamber and adjust the oxygen flowmeter to 0.8 - 1.5 l / min and the isoflurane vaporizer to 2 - 3% . remove the anesthetized animal from the chamber , let it breathe isoflurane from a mask and set the oxygen flowmeter to 0.4 - 0.8 l / min and the isoflurane vaporizer to 1.5% , then start the surgery . shave the surgical area with # 40 clippers ; remove hair from an area 2 times the surgical area , prepare the shaved skin with three antiseptic scrubs of povidone - iodine , followed by 70% ethanol , and cover with a sterile drape . expose the reproductive tract by an incision in the dorsomedial position directly above the ovarian fat pad . note : critical step : precise skin incision facilitates wound healing , the use of a scalpel is recommended in step 2.4 . using blunt fine forceps pull the ovarian fat pad carefully through the incision towards the midline , minimizing damage to nerves and major blood vessels . critical step : if bleeding occurs , stop the surgery and consider transplanting to a different host animal . under the control of the dissection microscope with help of a 28 gauge beveled needle make a 2 - 4 mm deep incision into the ovarian fat pad , 3 - 4 mm above the ovary . critical step : ensure that the incision only goes through half of the fat pad ; puncturing all the way through to the bottom side causes leakage . be swift and proceed without delay after this step . for cell transplantations , fill a syringe ( 30 gauge needle ) with 10 - 20 l of the cell - basement membrane matrix - mixture and inject into the fat pad incision . for uterine tube transplantation , pick up the uterine tube with fine forceps and place in 10 - 20 l basement membrane matrix kept on ice . using a 0.1 - 10/20 l xl graduated filter tip ( shortened by 3 mm ) pick up the tissue and basement membrane matrix suspension and release into the fat pad incision . wait 5 minutes for the basement membrane matrix to solidify and place the reproductive tract back into the peritoneum . close the muscles with 2 stiches of surgical suture and the skin with two small wound clips or surgical suture . repeat steps 2.4 - 2.8 to transplant a pbs - basement membrane matrix - mixture into the contra - lateral fat pad of the animal which will serve as control . critical step : after the surgery place the animal on a heating pad , because heat loss is rapid in anesthetized mice . let animal recover on a heating pad in the native cage and observe the animal until fully awake from the anesthesia . do not leave an animal unattended until it has regained sufficient consciousness to maintain sternal recumbence . do not return an animal that has undergone surgery to the company of other animals until fully recovered . place a handful of pre - wet food pellets inside the cage in addition to dry food on the cage after surgery . apply post - surgical analgesics if needed for the next few days and examine the wound daily . apply antibiotics according to the approved animal protocol if wound infection occurs . remove wound clips prepare 4% paraformaldehyde solution by mixing 26 ml ddh2o with 4 ml 10x pbs and 10 ml 16% paraformaldehyde solution.dissect in one block , the engrafted ovarian fat pad , ovary , uterine tube , 0.5 cm uterus as described in steps 1.1.1 - 1.1.4 . immediately place in 2 ml 4% paraformaldehyde and fix for 2 hr , at rt . from the same animal , dissect the non - engrafted contralateral ovarian fat pad system transplanted with pbs - basement membrane matrix mixture as a control ( see step 2.9 ) . fix and process in the same way.after fixation wash tissues three times with pbs for 5 min and incubate overnight in pbs at 4 c.for the whole - mount imaging of the ovarian fat pad proceed to step 3.2.1 . note : after the image acquisition tissues can be frozen ( 3.3.1 ) or processed for paraffin embedding ( 3.3.2 ) . overnight incubation in 30% sucrose in pbs at 4 c improves quality of frozen tissues . prepare 4% paraformaldehyde solution by mixing 26 ml ddh2o with 4 ml 10x pbs and 10 ml 16% paraformaldehyde solution . dissect in one block , the engrafted ovarian fat pad , ovary , uterine tube , 0.5 cm uterus as described in steps 1.1.1 - 1.1.4 . immediately place in 2 ml 4% paraformaldehyde and fix for 2 hr , at rt . from the same animal , dissect the non - engrafted contralateral ovarian fat pad system transplanted with pbs - basement membrane matrix mixture as a control ( see step 2.9 ) . after fixation wash tissues three times with pbs for 5 min and incubate overnight in pbs at 4 c . for the whole - mount imaging of the ovarian fat pad proceed to step 3.2.1 . note : after the image acquisition tissues can be frozen ( 3.3.1 ) or processed for paraffin embedding ( 3.3.2 ) . overnight incubation in 30% sucrose in pbs at 4 c improves quality of frozen tissues . image acquisition place whole - mount ovarian fat pad systems in pbs filled dishes and image using an inverted microscope equipped with epi - fluorescence attachment and high - definition color camera , with 4 , 10x objectives , and a stereomicroscope equipped with a fluorescence attachment , color camera and plan apo 1xwd70 , ed plan 1.5xwd45 objectives . place whole - mount ovarian fat pad systems in pbs filled dishes and image using an inverted microscope equipped with epi - fluorescence attachment and high - definition color camera , with 4 , 10x objectives , and a stereomicroscope equipped with a fluorescence attachment , color camera and plan apo 1xwd70 , ed plan 1.5xwd45 objectives . histology following whole - mount image acquisition ( 3.2.1 ) place a 200 - 500 l drop of embedding medium for frozen tissue specimens on a 2 x 1 cm piece of laboratory film and using forceps , transfer the tissue to the drop . pick up the film at one edge and transfer the tissue - medium drop to a 1.8 ml cryogenic vial . close the vial and plunge into liquid nitrogen . store frozen tissues at -80 c.alternatively , proceed with the standard paraffin embedding . immerse tissues once in 65% ethanol for 30 min , shaking gently at rt.immerse tissues once in 70% ethanol for 30 min , shaking gently at rt . at this stage samples can be stored for months at rt.immerse tissues once in 90% ethanol for 30 min , shaking gently at rt.immerse tissues once in 95% ethanol for 30 min , shaking gently at rt.immerse tissues twice in absolute ethanol ( 200 proof ) for 30 min , shaking gently at rt.immerse tissues twice in chloroform for 30 min , shaking gently at rt.immerse tissues once in paraffin for 30 min , shaking gently at 58 c.immerse tissues once in paraffin for 12 hr , shaking gently at 58 c.immerse tissues once in paraffin for 3 hr , at 58 c.place tissues in metal histology molds and fill molds with 58 c paraffin . add a plastic histology cassette on top of the paraffin and cool down paraffin to + 4 c . note : paraffin temperature should not exceed 58 c for optimal preservation of tissue suitable for immunohistochemical staining . preheat specimen processing gel to 60 c.pipette 200 l of the specimen processing gel onto a laboratory film - lined petri dish . using fine dissection forceps transfer the whole - mount tissue system to the specimen processing gel drop.allow the specimen processing gel plug to solidify at room temperature , or solidify the plug for 10 min at 4 c.place the specimen processing gel embedded tissue in histology tissue cassettes sandwiched between biopsy foam pads . note : specimen processing gel embedding prevents loss and allows preservation of small fragile tissue samples . note : tissues preserved by freezing or paraffin embedding are suitable for immunohistochemical staining . following whole - mount image acquisition ( 3.2.1 ) place a 200 - 500 l drop of embedding medium for frozen tissue specimens on a 2 x 1 cm piece of laboratory film and using forceps , transfer the tissue to the drop . pick up the film at one edge and transfer the tissue - medium drop to a 1.8 ml cryogenic vial . close the vial and plunge into liquid nitrogen . store frozen tissues at -80 c . immerse tissues once in 65% ethanol for 30 min , shaking gently at rt.immerse tissues once in 70% ethanol for 30 min , shaking gently at rt . at this stage samples can be stored for months at rt.immerse tissues once in 90% ethanol for 30 min , shaking gently at rt.immerse tissues once in 95% ethanol for 30 min , shaking gently at rt.immerse tissues twice in absolute ethanol ( 200 proof ) for 30 min , shaking gently at rt.immerse tissues twice in chloroform for 30 min , shaking gently at rt.immerse tissues once in paraffin for 30 min , shaking gently at 58 c.immerse tissues once in paraffin for 12 hr , shaking gently at 58 c.immerse tissues once in paraffin for 3 hr , at 58 c.place tissues in metal histology molds and fill molds with 58 c paraffin . add a plastic histology cassette on top of the paraffin and cool down paraffin to + 4 c . note : paraffin temperature should not exceed 58 c for optimal preservation of tissue suitable for immunohistochemical staining . immerse tissues once in 70% ethanol for 30 min , shaking gently at rt . at this stage samples can be stored for months at rt . immerse tissues once in 90% ethanol for 30 min , shaking gently at rt . immerse tissues twice in absolute ethanol ( 200 proof ) for 30 min , shaking gently at rt . place tissues in metal histology molds and fill molds with 58 c paraffin . add a plastic histology cassette on top of the paraffin and cool down paraffin to + 4 c . extract paraffin - tissue block and store at rt . note : paraffin temperature should not exceed 58 c for optimal preservation of tissue suitable for immunohistochemical staining . preheat specimen processing gel to 60 c.pipette 200 l of the specimen processing gel onto a laboratory film - lined petri dish . using fine dissection forceps transfer the whole - mount tissue system to the specimen processing gel drop.allow the specimen processing gel plug to solidify at room temperature , or solidify the plug for 10 min at 4 c.place the specimen processing gel embedded tissue in histology tissue cassettes sandwiched between biopsy foam pads . note : specimen processing gel embedding prevents loss and allows preservation of small fragile tissue samples . note : tissues preserved by freezing or paraffin embedding are suitable for immunohistochemical staining . pipette 200 l of the specimen processing gel onto a laboratory film - lined petri dish . using fine dissection allow the specimen processing gel plug to solidify at room temperature , or solidify the plug for 10 min at 4 c . place the specimen processing gel embedded tissue in histology tissue cassettes sandwiched between biopsy foam pads . embed in paraffin as in steps 3.3.2 - 3.3.2.10 . note : specimen processing gel embedding prevents loss and allows preservation of small fragile tissue samples . isolation and culture of primary tubal epithelium ( te ) cells euthanize donor 6- to 8-week - old virgin -actin - enhanced green fluorescent protein ( efgp ) or -actin - discosoma red fluorescent protein ( dsred ) mice by co2 administration followed by cervical dislocation . verify successful euthanasia by a toe pinch.place an individual mouse on an absorbent drape , ventral side up , and then wipe the abdomen with 70% ethanol . open the skin by making a lateral incision at the body midline and with fingertips pull the skin above and below the incision toward the head and tail of the mouse.hold the peritoneum using blunt forceps and make a cut with fine scissors to open the body cavity . gently push the coil of the intestine aside and locate the reproductive organs.with fine forceps pick up one uterine horn and cut 0.5 cm above the point where the uterine horns separate . while holding the uterine horn , dissect away connective tissue attached to the uterine horn , uterine tube , ovary and ovarian fat pad . place dissected reproductive tract in a dish with 6 ml sterile phosphate buffered saline ( pbs ) . proceed with the second reproductive tract.transfer the dish to a biosafety cabinet and wash the tissues 3 times in 6 ml sterile pbs . continue the work under a dissection microscope located in the biosafety cabinet . grab the uterine horn with fine tweezers and disconnect the uterine horn from the uterine tube by severing at the utero - tubal junction . note : after the ovarian bursa has been removed , the dissection is complete and the individual uterine tube remains in the pbs solution.transfer a single uterine tube in a 50 l drop of pbs to a 3.5 cm dish and mince into 0.1 mm pieces using 28 gauge needles . transfer to 200 l digestion buffer 1 ( dulbecco 's modified eagle 's medium ( dmem ) f12 ( ham 's ) medium supplemented with 300 units ml collagenase and 100 units ml hyaluronidase ) and incubate for 1 hr at 37 c in a 5% co2 incubator.after the incubation , add 1 ml 0.25% trypsin - ethylenediaminetetraacetic acid ( edta ) and suspend the solution with the help of a 1 ml pipette tip ( aka blue tip ) 20 times for 3 minutes . add 5 ml + 4 c dmem / f12 ( ham 's ) medium containing 2% fetal bovine serum.collect tissues by centrifugation ( 600 rcf , 5 min , room temperature ( rt ) ) , and add 1 ml digestion buffer 2 ( dmem f12 ( ham 's ) medium supplemented with 7 mg ml dispase ii and 10 g ml deoxyribonuclease i ( dnase i ) ) . suspend tissue pellet 20 times with help of a 1 ml pipette tip.add 5 ml serum free complete mouse tubal epithelium growth medium ( m - te - gm , table 1).collect cells by centrifugation ( 600 rcf , 5 min , rt ) . add 1 ml m - te - gm , suspend and count cells by hemocytometer . seed 1 x 10 cells in 1 ml per well in a 24-well low attachment plate and incubate in m - te - gm at 37c in a 5% co2 incubator for 4 days.change the medium every day.prepare single cell suspensions of cultured primary suspension te cells from -actin - egfp or -actin - dsred mice . centrifuge ( 600 rcf , 5 min , rt ) , and suspend cell pellets with 1 ml 0.25% trypsin - edta . incubate for 10 min at 37c in a 5% co2 incubator.stop trypsin activity by adding 5 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt ) . wash cell pellets twice with 4 ml of cold pbs ( 4c ) , add 1 ml pbs per cell pellet , and suspend . count cells by hemocytometer and transfer to 1.7 ml centrifugation tubes . working on ice , add 1 x 10 cells to 10 l pbs , then add 10 l basement membrane matrix . suspend and transport on ice to the animal room . note : perform all dissection and tissue culture work in a biosafety cabinet under sterile conditions . euthanize donor 6- to 8-week - old virgin -actin - enhanced green fluorescent protein ( efgp ) or -actin - discosoma red fluorescent protein ( dsred ) mice by co2 administration followed by cervical dislocation . place an individual mouse on an absorbent drape , ventral side up , and then wipe the abdomen with 70% ethanol . open the skin by making a lateral incision at the body midline and with fingertips pull the skin above and below the incision toward the head and tail of the mouse . hold the peritoneum using blunt forceps and gently push the coil of the intestine aside and locate the reproductive organs . with fine forceps pick up one uterine horn and cut 0.5 cm above the point where the uterine horns separate . while holding the uterine horn , dissect away connective tissue attached to the uterine horn , uterine tube , ovary and ovarian fat pad . place dissected reproductive tract in a dish with 6 ml sterile phosphate buffered saline ( pbs ) . transfer the dish to a biosafety cabinet and wash the tissues 3 times in 6 ml sterile pbs . grab the uterine horn with fine tweezers and disconnect the uterine horn from the uterine tube by severing at the utero - tubal junction . note : after the ovarian bursa has been removed , the dissection is complete and the individual uterine tube remains in the pbs solution . transfer a single uterine tube in a 50 l drop of pbs to a 3.5 cm dish and mince into 0.1 mm pieces using 28 gauge needles . transfer to 200 l digestion buffer 1 ( dulbecco 's modified eagle 's medium ( dmem ) f12 ( ham 's ) medium supplemented with 300 units ml collagenase and 100 units ml hyaluronidase ) and incubate for 1 hr at 37 c in a 5% co2 incubator . after the incubation , add 1 ml 0.25% trypsin - ethylenediaminetetraacetic acid ( edta ) and suspend the solution with the help of a 1 ml pipette tip ( aka blue tip ) 20 times for 3 minutes . add 5 ml + 4 c dmem / f12 ( ham 's ) medium containing 2% fetal bovine serum . collect tissues by centrifugation ( 600 rcf , 5 min , room temperature ( rt ) ) , and add 1 ml digestion buffer 2 ( dmem f12 ( ham 's ) medium supplemented with 7 mg ml dispase ii and 10 g ml deoxyribonuclease i ( dnase i ) ) . suspend tissue pellet 20 times with help of a 1 ml pipette tip . add 5 ml serum free complete mouse tubal epithelium growth medium ( m - te - gm , table 1 ) . add 1 ml m - te - gm , suspend and count cells by hemocytometer . seed 1 x 10 cells in 1 ml per well in a 24-well low attachment plate and incubate in m - te - gm at 37c in a 5% co2 incubator for 4 days . change the medium every day . prepare single cell suspensions of cultured primary suspension te cells from -actin - egfp or -actin - dsred mice . centrifuge ( 600 rcf , 5 min , rt ) , and suspend cell pellets with 1 ml 0.25% trypsin - edta . incubate for 10 min at 37c in a 5% co2 incubator.stop trypsin activity by adding 5 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt ) . centrifuge ( 600 rcf , 5 min , rt ) , and suspend cell pellets with 1 ml 0.25% trypsin - edta . stop trypsin activity by adding 5 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt ) . wash cell pellets twice with 4 ml of cold pbs ( 4c ) , add 1 ml pbs per cell pellet , and suspend . count cells by hemocytometer and transfer to 1.7 ml centrifugation tubes . working on ice , add 1 x 10 cells to 10 l pbs , then add 10 l basement membrane matrix . note : perform all dissection and tissue culture work in a biosafety cabinet under sterile conditions . preparation of immortalized human cell line separately grow lentivirus - egfp and -mcherry labeled human immortalized ovarian surface epithelium cell linehio118 until 80 - 90% confluency on 10 cm dishes at 37c in a 5% co2 incubator.wash dishes twice with 10 ml pbs , add 1 ml 0.25% trypsin - edta per dish and incubate for 10 min at 37c in a 5% co2 incubator . stop the reaction by adding 10 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt).wash cell pellets twice with 10 ml of cold pbs ( 4c ) , add 1 ml pbs per cell pellet , and suspend . count cells by hemocytometer and transfer to 1.7 ml centrifugation tubes.working on ice , add 1.0 x 10 lenti - mcherry labeled cells + 1.0 x 10lenti - egfp labeled cells to 10 l pbs . separately grow lentivirus - egfp and -mcherry labeled human immortalized ovarian surface epithelium cell linehio118 until 80 - 90% confluency on 10 cm dishes at 37c in a 5% co2 incubator . wash dishes twice with 10 ml pbs , add 1 ml 0.25% trypsin - edta per dish and incubate for 10 min at 37c in a 5% co2 incubator . stop the reaction by adding 10 ml dmem / f12 ( ham 's ) medium containing 5% fetal bovine serum . collect cell pellets by centrifugation ( 600 rcf , 5 min , rt ) . wash cell pellets twice with 10 ml of cold pbs ( 4c ) , add 1 ml pbs per cell pellet , and suspend . count cells by hemocytometer and transfer to 1.7 ml centrifugation tubes . working on ice , add 1.0 x 10 lenti - mcherry labeled cells + 1.0 x 10lenti - egfp labeled cells to 10 l pbs . preparation of the uterine tube dissect individual uterine tubes from 6- to 8-week old virgin -actin - dsred mice in pbs as described in steps 1.1.1 - 1.1.5 . transfer single uterine tubes into a 200 l drop of pbs under a dissection microscope . gently uncoil uterine tubes with the help of tweezers and 28 gauge needles by removing the mesosalpinx , a portion of the broad ligament which supports the segments of the uterine tube . place single uncoiled uterine tubes in a drop of 200 l ice - cold pbs until the recipient 's ovarian fat pad is exposed and prepared to receive the transplant . dissect individual uterine tubes from 6- to 8-week old virgin -actin - dsred mice in pbs as described in steps 1.1.1 - 1.1.5 . transfer single uterine tubes into a 200 l drop of pbs under a dissection microscope . gently uncoil uterine tubes with the help of tweezers and 28 gauge needles by removing the mesosalpinx , a portion of the broad ligament which supports the segments of the uterine tube . place single uncoiled uterine tubes in a drop of 200 l ice - cold pbs until the recipient 's ovarian fat pad is exposed and prepared to receive the transplant . note : disinfect instruments between each animal surgery . prepare and arrange all equipment in advance . dorsal transplantations to the right ovarian fat pad are preferential as this avoids the spleen . use syngeneic mice or severe combined immunodeficiency ( scid / ncr ) mice as recipients of primary cells . for human cells , such as hio118 cells , use nod / scid / gamma ( nsg ) mice or scid mice . anesthetize recipient mouse with a single intra - peritoneal injection of 2,2,2-tribromoethanol at a dosage of 0.15 ml/10 g body weight . place the animal on a heating pad , in the animal hood and confirm proper anesthetization by loss of pedal reflex ( toe pinch ) . apply vet ointment on eyes to prevent dryness while the animal is under anesthesia . inject the animal subcutaneously with the analgesic ketoprofen at a dosage of 4 mg/ g body weight to treat for post - surgical pain . place the animal in the induction chamber and adjust the oxygen flowmeter to 0.8 - 1.5 l / min and the isoflurane vaporizer to 2 - 3% . remove the anesthetized animal from the chamber , let it breathe isoflurane from a mask and set the oxygen flowmeter to 0.4 - 0.8 l / min and the isoflurane vaporizer to 1.5% , then start the surgery . shave the surgical area with # 40 clippers ; remove hair from an area 2 times the surgical area , prepare the shaved skin with three antiseptic scrubs of povidone - iodine , followed by 70% ethanol , and cover with a sterile drape . expose the reproductive tract by an incision in the dorsomedial position directly above the ovarian fat pad . note : critical step : precise skin incision facilitates wound healing , the use of a scalpel is recommended in step 2.4 . using blunt fine forceps pull the ovarian fat pad carefully through the incision towards the midline , minimizing damage to nerves and major blood vessels . critical step : if bleeding occurs , stop the surgery and consider transplanting to a different host animal . under the control of the dissection microscope with help of a 28 gauge beveled needle make a 2 - 4 mm deep incision into the ovarian fat pad , 3 - 4 mm above the ovary . critical step : ensure that the incision only goes through half of the fat pad ; puncturing all the way through to the bottom side causes leakage . , fill a syringe ( 30 gauge needle ) with 10 - 20 l of the cell - basement membrane matrix - mixture and inject into the fat pad incision . for uterine tube transplantation , pick up the uterine tube with fine forceps and place in 10 - 20 l basement membrane matrix kept on ice . using a 0.1 - 10/20 l xl graduated filter tip ( shortened by 3 mm ) pick up the tissue and basement membrane matrix suspension and release into the fat pad incision . wait 5 minutes for the basement membrane matrix to solidify and place the reproductive tract back into the peritoneum . close the muscles with 2 stiches of surgical suture and the skin with two small wound clips or surgical suture . repeat steps 2.4 - 2.8 to transplant a pbs - basement membrane matrix - mixture into the contra - lateral fat pad of the animal which will serve as control . critical step : after the surgery place the animal on a heating pad , because heat loss is rapid in anesthetized mice . let animal recover on a heating pad in the native cage and observe the animal until fully awake from the anesthesia . do not leave an animal unattended until it has regained sufficient consciousness to maintain sternal recumbence . do not return an animal that has undergone surgery to the company of other animals until fully recovered . place a handful of pre - wet food pellets inside the cage in addition to dry food on the cage after surgery . apply post - surgical analgesics if needed for the next few days and examine the wound daily . apply antibiotics according to the approved animal protocol if wound infection occurs . graft collection and preservation prepare 4% paraformaldehyde solution by mixing 26 ml ddh2o with 4 ml 10x pbs and 10 ml 16% paraformaldehyde solution.dissect in one block , the engrafted ovarian fat pad , ovary , uterine tube , 0.5 cm uterus as described in steps 1.1.1 - 1.1.4 . immediately place in 2 ml 4% paraformaldehyde and fix for 2 hr , at rt . from the same animal , dissect the non - engrafted contralateral ovarian fat pad system transplanted with pbs - basement membrane matrix mixture as a control ( see step 2.9 ) . fix and process in the same way.after fixation wash tissues three times with pbs for 5 min and incubate overnight in pbs at 4 c.for the whole - mount imaging of the ovarian fat pad proceed to step 3.2.1 . note : after the image acquisition tissues can be frozen ( 3.3.1 ) or processed for paraffin embedding ( 3.3.2 ) . overnight incubation in 30% sucrose in pbs at 4 c improves quality of frozen tissues . prepare 4% paraformaldehyde solution by mixing 26 ml ddh2o with 4 ml 10x pbs and 10 ml 16% paraformaldehyde solution . dissect in one block , the engrafted ovarian fat pad , ovary , uterine tube , 0.5 cm uterus as described in steps 1.1.1 - 1.1.4 . immediately place in 2 ml 4% paraformaldehyde and fix for 2 hr , at rt . from the same animal , dissect the non - engrafted contralateral ovarian fat pad system transplanted with pbs - basement membrane matrix mixture as a control ( see step 2.9 ) . after fixation wash tissues three times with pbs for 5 min and incubate overnight in pbs at 4 c . for the whole - mount imaging of the ovarian fat pad proceed to step 3.2.1 . note : after the image acquisition tissues can be frozen ( 3.3.1 ) or processed for paraffin embedding ( 3.3.2 ) . overnight incubation in 30% sucrose in pbs at 4 c improves quality of frozen tissues . image acquisition place whole - mount ovarian fat pad systems in pbs filled dishes and image using an inverted microscope equipped with epi - fluorescence attachment and high - definition color camera , with 4 , 10x objectives , and a stereomicroscope equipped with a fluorescence attachment , color camera and plan apo 1xwd70 , ed plan 1.5xwd45 objectives . place whole - mount ovarian fat pad systems in pbs filled dishes and image using an inverted microscope equipped with epi - fluorescence attachment and high - definition color camera , with 4 , 10x objectives , and a stereomicroscope equipped with a fluorescence attachment , color camera and plan apo 1xwd70 , ed plan 1.5xwd45 objectives . histology following whole - mount image acquisition ( 3.2.1 ) place a 200 - 500 l drop of embedding medium for frozen tissue specimens on a 2 x 1 cm piece of laboratory film and using forceps , transfer the tissue to the drop . pick up the film at one edge and transfer the tissue - medium drop to a 1.8 ml cryogenic vial . immerse tissues once in 65% ethanol for 30 min , shaking gently at rt.immerse tissues once in 70% ethanol for 30 min , shaking gently at rt . at this stage samples can be stored for months at rt.immerse tissues once in 90% ethanol for 30 min , shaking gently at rt.immerse tissues once in 95% ethanol for 30 min , shaking gently at rt.immerse tissues twice in absolute ethanol ( 200 proof ) for 30 min , shaking gently at rt.immerse tissues twice in chloroform for 30 min , shaking gently at rt.immerse tissues once in paraffin for 30 min , shaking gently at 58 c.immerse tissues once in paraffin for 12 hr , shaking gently at 58 c.immerse tissues once in paraffin for 3 hr , at 58 c.place tissues in metal histology molds and fill molds with 58 c paraffin . add a plastic histology cassette on top of the paraffin and cool down paraffin to + 4 c . note : paraffin temperature should not exceed 58 c for optimal preservation of tissue suitable for immunohistochemical staining . incubate at room temperature for 2 hr . in a water bath , preheat specimen processing gel to 60 c.pipette 200 l of the specimen processing gel onto a laboratory film - lined petri dish . using fine dissection forceps transfer the whole - mount tissue system to the specimen processing gel drop.allow the specimen processing gel plug to solidify at room temperature , or solidify the plug for 10 min at 4 c.place the specimen processing gel embedded tissue in histology tissue cassettes sandwiched between biopsy foam pads . note : specimen processing gel embedding prevents loss and allows preservation of small fragile tissue samples . note : tissues preserved by freezing or paraffin embedding are suitable for immunohistochemical staining . following whole - mount image acquisition ( 3.2.1 ) place a 200 - 500 l drop of embedding medium for frozen tissue specimens on a 2 x 1 cm piece of laboratory film and using forceps , transfer the tissue to the drop . pick up the film at one edge and transfer the tissue - medium drop to a 1.8 ml cryogenic vial . close the vial and plunge into liquid nitrogen . store frozen tissues at -80 c . immerse tissues once in 65% ethanol for 30 min , shaking gently at rt.immerse tissues once in 70% ethanol for 30 min , shaking gently at rt . at this stage samples can be stored for months at rt.immerse tissues once in 90% ethanol for 30 min , shaking gently at rt.immerse tissues once in 95% ethanol for 30 min , shaking gently at rt.immerse tissues twice in absolute ethanol ( 200 proof ) for 30 min , shaking gently at rt.immerse tissues twice in chloroform for 30 min , shaking gently at rt.immerse tissues once in paraffin for 30 min , shaking gently at 58 c.immerse tissues once in paraffin for 12 hr , shaking gently at 58 c.immerse tissues once in paraffin for 3 hr , at 58 c.place tissues in metal histology molds and fill molds with 58 c paraffin . add a plastic histology cassette on top of the paraffin and cool down paraffin to + 4 c . note : paraffin temperature should not exceed 58 c for optimal preservation of tissue suitable for immunohistochemical staining . immerse tissues once in 70% ethanol for 30 min , shaking gently at rt . at this stage samples can be stored for months at rt . immerse tissues twice in absolute ethanol ( 200 proof ) for 30 min , shaking gently at rt . place tissues in metal histology molds and fill molds with 58 c paraffin . add a plastic histology cassette on top of the paraffin and cool down paraffin to + 4 c . extract paraffin - tissue block and store at rt . note : paraffin temperature should not exceed 58 c for optimal preservation of tissue suitable for immunohistochemical staining . preheat specimen processing gel to 60 c.pipette 200 l of the specimen processing gel onto a laboratory film - lined petri dish . using fine dissection forceps transfer the whole - mount tissue system to the specimen processing gel drop.allow the specimen processing gel plug to solidify at room temperature , or solidify the plug for 10 min at 4 c.place the specimen processing gel embedded tissue in histology tissue cassettes sandwiched between biopsy foam pads . note : specimen processing gel embedding prevents loss and allows preservation of small fragile tissue samples . note : tissues preserved by freezing or paraffin embedding are suitable for immunohistochemical staining . pipette 200 l of the specimen processing gel onto a laboratory film - lined petri dish . using fine dissection forceps transfer the whole - mount tissue system to the specimen processing gel drop . allow the specimen processing gel plug to solidify at room temperature , or solidify the plug for 10 min at 4 c . place the specimen processing gel embedded tissue in histology tissue cassettes sandwiched between biopsy foam pads . embed in paraffin as in steps 3.3.2 - 3.3.2.10 . note : specimen processing gel embedding prevents loss and allows preservation of small fragile tissue samples . experimental cells and tissues can be accurately transplanted into the ovarian fat pad under a dissection microscope ( figure 1 ) . the examples include primary mouse tubal epithelium cells derived from mice ubiquitously expressing egfp ( figure 2a ) or dsred ( figure 2b ) and human immortalized ovarian surface epithelium cells hio118cells labeled with mcherry and egfp lentiviruses ( figure 2c - f ) . the approach is also applicable for long - term transplantation of organs , such as the mouse uterine tube ( figure 3 ) . according to immunohistochemical staining , both ciliated ( foxj1 positive ) and secretory ( pax8 positive ) cells are preserved in the tubal epithelium of transplanted tissues ( figure 3d and e ) . ( b ) an incision is made by a 28 g needle ( arrow ) . ( c ) ut / basement membrane matrix mixture engraftment by pipette tip ( arrow ) . ( d ) ut engrafted ( arrow , bright red , ut of -actin - dsred mice ) . figure 2 : detection of transplanted mouse primary tubal epithelium cells and human immortalized ovarian surface epithelium cells . ( a , b ) outgrowths of primary mouse tubal epithelium cells ( arrows ) of -actin - egfp mice ( a , green ) and -actin - dsred ( b , red ) 8 days after transplantation into a syngeneic mouse . ( c , d ) engraftments of mixed hio118 cells ( arrows ) labeled with either lenti - egfp ( green ) or lenti - mcherry ( red ) 10 days after transplantation into nsg mice . ( d ) enlarged area from ( c , arrow ) . ( e , f ) graft developed 43 days after transplantation of the same cells as in c , d to scid mouse ( arrows ) . a - d , f , fluorescence ; e , bright field , fp , fat pad ; ov , ovary ; ut , uterine tube . ( a , b , d - f ) scale bar = 500 m ; ( c ) scale bar = 1,600 m . figure 3 : characterization of uterine tube transplant.(a ) complete uterine tube ( arrow ) of -actin - dsred mouse 6 days after transplantation into the ovarian fat pad ( arrow , bright red ) . ( b ) fluorescent frozen section of the fat pad with transplant shown in ( a ) . ( c ) uterine tube graft ( arrow ) 40 days after transplantation into nsg recipient mouse ( arrow ) . paraffin section . note correct preservation of all principle uterine tube components , and lack of transplantation - associated fibrosis and inflammation . ( d , e ) detection of tubal epithelium markers paired - box gene 8 ( pax8 ) and forkhead box j1 ( foxj1 ; brown nuclear color , arrowheads ) in cells of the graft ( arrows ) shown in ( c ) . immunoperoxidase system . ( a ) scale bar = 1,000 m ; ( b ) scale bar = 200 m ; ( c - e ) scale bar = 100 m . table 1 : mouse tubal epithelim growth medium ( m - te - gm ) . components listed in the left column are dissolved in 1x dmem f12 ( ham 's ) medium at the indicated concentrations , right column . we have established an ovarian fat pad transplantation assay which allows for the accurate delivery and detection of epithelial cells and tissues . the ovarian fat pad assay transplantation procedure is less technically challenging than intrabursal injection and allows for more uniform and precise location of transplanted cells as compared to intraperitoneal injection . it is also well suited for long - term transplantation of an entire organ , such as the uterine tube . importantly , the ovarian fat pad provides a familiar microenvironment for epithelia of the female reproductive system . it should be particularly suitable for studies of the molecular and cellular properties of human and mouse ovarian and tubal epithelium cells during regeneration and malignant transformation . in contrast to other organs , few studies have focused on identification and characterization of stem cells in the epithelia of the female reproductive tract . such studies are of particular importance because many cancers are believed to originate from adult stem cells . epithelial ovarian cancers account for the majority of ovarian cancers and is in 5th place among all cancer related deaths of women in the us . thus development of an orthotopic assay with several advantages over the existing transplantation techniques should greatly facilitate studies in this area . given the superficial location of the ovarian fat pad , small animal imaging systems can be used to follow up on engraftments labeled with strong fluorescent or bioluminescent reporters . it also should be possible to establish minimally invasive high resolution live imaging assays , such as non - linear microscopy . the ovarian fat pad can also be kept in organ cultures , thereby allowing three - dimensional culture of normal and neoplastic epithelia under conditions closely recapitulating the organization of cells and the extracellular matrix . providing a heating pad and keeping rodents warm during surgery improves greatly the survival rate . sterility of instruments handling the fat pad ensures that the engrafted systems are kept sterile . in our experience , importantly , the fat pad incision should be made precisely because tearing the fat pad or puncturing it through causes bleeding . if engraftments do not develop , a higher concentration of injected cells should be considered . the first successful outgrowths can be observed as early as one week after the transplantation and most engraftments should be visible one month after the procedure . for transplantation , needles with larger diameter ( 23 - 25 g ) can be used to prevent shearing of large cells ( over 10 m in diameter ) . however , such needles may be more traumatic to the fat pad and their use should be tested in advance . for our experiments we have used 6 to 8 week old donor and recipient mice . for both purposes younger or the smaller size of ovarian fat pads in younger donors will also need to be considered . as with any methods , there are some limitations of the mouse ovarian fat pad transplantation assay . although syngeneic immuno - competent mice can be used for murine primary cells / tissues , our technique requires nsg or scid mice for transplantation of human material . it is likely possible to humanize the fat pad to support the growth of human epithelial cells . use of younger females may to lead to lower breeding costs ; however , mature virgin female mice ( age 8 to 10 weeks ) have a larger fat pad , thereby allowing transplantation of larger specimens . finally , laboratory personnel should be trained in animal surgery to ensure timely and successful execution of the procedure .

orthotopic transplantation assays in mice are invaluable for studies of cell regeneration and neoplastic transformation . common approaches for orthotopic transplantation of ovarian surface and tubal epithelia include intraperitoneal and intrabursal administration of cells . the respective limitations of these methods include poorly defined location of injected cells and limited space volume . furthermore , they are poorly suited for long - term structural preservation of transplanted organs . to address these challenges , we have developed an alternative approach , which is based on the introduction of cells and tissue fragments into the mouse fat pad . the mouse ovarian fat pad is located in the immediate vicinity of the ovary and uterine tube ( aka oviduct , fallopian tube ) , and provides a familiar microenvironment for cells and tissues of these organs . in our approach fluorescence - labeled mouse and human cells , and fragments of the uterine tube are engrafted by using minimally traumatic dorsal incision surgery . transplanted cells and their outgrowths are easily located in the ovarian fat pad for over 40 days . long - term transplantation of the entire uterine tube allows correct preservation of all principle tissue components , and does not result in adverse side effects , such as fibrosis and inflammation . our approach should be uniquely applicable for answering important biological questions such as differentiation , regenerative and neoplastic potential of specific cell populations . furthermore , it should be suitable for studies of microenvironmental factors in normal development and cancer .

in the case of non - spherical molecules the anisotropic nature of the intermolecular interactions can give rise to new phases ( liquid crystals ) @xcite that are absent when simple spherical molecules are considered . depending upon the shape and the size of molecules and upon the external parameters ( temperature , pressures , etc . ) a system may show a wide variety of phenomena and transitions in between the isotropic liquid and the crystalline solid . all these phases including that of the isotropic liquid and the crystalline solids are characterized by the average positions and orientations of molecules and by the intermolecular spatial and orientational correlations . the determination of phase diagram of such a system from the intermolecular potential is one of the most challenging problems of the statistical mechanics . the molecules of systems which exhibit liquid crystalline phases are generally large and have group of atoms with their own local features . in general it is difficult to know the true nature of the potential energy of interaction between such molecules . attempts have , however , been made to find the potential energy of interactions between two such molecules using different approximations . one such method is to sum the interatomic or site - site potentials between atoms or between interaction sites . in another and more convenient approach one uses rigid molecules approximation in which it is assumed that the intermolecular potential energy depends only on the position of the centre of mass and on their orientations . if , however , our interest is to relate the phases formed and their properties to the essential molecular factor responsible for the existence of liquid crystals , it is desirable to use a phenomenological description , either as a straightforward model unrelated to any particular physical systems or as a basis for describing by means of adjustable parameters between two molecules . most commonly used models are hard - ellipsoids of revolution , hard spherocylinders @xcite , cut - sphere , the kihara core model @xcite and the @xcite model . all these are single site models and refer to rigid molecules of cylindrical symmetry . even for these simple models calculating the complete phase diagram is difficult . the gay - berne potential , in particular , is proving to be a valuable model with which to investigate the behavior of liquid - crystals in recent years using computer simulation techniques @xcite . in this paper we consider a general gay - berne ( gb ) model with n-6 dependence on the shifted and scaled separation , r , between the uniaxial particles . u ( , , ) = 4 ( , , ) ( r^-n - r^-6 ) where @xmath2 while unit vectors @xmath3 indicate the orientations of symmetry axes of particles @xmath4 and @xmath5 , the orientation of the vector joining them is denoted by the unit vector @xmath6 . the dependence of the contact distance on the orientations of the particles and the interparticle vector is @xmath7^{-\frac{1}{2}}\ ] ] where @xmath8 is the contact distance for the cross configuration @xmath9 . the parameter @xmath10 is a function of the ratio @xmath11 , which is defined in terms of the contact distances when the particles are end - to - end ( e ) and side - by - side ( s ) , @xmath12 this vanishes for a sphere and tends to the limiting value of unity for an infinitely long rod . the orientational dependence of the potential well depth is given by a product of two functions , @xmath13 where the scaling parameter @xmath14 is the well depth for the cross configuration . the first of these functions @xmath15^{-\frac{1}{2}}\ ] ] clearly favours the parallel alignment of the particles and so aids liquid crystal formation . the second function has a form analogous to @xmath16 , _ i.e. _ @xmath17\ ] ] where the parameter @xmath18 is determined by the ratio of the well depths , @xmath19 , via @xmath20 the potential contains four parameters @xmath21 which determine the anisotropy in the repulsive and attractive forces , in addition to two parameters @xmath22 which scale the distance and energy , respectively . the ratio of the end - to - end and side - by - side contact distance , @xmath23 , is related to the anisotropy of the repulsive forces and it also determines the difference in the depth of the attractive well between the side - by - side and the cross configurations.the parameter @xmath24 is the ratio of the well depth for the side - by - side and end - to - end configurations . while @xmath23 determines the ability of the system to form an orientationally ordered phase , @xmath24 determines the tendency of the system to form a smectic phase @xcite.the other two parameters @xmath25 and @xmath26 influence nematic and smectic forming character of the anisotropic attractive forces in a more subtle way . in almost all of the simulation and theoretical studies to date n has been taken equal to 12 . the value of n defines the nature of the repulsion ; the higher the value of @xmath1 the harder is the nature of the repulsion . in fig.1 we plot @xmath27 as a function of separation for some fixed orientations with n=10 and 18 . it shows that as n increases the importance of attractive interaction increases for all orientations . in the present paper we investigate the effect of variation of n _ i.e. _ variation of the range of repulsion on the properties of molecular liquids and on its freezing transition . the paper is organized as follows : in sec.ii , we describe the solution of the ornstein- zernike equation using the percus yevick closure relation for pair correlation functions . section iii discusses the essential details of density functional formalism applied to study the freezing of molecular fluids into ordered phases . the results are given and discussed in section iv . the single particle density distribution @xmath28 defined as ( ) = ( , ) = _ i=1 ( -_i)(-_i ) where @xmath29 and @xmath30 give the position and the orientation of @xmath31 molecule , the angular bracket represents the ensemble average and the @xmath32 the dirac delta function , is constant independent of position and orientation for an isotropic fluid . it therefore contains no information about the structure of the system . the structural information of an isotropic fluid is contained in the two - particle density distribution @xmath33 which gives the probability of finding simultaneously a molecule in a volume element @xmath34 centered at @xmath35 and a second molecule in a volume element @xmath36 centered at @xmath37 . @xmath33 is defined as ( , ) ( _ 1 , _ 1 ; _ 2 , _ 2 ) = _ ij ( _ 1-_i)(_1-_i)(_2-_j ) ( _ 2-_j ) the pair correlation function @xmath38 is related to @xmath33 by the relation g ( , ) = since for the isotropic fluid @xmath39 where @xmath40 is the average number of molecules in volume @xmath41 , _ ( , _ 1 , _ 2 ) = ( , _ 1 , _ 2 ) where @xmath42 . in the isotropic phase @xmath33 depends only on the distance @xmath43 , the orientation of molecules with respect to each other and on the direction of vector @xmath44 is a unit vector along @xmath45 ) . the pair distribution function @xmath38 of the isotropic fluid is of particular interest as it is the lowest order microscopic quantity which contains informations about the translational and the orientational structures of the system and also has direct contact with intermolecular ( as well as with intramolecular ) interactions . for an ordered phase , on the other hand , most of the structural informations are contained in @xmath46 ( see sec . the values of the pair correlation functions as a function of intermolecular separation and orientations at a given and pressure are found either by computer simulations or by solving the ornstein - zernike equation @xmath47 d\bs \end{aligned}\ ] ] where @xmath48 and @xmath49 and @xmath50 are , respectively , the total and direct pair correlation functions , using a suitable closure relation . most commonly used closer relations are the ( py ) and the hyper netted chain ( hnc ) relations . approximations are introduced through these closure relations . the py and hnc integral equation theories are given by the oz equation coupled with the closure relation @xcite c^py ( , ) = f ( , ) [ 1 + ( , ) ] and c^hnc ( , ) = h ( , ) - -u ( , ) respectively . here @xmath51 - 1 $ ] and @xmath52 . both the py and hnc integral theories have been used to find the pair - correlations functions of model fluids of non - spherical molecules @xcite . it is found that while the py theory underestimates the correlations , particularly the angular correlation while the hnc theory overestimates them . in case of hard - core fluids we proposed a mixed integral equation which interpolates between the hnc and py theories and is thermodynamically consistent @xcite . such an approach is needed for the soft - core potential the one considered in this paper also . we , however , defer this approach for the future and confine ourselves here to solve the py equation to get the pair correlation functions for the gb(n-6 ) potential . the angle dependent function @xmath53 ( where a may be pair correlation function or pair potential ) is expanded in a basis set of rotational invariants @xcite in space fixed ( sf ) frame according to the equation @xmath54 where @xmath55 are the clebsch - gordon coefficients . for fully axially symmetric particles it is also possible to expand the function in products of spherical harmonics in body fixed ( bf ) frame according to the equation . @xmath56 where @xmath57 . numerically it is easier to calculate the bf harmonic coefficients than the sf harmonic coefficients . the two harmonic coefficients are related through a linear transformation , @xmath58 or @xmath59 in any numerical calculation we can handle only a finite number of the spherical harmonic coefficients for each orientation - dependent function . the accuracy of the results depends on this number . as the anisotropy in the shape of molecules ( or in interactions ) and the value of fluid density @xmath60 increases more harmonics are needed to get proper convergence . we have found that the series get converged if we truncate the series at the value of @xmath61 indices equal to 6 for molecules with @xmath62 @xcite . though it is desirable to include higher order harmonics _ i.e. _ for @xmath63 but it will increase computational time many fold . our interest is to use the data of the harmonics of pair correlation functions for freezing transitions where only low order harmonics are generally involved ( see sec . iii below ) . the only effect the higher - order harmonics appear to have on these low - order harmonics is to modify the finer structure of the harmonics at small values of @xmath64 whose contributions to the structural parameters ( to be define below ) are negligible . using the numerical procedure outlined elsewhere @xcite , we have solved the py equation for the gb(n-6 ) fluid having @xmath1 values 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 , 28 and 30 for @xmath65 and well depth ratio @xmath66 at reduced temperatures , @xmath67 and @xmath68 for a wide range of densities . the other two parameters @xmath25 and @xmath26 are taken to be @xmath69 and @xmath70 , respectively . the solutions could be found only upto certain density @xmath71 the value of which depend upon the and the value of @xmath1 . the value of @xmath71 is often close to the isotropic - nematic transition . because of this one faces problems in locating other less symmetric phases of the system using the theory to be discussed in sec . iii . in fig.2 we compare the values of @xmath72 in bf frame at @xmath73 and density @xmath74 for four sets of ( n-6 ) combinations . it is seen from this figure that the first peak becomes sharper and attains its maximum value at smaller value of @xmath75 as the hardness of the core increases . the cause of this becomes clear if we look at figs.3 and 4 which depict @xmath76 ] as a function of interparticle separation at @xmath77 , respectively . @xmath78 may be regarded as an averaged pair potential and , therefore , helps us in understanding the features of @xmath79 . @xmath78 seems to have two minimum ; one at @xmath80 and other at @xmath81 . the first minimum becomes deeper at higher @xmath1 and at lower and almost vanishes at lower @xmath1 and higher temperatures . the second minimum dependence on @xmath1 ( as well as on ) is weak . one may also note the shift to lower values of @xmath82 of first minimum as @xmath1 is increased . since the py theory is known to be reasonably accurate for systems interacting via pair potential which has hard repulsive core @xmath83 and weak attraction @xcite , the values of the pair correlation functions reported here are expected to be more accurate for higher values of @xmath1 and lower values of @xmath84 compared to values corresponding to lower @xmath1 and higher @xmath84 . in figs.5 - 6 we compare the two other projections of pcf in bf- frame at the same state conditions and observe similar behavior . in fig.7 we compare the value of @xmath79 at @xmath85 for gb(10 - 6 ) model at four different temperatures . here we see that the first peak gets sharper as the temperature decreases . such behavior is also seen ( see fig . 2 ) when @xmath1 is increased at the same temperature . this is due to increasing tendency of the molecules to form parallel configurations . as has already been mentioned , the py theory underestimates the molecular correlations . this can be seen from the pressure calculated using the values of the direct pair correlation function through the compressibility relation which is found to be lower than the simulated value as shown in fig.8 . for a system consisting of axially symmetric non - dipolar molecules the static kerr constant @xmath86 is given by @xcite k = ^-1 _ where @xmath87 is structural parameter defined as in eq.(3.22 ) and @xmath88 is a constant dependent only upon single particle properties . the divergence of @xmath86 may signal the absolute stability limit of the isotropic phase relative to orientationally ordered phase @xcite . thus the isotropic phase becomes orientationally unstable when the inverse kerr constant @xmath89 . it is , however , important to emphasize that the condition @xmath89 does not determine the thermodynamic phase transition , but rather a point on the spinodal line . this means that the density at which @xmath90 establishes a stability limit in the sense that at higher densities the isotropic phase can not exist even as a metastable state . _ the reduced kerr constants @xmath91 as a function of @xmath92 for the various @xmath1 values are plotted in figs . 9 & 10 at @xmath93 and @xmath68 . the structural informations of fluids at the level obtained above can be used to obtain information about their freezing . at the freezing point the spatial and orientational configurations of molecules undergo a modification . often abrupt change in the symmetries of the system takes place on the freezing . in contrast to the isotropic fluid , the molecular configurations of most ordered phases are adequately described by the single particle density ( singlet ) distribution @xmath94 provides us with a convenient quantity to specify an arbitrary state of a system . one may consider a variational thermodynamic potential as a functional of @xmath46 . the equilibrium state of the system at given @xmath95 and @xmath96 is described by the density @xmath97 corresponding to the minimum of the thermodynamic potential with respect to @xmath46 . this forms the basis of the density functional theory . in this article we investigate the freezing of the gb(n-6 ) fluid into the nematic and the smectic a ( sm a ) phases using density functional theory ( dft ) . in the nematic phase the full translational symmetry of the isotropic fluid phase ( denoted as @xmath98 ) is maintained but the rotational symmetry @xmath99 or @xmath100 ( depending upon the presence or absence of the centre of symmetry ) is broken . in the simplest form of the axially symmetric molecules the group @xmath99 ( or @xmath100 ) is replaced by one of the uniaxial symmetry @xmath101 ( or @xmath102 ) . the phase possessing the @xmath103 ( denoting the semi direct product of the translational group @xmath98 and the rotational group @xmath101 ) symmetry is known as uniaxial nematic phase @xcite . the smectic liquid crystals , in general , have a stratified structure with th long axes of molecules parallel to each other in layers . this situation corresponds to partial breakdown of translational invariance in addition to breaking of the orientational invariance . since a variety of molecular arrangement are possible within each layer , a number of smectic phases are possible @xcite . the simplest among them is the sm a phase . in it the centre of mass of molecules in a layer are distributed as in a two - dimensional fluid but the molecular axes are on the average along a direction normal to the smectic layer ( _ i.e. _ the director @xmath104 is normal to the smectic layer ) . the symmetry of the sm a phase is @xmath105 where @xmath106 corresponds to a two - dimensional liquid structure and @xmath107 for a one - dimensional periodic structure . the order parameters which characterize the ordered structures can be found from the singlet distribution @xmath108 . for this we express it in the fourier series and the wigner rotation matrices . thus ( * x * ) = ( , ) = _ 0 _ q _ lmn q_lmn ( g_q ) ( i*g*_q . ) d^l_mn ( ) where the expansion coefficients q_lmn(g_q ) = dd ( , ) ( -i*g*. ) d^l*_mn ( ) are the order parameters , @xmath109 the reciprocal lattice vectors , @xmath110 the mean number density and @xmath111 the generalized spherical harmonics or wigner rotation matrices @xcite . since we are interested in uniaxial systems of cylindrically symmetric molecules , @xmath112 in eqs.(3.1 ) & ( 3.2 ) . this leads to ( , ) = _ 0 _ l _ q q_lq ( i*g*_q . ) p_l ( ) and q_lq = dd ( , ) ( -i*g*. ) p_l ( ) where @xmath113 is the legendre polynomial of degree @xmath61 and @xmath114 is the angle between the cylindrical axis of a molecule and the director . since in the nematic phase the centres of mass of molecules are distributed as randomly as in the isotropic fluid but the molecular axes are aligned along a particular direction defined by the director @xmath115 ( a unit vector ) we have @xmath116 and q_l0 = ( 2l+1 ) p_l(())= ( 2l+1)|p_l where angular bracket indicates the ensemble average . it is often enough to use two orientational order parameters @xmath117 and @xmath118 to locate the isotropic - nematic transition as in almost all known cases the transition is weak first - order transition @xcite . to characterize the sm a phase we need three different class of order parameters ; ( i ) orientational , ( ii ) positional , ( iii ) mixed . these parameters are found from eq.(3.2 ) . for the orientational order we take @xmath117 and @xmath118 as in case of the nematic phase . for the positional order along the z - axis we choose one order parameter corresponding @xmath119 , @xmath120 being the layer spacing . thus = q_00(g_z ) = ( ) the coupling between the positional and orientational ordering is described by the ( mixed ) order parameter @xmath121 defined as = q_20(g_z ) = ( ) p_2 ( ) we therefore choose four order parameters to describe the ordering in a sm a phase and two for the nematic ordering . another way of writing the trial singlet distribution corresponding to the ordered phases of our interest is ( , ) = a_0 _ 0 where @xmath122 is a normalization constant , @xmath123 and @xmath124 are associated with the formation of layer in the sm a phase and @xmath125 and @xmath126 with orientational ordering . when @xmath127 and @xmath128 are zero but @xmath125 and @xmath126 are non zero the phase is nematic . in case of the isotropic fluid all the four parameters @xmath127 , @xmath128 , @xmath125 and @xmath126 are zero . if all the four parameters are non zero the phase is sm a. the four order parameters defined above can be found taking the expression of @xmath129 given by eq.(3.8 ) . thus & = & _ 0^d dz ( ) _ 0 ^ 1 dx ( s ) + & = & _ 0^d dz ( ) _ 0 ^ 1 dx ( s ) p_2(x ) + @xmath130 in the usual aapproach one uses the grand thermodynamic potential to locate the transition . the grand thermodynamic potential is defined as @xmath131 where a is the helmholtz free energy , @xmath25 the chemical potential and @xmath46 is a singlet distribution function . eq.(3.1 ) can be written as @xmath132 where @xmath133 is the grand thermodynamic potential of the isotropic fluid , and @xcite . @xmath134 - \delta \rho({\bf r } , { \bf \omega})}\right\ } \\ { \rm and } \nonumber \\ \frac{\delta w_2}{n } & = & -\frac{1}{2\rho_f } \int { d\bf r_{12 } } { d\bf \omega_1}{d\bf \omega_2}\delta\rho({\bf r_1 } , { \bf \omega_1 } ) c({\bf r_{12 } } , { \bf \omega_1 } , { \bf \omega_2})\delta\rho({\bf r_2 } , { \bf \omega_2 } ) \end{aligned}\ ] ] here @xmath135 , where @xmath60 is the density of the coexisting liquid . the ordered phase density is found by minimizing @xmath136 with respect to arbitrary variations in the ordered phase density subject to the constraint which corresponds to some specific features of the ordered phase . thus , @xmath137 where @xmath138 is lagrange multiplier which appears in the equation because of constraint imposed on the minimization . one attempts to find solution of @xmath46 of eq.(3.17 ) which have symmetry of the ordered phase . these solutions , inserted in eq.(3.14 ) give the grand thermodynamic potential difference between the ordered and liquid phases . the phase with the lowest grand potential is taken as the stable phase . phase coexistence occurs at the value of @xmath60 which makes @xmath139 for the ordered and liquid phases . substituting eq.(3.1 ) , into eq.(3.17 ) and eq.(3.14 ) and integrating results in , respectively @xmath140\ ] ] and @xmath141 where @xmath142 are the structural parameters related to the fourier transformed direct correlation function of the fluid phase . eq.(3.18 ) is the expression for the order parameters . this version of the is known as the second order density functional ( sodft ) because it considers only the and neglects the higher order correlations which might be present in the system at the transition point . in another version of the density functional approach in which higher order correlations are included and known as modified weighted density approximation @xcite , one uses the helmholtz free energy to locate the transition . for the helmholtz free energy we write a [ ( , ) ] = a_id [ ( , ) ] + a_ex [ ( , ) ] where both terms in eq.(3.23 ) are unique functionals of the one - particle density @xmath129 . the first term in the right hand side of eq.(3.23 ) is a non uniform ideal gas contribution of the form a_id [ ( , ) ] = ^-1_v dd ( , ) \{- 1 } where @xmath143 is the thermal de broglie wavelength . the second term in the right hand side of eq.(3.23 ) is the excess helmholtz free energy of the non uniform system . in the modified weighted - density approximation the excess free energy of a uniform system , but evaluated of a weighted density @xmath144 @xcite a^mwda_ex [ ] = n _ 0 ( ) where @xmath145 is the number of particles in the system @xmath146 is the excess free energy per particle of a uniform system at density @xmath147 . the weighted density @xmath148 is constructed from the actual inhomogeneous one - particle density @xmath46 and is defined by = _ v d*x*(*x*)_v d*x* ( * x*)(*x*-*x* ; ) introducing thereby the weighted function @xmath149 . it is an essential ingredient of the mwda that the weighted function @xmath150 which is used to determine the weighted density , depends itself on the sought function @xmath148 ; thus eq.(3.26 ) has to viewed as a self - consistency condition for the determination of the weighted density . to ensure that the approximation in the determination of @xmath148 becomes exact in the uniform limit , the weighted function has to be normalized , _ i.e. _ , d*x * ( * x*-*x* ; ) = 1 for any @xmath148 . the function @xmath150 can be then uniquely specified by requiring that the approximate functional @xmath151 $ ] is exact upto second order in the functional expansion , namely c(*x*-*x*;_0 ) = -__0 the conditions [ eqs.(3.25 - 3.28 ) ] result in a particularly simple expression for @xmath150 , namely ( * x*-*x* ; ) = -where @xmath41 is the volume of the sample , @xmath152 is the excess free energy per particle of an isotropic fluid of density @xmath148 and primes on @xmath152 indicate derivatives with respect to density . using expansion ( eq . 3.1 ) and ( eq.2.8 ) , respectively for @xmath46 and @xmath153 we find for the ordered phase @xmath154 -\rho_0{\hat \rho}\frac{\phi_0^{''}({\hat \rho})}{2\phi_0^{'}({\hat \rho})}\end{aligned}\ ] ] having computed @xmath148 , the next step in freezing analysis is to substitute @xmath148 into eq.(3.25 ) to compute @xmath155 . in terms of structural parameter , the excess free energy per particle of a uniform system at a density @xmath147 is given as _ 0 ( ) = -_0^ d _ 0^ c^0_00[ ] d the ideal gas part is calculated using the ansatz for @xmath129 given by eq.(3.8 ) . thus @xmath156 & = & \rho_0 \int d\br \sum_l \sum_q \frac{q_{lq}}{\sqrt { 2l+1 } } e^{i{\bf g}_q.\br } [ \{\ln(a_0\rho_0\lambda^3)-1\ } \delta_{l0 } -\alpha(z - x_0)^2\frac{\delta _ { 2l}}{\sqrt 5 } \nonumber \\ & & + \frac{\lambda_2\delta_{2l}}{\sqrt 5 } + \frac{\lambda_4\delta_{4l } } 3 - \alpha^1(z - x_0)^2 \delta_{l0 } ] \end{aligned}\ ] ] to determine the transition parameters , we first compute the effective density @xmath148 from eq.(3.30 ) and minimizing the free energy from eqs.(3.23 , 3.31 and 3.32 ) with respect to @xmath157 . in order to determine the transition density of the coexisting isotropic @xmath158 and anisotropic @xmath159 phases it is necessary to equate the pressure and chemical potentials ( maxwell construction ) of the two phases . we have used both versions of the density functional methods described above to locate the freezing transitions and calculate the values of the freezing parameters . the structural parameters defined by eq.(3.22 ) which appear in the as the input data are obtained from the harmonics of the direct evaluated using the py integral equation theory ( given in sec . ii ) . using these values of the structural parameters and the four order parameters @xmath160 we have solved eqs.(3.18 - 3.19 ) of the sodft and eqs.(3.23 - 3.32 ) of the mwda for the gb(n-6 ) fluid with @xmath0 for temperatures lying between @xmath161 to @xmath68 . all our results correspond to @xmath162 . our results show that for none of the cases studied here sm a phase gets stabilized . in the low temperature region for a given @xmath1 it , however , appeared as a metastable state having free energy lower than that of the isotropic phase but higher than the nematic ( see table i ) . since we have not included sm b and crystalline phases in our investigation for the reason already given , we found only the isotropic - nematic transition . for each @xmath1 we found a lower cut - off of the for the existence of the nematic phase . the nematic phase was not found to exist below this temperature . the lower cut - off for the nematic phase is found to increase with @xmath1 . for example , where for @xmath163 we found the nematic phase to exist at @xmath164 but not for @xmath165 . the computer simulation results of miguel _ et al _ @xcite show that for @xmath166 the cut - off is slightly above @xmath167 . our results , however , show that the nematic phase exists at @xmath167 . this may be due to error in the structural parameters values found from the py theory . both versions of the give similar results for the transition density @xmath168 but give the values of the order parameters including the change in density at the transition which are different from each other . more surprising is the way the values of the order parameters @xmath117 and @xmath118 vary with and with @xmath1 ( see tables ii - v ) found from the two version of the theory . while the sodft predicts that @xmath117 and @xmath118 decrease as the transition is increased , the mwda predicts them to increase . the computer simulation results @xcite do not give any clear indication as how these parameters vary with transition temperature . similar difference in the variation of the values of the order parameters with @xmath1 is also found . in table ii - v we give the values of the transition parameters found from the two theories . we also give the results found from the computer simulations at @xmath169 for @xmath170 . there is very good agreement between these results at @xmath171 . the transition density found from the theories are identical though somewhat higher than the value found from the simulation . the value of @xmath172 found from these methods are also in good agreement , though mwda predicts the value of @xmath172 which is lower than the sodft as well as simulation value . pressure and chemical potentials are in good agreement . but there is difference in the value of @xmath117 and @xmath118 . at @xmath173 both theories predict the transition density which is high compared to the md value . one of the possible reasons for this is , as pointed out in sec . ii , the inaccuracy in the values of c - harmonics at higher temperature . the py theory is known to underestimate the angular correlations and this defect of the py theory becomes more pronounced as is increased for a given @xmath1 . this may be the reason why the theory predicts the transition at higher density than the md value . as a consequence of this the transition pressure and the chemical potential are also substantially higher than the md values . this comparison at @xmath174 show that while the dft is good to predict the freezing parameters , the py values of structural parameters at higher are lower than the actual values . we hope to combine the py and hnc theories to generate accurate values of the harmonics of the and with these values to compute the full phase diagram . the work was supported by the department of science and technology ( india ) through project grant . one of us ( rcs ) thanks the director and management for providing some computational facility at miet . de gennes and j. prost , _ the physics of liquid crystals _ ( clarendon , oxford,1993 ) d. frenkel , j. phys . chem . * 91 * , 4912(1987 ) ; * 92 * , 3280(1988 ) t. kihara , _ intermolecular forces _ ( wiley , 1976 ) j. g. gay and b. j. berne , j. chem phys . * 74 * , 3316 ( 1981 ) e.d.miguel , l.f . rull , m.k . chalam , k.e . gubbins and e.v . swol , mol . phys . * 72 * , 593(1991 ) e.d.miguel , l.f . rull , m.k . chalam and k.e . gubbins , mol . * 74 * , 405(1991 ) m.a . bates and g.r . luckhurst , j. chem . phys . * 110 * , 7087(1999 ) j.p . hansen and i.r . mcdonald , _ theory of simple liquids _ ( academic press , london , 1976 ) ; c.g . gray and k.e . gubbins , _ theory of molecular fluids _ , vol . 1(clarendon , oxford , 1984 ) j. ram and y. singh , phys . a * 44 * , 3718 ( 1991 ) ; j. ram , r.c . singh and y. singh , phys . e * 49 * , 5117(1994 ) a. perera , p.g . kusalik and g.n . patey , j. chem . phys . * 87 * , 1295(1987 ) r.c . singh , j. ram and y. singh , phys . rev . e*54 * , 977(1996 ) a. perera , p.g . kusalik and g.n . patey , mol . phys.*60 * , 77(1987 ) s. kielich , _ dielectric and related molecular process _ ( chemical society of london , london , 1972 ) vol . 1 , chapt . 7 y. singh , phys . rep . * 207 * , 351 ( 1991 ) m.e . rose , _ elementary theory of angular momentum_(wiley , new york , 1957 ) a. r. denton and n. w. ashcroft , phys . a * 39 * , 426 , 4701 ( 1989 ) cccccccc @xmath168 & phase & @xmath175 & @xmath117 & @xmath118 & @xmath176 & @xmath177 & @xmath136 + + 0.293 & sm - a & 0.674 & 0.891 & 0.719 & 0.687 & 0.098 & -0.023 + & nematic & 0.000 & 0.843 & 0.562 & 0.000 & 0.058 & -0.093 + + 0.306 & sm - a & 0.647 & 0.888 & 0.741 & 0.677 & 0.088 & -0.157 + & nematic & 0.000 & 0.903 & 0.654 & 0.000 & 0.063 & -0.243 + + 0.312 & sm - a & 0.629 & 0.887 & 0.750 & 0.667 & 0.083 & -0.234 + & nematic & 0.000 & 0.923 & 0.691 & 0.000 & 0.065 & -0.333 ccccccccc potential model & theory & @xmath168 & @xmath178 & @xmath177 & @xmath117 & @xmath118 & @xmath179 & @xmath180 + + ( 8,6 ) & dft & 0.428 & 0.431 & 0.006 & 0.69 & 0.40 & 9.48 & 26.79 + & mwda & 0.412 & 0.416 & 0.009 & 0.56 & 0.27 & 7.77 & 22.71 + + ( 10 , 6 ) & dft & 0.29 & 0.301 & 0.038 & 0.72 & 0.41 & 1.30 & 3.96 + & mwda & 0.286 & 0.29 & 0.013 & 0.36 & 0.12 & 1.22 & 3.69 + ccccccccc potential model & theory & @xmath168 & @xmath178 & @xmath177 & @xmath117 & @xmath118 & @xmath179 & @xmath180 + + ( 10 , 6 ) & dft & 0.341 & 0.346 & 0.015 & 0.68 & 0.37 & 3.81 & 12.44 + & mwda & 0.339 & 0.341 & 0.007 & 0.40 & 0.15 & 3.71 & 12.16 + + ( 12 , 6 ) & dft & 0.282 & 0.295 & 0.046 & 0.74 & 0.43 & 1.38 & 4.11 + & mwda & 0.277 & 0.281 & 0.015 & 0.36 & 0.12 & 1.27 & 3.69 + + ( 14 , 6 ) & dft & 0.239 & 0.277 & 0.158 & 0.92 & 0.62 & 0.58 & 0.65 + & mwda & 0.237 & 0.241 & 0.019 & 0.27 & 0.08 & 0.55 & 0.54 + ccccccccc potential model & theory & @xmath168 & @xmath178 & @xmath177 & @xmath117 & @xmath118 & @xmath179 & @xmath180 + + ( 10 , 6 ) & dft & 0.381 & 0.385 & 0.009 & 0.68 & 0.38 & 8.26 & 25.63 + & mwda & 0.379 & 0.382 & 0.007 & 0.46 & 0.20 & 8.04 & 25.04 + + ( 12 , 6 ) & md & 0.308 & 0.314 & 0.019 & 0.50 & - & 3.50 & 12.70 + & dft & 0.322 & 0.328 & 0.02 & 0.67 & 0.37 & 3.40 & 11.28 + & mwda & 0.322 & 0.325 & 0.008 & 0.37 & 0.13 & 3.40 & 11.28 + + ( 14 , 6 ) & dft & 0.287 & 0.299 & 0.042 & 0.74 & 0.43 & 1.82 & 5.66 + & mwda & 0.283 & 0.288 & 0.017 & 0.37 & 0.12 & 1.69 & 5.21 + + ( 16 , 6 ) & dft & 0.261 & 0.283 & 0.085 & 0.82 & 0.51 & 1.06 & 2.59 + & mwda & 0.245 & 0.251 & 0.027 & 0.36 & 0.12 & 0.82 & 1.64 + ccccccccc potential model & theory & @xmath168 & @xmath178 & @xmath177 & @xmath117 & @xmath118 & @xmath179 & @xmath180 + + ( 10 , 6 ) & dft & 0.454 & 0.456 & 0.005 & 0.72 & 0.44 & 26.93 & 72.59 + & mwda & 0.435 & 0.437 & 0.005 & 0.62 & 0.30 & 21.26 & 59.84 + + ( 12 , 6 ) & md[5 ] & 0.323 & 0.331 & 0.025 & 0.50 & - & 5.70 & 20.90 + & dft & 0.378 & 0.382 & 0.009 & 0.68 & 0.38 & 10.90 & 34.27 + & mwda & 0.375 & 0.378 & 0.007 & 0.47 & 0.21 & 10.42 & 32.99 + + ( 14 , 6 ) & dft & 0.344 & 0.349 & 0.014 & 0.68 & 0.38 & 6.57 & 21.88 + & mwda & 0.343 & 0.346 & 0.009 & 0.44 & 0.20 & 6.52 & 21.71 + + ( 18 , 6 ) & dft & 0.306 & 0.315 & 0.028 & 0.72 & 0.41 & 3.43 & 11.52 + & mwda & 0.303 & 0.307 & 0.014 & 0.41 & 0.18 & 3.25 & 10.95 + + ( 24 , 6 ) & dft & 0.273 & 0.291 & 0.065 & 0.79 & 0.49 & 1.81 & 5.35 + & mwda & 0.267 & 0.274 & 0.026 & 0.37 & 0.13 & 1.65 & 4.78 + + ( 30 , 6 ) & dft & 0.249 & 0.283 & 0.137 & 0.90 & 0.61 & 1.11 & 2.38 + & mwda & 0.242 & 0.248 & 0.027 & 0.34 & 0.11 & 0.99 & 1.90 +

we have calculated the pair correlation functions of a fluid interacting via the gay - berne(n-6 ) pair potentials using the integral equation theory and have shown how these correlations depend on the value of n which measures the sharpness of the repulsive core of the pair potential . these results have been used in the density - functional theory to locate the freezing transitions of these fluids . we have used two different versions of the theory known as the second - order and the modified weighted density - functional theory and examined the freezing of these fluids for @xmath0 and in the reduced temperature range lying between 0.65 and 1.25 into the nematic and the smectic a phases . for none of these cases smectic a phase was found to be stabilized though in some range of temperature for a given @xmath1 it appeared as a metastable state . we have examined the variation of freezing parameters for the isotropic - nematic transition with temperature and @xmath1 . we have also compared our results with simulation results wherever they are available . while we find that the density - functional theory is good to study the freezing transitions in such fluids the structural parameters found from the theory need to be improved particularly at high temperatures and lower values of @xmath1 .

Romney and Cain closely matched near 20%, with Perry at 15% PRINCETON, NJ -- Republicans' support for Herman Cain has surged to 18%, their support for Rick Perry has sagged to 15%, and their support for Mitt Romney remains relatively stable at 20%. However, Romney's support is matched by the 20% of Republicans who are unsure which candidate they will back for the Republican nomination in 2012. Gallup's Oct. 3-7 update of Republicans' preferences for their party's 2012 presidential nominee shows that Romney since mid-September has regained a numerical lead over the rest of the field, mainly because Perry's support has dropped by half over the same period. At the same time, support for Cain has more than tripled, from 5% to 18%, creating a competitive three-way race for the nomination between Romney, Cain, and Perry -- all within five percentage points of each other. Prior to now, Gallup has had Romney out front, Perry out front, or a two-way battle between them. Also of note in the new results are Ron Paul's return to single-digit support levels, and the failure of Michele Bachmann, Newt Gingrich, Rick Santorum, and Jon Huntsman to make significant gains. Republicans Have Historically Nominated Early Front-Runners Republicans' current lack of consensus about who should face President Barack Obama next fall is in stark contrast to Republican primary contests over the past half century in which, in all but one case, the eventual nominee was the runaway leader by this point in the campaign. For instance, in early October 1999, George W. Bush led the Republican field, with 60% of Republicans preferring him for the 2000 nomination. Bob Dole led at a comparable point in 1995 with 46%, George H.W. Bush in 1987 with 41%, Ronald Reagan in 1979 with 41% (in a trial heat that did not include former President Gerald Ford), and so on back to Richard Nixon in 1959, when he led with 67%. The exception occurred in 2007, when the eventual Republican nominee, John McCain, was drawing just 16% support in early October, putting him in third place behind Rudy Giuliani (32%) and Fred Thompson (20%) for the 2008 nomination. Republicans in 2011 Are Following Democrats' Primary Pattern Republican trial-heat trends show that there has been a strong front-runner by this point in the campaign -- three to four months before the first primaries are held. In contrast, the Democratic fields in past elections tended to be more competitive, and thus may provide a better point of comparison for interpreting today's fractured Republican field. In the 10 presidential elections since 1960 that involved a competitive Democratic primary campaign, the Democrat with a significant lead in October of the year before the election won the nomination in only 2 cases: sitting Vice President Al Gore in 1999, with a 12-point lead over Bill Bradley, and former Vice President Walter Mondale in 1983, with a 19-point lead over John Glenn. In the remaining eight elections, the eventual front-runner's position at this point was tied for first (John F. Kennedy in 1959), second (Barack Obama in 2007 and Michael Dukakis in 1987), third (Hubert Humphrey in 1967), fourth (John Kerry in 2003 and George McGovern in 1971), sixth (Bill Clinton in 1991), or ninth (Jimmy Carter in 1975). In several cases (1991, 1971, and 1967), the Democrat leading at this point was someone who ultimately did not seek the nomination; however, in many cases (2007, 2003, 1991, 1987, 1975, 1971, and 1967), the eventual nominee still trailed one or more active candidates. Bottom Line Romney and Cain currently lead in Republicans' preferences nationally for the 2012 GOP presidential nomination. However, their 20% and 18% support levels, respectively, are well below where most previous Republican nominees stood in October of the year prior to the election. Today's Republican lineup is more akin to the history of Democratic primary campaigns than Republican campaigns. And it may be instructive to note that the Democrats' eventual nominees often ranked second or lower at this stage leading up to the election year. Of course, the media, political climate, and political system are quite different today from decades past, so the opportunity for candidates with lower support to surge into the lead as a result of early primary (or state party convention or caucus) wins may not be as great as it once was. In the meantime, Gallup is seeing plenty of surging and plunging of candidates as a result of the media exposure they are receiving from the Republican straw polls and debates. Given that, and the still-sizable percentage of Republicans who are undecided, history suggests the race may remain fluid for some time. Track every angle of the presidential race on Gallup.com's Election 2012 page. ||||| Mitt Romney's affection for Herman Cain has been well documented, at POLITICO and elsewhere. Romney took it to the next level at a New Hampshire town hall this evening. "We each have our own experiences, he’s a great guy. Vote for either one of us and you’ll be happy," Romney said, per POLITICO's Reid Epstein. Romney also called Cain a "terrific guy" and said voters should "give him a good look." That's not something Romney would say about a candidate he views as a real threat, and it's a reminder of how much Cain's rise has been mutually beneficial to both him and Romney.

– It’s not a hoax or a dream: Herman Cain really has surged to the upper echelon in GOP primary polls. Cain more than tripled his support in Gallup’s October poll, jumping from 5% in September to 18%, just a hair behind Mitt Romney’s 20%. Rick Perry, meanwhile, plummeted from 31% to 15%. The result is roughly in line with last week’s polls showing Cain’s surge. The rest of the candidates were all in the single digits. The tumult is unusual for Republicans, who have historically (with the exception of John McCain in 2008) picked a frontrunner early and stuck with him, Gallup notes. And given that a whopping 20% of the field is still undecided, “the race may remain fluid for some time." Romney for one plainly isn’t worried by Cain’s rise—last night he told a crowd in New Hampshire that Cain was a “terrific guy” and that they should “give him a look,” Politico reports. “Vote for either one of us and you’ll be happy."

dislocation is seen in 10% of the carpal bone injuries and occurs after high energy trauma while the wrist is in hyperextension.1 they tend to occur in young working age men.1 the perilunate injury was divided into four stages with a cadaveric study.2 the lunotriquetral ligament disruption and displacement of lunate are seen in stage 3 perilunate injury . the lunate is displaced dorsal while its articular surface with distal radius is normal or near - normal ( perilunate dislocation ) [ figure 1a ] . complete ligament disruption and volar dislocation of the lunate through the space of poirier are seen in stage 4 perilunate injury . the radiolunate articulation is disrupted ( lunate dislocation ) [ figure 1b ] . even though we can not see these images in antero - posterior ( ap ) x - ray , it helps us confirm whether there is a fracture ( e.g. styloid and carpal fractures ) . x - ray ( lateral view ) of wrist joint showing ( a ) stage 3 perilunate injury . ( b ) stage 4 perilunate injury radiological diagnosis is important and the lateral x - ray plays a key role . normally , the angle is between 30 and 60. if this angle exceeds 70 , there is said to be a scapholunate dissociation.2 the treatment choices for perilunate and lunate dislocations are closed reduction and casting , open reduction - internal fixation - ligament repair , trapeziolunate external fixation , limited wrist arthrodesis and proximal row carpectomy.1 closed reduction ( under appropriate anaesthesia ) and casting are recommended in the treatment of acute perilunate and lunate dislocations to prevent the increase of edema and to decrease neurovascular complications . if reduction is successful then the definitive treatment ( open surgery and internal fixation ) might be delayed otherwise these cases should undergo an emergency open reduction and internal fixation . this treatment is adopted from the treatment of fractures and ligament injuries.3 in open reduction and internal fixation there are several methods . in some , volar and dorsal approaches are handled together45 whereas in the others only volar6 or dorsal approaches are used.278 the aim of our study is to determine whether an isolated volar surgical approach is successful for the treatment of perilunate and lunate dislocation . 9 patients ( 6 males and 3 females average age of 34.5 3.6 years ) diagnosed with perilunate or lunate dislocation between january 2000 and january 2009 were involved in the study . the average time from the occurrence of the dislocation to surgery was 8.9 4.3 h. the mechanisms of injury were car accident for two patients , sports injury for three patients and falling from a height on the wrist for four patients . the left wrist affected in two and the right wrist was affected in seven patients . scaphoid fracture and perilunate dislocation was diagnosed in two patients , the radial styloid fracture and perilunate dislocation was diagnosed in one patient , pure perilunate dislocation was diagnosed in two patients and pure lunate dislocation was diagnosed in four patients [ figure 2 ] . all cases presented with stage 3 or 4 dislocation of which five of them were perilunate dislocations and four of them were lunate dislocations . three ( 33.3% ) patients had greater arc injuries , six ( 66.6% ) patients had lesser arc injuries . preoperative five patients ( 55.5% ) had hypoesthesia at 1 , 2 , 3 and radial side of 4 finger . preoperative x - ray of wrist joint anteroposterior and lateral views showing ( a ) scaphoid fracture with perilunate dislocation ( b ) a radial styloid fracture and perilunate dislocation ( c ) a pure lunate dislocation ( d ) a pure perilunate dislocation the palmar surgical approach was used via an extended carpal tunnel incision across the wrist in a zigzag fashion . median nerve and flexor tendons were retracted radially . after the exploration of palmar capsule , volar capsular rent and lunate dislocation would be visible . the lunate was reduced back in between the capitate and radius while applying gentle longitudinal traction on the hand . the deep volar luno triquetral ligament , scapho - lunate ligament and radiolunate ligaments were repaired [ figure 3 ] . ( b ) the deep volar luno - triquetral and scapho - lunate ligaments were ruptured . ( c ) the deep volar lunotriquetral and scapho - lunate ligaments have been repaired . ( d ) x - ray of wrist joint lateral view showing fixation with k - wires after open reduction of the lunatum the scaphoid fractures were fixed with a cannulated screw of 3.5 mm and grafted with the auto - graft . the radial styloid was fixed by a cannulated screw of 4.5 mm [ figure 4 ] . x - ray of wrist joint anteroposterior and lateral views showing ( a ) the postoperative 1 day x - ray of radial styloid fracture and perilunate dislocation . ( b ) the postoperative 12 month x - ray of a scaphoid fracture and perilunate dislocation showing 4.5 mm cannulated screw in situ , k - wires have been removed ( c ) the postoperative 24 month x - ray of a radial styloid fracture and perilunate dislocation . k - wires and the 4.5 mm cannulated screw were taken out after operation , the wrist movements of the patients were prevented for one and a half month by implementing short arm splint . k - wires were taken out on the 6 week and the exercises of movement expanding for wrist articulation and of isometric muscle restoration were started . wrist joint range of motion , fracture heal , carpal stability , the power of grasping , return to work were evaluated and also direct radiographs were taken routinely at each control . with these radiographs , evaluation of the clinical results was done using the dash , vas and modified mayo wrist scores . the palmar surgical approach was used via an extended carpal tunnel incision across the wrist in a zigzag fashion . median nerve and flexor tendons were retracted radially . after the exploration of palmar capsule , volar capsular rent and lunate dislocation would be visible . the lunate was reduced back in between the capitate and radius while applying gentle longitudinal traction on the hand . the deep volar luno triquetral ligament , scapho - lunate ligament and radiolunate ligaments were repaired [ figure 3 ] . ( b ) the deep volar luno - triquetral and scapho - lunate ligaments were ruptured . ( c ) the deep volar lunotriquetral and scapho - lunate ligaments have been repaired . ( d ) x - ray of wrist joint lateral view showing fixation with k - wires after open reduction of the lunatum the scaphoid fractures were fixed with a cannulated screw of 3.5 mm and grafted with the auto - graft . the radial styloid was fixed by a cannulated screw of 4.5 mm [ figure 4 ] . x - ray of wrist joint anteroposterior and lateral views showing ( a ) the postoperative 1 day x - ray of radial styloid fracture and perilunate dislocation . ( b ) the postoperative 12 month x - ray of a scaphoid fracture and perilunate dislocation showing 4.5 mm cannulated screw in situ , k - wires have been removed ( c ) the postoperative 24 month x - ray of a radial styloid fracture and perilunate dislocation . k - wires and the 4.5 mm cannulated screw were taken out after operation , the wrist movements of the patients were prevented for one and a half month by implementing short arm splint . k - wires were taken out on the 6 week and the exercises of movement expanding for wrist articulation and of isometric muscle restoration were started . wrist joint range of motion , fracture heal , carpal stability , the power of grasping , return to work were evaluated and also direct radiographs were taken routinely at each control . with these radiographs , evaluation of the clinical results was done using the dash , vas and modified mayo wrist scores . the average followup was 18.2 months ( range 12 - 28 months ) . in all patients , the radial styloid and scaphoid fracture union was observed at 3 month there were no cases of lunate avascular necrosis and radial styloid , scaphoid nonunion during followup period . hypoesthesia immediately after surgery was observed in five patients and the problem resolved in due course of time . the average flexion extension arc was 105.0 9.6 ( range 90 - 120 ) ( 74.6% of the other side ) , the average rotation arc was 138.8 7.8 ( range 130 - 150 ) ( 81.5% of the other side ) and the average radioulnar arc was 56.1 9.9 ( range 45 - 70 ) ( 86.4% of the other side ) . the grip strength was 0.55 bar and 83.2% of that of the uninjured arm . in the tests carried out for clinical evaluation , the modified mayo wrist score was very good for five patients and good for four patients . the preoperative vas which was measured 9.1 ( range 8 - 10 ) reduced to 0.5 ( range 0 - 1 ) in the final followup . in the final followup , the scapholunate interval was 2.1 mm ( range 1.6 - 2.4 mm ) and the scapholunate angle was found in normal limits of 51 ( range 47-58).9 all patients returned to work after 3 - 4 months postoperatively . even though dislocation in carpal bones is rarely seen , it might lead to instability and functional loss in the wrist if it is not treated properly.1011 misdiagnosis or late diagnosis of perilunate and lunate dislocations is reported up to 25%.1112 this delay affects the prognosis unfavorably in comparison with early treatment.12 untreated perilunate injury leads to painful limited range of motion , wrist joint arthritis and median nerve compression.13 although closed reduction is easy in acute perilunate and lunate dislocations , it is often difficult to maintain the reduction and the normal intercarpal integrity.1415 the ratio of reduction loss was 59% within 6 weeks of closed reduction and casting.15 most of the surgeons prefer open reduction due to the pain and loss of mobility resulting from residual carpal instability and progressive arthritis occurring frequently after closed reduction.1215 open reduction facilitates reduction and fixation and decrease possibility of residual instability . open surgical reduction is performed with volar , dorsal or combined volar and dorsal approaches . open surgical reduction of perilunate and lunate dislocation provides direct ligamentous repair and helps stability.245678 which surgical approach should be preferred ? the dorsal surgical approach provides a convenience in reduction of the scapholunate interval and repair of the dorsal ligaments , while the volar surgical approach allows to repair the important volar ligaments and to decompress the carpal tunnel.9 dorsal surgical approach could lead to scaphoid and lunate avascular necrosis.9 in volar surgical approach the deep volar lunotriquetral ligament , scapholunate ligament and radiolunate ligaments can be repaired . in the dorsal surgical approach the scapholunate ligament and dorsal luno - triquetral ligament can be repaired9 [ figure 5 ] . however , we obtained good results regarding stability without repairing the scapholunate ligament and dorsal lunotriquetral ligament as we used an isolated volar surgical approach . ( b ) scapholunate ligament , ( c ) lunotriquetral ligament extended carpal tunnel incision is preferred during volar surgical approach . the median nerve is retracted radially . the lunate and volar capsular rent will be visible in the space of poirier . some authors recommend combined approaches.4 they obtained high satisfactory results in 9 of 11 perilunate fracture - dislocations.4 in one study ( twenty five patients treated over an 11-year period for dorsal trans - scaphoid perilunate fracture - dislocations ) , the ratio of active range of wrist motion reduction was 20% in the patients treated via pure dorsal surgical approach . the range of flexion - extension arc was 104 , rotation arc was 152 and radioulnar deviation arc was 41.16 in our study we achieved similar results in terms of flexion extension arc , rotation arc and radio - ulnar deviation arc . the ratio of active range of wrist motion reduction was one - third compared with the opposite side , grip strength reduction ratio was 15 - 20% in the 25 patients ( 15 perilunate dislocations and ten perilunate fracture - dislocations ) treated via a combined volar and dorsal surgical approach.17 in our study we achieved better results in terms of both active range of wrist motion and grip strength . the dorsal surgical approach has a risk for lunate and scaphoid avascular necrosis due to disruption of the blood supply . combined approach increases the probability of adhesion formation at both volar and dorsal sides of the wrist . the volar surgical approach allows median nerve exploration and carpal tunnel decompression . also the perilunate and lunate dislocation and the fracture of the scaphoid the luno - triquetral ligament is important for volar intercalated instability.18 the volar approach allows repair of the luno - triquetral ligament . when the greater arc is injured together with the scaphoid fracture , nonoperative treatment of scaphoid fracture fails even if it is undisplaced . in those cases fixation of the scaphoid is recommended.19 in our study , two scaphoid fractures and radial styloid fracture healed without complications . it is suggested that a scapho - lunate gap > 3 mm leads to a poorer functional outcome.20 the scapholunate interval at the final control was measured as 2.1 mm ( range 1.6 - 2.4 mm ) and this was maintained throughout the routine controls . this is important for a satisfactory outcome including the grip strength and wrist joint range of motion . range of motion of the wrist might be limited even after anatomic reconstruction with rapidly developing painful radiocarpal osteoarthritis .

background : volar and/or dorsal surgical approaches are used for surgical treatment of perilunate and lunate dislocations . there are no accepted approaches for treatment in the literature . we evaluated the functional results of isolated volar surgical approach for the treatment of perilunate and lunate dislocation injuries.materials and methods:9 patients ( 6 male and 3 female patients average age 34.5 3.6 years ) diagnosed with perilunate or lunate dislocations between january 2000 and january 2009 were involved in the study . the reduction was performed through isolated volar surgical approach and k - wire fixation , fracture stabilization with volar ligament repair was performed . range of wrist joint motion , fracture healing , carpal stability , grip strength , return to work were evaluated and also direct radiographs were taken routinely at each control . the scapholunate interval and the scapholunate angle were evaluated radiographically . evaluations of the clinical results were done using the dash , vas and modified mayo wrist scores.results:the physical rehabilitation was started at 6th week , after the k - wires were removed . the average followup was 18.2 months ( range 12 - 28 months ) . at the final followup , the average flexion extension arc was 105.0 9.6 ( 74.6% of the other side ) , the average rotation arc was 138.8 7.8 ( 81.5% of the other side ) and the average radioulnar arc was 56.1 9.9 ( 86.4% of the other side ) . the grip strength was 0.55 bar ; 83.2% that the uninjured arm . according to the mayo modified wrist score , the functional result was excellent in five patients and good in four and the average dash score was 22.8 . the scapholunate interval was 2.1 mm and scapholunate angle was 51.conclusion:the clinical and radiological results of the isolated volar surgical approach were satisfactory . the dorsal approach was not needed for reduction of dislocations during operations . our results showed that an isolated volar approach was adequate .

one of the outstanding problems in star formation is the determination of the mechanisms that are responsible for the observed clumpiness in star forming regions . since the ratio , @xmath0 , of the thermal to magnetic pressure is observed to be small @xcite , it is natural to suppose that magnetohydrodynamic ( mhd ) waves play a crucial role . for this reason , there have been a number of three - dimensional ( 3d ) simulations of the effect of mhd waves on an isothermal plasma in which @xmath0 is small ( e.g. @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) . these do , indeed , show that density inhomogeneities can be formed in this way with statistical properties that are consistent with the observations . however , these calculations generally contain so many ingredients that they obscure the fundamental mechanisms . in two previous papers ( @xcite , hereafter fh02 and @xcite , hereafter lfh05 ) , we carried out 1d calculations of mhd waves in a low-@xmath0 plasma that were designed to elucidate the mechanism by which clumps are formed . in fh02 , we showed that clumps with a high - density contrast could be generated by the excitation of slow - mode waves due to the non - linear steepening of a fast - mode wave . in lfh05 , we explored how these effects were modified by the dissipation due to ion - neutral friction . the present paper is an extension of the work in fh02 to two dimensions . we find that the mechanism described in the previous paper works even better in two dimensions in the sense that the density contrasts are both larger and persist for longer . the governing equations and the initial condition are given in sect . [ sect : numerical calculations ] . we then discuss the results for a specific numerical model ( sect . [ sect : results ] ) and examine how these depend on the model parameters ( sect . [ sect : parameter study ] ) . finally , we conclude the paper by relating our results to observations of clumps and dense cores in gmcs ( sect . [ sect : discussions and conclusions ] ) . while fh02 considered only variations in the @xmath1-direction , we also allow changes in the @xmath2-direction . since we are only interested in magnetosonic waves , there is no need to introduce a @xmath3-component of either the magnetic field or the velocity . the mhd equations for an isothermal gas can then be written in the form @xmath4 where @xmath5^t\ ] ] is a vector of conserved variables , and @xmath6^t,\\ { \bf g } & = & [ \rho v_y , \rho v_y v_x - b_y b_x , \rho v_y^2 + p_g + b^2/2 - b_y^2 , v_y b_x - v_x b_y , 0]^t,\\ \end{array}\ ] ] are the corresponding fluxes . here we assume that @xmath7 , where @xmath8 is a constant sound speed . these equations were solved using the second order upwind scheme described in @xcite , except that we use the divergence cleaning technique described by @xcite . as in fh02 , we are interested in the generation of density inhomogeneities by fast - mode waves propagating in the positive @xmath1-direction . such a wave propagates with speed @xmath9 where the fast magnetosonic speed , @xmath10 , is given by @xmath11.\ ] ] the form of such a wave is most conveniently written in terms of the primitive variables @xmath12^t.\ ] ] we then have @xmath13 where @xmath14 is the right eigenvector for a fast - mode wave propagating in the positive @xmath1 direction for the system written in terms of the primitive variables , @xmath15 . note that we assume that the fast - mode wave is non - degenerate i.e. neither @xmath16 nor @xmath17 vanish . like fh02 , we use the above expression to superpose a small amplitude sinusoidal fast - mode wave propagating in the positive @xmath1-direction on a uniform background at rest . in order to make the flow two dimensional , we also introduce a shift with respect to the @xmath1-axis that depends on @xmath2 . the initial state is given by @xmath18\right\}{\bf r}_f , \label{eq : initial}\ ] ] where @xmath19 and @xmath20 are the amplitude and wavelength of the fast - mode wave and @xmath21 and @xmath22 the amplitude and wavelength of the phase shift . the homogeneous background state @xmath23 is as in fh02 : @xmath24 here @xmath25 is the equilibrium temperature of the isothermal gas . as in fh02 , we use @xmath26 ( or @xmath27 ) . since the amplitude is small , the fast - mode @xmath28 is calculated using the values of the unperturbed state and is normalised so that the amplitude of @xmath29 is @xmath19 . density inhomogeneities are generated for all values of @xmath30 . however , the highest contrasts are obtained when the initial wave propagates at a modest angle to the field ( fh02 ) . in our calculations we therefore limit ourselves to @xmath31 . we set @xmath32 since the transverse magnetic field changes sign for larger amplitudes . the non - linear steepening of the wave then leads to the formation of an intermediate shock , which is unphysical @xcite . we adopt @xmath33 for the amplitude of the phase shift . other values for the model parameters are being considered in sect . [ sect : parameter study ] . note that in the initial state , @xmath34 , @xmath17 is constant , while @xmath16 is a function of @xmath2 . this means that the divergence constraint @xmath35 is violated . however , for the adopted parameters ( see also below ) , we find that @xmath36 , which is of the same order of magnitude as the divergence errors that arise in numerical mhd calculations due to discretisation of the equations . as we include the divergence cleaning algorithm of @xcite to stabilize the numerical scheme , the initial violation of the divergence constraint is damped out . our initial state has an advantage over other models which introduce the two - dimensionality in a more natural way , i.e. a simple @xmath2-dependence of the primitive variables that allows an unambiguous interpretation of the initial stages of the simulations . a small density variation or a magnetic field @xmath17 that varies slightly with @xmath2 introduces a complex @xmath2-dependence for the primitive variables ( through @xmath10 and @xmath37 ) . calculations done with these alternative initial states , however , produce similar results to those of our model and hence provide a posteriori justification for our choice . the computational domain is @xmath38 and @xmath39 ( @xmath40 1000 ) with periodic boundary conditions . we use a uniform grid with @xmath41 mesh points . initially the solution is almost one dimensional : the gradients in the @xmath2-direction are of the order @xmath42 smaller than the gradients in the @xmath1-direction . although these variations are small , they can not be neglected . from eq . ( [ eq : initial ] ) we see that the gradients in the @xmath2-direction change sign when @xmath43 and @xmath44 ( for any given value of @xmath1 ) . this means that the domain can be divided into two regions with different temporal evolution : a central part with @xmath45 and the rest of the domain . in fig . [ fig : asymmetry ] we can clearly see these two regions . note that at this stage the variations in the @xmath2 direction are of the order of a few percent . after @xmath46 periods ( i.e. @xmath47 ) the fast - mode steepens into a shock , thereby exciting slow - mode components . fh02 showed that these slow modes produce inhomogeneities with large density contrasts . since there are as yet no significant variations in the @xmath2-direction , these high - density perturbations aligned with the @xmath2-axis . figure [ fig : shock ] shows the growth of one such high - density region and its subsequent decay . up to @xmath48 , the maximum densities in the computational domain do not differ significantly from those in 1d ( see fig . [ fig : rho_history ] ) . the density profiles of the perturbations are also similar to the 1d ones ( see fig . [ fig : shock ] and fh02 ) . we can also see from fig . [ fig : shock]b that the density perturbation is bounded by shocks as it expands . in contrast to the 1d case , the speed in the laboratory frame , @xmath49 , of these shocks is not constant along the shock front . the upstream fluid speed in the frame of the shock , @xmath50 , is roughly constant and equal to @xmath51 ( fh02 ) , where @xmath52 is the initial alfvn speed , whereas the upstream speed in the rest frame , @xmath53 , varies considerably along the shock front . since @xmath54 , it follows that @xmath49 must also vary along the shock front i.e. the shock front is curved . this effect can be seen clearly in fig . [ fig : curved_shocks ] . an important consequence of the curved shock front is the formation of clumps , rather than dense sheets . the dense regions are bounded by slow shocks that propagate predominantly in the @xmath1-direction . regions that are bounded by slowly moving shocks therefore retain a high density for longer than those bounded by faster shocks . at later times this produces variations in the @xmath2-direction that are larger than those that occurred before the initial decay . however , there is little motion in the @xmath2-direction because this is prevented by the magnetic field . once a clump forms , its long axes is orientated perpendicular to the magnetic field lines , but its aspect ratio is not particularly large ( see fig . [ fig : dense_cores ] ) . although the average density within clumps is nearly constant , the maximum density can have large fluctuations . as seen from fig . [ fig : rho_history ] , the maximum densities are a factor of two higher than obtained in 1d calculations . the initial fast - mode is still present and interacts with the clumps and its bounding shocks , thereby generating slow - mode waves . figure [ fig : fast mode decay ] shows a measure of the amplitude of fast and slow - mode waves as defined in fh02 . it shows clearly the correlation of the slow - mode waves with the density inhomogeneities . the slow modes are thus responsible for the fragmentation of the clump into high - density contrasts . figure [ fig : dense_cores ] shows a close - up of a clump with dense substructures . such fragmentation is , of course , not possible in 1d . the dense substructures in the clump are thus transient and have rather short lifetimes . they are generated because slow - mode waves are continuously excited by the fast - mode wave interacting with the clump . this explains why the time - scales of the density fluctuations are of the order of the time for a fast - mode wave to cross the computational domain , i.e. @xmath55 . as this wave dissipates , the amplitude of the slow modes decreases , resulting in lower density contrasts ( see fig . [ fig : fast mode decay ] ) . furthermore , the clump itself disperses . the 2d results show that a clump persists for a period of time that exceeds the lifetimes of the density perturbations in 1d by a factor of 10 . the ratio , @xmath0 , of the gas pressure to magnetic pressure increases in our simulations from its initial value of @xmath56 to @xmath57 . while the gas pressure can become a factor of 100 larger than initially since it scales like the density , the magnetic field does not vary much in strength . when @xmath0 approaches unity , the process of producing high - density contrasts by slow modes ceases to be effective . there is therefore an upper limit to the maximum density that can be produced . in the previous section , we focused on one specific numerical case with a set of specific parameters . as the results are parameter - dependent , we briefly discuss the influence of each parameter . [ [ balpha ] ] @xmath58 + + + + + + + + + + + + + + + + + + + + + * :* the fast - mode wave is most efficient in exciting slow - mode components for modest values of the angle , @xmath30 , between its direction of propagation and the magnetic field ( fh02 ) . when @xmath30 is too large , the shock is not effective in producing slow - mode components , whereas there is little steepening when @xmath30 is too small . moreover , the fast - mode wave is also responsible for the excitation of slow modes within the clumps . since it is the slow modes that generate the density inhomogeneities , this means that models with @xmath59 produce lower density contrasts . [ [ bf - a_1-and - bf - a ] ] @xmath60 and @xmath61 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + * :* both parameters affect the maximum density produced by the non - linear steepening of the fast - mode wave . fh02 showed that the maximum density is roughly proportional to @xmath62 . while the time - scale for the formation of the substructure is independent of @xmath8 , it depends on @xmath19 in two ways ( see fh02 ) . the wave amplitude determines the time for the fast - mode wave to steepen into a shock and also the time - scale for the subsequent decay . a lower value of @xmath19 means that dense cores arise later in the simulations . [ [ bf - a_2 ] ] @xmath63 + + + + + + + + + + + + + + + + + + + + + + + * :* the phase - shift of the fast - mode wave is responsible for the variations along the @xmath2-axis . the amplitude of this shift determines the time at which the simulations cease to be 1d . figure [ fig : rho_history2 ] shows the time evolution of the maximum density for an amplitude of @xmath64 . as the initial variations are a factor of 10 smaller than for @xmath65 , it takes longer to develop any significant deviation from 1d . this also means that the formation of substructure is deferred . note that the maximum density that can be attained is independent of @xmath21 ( see fig . [ fig : rho_history ] and fig . [ fig : rho_history2 ] ) . [ [ bf - l_1-and - bf - l_2 ] ] @xmath66 and @xmath67 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + * :* the wavelengths of the fast - mode wave and the phase shift determine the dimensions of the clump . its extent in the @xmath1-direction is roughly comparable with the size of density perturbations produced by excitation of slow modes . this means that it is @xmath68 , where @xmath69 is the initial density and @xmath70 the maximum density . the size in the @xmath2-direction is set by the wavelength of the phase shift . as mentioned in sect . [ sect : results ] , a sinusoidal phase shift divides the domain into two separate regions so that the @xmath2-extent is roughly @xmath71 . we have extended the fh02 model which describes the generation of density inhomogeneities by mhd waves in a low-@xmath0 environment , to two dimensions . we have followed the evolution of a fast - mode wave propagating in the positive @xmath1-direction with a small , but non - negligible , variation in the @xmath2-direction produced by a @xmath2-dependent shift along the @xmath1-axis . like fh02 , we find that the formation of density inhomogeneities is associated with the excitation of slow modes by the fast - mode wave . an important result is that the process of generating structure by slow modes works on different length - scales . while the larger structures arise due to the non - linear steepening of the fast mode , there are smaller structures generated by the interaction between the fast - mode wave and the larger structures . a limiting factor , however , is that @xmath0 increases within each level of substructure . when @xmath0 approaches unity , the mechanism ceases to be effective and produces no further substructures . @xmath0 is probably about unity in dense cores ( e.g. @xcite ) . although we made no attempt at reproducing any observational data , we can investigate the relevance of our simulations to observations of clumps and dense cores in gmcs . the structure of molecular clouds is often described as filamentary or clumpy ( e.g. @xcite ) . for example , observations of the @xmath72 oph a core show an arc - shaped ridge with 4 embedded cores @xcite . similar structures are obtained in our simulations . however , the shape of the clump depends on the properties of the initial fast - mode wave , i.e. its wavelength , and on the length - scale of perpendicular variations ( in our calculations determined by the sinusoidal phase - shift of the fast - mode wave ) . other shapes of clumps can then be reproduced by mhd waves with different properties . @xcite found that the clumps in the rosette molecular cloud , an archetypal gmc , are an order of magnitude denser than the mean cloud density . dense cores within the clumps typically have a density that exceeds the mean density by two orders of magnitude , but peak densities in pre - stellar cloud cores can range to values that exceed the mean density by 4 orders of magnitude ( e.g. @xcite ) . in our simulations , we find that the average density contrasts in the larger structures are in excess of 10 times the average background density of 1 . for the substructures , i.e. individual dense cores , this increases to 100 . we do not find the observed peak values , but this can be readily explained by the fact that we have restricted ourselves to modest amplitudes of the initial fast - mode wave . also we have not included self - gravity in our model . the inclusion of this effect will be investigated in a subsequent paper . however , we expect self - gravity only to act as an amplifier and not to have an influence on the fragmentation of the molecular cloud . recently , @xcite investigated the chemistry of transient dense cores within molecular clouds . using the results of fh02 to describe the growth and decay of the dense cores , they find a significant enhancement in chemical compositions of the cores as they disperse . this leads eventually to chemical enrichment of the molecular cloud . in our simulations , however , high - density clumps survive much longer than they do in fh02 . our results thus have serious implications for the chemical evolution and richness of clumps and dense cores . we thank the anonymous referee for a report that helped to improve the manuscript . svl gratefully acknowledges pparc for the financial support . 99 andr p. , ward - thompson d. , barsony m. , 1993 , apj , 406 , 122 ballesteros - 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using two dimensional simulations , we study the formation of structures with a high - density contrast by magnetohydrodynamic waves in regions in which the ratio of thermal to magnetic pressure is small . the initial state is a uniform background perturbed by fast - mode wave . our most significant result is that dense structures persist for far longer in a two - dimensional simulation than in the one - dimensional case . once formed , these structures persist as long as the fast - mode amplitude remains high . [ firstpage ] mhd stars : formation ism : clouds .

the causes of posterior shoulder dislocations are usually a strong traumatic event or a sudden violent internal rotatory muscles contraction such as what may happen during a convulsive crisis or electrocution [ 13 ] . in most of the cases , the dislocation is subacromial and posterosuperior ; the subspinatus and subglenoidea forms are very uncommon . anteromedial humeral head impaction fractures ( mclaughlin lesion or reverse hill sacs ) always complete this scenario . although posterior capsular or labral laceration seems to be constant , posterior tears of the rotatory cuff are not so much described in the literature [ 46 ] . most of the cases can be misunderstood because of being without a correct x - ray projection or the not - always clear presentation of the clinical signs , which essentially consist of pain and unability to do complete elevation and external rotation . anyway a posterior dislocation must be suspected when there is a lesser tuberosity fracture or a fixed internal rotation of the arm . the treatment depends on the delay of the diagnosis , on the associated bony and cartilaginous lesions , on the age and functional request of the patient , and finally on the surgeon 's experience . most of the authors agree that a dislocation can be considered inveterate if it is discovered 6 weeks after the trauma . it is very important to establish if it is inveterate or not because trying to reduce an inveterate luxation can lead to an epiphyseal fracture [ 610 ] . the goal of the treatment of the acute posterior dislocation of the shoulder must be to restore the patient 's ability to do his previous activities and to prevent posterior instability . we present the case of a 57-year - old man with right hemiparesis and epilepsy secondary to a stroke . the patient presented pain and impossibility at the elevation and extrarotation of his left shoulder soon after a convulsive crisis during his first hospitalization in the department of neurology of our hospital . it shows humeral head fractures with some very little fragments and internal rotation of the humerus . in order to confirm the posterior dislocation and to discover the associated fractures and the dimension of the reverse hill - sachs lesion it shows posterior dislocation and a damage of the cartilaginous surface of humeral head with loss of the bone that amounts between 20 and 30% of the articular surface . in order to prevent instability and to obtain an anatomical restoration that allows early mobilization and complete range of movement , we reduced the dislocation through a deltoid - pectoral incision , we stabilized the lesser tuberosity with a cancellous bone screw , and then we filled the reverse hill sachs with crioconserved femoral head contoured in the right shape to reconstruct the patient 's humeral head , maintaining his original bending radius . the allograft was fixed by using 2 herbert screws ( figure 3 ) . finally , we reduced and stabilized the posterior glenoid rim fracture with a herbert screw , through a posterior miniapproach . this treatment allowed the patient an early mobilization , and so he obtained a range of motion very similar to his previous condition . at 8-month followup , there are no signs of avascular necrosis ( figures 4 and 5 ) and the patient is satisfied with our operation . we did not perform the constant score because of the right hemiparesis . however , the patient is able to keep his left arm above his head and to rotate internally till sacral bone ( figures 6 and 7 ) . although the surgical techniques used for chronic posterior instability are quite the same for acute traumatic dislocations , it is important to make the right diagnosis soon after the trauma to avoid avascular necrosis [ 710 ] . sometimes it is quite difficult to obtain correct x - ray projection because of the pain that limits the patient 's mobility . a posterior dislocation must be suspected when there is a fracture of the anteromedial humeral head and when the arm is fixed in internal rotation . ct scan is always necessary to study the osteocartilaginous surface damage [ 5 , 6 ] . mclaughlin first had explained the relevance of the percentage of the articular humeral head cartilage loss to decide the treatment [ 7 , 8 ] . for less than 25% , hawkins reported his outcomes of 7 cases with no treatment . as shown by loebenberg , the decision depends on the age and on the functional request of the patient . for a cartilaginous loss that is between 25 and 40% , there is no universal agreement with reduction and osteosynthesis or prosthesis , while total or hemiarthroplasty is considered necessary for damage superior to 40% [ 4 , 7 , 8 ] . reconstruction of the shape of the humeral head by elevation of depressed cartilage and subchondral buttressing with cancellous bone graft has been advocated as a joint - preserving alternative [ 4 , 5 ] . dubouesset proposed the use of crioconserved allograft to restore the anatomy and to preserve the bone stock , preparing , that way , the patient for a probable future joint replacement . they had excellent results in 3 cases and 1 avascular necrosis at 1-year followup . beside the case discussed here , we treated this way other 2 chronic posterior shoulder dislocations , and in both of them we achieved satisfying results , so it is our opinion that using crioconserved bone to reconstruct the right shape of humeral head is a very valid method , and it is good in prevision of a future prosthesis . when crioconserved bone is not available , it is our opinion that using autologous transplantation from iliac crest is a good solution . maybe no delay in diagnosis can help to avoid avascular necrosis , but we believe that further studies are necessary .

posterior dislocation of the shoulder is an unfrequent event that often occurs as a consequence of a direct trauma or epileptic crisis . frequently the posterior dislocations are misunderstood , so they become chronic lesions . we reported a case of an acute posterior left shoulder dislocation with lesser tuberosity fracture and reverse hill - sachs lesions which involved more than 25% of the articular surface of the humeral head , in a 57-old - year man with right hemiparesis . we performed a synthesis of the lesser tuberosity with a screw , and we restored the shape of the humeral head with allograft . we achieved a good result that allows the patient to be able to do his previous activities of daily living .

a cilium which means an eyelash in latin , is motile ( although not all cilia motile ) hairlike slender appendage / sprotuberance that project from the free surfaces of certain cells ( e , g . eukaryotic cells ) and is present in almost all groups of the animal kingdom . because of its motility , it plays an important role in diverse physiological processes such as locomotion , alimentation , circulation , respiration and reproduction . there are two types of cilia namely motile cilia and non - motile or primary cilia . however , the motile cilia which do not beat randomly but are coordinated are taken into consideration in this study . this nature of the cilia gives extremely interesting aspects of ciliated epithelium . a summary of general observations and conclusions on the cilia of the gill of several aquatic species was given by rivera @xcite as : ( a ) in any given tissue , the rate of beat of all the cilia is remarkably uniform . ( b ) the lashings of a single cilium and of cilia on adjacent cells appear to be definitely coordinated . ( c ) a definite metachronal wave is established . metachronal rhythm is a movement where there is always a sequence of beat from row to row of cilia in a given row of cells and from one row of cells to the next , so that any small foreign body resting on the ciliated surface is progressively moved always in the same direction . since a metachronal wave provides a more `` steady progression of water over the ciliated surface or perhaps because it is not practical to excite a synchronous beat over a large area '' ( sleigh @xcite ) , it is widely believed that cilia beat in a metachronal wave rather than synchronously . however , the metachronal wave along a ciliated surface can change its pattern ( sleigh @xcite ) . the change depends on whether the metachronal waves travel in the same direction as the effective stroke of the ciliary beat ( symplectic metachronism ) , or the metachronal waves travel in the opposite direction to the effective stroke of the beat and thus opposite to the movement of fluid ( antiplectic metachronism ) , or the cilia beat at right angles to the line of wave progression ( diaplectic metachronism ) . satir @xcite showed an example of a diaplectic metaehronal wave in figure 6 of his study @xcite , while some data based on wave lengths , metachronal wave velocities and frequencies are available for lower animal forms ( sleigh @xcite ) . it is to be noted that data do not appear to be readily obtainable for higher animal species , especially mammals . however , it was measured that the beat frequency for cilia lining in the rabbit oviduct is approximately 20 - 30 beats / sec ( borell et al . it is important to mention that this order of magnitude of the frequency is comparable with frequencies of cilia beat of lower forms ( sleigh @xcite ) . it is to be noted that the investigations on the hydrodynamics of protozoa which use cilia for locomotion have being carried out by many investigators ( c.f . jahn and bovee @xcite and the references therein ) . blake @xcite considered a spherical envelope model for the swimming of the protozoan opalina and the swimming motion of either a two - dimensional or cylindrical ciliated body . miller @xcite worked on the problem of mucus transport in the trachea by the use of a mechanical simulation of the cilia in the trachea , while an analytical model for mucus transport in the trachea had been presented by barton and raynor @xcite without consideration of the metachronal wave motion . these studies in protozoology and mucus transport in the respiratory tract supplied information on the means of locomotion in protozoa and particle transport in the respiratory tract . however , only a little work has been done to relate the properties of the cilia and the metachronal wave to the net fluid transport in tubules . our motivation is coming from problems associated with the understanding of the transport of fluid through the ductus efferentes of the human male reproductive tract ( greep @xcite ) and the effect of cilia on ovum and sperm transport in the fallopian tubes ( blandau @xcite ) , ( sturgis @xcite ) . particularly , this paper will deal with a comparison of the results for the flow rates of our model to the flow rates estimated in the ductus efferentes of the male reproductive tract . it is to be noted that there are only a few data available on the flow rates due to ciliary activity . based on the experimental determinations ( tuck et al . @xcite , waites and setchell @xcite , setchell @xcite ) , lardner and shack @xcite estimated flow rate as @xmath5 with approximate values of @xmath6 , frequency of beat of the cilia as 20/sec for human testes , while the theoretical model of lardner and shack @xcite obtained a flow rate of @xmath7 . hence further studies are required for considerable improvements . past experimental observations indicate that most of the biological fluids possess non - newtonian behaviour @xcite . so , analysis on the basis of simple newtonian fluid non accurate results . the power law model is one of the simplest but the most widely used model for rheological fluid transports @xcite . the rheological nature of this model is strongly dependent on rehological fluid index @xmath4 and the model approximates both shear - thinning ( @xmath8 ) and shear - thickening ( @xmath9 ) fluids behaviour over a large range of flow conditions @xcite . viscous properties of human semen is experimentaly found to exhibit power law - behaviour [ dunn and picologlu @xcite , mendeluk et al . it has been reported experimently that semen proves to fit in a power - law model with pseudoplastic behavior @xcite . thus studies on fluid transport of the power law model by ciliary activity may be useful to draw some important conclusions . recently , siddiqui et al . @xcite have studied the flow of a power law fluid due to ciliary motion in an infinite channel and remarked that the power - law fluid gives results closer to the estimated one as @xmath5 . however , we believe that there are some drawbacks in their claim . they took @xmath10 , giving reference to agarwal and anawaruddin @xcite who reported an application of theirs model to fluid transport in vas deference considering @xmath10 . it is important to mention that ductus efferentes and vas deferens are quite different ducts , while we have no idea about the possibility of @xmath10 for the later case . however , @xmath0 , a non - dimensional measure with respect to mean radius @xmath1 of the tube and the cilia length , would be much less than @xmath10 @xcite . to the authors knowledge , the other drawbacks of the results in @xcite are : ( i ) they considered large favourable pressure gradient which was constant . it is well known that pressure gradient in small biological vessels ( at least when there is a wave like peristaltic wave @xcite , metachronal wave etc in the vessels ) varies with the length of the vessels and large favourable pressure gradient are physiologically insignificant , in general , and , at least , in the ductus efferentes ( @xcite ) ( ii ) dependence of flow characteristics on @xmath11 , wave number of the metachronal wave , is not true for higher values of @xmath11 as they have done their analysis for small values of @xmath11 etc . however , their power law model is somehow different and complex to the widely used power - law model . in view of all the above , a theoretical model for the flow in an axisymmetric tube due to metachronal wave of cilia motion has been taken into consideration for more realistic consequences . a study concerning the analysis of a non - linear problem of ostwald - de waele power - law fluid transport has been undertaken here by means of a sequence of cilia beat from row - to - row of cilia in a given row of cells and from one row of cells to the next ( metachronal wave movement ) under the conditions that the reynolds number is small and the wave number is large . based upon the analytical investigation , the velocity , pressure difference , flow rate have been formulated and extensive numerical calculations have been made thereafter . keeping in view a specific situation of fluid movement in micro - vessels by ciliary motion , the computational results are presented in graphical forms . the results presented for shear thinning and shear thickening fluids are quite relevant in the context of various studies of fluid transport due to ciliary activity . for example , semen usually behaves like shear thinning fluid when it contains a number of spermatozoa up to certain limit , however in the case of heavily concentrated spermatozoa suspensions , the fluid behaviour may be considered similar to that of a shear thickening fluid @xcite . moulik et al . @xcite reported that high viscosity of semen can be an indication of antibodies in the plasma and/or genital tract infection . some novel features may be reported in this study by which we can have a better insight of fluid motion by ciliary activity . ciliary pumping mechanism may be utilized in the study the hydrodynamics of protozoa which use cilia for locomotion . the results may find useful applications for the possible use of cilia - based actuators as micro - mixers , for flow control in tiny bio - sensors , or as micro - pumps for drug - delivery systems . in this investigation , the term cilia , as it is used , is limited to clliated epithelium and will not include flagella ; comparative physiology of flagella including sperm tails may be found in the papers by fawcett @xcite and by sleigh @xcite . a non - linear problem concerning the fluid transport characteristics in an axisymmetric tube under the action of ciliary beat that generate a metachronal wave will be studied here , by considering the fluid as an incompressible viscous non - newtonian fluid . let us consider an axisymmetric tube with ciliated walls of large length compared with its radius and a symplectic metachronal wave moves to the right with wave velocity c. the non - newtonian viscous fluid behaviour within the tube is treated as an incompressible viscous ostwald - de waele power law type of rheological fluids . we treat ( r,@xmath12,z ) as the cylindrical coordinates of the location of any fluid particle , r being the radius of the tube , the coordinate z measured in the direction of wave propagation and @xmath12 being the rotational coordinate . if @xmath13 be the stress tensor and @xmath14 the symmetric rate of deformation tensor , the constitutive equation of shear stress for the ostwald - de waele power law fluid can be written as @xmath15 @xmath16 in which @xmath17 and @xmath4 denote respectively the consistency factor and the power - law index parameter , depicting the behaviour of the fluid ; @xmath18 and @xmath19 are the velocity components in the @xmath20 and @xmath1 directions . it is well known that a shear thinning fluid is classified by @xmath8 , while for a shear thickening fluid , @xmath9 . based on the above consideration , the motion of an incompressible viscous ostwald - de waele power - law fluid in an axisymmetric tube together with equation of continuity may be considered to be governed by the equations @xmath21 @xmath22 @xmath23 where @xmath24 and @xmath25 are the density and pressure of the fluid . keeping the view on the geometry of the metachronal wave pattern , it is assumed that the envelope of the cilia tips can be written mathematically in the following form : @xmath26 which can be therefore assumed as the the equation of the extensible channel wall , where @xmath27 denotes the mean radius of the tube , @xmath0 is a non - dimensional measure with respect to ` @xmath27 ' of the cilia length , and @xmath28 and @xmath29 stand for the wave length and wave velocity of the metachronal wave . based upon the different patterns of cilia motion observed in sleigh ( 1968 ) , the cilia tips can be considered to move in elliptical paths such that the horizontal position of a cilia tip can be written as @xmath30 where @xmath31 represents a reference position of the particle and @xmath17 stands for a measure of the eccentricity of the elliptical motion . under the no slip conditions , the velocities imparted to fluid particles are just those of the cilia tips and hence the axial and vertical velocities of the cilia can be given by @xmath32 if equations ( [ cnsns_manuscript_envelope_cilia_tip ] ) and ( [ cnsns_manuscript_envelope_cilia_tip_horizontal ] ) are applied to equations ( [ cnsns_manuscript_cilia_velo_horizontal_equ ] ) and ( [ cnsns_manuscript_cilia_velo_vertical_equ ] ) , we have @xmath33 these boundary conditions enable us to distinguish between the effective stroke of the cilia and the slow less effective recovery stroke by approximately accounting for the shortening of the cilia . in other wards , we can say that the tube is narrower when @xmath18 is positive . for a wave frame ( @xmath34,@xmath35 ) moving with a velocity c away from a fixed frame ( @xmath20,@xmath1 ) , let us take the transformations @xmath36 in which ( @xmath37,@xmath38 ) and ( @xmath18,@xmath19 ) are the velocity components , @xmath39 and @xmath25 stand for pressure in wave frame and fixed frame of reference respectively . henceforward , we shall make use of the following non - dimensional variables : @xmath40 if we drop the bars over these symbols , the equations governing the flow of the fluid can be rewritten as @xmath41 @xmath42 @xmath43 @xmath44 whereas the boundary conditions are @xmath45 on @xmath46 . since in most of the cases of flow in small diameter tubules , reynolds numbers are very small ( @xmath47 ) , the analysis can be carried out by the approximation of the inertia - free flow . in this case , the governing equations under the consideration of the long - wavelength approximation can be simplified as follows : @xmath48 @xmath49 and also the forms of the boundary conditions will now be @xmath50 on @xmath46 . by solving ( [ cnsns_manuscript_zmomentum_lubrication ] ) subject to the boundary condition ( [ cnsns_manuscript_cilia_velo_horizontal ] ) , we have found the axial velocity in the form @xmath51 \label{cnsns_manuscript_cilia_axial_velocity}\ ] ] if we integrate the continuity ( 19 ) across the cross section of the tube , we get @xmath52 this shows that the volume flow rate @xmath53 in the wave frame of reference is constant . on integration ( [ cnsns_manuscript_cilia_axial_velocity ] ) across the cross section of the tube , the pressure gradient can be represented in terms of the volume flow rate by the following form . @xmath54 putting @xmath55 , obtained from ( [ cnsns_manuscript_cilia_flow_rate_pressure_grad ] ) , into ( [ cnsns_manuscript_cilia_axial_velocity ] ) we calculate @xmath56 \label{cnsns_manuscript_cilia_axial_velocity_containing_flow_rate}\ ] ] the instantaneous volume flow rate , @xmath57 , in the fixed frame of reference is found by integrating @xmath58 thus , the time - mean volume flow over a period is given by @xmath59 which , on integration for the sinusoidal wall of ( [ cnsns_manuscript_envelope_cilia_tip ] ) , gives @xmath60 after solving @xmath55 from ( [ cnsns_manuscript_cilia_flow_rate_pressure_grad ] ) and using ( [ cnsns_manuscript_cilia_time_averaged_flow_rate_fixed_frame ] ) , the pressure rise per wavelength can be calculated by the relation @xmath61 it may be noted that if we put @xmath62 , @xmath63 in equations ( [ cnsns_manuscript_cilia_axial_velocity ] ) , ( [ cnsns_manuscript_cilia_flow_rate_pressure_grad ] ) and ( [ cnsns_manuscript_cilia_pressure_rise_relation ] ) , the expressions reduce to those reported earlier in ref . if @xmath63 , the results also match well those of ref . @xcite when the peristaltic wave form in @xcite is replaced by the metachronal wave in this study in the fixed frame of reference . similarly , if the yield stress is set equal to zero and fluid flow is considered in an axisymmetric uniform vessel in @xcite , the expressions said above reduces to that obtained in @xcite . by solving the continuity equation ( [ cnsns_manuscript_continuity_non - dimensional ] ) subject to the boundary condition ( [ cnsns_manuscript_cilia_velo_vertical_simplified ] ) , we have found the radial velocity as @xmath64\frac{\partial u(h)}{\partial z}+\frac{(k+3)q}{(k+1)h^2}\left[\frac{r}{h}-\frac{r^{k+2}}{h^{k+2}}\right]\frac{\partial h}{\partial z } \label{cnsns_manuscript_cilia_radial_velocity}\ ] ] ) on @xmath0 , flow behaviour index @xmath4 and eccentricity @xmath17 . in all the figures , wave number @xmath65 , @xmath66 and @xmath4 has been varied from 1/3 to 5/3 to observe the changes taking place in @xmath67 relation . effect of @xmath0 on @xmath67 relation has been shown in figs . ( a - c ) by varing @xmath0 from 0.1 - 0.5.,title="fig:",width=321,height=172 ] ) on @xmath0 , flow behaviour index @xmath4 and eccentricity @xmath17 . in all the figures , wave number @xmath65 , @xmath66 and @xmath4 has been varied from 1/3 to 5/3 to observe the changes taking place in @xmath67 relation . effect of @xmath0 on @xmath67 relation has been shown in figs . ( a - c ) by varing @xmath0 from 0.1 - 0.5.,title="fig:",width=321,height=172 ] + @xmath68 ) on @xmath0 , flow behaviour index @xmath4 and eccentricity @xmath17 . in all the figures , wave number @xmath65 , @xmath66 and @xmath4 has been varied from 1/3 to 5/3 to observe the changes taking place in @xmath67 relation . effect of @xmath0 on @xmath67 relation has been shown in figs . ( a - c ) by varing @xmath0 from 0.1 - 0.5.,title="fig:",width=321,height=172 ] + ( c ) and @xmath0 relation on flow behaviour index @xmath4 by plotting graphs for n=1/3 - 5/3 . the other parameters are kept as @xmath69 , i.e. free pumping , @xmath65 , @xmath70.,width=321,height=172 ] and eccentricity @xmath17 relation on flow behaviour index @xmath4 by plotting graphs for n=2/3 - 4/3 . the other parameters are kept as @xmath69 , i.e. free pumping , @xmath65 , @xmath71.,width=321,height=172 ] with wave number @xmath11 and its dependence on flow behaviour index @xmath4 , which has been shown by plotting graphs for n=2/3 and 4/3 . the other parameters are kept as @xmath69 , i.e. free pumping , @xmath66 , @xmath71.,width=321,height=172 ] this section deals with a quantitative analysis of the mathematical model presented in the earlier sections . it may be noted that unlike the newtonian model , in ostwald - de waele power law model it has been not possible to find an explicit analytical expression of pressure difference @xmath72 in terms of time averaged flow rate @xmath73 due to the complexity of the problem of a rheological fluid when the wave shape is arbitrary . however , a numerical computation is required to express pumping characteristics or pumping performance of the rheological fluid for a clear understanding . in addition , it is a convention to exhibit velocity field in term of the pressure difference between the tube ends . hence , in view of those observations and to fulfill the demands , necessary computations have been carried out numerically by using the software mathematica . it is to be noted that there is only a few available data on the flow rates due to ciliary activity @xcite . for the quantitative study , we shall present theoretical estimates of different physical quantities that are of relevance to physical problems of the flows of rheological fluids under ciliarry activity . on the basis of the present analysis , the following non - dimensional data for the rheological fluids have been used @xcite : + @xmath74 to 0.5 , @xmath75 0.3 to 1 , @xmath76 to 0.2 , @xmath77 to 2 , @xmath78 to 1 . it is natural that pressure - flow characteristic ( i.e. the pumping characteristics ) can be determined through the variation of time averaged flow rate @xmath73 with difference in pressure @xmath79 across one wave length . the variations of volumetric flow rate of the fluid by cilia motion , for different values of @xmath0 , flow index number @xmath4 , wave number @xmath11 and eccentricity @xmath17 are exhibited in figs . [ cnsns_manuscript_pump7.1.1 - 7.4.1 ] . as expected to the linear nature of the case inertia - free flow ( @xmath80=0 ) of a newtonian fluid , the curve of @xmath79 versus @xmath73 is a straight line with negative slope and and positive intercepts ; however , for the aforesaid case of a rheological ( non - newtonian ) fluid the relationship between the pressure difference and the mean flow rate is nonlinear . the curves have three portions , namely , ( i ) free pumping zone , describing the region in which @xmath81 , ( ii ) pumping zone , indicating the region where @xmath82 and ( iii ) co - pumping zone , which regarded for the region where @xmath83 , the situation favourable for the flow to take place . from the above said relation , it is possible to calculate the amount of flow pumped by ciliarry activity , even in the absence of mean pressure gradient ( @xmath81 ) and also in the presence of adverse pressure gradient ( i.e @xmath82 ) up to certain a limit . if @xmath0 , @xmath4 , @xmath11 , @xmath17 are fixed at some values imposition of an adverse mean pressure gradient reduces the mean flow rate relative to the value obtained during free pumping and when it is large enough ( certain limit ) , it balances exactly the driving force for flow produced by the cilia motion , and the mean flow rate is zero . whereas if @xmath79 ( @xmath84 ) exceeds this limit , the flow will take place in the backward direction . figs . [ cnsns_manuscript_pump7.1.1 - 7.4.1](a - c ) show that the area of the pumping region and the length of the free pumping zone both increase significantly with a rise in @xmath0 for newtonian , shear thinning as well as shear thickening fluids and also these ( area , length ) enhance at a very high rate with an increase in the rheological parameter @xmath4 . in other wards , for fixed values of @xmath85 , time averaged flow rate @xmath73 rises with an increase in @xmath0 and @xmath4 . however , in the co - pumping zone , there is a critical value of @xmath79 for higher values of @xmath0 ( @xmath86 ) up to which @xmath73 for fixed values of @xmath79 can be raised with an increase in @xmath4 and if @xmath79 exceeds this critical value the reverse trend occurs . it is important to mention that for fixed values of parameters taken by lardner and shack together with @xmath62 , the flow rate in axisymmetric tube is two times more than the values reported by lardner and shack for a two - dimensional channel . in the case of free pummping , [ cnsns_manuscript_pump7.1.1 - 7.4.1](d ) clearly reveals that there is a remarkable enhancement of flow rate with increase in @xmath0 . it further explains that @xmath4 strongly influences the flow rate . the plots , presented in figs . [ cnsns_manuscript_pump7.1.1 - 7.4.1](e - f ) , indicate that for a non - newtonian fluid , @xmath73 increase as the wave number @xmath11 and @xmath0 increase and these parameters enhance @xmath73 at almost the same rate for both the shear thinning and shear thickening fluids . it is worthwhile to mention that an increase of @xmath0 corresponds to rise of cilia length and vice versa . again in the case of free pumping , when @xmath0=0 , there is no cilia to the inner surface of the tube , then @xmath73=0 . ) ) at different instants of time ( t=0.0 - 0.75 ) . the dark cploured curves represent envelop of cilia tips . arrows indicate the direction of velocity . reversal of flow corresponding a velocity profile has been indicated by reversed arrows in the vicinity of the envelop.,title="fig:",width=321,height=172 ] ) ) at different instants of time ( t=0.0 - 0.75 ) . the dark cploured curves represent envelop of cilia tips . arrows indicate the direction of velocity . reversal of flow corresponding a velocity profile has been indicated by reversed arrows in the vicinity of the envelop.,title="fig:",width=321,height=172 ] + @xmath68 ) ) at different instants of time ( t=0.0 - 0.75 ) . the dark cploured curves represent envelop of cilia tips . arrows indicate the direction of velocity . reversal of flow corresponding a velocity profile has been indicated by reversed arrows in the vicinity of the envelop.,title="fig:",width=321,height=172 ] ) ) at different instants of time ( t=0.0 - 0.75 ) . the dark cploured curves represent envelop of cilia tips . arrows indicate the direction of velocity . reversal of flow corresponding a velocity profile has been indicated by reversed arrows in the vicinity of the envelop.,title="fig:",width=321,height=172 ] + @xmath87 as shown in previous section , the mean flow is attributable solely to the motion of ciliary activity during free pumping and motion of cilia supplies the only driving force for fluid motion . the distributions of axial velocity for the present study are plotted in figs . ( [ cnsns_manuscript_velo7.1.1 - 7.1.4]-[cnsns_manuscript_velo7.5.1 - 7.5.13 ] ) for different values of @xmath0 , @xmath4 , @xmath11 and @xmath17 . since the flow is unsteady in the fixed frame of reference and the velocity profiles along with the radius of the blood vessels change with time , the distribution of velocity has been investigated at a time interval of a quarter of a metacronal wave period of cilia . when @xmath81.,title="fig:",width=321,height=172 ] when @xmath81.,title="fig:",width=321,height=172 ] + @xmath68 one can observe from fig . [ cnsns_manuscript_velo7.1.1 - 7.1.4 ] that at any instant of time , there exists a retrograde flow region and the maximum retrograde flow occurs at the narrowest portion of the tube , while the maximum forward flow occurs at the widest portion of the tube . however , the forward flow region is predominant in this case , since the time - averaged flow rate is positive for free - pumping ( cf . pumping characteristic in the previous section ) . moreover , the study further reveals that there exist two stagnation points on the axis . for example , at time t=0.75 , one of the stagnation points lies between z=0.0 and z=0.25 , while the other lies between z=0.25 and z=0.5 separating the central region of a retrograde flow from two forward flow regions . similar observations were made numerically and analytically by takabatake and ayukawa @xcite and maiti and misra @xcite , misra and maiti @xcite for a newtonian fluid and non - newtonian fluids respectively for a peristaltic transport . from the standpoint of ciliary pumping , this retrograde flow at the trough region is considered to be a kind of ineffective leakage . .,title="fig:",width=321,height=172].,title="fig:",width=321,height=172 ] + @xmath68 it is to be noted that the beat of a single cilium can be separated into two distinct phases . one being the effective stroke of cilia , when the cilium moves in the same direction as the general fluid movement and the reflux may occurs near the walls and in this case the portion of tube is wider . the other phase being the recovery stroke , when the cilium moves in opposite direction to general fluid movement and there may be forward flow near the walls and in this case the portion of the tube is narrower . .,title="fig:",width=321,height=172].,title="fig:",width=321,height=172 ] + @xmath68 .,title="fig:",width=321,height=172].,title="fig:",width=321,height=172 ] + @xmath87 the effects of @xmath0 , @xmath4 , @xmath11 and @xmath17 upon the velocities at the crest and the trough section of the tube are shown in figs . ( [ cnsns_manuscript_velo7.2.1 - 7.2.6]-[cnsns_manuscript_velo7.5.1 - 7.5.13 ] ) in the case of free - pumping . it may be observed from the fig . ( [ cnsns_manuscript_velo7.2.1 - 7.2.6 ] ) that there is a remarkable increase in magnitude of the axial velocity due to an increase in the value of @xmath0 for both sections . this implies that the increase of cilium length at least up to a certain limit can produce more driving force . ( [ cnsns_manuscript_velo7.3.1 - 7.3.6 ] ) illustrates that the magnitude of the axial velocity for both sections enhances significantly at the central region , while the reverse trend occurs at the boundary region if flow index number @xmath4 increases . that reverse trend might have been initiated due to the increase of friction at the boundary region of the tube if @xmath4 rises . as shown in figs . ( [ cnsns_manuscript_velo7.4.1 - 7.4.13]-[cnsns_manuscript_velo7.5.1 - 7.5.13 ] ) , for both sections , wave number @xmath11 and eccentricity @xmath17 of of the path of the cilia raise the magnitude of the axial velocity at the central region , while at the boundary region the trend is reversed indicating the rise of friction by increase in @xmath11 and @xmath17 . .,title="fig:",width=321,height=172].,title="fig:",width=321,height=172 ] + @xmath68 .,title="fig:",width=321,height=172].,title="fig:",width=321,height=172 ] + @xmath87 the ciliated walls of an axisymmetric tube have been modelled by an metachronal wave of cilium which is equivalent to a wavy wall of peristaltic transport . there is only a few available data in the existing literature on the flow rates due to the ciliary activity . the relationship between the pressure difference and the time - mean - volume flow through an axisymmetric tube is given in ( [ cnsns_manuscript_cilia_pressure_rise_relation ] ) . we have to test if the results of ( [ cnsns_manuscript_cilia_pressure_rise_relation ] ) are applicable to the flow rates observed in the ductus efferentes of the male reproductive tract . in the human , the ductuli efferentes are 10 - 15 tubules connecting the rete testis to the epididymis and the cells lining these tubules are ciliated . it is generally believed that the cilia are responsible for fluid transport @xcite . on the basis of experimental observations @xcite on the flow rates in the rete testis of rat , ram , and bull , the approximate flow rate in human rete testis per ductus efferentes was estimated by lardner and shack @xcite as @xmath881 0@xmath89 @xmath3 with approximate dimensions of @xmath90 , with frequency of beat of the cilia being 20/sec and @xmath91 . the said values justify the use of long wavelength and small reynolds number theory ( @xmath47 ) of the study . lardner and shack @xcite calculated the non - dimensional flow rate and dimensional flow rate as @xmath92 and @xmath9310@xmath89 @xmath3 respectively from their model in the case of free pumping assuming @xmath74 , @xmath65 and @xmath66 . however , if we consider all these values fixed with our model together with @xmath62 , our model gives the non - dimensional flow rate in an axisymmetric tube as @xmath94 and consequently the dimensional flow rate is @xmath9510@xmath89 @xmath3 ( cf . [ cnsns_manuscript_pump7.1.1 - 7.4.1]a ) . these values , for an axisymmetric tube are twice the values reported by lardner and shack @xcite for a two - dimensional channel . thus a considerable improvement is needed . however , @xmath0 is linearly proportional to the cilia length on the basis of the assumption and @xmath4 is linked to the rehological fluid ( widely known as non - newtonian fluid ) in the ductus efferentes of the male reproductive tract . it has been seen from fig . [ cnsns_manuscript_pump7.1.1 - 7.4.1 ] that the flow rates increase significantly with an increase in @xmath0 . the flow rates increase with cilia length was also reported in @xcite . moreover , for higher values of @xmath0 , rheological fluid index @xmath4 remarkably affect the fluid transport for adverse pressure gradient at pumping zone . in addition , if we consider @xmath96 , @xmath97 , @xmath81 , @xmath65 and @xmath66 then the non - dimensional flow rate and dimensional flow rate are calculated as @xmath98 and @xmath9910@xmath89 @xmath3 respectively which is close to the estimated value @xmath2 @xmath3 . but authors have no idea about the actual length of cilia and hence the value of @xmath0 , due to non - availibility of real physiological data of the concerned variables and parameters esed in the analysis . an analysis for the rheological fluid transport by means of a sequence of beat of cilia which are in an array and coordinated in such a way as to represent the metachronal wave is presented . the objective of the present study is related to the problems associated with the understanding of the fluid transport through the ductus efferentes of the human male reproductive tract ( @xcite ) and the effect of cilia on ovum and sperm transport in the fallopian tubes etc . however aonly n application of the our results for flow rates to the observed flow rates in the ductus efferentes of the reproductive tract is discussed here . on the basis of the derived analytical expressions , extensive numerical computations have been carried out . the effects of various parameters , such as @xmath0 , @xmath4 , @xmath11 , @xmath17 on pumping characteristic and velocity distribution are investigated in detail in the case of an axisymmetric tube flow . the study reveals that for a particular set of values , say @xmath74 , @xmath100 , @xmath66 , @xmath62 , @xmath81 , as considered in @xcite , flow rate in an axisymmetric tube is twice the value reported by lardner and shack @xcite for a two - dimensional channel . it further reveals that the flow rate changes remarkably with @xmath0 and @xmath4 and when @xmath0 is near by 0.5 our results of flow rate in human ductus efferentes are close to the estimated value @xmath2 @xmath3 as suggested by lardner and shack @xcite based on the experimental observations on the flow rates in the ductus efferentes in the other animals e.g. rat , ram , and bull . the considerable difference between the theoretical and the observed values indicates that the metachronal wave of cilia can not account for the total flow rate in ductus efferents and there must be some other important factors , responsible for the transport of semen . these factors may be ( cf . ilio and hess @xcite ) ( a ) contraction of smooth muscle ( b ) constant secretion of fluid by the seminiferous epithelium ( c ) contraction of the myoepithelial layer of the seminiferous tubule and tunica albuginea of the testis ( d ) the vacuum created by the ejaculation of sperm from the lower tract and by the absorption of fluid ( e ) increased pressure due to the pattern of branching and convergence of ductuli . consequently , to understand the mechanism involved in transport of semen in ductus efferentes of male repductive tract adequately , further theoretical and experimental investigations are essential . it is important to mention that forward flow takes place at the wider portion of the tube , while backward flow occurs at narrower portion of the tube in a similar fashion of peristaltic transport @xcite , although forward flow is dominant for positive time - averaged flow . + * acknowledgment : * _ one of the authors , s. maiti , is grateful to the university grants commission ( ugc ) , new delhi for awarding the dr . d. s. kothari post doctoral fellowship during this investigation . _ rivera , j. a , _ cilia , ciliated epithelium , and ciliary activity_. new york : pergamon press ( 1962 ) gray , j , _ ciliary movement _ , new york : academic press ( 1928 ) . lucus , a . m , ciliated epithelium , _ special cytology _ * 1 * ( 1932 ) , 409 - 473 . lardner t. j. and shack w. j. , cilia transport , _ bull . * 34 * ( 1972 ) , 325 - 335 . faure - fremiet , e , cils vibratiles et flagelles , _ biol . * 36 * ( 1961 ) , 464 - 436 . fawcett , d. , _ cilia and flagella _ , in the cell , braehet , j. and a. e. mirsky , eds . new york : academic press ( 1961 ) . satir , p. , structure and function in cilia and flagella , protoplasmatologia , iiie ( 1965 ) . satir , p. , studies of cilia ; 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the purpose of this paper is a theoretical study of a non - linear problem of rheological fluid transport in an axisymmetric tube by cilium . however , an attempt has been made to explain the role of cilia motion on the transport of fluid through the ductus efferentes of the male reproductive tract . ostwald - de waele power law viscous fluid has been considered to represent the rheological fluid to analyze pumping by means of a sequence of beat of cilia from row to row of cilia in a given row of cells and from one row of cells to the next ( metachronal wave movement ) under conditions for which the corresponding reynolds number is small enough for inertial effects to be negligible and the wavelength to diameter ratio is large enough for the pressure to be considered uniform over the cross - section . analyses and computations of the detailed fluid motions reveal that the time - averaged flow rates are directly dependent on @xmath0 , a non - dimensional measure involving the mean radius @xmath1 of the tube and the cilia length . thus , flow rate significantly varies with the cilia length . moreover , the flow rate has been reported close to the estimated value @xmath2 @xmath3 in human ductus efferentes when @xmath0 is near by 0.5 . the estimated value was suggested by lardner and shack @xcite in human based on the experimental observations on the flow rates in the ductus efferentes in the other animals , e.g. , rat , ram , and bull . in addition , the nature of the rheological fluid , i.e. , the value of the fluid index @xmath4 strongly influences various flow - governed characteristics . + _ keywords : non - newtonian fluid ; cilia movement ; metachronal wave ; flow reversal ; velocity at wave crest and trough . _ 0.8 cm -.1 in -.1 in 0.0 cm 22.5 cm [ section ] [ theorem]definition [ theorem]observation [ theorem ] [ theorem]proposition [ theorem]rule 22.5 cm = currsize

although the sm - like higgs boson has been discovered at the large hadron collider ( lhc ) @xcite , there are still a number of questions that call for physics beyond the sm ( bsm ) : ( i ) the origin of the mass of higgs particle or the origin of weak scale , ( ii ) the nature of non - baryonic dark matter ( dm ) , ( iii ) the origin of neutrino masses and mixing , ( iv ) matter - antimatter asymmetry of the universe , to name a few . the first question is often phrased as hierarchy problem , that addresses why the electroweak ( ew ) scale @xmath1 gev is much smaller than the planck scale . one of the nice ways to understand this is through quantum dimensional transmutation , which explains why the proton mass is much suppressed compared with the planck mass in quantum chromodynamics ( qcd ) @xcite . technicolor ( tc ) provides an answer in this way , but the naive version of it is strongly disfavored by the electroweak precision test ( ewpt ) @xcite . since the observation of w. bardeen @xcite , softly broken scale invariance has been considered as a possible solution for the hierarchy problem . if the model is scale invariant at classical level , no dimensionful parameters are allowed and the scale symmetry is broken only logarithmically through scale - anomaly . many authors have studies this type of models where the ew symmetry is dynamically broken via dimensional transmutation in the hidden sector with new confining strong interactions @xcite , or coleman - weinberg mechanism @xcite . some of the present authors have proposed a scale - invariant extensions of the sm with a strongly interacting hidden sector , namely hidden qcd models @xcite . at the classical level , the scale invariance is imposed so that all dimensionful parameters are forbidden in the classical lagrangian . the higgs mass term arises at quantum level through the dimensional transmutation driven by asymptotically free gauge theories in the hidden sector . hidden sector couples to the higgs through singlet scalar field only and there are stable or long - lived particles ( lightest hidden mesons and hidden baryons ) that can make good dm candidates . in those works , hidden qcd sector was studied in the chiral effective lagrangian approach and non - perturbative parameters were estimated by naive dimensional analysis . then the same model was analyzed in the nambu jona - lasinio ( njl ) approach in ref . @xcite . in this paper , we consider the same model using another approximation method , the ads / qcd @xcite , in order to analyze non - perturbative strong dynamics in the hidden qcd models . first we reformulate the hidden qcd sector in terms of the linear sigma model , in which the sigma and pi mesons are effective degrees of freedom . we consider a linear sigma model coupled with a scale - invariant higgs - singlet sector and analyzed the masses and mixing between the sm higgs boson , a singlet scalar messenger and the sigma meson . in the ads / qcd we successfully reduce the number of free parameters by matching the mass spectra of the lightest scalar , vector and axial vector mesons . next , we apply this model to dark matter phenomenology . in our model , since the hidden quarks do not couple to any u(1 ) gauge fields , the hidden pions can not decay through the u(1 ) anomaly and are found to be stable lightest particles coupling weakly with the sm fields . hence the hidden pions become candidates of the weakly interacting massive particle ( wimp ) dm . with the free parameters reduced by the ads / qcd , we identify the parameter space that satisfies the recent observations . then we study the distinctive features of the allowed parameter region and also some typical correlations among various observables . we address on the possible signatures of the model that can be further scrutinized in the future experiments such as lhc run - ii , ilc and so forth . this paper is organized as follows . in sec . [ sect - model ] , we revisit the original hidden qcd models @xcite by reformulating the hidden qcd sector with the linear sigma model . then in sec . [ sec : qcdqcd ] , we apply the idea of the ads / qcd to the linear sigma model described in sec . [ sect - model ] . in sec . [ sect - dm ] , numerical results on the higgs and the dark matter phenomenologies are presented . then sec . [ sect - summary ] is devoted to summary and discussions . scale - invariant extension of the sm with a strongly interacting hidden sector contains the sm fields plus a singlet scalar @xmath2 and a scale - invariant hidden qcd sector @xcite . the corresponding lagrangian is given by @xmath3 where @xmath4 is the mass parameter of the sm higgs boson . we have replaced all the mass parameters ( the higgs boson mass , the rh neutrino masses and the current quark masses of hidden - sector quarks ) by real singlet scalar operators @xmath2 or @xmath5 following the idea of classical scale invariance . @xmath6 is the field strength of the hidden qcd with @xmath7 gauge symmetry . the sm singlet scalar @xmath2 couples to the hidden - sector quarks @xmath8 through the yukawa interaction . since there are no dimensionful parameters in the lagrangian , this system is scale - invariant at the classical level . at quantum level and low - energy scale , the hidden - qcd quarks can condensate . such condensates @xmath9 induce a linear term in @xmath2 . then the potential of @xmath2 can be tilted and @xmath2 can develop a vev . the vev of the singlet scalar generates a higgs boson mass term @xmath10 , as well as the rh neutrino masses and the current quark masses of the hidden - sector quarks . thus all the mass scales in this model are generated by @xmath11 , which is a result of non - perturbative dynamics in the strongly interacting hidden sector . for this to happen , we assume that @xmath12 so that non - zero @xmath11 triggers the electroweak symmetry breaking . hereafter we consider the case in which @xmath13 and @xmath14 , for which we can use the known results from the hadronic system with @xmath15 and @xmath16 mesons . then @xmath17 and for simplicity we assume the hidden quarks have isospin symmetry @xmath18 . in such a case the low - energy effective theory of the hidden qcd is described by the pi meson triplets and the sigma meson . it would be written in the form of a linear sigma model @xmath19 where @xmath20 and @xmath21 represents sigma and pi meson fields . we parameterize the vevs and fluctuations of scalars as @xmath22 to minimize the potential energy @xmath23 three minimization conditions @xmath24 ( @xmath25 ) should be satisfied . these conditions reduce the number of free parameters . furthermore , two parameters @xmath26 , @xmath27 are traded with the pion mass @xmath28 and a sigma meson mass parameter @xmath29 . hence the scalar mass matrix @xmath30 takes the form of @xmath31 with @xmath32 where @xmath33 and @xmath34 . since a off - diagonal part @xmath35 satisfies @xmath36 , the higgs - singlet mixing can be large when @xmath0 is small . @xmath26 and @xmath27 are traded with pion mass @xmath28 and sigma meson mass @xmath29 by @xmath37 the couplings @xmath38 , @xmath39 are given by @xmath40 where @xmath41 . since one of the physical scalar should be the higgs boson with mass @xmath42 , @xmath43 is one of the eigenvalues of @xmath44 . thus a condition @xmath45 ( @xmath46 is a @xmath47 unit matrix ) yields @xmath48 + m_h^6 v_h^2 \tan^2\beta } { 3 \xi_\sigma^2 f_\pi^4 - f_\pi^2 [ 3 m_\pi^2 m_h^2 + m_\pi^4 + m_h^2 v_h^2 ( 1 + \tan^2\beta ) \xi_\sigma^2 ] + m_h^4 v_h^2 ( 1 + \tan^2\beta)},\end{aligned}\ ] ] where we have parameterized @xmath49 . the mixing matrix is defined as @xmath50 where @xmath51 is the sm - like higgs boson with @xmath52 gev and @xmath53 are extra scalar particles with @xmath54 . at this stage we have four free parameters : @xmath55 , @xmath56 , @xmath28 and @xmath29 ( or @xmath57 ) . to reduce the number of free parameters , in particular , to relate the @xmath29 with @xmath58 , we use a holographic treatment of the hidden qcd . in the ads / qcd @xcite , the hidden qcd sector is described by @xmath59 gauge theory on @xmath60 space with metric @xmath61 where @xmath62 and @xmath63 is the curvature radius of @xmath60 . @xmath64 breaks the conformal symmetry in the infrared ( ir ) regime , while one can take @xmath65 to be arbitrary small , @xmath66 . the non - perturbative breaking of chiral symmetry is regarded as the spontaneous breaking of @xmath59 symmetry by the vev of the bulk scalar @xmath67 which is a bi - doublet @xmath68 . the parity transformation corresponds to the exchange @xmath69 . then the 5d bulk lagrangian is given by @xmath70,\end{aligned}\ ] ] where @xmath71 , @xmath72 , and the bulk mass parameter @xmath73 is chosen so as to relate the bulk scalar field @xmath67 with the dimension - three operator @xmath74 . the profile of the vev is obtained by solving the zero - mode equation of motion . we have @xmath75 where @xmath76 and @xmath77 can be written in terms of the value of @xmath78 at boundaries @xmath79 from boundary conditions @xmath80 here nonzero @xmath77 corresponds to the spontaneous breaking of the chiral symmetry in the ir , while the boundary condition at @xmath81 corresponds to the explicit breaking of chiral symmetry . the boundary condition at @xmath82 is induced by the scalar potential localized on @xmath83 boundary . the boundary interaction is @xmath84 after the symmetry breaking @xmath85 , vector- and axial - vector gauge bosons @xmath86 , @xmath87 are expanded into kaluza - klein ( kk ) modes @xmath88 where @xmath89 , @xmath90 correspond to hadronic vector and axial - vector currents , respectively . the bulk scalar @xmath67 is decomposed into @xmath91 and gauge fixing conditions are @xmath92 and @xmath93 have the following kk expansions : @xmath94 where @xmath95 and @xmath96 are scalar and pseudo - scalar hadronic states , respectively . in particular @xmath97 corresponds to the pion . in the qcd the two point correlators for the scalars and pseudoscalars are defined as @xmath98 where the two - point correlator can be obtained from the generating function @xmath99 according to @xmath100 where @xmath101 and @xmath102 are the scalar and pseudoscalar external sources coupled to qcd : @xmath103 + h.c . , \quad \phi = m_q + \hat{s } + i\hat{p}_s.\end{aligned}\ ] ] according to the ads / cft correspondence , the generating function @xmath99 is obtained by integrating bulk fields restricted to a given ultraviolet(uv)-boundary value which play the role of the external sources coupled to qcd . for the 5d scalar field we have @xmath104 ( @xmath105 is a constant which will be determined in the matching of correlation in uv as @xmath106 @xcite ) or explicitly , @xmath107 since the quark masses are given by @xmath108 , the singlet scalar fluctuation @xmath109 can be related to the scalar source term as @xmath110 this correspondence can be used to obtain the couplings of @xmath109 to the meson states . this ads / qcd model has five relevant free parameters : @xmath111 , @xmath64 , @xmath112 , @xmath113 and @xmath114 . @xmath111 is traded with the pion mass @xmath28 by the gell - mann oaks renner relation @xmath115 \langle \bar{q } q \rangle , \label{gor}\end{aligned}\ ] ] or @xmath116 b_0 $ ] where @xmath117 . @xmath112 is related with the beta - function of the qcd and we fix @xmath118 where we consider the case @xmath119 . @xmath64 is related with the mass of the first kk state of @xmath120 which corresponds to the rho meson mass by @xmath121 . the value of @xmath113 can be fixed by adjusting the mass of the first kk of @xmath122 and the first kk vector meson mass @xmath123 with @xmath124 and @xmath125 , which yields @xcite @xmath126 the pion decay constant @xmath58 is written in terms of @xmath64 , @xmath113 , @xmath127 as @xmath128 when @xmath129 . here @xmath130 is the gamma function . with @xmath131 and @xmath13 one has @xmath132 which well agree with the experimental value @xcite @xmath133 when @xmath134 . hence for @xmath13 and @xmath135 we have @xmath136 . the hidden rho meson mass @xmath137 and hidden axial vector meson mass @xmath138 is estimated as @xmath139 now we fix the value of @xmath140 . in the original paper the author estimated @xmath141 and identified the lightest scalar meson as @xmath142 . in the present study , we regard sigma meson as lightest scalar resonance state , @xmath143 . in the ads / qcd , since the wave functions of @xmath95 , @xmath96 vanish at @xmath81 @xmath144 there are no direct interactions between meson states with source term . in the ads / qcd , source - pion - pion interactions are given by @xmath145 + \text{tr } [ ( \partial_\mu\pi)^2 \hat{s } ] \sum_n \frac{{g_{n\pi\pi } } f_{s_n } m_{s_n}}{p^2 + m_{s_n}^2 } , \label{source - int}\end{aligned}\ ] ] ( @xmath146 ) where @xmath147 , @xmath148 and @xmath149 is the mass , decay constant and the @xmath150 coupling . these terms arise due to the @xmath151 mixing . in particular , the first term of r.h.s . of eq . is induced by @xmath152 coupling through the @xmath16-source mixing . we assume that @xmath153 , @xmath154 and that the mixing is given by @xmath155 together with the gell - mann oaks renner relation eq . we obtain @xmath156 in the ads / qcd , @xmath157 and @xmath158 is obtained for @xmath13 , @xmath135 . @xmath147 and @xmath148 is obtained by formulas summarized in the appendix . we find numerically that eq . is satisfied when @xmath159 ( see fig . [ fig - fm ] ) , in the unit of @xmath160 for @xmath161 , @xmath13 . @xmath162 is indicated as black dashed line . ( a ) @xmath163 ( b ) @xmath164 . , title="fig:",width=264 ] in the unit of @xmath160 for @xmath161 , @xmath13 . @xmath162 is indicated as black dashed line . ( a ) @xmath163 ( b ) @xmath164 . , title="fig:",width=264 ] and hence we obtain a relation ( see fig . 2 ) @xmath165 when we take a scale normalized by @xmath166 so that we have @xmath167 , we obtain @xmath168 , @xmath169 ( fig . [ fig - msigma ] ) . scalar boundary coupling @xmath140 with @xmath161 , @xmath13 , @xmath166 . the shaded band indicates the mass range of @xmath170 @xcite . ( a ) @xmath163 ( b ) @xmath164 . , title="fig:",width=264 ] v.s . scalar boundary coupling @xmath140 with @xmath161 , @xmath13 , @xmath166 . the shaded band indicates the mass range of @xmath170 @xcite . ( a ) @xmath163 ( b ) @xmath164 . , title="fig:",width=264 ] this result well agree with the experimental bound @xmath171 @xcite , if we identify @xmath170 as the sigma meson . as a result of the previous sections , we now have three free parameters in this model : @xmath172 and @xmath173 . for numerical analysis , we scan the three - dimensional parameter space @xmath174 . note that the sm - like higgs boson with mass @xmath175 gev is termed as @xmath51 , and extra scalar particles as @xmath176 and @xmath177 with @xmath54 . we have considered several theoretical and experimental constraints . let us first consider the theoretical constraints . from the stability of the potential , the dimensionless couplings should satisfy the relation , @xmath178 which are translated into the following relation with the minimization conditions @xmath179 since the strongly interacting hidden sector are now treated as linear sigma model , the symmetry breaking condition in the @xmath16-sector would constrain the value of @xmath180 to be positive . with the help of eq . , the condition reads @xmath181 we also adopt the perturbativity bound on @xmath39 with our definition of the lagrangian : @xmath182 experimental constraints considered in the analysis are listed in the following : * signal strength for the sm higgs boson @xcite , @xmath183 * bounds for extra scalar particles from the lep @xcite and the lhc @xcite . * relic density from planck satellite @xcite . @xmath184 * neutrino signals through the dm capture by the sun , mostly from super - kamiokande for upward muon flux @xcite . * fermi - lat 6-year results for dm annihilation @xcite . * higgs invisible width from the lhc @xcite , @xmath185 * direct detection bound , mostly from lux @xcite , supercdms @xcite , and cresst - ii @xcite . we apply @xmath186 bounds with these experimental constraints except for the relic density , for which we use the measured value as an upper bound . this is because there could be additional contributions from hidden baryons to dm thermal relic density , which we do not include in this paper . we vary the @xmath58 up to 2 tev and the ranges for @xmath28 and @xmath0 are fixed with eq . and we use micromegas @xcite for evaluating dm - related observables . the result of scanning is depicted in fig . [ fig3 ] . here we see that there is definite lower bound for @xmath58 , around 100 gev . also @xmath0 is bounded from below , @xmath187 , mainly because of the perturbativity of @xmath39 since it can be written in the form @xmath188 so if @xmath0 is too small , @xmath39 will have very large value , above the perturbativity bound . the island on the leftmost side are the solution points where @xmath189 , _ i.e. _ the sm - like higgs resonances . other points include light scalar resonanaces with @xmath190 , heavy scalar resonances with @xmath191 and non - resonance solutions with @xmath192 . the non - resonance solutions favor relatively small @xmath0 . for example , if the hidden pion mass is away from both resonance regions more than @xmath193 , _ i.e. _ @xmath194 , then @xmath0 is constrained to be smaller than about @xmath195 . no points survive if the hidden pion mass is far away from the resonance regions , more than about @xmath196 . this is because when @xmath0 is small , the off - diagonal term of the mass matrix presented in eq . , @xmath197 , is enhanced compared with large @xmath0 case so that the mixing between the sm - like higgs boson and singlet scalar fields are enhanced . plane with color contours for @xmath0.,width=302 ] these features for the solution points can be more easily checked with another forms of plots . in fig . [ fig4 ] , the solution points are shown in @xmath198 plane . the thin branch in the left plot is the collection of solution points where @xmath199 , light scalar resonances . note that there is no solution points when @xmath200 , _ i.e. _ all extra scalar particles are heavier than the sm - like higgs boson . the right plot , where the points are shown in @xmath201 plane , also includes the thin branch that is corresponding to the solution points with heavy scalar resonances . the shape of the plot is almost same as fig . [ fig3 ] , since a relation @xmath202 generally holds in this model . as a result , @xmath203 has a definite lower bound @xmath204 as @xmath205 does . both plots also include the non - resonance cases , of which dm mass are far from both resonances and other parameters are tuned to satisfy the all constraints . plane ( left ) and @xmath201 plane ( right ) , with color contours for the hidden pion decay constant @xmath58.,title="fig:",width=302 ] plane ( left ) and @xmath201 plane ( right ) , with color contours for the hidden pion decay constant @xmath58.,title="fig:",width=302 ] as a distinctive observable , we show the deviation of the triple higgs coupling from the sm prediction in fig . the triple higgs coupling in the model can reach @xmath206 of the sm prediction for relatively small @xmath28 . if we take larger values for @xmath28 and @xmath58 , it approaches to the sm one and can not be a distinctive observable . especially when @xmath28 is larger than 1 tev , the triple higgs coupling is very close to the sm prediction and the deviation can not be detected . .,width=302 ] let us consider another observables . to be more specific , we separate the cases as the sm - like higgs resonance and the other cases . fig . [ fig6 ] shows the correlations between the higgs signal strength @xmath207 and dm - nucleon cross section in higgs resonance case . deviation of @xmath207 from 1 is generated by the mixing angle @xmath208 in eq . . in this case , the sm - like higgs boson can decay to a pair of dm s and these decay modes contribute to the higgs invisible decay width . as one can see in the left plot , the invisible decay width of the sm - like higgs boson increases when the signal strength decreases and vice versa , just like dm - nucleon cross section . we can understand this by the fact that the deviation of the signal strength is determined entirely by non - zero mixing angles among the sm - like higgs and other extra scalar particles . the more they are mixed , the more wide the channel between the visible and hidden sector is open . we show in the right plot the same correlation with relic density contours . the variation of the relic density is caused by the small variation of @xmath28 and @xmath58 as long as @xmath28 is close to @xmath209 . in both plots we apply @xmath210 bound for the signal strength @xmath207 such as @xmath211 . the same correlation is shown in fig . [ fig7 ] for the other cases than the sm - like higgs resonance . as mentioned before , the cases include light and heavy scalar resonances and non - resonance solutions . in this plot , the color contour represents the mass of the dm . unlike the higgs resonance case , relatively large values of the signal strength are favored , with generically larger values of dm - nucleon cross section . note that there is an upper limit for @xmath207 . this bound is originated from the @xmath212 mixing , that should be different from zero for avoiding the overclosure of the universe by the dm . [ fig8 ] is showing the correlation between the signal strength and triple higgs coupling normalized with the sm prediction . the left plot is for the sm - like higgs resonance solutions and the right one for other cases . both cases are predicting sharp linear correlations , but with different slopes . two solution points are disjoint with each other , so the measurements of them can be used for the identification of the scenarios , though their values are small . finally , some benchmark points are collected in table [ table1 ] . we classify the points as ( a ) sm higgs resonance solutions , ( b ) light scalar resonances , ( c ) heavy scalar resonances , and ( d ) non - resonance solutions . the solution points with large relic densities ( close to upper bound , @xmath213 ) are labelled as ( i ) and ( ii , iii ) correspond to the cases of small relic densities . note that the closer we take the dm mass to the exact resonance , @xmath214 ( or @xmath215 ) , the smaller the relic density becomes . .benchmark points for ( a ) sm - like higgs resonance , ( b ) light scalar resonance , ( c ) heavy scalar resonance and ( d ) non - resonance cases . [ cols="^,^,^,^,^,^,^,^,^,^,^",options="header " , ] in this paper , we have analyzed the scale - invariant extension of the sm with vector - like confining gauge theory in the hidden sector by using the ads / qcd proposed in refs . the model contains the singlet scalar field that connects the confining hidden sector and the scale - invariant sm sector . hidden sector fermions develop nonzero chiral condensates and generate the linear term in the potential of the singlet scalar field @xmath2 . as a result , the singlet scalar field @xmath2 develops a nonzero vev and it provides the tachyonic mass term for the sm higgs field . therefore the origin of the ewsb in the sm sector lies in the new strong dynamics in the hidden sector . we have used the ads / qcd approach to describe non - perturbative dynamics of the hidden qcd sector . by the ads / qcd , strongly interacting @xmath216 gauge theory in the hidden sector with two - flavors can be described by @xmath217 gauge theory on @xmath60 . the spectrum of the mesonic states then can be calculated up to overall scale by considering the two - point correlators . we first fixed the values of the ads / qcd parameters that reproduce the known spectra of the mesons by identifying first kk mode of the vector state as rho meson . we applied the results to the hidden qcd . in this case , hidden rho meson mass is be treated as overall scale of the hidden qcd . by this , we successfully found out the relation between hidden sigma meson mass and hidden pion decay constant etc . as a result , we reduced the number of free parameters of the model to three , _ i.e. _ @xmath218 and @xmath0 . the hidden pions can be the dm candidates since the hidden sector flavor symmetry becomes an accidental symmetry of hidden sector strong interaction . we have analyzed these `` hidden pion '' properties as the dm . many results of the dm search experiments were considered . in addition to the sm - like higgs boson , we have two extra neutral scalar fields in the model . those extended scalar sectors are constrained by the lhc data , for example higgs signal strengths and non - observation of another scalar particles , etc . by scanning the three - dimensional parameter space @xmath219 , we found that the non - resonance solutions are also possible in addition to the resonance solutions . we also considered various correlations among the experimental observables . for example , there is the correlation between the higgs signal strength @xmath207 and dm - nucleon cross section , and also between @xmath207 and the triple sm - like higgs coupling . especially for the latter , we found that their values and correlations behave differently depending on whether hidden pions have the sm - like higgs resonance or not . though the higgs signal strength @xmath207 has been measured quite precisely and seems to be consistent with the sm prediction , there is still room for the physics beyond the sm as discussed in this paper . if the higgs signal strength @xmath207 is measured more precisely , according to the sharp correlations we found , we can give peculiar predictions on the dm properties and others such as triple higgs coupling etc . this could be seen in the benchmark points we presented at the end of the analysis . let us comment on the future prospects . our model contains two extra neutral scalar bosons that mix with the sm - like higgs boson . mass spectra of those two scalar bosons are constrained by the up - to - date experimental results on the higgs signal strengths in such a way that both of them are heavier than the 125 gev sm - like higgs boson . besides the resonance solutions by the sm - like higgs , extra light and heavy scalar particles , the non - resonance solutions are also possible for moderate values of hidden pion mass and decay constant . in that case , the mass of the light extra scalar particle will be around a few hundred gev , which can be accessible at the lhc run - ii . the model also predicts the values of other observables such as relic density , dm - nucleon cross section and triple higgs coupling and so forth . especially , the higgs signal strength @xmath207 will be sharply determined . the more detailed study on the collider phenomenologies , for example , the pair production of the sm - like higgs boson , could be possible . in addition , more complete studies with the hidden baryons , another dm candidates , can be pursued with the ads / qcd . this work is supported in part by national research foundation of korea ( nrf ) research grant nrf-2015r1a2a1a05001869 ( hh , dwj , pk ) , nrf-2015r1d1a1a01059141 , nrf-2015r1a2a1a15054533 ( dwj ) and by the nrf grant funded by the korea government ( msip ) ( no . 2009 - 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in this paper , we revisit a scale - invariant extension of the standard model ( sm ) with a strongly interacting hidden sector within ads / qcd approach . using the ads / qcd , we reduce the number of input parameters to three , _ i.e. _ hidden pion decay constant , hidden pion mass and @xmath0 that is defined as the ratio of the vacuum expectation values ( vev ) of the singlet scalar field and the sm higgs boson . as a result , our model has sharp predictability . we perform the phenomenological analysis of the hidden pions which is one of the dark matter ( dm ) candidates in this model . with various theoretical and experimental constraints we search for the allowed parameter space and find that both resonance and non - resonance solutions are possible . some typical correlations among various observables such as thermal relic density of hidden pions , higgs boson signal strengths and dm - nucleon cross section are investigated . we provide some benchmark points for experimental tests .

glycogenosis type v , also known as glycogen storage disease type v ( gsd v ) , myophosphorylase deficiency , or mcardle disease ( online mendelian inheritance in man [ omim ; johns hopkins university , baltimore , md ] number 232600 ) , is a rare , mostly autosomal recessive disorder causing deficient myophosphorylation of glycogen in the skeletal muscles.1 patients with mcardle disease have mutations in both alleles of the pygm gene , which encodes myophosphorylase , the skeletal muscle isoform of glycogen phosphorylase.2 as the liver and heart isoforms of glycogen phosphorylase are unaffected , mcardle disease presents as a pure myopathy.3 here , we report the case of a 54-year - old man with mcardle disease who had a long history of fatigability and exercise intolerance ; he became unhappy and depressed because of not having an explanation for his symptoms for most of his life . we also summarize the main features of mcardle disease , including diagnostic tools and current therapeutic options . a 54-year - old man presented to our service with a lifelong history of fatigability that worsened on exertion . even as a child , he had experienced difficulty going up hills and lagged behind when he went out for a walk with friends . since his childhood , he had been labeled as lazy by family and friends . he consulted several doctors , who were unable to provide an explanation for his symptoms , adding to his unhappiness and resulting in depression . he presented to our service with early fatigue complaints and contractures triggered by dynamic exercise ( climbing stairs ) during a visit to his mother in hospital . he described a sensation of his legs becoming stiff like a board after walking for a while ; this symptom was relieved by rest . there were no diurnal fluctuations in symptoms , and findings of physical examination were unremarkable . he had been receiving long - term treatment with tianeptine , bromazepam , omeprazole , and silymarin . at presentation , results of routine blood and chemistry tests showed a creatine kinase ( ck ) level of 7924 u / l , a lactate dehydrogenase level of 624 u / l , and a myoglobulin level of 671 ng / ml . a repeat check performed after cessation of treatment revealed a ck level of 2945 u / l . results of tests for autoimmune disease - related antibodies such as antinuclear antibody and anti - ssa , anti - ssb , and topo - i antibodies were negative . needle electromyography findings were normal at rest but upon volunteer effort , showed a myopathic pattern characterized by reduced duration and amplitude , and increased recruitment of potential short polyphasic motor units in the biceps and deltoid muscles . a muscle biopsy specimen stained for glycogen showed subsarcolemmal accumulation of lakes of glycogen . results of enzyme histochemistry were completely negative for myophosphorylase , confirming the diagnosis of mcardle disease ( gsd v ) . a genetic study showed double heterozygosity of the pygm gene , with the mutation c.148c > t ( p.r49x ) in exon 1 and the change c.345 + 1 g > a in intron 2 , which , according to the bioinformatics simulations carried out , is a splicing mutation . myophosphorylase initiates the breakdown of muscle glycogen by removing ( 1,4)--glucosyl units from the outer branches of glycogen , leading to liberation of glucose-1-phosphate , which subsequently undergoes glycolysis . as a consequence of deficient myophosphorylase activity , patients with mcardle disease are unable to obtain energy from their muscle glycogen stores.4 given that glycolysis is blocked upstream , the skeletal muscle fibers of patients with mcardle disease can still take up glucose from the blood and convert it into glucose-6-phosphate , which then enters the downstream steps of glycolysis . therefore , muscle glycolysis is not totally impaired in these patients , and pre - exercise ingestion of carbohydrates can markedly improve their exercise tolerance.5 acute exercise can trigger episodes of reversible muscle crises that manifest mainly in the form of excessive , premature fatigue and contractures , frequently accompanied by marked muscle breakdown ( rhabdomyolysis ) and sometimes by myoglobinuria . potential differential diagnosis includes defects in phosphofructokinase ( pfk ; gsd vii or tarui disease ) , phosphorylase b kinase ( gsd viii ) , phosphoglycerate kinase ( gsd ix ) , phosphoglyceromutase ( gsd x ) , lactate dehydrogenase ( gsd xi ) , and -enolase ( gsd xiii ) . the time of onset of the typical disease symptoms and the degree of exercise intolerance vary between patients . another fact that might contribute to phenotypic heterogeneity is the patient s gender , with women generally being more severely affected than men.6,7 some patients can be oligosymptomatic , but in rare cases the disease can be profoundly incapacitating . disease severity has been correlated with genotype at the angiotensin - converting enzyme ( ace ) locus , where an in sertion / deletion variant ( the d allele ) associated with modestly increased ace activity is found more commonly in patients with more severe symptoms and reduced exercise tolerance.8 mcardle disease is not usually a life - threatening condition , although there are some exceptions . myoglobinuria occurs in about 50% of patients after intense exercise and about 50% of these patients also develop acute renal failure , which is almost always reversible but requires emergency treatment.9 the main diagnostic tools for mcardle disease are four features present in the majority of patients . the first is exercise intolerance , usually present from childhood , with or without actual fixed muscle weakness at the time of evaluation . another classic feature is a high serum level of total ck activity , even at rest , in the absence of heavy exercise in the previous hours or days . a third characteristic of the disease is one or more previous episodes of elevated ck serum levels after intense exercise . phenomenon , a pathognomonic feature of mcardle disease.10 first described by pearson et al , the second wind phenomenon denotes a sudden , marked improvement in the tolerance to aerobic , dynamic , large muscle mass exercise after approximately 10 minutes , that is , the disappearance of the excessive fatigue , breathlessness , and tachycardia that are triggered at the start of exertion.11 most patients describe this phenomenon as the ability to resume exercising if they take a brief rest at the appearance of premature fatigue early during exercise . this second wind can be explained by increased blood flow , enhanced delivery of free fatty acids with concurrent activation of fatty acid metabolism , and increased glucose utilization . in fact , haller and vissing showed that the second wind phenomenon is abolished by glucose infusion or sucrose ingestion before exercise.12 the first diagnostic test used for mcardle disease was a forearm ischemic test , but this can be painful and can produce false - negative results in the weakest patients or false - positive results in patients with other defects of glycogenolysis or glycolysis . biopsy of the vastus lateralis or biceps brachialis muscles is commonly conducted in patients with mcardle disease , in order to enable histochemical and biochemical analysis . in addition to subsarcolemmal or intermyofibrillar glycogen deposits , muscle specimens from patients with mcardle disease show a negative histochemical reaction for myophosphorylase and null activity of this enzyme.13 diagnosis based on molecular genetics can be very useful , where the required technology is available . around 100 different mutations have been described in pygm . the number of mutations continues to increase , highlighting the importance of complementary dna - based molecular studies for the diagnosis of mcardle disease.14 despite all efforts , no effective gene therapy is available to alleviate myophosphorylase deficiency in humans.15,16 at present , the most beneficial intervention for patients with mcardle disease , in combination with aerobic conditioning , is ensuring that sufficient blood glucose is constantly available to patients working muscles during the daytime . this is achieved by adopting a diet with a high proportion ( 65% ) of complex carbohydrates ( such as those found in vegetables , fruits , cereals , bread , pasta , and rice ) and a low proportion ( 20% ) of fat . in addition , the ingestion of simple carbohydrates ( 2040 g of glucose or fructose in adults and 20 g in children ) approximately 5 minutes before engaging in strenuous exercise , such as brisk walking or physical education in younger patients , can be helpful . in general , vigorous dynamic exercise should be performed only by the more fit patients and should be combined with pre - exercise carbohydrate ingestion . very intense exercises , particularly those involving high loads on low muscle mass , are strongly discouraged in these patients . increasing copies of the d allele at the ace locus is associated with disease severity , especially in women ; the preliminary results of a study based on this observation suggest that treatment with the ace inhibitor ramipril is beneficial.17 mcardle disease is a pure myopathy caused by an inherited deficit of the skeletal muscle isoform of glycogen phosphorylase . this syndrome is characterized by exercise intolerance , with most patients experiencing acute muscle crises after static or intense dynamic exercise . crises appear in the form of early muscle fatigue and contractures , sometimes with marked muscle breakdown ( rhabdomyolysis ) and myoglobinuria . no effective gene therapy is expected to be available in the short term . until a definitive cure is found , patients can benefit from adopting a diet rich in complex carbohydrates and ingesting simple carbohydrates before strenuous exercise . carefully supervised , regular , aerobic exercise of low - to - moderate intensity is a safe , recommended therapeutic option , but exercises that involve heavy static contractions or induce severe myalgia should be avoided . the benefits of creatine supplementation , treatment with ace inhibitors , and vitamin b6 supplementation remain unproven for patients with muscle phosphorylase deficiency.18

mcardle disease ( glycogen storage disease type v ) is a pure myopathy caused by an inherited deficit of myophosphorylase . the disease exhibits clinical heterogeneity , but patients typically experience exercise intolerance , acute crises of early fatigue , and contractures , sometimes with rhabdomyolysis and myoglobinuria , triggered by static muscle contractions or dynamic exercise . we present the case of a 54-year - old man with a lifelong history of fatigability , worsening on exertion . laboratory evaluation revealed significant elevations in levels of creatine kinase ( 7924 u / l ) , lactate dehydrogenase ( 624 u / l ) , and myoglobulin ( 671 ng / ml ) . a muscle biopsy confirmed the presence of mcardle disease . this case report illustrates how , due to embarrassment , the patient hid his symptoms for many years and was eventually extremely relieved and liberated once mcardle disease was diagnosed 40 years later .

in relativistic heavy - ion collisions large differences between the longitudinal and transverse expansion rates lead to large shear viscous effects , generating large anisotropies between the longitudinal and transverse pressures during the early stage of their evolution . these cause standard israel - stewart ( second - order ) viscous hydrodynamic theory ( see @xcite for a recent review ) to break down . anisotropic hydrodynamics @xcite ( ahydro ) deals with the large longitudinal / transverse pressure anisotropy , @xmath0 , `` non - perturbatively '' , thereby avoiding the occurrence of negative longitudinal pressures and improving the performance of hydrodynamics at early times @xcite . however , ahydro @xcite accounts only for one ( the largest ) of the five independendent components of the shear stress tensor @xmath1 . it can therefore not be used to compute the viscous suppression of elliptic flow which is sensitive to e.g. @xmath2 . on the other hand , since the four remaining components of the shear stress tensor never become as large as the longitudinal / transverse pressure difference ( with smooth initial density profiles they start out as zero , and with fluctuating initial conditions they are initially small ) , they can be treated `` perturbatively '' la israel and stewart , without running into problems even at early times . combining the non - perturbative dynamics of @xmath0 via ahydro with a perturbative treatment of the remaining viscous stress terms @xmath3 la israel - stewart defines our new vahydro scheme . it is expected to perform better than both is theory and ahydro during all evolution stages . the physics behind different hydrodynamic approximations to the underlying microscopic dynamics is best illustrated by starting from the boltzmann equation and considering conditions ( weakly coupled microscopic dynamics and small pressure gradients on the macroscopic level ) where both approaches are simultaneously valid . the form of the resulting hydrodynamic equations ( but not the value of the associated transport coefficients ) is independent of the coupling strength and remains unchanged for a strongly coupled liquid . we restrict ourselves to conformal systems with massless degrees of freedom generalizations to massive systems can be found in the literature @xcite . using the relaxation - time approximation ( rta ) for the collision term , with @xmath4 where @xmath5 is the local temperature , the boltzmann equation reads @xmath6.\ ] ] we define @xmath7-moments of the distribution function weighted with some momentum observable @xmath8 by @xmath9 ( @xmath10 is a degeneracy factor ) . the ( baryon-)charge current and energy momentum tensor are then written as @xmath11 they take their ideal fluid dynamical form @xmath12 and @xmath13 ( where @xmath14 is the spatial projector in the local rest frame ( lrf ) ) if we assume that the system is locally momentum isotropic : @xmath15 this ideal fluid decomposition does not require chemical equilibrium , nor does it require complete thermal equilibrium in the sense that the dependence of @xmath16 on its argument is exponential . if the dependence is non - exponential , the collision term in the boltzmann equation is non - zero , but its @xmath17-moment still vanishes , @xmath18 , due to energy - momentum conservation . the ideal hydrodynamic equations follow by inserting this ideal fluid decomposition into @xmath19 which one can solve for the local charge density @xmath20 , energy density @xmath21 , and flow velocity @xmath22 , with temperature @xmath23 , chemical potential @xmath24 and pressure @xmath25 following from the equation of state ( eos ) of the fluid . local deviations from chemical equilibrium result in a non - equilibrium value of the local chemical potential and a non - zero right hand side in the charge conservation equation . deviations from thermal equilibrium ( while preserving local isotropy ) must be accounted for by a non - equilibrium pressure in the eos @xmath26 . in both cases ( [ eq5 ] ) lead to a non - vanishing entropy production rate @xmath27 . israel - stewart ( is ) second - order viscous fluid dynamics @xcite is obtained by using in ( [ eq3 ] ) for @xmath28 the ansatz @xmath29 for later convenience we decompose @xmath17 into its temporal and spatial components in the lrf : @xmath30 where @xmath31 and @xmath32 . then @xmath33 and @xmath34 . the decomposition ( [ eq6 ] ) is made unique by landau matching : first , define the lrf by solving the eigenvalue equation @xmath35 with the constraint @xmath36 . this fixes the flow vector @xmath22 and the lrf energy density . next , we fix @xmath23 and @xmath24 by demanding that @xmath37 gives no contribution to the local energy and baryon density : @xmath38 . inserting ( [ eq6 ] ) into ( [ eq3 ] ) we find the general decomposition @xmath39 with a non - zero charge flow @xmath40 in the lrf , a bulk viscous pressure @xmath41 , and a shear stress @xmath42 ( where @xmath43 indicates moments taken with the deviation @xmath37 from @xmath16 ) . in the last equation we introduced the notation @xmath44 , with @xmath45 , for the traceless and transverse ( to @xmath46 ) part of a tensor @xmath47 . the shear stress tensor @xmath48 has 5 independent components . altogether , the deviation @xmath37 has introduced 9 additional dissipative flow degrees of freedom . their corresponding 9 equations of motion are controlled by microscopic physics and can be derived from approximate solutions of the boltzmann equation @xcite . anisotropic hydrodynamics @xcite is obtained from ( [ eq5 ] ) by using in ( [ eq3 ] ) the spheroidally deformed local momentum distribution @xmath49 where @xmath50 , @xmath51 being a unit vector in @xmath52 direction in the lrf . this distribution is characterized by 3 flow parameters @xmath22 and three `` thermodynamic '' parameters : the `` transverse temperature '' @xmath53 , the effective chemical potential @xmath54 , and the momentum - anisotropy parameter @xmath55 . inserting ( [ eq8 ] ) into ( [ eq3 ] ) yields the ahydro decomposition @xmath56 for massless systems , the local momentum anisotropy effects factor out via the @xmath57-functions , given in @xcite . the isotropic pressure is obtained from a locally isotropic eos @xmath58 . for massless noninteracting partons , @xmath59 independent of chemical composition . to compare with ideal and is viscous hydrodynamics , we need to assign the locally anisotropic system an appropriate temperature @xmath60 and chemical potential @xmath61 , thinking of @xmath62 as an expansion around the locally isotropic distribution @xmath63 . for this we impose the generalized landau matching conditions @xmath64 and @xmath65 . for example , using an exponential ( boltzmann ) function for @xmath16 with @xmath66 , one finds @xmath67 . with this matching we can write @xmath68 we see that @xmath69 has only one independent component , @xmath70 , so ahydro leaves 4 of the 5 components of @xmath1 unaccounted for . for massless particles we have @xmath71 , so the equation of motion for @xmath69 can be replaced by one for @xmath72 . for @xmath73 we need an additional `` anisotropic eos '' for @xmath74 , in order to separate @xmath75 from the viscous bulk pressure @xmath76 . * 4 . * finally , vahydro @xcite is obtained by generalizing the ansatz ( [ eq8 ] ) to include arbitrary ( but small ) corrections to the spheroidally deformed @xmath77 : @xmath78 the parameters @xmath79 and @xmath80 are landau - matched as before , _ i.e. _ by requiring @xmath81 ; to fix the value of the deformation parameter @xmath72 we demand that @xmath82 does not contribute to the pressure anisotropy @xmath70 , which requires @xmath83 . then , upon inserting ( [ eq14 ] ) into ( [ eq3 ] ) , we obtain the vahydro decomposition @xmath84 subject to the constraints @xmath85 . clearly , the additional shear stress @xmath86 arising from @xmath37 has only 4 degrees of freedom . the strategy in vahydro is now to solve hydrodynamic equations for ahydro ( which treat @xmath70 nonperturbatively ) with added viscous flows from @xmath87 , together with is - like `` perturbative '' equations of motion for @xmath88 , and @xmath86 . the hydrodynamic equations are obtained by using the decomposition ( [ eq15 ] ) in the conservation laws ( [ eq5 ] ) . the evolution equations for the dissipative flows @xmath89 , and @xmath86 are derived by generalizing the procedure in @xcite to an expansion of the distribution function around the spheroidally deformed @xmath90 in ( [ eq8 ] ) , using the 14-moment approximation . the equations are lengthy and found in @xcite . we give their simplified form for ( 0 + 1)-d expansion in the next section . especially at early times @xmath87 is much smaller than @xmath37 , since the largest part of @xmath37 is already accounted for by the momentum deformation in ( [ eq8 ] ) . the inverse reynolds number @xmath91 associated with the residual shear stress @xmath86 is therefore strongly reduced compared to that associated with @xmath1 , significantly improving the range of applicability of vahydro relative to standard second - order viscous hydrodynamics . for ( 0 + 1)-d longitudinally boost - invariant expansion of a transversally homogeneous system , the boltzmann equation can be solved exactly in rta @xcite , and the solution can be used to test the various macroscopic hydrodynamic approximation schemes . setting homogeneous initial conditions in @xmath92 and space - time rapidity @xmath93 and zero transverse flow , @xmath86 reduces to a single non - vanishing component @xmath94 : @xmath95 at @xmath96 . we use the factorization @xmath97 etc . to get equations of motion for @xmath98 @xcite : @xmath99 -\lambda(\xi)\frac{\tilde\pi}{\tau } + 12\biggl [ \frac{\dot{\lambda}}{3\lambda}\bigl({\cal r}_{\rm l}(\xi){\,-\,}{\cal r}(\xi)\bigr ) + \bigl(\frac{1{+}\xi}{\tau}-\frac{\dot{\xi}}{2}\bigr ) \bigl({\cal r}^{zzzz}_{-1}(\xi){\,-\,}\frac{1}{3}{\cal r}^{zz}_{1}(\xi)\bigr ) \biggr ] p_\mathrm{iso}(\lambda),\end{aligned}\ ] ] where @xmath100 and all the @xmath101-functions can be found in @xcite . @xmath102 and the ratio of shear viscosity @xmath103 to entropy density @xmath104 , @xmath105 , are related by @xmath106 . in @xcite we solved these equations and compared with the exact solution , and also with the other hydrodynamic approximation schemes discussed above plus a 3rd - order viscous hydrodynamic approximation derived in @xcite . as an example , we show in fig . [ f1 ] the entropy production ( measured by the increase in particle number @xmath107 ) between start and end of the dynamical evolution from an initial temperature of 600mev to a final one of 150mev . for this extreme ( 0 + 1)-d scenario , where the difference between longitudinal and transverse expansion rates is maximal , vahydro is seen to reproduce the exact solution almost perfectly , dramatically outperforming all other hydrodynamic approximations . as a function of @xmath108 . the black points , red dashed line , blue dashed - dotted line , green dashed line , and purple dotted line correspond to the exact solution of the boltzmann equation , vahydro , ahydro , third - order viscous hydrodynamics @xcite , and second - order viscous hydrodynamics @xcite , respectively . the initial conditions are @xmath109mev , @xmath110 , and @xmath111 at @xmath112fm/@xmath113 . the freeze - out temperature was taken to be @xmath114mev.[f1 ] ] * acknowledgments : * this work was supported in part by the u.s . department of energy , office of science , office of nuclear physics , under awards no . de - sc0004286 and ( within the framework of the jet collaboration ) de - sc0004104 . clarifying discussions with gabriel denicol and dirk rischke are gratefully acknowledged . c. gale , s. jeon and b. schenke , int . j. mod . phys . a 28 ( 2013 ) . m. martinez and m. strickland , nucl . phys . a 848 ( 2010 ) 183 ; m. martinez , r. ryblewski and m. strickland , phys . c 85 ( 2012 ) 064913 . w. florkowski and r. ryblewski , phys . c 83 ( 2011 ) 034907 ; r. ryblewski and w. florkowski , eur . j. c 71 ( 2011 ) 1761 ; l. tinti and w. florkowski , phys . rev . c 89 ( 2014 ) 034907 . w. israel and j. m. stewart , annals phys . 118 ( 1979 ) 341 . g. s. denicol , h. niemi , e. molnar and d. h. rischke , phys . d 85 ( 2012 ) 114047 . w. florkowski , r. ryblewski , m. strickland and l. tinti , phys . rev . c 89 ( 2014 ) 054909 . d. bazow , u. heinz and m. strickland , arxiv:1311.6720 [ nucl - th ] . w. florkowski , r. ryblewski and m. strickland , phys . c 88 ( 2013 ) 024903 . a. jaiswal , phys . c 88 ( 2013 ) 021903 .

a new formulation of second - order viscous hydrodynamics , based on an expansion around a locally anisotropic momentum distribution , is presented . it generalizes the previously developed formalism of anisotropic hydrodynamics ( ahydro ) to include a complete set of dissipative currents for which equations of motion are derived by solving the boltzmann equation in the 14-moment approximation . by solving the vahydro equations for a transversally homogeneous , longitudinally boost - invariant system ( ( 0 + 1)-dimensional expansion ) and comparing with the exact solution of the boltzmann equation in relaxation - time approximation we show that vahydro performs much better than all other known second - order viscous hydrodynamic approximations . viscous relativistic fluid dynamics , boltzmann equation , relaxation - time approximation , anisotropic hydrodynamics

filariasis is an endemic disease in most tropical and subtropical countries and is known to infect humans with various clinical manifestations . knowledge of endemic areas with poor vector control due to improper sanitation and overpopulation is often helpful in diagnosis . a 54-year - old female school teacher reported with a complaint of intermittent swelling inside the mouth on the left side . repeated exacerbations of the swelling occurred 4 - 5 times in a span of 8 months . itching of the cheek always preceded the swelling , which got resolved within 1 - 2 days . she had consulted many clinicians prior to reporting to our hospital and had taken medications . she gave a medical history of hypertension and dyslipidemia for which she was on medication since 5 years . extra - orally , diffuse swelling of left cheek was noted with no color changes . intra - orally , examination of the left buccal mucosa revealed a hard movable mass of 1 cm 0.5 cm anterior to the anterior border of ramus almost at the level of 27 [ figure 1 ] . swelling on the left buccal mucosa without any inflammatory signs an occlusal radiograph placed vertically in the upper gingival sulcus in contact with the buccal mucosa to check for any soft - tissue calcifications did not reveal any findings . differential diagnoses of a parotid sialolith , minor salivary gland tumor , cysticercosis , calcified facial node , and lipoma were made . ultrasound scan of the cheek revealed a well - defined round hypo - echoic lesion in the muscular layer of the left cheek measuring 0.8 cm 0.5 cm , with small specks of calcification . there were no obvious vascularity within the lesion and no perilesional edema [ figure 2 ] . ultrasound scan of cheek showing a small well - defined round hypo - echoic lesion excisional biopsy of the nodule was carried out . histological examination revealed a dense fibrous capsule showing infiltrate of mixed inflammatory cells consisting of lymphocytes , macrophages , eosinophils , and neutrophils . within the capsule , a single female filarial worm showing further , magnification revealed a thick layed cuticle with multiple longitudinal ridges and centrally placed intestinal tubule within the well - developed musculature [ figures 4 and 5 ] . double uterus appearance : scanner view centrally placed intestinal tubule in the worm with thick cuticle ( c ) and muscular layer ( m ) : h and e , 10 filarial worm with numerous larval forms ( l ) : h and e , 45 patient was treated with diethylcarbamazine ( dec ) 100 mg tid for 3 weeks , albendazole 400 mg hs and cetrizine 5 mg once daily for 5 days . following medication , patient dirofilariasis is an endemic disease in certain parts of africa , asia , europe and america . although nearly forty species of dirofilaria have been identified , only a few have been reported to cause human infection ; the most common being dirofilaria immitis , a parasite of dogs , d. tenuis a parasite of raccoons , dirofilaria repens , a parasite of dogs and cats , and d. ursi a parasite of bears . dirofilaria repens infection is endemic in india and srilanka and in the present case , the infection was localized intra orally in the buccal mucosa . these are nematodes that have a long , thin , filariform appearance and a rounded anterior end with an oral cavity . once the infected larvae penetrate through the wound into the human body , they migrate into the subcutaneous tissue and develop into the adult form in 6 months . in humans , a strong inflammatory reaction in the surrounding tissue is seen . patients with skin involvement present with subcutaneous lumps found in the trunk , breast conjunctiva , and joints . respiratory infection results in solitary or multiple pulmonary lesions called coin lesions , seen on chest radiographs . dirofilariasis of the oral cavity is extremely rare , but when present , is usually seen in the buccal mucosa as sub mucosal nodules . tilakaratne and pitakotuwage has reported the most common site to be the buccal mucosa in his study of 7 cases . swelling of the lips and interdental papillae have been reported in a young patient with microfilaraemia . diagnosis is confirmed with biopsy , where the pathognomonic nematode is found in the center of dense inflammatory response . worms belonging to the genus dirofilaria are identified by their thick laminated cuticle , broad lateral ends and large muscle cells . d. immitis also causes microfilaremia in human , presents clinically as pulmonary lesions and requires anti - helminthic drugs , whereas microfilaremia is absent in human cases of infection caused by dirofilaria repens and mostly presents intra - ocularly . polymerase chain reaction based diagnosis of human dirofilariasis on samples embedded in paraffin were first studied in pulmonary lesions in 2006 . this was useful in cases of uncertain identification of dirofilarial species due to poor preservation of the worm . the definitive treatment of dirofilaria infection in humans is surgical removal of the adult worm . the safety and tolerability of these treatments have been evaluated through many clinical and laboratory assessments . both the dec and albendazole are well - tolerated when given alone or in combination with no adverse events observed and these drugs are rapidly absorbed from the gastro - intestinal tract . the most important action of dec appears to be an alteration of microfilariae membranes so that they are readily phagocytosed by tissue fixed monocytes . ivermectin , a parasiticide , is effective against microfilariae ( blocking their transmission ) and can be administered annually as a single oral dose with virtually no side - effects . cases of intra - oral nematode often pose a diagnostic dilemma leading to improper management and thereby poorer prognosis to the patient . medical awareness of the risk of infection is essential and very often a detailed travel history is helpful in diagnosis . hence , oral filariasis should be considered in the differential diagnosis of a recurrent intra oral or facial swelling that may not have overt inflammatory signs and symptoms or swellings that do not respond to routine therapy and those seen in patients from endemic areas .

filariasis is an endemic disease in tropical and subtropical countries . filarial nematodes can infect humans through vectors , commonly mosquitoes . human infection can manifest as lymphatic filariasis , subcutaneous or pulmonary nodules and with eye involvement . intra - oral presentation is very rare and often poses a diagnostic dilemma to the dentist . we report a case of intra - oral dirofilaria repens infection in a 54-year - old female patient , involving the buccal mucosa . history was unremarkable and on clinical examination , a diffuse swelling with no significant signs and symptoms was seen . laboratory investigations and radiographs were non - contributory to diagnosis . ultrasound findings revealed a hypo - echoic lesion in the muscular layer of the left cheek . differential diagnoses considered were minor salivary gland tumor , parotid sialolith , and cysticercosis among others . the presence of a dirofilaria worm in the excised nodule confirmed the diagnosis . medical awareness of the risk of intra - oral nematode infection is essential . a detailed travel history , awareness of endemic status of certain diseases , proper diagnosis and management helps in better prognosis for the patient .

force measurements on a scaled hair - bundle model respected the physiological character of the liquid flow . the finite - element method provided approximate solutions to partial differential equations reflecting the hair bundle 's geometry . the velocity variable of the liquid was substituted by the time derivative of the displacement ; fluid pressure was approximated by linear shape functions and the displacements of liquid and solid by quadratic ones . the hydrodynamic forces between stereocilia were estimated analytically by solving the stefan - reynolds equations under the lubrication approximation , which is valid when the gaps between adjacent stereocilia are much smaller than their diameter . stochastic simulations based on these results were performed for a system of linearly coupled dynamic variables following a langevin description with gaussian white noise at room temperature . the integration procedure was validated by choosing time steps small enough to assure that the results were independent of the increment . we tested the effects of inertia and of the estimated top - connecter stiffness and confirmed the validity of our conclusions for mammalian hair bundles . dual - beam differential interferometry was used to record stereociliary motions with sub - nanometre spatial and sub - millisecond temporal resolution . fourier analysis of the records was performed with the multitaper method to obtain coherence spectra as well as stiffness and drag coefficients . these results were used to verify the predictions of the numerical model and to measure directly the relative mode of motion between stereocilia .

the detection of sound begins when energy derived from an acoustic stimulus deflects the hair bundles atop hair cells1 . as hair bundles move , the viscous friction between stereocilia and the surrounding liquid poses a fundamental physical challenge to the earfs high sensitivity and sharp frequency selectivity . part of the solution to this problem lies in the active process that uses energy for frequency - selective sound amplification2,3 . here we demonstrate that a complementary part of the solution involves the fluid - structure interaction between stereocilia and the liquid within the hair bundle . using force measurement on a dynamically scaled model , finite - element analysis , analytical estimation of hydrodynamic forces , stochastic simulation , and high - resolution interferometric measurement of hair bundles , we characterize the origin and magnitude of the forces between individual stereocilia during small hair - bundle deflections . we find that the close apposition of stereocilia effectively immobilizes the liquid between them , which reduces the drag and suppresses the relative squeezing but not the sliding mode of stereociliary motion . the obliquely oriented tip links couple the mechanotransduction channels to this least dissipative coherent mode , whereas the elastic horizontal top connectors that stabilize the structure further reduce the drag . as measured from the distortion products associated with channel gating at physiological stimulation amplitudes of tens of nanometres , the balance of viscous and elastic forces in a hair bundle permits a relative mode of motion between adjacent stereocilia that encompasses only a fraction of a nanometre . a combination of high - resolution experiments and detailed numerical modelling of fluid - structure interactions reveals the physical principles behind the basic structural features of hair bundles and shows quantitatively how these organelles are adapted to the needs of sensitive mechanotransduction .

a reasonable understanding of the kondo problem was achieved in the case of isolated kondo impurities by the anderson impurity model ( aim ) . despite the fact that many heavy electron systems are stoichiometric with a local moment in each unit cell , many of their physical properties can be well accounted for by the aim . on the other hand , some low - temperature properties such as optical conductivity are fundamentally different than those expected of the aim . these are consistent with the renormalized band behavior , captured by the anderson lattice model . here hybridization of local moments and conduction electrons leads to the presence of the hybridization gap ( hg ) in the vicinity of the fermi level,@xcite where in heavy fermions the fermi level lies close to the edge of the lower hybridized band.@xcite recent experiments on the photoexcited carrier relaxation dynamics in several heavy electron compounds have shown that the relaxation of the electronic system back to equilibrium is extremely sensitive to the underlying low energy electronic structure and strongly depends on the temperature ( @xmath5 ) and excitation level.@xcite it has been shown , that the bottleneck in carrier relaxation is governed by the presence of the hg near the fermi level.@xcite both @xmath5 and excitation density dependence of the relaxation process can be well accounted for by the phenomenological rothwarf - taylor ( rt ) model @xcite which was originally developed to describe the relaxation in superconductors driven out of equilibrium.@xcite we should note that the alterantive model presented in refs . [ 6,7 ] is esentially also a bottleneck model . here the energy and momentum conservation law leads to the suppression of e - ph scattering near e@xmath6 in the case of sound velocity exceeding the fermi velocity . this suppression of e - ph scattering near e@xmath6 effectivly acts as a gap in the dos . however , since the temperature and excitation dependence of the relaxation dynamics in a kondo insulator smb@xmath7 is nearly identical to that of heavy fermion systems,@xcite it was naturally to assume that the origin of the bottleneck in the entire class of materials was in the presence of the indirect hybridization gap.@xcite in this paper we report first systematic studies of photoexcited carrier relaxation dynamics in an intermediate - valence system yb@xmath0lu@xmath1al@xmath2 . in yb@xmath0lu@xmath1al@xmath2 concentration of local f moments can be continuously varied between 1 ( ybal@xmath2 is a heavy fermion with the kondo temperature of 600 - 700 k ) and 0 by replacing yb with open f - shell with lu with closed f - shell ( lual@xmath2 is a normal metal ) . dilution by doping with non - magnetic ions should give rise to the disappearance of the long range order , and the associated hg at some critical doping . moreover , in ybal@xmath2 the low - temperature anomalies observed in susceptibility and specific heat suggest the presence of a second energy scale of the order of 40 k.@xcite the observed anomalies are quickly suppressed by doping @xcite suggesting that this energy scale is related to the onset of fermi liquid coherence.@xcite using optical pump - probe spectroscopy in the low perturbation regime we show that at high @xmath5 and doping levels @xmath8 the relaxation rate decreases with decreasing @xmath5 much like in other heavy electron systems studied so far.@xcite this behavior is consistent with the relaxation bottleneck due to the presence of the hg.@xcite the hg does not change significantly in the doping range @xmath8 , and the disappearance of the long range order appears near @xmath9 . at some characteristic doping dependent temperature @xmath4 , the slowing down of relaxation is truncated and the relaxation rate becomes constant below @xmath10 . this behavior is explained by the competition between the relaxation across the hg and the ballistic electron transport , when at low @xmath5 the electron mean free path @xmath11 becomes larger than the optical penetration depth @xmath12 . we derived the theoretical model that describes the functional form of relaxation for such a case and discuss the striking doping dependence of the low temperature relaxation rate . the experiments were performed in the standard pump - probe configuration using a mode - locked ti : sapphire laser as the source for both photoexcitation and probe laser pulse trains . the pump and probe pulses had a duration of @xmath13 fs at the center wavelength of 800 nm . the experiments were performed in the very weak excitation regime with the excitation fluence of @xmath14 @xmath15j/@xmath16.@xcite from the literature values @xcite of the complex conductivity at 1.5 ev we estimated the corresponding absorbed energy densities to be @xmath17 mj/@xmath18 in ybal@xmath2 . based on the known values of the sommerfeld constant we estimated the corresponding increase in the electronic temperature after excitation to be less than 10 k over the entire @xmath5 range implying that the dynamics being studied is near the thermal equilibrium . the yb@xmath0lu@xmath1al@xmath2 samples ( 10 doping levels were studied ) were grown by the self - flux method in excess al.@xcite figure 1 shows the dynamics of photoinduced reflectivity change in ybal@xmath2 and yb@xmath19lu@xmath20al@xmath2 in the @xmath5 range between 4 k and 300 k. at 300 k , the rise time of about 70 fs is followed by fast electronic relaxation which can be well described by a single exponential decay with the relaxation time @xmath21 fs . following this initial electronic relaxation the system recovers to equilibrium on the timescale of several 100 ps , which is attributed to heat flow out of the excitation volume . upon lowering @xmath5 , changes in both the amplitude of the transient , , and @xmath22 are observed . upon cooling @xmath22 gradually increases in the same fashion as in previously studied heavy electron compounds,@xcite reaching 3.2 ps at @xmath23 k. there the anomalous increase in @xmath22 is truncated and @xmath22 remains constant below @xmath23 k. the amplitude of transient , also shows a pronounced @xmath5 dependence similar to early reports.@xcite at low temperatures is being nearly constant up to @xmath23 k and showing a pronounced suppression upon further @xmath5 increase . qualitatively similar results are obtained for all @xmath24 , except that the temperature where the relaxation time divergence is truncated , @xmath10 , is doping dependent , as discussed below . in lual@xmath2 , however , the dynamics follows the behavior seen in normal metals , where the relaxation is only very weakly temperature dependent with the relaxation time slightly increasing upon increasing the temperature.@xcite similarly , virtually no t dependence of @xmath25 is observed . at selected temperatures and b ) in yb@xmath19lu@xmath20al@xmath2 from 6 - 280 k ( in 6k steps between 6 - 140k and 10k steps from 140 - 280 k ) . ] the @xmath5 dependence of @xmath22 in ybal@xmath2 is shown in figure 2 . above @xmath23 k it is consistent with the relaxation bottleneck scenario due to the presence of the narrow hg , @xmath26 , in the density of states.@xcite the relaxation process can be described by the rt model . here following photoexcitation and the initial electron - electron and electron - phonon collisions which proceed on a sub - ps timescale , the system is characterized by excess densities of electron - hole pairs ( ehps ) and high frequency phonons ( hfp ) . when an ehp with an energy @xmath27 recombines , a high frequency phonon ( @xmath28 ) is created . since hfp can subsequently excite ehp , the recovery is essentially governed by the decay of the hfp population.@xcite in the low excitation limit , as in this case , the @xmath5 dependencies of both amplitude of the induced reflectivity change and @xmath22 are governed by the @xmath5 dependence of the number density of thermally excited ehps , @xmath29 . it was shown @xcite that @xmath30 , where @xmath31 @xmath32@xmath33 and @xmath34^{-1}\text { \ , } \label{tautdep}\ ] ] where @xmath35 is a constant that depends only on the photoexcitation intensity . in a narrow band semiconductor @xmath29 depends on the shape of the dos in the energy range @xmath36 around the chemical potential ( here and further @xmath37 ) . generally , the number density of thermally excited ehps across the gap ( in this case indirect hybridization gap , @xmath26 ) is given by @xmath38 where @xmath39 is of the order of 1 ( 0.5 for a bcs superconductor ) , depending on the shape of the dos near the gap edge . neither the size of @xmath26 , the exact shape of the low energy dos ( anisotropy , possible impurity levels within the gap ) , or the @xmath5 dependence of @xmath26 is well known in intermediate valence systems , therefore there is some ambiguity in determining @xmath26 . however , as the main @xmath5 dependence in @xmath29 comes from the exponential term , a rough estimate of the size of @xmath26 can be obtained . for @xmath40 k a good agreement of the data with this simple model can be obtained . since @xmath22 was found to be independent on @xmath41 over the range of @xmath41 studied @xcite we can assume that @xmath42 . indeed fig . 2 shows that there is a good agreement between @xmath43 and @xmath44 . fit with @xmath45 gives a values for the indirect hg of @xmath46 mev . this value is lower than the values of the pseudogap obtained from the inelastic neutron scattering data ( 30 mev),@xcite as well as the value inferred from the optical conductivity data on ybal@xmath2 ( 60 mev).@xcite the relationship between the observed pseudogaps in the spin ( neutrons ) and charge ( optical ) excitation spectra is unclear . on the other hand , the interpretation of the optical conductivity data is also not straightforward,@xcite since the indirect transitions are forbidden by the momentum conservation law . furthermore , the relaxation dynamics bottleneck is expected to be governed by the gap minimum , therefore taking the uncertainties in the interpretation of both experimental results the agreement is reasonable . given the fact , that the mid infrared peak at 0.25 ev,@xcite which is in the intermediate valence systems commonly interpreted as the direct optical transition across the hybridization gap,@xcite is in ybal@xmath2 present way above room temperature,@xcite it is expected that the same is true also for the indirect gap , as implied by the present study . and the inverse density of thermally excited quasiparticles , @xmath47 , for ybal@xmath2 . @xmath47 was determined from the t dependence of the normalized amplitude of the photoinduced reflectivity change , @xmath25 ( inset ) , via @xmath30 . the data are fit with @xmath48 , where @xmath49 mev is the size of the indirect hg . ] figure 3 presents the @xmath5 dependence of @xmath22 , obtained by the single exponential fit , on a series of yb@xmath0lu@xmath1al@xmath2 samples . over a large range of doping , @xmath8 , all @xmath50 fall almost on the same curve . since @xmath50 can be well understood in terms of the rt scenario,@xcite the results imply that the hg persists over wide range of doping . we should note that there is some variation in the gap extracted from the fit to the relaxation times of individual doping levels ( 10 mev @xmath51 21 mev ) - see the two fits in figure 3 . however , there is no systematic dependence of @xmath52 . at @xmath53 , however , a qualitative change in the relaxation dynamics is observed , with relaxation showing a very weak temperature dependence , much like in the metallic lual@xmath2 . this observation can be attributed to the loss of the long range order at @xmath53 , consistent with the inelastic neutron scattering data.@xcite based on the above we argue that the hybridization gap in yb@xmath0lu@xmath1al@xmath2 persists , nearly unchanged , up to @xmath54 , with the loss of the long range order to appear only near @xmath55 . , extracted using a single exponential decay fit , for yb@xmath0lu@xmath1al@xmath2 series . the dashed and dotted lines present fits with @xmath56 with @xmath57 mev and @xmath58 mev , respectively . ] below @xmath4 , however , @xmath22 saturates at @xmath59 . generally , the saturation of @xmath22 at low @xmath5 is expected within the rt model when @xmath60 becomes smaller than @xmath61- see eq.([tautdep ] ) . however in this case the low temperature relaxation time , @xmath62 , should depend on the excitation fluence . the fact that relaxation dynamics in this low perturbation experiment is found to be independent of excitation intensity effectively rules out this interpretation.@xcite alternatively , we can assume ( quite generally ) , that the relaxation of the excited state proceeds via two independent channels . in the case of two competing relaxation processes the recovery dynamics will always be governed by the fastest of the two . if one of the processes is slow and temperature independent , while the other shows strong temperature dependence , becoming slower and slower as the temperature is reduced , one would expect to observe a crossover from the temperature dependent to a temperature independent relaxation at the temperature where the two timescales become comparable . clearly , this scenario is consistent with the experimentally observed temperature dependence of the relaxation time . while at temperatures above @xmath10 the temperature dependence of both amplitude and relaxation time are in very good agreement with the relaxation bottleneck model - see fig . ( 2 ) , where the bottleneck in relaxation is a result of the presence of the hybridization gap near the fermi level , the question arises which temperature independent relaxation process could lead to the observed crossover into t - independent relaxation below @xmath10 ? measurements of the de haas - van alphen ( dhva ) effect in ybal@xmath2 and lual@xmath2 indicate a large mean free path , @xmath63 nm,@xcite several times larger than the optical penetration depth @xmath12 ( @xmath64 nm and @xmath65 nm).@xcite from the t dependence of resistivity ( inset to fig . 5 ) it follows that @xmath66 up to @xmath23 k , well into experimentally accessible @xmath5 range . hence one can expect that in addition to the recombination process with characteristic time @xmath22 a ballistic transport of hot electrons @xcite will take place on a timescale of @xmath67 , where @xmath68 is the fermi velocity . from the dhva data @xcite one obtains @xmath69 @xmath70 ( @xmath71 @xmath72 ) m / s in ybal@xmath2(lual@xmath2 ) giving the characteristic timescale for the ballistic transport out of the probed volume of @xmath73 ps and @xmath74 fs , respectively . since @xmath68 is a weak function of temperature , the competition between the strongly @xmath5 dependent recombination across the hg and a t - independent ballistic transport can account for the observed temperature dependence of the relaxation time in yb@xmath0lu@xmath1al@xmath2 . to describe the relaxation process for such a case we use the boltzmann kinetic equation with the collision integral in the @xmath22-approximation,@xcite @xmath75 here @xmath76 is the non - equilibrium correction to the equilibrium distribution function , which depends on time @xmath77 , distance from the surface @xmath78 , energy @xmath79 relative to the fermi energy , and the angle @xmath80 between the velocity and the transport direction , @xmath78 . the relaxation time @xmath22 in general depends on the energy and the angle . here we assume that the particle - hole symmetry is preserved , so that there is no electric field . also , if the fermi energy is large compared to the photon energy , one can neglect the dependence of the speed of hot electrons and holes on their relative energy , i.e. @xmath81 . eq.([eq1 ] ) , supplemented by the initial condition @xmath82 , describing the initial distribution of the hot quasiparticles after photoexcitation , has the solution : @xmath83 the spatial and time distribution of the electron - hole pair density is found as @xmath84 for comparison with the experimental data we assume that @xmath22 is energy and angle independent , @xmath85 and take the gaussian form of the energy integrated excitation profile at @xmath86 , @xmath87.@xcite @xmath88 is proportional to the number of photoinduced carriers within @xmath89 . integrating eq.([n ] ) with the gaussian probe profile , @xmath90,@xcite and normalizing to @xmath71 at @xmath86 one obtains @xmath91 eq.([ballistic ] ) has two regimes . on a short time scale , @xmath92 , it reduces to @xmath93 while for @xmath94 we have@xmath95 at selected temperatures fit with single exponential decay ( dashed blue line ) and with eq.([ballistic ] ) ( solid red line ) , where @xmath96 ps . at low temperatures the fit is entirely governed by the @xmath67 term ( with @xmath97 ps ) , while above 50 k the relaxation is best fit with a single exponential decay . ] figure 4 presents the photoinduced reflectivity traces in ybal@xmath2 at a few selected temperatures . we fit the photoinduced reflectivity traces with eq.([ballistic ] ) - solid lines and compare it to the single exponential decay ( dashed ) . at @xmath98 the model clearly describes the experimental data much better than a single exponential decay . in fact , the fit is mainly governed by the @xmath67 ratio ( best fit gives @xmath99 ps in good agreement with the above estimate ) while @xmath100 can be anywhere between 5 - 100 ps . the situation is reversed at @xmath101 , where the fit is entirely governed by @xmath100 . since the mean free path quickly decreases below @xmath12 upon increasing t , e.g. in ybal@xmath2 this should happen at @xmath23 k ( see inset to fig . 5 ) , the ballistic transport becomes ineffective . correspondingly , the fit to the 70 k data in fig . 4 with fixed @xmath96 clearly becomes inadequate . in fact , the data are much better fit with the single exponential decay ( dashed blue line ) . thus , @xmath10 can be thought of as the temperature where @xmath102 ; below @xmath10 the relaxation is dominated by the ballistic transport , while above this temperature relaxation is governed by the recombination across the indirect hg . in earlier studies @xcite such a saturation of @xmath22 at low @xmath5 was not observed . this can be understood , since at experimentally accessible temperatures of @xmath103 k the mean free path in ybal@xmath2 is by far the largest among the systems studied . still , comparison of dynamics in ybcdcu@xmath104 and ybagcu@xmath104 ( fig . 5 of ref . [ 4 ] ) shows an onset of saturation at @xmath105 k in ybagcu@xmath104 . this feature is absent in ybcdcu@xmath104 . since the mean free path in ybcdcu@xmath104 is considerably smaller than in ybagcu@xmath104,@xcite this observation is consistent with the proposed scenario . for yb@xmath0lu@xmath1al@xmath2 . inset shows the @xmath5 dependence of resistivity for several doping levels . ] the doping dependence of the low temperature relaxation rate , @xmath106 , is plotted in fig . 5 . initially @xmath107 shows a weak decrease from @xmath108 ps@xmath109 , followed by a rapid drop at @xmath110 . further increase in @xmath78 results in an increase in @xmath111 up to @xmath112 5 ps@xmath109 . within the above scenario , following the @xmath67 ratio , one would expect @xmath107(lual@xmath2 ) @xmath105 @xmath107(ybal@xmath2 ) , as observed . the strong drop in @xmath107 near @xmath110 can be understood as being a result of the decrease of @xmath11 below @xmath12 , consistent with the resistivity data ( see insert to fig . 5 ) . indeed , in yb@xmath113lu@xmath114al@xmath2 the expected low @xmath5 divergence of @xmath22 due to the relaxation bottleneck @xcite is largely recovered ( see fig.3 ) . thus , the qualitative doping dependence of @xmath107 in yb@xmath0lu@xmath1al@xmath2 can be understood as a competition between decreasing @xmath115 ratio and doping induced disorder . still , the underlying origin of the very sharp anomaly at @xmath116 is unclear . noteworthy , this doping level corresponds well with the doping level where low temperature coherence effects are strongly suppressed.@xcite we studied the carrier relaxation dynamics in yb@xmath0lu@xmath1al@xmath2 , an intermediate valence heavy fermion system where doping was continuously tuned between a heavy fermion and normal metal . in ybal@xmath2 there seems to be an overall agreement that its low temperature properties are governed by a hybridization of conduction electrons with spatially extended wave functions and localized f orbitals , which can be described by the anderson lattice model . since photoexcited carrier relaxation was found to be very sensitive to the appearance of the gap in the charge excitation spectrum , the aim of this work was to utilize time - resolved optical spectroscopy to determine the doping level at which long range order , leading to the indirect hybridization gap in intermediate valence heavy electron systems , is suppressed . by performing systematic studies of photoexcited carrier relaxation dynamics in yb@xmath0lu@xmath1al@xmath2 system , where doping was continuously varied between @xmath117 , we show that the hybridization gap persists up to the critical doping @xmath9 . this is consistent with inelastic neutron scattering data.@xcite indeed , the percolation threshold for the cubic system is @xmath118.@xcite this observation implies that the kondo lattice is a very robust feature , and suggest the anderson lattice model to be a minimum model for the description of this class of materials . in yb@xmath0lu@xmath1al@xmath2 , below some doping dependent temperature @xmath4 , the relaxation time divergence due to the relaxation bottleneck is cut . this observation can be naturally explained by considering a parallel temperature independent relaxation channel . since ybal@xmath2 is known for its large electronic mean free path , we consider ballistic electronic transport out of the probed volume as a possible competing process . we developed a theoretical model , describing the dynamics of excess quasiparticle density for such a case . comparison with the experimental data showed that the functional form of relaxation below @xmath4 , the temperature dependence of relaxation time , as well as the doping dependence of the low temperature relaxation rate in yb@xmath0lu@xmath1al@xmath2 can be well accounted for by this model with the dominant ballistic electron transport at low @xmath5 . the strikingly sharp anomaly in @xmath119 at @xmath116 clearly requires further experimental and theoretical work . this work was supported by sofja - kovalevskaja award from the alexander von humboldt foundation , zukunftskolleg and center for applied photonics at the uni . konstanz , the laboratory directed research and development program at los alamos national laboratory , and center for integrated nanotechnologies at lanl . such choice of the excitation profile is used to satisfy the condition @xmath122 at @xmath123 . this condition means that quasiparticles can not escape from the sample through the surface . the results are independent of the particular choice of excitation profile .

femtosecond time - resolved optical spectroscopy was used to systematically study photoexcited carrier relaxation dynamics in the intermediate - valence heavy fermion system yb@xmath0lu@xmath1al@xmath2 ( @xmath3 ) . given the demonstrated sensitivity of this experimental technique to the presence of the low energy gaps in the charge excitation spectrum , the aim of this work was to study the effect of dilution of the kondo lattice on its low energy electronic structure . the results imply that in yb@xmath0lu@xmath1al@xmath2 the hybridization gap , resulting from hybridization of local moments and conduction electrons , persists up to 30% doping . interestingly , below some characteristic , doping dependent temperature @xmath4 the relaxation time divergence , governed by the relaxation bottleneck due to the presence of the indirect hybridization gap , is truncated . this observation is attributed to the competing ballistic transport of hot electrons out of the probed volume at low temperatures . the derived theoretical model accounts for both the functional form of relaxation dynamics below @xmath4 , as well as the doping dependence of the low temperature relaxation rate in yb@xmath0lu@xmath1al@xmath2 .

the pulmonary arterial and venous structures deliver deoxygenated blood to the lung periphery and return oxygenated blood to the systemic circulation . these highly complex branching structures support the primary function of the lung that is to bring blood into close proximity with incoming fresh gas delivered to the terminal air sacs ( alveoli ) through the process of respiration . in clinical practice , it is of great importance , for instance , to be able to characterize the vascular trees for the detection of pulmonary emboli ( localized blockages ) , detection of signs of pulmonary hypertension , and for the differentiation between vasculature and focal opacities ( for detection of lung cancer and other localized pathologies ) . the vascular trees can also serve as a roadmap for the tracking of lung tissues across lung volume changes or across time as the lung is serially monitored . recent advances in mdct scanner technology enable the scanning of the entire lung with nearly isotropic submillimeter voxel dimensions ( on the order of 0.4 mm ) . vessel segments with radii of 2 mm or less are readily detectible in those images . while detectible , manual segmentation of these complex tree structures , even if an individual were willing to take the time , has been found to present a near impossible task due to the following reasons . it is difficult to determine boundaries of a vessel consistently , especially thin segments , due to the partial volume effects and image noise . volumetric lung scans of the adult human consist of more than 500 slices and the vascular tree , in a bipodial fashion , rapidly branch as one tracks the vessels from their central to peripheral locations , with the full tree structure consisting of more than 23 generations . in addition , manual measurements of the vessels for assessment of diameters and branching angles are unreliable . the measurement of diameter requires the determination of cross - sectional planes perpendicular to the local segment centerlines . similarly , a plane that includes both parent and child segments around the branchpoint needs to be localized for branching angle measurements . both measurements are difficult to perform manually via 2d images because of problems of for - shortening in projected view . therefore , highly automated segmentation of the pulmonary vascular tree based on 3d image analysis plays an important role in detecting and characterizing the vessel structure . the segmentation results are sought as we seek to build a lung atlas in which we will establish normative values against which an individual can be compared for the detection of disease . there is great interest in identifying branchpoints of the vascular trees as a set of landmarks that may allow matching of the lung across volume changes . during a respiratory cycle , even though the registration may require separation of arterial and venous trees , segmentation of the entire vascular trees provides branchpoint information required for this purpose . eventually the arterial and venous trees can readily be separated by scanning during the infusion of iodinated contrast agent and scanning during the arterial phase of the infusion . tube enhancement filters based on a combination of the eigenvalues of a hessian matrix have been reported in [ 35 ] . reported a vessel segmentation algorithm based on a codimension two level set method . vasilevskiy and siddiqi used gradient flows implemented using a level set method for 2d and 3d vessel segmentation . a tracking direction was estimated by an eigenvector of the hessian matrix at each tracking front position . used cores [ 12 , 13 ] to track the vascular tree from a seed point . reported a method for vascular tree segmentation using correlation - based enhancement filters and a fuzzy shape representation of the data . an approach based on mathematical morphology and discrete geometry operators use of vascular tree segmentation for detection , segmentation , and analysis of pulmonary lobes and sublobes was presented in . the eigenvalues and eigenvectors of the hessian matrix are implicitly or explicitly used in some of the above algorithms and the algorithms have worked well for extracting vessels in several organ systems imaged by ct or mr . the tube enhancement filters can extract both thin segments and thick segments without using seed points . however , such filters produce disconnections around the junctions since they are based on a cylindrical vessel segment model . segmentation results obtained from vessel traversal algorithms generally have better connectivity between segments but often miss peripheral thin segments . our goal outlined in this paper has been to develop an algorithm that extracts peripheral thin segments as well as thick segments from thoracic ct images with better connectivity . the major contribution of the reported work is the development of an algorithm which extracts detailed pulmonary vascular trees by a novel integration of the tube enhancement filter and vessel traversal approaches . our approach builds on several previously developed and proven methods for vessel enhancement and vessel traversal . however , when applying these algorithms individually to extract pulmonary vessels , several additional issues need to be resolved , which is the topic of this paper . the presented method integrates existing conceptual modules in a way that the final approach is free of the inherent limitations of the individual building blocks . our integrated algorithm consists of three major steps : ( 1 ) tube enhancement based on the cylindrical shape model using an eigenvalue of the hessian matrix serves as a filter to extract vessels and to produce information that is used to determine a set of seed points in the following vessel traversal step . ( 2 ) the traversal step starts from each seed point until one of the eigenvalues of the hessian matrix changes its sign twice , signifying that the front point of a trajectory has reached a junction . ( 3 ) branchpoint analysis is accomplished by applying a thinning method which then allows for the selection of objects with many branchpoints , serving as a means of distinguishing between vascular trees and noise components . a vessel segment in a 3d image is often modeled as having a cylindrical shape with a 2d gaussian - like intensity distribution within its cross - sectional plane . a combination of the eigenvalues of the hessian matrix is often used to characterize and enhance its shape in the image . since pulmonary vessels consist of segments with a wide range of radii , a multiscale approach needs to be considered . in this vessel enhancement process , segment radius information for multiscale integration . based on the cylindrical vessel model , the eigenvalues of the hessian matrix are commonly employed recently as efficient criteria to differentiate tube structures from other image components . let three eigenvalues of the hessian matrix at a point be 1 , 2 , and 3 and let their corresponding eigenvectors be e1 , e2 , and e3 , respectively . when a point is close to the center of a segment , 1 and 2 take on large negative values whereas 3 takes on a small value . figure 1 illustrates a cylindrical vessel model , with the eigenvalues / eigenvectors at the center of the model . according to the model , the following criteria are typically used to construct a filter output function . elongation : 3 is much less than 1 and 2 ( 3/1 0 or 3/2 0 ) . symmetry : 1 and 2 are of almost the same values when a point is close enough to the center of a segment ( 2/1 1 ) . these criteria capture the characteristics of the model so as to differentiate tube structures from sheet and blob shaped structures when a point is within a vessel segment and close to its center . however , pulmonary vascular trees include many junctions , and criteria 2 and 3 above are not always satisfied around the branchpoints . 1 and 2 do not always satisfy criterion 3 above , especially in the thin segments and around the junctions . in addition , 3 sometimes takes large positive values even when a point is within a straight segment , which implies criterion 2 is not always met . figure 2(a ) shows a trajectory by a white tube starting from a point demarcated by the left most white arrow . the gray parts on the trajectory indicate the points where 3 takes on negative values . figure 2(b ) shows changes of the three eigenvalues of the hessian matrix as the front point of the trajectory advances . intensity gradually changes towards junctions when the point is in a straight segment and it may cause 3 to take on a positive value . when the point is around a junction , intensity decreases rapidly towards the segmental direction and it causes 3 to take on a negative value . for these reasons , 3 fluctuates along the trajectory . also , 2 oscillates with its phase opposite to 3 since 2 takes relatively smaller values when the point is around junctions . based on this observation , the filter output function f(x ) is defined as follows : ( 1)f(x)=max fsf22i(x ) , where f is the standard deviation of a gaussian function convoluted with an image so as to take second derivatives in the volume coordinate , and i(x ) is the intensity value at the point . thus , it may also enhance blob structures , typically image noise as well as cylindrical structures . according to our experience , in thoracic ct images , the noise will not be enhanced to the same degree as are vessels since contrast between parenchymal background and pulmonary vessels is relatively high compared to the noise . ( hounsfield units ) while lung parenchyma is typically between 800 and 900 h.u . since gaussian noise with standard deviation = 20 can be considered typical for ct images , a difference greater than 100 h.u . f(x ) takes a maximum value when f is the closest to the radius of a target segment among other f in the range s. therefore , s should include appropriate values that cover all the radii of the vessel segments in the lung . however , when s contains a wide range of values , and the filter output is calculated at a nonvessel point close to a junction or multiple thin segments are close to each other , f(x ) gets larger than it should . this is caused by a gaussian function with a large f that excessively smoothes the region . figure 3(b ) shows the result when a fixed range of s was used for all voxels in the image . the filter overly extracted nonvessel regions around the junction . in order to avoid the inappropriate enhancement , large f should be included in s only when it needs to be used for the detection of a thick segment . we applied thresholding with a fixed value to obtain thick segments , and a discrete distance transform is applied to estimate an approximate radius r. by using a distance transform value d , the radius r is estimated as r = d+1 - 1 [ voxel ] . we used 600 [ h.u . ] for both tlc and frc scans as the threshold value . using the radius information , range s is determined depending on the distance d as follows : ( 2)s={{1},0<r1,{1,2,2},1<r2,{1,2,2,22},2<r22,{1,2,2,22,4},22<r . the filter output function takes large values not only at the tube structures but also at the edges of large concave structures such as bones and the heart . in addition , the function takes a relatively long time to be calculated for a whole volume . for simplicity , a lung segmentation method based on intensity thresholding and 3d labeling is employed . obviously any existing lung segmentation algorithms such as can also be used for this purpose . they should be located in the left lung , right lung and trachea , respectively . both left and right lungs are extracted by a simple thresholding with a fixed value and 3d labeling with the two seed points in the lung . the trachea and two or three subsequent branches are also segmented by thresholding with a fixed value and 2d labeling based upon connectivity between neighboring slices and the seed point . although the segmentation results from this very simple approach often contains part of the mediastinal region , it significantly reduces the number of voxels outside of the lung which would have otherwise been processed in the filtering step . it also greatly reduces the possibility of extracting false vessels caused by structures outside of the lung region . in our experiments , it took well under a minute to perform the lung segmentation while the lung segmentation served to reduce the tube enhancement filter processing time by more than four minutes . initial segmentation can be obtained by thresholding the filter output . however , since the segmentation works on a voxel - by - voxel basis , the result contains local disconnections and small holes . these are caused mainly by image noise and the difference of the intensity distribution on a cross - sectional plane between straight segments and junctions . the cross - sectional shape of a vessel contour at a junction becomes an ellipse . it causes lower filter output and local disconnections around junctions , especially where very thin segments bifurcate from a thick segment . the vessel traversal approach is suitable for improving connectivity and for filling small holes in a segment . the connectivity improvements include the following processes : initialization including automated localization of seed points , tracking terminations at junctions , radius estimation for boundary recovery . since points near the center of a segment are generally less influenced by noise , seed points are preferentially identified at segment centers . according to the vessel model , the intensity function takes a local maximum at the center of a segment . the local maximum position xmax in the volume coordinate can then be calculated by the following equation : ( 3)xmax = x+p = x(i , e1)1e1(i , e2)2e2 , where i is a gradient vector at x , e1 and e2 are eigenvectors corresponding to the eigenvalues 1 and 2 . the operator ( , ) takes the inner product of the two vectors in the equation . i is estimated by using f which maximizes ( 1 ) in s ( i.e. , the gradient is calculated as a convolution of the first derivative of a 3d gaussian function and f ) . since estimation of xmax is sensitive to image noise , x is considered to be located close enough to the center when the following conditions are met : ( 4)px0.5 , py0.5 , pz0.5 , where px , py , and pz are the components of the vector p. nonetheless , many points in the airway wall are also included as tracking seed points if only these conditions are taken into account , because the local intensity structure on the airway wall is quite similar to that of a thin segment . many of those points in the airway wall can be differentiated since the cross - sectional shape at the points is elliptical compared to that of the thin vessel segments . since ( 3 ) is based on the cylindrical vessel model , estimation of the local maximum position is inaccurate if a point is close to a junction . in that case if the eigenvalues satisfy conditions ( 4 ) , ( 5 ) and ( 6 ) , then the point is considered to be the center of a vessel segment and is registered as a seed point for the tracking process . starting from a seed point , the front position of a trajectory advances in the continuous 3d space of the volume coordinate according to the estimated tangent direction with the step size of 0.2 voxel . at the seed point , 3 is a positive value since the seed point satisfies condition ( 6 ) . as the front position advances , 3 takes a negative value around the branchpoints and becomes positive when the front is remote from the junctions . thus , once a segment is connected to its parent segment , tracking can be terminated . this will prevent performing the tracking multiple times for a segment . at a seed point , one of them leads to a thicker segment and the other leads to a peripheral child branch . local disconnection is often observed at a junction of a thick and a thin segment . therefore , the tracking front should advance towards the thick segment in order to fill the potential gap between the two segments . since a thick segment generally has higher ct values , the intensity value at the terminated point can be the criterion for selecting the trajectory which leads to the thicker segment . after tracking in both directions , the trajectory whose intensity value at the termination point is higher than the other is selected for radius estimation and the other is discarded . after tracking , spheres with an estimated radius are drawn at each tracking front position to fill possible holes and gaps between two segments . the intensity value around a point x can be estimated using the gradient i and the hessian matrix by the following quadratic equation ; ( 7)i(x+x)i(x)+(i,x)+12(x , hx ) . we determined x as the radius of the sphere at the point when the estimated intensity value i(x + x ) reaches half value of i(x ) from background value . intensity decreases toward both the e1 and e2 directions and it tends to decrease faster along either e1 or e1 compared with any other direction since the absolute value of 1 is bigger than 2 . therefore , x is made parallel to e1 to estimate the smallest distance to the outside of the vessel from the point . then , x can be expressed as x = te1 , where t is the minimum absolute value of the following equation : ( 8)t=(i , e1)(i , e1)21(i(x)ibg)1 . the background value is determined by ibg = min i(x iopte1 ) where i = 1,2 , 3 and opt is the optimal f which maximizes the filter output function ( 1 ) at the closest voxel from x. opt at each voxel can be obtained in the vessel enhancement step and is reused to avoid expensive multiscale filtering in this step . the hessian matrix and gradient vector are calculated by convoluting the second- and first- order derivative of gaussian function with opt . the intensity value i(x ) is obtained by convoluting gaussian function with opt at x , and ibg is evaluated directly from the image using trilinear interpolation . the minimum estimated radius along a trajectory is used for drawing spheres at each positions on the trajectory . an object that contains small numbers of branchpoints can be considered as noise or part of other structures . therefore , a thinning algorithm is applied to each object in the result to obtain the number of branchpoints in the object from its graph representation . empirically determined , an object which has 100 or more branchpoints , is extracted as a vascular tree . the value 100 is chosen empirically by taking into account that the thinning algorithm may produce false branches . figure 5 shows the surface model of the tree structure and a cross - sectional image of one of the noisy phantom instances . this model was originally developed to represent an airway tree , yet it is appropriate also for use as a model for simulating a pulmonary vascular tree since the pulmonary arterial tree follows the airway tree out into the lung periphery and thus has the same general geometric relationships as the airway tree . each segment was characterized by a starting point , an end point and the associated radius . 3d gaussian spheres were moved along the linear segments to generate the tree structure in a 3d image whose dimension was 250 250 250 voxels . the radius of a segment decreases from the starting point to the end point of a segment so that it becomes the same as the radius of a child segment in order to allow smooth connection . standard deviation of the 3d gaussian spheres r changes as the radius varies . in this phantom setting , maximum r was six voxels and minimum r was approximately one voxel in the volume . we also rotated the model in 11 different angles in 3d space and generated the structure in 3d images . intensity value at the center of a segment mildly decreased from the starting point of a segment toward its end point along the tangent direction . ] at the center whereas the thinnest had a value of 700 [ h.u . the background value was 900 [ h.u . ] to simulate a typical background intensity in the parenchymal region in lung ct images . gaussian noise with a standard deviation = 20 , 30 , 40 was added to each image . after the result was obtained , a thinning method was applied to obtain its graph representation so as to evaluate how many branches were correctly extracted and how many false branches were extracted by the segmentation algorithm . both missing and extra branches were counted manually . the segmentation algorithm was applied to 44 ct scans from a total of 22 human subjects with lung volume held at 85% ( for simplicity referred to as total lung capacity or tlc ) and 20% ( referred to functional residual capacity or frc ) of the subject 's vital capacity . both tlc and frc scans subjects were healthy volunteers except for three who had mild chronic obstructive pulmonary disease ( copd ) judged both by pulmonary function tests and visual assessment of the ct images . all images were scanned by a 4-slice mdct scanner ( philips mx8000 , philips medical systems , cleveland , ohio ) . in - plane pixel sizes of the ct images ranged from 0.52 mm to 0.88 mm , slice thickness was 1.3 mm , and slice increment was 0.65 mm . approximately 550 and 500 slices per case were available for each tlc and frc scan , respectively . in order to evaluate the segmentation results quantitatively , more than 1000 points in the vessels were manually identified in each ct data set to form a validation set to assess the true positive ( tp ) rate . tp rate is defined as the ratio between the total number of points detected by the algorithm and the total number of points in the data set . we consistently chose the center point of the vessels as a member of the tp point set because the center line is more important than vessel borders in defining the vessel geometry . each lung was divided into four distinct regions in terms of radial distance from the hilum so as to avoid biased distribution of the test points . region a is the closest to the hilum and region d is close to the pleural surface . region a contains a greater number of thicker segments than the other regions . to evaluate the false positive ( fp ) rate , 150 points were randomly placed in each region , and the points within the vessels were manually eliminated such that all points represented nonvessel regions . this left approximately 120 points per region which were located in the parenchyma , airway walls and pulmonary fissures . false positive rate is defined as the ratio between the total number of points included by the segmentation result and the total number of points in the data set . we implemented this algorithm with a multithreaded process for the tube enhancement filter and the vessel traversal . since the filter works on a voxel - by - voxel basis , it can be processed in parallel . similarly , the vessel traversal from a seed point can be executed in parallel without depending on other seed point locations . other processes such as lung segmentation and connected component analysis were implemented as serial processes . we used a linux - based computer with dual xeon 3.6 ghz processors ( hyperthreading on ) and 4 gb of memory for our experiment . the processing time varies depending on the size of the lung to be processed . therefore , tlc scans take longer time than processing frc scans . it took less than one minute ( 30 to 50 seconds ) to obtain lung segmentation result . then it took about one to three minutes to complete the tube enhancement filter process . the memory requirement is on the order of three times that required to hold the original volume . in our implementation , the program required approximately 900 mb for processing a volume consisting of 512 512 595 voxels . the segmentation algorithm has one major parameter , the threshold of the filter output used to obtain the initial segmentation . when it is decreased , more vessels and noise elements are extracted , increasing the tp rate as well as the fp rate . on the contrary , less vessels ( and noise elements ) are extracted if the threshold is increased , causing a lowering of the tp and fp rates . since the threshold is a tradeoff between tp and fp rates , four thresholds were selected empirically and were tested by use of the simulation . figure 7 shows average number of false ( extra ) branches and missing branches as a function of the threshold value . when the threshold setting was 0.06 , the segmentation results were missing less than one branch per volume on average . however , the number of extra branches increased rapidly when noise levels went up . on the contrary , when the threshold was 0.09 , the results missed 3.5 to 4.5 out of 125 branches on average whereas they had less extra branches than other threshold settings . in , a noise level = 20 was used to represent typical noise in ct images . for comparison , when the threshold was 0.07 , the algorithm missed less than one branch on average for all noise levels and the results contained one or less extra branches in the case of = 20 , 30 . derived from this result , a threshold value of 0.07 was used for the following experiments using the clinical data sets . figure 8 shows volume - rendered images of the segmentation results from both tlc and frc scans of one subject . since the scale of these images is the same , they also show how the lung geometry changes between the two volumes scanned . table 1 shows a summary of the tp rate for both tlc and frc scans . tp rate for tlc scans was 99.6% from the total of 16933 validation points and 99.5% from 15,281 points in right and left lungs , respectively . similarly , tp rate for frc scans was 99.0% from 13356 points and 98.2% from 10646 points in right and left lungs , respectively . since the lung volume of frc scans is less than that of tlc scans , there were less validation points for frc data sets . also , especially in the frc scans due to increased compliance , motion artifacts may have contributed to a small increase in the error rate . table 2 shows a summary of the fp rates for both tlc and frc scans . a total of 11,925 points and 9620 points were used in right and left lung of the tlc scans , respectively , yielding fp rates of 1.21% in the right and 0.99% in the left lung . for frc scans , a total of 11752 points in right lung and 8722 points in left lung were used and fp rates of 0.96% and 0.88% in the right and left lungs were obtained . in this section , the parameters affecting segmentation results will be discussed first followed by the performance difference between the left and right lungs . we will also discuss the difference of the validation results between tlc and frc scans . the threshold for obtaining initial segmentation from the filter output influences the final result when set close to zero , more objects including noise and other structures are obtained ; less vessel segments and less noise result for larger threshold values . , four different values were used to determine an appropriate value for pulmonary vascular segmentation from clinical ct images . 0.07 was empirically determined to be the best choice and was used for in vivo human images ; 0.08 was shown to be an alternative based on the results of the simulation . when 0.08 is used for in vivo human lung images , the tp rate was 99.3% and 97.0% for tlc and frc scans , respectively . in tlc images , the tp rate decreased merely 0.3% whereas the fp rate dropped by 0.45% . the tp rate in the region a for both tlc and frc scans was lower than in the other regions . this region also contains thin segments bifurcating from the thick segments , some of which were missed by the segmentation . radii of those missing segments were typically 1 to 2 mm and they emanated from segments whose radii were 5 to 8 mm . vessel traversal was sometimes terminated prematurely before the front merged to the centerline of the thick segments . in addition , some data sets had cardiogenic motion artifacts , particularly in the left lung regions , which caused branches to be missed . anatomically , many arterial segments run along with the airway segments , and sometimes they appear attached to each other in the ct image . complete elimination of the airway wall may require a priori knowledge of the location of the airway tree . an integration of the airway tree segmentation [ 21 , 22 ] will likely solve this problem . the lung is less dense at tlc than frc and parenchymal density at tlc is more homogeneous . in frc scans , parenchymal density increases and the density of the parenchyma increases typically by 100 to 200 hounsfield units compared to that in the tlc scans . the image quality of frc scans is also degraded by motion artifacts caused largely by cardiogenic motion which is accentuated by the fact that the lung is more compliant . the motion artifacts are more prominent in the left lung both because the heart is usually leftward shifted within the thorax . the overall tp rate in the frc scans was less than that in the tlc scans by 0.6% . the pulmonary arterial tree feeds the pulmonary capillaries which in turn drain into the pulmonary veins . the segmentation results demonstrated here contain only one or two connected trees in each lung , inferring that they may be implicitly connected in some locations . the total number of generations in the segmented trees can serve as a clinically important index . it is difficult to automatically estimate the number of generations in the segmented trees because of the implicit connections . the visual evaluation of the segmentation results indicates inclusion of peripheral thin segments close to the pleural surface . the algorithm , as currently completed and described , can be useful for clinical applications which do not require arterial and venous separation such as the detection of pulmonary emboli , the evaluation of the pulmonary vasculature in pulmonary hypertension and in the characterization of pulmonary nodules . an interesting byproduct of the vascular tree segmentation is that it depicts the pulmonary fissures as regions void of the vessel segments . pulmonary fissures are visible structures in the lung , which separate each lung into lobes . lobe segmentation has required fissure detection based upon identification of the fissure itself as has been reported in [ 25 , 26 ] . rough localization of pulmonary fissures using the vascular tree segmentation results avoids detection of the fissure itself and can be performed by searching in the sparse region of the vessel segments . this helps in limiting the region of interest to search for exact pulmonary fissure locations and may help to provide a fissure definition in the cases where the actual fissure is incomplete . the main purpose of the presented paper was to report on a practical method for extraction of pulmonary vessels together with its validation on clinical ct images . development of a simple yet practical tube enhancement filter output function ( 1 ) . we have developed an algorithm to extract the pulmonary vascular trees from thoracic 3d ct images . the algorithm was applied to 44 volumetric ct scans consisting of 22 high volume scans and 22 low volume scans . it yielded 99.6% tp rate and 1.2% fp rate for the high volume scans , 98.6% tp rate and 0.9% fp rate for the low volume scans . the values for the tp and fp evaluations of these in vivo human data sets show a reliable performance and suitability of the proposed algorithm for future clinically relevant applications .

this paper describes an algorithm for extracting pulmonary vascular trees ( arteries plus veins ) from three - dimensional ( 3d ) thoracic computed tomographic ( ct ) images . the algorithm integrates tube enhancement filter and traversal approaches which are based on eigenvalues and eigenvectors of a hessian matrix to extract thin peripheral segments as well as thick vessels close to the lung hilum . the resultant algorithm was applied to a simulation data set and 44 scans from 22 human subjects imaged via multidetector - row ct ( mdct ) during breath holds at 85% and 20% of their vital capacity . a quantitative validation was performed with more than 1000 manually identified points selected from inside the vessel segments to assess true positives ( tps ) and 1000 points randomly placed outside of the vessels to evaluate false positives ( fps ) in each case . on average , for both the high and low volume lung images , 99% of the points was properly marked as vessel and 1% of the points were assessed as fps . our hybrid segmentation algorithm provides a highly reliable method of segmenting the combined pulmonary venous and arterial trees which in turn will serve as a critical starting point for further quantitative analysis tasks and aid in our overall goal of establishing a normative atlas of the human lung .

SECTION 1. PRIVACY AND DATA PROTECTION POLICIES OF FEDERAL AGENCIES. (a) Short Title.--This Act may be cited as the ``Federal Privacy and Data Protection Policy Act of 2002''. (b) Definitions.--In this Act, the term ``agency'' has the meaning given that term under section 551(1) of title 5, United States Code. (c) Findings.--Congress finds that-- (1) in the wake of the attacks on the United States on September 11, 2001, Federal agencies are collecting an increasing amount of personal information from and on individuals as part of the expanded war on terrorism; (2) the worthwhile goals of those data collection initiatives are to help ensure homeland security and protect the people of the United States from future acts of terrorism; (3) protecting homeland security and fighting terrorism requires not only seeking to protect lives and property in the United States, but also ensuring that individual rights and essential liberties are safeguarded; (4) in order to achieve these goals, it is essential that agencies properly manage, maintain, and secure personal information on people in the United States from inappropriate use, disclosure, or dissemination to third parties; (5) because of the leading role of the Federal Government in the expanded war on terrorism, the Federal Government should serve as a role model for State and local government, and the private sector, by establishing effective safeguards and procedures to protect personal data of people in the United States; (6) in order to ensure that people in the United States understand and have confidence in the proper use and safety of personal information, it is essential for agencies to implement effective privacy policies and procedures and to state those privacy policies, both online and offline; and (7) an essential part of ensuring that the people in the United States have full confidence in the privacy and security of personal information is to-- (A) have agencies confirm adherence by those agencies to the stated policies; and (B) have independent, third party review, and confirmation of adherence. (d) Purpose.--The purpose of this Act is to provide a framework for ensuring effective data and privacy management by Federal agencies to-- (1) ensure public confidence and trust in how agencies collect, maintain, and use personal information; (2) ensure continued adherence to data protection and privacy policies and procedures; (3) ensure that individual rights and essential liberties are protected; and (4) provide for effective oversight of the collection and use of individual information. (e) Privacy Manager.-- (1) In general.--Each agency shall designate an employee of that agency as the agency privacy manager to-- (A) be responsible for effective data protection and management within that agency; and (B) ensure compliance with the privacy and data security policies. (2) Additional responsibilities.--Each privacy manager shall be responsible for-- (A) training and education for employees to promote awareness of and compliance with the privacy and data security policies; and (B) developing recommended practices and procedures to ensure compliance with the privacy and data security policies. (f) Benchmark Assessment.-- (1) In general.--Not later than 1 year after the date of enactment of this Act, each agency shall conduct a detailed benchmark assessment of the privacy and data protection policies and practices of that agency with regard to the collection, use, sharing, disclosure, transfer, and security of personally identifiable information relating to the agency employees and the public. Such practices shall be accurately and clearly stated in written policies governing the data collection and use practices of the agency, both online and offline. (2) Content.--At a minimum, each benchmark assessment shall determine and state-- (A) the personally identifiable information the agency collects on-- (i) employees of the agency; and (ii) members of the public; (B) any purpose for which the personally identifiable information is collected; (C) any notice given to individuals regarding the collection and use of personal information, relating to that individual; (D) any access given to individuals to review, amend, correct, supplement, or delete personal information relating to that individual; (E) whether or not consent is obtained from an individual before personally identifiable information is collected, used, transferred, or disclosed and any method used to obtain consent; (F) the policies and practices of the agency for the security of personally identifiable information; (G) the policies and practices of the agency for the proper use of personally identifiable information; (H) the training and education procedures of the agency to adequately train personnel on agency policies and procedures for privacy and data protection; (I) the policies and procedures of the agency for monitoring and reporting violations of privacy and data protection policies; and (J) the policies and procedures of the agency for assessing the impact of technologies on the stated privacy and security policies. (g) Recording.--A written report of each benchmark assessment shall be prepared and recorded with the Inspector General of the agency to serve as a benchmark for the data protection and privacy practices and policies of the agency. Each benchmark assessment shall be signed by the agency privacy manager, verifying that the agency is in good faith compliance with the policies and practices stated in the benchmark assessment. (h) Independent, Third-Party Review.-- (1) In general.--At least every 3 years, each agency shall have performed an independent, third-party review of the privacy and data protection practices of the agency to-- (A) determine the effectiveness of the privacy and data protection policies, practices, and procedures; and (B) ensure compliance with the stated privacy policy of the agency. (2) Purposes.--The purposes of reviews under this subsection are to-- (A) measure privacy and data protection practices against the original benchmark assessment of the agency; (B) ensure compliance and consistency with both online and offline stated privacy policies; and (C) provide agencies with ongoing awareness and recommendations regarding privacy and data protection practices. (3) Requirements of review.--The Inspector General of each agency shall contract with an independent, third party that is a recognized leader in privacy consulting, privacy technology, and data collection and use management to-- (A) evaluate the privacy and data protection practices of the agency; and (B) recommend strategies and specific steps to improve privacy and data protection management. (4) Content.--Each review under this subsection shall include-- (A) a review of the original benchmark assessment concerning the privacy and data protection practices of the agency with regard to the collection, use, sharing, disclosure, transfer, and security of personally identifiable information relating to agency employees and the public; (B) a detailed review of the current offline privacy and data protection practices of the agency with regard to the collection, use, sharing, disclosure, transfer, and security of personally identifiable information of the employees of the agency and the public to check for compliance with the original benchmark assessment, especially concerning whether those practices are accurately reflected in the written policies of the agency; and (C) a detailed electronic scan of any website of the agency with a technology product that alerts an agency to the privacy vulnerabilities on that web page, including-- (i) possible noncompliance with the benchmark assessment; (ii) whether the privacy and data protection practices of the agency comply to the written privacy policy of the agency; and (iii) whether there are any risks for inadvertent release of personally identifiable information from the website of the agency. (5) Restrictions to avoid conflict of interest.--An independent contractor that has substantial business with an agency may not perform a review under this subsection for that agency. (6) Report.--Upon completion of a review, the Inspector General of an agency shall submit to the head of that agency a detailed report on the review, including recommendations for improvements or enhancements to privacy and data protection practices of the agency. (i) Internet Availability.--Each agency shall make each agency benchmark assessment, each independent third party review, and each report of the Inspector General relating to that review available to the public on the website of the agency.

Federal Privacy and Data Protection Policy Act of 2002 - Requires each Federal agency to designate an employee as privacy manager to: (1) be responsible for data protection and management within that agency; (2) ensure compliance with the privacy and data security policies; and (3) be responsible for training and educating employees about such policies and developing practices and procedures to ensure compliance.Requires each agency to conduct and record with its Inspector General a benchmark assessment of privacy and data protection policies and practices for the collection, use, sharing, disclosure, transfer, and security of personally identifiable information relating to employees and the public.Requires each agency to perform an independent, third-party review of privacy and data protection practices every three years to: (1) determine the effectiveness of policies, practices, and procedures; and (2) ensure compliance with its stated privacy policy.Requires each Inspector General to: (1) contract with an independent, third party to evaluate privacy and data protection policies and recommend strategies and steps to improve privacy and data protection management; and (2) report to the head of the agency on such review.Requires agencies to make such assessments, reviews, and Inspector General reports available to the public on their websites.

at a distance of @xmath7 kpc ( e.g. , * ? ? ? * ) , the andromeda galaxy m31 is the nearest giant spiral to the milky way . together , these two galaxies dominate the mass and dynamics of the local group . it is therefore of tremendous interest to determine the velocity vector of m31 with respect to the milky way . while the line - of - sight velocity of m31 is well - known from doppler measurements , a determination of its proper motion ( pm ) has so far remained elusive . the pm of m31 has been sought for almost a century ( e.g. , * ? ? ? * ) , but _ very high _ astrometric accuracy is required to accomplish this . at the distance of m31 , 100 km s@xmath2 corresponds to 0.027 mas yr@xmath2 this is well beyond the accuracy limit of current ground - based optical observations even for long time baselines ( e.g. , @xmath8 year ; e.g. , * ? ? ? the two most accurate ( @xmath9 mas yr@xmath2 ) pm measurements in the local group come from studies of water masers in m33 @xcite and ic 10 @xcite . however , water masers in m31 have only recently been discovered @xcite , and it will take time until a sufficient baseline has been established to enable pm measurements . theoretical modeling of the local universe has suggested that the galactocentric rest - frame velocity of m31 must have a tangential component @xmath10 km s@xmath2 . however , within this limit many different orbits are still possible @xcite . @xcite recently presented an estimate of m31 s transverse velocity based on indirect arguments , using the known kinematics of satellite galaxies of m31 and the local group . their estimate implies that @xmath11 km s@xmath2 , at 68.3% confidence . in other words , m31 may be moving directly ( radially ) towards the milky way . this might have drastic implications for the future of the milky way , and even for the sun itself @xcite . however , all theoretical and indirect estimates of @xmath12 make assumptions about the structure and equilibrium of the local group that may not hold true in our hierarchically - evolving universe . therefore , only a direct pm measurement will yield a robust determination of the m31 velocity vector . the _ hubble space telescope _ ( ) is an observing platform in space with unparalleled astrometric capabilities . whereas the _ absolute _ astrometric accuracy of is limited by the accuracy of the guide star catalog ( @xmath13 arcsec for gsc2.3 ; * ? ? ? * ) , the current onboard imagers of ( e.g. , acs and wfc3 ) are capable of measuring _ relative _ positions of multiple sources in a field to better than 0.5 mas . therefore , it is possible to measure very accurate absolute pms of stars by measuring their displacement over time relative to stationary background reference source(s ) in the same field . quasi - stellar objects ( qsos ) have conventionally served as reference sources in pm studies , due to their star - like appearance and luminous nature . such a strategy has been used in several studies for measuring absolute pms of milky way satellite galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ) . however , the accuracies thus achieved are not sufficient at the distance of m31 . this is due in part to drawbacks of using qsos . not only must they be spectroscopically identified in advance , but their distribution on the sky is sparse . for the small field of view of imagers , these limits require the observer to find a qso behind the field of interest . if one exists , one must deliberately image the field containing the qso at two or more different epochs to measure the displacement of the stars relative to the qso . even then , the pm uncertainty is limited by the positional accuracy of a single qso . instead of using qsos , one can use background galaxies as reference objects in studies of absolute pms . at the spatial resolutions of interest here , these sources are also stationary due to their large distances . one great advantage of background galaxies is their ubiquity : background galaxies are found in nearly every deep astronomical image . moreover , using many background galaxies can provide higher accuracy than using a single qso . while the individual positional accuracy is somewhat poorer for galaxies , their much larger number provides an important @xmath14 advantage in averaging . for example , @xcite and @xcite used background galaxies to derive an accurate pm of the galactic globular cluster ngc 6397 , at the distance of @xmath15 kpc from the sun . similarly , @xcite used background galaxies to determine the absolute pm of a hypervelocity star in the milky way halo . unlike the situation with qsos , galaxy positions are difficult to measure one can adopt a simple centroiding algorithm , but such algorithms have limited accuracy in the undersampled images of s wide - field detectors @xcite . furthermore , the resolved galaxies and the unresolved stars would be expected to have different centroid biases , leading to spurious apparent pms . as a better alternative , @xcite developed a template - fitting method to measure accurate positions of resolved background galaxies . in this method , a tailor - made template is constructed for each individual object , and the same template is used to measure a consistent position for that object in each exposure . this is conceptually similar to the effective point spread function ( epsf ) approach widely used for stars @xcite . even for bright background galaxies , the template - fitting method is able to measure positions at least twice as well as with simple centroids @xcite . in this paper we present the first proper motion measurements for the galaxy m31 , based on new acs / wfc and the wfc3/uvis imaging of three fields with deep pre - existing data . we use the template - fitting method of @xcite as our basis , but make several innovations in the analysis to minimize systematic errors and ensure robustness of the results . the final accuracy of only @xmath6as yr@xmath2 is significantly better than what has been achieved by for other nearby galaxies , and is comparable to what has been achieved for other local group galaxies using vlba observations of water masers . this paper is organized as follows . section 2 describes the observations . section 3 describes the analysis steps that lead to the pm measurements . section 4 presents and discusses the pm results thus obtained for the three target fields . concluding remarks are presented in section 5 . this is the first paper in a series of three . in paper ii @xcite we derive the velocity vector of the m31 center of mass by correcting the pm results presented here for the internal motions of stars within m31 and for the reflex solar motion . we then combine the result with other estimates to determine the galactocentric velocity and orbit of m31 , and use this to estimate the mass of the local group . in paper iii ( van der marel et al . 2012b , in preparation ) we use the results to study the future dynamical evolution of the local group , and the expected merging of the milky way - m31-m33 system . the data set we used for measuring the pm of m31 consists of images of three fields obtained in two separate epochs . the fields are the * spheroid * , * outerdisk * , and * tidalstream * fields of @xcite obtained under the science programs go-9453 and go-10265 ( pi : t. brown ) . figure [ fig : targetfields ] shows the location of the three m31 target fields . the observation details for the first epoch data are given in @xcite ; field coordinates and total exposure times are listed in their table [ tab : obslog ] . in brief , the target fields were observed between december 2002 and january 2005 in two filters ( f606w and f814w ) with hst acs / wfc to create color - magnitude diagrams ( cmds ) that reach well below the m31 main sequence turn - off . for each field , all exposures were obtained within 40 days so they can be safely treated as a single epoch of data . total per - field per - filter exposure times ranged from 53 - 161 ksec . individual images had exposure times ranging from 1,100 to 1,300 sec , and were dithered such that no two exposures placed a star on the same pixel . in addition to the whole - pixel offsets , the dithering strategy also included sub - pixel shifts so that every object was observed at a range of locations relative to the pixel boundaries ; such `` pixel phase '' coverage is critical for our program . the very deep first - epoch f606w data were used by us for constructing super - sampled stacked images , identifying stars and galaxies , building templates for the template - fitting method , and providing reference positions of stars and galaxies , as described in section [ sec : measuringpm ] below . our second - epoch data were observed between january 2010 and august 2010 using acs / wfc and wfc3/uvis in f606w ( hst program go-11684 , pi : van der marel ) . we designed our observations to minimize random and systematic errors with the following strategies in mind . pre - analysis of the first - epoch data revealed that the f606w filter provides slightly better astrometric handle on the background galaxies than the f814w filter , so we chose to obtain second - epoch images only with f606w . furthermore , we decided to observe the three target fields with two different instruments instead of just one . this yields comparable random error , but allows additional consistency checks on our pm results . since the purpose of the second - epoch observations was astrometry , and not deep photometry , the total second - epoch exposure time was much less than in the first - epoch . we observed each target field for two orbits ( four half - orbit exposures ) with wfc3/uvis and one orbit ( two half - orbit exposures ) with acs / wfc . individual images had exposure times ranging from @xmath161,300 to 1,500 sec , slightly longer than in the first epoch , and were dithered in similar fashion . the baselines between the two epochs are in the range of 57.5 years . for the acs observations , we used the same orientations and coordinates as used by the first - epoch observations to maximize the overlapping area and so that any errors in the static distortion solution would naturally cancel out . due to different sets of guide stars being used between the first- and second - epoch observations , the second - epoch acs images were slightly offset and rotated with respect to the first - epoch images . however , the offsets are all within a negligible fraction of the acs / wfc field of view ( fov ) , and the orientations are within 01 of each other . for the wfc3 observations , we pointed the telescope so that the resulting images roughly share the same centers with the first epoch , but the wfc3 images were rotated by roughly 45 with respect to the acs images . this was to place the parallel acs / wfc fields overlapping with the first epoch parallel wfpc2 images , but the parallel fields will not be discussed in this paper as they are not useful for astrometry at the accuracy that we need . because the fov of wfc3/uvis is 64% of that of the acs / wfc , the observed wfc3 images are fully contained within the acs images despite the @xmath17difference in their orientations . the details of our second - epoch data are summarized in table [ tab : obslog ] . measurement of proper motions involves measuring the displacement between the position of an object at one time and its position at another . if this displacement can be measured with respect to objects for which we know the absolute motion , then we can obtain absolute pms . in our case , we will measure the displacement of m31 stars with respect to the background galaxies in the field to obtain an absolute pm . our strategy is to first align the stars in the first- and second - epoch images , restricting the alignment to those stars confirmed to belong to m31 . then we measure the average displacement of the background galaxies with respect to this moving frame of reference . the negative of this relative displacement yields the mean absolute pm of the m31 stars . this measurement of the mean does not require knowledge of the exact pm _ distribution _ of the m31 stars . this distribution can be complex , because different structural components of m31 contribute to each field . however , to transform the mean pm of the m31 stars in a field to an estimate of the m31 center of mass , one does need to construct a model for the internal kinematics of m31 , which is addressed in paper ii of this series . the overall pm derivation process is summarized below . 1 . we first create a high - resolution stacked image using the deep and well - dithered first - epoch images for each target field using the distortion - corrected first exposure as the reference frame . 2 . stars and galaxies are then identified from the stacked image for each field , and photometric measures and the cmd are used to specifically identify m31 reference stars . we construct a template for each star and galaxy from the high - resolution image . we then use the template to measure in a consistent fashion a position for each star / galaxy in each individual exposure of each epoch . we redefine the first - epoch reference frame using the template - based positions of the stars , and determine the average first - epoch position of each galaxy in this frame . we determine the template - measured positions of the stars in each of the six second - epoch exposures for each field and use them to transform the template - measured positions of the galaxies into the first - epoch frame . 7 . we then take the difference between the second- and first - epoch positions of the galaxies to obtain the relative displacement of the galaxies with respect to the m31 stars . 8 . finally , we multiply the relative displacements of the galaxies by @xmath18 to obtain the mean absolute displacement of the m31 stars , since in reality the galaxies are stationary and the stars are moving . division by the time baseline turns the displacements into pms . the following sections provide the details of each step . we downloaded all the required data in the form of _ flt.fits images from the stsci archive . these images are already bias - subtracted , dark - subtracted , and flat - fielded by the stsci data - reduction pipelines using the best available calibration data at the time of data inquiry . each multi - extension _ flt.fits file was converted to a single 4,096@xmath194,096 image where the top chip scene is directly abutted to the bottom chip scene . this single - format image allows a more efficient way of handling the data , and all computer software we used throughout our analysis were specifically programmed to deal with this image format . the detectors suffer from significant degradation in charge - transfer efficiency ( cte ) as time progresses . this impacts the astrometry of objects by effectively shifting the centroid position of the flux distribution . this can be a particularly serious problem for our second - epoch acs / wfc data , taken almost 9 years after the installation of acs . a pixel - based cte correction routine has recently been developed by @xcite for the acs / wfc , and @xcite demonstrated that this correction works very well for astrometric purposes . all first - epoch acs / wfc images were processed through this routine . for the second - epoch acs / wfc images , we used a modified version of the cte correction code that also included a correction for @xmath20-cte , in addition to the publicly available correction for @xmath21-cte . we found that the @xmath20-cte correction made very little difference to the positions measured in the images , compared to the other uncertainties in the results . a cte correction routine was not available for the wfc3/uvis at the time of writing this paper , so no correction was made to the wfc3 images . however , since at the time of the observations , uvis had spent only @xmath22% as much time as acs in the space environment , the cte degradation of our uvis images is expected to be quite small . although uvis appears to be losing charge - transfer efficiency faster than acs did , the studies that show this have focused on low - background images ( e.g. , * ? ? ? as our backgrounds are quite high , we expect cte losses to be very low for our images . hence , the cte degradation should only have a minimal effect on our wfc3 pm measurements . a direct post - facto consistency check of this is provided by comparison our acs / wfc and wfc3/uvis pms derived for the same fields ( see section [ sec : checks ] below ) . as the final step of the initial processing of individual images , we measured each star using the img2xym_wfc_9x10 program @xcite on the acs / wfc images , and using a similar program on the wfc3/uvis images . both programs utilize library psfs to determine a position and a flux for each star . we will use these psf - based star positions to provide our initial handle on the coordinate transformations from one image to another . the positions of objects on the detectors must be corrected for geometric distortions before they can be used for any astrometric measurement . for the acs / wfc detector , the distortion - correction solutions by @xcite have been used in several astrometric studies . these solutions are known to be better than 0.01 pixel or @xmath160.5 mas , and were shown to be stable between 2002 and 2007 @xcite . these available solutions were directly applied to the positions measured in our first - epoch acs / wfc images . while reducing data for another program ( go-11677 , pi : h. richer ) , one of us ( j.a . ) found that the acs distortion solution appears to have changed by @xmath23 pixel relative to the solution before the _ hst service mission 4 _ ( sm4 ) . this may be related to a similar variation of the psf ( anderson et al . , in prep . ) . it is unclear what caused these variations , but they appear to be stable over time . we used the go-11677 data set to develop a correction to the pre - sm4 acs / wfc distortion solution and applied it to the second - epoch data . for the wfc3/uvis data , we used the distortion corrections provided by @xcite . these corrections are better than 0.008 pixel or @xmath160.3 mas and appear to be stable over the uvis lifetime so far . the accuracies of the distortion corrections are comparable to our final measured motions ( as will be shown later ) . however , geometric distortion affects both star and galaxy positions similarly , and hence drops out in a differential measurement to lowest order . this is true in particular if each galaxy position is measured with respect to that of nearby stars that fall on the same area of the detector . this is what we do in section [ sec : derivingpms ] below , to ensure that higher order geometric distortion correction residuals do not affect our final results . the deep and well - dithered first - epoch acs / wfc data are well - suited for constructing high - resolution stacked images . to do this , we first apply the distortion corrections ( see section [ sec : distcor ] ) to the positions of stars measured in section [ sec : initialprocessing ] . we then adopt the first exposure of each field as the frame of reference , cross - identify stars in this exposure and stars in the other exposures , and use their distortion - corrected positions to construct a six - parameter least - squares linear transformation between the two frames . the six parameters involve x - y translation , scale , rotation , and two components of skew . the need for these linear transformations is discussed in section 3.6.4 of @xcite . we use these transformations to convert the star positions measured in the various images into the reference frame , giving us many estimates of the position of each star in the reference frame . we average these positions to refine the reference - frame positions for all the stars , and use these new average positions to improve the transformations ( which had initially been based on the positions as measured in the first frame itself ) . this procedure is iterated 23 times to improve the positions of both the stars and the transformations . we use the star - based transformations to construct the stacked images . in order to get better sampling , we super - sample the stacked image by a factor of 2 relative to the native acs / wfc pixel scale . the image - stacking process we used is similar to the commonly used drizzle algorithm @xcite with a point kernel , except that we included an iterative procedure to regularize the sampling in a manner similar to idrizzle @xcite . the procedure involves no deconvolution , and as such the resulting image at every point simply represents the flux that an actual _ flt image pixel would receive if it were centered at that location in the frame . it is this property that allows us to construct empirical templates ( see section [ sec : templatefittingmethod ] ) for our stars and galaxies . figure [ fig : stackedimage ] shows a 25@xmath1925 portion of the 2@xmath19 super - sampled stacked image for the _ spheroid _ field with m31 stars and background galaxies identified , as described in the following sections . all of our target fields are dominated by m31 stars , but there are also other sources , such as foreground stars and background galaxies . since our strategy for deriving the pm of m31 is to measure the displacement of the background galaxies relative to the co - moving frame of reference defined by the m31 stars , it is important to accurately identify both background galaxies and m31 stars before we proceed any further . the selection of m31 stars was carried out following the procedure below . for each target field , we use the star list compiled in section [ sec : stackedimages ] . our initial star lists include only sources that are found independently in a large number of first - epoch f606w exposures ( typically , @xmath24% ) ; as such , the list is almost entirely free of cosmic rays and image defects . there are , however , a large number of resolved sources , which could be either blended stars or extended background galaxies . to identify them , we made use of the mean quality - of - psf - fit parameter ( qfit ) reported by the img2xym_wfc_9x10 program ( see figure [ fig : starid]a ) . selecting the objects with low values of qfit allows us to filter out extended objects as well as stars that are too close to other stars to provide accurate position measurements . to ensure that all of the stars in the list are m31 members , we reduced the f814w images and constructed a cmd ( see figure [ fig : starid]b ) . from this , we selected stars that lie roughly on the m31 sequences . although small in number , field stars in the milky way halo may be included in our selection , but we believe that most of them will be filtered out in our next step of selection . finally , reference stars were selected based on their lack of motion with respect to the other m31 stars . this was done by aligning the second - epoch star positions with the first - epoch positions and iteratively rejecting the objects that have moved between the epochs ( see figure [ fig : starid]c ) . for any given acs / wfc target field , the m31 stars should all be moving towards the same direction in space . differential motions due to the internal kinematics of m31 within a single acs / wfc field should be negligible compared to the observational uncertainties ( see paper ii for details ) . we note that , in principle , better detection and photometry of fainter stars can be achieved by measuring stars directly from the stacked images as has been demonstrated by @xcite . however , as our main goal is doing astrometry , we are only interested in stars for which positions can be reliably measured in _ individual exposures_. our final lists of m31 reference stars include @xmath25 stars for the * spheroid * and * outerdisk * fields , and @xmath26 stars for the * tidalstream * field . a quick visual inspection of the super - sampled stacked images of our target fields reveals that there are hundreds of background galaxies . we have already identified sources using the img2xym_wfc_9x10 program , but because that program is specifically designed to measure stars , it neglects many of the extended sources . for this reason , sextractor @xcite was separately run on the stacked images to detect and measure extended sources . we generated a candidate list of galaxies by selecting sources from the sextractor output mainly based on their mag_auto , class_star , and flux_max parameters . for each field , this candidate list included more than 1,000 sources , but we found that many of the candidates are in fact multiple stars clustered together . we carefully identified sources in the candidate list one by one , basing our judgment on their 2-d contours and 3-d surface profiles . whenever the identification was unclear , we excluded the source from our selection to stay on the conservative side . we note that we desire the background galaxy list to be as free of contamination by stars as possible because the pm measurements are sensitive to the reference sources we choose to use . finally , we considered only objects for which the template - fitting method , described in the next section , yields position uncertainties of less than 0.25 pixel in both @xmath20 and @xmath21 . the final lists contain 368 , 339 , and 374 galaxies for the * spheroid * , * outerdisk * , and * tidalstream * fields , respectively . our goal is to measure accurate pms . the most crucial part of our analysis is therefore to measure the positions of objects in the individual images as accurately as possible . simple methods such as fitting the objects with a two - dimensional gaussian function or finding the flux centroid are accurate only if the objects have well - sampled peaks . this is not the case for most of the background galaxies in our target fields . to measure the positions of objects , we therefore adopt the template - fitting method developed by @xcite . the details and general diagnostics of the template - fitting method are documented in @xcite . here we summarize only the basic concepts behind the method . the distortion corrections in section [ sec : distcor ] and the linear transformations derived in section [ sec : stackedimages ] allow us to associate a position @xmath27 in a given individual image @xmath28 with a position @xmath29 in the stacked image , and _ vice versa_. we are thus able to build a model of what the galaxy or star should look like in an individual image by proper sampling of the stacked image . the goal is to measure in consistent fashion a position for each object ( star or galaxy ) in each individual exposure . to do this , we construct a template model for each object , and use it to measure that object in every exposure . the location within the template that we will define to be its center is arbitrary , since in the end we care only about differences in position . so we define the center of the brightest pixel in the stacked image to be the object center ( or `` handle '' in the parlance of mahmud & anderson ) . with the center so defined , we interpolate the stacked image at a super - sampled array of points , with the center at ( 0,0 ) but with a pixel orientation and spacing that corresponds to the transformed exposure s _ flt coordinate system . the result is a template that can be interpolated at an array of locations to tell us how much flux we would expect in an array of _ flt pixels for a presumed object center . the template is custom - made for each individual exposure , based on the mapping of that exposure s pixel coordinate system into the master frame . the template centers are all the same . for each object in each exposure , we use the previously established transformations to identify the location of the object in the exposure to within one pixel . we then evaluate an array of trial locations for the center , covering an area of 1@xmath191 pixels with a spacing of 0.01 pixel . at each trial location , interpolation of the template with a bicubic interpolation algorithm tells us how much flux we should expect to measure in each pixel of the exposure . we compare this model to the actual observed pixel values to obtain a quality - of - fit quantity , @xmath30 for each trial offset @xmath31 . the position of the galaxy or star then corresponds to the location of the template center that gives the minimum @xmath32 . in section [ sec : initialprocessing ] we used empirical `` library '' psf fits to the stars to define the transformations for construction of the stacked images . however , for the final pm measurements we use the template procedure for both galaxies and stars . this minimizes any potential for systematic errors due to differences in measurement techniques between different types of objects . the sums in equation ( [ eq : qfit ] ) were chosen to extend over the @xmath33 pixel raster centered on the object s brightest pixel in the individual exposure . the size of this region was deliberately chosen to be small , since most of the positional information for the stars and compact galaxies of interest here is contained in the central core pixels . we applied the template - fitting method to all stars and galaxies in the first - epoch acs / wfc data , to determine their positions in each exposure . to illustrate the quality of the template - fitting method , we show in figure [ fig : templatefittingacsep1 ] the best fit @xmath34 ( as defined in section [ sec : templatefittingmethod ] ) versus instrumental magnitude for the background galaxies in one of the first - epoch images . the top row of figure [ fig : templatefits ] shows the data , template fits , and residuals for three galaxies of different brightness , and for one star . the stacked images constructed in section [ sec : stackedimages ] represent the astronomical scene convolved with the average effective psf _ appropriate for the first - epoch data_. the effective psf represents the convolution of the instrumental psf with the sensitivity profile of a pixel . the astronomical scene for any given object should not change between our epochs of data , but the effective psf might change . this is certainly the case for the second - epoch wfc3/uvis data , discussed below , since both the instrumental psf and the pixelization are different than for the first - epoch acs / wfc data . however , we also found that the effective psf for the second - epoch acs / wfc data was not the same as for first - epoch acs / wfc data . even though the pixelization remained the same , we found that a subtle change occurred in the acs psf since sm4 ( see section [ sec : distcor ] ) . it is important that any change in the effective psf be explicitly accounted for in the analysis . psf changes can introduce centroid shifts , and these shifts can be different for point sources and for extended sources . our technique for measuring the m31 pm relies on positional differences between stars and background galaxies . psf changes can therefore produce spurious pm results . in order to deal with the differences in the effective psf between epochs , we model each object in a given second - epoch image as follows . first , we select bright and isolated stars from the m31 reference star list compiled in section [ sec : staridentification ] , and use them to derive a 7@xmath197-pixel kernel that accounts for differences in effective psf between the stacked image and the individual exposure . next , we interpolate the first - epoch template onto the _ flt pixel grid of the second epoch image , as we did in section [ sec : firstepochacs ] . we then convolve the template with the kernel derived in the earlier stage , and finally evaluate the goodness - of - fit quantity @xmath34 to find the object position that provides the minimum @xmath34 . the middle row of figure [ fig : templatefits ] shows the data , template fits , and residuals for three galaxies of different brightness , and for one star , obtained with this procedure for one of the second - epoch acs / wfc images ( jb4404vuq ) . the complexity in this procedure lies in the determination of the kernel . each kernel has 49 free parameters . however , it is constrained by 5@xmath195-pixel patches centered around _ all _ the objects in each image . this is an over - determined problem that can be solved to find the best - fitting kernel . we cast the problem into the form of a least - squares matrix equation , and solved for the kernel using the observed pixel values for several thousand bright and isolated stars distributed throughout the target fields . the solution was obtained through _ singular value decomposition _ @xcite . to fit the kernels , we first determined the stellar positions of the bright and isolated stars without any kernel . then we kept those positions fixed , and optimized the kernels . we ended up using a single kernel for each second - epoch image . we experimented with using different kernels for different parts of each image ( to deal with potential field - dependent psf variations ) , but found that this did not change the main results . in deriving the kernel , we recognized that there is a degeneracy between shifting the kernel and shifting the astronomical scene . we removed this degeneracy by constructing the pixel residuals that went into the kernel with respect to the library - psf - measured position ( see section [ sec : initialprocessing ] ) for each star . this ensured that the kernel would reproduce on average the psf - based positions for the stars , and that it would properly account for changes in source shape due to known psf variations between epochs . either way , the degeneracy does not affect absolute pms that are based on relative differences in position between stars and background galaxies . the top panels of figure [ fig : kernel_diag ] show the average of the derived normalized kernels for the second - epoch acs / wfc images . slight asymmetries are evident , primarily in the @xmath20 direction . without our kernel - based corrections , such asymmetric psf differences would bias astrometry . our second epoch wfc3/uvis images are rotated by @xmath17 deg with respect to the acs images . because we have many bright m31 stars in the field , we are able to derive six - parameter linear transformations that relate the undistorted wfc3 positions to the stacked image without difficulty . to determine the positions of all objects in the field we used the same kernel - based template - matching approach as for the second - epoch acs data . in this case , the kernel accounts not only for psf variations , but also for variations in the psf size and orientation between epochs . the bottom row of figure [ fig : templatefits ] shows the data , template fits , and residuals for three galaxies of different brightness , and for one star , obtained with this procedure for one of the second epoch wfc3/uvis images ( ib4401s1q ) . the kernel size for the wfc3/uvis data was chosen to be the same as for the acs data , and we used over 1,000 stars to derive the kernels . the bottom panels of figure [ fig : kernel_diag ] show the average of the derived normalized kernels for the second - epoch wfc3/uvis images . there are slight asymmetries in both coordinate directions . this differs from the situation for the second - epoch acs / wfc data , because the wfc3/uvis detector is rotated by @xmath35 in the hst focal plane with respect to the acs / wfc detector . also , the symmetric part of the kernels differs between the second - epoch acs / wfc images and the second - epoch wfc3/uvis images . this is because of the difference in psf shapes between the different detectors . our kernel - based approach minimizes potential systematics arising from measuring positions of stars and galaxies in images with different psf characteristics . our pm measurement technique for each field compares the high - resolution stacked image from the first - epoch to the individual exposures from the second epoch . the derived kernels account for variations in the average psf between the epochs , as well as exposure - to - exposure psf variations within the second epoch . we do not compare second - epoch exposures to individual first - epoch exposures , but only to the high - resolution stacked image . the stacked image is constructed from the first - epoch images , so on average , the psf does not change between the stacked image and the individual first - epoch images . therefore , any exposure - to - exposure psf variations that may exist within the first epoch do not affect the derived pms . for this reason , there was no need to study or correct explicitly psf variations within the first epoch data set . the processes outlined above lead to accurate positions of stars and galaxies in each individual exposure . we align the star positions between exposures using the same iterative approach described in section [ sec : stackedimages ] , but this time using the newly derived positions based on the template - fitting method instead of the initial library - psf - based positions . for each exposure for a given field , this procedure yields a six - parameter linear - transformation with respect to the first exposure in the first epoch for that field . for all objects ( stars and background galaxies ) in all exposures , we apply the known geometric distortion solutions and these linear - transformations , to obtain the position in the distortion - corrected frame of the first exposure ( i.e. , j8f801abq , j92c01b4q , and j92c28ccq for * spheroid * , * outerdisk * , and * tidalstream * , respectively ) . these distortion - corrected frames serve as our reference frames . in the first - epoch data we have many exposures . this yields multiple determinations for the position of each star or galaxy in the reference frame . the rms scatter among these determinations provides a measure of the random positional uncertainty in a single measurement for each object . figure [ fig : plot_sigxy ] shows the one - dimensional errors in positions for m31 stars ( upper panels ) and background galaxies ( lower panels ) as a function of instrumental magnitude ( defined as @xmath36 $ ] ) in the three separate target fields . brighter objects have a higher signal - to - noise ratio than fainter objects , and therefore have more accurately determined positions . stars are more compact than background galaxies , and therefore also have more accurately determined positions . at fixed magnitude , the scatter in positional accuracy is larger for the galaxies than for the stars . this is because galaxies have a large variation in sizes and shapes , with the morphology also depending on wavelength . the dependence of astrometric accuracy on size and shape was discussed in @xcite , and the dependence on wavelength was discussed in @xcite . at the bright end in figure [ fig : plot_sigxy ] , the per - exposure accuracies level off at 0.010.02 wfc pixels for both stars and galaxies . when many measurements are averaged , the positional errors decrease as @xmath37 . using the above procedure , we determine for each object its average first - epoch position in the reference frame . in a similar way , we measure template - based positions for each second - epoch exposure , correct these positions for distortion , and transform them into the reference frame using the template - measured star positions . we then compare these positions with the first - epoch averages to estimate the pm displacement for that object . division by the time baseline of the observations then yields an estimate of the actual pm . by construction , our method aligns the star fields between epochs . m31 stars will therefore have zero pm on average . figures [ fig : starpm1 ] and [ fig : starpm2 ] show the residual motion of each star in @xmath20 and @xmath21 ( @xmath38 and @xmath39 ) as a function of chip coordinates for one of the second - epoch acs / wfc images , and for one of the second - epoch wfc3/uvis images . these plots show that the `` average star '' ( given our selection criteria and brightness limits ) is measured with a precision of @xmath40 pixel ( but as shown in figure [ fig : plot_sigxy ] , this is a strong function of brightness ) . when averaging over an ensemble of @xmath41 stars in @xmath42 exposures , the accuracy of the average pm is in principle smaller by a factor @xmath43 . the stellar pms show that there remain some small systematic trends with position on the detector , at levels @xmath44 pixel . these trends may be related to small changes in the distortion solution between the first and second epochs , or other low - level systematic effects that are not accounted for in our analysis . such systematic trends might affect pm results . it is therefore important that we correct for them . we note that we found similar residual trends in all three target fields . this indicates that whatever is causing the low - level systematic trends is related to the detector characteristics rather than the internal kinematics of m31 . the background galaxies were not used to define any transformations between the first - epoch and second - epoch data . any motion between the galaxies and stars should therefore show up as a displacement between the first- and second - epoch galaxy positions in the reference frame . we measure these displacements in a two step process to remove any systematic pm trends related to the position on the detector , such as those visible in figures [ fig : starpm1 ] and [ fig : starpm2 ] . first , we calculate the difference between the first- and second - epoch positions for each background galaxy in the reference frame . then , for each galaxy , we compute the average displacement of stars in the vicinity of the galaxy . we subtract this displacement from the galaxy displacement . this `` local correction '' ensures that the displacement of each background galaxy is measured only with respect to the m31 stars that fall on the same part of the detector . this removes any remaining systematic pm residual associated with detector position . each local correction is constructed using stars of similar brightness ( @xmath45 mag in the inner 5@xmath195 pixels area ) and within a 200 pixel region centered on the given background galaxy . the matching of the stars and background galaxies in brightness was motivated by the fact that some known detector effects ( such as cte ) , depend not only on detector position , but also on the source brightness . in the top panels of figures [ fig : glxypm1 ] and [ fig : glxypm2 ] , we show the @xmath20 and @xmath21 proper motions ( @xmath38 and @xmath39 ) of each galaxy as a function of chip locations ( @xmath20 and @xmath21 ) , for the same second - epoch exposures as in figures [ fig : starpm1 ] and [ fig : starpm2 ] . there are many more stars than background galaxies in each frame , and the positions of the stars are generally more accurately determined than those of the galaxies ( see figure [ fig : plot_sigxy ] ) . the final pm error for each second - epoch exposure is therefore dominated entirely by the astrometric accuracy for the background galaxies . to determine an average pm of the m31 stars in each field , we start with the measured pm displacements of the background galaxies in the reference frame ( including local corrections as described above ) . for each of the 18 different second - epoch images , we calculate the weighted average using the positional errors determined from the rms among the first - epoch measurements . outliers were rejected in this process with an iterative 3-@xmath46 rejection scheme applied to the 2-d pm distribution . the uncertainty of the average was computed using the bootstrap method @xcite with 10,000 bootstrap samples for each case . this provides a rigorous error estimate , which is ultimately based on the actual scatter between results inferred from different background galaxies . this naturally includes any random errors due to photon - counting statistics , as well as any potentially remaining systematic errors that lead to increased scatter ( but any systematic errors that affect all sources equally would not be quantified by this ) . we then transformed the results to average pms ( and their associate errors ) of m31 stars in the directions north and west , in units of mas yr@xmath2 . to do this , we used the orientation of the reference image ( see section [ sec : firstepochacs ] ) with respect to the sky ( using the fits header keyword orientat ) , the time baseline , and the fact we are measuring the relative displacement of the background galaxies with respect to the m31 stars in our target fields . in table [ tab : results1 ] , we tabulate the pm is defined to be positive for an object moving towards the west , and therefore has the opposite sign of the pm in the ra direction . ] @xmath47 inferred from each second - epoch image and the corresponding error , along with the number of background galaxies used for the pm derivation . figure [ fig : pmdiagrams ] shows for each of the three target fields the pm estimates inferred from the six independent second - epoch exposures ( 2 acs / wfc @xmath48 4 wfc / uvis ) . the final estimate of the average pm of the m31 stars in each field is calculated by taking the error - weighted mean of the six independent measurements listed in table [ tab : results1 ] . the results are shown in red in figure [ fig : pmdiagrams ] , and they are tabulated in table [ tab : results2 ] . figure [ fig : pmall ] compares the final pm results for the three different m31 fields . the weighted average of the results is shown in black . this weighted average is also listed in table [ tab : results2 ] . the figure shows results in physical units of km s@xmath2 , instead of mas yr@xmath2 . to transform the units , we assumed a distance of 770 kpc ( see references in * ? ? ? * ) , so that @xmath49 mas yr@xmath50 km s@xmath2 . distance errors were not propagated in this conversion . the final weighted average pm differs from zero at the @xmath51-@xmath46 level . therefore , we have actually measured a motion , and we have not merely put an upper limit on any motion . to have faith in the results , it is important to assess the internal consistency of the measurements . there are many checks available for this , since we have performed measurements using different exposures , with different instruments , and for different fields . for a given field @xmath52 ( * spheroid * , * outerdisk * , or * tidalstream * ) , second - epoch instrument @xmath28 ( acs / wfc or wfc3/uvis ) , and coordinate direction @xmath53 ( west or north ) , we identify the set of @xmath54 pm measurements @xmath55 ( either four or two measurements , depending on the instrument ) with random errors @xmath56 . there are a total of 36 measurements ( see table [ tab : results1 ] ) . we combine the different measurements @xmath54 to obtain the 12 weighted averages @xmath57 with random errors @xmath58 . the quantity @xmath59 provides a measure of the extent to which different measurements for the same field and with the same instrument agree to within the random errors . we find that @xmath60 . in absence of systematic errors , one expects @xmath61 to follow a @xmath62 probability distribution with @xmath63 degrees of freedom . the expectation value for such a distribution is @xmath64 , and the dispersion is @xmath65 . hence , the measurements for the same field with the same instrument are statistically consistent with each other . this is also visually evident from inspection of figure [ fig : pmdiagrams ] , which shows furthermore that the agreement is least good for the * outerdisk * field . the quantity @xmath66 provides a measure of the extent to which measurements for the same field with different instruments agree to within the random errors . we find that @xmath67 . in this case @xmath68 , so the measurements for the same field with the different instruments are also statistically consistent with each other . finally , the quantity @xmath69 provides a measure of the extent to which measurements for different fields agree to within the random errors . here @xmath70 with random errors @xmath71 are the weighted averages over all exposures for given field ( top three lines of table [ tab : results2 ] ) . the @xmath72 are the weighted averages over all fields ( bottom line of table [ tab : results2 ] ) ) . we find that @xmath73 . in this case @xmath74 , so the measurements for different fields are also statistically consistent with each other . this is also visually evident from inspection of figure [ fig : pmall ] . the fact that all measurements are statistically consistent indicates that there is no additional scatter in the data that is unaccounted for by the random errors . this justifies the use of weighted averages in combining the different measurements ( which propagates only random errors ) . the final weighted average pm corresponds to a displacement of 0.0074 acs / wfc pixel over the @xmath75 year time baseline for the * spheroid * field . the per - coordinate error in the displacement is only 0.0024 pixel . the displacement errors are even lower for the other fields , which have shorter time baselines . these displacements are very small , but they can nonetheless be accurately measured . this can be understood based on first principles . a single source can be centroided to an accuracy of order @xmath76 , where @xmath46 is the gaussian dispersion of the object size , and @xmath77 is the signal - to - noise ratio of the observation . for a compact source with @xmath78 , this yields uncertainties of @xmath79@xmath80 pixels , consistent with what we found in figure [ fig : plot_sigxy ] . therefore , even a single bright compact source in a single exposure can provide an accuracy comparable to the m31 pm displacement . averaging over multiple sources in many exposures / fields reduces the random uncertainties to thousandths of a pixel and hence allows a solid measurement of the pm displacement . the key to our robust measurement is , though , control of _ systematic errors _ , since those are not guaranteed to decrease by averaging multiple measurements . we have paid careful attention throughout our observation planning and subsequent analysis to identify possible sources of systematic errors and adjusted our methodology to minimize them as following : * the observations were obtained with the f606w filter , which has the best psf and distortion models for both acs / wfc and wfc3/uvis ( see section [ sec : data2 ] ) . * the acs / wfc images were obtained using the same telescope orientation and pointing in both epochs ( see section [ sec : data2 ] ) . this allows any static astrometric residuals that depend on the position on the detector ( e.g. , static geometric distortion solution errors ) to cancel out in the differential pm measurement . * the acs / wfc data were explicitly corrected for the effects of imperfect cte , reducing any potential astrometric impact ( see section [ sec : initialprocessing ] ) . * we used different geometric distortion solutions for the different epochs of data , thus minimizing any impact due to potential time - variations in the geometric distortion solutions ( see section [ sec : distcor ] ) . * we carefully selected our samples of m31 stars and background galaxies to minimize any bias introduced by interlopers ( see section [ sec : stargalaxyid ] ) . * we built a unique template for every individual source that was measured , thus avoiding any ad hoc assumptions about the properties of psf or galaxy shapes ( see section [ sec : templatefittingmethod ] ) . * we fitted and accounted for psf variations between different epochs , thereby minimizing any potential pm biases ( see section [ sec : secondepochacs ] ) . * we measured the relative pm of each background galaxy with respect to only its neighboring stars ( the `` local correction '' ) , thus minimizing the impact of spurious spatially varying pm residuals ( see section [ sec : derivingpms ] ) . * the above local measurement was made with respect to only stars of similar brightness , thus minimizing the impact of magnitude - dependent pm residuals , including cte effects ( see section [ sec : derivingpms ] ) . * we obtained the final pm for each field by averaging over background galaxies at many different locations on the detector . this minimizes the potential impact of local peculiarities in detector properties or the astronomical scene ( see section [ sec : final ] ) . our approach is significantly advantageous over pm studies that use only a single background quasar in an image . * we determined the random pm error for each exposure from the actual scatter between results from different background galaxies . the resulting errors include all sources of scatter , and not just those from photon - counting statistics ( see section [ sec : final ] ) . * we used robust statistical measures with outlier rejection throughout our analysis , thus minimizing the potential influence of individual erroneous measurements ( e.g. , section [ sec : final ] ) . * we showed that pm measurements with different instruments , taken at different times and with different telescope orientations , as well as measurements of different fields , all yield statistically consistent results ( see section [ sec : checks ] ) . this rules out a large range of possible residual systematic errors , including most possible astrometric residuals specific to a given instrument or detector . in summary , there is strong reason to believe that the pm measurements and the quoted uncertainties are robust and free of the potential systematics considered in this section . the results presented thus far do not directly measure the pm of the m31 center of mass ( com ) . instead , in every field we measure the sum of the internal kinematics of the m31 stars and the com motion . the rotation curve of m31 has an amplitude of @xmath81 km s@xmath2 @xcite . the contributions from internal kinematics are therefore not necessarily negligible compared to the uncertainties in our measurements ( see figure [ fig : pmall ] ) . in paper ii we model the internal kinematics explicitly , and we derive an unbiased estimate for the com pm . as it turns out , this estimate is not very different from the weighted average presented in table [ tab : results2 ] . we also show in paper ii that this estimate is statistically consistent with the estimate for the transverse motion of m31 derived with the independent methods of @xcite , based on the kinematics of m31 and local group _ satellites_. this is a further indication that any remaining systematic uncertainties in our measurements are likely to be small . the observed pms presented here are heliocentric motions , i.e. , _ not _ corrected for the reflex solar motion in the milky way . this known reflex motion falls in the same quadrant of pm space as our measurements ( see * ? ? ? the actual transverse motion of m31 with respect to the milky way is therefore closer to zero than what we show in figure [ fig : pmall ] . this provides another useful consistency check on our measurements , since there are theoretical reasons to suspect that the transverse motion of m31 with respect to the milky way should be small ( e.g. , * ? ? ? in fact , we show in paper ii that the transverse motion implied by our data is consistent with zero , meaning that m31 is likely moving on a nearly direct radial orbit towards the milky way . we have presented the first direct absolute pm measurements of three fields in m31 , our nearest giant companion galaxy in the local group . we used new second - epoch data obtained with two different instruments , combined with very deep pre - existing first - epoch data , spanning a time baseline of 57 years . with state - of - the - art analysis methods , using background galaxies as stationary reference frame , we achieved a final pm accuracy of @xmath82as yr@xmath2 . this is comparable to the accuracies that have been achieved for other local group galaxies using vlba observations of water masers @xcite . water masers were recently discovered in m31 @xcite , but have yet to be used for a pm determination . we have paid careful attention to control of systematic errors throughout our analysis . a large range of consistency checks indicates that our pm measurements and the quoted uncertainties are robust and free of unknown systematics . the new pm results provide improved insights into the history , future , and mass of the local group . these topics are explored in detail in papers ii and iii of this series . the techniques presented here for measuring the pm of stars with respect to background galaxies are not only applicable to m31 , but can be applied to a wide range of other problems . for example , our group has ongoing observing programs to use the same techniques to measure the pm of leo i ( go-12270 , pi : s. t. sohn ) , the pm of dwarf galaxies near the local group turn - around radius ( go-12273 , pi : r. p. van der marel ) , and the pm of stars in the sagittarius stream ( go-12564 , pi : r. p. van der marel ) . more generally , any deep wide - field space - based imager with a stable configuration , including future missions such as wfirst and euclid , might be able to use the techniques presented here to measure the pms of foreground objects from multiple epochs of data . for m31 itself , it would be possible to improve the results presented here through additional observations by , e.g. , increasing the available number of fields , time baselines , or signal - to - noise ratio per epoch . meanwhile , water masers hold the potential to soon provide pm measurements for individual sources in m31 @xcite . they will yield constraints on the transverse motion of the m31 center - of - mass that are independent from those presented here and in paper ii . furthermore , water masers might allow measurement of additional effects , such as the m31 pm rotation , and the increase in m31 s apparent size caused by its motion towards us . support for this work was provided by nasa through a grant for program go-11684 from the space telescope science institute ( stsci ) , which is operated by the association of universities for research in astronomy ( aura ) , inc . , under nasa contract nas5 - 26555 . the authors are grateful to rachael beaton , gurtina besla , tom brown , t. j. cox , mark fardal , and raja guhathakurta for contributing to the other papers in this series , and for comments that helped improve the presentation of the present paper . kalirai , j. s. , anderson , j. , richer , h. b. , king , i. r. , brewer , j. p. , carraro , g. , davis , s. d. , fahlman , g. g. , hansen , b. m. s. , hurley , j. r. , lpine , s. , reitzel , d. b. , rich , r. m. , shara , m. m. , & stetson , p. b. 2007 , , 657 , l93 sohn , s. t. , anderson , j. , & van der marel , r. p. 2010 , in 2010 space telescope science institute calibration workshop - hubble after sm4 . preparing jwst , ed . s. deustua , & c. oliveira ( baltimore , md : stsci ) van der marel , r. p. , anderson , j. , cox , c. , khozurina - platais , v. , lallo , m. , & nelan , e. 2007 , acs / isr 2007 - 07 , calibration of acs / wfc absolute scale and rotation for use in creation of a jwst astrometric reference field ( baltimore : stsci ) and [ fig : glxypm2 ] . measurements using acs / wfc ( open squares ) and wfc3/uvis ( open triangles ) are indicated with different symbols . the solid red data point is the weighted average of the six separate measurements for each field . [ fig : pmdiagrams],title="fig : " ] and [ fig : glxypm2 ] . measurements using acs / wfc ( open squares ) and wfc3/uvis ( open triangles ) are indicated with different symbols . the solid red data point is the weighted average of the six separate measurements for each field . [ fig : pmdiagrams],title="fig : " ] and [ fig : glxypm2 ] . measurements using acs / wfc ( open squares ) and wfc3/uvis ( open triangles ) are indicated with different symbols . the solid red data point is the weighted average of the six separate measurements for each field . [ fig : pmdiagrams],title="fig : " ] l l c r@. l l r@. l target field & data set & detector & & exposure time ( s ) & + * * spheroid * & jb4404vsq , jb4404vuq & acs / wfc & 75 & 07 & 1289 , 1289 & 7 & 10 + & ib4401rsq , ib4401ruq , ib4401rxq , ib4401s1q & wfc3/uvis & 255 & 14 & 1379 , 1379 , 1450 , 1450 & 7 & 57 + * * outerdisk * & jb4405jgq , jb4405jiq & acs / wfc & 247 & 17 & 1289 , 1289 & 5 & 06 + & ib4402urq , ib4402uwq , ib4402vqq , ib4402vuq & wfc3/uvis & 67 & 08 & 1420 , 1420 , 1491 , 1491 & 5 & 55 + * * tidalstream * & jb4406muq , jb4406mwq & acs / wfc & 21 & 85 & 1299 , 1299 & 5 & 99 + & ib4403enq , ib4403epq , ib4403esq , ib4403ewq & wfc3/uvis & 216 & 92 & 1379 , 1379 , 1450 , 1450 & 5 & 47 + cl [email protected] [email protected] [email protected] [email protected] c & & & & & & + field & data set & & & & & @xmath83 + & jb4404vsq & @xmath84 & 0839 & @xmath84 & 0212 & 0 & 0512 & 0 & 0327 & 308 + & jb4404vuq & @xmath85 & 0012 & @xmath84 & 0982 & 0 & 0297 & 0 & 0299 & 306 + * spheroid * & ib4401rsq & @xmath84 & 0085 & @xmath85 & 0184 & 0 & 0606 & 0 & 0530 & 176 + & ib4401ruq & @xmath84 & 0564 & @xmath84 & 0379 & 0 & 0332 & 0 & 0442 & 176 + & ib4401rxq & @xmath84 & 0772 & @xmath84 & 0104 & 0 & 0660 & 0 & 0495 & 186 + & ib4401s1q & @xmath84 & 0895 & @xmath84 & 0126 & 0 & 0369 & 0 & 0339 & 172 + & jb4405jgq & @xmath84 & 0706 & @xmath85 & 0085 & 0 & 0501 & 0 & 0504 & 310 + & jb4405jiq & @xmath84 & 1105 & @xmath84 & 0043 & 0 & 0547 & 0 & 0501 & 286 + * outerdisk * & ib4402urq & @xmath84 & 0123 & @xmath85 & 0993 & 0 & 0679 & 0 & 0681 & 156 + & ib4402uwq & @xmath84 & 0668 & @xmath84 & 1609 & 0 & 0649 & 0 & 0759 & 152 + & ib4402vqq & @xmath84 & 0641 & @xmath85 & 1353 & 0 & 0761 & 0 & 0757 & 161 + & ib4402vuq & @xmath85 & 0237 & @xmath84 & 1112 & 0 & 0589 & 0 & 0553 & 152 + & jb4406muq & @xmath85 & 0425 & @xmath84 & 0895 & 0 & 0574 & 0 & 0601 & 321 + & jb4406mwq & @xmath85 & 0104 & @xmath85 & 0098 & 0 & 0564 & 0 & 0518 & 317 + * tidalstream * & ib4403enq & @xmath84 & 1116 & @xmath84 & 0572 & 0 & 0670 & 0 & 0752 & 185 + & ib4403epq & @xmath84 & 0792 & @xmath84 & 0358 & 0 & 0766 & 0 & 0812 & 196 + & ib4403esq & @xmath84 & 0445 & @xmath84 & 0474 & 0 & 0883 & 0 & 0731 & 175 + & ib4403ewq & @xmath85 & 0298 & @xmath84 & 0148 & 0 & 0794 & 0 & 0728 & 185 + l [email protected] [email protected] [email protected] [email protected] & & & & + field & & & & + & @xmath84 & 0458 & @xmath84 & 0376 & 0 & 0165 & 0 & 0154 + * outerdisk * & @xmath84 & 0533 & @xmath84 & 0104 & 0 & 0246 & 0 & 0244 + * tidalstream * & @xmath84 & 0179 & @xmath84 & 0357 & 0 & 0278 & 0 & 0272 + weighted av . & @xmath84 & 0422 & @xmath84 & 0309 & 0 & 0123 & 0 & 0117 +

we present the first proper motion measurements for the galaxy m31 . we obtained new @xmath0-band imaging data with the _ hubble space telescope _ acs / wfc and the wfc3/uvis instruments of three fields : a spheroid field near the minor axis , an outer disk field along the major axis , and a field on the giant southern stream . the data provide 57 year time baselines with respect to pre - existing deep first - epoch observations of the same fields . we measure the positions of thousands of m31 stars and hundreds of compact background galaxies in each field . high accuracy and robustness is achieved by building and fitting a unique template for each individual object . the average proper motion for each field is obtained from the average motion of the m31 stars between the epochs with respect to the background galaxies . for the three fields , the observed proper motions @xmath1 are , in units of mas yr@xmath2 , @xmath3 , @xmath4 , and @xmath5 , respectively . the ability to average over large numbers of objects and over the three fields yields a final displacement accuracy of a few thousandths of a pixel , corresponding to only @xmath6as yr@xmath2 . this is comparable to what has been achieved for other local group galaxies using vlba observations of water masers . potential systematic errors are controlled by an analysis strategy that corrects for detector charge transfer inefficiency , and spatially- and time - dependent geometric distortion and point - spread - function variations . the robustness of the proper - motion measurements and uncertainties are supported by the fact that data from different instruments , taken at different times and with different telescope orientations , as well as measurements of different fields , all yield statistically consistent results . papers ii and iii of this series explore the implications of the new measurements for our understanding of the history , future , and mass of the local group .

for a long time , laboratory experiments and observations in space have been stirring up a dispute concerning the mechanisms of the magnetic - field evolution in plasma and the associated plasma dynamics . estimates of the plasma collisionality in plasma opening switches ( pos ) , for example , indicate that the magnetic field diffusion should be small while the plasma pushing by the magnetic - field pressure should be dominant . however , magnetic - field penetration has been observed in pos experiments @xcite , and , moreover , it is found to be significantly faster than expected from diffusion @xcite . the magnetic - field penetration was also found to be higher than , or of a comparable velocity to the plasma pushing . in an early experiment @xcite a fast magnetic - field penetration into a plasma where the ions are nearly immobile was observed . this was explained by the generation of an electric hall field based on the electron magnetohydrodynamics theory @xcite . the relative importance of the two governing processes , i.e. , the plasma pushing and the magnetic - field penetration , was further analyzed in a series of additional experiments with different plasma parameters , in which comprehensive measurements of spatial distributions of the magnetic field , of the ion velocity , and of the electron density in the plasma were performed . these detailed measurements , performed in multi - ion species plasma , have revealed that the fast magnetic field penetration into the plasma is accompanied by a specular reflection of the light - ion plasma and a slow pushing of the heavy - ion plasma penetrated by the field @xcite , resulting in ion - species separation @xcite . the electric field plays a crucial role in the interaction of the magnetic field with the plasma . the electric field transfers energy to the current - carrying plasma through the joule heating , the electric field that is generated by the space - charge separation due to the magnetic field accelerates the ions , and the ( hall ) electric field may induce the magnetic - field penetration into the plasma . however , previous studies of the electric fields in plasmas under application of pulsed currents ( e.g. , refs . @xcite ) lacked the temporal and spatial resolutions and , thus , only provided an averaged view . in this paper we describe an application of 3d - resolved spectroscopy to investigate the time evolution of electric fields in plasmas under high - current pulses . our method is based on laser spectroscopy combined with plasma doping by lithium , which allows for electric field measurements from the lithium emission - line shape . in the following sections we first discuss the physics underlying the diagnostic method and the measurements of the initial conditions of the plasma prior to the application of the current . then , measurements of the electric field in the plasma under a current pulse are described , followed by a discussion on the relation between the measured electric field , the magnetic field , and the plasma dynamics . it is found that the measured electric field magnitude is consistent with the hall electric field calculated on the basis of the magnetic field and the plasma density measured in a separate study . the stark effect has proven to be of a great utility for non - intrusive measurements of the frequency and amplitude of local electric fields in plasmas , as first suggested by baranger and mozer @xcite and shortly later experimentally verified by kunze and griem @xcite . the advantages of the lithium atomic system for electric fields measurements have been previously demonstrated @xcite . lithium was employed for measurements of electric fields in dilute plasmas of gas discharges @xcite and in the vacuum gap of a high - voltage diode @xcite . in our experiment , high spatial and temporal resolutions in measuring the electric fields in relatively dense ( @xmath0 ) plasma are achieved . at such densities , extracting the information from the spectral line - profiles becomes more difficult due to the increased stark broadening and the faster ionization processes that reduce the neutral lithium line emission . the e - field diagnostic is based on the analysis of the line - shape of a forbidden transition and its intensity relative to an allowed transition . the neutral - lithium atomic system is most suitable for applying the method since the 2p-4f dipole - forbidden transition ( 4601.5 ) and the 2p-4d allowed transition ( 4603 ) are very close in wavelength , and therefore , both lines can be recorded simultaneously . this is particularly useful for investigating a highly transient plasma , such as the present one , where a reliable measurement requires obtaining the information on the e - field in a single discharge . in the presence of an electric field , a configuration mixing of the 4d and 4f levels occurs , making possible an electric dipole transition from the 4f level to the 2p level . since the 4d-4f mixing coefficient depends on the electric field amplitude , the intensity of the forbidden transition can serve as a measure of the electric field strength . the mixing coefficient is larger for smaller energy - level difference , thus the small energy separation between the 4f and the 4d levels ( @xmath1 ) makes these transitions in lithium suitable for measurements of relatively low electric field . the time dependence of the electric field magnitude and direction also affects the spectral line - profiles , and thus , using a detailed line - shape analysis allows for obtaining additional information on the frequency spectrum of the e - fields . in the case of a harmonic perturbation with frequency @xmath2 , a dipole - forbidden transition is split into two satellites , displaced from the unperturbed position by @xmath3 @xcite . generally , for a non - harmonic perturbation the linewidth is roughly @xmath4 , where @xmath5 is the typical field frequency . therefore , taking into consideration also the contributions of the doppler and instrumental broadenings to the total line widths , it is possible to conclude that for the present case of li i spectrum , the forbidden line would be unresolved from the strong allowed line for e - field frequencies above @xmath6 . our detailed modeling confirms this . under the relevant plasma conditions the populations of the 4d and 4f levels are insufficient to produce strong spectral lines required for accurate measurements . laser - induced - fluorescence ( lif ) technique is employed to increase the 4d and 4f level populations by the laser pumping . pumping of these levels directly from the ground state ( 2s ) is inefficient since the 2s4d and 2s4f transitions are dipole - forbidden . instead , the laser emission is employed for pumping the 4p level from the ground state , and electron - collisional transfer from the 4p level leads to the increase of the 4d and 4f levels populations . the knowledge of the relative populations of the 4d and 4f levels is important for proper interpretation of the relative line intensities . due to the small energy separation between the 4d and 4f levels , it is expected that the electron - collision processes between these two levels dominate the relative populations of these levels , leading to a population distribution in accordance to the level statistical weights . this is verified by collisional - radiative calculations @xcite . the collisional excitations and de - excitations from the pumped 4p level lead to an increased population also of the levels of the neighboring n=3 configuration . the resulting rise in the line intensities is advantageous , since different lines are used to obtain simultaneously both the stark and the doppler contributions to the line shapes . for example , due to the different sensitivity of the 4d and 3d states to the stark effect , a comparison of the 2p3d and 2p4d line shapes allows for inferring the doppler broadening and the rather small stark - broadening contribution to the 2p4d shape . in the present experiments a lithium beam , produced by applying a nd : yag laser pulse onto a solid lithium target , is injected into the plasma region of interest . another laser beam , which is used for the pumping , intersects the lithium beam at the point of interest to produce the lif emission ( see fig . [ doping ] ) . the lithium beam density is so selected that it introduces a minimal disturbance in the region of diagnostics , while , on the other hand , is sufficient for yielding a satisfactory intensity of the desired transitions . for the line - shape modeling , the method described in ref . @xcite was used . this method is capable of calculating line shapes under the simultaneous effects of the plasma micro- and macro - fields ( both electric and magnetic ones ) . the forbidden transition from the @xmath7 to the @xmath8 level of is caused mostly by the 4f4d level mixing . the mixing of the 2p and 4f levels with other levels is negligible since the energy separations between these levels and 2p and 4f are significantly larger than the 4d4f separation . therefore , the 4f4d energy separation is crucial for an accurate modeling . we have measured its value independently @xcite in order to resolve the ambiguity in light of the large spread in the values of this quantity in the available data sources . in this experiment we employ a coaxial plasma configuration , shown in fig . [ posdiag ] , in which plasma is initially injected to fill up the volume between the two coaxial electrodes . the cathode and anode diameters are 3.8 and 8.9 cm , respectively , and the plasma is injected over an axial length of 10 cm . a current pulse applied at one side of the coaxial line propagates through the plasma until the current channel reaches the vacuum section of the transmission line that is followed by a shorted end . this experimental configuration is commonly referred to as plasma opening switch ( see e.g. @xcite and reference therein ) and has been recently used for studying the interaction of the plasma with the propagating magnetic field @xcite . the plasma prefill in the present experiment is produced by a flashboard plasma source and is injected inward through the transparent anode to fill up the a - k gap ( see fig . [ posdiag ] ) . the flashboard plasma with an electron density @xmath9 and electron temperature @xmath10 ev , almost uniform across the a - k gap , is mainly composed of protons and carbon ions ( mainly c iii - v ) . since the heavier carbon ions flow at lower velocities than the protons , the carbon / proton relative abundance decreases towards the cathode . the coaxial line is powered by an lc - water - line marx generator . a current pulse of @xmath11 with a rise time of @xmath12 is then driven through the coaxial line . the upstream and downstream currents are measured by rogowski coils placed at the output of the water - line and at the shorted end . in the diagnostic technique here employed , the flashboard prefill plasma is doped with lithium using a laser - produced lithium beam ( see fig . [ poscross ] ) . for the generation of the lithium beam , a nd : yag laser pulse ( 6 ns ) is focused onto a surface of a metallic lithium target attached to one of the coaxial electrodes . the laser intensity was @xmath13 on the target surface . the particle velocities in the laser - produced plasma plume were found to be @xmath14 . at the distance of @xmath15 from the target , at which the electric field measurements are performed , the density of the lithium beam was @xmath16 with an ionization degree of @xmath17 , i.e. , the electron density was @xmath18 . the electron temperature was @xmath19 ( see sec . [ optim ] ) . for the photopumping of the 4p state , a tunable dye laser is used . this laser is pumped by an additional nd : yag laser pulse of 15 ns duration . in order to obtain the wavelength required for the photopumping ( @xmath20 ) , a wavelength extender for the generation of the second harmonic of the dye laser pulse is employed . thus , the dye laser is tuned to generate a pulse at @xmath21 ( using a solution of ` fluorescein 548 ` dye in methanol ) . the energy achieved at 2741.2 is @xmath221 mj . the laser spectral width is 0.2 . for measurements where recording of accurate spectral line profiles are important , experimental conditions for which the doppler broadening is relatively small are preferable . the doppler broadening that affects the line shapes in these measurements results from the lithium atom velocities in the axial ( _ z _ ) direction ( along the line of sight ) . in order to minimize this effect it is required to use a sufficiently long time delay between the laser pulse for target evaporation and the current pulse application . the reason is that the lithium atoms ejected from the target surface due to the laser pulse move away from the surface with velocities varying along the plasma column produced . therefore , slow atoms reach the measurement region with longer delays . generally , lower velocities in the propagation direction normal to the target surface are correlated with lower velocities in the transverse directions , which enabled us to achieve a satisfactorily low doppler broadening in the axial direction . in the present experiment we used a time delay of 450 ns between the laser pulse employed for the target evaporation and the laser pulse employed for photopumping . selecting longer time - delays decreases the amount of the atoms due to the lithium ionization processes that take place in the prefill plasma , thereby , reducing the signal - to - noise ratio . therefore , the optimal delay was determined according to the requirement of minimal doppler broadening but high enough signal intensity . the diagnostic system consists of two 1-m uv - visible spectrometers equipped with 2400 grooves / mm gratings ( see fig . [ posdiag ] ) . the output of one spectrometer is collected by an optical - fiber array and transmitted to 10 photomultiplier tubes that allow the recording of the line - profile time - dependence ( temporal resolution of 7 ns ) , while the output of the second spectrometer is recorded by a gated ( down to 5 ns ) intensified charge - coupled device ( iccd ) camera , allowing for recording single gated broadband spectra . the spectral resolutions of both systems are @xmath23 in the spectral range used . since the induced fluorescence originates from the region along the pumping - laser path , observing the emitted radiation perpendicular to the pumping - beam direction allows for measurements with a high spatial resolution in 3 dimensions . in this case the spatial resolution along the line of sight is determined by the width of the pumping laser beam , which is @xmath24 , whereas the resolution in the plane perpendicular to the line of sight is chosen by the spectrometer slit dimension ( sub - mm scale ) . a detailed discussion of the spectral calibration and the determination of the instrumental response of the system can be found in ref . the measurements are performed in three stages . in the first stage we characterize the laser - produced lithium plasma used as a dopant . in principle , the dopant plasma could perturb the local conditions of the main prefill plasma , introducing uncertainties in the measurements . in order to minimize this perturbation , the dopant density must be kept lower than that of the main plasma . however , lowering the lithium density results in weakening the spectral lines of interest , thereby reducing the signal - to - noise ratio that is crucial for resolving the spectral profiles required for the determination of the electric field . to optimize the dopant density , measurements of the lithium density , ionization degree , and expansion velocity were first performed with no plasma prefill . in the second stage , with the optimal configuration of the lithium doping , the electric fields are measured in the plasma prefill ( still without the application of the current pulse ) . these experiments yield the initial level of the electric field present in the plasma prior to the application of the current pulse . we refer to this field as a `` background '' electric field . finally , we measure the evolution of the electric fields generated during the conduction of the pulsed current . details of the measurements aimed at the diagnostics of the laser - produced lithium beam will be published separately @xcite . here , we briefly describe the main results . measurements were performed to determine the temporal evolution of the plasma parameters in the lithium beam at different distances from the target for various laser intensities in the range of @xmath25 - @xmath26 a typical spectrum in the wavelength range of interest ( 4603 ) , obtained at a distance of 2.5 mm from the target , is presented in fig . [ profile_las ] . it is recorded by the iccd camera with a time - gate of 10 ns correlated with the peak of the lif signal . the figure shows the measured and simulated line shapes of the allowed 2p-4d and the nearby forbidden 2p-4f transitions . the line shape simulation , similar to that described in ref . @xcite , show the individual contribution of each of the three broadening mechanisms : the stark effect , doppler , and instrumental . the doppler broadening can be estimated from the velocities obtained from time - of - flight measurements . for the present measurements we used a time delay of 450 ns between the evaporating laser pulse and the photopumping laser pulse . at a distance of 2.5 mm from the electrode this delay corresponds to a velocity of @xmath27 . since the plume expands into a large solid angle , the transverse velocities are of the order of the longitudinal velocities . indeed , a doppler broadening of 2 ev , consistent with the velocities mentioned above , is obtained by deconvolving the known instrumental broadening function from the total line shape of the 2p3d transition ( 6104 ) that is insensitive to the stark effect under the present conditions . subsequently , the stark - broadened spectrum for various values of the electron density @xmath28 is calculated , and convolved with the instrumental and the doppler broadening functions . for these calculations , we used @xmath29 , adopted from the results of a collisional - radiative modeling of the temporal behavior of the line intensities ( described in ref . @xcite ) . from the line - shape calculations it is found that the measured spectrum can not be satisfactorily fitted for any electron density . a good fit is rather obtained by assuming a combination of @xmath30 and low frequency ( @xmath31 ) oscillations with an amplitude of @xmath32 ( see fig . [ profile_las ] ) . although assuming a higher electron density of @xmath33 ( with no waves in the plasma ) provides a satisfactory fit to the total intensity ratio of the allowed line to the forbidden line , the width of the 2p-4f line becomes significantly larger due to the wide spectrum of the microfield amplitudes under this assumption . this results in flattening of the forbidden peak , which is in disagreement with the observations . we now describe the experiments in which the lithium beam is locally injected into the flashboard plasma that prefills the inter - electrode gap ( still , without applying the main pulsed - current ) . the lithium target is attached to the cathode ( the inner electrode , see fig . [ poscross ] ) . the plasma prefill parameters were obtained in a previous work from emission spectroscopy @xcite . the plasma is found to have a nearly uniform electron density across the inter - electrode gap with @xmath34 and @xmath35 . under these conditions the lithium atoms undergo substantial ionization and the density of neutral lithium arriving at the observation point is expected to be significantly lower than when the dopant is injected into vacuum , leading to reduced line intensities . indeed , the intensity of the 4603-line in the plasma prefill is found to be an order of magnitude lower than when the lithium beam is expanding in vacuum . nevertheless , this intensity is still sufficient to provide a signal - to - noise ratio that is adequate for resolving the line profiles of interest . in these experiments the 2p-3d line is not useful for measuring the doppler broadening since its upper level is no longer populated from the decay of the @xmath36 levels , as the latter are significantly depopulated through collisional ionization due to the higher prefill plasma density . instead , here we use the 2s-2p line at 6708 that is also insensitive to the stark effect . this line exhibits somewhat larger doppler width than in the case of expansion into vacuum , corresponding to a temperature of @xmath37 . in fig . [ fb_2p-4d ] we present a comparison of the profiles of the allowed 2p4d and the forbidden 2p4f lines emitted when the lithium beam is expanding in vacuum with those emitted with the flashboard plasma prefill . it is clearly seen that in the presence of the flashboard plasma the forbidden line has a substantially higher relative intensity and both lines are relatively broadened . similarly to the previous case , also here we find that electric microfields , arising from the thermal electrons and ions , can not explain the observations . the best fit is obtained by considering a combination of micro electric fields due to @xmath38 and the presence of a low frequency electric field of @xmath39 . we note that under these higher density conditions , the line profiles are less sensitive to the density , but the inferred density range agrees well with that found in a previous work @xcite . the simulations also give an upper limit for the oscillation frequency of the additional electric field , @xmath40 . this upper limit is of the order of @xmath41 of the flashboard plasma , indicating that these oscillations can possibly be of the ion - acoustic type . similar e - field intensities were measured in several positions , particularly in the positions where the e - field measurements were performed during the current application , as described in the next paragraph . we take this observed electric field of @xmath42 to be the upper limit of the collective fields present in the plasma prefill prior to the application of the high - current pulse ; hereafter referred to as the `` background '' electric field . for performing measurements of electric fields also in the vicinity of the anode , the lithium target is attached to the anode and the evaporating laser beam is focused onto the target through a port in the vacuum chamber at the opposite side of the anode . the two different setups , allowing for measurements in the vicinity of the cathode and the anode , are schematically described in fig . [ beam_injection ] . since the flashboard plasma source is located on an outside cylinder and its plasma flows radially inward , attaching the dopant - lithium target to the anode results in evaporated li atoms flowing mostly in the same direction as the flashboard plasma flow , whereas when the li target is attached to the cathode , the li atoms flow opposite to the direction of the flashboard plasma flow . the line profiles obtained near the anode are compared to those obtained near the cathode . the comparison of the line profiles is performed for azimuthal and radial polarizations ( the line of sight is along the axial direction ) . interestingly , as shown in fig . [ fb_pol ] , the change of the dopant injection direction with respect to the flashboard plasma flow is found to affect the line profiles only in the azimuthal polarization . for the azimuthal polarization , the 2p4f forbidden - line intensity is noticeably higher for the case where the dopant atoms are injected opposite to the direction of the flow of the flashboard plasma ( measurements near the cathode ) , while for the radial polarization the line profiles are found to be similar for the two cases of the dopant injection . the explanation for this effect is not clear yet . for the e - field measurements in the present study only the radial - polarization line - emission is used , for which no effect of the switching of the lithium injection direction on the line shapes is observed . knowledge of the effect of the prefill plasma on the dopant lithium line shapes and the corresponding electric fields allows for investigating the electric fields formed during the flow of the pulsed - current in the plasma . the measurements are performed at a distance of 2.5 mm from the electrodes ( either the cathode or the anode ) inside the inter - electrode gap at different axial positions . the field of view of the optical system covers a region between 2.2 and 2.8 mm from the electrodes . we note that estimates of the maximal sheath size give a much smaller distance from the electrodes , based on the known system inductance and the measured current . the electric field measured is thus in the plasma and not in the sheath . the arrangement of the measurement positions is shown in fig . [ e_pos_setup ] . the measurement positions are located symmetrically near the anode and near the cathode separated axially by 35 mm . the positions * 1 * and * 4 * in the plasma are located at a distance of @xmath43 cm from the generator - side plasma boundary . the boundary position is defined as the position beyond which ( towards the generator ) @xmath28 drops by more than a factor of 3 relative to that in the main part of the plasma . due to the plasma expansion towards the cathode the plasma boundary is slightly farther from the measurement positions near the cathode than near the anode . . the total length of the plasma is @xmath44 . ] this setup allows for determining the velocity of the electric - field axial propagation at the two radial positions ( near the anode and of the cathode ) . the temporal evolution of the electric field at each position is obtained by performing consecutive experiments , varying the time delay between the application of the current pulse and the application of the photo - pumping laser . the temporal resolution of the measurements ( 10 ns ) is determined by the time - gate of the iccd camera . in order to cover the entire duration in which the current flows through the plasma , the e - field is obtained at a minimum of 6 consecutive time intervals in each position . for overcoming the shot - to - shot irreproducibility , the results at each time are averaged over several discharges . , corresponding to time of maximum e - field at point * 2*. ] figure [ fb_pos_profiles ] shows a comparison between the spectral profiles obtained at point * 2 * prior and after the current - pulse application . it is clearly seen that the lines broaden during the current conduction in the plasma , with the forbidden component rises in intensity relative to the allowed line and becomes shifted to shorter wavelengths . this demonstrates the rise of the e - field in the plasma during the current conduction . the recorded profiles are analyzed in the manner described in sec . [ method ] , taking into account the effects of the plasma microfields , the doppler broadening , and the instrumental broadening . this analysis yields the electric field amplitude as a function of time . the inferred evolution of the e - fields at the 3 axial positions near the cathode and the anode are shown in fig . [ e - field_anodevscathode ] . the error - bars in the figure reflect the statistical errors due to the shot - to - shot irreproducibility . in addition , a systematic error of up to 10% can be expected due to the finite accuracy of the line - shape modeling . for clarity , these have been omitted from the figure . thus , the absolute value of the measured e - field has an additional error of 10% . the rise of the e - field in the vicinity of the cathode ( fig . [ e - field_anodevscathode]a ) is observed to be delayed between the different axial positions . this allows for determining the axial propagation velocity of the electric field , which is found to be @xmath45 . the velocity is found to be approximately the same between points * 1 * * 2 * and * 2 * * 3 * , therefore , the e - field propagation velocity is concluded to be constant over the entire pulse . based on the 10-ns temporal resolution , the rise time of the e - field is inferred to be less than @xmath46 . the product of the field rise - time and the propagation velocity gives an estimate of the axial scale of the changes of the electric field . this scale of @xmath47 could possibly be related to the width of the current channel , which in previous experiments was found to exhibit a similar scale , @xmath48 cm @xcite . in the vicinity of the anode one might expect somewhat lower e - field values . this is plausible due to the lower b - field near the anode and the higher fraction of heavy ions , since the latter leads to a higher electron density following the reflection of the protons by the propagating magnetic front . however , the e - field at point * 4 * was found to have an amplitude similar to the maximum obtained near the cathode , whereas at points * 5 * and * 6 * no rise in the field is observed within the measurement accuracy ( see fig . [ e - field_anodevscathode]b ) . the e - field in point * 4 * rises at a delay compared to point * 1 * , demonstrating a slower propagation of the e - field near the anode . thus , when the current channel near the cathode reaches the vacuum section near the shorted end of the transmission line and as a result ceases to flow through the plasma , the current near the anode has still not reached point * 5 * , and no e - field is generated at points * 5 * and * 6*. an upper limit for the field propagation velocity near the anode can thus be estimated by dividing the distance between point * 4 * and point * 5 * by the time interval between the field arrival at point * 4 * and the field arrival to the plasma - vacuum boundary ( at the shorted - end side ) . this gives a velocity of @xmath49 . is the start of the current pulse . ] we now estimate the net rise in the e - field due to the application of the current pulse , by subtracting from the measured total e - field ( @xmath50 ) the background field @xmath51 , found in the plasma prefill prior to the current application ( see sec . [ sec_fb ] ) . a simple subtraction of this background from the measured e - field is not always correct . in order to demonstrate this fact , let us assume that some external quasi - static field @xmath52 at a certain direction ( e.g. , the hall field ) is formed in the plasma in addition to the already present randomly directed , fluctuating background field . on a spatial scale smaller than the typical scale of the fluctuations , where the background field has a distinguished orientation , the background and the external fields should be summed up as vectors . then , the sum of the fields must be averaged over all possible directions of the background field , since in the measurements the field of view of the optical system is assumed to be larger than the fluctuation scale . as a result , the mean value of the total measured field is given by @xmath53 . table [ e - res ] summarizes the results of the e - field measurements . the first column presents the position of the measurement . the other columns give the total measured e - field and the field obtained after the subtraction of the background field of @xmath54 near the cathode and @xmath55 near the anode . the table also gives the inferred axial propagation velocity of the field ( @xmath56 ) . .summary of the peak e - field parameters . [ cols="^,^,^,^",options="header " , ] in a quasi - neutral plasma the electric field is given by ohm s law : @xmath57 where @xmath58 is the magnetic field , @xmath59 is the current density , @xmath60 is the ion velocity , @xmath61 is the plasma conductivity , and @xmath62 is the speed of light in vacuum . here , the electron inertia and pressure are neglected . we now show that the measured electric field in the vicinity of the cathode is close to the electric field calculated by this expression when only the first ( hall ) term on the right - hand - side is considered . the second term , which results from ion pushing @xcite is shown to be smaller than the hall term . the contribution of the third term is discussed in sec . [ anomalous ] . for evaluating the hall term and comparing it to the present electric field measurements we use previous measurements of the magnetic field and density @xcite . although the b - field measurements are highly informative , they do not allow for the reconstruction of the spatial distribution of the b - field due to the small number of the measurement positions in the a - k gap . nevertheless , these measurements demonstrate a strong correlation between the rise of the magnetic field at each measurement position and a drop of the electron density ( see , e.g. , @xcite ) . we note that the prominent density drop is closely related to the phenomenon of ion - species separation @xcite , mentioned in sec . [ introduction ] , in which the magnetic field only penetrates into the heavier component of the plasma ( carbon ions ) while the light ions ( protons ) are reflected ahead by the magnetic field front . in ref . @xcite a map of the electron density distribution was measured at different instants of the current conduction in an experimental setup similar to the present one . these data show that the density drop propagates axially , exhibiting different propagation velocities at different radial positions . thus , assuming the density drop in the a - k gap is correlated with the arrival of the magnetic field front everywhere , the measured evolution of the density map can be used to determine the distribution of the b - field front . we now fit an analytical expression for the magnetic field temporal distribution . based on the previous measurements @xcite we approximate the b - field axial distribution at each radial position by a step - like function of a front width @xmath63 , i.e. , the b - field rises within a distance @xmath63 that corresponds to the current - channel width . this step front propagates axially with a constant velocity . the propagation velocity is lower at larger radii , similarly to the density drop @xcite . at the plasma boundary , @xmath64 , the magnetic - field temporal behavior was found to be similar to that of the generator current , approximated by @xmath65 , where @xmath66 is the time corresponding to the peak - current . therefore , we assume that the amplitude of the field in the back of the step - front ( which is the height of the step ) also rises in time as @xmath67 . for the radial distribution of the magnetic field we assume that the field at the rear of the field - front decreases towards the anode as @xmath68 , due to the cylindrical geometry of the experiment . under these assumptions we find that the magnetic field can be approximated by : @xmath69,\end{aligned}\ ] ] where @xmath70 is the peak magnetic field , @xmath71 and @xmath72 are the cathode and anode radii , @xmath73 ( here we focus on the period of the current flow through the plasma lasting until @xmath74 that denotes the arrival of the current channel at the plasma transmission - line boundary ) , @xmath75 is the b - field propagation velocity near the cathode , and @xmath76 is the current - channel width . in our experiment @xmath77 . the variables @xmath78 and @xmath79 are limited by @xmath80 and @xmath81 , where @xmath82 is the position of the plasma transmission - line boundary . in the calculations , the current channel width @xmath63 , which is assumed to be broadened by diffusion , varies in time as @xmath83 , where @xmath84 is the electron skin depth . the term @xmath85 is the front - width at the instant @xmath86 . since at time @xmath86 @xmath63 is measured to be about @xmath87 , which is much larger than @xmath84 , we obtain @xmath88 . the comparison of the map of the b - front propagation determined from the previous measurements of the electron density drop to the map generated using the semi - analytical formula ( 2 ) is shown in fig . [ b - front ] , demonstrating a good agreement between the two approaches . ) ( here the contours are the locations where the magnetic field is 0.2 t ) . the numbers on the plot represent the time in nanoseconds relative to the beginning of the current pulse . the solid circles in ( b ) represent the positions of the present e - field measurements . ] using the analytic form of the magnetic field and the fact that @xmath89 , the hall electric field is expressed by : @xmath90}{4 \pi\ : n_{e}\ : e}= & \nonumber \\ & ~ & \nonumber \\ & \displaystyle = \frac{1}{4\pi\ : n_{e}\ : e}\left[\vec e_r\left(b\:\frac{1}{r}\frac{\partial ( rb)}{\partial r}\right)+\vec e_z \left(b\frac{\partial b}{\partial z}\right)\right]&.\end{aligned}\ ] ] finally , by inserting eq . ( [ bmap_fun ] ) into eq . ( [ eh ] ) , the axial ( @xmath91 ) and radial ( @xmath92 ) components of the electric field are found to be : @xmath93 \times \nonumber \label{er } \\ { ~ } & \times \left [ 1-\tanh ^{2}(\zeta ) \right ] , & \\ & ~ & \nonumber \\ & \displaystyle e_{hall , r}=\frac { b_{0}^{2}\:r_{c}^{3}\:v_{c}\:t\:\sin ^{2}\left ( \frac{\displaystyle\pi t}{2\tau } \right ) } { 8\pi \:n_{e}\:e\:r^{4}\:\delta } \:\left [ 1-\tanh ( \zeta ) \right ] \times \nonumber \\ & \times \left [ 1-\tanh ^{2}(\zeta ) \right ] , & \label{ez}\end{aligned}\ ] ] where @xmath94 . we now compare the magnitude of the measured e - field with the calculated @xmath95 using the expressions ( [ er ] ) and ( [ ez ] ) . we note that for this comparison , knowledge of the electron density is essential . here , again , we use the previous measurements by weingarten _ et al . _ we assume that the magnetic field reflecting the protonic component of the plasma and thereby causing the density to drop , penetrates only into the carbon plasma @xcite . the electron density of the carbon plasma ( penetrated by the magnetic field ) is determined here for each position at the time of the arrival of the magnetic front at the transmission - line boundary of the plasma . at this time , at the generator side of the plasma , namely at point * 1 * , the electron density drops from @xmath96 to @xmath97 . in the middle of the plasma ( at point * 2 * ) the density only drops to @xmath98 , and at the transmission - line boundary of the plasma ( at point * 3 * ) no density drop is found , rather a slight rise to @xmath99 is observed . using these data , the evolution of @xmath100 is incorporated into the calculations of @xmath95 by synchronizing the change of the local value of the electron density with the rise of the local magnetic field , namely @xmath101 . here , @xmath102 denotes the density drop at the particular position for which the electric field evolution is calculated , and @xmath103 . and @xmath92 . the background e - field of 8 kv / cm , found in the flash - board plasma , is added to the calculated values in the manner described in sec . [ sec_fb ] . ] thus , the evolution of the hall electric field is calculated for the three different axial positions at which the electric field measurements were performed . figure [ evsmodel ] gives a comparison between the calculation results and the experimental data near the cathode . the hall field presented is the magnitude of the electric field including its axial and radial components , to which the @xmath42 turbulent background has been added according to @xmath104 ( see sec . [ sec_fb ] ) . it is seen that the calculated hall - field fits well the measured values , except for point * 1 * at relatively late times . the relatively large deviation seen for point * 1 * can possibly be explained by the more pronounced @xmath100 drop observed at this point , which may reduce the turbulent background e - field , contrary to our assumption in the model that the background field is constant . such a good agreement between the experimentally measured electric field and the calculated hall electric field , based on the b - field and density measurements , as shown in fig . [ evsmodel ] , suggests that the observed e - field is most likely the hall field , generated by the current . although a thorough understanding of the field evolution requires a self - consistent modeling that , for example , would also consider the ion reflection and species separation observed in the experiment , this agreement indicates that the hall field could play a crucial role in the magnetic field penetration . the model discussed here predicts the e - field near the anode ( point * 4 * ) to be a factor of 4 lower than that near the cathode at point * 1 * ( b - field drops by a factor of 2 near the anode , see table [ param_table ] ) , in disagreement with the measurements ( see fig . [ e - field_anodevscathode ] ) . a possible explanation is a rise of the turbulence near the anode during the current flow . in order to test this explanation , one could measure the axial velocities of the accelerated ions both near the anode and near the cathode . since the ions accelerate axially mostly due to the hall - field , if indeed the electric field is mostly turbulent near the anode then the axial ion velocities near the anode will be substantially lower than they are near the cathode , but the velocity distribution will be much broader . the contribution of the ion motion to the electric field in ohm s law ( the second term of the rhs of eq . ( [ ohms_law ] ) ) is small . this contribution can be estimated by comparing @xmath105 to @xmath106 . approximating the magnitude of the current density by @xmath107 , using the measured ion velocities from ref . @xcite , and assuming the ions are accelerated in the direction perpendicular to the b - field front , we find the contribution of the convective term in eq . ( [ ohms_law ] ) to be much smaller than the contribution of the hall term . if instead of using the measured ion velocities we use the mhd velocity @xmath108 ( where @xmath109 is the mass density ahead of the current front ) as the maximal ion velocity , we find that the contribution of the hall term is larger than that of the ion motion as long as @xmath110 ( the effective ion skin depth ) . here , @xmath111 yields an effective ion skin depth of @xmath112 that is much larger than @xmath113 ( the current - channel width observed in the experiments ) , thus the ion term is expected to be smaller . as suggested in sec . [ sec_fb ] , the background electric field may be attributed to an ion - acoustic instability in the plasma . in this case , this electric field should cause a relatively strong electron collisionality in the plasma prior to the application of the current . here we describe the effect of such a strong collisionality on the magnetic - field evolution and the current distribution . following ref . @xcite , the effective collision frequency @xmath114 associated with the ion - acoustic turbulent electric fields in the plasma is : @xmath115 assuming that the turbulent e - field is of the order of the background e - field of @xmath42 measured prior to the current application , and using @xmath116 and @xmath117 ( @xmath118 being the upper limit of the electron temperature in the plasma prefill ) , the expected collision frequency is @xmath119 . this frequency is much higher than spitzer s collision frequency , which for the above parameters is @xmath120 . such a high collision frequency is expected to increase the rate of magnetic field penetration into the plasma and also to broaden the current channel . in spite of the relatively high anomalous collision frequency suggested here , it is still insufficient to explain the fast b - field penetration by diffusion that requires collision frequency of about @xmath121 @xcite . in addition , step - like spatial profile of the magnetic field is inconsistent with the exponential decay predicted by diffusion . a different mechanism , such as the hall - field induced mechanism @xcite , is thus expected to cause the fast magnetic field penetration . still , the high anomalous collision frequency may help to explain the observed broad current - channel , not understood thus far . according to ref . @xcite , in a steady hall - induced penetration the current - channel width is estimated to be : @xmath122where @xmath123 is the alfvn velocity of electrons , @xmath124 ( @xmath125 is the electron mass ) , and @xmath126 is the inter - electrode spacing . although in the present experiment the plasma and field dynamics do not reach a steady state , we use this relation to obtain an estimate for the current - channel width , assuming hall - induced penetration . for @xmath127 and the anomalous collision frequency estimated above , we find that @xmath128 . this value is an order of magnitude larger than the electron skin - depth @xmath129 and consistent with the measurements @xcite used for our model ( @xmath130 ) . thus , while the anomalous collision frequency estimated from the turbulent electric fields is insufficient to explain the rate of magnetic field penetration , it does explain reasonably well the current channel width . we note that in a previous investigation @xcite it was concluded otherwise , based on an estimated upper level of a @xmath131 electric field . however , in that experiment the plasma source was a plasma gun rather than a surface flashover as in the present work . also , the previous e - field measurements might have been related to a secondary plasma , since they were based on hydrogen line - emission that also originated at electrode sputtering @xcite . the anomalous collision frequency predicted above is about three times higher than the minimal collision frequency required for a collisional current channel dominated by the hall - field penetration @xcite , @xmath132 $ ] , which is estimated to be @xmath133 this further supports the possibility of a hall - field induced magnetic - field penetration . we note that for @xmath134 the value of @xmath114 is larger than the electron gyrofrequency , meaning there is no electron magnetization and the resistive term ( the third term on the rhs of eq . ( [ ohms_law ] ) ) is thus dominant in determining the electric field at the beginning of the current conduction . therefore , the hall mechanism is not applicable in these conditions . the collisionality , though rather high , also can not explain the velocity of the magnetic field penetration at this early stage of the pulse and the question regarding the mechanism of the initial magnetic field penetration remains open . for the first time the electric fields in current - carrying plasmas are measured with high spatial and temporal resolutions . this is achieved by a diagnostic method that is based on line - shape analysis of dipole - forbidden transitions combined with laser spectroscopy . the measured electric fields exhibit a good agreement with the hall field calculated using measurements of the time - dependent magnetic - field and density distributions in the current - carrying plasma . these results indicate that in the present experiment the hall mechanism can be dominant in the magnetic field penetration into the plasma . moreover , it is noteworthy that the modeled hall field , which depends linearly on @xmath135 , reproduces well the present e - field measurements , particularly in light of the sharp density drop observed due to the ion - species separation phenomenon . it is important to note , however , that in order to further conclude that the hall electric field induces the magnetic field penetration , as suggested in refs . @xcite , it is yet to be shown that the evolution of the electric fields must be consistent with the magnetic field propagation in accordance with faraday s law : @xmath136 a rather high level of the electric field ( @xmath137 kv / cm ) is observed in the plasma prefill prior to the pulsed current application . such electric fields , if present in the entire prefill plasma , may give rise to an anomalous collisionality that is consistent with the hall mechanism and may help explaining the observed current channel width . a clarification of this effect and the nature of this possible turbulence can be a subject of future investigations . the authors thank r. arad for useful comments and are grateful to yu . v. ralchenko for his help in the collisional - radiative calculations . highly valuable discussions with h .- j . kunze and h. r. griem are appreciated . we thank p. meiri for his skilled technical assistance . this work was supported in part by the german - israeli project cooperation foundation ( dip ) , the u.s .- israel binational science foundation ( bsf ) , the israel science foundation ( isf ) , and by sandia national laboratory ( usa ) . s. kingsep , yu . v. mochov , and k. v. chukbar , sov . j. plasma phys . * 10 * , 495 ( 1984 ) ; a. s. kingsep , k. v. chukbar , and v. v. yankov , in reviews on plasma physics , edited by b. kadomtsev ( consultants review , new york , 1990 ) , vol . 16 , p. 243 .

electric fields in a plasma that conducts a high - current pulse are measured as a function of time and space . the experiment is performed using a coaxial configuration , in which a current rising to 160 ka in 100 ns is conducted through a plasma that prefills the region between two coaxial electrodes . the electric field is determined using laser spectroscopy and line - shape analysis . plasma doping allows for 3d spatially resolved measurements . the measured peak magnitude and propagation velocity of the electric field is found to match those of the hall electric field , inferred from the magnetic - field front propagation measured previously .

during the cardiac device implantation procedure , selection of the appropriate vein puncture site is important to reduce the risk of vascular and lead - related complications.1 ) nerve injuries that arise during device implantation procedures are sparsely reported in the literature.2)3 ) here , we report a case of brachial plexus injury caused by indwelling transvenous pacing leads . a 64-year - old male patient underwent cardiac resynchronization therapy ( crt ) device with defibrillator implantation for dilated cardiomyopathy and recurrent ventricular tachycardia . during the implantation procedure , it was difficult to determine the location of the left axillary vein as although the left subclavian vein was punctured and a guide wire could be inserted , we could not insert a peel - away introducer across the costoclavicular junction and handle the inserted right ventricular lead due to mechanical resistance at the costoclavicular junction . to avoid the risk of difficult lead handling and future subclavian crush syndrome , a second puncture was performed at a more lateral site approximately two fingers away from the initial puncture point . although a puncture needle should be inserted almost vertically in order to reach the lateral axillary vein near the junction of the cephalic and brachial veins , we were able to insert peel - away introducers and the left ventricle ( lv ) and right atrium ( ra ) leads without any difficulty . the lv and ra leads were positioned where the optimal values of sensing and pacing parameters were obtained . after starting biventricular pacing , the episodes of ventricular tachycardia decreased remarkably , suggesting successful electrical remodeling . the patient was discharged without overt complications . however , two weeks after the implantation of the crt device , the patient started complaining of " electric shock - like " pain in the left axillary area radiating to the medial border of the left arm . the patient described the pain as being usually triggered by active shoulder movements , especially when pulling up his pants . during physical examination , typical pain in the left axillary area was reproduced whenever his left shoulder was passively abducted more than 60 degrees . chest computed tomography scans showed the lv and ra leads running together into the lateral axillary vein along the lateral side of the pectoralis minor muscle causing a curvature with an acute angle ( fig . fluoroscopic examination in the supine position showed that the lv and ra leads were positioned at an acute angle directing towards the left brachial plexus whenever the patient 's shoulder was passively abducted more than 60 degrees ( fig . 2 ; video in the online - only data supplement ) . severe left axillary and radiating arm pain recurred whenever the lv and ra leads formed such an acute angulation on fluoroscopic examination . analgesics and antibiotics were prescribed to control the pain and to treat the possible subclinical device - related infection . however , the patient complained of gradual worsening of the pain despite continued administration of high - dose pain killers . six months after implantation of the crt device , the patient was readmitted for adjustment of lead angulation due to worsening of the left axillary and radiating arm pain which impeded the patient 's daily physical activities . due to the fact that the lv and ra leads were inserted across the pectoralis major and minor muscles into the lateral axillary vein , which was located deep in the patient 's chest , correction of the lead angulation by generator repositioning was technically impossible . operators had to move the entry site of the lv and ra leads from the distal to the proximal axillary vein using the cut - down method . under general anesthesia , the pectoralis minor muscle was cut and the axillary vein was exposed . after disconnection of the lv and ra leads from the generator , we attempted to manually extract the disconnected leads through the transverse incision line . however , the leads were tightly adhered to the axillary venous wall , and the possibility of vascular injury and lv lead malpositioning due to extraction force was considered . finally , we had to open the left axillary vein to separate the leads safely . the left axillary vein was incised longitudinally from the initial insertion site of the lv and ra leads to the more proximal site which was 3 cm away ( figs . 2d and 3b ) . separated leads were moved to the proximal site through the longitudinal incision line and the remaining incision lines were closed . after adjusting the lv and ra lead insertion site , acute angulation was not observed during passive shoulder abduction more than 60 degrees on fluoroscopic examination ( fig . although curvatures of the lv and ra leads were slightly modified after the correction surgery , there was no significant change in the lv lead tip location and lv capture threshold . neuropathic pain decreased remarkably two weeks later and analgesic agents could be withheld two months later . the ranges of passive and active shoulder movements increased gradually but were nearly completely normalized at six months after the surgery . during the cardiac device implantation procedure , selection of the appropriate vein puncture site is important to avoid the risk of vascular or pacing lead - related complications.1 ) in the present case , to avoid the risk of subclavian crush syndrome , the lv and ra leads were inserted into the lateral axillary vein which is close to the brachial plexus , under the guidance of contrast venography.4 ) unfortunately , the inappropriately inserted crt device leads caused brachial plexus injury . although transvenous pacing lead - induced nerve injury is not a frequent complication seen in clinical practice , this possibility should be kept in mind by the operators . if this type of complication occurs , correction surgery for the lead insertion site using the cut - down method can be considered as a therapeutic option . understanding the vascular anatomy with adjacent nerve structures and carefully selecting the vein puncture site are necessary for minimizing the risk of pacing lead - induced nerve injury .

a 64-year - old male patient underwent cardiac resynchronization therapy ( crt ) device implantation via the axillary venous approach . two weeks later , the patient started complaining of " electric shock - like " pain in the left axillary area . during physical examination , typical pain in the left axillary area was reproduced whenever his left shoulder was passively abducted more than 60 degrees . fluoroscopic examination showed that the left ventricle ( lv ) and right atrium ( ra ) leads were positioned at an acute angle directing towards the left brachial plexus whenever the patient 's shoulder was passively abducted . brachial plexus irritation by the angulated crt leads was strongly suspected . to relieve the acute angulation , we had to adjust the entry site of the lv and ra leads from the distal to the proximal axillary vein using the cut - down method . after successful lead repositioning , the neuropathic pain improved rapidly . although transvenous pacing lead - induced nerve injury is not a frequent complication , this possibility should be kept in mind by the operators .

dis and ns were responsible for drafting the article and revising it critically for important intellectual content .

in this issue of the journal , erqou and colleagues ( doi 10.1007/s00125 - 014 - 3374-x ) report , in a systematic review and meta - analysis of randomised trials , a very modest ( 1.3 mmol / mol or 0.12% ) albeit significant increase in hba1c in patients with diabetes treated with statins , compared with control . here , we discuss the clinical relevance of the findings . given the overwhelming benefit of statins on cardiovascular outcomes in diabetes , current guidelines recommending statins for primary prevention in type 2 diabetes should not change , and any effect on microvascular risk is likely to be minimal . of course , all patients recommended for statin treatment , whether they have diabetes or not , should now be warned of a slight potential for dysglycaemia on starting statins , but at the same time they should be told that very modest lifestyle improvement will help offset this dysglycaemia risk . finally , we remind colleagues that nearly all drugs have side effects and we should not be surprised by this statin dysglycaemia effect , which can be easily managed .

most of our current understanding of surface morphology is based on the step - continuum model,@xcite which treats the step itself as the fundamental unit controlling the evolution of a surface . in this model , the step stiffness @xmath0 serves as one of the three fundamental parameters ; it gauges the resistance " of the step to meandering and ultimately accounts for the inertia of the step in the face of driving forces . the stiffness can be derived from the step line tension @xmath1 , the excess free energy per length associated with a step edge of a specified azimuthal orientation @xmath2 . from @xmath3 , the two - dimensional equilibrium crystal shape ( i.e. , the shape of the islands ) is determined . the goal of this paper is to find low - temperature ( @xmath4 ) formulas for @xmath1 and thence @xmath5 as functions of the azimuthal misorientation @xmath2 , assuming just nearest - neighbor interactions in plane and an underlying \{111 } surface . such surfaces are characterized by a six - fold symmetric triangular ( hexagonal ) lattice , allowing all calculations to be done in the first sextant alone ( from @xmath6 to @xmath7 ) . in contrast to @xmath1 , we shall find that at low @xmath4 , @xmath8 is insensitive , under plausible assumptions , to the symmetry - breaking by the second substrate layer , so that plots from @xmath6 to @xmath9 suffice . although an analytic solution exists for the orientation dependence of @xmath1 on a square lattice,@xcite only an implicit solution to a 6@xmath10-order equation has been found for a hexagonal lattice.@xcite this makes comparisons to experiment rather arduous , particularly when trying to compare data on @xmath8 , which is related to @xmath1 through a double derivative with respect to @xmath2 . fortunately , we will see that a remarkably simple formula exists for the orientation dependence of @xmath0 at temperatures which are low compared to the characteristic energy of step fluctuations ( i.e. the kink energy or the energy per length along the step ) . for noble metals , room temperature lies in this limit , facilitating direct comparisons to experiment . motivating this work is a recent finding@xcite that the square - lattice nearest - neighbor ( nn ) ising model underestimates @xmath0 by a factor of @xmath11 away from close - packed directions on cu\{001}. later work@xcite showed that much ( but not all ) of this discrepancy could be understood by considering the addition of next - nearest - neighbor ( nnn ) interactions . for the triangular lattice , we will see that such a longer - range interaction is not required to describe the orientation dependence of @xmath0 . in the following section , we characterize steps on a hexagonal lattice and perform a low - temperature expansion of the lattice - gas partition function , assuming only nn bonds are relevant , and derive both @xmath1 and @xmath8 . we obtain a remarkably simple expression for the latter in eq . ( [ eq : stiffness ] ) . since this low-@xmath4 limit is determined by geometric / configurational considerations , it becomes problematic near close - packed orientations ( @xmath12 ) , where the kinks must be thermally activated . therefore , we make use of exact results to assess in several ways how small @xmath2 can be before the simple expression becomes unreliable . in section iii , we present three general results for island stiffness that are valid in the experimentally - relevant low-@xmath4 limit when configurational considerations dominate the thermodynamics . we show that the line tension can not be [ re]generated from the stiffness and that the stiffness can have full 6-fold symmetry even though the substrate and the line tension have just 3-fold symmetry . accounting for such 3-fold symmetry with a lattice - gas model on a hexagonal grid requires an extension from the conventional parametrization ; we posit an _ orientation - dependent _ interactions between 3 atoms at the apexes of an equilateral triangle with nn legs . in section iv , we compare our results to experiments on ag and cu\{111 } surfaces , showing that eq . ( [ eq : stiffness ] ) provides a good approximation and , thus , that nnn interactions are much less important than on cu\{001}. the final section offers a concluding discussion . three appendices give detailed calculations of the leading correction of the low-@xmath4 expansion , of explicit analytic and numerical results based on zia s exact implicit solution , @xcite and of eq . ( [ eq : stiffness ] ) as the low-@xmath4 limit of zia s solution . the orientation dependence of @xmath3 on \{111 } surfaces can be determined by first calculating the free energy @xmath13 of a single step oriented at a fixed angle @xmath2 . to approximate this , we perform a low - temperature ising expansion of the partition function , similar to the one used by rottman and wortis.@xcite they considered a step on a square lattice with one end fixed to the origin and the other end , a distance @xmath14 away , fixed to the point ( @xmath15 , @xmath16 ) . such a step is shown in fig . [ fig : brokenbonds]a . the single - layer island ( or compact adatom - filled region ) is in the lower region , separated by the step edge which is drawn as a bold solid line from the upper part of the figure , representing the plain " region . they found the step energies associated with the broken bonds of the step - edge to be @xmath17 where @xmath18 , sometimes@xcite called the ising parameter , " is the bonding energy associated with the severed half " of the nn lattice - gas bond : since the nn lattice - gas energy @xmath19 is attractive ( negative ) , and half of it is attributed to the atom on each end , it costs " a positive energy @xmath20 for each step - edge atom . because longer steps require more step - edge atoms , the step energy is only a function of the step length : @xmath21 . thus , @xmath22 corresponds to the shortest possible step . to increase the length of this step , two more step - edge links corresponding to one more step - edge atom must be added , one going away from the fixed endpoint and one going toward it . because this corresponds to two more broken bonds , in general , @xmath23 . with these energies , we can write down the partition function @xmath24 , assuming @xmath2 is fixed but @xmath14 is large enough so that integer values of @xmath25 and @xmath26 can be found : @xmath27 where @xmath28 corresponds to the number of ways a step of length @xmath29 can be arranged between the two endpoints . for low temperatures , only the first term in eq . ( [ eq : partitionfun ] ) need be considered ( appendix i provides the leading correction term , which gives a correction of order @xmath30 ) . to lowest order , then , @xmath13 is @xmath31 where we have inserted the value of @xmath32 obtained from a simple combinatorial analysis.@xcite after taking the thermodynamic limit ( @xmath25 , @xmath26 @xmath33 @xmath34 ) and using stirling s approximation , @xmath13 becomes @xmath35\end{aligned}\ ] ] and the shortest distance steps connecting points on a triangular lattice [ ( b ) , right panel ] . this figure shows two corresponding steps . analogous to the @xmath36 broken bonds oriented at @xmath6 and @xmath37 on a square lattice , there are @xmath38 broken bonds oriented at @xmath6 and at @xmath7 on a triangular lattice . however , there are another @xmath38 broken bonds oriented at @xmath39 on a triangular lattice . , width=8 ] [ fig : brokenbonds ] in order to extend this result to a step on a triangular lattice , we need to make a few minor adjustments . first , we introduce a linear operator @xmath40 that transforms the coordinates of a point on a square lattice ( @xmath25,@xmath26 ) to those on a triangular lattice ( @xmath41,@xmath42 ) ; cf . [ fig : brokenbonds]b . this operator finds the position of a point in a coordinate system whose positive y - axis is bent at @xmath7 with respect to the positive x - axis : @xmath43 with the aid of @xmath40 , we can see how @xmath22 changes on a triangular lattice . to begin , we imagine a step in the first sextant ( from @xmath6 to @xmath7 degrees in the plane ) starting at ( 0,0 ) and ending at ( @xmath44 , @xmath45 ) . such a step is shown in fig . [ fig : brokenbonds]b . as before , the bold solid line represents the step edge with the bottom region a layer higher than the top ( or , alternatively phrased , it separates the upper , adatom - free region from the lower , adatom - filled region ) . the broken bonds required to form the step will have only three orientations : @xmath6 , @xmath7 , and @xmath39 . if we consider the shortest step between the two points ( corresponding to energy @xmath22 ) , then there will be exactly @xmath38 broken bonds oriented at @xmath6 and @xmath7 ( these bonds are analogous to those oriented at @xmath6 and @xmath37 on a square lattice ) . there will be another @xmath46 broken bonds oriented at @xmath39 ( drawn as bold , dashed lines in fig . [ fig : brokenbonds ] ) . in total , there will be @xmath47 broken bonds . since @xmath18 is the energy of these severed bonds , @xmath48 . thus , the energy is proportional to the step length , as was the case on a square lattice . using @xmath40 to write @xmath41 and @xmath42 in terms of @xmath25 and @xmath26 gives @xmath49 next we consider the degeneracy factors @xmath50 on a triangular lattice . for the ground state @xmath51 there is a one - to - one correspondence between the shortest distance steps connecting two points on a square lattice and the corresponding steps on a triangular lattice ( see fig . [ fig : brokenbonds ] ) . therefore , we know that the degeneracy factor @xmath52 for steps of energy @xmath53 on a triangular lattice must be identical to @xmath54 implicit in eq . ( [ eq : freeenergy0 ] ) ! more precisely , if we assume the point ( @xmath25,@xmath26 ) is in the first quadrant , and ( @xmath41 , @xmath42 ) is in the first sextant , then on a square lattice , shortest - distance step - links are oriented at either @xmath6 or @xmath37 , whereas on a triangular lattice they are oriented at either @xmath6 or @xmath7 ( i.e. in the first sextant , the shortest path can not have links oriented at @xmath39 ) . in both cases , the individual step - links can only be oriented in one of two directions and , therefore , besides the transformation between coordinates , the total number of path arrangements is the same . using eq . ( [ eq : freeenergy0 ] ) and stirling s approximation , we find the low - temperature free energy ( appendix i provides the lowest - order correction ) : @xmath55 \approx e_0^\vartriangle - k_bt \times } \nonumber \\ & & \times \left [ ( m ' \ ! + \ ! n ' ) \ln ( m'\ ! + \ ! n ' ) - m ' \ln m ' - n ' \ln n ' \right ] . \end{aligned}\ ] ] alternatively , we can transform eq . ( [ eq : freeenergy ] ) for the square lattice to the triangular lattice by just replacing @xmath56 with @xmath57 . ( this ratio is just @xmath58 , so it might be termed @xmath59 . ) [ we must also make a simple ( and ultimately inconsequential ) change to @xmath22 . ] we now take the thermodynamic limit ( @xmath41 , @xmath42 @xmath33 @xmath34 ) and write @xmath44 and @xmath45 in terms of @xmath15 and @xmath16 via eq . ( [ eq : ldef ] ) . then dividing by @xmath14 and defining@xcite @xmath60 all non - negative in the first sextant , we straightforwardly find the step - edge line tension ( or free - energy per unit length@xcite ) @xmath1 : @xmath61,\end{aligned}\ ] ] where @xmath62 is the nearest - neighbor spacing and @xmath63 for the special case of the maximally kinked orientation , eqs . ( [ eq : etas ] ) ( [ eq : tpm0 ] ) reduce to @xmath64 where @xmath65 for the \{111 } surface . this result for the maximally kinked case ( including steps at @xmath66 on a square lattice ) was derived earlier from a direct examination of entropy.@xcite for specificity , we recall some established results . for a hexagonal lattice with just nearest - neighbor attractions , the critical temperature @xmath67 is long known:@xcite @xmath68 from the equilibrium shape of islands over a broad temperature range , giesen _ et al._@xcite deduced that the free energy per lattice spacing in the maximally kinked directions is 0.27 @xmath69 0.03ev on cu\{111 } and slightly smaller , 0.25 @xmath69 0.03ev , on ag\{111}. combining these results with eq . ( [ eq : sgi ] ) , we find @xmath18 is 0.126ev on cu\{111 } and 0.117ev on ag\{111}. in both cases , then , room temperature is somewhere between @xmath70 and @xmath71 . as shown just above , the step - stiffness @xmath72 computed from eq . ( [ eq : linetensiontheta ] ) depends to leading order only on the combinatoric entropy terms @xmath73 and @xmath74 of eqs . ( [ eq : linetensiontheta ] ) and([eq : tpm0 ] ) . hence , @xmath75 so that@xcite @xmath76 with this notation , the reduced stiffness is @xmath77 where @xmath78 adding these terms together gives our _ main _ result a remarkably simple form for the reduced stiffness in the low - temperature ( @xmath79 ) limit : @xmath80 where @xmath81 . ( just below room temperature for cu and ag\{111 } surfaces ) , the numerical evaluation of the exact stiffness@xcite approaches the solid line representing the low - temperature approximation given in eq . ( [ eq : stiffness ] ) . the small circles indicate evaluations using the exact results of eqs . ( [ eq : highsym2 ] ) and ( [ eq : highsym4 ] ) . at @xmath70 , when @xmath2 decreases , the exact solution begins to deviate from the approximation when its curvature changes sign near @xmath82 . the scale here is linear , in contrast to the logarithmic scale of fig . 2 of ref . the inset shows more fully how the exact stiffness approaches the low - temperature limit for the particular azimuthal angle @xmath83 . , width=8 ] to test how low the temperature should be for eq . ( [ eq : stiffness ] ) to be a good approximation , we compare it to a numerical evaluation of the exact implicit solution of the ising model . the derivation of this solution , outlined by zia,@xcite gives a @xmath84 order equation for @xmath1 . in essence , after conversion to our notation , his key result for the step free energy @xmath3 is given by@xcite @xmath85 where the @xmath86 s are the solutions of the pair of simultaneous equations for the angular constraint , @xmath87 and the thermal constraint , @xmath88 where @xmath89 , via eq . ( [ eq : hextc ] ) . the ratio @xmath90 of eq . ( [ eq : psithetzia ] ) is a monotonically decreasing function which is @xmath91 at @xmath2=0@xmath92 , 1 at @xmath2=30@xmath92 , and 0 at @xmath2=60@xmath92 . in these high - symmetry directions , ( [ eq : psithetzia ] ) and ( [ eq : psitzia ] ) yield analytic solutions for @xmath3 and @xmath0 : @xmath93 details are provided in appendix ii . akutsu and akutsu @xcite also derived these equations , in different notation @xcite and from the more formal perspective of the imaginary path - weight method . symmetry dictates that the solution at @xmath94 is the same solution as that at @xmath95 . furthermore , at @xmath96 , @xmath97 , so eqs . ( [ eq : highsym1])-([eq : highsym4 ] ) all go to @xmath98 , as expected . , below which the approximation given in eq . ( [ eq : stiffness ] ) begins to fail , as a function of @xmath99 . the black dots connected by the solid , blue line represent the first estimate , defined to be the angle @xmath100 at which the curvature of the numerically determined inverse stiffness changes sign . the dashed , red line represents the second estimate , @xmath101 $ ] . at angles below @xmath102 , the three theorems of section [ sec:3thrm ] break down , and higher order terms are required in the expansion of the step partition function . at temperatures between @xmath70 and @xmath71 ( roughly room temperature for cu and ag\{111 } surfaces ) , @xmath102 is on the order of a few degrees . , width=8 ] to find @xmath0 in general directions , we solve eqs . ( [ eq : psithetzia ] ) and ( [ eq : psitzia ] ) [ or , equivalently , eq . ( [ eq : stiffgensimp ] ) ] numerically . as fig . [ fig : stiffnesscompare2 ] shows , once @xmath4 decreases to nearly @xmath70 , eq . ( [ eq : stiffness ] ) more or less coincides with the exact numerical solution for the stiffness . at such low temperatures ( compared to @xmath67 ) , the approximation only fails below some very small , temperature - sensitive critical angle @xmath102 . although it might seem easy to determine this angle by eye , estimating it quantitatively turns out to be a subtle and somewhat ambiguous task . we discuss two possible estimation techniques below . in the first approach , we estimate @xmath102 to be the angle @xmath100 at which the _ curvature _ of the exact solution changes sign . the points on the solid curve in fig . [ fig : thetac ] show @xmath100 at several temperatures ranging from @xmath70 to @xmath103 . at temperatures near and above @xmath103 , @xmath100 does not reliably estimate @xmath102 because there is a sizable curvature - independent difference between the exact solution and the approximation given in eq . ( [ eq : stiffness ] ) evident even at @xmath104 ( see fig . [ fig : stiffnesscompare2 ] ) . on the other hand , as the temperature dips below @xmath105 , this difference fades , and the use of @xmath100 to estimate @xmath102 becomes ever more precise . a second , more fundamental way to estimate @xmath102 comes from an examination of the assumptions required to derive the simple expression for the low - t limit eq . ( [ eq : stiffness ] ) directly from the exact solutions eqs . ( [ eq : psithetzia ] ) and ( [ eq : psitzia ] ) . in appendix iii we show that to do so @xmath2 must be greater than some @xmath106 satisfying @xmath107 to give definite meaning to this inequality , we estimate @xmath102 directly from fig . [ fig : stiffnesscompare2 ] at a single temperature , say @xmath105 . at that temperature , @xmath102 is nearly @xmath108 . if @xmath106 is to accurately represent @xmath102 , it should also be around @xmath108 at @xmath105 . we enforce this by interpreting the ` @xmath109 ' in eq . ( [ eq : thetac ] ) to mean ` @xmath110 . ' the dashed ( red online ) curve in fig . [ fig : thetac ] shows the resulting @xmath106 as a function of temperature . and the free energy per length [ dashed blue curve , right axis ] for edges oriented in the maximally zig - zagged ( @xmath111 ) and close - packed ( @xmath112 ) directions , based on taking the ratios of eqs . ( [ eq : highsym4 ] ) and ( [ eq : highsym2 ] ) and of eqs . ( [ eq : highsym3 ] ) and ( [ eq : highsym1 ] ) , respectively . the line - tension ratio increases slowly but monotonically to the @xmath4=0 limit @xmath113 . in contrast , the stiffness ratio plummets toward 0 , the value predicted by eq.([eq : stiffness ] ) , providing an indicator how low @xmath4 must be for this simple low-@xmath4 formula to be a good approximation at all angles . , width=8 ] [ fig : ratio0 - 30 ] clearly @xmath100 and @xmath106 are very different estimates for @xmath102 . while @xmath106 is reliable at all temperatures ( unlike @xmath100 ) , it is less precise than @xmath100 at lower temperatures . a combination of @xmath100 and @xmath106 is therefore the best estimate for @xmath102 , being closer to @xmath100 at lower temperatures , and closer to @xmath106 at higher temperatures . in essence , @xmath102 is no more than a few degrees between @xmath70 and @xmath71 , regardless of which estimation technique is used . we therefore reach the practical conclusion that eq . ( [ eq : stiffness ] ) is valid for almost all angles at temperatures near and below @xmath71 , which fortunately happens to be around room temperature for cu and ag\{111}. finally , we emphasize that @xmath0 varies significantly with angle , especially at lower temperatures ( where the equilibrium crystal shape ( ecs ) is hexagonal rather than circular ) . if one wants to approximate @xmath0 as isotropic rather than using eq . ( [ eq : stiffness ] ) , one should not pick its value in the close - packed direction ( viz . @xmath112 ) ; fig . [ fig : ratio0 - 30 ] provides stunning evidence of this conclusion . from eq . ( [ eq : stiffness ] ) we also see that at low - temperatures the stiffness actually _ increases _ linearly with temperature . this contrasts with its behavior at high temperatures , where @xmath0 must ultimately decrease as the ecs becomes more nearly circular and the steps fluctuate more easily . in this section we present three theorems that are valid under two conditions : first , the energy term in the free energy must be a linear combination of @xmath114 and @xmath115 . from eq . ( [ eq : e_0final ] ) and [ implicitly ] eq . ( [ eq : freeenergy0 ] ) we see that this property holds true in general for lattice - gas models , even when considering next - nearest neighbors and beyond.@xcite second , the temperature must be low enough so that the entropy is adequately approximated by the contribution of the lowest order term , @xmath116 . this entropic contribution is due exclusively to geometry or combinatorics of arranging the fixed number of kinks forced by azimuthal misorientation . hence , it must vanish near close - packed directions ( 0@xmath92 and 60@xmath92 in the first sextant ) . for angles sufficiently close to these directions , in our case less than @xmath102 , the leading term becomes dominated by higher - order terms , and the three results no longer apply . the first theorem is a remarkable consequence of the first condition , that the energy term in the free energy is a linear combination of @xmath114 and @xmath115 . since the stiffness @xmath117 and since @xmath118 and @xmath119 , we see that _ the lattice - gas energy makes no contribution whatsoever to the low - t limit of reduced stiffness _ , as shown explicitly for square lattices long ago.@xcite thus , we retrieve the result that the leading term in a low - temperature expansion of the reduced stiffness @xmath120 depends only on @xmath121 , which is determined solely by geometric ( combinatoric ) properties . of course , higher - order terms ( which are crucial near close - packed directions ) do have weightings of the various configurations that depend on boltzmann factors involving the characteristic lattice - gas energies . furthermore , next - nearest - neighbor interactions can ( at least partially ) lift the @xmath121-fold degeneracy of the lowest energy paths.@xcite an important corollary is that from the stiffness it is impossible to retrieve the energetic part of the step free energy , the major component of @xmath1 at lower temperatures when the islands are non - circular ! thus , contrary to a proposed method of data analysis,@xcite one can not regenerate @xmath1 from @xmath8 by fitting the stiffness to a simple functional form and then integrating twice . in this framework , the linear coefficients of @xmath114 and @xmath115 can be viewed as the two integration constants associated with integrating a second - order differential equation.@xcite another important result is that the leading term in the stiffness at low temperature has the full symmetry of the 2d net of binding sites rather than the possibly lower symmetry associated with the full lattice . specifically , for the present problem of the \{111 } face of an fcc crystal , the stiffness @xmath8 to lowest order has the full 6-fold symmetry of the top layer rather than the 3-fold symmetry due to symmetry breaking by the second layer . in contrast , the step energy of b - steps ( \{111 } microfacets ) differs from that of a - steps ( \{100 } microfacets ) , leading to islands with the shape of equiangular hexagons with rounded corners , but with sides of alternating lengths ( i.e. , ababab ) . to see the origin of the 6-fold symmetry of the stiffness , suppose without loss of generality that steps in the @xmath122 direction have energy @xmath123 per lattice spacing , so that those in the @xmath124 direction have energy @xmath125 . furthermore , we must make the crucial assumption that any corner energy is negligible . then all shortest paths to ( @xmath126 ) have the same energy @xmath127 , with degeneracy still @xmath54 . thus , the free energy is @xmath128 , while that of its mirror point ( through the line at @xmath111 ) is @xmath129 . the crux of the proof is that @xmath130 . thus , while the free energies at the pair of mirror points differ , the energy parts are obliterated when the stiffness is computed ( since @xmath44 and @xmath45 are linear combinations of @xmath114 and @xmath131 ) , leaving just the contribution from the entropies , which are the same to lowest order . within lattice - gas models with only pair interactions , there is no obvious way to distinguish a and b steps ; the minimalist way to obtain different step energies for a and b steps within the lattice - gas model is to invoke a non - pairwise 3-site trio " interaction associated with three [ occupied ] sites forming an equilateral triangle with nn sides . in contrast to the ones considered heretofore,@xcite these novel trio interactions must be _ orientation - dependent _ : if the triangle points in one direction , say up , the interaction energy is positive , while if it points in the opposite direction , it has the opposite sign . ( of course , there could be a standard orientation - independent 3-site term in the hamiltonian . as in the analogous situation for squares , we expect that such a term would simply shift the pair interactions , at least in the sos approximation as discussed in ref . . ) the contributions from such a symmetry - breaking interaction would cancel in the interior of an island ( in the 2d bulk ) , but would distinguish a and b edges . specifically , each side of the equilateral triangle is associated with a link , so that 1/3 of its strength can be attributed to each . each link has a triangle on both sides , one of each orientation . hence , the difference between the energy per @xmath62 of a and b steps is 1/3 the difference between the trio interactions in the two opposite orientations . for the ground - state , minimum - number - of - links configurations , such a term will not lift the degeneracy since each configuration has the same 1 ) number of horizontal ( @xmath122 ) links , 2 ) number of right - tilted diagonal links ( @xmath124 ) , and 3 ) _ difference _ between the number of convex and concave kinks " ( i.e. , bends ) . since this statement is not true for higher - energy configurations , the 6-fold symmetry is not preserved at higher orders . nonetheless , at low @xmath4 it should be a decent approximation for the stiffness ( much better than for the island shape ) . thus , our result that the breaking of 6-fold symmetry on an fcc \{111 } is much smaller for the stiffness than for the free energy , is more general than the nearest - neighbor lattice gas model which underlies eqs . ( [ eq : linetensiontheta ] ) ( [ eq : tpm0 ] ) and the resulting eq . ( [ eq : stiffness ] ) derived below . we reemphasize that the necessary assumptions are 1 ) that the orientational dependence of the step energy be just a linear combination of @xmath131 and @xmath114 and 2 ) that no interaction break the degeneracy of the shortest path corresponding to orientation @xmath2 . as above , for angles near close - packed directions , the higher - order terms become important at lower temperatures than for general directions . this feature is illustrated in fig . [ fig : stiffnesscompare2 ] and its associated formalism is given in appendices i and iii . ) and experiments on cu and ag\{111}. eq . ( [ eq : stiffness ] ) appears as a solid black line , while the average of the experimental data is a thick dashed blue line . the agreement is reasonable at all angles . in either case the thin dashed red line is a [ smoothed ] average of the data for the given angle while the thin solid purple line corresponds to the angle mirror - reflected through a radial at 30@xmath92 , i.e. at 60@xmath132 . , title="fig:",width=9 ] ) and experiments on cu and ag\{111}. eq . ( [ eq : stiffness ] ) appears as a solid black line , while the average of the experimental data is a thick dashed blue line . the agreement is reasonable at all angles . in either case the thin dashed red line is a [ smoothed ] average of the data for the given angle while the thin solid purple line corresponds to the angle mirror - reflected through a radial at 30@xmath92 , i.e. at 60@xmath132 . , title="fig:",width=9 ] [ fig : giesen111 ] in fig . [ fig : giesen111 ] we compare eq . ( [ eq : stiffness ] ) to measurements on cu\{111 } and ag\{111}. the experimental data were derived from the equilibrium shape of 2d islands using the method described in ref . . the solid black line corresponds to eq . ( [ eq : stiffness ] ) , while the thick dashed blue line corresponds to the average of the experimental measurements . ( [ eq : stiffness ] ) captures the overall trend and is satisfactory at most angles and temperatures . as expected , eq . ( [ eq : stiffness ] ) somewhat overestimates @xmath0 near @xmath133 ( since the @xmath134 singularity remains ) . furthermore , near @xmath111 eq . ( [ eq : stiffness ] ) somewhat underestimates the experimental @xmath0 , but only by a factor of 1/6 for cu\{111 } and 1/4 for ag\{111}. this is in striking contrast to the analogous nn theory for cu\{001 } near 45@xmath92 , which underestimates @xmath0 by a factor of 4 . finally , notice there is no clear temperature dependence in the measured data . this is further evidence that @xmath135 is a constant at low - temperatures , as eq . ( [ eq : stiffness ] ) suggests . the agreement between theory and experiment is a pleasant surprise considering analogous comparisons made for cu\{001}@xcite found @xmath0 to be four - times larger than the theoretical value at large angles ( near @xmath136 ) . it was later shown@xcite that this discrepancy could be partially accounted for by considering next - nearest - neighbor ( nnn ) interactions ( or right - triangle trio interactions , which turn out to affect @xmath0 at low temperatures in the same way ) . clearly , the success of eq . ( [ eq : stiffness ] ) suggests that these interactions are less relevant for \{111 } surfaces . this is reasonable because the ratio of nnn distance to nn distance is smaller by a factor of @xmath137 on a triangular lattice compared to on a square lattice . furthermore , in the close - packed direction ( @xmath112 ) , for every broken nn - bond there are only one and a half broken nnn bonds on a triangular lattice , compared to two broken nnn bonds on a square lattice . these simple arguments help explain why nnn - interactions may increase @xmath0 by only @xmath138 to @xmath139% on cu / ag\{111 } , as opposed to @xmath140% on cu\{001 } surfaces . by generalizing the low - temperature expansion of the nearest - neighbor square lattice - gas ( ising ) model to a triangular lattice , we have found a remarkably simple formula for the orientation dependence of the \{111 } surface step stiffness . this formula , unlike its square lattice analog , fits experimental data well at general angles , suggesting that nnn - interactions are relatively unimportant on \{111 } surfaces . to corroborate this picture and explain the success of eq . ( [ eq : stiffness ] ) , we are currently using the vasp package@xciteto perform first - principle calculations . in particular , we are examining the ratio of the nnn to nn interaction strength . preliminary results@xcite suggest that this ratio is roughly an order of magnitude smaller on cu\{111 } than on cu\{001 } , and essentially indistinguishable from zero . this tentative finding is consistent with expectations from the semiempirical embedded atom method , which predicts that indirect interactions are insignificant / negligible between atoms sharing no common substrate atoms.@xcite we are also calculating the difference in trio interactions between oppositely oriented triangle configurations . we expect that our formula , as well as the general 6-fold symmetry of the stiffness ( except in close - packed directions ) , should be broadly applicable to systems in which multisite or corner energies are small and for which the bond energies are considerably higher than the measurement temperature . studies which ignore the 3-fold symmetry breaking on metallic fcc \{111 } substrates , such as a recent investigation of nanoisland fluctuations on pt\{111},@xcite should be good representations . many recent investigations@xcite focus on the larger asymmetry of the kinetic coefficient,@xcite taking the stiffness to be isotropic . in such cases , this stiffness should not be characterized by its value in close - packed directions . in this appendix we discuss the lowest - order correction to the ground state entropy of the step running from the origin to an arbitrary particular point . first we review results for a square lattice . we can rewrite eq . ( [ eq : partitionfun ] ) as @xmath141 . \end{aligned}\ ] ] then , assuming the exponential is small , we have @xmath142+\frac{g_{m , n}(1)}{g_{m , n}(0 ) } e^{-2\varepsilon / k_bt}\right\}. \end{aligned}\ ] ] a combinatorial analysis@xcite shows that @xmath143 then eq . ( [ eq : freeenergy ] ) generalizes to @xmath144 . % \frac{m(m+1)^2 + n(n+1)^2}{(m+1)(n+1)}\end{aligned}\ ] ] for the triangular lattice we find important differences from the square lattice for the higher - order terms . specifically , we consider how @xmath145 changes . in contrast to @xmath121 , we can not simply replace @xmath25 and @xmath26 with @xmath41 and @xmath42 . there is no one - to - one correspondence between paths of energy @xmath146 on a square lattice and those of energy @xmath147 on a triangular lattice . this failed correspondence for higher terms follows from the observation that @xmath147-configurations are only one link longer than @xmath53-steps , whereas @xmath146-configurations are two links longer than @xmath22-steps : @xmath148 , or @xmath149 hence , we require a separate combinatorial analysis . . the dashed step contains ( @xmath150 ) x - links , ( @xmath151 ) y - links , and one @xmath152-link , while the solid step contains ( @xmath153 ) x - links , ( @xmath154 ) y - links , and one @xmath152-link.,width=6 ] [ fig : e1paths ] we imagine a step of energy @xmath146 in the first sextant . such a step ( see fig . [ fig : e1paths ] ) will have either : ( 1 ) ( @xmath155 ) links oriented at @xmath6 ( denoted x - links " ) , ( @xmath156 ) links oriented at @xmath7 ( denoted y - links " ) , and one link oriented at @xmath39 ( denoted @xmath152-links " ) , or ( 2 ) ( @xmath157 ) links oriented at @xmath6 , ( @xmath158 ) links oriented at @xmath7 , and one link oriented at @xmath159 . in the first case , the problem can be reworded as follows : how many ways to arrange an ( @xmath160)-lettered word with ( @xmath150 ) x s , ( @xmath161 ) y s , and one @xmath152 . in the second case , the problem is the same , only with @xmath25 and @xmath26 switched . thus , the solution of this traditional combinatorial problem gives the total number of next - to - shortest paths @xmath162 : @xmath163 with @xmath164 and @xmath165 in hand , we can write the low - temperature partition function expansion for a triangular lattice . using eq . ( [ eq : freeenergy0 ] ) and expanding the logarithm as in eq . ( [ eq : freeenergy0a ] ) , we have @xmath166 + \frac{g^\vartriangle(1)}{g(0 ) } e^{-\delta e^\vartriangle / k_bt}\right\}. \end{aligned}\ ] ] taking the thermodynamic limit ( @xmath41 , @xmath42 @xmath33 @xmath34 ) and using stirling s approximation gives @xmath167 \ ! . \hspace{-2 mm } f \ ! & \approx & \ ! e_0^\vartriangle \ ! - \ ! k_b t \left [ ( m ' \ ! + \ ! n ' ) \ln ( m ' \ ! + \ ! n ' ) \ ! - \ ! m ' \ln m ' \ ! - \ ! n ' \ln n ' \right . \nonumber \\ \ ! & + & \ ! \left . e^{-\varepsilon / k_bt } \frac{m'^3 \ ! + \ ! n'^3 \ ! + \ ! m ' n'^2 \ ! + \ ! n ' m'^2}{m'n ' } \right ] \ , . \end{aligned}\ ] ] the pair of cross - factors in the last coefficient are absent in eq . ( [ eq : freeenergya ] ) for the square lattice . the correction term becomes non - negligible when the final term in eq . ( [ eq : freeenergytri ] ) becomes of order unity . at low @xmath4 this occurs only near close - packed directions , so for small values of @xmath2 . in this regime , to lowest order in @xmath2 , @xmath168 and @xmath169 . then the critical value of @xmath2 is @xmath170 specifically , based on eq . ( [ eq : crossover ] ) and using @xmath171 ev for cu\{111 } , we find that @xmath172 is 0.353@xmath92 , 3.18@xmath92 , and 5.51@xmath92 for t / t@xmath173 of 1/9 , 1/5 , and 1/4 , respectively . as clear from fig . [ fig : thetac ] , this criterion turns out to underestimate the values for @xmath102 obtained in section ii.d , mainly because eq . ( [ eq : crossover ] ) was derived from an expression for @xmath1 instead of @xmath8 ( which should depend more sensitively on @xmath2 ) . over the plotted thermal range . in this appendix , we derive eqs . ( [ eq : highsym1 ] ) ( [ eq : highsym4 ] ) for the mirror - line directions @xmath95 and @xmath174 from zia s implicit exact solution.@xcite to begin , because @xmath175 ( where the prime represents differentiation with respect to @xmath2 ) , it follows from eq . ( [ eq : betazia ] ) that @xmath176 we can simplify eq . ( [ eq : stiffgen ] ) by finding relationships between the various derivatives of the @xmath86 s . differentiating eq . ( [ eq : psitzia ] ) with respect to @xmath2 , regrouping , and using eq . ( [ eq : psithetzia ] ) , we get @xmath177 differentiating again yields @xmath178 using eq . ( [ eq : ddpsitzia ] ) , we rewrite the last part of eq . ( [ eq : stiffgen ] ) ( containing @xmath179 and @xmath180 ) in terms of just @xmath181 and @xmath182 . then , using eq . ( [ eq : dpsitzia ] ) we eliminate @xmath182 in favor of @xmath181 . we are then left with an equation relating @xmath0 to only @xmath181 : @xmath183 for general angle , we must evaluate @xmath181 numerically . however , for the two high - symmetry directions we can obtain analytic results that allow us ( with the aid of eq . ( [ eq : betazia ] ) for @xmath3 ) to write explicit expressions for @xmath0 , as presented in the next two subsections . ( dashed red curve ) and @xmath184 ( solid blue curve ) as functions of angles at temperature @xmath71 equivalent to room temperature for the experimental systems cu and ag \{111}. note that the linear behavior near one limit and the divergent slope near value zero at the other . at higher temperatures the curves are qualitatively similar but progressively smaller in magnitude . , width=8 ] [ fig : psiplot ] at @xmath95 , eq . ( [ eq : betazia ] ) reduces to @xmath185 assuming that @xmath186 is finite . furthermore , near @xmath95 , eq . ( [ eq : psithetzia ] ) can be inverted and the @xmath187 s combined to get @xmath188 for eq . ( [ eq : betazia2 ] ) to hold at @xmath95 , @xmath189 eq . ( [ eq : psitzia ] ) therefore becomes : @xmath190 solving this for @xmath191 and taking the positive root , we find : @xmath192 consistent with the assumption of finite @xmath186 . solving for @xmath193 and combining with eq . ( [ eq : betazia0 ] ) yields eq . ( [ eq : highsym1 ] ) . correspondingly for @xmath0 , at @xmath95 eq . ( [ eq : stiffgensimp ] ) becomes @xmath194 while eq . ( [ eq : dpsitzia ] ) becomes @xmath195 provided @xmath196 is finite . we obtain @xmath196 by differentiating eq . ( [ eq : betazia2 ] ) with respect to @xmath2 and then setting @xmath95 so that eqs . ( [ eq : psi0 ] ) and ( [ eq : psi2prime0 ] ) apply . this give @xmath197.\end{aligned}\ ] ] by combining this with eq . ( [ eq : psi10f ] ) for @xmath191 , we see that @xmath196 is indeed finite , as we earlier assumed . thus , eq . ( [ eq : stiffzia0simp ] ) becomes eq . ( [ eq : highsym2 ] ) , as desired . at @xmath199 , ( [ eq : betazia ] ) becomes @xmath200 . \label{eq : betazia30}\end{aligned}\ ] ] furthermore , near @xmath201 , @xmath202 , where @xmath203 . inverting eq . ( [ eq : psithetzia ] ) we therefore have @xmath204 by inspection , at @xmath201 ( @xmath205 ) , one solution to this equation is just @xmath206 plugging this result into eq . ( [ eq : psitzia ] ) and solving for @xmath207 gives , @xmath208 combining this with eq . ( [ eq : betazia30 ] ) ( where we now know @xmath209 ) results in eq . ( [ eq : highsym3 ] ) . as for @xmath0 , at @xmath201 , eq . ( [ eq : stiffgensimp ] ) becomes @xmath210 while eq . ( [ eq : dpsitzia ] ) becomes @xmath211 like before , we can find @xmath212 by differentiating eq . ( [ eq : psithetzia30 ] ) with respect to @xmath2 . taking the result and setting @xmath201 , so that eqs . ( [ eq : psi30 ] ) and ( [ eq : dpsitzia30 ] ) apply , gives @xmath213 finally , we combine this result with eq . ( [ eq : psi230 ] ) for @xmath214 and eq . ( [ eq : stiffgensimp30 ] ) , to get eq . ( [ eq : highsym4 ] ) , as desired . in this appendix , we re - derive eq . ( [ eq : stiffness ] ) directly from the exact solution for @xmath1 given in eqs . ( [ eq : psithetzia ] ) and ( [ eq : psitzia ] ) . to do so , we just assume @xmath215 ( remember that @xmath90 decreases from @xmath91 at @xmath112 to 1 at @xmath104 , so that , between these angles , this condition also implies that @xmath216 ) . in this case , eq . ( [ eq : psithetzia ] ) can be solved to give @xmath217 thus , if @xmath218 , then @xmath219 . we show here that these assumptions for @xmath220 , together with the low - temperature replacement of @xmath221 by @xmath222 in eq . ( [ eq : psitzia ] ) , are enough to derive eq . ( [ eq : stiffness ] ) . when @xmath223 , then @xmath224 . with these approximations , ( [ eq : psithetzia ] ) and ( [ eq : psitzia ] ) become remarkably simple : @xmath225 solving this pair of equations for @xmath226 and @xmath227 gives @xmath228 if we then replace @xmath221 by its low - temperature limit , @xmath229 , eq . ( [ eq : betazia ] ) becomes @xmath230 + \eta_- \ln \left [ \frac{\eta_-}{z(\eta_0+\eta_- ) } \right].\\ \nonumber\end{aligned}\ ] ] by deriving the approximation given in eq . ( [ eq : linetensiontheta ] ) ( and thus eq . ( [ eq : stiffness ] ) ) in this way , we can determine when the approximation becomes invalid . specifically , we require @xmath223 . as we showed , the more restrictive of these inequalities is the one involving @xmath233 , since @xmath233 is necessarily smaller than @xmath234 in the first sextant by a factor of @xmath235 ( which is less than 1 ) . thus , the main assumption is @xmath236 , which , from eq . ( [ eq : psisollowt ] ) , is just @xmath237 the solution to this equation , which we call @xmath106 , is given by the following inequality : @xmath238 because @xmath239 decreases from @xmath91 at @xmath240 to @xmath241 at @xmath242 , we know that angles in the first sextant that are greater than @xmath106 will also satisfy the inequality in eq . ( [ eq : restrictang ] ) . thus , eqs . ( [ eq : linetensiontheta ] ) and ( [ eq : stiffness ] ) are valid in the first sextant at all angles above @xmath106 . work at the university of maryland was supported by the nsf - mrsec , grant dmr 00 - 80008 . tle acknowledges partial support of collaboration with isg at fz - jlich via a humboldt u.s . senior scientist award . we are very grateful to r. k. p. zia for many insightful and helpful comments and communications . we have also benefited from ongoing interactions with e. d. williams and her group . this simple equivalency does not hold for stepped surfaces in an electrochemical system , where the electrode potential @xmath245 is fixed rather than the surface charge density conjugate to @xmath245 . h. ibach and w. schmickler , phys . * 91 * , 016106 ( 2003 ) . other noteworthy subtleties in the free energy are discussed by n. akutsu and y. akutsu , j. phys . . jpn . * 64 * , 736 ( 1995 ) . the calculation can be facilitated by writing @xmath246 and then using eq . ( [ eq : dt_i ] ) to show @xmath247/[a_i \cos \theta + b_i \sin \theta]$ ] ( [ eq : psitzia ] ) bypasses several intermediate quantities that are important for zia s [ ] general treatment but cumbersome here . our @xmath184 has the opposite sign from zia s , and our angle @xmath2which vanishes for close - packed step orientations differs by 30@xmath92 from his . note also that interchanging @xmath248 and @xmath184 on the lhs of eq . ( [ eq : psithetzia ] ) inverts the lhs , from which it is easy to see that @xmath1 of eq . ( [ eq : betazia ] ) is symmetric about @xmath111 . the lhs of eq . ( [ eq : psitzia ] ) is obviously invariant under the interchange of @xmath248 and @xmath184 .

for hexagonal nets , descriptive of \{111 } fcc surfaces , we derive from combinatoric arguments a simple , low - temperature formula for the orientation dependence of the surface step line tension and stiffness , as well as the leading correction , based on the ising model with nearest - neighbor ( nn ) interactions . our formula agrees well with experimental data for both ag and cu\{111 } surfaces , indicating that nn - interactions alone can account for the data in these cases ( in contrast to results for cu\{001 } ) . experimentally significant corollaries of the low - temperature derivation show that the step line tension can not be extracted from the stiffness and that with plausible assumptions the low - temperature stiffness should have 6-fold symmetry , in contrast to the 3-fold symmetry of the crystal shape . we examine zia s exact implicit solution in detail , using numerical methods for general orientations and deriving many analytic results including explicit solutions in the two high - symmetry directions . from these exact results we rederive our simple result and explore subtle behavior near close - packed directions . to account for the 3-fold symmetry in a lattice gas model , we invoke a novel orientation - dependent trio interaction and examine its consequences .

There is no safe space in America where the country’s culture wars aren’t being waged — not even the make-believe workshop of a shopping mall Santa Claus — and no ears so innocent that they haven’t heard about the sexual misdeeds of some prominent men and accusations against others. That, at least, was the twisted Christmas spirit of the “Saturday Night Live” cold open this weekend, in an episode hosted by James Franco and featuring the musical guest SZA. Indeed, the first half of the show frequently returned to the many sexual misconduct scandals roiling powerful men and the institutions that once protected them — including Senator Al Franken, the “S.N.L.” alumnus who said on Thursday that he would resign his seat as he faced allegations from at least six women of groping and improper advances. The show’s pointed and effective opening sketch, which featured Kenan Thompson as the would-be Santa and Kate McKinnon as his elfin assistant, began with a boy asking Mr. Thompson for traditional gifts like Mega Bloks and Lazer Tag. “And,” the boy added, “can you tell me, what did Al Franken do?” Mr. Thompson was understandably taken aback. “O.K., wow, let’s see,” he said. “I think I can handle the Mega Bloks and the Lazer Tag. Can you take the Al Franken thing, Sugarplum?” ||||| UPDATE, with video No political impressions or surprise guests to kick off tonight’s Saturday Night Live cold open – instead, the NBC comedy went with a Christmas bit that had a bunch of wised-up kids asking Kenan Thompson’s shopping mall Santa questions like, “Can you tell me, what did Al Franken do?” Asked the little boy in a reindeer sweater, “And what kinda list is Roy Moore on?” “It’s more of a registry,” replied Kate McKinnon’s helpful elf, asking Santa to refrain from calling her Sugar Plum “in this climate.” (Take a look at a couple brief clips below.) Asked another little boy, why do all those football players kneel – do they hate the troops or are they just tired from all the brain injuries? Then a little girl complained about feminazis taking away her Barbie, and another stumbling over the words “embassy” and “Tel Aviv.” (Another little girl missed her set-up entirely, leaving Thompson – who may or may not have been to blame – to land a Chuck Schumer punchline as a non sequitur. NOTE: As a Deadline commenter noticed, the clip above must be of the dress rehearsal. It’s mistake-free). And there was the inevitable inside-NBC joke when Santa asked a boy what kind of toy he wanted for Christmas. “You mean like the one Matt Lauer gave to his co-worker?” the kid asked. Finally, a little girl named Jenny said all she wanted for Christmas was for everything to be okay. Consoled not-Sugar Plum the elf, all will be fine – in “three years, 42 days and 24 minutes.” Tonight’s episode is hosted by James Franco, with musical guest SZA.

– It's that time of the year to determine who's been naughty and who's been nice, and Saturday Night Live jumped in with its two cents on the seemingly endless sexual harassment scandals in its Cold Open. With Kenan Thompson as Santa and Kate McKinnon as an elf, a line of children asked things like, "Can you tell me, what did Al Franken do?" Per the New York Times, Thompson replies that he's got that particular boy's toy requests, but says to McKinnon, "Can you take the Al Franken thing, sugarplum?" McKinnon refuses, adding, "in this climate, can you just call me Amy?" When the boy's line of questioning turns to Roy Moore, McKinnon says he's not so much on Santa's naughty "list. It's more of a registry," adds Deadline. Others taking a hit included President Trump ("Nineteen accusers. Google it," says McKinnon) and Matt Lauer (one boy asked if he wanted a toy responded, "Oh, you mean toy like the one Matt Lauer gave to his co-worker?" The episode was guest-hosted by James Franco.

it has been well established that alcohol use or cigarette smoking or both are the most significant risk factors for the development of head and neck squamous cell carcinomas ( hnsccs ) . however , nearly every head and neck oncologist has come across patients , most of them young , with little or no tobacco or alcohol consumption ( up to 20% in some cases ) . sturgis and cinciripini demonstrated decreasing incidence rates for tobacco - associated oral , pharyngeal , and laryngeal cancers since the mid-1980s , and these rates trailed the declines in smoking prevalence by 10 - 15 years . on the other hand , oropharyngeal cancer is not demonstrating a similar decline . shiboski et al . found a dramatic rise in the incidence rates of oropharyngeal cancer in adults younger than 45 years of age in the us ( 2% per year for base - of - tongue cancer and 4% per year for tonsil cancer ) . as far back as 1982 , the presence of human papillomavirus ( hpv ) antigens in 36% of pathologic specimens of laryngeal cancers was demonstrated . since then , several hundred papers on this topic have been published . hpv genomic dna was detected in 26% of all hnsccs , whereas approximately 50% of oropharyngeal cancers contained the hpv genome . by contrast , in a multinational study , only 18% of oropharyngeal tumors were hpv , indicating that this proportion varies with geography and sexual behavior ( history of performing oral sex and oral - anal contact ) . some studies found that patients who had sexual intercourse at an early age and more than six oral sexual partners in their lifetime had a fivefold risk of having hpv in their tumor compared with patients with no oral sexual partners . also , a significant racial difference in hpv positivity was found in a clinical trial of induction chemotherapy followed by concurrent chemoradiation therapy between white patients ( 35% ) and black patients ( 4% ) . several studies demonstrated an improved prognosis for patients with hpv tumors versus patients with hpv tumors with ( chemo)radiation treatment . other studies found the same results in both patients treated with radiation or surgery and radiation [ 15 - 18 ] . investigating the correlation between hpv infection and p53 mutation in hnsccs , found that patients with p53 mutations had a history of heavier smoking in comparison with patients with hpv infection , who conversely had a more advanced stage at diagnosis . in a paper from our institution , we analyzed a homogenous group of surgically treated oropharyngeal cancers with or without postoperative radiotherapy according to commonly accepted pathologic risk factors . patients were divided into three groups according to hpv , tp53 ( tumor protein p53 ) , and p16 status . patients harboring high - risk hpv showed a significant improvement in terms of survival and occurrence of relapse and a lower incidence of smoking - related second primary tumors , independently of tumor stage and delivered treatment ( surgery alone or surgery and postoperative radiotherapy ) , thus confirming that hpv tumors represent a distinct disease among oropharyngeal cancers . in contrast , p53 mutation and p16 status seemed to lack prognostic significance in the absence of hpv infection . detected hpv-16 in 22 of 68 ( 32% ) lymph node metastases in patients with hnscc and found that all hpv-16 lymph nodes were metastases from the oropharynx . goldenberg et al . found a correlation between patients with cystic lymph node metastases and the presence of hpv dna . the quoted retrospective analyses must be interpreted with caution because of possible confounding data . for example , schwartz et al . analyzed hpv infection and survival in oral cancers , but 31.5% of their patients had an oropharyngeal tumor ( tonsil and base of the tongue ) . nevertheless , the association between hpv status and prognosis seems to be indisputable , with a better disease - specific survival for patients with hpv oropharyngeal cancers in comparison with hpv patients , whereas disease - specific survival was similar for hpv or hpv patients with nonoropharyngeal cancer . some authors even demonstrated a worse prognosis for hpv patients with laryngeal and hypopharyngeal carcinomas in comparison with hpv patients . hence , the matter seems to be restricted to oropharyngeal cancer , and the diagnosis of hpv positivity should enter as a routine test for these patients . the most clinically useful test , in situ hybridization , is available in only a few centers which is unfortunate , even if p16 immunohistochemistry may serve as a reasonable surrogate . another possible bias in the interpretation of the results of some studies is due to the staging of the presented patients , as some authors used the ajcc - uicc ( american joint cancer committee / union internationale contre le cancer ) stage grouping . it is well known that in stage iii there are t1-n1 and t3-n0 tumors , and in stage iva there are t1-n2 and t4a - n0 , and these are clearly different tumors . looking to those papers reporting t stage , we may realize that although overall tnm ( tumor , node , metastasis ) stage does not differ by hpv status , hpv tumors are more likely than hpv tumors to have a lower t stage , whereas advanced t stage is a significant risk factor for recurrence and death , independently of hpv status . some historic papers on results of radiation therapy for oropharyngeal tumors demonstrated that vegetating tumors ( t1-t2 ) are more curable than infiltrating tumors ( t4 ) . . demonstrated that patients with p16 oropharyngeal tumors are less likely to have a persistent viable tumor in neck lymph nodes after ( chemo)radiotherapy and hypothesized that a post - treatment planned neck dissection may perhaps be avoided in p16 patients . in conclusion , several authors indicate that the impact of hpv status must be evaluated in prospective clinical trials and included as a stratification factor to avoid potential confusion . the current ajcc - uicc staging system for oropharyngeal cancer needs to be modified in order to better reflect different prognoses for patients with hpv or hpv tumors and those with vegetating or infiltrating tumors .

human papillomavirus ( hpv ) is detected in a subset of patients with head and neck squamous cell carcinoma , most frequently in tumors in the waldeyer 's ring ( palatine tonsil and base of tongue ) . several studies suggest that patients with hpv - positive tumors have better survival with either concurrent chemoradiation therapy or surgery followed by radiation compared with hpv - negative patients . however , some possible confounding clinicopathologic variables may challenge the validity of this statement , for example , some authors used the tnm ( tumor , node , metastasis ) grouping stage while others used the primary tumor ( t stage ) , and other studies have demonstrated that tumors with advanced t stage were less likely to be infected with hpv . a large clinical trial with stratification of patients according to all known tumor prognostic factors is crucial to solve the question .

the magnetism of fermi gases has always received considerable attention in solid - state physics , such as localized and itinerant electrons . while the magnetic properties of bose gases has been less studied . but since the realization of bose - einstein condensation ( bec ) in ultracold atomic gases @xcite , more interests have been cast to this system . the bose gases plays an important role in understanding some exotic quantum phenomena , such as superconductivity and superfluid . the ideal charged bosons were used originally to describe the superconductivity . it has been shown by schafroth @xcite , blatt and butler @xcite that an ideal gas of charged bosons exhibits the essential equilibrium features of superconductor . although the bardeen - cooper - schrieffer ( bcs ) theory @xcite explained the microscopic nature of conventional superconductivity , the charged bose gas exhibits strong diamagnetism at low temperature , which can be attributed to meissner effect . in recent years , the normal - state diamagnetism of high - temperature cuprate superconductors has been explained by real - space charged bosons @xcite . this also recasts new research interest in charged bose gases . experimentally , since the realization of _ spinor _ bec in optical traps @xcite the magnetic properties of _ spinor _ bose gases has received considerable attention . moreover , an ultracold plasma can be created by photoionization of laser - cooled neutral atoms @xcite . the temperatures of electrons and ions can reach as low as 100 mk and 10 @xmath5k , respectively . the ions can be regarded as charged bosons if their spins are integers . the lande - factor for different magnetic ions could also be different . it is known that paramagnetism is from the spin degree of freedom of particles . while charged spinless bose gases can exhibit strong diamagnetism , similar to meissner effect , which comes from the orbital motion of charge degree of freedom in magnetic field . theoretically , both the paramagnetism @xcite in neutral spin-1 bose gases and the diamagnetism of the charged spinless bose gases @xcite have been studied . moreover , we @xcite have discussed the competition of paramagnetism and diamagnetism in charged spin-1 bose gases in external magnetic field , using the lande - factor @xmath1 to evaluate the strength of paramagnetic ( pm ) effect . it is shown that the gas exhibits a shift from diamagnetism to paramagnetism as @xmath1 increases . the ferromagnetism and superconductivity are not compatible in conventional physical models . the meissner - ochsenfeld effect shows the conventional superconductor cancels all magnetic field inside when the temperature below the superconducting transition temperature , which means they become perfectly diamagnetic . the discovery of several ferromagnetic ( fm ) superconductors in experiments @xcite stimulates the research interest in the exotic magnetic properties of fm superconductors . the state of the cooper pairs in the fm superconductors has been wildly studied @xcite . a stronger spin - orbit interaction in uge@xmath6 results in an abnormal huge magnetocrystalline anisotropy @xcite . monthoux et al.@xcite indicates that the favorite superconducting pairing type of this anisotropy is triplet . although the exact symmetry of the paired state has not yet been identified , a spin - triplet pairing is more likely than the spin - singlet pairing in these superconductors @xcite . these behaviors are somewhat like charged spin-1 bosons . thus the charged spin-1 boson model helps to understand the exotic magnetic properties observed in such materials . although the ferromagnetism @xcite in a chargeless spinor bose gas has also been involved in theory , it is little discussed when fm interaction exists in a charged spin system . accordingly the magnetic behavior will become more complex in charged spin systems with fm interactions , where diamagnetism , paramagnetism and ferromagnetism compete with each other in such case . in this paper , the magnetic properties of a charged spin-1 bose gas with fm interactions are studied via mean - field theory . alexandrov et al . found that the coulomb or any other scattering may make charged bose gases superconducting below a critical field @xcite with a specific vortex matter @xcite . superconducting is not obtained in our paper , probably because we used the mean - field approximation to deal with the fm interaction . in despite of this , mean - field theory is still effective to point out the main physics of the magnetism , especially the ferromagnetic transition @xcite . the remainder of this paper is structured as follows . in section 2 , we construct a model including landau diamagnetism , pauli paramagnetism and fm effect . the magnetization density is obtained through the analytical derivation . in section 3 , the results is obtained and the discussions of our results is presented . a summary is given in section 4 . the spin-1 bose gas with fm couplings is described by the following hamiltonian : @xmath7 where @xmath5 is the chemical potential and the landau levels of bosons with charge @xmath8 and mass @xmath9 in the effective magnetic field @xmath10 is @xmath11 where @xmath12 labels different landau levels and @xmath13 is the gyromagnetic frequency . the energy level is degenerate with degeneracy @xmath14 where @xmath15 and @xmath16 are the length in @xmath17 and @xmath18 directions of the system , respectively . the intrinsic magnetic moment associated with the spin degree of freedom leads to the zeeman energy levels split in the magnetic field , @xmath19 where @xmath1 is the lande - factor and @xmath20 denotes the spin - z index of zeeman state @xmath21 ( @xmath22 ) . the contribution to the effective hamiltonian from the fm couplings is @xmath23 where @xmath24 denotes fm coupling and spin polarization @xmath25 . the grand thermodynamic potential is expressed as @xmath26,\end{aligned}\ ] ] where @xmath27 . through converting the sum over @xmath28 to continuum integral , we obtain @xmath29}\},\nonumber\\\end{aligned}\ ] ] where @xmath30 is the volume of the system . ( [ t3 ] ) can be evaluated by taylor expansion , and then performing the integral over @xmath31 . we get @xmath32}}{1-e^{-l\beta\hbar \omega}}.\nonumber\\\end{aligned}\ ] ] for convenience s sake , we introduce some compact notation for the class of sums . it can be defined as @xmath33=\sum_{l=1}^{\infty}\frac{l^{\alpha/2}e^{-l x(\varepsilon+\delta)}}{(1-e^{-l x})^{\kappa}},\end{aligned}\ ] ] where @xmath34 and @xmath35 . within this notation , eq . ( [ t2 ] ) can be rewritten as @xmath36.\end{aligned}\ ] ] with @xmath37 . the particle density @xmath38 can be expressed as @xmath39.\end{aligned}\ ] ] the magnetization density @xmath40 can be obtained from the grand thermodynamic potential , @xmath41 \nonumber\\ & + & x(g\sigma-\frac{1}{2 } ) \sigma_{1\sigma}[2-d,0]- x\sigma_{2\sigma}[2-d,1]\biggr\}.\nonumber\\\end{aligned}\ ] ] the relation among effective magnetic field @xmath10 , external magnetic field @xmath42 and magnetization density @xmath43 is formally expressed as @xmath44 for computational convenience , some dimensionless parameters are introduced below . @xmath45 , @xmath46 , @xmath47 , @xmath48,@xmath49 , @xmath50 , @xmath51 and @xmath52 , and then @xmath53 , where @xmath54 is the characteristic temperature of the system , which is given by @xmath55 . the mean - field self - consistent equations are derived , @xmath56,\\ \label{eq1 } 1&=&\overline \omega t^{1/2}\sum_{\sigma=1,0,-1}\sigma_{1\sigma}^{\prime}[2-d,0],\\ \label{eq2 } \overline m_{t\neq 0}&=&t^{3/2}\sum_{\sigma}\biggl\{\sigma_{1\sigma}^{\prime}[-d,0 ] + x(g\sigma-\frac{1}{2 } ) \sigma_{1\sigma}^{\prime}[2-d,0]\nonumber\\ & -&x\sigma_{2\sigma}^{\prime}[2-d,1]\biggr\},\\ \label{eq3 } \overline \omega&=&h+4\pi\gamma \overline m , \label{eq4}\end{aligned}\ ] ] where @xmath57 , and @xmath58=\sum_{l=1}^{\infty}\frac{l^{\alpha/2}e^{-lx(\overline \varepsilon+\delta)}}{(1-e^{-lx})^{\kappa}},\end{aligned}\ ] ] with @xmath59 . similar method has been used to study the diamagnetism of the charged spinless bose gas @xcite . furthermore , we have extended it to investigate the magnetic properties of charged spin-1 bose gas @xcite . , ( b)@xmath60 versus @xmath61 at reduced temperature @xmath62 and magnetic field @xmath63 . the lande - factor g is chosen as : @xmath64(solid line ) , 0.3(dashed line ) , 0.5(dotted line ) . , scaledwidth=45.0% ] in the following calculations from fig . 1 to fig . 6 , the characteristic parameter @xmath65 has been set as @xmath66 , which is estimated for a system with the charge and mass of @xmath67he , and the particle density being set as @xmath68 . 1 is plotted in a very weak magnetic field @xmath63 . as shown in fig . 1(a ) , the value of total magnetization density @xmath2 presents a turning point from zero to nonzero . it is shown that the zero - field spontaneous magnetization exists in this system with increasing @xmath3 , where @xmath3 is the reduced fm coupling of charged spin-1 bose gases . the curves of @xmath69 versus @xmath3 in fig . 1(b ) are superposed for different lande - factors ( @xmath64 , 0.3 and 0.5 ) . it suggests that @xmath70 is independent with the lande - factor , so @xmath0 at a certain temperature are equal for any lande - factor . here @xmath0 is the critical value of reduced fm coupling of pm phase to fm phase transition . @xmath71 in this situation . when @xmath72 @xmath69 equals 0 , and the value of @xmath69 increases with increasing @xmath3 while @xmath4 until saturate . in the region of @xmath4 , the magnetization density @xmath73 increases with lande - factor for fixed @xmath3 , which is attributed to the pm effect @xcite . diamagnetism , paramagnetism and ferromagnetism compete with each other in such system . the diamagnetism of charged bose gases , which is due to the internal field induced by the spontaneous magnetization , can not overcome ferromagnetism in very weak magnetic field . while the competition between paramagnetism and diamagnetism has been discussed in ref . vs reduced temperature @xmath74 phase diagram of charged spin-1 bose gases at magnetic field @xmath63.,scaledwidth=45.0% ] fig . 2 plots the @xmath0 dependence of temperature at magnetic field @xmath63 . the region below @xmath0 is pm phase , while the region above it is fm phase . as the temperature increases , @xmath0 increases monotonically . it is shown that spontaneous magnetization is hard to occur at high temperature , when the bose statistics reduces to boltzmann statistics . , ( b)@xmath60 as a function of lande - factor @xmath1 of charged spin-1 bose gases at reduced temperature @xmath62 and magnetic field @xmath63 . the reduced fm coupling @xmath3 is chosen as : @xmath75(solid line ) , 0.1(dashed line ) , 0.2(dotted line ) , 0.3(dash dotted line ) , and 0.5(dash dot dotted line).,scaledwidth=45.0% ] it is supposed that @xmath69 will reach to a nonzero equivalence at @xmath76 for arbitrary value of lande - factor for the situation of fig . 1 . to further study the influence of fm coupling to spontaneous magnetization , fig . 3 is plotted . it is shown when @xmath77 , the value of @xmath69 will be zero for any lande - factor values . so the evolution of @xmath69 with lande - factor @xmath1 are superposed and keeps zero for @xmath75 and @xmath78 . for fixed @xmath3 when @xmath79 , the magnetization density @xmath2 increases monotonically with @xmath1 . while @xmath69 maintains a constant in despite of @xmath1 . our results also show that diamagnetism gives little contribution to the magnetism in the weak magnetic field , while paramagnetism and ferromagnetism play significant roles in the magnetization density in the region for @xmath4 . the interaction between paramagnetism and ferromagnetism is intricate . the increase of @xmath69 due to increasing the reduced fm coupling @xmath3 will contribute to the paramagnetism . , ( b)@xmath60 as a function of lande - factor @xmath1 of charged spin-1 bose gases at reduced temperature @xmath80 and magnetic field @xmath81 . the reduced fm coupling @xmath3 is chosen as : @xmath75(solid line ) , 0.01(dashed line ) , 0.1(dotted line ) , 0.3(dash dotted line ) , and 0.5(dash dot dotted line).,scaledwidth=45.0% ] above we have discussed the very weak magnetic field situation , now we turn to investigate the magnetic properties of charged spin-1 bose gases at finite magnetic field , where diamagnetism will emerges clearly . the result of the dependence of the total magnetization density @xmath2 and @xmath82 with lande - factor @xmath1 at a definite magnetic field @xmath81 at reduced temperature @xmath80 is shown in fig . 4 . at low temperature in the definite magnetic field , there is a competition among the paramagnetism , diamagnetism and ferromagnetism . it is shown that diamagnetism dominates in the small @xmath1 region , and therefore the magnetization density exhibits negative value . when @xmath83 , the system presents paramagnetism which is independent of reduced fm coupling @xmath3 . as seen from fig 4 , the curves of @xmath78 , @xmath84 and @xmath85 match together . it means that @xmath69 tends to saturate if @xmath3 is greater than a critical value . the increase of @xmath3 after this critical value does not contribute to the magnetization density . then the system exhibits similar magnetization density at @xmath78 , @xmath84 and @xmath85 . , ( b)@xmath60 as a function of magnetic field @xmath86 of charged spin-1 bose gases at reduced temperature @xmath62 with lande - factor @xmath87 . the reduced fm coupling @xmath3 is chosen as : @xmath75(solid line ) , 0.1(dashed line ) , 0.3(dotted line ) , and 0.5(dash dotted line).,scaledwidth=45.0% ] the discussions above all focused on fixed magnetic field . next we study the influence of magnetic field on magnetism . the evolution of the total magnetization density @xmath2 and @xmath70 with magnetic field at reduced temperature @xmath62 with @xmath87 is shown in fig . the gas always manifests paramagnetism no matter what the values of @xmath3 are . it indicates that in the case of @xmath87 , diamagnetism can not overcome paramagnetism no matter how strong the magnetic field is . this behavior is qualitatively consistent with the result of charged spin-1 bose gases @xcite . in this region , the stronger ferromagnetism induce larger @xmath69 , which will enhance paramagnetism . with increasing the magnetic field , diamagnetism also increases . while this will not change the paramagnetism of this system . whether diamagnetism can increase infinitely with magnetic field is an important issue . , ( b ) the paramagnetization density @xmath88 , and ( c ) the diamagnetization density @xmath89 as a function of magnetic field @xmath86 of charged spin-1 bose gases with @xmath87 and @xmath85 , at reduced temperature @xmath62.,scaledwidth=45.0% ] in order to manifest the paramagnetism and diamagnetism in detail , in fig . 6 we study the dependence of the total magnetization density @xmath2 , the paramagnetization density @xmath88 and the diamagnetization density @xmath89 with magnetic field in reduced temperature @xmath62 with @xmath87 and @xmath85 . @xmath88 holds a constant since fm coupling is larger . @xmath89 tends to saturate with magnetic field . it indicates that diamagnetism will not increase infinitely with magnetic field . this is why in fig . 5 the gas preserves paramagnetism even though the magnetic field is large . it is significant to evaluate the diamagnetic behavior at high magnetic field limit . without consideration of spin , the diamagnetization density , @xmath90,\end{aligned}\ ] ] when @xmath91 , @xmath92 can be reduced to , @xmath93 from equation ( 14b ) , we can obtain , @xmath94 substituting equation ( [ lim3 ] ) into ( [ lim2 ] ) , @xmath95 can be obtained . this analytical result illustrate the diamagnetization density @xmath89 tends to a finite value at high magnetic field . , ( b)@xmath60 versus reduced temperature @xmath74 of charged spin-1 bose gases with @xmath96 and @xmath97 , at magnetic field @xmath63 . the reduced fm coupling @xmath3 is chosen as : @xmath75(solid line ) , 0.1(dashed line ) , 0.3(dotted line ) , 0.5(dash dotted line).,scaledwidth=45.0% ] in order to investigate the magnetic properties of the charged spin-1 bose gas in low temperature , we suppose @xmath96 . the evolution of the total magnetization density @xmath2 and @xmath60 with reduced temperature at @xmath63 and @xmath97 is shown in fig . it is shown that @xmath2 increases with increasing temperature , and reaches a maximum , then decreases at high temperature region . the upward trend at low temperature reflects the diamagnetism , comparing with our results in ref . 21 , which shows a flat trend at the same temperature region . a sharp decline can be seen when @xmath2 close to zero . this suggests that there is a pseudo - condensate temperature in the transition from ferromagnetism to paramagnetism . although condensation has not been considered , the magnetic field is faint in such a case . it is reasonable that the pseudo - critical temperature increases with increasing reduced fm coupling @xmath61 therefore , the temperature region of ferromagnetism enlarges from @xmath75 to @xmath85 in turn . in summary , we study the interplay among paramagnetism , diamagnetism and ferromagnetism of charged spin-1 bose gas with fm coupling within the mean - field theory . in very weak magnetic field , it is shown that the ferromagnetism is stronger than the diamagnetism , where the diamagnetism is related with spontaneous magnetization . the critical value of reduced fm coupling @xmath0 of pm phase to fm phase transition increases with increasing temperature . the lande - factor @xmath1 is supposed as a variable to evaluate the strength of the pm effect . the gas exhibits a shift from diamagnetism to paramagnetism as @xmath1 increases at a finite magnetic field . ferromagnetism plays an important role in the magnetization density in the weak magnetic field . diamagnetism can not increase infinitely with magnetic field at high magnetic field . condensation is predicted to occur through studying the low - temperature magnetic properties in a weak magnetic field . jq would like to thank professor huaiming guo for the helpful discussions . this work was supported by the national natural science foundation of china ( grant no . 11004006 ) , and the fundamental research funds for the central universities of china . 10 anderson m h , ensher j r , matthews m r , wieman c e and cornell e a 1995 _ science _ * 269 * 198 ; davis k b , mewes m - o , andrews m r , druten n j v , durfee d s , kurn d m and ketterle w 1995 _ phys . lett . _ * 75 * 3969 ; bradley c c , sackett c a , tollett j j and hulet r g 1995 _ phys . rev . lett . _ * 75 * 1687 daicic j , frankel n e and kowalenko v 1993 _ phys . * 71 * 1779 ; daicic j , frankel n e , gailis r m and kowalenko v 1994 _ phys . rep . _ * 237 * 63 ; daicic j and frankel n e 1996 _ phys . _ d * 53 * 5745 saxena s s , agarwal p , ahilan k , grosche f m , haselwimmer r k w , steiner m j , pugh e , walker i r , julian s r , monthoux p , lonzarich g g , huxley a , sheikin i , braithwaite d and flouquet j 2000 _ nature _ * 406 * 587

magnetic properties of a charged spin-1 bose gas with ferromagnetic interactions is investigated within mean - field theory . it is shown that a competition between paramagnetism , diamagnetism and ferromagnetism exists in this system . it is shown that diamagnetism , being concerned with spontaneous magnetization , can not exceed ferromagnetism in very weak magnetic field . the critical value of reduced ferromagnetic coupling of paramagnetic phase to ferromagnetic phase transition @xmath0 increases with increasing temperature . the lande - factor @xmath1 is introduced to describe the strength of paramagnetic effect which comes from the spin degree of freedom . the magnetization density @xmath2 increases monotonically with @xmath1 for fixed reduced ferromagnetic coupling @xmath3 as @xmath4 . in a weak magnetic field , ferromagnetism makes immense contribution to the magnetization density . while at a high magnetic field , the diamagnetism inclines to saturate . evidence for condensation can be seen in the magnetization density at weak magnetic field .

SECTION 1. SHORT TITLE. This Act may be cited as the ``IDEA Full Funding Act''. SEC. 2. AMENDMENT TO IDEA. 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``(C) $16,134,207,000 or 21.2 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2018, and there are hereby appropriated $4,636,359,000 or 5.1 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2018, which shall become available for obligation on July 1, 2018, and shall remain available through September 30, 2019; ``(D) $18,063,059,000 or 23.2 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2019, and there are hereby appropriated $6,565,211,000 or 7.1 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2019, which shall become available for obligation on July 1, 2019, and shall remain available through September 30, 2020; ``(E) $20,222,507,000 or 25.4 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2020, and there are hereby appropriated $8,724,659,000 or 9.3 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2020, which shall become available for obligation on July 1, 2020, and shall remain available through September 30, 2021; ``(F) $22,640,117,000 or 27.8 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2021, and there are hereby appropriated $11,142,269,000 or 11.7 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2021, which shall become available for obligation on July 1, 2021, and shall remain available through September 30, 2022; ``(G) $25,346,755,000 or 30.5 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2022, and there are hereby appropriated $13,848,907,000 or 14.4 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2022, which shall become available for obligation on July 1, 2022, and shall remain available through September 30, 2023; ``(H) $28,376,972,000 or 33.4 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2023, and there are hereby appropriated $16,879,124,000 or 17.3 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2023, which shall become available for obligation on July 1, 2023, and shall remain available through September 30, 2024; ``(I) $31,769,453,000 or 36.5 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2024, and there are hereby appropriated $20,271,605,000 or 20.4 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2024, which shall become available for obligation on July 1, 2024, and shall remain available through September 30, 2025; and ``(J) $35,567,506,000 or 40 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2025 and each subsequent fiscal year, and there are hereby appropriated $35,567,506,000 or 40 percent of the amount determined under paragraph (2), whichever is greater, for fiscal year 2025 and each subsequent fiscal year, which-- ``(i) shall become available for obligation with respect to fiscal year 2025 on July 1, 2025, and shall remain available through September 30, 2026; and ``(ii) shall become available for obligation with respect to each subsequent fiscal year on July 1 of that fiscal year and shall remain available through September 30 of the succeeding fiscal year. ``(2) Amount.--With respect to each subparagraph of paragraph (1), the amount determined under this paragraph is the product of-- ``(A) the total number of children with disabilities in all States who-- ``(i) received special education and related services during the last school year that concluded before the first day of the fiscal year for which the determination is made; and ``(ii) were aged-- ``(I) 3 through 5 (with respect to the States that were eligible for grants under section 619); and ``(II) 6 through 21; and ``(B) the average per-pupil expenditure in public elementary schools and secondary schools in the United States.''. SEC. 3. OFFSETS. The amounts appropriated in 611(i) of the Individuals with Disabilities Education Act (20 U.S.C. 1411(i)), as amended by section 2 of this Act, shall be expended consistent with pay-as-you-go requirements.

IDEA Full Funding Act Amends the Individuals with Disabilities Education Act (IDEA) to reauthorize and make appropriations for the grant program to assist states and outlying areas in providing special education and related services to children with disabilities. Sets the amount to be authorized and the amount to be appropriated for each fiscal year from FY2016-FY2024 as the greater of: (1) a specified amount, or (2) a specified percentage of an amount determined pursuant to a formula that multiplies the number of children receiving special education services by the average per-pupil expenditure in public elementary and secondary schools. Authorizes and appropriates funds for FY2025 and each subsequent fiscal year equal to the greater of a specified amount or 40% of the amount determined using such formula. Requires amounts appropriated to be expended consistent with pay-as-you-go requirements.

As more and more companies develop smartwatches, we're starting to see which will stick around and which will fall behind. Pebble is hoping that it could become one of the former companies—but it's cutting costs to stay afloat. In an interview with Tech Insider, Pebble CEO Eric Migicovsky revealed the company would lay off 40 employees, or about 25 percent of its entire workforce. Migicovsky was slightly cryptic when explaining the reason for the layoffs, but he did say that Pebble would be carefully considering how to spend its money over the next year. "We've definitely been careful this year as we plan our products," Migicovsky told Tech Insider. "We got this money, but money [among VCs in Silicon Valley] is pretty tight these days." According to the interview, Pebble has raised $26 million over the past eight months, which is in addition to its original $20 million raised back in February of 2015 when it launched its Pebble Time Kickstarter campaign. Migicovsky claims Pebble will focus its wearable device efforts on the health and fitness market going forward, and it will also start selling smartwatches in India via Amazon next month. Since the beginning, Pebble's success has always been heavily based on its community of followers and developers. The Kickstarter for the original Pebble pulled in over $10 million, and since then the company has created upgraded, all-metal designs of its first smartwatch, redesigned its interface, and even designed a round version meant to appeal to the more fashion-conscious shopper. But now it appears even a strong community cannot prevent the shakiness of the wearable industry from affecting Pebble. The market for smartwatches and smartwatch hybrids continues to get crowded: Fitbit's Blaze debuted recently, and we saw the company's stock fall shortly after, and Apple lowered the price of its Watch to $299 this week. Pebble hasn't disclosed any sales figures recently; it's too early to know sales of Fitbit's Blaze; and aside from analyst projections, Apple Watch sales numbers are still shrouded in mystery. Despite that uncertainty, experts do predict that in the wearables category, smartwatches will be the device in highest demand over the next few years. Pebble plans to be around to see that reality. "We want to be careful," Migicovsky told Tech Insider. "Pebble is in this for the long haul. We have a vision where wearables will take us in five to 10 years, and this is setting us up for success." ||||| Pebble, the buzzy startup credited for being one of the first companies to launch a modern smartwatch, is laying off 40 employees this week, CEO Eric Migicovsky told Tech Insider in an interview. That's about 25% of its total staff. Migicovsky also said the company has raised $26 million over the last eight months on top of its $20 million Kickstarter campaign that started in February 2015. He wouldn't disclose the investors, but did say Pebble has raised a mix of debt and venture capital from private investors. Migicovsky blamed a chilly fundraising environment in Silicon Valley for the layoffs. "We've definitely been careful this year as we plan our products," Migicovsky said. "We got this money, but money [among VCs in Silicon Valley] is pretty tight these days." Moving forward, Migicovsky said he wants Pebble to focus on the health and fitness aspects of the company's wearables, which he says most users are interested in. The company will also start selling its products in India next month through a partnership with Amazon. The Pebble layoffs come at a shaky time for the wearable technology market. FitBit, the leader in the wearable category, has seen its stock fall dramatically in recent months. Apple dropped the price of the Apple Watch by $50 to $299 on Monday, a sign that it's not selling as well as hoped. "We want to be careful," Migicovsky said. "Pebble is in this for the long haul. We have a vision where wearables will take us in five to 10 years, and this is setting us up for success." Migicovsky wouldn't disclose sales figures for Pebble. The last time the company announced sales was in February 2015 when it said it had sold 1 million smartwatches since 2013. By contrast, estimates for Apple Watch sales are all over the place — Apple has never disclosed sales figures — but even the most conservative analysts think Apple sold about 10 million units in 2015. (The Apple Watch isn't even a year old yet.) Pebble targets the lower end of the smartwatch market. Its watches start at $100 and go up to $250. Smartwatches were once considered to be the "next big thing" in consumer technology, but so far no one has created a must-have gadget in the category. They're nice to own, but still not as capable or essential as a smartphone. ||||| Pebble, the company that helped usher in the smartwatch era, is tightening spending through a round of layoffs. On Wednesday, Pebble CEO Eric Migicovsky told Tech Insider that 40 employees, equating to roughly 25% of his company’s workforce, would be let go this week. According to Migicovsky, the layoffs are required due to “a chilly fundraising environment” in Silicon Valley. Pebble originally saw success with its first smartwatch on Kickstarter, where the company’s campaign raised over $10 million in 2012. Get Data Sheet, Fortune’s technology newsletter. The firm later raised another $20 million via its second Kickstarter campaign for its current crop of Pebble Time smartwatches. In addition to its Kickstarter success, Migicovsky told Tech Insider that Pebble raised another $26 million over the last eight months. By letting employees go when raising money is getting tougher, the company can focus on its future. Migicovsky says his company has a vision for “where wearables will take us” over the next five to 10 years. Earlier this month, Pebble dropped the price of its Pebble Time and Time Round smartwatches by $50. The price drop rounds out Pebble’s product offering, which ranges from $100 to $250, depending on the model. Read more: Why Pebble’s Smartwatch Price Drop Is a Smart Move In December, the company added fitness tracking capabilities to its Pebble Time lineup of watches. Through a health app, the watch gained the ability to count steps and track sleep. According to Migicovsky, Pebble’s focus going forward will continue to be development of health and fitness features as well as an expansion to India through a partnership with Amazon.

– Is the smartwatch's time already over? Tech Insider reports Pebble—one of the first companies to release a smartwatch—is laying off 40 employees, about 25% of its total staff. Pebble raised $26 million this year, in addition to the $30 million it has raised on Kickstarter since its founding, according to Fortune. Regardless, CEO Eric Migicovsky says fundraising has been difficult in Silicon Valley, necessitating the layoffs. "Money is pretty tight these days," he tells Tech Insider. Despite the layoffs, Migicovsky says Pebble "is in this for the long haul." "We have a vision where wearables will take us in five to 10 years," he says. In the near future, that includes focusing on health and fitness functions popular with consumers. The problems at Pebble are just another sign of dark clouds looming for the wearable technology industry, Tech Insider reports. FitBit, the industry leader in wearable tech, recently had its stock fall "dramatically." Apple reduced the price of its Apple Watch by $50 this week, signs that sales aren't going well. Pebble also dropped the price of its watches this month. Despite these warning signs, more and more companies are getting into the smartwatch game, according to Ars Technica. And experts believe smartwatches will still be the most-purchased piece of wearable technology for at least the next few years.

The Occupy Wall Street protests are moving into the neighborhood. Finding it increasingly difficult to camp in public spaces, Occupy protesters across the country are reclaiming foreclosed homes and boarded-up properties, signaling a tactical shift for the movement against wealth inequality. Deb Austin, right, who has received an eviction notice, speaks in front of her house surrounded by other homeowners, neighbors and demonstrators in Portland, Ore., Tuesday, Dec. 6, 2011. Following tactics... (Associated Press) In this photo shot Monday, Dec. 5, 2011, the electric meters of a formerly boarded-up duplex are covered with graffiti from members of an Occupy Seattle group that took over the house in Seattle. Following... (Associated Press) In this photo shot Monday, Dec. 5, 2011, a Occupy Seattle protester who goes by the name "Mufasa" sits on the steps of a formerly boarded-up duplex members of the group have taken over in Seattle. Following... (Associated Press) Police officers stand guard during a tour of foreclosed homes by Occupy Wall Street activist in the East New York neighborhood of the Brooklyn borough of New York, Tuesday, Dec. 6, 2011. Finding it increasingly... (Associated Press) Groups in more than 25 cities held protests Tuesday on behalf of homeowners facing evictions. In Atlanta, protesters held a boisterous rally at a county courthouse and used whistles and sirens to disrupt an auction of seized houses. In New York, they marched through a residential neighborhood in Brooklyn carrying signs that read "Foreclose on banks, not people." Southern California protesters rallied around a family of six that reclaimed the home they lost six months ago in foreclosure. "It's pretty clear that the fight is against the banks, and the Occupy movement is about occupying spaces. So occupying a space that should belong to homeowners but belongs to the banks seems like the logical next step for the Occupy movement," said Jeff Ordower, one of the organizers of Occupy Homes. The events reflect the protesters' lingering frustration over the housing crisis that has sent millions of homes into foreclosure after the burst of the housing bubble that helped cripple the country's economy. Nearly a quarter of all U.S. homeowners with mortgages are now underwater, representing nearly 11 million homes, according to CoreLogic, a real estate research firm. Protesters say that banks and financial firms own abandoned foreclosed houses that could be housing people. Seattle has become a leader in the anti-foreclosure movement as protesters took over a formerly boarded-up duplex last month. They painted the bare wood sidings with green, black and red paint, and strung up a banner that says "Occupy Everything - No Banks No Landlords." While arrests have already been made in a couple of squatting cases in Seattle and Portland, it remains to be seen how authorities will react to this latest tactic. In Portland, police spokesman Sgt. Pete Simpson said he's aware that the movement called for people to occupy foreclosed homes, but said it's difficult to distinguish between the people who would squat in homes as a political statement and those that do it for shelter. "The vacant property issue is of concern in cities nationwide," Simpson said. "We'll treat them all as trespassers." In Seattle, protesters took over a boarded-up warehouse slated for demolition last weekend. In an announcement, the protesters said they planned to make the warehouse into a community center, and hosted a party the night they opened the building. Police moved in soon after, arresting 16 people in the process of clearing it out. Seattle police spokesman Sgt. Sean Whitcomb said his department sees squatting in private properties as the same violation of trespassing Occupy Seattle made when it camped in a downtown park. "It's no different than when people were trespassing (in the park)," Whitcomb said. "We went nights and days, letting people camp in the park. We relied on education and outreach, rather than enforcing the law to the letter." Atlanta protesters took a more aggressive approach in trying to disrupt the home auction. The auction went on but the whistles and sirens made it difficult for the auctioneers to communicate, said Occupy Atlanta spokesman Tim Franzen. "We don't know how many homes we saved for one more month during the holiday season," he said. "It was kind of a Christmas gift to the people." In Riverside, Calif., Art de los Santos arrived in a U-Haul with assorted furniture and about three dozen supporters at his former three-bedroom, three bathroom home. He broke the lock and moved back in. Reclaiming his old home is his last resort to get the attention of bank JP Morgan Chase after he applied three times for a loan modification to no avail. "I'm getting down to my last option," he said. "Nothing seems to work. Maybe if I protest, it'll get their attention." The home, which was foreclosed on, is sitting empty while he, his wife and four children, aged 11 to 7, are squeezed into an Orange County rental apartment. He's also renting a storage unit. "It's sad because you have all these memories there," said the 46-year-old. "My kids were running around the neighborhood on their bikes. It's a nice little community." Tom Kelly, spokesman for JPMorganChase, had no immediate knowledge of de los Santos' case and could not comment, but noted that he is trespassing. New York protesters introduced members of a homeless family at the end of their rally and said they plan renovate and clean up the house so the family can live in a house they said had been abandoned by a bank. In Portland, a press conference was held at the home of a woman facing foreclosure next March. She vowed to stay in her house until authorities take her out. "We belong here," said Deb Austin, who said she fell behind in payments after a cancer diagnosis and after her husband lost her second job. "And we're not leaving." ___ Associated Press writers Nigel Duara in Portland, Ore., Cristina Silva in Las Vegas, Leonard Pallats in Atlanta, Deepti Hajela in New York, and Christina Hoag in Los Angeles contributed to this report. ||||| Occupy San Francisco demonstrators clashed with police Wednesday night after they returned to Justin Herman Plaza following the clearing of their encampment by police in an early morning raid. About a half dozen Occupy protesters were arrested and later released during the evening, but police eventually pulled back after demonstrators refused to leave the plaza. The group greeted the police retreat with cheers and chants of "our park" and "cops are the 99 percent." "I feel like we're all refugees of the 1 percent and the police were trying to kick people out of a public space," said Michael Sampson, 25, who was part of the Occupy Oakland protest, as he set up a tent in the plaza. "This belongs to the people." Demonstrator Amy Oh, 32, called Wednesday's activities a "partial victory." "The problem with all the constant raids and evictions is that it distracts from our original purpose," said Oh, referring to the movement centered on the global frustration over major banks, multinational corporations and the economy. Late Wednesday, occupiers had set up about four tents at the site of their former encampment but eventually took them all down. The number of protesters had dwindled to about 40, but police remained nearby. Demonstrators were upset that police raided the Occupy SF camp at about 1:30 a.m. Wednesday, arresting 70 campers and protesters and clearing out the 2-month-old, 142-tent encampment. At least three demonstrators were arrested Wednesday afternoon after they reportedly blocked traffic outside the Federal Reserve building on Market Street. More than 100 police officers, along with sheriff's deputies, firefighters and public works crews, converged on the camp at the foot of Market Street early Wednesday and gave protesters five minutes to clear out. The city took action after police and city officials stopped being able to communicate with the protesters. The 70 were arrested on suspicion of illegal lodging and camping in a public park. Two were also arrested on suspicion of felony assault on a police officer after they threw a metal chair at him, hitting him on his face shield and causing minor injuries, Officer Albie Esparza said. Police moved in after Mayor Ed Lee gave up hope of negotiating a voluntary departure from the plaza with the leaderless Occupy movement. The mayor, who had said repeatedly that tents would not be allowed in the plaza, repeated that warning Wednesday and said he meant it. Lee noted that the city had given the protesters repeated warnings to move somewhere else. He said the protests have cost the city $950,000. Although protests will be allowed at the plaza, the tents won't rise again, Lee said. "Everyone in the city has the right to protest," Lee said. "But overnight sleeping will not be allowed." A separate offer to move the encampment to a vacant lot owned by the school district near 16th and Mission streets is also off the table, Lee said. Supporters and members of the encampment regrouped during the evening. They held a rally at about 5 p.m. and returned to their former campsite, intending to hold a meeting to discuss where they might next set up camp. A large contingent of police arrived as the general assembly was getting started. They issued an order to disperse and police in riot gear encircled protesters on the plaza. Police arrested two young men, including one who was injured, who were in the perimeter of the circle. They also arrested a man and a woman who tried to cut him free from hand bonds. Protester Jed Holtzman, 34, said he thinks the police response was overblown. "Given that it's a public park that's open, it is not only an overblown reaction, it is a 100 percent misplaced reaction," he said, pointing out that they were only there to have their general assembly. "If there were 10 folks in here having a picnic, do you think this would be happening?" This article appeared on page C - 1 of the San Francisco Chronicle

– Another Occupy encampment was cleared out early today, as police raided Occupy SF and arrested 70 people who had been camping at Justin Herman Plaza. Protesters at the 2-month-old encampment were given five minutes to leave shortly after 1am; most did, but 30 who did not were arrested. The other 40 arrests came when protesters who objected to the eviction blocked Market Street. The San Francisco Chronicle reports that a few clashes occurred, and two people allegedly threw a metal chair at a police officer. Meanwhile, the AP reports on the shift from "Occupy Wall Street" to "Occupy Our Homes." As protesters are finding their public camping options increasingly limited, Occupiers are moving into foreclosed homes and properties. More than 25 cities saw "Occupy Our Homes" protests yesterday on behalf of evicted homeowners. "It's pretty clear that the fight is against the banks, and the Occupy movement is about occupying spaces," says an organizer. "So occupying a space that should belong to homeowners but belongs to the banks seems like the logical next step for the Occupy movement."

WASHINGTON (Reuters) - President Donald Trump said on Sunday he will offer details on how he would like to overhaul President Barack Obama’s signature healthcare law in a speech to the U.S. Congress on Tuesday. U.S. President Donald Trump speaks during the Governor's Dinner in the State Dining Room at the White House in Washington, U.S., February 26, 2017. REUTERS/Joshua Roberts Since they now control the White House and Congress, Republicans are under pressure to fulfill their pledge to repeal and replace the Obamacare law although they have found no easy way to do it. The law has proven popular in many states, even those controlled by Republicans, and it enabled millions of previously uninsured people to get affordable coverage, although steep premium increases angered some. Trump is to talk about healthcare, among other topics, in a nationally televised address on Tuesday night to a joint session of Congress. Trump reiterated his pledge to repeal and replace the Obamacare law in remarks at a black-tie dinner for the National Governors Association. “We’re going to be speaking very specifically about a very complicated subject,” Trump said. “I think we have something that is really going to be excellent.” Republicans have yet to agree on a single detailed policy proposal to repeal and replace the Affordable Care Act. Some moderates want to revise the law and not abandon it entirely while conservatives want to repeal it completely. Still to be worked out are details including the future of Medicaid, the government health insurance program for the poor that was expanded in more than 30 states under Obamacare, and how a new healthcare law would be funded. Trump said he would be discuss healthcare on Monday when he meets some of the governors who are in Washington for the National Governors Association’s annual meeting. Trump cast his first weeks in office in a positive light despite stumbles including an executive order aimed at banning people from seven Muslim-majority nations that was immediately embroiled in a court challenge. “We’ve made a lot of promises over the last two years, and many of those promises already are kept so we’ve very honored by that,” he said. Trump turned the microphone over to Virginia Governor Terry McAuliffe, a Democrat who chairs the governors association. McAuliffe is a long-time supporter of former President Bill Clinton and his wife, Hillary, whom Trump defeated in the Nov. 8 presidential election. McAuliffe told Trump, “We want to work with you” on creating jobs and strong healthcare system. ||||| poster="http://v.politico.com/images/1155968404/201702/2990/1155968404_5339620683001_5339588189001-vs.jpg?pubId=1155968404" true Trump: ‘Nobody knew that health care could be so complicated’ The president appears to nod to the grim political reality around repealing and replacing Obamacare. President Donald Trump on Monday claimed that “nobody knew that health care could be so complicated,” and again flirted with the idea that Republicans should let Obamacare “implode” so that Democrats shoulder the blame. Even as he re-upped his commitment to repealing and replacing Obamacare during separate gatherings with governors and insurance CEOs, Trump appeared to nod to the grim political reality of yanking away the increasingly popular law. Story Continued Below "Let it be a disaster, because we can blame that on the Dems that are in our room -- and we can blame that on the Democrats and President Obama," Trump said in remarks to the National Governors Association. "But we have to do what's right, because Obamacare is a failed disaster." He also used some strained logic to explain why Obamacare’s popularity has continued to generally tick up, with a Wall Street Journal/NBC News poll released last week finding that 43 percent of voters think the law was a good idea, while 41 percent said it was a bad idea. (It was a slight dip from January, in which 45 percent said the law was a good idea, but overall, the law’s popularity has been steadily rising over the past two years). Trump on Monday theorized that polls show the program’s approval rating climbing not because people like it, but because they know Republicans will soon repeal it. He did not offer more of an explanation for the claim. “People hate it, but now they see that the end is coming, and they're saying, ‘Oh, maybe we love it,’” Trump said. “There's nothing to love. It's a disaster, folks.” He also seemed to express surprise at the complexity of the reform process. “I have to tell you, it’s an unbelievably complex subject,” Trump said. “Nobody knew that health care could be so complicated.” Trump throughout his campaign publicly pledged to quickly kill and replace Obamacare, while never getting specific about what the alternative would look like. After the election, however, he’s appeared at times to waffle about yanking the law, tweeting on Jan. 4 that it would be more politically savvy to let Democrats own the Obamacare “disaster.” Recently he’s promised to release his Obamacare alternative plan by early to mid-March, but there’s been trepidation among some Republicans, especially after many GOP lawmakers were forced to confront angry constituents at recent town halls who are worried about losing their health care. Republicans, who have blamed Obamacare for industry problems like increases in premiums and say the law represents government overreach, are now running into trouble agreeing what to put in its place if they kill it. Some 20 million people depend on the law for their insurance, and Republicans worry about the further backlash they may face if some of those people lose their coverage under a new plan. On Monday, Trump gave more mixed signals, both expressing political reservations and emphasizing his commitment to repeal and replace former President Barack Obama’s signature achievement, which is formally known as the Affordable Care Act. As he met on Monday with insurance company chief executives, Trump reiterated his description of Obamacare as a "disaster" that is "only getting worse." He also discussed his own upcoming plan, pledging that it will be competitive and "great" for "the patients, for the people and hopefully for the companies." "Costs will come down, and I think the health care will go up very, very substantially," the president said. "I think people are gonna like it a lot. We've taken the best of everything we can take." Trump also told the group that he has instructed his health and human services secretary, Tom Price, to work with industry leaders to "stabilize the insurance markets and to ensure a smooth transition to the new plan." ||||| Donald Trump is learning. If there’s one thing almost everybody across the political spectrum knows about health-care reform, it’s that it’s really hard. People who study the issue closely know it. People who don’t follow the issue know. (That’s why lots of smart people don’t follow the issue closely — it’s really hard!) But there is apparently a category of people who did not realize until very recently that the issue is hard, and that category consists of Donald J. Trump, who told reporters today, “It’s an unbelievably complex subject. Nobody knew health care could be so complicated.” Health-care reform is extremely complicated even under the best of circumstances. But when you combine the inherent complexities of the subject with the ideological rigidities of the conservative movement, the problem goes from hard to prohibitively impossible. Providing access to medical care to the tens of millions of Americans who can’t afford it on their own, because they’re too poor or too sick, is arithmetically futile if you’re bound by a dogma that opposes redistribution from the rich and healthy to the poor and sick. House Republicans have decided to resolve the contradiction between party dogma and the promise not to harm the public in favor of the former. A study prepared by the National Governors Association, and which leaked to the media Saturday evening, finds that the House Republicans leadership’s formative plan to replace Obamacare will deprive millions of people of their insurance. The Wall Street Journal reports that Paul Ryan and Mitch McConnell, lacking the votes for a plan that would create massive humanitarian and economic damage to the health-care sector and millions of voters who would lose their access to care, want to just push the bill ahead anyway. Their purported calculation is that they can force wavering Republicans to go along with the bill for fear of betraying the noble cause of Obamacare repeal that has animated the base for years. “You’re a Republican, you’ve been running to repeal Obamacare, they put a repeal bill in front of you … Are you going to be the Republican senator who prevents Obamacare repeal from being sent to a Republican president who is willing to sign it?” said Doug Badger, a longtime Republican leadership health-policy adviser, tells the Journal. Juliet Eilperin and Amy Goldstein report that many of the most orthodox members of Trump’s administration, including Mike Pence, who is close to Paul Ryan, side with this strategy. On the other hand, they report, numerous Trump advisers are concerned about the political fallout of blowing up the health-care system. These advisers include Jared Kushner, NEC director Gary Cohn, senior policy adviser Stephen Miller and chief strategist Stephen K. Bannon. And the reason they fear that is that Trump did not just run on repeal. He ran for president making irreconcilable promises on health care. To win support from voters, he promised “terrific” insurance that would “take care of everybody.” But to remain acceptable to Republican elites, he avoided embracing any policies that would violate party dogma against tax increases. The actual details of his health-care plan were fuzzy and usually ignored, but to the extent they existed at all, they consisted mainly of warmed-over conservative platitudes that would mostly resemble the old, pre-Obamacare system and do little or nothing to cover the uninsurable. Trump held together the contradiction by simply pretending the solution would reveal itself over time and would be extremely easy. Quite likely Trump believed this himself — as a committed nonreader, and a narcissistic devotee of his own negotiating prowess, he surely believed that he could broker a deal that would satisfy both the moral objective of universal coverage and the specific ideological hang-ups that had prevented his party from ever supporting a plan that would accomplish it in the past. The only thing that held Trump’s position together was a refusal to engage with the substance of the issue, and a magical belief that it could all be waved away. At best, he will keep either his promise to the Republican elite or his promise to the electorate. At worst he will keep neither. His offhand comment that the issue is hard is a window into the mind of a man who realizes the jig is almost up. ||||| Republican leaders who are preparing a bill to repeal Obamacare have a new strategy: betting that fellow GOP lawmakers will think twice about blocking it. WSJ's Louise Radnofsky explains on Lunch Break with Tanya Rivero. Photo: Reuters WASHINGTON—Republican leaders are betting that the only way for Congress to repeal the Affordable Care Act is to set a bill in motion and gamble that fellow GOP lawmakers won’t dare to block it. Party leaders are poised to act on the strategy as early as this week, after it has become obvious they can’t craft a proposal that will carry an easy majority in either chamber. Lawmakers return to Washington Monday after a week of raucous town halls in their districts that amplified pressure on Republicans to forge ahead with their...

– President Trump will lay out details of his plan to repeal and replace ObamaCare in his State of the Union speech Tuesday night, reports Reuters, but he acknowledged Monday that things are moving more slowly than he'd hoped. "I have to tell you, it's an unbelievably complex subject," he said during a meeting with governors at the White House, per Politico. "Nobody knew that health care could be so complicated." (That last line is drawing scorn from critics, as in this post at New York from Jonathan Chait. He faults Trump for "simply pretending the solution would reveal itself over time and would be extremely easy.") Still, Republican leaders remain committed to keeping their promise, and the Wall Street Journal reports that they're moving closer to a risky strategy in the House and Senate: Call a vote and "dare" rank-and-file Republicans to oppose them. The strategy is a gamble because GOP leaders can afford only two defections in the Senate and 22 in the House, and different factions have threatened to defect over a slew of reasons, including tax credits and Medicaid funding. But a GOP health policy adviser puts it this way: “You’re a Republican, you’ve been running to repeal ObamaCare, they put a repeal bill in front of you," says Doug Badger. "Are you going to be the Republican senator who prevents ObamaCare repeal from being sent to a Republican president who is willing to sign it?” Meanwhile, a new survey suggests that ObamaCare is more popular than ever, but Trump belittled that notion. "People hate it, but now they see that the end is coming and they're saying, 'Oh, maybe we love it,'" he said. "There's nothing to love. It's a disaster folks, OK? So you have to remember that."

The New York Times is due to introduce a 'metered' paywall in early 2011 . Readers will be allowed to access a certain number of articles free each month, then will be asked to pay. "This has the benefit of allowing our millions of readers who come to us through search engine to still find our content," Sulzberger specified, while those who use the site heavily will be charged. Chairman and publisher of the, stressed the need to take risks and not be afraid of failure in the quest to find a business model that can adequately support high quality journalism. He was speaking at thein London. He confirmed that the paper will work with Google to implement First Click Free, stressing that "we want to ensure that NYTimes.com continues to be part of the open web ecosystem." Many details of the pay strategy are yet to be decided, however. "We are still working on deciding what type of content will count towards the metre," as photos and graphics may well require different considerations. "We are in the process of conducting extensive research to decide on pricing and the extent of the metre," he continued, adding that "we will be refining all these policies as we get ready to launch in the near future." "Our pursuit of the pay model is a step in the right direction for us," Sulzberger said. "We believe that serious media organisations must start to collect additional revenue from their readers," and "information is less and less yearning to be free." Readers are becoming increasingly willing to buy information on the web if it enhances their lives, he said. A further incentive towards experimentation is that in the digital age, the cost of changing is low. "If we discover that we've tried something that's not working, we could change it." This should not be seen as failure, he emphasised, but as a willingness to adapt and learn. The TimesSelect experiment in 2007 was not aborted because of a failure to succeed, Sulzberger insisted, but because the paper thought it could make more money from advertising revenue. "Don't lock yourself into a direction," he warned. Putting up a paywall does not in itself comprise a business model, however, rather "we must reconsider the very nature" of user engagement. Sulzberger noted many ways in which the NYT is beginning to engage further its readers by producing abundant multimedia and graphics, and by inviting them to join crowdsourcing initiatives. The paper recently developed a tighter level of integration with Facebook, and Sulzberger hopes that the NYT will be able to build a tighter emotional bond with their readers by encouraging them to come to NYTimes.com with their own identities, and by allowing them to find NYT content wherever they might be. Asked about his response to the suggestion that the NYT might print its last edition in 2015, Sulzberger said he saw no point in making such predictions and said all he could say was that "we will stop printing the New York Times sometime in the future, date TBD." [CLARIFICATION: Sulzberger was not making an announcement that the New York Times has definite plans to stop printing in the near future; rather making the point, in a joking fashion, that it is impossible and fruitless to predict exactly when printed newspapers might come to an end.] ||||| At a conference in London, Arthur Sulzberger Jr conceded that someday the New York Times Company will be forced to stop publishing a printed paper.* This sounds obvious, but it's a big deal. The economics of the online news business will not support the infrastructure or newsroom that the printed paper supports. Unless the New York Times Company can come up with a miracle new digital revenue stream, therefore, it will eventually have to be restructured and downsized (or sold to a deep-pocketed Sydney Harmon-type who runs it at a loss out of love). Importantly, even a successful online paywall will not allow the paper to maintain its current cost structure. We estimate that the NYT currently spends about $200 million a year on its newsroom and generates about $150 million of online revenue. If the paywall is highly successful--attracting, say, 1 million subscribers who pay $100 a year--this will add another $100 million of online subscription revenue (assuming the company doesn't lose ad revenue). With $250 million of revenue, the NYT might be able to sustain newsroom costs of about $100 million. Now, a $100 million newsroom budget is a HUGE newsroom budget--one that most online publications would kill for. So the New York Times isn't going anywhere. But $100 million is also a lot less than the New York Times's current newsroom budget. So if Arthur Sulzberger is right that the New York Times will eventually have to stop printing the print paper--and we certainly think he is--his company is likely to have to be restructured. That is, unless NYTCo can find a Bloomberg-like sugar-daddy to run it at a loss indefinitely. * Here's what Arthur said, exactly, as reported by Emma Heald of editorsweblog: Asked about his response to the suggestion that the NYT might print its last edition in 2015, Sulzberger said he saw no point in making such predictions and said all he could say was that "we will stop printing the New York Times sometime in the future, date TBD." That's the first time we've heard him say that. And we suspect it's news to a lot of folks who have been telling us that we're wrong about the NYT because the company will be printing papers forever. ||||| News Corp rolled out a paywall at two of its major UK papers. It's not going well. The New York Times is scheduled to roll out its own paywall in January. Should anyone there be having second thoughts? Rupert Murdoch, of course, can afford to absorb short-term losses in his newspaper properties. He's famous for it, actually. But Techdirt points out two ongoing drawbacks of the paywalls at the Times UK: one, advertisers are fleeing the paper as its online traffic plummets; and two, its reporters are being passed over for those at other papers by sources who want to get their stories out more widely. Those are both serious problems that could persist long-term in the coming online media universe, where major generators of original content will mostly have paywalls, and the meta-media of bloggers and aggregators will mostly remain free. In a speech yesterday, NYT chairman Arthur Sulzberger gave no indication that the paper was anything other than full speed ahead on its upcoming paywall, though he did say "If we discover that we've tried something that's not working, we could change it." And in a comment that perked up the ears of futurists, he added, "we will stop printing the New York Times sometime in the future, date TBD." That shouldn't surprise anyone, though. Of course the New York Times will stop printing at some point in the future. As will most every newspaper, because print is an outmoded technology. It might take 20 years, but it will surely happen. And when all news is online, newspapers will have to charge for online news. It's quite simple. Online advertising can generate enough revenue to support an operation like Gawker Media, but not an operation like the New York Times. The great newspapers will surely shrink their staffs and become more efficient, but ultimately, expensive enterprise journalism requires paying subscribers. The debate over fair use will be messy, but it will be settled eventually. Both sides—those first-line journalism operations who write up the news, and those second-line web operations that aggregate, parse, discuss, and promote that news—know that they need each other. Some fair agreement for the sharing of content and revenue will come to pass, one in which the details will ultimately be hammered out in response to how dire the financial straits of newspapers and their ilk becomes. It's not a make-or-break situation at the moment, but eventually it will be untenable to give everything away online for free. All this is just to say: paywalls are coming. Yes, they're a risk—especially for the early adopters—but better to give it a shot now and tweak it until it's right than to wait until the situation grows even more alarming. (Assuming the quality is there. For the bad newspapers throwing up paywalls, all hope is lost). The New York Times itself today reports that newsprint is useful for gardening. For distribution of journalism, not so much.

– This from Arthur Sulzberger Jr.: "We will stop printing the New York Times sometime in the future, date TBD." OK, "this sounds obvious," writes Henry Blodget at Business Insider, "but it's a big deal." Unless the paper finds a "sugar-daddy," it will surely have to downsize over time given the realities of online revenue. Blodget estimates the Times spends $200 million a year on its current newsroom, a figure that will likely be cut in half even if the coming paywall is "highly successful" with 1 million or so subscribers. More on Sulzberger's comments at EditorsWeblog. At Gawker, Hamilton Nolan weighs in: "Online advertising can generate enough revenue to support an operation like Gawker Media, but not an operation like the New York Times. The great newspapers will surely shrink their staffs and become more efficient, but ultimately, expensive enterprise journalism requires paying subscribers." As for fair use in the new age: "Both sides—those first-line journalism operations who write up the news, and those second-line web operations that aggregate, parse, discuss, and promote that news—know that they need each other. Some fair agreement for the sharing of content and revenue will come to pass."

Skip in Skip x Embed x Share USA TODAY's Shannon Rae Green talks with Politics Editor Paul Singer about how likely Obama's proposals for tax credits for child care, breaks for community college student and more bipartisan deals are to pass in a Republican-controlled Congress. (USA NEWS, USA TODAY) President Obama delivers his State of the Union speech before members of Congress in the House chamber on Jan. 20, 2015. (Photo: Alex Wong, Getty Images) President Obama largely stuck to the facts in his State of the Union address, although he did cherry-pick data and exaggerate at times to put the best spin on his accomplishments. Some highlights: • Obama made the inflated claim that "more than half of manufacturing executives have said they're actively looking to bring jobs back from China." A survey showed most "expressed interest" in it, but are not "actively looking" at doing it. • Obama exaggerated when he said the U.S. is "the only advanced country on Earth that doesn't guarantee paid sick leave." Canada and Japan also don't mandate paid short-term sick leave, which is what Obama is seeking for the U.S. • The president boasted that the U.S. has gained 11 million private sector jobs in five years. Yes, but that ignores his first 13 months in office and a net loss of public sector jobs. Total employment growth during his time in office is about 6.4 million. • Obama also boasted that "more of our people are insured than ever before." But that's based on an administration analysis that compares the second quarter of 2014 to years past. We don't have the full 2014 federal numbers yet. The president delivered his sixth State of the Union address at a joint session of Congress on Jan. 20. But it was his first under a Congress controlled by Republicans. Much of his speech was devoted to the improving economy. MANUFACTURING JOBS Obama made the inflated claim that "more than half of manufacturing executives have said they're actively looking to bring jobs back from China." The president was referring to an August 2014 survey of 252 senior manufacturing executives in the U.S. conducted by the Boston Consulting Group. But the survey's findings don't exactly back up the president's claim. While 54% of those surveyed "expressed interest in reshoring," only 16% said they are "already bringing production back from China to the United States," a 20% increase from the 2013 survey. And 20% of those polled said that "they would consider returning production in the near future," up 24% from 2013. Obama also said that since 2010 "[o]ur manufacturers have added almost 800,000 new jobs." That's true enough, but there has been a net loss of manufacturing jobs during the president's time in office. Since January 2010, the time frame used by the president, the U.S. has seen an increase of 777,000 manufacturing jobs, according to the Bureau of Labor Statistics. But since January 2009, when Obama took office, the U.S. has seen a net decline of 321,000 manufacturing jobs, the same BLS data show. In a recent study, the Information Technology & Innovation Foundation rejected talk of a "manufacturing renaissance," calling it a "myth," and noting there still is a long way to go. Even with the recent increase in manufacturing jobs, there are still nearly 1.8 million fewer manufacturing jobs than there were in January 2007, BLS figures show. "Much of the growth since 2010 appears to be caused by a cyclical recovery as demand, particularly for motor vehicles and other durable goods, returns," the ITIF report said. Skip in Skip x Embed x Share During President Obama's 2015 State of the Union Address, he described America's growing economy and rising wages, but said middle-class economic policies work as long as politics don't get in the way. VPC ECONOMIC GROWTH The president fudged a bit when he said economic growth and job gains are the best in 16 years. Obama: Tonight, after a breakthrough year for America, our economy is growing and creating jobs at the fastest pace since 1999. Not quite. As for how fast "our economy is growing," official figures from the U.S. Bureau of Economic Analysis put the gain in real gross domestic product at an annual rate of 5.0% in the third quarter of last year. Those are the most recent figures available, and they represent the best quarterly gain in some time. But not since 1999. The BEA's figures show real GDP grew at a rate of 6.9% in the third quarter of 2003, and at 7.8% in the second quarter of 2000. And as for "creating jobs," the White House has pointed to a preliminary figure of 2.95 million jobs gained in 2014, which is the best since 1999 if it holds up when the BLS completes its normal revisions of job figures, which could go up or down. But the president spoke in present tense — saying the economy "is … creating jobs" at the fastest clip since 1999. And by more immediate measures the pace is not quite the most rapid since 1999. BLS puts the gain in total nonfarm employment during the most recent three-month period (ending in December) at 866,000 jobs. That's a respectable number, but not the best three-month gain since 1999. The BLS figures show other three-month stretches in 2010, 2006, 2004 and 2000 when even more jobs were added. SICK PAY Obama exaggerated when he said the United States was "the only advanced country on Earth that doesn't guarantee paid sick leave." While Canada and Japan have social insurance programs that would cover an extended leave for cancer treatment, they don't have guaranteed paid leave for an illness that lasts a few days. And Obama made the claim in calling for "a bill that gives every worker in America the opportunity to earn seven days of paid sick leave." A 2009 report by the Center for Economic and Policy Research, a group funded by various labor groups and foundations, examined policies in 22 countries "ranked highly in terms of economic and human development." It says in the first paragraph that the U.S. is "the only country that does not guarantee that workers receive paid sick days or paid sick leave," but it goes on to say that neither Canada nor Japan has a policy for financial support for short-term leave, for an illness such as a five-day flu. Those countries do have social insurance that would cover some of the pay for an employee needing 50 days off for cancer treatment. Those are the two scenarios examined in the study. The report says that 11 countries guaranteed full pay for an illness requiring five sick days. Others paid for some missed time, but not all five days (and in a few cases not even one full day), because of waiting periods before the financial support would kick in. Obama also said that the U.S. was the "only advanced country on Earth that doesn't guarantee … paid maternity leave to our workers." A 2014 report from the United Nation's International Labour Organization found: "Only two out of 185 countries and territories currently provide no statutory cash benefits during maternity leave." The two countries were Papua New Guinea and the United States, both of which provide some kind of maternity leave but no requirement for paid leave. The U.S. Family and Medical Leave Act requires 12 weeks of unpaid leave for new mothers who have worked for one year for employers with more than 50 workers. Employers may require a substitution of paid sick or vacation days for the FMLA leave. However, the International Labour Organization report went on to say that the benefits in more than half of those 185 countries "were neither generous nor sufficiently long-lasting." It calls for 14 weeks of pay equal to two-thirds of previous earnings, a standard met by 85% of developed countries. And not all women are eligible for benefits. "Only 28.4 per cent of employed women worldwide would receive cash benefits in case of maternity," the report said. Skip in Skip x Embed x Share Watch all the highlights of President Obama's 2015 State of the Union Address. VPC PRIVATE SECTOR JOB GROWTH The president was correct when he said the U.S. has gained 11 million private sector jobs in the past five years. Obama: And over the past five years, our businesses have created more than 11 million new jobs. That's true as far as it goes. The economy gained 11,215,000 private sector jobs between February 2010 and the preliminary figures for December of last year. Of course, the president said nothing of the 4,210,000 private sector jobs that were lost during the first 13 months of his tenure as president, due to the savage recession that was raging at the time he took office. Overall, since Obama took office, the net gain in private sector employment is just over 7 million. And the gain in total employment during his time in office is lower than that — just under 6.4 million. That's because of a net loss in government jobs, particularly in local school systems. (Photo: Pablo Martinez Monsivais, AP) ABORTION AND TEEN PREGNANCIES IN DECLINE Obama was right when he said "teen pregnancies and abortions are nearing all-time lows." Obama: We still may not agree on a woman's right to choose, but surely we can agree it's a good thing that teen pregnancies and abortions are nearing all-time lows, and that every woman should have access to the health care she needs. The rate of teen pregnancies in the U.S. has been on the decline for decades, according to the Centers for Disease Control and Prevention's Division of Vital Statistics. In 2013, there were 274,641 babies born to females aged 15 to 19, a rate of 26.6 births for every 1,000 teen mothers. That was a 10% decline from 2012 and "the lowest number of teen births ever reported for the United States." According to CDC, it was also 57% lower than in 1970, the peak year for teen births. However, despite this progress, teen pregnancies in the U.S. still outpace many other developed countries including Canada and the United Kingdom, according to United Nations statistics. As for abortions, the Guttmacher Institute reported in July 2014 that the rate of abortions in 2011 was the lowest since 1973. In 2011, "1.06 million abortions were performed, down 13% from 1.21 million in 2008." CHINA'S 'COMMITMENT' ON EMISSIONS In a section of his speech dealing with efforts to address climate change, Obama touted a recent agreement with China. Obama: In Beijing, we made an historic announcement – the United States will double the pace at which we cut carbon pollution, and China committed, for the first time, to limiting their emissions. Committed? Not exactly. In a joint announcement on Nov. 12, 2014, both the U.S. and China said they "intend to achieve" emissions targets. For its part, the U.S. said it "intends to achieve an economy-wide target of reducing its emissions by 26%-28% below its 2005 level in 2025 and to make best efforts to reduce its emissions by 28%." China, meanwhile, said it "intends to achieve the peaking of CO2 emissions around 2030 and to make best efforts to peak early and intends to increase the share of non-fossil fuels in primary energy consumption to around 20% by 2030." The agreement was hailed by the Natural Resources Defense Council as "a turning point in the fight against global warming." But the deal was derided by many Republican leaders, including Sen. Jim Inhofe, a Republican senator from Oklahoma and new chair of the Senate Environment Committee, who released a statement condemning the deal as a "non-binding charade." As we wrote in a story about the climate deal with China, it's true, as Inhofe said, that the deal is not a legally binding treaty, which would need Senate ratification. As the language in the announcement makes clear, the countries said they "intend to achieve" specific targets, but that's not quite a binding commitment. HEALTH INSURANCE Obama's boast about the decline in the uninsured is supported by early estimates from inside and outside his administration. Obama: And in the past year alone, about 10 million uninsured Americans finally gained the security of health coverage. That figure is echoed by a quarterly survey conducted by the Urban Institute and a report by researchers with the Department of Health and Human Services and Harvard School of Public Health. But we don't yet know if Obama can claim that "more of our people are insured than ever before," as he said earlier in his speech. An analysis of the percentage of uninsured by the White House's Council of Economic Advisers shows that, but compares the second quarter of 2014 to years past. We don't have the full 2014 federal numbers yet. The Urban Institute's Health Reform Monitoring Survey says the number of the uninsured dropped by 10.6 million nonelderly adults between September 2013 and September 2014. (The Affordable Care Act's first open enrollment period for policies purchased by individuals was from Oct. 1, 2013, through March 31, 2014.) An earlier estimate from researchers with the Department of Health and Human Services and Harvard School of Public Health put the decline of the uninsured at 10.3 million adults from January 2012 through June 2014. Their report, published in The New England Journal of Medicine, noted that "depending on the model and confidence intervals, our sensitivity analyses imply a wide range from 7.3 to 17.2 million adults." Estimates from the most recent National Health Interview Survey conducted by the Centers for Disease Control and Prevention's National Center for Health Statistics show a drop of 6.8 million people (of all ages) who were without health insurance at the time they were interviewed in the first six months of 2014, compared with 2013 (see Table 2). Those numbers were just released in December, so we won't have a fuller look at the changes between 2013 and 2014 overall for some months. Obama cited a statistic from his own Council of Economic Advisers in saying that "more of our people are insured than ever before." The CEA used National Center for Health Statistics data and estimated that "the nation's uninsured rate is now at or near the lowest level recorded across five decades of data." The data go back to 1963, and CEA had to make some adjustments due to changes in survey construction over the years. As we said, figures for all of 2014 aren't yet available, so CEA compares the percentage of uninsured for the second quarter of 2014 (11.3%) to figures from past years. That's the lowest rate in CEA's chart, but only 0.1 percentage points below the rate in 1974, 1978 and 1980 (see the table on page 11). The figure for the first six months of 2014, not just the second quarter, is higher, however, at 12.2% (see Table 1). It remains to be seen how 2014 as a whole will compare to the past. The National Center for Health Statistics' trend numbers for those without health insurance under age 65 (see Table 3) show that the first six months of 2014 had a lower percentage of uninsured than most of the past years — but not all. The percentage of the uninsured under age 65 was lower in 1974, 1978, 1980 and 1982. DEFICITS In ticking off his accomplishments, Obama listed this one: "our deficits cut by two-thirds." That's accurate, but as we have written before, the deficits have fallen from high levels and are on pace to return to high levels. When Obama took office in January 2009, the federal deficit for fiscal year 2009 was already on pace to be $1.2 trillion and topped $1.4 trillion by the end of the fiscal year on Sept. 30, 2009. Annual deficits remained above $1 trillion for three more years before dropping to $680 billion in fiscal 2013. The U.S. finished the most recent fiscal year with a deficit of $483 billion — roughly down two-thirds from what it was in fiscal 2009, as the president said. But, as we noted in our quarterly report on Obama's presidency, the nonpartisan Congressional Budget Office projects that annual deficits will soon rise again if Congress doesn't act. In a report it issued in August, CBO projected that under current law the deficit will rise above $500 billion in fiscal 2016 and hit nearly $950 billion by 2022. DRONES Obama said his administration has "worked to make sure our use of new technology like drones is properly constrained." Whether the use of drones has been "properly constrained" is a subjective matter. The Stimson Center, a global security think tank, for one, warned in 2014 that heavy reliance on drones "risks increasing instability and escalating conflicts." But as a matter of independent analysis, Obama has ordered many more drone strikes than his predecessor, George W. Bush. Obama: As Americans, we respect human dignity, even when we're threatened, which is why I've prohibited torture, and worked to make sure our use of new technology like drones is properly constrained. No official figures are available, and for a time the Obama administration would not even publicly admit that such CIA-controlled attacks were taking place. But independent reports have found a dramatic increase in the use of covert, remote-controlled drones and missiles to attack targets in Pakistan and Yemen. An independent estimate by the nonpartisan New America Foundation, based on what it deems to be "credible news reports," puts the number of attacks at more than 450 since Obama took office, more than nine times as many as took place while Bush was in office. In Pakistan, the group concludes, somewhere between 1,838 and 3,041 people were killed by drones approved by Obama. Most of them were militants, the report states, but about 150 of them were civilians. As we noted in a story in April 2013, estimates by the Bureau of Investigative Journalism in Britain, while slightly different, give a similar picture. — Eugene Kiely, Brooks Jackson, Lori Robertson, Robert Farley, D'Angelo Gore, Carolyn Fante and Eden Everwine For a full list of sources, see FactCheck.org. Read or Share this story: http://usat.ly/1JcEXxV ||||| President Barack Obama’s State of the Union address Tuesday provided a prime-time opportunity to contrast his lame duck vision for the economy, terrorism and foreign policy against a new Republican-led Congress eager to prevent any big victories. But with such high political stakes — and a television audience of tens of millions — also comes the allure to stretch the facts for even a small boost in public opinion polls. Story Continued Below Here’s POLITICO’s look at some of the key parts of Obama’s speech, and where he made some of his edgiest claims: What’s the definition of “combat”? Obama: “Tonight, for the first time since 9/11, our combat mission in Afghanistan is over.” Actually, the bullets are still flying in Afghanistan. Administration officials stress they’ve been given two “narrow” tasks: help train the Afghan National Security Forces and continue to go after Al Qaeda and other terrorist groups so they can’t use Afghanistan as a base from which to launch attacks on the U.S. But there’s little doubt those missions will involve what almost anyone would consider “combat” — American forces coming into contact with the enemy. In fact, Obama late last year issued an order explicitly authorizing U.S. commanders in Afghanistan to order air strikes if U.S. or allied troops are threatened by the Taliban. And the “counterterrorism” mandate Obama has cited in the past could include raids by special operations troops on terrorist hideouts. Republicans wasted no time Tuesday night pouncing on Obama’s “combat mission” claim: House Speaker John Boehner has long argued Obama’s policy of withdrawing troops from Afghanistan is only setting the stage for a second Iraq-style collapse. The Afghan force isn’t ready to stand on its own without its American mentors, Boehner and others argue, so Obama’s plan to continue cutting U.S. troops there by the time he leaves office is a disaster in the making. “President Obama is more interested in keeping arbitrary, political deadlines than defeating the terrorist threat in Afghanistan,” Boehner’s office said in an email blasted out just minutes after Obama’s speech started. Economy improving? Not for everyone Obama: “The shadow of crisis has passed, and the State of the Union is strong.” This was perhaps the key line of the speech, with Obama declaring the effects of the financial crisis and Great Recession over and the economy moving into a period of renewed strength. But it still might take a little while longer. Median family income dropped nearly 4 percent, to $51,939, in 2013, from when Obama took office in 2009, according to Census data. And while the jobless rate is in fact nearly half the 10 percent peak of October 2009, the size of the labor force has also continued to shrink through the Obama presidency. That reflects some baby boomer retirements but also the frustration of workers giving up on ever finding a decent-paying job. The labor force participation rate is now 62.7 percent, the lowest level since 1978. Wages are not really growing much either. Over the last year, average hourly wages rose just 40 cents, or 1.65 percent, to $24.57 an hour. The economy is certainly better, but the shadow of the crisis is likely to be with the U.S. for at least a couple more years. America’s allies against ISIL Obama: “We’re also supporting a moderate opposition in Syria that can help us in this effort, and assisting people everywhere who stand up to the bankrupt ideology of violent extremism.” There’s little risk for Obama to use his speech to go hard after the Islamic State of Iraq and the Levant. But in making the claim that American leadership “is stopping ISIL’s advance” with aid to future Middle East fighters, the president left out the fact that U.S. forces have not yet begun “vetting” or training the very “moderate opposition” that he eventually wants fighting in Iraq and Syria. Sure, Obama acknowledged that “this effort will take time.” And the Pentagon has said as many as 1,000 American trainers and support troops could begin deploying this month to Qatar, Turkey and Saudi Arabia to begin arming and training the Syrian fighters. But defense officials have also confirmed they haven’t cleared or recruited any of those fighters. In a best-case scenario, defense officials say, the first Syrian fighters could begin training by March, and they could be back in the fight by the beginning of 2016. Obama wants to train about 5,400 “moderate” Syrian opposition fighters in the first year, then deploy them in units that could defend their homes and villages against ISIL. Eventually the U.S. hopes these groups can take the offense against ISIL and then be part of a negotiated, political settlement to end the Syrian civil war — a deal in which President Bashar Assad would leave power. It’s been widely reported that Obama’s top national security aides have clashed behind the scenes over this strategy. In particular, outgoing Defense Secretary Chuck Hagel asked pointed questions of National Security Adviser Susan Rice about what happens when U.S.-backed fighters get into direct contact with Assad’s military. To what degree, Hagel asked, would American troops or warplanes support them? There are also open questions about whether the U.S.-backed fighters would actually follow Washington’s “ISIL-first” strategy — or whether they’d immediately go after Assad. Ultimatum on cybersecurity legislation Obama: “If we don’t act, we’ll leave our nation and our economy vulnerable. If we do, we can continue to protect the technologies that have unleashed untold opportunities for people around the globe.” Talk about setting himself up for failure. For starters, there are no guarantees, even with the best-written bill, that hackers can be stopped from wreaking havoc on government departments or private companies. Cyber-attackers don’t need to be all that sophisticated to succeed — sometimes it’s enough to be lucky, or to pick a weak target. Privacy activists are also far from enthusiastic about Obama’s proposals, including one that would expand information sharing between the government and private sector. Mindful of what Edward Snowden exposed in 2013 about the National Security Agency, they are concerned about private information making its way from the Department of Homeland Security into the hands of government surveillance or law enforcement agencies. White House officials insist they would have privacy protections in place. But Snowden’s revelations haven’t exactly left much goodwill and faith in such assurances. There are also plenty of questions about whether the information sharing is really necessary. Obama’s proposed Computer Fraud and Abuse Act may very well make things much worse for hackers — a good thing if you happen to be a federal prosecutor confident in government law enforcement and who wants an even larger stick. But it’s a frightening thing for many in the security community who say innocent behavior would be criminalized as a result. Charlie Hebdo condemnation Obama: “As Americans, we respect human dignity, even when we’re threatened. … It’s why we continue to reject offensive stereotypes of Muslims — the vast majority of whom share our commitment to peace.” The White House has spoken out against anti-Muslim messages in the past, but its voice wavered recently in the wake of the deadly attack on the satirical French publication Charlie Hebdo. The magazine published a raft of cartoons in recent years mocking Muhammad, the central prophet in Islam. Back in 2011, then-White House press secretary Jay Carney questioned the wisdom and perhaps the taste of sketches of Muhammad in the same magazine. “Obviously, we have questions about the judgment of publishing something like this. We know that these images will be deeply offensive to many and have the potential to be inflammatory,” Carney said at the time. “We don’t question the right of something like this to be published. We just question the judgment behind the decision to publish it.” Obama said nothing about anti-Muslim stereotyping in his public remarks right after the Paris attacks. And current White House press secretary Josh Earnest talked in general terms about the duties of publishers, but he did not repeat Carney’s earlier, direct criticism of Charlie Hebdo. “It would not be the first time that there has been a discussion in this country about the kinds of responsibilities that go along with exercising the right to freedom of speech,” Earnest said a couple of days after the attacks. “In the circumstances in which my predecessor was talking about this issue, there was a genuine concern that the publication of some of those materials could put Americans abroad at risk, including American soldiers at risk.” Obama did try to couple the expression of concern for Muslims on Tuesday with a comment aimed at those more concerned about free expression, quickly adding that part of American values is to “defend free speech.” What’s your definition of “advanced economies”? Obama: “Since 2010, America has put more people back to work than Europe, Japan and all advanced economies combined?.” Hate to be technical here, but Obama’s choice of words here makes a difference. According to PolitiFact, the International Monetary Fund classifies 36 countries as advanced economies, and seven of those — the G7 — as major advanced economies. The number of people employed in the U.S. has grown by roughly 6 million people since 2009. That’s much more than the other G7 countries — Canada, France, Germany Italy, Japan and the UK combined. But the president didn’t say “major advanced economies.” He said “advanced economies.” U.S. job growth exceeds the combined job growth of the 36 advanced economies, but only if you exclude Hong Kong and Taiwan. And remember, job growth since 2009 would be greater than job growth since 2010. Blowing in the wind Obama: “America is No. 1 in wind power.” We’re No. 1! Or No. 2 — depending on how the wind blows. The U.S. gets more electricity from wind power than China, at least in 2013. The U.S. produced 167 billion kilowatt-hours from wind power in 2013, significantly more than China’s 138 billion kilowatt-hours of wind electricity that year, according to the American Wind Energy Association. For the first three quarters of 2014, the U.S. got 133.5 billion kilowatt-hours of electricity from wind power, according to the most recent data available from the Energy Information Administration. That’s 7.7 percent more than the 124 billion kilowatt-hours of wind electricity produced over the same period of 2013. But China leads on total installed capacity, according to the Global Wind Energy Council. As of the end of 2013, China had a total of 91,412 megawatts of wind power capacity installed, more than a quarter of the entire world’s installed wind capacity. The U.S. trailed in second place with 61,091 megawatts installed, just over 19 percent of the world’s total. China may have added as much as 20,000 new megawatts of wind power in 2014, which would be a record, according to an October Bloomberg report. The American Wind Energy Association has not yet released full-year 2014 data, but in the first three quarters of last year the U.S. added only 1,254 megawatts, bringing total U.S. capacity to around 62,300 megawatts. U.S. installations peaked in 2012, but have been significantly less since then because of uncertainty over the production tax credit. Obama can gloat that the U.S. does beat out Germany (34,250 megawatts of capacity), Spain (22,959 megawatts) and India (20,150 megawatts). An understatement on the newly insured Obama: “In the past year alone, about 10 million uninsured Americans finally gained the security of health coverage.” There are a lot of surveys — and disputes — about how many people got covered because of the Affordable Care Act, but the 10 million newly insured may well be an understatement. The president’s figures are supported by a New England Journal of Medicine study published in July. Using Health and Human Services data and Gallup polling, the researchers calculated that about 10.3 million previously uninsured people had gained coverage through the exchanges and Medicaid. That doesn’t include people who began signing up in the second enrollment season, which began in November and runs through Feb. 15. Other studies that came out during the summer offered similar estimates, including a Commonwealth Fund report pegging the newly insured at 9.5 million. A Gallup poll estimated the national uninsured rate dropped to 12.9 percent in the fourth quarter of 2014. Ben White, Josh Gerstein, Marianne LeVine, Alex Guillén and Sarah Wheaton contributed to this report. ||||| During his 2015 State of the Union address, President Obama acknowledged the nation's struggles over the past 15 years, but said it is time "we turn the page." (AP) A State of the Union address is often difficult to fact-check, no matter who is president. The speech is a product of many hands and is carefully vetted, so major errors of fact are relatively rare. But State of the Union addresses often are very political speeches, an argument for the president’s policies, so context is sometimes missing. Here is a guide through some of President Obama’s most interesting claims, in the order in which he made them. There are some statements we are still checking and so will publish additional information in the coming days. As is our practice with live events, we do not award Pinocchio rankings, which are reserved for complete columns. “Over the past five years, our businesses have created more than 11 million new jobs.” The low point in jobs was reached in February 2010, and there has indeed been a gain of more than 11 million private-sector jobs since then, according to Bureau of Labor Statistics data. Note that the president carefully referred to “businesses,” as in the same period the number of federal, state and local government jobs has actually declined by more than 500,000. So adding in government jobs slightly reduces the total number of new nonfarm jobs to 10.7 million jobs. While Obama has touted what he often calls the “longest stretch of uninterrupted private sector job growth” in U.S. history, the average number of jobs created in this period is significantly lower than under either Bill Clinton or Ronald Reagan. (When you exclude a single month of decline, in fact, Clinton and Reagan had streaks of 85 and 71 months, respectively.) Still, the president finally has some bragging rights about the state of the economy. With the rate of job creation averaging almost 250,000 jobs a month in 2014, this is the first State of the Union address given by Obama in which the number of jobs in the United States is actually higher than when the recession began in December 2007. Even with the massive jobs losses at the start of his presidency, Obama can claim that nearly 6.4 million jobs were added since he took office. At this point in George W. Bush’s presidency, the comparable number was 4.5 million – and for Bill Clinton and Ronald Reagan, the figure was 18 million and 9.4 million, respectively. “Thanks to lower gas prices and higher fuel standards, the typical family this year should save $750 at the pump.” This looks like a big number, but it comes out of the Short-Term Energy Outlook published this month by the Energy Information Administration: “The average household is now expected to spend about $750 less for gasoline in 2015 compared with last year because of lower prices.” Although that report did not specifically cite Obama’s fuel-efficiency standards, a December EIA report (predicting an annual savings of $550) said “lower fuel expenditures are attributable to a combination of falling retail gasoline prices and more fuel-efficient cars and trucks that reduce the number of gallons used to travel a given distance.” “Today, our younger students have earned the highest math and reading scores on record. Our high school graduation rate has hit an all-time high. And more Americans finish college than ever before.” In his statement on “younger students,” Obama likely is referring to the National Assessment of Educational Progress report on fourth- and eighth-grade reading and math scores. The Nation’s Report Card, released in 2013, showed improvement in national math and reading tests administered by the federal government every two years. The 2013 reading score was the highest among all previous assessments for students in eighth grade. For fourth-graders, the 2013 reading score was the highest out of all previous years except for 2011. Still, the biennial increases in fourth- and eighth-grade students’ reading and math scores during Obama’s administration have been incremental. For high school graduation rates, Obama’s claim is on point. The data on average public high school graduation and dropout rates are collected by the Department of Education’s National Center for Education Statistics. For the class of 2011-2012, 81 percent of public high school students graduated. It was the highest percentage of high school graduates since 1995. The geographical breakdown shows 22 states had a graduation rate of 80 percent or higher, and another 22 states had a graduation rate of 70 to 79.9 percent. Seven states had a graduation rate of less than 70 percent. U.S. high school dropout rates reached record lows, according to the Pew Research Center. As our colleague Lyndsey Layton pointed out, the high school graduation rate is just one measure of success. Despite the high percentages in the report, there were disparities in graduation rates based on socioeconomic status, race and ethnicity. When it comes to college graduation rates, however, there is some context missing in his statement. Obama said “more Americans finish college than ever before.” Education Department data show a steady increase in graduation rates for first-time, full-time bachelor’s-degree-seeking students at four-year colleges, from the class of 1996 to the class of 2006. However, recent studies show an increase in the number of students graduating in six years rather than four. Graduating in six years is more expensive for students and adds to their debt. In addition, the Education Department records do not take into consideration a separate category of students: transfer students. — Michelle Ye Hee Lee “Forty-three million workers have no paid sick leave — 43 million.” This statistic comes from Labor Department survey released in September, which found that 39 percent of 109 million private sector workers were not given paid sick leave. That adds up to 43 million workers. “Our deficits cut by two-thirds” The improvement in the economy, coupled with the spending cuts in the sequester, has yielded a significantly lower deficit than just a few years ago. The deficit for the fiscal year that ended Sept. 30 was $483 billion, a decline of nearly $200 billion from the year before. For economists, raw numbers mean less than the percentage of the gross domestic product, and here, too, there has been an improvement. As a percentage of the GDP, the deficit in fiscal year 2014 was 2.8 percent, the lowest level since 2007. For fiscal year 2009, when Obama took office, the deficit was 9.8 percent, so that’s a 71 percent reduction. Interestingly, Obama’s 2010 budget, introduced in 2009 when deficits were soaring, predicted that the deficit in 2014 would be $535 billion and 2.9 percent of GDP — meaning the administration beat its five-year deficit target. “Thanks to a growing economy, the recovery is touching more and more lives. Wages are finally starting to rise again. We know that more small-business owners plan to raise their employees’ pay than at any time since 2007.” A December 2014 survey by the National Federation of Independent Businesses reported the highest Small Business Optimism Index since October 2006. The survey found a seasonally adjusted net 17 percent of businesses planned to raise wages in coming months – a two-percentage-point increase from the previous month. Three percent of businesses reported reductions in worker compensation, compared with 24 percent that reported a boost in compensation. The net 25 percent of businesses reporting higher wages was up four percentage points from the previous month. But it is too early to say that this positive response from small businesses means “wages are finally starting to rise again.” According to the Bureau of Labor Statistics, the seasonally adjusted average hourly earnings in December 2014 for all businesses was $24.57 – just 40 cents higher than December 2013. Average weekly earnings between December 2013 and December 2014 increased by 2.5 percent. However, the median weekly earnings between third-quarter 2013 and third-quarter 2014 remained flat. — Michelle Ye Hee Lee “Since 2010, America has put more people back to work than Europe, Japan and all advanced economies combined.” Once again, the president relies on a data point from 2010; after all, in 2009, the United States was shedding hundreds of thousands of jobs a month in the early days of his presidency. He also uses a somewhat unusual phrase — “advanced economies” — because he is relying on an International Monetary Fund listing of “advanced economies” that includes some entities, such as Hong Kong, that are not considered independent countries. But it does not include such fast-growing nations as China. But under that specific data set, Obama is right. From the first quarter of 2010 through the second quarter of 2014, the United States created 7.5 million new jobs — compared with 7.4 million in the other advanced economies. “Our manufacturers have added almost 800,000 new jobs.” The low point for manufacturing jobs was reached in January 2010, and there has been a gain of 786,000 jobs since then. But Bureau of Labor Statistics data show that the number of manufacturing jobs is still more than 300,000 fewer than when Obama took office in the depths of the recession — and 1.5 million fewer than when the recession began in December 2007. “In Iraq and Syria, American leadership — including our military power — is stopping ISIL’s advance.” The president can certainly make a case that progress is being made in Iraq against militants of the Islamic State (which is also known as ISIS or ISIL), but he goes too far when he lumps Syria into the same sentence. Just last week, the Wall Street Journal documented that three months of U.S. airstrikes in Syria had failed to prevent the group from expanding its territory in the country. The article quoted a senior defense office as saying that “certainly ISIS has been able to expand in Syria, but that’s not our main objective.” Col. Patrick Ryder, a spokesman for the U.S. Central Command, told the newspaper that airstrikes weren’t intended to prevent Islamic State fighters from gaining ground in most of Syria. “Gaining territorial control in Syria has never been our mission,” he said. “That wasn’t the objective of our airstrikes.” U.S. military officials have been more forthright about saying they have made progress against Islamic State in Iraq. “We’re starting to see what they’re doing is they’re trying to protect the areas they are in control of now, which I might add is some 700 square kilometers less than it was about six months ago,” Navy Rear Adm. John Kirby, the Pentagon press secretary, told reporters in January. He said he was not able to provide a breakdown as to how much was in Iraq and how much was in Syria. In another news briefing, Kirby said that Syria opposition fighters would be trained “to eventually go on the offensive against ISIL inside Syria.” “It makes no sense to spend $3 million per prisoner to keep open a prison that the world condemns and terrorists use to recruit.” In fiscal 2014, the total cost of the Guantanamo Bay facility was $397 million, according to a Defense Department report. With about 155 detainees during the year, that averages out to about $2.6 million per detainee. Over the course of the past decade, the prison has cost a total of $8.2 billion, the report says. “2014 was the planet’s warmest year on record. Now, one year doesn’t make a trend, but this does – 14 of the 15 warmest years on record have all fallen in the first 15 years of this century.” Obama correctly cited research from U.S. government scientists. UPDATE: Obama earns Three Pinocchios for State of the Union remarks on Iran: “Our diplomacy is at work with respect to Iran, where, for the first time in a decade, we’ve halted the progress of its nuclear program and reduced its stockpile of nuclear material.” UPDATE: Obama earns One Pinocchio for State of the Union remarks on crime and incarceration: “For the first time in 40 years, the crime rate and the incarceration rate have come down together.” (About our rating scale) Send us facts to check by filling out this form Follow The Fact Checker on Twitter and friend us on Facebook

– Last night's State of the Union address has been described as "defiant" and "assertive," but how about "accurate"? The media this morning is questioning a few of President Obama's bigger claims. Among the shakier ones: "Our combat mission in Afghanistan is over." Not if you define "combat" as direct confrontation with the enemy. In addition to helping train Afghan forces, the US is still tasked with preventing a resurgence of al-Qaeda and other militant groups in Afghanistan, Politico reports. "Our economy is growing and creating jobs at the fastest pace since 1999." The US Bureau of Economic Analysis says that the most recent figures available—for the third quarter of last year—show the real GDP was growing at an annual rate of 5.0%. It was actually higher than that in 2003, at 6.9%, and 2000, at 7.8%. And regarding the speed of job growth, that appears to have been a reference to a preliminary, not a final, figure for 2014, USA Today reports. "Since 2010, America has put more people back to work than Europe, Japan, and all advanced economies combined." Well, that figure comes from the International Monetary Fund's list of “advanced economies," which includes some spots, like Hong Kong, that aren't independent countries—and it doesn't count China, the Washington Post reports. "We can continue to protect the technologies that have unleashed untold opportunities for people around the globe." This line in cybersecurity is highly questionable, Politico reporters write: "There are no guarantees, even with the best-written bill, that hackers can be stopped from wreaking havoc on government departments or private companies." "In the past year alone, about 10 million uninsured Americans finally gained the security of health coverage." Here, Obama may actually be underselling himself, Politico reports. The study in the New England Journal of Medicine that offers the 10 million figure doesn't include sign-ups under ObamaCare since November.

SECTION 1. SHORT TITLE. This Act may be cited as the ``ATM Public Safety and Crime Control Act''. SEC. 2. ENHANCED SECURITY MEASURES REQUIRED AT DEPOSITORY INSTITUTIONS. (a) Banks and Savings Associations.--Section 3 of the Bank Protection Act of 1968 (12 U.S.C. 1882) is amended by adding at the end the following new subsection: ``(c) Enhanced Surveillance Requirements.--With respect to each surveillance camera which a depository institution is required to maintain under the regulations prescribed under subsection (a), each Federal supervisory agency shall prescribe, on the basis of recommendations made by the Director of the Federal Bureau of Investigation pursuant to section 540C(c) of title 28, United States Code, regulations which require the depository institution to-- ``(1) provide lighting and a surveillance camera of sufficient quality to produce surveillance pictures which can be used effectively as evidence in a criminal prosecution of illegal activities at the location monitored by the camera; and ``(2) operate such camera in a manner which does not compromise the quality of the surveillance pictures.''. (b) Credit Unions.--Section 205(e) of the Federal Credit Union Act (12 U.S.C. 1785(e)) is amended-- (1) by redesignating paragraph (3) as paragraph (4); and (2) by inserting after paragraph (2), the following new paragraph: ``(3) Enhanced surveillance requirements.--With respect to each surveillance camera which an insured credit union is required to maintain under the regulations prescribed under paragraph (1), the Board shall prescribe, on the basis of recommendations made by the Director of the Federal Bureau of Investigation pursuant to section 540C(c) of title 28, United States Code, regulations which require the credit union to-- ``(A) provide lighting and a surveillance camera of sufficient quality to produce surveillance pictures which can be used effectively as evidence in a criminal prosecution of illegal activities at the location monitored by the camera; and ``(B) operate such camera in a manner which does not compromise the quality of the surveillance pictures.''. SEC. 3. STUDY AND TECHNICAL RECOMMENDATIONS BY FBI. (a) In General.--Chapter 33 of title 28, United States Code, is amended by adding at the end the following: ``Sec. 540C. Technical recommendations on surveillance equipment ``(a) Review of Crime Prevention Standards and Procedures.--In order to reduce the incidence of crimes under section 2113 of title 18, other violations of such title, and other criminal activity on the property of or in the vicinity of financial institutions (as defined in section 20 of such title) and to facilitate more effective prosecutions of such crimes, the Director of the Federal Bureau of Investigation shall periodically review the standards and procedures applicable with respect to security requirements established under section 3 of the Bank Protection Act of 1968 and section 205(e) of the Federal Credit Union Act. ``(b) Consultation With Attorney General.--In conducting any review under subsection (a), the Director of the Federal Bureau of Investigation shall consult with the Attorney General to ascertain the extent to which inadequate security measures, or improperly maintained security equipment, at financial institutions has hindered effective prosecutions under section 2113 of title 18, United States Code, or other criminal provisions. ``(c) Recommendations.--Before the end of the 6-month period beginning on the date of the enactment of the ATM Public Safety and Crime Control Act and at such times after such date as the Director of the Federal Bureau of Investigation may determine to be appropriate, the Director shall make technical recommendations to the Federal banking agencies (as defined in section 3 of the Federal Deposit Insurance Act) and the National Credit Union Administration Board on standards and procedures for meeting the purposes of section 3 of the Bank Protection Act of 1968 and section 205(e) of the Federal Credit Union Act.''. (b) Report to Judiciary Committees.--The Director of the Federal Bureau of Investigation shall submit a copy of any recommendations made in accordance with section 540C(c) of title 28, United States Code, to the Committee on the Judiciary of the House of Representatives and the Committee on the Judiciary of the Senate at the same time such recommendations are transmitted to the Federal banking agencies and the National Credit Union Administration Board in accordance with such section. (c) Clerical Amendment.--The table of sections for chapter 33 of title 28, United States Code, is amended by inserting after the item relating to section 540B the following new item: ``540C. Technical recommendations on surveillance equipment.''. SEC. 4. INITIAL IMPLEMENTATION OF REGULATIONS. (a) Timetable for Regulations.--The Federal banking agencies and the National Credit Union Administration Board shall prescribe final regulations pursuant to section 3(c) of the Bank Protection Act of 1968 and section 205(c)(3) of the Federal Credit Union Act, respectively, before the end of the 6-month period beginning on the date the technical recommendations of the Director of the Federal Bureau of Investigation are received by such agencies in accordance with section 540C(c) of title 28, United States Code. (b) Effective Date of Regulations.--The regulations referred to in subsection (a) shall require depository institutions and credit unions to achieve compliance with such regulations by the end of the 6-month period beginning on the date the final regulations are published in the Federal Register. SEC. 5. AMENDMENTS TO DEFINITIONS. Section 2 of the Bank Protection Act of 1968 (12 U.S.C. 1881) is amended to read as follows: ``SEC. 2. DEFINITIONS. ``The following definitions shall apply for purposes of this Act: ``(1) Depository institution.--The term `depository institution' has the meaning given to such term in section 3(c) of the Federal Deposit Insurance Act. ``(2) Federal supervisory agency.--The term `Federal supervisory agency' has the meaning given to the term `appropriate Federal banking agency' in section 3 of the Federal Deposit Insurance Act.''.

ATM Public Safety and Crime Control Act - Amends the Bank Protection Act of 1968 and the Federal Credit Union Act to direct each Federal banking supervisory agency and the National Credit Union Administration Board (NCUAB), respectively, to require a depository institution to: (1) provide lighting and a surveillance camera of sufficient quality to produce surveillance pictures which can be used effectively as evidence in a criminal prosecution of illegal activities at the location monitored by the camera; and (2) operate such camera in a manner which does not compromise the quality of the surveillance pictures.Amends the Federal Judicial Code to instruct the Director of the Federal Bureau of Investigation to: (1) periodically review the standards and procedures applicable to such surveillance and security requirements; and (2) make technical recommendations to the Federal banking agencies and the NCUAB on standards and procedures to implement this Act.Sets forth a timetable for the Federal banking agencies and the NCUAB to prescribe final regulations that require depository institutions and credit unions to achieve compliance with this Act.

a technique known as the colony overlay procedure for peptidases ( copp assay ) was previously developed as the first test to enumerate total vibrionaceae in shellfish , seawater , and well water [ 1 , 2 ] . this assay has been recommended for use in monitoring molluscan shellfish and for potentially regulating their harvest based on the levels of total vibrionaceae . this total vibrionaceae approach is similar in concept to traditional sanitary surveys of shellfish harvesting areas , which are based on the total number of fecal coliforms or e. coli present in either the shellfish or their surrounding waters [ 3 , 4 ] . in the original copp assay , a substrate , l - lysyl-7-amino-4-trifluoromethylcoumarin ( l - lys - afc ) , is bound to a cellulose acetate membrane and the membrane is overlaid for 10 minutes onto an overnight culture grown on nonselective agar media . a lysyl aminopeptidase that is present in all vibrionaceae family members tested to date cleaves the substrate to produce fluorescent foci on the membrane when viewed under longwave uv . in the present study , we extended this overlay concept to produce similar assays for total and fecal e. coli . these assays are based on the presence of -glucuronidase ( gud ) activity , which is found in most non - o157:h7 e. coli and results in cleavage of the substrate 4-methyl--d - glucuronide ( mug ) into the fluorescent 4-methylumbelliferone . mug - based fluorescence assays for e. coli have been previously developed for food and water [ 612 ] . mug - based assays of foods and particularly molluscan shellfish often involve the most probable number ( mpn ) procedure , which is labor intensive , relatively costly , and requires up to three days for results to be obtained . consequently , simpler , more rapid , less expensive , and more direct enumerative procedures are needed to monitor for total and fecal e. coli , particularly in perishable foods , like shellfish . in this study , we report on simple membrane overlay methods to separately enumerate total e. coli ( capable of growing at 37c ) , fecal e. coli ( capable of growing at 44.5c ) , and total vibrionaceae ( capable of growing at 37c ) , and a fourth multiplex method to enumerate total e. coli and total vibrionaceae simultaneously . these methods are applicable for use in monitoring the presence of these organisms in shellfish and other foods , water , and environmental samples . stock cultures consisted of 37 strains of non - o157:h7 e. coli , as described in table 1 , and 22 enterobacteriaceae within the genera citrobacter , klebsiella , pseudomonas , salmonella , shigella , serratia , and yersinia ( table 2 ) . human pathogenic vibrios consisted of v. cholerae o1 and v. vulnificus ( vv1003 ) , as previously described , and v. parahaemolyticus o3:k6 , a pandemic strain obtained from e. fidelma boyd at the university of delaware , newark , delaware . eastern oysters ( crassostrea virginica ) were obtained from a commercial source in rhode island and from a tidal river at the university of delaware marine laboratory in lewes , delaware . the oysters were naturally contaminated with low levels of e. coli and moderate levels of vibrionaceae . they were collected principally during the warm , summer months when vibrionaceae were present in the water column . seawater was also obtained from the university of delaware marine laboratory during the summer . the mpn procedure using mug in the ec broth tubes was performed on dilutions of pure cultures and on seawater and oyster homogenates according to the protocol published in the u.s . the mug membrane overlay procedure was developed and its specificity was determined using e. coli serotypes and other enterobacteriaceae as listed in tables 1 and 2 . the bacteria were grown in tryptic soy broth ( becton , dickinson and co. , sparks , maryland ) supplemented with an additional 0.5% nacl ( 1% total nacl ) and were streaked onto 100 mm plates of tryptic soy agar ( becton , dickinson and co. ) containing a total of 1% nacl ( tsa - n ) using a flamed and cooled metal triangle . plates were incubated overnight ( ~18 hours ) at 37c . after culture incubation , cellulose chromatography papers ( whatman international , maidstone , uk ) or whatman no . 1 , 4 , or 54 cellulose filter paper discs ( referred to as cellulose membranes ) were cut to the desired size ( of the petri dish or colonies to be overlaid ) and soaked in 20 mm tris buffer , ph 8.0 containing 50 mg / l mug for about 10 seconds . excess buffer was allowed to drip from the membranes for 5 seconds , and the membranes were overlaid onto colonies growing on the surface of the tsa - n plates . unused substrate was retained at 4c for future use and has a shelf life of several weeks . membranes were removed with forceps and placed in empty petri dishes and examined for fluorescent foci using either a hand - held uv lamp at a wavelength of 364 nm or a uv light box at the same wavelength . alternatively , membranes could be viewed with the hand - held uv lamp while still overlaying the colonies . the copp assay was performed with cellulose acetate membranes as previously described [ 1 , 2 ] or with cellulose chromatography paper ( whatman international ) . in essence , a substrate l - lysyl-7-amino-4-trifluoromethylcoumarin ( l - lys - afc ; cat . afc-008 , mp biomedicals , salon , oh ) was dissolved in dimethylsulfoxide ( dmso ) to 20 mm ( 2140 l of dmso to 25 mg of l - lys - afc ) and the stock was stored at 20c until needed . a 250 m substrate working solution was prepared by combining 25 l of thawed substrate and 2 ml of 20 mm tris , ph 9.0 . substrate stock solution may be refrozen and thawed multiple times without appreciable deterioration of the substrate . a cellulose acetate membrane or a plain cellulose membrane ( chromatography paper ) was cut to the desired size and placed in the working solution for 1015 seconds . the membrane was lifted with forceps , allowed to drip excess fluid for 5 seconds , and overlaid onto overnight bacterial colonies grown at 37c on tsa - n plates . each membrane was removed from the plate , placed in a clean petri dish , immediately viewed under longwave ( 364 nm ) uv , and fluorescent foci were counted . alternatively , the foci could be visualized with a hand held uv lamp while the membrane was still covering the colonies . the appearance of bright white or pale blue fluorescence on cellulose acetate membranes or green fluorescence on cellulose chromatography paper signifies the presence of a lysyl aminopeptidase , which cleaves the substrate . positive controls consisted of v. cholerae , v. parahaemolyticus , and v. vulnificus and were propagated at 37c . the overlay of enterobacteriaceae was also performed at 37c for 10 minutes to determine if any of the species contained a lysyl aminopeptidase activity similar to that found in the vibrionaceae . a method to simultaneously detect total vibrionaceae and total e. coli was evaluated using cellulose chromatography paper that was soaked in 20 mm tris , ph 8.0 containing 250 m l - lys - afc and 50 mg / l mug . oysters were either 1 : 10 homogenates or dilutions of the homogenates that were prepared in 0.1% peptone buffer . plates were prepared using 100 l of each homogenate or dilutions of the homogenates , which were spread over tsa - n plates with a flamed and cooled metal triangle . after overnight incubation at 37c , membranes containing both substrates were overlaid onto the culture plate . vibrionaceae were enumerated in situ after 10 minutes followed by the enumeration of mug - positive ( gud - positive ) colonies after an additional 20 minutes ( 30 minutes total ) . it was anticipated that total e. coli could be easily distinguished from total vibrionaceae based on the color of the fluorescent foci . forty - three principally food - borne outbreak strains of e. coli o157:h7 were screened for gud activity by both the mpn - mug assay and by the mug overlay of colonies that were grown on tsa - n and incubated at 37c for 2 hours followed by 44.5c overnight . plates were overlaid for 30 minutes and the membranes were viewed on a uv light box . oysters and seawater were screened by the membrane overlay assay for total e. coli and total vibrionaceae and by multiplex assays for both by spread plating 100 l of a 1 : 10 or 1 : 100 oyster homogenate , prepared in 0.1% peptone buffer , or 100 l of undiluted seawater onto tsa - n plates . the plates were allowed to incubate at either 37c for total e. coli and total vibrionaceae overlays or at 37c for 2 hours followed by 44.5c overnight for e. coli overlays using cellulose membranes containing mug and copp separately and combined . samples were occasionally plated in duplicate and one plate incubated at 37c for the multiplex assay of total vibrionaceae and total e. coli while the other plate was incubated at 37c for 2 hours and then at 44.5c overnight for fecal e. coli enumeration . initial tests showed that overnight colonies of e. coli growing on tsa - n plates could be overlaid with cellulose membranes ( chromatography paper or whatman no . 1 , 4 , or 54 filter paper discs ) soaked in mug to produce strong blue fluorescent foci on the membranes , corresponding with the site of contact between the colony and the membrane . comparable results were obtained regardless of which type of membrane was used . consequently , we selected the chromatography paper to perform mug overlays throughout this study . an evaluation of substrate concentrations showed that strong fluorescence intensity was achieved when membranes were saturated in 50 mg / l mug . membranes were incubated for 1560 minutes , and then viewed for fluorescent foci in situ with a hand - held uv lamp , or the membrane could be removed to a petri dish and viewed with the hand - held uv lamp or placed on a uv light box for viewing . optimal results were obtained after a 3060-minute overlay and 30 minutes was selected for the remainder of the study . in contrast , colonies to be screened for total vibrionaceae by the copp assay were saturated in 250 m of l - lys - afc and overlaid for only 10 minutes to preclude weak enzyme activity , which is present in some enterobacteriaceae and other non - vibrionaceae , from producing false positive fluorescent foci . figures 1(a)1(d ) show mug and copp fluorescence on cellulose membranes after overlaying colonies of three serotypes of non - o157 : h7 e. coli ( top row in each panel ) and three vibrionaceae ( bottom row in each panel ) . edges of the foci are not distinct and sharp , but somewhat fuzzy because enzyme activity is via diffusion of the enzymes within the membranes . examples of representative mug fluorescence on the membranes are shown for total e. coli that had been incubated at 37c overnight and overlaid for 30 minutes with mug - containing membranes ( figure 1(a ) ) , and for fecal e. coli grown at 37c for 2 hours , incubated overnight at 44.5c , and overlaid for 30 minutes with a mug membrane ( figure 1(b ) ) . these same vibrios are strongly copp positive after overnight incubation at 37c and overlay for 10 minutes with l - lys - afc , producing green fluorescence on cellulose membranes , as depicted in figure 1(c ) . very weak copp fluorescence is occasionally observed in the e. coli ( arrow , figure 1(c ) ) , and such foci should not be counted as vibrionaceae because of the weak signal . this fluorescence may be minimized by enumerating the foci immediately after the 10-minute overlay . results of the multiplex assay on cultures incubated at 37c overnight , followed by a 30-minute overlay with mug and l - lys - afc ( combined ) are shown in figure 1(d ) with blue fluorescence from the e. coli on the top row and green fluorescence from the vibrios on the bottom row . the arrow in figure 1(d ) indicates the blockage of uv light from an opaque colony of v. parahaemolyticus which inadvertently transferred to the membrane and blocked the passage of the uv light from the light box through the membrane . such transfer of opaque colonies to the membranes occasionally occurs and appears to be a function of the stickiness of the colony . in such cases , foci may be readily observed by holding a hand - held uv lamp on the opposite side of the membrane ( the side without the opaque material ) . the mug overlay and the mpn - mug assays were compared for 37 strains of e. coli ( non - o157:h7 ) . twenty - four ( 65% ) of the 37 strains were positive by the mug overlay and 23 ( 62% ) were positive by the mpn - mug assay ; however , four colonies that were mug - negative by overlay were positive or weakly positive by the mpn - mug method , specifically strains o14:nm , o42:h2 , o103:h2 , and o111:nm ( table 1 ) . likewise , five isolates that were mug - negative according to the mpn - mug method were positive by the overlay method , specifically one each of the o4:nm and o26:h11 strains , and o78:h11 , o91:h , and o91:h14 ( table 1 ) . mpn - mug often gave weak fluorescence signal ( listed as in table 1 ) . repeat assays of these isolates showed variability in the perceived fluorescence intensities for those cultured in mpn - mug media . no variability was seen on the overlays , which consistently produced bright blue foci . copp overlays of these cultures were performed for 10 minutes with readings taken immediately after overlay , and weakly positive results were obtained for four of the isolates ( table 1 ) . differentiation of the shigella spp . was possible using individual mug and copp assays where one sh . boydii was both mug and copp positive , sh . flexneri was both mug and copp negative , sh . dysenteriae was mug negative and copp positive , and sh . sonnei was mug positive and copp negative with cultures propagated at 37c ( table 2 ) . shigella boydii , sh . dysenteriae , and y. enterocolitica were copp positive indicating an enzyme analogous to the lysyl aminopeptidase that was found in vibrionaceae family members . this is the first time we detected strong copp positive colonies associated with bacteria that were unrelated to the vibrionaceae . forty - three e. coli o157:h7 strains were tested in triplicate and were mug negative by both the overlay and mpn - mug assays ( data not shown ) . it is well known that o157:h7 strains lack gud activity and are therefore mug negative with few exceptions . membranes simultaneously soaked in mug and l - lys - afc were used in a multiplex format to detect total e. coli and total vibrionaceae on plates that were grown overnight at 37c ( figures 1(e ) and 1(f ) ) . in the multiplex assay of oyster homogenates , green and dark blue foci are obtained for vibrionaceae and total e. coli , respectively , when incubated at 37c ( figures 1(e ) and 1(f ) ) . for accurate enumeration , fluorescent foci must be counted in stages . membranes were incubated for 10 minutes on the plates and viewed with a hand - held uv . green fluorescent foci , representing the vibrionaceae colonies , were counted immediately , to avoid low levels of enzymes in some non - vibrionaceae from leading to false positive results . the plate was then incubated for an additional 20 minutes or longer at 37c for blue fluorescence development , which is indicative of colonies of total e. coli . for illustration purposes only , membranes shown in figures 1(e ) and 1(f ) were illuminated on a uv light box and photographed after a 30-minute overlay , which was sufficient to give bright blue fluorescence from the gud - positive colonies but was longer than recommended for accurate vibrionaceae enumeration . simultaneous detection is only practical if countable levels of total e. coli and total vibrionaceae are present on the same dilution plate , although figures 1(e ) and 1(f ) demonstrate the ease with which total e. coli colonies may be identified , even on crowded plates . multiplex assays are not appropriate for cultures incubated at 44.5c , since many vibrionaceae may not grow at elevated temperatures . one exception was our v. cholerae o1 which produced typical copp fluorescence when grown at 44.5c . if total vibrionaceae and total and fecal e. coli enumeration are desired for a sample , duplicate plating allows one plate to be incubated at 37c for total vibrionaceae and total e. coli while the other plate is incubated at 37c for 2 hours and then at 44.5c overnight for fecal e. coli enumeration . the 2 hours incubation at 37c constitutes a resuscitation step , as oysters may contain stressed bacteria which need to be resuscitated . higher e. coli counts were obtained in our assays when the resuscitation step was employed . from a safety standpoint , the mug assay offers additional protection against pathogens , by detecting some strains of salmonella and shigella which were mug positive and could grow at 44.5c , specifically , s. montevideo , sh . seawater produced bacterial colonies that gave a fluorescence signal comparable to that found in oyster homogenates for total and fecal e. coli and total vibrionaceae ; however , the levels of bacteria were generally 10- to 100-fold less than in filter - feeding molluscan shellfish , which bioconcentrate bacteria from the seawater within their edible tissues . by definition , fecal coliforms , including fecal e. coli , are gram - negative bacteria which ferment lactose with the production of acid and gas at 44.545.5c . such organisms are indicative of human gut bacteria and can be used as indicators for the possible presence of human fecal pathogens in foods and water . the mpn procedure capitalizes on the use of lactose - containing media , the collection of gas , and growth at 44.545.5c , so that positive isolates meet the classical definition for fecal coliforms . mpn - mug procedures use mug as an indicator for the presence of e. coli , since e. coli are the primary producers of gud at these elevated temperatures ; therefore , positive mpn results in the presence of mug are considered confirmatory for the presence of e. coli . current mpn assays for total and fecal coliforms , or e. coli , are tedious , costly , and time consuming . the incorporation of mug into ec broth for the mpn detection of e. coli has hastened the analysis over previous mpn methods but is still complex and produces false positives which can compromise results . according to the u.s . food and drug administration 's bacteriological analytical manual , the mpn - mug assay requires the use of new borosilicate glass tubes as well as new gas collection ( durham ) tubes and the tubes must be prescreened for fluorescence , as some tubes exhibit autofluorescence . in our hands , autofluorescence was a problem and may have contributed to the weakly positive mpn - mug results for e. coli o14:nm , o42:h2 , o103:h2 , and o111:nm , which were consistently negative by the mug overlay procedure ( table 1 ) . in the united states , oysters and their growing waters are monitored for fecal coliforms or e. coli using a 5-tube mpn approach , which means that 1530 or more new tubes may be required for a single analysis , depending on the number of dilutions required and the number of presumptive positive tubes that need to be transferred from lauryl sulfate tryptose broth to ec broth , thus making this procedure costly and impractical for routine use . since one of the major obstacles in monitoring for environmental contamination and food safety is the lack of practical and cost effective assays , our goal was to produce simple , more rapid , and inexpensive procedures to enhance monitoring efforts . this paper provides new tools to monitor for total and fecal e. coli and total vibrionaceae levels . in this study , we developed a simple plate cultivation and mug - membrane overlay technique to detect bacteria that are likely fecal e. coli based on gud production and their ability to grow at 44.5c . for our overlay procedure for total e. coli , we recognize that occasional pathogens other than e. coli may be gud positive , like some salmonella and shigella strains ( table 2 ) , or some streptococci ; however , the detection of other occasional pathogens simply enhances the benefits of using this test as a potential regulatory tool . endogenous levels of gud , which are high in some fish and shellfish [ 8 , 17 ] , are not a problem in our plate - based membrane overlays , since the overnight incubation of the plates at either 37c or 44.5c degrades endogenous , tissue - specific enzymes well before the plate is overlaid with the membrane containing the fluorogenic substrate . consequently , in the many assays we performed on oysters , we saw no background fluorescence , even though oyster tissues are known to contain gud . in addition to the complexities of performing traditional mpn - based assays , analyses for vibrionaceae in seawater and shellfish are usually complex and are generally limited to picking a few isolates from a plate for complex biochemical or molecular biological testing for specific pathogenic strains . monitoring of shellfish or seawater for pathogenic vibrios has failed to stop outbreaks of v. parahaemolyticus , while routine monitoring programs for v. vulnificus are nonexistent in spite of the fact that v. vulnificus in oysters causes occasional illness and death . acceptable baseline or threshold levels of vibrionaceae and total or fecal e. coli should be determined for implementation into regulations for harvesting or distribution of shellfish . threshold levels currently exist for coliforms in harvesting area waters and shellfish meats [ 3 , 4 ] but are based on mpn approaches . no methods have been established to date for regulation of shellfish harvesting or distribution based on total vibrionaceae levels or e. coli levels using simple overlay methods . in screening 37 strains of non - o157:h7 e. coli that were associated with major foodborne outbreaks of illness , 24 ( 65% ) were positive by the mug overlay and 23 ( 62% ) were positive by the mpn - mug assay . in contrast , other studies showed the recovery of gud in 95.5% , 96.5% , and 91% of the isolates examined . potential reasons for these differences in gud distribution among the isolates were suggested by chang et al . , but there have been no conclusive studies explaining such variability . in addition to a subset of non - o157:h7 isolates that were mug negative , 43 isolates of e. coli o157:h7 that were derived from a wide variety of food - borne outbreaks were mug negative . the failure to detect o157:h7 strains is a limitation of both mpn - mug and the mug overlay methods . this finding does not lessen the importance of the mug membrane overlay procedure , since o157:h7 strains constitute a minority of the e. coli in environmental isolates and other mug - based cultural assays , like the u.s . food and drug administration - recommended mpn - mug assay for e. coli , also fail to detect the o157:h7 serotype . escherichia coli o157:h7 strains do not contain enzymatically active gud , although these strains contain the gusa ( uida ) gene , which encodes gud and two regulatory regions . there does not appear to be regulatory repression to restrict gud formation , since antibody against gud detects the enzyme ; however , the gud is in an inactive form lacking hydrolytic activity . the cause for this inactive protein is the presence of a guanosine - guanosine insertion causing a frameshift resulting in the introduction of a premature termination codon in the gusa gene in all strains of e. coli o157:h7 tested , but not in other serotypes . this mutation accounts for the presence of an incomplete protein lacking gud activity ; therefore , mug - based assays are not appropriate for the detection of o157:h7 isolates . advantages of the overlays are that they are far simpler , less expensive , and directly quantitative , unlike mpns which give statistical probabilities of counts . culturing bacteria on nonselective tsa - n also has an advantage over selective media , like mcconkey agar with or without mug , since selective media are often inhibitory to environmentally stressed bacteria . with multiplex overlays , we have consolidated assays to simplify monitoring in order to drive down costs for screening and to promote more frequent testing for total e. coli and vibrionaceae . both the mug overlay and the copp assays are relatively fast , with results derived within 24 hours . mpn assays require up to 3 days for completion ( 2448 hours incubation in lst broth followed by 24 hours in ec broth ) and additional time if e. coli confirmation via biochemical testing is desired . together , the mug and copp overlay methods provide new options for quantifying total and fecal e. coli and vibrionaceae in seawater , shellfish , and other food and environmental matrices . unlike the original copp assay , which used cellulose acetate membranes that could be prepared in advance , dried for storage , and soaked in buffer before overlay [ 1 , 2 ] , the cellulose membranes used for copp and mug assays in this paper can not be prepared in advance or dried . this is because copp substrate covalently bonds to cellulose acetate membranes , but not to plain cellulose membranes , and mug does not bind to either membrane . although we used cellulose acetate and plain cellulose membranes to screen stock cultures for lysyl aminopeptidase activity , we used cellulose membranes exclusively for multiplex assay for total coliforms and total vibrionaceae . this was because copp assays on cellulose acetate membranes produced a bright light blue fluorescence while mug produced a stronger blue fluorescence ; thus , differentiation of the two colors was difficult at times . it became clear that the green and blue fluorescence obtained on the plain cellulose membranes was easier to discriminate between than blue and light blue fluorescence on the cellulose acetate membranes . multiplex overlays for the simultaneous detection of both total e. coli and total vibrionaceae may be performed when both groups of bacteria are in relatively the same proportion ; that is , both can be enumerated from the same dilution plate . methods to monitor molluscan shellfish harvesting and distribution , much like methods for other foods , water , or environmental samples , are often outdated and out of touch with today 's needs . it is necessary to shift analytical and regulatory paradigms to simpler , more practical , and cost effective measures to monitor relative levels of contamination . given the development of simple membrane overlay assays , we propose the establishment of membrane overlay - based monitoring for total and fecal e. coli and total vibrionaceae . for routine monitoring purposes , it may be time to shift from a search for specific vibrio pathogens to the enumeration of total vibrionaceae . environmental factors responsible for increases in human pathogenic vibrios within shellfish or their growing waters will likely cause an increase in the levels of many other vibrionaceae family members , including pathogenic strains ; therefore , the copp assay could prove useful in regulating shellfish harvesting based on total vibrionaceae counts . european standards for shellfish harvesting , where coliform levels are currently used to regulate shellfish harvesting and distribution [ 3 , 4 ] . in an aquaculture setting , the simple copp assay may serve as an index of fish health and disease , where spikes in vibrionaceae levels over what is normal and customary would suggest a need for more refined assays for specific pathogens and for corrective actions to be implemented within the aquaculture or hatchery setting . membrane overlays are simple and practical for routine monitoring and could enhance food safety by allowing increased numbers of samples to be tested at a reduced cost or by providing a simple alternative to procedures that are too rigorous for routine use .

three assays were developed to enumerate total and fecal escherichia coli and total vibrionaceae in shellfish , seawater , and other foods and environmental samples . assays involve membrane overlays of overnight colonies on nonselective agar plates to detect -glucuronidase and lysyl aminopeptidase activities for e. coli and vibrionaceae , respectively . cellulose membranes containing the substrates 4-methylumbeferyl--d - glucuronide ( mug ) produced a bright blue fluorescence when overlaid onto e. coli , while l - lysyl-7-amino-4-trifluoromethylcoumarin produced green fluorescent foci when overlaid onto vibrionaceae family members . a multiplex assay was also developed for simultaneously enumerating total e. coli and total vibrionaceae in oysters and seawater . overall , 65% of overlaid e. coli ( non - o157:h7 ) were mug - positive , compared with 62% as determined by the most - probable - number - mug assay . the overlays are rapid , simple , and cost effective for quantification purposes . this research provides practical alternatives for monitoring bacterial indicators and potential pathogens in complex samples , including molluscan shellfish .

pancreatic pseudocysts developed in 23% of patients following pancreatic trauma and endoscopic retrograde pancreatography demonstrated duct injury in half of these ( grade iii pancreatic injury ) ( table 1 ) [ 13 ] . percutaneous radiologically guided drainage is an alternative but has a failure rate of 55% , and it is not suitable for the communicating mature pseudocyst . external drainage has the disadvantage that it may introduce infection and leave the patient with an external fistula [ 1 , 4 , 5 ] . endoscopic or endoscopic ultrasound ( eus)-guided drainage of pancreatic pseudocyst that bulges into the gut lumen via a cystgastrostomy , cystduodenostomy or transpapillary method is another alternative , but requires careful patient selection and skill . these methods are gaining popularity , but no randomized trials have been done to compare them with traditional methods [ 1 , 57 ] . table 1:pancreas injury scale.gradetype of injurydescription of injuryihaematomaminor contusion without duct injurylacerationsuperficial laceration without duct injuryiihaematomamajor contusion without duct injury or tissue losslacerationmajor contusion without duct injury or tissue lossiiilacerationdistal transection or parenchymal injury with duct injuryivlacerationproximal transection or parenchymal injury involving ampullavlacerationmassive disruption of pancreatic headproximal pancreas is to the patient 's right of the superior mesenteric vein.advance one grade for multiple injuries up to grade iii . a 27-year - old african woman who is non - alcoholic presented with an enlarging epigastric mass of 8-year duration following blunt abdominal trauma from a fall off a motorbike . apart from post - prandial bloating , early satiety and difficulty while lying supine , she was clinically well . physical examination revealed a tense , forward bulging , epigastric mass of 20 cm diameter with a palpable smooth upper border but impalpable lower border . blood tests revealed a raised serum amylase of 151 u / l ( normal 70300 u / l ) and a haemoglobin level of 11 g / dl ( normal 1215 ) . a computed tomography ( ct ) scan confirmed a retroperitoneal cystic mass within the body and tail of pancreas with the main differential diagnosis of a pancreatic pseudocyst ( fig . 1 ) . , a nasogastric tube was passed because gastric emptying is often impaired . following an upper midline incision , the lesser sac was entered through the gastrocolic omentum and the large , tense , smooth thick - walled mature cyst of 25 cm in diameter was found attached to the body and tail of the pancreas . a laparotomy revealed a normal gall bladder and excluded gallstones as a possible cause of the pancreatitis . taking care to avoid vessels densely adherent to the pseudocyst , a 5-cm incision of the anterior wall of the cyst with cutting diathermy drained 2.8 l of thick creamy fluid consistent with pancreatic juice . loculi within the cyst were broken down with the suction catheter ( fig . 3 ) . the upper end of a retrocolic roux loop of jejunum with its closed end was approximated to the front of the cyst without tension ( fig . side - to side two - layer anastomosis between the opening into the cyst and a longitudinal jejunostomy was fashioned . this entailed an inner all coats continuous suture of non - absorbable material ( nylon ) and an outer layer of interrupted absorbable ( vicryl ) to ensure serosal apposition ( fig . 5 ) . the distended transverse colon was decompressed by suction aspiration of colonic gas using a 22-g i.v . the patient lost 200 ml of blood and received a unit of whole blood intraoperatively . following abdominal lavage , a corrugated ( r ) paracolic drain was inserted and the midline wound closed by a mass closure technique with a monofilament non - absorbable 1.0 nylon , and interrupted nylon sutures for the skin . the nasogastric tube was removed on the second day as her serum amylase was within the normal range . her bowels moved on the second day and the drain removed on the fifth postoperative day . the patient was discharged on the 10th postoperative day and long - term follow - up planned . figure 1:ct showing a large pancreatic pseudocyst in the body and tail of pancreas bulging into the anterior abdominal wall and displacing loops of the small bowel . ct showing a large pancreatic pseudocyst in the body and tail of pancreas bulging into the anterior abdominal wall and displacing loops of the small bowel . traumatic pancreatic pseudocysts associated with peripheral ductal injury may resolve spontaneously or be treated successfully by percutaneous aspiration , whereas those associated with injuries to the proximal duct ( head of pancreas ) require internal drainage by roux - en - y cystjejunostomy . the optimal point of drainage can be inferred from the ct scan , where the cyst wall is thin and extrapancreatic but careful intraoperative assessment for dependent drainage is desirable [ 1 , 5 , 8 , 9 ] . a common misdiagnosis for pseudocysts are mucinous cystic tumours , which make 4050% of pancreatic cysts and are radiologically similar to pseudocysts . a sample of the pseudocyst wall is sent routinely for histological examination to exclude the presence of an epithelial lining and confirm that the collection was inflammatory rather than neoplastic [ 1 , 5 ] . an inferior pseudocyst that bulges through the transverse mesocolon as in this case is preferentially drained into a roux loop of jejunum . this obtains dependent drainage and excludes the cyst contents from food and bile , and should prevent activation of the pancreatic secretions until they are within the jejunum . more rarely , those at the head of the pancreas may be drained into the duodenum by a cystoduodenostomy , and those related to the tail of the pancreas are best managed by distal pancreatectomy with a splenectomy [ 2 , 3 , 5 ] . if possible , surgical intervention should be avoided until the pseudocyst is at least 6 weeks old , by which time the wall will usually be fibrotic enough to hold sutures [ 1 , 5 ] . continuous sutures are mostly used for cystgastrostomy so as to control haemorrhage from the pseudocyst wall or inflamed wall of the stomach [ 1 , 5 ] . postoperative complications may include a flare up of acute pancreatitis , haemorrhage from the suture lines or from the vessels of the wall of the pseudocyst as it collapses , pancreatic ascites , external pancreatic fistulae and recurrent pseudocyst formation [ 1 , 3 , 5 ] . the reported pseudocyst recurrence rate of 1020% following internal drainage is due either to inadequate stoma size , failure to break down loculi within the pseudocyst or to a persistent communication to the pancreatic duct [ 5 , 8 ] . the latter is characteristic of the post - traumatic pancreatic pseudocyst due to associated duct injury . after excluding a mucinous cystic tumour via an eus - guided fine needle aspiration of cyst fluid for analysis , a pancreatic sphincterotomy with or without stenting of the main pancreatic duct disruption would manage a persistent communicating pancreatic pseudocyst [ 1 , 3 , 5 , 6 , 9 ] . written informed consent was obtained from the patient for publication of the case report and any accompanying images . a copy of the written consent is available for review by the editor of this journal .

a pancreatic pseudocyst is a collection of serous fluid in relation to the pancreas following acute pancreatitis . if pancreatography is performed , most pseudocysts will be found to have a connection with the pancreatic ductal system . most will resolve spontaneously but clinically significant pseudocysts ( 5% ) may require surgical intervention . surgical ( laparoscopic or open ) direct drainage of pancreatic pseudocysts into the upper gastrointestinal tract is the mainstay of treatment with the possibility of pancreatic resection if malignancy is suspected . we report a persistent post - traumatic pancreatic pseudocyst of 8-year duration , despite recurrent percutaneous aspiration that was finally managed by a roux - en - y drainage .

the single participant of this study was a man with left severe hemiplegia resulting from a stroke six years ( 72 months ) earlier . his arm and hand were at stage 1 on chedoke - macmaster stages of movement recovery with no voluntary movement . he was 64 years old and every other rehabilitation intervention in which he participated , including fest ( without bci activation ) , had failed to produce any change in his ability to move his affected upper limb . we created a neuroprosthesis for reaching using a four - channel stimulator ( compex , switzerland ) , which was programmed to perform forward reaching ( making it possible to reach to the right knee as well ) for which the anterior deltoid and triceps brachii were stimulated , with arm retreival produced by stimulating the posterior deltoid and biceps brachii.reaching to the mouth ( which also allowed reaching to the right shoulder ) achieved by aplying stimulation to the anterior deltoid and biceps brachii , while retrieval was produced by stimulation the posterior deltoid and triceps brachii.lateral reaching produced by stimulating biceps brachii followed by anterior and posterior deltoid and finally by the triceps brachii , while retrieving was achieved by stimulating the biceps brachii muscle , discontinuing deltoid stimulation , and stimulating the triceps brachii to produce arm extension while lowering the arm . forward reaching ( making it possible to reach to the right knee as well ) for which the anterior deltoid and triceps brachii were stimulated , with arm retreival produced by stimulating the posterior deltoid and biceps brachii . reaching to the mouth ( which also allowed reaching to the right shoulder ) achieved by aplying stimulation to the anterior deltoid and biceps brachii , while retrieval was produced by stimulation the posterior deltoid and triceps brachii . lateral reaching produced by stimulating biceps brachii followed by anterior and posterior deltoid and finally by the triceps brachii , while retrieving was achieved by stimulating the biceps brachii muscle , discontinuing deltoid stimulation , and stimulating the triceps brachii to produce arm extension while lowering the arm . transitioning between movement phases ( i.e. , reach and retrieve ) could be triggered using a ttl - level signal provided by an external switch or a bci . the bci was implemented as a simple brain - switch , which was activated whenever the power within the beta range ( 13 hz- 30 hz ) of the participant s eeg decreased below a threshold , indicating the participant s intention to move his arm . this frequency range was selected by identifying spectral components displaying erd using data collected when the participant attempted repeatedly to perform hand ( palmar and lateral grasps , precision pinch , and hand opening ) movements following a ready - go - stop experimental cue . the analysis was performed using a total of 104 attempted movement repetitions and applied to six eeg electrode positions ( f3 , fz , f4 , c3 , cz , c4 of the 10 - 20 electrode placement system ) . the frequency band between 18 hz and 28 hz at the fz location were found to be the most suitable for implementing the bci . eeg recordings for this process were performed using a synamprt eeg amplifier ( compumedics , u.s.a . ) at a sampling rate of 1 khz and filtered between 0.05 hz and 40 hz . erd estimation was performed with custom - made software ( matlab , mathworks , u.s.a . ) . to create the bci , acquisition of eeg activity was performed using a desktop biopotential amplifier ( qp511 , grass telefunken , germany ) and a data acquisition system ( usb-6363 , national instruments , u.s.a . ) using a sampling frequency of 300 hz . the eeg signal from electrode fz was band - pass filtered ( 10-hz - 100 hz ) and amplified ( 20,000x ) prior to its digital acquisition . all processing was implemented using custom - made software ( labview , national instruments , u.s.a . ) . the bci estimated a moving average ( over a 500 ms period ) of the eeg rms value measured every 125 ms . for an activation to take place , the moving average had to decrease below a threshold for a pre - specified duration ( 500 ms to 1,200 ms ) . the experimenters could adjust both parameters at any moment during the operation of the system . this pulse was delivered to the neuroprosthesis for reaching where it triggered a transition in the state of the electrical stimulation ( e.g. , from active reaching to retrieving the arm ) . in addition , an external manual switch could also be used by the experimenters bypassing the bci altogether in cases in which the brain interface failed to identify the intention to move . one of them guided the arm in motion ( assisted by the electrical stimulation ) and could trigger the stimulation manually bypassing the bci completely . the second experimenter demonstrated the movement to perform at every repetition and could also adjust the bci activation parameters ( i.e. , activation threshold and latency ) . the intervention consisted of 40 90-minute sessions ( 30-minute setup and 60-minute active therapy ) delivered three times a week . during each session the participant attempted to reach to different targets ( listed above in the neuroprosthesis implementation ) repeatedly following the experimenters instructions . each movement was performed with a brief pause between phases ( i.e. , the participant would reach , hold the reaching position for a few seconds , and then return his arm to a starting position followed by a few moments of relaxation with no stimulation ) . we measured the effects of the intervention using five assessments , measured at beginning , midpoint and end of the study . the assessments were the toronto rehabilitation institute - hand function test ( trihft ) , the action research arm test ( arat ) , functional independence measure ( fim ) , self - care component of the functional independence measure , and fugl - meyer assessment upper extremity sub - score . the single participant of this study was a man with left severe hemiplegia resulting from a stroke six years ( 72 months ) earlier . his arm and hand were at stage 1 on chedoke - macmaster stages of movement recovery with no voluntary movement . he was 64 years old and every other rehabilitation intervention in which he participated , including fest ( without bci activation ) , had failed to produce any change in his ability to move his affected upper limb . we created a neuroprosthesis for reaching using a four - channel stimulator ( compex , switzerland ) , which was programmed to perform forward reaching ( making it possible to reach to the right knee as well ) for which the anterior deltoid and triceps brachii were stimulated , with arm retreival produced by stimulating the posterior deltoid and biceps brachii.reaching to the mouth ( which also allowed reaching to the right shoulder ) achieved by aplying stimulation to the anterior deltoid and biceps brachii , while retrieval was produced by stimulation the posterior deltoid and triceps brachii.lateral reaching produced by stimulating biceps brachii followed by anterior and posterior deltoid and finally by the triceps brachii , while retrieving was achieved by stimulating the biceps brachii muscle , discontinuing deltoid stimulation , and stimulating the triceps brachii to produce arm extension while lowering the arm . forward reaching ( making it possible to reach to the right knee as well ) for which the anterior deltoid and triceps brachii were stimulated , with arm retreival produced by stimulating the posterior deltoid and biceps brachii . achieved by aplying stimulation to the anterior deltoid and biceps brachii , while retrieval was produced by stimulation the posterior deltoid and triceps brachii . lateral reaching produced by stimulating biceps brachii followed by anterior and posterior deltoid and finally by the triceps brachii , while retrieving was achieved by stimulating the biceps brachii muscle , discontinuing deltoid stimulation , and stimulating the triceps brachii to produce arm extension while lowering the arm . transitioning between movement phases ( i.e. , reach and retrieve ) could be triggered using a ttl - level signal provided by an external switch or a bci . the bci was implemented as a simple brain - switch , which was activated whenever the power within the beta range ( 13 hz- 30 hz ) of the participant s eeg decreased below a threshold , indicating the participant s intention to move his arm . this frequency range was selected by identifying spectral components displaying erd using data collected when the participant attempted repeatedly to perform hand ( palmar and lateral grasps , precision pinch , and hand opening ) movements following a ready - go - stop experimental cue . the analysis was performed using a total of 104 attempted movement repetitions and applied to six eeg electrode positions ( f3 , fz , f4 , c3 , cz , c4 of the 10 - 20 electrode placement system ) . the frequency band between 18 hz and 28 hz at the fz location were found to be the most suitable for implementing the bci . eeg recordings for this process were performed using a synamprt eeg amplifier ( compumedics , u.s.a . ) at a sampling rate of 1 khz and filtered between 0.05 hz and 40 hz . erd estimation was performed with custom - made software ( matlab , mathworks , u.s.a . ) . to create the bci , acquisition of eeg activity was performed using a desktop biopotential amplifier ( qp511 , grass telefunken , germany ) and a data acquisition system ( usb-6363 , national instruments , u.s.a . ) using a sampling frequency of 300 hz . the eeg signal from electrode fz was band - pass filtered ( 10-hz - 100 hz ) and amplified ( 20,000x ) prior to its digital acquisition . all processing was implemented using custom - made software ( labview , national instruments , u.s.a . ) . the bci estimated a moving average ( over a 500 ms period ) of the eeg rms value measured every 125 ms . for an activation to take place , the moving average had to decrease below a threshold for a pre - specified duration ( 500 ms to 1,200 ms ) . the experimenters could adjust both parameters at any moment during the operation of the system . this pulse was delivered to the neuroprosthesis for reaching where it triggered a transition in the state of the electrical stimulation ( e.g. , from active reaching to retrieving the arm ) . in addition , an external manual switch could also be used by the experimenters bypassing the bci altogether in cases in which the brain interface failed to identify the intention to move . one of them guided the arm in motion ( assisted by the electrical stimulation ) and could trigger the stimulation manually bypassing the bci completely . the second experimenter demonstrated the movement to perform at every repetition and could also adjust the bci activation parameters ( i.e. , activation threshold and latency ) . the intervention consisted of 40 90-minute sessions ( 30-minute setup and 60-minute active therapy ) delivered three times a week . during each session the participant attempted to reach to different targets ( listed above in the neuroprosthesis implementation ) repeatedly following the experimenters instructions . each movement was performed with a brief pause between phases ( i.e. , the participant would reach , hold the reaching position for a few seconds , and then return his arm to a starting position followed by a few moments of relaxation with no stimulation ) . we measured the effects of the intervention using five assessments , measured at beginning , midpoint and end of the study . the assessments were the toronto rehabilitation institute - hand function test ( trihft ) , the action research arm test ( arat ) , functional independence measure ( fim ) , self - care component of the functional independence measure , and fugl - meyer assessment upper extremity sub - score . the recorded values are displayed in table 1 . the fugl - meyer assessment upper extremity sub - score had a clinically significant change ( 6 points ; 13 points at baseline and 19 points at the end of the intervention ) . the fim self - care subscores registered non - significant improvements ( 28 and 35 at baseline and end , respectively ) . all the other assessments remained unchanged ( table 1 ) , likely due to the fact that the trihft and arat require hand function beyond the functional gains observed . in addition , although the fma - ue sub - score and fim self - care subscores were very similar ( or the same ) between the midpoint and discharges assessments , it was evident that the quality of the movement ( e.g. , speed and smootheness ) improved between these two measurements qualitatively , the bci was able to detect the participant s intention to move and consequently trigger the neuroprosthesis when required . our preliminary results suggests that the bci was able to trigger the neuroprosthesis for the majority of reaching movement repetitions ( sometimes with accuracies as high as 90% ) , although a full data analysis is yet to be completed . the most common source of interference that affected the bci was electrical interference originating from activation of facial muscles ( i.e. , reflective of the participants physical effort ) . in conclusion , the results of this study suggest that integration of a simple single - channel bci with fest may help individuals with severe hemiplegia resulting from stroke regain voluntary arm reaching function , even 6 years ( 72 months ) after having a stroke . further testing is required to verify the findings presented here including a large number of participants .

we present here the integration of brain - computer interfacing ( bci ) technology with functional electrical stimulation therapy to restore voluntary function . the system was tested with a single man with chronic ( 6 years ) severe left hemiplegia resulting from a stroke . the bci , implemented as a simple brain - switch activated by power decreases in the 18 hz 28 hz frequency range of the participant s electroencephalograpic signals , triggered a neuroprosthesis designed to facilitate forward reaching , reaching to the mouth , and lateral reaching movements . after 40 90-minute sessions in which the participant attempted the reaching tasks repeatedly , with the movements assisted by the bci - triggered neuroprosthesis , the participant s arm function showed a clinically significant six point increase in the fugl - meyer asessment upper extermity sub - score . these initial results suggest that the combined use of bci and functional electrical stimulation therapy may restore voluntary reaching function in individuals with chronic severe hemiplegia for whom the rehabilitation alternatives are very limited .

dolichoectatic and fusiform aneurysms represent a small subset of cerebral aneurysms and are among the most difficult to treat . the pathophysiology of fusiform cerebral aneurysms includes a disrupted internal elastic lamina and muscle layer that might be susceptible to mechanical injury by hemodynamic strain , causing progressive attenuation of the arterial wall . the treatment of fusiform aneurysms of the basilar artery is challenging for several reasons , including the presence of perforating vessels , the proximity to the brain stem and the exiting cranial nerves , and the surgical approaches necessary to access the basilar artery . we present the case of a patient with acute brain stem ischemic stroke who had a fusiform basilar artery aneurysm complicated by a massive subarachnoid hemorrhage . our objective is to discuss the difficulties in the acute management of this disease , its potential treatments and complications . a 53-year - old man with a previous history of hypertension and obesity was admitted to our emergency department with sudden right hemiplegia , hemianopsia , and dysarthria within 2 h from symptom onset . his national institutes of health stroke scale ( nihss ) score at admission was 19 , and he had no previous history of stroke or transient ischemic attacks . the patient 's neurological symptoms progressively improved during the first hour after admission , with only a right facial palsy ( nihss 2 ) remaining . a head ct at admission showed a hyperdense basilar artery , and a ct angiography ( cta ) confirmed a basilar fusiform aneurysm with a thrombus within the vessel and no signs of acute dissection ( fig . he was treated with antiplatelets and transferred to our intensive care unit . due to his clinical improvement a head ct revealed an extensive subarachnoid hemorrhage in the basal cisterns and posterior fossa ( fisher grade 3 ; fig . basilar artery fusiform aneurysms pose difficulties to treatment because , during the course of the disease , both bleeding and thrombosis can occur . in addition , bleeding may be a complication of a basilar artery fusiform aneurysm in patients initially presenting with brain ischemia , even when anticoagulation and thrombolytic treatments are not used , as happened in our patient . fusiform cerebral aneurysms can be divided into acute dissecting aneurysms , which usually cause subarachnoid hemorrhage or cerebral ischemia , and chronic fusiform or dolichoectatic aneurysms , which slowly enlarge with time and can be asymptomatic or associated with cranial nerve dysfunction , ischemic stroke , subarachnoid hemorrhage , pseudotumor , or hydrocephalus . although important for the treatment decision - making , the differentiation between a dissecting and a chronic fusiform aneurysm is often difficult , even with advanced neuroimaging techniques [ 1 , 4 , 6 ] . in our patient , regardless of the acute presentation of an ischemic event and posterior bleeding , no signs of dissection were seen on the cta or the mri / mra of the brain . more than half of large cerebral aneurysms with a diameter of 20 mm or more are known to have thrombi like the one seen in our patient . the mortality rate of patients with fusiform basilar aneurysms is approximately 70% if the basilar artery has become occluded [ 8 , 9 ] . conversely , the occurrence of hemorrhagic events is associated with the degree of ectasia of the basilar artery . anticoagulation therapy at conventional doses seems to increase the risk of intracranial bleeding [ 11 , 12 ] . the role of antiplatelet agents in promoting hemorrhagic strokes in such patients is less clear . the treatment of such lesions can be a dilemma , as in the case described . in patients with vertebrobasilar dolichoectasia considering that the current treatment risks can exceed the natural risk of basilar rupture or occlusion , a better understanding of the pathophysiology is required to help select patients at higher risk of hemorrhagic or ischemic events for invasive treatments [ 4 , 5 ] .

we present the case of a patient with acute brain stem ischemic stroke who was found to have a fusiform basilar aneurysm with a thrombus within the dilated vessel . three days after the ischemic stroke , the patient had a massive subarachnoid hemorrhage and died . this case illustrates the difficulties in the acute management of ischemic events in patients with basilar fusiform aneurysms , because the natural history of this disease encompasses both bleeding and thrombosis .

On the morning he was being ousted as Donald Trump’s chief strategist last Friday, Steve Bannon had already turned the page. “Why do you sound unfazed?” a friend asked Bannon as news of his demise ricocheted across the web. “Because,” Bannon replied, “we’re going to war.” Hours later, Bannon was calling into the editorial meeting at Breitbart News, rallying his troops to continue the battles he waged inside the White House. “We have a duty to the country to be the vanguard of ‘The Movement,’” he told his staff, according to one person on the call. Bannon’s main targets are the West Wing’s coterie of New York Democrat “globalists”—Ivanka Trump, Jared Kushner and former Goldman Sachs president Gary Cohn—as well as the “hawks,” comprised of National Security Adviser H.R McMaster and his deputy, Dina Powell. “He wants to beat their ideas into submission,” Breitbart News Editor-in-Chief Alex Marlow told me. “Steve has a lot of things up his sleeve.” The chaotic, war-torn West Wing of the past six months will be prologue, but the coming struggles will be as personal as they are ideological, waged not with leaks but with slashing Breitbart banners. On Sunday, Breitbart took renewed aim at McMaster, with a headline claiming he advocated “Quran Kissing.” But most of all, there’s a deep animosity between Bannon and Kushner, amplified by a lack of respect. Bannon finds Kushner’s political instincts highly questionable. “He said Jared is a dope,” one Bannon ally recalled. The two clashed fiercely on personnel decisions and policy debates, both domestic and international, many of which Bannon lost. But Bannon, who was the only West Wing advisor to publicly support the president’s response to the violence in Charlottesville, is especially galled at being scapegoated as an anti-Semite in its wake. “It’s one of the attacks he takes most personally because it’s not true,” a Breitbart staffer told me. Bannon’s allies lay out a more complicated backstory. Bannon, they say, lobbied Trump aggressively to move America’s embassy in Israel from Tel Aviv to Jerusalem, but was blocked by Kushner. And, according to three Bannon allies, Bannon pushed a tougher line against the Palestinians than Kushner did. In May, when Palestinian President Mahmoud Abbas visited the White House, Bannon stayed home. “I’m not going to breathe the same air as that terrorist,” Bannon texted a friend. In the final weeks, Bannon was relentlessly tarred as a prime West Wing leaker, but Bannon’s allies make a similar case about Kushner. Specifically, they believe that Kushner cultivated a relationship with Matt Drudge, who frequently pushed anti-Bannon headlines—“The Total Eclipse of Steve Bannon”; “Bannon ‘Is the Real President”—in the weeks leading up to Trump’s decision to defenestrate him. Bannon also told friends that he believed Kushner encouraged Fox News chairman Rupert Murdoch to lobby Trump to fire him. Last week, The New York Times reported that Murdoch told Trump over a private dinner with Kushner that Trump needed to jettison his chief strategist. The Bannon camp believes that Murdoch was especially receptive to Kushner’s lobbying because Murdoch is worried about the rise of Sinclair Broadcasting as a competitor to Fox, and blames Bannon for Trump’s decision so far not to block the Sinclair’s $3.9 billion takeover of Tribune Media in May. Bannon has media ambitions to compete with Fox News from the right. Last week in New York, he huddled with his billionaire benefactor, Robert Mercer, and discussed ways to expand Breitbart into TV, sources said. “Television is definitely on the table,” a Bannon adviser told me. A partnership with Sinclair remains a possibility. In recent days, Sinclair’s chief political analyst Boris Epshteyn has spoken with Breitbart editors about ways to form an alliance, one Breitbart staffer said. “All the Sinclair guys are super tight with Breitbart. Imagine if we got together Hannity and O’Reilly and started something?” Meanwhile, the next phase has already begun. On Sunday, the website’s lead story was based on a Daily Mail report that said Ivanka was behind Bannon’s removal. “Trump’s daughter Ivanka pushed out Bannon because of his ‘far-right views’ clashing with her Jewish faith,” the article noted. Another piece was headlined: “6 TIMES JAVANKA’S DISPLEASURE WITH POTUS LEAKED TO PRESS.” In his feud with Kushner, Bannon may have a powerful ally: Reince Priebus, also recently departed from the White House with a quiver of grudges. Recently, according to several sources, Bannon has told friends he wants Priebus to give his account of the James Comey firing to special prosecutor Robert Mueller. According to a source close to Priebus, the former chief of staff believes that the decision was made during an early May weekend in Bedminster, where Kushner, Ivanka Trump, and Stephen Miller were with the president. Trump returned to the Oval Office on Monday, May 8 and told other aides he intended to fire Comey. At Breitbart, Bannon has a brigade of similarly happy warriors. “We’re in a loud bar celebrating the return of our captain!” Breitbart’s Washington editor Matt Boyle told me on Friday night. Breitbart’s defense of Trump has so far helped keep the Russia scandal from gaining traction on the right. But that could swiftly change if Trump, under the influence of Kushner and Cohn, deviates too far from the positions he ran on. If that happens, said one high-level Breitbart staffer, “We’re prepared to help Paul Ryan rally votes for impeachment.” ||||| President Trump decided to dismiss Stephen K. Bannon, after weeks of White House upheaval and racial unrest. The ousted chief strategist returned to Breitbart News on Aug. 18. (Peter Stevenson,Jenny Starrs/The Washington Post) President Trump decided to dismiss Stephen K. Bannon, after weeks of White House upheaval and racial unrest. The ousted chief strategist returned to Breitbart News on Aug. 18. (Peter Stevenson,Jenny Starrs/The Washington Post) President Trump’s most unconventional senior adviser, Stephen K. Bannon, may have left the White House, but the political turbulence that has characterized the first seven months of Trump’s presidency doesn’t appear to be going anywhere. The tenure and departure of Bannon, the president’s chief strategist and champion of his nationalist impulses, exposed deep fissures in the Trump-era Republican Party, within the White House and beyond. Those differences are still harming Trump’s effectiveness as he tries to kick-start a sputtering legislative agenda at a time when relationships with Republican congressional leaders are seriously frayed — largely because of the president’s behavior, including his response to hate-fueled deadly violence in Charlottesville last weekend. While Bannon’s ouster was the latest move by new Chief of Staff John F. Kelly to bring a greater sense of normalcy to the White House, even some of Trump’s allies question how likely that is to take hold, particularly under a president who relishes changing the national conversation with a provocative tweet — a practice Kelly has not been able to curb. Trump — nearing the end of a working vacation at his Bedminster, N.J., golf resort — has made a habit of continuing to solicit advice from former staffers, often through late-night calls when he is no longer under the watchful eye of Kelly. Bannon also has made clear since he left Friday that he is going to use Breitbart News, the pugilistic conservative website, to try to advance his agenda from outside the White House. The Post's Dan Balz says the firing of chief strategist Stephen K. Bannon simultaneously changes everything and nothing for the Trump administration. (Bastien Inzaurralde,Jhaan Elker/The Washington Post) In an interview in Washington on Saturday, Bannon warned Republican leaders to enthusiastically support Trump’s priorities on taxes, trade and funding a massive border wall — or risk the wrath of the president’s base, including Breitbart, to which Bannon returned Friday as executive chairman. “If the Republican Party on Capitol Hill gets behind the president on his plans and not theirs, it will all be sweetness and light, be one big happy family,” Bannon said. [After Charlottesville, Republicans remain stymied over what to do about Trump] But Bannon added with a smile that he does not expect “sweetness” anytime soon — and described the turbulent political moment in the Republican Party and the country as a necessary battle over Trump’s priorities. “No administration in history has been so divided among itself about the direction about where it should go,” Bannon said, adding that Trump’s base is frustrated by a congressional agenda that has dovetailed more with traditional Republican priorities than the agenda Trump championed. In a pair of tweets on Saturday, the president wished Bannon well and thanked him for his service. “He came to the campaign during my run against Crooked Hillary Clinton — it was great!” Trump said in the first, referring to Bannon’s role during the general election. Several hours later, Trump predicted Bannon would be “a tough and smart new voice at @BreitbartNews . . . maybe even better than ever before,” adding: “Fake News needs the competition!” Trump and Bannon had not yet spoken by phone as of early Saturday, according to people close to both men. It was not clear who had been reaching out to whom, the people said. Bannon spent the day in Washington meeting with friends and allies, and talking with Breitbart writers and executives, according to people close to him. Several friends and former co-workers said that they expect Bannon to use the platform to attack his political opponents, including those he has derided as “globalists” and Democrats inside the White House. “I think Steve is going to be more effective on the outside,” said Matt Schlapp, chairman of the American Conservative Union and a longtime friend of Bannon. “On the outside, if you are well-funded and you are feared and you have a platform, you are going to be a power player. Steve has all of that in spades.” Trump and Bannon associates also expect Bannon to continue to have Trump’s ear, as has been the case with some other fired staffers such as Corey Lewandowksi, Trump’s first campaign manager, who periodically shows up at the White House. “With Donald Trump, once he likes you, you’re either in his inner orbit, or you’re in his outer orbit,” said Christopher Ruddy, chief executive of Newsmax Media and a member of Trump’s Mar-a-Lago Club in Palm Beach, Fla. “You never leave altogether.” In a White House that has had competing power centers, some Trump confidants argued that Bannon’s removal was necessary to bring a more regimented system to the White House, as Kelly has sought. They argued that with Bannon, who had a reputation of trying to undermine colleagues with more establishment views, this made particular sense. [Trump, first lady to skip Kennedy Center Honors over concerns of ‘political distraction’] “I think it raises the morale of staffers and brings more of a sense of normalcy to the White House on a day-to-day basis,” said one Republican strategist close to the White House, who spoke on the condition of anonymity to speak more candidly. “You don’t have such an un­or­tho­dox staffer breathing down people’s necks and creating tension every day.” “What it does not do is remove the person who’s creating the most drama in the White House, and that’s Donald Trump,” the strategist added. “He’s going to continue to do what he’s going to do.” The coming weeks should bring no shortage of drama. Fallout is continuing from Trump’s remarks on Charlottesville, in which he blamed “both sides” for the violence and said some “fine people” marched alongside the neo-Nazis and white supremacists protesting the removal of a Confederate statue. The investigations into the Trump campaign’s ties with Russia also continue. And next month, Congress returns to a full set of challenges, including legislation to raise the nation’s debt ceiling. If Trump and lawmakers become paralyzed by the task, they could spark an international crisis. Trump also wants Congress to try to resurrect health-care legislation and take up tax reform, another shared priority but one also rife with intraparty division. He is also seeking funding for his marquee campaign promise of a wall on the U.S.-Mexico border. On most of these issues, there is no evident strategy among Republicans on either side of Pennsylvania Avenue for bridging divisions and bringing Trump and congressional Republicans together. “The reality of it is that even if there were no issues inside the White House, you still have an underlying divide in the Republican Party about how we’ll approach some of these issues,” said former Republican National Committee chairman Michael Steele. “To me, that’s the most disheartening part of this.” While Bannon’s influence has been evident on some Trump policies — including trade, immigration and a decision to pull out of the Paris climate accord — he was much less a presence on health care, the issue that has most come to symbolize GOP dysfunction at a time when the party controls the presidency and both chambers of Congress. In recent weeks, Trump has grown increasingly unhappy with Senate Majority Leader Mitch McConnell (R-Ky.) and rarely mentions House Speaker Paul D. Ryan (R-Wis.) in private conversations, blaming both for his legislative troubles, according to two people who have spoken with Trump. On Friday, a flurry of bravado-filled interviews with Bannon appeared on various websites, including one in which he said he felt as if “I’ve got my hands back on my weapons” and was prepared to “crush the opposition.” Advisers to senior congressional Republicans were taken aback that none of the combative language was countered by the White House. “They just sat out there,” said one Republican aide. “That told me everything about whether the White House actually cares about making clear it’s on our side.” Other Republican aides pointed out that there were other consequential openings on the staff beyond Bannon. While Bannon has been close to the conservative House Freedom Caucus, it was former chief of staff Reince Priebus and outgoing press secretary Sean Spicer who had deep friendships in the party going back to their days at the Republican National Committee. Ever since Priebus left, many Republican officials have found it harder to engage the White House and to feel assured that the administration “understands the language of Republicans,” as one veteran Republican operative described the dynamic. [The Fix: Where Republican senators stand on Trump’s views] Bannon said he sees the roiling feuds inside the West Wing and in the GOP leadership ranks as somewhat but not entirely distinct from broader national divisions. “The tensions in the White House are slightly different than the tensions in the country. It’s still a divided country. Fifty percent of the people did not support President Trump. Most of those people do not support his policies in any way, shape or form,” Bannon said. Bannon said both Republicans and Democrats will need to pay close attention to the anxiety among many working people in the country over economic opportunity and national identity, even as they work to settle their turf fights in Washington. The showdown in a special Senate race in Alabama offers a harbinger of the discord facing the GOP in 2018. In a Sept. 26 primary runoff, Sen. Luther Strange (R-Ala.), an ally of Senate GOP leaders, has been endorsed by Trump but is disliked by many right-wing leaders, including Breitbart and talk-radio hosts such as Laura Ingraham. Strange faces Roy Moore, a former state Supreme Court justice and longtime favorite of conservatives for his hard-line stands on same-sex marriage and allowing the Ten Commandants to be displayed in public. Rather than rally behind Strange, several conservative leaders said privately Saturday that they expect their supporters to get behind Moore as a way of sending a signal to Trump that while they are with him philosophically, they will not follow his decisions blindly ahead of the 2018 mid-term elections. Rep. Mo Brooks (R-Ala.), who finished third in last week’s Senate vote and did not make the runoff, acknowledged that many conservatives are urging him to get behind Moore to stop Strange and rattle GOP leaders. “Have I made a decision? No, I have not,” Brooks said coyly in an interview. “But it looks like the establishment and Washington swamp have taken control of the White House with Bannon’s departure and with Luther Strange.” Wagner reported from Bedminster, N.J. Paige Winfield Cunningham contributed to this report. ||||| Mr. Bannon fed Mr. Trump’s paranoid streak and shared the president’s penchant for believing in conspiracies. He viewed not just intelligence agencies but most of government as stocked with a devious bureaucratic underbelly, the “deep state.” Mr. Trump, who has never worked in government, eagerly adopted that view. Mr. Bannon was notorious for maintaining his own, shadowy presence within the White House. He would frequently skip meetings where policy was discussed, injecting his views into the process in other ways, according to two administration officials. He did not use a computer, preferring to have paper printed and handed to his assistant to stay outside the formal decision-making process. Mr. Bannon favored a culture similar to the one Mr. Trump brought with him from the business world to the White House — a flat structure with blurred lines of responsibility and competing power centers. And early on Mr. Bannon benefited from that structure, sitting at the top, free to slip unvetted materials to the president without a gatekeeper to get past. “Theoretically, a more coherent staff should produce a more coherent policy,” said David Axelrod, who was President Barack Obama’s senior adviser and the person in a comparable role to Mr. Bannon in the White House. “But that presupposes a president who embraces the process and the policy.” With little process to speak of, tensions over policy swelled. Ideological differences devolved into caustic personality clashes. Perhaps nowhere was the mutual disgust thicker than between Mr. Bannon and Mr. Trump’s daughter and son-in-law. Mr. Bannon openly complained to White House colleagues that he resented how Ms. Trump would try to undo some of the major policy initiatives that he and Mr. Trump agreed were important to the president’s economic nationalist agenda, like withdrawing from the Paris climate accords. In this sense, he was relieved when Mr. Kelly took over and put in place a structure that kept other aides from freelancing. “Those days are over when Ivanka can run in and lay her head on the desk and cry,” he told multiple people.

– Steve Bannon had planned an orderly departure from the White House, but it was scuppered by the violence in Charlottesville, insiders say. Sources tell the New York Times that new White House chief of staff John Kelly told the White House strategist in July that he would have to leave and they agreed on a date in mid-August, marking a year since Bannon joined the Trump team. But after Charlottesville, Bannon sought to push back the Aug. 14 departure date and stay on until at least Labor Day, worried that it would look like his departure was a response to events, the insiders say. He ended up leaving within days anyway after contradicting Trump's foreign policy in an interview with a liberal magazine. The insiders say that Bannon's departure was hastened by the "mutual disgust" between himself and the couple he called "Javanka" behind their backs: Jared Kushner and Ivanka Trump. Bannon, who has now returned to Breitbart News, tells the Washington Post that he expects the turbulence in the Republican Party and the White House to continue. "No administration in history has been so divided among itself about the direction about where it should go," he says. According to Vanity Fair, Bannon now plans to use Breitbart to continue his feud with Kushner, Ivanka Trump, and other administration figures including National Security Adviser HR McMaster. (Here's what President Trump had to say about Bannon's departure.)

its socioeconomic relevance is characterized by a high prevalence in industrialized countries combined with the productivity loss associated with the disease . methotrexate ( mtx ) is the most commonly used disease - modifying antirheumatic drug ( dmard ) . tumor necrosis factor ( tnf- ) inhibitors are the most popular biological agents approved for the treatment of ra after failure of conventional dmards . germany is the most populous country in the european union and its most important market for biological agents . the main payer in the german health care system is the statutory health insurance ( shi ) . the shi funds have more than 70 million members . with more than eur 1 billion expenditure , tnf- inhibitors ranked highest in the shi funds ' pharmaceutical expenditure in 2011 . for the german population , overall prevalence of inflammatory arthritis is estimated at 3.4 % . the percentage of patients treated with tnf- inhibitors has been rising from 2 % in 2000 to 20 % in 2008 . in 2011 , high prevalence and high pharmaceutical spending motivate a cost - effectiveness analysis ( cea ) of tnf- therapies for the german setting . we aim to conduct a cea considering the special requirements for health economic analysis in germany . we choose cost per responder as the most suitable measure of cost - effectiveness for the german setting . quality - adjusted life years are not used in the german context due to legal concerns . cost - effectiveness in terms of cost per function score unit is problematic as the commonly used health assessment questionnaire is not cardinally scaled . reporting from the main payer 's perspective has been suggested by the institute for quality and efficiency in health care for cea in germany . for inclusion of effectiveness studies , we require results in terms of response rates as defined either by european league against rheumatism ( eular ) criteria ( eular good response , eular moderate to good response ) or by american college of rheumatology ( acr ) criteria ( acr50 response , acr70 response ) . first - line biological therapy is not reimbursed by the german shi funds unless individual reasons imply poor response or toxicity of dmards . german guidelines require treatment for at least 6 months and failure of at least two dmards including mtx before the initiation of biological therapy . while mtx monotherapy is chosen as the comparator in most ceas of biological treatments , this would not reflect german clinical practice . by definition , patients who are eligible for mtx monotherapy would not be treated with tnf- inhibitors in the german setting . only mtx refractory patients would be treated with biological therapies . the german federal joint committee 's ( gemeinsamer bundesausschuss ( gba ) ) requirements include identification of the correct comparator for the specific patient population . if mtx monotherapy is not effective , dmard combination therapy can be initiated as an alternative to biological treatments . we identify conventional triple therapy as the most clinically relevant alternative to biological therapy as shown by 2011 shi prescription data . the combination of mtx , sulfasalazine , and hydroxychloroquine has been shown to be more effective than mtx monotherapy by o'dell . it is the most suitable comparator to reflect a treatment alternative to biological therapy in german clinical practice . direct clinical comparisons offer a higher level of evidence than indirect comparisons according to gba 's requirements . all clinical trials are included if they feature at least one study arm with biological therapy and one arm with triple therapy . initial treatment needs to be mtx monotherapy or failure of mtx monotherapy has to be an inclusion criterion for patients . we search pubmed for the search terms adalimumab , sulfasalazine , hydroxychloroquine , and rheumatoid arthritis . application of the same search terms to infliximab and etanercept produced 40 and 34 hits . screening of the hits resulted in the identification of three clinical trials for infliximab [ 1317 ] and two clinical trials for etanercept [ 18 , 19 ] . we calculate cost per responder based on german direct medical costs for the treatments applied in the trials . cost calculations include 2013 drug costs and treatment costs ( administration and monitoring cost and screening cost before initiation of the therapy ) according to german shi payment conditions . contrary to other countries , germany applies the full 19 % value - added tax ( vat ) to all pharmaceuticals . we provide results without vat for better international comparability as shown in table 1.table 1direct costsdrug costs [ ] administration and screening costs [ ] total costs [ ] total costs , vat deducted [ ] total costs , rebates deducted [ ] total costs , rebates and vat deducted [ ] therapyq1qnq1qnq1qnq1qnq1qnq1qntriple therapy175.78178.9544.5644.56220.34223.51192.27194.94187.37190.15159.31161.57ifx + mtx8,387.804,555.97247.8075.528,635.604,631.497,296.373,904.077,536.224,031.786,197.003,304.36etn + mtx5,691.385,694.55201.0057.355,892.385,751.904,983.674,842.695,154.795,013.924,246.094,104.70 ifx infliximab , etn etanercept , mtx methotrexate , q1 first quarter of treatment , qn following quarters of treatment ifx infliximab , etn etanercept , mtx methotrexate , q1 first quarter of treatment , qn following quarters of treatment in the last decade , the german legislator has routinely applied mandatory rebates to nonreference price group pharmaceuticals . the shi funds ' savings due to mandatory rebates are not reflected by manufacturers ' list prices . the manufacturers currently have to reimburse the shi funds for 16 % of list prices . we report results reflecting the 16 % rebate as shown in table 1 . four out of six identified trials were excluded because they compared combinations of biological and triple therapy rather than comparing biological to triple therapy . the opera study compares adalimumab and mtx combination therapy plus possible step - up odell triple therapy to mtx ( and adalimumab placebo ) therapy plus possible step - up odell triple therapy . while the placebo arm reflects german clinical practice , the adalimumab arm includes both biological and triple conventional therapy . the neo - raco study added infliximab on top of an existing triple therapy strategy . the best study includes four actively managed study arms ( dmard sequential monotherapy , dmard step - up combination therapy , dmard initial combination therapy , initial infliximab , and mtx combination therapy ) [ 13 , 14 ] . while providing a valuable comparison of four different treatment approaches , the active study design ultimately leads to infliximab combination therapy in all study arms . each study arm has an individual treatment plan that differs both in medication and timing . the study designs are not suitable to compare biological therapy to conventional therapy for the purpose of our analysis . the swefot trial compares o'dell 's triple therapy to infliximab and mtx combination therapy after failure of mtx monotherapy [ 16 , 17 ] . the swefot trial reflects two important characteristics of german practice : failure of mtx therapy ( even though failure of a second dmard would be required in germany ) and comparison to o'dell 's triple treatment . the swefot trial reports response rates according to both acr criteria and to eular criteria . cost of the study medication in the german setting is shown in table 1 . given the 12 months results of the swefot trial , the incremental cost - effectiveness ratios ( icer ) for acr response under infliximab combination therapy compared to o'dell 's triple therapy are 216,392 euros ( acr50 ) and 432,784 euros ( acr70 ) . for eular criteria , the icers are 154,566 euros for a good response and 196,720 euros for a good to moderate response ( table 2).table 2cost per responder for infliximab combination therapy compared to conventional triple therapyresponseacr20acr50acr70eular ( good)eular ( moderate good)cost per responder [ ] 154,566216,392432,784154,566196,720cost per responder , vat deducted [ ] 130,225182,315364,629130,225165,741cost per responder , rebates deducted [ ] 134,813188,738377,475134,813171,580cost per responder , vat and rebates deducted [ ] 110,472154,660309,321110,472140,600 cost per responder for infliximab combination therapy compared to conventional triple therapy the treatment of early aggressive rheumatoid arthritis ( tear ) trial compares o'dell 's triple therapy to etanercept and mtx combination therapy , both as initial therapies and as step - up therapies after the failure of initial mtx monotherapy after 6 months . like the swefot trial , the two step - up arms reflect the failure of one dmard . the icer for a acr70 response is 321,527 euros ( projected for 1 year ) ( table 3).table 3cost per responder for etanercept combination therapy compared to conventional triple therapyresponseacr70cost per responder [ ] 321,527cost per responder , vat deducted [ ] 270,476cost per responder , rebates deducted [ ] 280,680cost per responder , vat and rebates deducted [ ] 229,628 cost per responder for etanercept combination therapy compared to conventional triple therapy a similar analysis for the usa estimated cost per responder for infliximab at $ 92,081 by acr50 criteria and at $ 152,471 by acr70 criteria and for etanercept at $ 63,137 ( acr50 ) and at $ 135,085 ( acr70 ) against placebo . this difference can mainly be attributed to the use of triple therapy rather than placebo as a comparator for the german setting . our results show that cost per responder would be underestimated if the relevant comparator was not taken into account . however , all german results are overestimated by 40 % when including vat and mandatory rebates in the cost calculations . this needs to be taken into account when reporting results based on german list prices . if drug costs are adapted and the specific relevant comparator is taken into account , our results can be transferred to many other countries , which do not use quality - adjusted life years as part of policy decisions due to legal or political concerns . however , both trials show little evidence for any significant clinical advantage of tnf- therapy after 2 years . under the conditions of these trials , a more prominent role of conventional combination therapy could contribute to significant direct medical cost savings . at 5 years , the best study has shown that 19 % of patients are in drug - free remission after initial treatment with infliximab . the possibility for drug - free remission could have an important impact on the results of cea . accounting for prevented disability in long - term analysis can substantially change the results of cea if conducted from a societal perspective . initial biological therapy with adalimumab showed an advantage in radiographic progression over mtx monotherapy even if adalimumab therapy was discontinued after 1 year . if no response could be achieved , the swefot trial allowed switching the therapy from infliximab to etanercept and from triple therapy to cyclosporin a. these adjustments are not reflected by our cost calculations . the huge cost difference between biological and conventional therapy does not significantly change for either switch . the same critique applies to cea based on the tear trial with 379 patients in the step - up arms . cea by cost per responder is a viable option for jurisdictions , which do not use quality - adjusted life years . our results reflect gba 's requirements for relevant comparators as currently practiced in its early benefit assessments for new approvals in germany . while our analysis focused on the agents with the highest budget impact in 2011 , gba selected tocilizumab , golimumab , and certolizumab pegol for the first benefit assessment of biological agents for ra in 2014 . these agents are in an earlier stage of their product lifecycle . due to their expected future budget impact , their manufacturers are required to negotiate a rebate with the shi funds based on gba 's benefit assessment . our analysis has shown that the choice of the comparator will play a critical role . cost per responder for the german setting is more than double the cost estimated in a similar analysis for the usa , which measured against placebo . however , german results are overestimated by 40 % when calculating based on the drugs ' list prices . recent research has shown the possibilities of long - term drug - free remission and improved radiographic progression with early biological treatment . further research is required to determine the long - term cost - effectiveness of biological approaches to treatment of ra .

tumor necrosis factor ( tnf- ) inhibitors ranked highest in german pharmaceutical expenditure in 2011 . their most important application is the treatment of rheumatoid arthritis ( ra ) . our objective is to analyze cost per responder of tnf- inhibitors for ra from the german statutory health insurance funds ' perspective . we aim to conduct the analysis based on randomized comparative effectiveness studies of the relevant treatments for the german setting . for inclusion of effectiveness studies , we require results in terms of response rates as defined by european league against rheumatism ( eular ) or american college of rheumatology ( acr ) criteria . we identify conventional triple therapy as the relevant comparator . we calculate cost per responder based on german direct medical costs . direct clinical comparisons could be identified for both etanercept and infliximab compared to triple therapy . for infliximab , cost per responder was 216,392 euros for acr50 and 432,784 euros for acr70 responses . for etanercept , cost per acr70 responder was 321,527 euros . cost was lower for response defined by eular criteria , but data was only available for infliximab . cost per responder is overestimated by 40 % due to inclusion of taxes and mandatory rebates in german drugs ' list prices . our analysis shows specific requirements for cost - effectiveness analysis in germany . cost per responder for tnf- treatment in the german setting is more than double the cost estimated in a similar analysis for the usa , which measured against placebo . the difference in results shows the critical role of the correct comparator for a specific setting .

several lines of evidence suggest that the amygdala is structurally and functionally altered in patients with bipolar disorder [ 12 , 14 ] . in adult patients with bipolar disorder in contrast to this , studies investigating adolescent patients reported a decreased amygdala volume . a meta - analysis of volumes of regional brain structures in bipolar disorder , however , could not observe any significant change of amygdala volume . another recent systematic review and meta - analysis of amygdala volume in adolescent and adult patients with bipolar disorder included 14 mri studies . this study revealed a bilaterally reduced amygdala volume in the overall sample of patients with bipolar disorder , but the results of the individual studies and the pediatric and adult subsamples were heterogeneous . an additional meta - regression analysis revealed a positive correlation between mean age and amygdala volume in patients with bipolar disorder . therefore , the authors concluded that amygdala volume is decreased at the beginning of the disorder and increases with illness duration . this hypothesis is supported by chen and coworkers who reported a positive correlation of age and amygdala volume in patients with bipolar disorder in contrast to a negative correlation in healthy control subjects . functional imaging studies with depressed patients suffering from bipolar disorder exhibited a disturbed cortical - limbic network with increased metabolism in amygdala and other subcortical structures . another study observed a reduced dorsolateral prefrontal cortical activation corresponding with increased amygdala activation in a facial affect discrimination task in patients with bipolar disorder . taken together , these results suggest an involvement of the amygdala in the pathophysiology of bipolar disorder . the neurotransmitter serotonin ( 5-hydroxytryptamine ; 5-ht ) is an essential modulator of emotional behaviour and an abnormal function of 5-ht is found in mood disorders . the serotonin transporter plays an important role in regulating 5-ht levels in the brain by transporting 5-ht from the synaptic cleft to the pre - synaptic neuron . a recent study reported a 26% lower serotonin transporter binding potential in the amygdalae of depressed medication - free patients with bipolar disorder . a polymorphism ( 5-ht transporter - linked polymorphic region ; 5-httlpr ) in the transcriptional control region upstream of the coding sequence of the serotonin transporter gene ( slc6a4 ) results in short ( s)- or long ( l)-alleles . the s - allele is associated with significant lower serotonin transporter binding and mrna expression . functional imaging studies in healthy individuals revealed an association between 5-httlpr genotype and neuronal activity in the amygdala . carriers of the s - allele showed reduced serotonin expression and an increased fear and anxiety - related behaviour . furthermore , in functional magnetic resonance imaging it could be shown that carriers of the s - allele exhibited greater amygdala neuronal activity in response to fearful stimuli or aversive pictures compared to individuals with the homozygous l genotype . pezawas and colleagues observed an uncoupling of a cingulate - amygdala feedback circuit in healthy carriers of the s - allele . moreover , in this study a structural analysis using optimized voxel - based morphometry showed a significantly reduced gray matter volume of the right and left amygdala in s - allele carriers . taken together , these studies suggest that the 5-httlpr genotype might modulate serotonergic function and , moreover , amygdala function as well as structure in healthy individuals . we hypothesized that the 5-httlpr genotype might impact the amygdala volume generally in patients with bipolar disorder as well as in healthy individuals . in the above mentioned studies on amygdala volume in bipolar disorder the influence of the 5-httlpr genotype were not considered . the aim of this study was to clarify the role of the 5-httlpr genotype on amygdala volume in patients with bipolar i disorder and healthy control subjects . firstly we tested the overall effect of the 5-httlpr genotype on amygdala volume and secondly we looked for a diagnosis specific influence . thirty - seven euthymic patients with bipolar i disorder and 37 healthy control subjects participated in the study ( table 1 ) . written informed consent was obtained from all subjects and the study was approved by the local ethical committee . subjects were recruited from the outpatient unit of the department of psychiatry and psychotherapy of the saarland university hospital . the diagnosis of bipolar i disorder and the condition as healthy subjects was confirmed by using the german version of the structural clinical interview for dsm - iv . the healthy control subjects exhibited no past or present psychiatric , neurological or medical disorder and had no positive family history of psychiatric disorders . table 1demographic and genotype data5-httlpr genotypedff / chipllslssbipolar disorder ( n)8236controls ( n)18145all individuals ( n)263711all individuals ( n)264815.930.01age ( years ; mean sd)39.7 14.544.0 11.41 , 721.980.16education ( years ; mean sd)13.7 2.413.9 2.61 , 720.090.77gender ( male / female)7/1926/2215.070.02handedness ( right / not right)20/642/611.390.24subjects are separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl are combined and compared with the group ll . number ( n ) of subjects and demographic data are shown demographic and genotype data subjects are separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl are combined and compared with the group ll . number ( n ) of subjects and demographic data are shown mri scanning was performed on a 1.5 tesla magnetom ( siemens , erlangen ) and a t1-weighted , mprage sequence of 176 consecutive slices with a voxel size of 1 mm was acquired . one rater blind to diagnosis and genotype ( pm ) determined amygdala volume by direct manual tracing of the boundaries as previously described by brambilla and colleagues . the intra - rater intra - class correlation coefficients ( icc ) , established by double tracing of 14 scans , were icc = 0.980 for the right and icc = 0.978 for the left amygdala . 5-httlpr ( slc6a4)-specific primers ( forward , 5-tagagggactgagctggacaaccac-3 ; reverse , 5-ggtgttgccgctctgaatgc-3 ) were used for polymerase chain reaction ( pcr ) . the thermocycler protocol involved an initial denaturation cycle ( 4 min , 94c ) , 35 cycles of denaturation ( 30 s , 94c ) , annealing ( 30 s , 61.4c ) , and extension ( 30 s , 72c ) , followed by a final extension step ( 7 min , 72c ) , and terminating at 10c . this procedure resulted in fragments of 585 ( short , s ) and 628 ( long , l ) bp in length . fragments were amplified by pcr in a final volume of 50 l containing 100 ng genomic dna , 50 mm kcl , 10 mm tris hcl ( ph 8.3 ) , 0.025 % tween 20 , 0.025 % bsa , 10 pmol of each primer ( mwg biotech ) , 0.2 mm of each dntp ( mbi fermentas ) , 7.5 mm mgcl2 , 5 % dmso and 2 unit of taq polymerase ( eurogentec , seraing , belgium ) . for analysis , 10 l of pcr product were visualized on 1.5 % agarose gels stained with ethidium bromide . the subjects were separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl were combined and compared with the group ll . with this approach we follow several previous studies which combined all individuals with at least one s - allele in one group [ 5 , 6 , 11 ] . the groups divided by genotype ( table 1 ) or by genotype and diagnosis ( table 2 ) did not show significant differences regarding age , education or handedness . however , the female fraction in the group ll was disproportionately high ( table 1 ) , in particular in the control group ( table 2 ) . therefore , we adjusted the main analyses for gender . additionally , we adjusted for age considering the negative correlation between brain volume and age and the hypothesized positive correlation between age and amygdala volume in bipolar disorder . multivariate analyses of covariance ( mancova ) with 5-httlpr polymorphism and gender as independent factors , age as covariate and right and left amygdala volume as dependent variables were calculated ( table 3 ) . additionally , the factor diagnosis was entered into the model to assess whether interactions between genotype and diagnosis could be found ( table 4 ) . table 2demographic data divided by diagnosis and genotypecontrolsbipolar disorderllsl or ssllsl or ss(a ) demographic data age ( years ; mean sd)39.6 15.142.3 10.839.8 14.145.1 11.8 education ( years ; mean sd)13.8 2.414.2 2.813.6 2.613.8 2.5 gender ( male / female)3/1512/74/414/15 handedness ( right / not right)14/415/46/227/25httlpr genotypediagnosisdffpdffp(b ) statistics age ( years ; mean sd)1 , 701.460.231 , 700.210.65 education ( years ; mean sd)1 , 700.150.71 , 701.170.68controlsbipolar disorderdfchipdfchipgender ( male / female)18.290.004 * 10.010.93handedness ( right / not right)10.010.9310.440.51(a ) subjects are separated according to diagnosis and 5-httlpr genotype . ( b ) the statistical analyses exhibited no difference of age , education and handedness between groups . gender allocation was different between groups*significant group differencestable 3mancova with variables of right / left amygdala volume and independent factor 5-httlpr - genotype adjusted for gender and age5-httlpr genotypedffpllsl / ss gray matter volume ( cm)714.7 80.5716.3 74.51 , 690.00.85 absolute amygdala volumes multivariate2 , 683.90.026 * right ( cm ; mean sd)1.23 0.221.38 0.301 , 695.90.018 * left ( cm ; mean sd)1.20 0.251.24 0.251 , 691.60.22 relative amygdala volumes multivariate2 , 683.50.034 * right ( 10 ; mean sd)0.17 0.030.19 0.041 , 695.60.021 * left ( 10 ; mean sd)0.17 0.030.17 0.031 , 691.50.22subjects are separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl are combined and compared with the group ll . right relative amygdala volume is significant increased in s - allele carriers*significant group differencestable 4mancova with independent factors 5-httcpr - polymorphism , diagnosis , gender and covariant agecontrolsbipolar disorderllsl or ss ( % ) llsl or ss ( % ) ( a ) amygdala volume divided by diagnosis and genotype gray matter volume ( cm)707.3 72.8718.2 85.5 + 1.5731.4 99.2714.9 67.52.2 absolute amygdala volumes right ( cm ; mean sd)1.21 0.251.35 0.37 + 11.01.27 0.141.40 0.26 + 10.0 left ( cm ; mean sd)1.19 0.271.26 0.29 + 5.71.21 0.211.24 0.22 + 2.1 relative amygdala volumes right ( 10 ; mean sd)0.171 0.030.187 0.05 + 9.50.176 0.030.196 0.04 + 11.4 left ( 10 ; mean sd)0.168 0.030.176 0.04 + 4.50.166 0.020.173 0.03 + 4.4factor 5httlpr genotypefactor diagnosisinteraction 5htt diagnosisdffpdffpdffp(b ) mancova ( 5httlpr , diagnosis , gender , age ) gray matter volume ( cm)1 , 650.390.531 , 651.000.321 , 650.130.72 absolute amygdala volumes multivariate2 , 642.640.0792 , 640.740.482 , 640.330.72 relative amygdala volumes multivariate2 , 642.030.142 , 640.870.422 , 640.240.79subjects are separated according to 5-httlpr genotype and diagnosis . for statistical analyses the groups ss and sl are combined and compared with the group llsd standard deviation , % difference ss / sl versus ll in percent terms demographic data divided by diagnosis and genotype ( a ) subjects are separated according to diagnosis and 5-httlpr genotype . ( b ) the statistical analyses exhibited no difference of age , education and handedness between groups . gender allocation was different between groups * significant group differences mancova with variables of right / left amygdala volume and independent factor 5-httlpr - genotype adjusted for gender and age subjects are separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl are combined and compared with the group ll . right relative amygdala volume is significant increased in s - allele carriers * significant group differences mancova with independent factors 5-httcpr - polymorphism , diagnosis , gender and covariant age subjects are separated according to 5-httlpr genotype and diagnosis . for statistical analyses the groups ss and sl are combined and compared with the group ll sd standard deviation , % difference ss / sl versus ll in percent terms thirty - seven euthymic patients with bipolar i disorder and 37 healthy control subjects participated in the study ( table 1 ) . written informed consent was obtained from all subjects and the study was approved by the local ethical committee . subjects were recruited from the outpatient unit of the department of psychiatry and psychotherapy of the saarland university hospital . the diagnosis of bipolar i disorder and the condition as healthy subjects was confirmed by using the german version of the structural clinical interview for dsm - iv . the healthy control subjects exhibited no past or present psychiatric , neurological or medical disorder and had no positive family history of psychiatric disorders . table 1demographic and genotype data5-httlpr genotypedff / chipllslssbipolar disorder ( n)8236controls ( n)18145all individuals ( n)263711all individuals ( n)264815.930.01age ( years ; mean sd)39.7 14.544.0 11.41 , 721.980.16education ( years ; mean sd)13.7 2.413.9 2.61 , 720.090.77gender ( male / female)7/1926/2215.070.02handedness ( right / not right)20/642/611.390.24subjects are separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl are combined and compared with the group ll . number ( n ) of subjects and demographic data are shown demographic and genotype data subjects are separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl are combined and compared with the group ll . mri scanning was performed on a 1.5 tesla magnetom ( siemens , erlangen ) and a t1-weighted , mprage sequence of 176 consecutive slices with a voxel size of 1 mm was acquired . one rater blind to diagnosis and genotype ( pm ) determined amygdala volume by direct manual tracing of the boundaries as previously described by brambilla and colleagues . the intra - rater intra - class correlation coefficients ( icc ) , established by double tracing of 14 scans , were icc = 0.980 for the right and icc = 0.978 for the left amygdala . 5-httlpr ( slc6a4)-specific primers ( forward , 5-tagagggactgagctggacaaccac-3 ; reverse , 5-ggtgttgccgctctgaatgc-3 ) were used for polymerase chain reaction ( pcr ) . the thermocycler protocol involved an initial denaturation cycle ( 4 min , 94c ) , 35 cycles of denaturation ( 30 s , 94c ) , annealing ( 30 s , 61.4c ) , and extension ( 30 s , 72c ) , followed by a final extension step ( 7 min , 72c ) , and terminating at 10c . this procedure resulted in fragments of 585 ( short , s ) and 628 ( long , l ) bp in length . fragments were amplified by pcr in a final volume of 50 l containing 100 ng genomic dna , 50 mm kcl , 10 mm tris hcl ( ph 8.3 ) , 0.025 % tween 20 , 0.025 % bsa , 10 pmol of each primer ( mwg biotech ) , 0.2 mm of each dntp ( mbi fermentas ) , 7.5 mm mgcl2 , 5 % dmso and 2 unit of taq polymerase ( eurogentec , seraing , belgium ) . for analysis , 10 l of pcr product were visualized on 1.5 % agarose gels stained with ethidium bromide . the subjects were separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl were combined and compared with the group ll . with this approach we follow several previous studies which combined all individuals with at least one s - allele in one group [ 5 , 6 , 11 ] . the groups divided by genotype ( table 1 ) or by genotype and diagnosis ( table 2 ) did not show significant differences regarding age , education or handedness . however , the female fraction in the group ll was disproportionately high ( table 1 ) , in particular in the control group ( table 2 ) . therefore , we adjusted the main analyses for gender . additionally , we adjusted for age considering the negative correlation between brain volume and age and the hypothesized positive correlation between age and amygdala volume in bipolar disorder . multivariate analyses of covariance ( mancova ) with 5-httlpr polymorphism and gender as independent factors , age as covariate and right and left amygdala volume as dependent variables were calculated ( table 3 ) . additionally , the factor diagnosis was entered into the model to assess whether interactions between genotype and diagnosis could be found ( table 4 ) . table 2demographic data divided by diagnosis and genotypecontrolsbipolar disorderllsl or ssllsl or ss(a ) demographic data age ( years ; mean sd)39.6 15.142.3 10.839.8 14.145.1 11.8 education ( years ; mean sd)13.8 2.414.2 2.813.6 2.613.8 2.5 gender ( male / female)3/1512/74/414/15 handedness ( right / not right)14/415/46/227/25httlpr genotypediagnosisdffpdffp(b ) statistics age ( years ; mean sd)1 , 701.460.231 , 700.210.65 education ( years ; mean sd)1 , 700.150.71 , 701.170.68controlsbipolar disorderdfchipdfchipgender ( male / female)18.290.004 * 10.010.93handedness ( right / not right)10.010.9310.440.51(a ) subjects are separated according to diagnosis and 5-httlpr genotype . ( b ) the statistical analyses exhibited no difference of age , education and handedness between groups . gender allocation was different between groups*significant group differencestable 3mancova with variables of right / left amygdala volume and independent factor 5-httlpr - genotype adjusted for gender and age5-httlpr genotypedffpllsl / ss gray matter volume ( cm)714.7 80.5716.3 74.51 , 690.00.85 absolute amygdala volumes multivariate2 , 683.90.026 * right ( cm ; mean sd)1.23 0.221.38 0.301 , 695.90.018 * left ( cm ; mean sd)1.20 0.251.24 0.251 , 691.60.22 relative amygdala volumes multivariate2 , 683.50.034 * right ( 10 ; mean sd)0.17 0.030.19 0.041 , 695.60.021 * left ( 10 ; mean sd)0.17 0.030.17 0.031 , 691.50.22subjects are separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl are combined and compared with the group ll . right relative amygdala volume is significant increased in s - allele carriers*significant group differencestable 4mancova with independent factors 5-httcpr - polymorphism , diagnosis , gender and covariant agecontrolsbipolar disorderllsl or ss ( % ) llsl or ss ( % ) ( a ) amygdala volume divided by diagnosis and genotype gray matter volume ( cm)707.3 72.8718.2 85.5 + 1.5731.4 99.2714.9 67.52.2 absolute amygdala volumes right ( cm ; mean sd)1.21 0.251.35 0.37 + 11.01.27 0.141.40 0.26 + 10.0 left ( cm ; mean sd)1.19 0.271.26 0.29 + 5.71.21 0.211.24 0.22 + 2.1 relative amygdala volumes right ( 10 ; mean sd)0.171 0.030.187 0.05 + 9.50.176 0.030.196 0.04 + 11.4 left ( 10 ; mean sd)0.168 0.030.176 0.04 + 4.50.166 0.020.173 0.03 + 4.4factor 5httlpr genotypefactor diagnosisinteraction 5htt diagnosisdffpdffpdffp(b ) mancova ( 5httlpr , diagnosis , gender , age ) gray matter volume ( cm)1 , 650.390.531 , 651.000.321 , 650.130.72 absolute amygdala volumes multivariate2 , 642.640.0792 , 640.740.482 , 640.330.72 relative amygdala volumes multivariate2 , 642.030.142 , 640.870.422 , 640.240.79subjects are separated according to 5-httlpr genotype and diagnosis . for statistical analyses the groups ss and sl are combined and compared with the group llsd standard deviation , % difference ss / sl versus ll in percent terms demographic data divided by diagnosis and genotype ( a ) subjects are separated according to diagnosis and 5-httlpr genotype . ( b ) the statistical analyses exhibited no difference of age , education and handedness between groups . gender allocation was different between groups * significant group differences mancova with variables of right / left amygdala volume and independent factor 5-httlpr - genotype adjusted for gender and age subjects are separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl are combined and compared with the group ll . right relative amygdala volume is significant increased in s - allele carriers * significant group differences mancova with independent factors 5-httcpr - polymorphism , diagnosis , gender and covariant age subjects are separated according to 5-httlpr genotype and diagnosis . for statistical analyses the groups ss and sl are combined and compared with the group ll sd standard deviation , % difference ss / sl versus ll in percent terms the multivariate analyses with independent factors 5-httlpr polymorphism and gender and covariate age revealed a significant effect for 5-httlpr genotype on absolute ( df = 2 , 68 , f = 3.9 , p < 0.05 ) and relative ( df = 2 , 68 , f = 3.5 , p < 0.05 ) amygdala volume ( table 3 ) . following univariate tests showed that the absolute ( + 12% , df = 1 , 69 , f = 5.9 , p < 0.05 ) and relative volume of the right amygdala ( + 12% , df = 1 , 69 , f = 5.6 , p < 0.05 ) were increased in s - allele carriers compared to individuals with the homozygous l - genotype ( table 3 ; fig . 1 ) . absolute and relative volumes of the right amygdala were increased in s - allele carriers for both groups investigated in this study ( healthy controls : absolute volume + 11% , relative volume + 9.4% ; patients with bipolar disorder : absolute volume + 10% , relative volume + 11.4% ) . the additional mancova with the independent factors 5-httlpr - polymorphism , diagnosis , gender and covariate age was only able to show a statistical trend for the multivariate analysis of the factor 5-httlpr on absolute amygdala volumes , though . with respect to the factor diagnosis or the interaction between genotype and diagnosis no significant effect was found ( table 4 ) . the right relative amygdala volume is increased in s - allele carriers compared to subjects with homozygous l genotype ( p < 0.05 ) . the right relative amygdala volume is increased in s - allele carriers compared to subjects with homozygous l genotype ( p < 0.05 ) . in this study we investigated the influence of the 5-httlpr polymorphism on amygdala volume in healthy individuals and patients with bipolar disorder . the analyses revealed increased absolute and relative volumes of the right amygdala in all s - allele carriers of the 5-httlpr polymorphism . these findings indicate that the 5-httlpr genotype has an impact on amygdala volume both in patients with bipolar disorder and healthy control subjects . further analyses with the additional factor diagnosis were unable to show an effect of genotype or diagnosis on absolute or relative amygdala volume . even though no interaction between genotype and diagnosis was found , we were not able to show that the increased amygdala volume depends on the genotype only . however , as both healthy individuals and patients with bipolar disorder displayed an increased amygdala volume in the first analysis , we hypothesize a potential general influence of the 5-httlpr polymorphism on amygdala volume . the statistical not significant findings of the second analyses might result from the relatively small sample size of 74 subjects . nevertheless , we interpret these data as an indication for a possible interaction between 5-httlpr - genotype and amygdala volume . further analyses with a larger sample size might be able to verify these first results . an increased volume of the amygdala derived from mri could indicate an increased number of neurons in this brain region . it has been discussed that variations in mri measurements potentially reflect alterations of neuronal and non - neuronal tissue compartments , physiological alterations in brain tissue or changes in other chemical constituents . however , a recent study using post mortem tissue of the pulvinar from patients with major depressive disorder , bipolar disorder , schizophrenia and healthy controls reported a higher number and volume of pulvinar neurons in subjects with the homozygous short 5-httlpr genotype . as both the pulvinar and amygdala contain high levels of serotonin transporter and are connected with each other the possible effects of 5-httlpr genotype on neurons might be comparable . we hypothesize , therefore , that the increased amygdala volume in s - allele carriers may reflect a higher number of neurons or an increased volume of neurons in the right amygdala . as we found this relatively increased volume both in healthy control subjects and patients with bipolar disorder we hypothesize furthermore that it might reflect a basic regulatory mechanism between serotonin transporter function and neuronal number or size in amygdala and maybe in other regions of the human brain . as a relatively increased volume may also account for increased activity observed in functional mri studies , our data is in accord with prior findings of higher amygdala activity in healthy carriers of the s - allele [ 5 , 6 ] . by contrast , another study using voxel - based morphometry observed a reduction of amygdala gray matter volume in healthy s - allele carriers . investigation with voxel - based morphometry ( vbm ) allows structural analyses free from hypotheses and user - bias . despite these advantages , its general application in structural mri studies a recent study concluded that manual tracing of the corpus callosum was more sensitive in detecting discrete structural changes than vbm . therefore , the different findings in the vbm and the present study may be caused by methodological differences . however , an increased volume of the amygdala with a higher number of neurons or an increased neuronal size could explain the observed higher activation in these subjects . taken together , the present findings are consistent with the view that the 5-httlpr polymorphism may modulate neuronal size or number in the amygdala . it seems to be worthwhile to investigate the relationship between serotonin transporter function and amygdala function and volume in further studies . moreover , 5-httlpr genotype might be used as a covariate in further structural mri investigations .

backgroundfunctional imaging studies in healthy individuals revealed an association between 5-httlpr genotype and neuronal activity in the amygdala . the aim of this study was firstly to investigate a possible overall impact of the 5-httlpr on amygdala volume in patients with bipolar disorder and healthy individuals and secondly to test a diagnosis specific influence of the 5-httlpr on amygdala volume.methodswe performed a region of interest analysis of amygdala volume in 37 patients with bipolar i disorder and 37 healthy control subjects . the 5-httlpr genotype of each proband was determined and the subjects were separated according to 5-httlpr genotype and for statistical analyses the groups ss and sl were combined and compared with the group ll.resultsthis study shows that carriers of the short allele ( sl or ss ) of the 5-httlpr polymorphism exhibit a relatively increased volume of the right amygdala compared to homozygous l - allele carriers irrespective of diagnosis status . however , further analyses with the factors genotype and diagnosis were not able to reproduce this result.conclusionsthe present findings are consistent with the view that the 5-httlpr polymorphism might modulate neuronal size or number in the amygdala . it would be worthwhile investigating the relationship between serotonin transporter function and amygdala function and volume in further studies .

there has been considerable interest in the emergence of non - trivial paramagnetic ground states of quantum magnets with interacting spin @xmath2 local moments . such non - trivial quantum paramagnets would occur in low dimensional systems or on geometrically frustrated lattices . two prominent examples of such quantum paramagnetic ground states are quantum spin liquids and valence bond solids.@xcite the determination of the underlying hamiltonian in such systems , however , has been a challenge as this often requires the detailed information about the spectra of the elementary excitations as well as the ground state . more specifically , the dispersion of the @xmath2 charge - neutral spinon excitations or more accurately the two - spinon continuum would be an essential information to determine the hamiltonian for quantum spin liquids . in the case of the valence bond solids , the triplon dispersions and dynamics would play similar roles . in two- and three - dimensional quantum magnets , such information is quite scarce and this has remained as one of the main challenges both in experimental and theoretical studies of these systems . this is in contrast to magnetically ordered systems where accurate determination of spin wave spectrum has been around for a long time , which is often used to infer the minimal spin hamiltonian . in this work , we present a theoretical study of triplon dynamics in the valence bond solid ground state of the coupled spin - ladder system , designed to explain magnetic properties of bicu@xmath0po@xmath1.@xcite in particular , we investigate a possible minimal spin hamiltonian that is consistent with previous experimental results . the recent high quality neutron scattering experiments reported in ref . [ ] enable us to construct the model using the valuable information on triplon dispersions and two - triplon continuum . combining the theoretical results obtained in the bond operator formulation@xcite of the spin model and the spectra of the collective modes measured in the experiments , we determine various anisotropic spin interactions . it is found that the low energy properties of the triplons can only be explained in the presence of substantial dzyaloshinskii - moriya and symmetric anisotropic spin interactions.@xcite it is shown that the interactions between the triplons renormalize the triplon dispersions and more importantly the anisotropic spin interactions are primarily responsible for the triplon decay into two - triplon continuum . our study of the triplon dynamics in this system provides a useful framework to understand the roles of various anisotropic spin interactions and presents an opportunity to determine the spin hamiltonian of the valence bond solid ( vbs ) ground states in considerable details . the rest of the paper is organized as follows . we introduce our model hamiltonian for bicu@xmath0po@xmath1 and the vbs ground state in sec . [ sec : model_vbs ] . the vbs state and its triplon excitations are described using the bond operator formulation in sec . [ sec : quadratic ] , where the importance of anisotropic spin interactions is discussed in comparison with the experimentally measured triplon dispersions . in sec . [ sec : decay ] , it is shown that the anisotropic spin interactions are responsible for the triplon decay into the two - triplon continuum . finally our results are summarized with an outlook in sec . [ sec : conclusion ] . we start by describing our model hamiltonian for bicu@xmath0po@xmath1 and the vbs ground state . po@xmath1.[fig : lattice ] ] we consider the lattice structure in fig . [ fig : lattice ] and introduce the spin model described in eq . ( [ eq : spin_model ] ) with two types of anisotropic spin interactions , which are the dzyaloshinskii - moriya ( @xmath3 ) and anisotropic & symmetric ( @xmath4 ) interactions , as well as the isotropic heisenberg interactions ( @xmath5 ) . @xmath6 where @xmath7 is a @xmath2 moment at site @xmath8 , @xmath9 , and summation convention for repeated greek indices is assumed . we set the @xmath10 directions along the crystallographic @xmath11 axes ( fig . [ fig : lattice ] ) , respectively . based on the crystal symmetry @xmath12 of bicu@xmath0po@xmath1,@xcite there are five independent links as denoted with different colors in the figure . accordingly , there are five independent heisenberg interactions : @xmath13 along the zigzag legs ( magenta ) , @xmath14 and @xmath15 along the straight legs ( green and orange , respectively ) , @xmath16 on the rungs of the ladders ( blue ) , and @xmath17 as the inter - ladder couplings ( gray ) . distinction between @xmath14 and @xmath15 arises from the existence of two inequivalent cu sites ( denoted with different colored balls ) . the antiferromagnetic couplings @xmath13 , @xmath14 , @xmath15 form triangular structures on the lattice and generate magnetic frustration in the system . superexchange pathways are given by cu - o - cu for @xmath13 and @xmath17 , and cu - o - o - cu for @xmath14 , @xmath15 , and @xmath16.@xcite as pointed out in refs . [ ] and [ ] , the cu - o - cu bond angle for the @xmath17 exchange is close to 90@xmath18 in contrast to the other exchange interactions , implying that @xmath17 can be weak antiferromagnetic or ferromagnetic according to the goodenough - kanamori rule.@xcite we assume that the coupling @xmath17 is weak in magnitude compared to the other exchange interactions , @xmath13 , @xmath14 , @xmath15 , @xmath16 , dominated by the antiferromagnetic superexchange . the dzyaloshinskii - moriya ( dm ) vectors @xmath19 can also be determined by the crystal symmetry.@xcite we list the symmetry - constrained dm vectors in table [ tab : indep_coupling ] for twelve links in a unit cell . in the table , dm vectors are decomposed along the @xmath11 axes : @xmath20 with @xmath21 being orthonormal vectors along the crystallographic axes . the minus signs and zero values in the vector components arise from the pseudo - vector nature of @xmath3 , and _ mirror _ & _ inversion _ symmetries in the system . ccccc @xmath22 & @xmath5 & @xmath23 & @xmath24 & @xmath25 + @xmath26 & @xmath13 & @xmath27 & @xmath28 & @xmath29 + @xmath30 & @xmath13 & @xmath27 & @xmath31 & @xmath29 + @xmath32 & @xmath13 & @xmath27 & @xmath31 & @xmath29 + @xmath33 & @xmath13 & @xmath27 & @xmath28 & @xmath29 + + @xmath34 & @xmath14 & @xmath35 & @xmath36 & @xmath37 + @xmath38 & @xmath14 & @xmath35 & @xmath36 & @xmath37 + + @xmath39 & @xmath15 & @xmath40 & @xmath36 & @xmath41 + @xmath42 & @xmath15 & @xmath40 & @xmath36 & @xmath41 + + @xmath43 & @xmath17 & @xmath36 & @xmath44 & @xmath36 + @xmath45 & @xmath17 & @xmath36 & @xmath44 & @xmath36 + + @xmath46 & @xmath16 & @xmath36 & @xmath47 & @xmath36 + @xmath48 & @xmath16 & @xmath36 & @xmath47 & @xmath36 + we constrain the coupling constant matrix @xmath4 of the anisotropic & symmetric interaction by requiring the following condition : @xmath49 here underlying assumption is that the spin exchange interaction is generated by the antiferromagnetic superexchange mechanism . then , the condition comes from the fact that both of @xmath50 and @xmath51 interactions originate from the spin - orbit coupling in the microscopic hubbard model ( see ref . [ ] or appendix [ app : dm ] ) . as mentioned earlier , @xmath17 is not dominated by the antiferromagnetic superexchange . hence , eq . ( [ eq : gamma ] ) is not applied to the @xmath17 links ( gray in fig . [ fig : lattice ] ) . we find that @xmath52 and @xmath53 are not essential for describing overall magnetic anisotropies in the system so that we will ignore @xmath52 and @xmath53 afterwards ( @xmath54 ) . we will investigate the magnetic field response of the system later . in this case , we consider the zeeman interaction : @xmath55 with @xmath56 being the magnetic field . in principle , we could consider symmetry - allowed @xmath57-tensors for two inequivalent cu@xmath58 ions to allow anisotropy in the zeeman interaction as well . however , this will introduce more parameters needed to be determined , rendering the theory more complicated . for simplicity , we assume an isotropic @xmath57-factor with @xmath59 . ] now we discuss the valence bond solid phase as the ground state of bicu@xmath0po@xmath1 . the vbs phase is depicted in fig . [ fig : vbs ] . here , the valence bonds are formed at the @xmath16-links or the rungs of the spin ladders ( denoted with thick black lines ) . we call this phase the rung - vbs in this paper . the existence of a vbs phase in bicu@xmath0po@xmath1 has been hinted through earlier studies . a finite spin gap and elementary spin-1 excitations in the compound are evidences for a vbs state . the finite spin gap was observed in various experiments such as the heat capacity , magnetic susceptibility , nmr , and neutron scattering.@xcite the spin-1 excitations have been detected in recent inelastic neutron scattering experiments.@xcite the spin-1 character of the excitations was inferred by investigating their behaviours under external magnetic fields . the structure of the vbs state was investigated in the elaborate work by tsirlin _ et al._@xcite they constructed a heisenberg spin ladder model and studied it by using various numerical techniques and experimental informations . it was shown that the ground state of the heisenberg spin ladder model has strong bond strength @xmath60 at the rungs in the exact diagonalization studies . this numerical result suggests that the rung - vbs phase arises in their model , where they did nt consider anisotropic spin interactions . the spin model in eq . ( [ eq : spin_model ] ) is a generalization of the heisenberg spin ladder model with anisotropic spin interactions , which turns out to be extremely important to describe the neutron scattering data . in the next section , we show that the model in eq . ( [ eq : spin_model ] ) provides an excellent description of the triplon excitations seen in the scattering experiments on bicu@xmath0po@xmath1 . in the following , we will describe the triplon excitations in the bond operator theory developed for the rung - vbs phase . bond operator theory@xcite is a useful framework for describing a valence bond solid phase and its spin-1 triplon excitations . the theory is built upon the bond operator representation of the spin operators @xmath61 forming a valence bond . @xmath62 where @xmath63 , and @xmath64 is the totally antisymmetric tensor . the bond operators @xmath65 and @xmath66 create the spin - singlet and spin - triplet states of @xmath61 , respectively , and follow the boson statistics . in order to keep the physical hilbert space consisting of the four states ( the singlet and triplet ) , the hardcore constraint should be imposed : @xmath67 . we express the original spin hamiltonian eq . ( [ eq : spin_model ] ) in terms of the bond operators by using the representation eq . ( [ eq : bond_op ] ) with the dimer covering for the rung - vbs state in fig . [ fig : vbs ] . in the resulting bond operator hamiltonian , the rung - vbs state can be described by condensing the @xmath68-bosons at all the dimers : @xmath69 . the hardcore constraint is incorporated at each dimer with the lagrange multiplier @xmath70 as @xmath71 . exploiting the crystal symmetry of bicu@xmath0po@xmath1 , we set the parameters @xmath72 to be uniform across all the dimers . then , we end up with the following form of the bond operator hamiltonian . @xmath73 here , the hamiltonian is arranged according to the order of the @xmath74-boson operator . @xmath75 consists of the quadratic terms like @xmath76 , @xmath77 , and their hermitian conjugates . @xmath78 contains the cubic terms @xmath79 and @xmath80 . @xmath81 has the quartic terms of the form @xmath82 . in the above expression , we also included the zeeman interaction [ eq . ( [ eq : zeeman ] ) ] , which only has quadratic terms since possible linear terms are cancelled . below , we develop a simple quadratic bond operator theory by keeping only the quadratic part @xmath75 in the hamiltonian . via this quadratic theory , we describe the low energy triplon excitations around the spin gap observed in experiments . we will consider higher order interactions later in this paper . the quadratic bond operator hamiltonian has the following form in the momentum space after the fourier transformation . @xmath83 where @xmath84 is a function of @xmath85 and @xmath70 , and @xmath86 with @xmath87 and similarly for @xmath88 and @xmath89 . here , the subscripts , 1 and 2 , in the @xmath74-operators indicate the two dimers in a unit cell ( shown in fig . [ fig : vbs ] ) . as mentioned earlier , the @xmath10 directions are taken parallel to the crystallographic @xmath11 axes . the @xmath90 , @xmath50 , @xmath51 , and @xmath91 interactions in the original spin hamiltonian are transformed to the triplon hopping and pairing amplitudes contained in the 12@xmath9212 matrix @xmath93 . the quadratic hamiltonian has two notable features : ( i ) its dependences on @xmath14 and @xmath15 appear only through the sum @xmath94 , and ( ii ) the @xmath95 interactions cancel each other at the quadratic level without any contribution to @xmath75 . these features will be discussed again later . the detailed form of @xmath75 is provided in appendix [ app : matrix ] . the quadratic hamiltonian is diagonalized via the bogoliubov transformation leading to the following form : @xmath96 here , @xmath97 is the bogoliubov quasiparticle operator or the _ triplon _ with the excitation energy @xmath98 . the constant term corresponds to the ground state energy , @xmath99 . with this setting , the parameters @xmath85 and @xmath70 for the ground state are determined by the saddle point equations : @xmath100 in the ground state , we also compute the magnetization , @xmath101 , under nonzero magnetic fields as follows . @xmath102 with @xmath103 being the number of the spin moments . before discussing the results of the quadratic theory , we comment on our conventions about the brillouin zone and momentum vectors . for direct comparisons of our theoretical computations with experimental results , we use the extended zone scheme for the brillouin zone and denote momentum vectors in reciprocal lattice unit as @xmath104 , which means @xmath105 with @xmath106 being the reciprocal lattice vectors corresponding to the lattice vectors @xmath107 along the @xmath11 axes , repsectively . , in the quadratic bond operator theory . the dispersions are compared with the neutron scattering results in ref . [ ] ( denoted wth color dots ) . the spin gap positions , @xmath108 , are marked by the arrows . the gray region indicates the multi - triplon continuum computed with eq . ( [ eq : two - triplon ] ) . error bars in the neutron scattering data represent the energy widths ( or decay rates ) of the measured quasiparticle peaks . [ fig : quad_band ] ] the triplon dispersions obtained in the quadratic theory can be fitted with the experimental results@xcite by controlling the coupling constants @xmath109 . figure [ fig : quad_band ] shows the best fit ( black lines ) with the neutron scattering data ( color dots ) along the momentum direction @xmath110 , yielding the following set of the coupling constants . @xmath111 the other coupling constants not shown here are set to zero since they are found to be irrelevant for describing essential features of the neutron scattering data . as mentioned earlier , the @xmath95 couplings cancel each other in the quadratic hamiltonian @xmath75 whereas the @xmath112 couplings survive at the quadratic level . hence , we control the @xmath112 couplings instead of the @xmath95 couplings . the @xmath95 couplings in eq . ( [ eq : coupling_const ] ) are the values obtained from the @xmath112 couplings and the relationship eq . ( [ eq : gamma ] ) . as will be shown later , the @xmath95 interactions appear in the cubic terms of @xmath78 . their effects on the triplon excitations will be investigated in a later part of this paper . further discussions on the parameter regime of eq . ( [ eq : coupling_const ] ) are provided in appendix [ app : fitting ] . the quadratic theory with the coupling constants in eq . ( [ eq : coupling_const ] ) yields _ six nondegenerate _ , triplon dispersions ( see fig . [ fig : quad_band ] ) . it is due to the fact that the anisotropic and symmetric couplings , @xmath112 , completely break the so(3 ) spin rotation symmetry existing at the level of heisenberg model , and there are two dimers in a unit cell . the spin gap ( minimum excitation energy ) occurs at the incommensurate momentum positions : @xmath108 and their equivalent momenta translated by reciprocal lattice vectors ( denoted with arrows in the figure ) . we find that the lowest three dispersions are in good agreement with the neutron scattering results around the spin gap . among the other higher - energy three dispersions , only one of them is experimentally observed and qualitatively consistent with the theoretical result ( see the highest line of blue dots ) . in regions away from the spin gap , however , the quadratic theory can not fully explain the results from the experimental measurements . to be specific , inside the gray region , the lowest dispersion bends downward ( red ) , and the lowest two triplon modes decay at certain momenta ( red and green ) . these features are believed to be the effects of triplon interactions coming from , for example , the cubic terms generated by the @xmath95 interactions . these effects will be discussed later . at the moment , we focus on the low energy part around the spin gap ( below the gray region ) and see if the quadratic theory provides a satisfactory description of the low energy spin dynamics in bicu@xmath0po@xmath1 . as we have already seen , the theory is in good agreement with the neutron scattering results in the low energy region . this fact supports the idea that the spin excitations observed in the neutron scattering are triplon excitations , confirming the rung - vbs state in bicu@xmath0po@xmath1 . below we provide more evidences for this conclusion . as another mean to check that the observed excitation modes are the triplons in the rung - vbs phase , their field responses can be examined in the theory and compared with the experimental data . turning on the zeeman interaction in the quadratic bond operator hamiltonian , we compute the triplon excitation spectrum as a function of the magnetic field . the obtained spectra are plotted in fig . [ fig : zeeman ] at the spin gap positions , @xmath113 . existing experimental data@xcite is only for the fields along the @xmath114 axis , which is also denoted in the figure with color dots . one can find that the theoretical result is consistent with the experimental data both qualitatively and quantitatively ( left panel ) . for example , it was observed in experiments that the lowest mode ( red ) is almost not reacting to the magnetic field whereas the other two higher energy modes are moving downward ( green ) and upward ( blue ) , respectively . these behaviours are well captured in the theoretical result . the observed magnetic field response also tells us that the triplon modes do not possess any degeneracy as predicted in the theory . notice that , in general , the magnetic field dependence of the triplon dispersion is not linear in magnetic field , especially for the two higher energy triplon modes ( green and blue dots in fig . [ fig : zeeman ] ) . indeed the magnetic field dependence of the two higher energy modes follows @xmath115 behaviour . this is due to the fact that the triplon modes do not possess well - defined spin quantum number ( @xmath116 , spin component along the field direction ) as a result of magnetic anisotropies . instead the usual spin quantum numbers ( @xmath117 ) in the spin isotropic case are mixed in the triplon modes . the non - linear magnetic field dependence can also be found in other field directions . it can be seen that certain triplon modes have almost constant energy in magnetic field . for instance , when the magnetic field is applied along the @xmath114 axis , the energy of the lowest energy triplon mode is basically constant ( red dots in fig . [ fig : zeeman ] ) , implying that the spin character of this mode is dominated by the quantum number @xmath118 . similar behavior is also found in the second / third lowest mode under the magnetic field along @xmath119/@xmath120 axis ( see the middle and right panels in fig . [ fig : zeeman ] ) . accordingly , we can characterize three triplon modes approximately as the @xmath118 , @xmath121 , @xmath122 states from the lowest to the highest energy modes ( the spin characters can be directly identified by taking the spin projections of the triplon mode eigenvectors ) . in other words , three triplon modes have their own approximate spin quantization axes . if the applied magnetic field is not along the quantization axis , triplon modes follow non - linear magnetic field dependence and can be characterized by mixed spin states . , as a function of magnetic field , @xmath91 , obtained in the theory . the magnetization is computed with eq . ( [ eq : magnetization ] ) for the magnetic fields along the @xmath11 axes . the figure shows the the magnetization components along the field directions . other components perpendicular to the field are zero . [ fig : magnetization ] ] we now discuss the magnetization process of the system . recent high magnetic field experiments in ref . [ ] show that bicu@xmath0po@xmath1 undergoes a cascade of field - induced phase transitions with anisotropic magnetic responses to different field directions . upon increasing the field , the magnetization monotonically increases with different slopes depending on the field direction until the system reaches the transition where the spin gap is closed . the average slope or susceptibility , @xmath123 , has the sequence of @xmath124 and concomitantly the critical field , @xmath125 , has the opposite sequence of @xmath126 , where the superscripts denote the applied field direction . the above experimental features can be explained in the quadratic bond operator theory . figure [ fig : magnetization ] shows the magnetizations predicted from the theory , which are consistent with the susceptibility sequence pattern observed in the experiments . on the other hand , the critical fields can be read from the previous triplon energy plots in fig . [ fig : zeeman ] . extrapolating the triplon spectra ( gray dashed lines ) , we find that @xmath127 in the quadratic theory . although the value of @xmath128 is a bit larger than the measured value , the right trend in the sequence of the critical fields is well captured in the theory . in the previous sections , we have observed remarkable consistency between the quadratic bond operator theory and experiment in the low energy regions . this fact implies that bicu@xmath0po@xmath1 has the rung - vbs ground state with the triplons as the elementary excitations . moreover , the theory tells us that the couplings in eq . ( [ eq : coupling_const ] ) are minimal interactions . on the other hand , the experimental data deviates from the theoretical calculations in the gray region of fig . [ fig : quad_band ] with the following features : ( i ) downward bending of the lowest triplon dispersion ( red ) , ( ii ) abrupt decays of the lowest two triplon modes at certain momenta ( red and green ) , and ( iii ) broadened energy width or increased decay rate in the third lowest dispersion ( blue ) . notice that the gray region in the figure denotes multi - triplon continuum with the lower boundary computed as the minimum energy of two - triplon excitations : @xmath129 , \label{eq : two - triplon}\ ] ] where @xmath130 is the single - triplon dispersion in the quadratic theory with @xmath131 being band indices . this fact proposes a picture that the triplons are strongly interacting within the triplon continuum region so that they lose their prominence as quasiparticle modes inside the region . thus , we need to consider the interactions between triplons to capture triplon decay processes . now we consider the influence of triplon interactions on the triplon dynamics in bicu@xmath0po@xmath1 . two main effects are expected from the triplon interactions : triplon energy renormalization and decay.@xcite these two effects are closely related with the triplon phenomenology observed in the neutron scattering experiments ( substantial energy splittings around the spin gap and decay phenomena inside the triplon continuum ) . the triplon interactions are taken into account by extending the previous quadratic bond operator theory . for the spin hamiltonian [ eq . ( [ eq : spin_model ] ) ] with the couplings in eq . ( [ eq : coupling_const ] ) , we arrange the corresponding bond operator hamiltonian in the following way : @xmath132 + \mathcal{h}_{cubic}[d_1 ] + \mathcal{h}_{quartic}[d_1,\gamma_1],\ ] ] where we have denoted the dependence on the anisotropic couplings in the square brackets . we will take the mean - field approximations for @xmath81 and use the cubic interactions , @xmath78 , to describe the triplon decay processes . in this approach , the triplon modes and their decays are identified via the peak structures in the spectral weight function of the triplon green s function . this approach reveals that the @xmath95 couplings have noticeable contributions on the energy splittings around the spin gap as well as the decay phenomena inside the triplon continuum . readers interested in the results rather than the calculational details are advised to directly move to sec . [ sec : result ] . the quartic terms in @xmath81 provide two - body scatterings of the @xmath74-bosons . we include the two - body interactions in the mean - field approximations , leading to the following mean - field hamiltonian : @xmath133 for the mean - field decouplings , we employ particle - particle ( @xmath134 ) and particle - hole ( @xmath135 ) channels . details of the decoupling scheme are explained in appendix [ app : mf ] . the cubic terms in @xmath78 provide decay and fusion processes of the @xmath74-bosons ( @xmath136 ) . the processes are induced by the cubic terms from the @xmath95 and @xmath17 couplings whereas the other couplings , @xmath13 , @xmath137 , @xmath16 , and @xmath112 , do not have such cubic terms because of symmetry reasons . more details about the existence of the cubic terms and the associated symmetry are provided in appendix [ app : decay ] . we will investigate the effects of the cubic interactions via the green s function approach.@xcite in this approach , the triplons determined from the mean - field hamitonian , @xmath138 , are taken as the bare particles . we express the interaction part @xmath78 in terms of the bare triplons ( @xmath139 ) from @xmath138 , which leads to the following form : @xmath140 here , we use the shorthand notations : @xmath141 , and so forth for @xmath142 , @xmath143 . in addition to the decay and fusion terms for the triplons ( @xmath144 and @xmath145 ) , we have the source and sink terms for the @xmath139-triplons ( @xmath146 and @xmath147 ) in the above expression . the vertex functions , @xmath148 and @xmath149 , are functions of the singlet - condensation ( @xmath85 ) , the bogoliubov transformation matrix of @xmath138 , the coupling constants ( @xmath90 s , @xmath95 , @xmath112 ) , and the lattice vectors ( @xmath150 ) . the vertex function @xmath149 is totally symmetric whereas the other @xmath148 is symmetric only for the first two arguments : @xmath151 . it is convenient to recast the total hamiltonian as follows . @xmath152 with the kinetic part @xmath153 ( from @xmath154 and the interaction part @xmath155 . we now define the triplon green s function : @xmath156 \rangle , \end{aligned}\ ] ] where the average @xmath157 is taken for the ground state of @xmath158 with the time - ordering operator @xmath159 . here , we set @xmath160 , and @xmath161 with @xmath162^t$ ] . the green s function is written as the following 12@xmath9212 matrix : @xmath163 , \label{eq : g - fun}\ ] ] with the normal green s function parts @xmath164 and the anomalous function parts @xmath165 as the 6@xmath926 submatrices . the triplon self energy has the same matrix structure : @xmath166.\ ] ] the green s function and the self energy are related by the dyson equation : @xmath167 in the momentum - frequency space , the bare green s function @xmath168 for the hamiltonian @xmath169 is a diagonal matrix with the matrix elements @xmath170_{mn } = \frac{\delta_{mn}}{\omega-\omega_{m}({\bf k})+i\eta},\ ] ] where @xmath171 are the triplon eigenvalues obtained from @xmath138 and @xmath172 . the other piece of the diagonal elements is given by the relationship @xmath173 . using the dyson equation , we can express the full green s function in terms of the bare green s function and the self energy . for example , one can obtain @xmath174^{\textup{-}1 } \boldsymbol{\sigma}^{21 } , \\ \\ { \bf g}^{21}= [ ( { \bf g}_0^{22})^{\textup{-}1}-\boldsymbol{\sigma}^{22}]^{\textup{-}1}\boldsymbol{\sigma}^{21}{\bf g}^{11 } , \end{array } \label{eq : dyson2}\ ] ] and similarly for @xmath175 . .[fig : one - loop ] ] the green s function can be calculated by inserting the one - loop self energy into the dyson equation [ eq . ( [ eq : dyson1 ] ) or ( [ eq : dyson2 ] ) ] . we will extract information about the triplon modes by computing the spectral weight function of the green s function . for positive frequencies of our interest , the spectral function is defined as @xmath181 \right\ } . \label{eq : spectral}\end{aligned}\ ] ] as a simple example , one can check that @xmath182 $ ] for the noninteracting hamiltonian @xmath169 . with the triplon interaction @xmath183 , the delta - function peaks representing the bare triplon modes are modified into finite - size peaks having renormalized energy and nonzero width . if the peak is still well - defined with large height and narrow width , the associated triplon mode survives as a quasiparticle with a finite life time . in the next section , we analyze the triplon modes and their decay processes by looking at the peak structures of the spectral function . here we present the results of the interacting triplon theory . we control the coupling constants such that the quasiparticle peak structures in the spectral function @xmath184 match the neutron scattering data . the resulting renormalized coupling constants are then obtained as follows . @xmath185 compared to the previous estimation in eq . ( [ eq : coupling_const ] ) , the heisenberg couplings have been increased and the anisotropic couplings , @xmath95 and @xmath112 , have been somewhat reduced with the inclusion of the triplon interactions . such reductions of the anisotropic couplings reflect the fact that the @xmath95 couplings have sizeable energy renormalization effects contributing to the energy splittings around the spin gap . the spectral function , @xmath184 , calculated for the coupling constants [ eq . ( [ eq : coupling_const2 ] ) ] , is plotted in fig . [ fig : spectral ] with the two different styles , ( a ) line and ( b ) color map . in fig . [ fig : spectral ] ( a ) , we find that the triplon phenomenology mentioned before is well captured in the spectral function . first of all , the spin gap is found at @xmath186 with the energy , @xmath187 , which is comparable to the measured value , @xmath188 . around the spin gap , three separated triplon modes are found with the energy splittings of @xmath189 mev consistently with the experimental result , @xmath190 . the energy splittings around the spin gap are mainly the energy renormalization effects of the @xmath95 couplings among the anisotropic couplings in eq . ( [ eq : coupling_const2 ] ) . one can notice this from the comparable sizes of @xmath191 and @xmath192 , and the small ratio @xmath193 . next , moving inside the triplon continuum region ( gray ) , the triplon modes undergo substantial decay processes as shown in significantly broadened quasiparticle peak structures . remarkably , the triplon continuum predicted in the bond operator theory matches well the region where the decay processes are found in the neutron scattering experiments . this can be seen in comparison with the experimental data in fig . [ fig : spectral ] ( b ) . the second ( green ) and third ( blue ) lowest triplon modes observed in the experiments disappear or lose its prominence above the solid gray line that represents the lower boundary of the triplon continuum calculated with @xmath138 . for comparison , we also show the lower boundary obtained in the quadratic theory ( dashed gray line ) in the same plot . the decay processes are mainly caused by the @xmath95 couplings with a minor contribution from the @xmath17 coupling ( see sec . [ sec : decay_channel ] ) . it is confirmed by conducting computations with one of the two couplings being turned off . among several experimental features in the triplon dynamics , the downward bending of the lowest triplon energy dispersion [ red dots in fig . [ fig : spectral ] ( b ) ] is not clearly explained in the current theory . for the bended part of the dispersion , we can think of two possibilities : ( i ) two - triplon bound state and ( ii ) the level repulsion by the triplon - continuum . the former idea naturally arises by noting that the bended part has a similar shape to that of the gray line . although the bended part disappears at certain momentum , it could be a matrix element effect . such two - triplon state contributions to the spin structure factor have been observed in the compound srcu@xmath0(bo@xmath194)@xmath0.@xcite on the other hand , the bended dispersion could be an effect of the level repulsion by the continuum as proposed in ref . [ ] . in our theory , the effects of the couplings between the single- and two - triplon excitations were implemented via the one - loop self energy in the single - triplon propagator ; the level repulsion effect appears to be rather small at the one - loop level . to investigate the full level repulsion effect , it may be necessary to take into account higher order corrections or consider the single- and two - triplon sectors on equal footing . in both cases , these considerations would provide a unique opportunity to investigate interesting multi - particle dynamics caused by anisotropic spin interactions . we leave this problem as an interesting subject of future study . .comparison of our work with ref . the second and third rows indicate experimental results and theoretical approaches employed in the two works . [ tab : coupling - comparison ] [ cols="^,^",options="header " , ] now we comment on the coupling constants estimated from the triplon theory . due to many independent exchange couplings in the spin model , we considered the simplest parameter regime [ eq . ( [ eq : coupling_const2 ] ) ] that captures essential features of the neutron scattering data ( see appendix [ app : fitting ] ) . nonetheless , we find that the overall energy scale of the parameter regime is consistent with a previous estimation in ref . table [ tab : coupling - comparison ] shows our results in comparison with theirs . despite various differences between the two works , both results have an almost same average value of the heisenberg couplings per a unit cell : @xmath195 8.6 mev . a major difference is that in ref . [ ] @xmath15 is evaluated to be much smaller than @xmath14 while in our triplon theory such a dissimilarity between @xmath14 and @xmath15 is not crucial for describing the neutron data . we hope this point is clarified in future studies . the dm interactions responsible for magnetic anisotropies in bicu@xmath0po@xmath1 were estimated in our study . although various experimental results could be well described and understood by our theory , the magnitudes of the estimated dm interactions are quite large ( @xmath196 ) compared to the values usually found in copper oxides . this may change once higher order contributions are taken into account in the triplon self - energy ( beyond the one - loop level ) . for a more accurate estimation of the coupling constants , the microscopic spin model may be directly studied with numerical techniques . further experimental information such as electron spin resonance ( esr ) measurements will be also helpful for determining the dm interactions more precisely.@xcite in this paper , we provided theoretical analysis of the rung - vbs ground state in bicu@xmath0po@xmath1 by constructing a minimal spin hamiltonian and developing a comprehensive theory of triplon dynamics . in comparison with the neutron scattering experiment data , it is shown that the anisotropic spin interactions ( @xmath95 and @xmath112 ) are crucial to explain the unusual quantum numbers carried by the triplons and the decay processes of the triplons to the multi - triplon continuum . our results would provide essential information for various ongoing studies of bicu@xmath0po@xmath1 . in particular , the recent high - field experiments found a series of field - induced quantum phase transitions.@xcite nature of the field - induced phases has not been clearly understood , in part due to the lack of the spin hamiltonian incorporating anisotropic spin interactions . we believe that the spin hamiltonian presented here , together with the information about the spin content of the triplons , is a good starting point for the study of the field - induced phases . we thank kemp plumb and young - june kim for sharing their neutron scattering data on bicu@xmath0po@xmath1 and many helpful discussions . this work was supported by the nserc of canada and the canadian institute for advanced research . this research was also supported in part by perimeter institute for theoretical physics . research at perimeter institute is supported by the government of canada through industry canada and by the province of ontario through the ministry of research and innovation . computations were performed on the gpc supercomputer at the scinet hpc consortium . scinet is funded by : the canada foundation for innovation under the auspices of compute canada ; the government of ontario ; ontario research fund - research excellence ; and the university of toronto . the low energy spin hamiltonian in eq . ( [ eq : spin_model ] ) can be derived from the microscopic hubbard model consisting of the electron hopping @xmath197 and the on - site coulomb repulsion @xmath198 : @xmath199 the electron hopping amplitude generically consists of the spin - independent ( @xmath74 ) and spin - dependent ( @xmath200 ) parts : @xmath201 where @xmath202 are the pauli matrices and @xmath203 are the spin indices . the spin - dependent hoppings have their origin in the atomic spin - orbit coupling . the corresponding hopping amplitude @xmath204 is a three - component pseudo - vector satisfying @xmath205 . taking the large coulomb interaction limit ( @xmath206 ) with the half electron filling ( one electron per site ) and developing a degenerate perturbation theory , one can obtain the spin hamiltonian in eq . ( [ eq : spin_model ] ) as a low energy effective model.@xcite the coupling constants are defined in the following way . @xmath207 it is clear from the expressions that the dzyaloshinskii - moriya and anisotropic @xmath208 symmetric interactions share the same origin in the spin - orbit coupling . their relationship in eq . ( [ eq : gamma ] ) is obtained from the above microscopic expressions for the coupling constants . the quadratic hamiltonian takes the following form . @xmath209 + \sum_{\bf r } \sum_{m=1}^2 \left(\frac{1}{4 } j_4-\mu \right ) t_{m\alpha}^{\dagger}({\bf r } ) t_{m\alpha}({\bf r } ) \nonumber\\ & - & \frac{\bar{s}^2}{4 } \sum_{\bf r } ( \mathcal{j}_1^{\alpha\beta } + \mathcal{j}_1^{\beta\alpha } ) [ t_{1\alpha}^{\dagger}({\bf r } ) t_{2\beta}({\bf r } ) + t_{1\alpha}^{\dagger}({\bf r } ) t_{2\beta}^{\dagger}({\bf r } ) ] + \textup{h.c . } \nonumber\\ & - & \frac{\bar{s}^2}{4 } \sum_{\bf r } ( \tilde{\mathcal{j}}_1^{\alpha\beta } + \tilde{\mathcal{j}}_1^{\beta\alpha } ) [ t_{1\alpha}^{\dagger}({\bf r } ) t_{2\beta}({\bf r}-{\bf r}_{\bf b } ) + t_{1\alpha}^{\dagger}({\bf r } ) t_{2\beta}^{\dagger}({\bf r}-{\bf r}_{\bf b } ) ] + \textup{h.c . } \nonumber\\ & + & \frac{\bar{s}^2}{4 } \sum_{\bf r } ( \mathcal{j}_2^{\alpha\beta } + { \mathcal{j}'}_2^{\beta\alpha } ) [ t_{1\alpha}^{\dagger}({\bf r } ) t_{1\beta}({\bf r}+{\bf r}_{\bf b } ) + t_{1\alpha}^{\dagger}({\bf r } ) t_{1\beta}^{\dagger}({\bf r}+{\bf r}_{\bf b } ) ] + \textup{h.c . } \nonumber\\ & + & \frac{\bar{s}^2}{4 } \sum_{\bf r } ( \mathcal{j}_2^{\alpha\beta } + { \mathcal{j}'}_2^{\beta\alpha } ) [ t_{2\alpha}^{\dagger}({\bf r } ) t_{2\beta}({\bf r}-{\bf r}_{\bf b } ) + t_{2\alpha}^{\dagger}({\bf r } ) t_{2\beta}^{\dagger}({\bf r}-{\bf r}_{\bf b } ) ] + \textup{h.c . } \nonumber\\ & - & \frac{\bar{s}^2}{4 } \sum_{\bf r } \mathcal{j}_3^{\alpha\beta } [ t_{1\alpha}^{\dagger}({\bf r } ) t_{1\beta}({\bf r}-{\bf r}_{\bf c } ) + t_{1\alpha}^{\dagger}({\bf r } ) t_{1\beta}^{\dagger}({\bf r}-{\bf r}_{\bf c } ) ] + \textup{h.c . } \nonumber\\ & - & \frac{\bar{s}^2}{4 } \sum_{\bf r } \mathcal{j}_3^{\alpha\beta } [ t_{2\alpha}^{\dagger}({\bf r } ) t_{2\beta}({\bf r}+{\bf r}_{\bf c } ) + t_{2\alpha}^{\dagger}({\bf r } ) t_{2\beta}^{\dagger}({\bf r}+{\bf r}_{\bf c } ) ] + \textup{h.c . } \nonumber\\ & - & \frac{\bar{s}^2}{4 } \sum_{\bf r } \sum_{m=1}^2 ( \mathcal{j}_4^{\alpha\beta}-j_4 \delta^{\alpha\beta } ) [ t_{m\alpha}^{\dagger}({\bf r } ) t_{m\beta}({\bf r } ) + t_{m\alpha}^{\dagger}({\bf r } ) t_{m\beta}^{\dagger}({\bf r } ) ] + \textup{h.c . } \nonumber\\ & + & i \sum_{\bf r } \sum_{m=1}^2 g \mu_b h^{\alpha } \epsilon_{\alpha\beta\gamma } t_{m\beta}^{\dagger}({\bf r } ) t_{m\gamma}({\bf r } ) .\end{aligned}\ ] ] here , @xmath210 is the number of unit cells and @xmath211 denotes a lattice vector . the coupling constant matrices denoted with @xmath212 s are combinations of the @xmath90 , @xmath50 , @xmath51 couplings . for example , @xmath213 with @xmath112 related to @xmath13 and @xmath95 through eq . ( [ eq : gamma ] ) . the @xmath214 matrix is defined by flipping the sign of @xmath28 ( @xmath215 ) in the expression of @xmath216 . the other @xmath212 matrices are defined in similar fashions . as mentioned in sec . [ sec : quadratic_theory ] , the @xmath95 couplings cancel each other in the quadratic hamiltonian . to be specific , due to the antisymmetric nature of the dm matrix ( @xmath217 ) , we have @xmath218 and similarly for @xmath219 . in the quadratic theory , we focus on a low energy region around the spin gap . the measured spin gap positions [ @xmath108 ] provide a useful constraint on the heisenberg coupling constants . the constraint can be obtained by comparing the measured value with the analytic expression for the spin gap position : @xmath221 notice that @xmath222 only depends on the ratio of @xmath13 to @xmath94.@xcite the above expression is derived from the quadratic bond operator theory only with the heisenberg interactions . upon the inclusion of anisotropic interactions , the spin gap position remains almost the same with a slight shift , which means that the position is determined mainly by the heisenberg interactions , @xmath13 , @xmath14 , @xmath15 , that generate frustration in the system . comparison of the theory prediction @xmath222 with the measured value @xmath223 leads to the condition @xmath224 . we choose the simplest case @xmath225 that satisfies the condition . additionally , we impose another condition @xmath226 . these constraints are overall consistent with the previous estimation for the heisenberg couplings in ref . although the latter argued that @xmath227 with @xmath228 being comparable to each other , @xmath14 and @xmath15 are not distinguished in the bond operator hamiltonian ( as pointed out in sec . [ sec : quadratic_theory ] ) . for simplicity , we set @xmath229 . we find that the relatively weak coupling @xmath17 should be antiferromagnetic ( @xmath230 ) to reproduce experimentally observed curvatures of the triplon dispersions at @xmath113 . as for the dm vectors , at least two components along different directions are necessary in order to completely break the spin rotation symmetry as observed in the neutron scattering experiments . @xmath27 and @xmath28 ( and associated @xmath112 ) are found to be enough to describe low energy triplon physics as shown in sec . [ sec : triplon_dispersions ] and [ sec : triplon_magnetic_behaviors ] . we explain the mean - field decouplings of the quartic terms in @xmath81 . the quartic terms of the spin interactions at the link @xmath231 are given as follows . @xmath232 where @xmath233 is a coupling constant matrix containing all the couplings ( @xmath234 ) at the link @xmath231 . the quartic term is decoupled with two mean - field channels in the following way . @xmath235 \nonumber\\ & + & \frac{1}{2 } \left [ p_{ij}^{\nu\rho } t_{i\mu}^{\dagger } t_{j\sigma } + p_{ij}^{*\mu\sigma } t_{i\nu } t_{j\rho}^{\dagger } - p_{ij}^{*\mu\sigma } p_{ij}^{\nu\rho } \right],\end{aligned}\ ] ] where the mean - field parameters are defined as @xmath236 although we used the site notation @xmath237 in the above for notational simplicity , in practice the computation is done with dimer indices , _ e.g. _ @xmath238 with the dimer index @xmath239 and the spin index @xmath240 in the dimer . at each inter - dimer interaction link , there are two mean - field parameters , @xmath241 and @xmath242 , each of which is represented by a 3@xmath923 matrix . cubic terms in the bond operator theory survive when the system has couplings that are not invariant under the global site interchange at each dimer . under the site interchange , the bond operators , based on the spin - singlet and spin - triplet basis , transform as @xmath243 with @xmath244 . since each cubic term contains one @xmath68-boson and three @xmath74-bosons , the cubic term changes its sign under the site interchange . if all the couplings in the system are invariant under the site interchange , then the cubic terms vanish . however , the spin model eq . ( [ eq : spin_model ] ) has various couplings that can generate the cubic terms . we list below such couplings with the conditions for the nonzero cubic terms . f. casola , t. shiroka , a. feiguin , s. wang , m. s. grbi , m. horvati , s. krmer , s. mukhopadhyay , k. conder , c. berthier , h .- ott , h. m. rnnow , c. regg , and j. mesot , phys . lett . * 110 * , 187201 ( 2013 ) . as we approach the critical points , it takes a longer and longer time to obtain a converged solution of the saddle point equations [ eq . ( [ eq : saddle - point - eq ] ) ] . rather than solving the equations directly around the critical points , we estimate the critical fields by extrapolation .

we provide a theory of triplon dynamics in the valence bond solid ground state of the coupled spin - ladders modelled for bicu@xmath0po@xmath1 . utilizing the recent high quality neutron scattering data [ http://www.nature.com/nphys/journal/v12/n3/full/nphys3566.html[nature physics * 12 * , 224 ( 2016 ) ] ] as guides and a theory of interacting triplons via the bond operator formulation , we determine a minimal spin hamiltonian for this system . it is shown that the splitting of the low energy triplon modes and the peculiar magnetic field dependence of the triplon dispersions can be explained by including substantial dzyaloshinskii - moriya and symmetric anisotropic spin interactions . taking into account the interactions between triplons and the decay of the triplons to the two - triplon continuum via anisotropic spin interactions , we provide a theoretical picture that can be used to understand the main features of the recent neutron scattering experimental data .

the incidence of blunt cardiac rupture among hospital admissions for trauma is only approximately 0.16%2% [ 46 ] . however , the actual incidence may be higher because many victims may die before arrival at the hospital . with advances in traumatology , several studies have investigated the prognostic factors associated with traumatic cardiac rupture . in this study , we attempted to find factors affecting the prognosis of patients with blunt traumatic cardiac rupture . this retrospective study was reviewed and approved by the institutional ethics committee of our institution ( ethical committee of sungkyunkwan university of samsung changwon hospital , approval number 2015-scmc-037 - 00 ) . between 1999 and 2015 , a total of 107,657 patients were admitted to our hospital due to trauma . ultimately , we analyzed 21 patients who were diagnosed with blunt traumatic cardiac rupture and required emergency surgery . in our analysis of these 21 patients all operations were performed via median sternotomy . in each case , cardiopulmonary bypass ( cpb ) or extracorporeal membrane oxygenation was prepared as a precaution . if the patient was hemodynamically unstable , 2 cardiovascular surgeons operated together to perform the median sternotomy and femoral cannulation simultaneously . after the sternotomy , surgeons opened the pericardium for prompt decompression of the heart , rapidly removed the hematoma , and attempted to find the injury site . the injury sites were primarily repaired using double - arm monofilament stitches with pledgeted , interrupted sutures . after the injury sites were primarily repaired , we weaned the patients from cpb as soon as possible . categorical variables were compared using the chi - square test or the fisher exact test . all p - values < 0.05 were considered to indicate statistical significance . this retrospective study was reviewed and approved by the institutional ethics committee of our institution ( ethical committee of sungkyunkwan university of samsung changwon hospital , approval number 2015-scmc-037 - 00 ) . between 1999 and 2015 , a total of 107,657 patients were admitted to our hospital due to trauma . ultimately , we analyzed 21 patients who were diagnosed with blunt traumatic cardiac rupture and required emergency surgery . in our analysis of these 21 patients all operations were performed via median sternotomy . in each case , cardiopulmonary bypass ( cpb ) or extracorporeal membrane oxygenation was prepared as a precaution . if the patient was hemodynamically unstable , 2 cardiovascular surgeons operated together to perform the median sternotomy and femoral cannulation simultaneously . after the sternotomy , surgeons opened the pericardium for prompt decompression of the heart , rapidly removed the hematoma , and attempted to find the injury site . the injury sites were primarily repaired using double - arm monofilament stitches with pledgeted , interrupted sutures . after the injury sites were primarily repaired , we weaned the patients from cpb as soon as possible . categorical variables were compared using the chi - square test or the fisher exact test . all p - values < 0.05 were considered to indicate statistical significance . most blunt traumatic cardiac injuries resulted from traffic accidents ( 81% ) , and most patients had combined trauma . the combined trauma included liver laceration , spleen injury , pelvic bone fracture , spinal fracture , and fractures of the extremities ( table 2 ) . the mean injury severity score ( iss ) was 2817.4 ( range , 16 to 97 ) . among the 21 patients , the mean central venous pressure ( cvp ) and systolic blood pressure of the 3 patients who died were 28 cm h2o and 67 mm hg , respectively . in contrast , the mean cvp and systolic blood pressure of the 7 surviving patients were 26 cm h2o and 81 mm hg , respectively . three of them had left ventricle injuries , and the other had a right atrium ( ra)/inferior vena cava ( ivc ) junction injury . among these 4 patients , therefore , they underwent a co - operation ( open reduction and vessel repair ) to prevent additional bleeding due to systemic heparinization . the preoperative lab findings , systolic blood pressure , and elapsed time from arrival to surgery are summarized in table 3 . myocardial band ( ck - mb ) levels ( 13.49.2 ng / ml ) were elevated in most patients . in contrast , the preoperative creatinine levels ( 1.10.3 mg / dl ) were nearly normal in all patients . in addition , the mean blood transfusion amount in survivors was 6.3 units , as compared to 9 units in fatalities ( p=0.900 ) . no instances of intraoperative mortality occurred , but the in - hospital mortality rate was 24% ( 5 of 21 ) . the causes of death included pneumonia ( 1 ) , inadequate myocardial protection - related low cardiac output ( 1 ) , and massive bleeding - related disseminated intravascular coagulation ( 3 ) . all fatalities showed liver and renal failure , and 2 of them showed brain death . significant differences were found in preoperative ck - mb levels ( p=0.042 ) and platelet counts ( p=0.004 ) between the survivors and fatalities . in addition , the preoperative glasgow coma scale score ( p=0.007 ) , trauma and injury severity score ( p=0.007 ) , and iss were significantly worse in the fatalities than in the survivors ( p=0.004 ) . no significant differences were found between the two groups in preoperative creatinine levels ( p=0.495 ) or elapsed time to surgery ( p=0.445 ) . similarly , no significant differences were found in injury location ( p=0.437 ) , cpr history ( p= 0.372 ) , use of cpb ( p=0.182 ) , amount of blood transfusion ( p=0.900 ) , or shock index ( p=0.186 ) between the two groups . most patients who experience blunt traumatic cardiac rupture die before arrival to the hospital . according to one japanese study , 91% of patients with blunt traumatic cardiac rupture died within 30 minutes of the accident . we analyzed 21 patients who experienced blunt traumatic cardiac rupture and compared our results with those of previous studies . traffic accidents were the most common cause of blunt traumatic cardiac rupture ( 80% ) , and the most common site of injury was the right atrium ( 43% ) [ 2,5,79 ] . when a patient arrived at the hospital , we first focused on the vital signs , peripheral circulation , presence of an open wound , neck vein distension , and facial plethora . if cardiac rupture was suspected , we performed chest computed tomography , focused assessment with sonography for trauma , or transthoracic echocardiography as soon as possible . if patients had unstable vital signs , we performed intubation and transfusion , using intravenous inotropics as needed . if patients had hemopneumothorax , we inserted a chest tube at the emergency department and then rapidly transferred the patients to the operating room . ten of the 21 patients were suspected to have cardiac tamponade because they had hypotension , high cvp , and echocardiographic signs of tamponade ( the presence of pericardial effusion , diastolic collapse of the right ventricle , ivc dilatation , etc . ) . when we suspected cardiac tamponade , we rapidly moved the patient to the operating room rather than trying to insert a pericardial catheter in the emergency room , because it takes almost the same time to perform a pericardial catheter insertion as to prepare the operating room in our hospital . the average elapsed door - to - surgery time in patients with cardiac tamponade was 29 minutes . in contrast , when cardiac tamponade was not suspected , further evaluations were performed prior to surgery . if a patient s vital signs are unstable , we consider an emergency department thoracotomy to have several advantages , including the prompt decompression of pericardial pressure and the rapid restoration of hemodynamics . cpb was applied in 4 patients with left ventricular rupture , and in 1 patient with an ra / ivc junction injury . the overall survival rate was similar to that of a prior study , which found that 70%80% of patients who were transferred to trauma centers survived after blunt cardiac injury . they found significant differences between survivors and fatalities in preoperative creatinine levels , but no differences in preoperative ck - mb or platelet count . in contrast , we found no significant difference in preoperative creatinine levels between survivors and fatalities . in addition , our results revealed significant differences in preoperative ck - mb levels and platelet counts between the two groups . patients with impaired renal function preoperatively would be expected to have poorer postoperative outcomes than those with normal renal function . in our study , however , all patients had normal preoperative creatinine levels . this may explain why we did not identify a significant difference between survivors and fatalities . this enzyme is not specific for cardiac injury , but can reflect severe muscle injury and potentially predict rhabdomyolysis . according to a 1998 study by swaanenburg et al . , among 38 patients with thoracic injuries , 1830 had increased ck - mb levels , increased ck - mb activity , an elevated ratio of ck - mb activity to total ck , or an elevated ratio of ck - mb mass to total ck upon admission . although elevated ck - mb levels are not specific for cardiac injury , they can be indicative of severe combined injuries and be associated with a poor prognosis . in addition , a low preoperative platelet count may also be associated with a poor prognosis . recently reported that the early - stage platelet count was independently related to mortality in blunt trauma patients . a low platelet count reflects increased platelet consumption as well as massive blood loss and hemodilution . increased platelet consumption can lead to a systemic inflammatory response or disseminated intravascular coagulation . early platelet consumption can be explained based on the fact that platelet aggregation and blood clot formation begins within 1520 seconds of a major vessel rupture . we did not find any significant difference in elapsed time from hospital arrival to surgery between fatalities and survivors . for instance , when a patient was suspected to have cardiac tamponade , surgery was promptly performed within 30 minutes . this was a case - control study , and case - control studies are prone to bias and confounding . although we were able to identify some characteristics of survivors , we were not able to clearly confirm causality . given this limitation , we attempted to identify factors associated with a poor prognosis . few prior studies have investigated blunt traumatic cardiac rupture due to the rarity of such cases . we found that elevated ck - mb levels , a low platelet count , and multi - organ traumatic injury were associated with a poor prognosis ( fig . if a patient with blunt traumatic cardiac rupture exhibits these factors , clinicians should be especially attentive and respond promptly to save the patient s life . this was a case - control study , and case - control studies are prone to bias and confounding . the small , heterogeneous study population is a major limitation of this study . although we were able to identify some characteristics of survivors , we were not able to clearly confirm causality . given this limitation , we attempted to identify factors associated with a poor prognosis . few prior studies have investigated blunt traumatic cardiac rupture due to the rarity of such cases . we found that elevated ck - mb levels , a low platelet count , and multi - organ traumatic injury were associated with a poor prognosis ( fig . if a patient with blunt traumatic cardiac rupture exhibits these factors , clinicians should be especially attentive and respond promptly to save the patient s life .

backgroundblunt traumatic cardiac rupture is rare . however , such cardiac ruptures carry a high mortality rate . this study reviews our experience treating blunt traumatic cardiac rupture.methodsthis retrospective study included 21 patients who experienced blunt traumatic cardiac rupture from 1999 to 2015 . every patient underwent surgery . several variables were compared between survivors and fatalities.resultssixteen of the 21 patients survived , and 5 ( 24% ) died . no instances of intraoperative mortality occurred . the most common cause of injury was a traffic accident ( 81% ) . the right atrium was the most common location of injury ( 43% ) . ten of the 21 patients were suspected to have cardiac tamponade . significant differences were found in preoperative creatine kinase myocardial band ( ck - mb ) levels ( p=0.042 ) and platelet counts ( p= 0.004 ) between the survivors and fatalities . the patients who died had higher preoperative glasgow coma scale scores ( p=0.007 ) , worse trauma and injury severity scores ( p=0.007 ) , and higher injury severity scores ( p=0.004 ) than those who survived.conclusionwe found that elevated ck - mb levels , a low platelet count , and multi - organ traumatic injury were prognostic factors predicting poor outcomes of blunt cardiac rupture . if a patient with blunt traumatic cardiac rupture has these factors , clinicians should be especially attentive and respond promptly in order to save the patient s life .

tularemia is a potentially fatal , multisystemic disease in humans , and it is caused by francisella tularensis and is primarily observed in the northern hemisphere including europe , north america , and asia . pneumonic tularemia occurs after exposure to aerosolized f tularensis particles or from hematogenous spread from a distal site ; it has remained the most lethal form of tularemia.f tularensis has two predominant subspecies , namely subsp tularensis ( type a ) and subsp holarctica ( type b ) . type b is much less virulent compared with type a and almost never causes lethal infection in humans . tularemia pneumonia was a more invasive form of infection and more likely to be caused by f tularensis type a previously . in this report , we present a 68-year - old man californian resident with tularemic bacteremic pneumonia caused by type b tularemia following treatment for 5 months with steroids for hypersensitivity pneumonitis . this case suggests that low virulence f tularensis should be included in the differential diagnoses of bacteremic pneumonia in immune - compromised hosts , particularly for those with endemic tularemia . in june , a 68-year - old man with a 3-day history of high fever was admitted to our hospital . the patient lived in a californian metropolitan area for the past few decades and arrived in taiwan 1 day before admission . he had been diagnosed with diabetes ; dry cough , and progressive shortness of breath were observed for 6 months . hypersensitivity pneumonitis was diagnosed after extensive studies involving high - resolution chest computed tomography ( ct ) and lung biopsy in addition to the exclusion of toxoplasma , rubella , cytomegalovirus , and herpes simplex virus type 1 and 2 . thereafter , a high dose of steroids with prednisolone 60 mg per day was prescribed for 5 months . , laboratory examinations revealed leukocytosis and considerably elevated c - reactive protein levels ( 260.1 mg a chest radiograph revealed left lower lung opacities ( figure 1 ) . despite the administration of empiric therapy with ceftriaxone plus clindamycin for community - acquired pneumonia , the fever persisted , and admission chest radiograph : left lower lung consolidation and pleural effusion . initial chest computed tomography ( ct ) : left lower lung air - bronchial ground with pleural effusion . a blood culture was performed in 2 sets , and both sets were positive for gram - negative bacilli after 1 day . a polymerase chain reaction ( pcr ) analysis for the 16s rrna showed the presence of f tularensis on detection of the lpna encoding a 17-kda lipoprotein which is specific for strains of the genus francisella . using the primer of 5-aggcggagatctaggaa - ccttt-3 and 5-agcccaagctgactaaaatcttt-3 , holarctica was confirmed by the amplification of ft - m19 , which is located between the genes dead and ppic , showing the specific 30-bp deletion ( figure 3 ) . the serology test for tularemia by the capture enzyme - linked immunosorbent assay , which was based on antigen binding to a monoclonal antibody ( mab ) coated onto a solid phase ( microtitre plate ) and detection of the bound antigen using the same mab ( peroxidase labeled ) , had been prescribed but were negative result at that time . sputum , bronchial washing , and pleural effusion cultures were negative for bacteria , fungi , and tuberculosis . in addition , tests for mycoplasma , legionella , and human immunodeficiency virus were negative . streptomycin ( 1 g every 12 h ) and doxycycline ( 100 mg every 12 h ) were administered for severe tularemia with bacteremic pneumonitis . the fever subsided after 1 day , and parenchymal changes in the lung improved steadily thereafter . although no pathogen was isolated from the lung or associated specimen , the clinical course of concomitant bacteremia and fulminant pneumonia suggested that they were caused by the same pathogen of f tularensis . the fever , pneumonia , and pleural effusion were progressive at first even under coverage with extended - spectrum antibiotics . subspecies identification with ft - m19 assay , the pcr product has a band over 220 bp area . assessment of risk exposures regarding this case revealed no history of hunting , skinning , farming , lawn mowing , brush cutting , or contaminated food ( such as hares ) consumption . the patient is a biochemist who oversees his own biochemistry company , which manufactures products from the ascites of mice and the serum of rabbits . during the past 6 years , he was in frequent contact with the secretion of the animals ( either ascites or serum ) during routine laboratory procedures . tularemia is a zoonotic infection primarily observed in the northern hemisphere , and it is caused by f tularensis , a strictly aerobic , gram - negative coccobacillus . it is associated with rodents and hares and is transmitted to humans by direct contact with animals , aerogenic exposure , contaminated food or water consumption , and arthropod bites . laboratory - acquired tularemia has been frequently reported , and it remains a threat for laboratory personnel . the most common ( 80% of cases ) clinical manifestation of tularemia is ulceroglandular tularemia . pneumonia occurs in approximately 30% of patients with ulceroglandular tularemia and 80% of those with typhoidal tularemia ( prevalence varies widely between clinical series ) . f tularensis has two predominant subspecies : subsp tularensis ( type a ) and subsp . type a is predominantly isolated in north america , highly virulent , and can cause invasive diseases such as pneumonia and bacteremia . before the advent of effective antibiotics , type b spreads more widely over the northern hemisphere , and it is the predominant subspecies in europe , japan , and north america . type b is much less virulent compared with type a. it is rarely invasive and almost never causes lethal infection in humans , even when early appropriate treatment is not applied . primary pneumonia is associated with pulmonary involvement because of inhalation , whereas secondary pneumonia is considered to be caused by hematogenic spread during the course of the disease . bacteremic tularemia is rare , and most cases were due to type a. by contrast , pulmonary involvement with type b infection has been of much lower incidence , even in outbreaks or epidemics . type b tularemia with bacteremia was reported only in immune - compromised hosts , including those with acquired immune deficiency syndrome , and in patients who have undergone liver transplantation . serology is the most frequently ordered diagnostic test for f tularensis infection ; however , it is limited by poor sensitivity because of undetectable antibody levels until the second week of illness . blood cultures remain useful for an early diagnosis of severe forms of tularemia , whereas serological tests are not yet positive . molecular subtyping assays are directed against an upstream region of an ribonucleic acid ( ribonucleic acid ) helicase ( the ft - m19 assay ) , the presence or absence of the isftu2 insertion sequence element ( isftu2 assay ) , the f tularensis region of difference 1 ( rd1 assay ) , and the pdpd gene ( pdpd-2 assay ) . we report an immune - compromised patient who presented with severe bacteremic tularemic pneumonia caused by low virulence f tularensis ( type b ) and was administered high doses of steroids . this case suggests that low virulence f tularensis should be included in the differential diagnoses of bacteremic pneumonia for endemic tularemia . real - time pcr can facilitate the early diagnosis of tularemia , particularly in patients with less frequent clinical manifestations and those from endemic regions .

abstracttularemia is a zoonotic infection seen primarily in the northern hemisphere . it is caused by the bacteria francisella tularensis . although the ulceroglandular form of the disease is the more common manifestation of infection , f tularensis is known to cause pneumonia . f tularensis has two predominant subspecies , namely subsp . tularensis ( type a ) and subsp . holarctica ( type b ) . type b tularemia is considered to be much less virulent than type a and barely caused lethal disease and pneumonia.we reported a case with a 68-year - old man immune - compromised patient diagnosed with bacteremic pneumonia engendered by type b tularemia with initial presentation of high fever , pneumonia with pleural effusion ; the diagnosis was performed using 16s rrna gene sequence analysis . the patient 's fever , pneumonia , and pleural effusion were resolved with appropriate antibiotics for tularemia . this case involving severe bacteremic pneumonia in an immune - compromised patient is rare.this case suggests that low virulence f tularensis should be included in the differential diagnoses of bacteremic pneumonia for endemic tularemia .

during the last decade of the past century there has been a vivid discussion about the opacity of spiral galaxies . this discussion was initiated by disney , davies & phillipps ( 1989 ) and valentijn ( 1990 ) , who countered the conventional view that spiral galaxies are optically thin over their entire optical discs ( holmberg 1958 ; de vaucouleurs , de vaucouleurs & corwin 1976 ; sandage & tammann 1981 ) . this issue has not yet been settled , although an overall consensus seems to be emerging that spiral galaxies are , in general , at least moderately optically thick within their optical disc , i.e. that they have central face - on optical depth of at least unity . we will not repeat a detailed overview of the different points of view and the large variety of observational tests , and refer to davies & burstein ( 1995 ) , xilouris et al . ( 1997 ) , kuchinski et al . ( 1998 ) and calzetti ( 2001 ) for excellent reviews . we just wish to point out an important observational constraint which , in our opinion , is not always given enough attention : the far - infrared ( fir ) emission of spiral galaxies . this emission originates from the absorption of starlight by dust grains , which is thermally re - emitted at longer wavelengths . the most recent results show that about 30 per cent of the bolometric luminosity of late - type galaxies is fir emission by interstellar dust ( popescu & tuffs 2002 ) . notice that this figure refers to normal quiescent spiral galaxies ; special classes of galaxies such as starburst galaxies emit even higher fractions of their energy at fir wavelengths . these facts demonstrate quite convincingly that interstellar dust forms an important constituent of spiral galaxies . the physical processes of absorption and scattering by dust grains should hence be taken into account when interpreting and modelling the observed optical properties of galaxies . we would like to stress that _ all _ optical observables will to some extent be affected by dust , including the observed kinematics . indeed , when interstellar dust grains absorb or scatter photons , the kinematical information contained within these photons , in the form of the doppler shift , will also be absorbed or scattered . it is important to realize that most of the kinematical data of galaxies are optical measurements . firstly , stellar kinematics are always measured from optical absorption lines . in principle , the attenuation effects of interstellar dust could be minimized by using the sensitive @xmath0co absorption feature at 2.29 @xmath1 m ( gaffney , lester & doppmann 1995 ) . measuring stellar kinematics at near - infrared ( nir ) wavelengths is , however , observationally extremely difficult due to the high sky surface brightness . secondly , the vast majority of spatially resolved rotation curves of spiral galaxies have been measured using optical emission lines ( usually the h@xmath2 line ) . they can also be measured using the hi or co lines , where dust extinction is not an issue . however , these methods are observationally much more expensive than the more straightforward h@xmath2 observations . currently , the only way to investigate the effects of dust attenuation on the observed kinematics of galaxies is by means of detailed radiative transfer modelling . many different approaches exist to handle the radiative transfer problem , and various teams have adopted different techniques to study the effect of dust on the photometry and spectral energy distributions ( seds ) of galaxies ( e.g. bruzual , magris & calvet 1988 ; witt , thronson & capuano 1992 ; byun , freeman & kylafis 1994 ; wise & silva 1996 ; bianchi , ferrara & giovanardi 1996 ; corradi , beckman & simonneau 1996 ; baes & dejonghe 2001a ) . the effect of dust attenuation on the observed kinematics , however , is largely unexplored , and limited to the rotation curves of spiral galaxies . davies ( 1990 ) argued that the effects of dust absorption on the observed optical rotation curve of a disc galaxy can lead to a severe underestimation of the true rotational velocity in the inner regions . this argument was quantified by bosma et al . ( 1992 ) , who calculated the effect of dust absorption on the observed rotation curve of edge - on galaxies . the most detailed work on this subject comes from matthews & wood ( 2001 ) , who calculate the effects of dust attenuation on the rotation curve of low surface brightness ( lsb ) galaxies through monte carlo simulations . we have embarked on a program to systematically investigate the effects of dust on the observed kinematics of galaxies . in previous papers we focused on the effects of dust attenuation on the observed stellar kinematics of elliptical galaxies . initially , we only considered absorption by dust grains in our models ( baes & dejonghe 2000 ; baes , dejonghe & de rijcke 2000 ) . the inclusion of absorption in the calculation of the observed kinematics is a fairly simple procedure : it basically adds a weight to the contribution of each individual star along a line of sight . the radiative transfer problem becomes much more complicated however when scattering is also included . in this case , photons can leave their original path , such that any star can contribute to the observed kinematics in any line of sight . moreover , not only the stellar velocities but also the individual dust grain velocities should be taken into account in the calculation of the observed kinematics . we argue that the monte carlo method is the only radiative transfer modelling method in which kinematical information can be included in an elegant and straightforward way . using a one - dimensional spherical monte carlo code , we found that the effects of dust scattering are fairly important : dust attenuation can serve as an additional or alternative explanation for the stellar kinematical evidence of a dark matter halo around ellipticals ( baes & dejonghe 2001b , 2002a ) . in this paper , we tackle the more complicated problem of investigating the effect of dust attenuation on the observed kinematics of disc galaxies . we have written a new monte carlo code ( skirt , acronym for stellar kinematics including radiative transfer ) that can handle any geometry of stars and dust . this code is presented in section [ skirt.sec ] , and tested in section [ test.sec ] . we present our model and the results of our monte carlo simulations in section [ results.sec ] . these results are discussed in section [ discussion.sec ] , and section [ conclusions.sec ] presents our conclusions . the basic characteristics of monte carlo radiative transfer have been explained at length by various authors ( e.g. cashwell & everett 1959 ; mattila 1970 ; witt 1977 ; fischer , henning & yorke 1994 ; bianchi et al . in essence , a monte carlo radiative transfer code follows the life of a very large number of individual photons . a photon is , at each stage in its existence , characterized by various quantities , such as its position @xmath3 , propagation direction @xmath4 , wavelength @xmath5 and doppler shift @xmath6 as measured in a frame of rest . and the corresponding line - of - sight velocity @xmath6 , which are related by the expression @xmath7 . ] after being emitted , photons propagate on straight lines through the interstellar medium until they either interact with a dust grain or leave the galaxy . the various interactions alter the properties of the photon , according to random numbers generated from the appropriate probability functions . when at last the photon escapes from the galaxy , its final properties are recorded . after recording a large numbers of photons in this way , the global observed properties of the system can be calculated . we will not repeat an in - depth description of the principles and the numerous equations of monte carlo radiative transfer here , as they are well described in the articles listed above . instead , we will focus on a number of aspects which make our code different from the existing ones . these differences are mainly our choice of the dust grid and the possibility to include kinematical information into the radiative transfer calculations . when no kinematical information is included in the radiative transfer calculations , photons are characterized at each moment by a wavelength @xmath5 , a position @xmath3 and a direction @xmath4 . initial values for these quantities must be generated randomly from the emitting stellar system , which can be composed of several stellar components . the initial emission direction @xmath8 can be sampled from the unit sphere , the initial position @xmath9 is sampled from the spatial distribution of the stellar component , and the initial wavelength @xmath10 is sampled from the sed of the stellar component at the position @xmath9 . the skirt code contains a library with a set of common stellar components ( including spherical jaffe , hernquist , plummer and de vaucouleurs models , and axisymmetric exponential , sech , isothermal disc models ) , from which it is straightforward to sample a random position ( see appendix a ) . another library contains a set of seds , including planck functions and realistic tabulated stellar and galaxy seds ( kinney et al . 1996 ; pickles 1998 ) . this library also contains so - called monochromatic seds , which are described by a dirac delta function . sampling a random wavelength from the latter is trivial , because all photons are emitted with the same wavelength . when the skirt code is used to calculate the observed kinematics of a dusty galaxy , photons must also carry with them the kinematic signature of the star that has emitted them , in the form of a doppler shift . because this is a one - dimensional quantity , not all kinematical information of the star can be transmitted to the observer , and it is important to consider how the observed doppler shift relates to the velocity vectors of the star and the scattering dust grains . this problem was discussed in detail in section 2.3 of baes & dejonghe ( 2002a ) , where it is shown that the general expression for the doppler shift after @xmath11 scattering events is @xmath12 where @xmath13 and @xmath14 are the velocity vectors of the emitting star and the @xmath15th dust grain respectively . the initial value of the doppler shift attached to the photon is hence the component of the star in the direction of the original emission , @xmath16 . to complete the initialization of a photon , we also need to generate a line - of - sight velocity from the appropriate probability distribution . in this case , this function is the spatial line - of - sight velocity distribution ( losvd ) @xmath17 , which describes the probability for a star at a position @xmath9 to have a velocity component @xmath6 in the direction @xmath8 . in general , the spatial losvd is a marginal probability distribution of the stellar distribution function @xmath18 , which describes the probability density of the stellar component in six - dimensional phase space , @xmath19 where @xmath20 is the stellar number density and the integration covers the entire velocity space perpendicular to the direction @xmath4 . thus , in order to be of use for a kinematical monte carlo run , each stellar component must allow the generation of a velocity from its spatial losvds for arbitrary @xmath3 and @xmath4 . the spatial losvds can be calculated analytically for a number of self - consistent spherical models . apart from isotropic models ( e.g. plummer 1911 ; hnon 1959 ; jaffe 1983 ; hernquist 1990 ) , this is possible for the anisotropic families of plummer and hernquist models described by dejonghe ( 1987 ) and baes & dejonghe ( 2002b ) . for more complicated dynamical models , however , an analytical evaluation of the spatial losvds is not possible . for such models , we approximate the velocity distribution at each position in the galaxy as a local gaussian distribution . this means that at each position @xmath3 , the distribution function can be written as @xmath21 . \label{gaussf}\end{gathered}\ ] ] here @xmath22 and @xmath23 represent the mean velocities and velocity dispersions in the directions @xmath24 , the principle axes of the velocity ellipsoid at the position @xmath3 . the orientation of the velocity ellipsoid and the values of the mean velocities and velocity dispersions can vary from position to position , such that the distribution function ( [ gaussf ] ) represents a fairly general distribution function . but a distribution function of this form has the advantage that the spatial losvds can be calculated exactly for any direction @xmath4 by applying the formula ( [ defslosvd ] ) . we find that the spatial losvd will also be a gaussian distribution , @xmath25 , \label{gaussianslosvd}\ ] ] with parameters @xmath26 where obviously @xmath27 are the components of the vector @xmath4 with respect to the orthonormal reference system @xmath24 . if hence , for each stellar component , we specify the orientation and parameters of the velocity ellipsoid at each position @xmath3 , we can easily sample line - of - sight velocities from the spatial losvds in an arbitrary direction , and hence initialize the photons initial doppler shifts . the life of a single photon can be thought of as a loop , whereby at each iteration ( representing a physical process ) we must update its position @xmath3 , propagation direction @xmath4 , wavelength @xmath5 and doppler shift @xmath6 . the initial values are determined randomly at the emission phase , and change at every scattering event . as we only consider coherent scattering , and we are not taking into account the re - emission of photons at longer wavelength , the only wavelength change of a photon along its path is due to the varying doppler shift . these wavelength variations are so tiny that the optical properties of the dust ( extinction curve , dust albedo and asymmetry parameter ) do not vary . the wavelength of a photon can hence be considered fixed throughout its lifetime . we must therefore only update the three quantities @xmath3 , @xmath4 and @xmath6 at each iteration , from their old values ( @xmath28 ) to the new ones ( @xmath29 ) . this proceeds in several steps . the first step in the iteration consists of determining whether an interaction with a dust grain will take place or whether the photon will leave the galaxy . to do this , we sample an optical depth @xmath30 from an exponential distribution and compare it to @xmath31 , the total optical depth along the path . when @xmath32 , the photon will leave the galaxy ; in the other case , the photon will interact with a dust grain . this interaction can either be a scattering or an absorption event , which is determined by the scattering albedo . in the former case , the photon will continue its journey through the galaxy , in the latter case , the loop is ended . the second step in the loop , if the photon is scattered , is the determination of the position of the scattering . therefore we have to translate the sampled optical depth @xmath30 to a physical path length @xmath33 . with this path length known , the new position is @xmath34 . the third step in the iteration is the determination of the new propagation direction @xmath35 of the photon . it is found by sampling a direction from the probability density @xmath36 , which represents the scattering phase function . various phase functions are built into the skirt code , including the isotropic phase function and the anisotropic henyey - greenstein phase function . the sampling of a direction from these phase functions can be performed analytically . the final step is to update the photon s doppler shift . the relative orientation of the propagation directions before and after the scattering event cause a change in doppler shift [ from equation ( [ vp ] ) ] @xmath37 to calculate the updated doppler shift , we need to sample a dust grain velocity from the dust velocity distribution . therefore , the dust components in the skirt library must not only be specified by a spatial distribution , but also by the entire phase space distribution @xmath38 . analogous to the stellar distribution function , we assume that the dust velocity field can be described by a trivariate gaussian distribution . because the dispersions in the interstellar medium are fairly small compared to the rotational velocities however , we restrict ourselves to assuming an isotropic dispersion tensor , such that @xmath39,\ ] ] with @xmath40 and @xmath41 being the mean velocity vector and the velocity dispersion of the dust . similarly as in the stellar case , we do nt have to sample a full three - dimensional velocity vector for the dust , but only a component in the direction @xmath42 this means that we just have to sample a velocity from a one - dimensional gaussian distribution with mean velocity @xmath43 and dispersion @xmath44 . the first step in the iteration described in the previous subsection requires the calculation of the total optical depth along a given path . it is found through the integral @xmath45 where @xmath46 represents the total ( absorption plus scattering ) opacity of the dust at a position @xmath3 . to execute the second step in the iteration , we need to convert an optical depth @xmath30 into a physical path length @xmath47 along a given path , which is done by solving the equation @xmath48 for @xmath49 . only for a few simple geometries , such as constant density or some spherical dust distributions , can these integrations be performed analytically . in general , the calculation of the two quantities @xmath50 and @xmath47 must be performed numerically . these integrations are usually the most time - consuming part of monte carlo codes . therefore , it is important to think about an efficient and flexible way to do this ; we have considered two approaches . in order to allow a completely arbitrary distribution of dust ( including clumpy dust distributions ) , most modern radiative transfer monte carlo codes adopt an approach that can be described as a uniform dust density ( udd ) grid . it consists of dividing space into a number of cells , and attaching a uniform dust density to each cell , for example the value at the centre of the cell . this uniform density ( and hence opacity ) makes it very easy to calculate the optical depth [ equation ( [ task1 ] ) ] along a given path : simply calculate the distance that the photon runs through each cell it crosses , multiply this distance with the opacity in the cell , and add all the pieces together . the inversion of the equation ( [ task2 ] ) is not much more difficult . first , look for the cell in which the interaction will take place . since the opacity increases linearly with path length within a single cell , this inversion of the equation is then straightforward . in the skirt code , a udd grid is included based on a three - dimensional cartesian grid . the grid cells can be chosen arbitrarily , in order to achieve an efficient grid for a variety of dust distributions . an algorithm is included to construct clumpy dust distributions from an underlying smooth dust distribution , as described in witt & gordon ( 1996 ) and bianchi et al . ( 2000 ) . in addition to the udd grid , we explore a new approach to handle the integration through the dust : an interpolated dust density ( idd ) grid . the basis is the same : we divide space into a number of cartesian grid cells , but , instead of attaching a uniform opacity to each cell , we use the correct values of the opacity at the eight border points of the cells , and we apply a simple trilinear interpolation routine to determine the opacity in each of the points within a grid cell . consider a photon at the position @xmath51 , a position within the @xmath52th cell with border points @xmath53 , etc . we define the dimensionless quantities @xmath54 , @xmath55 and @xmath56 as @xmath57 since @xmath54 increases linearly from 0 to 1 as @xmath58 moves linearly from @xmath59 to @xmath60 , and similarly for @xmath55 and @xmath56 , the trilinear interpolation rule for the opacity simply reads @xmath61 where @xmath62 , etc . represent the opacity in the border points . now consider the fraction of the path that remains in this cell . this path can be parametrized using the expression @xmath63 , with the path length @xmath33 as a free parameter . in each of the points along this path ( as long as we remain in the same cell ) , we can calculate the opacity by a similar formula as ( [ kappaintpol ] ) , @xmath64 \left[1-q(s)\right ] \left[1-r(s)\right ] \kappa_{i , j , k } \nonumber \\ & \quad+ \left[1-p(s)\right ] \left[1-q(s)\right ] r(s)\ , \kappa_{i , j , k+1 } \nonumber \\ & \quad+ \cdots \nonumber \\ & \quad+ p(s)\,q(s)\,r(s)\,\kappa_{i+1,j+1,k+1},\end{aligned}\ ] ] where the parameters @xmath54 , @xmath55 and @xmath56 are now linear functions of the path length @xmath33 , @xmath65 along a path within a single cell , the opacity is thus a cubic polynomial in @xmath33 , the distance traveled along the path , @xmath66 with constant coefficients @xmath67 . with this expression for the opacity , the calculation of the optical depth @xmath50 is very straightforward . indeed , it is sufficient to calculate , for each cell the path passes through , the two boundary positions . this enables us to calculate the path length @xmath33 within the cell and the coefficients @xmath67 . given these coefficients , the portion of the optical depth in that cell is found by substitution into the quartic polynomial @xmath68 also , the calculation of the path length @xmath47 is straightforward . first , we determine the cell in which the optical depths at the border points bracket the value of @xmath30 , in a similar way as described above to calculate the total optical depth along the path . the determination of @xmath33 then comes down to finding the root of a quartic equation . the obvious way of finding this root is by means of a newton - raphson iteration , because we can easily compute both the function values and the derivatives of this function . this routine has a very fast quadratic convergence ( the number of significant digits approximately doubles with each iteration ) . usually , no more than two iterations are necessary . to compare the accuracy and efficiency of the two approaches , we applied both techniques to a simple spherical dust geometry , characterized by an opacity @xmath69 the integrations through the dust , i.e. the calculation of the two functions @xmath50 and @xmath47 , can be performed exactly for such a dust component with @xmath70 , 3 or 5 [ see baes ( 2001 ) for details ] . these exact results were compared with the results from the udd and idd grids . in figure [ grid.eps ] we plot the relative error of the calculated values of the opacity , the total optical depth along a path and the path length corresponding to a given optical depth for 1000 randomly generated photons for such a model . for a given number of dust grid cells , the accuracy of the integrations in the idd grid is much better than those in the udd grid . however , in terms of computational efficiency , comparing the two grids with the same numbers of cells is not fair , because the integrations in the udd grid are less complicated and hence faster . we found that the idd grid integrations are a factor 3 slower in the mean . on the other hand , in order to reach a similar accuracy as the idd grid , many more cells are necessary in the udd grid . apart from slowing down the integrations , this will also increase the memory requirements significantly . after several tests , we found that the idd grid is computationally preferable above the udd grid , in particular when the system harbours a large dynamical range of dust densities ( such as an exponential profile which is appropriate in disc galaxies ) . it should be noted however , that the udd grid still remains a very useful alternative , in particular to include clumpy dust distributions into the skirt code . the procedure described at the beginning of the previous section is the most basic version of a monte carlo iteration step . when executed as such , however , it would be very inefficient . throughout the years a number of intelligent tricks have been presented which increase the computational efficiency considerably . most of them attach a weight to each photon , which can be altered during its lifetime . we incorporate three such techniques into our skirt code . the first optimization to the basic monte carlo scenario is to turn all interactions into scattering events . in reality , of course , the interaction between a photon and a dust grain can either be an absorption or a scattering event ; the nature of this event is determined by the albedo @xmath71 of the dust grains . the problem with absorptions is that the photon is lost , and therefore does not contribute to the observed radiation field anymore . to overcome this problem , we force each interaction to be a scattering event and alter the weight of the photon after each scattering by a factor @xmath71 in order to compensate for the fraction of absorbed photons . the second technique is the peeling - off procedure introduced by yusef - zadeh et al . in the basic monte carlo iteration , each photon leaves the galaxy at a certain stage , and it can be classified in bins according to its position and direction . this approach has a number of disadvantages . firstly , if we are interested in only one single observing position , most of the photons are not used . secondly , if the observer has the misfortunate of being located in a direction in which not many photons leave the galaxy , he might have to wait for a very long time to detect enough photons to obtain good statistics . thirdly , if one wants to compare the view of a system from two observing positions close to each other , the direction bins must be chosen to be very small , which requires a very large number of photons . the peeling - off technique can be used to tackle these problems . it consists of creating a new photon during each scattering [ resp . emission ] process , which is scattered [ resp . emitted ] exactly in the direction of the observer . this photon will be detected by the observer . its weight is altered by a factor @xmath72 [ resp . 1 ] to compensate for the probability of scattering [ resp . emission ] in the direction @xmath73 , and a factor @xmath74 $ ] to compensate for extinction along the line - of - sight . the third optimization we apply is the principle of forced first scattering ( witt 1977 ) , which is useful in the relatively low optical depth regime . a problem in such systems is that most of the photons leave the galaxy directly without a single interaction with a dust grain , and therefore many photons need to be generated in order to have a good statistics of the scattered radiation . to overcome this problem , we split the emitted photon into two parts . the first part of the photon directly leaves the galaxy and obtains a weight @xmath75 ( because we adopt the peeling - off technique , we do nt have to consider this fraction anymore ) . the other part of the photon with the remaining weight is forced to be scattered at least once , which is achieved by sampling an optical depth @xmath30 such that @xmath76 . this technique is called the principle of forced first scattering , but nothing prevents us applying it only to freshly emitted photons : it can equally well be applied to scattered photons ( bianchi et al . the number of forced scatterings we apply in our calculations is usually 3 , but this value can be set arbitrarily according to the studied system . the last phase in the monte carlo cycle is the detection phase , whereby the information contained in the photon is transmitted to the observer . because of the peeling - off procedure , the number and position of the observers can be chosen randomly . at each observing position , the user can choose from several simulated instruments to detect the photons : photometers , low - resolution and high - resolution spectrographs . each instrument consists of a number of pixels on the plane of the sky and they come in two geometries : rectangular and circular . each pixel contains a detector , the nature of which depends on the kind of instrument . the photometers are the most simple instruments , whereby the detector in each pixel is just a counter . every time a photon hits the pixel and its wavelength is within the detector s bandwidth , its weight is added to the intensity . at the end of the simulation , the 2d surface brightness image of the system is directly obtained . the photometers are designed such that each photon remembers the number of scatterings it has undergone , and this information is also used by the photometric detectors . this allows us to construct images for each individual scattering ( direct emission , photons that have been scattered once , etc . ) , which can be useful to disentangle the effects of absorption and scattering . the low - resolution spectrographs work in a very similar way , except that there is not just one detector , but a range of detectors corresponding to different wavelength bins . in this way a data cube is produced ( actually a set of data cubes , one for every scattering ) , very similar to the data cubes obtained by radio or fabry - perot observations . the high - resolution spectrographs basically produce similar data cubes , with doppler shift bins replacing the wavelength bins . combining the different doppler shift bins at a given position @xmath77 on the sky , we obtain the losvd or line profile @xmath78 , which describes the entire projected velocity distribution . from the losvds , the 2d mean projected velocity field @xmath79 and projected velocity dispersion field @xmath80 can be calculated . from a conceptual point of view , high - resolution and low - resolution spectrographs work in a very similar way . both separate the incoming photons in different bins according to the extra information carried by the photon , which is the wavelength in the former and the doppler shift in the latter case . from a computational point of view , however , there is an important difference between the two . indeed , the wavelength of the photon is actively used throughout the monte carlo iteration , because the optical properties of the dust grains depend on the photon s wavelength . on the contrary , a photon s path does not depend on its doppler shift . moreover , the changes in doppler shift experienced by a photon when it moves through the dust are independent of the initial stellar doppler shift . therefore , we can optimize our code in the following way . instead of initializing the photon s doppler shift by generating a @xmath81 from the stellar spatial losvd , we postpone this contribution of the stellar velocity until later and initialize @xmath81 to zero . when the photon leaves the galaxy after @xmath11 scattering events , it will then carry a doppler shift @xmath82 where we still have to add the stellar doppler shift in order to obtain the correct value . instead of generating a single initial stellar doppler shift @xmath81 from the spatial losvd @xmath17 , we split the photon over all velocity bins . each fraction will then be weighted by a weight factor that represents the probability that the final doppler shift of the photon will fall within the corresponding bin . in order to fall within a bin with boundaries @xmath83 and @xmath84 , the photon must have an initial stellar doppler shift satisfying @xmath85 . the weight factor corresponding to the @xmath86th bin will hence equal @xmath87 when we substitute the gaussian spatial losvd ( [ gaussianslosvd ] ) into this expression , we can evaluate this weight factor exactly @xmath88.\ ] ] this method is of the same kind as the optimization techniques described in section [ opt.sec ] and also increases the efficiency of the skirt code in a significant way . the skirt code is implemented in the ansi standard c++ language and makes optimal use of the object - oriented structure of this language . the output of the code consists of fits files , which are created by means of the fitsio and ccfits packages . the run time of the skirt code with reliable output depends critically on the number of photons , the number of observing directions , the spatial and velocity resolution of the instruments and the number of cells in the dust grid . for the simulations described in section [ results.sec ] , we found that about @xmath89 photons are necessary to obtain accurate results . the code spends 60 per cent of the time moving through the dust grid , while most of the remaining time is spent in the calculation of the spatial losvds . when run on a modern pentium iv pc , the run time of a single simulation ( with 7 observing positions ) is of the order of 50 to 100 hours . the code was first run without dust included in order to test the projection algorithm and the calculation of the observed kinematics . we used simple non - rotating spherical geometries which allow an analytical expression of the surface brightness and projected velocity dispersion profiles ( dejonghe 1987 ; hernquist 1990 ; jaffe 1983 , baes & dejonghe 2002b ) . also the surface brightness profiles of face - on and edge - on exponential discs ( which can be calculated analytically ) are accurately recovered . moreover , when we attach a simple velocity structure to an exponential disc , with a flat rotation curve and exponentially decreasing velocity dispersions , the observed kinematics can be also calculated analytically in the face - on and edge - on directions . these are recovered very well , proving the correct behaviour of the code . next , we compared the results of the skirt code with our previous monte carlo calculations of the observed kinematics of elliptical galaxies ( baes & dejonghe 2001b , 2002a ) . the monte carlo code used in these papers also allowed for the calculation of the observed kinematics , but only for spherical models , chosen such that the integrations through the dust could be performed analytically . we found an excellent agreement between these results and those calculated with the new skirt code . -band surface brightness distribution of an edge - on disc galaxy , for various values of the optical depth . the model is similar to the bt0.3 model described by byun et al . ( 1994 ) , i.e. an exponential stellar disc with scale length @xmath90 kpc and scale height @xmath91 kpc , a de vaucouleurs bulge with @xmath92 kpc and a bulge - to - total luminosity ratio of 0.3 . the dust is also exponential with scale length @xmath93 kpc and @xmath94 kpc , and the face - on central optical depths in the different plots are @xmath95 , 0.5 , 1 , 2 , 5 and 10 ( from top to bottom ) . surface brightness contours are shown with a step of @xmath96 mag / kpc@xmath97 . , scaledwidth=40.0% ] finally , we compared our ( photometric ) results with the radiative transfer calculations of other authors . in figure [ byun.eps ] we plot the two - dimensional edge - on surface brightness distribution of an sb galaxy model in the @xmath98 band for various values of the optical depth . the models are the same models as the bt0.3 models of byun et al . ( 1994 ) , and they consist of a stellar disc , a stellar bulge and a dust disc . comparing this figure with their figure 4b , we find an excellent agreement between the two results . notice that byun et al . ( 1994 ) adopted a completely different approach to solve the radiative transfer problem . we apply the skirt code to investigate the effect of dust absorption and scattering on the photometry and the stellar kinematics of normal galactic discs . we limit our modelling only to a stellar disc and do not include a bulge , because we are primarily interested in the disc kinematics . our model consists of a simple axisymmetric double exponential disc galaxy , with stellar emissivity @xmath99 the luminosity @xmath100 is a free scaling parameter in our models , as both the input emissivity and the output light profile scale with the luminosity . for the scale length and scale height we chose the values adopted by byun et al . ( 1994 ) to describe the milky way , @xmath90 kpc and @xmath101 pc . as we focus on the observed kinematics , which are always measured in a very narrow wavelength region , we chose a trivial monochromatic sed centered on the @xmath102 band . in order to run a kinematical simulation for such a disc galaxy , we also need to provide details on the kinematical structure of the disc . we assume that the stellar velocities at each position in the disc can be represented by a trivariate gaussian distribution , @xmath103.\ ] ] such a velocity distribution was first proposed by schwarzschild ( 1907 ) to describe the distribution of stellar velocities in the solar neighbourhood . the mean azimuthal velocity and the three velocity dispersion components can vary from position to position . the entire kinematical structure of the disc will be completely determined if we have expressions for the four functions @xmath104 , @xmath105 , @xmath106 and @xmath107 . since the system is axisymmetric , these quantities will depend only on the cylindrical radius @xmath108 and the height @xmath109 . moreover , because stellar discs are thin and the contribution of photons high above or under the symmetry plane of the galaxy will be quite small due to the vertical exponential decrease , we will assume that these four functions are a function of @xmath108 only . for the @xmath110 profile , we assume the arctan profile , a simple two - parameter fitting function that fits the observed rotation curves of disc galaxies fairly well ( e.g. courteau 1997 ) , @xmath111 we have adopted an amplitude @xmath112 km / s and a scale radius @xmath113 kpc , which results in a rotation curve that has a steep initial gradient and reaches its flat part fairly quickly . the internal velocity dispersion profiles in disc galaxies are not well constrained . for a thin self - gravitating disc , the jeans equations yield that the vertical velocity dispersion scales with the square root of the surface density . if we assume a constant mass - to - light ratio , we obtain the following parametrization , @xmath114 as all dispersions in a stellar disc are thought to exist from the gradual stellar heating of an initial cold disc , it makes sense to assume that the velocity dispersions in the other direction are intimately coupled to the vertical dispersion . therefore , we assume a constant axis ratio of the velocity ellipsoid in our model , such that @xmath115 and @xmath116 have the same spatial variation as @xmath117 . notice that such behaviour is found to be in agreement with the sparse existing data on the velocity dispersions in external galaxies ( gerssen et al . 1997 , 2000 ) . the only remaining quantities that need to be set are normalizations of the dispersions . we adopted the values @xmath118 km / s . at a galactocentric radius of 8 kpc , this gives velocity dispersions of ( 37,28,18 ) km / s , which roughly corresponds to the measured velocity dispersions in the solar neighbourhood . the dust was chosen to be distributed in a similar way as the stellar distribution , @xmath119 whereby @xmath30 ( here ) represents the face - on optical depth through the centre of the galaxy , @xmath120 for the dust scale length and scale height , we again choose the values from byun et al . ( 1994 ) , @xmath93 kpc and @xmath121 pc . notice that the dust is hence significantly more confined to the plane of the galaxy , a feature which gives rise to the well - known dust lanes in edge - on galaxies . for the velocity field of the dust grains , we assumed an isotropic gaussian distribution , @xmath122.\ ] ] we assumed the same mean velocity as the stellar distribution , and a velocity dispersion @xmath123 km / s , which is a typical value for the dispersion of the cold gas in the interstellar medium ( sofue & rubin 2001 ) . finally , for the optical properties of the dust we took the average galactic values ( gordon , calzetti & witt 1997 ) . these functions and parameters completely determine our model , except for the one free parameter @xmath124 , the central face - on optical depth in the @xmath102 band ( the corresponding optical depth at other wavelengths is determined by the assumed optical properties of the dust ) . as discussed in the introduction , the optical depth in spiral galaxies is still a matter of debate . we ran our models for the optical depth values @xmath95 , 0.5 , 1 , 2 , 5 and 10 , in order to cover a wide range of possible scenarios . in this section we present and describe the results of our monte carlo simulations . we will not discuss the effects of dust on the photometry , since such results have been discussed at length by other authors , such as byun et al . ( 1994 ) , corradi et al . ( 1996 ) and bianchi et al . instead we concentrate on the effects of dust on the observed kinematics , in particular on the mean projected velocity @xmath79 and the projected velocity dispersion @xmath80 . in figures [ mw_vp.eps ] and [ mw_sigp.eps ] we compare , at various inclination angles , the 2d mean projected velocity and projected velocity dispersion fields of an optically thin galaxy ( left ) with the corresponding fields of a dusty galaxy with optical depth @xmath125 ( centre ) and @xmath126 ( right ) respectively . notice that the mean projected velocity field is not plotted in the face - on direction , as there is no rotation perpendicular to the galactic plane . to facilitate the interpretation of these 2d kinematical fields , we plotted in figure [ mwkin.eps ] the major and minor axis kinematical profiles of our models at various inclination angles , explicitly as a function of the optical depth . .the effect of dust attenuation on the slope of the mean projected velocity curve . this slope is expressed through the major axis radius at which the rotation curve reaches half of the asymptotic value @xmath127 these radii are tabulated for the various inclinations and optical depths considered in our simulations . for a infinitely thin and dust - free galaxy , the intrinsic value would be 0.5kpc , independent of the inclination angle . [ cols="<,>,>,>,>,>",options="header " , ] [ rot.tab ] for edge - on galaxies , the effects of dust on both the mean projected velocity and the projected velocity dispersion are very strong , as is obvious from the bottom row panels of figure [ mw_vp.eps ] and [ mw_sigp.eps ] , and the panels in the right column of figure [ mwkin.eps ] . the projected mean velocity profile along the major axis rises more and more slowly as the optical depth increases , and tends towards a solid body rotation . these trends were expected , and in agreement with the arguments of davies ( 1990 ) and the absorption - only calculations of bosma et al . ( 1992 ) . to quantify this change of slope , we have calculated , for each optical depth , the major axis radius at which the mean projected velocity reaches half of its maximum value @xmath127 kms@xmath128 . these values are tabulated in the second column of table [ rot.tab ] , and demonstrate that the effects of dust attenuation are very severe , even for small optical depths . the reason for this shallower slope of the rotation curve is that we mainly see the radiation from the optically thin part of the galaxy , which is more and more restricted to the outer part of the galaxy as the optical depth increases . in the same way , we can understand the effects of dust attenuation on the projected velocity dispersion profile , where also a prominent dust lane is visible in the contour plot : we mainly see the light ( and hence the doppler shift ) of the stars from the outer part of the disc , where the intrinsic velocity dispersion is much smaller . bosma et al . ( 1992 ) found that the signature of dust absorption on the rotation curve depends strongly on the inclination angle . for inclinations which deviate as few as 5 degrees from purely edge - on , they found that the effects of dust on the rotation curve is already severely reduced , even for optical depths up to @xmath129 . this result remains the same if scattering is also taken into account , because the absorption effects of dust strongly dominate in highly inclined galaxies . table [ rot.tab ] quantitatively demonstrates these results . for the projected velocity dispersion , a similar effect is valid , at least for the major axis dispersion profile . when the entire projected velocity dispersion field ( or just the minor axis dispersion profile ) is taken into account , the asymmetrical signature of the dust can still be recognized for inclinations down to 80 degrees . moving to intermediate inclinations , the effects of dust attenuation on the observed kinematics quickly become very limited . for example , there is hardly any effect noticeable for an inclination of 60 degrees , which can easily be seen by comparing the corresponding panels in figure [ mw_vp.eps ] and [ mw_sigp.eps ] . in the light of the previous results , we would expect that the effects of dust attenuation on the observed kinematics of face - on galaxies are completely neglegible . and indeed , on the mean projected velocity there is no effect at all : the projected mean velocity is zero for face - on galaxies , regardless of whether dust is present or not . however , we do see a conspicuous effect of dust attenuation on the projected velocity dispersion : it increases with increasing optical depth . this can not be an absorption effect , because all stars along a given line of sight in our face - on galaxy discs have the same velocity dispersion @xmath117 in the direction of the observer . the effect arises as a result of photons emitted in the central regions in a direction parallel to the plane of the galaxy . when these photons are scattered into a vertical direction , they have a large probability to leave the galaxy . they will then contribute the high - velocity information of the stars in the central regions to the losvds , causing high - velocity wings and hence an increased velocity dispersion . the effect is similar to what we found for the projected velocity dispersion profile of elliptical galaxies containing a diffuse dust component ( baes & dejonghe 2002a ) . compared to these models , where the signature of the dust is very significant , it is fairly modest for the face - on discs . the reason for this weaker impact is the fact that the velocity dispersion profile in our disc galaxy models have a fairly shallow slope , compared to the elliptical galaxy models of baes & dejonghe ( 2002a ) . in disc galaxies , the doppler shifts contributed by the scattered photons will in the mean differ less from the doppler shifts contributed by the direct photons as in elliptical galaxies . we could ask ourselves the question whether this conclusion is biased by the chosen star - dust geometry of our disc galaxy models . indeed , baes & dejonghe ( 2002a ) found their results depended strongly on the relative star - dust geometry : the scattering effect was strong only for models in which the dust was more extended than the stars . in our disc galaxy models , the dust distribution has the same scale length as the stars , whereas the scale height is smaller , such that the dust is always sandwiched between the stars . recently however , evidence has been found for extended distributions of cold dust in spiral galaxies , both from the radiative transfer modelling of the dust lanes in edge - on galaxies ( xilouris et al . 1997 , 1998 , 1999 ) and from iso and scuba dust emission ( alton et al . 1999 ; davies et al . 1999 ) . in order to investigate whether this would bias our results , we considered a new set of models with an extended dust distribution . they were constructed by increasing the dust scale length or the dust scale height by factors up to three , while keeping the face - on optical depth fixed . running new face - on simulations for these models , we found that the strength of the scattering effect on the projected velocity dispersion increases only minimally , with deviations of the order of a few per cent . the modest effects found in figure [ mwkin.eps ] are hence representative for disc galaxies . one of the most useful and promising applications of stellar kinematics in disc galaxies is their contribution to mass modelling . in its simplest form , this mass modelling consists of decomposing the observed rotation curve into contributions by the disc and the dark halo ( assuming the contributions of a bulge and molecular / atomic gas are negligible ) . even in this most simple scenario , there is still a virtually complete degeneracy : the mass - to - light ratio of the disc . authors have often adopted a solution in which the contribution of the disc is maximized , leading to the so - called maximum disc hypothesis ( van albada & sancisi 1986 ) . there are however , no convincing arguments to favour a particular value for the stellar mass - to - light ratio , and often scenarios in which the dark matter halo dominates the disc are equally possible ( e.g. lake & feinswog 1989 ) . stellar kinematics can , in principle , provide the necessary additional constraint to break this degeneracy . indeed , for a self - gravitating disc , the vertical velocity dispersion scales linearly with the square root of the surface density of the disc , and can therefore be used to constrain the mass - to - light ratio of the disc . the most obvious candidates for such an analysis would be face - on galaxies , because their projected velocity dispersion directly reflects the vertical velocity dispersion in the disc . we found that for a dusty disc galaxy , the observed velocity dispersion is affected by scattering . the effects are modest , however , even for models with an extended dust distribution . alas , face - on galaxies do have strong observational disadvantages . foremost , their low surface brightness make it very hard to obtain the stellar kinematics out to sufficiently large distances to isolate the disc component . moreover , the shape and amplitude of the rotation curve can not be measured directly . the amplitude can be estimated fairly accurate using the tully - fisher relation , whereas the shape could be approximated through the ( controversial ) universal rotation curve formalism ( persic , salucci & stel 1996 ) . this is unsatisfactory , however , because there is a large spread in universal rotation curves , and the details of mass modelling usually depend crucially on small scale features of the rotation curve which statistical methods can not incorporate . edge - on galaxies do nt suffer from these observational problems : their surface brightness is much higher , and their apparent rotation curve can be determined directly . however , the interpretation of the kinematical data is non - trivial . firstly , the vertical velocity dispersion must be linked to the observed dispersion , which is a mixture of contributions from the radial and tangential velocity components . based on the observed axis ratio of velocity ellipsoid in the solar neighborhood , bottema ( 1993 ) estimated the vertical velocity dispersion in edge - on galaxies by means of the radial velocity dispersion evaluated at one scale length . it has been shown , however , that the velocity ellipsoid axis ratios in disc galaxies can vary substantially ( gerssen et al . secondly , our modelling indicates that both the projected mean velocity and the projected velocity dispersion field in edge - on galaxies are strongly affected by interstellar dust . galaxies of an intermediate inclination ( @xmath130 ) , however , are most suitable for such an analysis . gerssen et al . ( 1997 ) have shown that for galaxies with an intermediate inclination , the three components of the velocity ellipsoid can , in principle , be determined by studying the kinematics along major and minor axes . also , because the rotation curve of inclined galaxies can directly be determined and their surface brightnesses are high enough to allow the measurements of their kinematics in a reasonable time , they form ideal targets for such a study . moreover , determining the three components of the velocity ellipsoid is very useful to constrain the dynamical history of disc galaxies , because the various proposed mechanisms leave a different imprint on the velocity ellipsoid . our modelling demonstrates that the observed kinematics of inclined disc galaxies can be directly interpreted and are not biased by dust attenuation . we argue that studying the observed kinematics of a substantial set of optically smooth inclined galaxies could thus greatly contribute to understanding the mass structure and dynamical history of spiral galaxies . the results of our modelling are important concerning the derivation of the rotation curve of spiral galaxies . whereas the outer parts of the rotation curves of spirals were the preferred field of interest for nearly three decades , it is the inner slope of the rotation curve which nowadays stands in the spotlight . to measure the slope in this inner region accurately , a high spatial resolution is required , which makes the usual 21-cm measurements less suitable , except for the most nearby galaxies . a useful alternative are co rotation curves , which can achieve a high resolution in both the spatial and velocity directions , but these observations are quite costly in observing time . the main alternative remains optical h@xmath2 observations , either long - slit or fabry - perot . using h@xmath2 rotation curves , several authors ( blais - ouellette , amram & carignan 2001 ; borriello & salucci 2001 ; de blok , mcgaugh & rubin 2001 ; de blok & bosma 2002 ) have recently found shallow slopes for the inner rotation curve of a significant number of ( mainly lsb and dwarf ) galaxies . such slopes are not in agreement with the results of high - resolution cosmological n - body simulations , where it is found that dark matter halos have a strong cusp , and hence that rotation curves of dark matter dominated galaxies should be steeply rising ( navarro , frenk & white 1997 ; moore et al . a number of `` solutions '' have been proposed to explain this discrepancy , amongst them the suggestion that the internal extinction in the centre of galaxies could be a major source of uncertainty . our models show that , indeed , an edge - on galaxy with an observed slowly rising rotation curve could in principle be a _ dusty _ galaxy with an intrinsically steep rotation curve . we found , however , that this effect can not be obtained with realistic amounts of dust if the galaxies deviate more than a few degrees from exactly edge - on , confirming the results of bosma et al . ( 1992 ) and matthews & wood ( 2001 ) . in addition , because lsb galaxies are assumed to be dust poor ( mcgaugh 1994 , tully et al . 1998 ; matthews et al . 1999 ) , we have demonstrated that dust effects can not explain the observed discrepancies . we do however demonstrate that dust effects are important for galaxies within a few degrees from edge - on , and that dust attenuation must be seriously taken into account in such cases . the calculation of the final doppler shift of a photon in the skirt code takes into account the velocity information of the star and the individual velocity vectors of each individual scattering dust grain . this means that for every scattering event , we need to sample a velocity from the dust velocity field , and this is a costly operator . it would be very convenient from a computational point of view , if we could neglect the dust grain velocities . we have done this in our previous monte carlo simulations ( baes & dejonghe 2001b , 2002a ) , where we studied the observed stellar kinematics of elliptical galaxies . in these models , both stars and dust grains are supported by random motions , and because the dust is colder than the stars , the extra doppler shifts due to scattering are generally smaller than the stellar doppler shift . in a spiral galaxy , however , this argument does not hold anymore , because the velocities of both stars and dust grains are dominated by the rotation and are therefore of the same magnitude . in order to investigate the importance of including the individual dust grain velocities into the code , we ran the same models again but without taking the dust velocities into account . in figure [ mwappkin.eps ] we plot the major and minor axes mean projected velocity and projected velocity dispersion profiles of our models calculated this way . comparing this figure with the corresponding this figure with figure [ mwkin.eps ] , we find that the effects of dust on the mean projected velocity profiles are significantly overestimated when the dust grain velocities are not taken into account , in particular for inclined galaxies . the differences between the projected velocity dispersion curves in both figures are even worse : when the dust grain velocities are neglected , the apparent effect of dust attenuation is to increase the dispersion at nearly all radii and all inclinations , by factors of up to 200 per cent or more for realistic optical depths . to understand this behaviour , consider a photon emitted by a star with velocity @xmath13 in the direction @xmath8 , and assume this photon is scattered by a dust grain with velocity @xmath131 into the direction @xmath132 , whereafter it manages to escape the galaxy . when we do not take the dust grain velocity into account , the observed doppler shift of the photon will simply be @xmath133 . on the contrary , the correct observed doppler shift of the photon reads @xmath134 in a disc galaxy , the motion of both stars and dust grains is dominated by the same rotation . if the pathlength of the photon between its emission and scattering is short , the velocity vectors of the star and dust grain will therefore be very similar , @xmath135 , such that @xmath136 . the new correct doppler shift is hence a typical line - of - sight velocity of a star in the new propagation direction @xmath132 of the photon . therefore , taking the dust motion into account more or less forces the dust grain to adopt a doppler shift that is `` appropriate '' for the new propagation direction . along a given line - of - sight , the velocity information carried by scattered photons will , in the mean , only modestly deviate from the velocity information carried by photons directly emitted in same direction . if we do nt take the dust grain velocities into account , the photon can contribute , to the observed kinematics in a given direction , a line - of - sight velocity typical for a completely different direction . in the elliptical galaxy models from baes & dejonghe ( 2002a ) , this does not make much difference , because the velocities of the stars have similar magnitudes in the different directions . in a rotating disc galaxy however , this makes a huge difference because the stars have hugely different velocities in different directions : the vertical and radial motions are determined by the dispersion and are of the order of a few tens of km / s , whereas the azimuthal motion is dominated by the rotation and is of the order of 200 km / s . if the dust grain velocities are not correctly taken into account , scattered photons can thus cause erroneous extremely - high - velocity wings in the losvds . these give rise to modest but significant errors in the mean projected velocity , and very large errors in the projected velocity dispersion . as a remark , we want to point out that matthews & wood ( 2001 ) found that `` also including the doppler shifts arising from the relative bulk motion of the scattering dust particles had a negligible effect on the final rotation curves '' . whereas this statement is indeed true for the mean projected velocity of highly inclined galaxies , we nevertheless judge that this could easily be misinterpreted as a justification to neglect dust velocities altogether . it must be realized that for the calculation of the entire losvds , and for the projected velocity dispersion in particular , the dust velocities do play a crucial role , and must be taken into account . in this paper we have presented a novel monte carlo code that can take velocity information into account , and can hence be used for kinematical modelling of dusty objects . we applied this code to calculate the observed kinematics of dusty disc galaxies . the main results of this paper can be summarized as follows . 1 . a correct inclusion of kinematical information into radiative transfer problems requires the inclusion of the velocities of both the emitting stars and the scattering dust grains . we see no other way of tackling this problem except with monte carlo techniques . a new approach is presented to optimize the integration through the dust in a monte carlo code , using a trilinear interpolation instead of a constant opacity within each cell . we compared both kinds of grids , and find that , to obtain a similar accuracy , the new approach is more efficient in terms of computation time and memory . the effects of dust attenuation on the kinematics of edge - on disc galaxies are severe . both the mean projected velocity and the projected velocity dispersion are severely affected , even for modest optical depths . therefore we strongly advise to always interprete the stellar kinematics and optical rotation curves of edge - on galaxies very cautiously . 4 . for galaxies which are more than a few degrees from strictly edge - on , the effects of interstellar dust on the observed kinematics are much weaker . therefore , we argue that dust attenuation can not be invoked as a possible mechanism to reconcile the observed slope of lsb galaxies with the predicted cdm cosmological models . 5 . dust attenuation does not affect the kinematics of intermediately inclined galaxies . such galaxies hence form the ideal targets for stellar kinematical studies , in particular to constrain the mass structure and to study the kinematical history of disc galaxies . . the projected velocity dispersion of face - on galaxies increases slightly due to scattering of dust grains into the line of sight . the effects are relatively small , however , even for extended dust distributions . 7 . neglecting the extra doppler effect caused by the scattering medium results in incorrect projected kinematics , in particular if the velocity components of the stars ( and dust grains ) in the galaxy differ considerably , such as in a rotating disc . if the dust grain velocities are neglected , the mean projected velocity is significantly underestimated , and the projected velocity dispersion field is completely overestimated . m.b . gratefully thanks the fund for scientific research for financial support . alton p. , bianchi s. , rand r. , xilouris e. , davies j. , trewhella m. , 1999 , apj , 507 , l125 baes m. , ph.d . thesis , univ . gent , belgium baes m. , dejonghe h. , 2000 , mnras , 313 , 153 baes m. , dejonghe h. , 2001a , mnras , 326 , 722 baes m. , dejonghe h. , 2001b , apj , 563 , l19 baes m. , dejonghe h. , 2002a , mnras , 335 , 441 baes m. , dejonghe h. , 2002b , a&a , 393 , 485 baes m. , dejonghe h. , de rijcke s. , 2000 , mnras , 318 , 798 bianchi s. , ferrara a. , davies j.i . , alton p.b . , 2000 , mnras , 311 , 601 bianchi s. , ferrara a. , giovanardi c. , 1996 , apj , 465 , 127 blais - 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zadeh f. , morris m. , white r.l . , 1984 , apj , 278 , 186 in this appendix , we show how the skirt code generates a random position from the exponential disc model , i.e. how a random position is drawn from the three - dimensional probability density @xmath137 as this probability density is a separable function of @xmath108 , @xmath138 and @xmath109 , we can generate a random position by independently generating each of these three coordinates , whereby the generation of an azimuth is trivial . to generate a random radius and height , we use the transformation technique , which says that a random variable @xmath58 can be drawn from a probability density @xmath139 by generating a uniform deviate @xmath140 and solving the equation @xmath141 for @xmath58 . the calculation of a random @xmath109 is easy using this principle and results in @xmath142 this procedure works equally well when we introduce a cut - off , or when a sech or isothermal profile is used instead of the exponential profile to describe the vertical distribution of the stars ( e.g. bianchi et al . 1996 ) . applying the same technique to generate a random @xmath108 , we can find @xmath108 by solving the equation @xmath143 bianchi et al . ( 1996 ) invert this transcendental equation numerically to find @xmath108 . however , this equation can be solved exactly by means of the lambert function , yielding @xmath144.\ ] ] the lambert function , also known as the product log function , is generally defined as the inverse of the function @xmath145 , and @xmath146 represents the only real branch of this complex function besides the principle branch . the lambert function can be computed in a very efficient way by means of halley iteration ; for more information on this function see corless et al .

we present skirt ( stellar kinematics including radiative transfer ) , a new monte carlo radiative transfer code that allows the calculation of the observed stellar kinematics of a dusty galaxy . the code incorporates the effects of both absorption and scattering by interstellar dust grains , and calculates the doppler shift of the emerging radiation exactly by taking into account the velocities of the emitting stars and the individual scattering dust grains . the code supports arbitrary distributions of dust through a cellular approach , whereby the integration through the dust is optimized by means of a novel efficient trilinear interpolation technique . we apply our modelling technique to calculate the observed kinematics of realistic models for dusty disc galaxies . we find that the effects of dust on the mean projected velocity and projected velocity dispersion are severe for edge - on galaxies . for galaxies which deviate more than a few degrees from exactly edge - on , the effects are already strongly reduced . as a consequence , dust attenuation can not serve as a possible way to reconcile the discrepancy between the observed shallow slopes of the inner rotation curves of lsb galaxies and the predictions of cdm cosmological models . for face - on galaxies , the velocity dispersion increases with increasing dust mass due to scattering , but the effects are limited , even for extended dust distributions . finally , we show that serious errors can be made when the individual velocities of the dust grains are neglected in the calculations . dust , extinction galaxies : kinematics and dynamics galaxies : spiral radiative transfer

to determine the trajectory of a photon being observed in the human cornea , from a point within the anterior central corneal epithelium to a point within the posterior stroma . refractive error places an enormous disease burden on society , with net estimates of over two billion people affected worldwide @xcite . myopia , hyperopia , presbyopia , astigmatism , and cataracts are among the most common forms of refractive error . refractive surgery is an effective and growing method of correcting refractive error . there are a high volume of cases performed annually , including cataract extractions with intraocular lens placement , laser - assisted in - situ keratomileusis ( lasik ) by microkeratome incision or by femtosecond laser incision , photorefractive keratectomy ( prk ) , and laser - assisted sub - epithelial keratomileusis ( lasek ) . refractive surgery techniques and technologies have seen significant advances over the years including current reports of greater than 90% patient satisfaction post - operatively @xcite . however , outcomes remain suboptimal and patients are often still left to manage imperfect vision following surgery . most modern refractive surgery techniques involve direct modification of the corneal epithelium and stroma . it is therefore important to have a precise and detailed understanding of the refractive properties along this path . it is additionally imperative to understand how those properties govern the behavior of light both as a source of visual stimulus , and in amplified form , as lasers for refractive and other ophthalmic intervention . furthermore , a precise quantitative mapping of the refractive properties of the human cornea is requisite for good design of keratoprosthetic implants . in this paper , we embark on a mathematical exploration of the photon trajectory from the anterior central corneal epithelium to the posterior stroma . we operate within the realm of geometric optics , which assumes the limit of short wavelength , where light propagation can be approximated by rays and studied using geometry . we introduce the trajectron algorithm for computing the photon trajectory in a model respectful of the cornea s axial grin nature . meridional intra - corneal grin is of significantly less magnitude than axial intra - corneal grin , and is assumed to be zero in this model . trajectron uses a closed form solution of the ray equation of constant axial grin media , and evaluates over piece - wise constant grin . one advantage of trajectron is that it is not restricted to the paraxial regime . this makes it eligible for the study of non - paraxial optical phenomena such as peripheral visual field analysis , as well as higher - order aberrations before and after refractive surgery . previous mathematical models of the human eye assumed the corneal refractive index to be constant @xcite . such models were proposed when less was known about the intra - corneal grin nature . a few recent models based on ray - transfer matrix ( abcd ) analysis incorporate the intra - corneal grin nature . barbero proposed a multilayer model of cornea and tear - film to calculate corneal power . his global ray - transfer matrix was a product of 7 matrices representing ray transfer through 4 interfaces and 3 media which included a grin stroma @xcite . flores - arias et al proposed a linear cascade model expressing the generalized fresnel integral transform kernel in terms of paraxial coefficients ; where the global ray - transfer matrix was a product of anterior chamber , grin cornea , and grin lens component ray - transfer matrices @xcite . these newer models incorporating the grin nature represent a significant advance . one disadvantage however , is that they are restricted to the paraxial regime , and this limits their validity for peripheral visual field analysis and non - paraxial photon tracking . in contrast , our current work is useful for investigating interesting non - paraxial optical phenomenology , because it respects the intra - corneal grin nature , and is not restricted to the paraxial regime . in this paper we make the following technical and biophysical contributions : * the first quantitative demonstration of non - paraxial light - bending within the human cornea . * an analytico - numerical algorithm , trajectron , for determining the photon trajectory within the human cornea , respecting axial grin and assuming zero meridional grin . * a method for studying non - paraxial optical phenomena in the human cornea . for example : * * peripheral visual field analysis * * higher order aberrations pre and post refractive surgery * an approach towards describing the angular domain over which the paraxial approximation is clinically useful in the human cornea . we use a hybrid approach inter - weaving between analytical and numerical processes . our objective is to determine the ray path from a point in the anterior central corneal epithelium to a point in the posterior stroma . the human cornea has an axial grin of non - constant magnitude @xcite , and we approximate it as also having zero meridional grin . this approximation is made because , although meridional intra - corneal grin has been demonstrated in - vivo in humans @xcite , it is significantly less than the axial intra - corneal grin @xcite . to achieve our objective , we introduce trajectron , a new algorithm which evaluates a closed form solution of the ray equation of constant axial grin media , over piece - wise constant axial grin . the details of the trajectron algorithm are presented in section ( [ sec : rslt ] ) below . discrete measurements of corneal refractive indices are obtained from the literature , and a continuous distribution is generated by curve fitting . trajectron is prototyped in matlab ( the mathworks inc . , natick , ma ) . the remainder of this paper is organized as follows : section ( [ sec : physfor ] ) outlines the physical formalism of lagrangian optics and includes a known closed form solution of the ray equation of constant axial grin media ; section ( [ sec : msmt ] ) describes structure , thickness , and refractive index measurements within the human cornea ; section ( [ sec : compu ] ) introduces the trajectron algorithm ; section ( [ sec : rslt ] ) presents the results of our numerical experiments ; section ( [ sec : disc ] ) discusses the findings , the study limitations , and the clinical angular domain of the paraxial and non - paraxial regimes ; and section ( [ sec : conclu ] ) concludes the paper . fermat s principle of stationary time asserts that light travels along the path that takes the least ( or greatest ) time . in the context of a classical mechanics treatment , fermat s principle is fully described by the lagrangian of geometric optics , given by , @xmath0 where @xmath1 is the refractive index distribution , @xmath2 , @xmath3 , and @xmath4 are spatial coordinates , and @xmath5 . while @xmath2 and @xmath3 take the role of generalized coordinates , @xmath4 describes the optical axis and takes the role of parameter . the corresponding euler - lagrange equations are given by , @xmath6 where equation ( [ fermat_e - l ] ) encodes three equations : with @xmath7 , @xmath8 , and @xmath9 . applying equation ( [ fermat_e - l ] ) above to the optical lagrangian , equation ( [ optical_lagrangian ] ) , yields the ray equation , @xmath10 which represents the equations of motion for propagation of a light ray through a medium of refractive index distribution @xmath11 . in equation ( [ ray_eqn ] ) , @xmath12 is the spatial position vector @xmath13 $ ] of the ray , @xmath14 is the gradient operator , and @xmath15 is the arc length along the ray trajectory , and is given by @xmath16 . in the case of constant refractive index gradient , @xmath17 , along the optical axis direction , and zero refractive index gradient along the other two cardinal directions , equation ( [ ray_eqn ] ) can be written as , @xmath18 the ray @xmath19 $ ] is embedded in a 2-dimensional plane . this plane of propagation is defined by the optical axis and @xmath20 , where @xmath21 denotes the point along the optical axis in the anterior corneal epithelium where we initiate observation , and @xmath20 denotes the ray direction at @xmath21 . the embedding , @xmath22 , is given by , @xmath23 where @xmath24 is the angle the propagation plane makes with the positive @xmath3-axis . the components of the canonical optical momentum are given by , @xmath25 and as follows for direction cosines , sum of squares equals one , hence , @xmath26 equations ( [ ray_eqn_const_grad ] ) and ( [ canonical_optical_momenta ] ) together state that @xmath27 and @xmath28 are constant along the ray trajectory . equation ( [ ray_eqn_const_grad ] ) in conjunction with the constancy of @xmath27 and @xmath28 , constrain the ray @xmath29 to the @xmath30 plane . applying the fundamental theorem of calculus to the conservation relation for optical momentum shown in equation ( [ momentum_conservation ] ) , one obtains the following known closed form solution of the ray equation in constant axial grin media @xcite , @xmath31 where @xmath32 is the refractive index at the initial observation point of the photon , @xmath33 is a function of @xmath4 given by , @xmath34 @xmath35 is a constant given by , @xmath36 and @xmath37 is the angle between @xmath20 and the positive @xmath38 axis . the angle between the optical axis and @xmath20 is denoted by @xmath39 . in this paper we are primarily interested in rays entering the cornea , and will therefore focus on photon trajectories for which @xmath40 . closed - form and numerical solutions of the ray equation of axial grin media require knowledge of the grin . the gradients can be approximated by the difference quotients . this requires appropriately sampled measurements of refractive index and thickness . below , we examine the literature for the required measurements in the four corneal layers along the photon trajectory of interest : ( i ) corneal epithelium , ( ii ) bowman s layer , ( iii ) anterior stroma , and ( iv ) posterior stroma . the corneal epithelium is a non - keratinized stratified squamous epithelium @xcite of 5 - 7 cell layers with rapid surface turn over . the corneal epithelium is covered by mucinous tear film anteriorly , and is adjacent to bowman s layer posteriorly . the morphology of the air - tear film interface approximately conforms to the corneal epithelial surface . corneal epithelial surface layer abrasions can cause significant visual distortion , and can manifest photophobia and moderate to severe amounts of pain . however as a result of limbal stem cell activity @xcite , abrasions typically heal in 24 - 48 hours in healthy individuals . both lasek and prk procedures involve manipulation of the corneal epithelium . in prk , the epithelial layer is removed entirely by mechanical or alcohol debridement , to allow for laser ablation of the anterior stroma @xcite . in lasek , an alcohol solution is used to disrupt the epithelial layer , creating a flap which is then replaced following laser ablation of anterior stroma @xcite . there have been several measurements of human central corneal epithelial thickness by various modalities . significant variation exists in the findings , but almost all the results have been in the 49 - 60 @xmath41 m range . the following is a sample of prior work in this area . king - smith et al used interferometry to make measurements on 6 healthy eyes , and found a corneal epithelial thickness of @xmath42 @xcite ; li et al used confocal microscopy through focusing ( cmtf ) on 7 healthy subjects and found a thickness of @xmath43 @xcite ; and reinstein et al used very high frequency ultrasound ( vhfu ) on 110 eyes in 56 subjects who presented for refractive surgery , and they found a thickness of @xmath44 @xcite . ladage et al conducted a prospective randomized double - blind study on 246 subjects , assessing the effects of contact lens type and oxygen transmissibility on corneal epithelium in daily wear @xcite . the study consisted of three treatment groups : high oxygen - transmissible soft lenses ( n= 36 subjects ) , hyper oxygen - transmissible soft lenses ( n=135 subjects ) , and hyper oxygen - transmissible rigid gas permeable lenses ( n=75 subjects ) , in each of which baseline central corneal epithelial thickness was measured using cmtf and found to be @xmath45 , @xmath46 , and @xmath47 respectively . there have been a number of studies using optical coherence tomography ( oct ) @xcite to estimate central corneal epithelial thickness in humans . wang et al used oct on 20 healthy eyes in 40 subjects and found a thickness of @xmath48 @xcite ; feng et al used oct on 10 healthy subjects and found a thickness of @xmath49 ; and radhakrishnan et al used 1310 nm real - time oct to make measurements on 5 healthy subjects , and found a thickness of @xmath50 m @xcite . table ( [ table : epithelial_thickness ] ) summarizes the central corneal epithelial thickness for the above mentioned studies . [ table : epithelial_thickness ] patel et al used a modified hand - held refractometer to measure the refractive index in 10 human eyes in - vivo , and found a value of 1.401 ( @xmath510.005 ) @xcite . there have been few if any other in - vivo estimations of corneal epithelium refractive index in humans . in humans , bowman s layer sits posterior to the corneal epithelium and contains randomly arranged collagen fibrils , which on transmission electron microscopy ( tem ) , appear to be continuous with the more regularly arranged fibrils of the stroma . fibrils in bowman s layer were only half to two thirds the diameter of those in the stroma , suggesting that bowman s layer fibrils may be a condensation of stromal fibrils @xcite . using tem , hayashi et al found the collagen fibril diameter to be 20 nm @xcite in bowman s layer and 20 - 30 nm in the stroma @xcite ; and komai et al found fibril diameters of 25 nm in bowman s layer and 25 - 35 nm in the stroma @xcite . there have been few measurements of human bowman s layer thickness , most of which have fallen in the @xmath52 m range . in hayashi et al s tem studies , measurements were made on an excised conical cornea and found a central thickness of @xmath53 m . li et al s cmtf studies on 7 healthy subjects found a thickness of @xmath54d @xcite ; king - smith et al s interferometry measurements on 6 healthy eyes found a thickness of @xmath55 @xcite ; and komai et al s tem studies on 8 eye - bank eyes found a thickness of 8 - 12 @xmath41 m @xcite . table ( [ table : bowman_thickness ] ) summarizes results from the above sample of work in this area . [ table : bowman_thickness ] there have been no reported measurements of the refractive index function of bowman s layer in humans . however , anterior stroma is intermediate between bowman s layer and posterior stroma , in terms of several structural features such as axial depth , susceptibility to hydration swelling @xcite , degree of hydration @xcite , collagen fibril diameter @xcite , and regularity of fibril arrangement @xcite . it is therefore reasonable to conjecture that the refractive indicex function of the anterior stroma is intermediate between those of bowman s layer and posterior stroma . this is premised on the notion that the group refractive index of a substance is a function of the refractive indices of the biochemical constituents of that substance . hence the group refractive index can be estimated by a weighted summation rule such as the gladstone - dale relation ; or it can be estimated by interpolation , as we do here . the stroma constitutes approximately 90% of the corneal thickness , and the anterior stroma is the major target for ablation and remodelling in most refractive surgery procedures . the anterior stroma consists of intermediate regularity type i collagen fibrils , 20 - 35 nm in diameter @xcite . on scanning electron microscopy ( sem ) , the collagen fibrils are seen bundled into lamellae which are piled in parallel stacks of about 300 lamellae in the central cornea and about 500 at the limbus @xcite . the anterior stromal lamellae are 0.21.2 @xmath41 m thick and 0.530 @xmath41 m wide @xcite , and are interconnected at points either via interlamellae crossing collagen fibrils or via anastomosing sublamellae @xcite , consistent with maurice and gallagher s earlier findings in the rabbit cornea @xcite . the architecture of the anterior stroma confers shape , curvature , rigidity , and hydration resistance to the cornea @xcite . the anterior corneal stroma has no conventionally defined thickness or demarcation , but the anterior @xmath56 m of the stroma has been shown to be physiologically distinguishable from more posterior stroma @xcite . the refractive index of anterior stroma was observed as @xmath57 by patel et al , using a bench abb refractometer to make measurements on bare stroma of fresh human corneas @xcite . the posterior stroma differs from anterior stroma in a number of ways . ultrastructural studies done in rabbit and humans corneas found the posterior stroma to have a greater degree of regularity of collagen fibril arrangement than the anterior stroma @xcite . unlike anterior lamellae , posterior lamellae may course the entire length of the cornea without branching , and they are typically 1.0 2.5 @xmath41 m thick and 100200 @xmath41 m wide , which is larger in dimension than anterior lamellae @xcite . horizontal branching occurs among both anterior and posterior lamellae , however only anterior lamellae exhibit axial branching @xcite . in addition , the posterior stroma has been found to be more susceptible to hydration and swelling than the anterior stroma @xcite . though the posterior stroma is largely spared in current refractive surgery procedures , it becomes the cornea s primary source of structural support and bulk following laser ablation of the anterior stroma . the posterior stroma can be reasonably designated as the posterior two - thirds to three - quarters of the stroma . reinstein et al used vhfu to measure net stromal thickness across the central 10 mm of the cornea in 110 normal eyes , and they found a vertex thickness of @xmath58 m and a thickness of @xmath59 m at the thinnest point @xcite . erie et al used in - vivo confocal microscopy on 18 eyes of 12 patients presenting for lasik , and they found a net stromal thickness of @xmath60 m pre - operatively @xcite . patel et al used a bench abb refractometer on bare stroma of fresh human cornea , and found a posterior stroma refractive index of @xmath61 . this differed from the refractive index of the anterior stroma which they found to be @xmath57 @xcite . we fit a curve , shown in figure ( [ fig : ri ] ) , to patel s experimentally measured data points @xcite shown in table [ table : ri_human_cornea_radial ] . the fit curve s expression is given by , @xmath62 where @xmath63 is the displacement ( in @xmath41 m ) along the optical axis , @xmath64 is the refractive index at @xmath4 , and we have chosen @xmath65 m as the central corneal epithelial surface , @xmath66 as the initial observation point of the photon in the corneal epithelium , @xmath67 m as the observation point in the anterior stroma , and @xmath68 m as the observation point in the posterior stroma . these choices are consistent with the literature data . [ table : ri_human_cornea_radial ] here we describe the trajectron algorithm for computing the trajectory of a photon in the human cornea , based on geometric optics and the following two assumptions : ( i ) non - zero axial grin , and ( ii ) zero meridional grin . we discretize the optical axis into @xmath69 segments , with finer segments over bowman s layer because it has a faster changing refractive index gradient than both the corneal epithelium and stroma . to compute the photon trajectory over the @xmath70th segment we require : ( i ) the incident refractive index , @xmath71 , ( ii ) the incident location of the ray , @xmath72 , ( iii ) the refractive index difference quotient @xmath73 , and ( iv ) the angle @xmath74 which the incident optical momentum , @xmath75 , makes with the optical axis . in the above notation we have used the domain parametrization , @xmath76 , over each discrete segment @xmath77 , such that @xmath78 denotes the restriction of an arbitrary function @xmath79 over the @xmath70th segment , @xmath80 denotes the value of @xmath79 at the start point of the @xmath70th segment , and @xmath81 denotes the value of @xmath78 at endpoint of the @xmath70th segment . domain segment boundary points are related by , @xmath82 , for every @xmath70 . \(i ) we obtain @xmath71 simply by evaluating the fit curve in equation ( [ ri_fcn ] ) . ( ii ) the incident ray location is given by , @xmath83 where @xmath84 , is the ray location at the end of the previous segment and is available from the previous computation . \(iii ) the difference quotient is readily computed by , @xmath85 \(iv ) we then determine the angle the optical momentum @xmath86 makes with the axial direction by , @xmath87 , \label{theta_eqn}\ ] ] where , @xmath88 @xmath35 is a constant defined in equation ( [ a_const ] ) , and @xmath33 is a function of @xmath4 defined in equation ( [ g_eqn ] ) . it follows that , @xmath89 where @xmath90 is an evaluation of the closed form solution using the @xmath70th segment parameters obtained as described above . the trajectron algorithm is summarized in table ( [ trajectron ] ) . [ trajectron ] we conducted 40 numerical experiments with @xmath91 , each of which demonstrated bending of the photon trajectory within the human cornea . results of the first 20 numerical experiments are displayed in table ( [ table : light bending ] ) . the @xmath92 values ranged from 2.21 to 79.05 degrees and resulted in @xmath93 values which ranged from 2.25 to 90 degrees . a photon with a @xmath92 of @xmath94 degrees will proceed along a straight line trajectory . however , for all other @xmath92 values , some degree of bending occurs . figure ( [ fig : bendometer ] ) plots both the photon trajectory ( solid line ) and the ray initial tangent ( dashed line ) for a photon with a @xmath92 of 78.97 degrees . as the @xmath92 values approach 90 degrees , the bending of the photon trajectory increases , and becomes increasingly and exquisitely dependent on angle . the difference , @xmath95 , between the initial tangent line and the photon trajectory is a measure of the extent of bending . we use @xmath96 to denote the displacement along the r - axis at position @xmath97 m due to light bending . table ( [ table : light bending ] ) shows the @xmath96 values at @xmath98 m , @xmath99 m , @xmath100 m , and @xmath101 m . in the next 20 numerical experiments , we computed photon trajectories with @xmath92 values clustered closer to 90 degrees . specifically , the @xmath92 values ranged from 77.68 to 78.72 degrees and resulted in @xmath93 values ranging from 85 degrees to 89.75 degrees . the photon trajectories were noted to bend away from the optical axis in a concave upwards direction as shown in figure ( [ fig : l_broom_1black ] ) . [ table : light bending ] until recently , schematic eye models assumed a constant or average corneal refractive index @xcite . since emerging evidence of corneal grin nature , a few newer models have respected the grin . but like their older counterparts , these newer models are based on paraxial approximation and ray transfer matrix analysis @xcite . the first - order paraxial approximation of the wave equation in shortwavelength limit , is one whose solutions are rays propagating along straight lines . and this linearity allows an optical system to be modelled using ray - transfer matrix analysis . the fitness of these ray - transfer matrix analyses depend on the magnitude of high frequency coefficients in the fourier transform of the refractive index function . in the case of highly varying refractive index gradient and consequently highly varying ray spatial gradient , linear approximations have limited validity . and a prohibitively large number of optical elements or ray transfer matrices may be required to obtain a good approximation of the ray path . the transition zone between the corneal epithelium and bowman s layer is an example of such a steep gradient , where finer linearization granularity is required . there is not a general notion of when linear approximation approaches may begin to lose validity , as the small angle approximation , sin@xmath102 , has no defined boundary . for this reason the angular domain over which the paraxial approximation is clinically applicable is not clear . yet clinically , refractive error measurements and correction are based on paraxial approximation . results of our numerical experiments shown in figure ( [ fig : l_broom_1black ] ) may help us gain some traction on this issue . we see an increase in non - linearity with @xmath92 . this increase in non - linearity is correlated with a loss of paraxial approximation validity . also from figure ( [ fig : l_broom_1black ] ) , we see that linear - like form is preserved over a much wider angle than only those for which sin@xmath102 . this suggests that the angular domain over which the paraxial approximation is clinically applicable is more broad than suggested by the small angle approximation alone . for instance , for a @xmath92 of 50 degrees , the @xmath103 is @xmath104 m , which is a relatively small displacement . in addition to exhibiting such preservation of linear - like form over broad angle , the paraxial approximation is a potent simplification device in theory and practice . for these reasons , it has enjoyed much success and longevity in the clinic . however , its domain of validity is limited . for instance , for @xmath105 75 degrees , the corresponding @xmath103 exceeds @xmath106 mm and increases rapidly and non - linearly with @xmath107 ; such that by @xmath108 degrees , the @xmath103 has reached 5 mm , which is almost the entire radius of the cornea . this is clearly non - paraxial territory over which the paraxial approximation is invalid . clinically , this zone is at the fringes of peripheral vision . loss of vision here is not likely to interfere significantly with daily life , and may even go unnoticed . however , such subtle peripheral vision loss is often the first sign of an insidious optic neuropathy such as primary open angle glaucoma . in the numerical experiments presented here , the scope of the photon trajectories studied are exclusively intra - corneal , with @xmath109~\mu$]m . based on these purely intra - corneal photon trajectories , we have made inference involving the visual field . this is justified by a reasonable assumption of continuity . we have assumed that there exists a correspondence between the intra - corneal angle , @xmath110 , and the @xmath110 of the originating ray source in the visual field . in other words , relatively wide angles in the field give rise to relatively wide angles within the cornea , and relatively narrow angles in the field give rise to relatively narrow angles within the cornea . however , while we have relied on this angular correspondence to make inference on field source , it is important to note that what we have shown in this paper is that this correspondence is non - linear . and more specifically , we have shown that wide intra - corneal angles give rise to wider intra - corneal angles , while narrow intra - corneal angles remain relatively constant . limitations of the current study include the assumption of gradient zero in the meridional directions . vasudevan et al showed naso - temporal gradients in the human corneal epithelium @xcite . using a portable abb refractometer mounted on a slit - lamp to make measurements on 10 human subjects , they found corneal vertex , nasal , and temporal refractive indices of @xmath111 , @xmath112 , and @xmath112 respectively . these gradients are significantly less than those found by patel @xcite in the axial direction , and hence were assumed to be zero . the naso - temporal gradients were in the direction of the corneal vertex , and their incorporation into the model can be expected to attenuate the concavity of the photon trajectory to some degree . however , the overall non - linearity and angular - dependence behavior shown here will be unchanged . a second limitation of the current work is the non - uniform specimen preparation and measurement method of the axial refractive index . the epithelial refractive index was measured in - vivo using a modified hand - held refractometer , while the stroma was prepared as bare fresh cornea and measured in - vitro using a bench - top abb refractometer @xcite . a third limitation of the current study is the sparsity of refractive index data points currently available to us in the literature . this sparsity is due to the technological difficulty of making fine high precision refractive index measurements in the human cornea . most of this challenging work has been done by patel and by vasudevan . both patel s axial measurements and vasudevan s naso - temporal measurements contained only three data points each , which points towards the challenging nature of the work . unfortunately , mathematical models based on such sparse data may be susceptible to the aliasing problem . for instance , in the current study we only had one data point available for the refractive index gradient in the corneal epithelium . however , the corneal epithelium is @xmath50 m thick on average with 5 - 7 cell layers and contains histophysiological gradients . the cells are older , flatter , and closer to apoptosis anteriorly than posteriorly the epithelium is bathed in the tear film mucinous phase anteriorly and continuous with bowman s layer posteriorly . these histophysiological gradients suggest that the corneal epithelium contains non - zero refractive index gradients . if a gradient does exists , its direction and form beg investigation . more generally , finer sampling granularity of the refractive index is needed in the human cornea in each of the three principal axis directions . in - spite of the above limitations , the current study has provided a clear first demonstration of non - paraxial intra - corneal light - bending , and highlighted potential areas for further experimental and theoretical collaboration in addressing the global disease burden of refractive error . in this paper , we have provided the first quantitative demonstration of non - paraxial light - bending within the human cornea . we have also introduced the trajectron algorithm for computing photon trajectories in the human cornea . and we have initiated steps towards describing the angular domain over which the paraxial approximation is clinically applicable . these demonstrations have significant implications in the development of refractive surgery algorithms . i would like to express gratitude to my wife lisa for her moral support . i would like to thank my friend peter blair for reading this manuscript and providing helpful suggestions on its technical presentation . 10 m. m. abdull , s. sivasubramaniam , g. v. s. murthy , c. gilbert , t. abubakar , c. ezelum , and m. m. rabiu , _ causes of blindness and visual impairment in nigeria : the nigeria national blindness and visual impairment survey _ , investigative ophthalmology & visual science * 50 * ( 2009 ) , no . 9 , 4114 . d. a. atchison and g. smith , _ optics of the human eye _ , butterworth - 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in this article , we follow the trajectory of a photon in the human cornea . prior to experimental evidence of the cornea s gradient refractive index ( grin ) nature , schematic eye models used a constant or average as the corneal refractive index . a few recent models respect the intra - corneal grin , but are based on the paraxial approximation , and thereby have limited validity in peripheral visual field analysis and non - paraxial photon tracking . here , we introduce the trajectron algorithm . it uses a closed form solution of the ray equation of constant axial grin media , and evaluates over piece - wise constant grin . using trajectron , we present the first quantitative demonstration of non - paraxial intra - corneal light - bending phenomena . this demonstration has significant implications in the development of refractive surgery algorithms . ( 1,0)300

LANSING, Mich. (AP) — One socially conservative Michigan lawmaker was expelled from office and another resigned early Friday after they were embroiled in scandal over their extramarital affair and an attempt to hide it with a strange fictional email. State Rep. Ben Glardon, front, puts his head in his hands as State Rep. Todd Courser, behind, speaks before the vote, Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan House was at a standstill... (Associated Press) Rep. Todd Courser, R-Lapeer, listens during House hearings Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan House was at a standstill Thursday over whether to expel Rep. Todd Courser and Rep. Cindy... (Associated Press) Republican state Reps. Cindy Gamrat, left, and Todd Courser listen Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan House was at a standstill Thursday over whether to expel Courser and Gamrat,... (Associated Press) State Rep. Cindy Gamrat watches the votes in the House of Representatives, Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan House was at a standstill Thursday night over whether to expel, Rep.... (Associated Press) State Rep.Cindy Gamrat watches the voting board as house members vote Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan House was at a standstill Thursday night over whether to expel, Rep. Cindy... (Associated Press) House Democratic Leader Rep. Tim Greimel, left, and House Speaker Rep. Kevin Cotter, right, speak, Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan House was at a standstill Thursday night over... (Associated Press) State Rep. Todd Courser watches the vote board as votes roll in Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan House was at a standstill Thursday night over whether to expel, Rep. Cindy Gamrat... (Associated Press) State Rep. Cindy Cindy Gamrat looks at the voting board during House hearings Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan House was at a standstill Thursday over whether to expel Rep. Todd... (Associated Press) Republican state Reps.Todd Courser, foreground, and Cindy Gamrat, background, listen in the House Appropriations committee room at the Capitol, Thursday, Sept. 10, 2015 in Lansing, Mich. The Michigan... (Associated Press) Republican Rep. Cindy Gamrat became just the fourth legislator to be kicked out in state history shortly after 4 a.m. An hour earlier, GOP Rep. Todd Courser resigned, effective immediately, when it became clear majority Republicans had secured votes from enough Democrats for his expulsion in exchange for the House asking the attorney general and state police to investigate the lawmakers. Both were immediately escorted out of the chamber. "I put everybody through a whole bunch — across the state, my own family, the constituents, the people in this room," Courser told reporters. "Whether it was the third vote or the fourth vote or the fifth vote, they were going to eventually get me." Gamrat, who was tossed on a 91-12 vote, declined comment while leaving the Capitol. "I have done everything I can to redeem the situation," she said shortly before in her speech asking for a censure, which would have let her stay on the job with restrictions. "I am sincerely sorry for what it's caused." Courser, 43, of Lapeer in Michigan's Thumb region, admitted sending an "outlandish" phony email to GOP activists and others in May claiming he was caught with a male prostitute. The email was intended to make his affair with the 42-year-old Gamrat appear less believable if it were exposed by an anonymous blackmailer who Courser said was demanding his resignation. The self-smear email called Courser a "bi-sexual porn addicted sex deviant" and "gun toting Bible thumping ... freak" and Gamrat a "tramp." Gamrat, from Plainwell in the southwestern part of the state, said she discussed the plot with Courser but did not know the email's sexually explicit content before it was sent. On Thursday, a special House committee recommended the expulsion of both legislators. But the full chamber then deadlocked for hours, as more than two dozen Democrats refused to vote. They attacked the "sham" investigation as rushed and self-serving. They questioned why two "whistleblower" aides to Courser and Gamrat were allowed to be fired by GOP leadership, since the speaker's office had known of problems in the lawmakers' combined office. The House was six votes short of the two-thirds supermajority needed under the state constitution. More than two dozen minority Democrats initially abstained from voting and criticized the process. In calling for both legislators' expulsion, Rep. Ed McBroom, a Republican from Vulcan in the Upper Peninsula who chaired the disciplinary panel, said: "These two members have obliterated the public trust. They've obliterated the trust of their colleagues. And each day that they continue here they reduce the public trust in this institution." The scandal unfolded last month after a staffer the couple shared was fired in July. Ben Graham gave The Detroit News a secret audio recording of Courser demanding that he send the email to "inoculate the herd," an apparent reference to Courser's supporters. While Graham refused and the email was likely legal, the plot was unethical, according to a House Business Office probe that alleged dishonesty, misconduct and misuse of public resources extending beyond the affair and fictional email. State police are investigating the alleged blackmail and this week obtained a warrant for records from a phone company related to a prepaid, or "burner," phone from which Courser said he received threatening text messages. Republican Speaker Kevin Cotter said it was a "sad day," but it was important to address a "cloud hanging over us for some time." ___ Follow David Eggert on Twitter: https://twitter.com/DavidEggert00 ||||| CLOSE State Rep. Todd Courser, R-Lapeer, resigned from the House if Representatives early Friday morning State Rep. Todd Courser talks with attorney Daniel Randazzo as the House Select Committee breaks to go back to caucus and the house session Capitol Wednesday 9/9/2015. (Photo: Rod Sanford / Lansing State Jour) LANSING — It took 14 hours, two failed votes and a day full of drama, but at 3:12 a.m. Friday, state Rep. Todd Courser resigned from his state House seat, and an hour later, Rep. Cindy Gamrat was expelled on a 91-12 vote, ending a controversial sex and cover-up scandal that has rocked Lansing for the last month. "I felt is was the appropriate thing to do. I put everybody through a whole bunch, my family, constituents and the people in this room," Courser said. "You go 14-15 hours later, they would have been doing a third vote. I felt they were just going to go until they got their answer." His resignation letter was short and simple: "I hereby tender my resignation from the Michigan House of Representatives effective immediately.. It has been an honor serving with the dedicated members and staff of the House of Representatives." Gamrat decided to stick it out and asked her colleagues to censure, rather than expel her. "I firmly believe in restoration and redemption," she said." I have done everything I can to redeem this situation and I'm sincerely sorry for what this has caused. I still believe my actions warrant censure, but not expulsion.". Her colleagues disagreed, voting 91-12 to expel her with five Democrats declining to vote on the matter. It appeared throughout the evening that Courser and Gamrat, two tea party Republicans caught up in a sex and cover-up scandal, might save their jobs, thanks to Democrats. Twenty-six Democrats initially refused to vote on a resolution to expel Courser, leaving the expulsion vote six votes shy of the 73 votes needed to remove the lawmaker from office. After a 67-14 vote, with 26 Democrats refusing to vote and two Democrats absent, Republicans called for a reconsideration of the vote and the board stayed open until it was cleared shortly before midnight, so the House could adjourn for the day and reconvene a minute later. "It's sort of Shakespearean, if you look at it: My fate rests in the hands of the Democrats," Courser said late Thursday. But the lengthy and passionate debate took its toll. Courser said, leading to his decision to resign. "It's an unfortunate chapter where we're at, but it's time to turn a page and go in a different direction and obviously heal, in my own house and in this body as well," he said. "It's been hell." Many Democrats said, while they found the actions of Courser and Gamrat "disgusting and despicable," they wouldn't vote on the measure because of the process that was used to get to an expulsion. They wanted more information on what Speaker of the House Kevin Cotter, R-Mt. Pleasant knew and when he found out about the affair and bizarre cover-up engineered by Courser and Gamrat. They wanted to hear from two staffers -- Ben Graham and Keith Allard -- about the process they went through to reveal the cover-up to Republican leadership. "The issue is much larger than the very narrow scope given to the committee. I really want to know when the staff went to leadership, what they said and when they said it," said state Rep. Sarah Roberts, D-St. Clair Shores. "The gravity of this issue truly deserves to be looked at in a much broader scope and in brighter light. People deserve that due diligence before we make this decision." In the end, an amendment was added onto the Gamrat expulsion resolution, calling for a Michigan State Police investigation into the controversy. Another resolution called on the Attorney General's office to looking into the matter. With those amendments, Democrats switched from voting no or not voting to supporting the expulsion. CLOSE State Rep. Cindy Gamrat, R-Plainwell, was expelled from the House of Representatives early Friday morning "House Democrats have called for weeks for an independent law enforcement investigation of these very serious allegations regarding Reps. Courser and Gamrat," said House Minority Leader Tim Greimel, D-Auburn Hills. John Sellek, a spokesman for Attorney General Bill Schuette, said Friday morning, that an investigation into the Courser Gamrat controversy has already been opened. "The Attorney General has discussed this issue with Col. Kriste Etue of the Michigan State Police," Sellek said in a statement. "We will work with the Michigan State Police and conduct a joint investigation, which will be complete and thorough, without fear or favor.” Republicans said the 833-page report and testimony from both Courser and Gamrat, who both admitted misconduct in office and misuse of taxpayer resources but asked for censure rather than expulsion, clearly laid out plenty of reason to expel the two members. "The oath that we all take is the sole protection against an unjust expulsion," said state Rep. Ed McBroom, R-Vulcan, chairman of the special committee that voted 4-0 earlier Thursday to expel both members. "They have both admitted their guilt. They both agreed to the damage they've done. And neither can offer a reasonable argument that they're being honest now, or the disdain they have shown to this body and its members is the outlier and not the norm." Rep. Gary Glenn, R-Midland, was once tight with Courser and Gamrat, but supported the expulsion as a way to end the controversy that has consumed Lansing and Michigan. "I would say that all the evidence I've seen...the public, both Republicans and Democrats, can safely say is not in doubt; and honestly the public will hold accountable anyone who acts at odds to the actual substantive question before us," he said. "I appeal to the compassion, humanity and decency of my friends on both sides of the aisle: End the damage to the families, to the constituents, to the House of Representatives. We know what's right and what's wrong." State Rep. Cindy Gamrat watches the votes roll in to expel Gamrat and fellow Rep. Todd Courser in the House of Representatives Thursday, Sept. 10, 2015. (Photo: Rod Sanford, Lansing State Journal) The resignation and expulsion capped a day of drama for the two lawmakers and the entire Legislature. Republicans held the board open for more than seven hours, waiting for the Democrats who chose not to vote to change their mind. They invoked "Rule 32," which requires members to stay in their seats indefinitely. They repeatedly ran down the list of Democratic members who weren't voting to ask if they changed their mind. When the first vote failed 67-14, with 26 Democrats not voting and two Democrats absent, they tried again; reconsidering the vote and keeping the board open with the hopes that they could come up with the necessary 73 votes. "No time was wasted, it was never about running the clock out to try and apply pressures. there was so much negotiation during all of that time.," said Cotter. The day of drama began with the committee's 4-0 vote to expel both Courser and Gamrat. The two Democrats on the committee passed on the vote. Gamrat then began talking to the media, saying she was shocked by the expulsion recommendation vote because she thought she had worked out a deal with House leadership for a censure rather than being removed from office. "I had a clear understanding that if I were to plead guilty to everything that there would be a censure. I didn't want to sign the statement, but I was told that it would be ugly if I didn't," she said. But McBroom blasted her for the allegation. "To allege that we twisted arms to get a statement is completely disrespecting the truth and maligning the committee," he said. "Perhaps I did not speak clearly enough: There was no deal with that member." And the mysterious "texter," who sent Courser and his brother messages from a burner cell phone calling on him to resign or risk having the affair become public knowledge, came into play during the day that stretched into night. A magistrate said Thursday he issued a search warrant Wednesday ordering AT&T to turn over all information they have about a prepaid phone that Courser claims was used to blackmail him over his extramarital affair with Gamrat. Magistrate Greg Wise of 71A District Court in Lapeer told the Free Press he issued the search warrant at the request of the Michigan State Police, confirming that a police investigation into Courser's blackmail claims was active as the House deliberated over whether to expel Courser and Gamrat. The scandal swirling around Courser and Gamrat had been rumored for months, but burst onto the public scene last month when audio recordings surfaced and revealed that Courser had asked his staff to send an anonymous, "false flag" e-mail that he had written, saying he was addicted to drugs and pornography, and paid for sex with men outside a Lansing bar. His staff refused to participate in the attempt to make it appear that Courser was the victim of a smear campaign and to downplay the affair he was having with Gamrat. But the e-mail still was widely sent around Lansing. Courser, in the recordings and Facebook posts, has said he was being blackmailed and that the phony e-mails were an attempt to smoke out the person who was trying to get him to resign from office or risk having the evidence of the affair released to the public. He has released text messages he says both he and his brother have received from the supposed blackmailer. Staff Writer Paul Egan contributed to this report. Contact Kathleen Gray: 517-372-8661, [email protected] or on Twitter @michpoligal. Copyright 2015 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed. Read or Share this story: http://on.freep.com/1UIYfAM

– At 3:12am today, Michigan state Rep. Todd Courser resigned from his seat in the legislature, though it appears he had no intention of doing so when he entered the room 14 hours earlier. The move came after two failed votes to expel Courser, 43, as well as a lengthy debate about his affair with Rep. Cindy Gamrat, 42, who was expelled shortly after Courser gave his resignation, reports the Detroit Free Press. The affair came to light after Courser sent an anonymous, phony email to GOP activists in May claiming he was a "bi-sexual porn-addicted sex deviant" who paid for sex with men, per the AP. The email was apparently intended to make Courser's affair with Gamrat seem less egregious or even unbelievable if it became known. Courser says he and his brother had received texts from someone who threatened to expose the affair. Both Courser and Gamrat admitted to misconduct and misuse of taxpayer resources but hoped they would only be censured. A special committee had voted 4-0 to expel the pair, but the first vote in the House failed 67-14 as many Democrats chose not to vote; a second vote also failed. Only when an amendment calling for police and AG investigations into the controversy were added to Gamrat's expulsion resolution did it pass 91-12 around 4am. "I just felt like it was the appropriate moment to do it," Courser says of his resignation. "Whether it was the third vote or the fourth vote or the fifth vote, they were going to eventually get me." A magistrate has issued a search warrant ordering AT&T to give up information about the prepaid phone used in the apparent blackmail scheme.

arsenic exposure with drinking water and the food is very common in west bengal particularly in rural parts of north and south 24 parganas district . around 150 million people are at risk from arsenic contaminated ground water in the combined areas of west bengal and its neighboring country bangladesh . while toxicological mechanisms for pulmonary effects of inorganic arsenic are not known , some reports have demonstrated that arsenic can accumulate in human lung tissue thus enhancing the possibility that the metal can produce respiratory effects . . however , arsenic - induced diffuse parenchymal lung disease ( dpld ) is a very rare presentation of arsenicosis which has been reported here . a 42-year - old nondiabetic nonhypertensive housewife was admitted to the chest department of a tertiary care hospital with gradually progressive exertional dyspnea ( modified medical research council grading 2 ) associated with a dry cough for last 3 years . there was no seasonal or diurnal variation of symptoms , no h / o wheeze , allergic rhinitis , or suggestive features of paroxysmal nocturnal dyspnea and orthopnea . there was no history of any joint pain , dry eye , oral ulceration , or history suggestive of raynaud 's phenomenon . systemic examination revealed bilateral scattered end - inspiratory crepitations not altered by coughing and posture change . routine blood analysis including complete hemogram , glycemic status , renal hepatic , and thyroid profile were all within normal range . blood for hiv i and ii was negative , and there was no evidence of any immunosuppression . work up for connective tissue disorders namely serum anti - nuclear antibody by hep2 cell line , rheumatoid factor , anti - ccp , anti - ds - dna antibody , anti - phospholipid antibody , anticentromere antibody , anti - ro , and anti u1 rnp antibody all were negative and serum angiotensin converting enzyme was normal . her chest x - ray ( posteroanterior ) showed reticular opacities of both lung fields [ figure 1 ] . we did a high - resolution computed tomography scan of thorax which revealed bilateral interstitial septal thickening and ground glass opacities suggestive of dpld [ figures 2 and 3 ] . chest x - ray ( posteroanterior ) showing bilateral reticular opacities high - resolution computed tomography scan of thorax showing bilateral interstitial septal thickening and ground glass opacities suggestive of diffuse parenchymal lung disease high - resolution computed tomography scan of thorax showing bilateral patchy ground glass opacities and reticulonodular patterns her spirometry showed a restrictive pattern ( forced expiratory volume in 1 s / forced vital capacity [ fvc ] : 82.03 , fvc : 58% ) and 6-min walk distance ( 6mwd ) was 250 m with 2% desaturation in resting o2 saturation ( spo2 ) ( pretest value 98% whereas posttest value was 96% ) . the arterial blood gas ( abg ) analysis was normal with ph 7.43 , pco2 39 mmhg , and po2 78 mmhg . at that stage , patient was diagnosed as a case of dpld of unknown cause . as the patient complaining of progressively increasing distress , we went for a close look up for the etiology . we noticed generalized darkening of skin and keratotic lesions over the palms and fissures and cracks over the soles which was present for last 7 years and progressively increasing . on further enquiry , we came to know that many other villagers of her village were also having similar skin lesions . she resides in a village of north-24-parganas and used to drink water from a local tube well where arsenic contamination of drinking water is known . skin of hands showed hyperpigmentation , palmar keratosis [ figure 4 ] and skin over leg showed raindrop pigmentation we asked for consultation from our dermatological department who confirmed it as arsenic - induced skin lesions . both palmar surface showing keratoses in the form of diffuse thickening and nodular pigmented elevations skin over the leg showing raindrop pigmentation bronchoalveolar lavage ( bal ) fluid was taken after wedging the bronchoscope into the subsegmental bronchi both in right and left side and sent for routine examinations along with arsenic level determination . the bal fluid report showed 22% lymphocyte , 76% macrophage , and neutrophils 2% ; gram stain and afb stain negative with mycobacterial culture being negative . however , the arsenic level in the bal fluid was 0.09 g / g in both samples ( normally lung may contain up to 0.01 g / g of arsenic ) . we also sent the local drinking water used by the patient , hair , and nail of the patient for arsenic level determination . the drinking water , hair , and nail contained 0.18 mg / l ( normal = up to 0.05 mg / l),5.34 g / g , 8.93 g / g ( normal up to 0.5 g / g ) of arsenic , respectively . the patient again later presented to us around 7 months later with severe respiratory distress with bilateral pitting pedal edema . the patient had cyanosis , spo2 86% at room air , tachycardia , angorged and pulsatile internal jugular vein . systemic examination showed left parasternal heave and a loud pulmonary component of 2 heart sound ( p2 ) with a closed split . subsequent echocardiography revealed right atrial dilatation and right ventricular hypertrophy , grade 2 tricuspid regurgitation and mean pulmonary artery pressure of 42 mmhg . the patient was put on high flow oxygen , inhaled bronchodilators , and diuretic , by which she improved symptomatically . she is on regular follow - up in our opd and no further exacerbations occurred till now over last 6 months . on follow - up , spirometry , 6 min walk test , and abg did not reveal any significant improvement ; but echocardiography showed favorable response in terms of mean pulmonary artery pressure ( comparison done with reports at initial visit and reports at 14 months later i.e. , around 6 months after starting treatment for pulmonary hypertension ) . l to 1.26 l ; 6mwd almost remaining same with 1% desaturation ; abg showed ph 7.36 , pco2 48 mm hg , po2 80 mmhg . thus , we concluded that it was a case of dpld with cor pulmonale in a case of chronic arsenic exposure . though lung biopsy is imperative to confirm the diagnosis but in our case it was not possible due to the poor functional status of the patient due to pulmonary artery hypertension . dplds represent a large number of conditions that involve the parenchyma of lung the alveoli , alveolar epithelium , capillary endothelium , and spaces between those structures as well as the perivascular and lymphatic tissue . chronic arsenic poisoning or arsenicosis is a major health problem in eastern india and bangladesh . arsenic , a metalloid occurring naturally , is the 20 most abundant element in the earth 's crust , and a component of more than 245 minerals . humans are exposed to this toxic arsenic primarily from air , food , and water . drinking water and natural groundwater may be contaminated with arsenic from arsenical pesticide , natural mineral deposits or improperly disposed arsenical chemicals , industrial effluent , and drainage problems . arsenicosis is a multisystem disorder that may involve the skin , lung , gastrointestinal tract , cardiovascular , nervous , hematological , and endocrine system . symptoms include weakness , paresthesia , cough , burning eye , pain abdomen , etc . hyperkeratosis of palms and soles , rain - drop like spotty pigmentation and depigmentation or diffuse melanosis affecting the whole body are the characteristic features . diffuse thickening of palms and soles with or without nodular elevations are diagnostic of arsenic - induced keratosis . arsenicosis may result in both malignant and nonmalignant lung diseases including obstructive airway disease , bronchiectasis , and bronchitis . in a hospital - based study carried out on 29 cases of chronic arsenic toxicity with nonmalignant lung disease in kolkata , west bengal , obstructive lung disease was most prevalent being diagnosed in 17 ( 58.6% ) cases . however , till now no confirmed case of dpld due to arenic , substantiated by demonstration of significantly high level of arsenic in bal fluid as well as in hair , nail , and drinking water source has been reported in the literatures . henceforth , it should be a learning curve for physicians particularly belonging to the highly endemic belt of arsenic to consider arsenicosis as a potential etiology in cases of dpld with no identifiable cause . careful attention to such cases may enlighten more evidence of association between these two conditions in near future .

a 42-year - old housewife , the resident of rural part of west bengal , presented with gradually progressive exertional dyspnea associated with a dry cough for last 3 years clinical features were suggestive of diffuse parenchymal lung disease ( dpld ) . her chest x - ray posteroanterior view and high resolution computed tomography scan of the thorax showed bilateral patchy ground glass opacities and reticulonodular pattern . search for the etiology revealed classical skin findings of chronic arsenic exposure in the form of generalized darkening and thickening of skin and keratotic lesions over the palms and soles and classical raindrop pigmentation over leg which was present for last 7 years subsequently her bronchoalveolar lavage fluid , hair , nail , and drinking water showed significant amount of arsenic contamination . by exclusion of all known causes of dpld , we concluded that it was a case of dpld due to chronic arsenic exposure . to the best of our knowledge , only few case report of dpld in chronic arsenicosis has been reported till date .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Family and Medical Leave Enhancement Act of 2001''. SEC. 2. ELIGIBLE EMPLOYEE. Section 101(2)(B)(ii) of the Family and Medical Leave Act of 1993 (29 U.S.C. 2611(2)(B)(ii)) is amended by striking ``less than 50'' each place it occurs and inserting ``fewer than 25''. SEC. 3. ADDITIONAL LEAVE FOR PARENTAL INVOLVEMENT. (a) Leave Requirement.--Section 102(a) of the Family and Medical Leave Act of 1993 (29 U.S.C. 2612(a)) is amended by adding at the end the following: ``(3) Entitlement to additional leave for parental involvement.-- ``(A) In general.--Subject to section 103(f), in addition to leave available under paragraph (1), an eligible employee shall be entitled to a total of 4 hours of leave during any 30-day period, and a total of 24 hours of leave during any 12-month period to participate in or attend an activity that-- ``(i) is sponsored by a school or community organization; and ``(ii) relates to a program of the school or organization that is attended by a son or daughter or a grandchild of the employee. ``(B) Definitions.--As used in this paragraph: ``(i) School.--The term `school' means an elementary school or secondary school (as such terms are defined in the Elementary and Secondary Education Act of 1965 (20 U.S.C. 6301 et seq.)), a Head Start program assisted under the Head Start Act (42 U.S.C. 9831 et seq.), and a child care facility licensed under State law. ``(ii) Community organization.--The term `community organization' means a private nonprofit organization that is representative of a community or a significant segment of a community and provides activities for individuals described in subparagraph (A) or (B) of section 101(12), such as a scouting or sports organization.''. (b) Schedule.--Section 102(b)(1) of such Act (29 U.S.C. 2612(b)(1)) is amended by inserting after the second sentence the following: ``Leave under subsection (a)(3)(A) may be taken intermittently or on a reduced leave schedule.''. (c) Substitution of Paid Leave.--Section 102(d)(2)(A) of such Act (29 U.S.C. 2612(d)(2)(A)) is amended-- (1) by striking ``under'' and inserting the following: ``under-- ``(i)''; and (2) inserting before the period at the end the following: ``; or ``(ii) subsection (a)(3)(A) for any part of the 24-hour period of such leave under such subsection''. (d) Notice.--Section 102(e)(1) of such Act (29 U.S.C. 2612(e)(1)) is amended by adding at the end the following: ``In any case in which an employee requests leave under subsection (a)(3)(A), the employee shall provide the employer with not less than 7 days' notice, before the date the leave is to begin, of the employee's intention to take leave under such subsection.''. (e) Certification.--Section 103 of such Act (29 U.S.C. 2613) is amended by adding at the end the following: ``(f) Certification for Parental Involvement Leave.--An employer may require that a request for leave under section 102(a)(3)(A) be supported by a certification issued at such time and in such manner as the Secretary may by regulation prescribe.''. SEC. 4. PARENTAL INVOLVEMENT LEAVE FOR CIVIL SERVANTS. (a) Leave Requirement.--Section 6382(a) of title 5, United States Code, is amended by adding at the end the following: ``(3)(A) Subject to section 6383(f), in addition to leave available under paragraph (1), an employee shall be entitled to a total of 4 hours of leave during any 30-day period, and a total of 24 hours of leave during any 12-month period to participate in or attend an activity that-- ``(i) is sponsored by a school or community organization; and ``(ii) relates to a program of the school or organization that is attended by a son or daughter or a grandchild of the employee. ``(B) For the purpose of this paragraph: ``(i) The term `school' means an elementary school or secondary school (as such terms are defined in the Elementary and Secondary Education Act of 1965 (20 U.S.C. 6301 et seq.)), a Head Start program assisted under the Head Start Act (42 U.S.C. 9831 et seq.), and a child care facility licensed under State law.''. ``(ii) The term `community organization' means a private nonprofit organization that is representative of a community or a significant segment of a community and provides activities for individuals described in subparagraph (A) or (B) of section 6381(6), such as a scouting or sports organization.''. (b) Schedule.--Section 6382(b)(1) of such title is amended by inserting after the second sentence the following: ``Leave under subsection (a)(3)(A) may be taken intermittently or on a reduced leave schedule.''. (c) Substitution of Paid Leave.--Section 6382(d) of such title is amended by inserting before ``, except'' the following: ``, or for leave provided under subsection (a)(3)(A) any of the employee's accrued or accumulated annual leave under subchapter I for any part of the 24-hour period of such leave under such subsection''. (d) Notice.--Section 6382(e)(1) of such title is amended by adding at the end the following: ``In any case in which an employee requests leave under subsection (a)(3)(A), the employee shall provide the employing agency with not less than 7 days' notice, before the date the leave is to begin, of the employee's intention to take leave under such subsection.''. (e) Certification.--Section 6383 of such title is amended by adding at the end the following: ``(f) An employing agency may require that a request for leave under section 6382(a)(3)(A) be supported by a certification issued at such time and in such manner as the Office of Personnel Management may by regulation prescribe.''. SEC. 5. CLARIFICATION OF LEAVE ENTITLEMENT. Section 102(a)(1) of the Family and Medical Leave Act of 1993 (29 U.S.C. 2612(a)(1)) and section 6382(a)(1) of title 5, United States Code, are each amended by adding at the end the following: ``(E) In order to meet routine family medical needs, including transportation of a son or daughter or a grandchild for medical and dental appointments for annual checkups and vaccinations. ``(F) In order to meet the routine medical care needs of elderly individuals who are related to the eligible employee, including visits to nursing homes and group homes.''. SEC. 6. DEFINITION OF GRANDCHILD. (a) Non-Civil-Service Employees.--Section 101 of the Family and Medical Leave Act (29 U.S.C. 2611) is amended by adding at the end the following new paragraph: ``(14) Grandchild.--The term `grandchild' means a son or daughter of an employee's child.''. (b) Civil Service Employees.--Section 6381 of title 5, United States Code, is amended-- (1) in paragraph (5)(B), by striking ``and'' at the end; (2) in paragraph (6)(B), by striking the period at the end and inserting ``; and''; and (3) by adding at the end the following new paragraph: ``(7) the term `grandchild' means a son or daughter of an employee's child.''.

Family and Medical Leave Enhancement Act of 2001 - Amends the Family and Medical Leave Act of 1993 (FMLA) to expand the Act's coverage by reducing from 50 to 25 the threshold minimum number of employees of an employer necessary for the Act to apply.Allows employees covered by FMLA to take up to four hours during any 30-day period, and up to 24 hours during any 12-month period, of parental involvement leave to participate in or attend their children's or grandchildren's educational and extracurricular activities.Amends Federal civil service law to apply the same parental involvement leave allowance to Federal employees.Provides that leave under FMLA may be taken to meet: (1) routine family medical needs, including transportation of children or grandchildren for medical and dental appointments for annual checkups and vaccinations; and (2) the routine medical care needs of elderly relatives of the eligible employee, including visits to nursing homes and group homes.

ORLANDO, Fla. - A 22-year-old Arizona man was arrested early Monday after he falsely told guests at Walt Disney World’s Contemporary Resort that there was an active shooter inside the hotel to get reactions out of them, according to the Orange County Sheriff’s Office. Deputies said it was shortly after midnight when Dillion Burch told the woman at the front desk of the hotel, located at 4600 North World Drive, that he was telling guests that something had been happening on the property because he has a YouTube channel, according to an arrest report. The woman then notified the on-duty manager that Burch had been going up to guests and telling them that the resort was on lockdown because of a shooter, the report said. Other guests told authorities they had been approached by a man who was intoxicated and was saying there was an active shooter or an emergency, and that they needed to evacuate. He later admitted that it was a joke, the witnesses told authorities, and that he was doing an experiment for his YouTube channel. When the manager approached Burch and asked him why, he said he was working on a school project in which he had to record people’s reactions when they find out an emergency is happening, deputies said. According to the report, the manager told Burch he couldn’t do that and that deputies were on their way to talk to him. Burch told the manager he would leave on his own and asked him not to follow him, the report said. He then walked out of the hotel lobby, saw deputy’s lights and began running into the parking lot, authorities said. Security later found Burch hiding in a row of bushes on hotel property and called deputies to make contact with him, according to the report. Deputies arrived and found Burch crawling out from his hiding spot, the report said. Burch was searched and taken into custody by deputies. During the search, authorities located a beer in his red backpack, deputies said. Burch is charged with disturbing the peace at a public lodging and disorderly intoxication. He was evicted from his hotel room and banned from Walt Disney World property, the report said. During his first appearance Tuesday, Burch pleaded no contest to both charges and was sentenced to three days in jail. Copyright 2018 by WKMG ClickOrlando - All rights reserved. ||||| Disney Contemporary Resort. (iStock) Erin Taylor was taking a stroll in the sand along the water at Disney’s Contemporary Resort in Orlando when a young man rushed up to her with terrifying news: The resort was in a state of emergency, he said. She needed to evacuate immediately. There was an active shooter on the property. Taylor worked as a manager at the resort but somehow did not know anything about this. She started to panic. That’s when the young man said he was just joking. He had been going around scaring people just to record their reactions as an experiment for a YouTube video, he said, according to court records. The police would not find his prank very funny. Dillion Burch. (Orange County Jail) Dillion Burch, 22, was arrested by Orange County sheriff’s deputies in the early-morning hours Monday after creating a brief panic at the resort. He pleaded no contest to charges of disturbing the peace and disorderly intoxication Tuesday and was sentenced to three days in jail. According to the arrest affidavit, Burch started telling people standing at the resort bus stop that there was an active shooter inside the hotel. Sometime afterward, he alarmed Taylor on the mini beach and approached two others. One of the people he spooked called 911 to report Burch’s claims of an active shooter, sending an Orange County sheriff’s deputy zooming on his way. Then Burch went back into the lobby to chat up the front desk worker, telling her about his YouTube channel. According to the affidavit, he said, “they are probably looking for me.” “Why?” the front desk worker asked. Burch allegedly then told her about his fake active-shooter prank. Confronted by the hotel manager, Jose Castillo, Burch claimed the YouTube video was for a school project, the affidavit said. He was tasked with recording people’s reactions when they find out there is an emergency occurring. Castillo told him that he was not allowed to do that and that the police were on their way to speak with him. Burch allegedly fled, telling Castillo not to follow him. He could hear the sirens as he left the lobby, so he took off to hide in the bushes, according to the affidavit. Police say he soon crawled out from where he was hiding and announced that he was the one they were looking for. Burch told police he was intoxicated, and police say they found a beer in his backpack. Burch has been banned from Walt Disney World property. More from Morning Mix: He convinced people he was a rich ‘Saudi prince.’ He was really a poor street kid from Bogota. ||||| A 22-year-old Arizona man was arrested Monday after he told guests at a Disney resort there was an active shooter so he could record their reactions and post it to YouTube, according to an arrest affidavit. Dillion Burch was “highly intoxicated” and running up to guests at Disney's Contemporary Resort and telling them they had to evacuate because of the shooter shortly after midnight, the affidavit said. Burch then told the people he was joking and wanted to see what their reactions were for a school project, according to the affidavit. The incident caused a “significant disturbance” and the resort had to go on lock down, the affidavit said. Deputies found Birch hiding in some bushes and arrested him. He was taken to the Orange County Jail on disturbing the peace and disorderly intoxication charges. He has since bonded out of the jail, records show. [email protected], 407-420-5471 or @DavidHarrisOS

– Police in Orlando say an Arizona man caused a panic at a Disney resort by going around telling people about an active shooter—all so he could record their reactions for his YouTube channel. Dillion Burch, 22, allegedly told residents at Disney's Contemporary Resort they had to evacuate in the early morning hours of Monday, reports the Orlando Sentinel. At least one worried person then called police about a shooter on the loose, reports the Washington Post, and the arrest affidavit accuses Burch of causing a "significant disturbance" that resulted in the resort going on lockdown. Burch told a front-desk worker what he was doing; she alerted a manager who confronted Burch. He then claimed to the hotel manager that it was all for a school project, police say. He left the hotel upon hearing that the police were on the way, and officers soon found him hiding in the bushes, reports WKMG. Police found beer in his backpack. Burch pleaded no contest to disturbing the peace and disorderly intoxication and earned a sentence of three days in jail.

nonribosomal peptides ( nrps ) are of great pharmacological importance , but there is currently no technology for high - throughput nrp dereplication and sequencing . we employ multi - stage mass spectrometry followed by spectral alignment algorithms for sequencing of cyclic nrps . we also present an algorithm for comparative nrp dereplication that establishes similarities between newly isolated and previously identified similar but non - identical nrps , substantially reducing dereplication efforts ..

consider the system of differential equations @xmath0\psi_1-\dfrac{{{\mathrm{\,d}}}\psi_2}{{{\mathrm{\,d}}}x}&=0,\\ \dfrac{{{\mathrm{\,d}}}\psi_1}{{{\mathrm{\,d}}}x}+\bigl[v(x)-(\lambda+k)\bigr]\psi_2&=0 , \end{aligned}\ ] ] on @xmath1 , where @xmath2 are parameters and @xmath3 is a potential . equivalently one may define a self - adjoint operator by @xmath4 where @xmath5 and @xmath6 are pauli matrices . then becomes the eigenvalue equation @xmath7 , where @xmath8 . for a given potential @xmath3 let us set @xmath9 and introduce the _ @xmath10-spectrum _ associated with @xmath3 : @xmath11 equivalently @xmath12 is the spectrum of the linear operator pencil @xmath13 . our goal is to understand the properties of @xmath12 , such as symmetries , existence of real and complex ( non - real ) eigenvalues , eigenvalue estimates and asymptotics . similar problems , as well as some other related questions , have been studied in a variety of situations in mathematical literature see , for instance , @xcite , @xcite , @xcite , @xcite , @xcite . whilst the general asymptotic behaviour and estimates in our case are generally in line with earlier results ( see theorems [ thm : lowerasym ] and [ thm : singsigngvalasym ] ; we should note that our methods allow the widest class of potentials ) , some unexpectedly subtle phenomena occur depending on the properties of @xmath3 . in particular , @xmath12 may have a totally different structure for single - sign and variable - sign potentials ( compare theorems [ thm : singsignreal ] and [ thm : oddv0 ] ) , as well as for potentials having gaps ( that is , whose support is not connected ) and for no - gap potentials ( see examples [ ex : ex3 ] and [ ex : ex4 ] ) . also , variable - sign potentials can produce some ( or even all ) non - real eigenvalues , which have not been studied previously ( see theorem [ thm : oddv0 ] and example [ ex : ex2 ] ) . in physical literature this problem appears in the study of electron waveguides in graphene ( see @xcite , @xcite and references therein ) . note that the electron dynamics in graphene is governed by the two - dimensional massless dirac operator , and the one - dimensional system is obtained as a result of the separation of variables : the parameter @xmath14 corresponds to the frequency of the wavefunction @xmath15 in the direction parallel to the waveguide . from the physical viewpoint solutions @xmath16 are of particular interest ; these are called _ confined modes_. among them , especially important in the study of conductivity properties of graphene are _ zero modes _ : @xmath17-solutions corresponding to @xmath9 . ( see section [ sec : nzmodes ] for discussion of modes corresponding to @xmath18 . ) zero - energy states in graphene have also been studied for potentials of other types see , for instance , @xcite , @xcite . it was shown in @xcite that for the potential @xmath19 the solutions of the system can be found explicitly in terms of special functions . moreover , there exists an infinite sequence of coupling constants @xmath10 such that @xmath20 is an eigenvalue of the operator @xmath21 . an attempt to formulate and prove precise mathematical statements confirming and generalising the results of @xcite was the starting point of our research . to state precise results we need to make some basic restrictions on the local regularity and global decay of the potential @xmath3 . we shall assume all potentials are real valued and locally @xmath17 . let @xmath22 denote the class of such potentials which additionally satisfy @xmath23 roughly , @xmath24 if it decays at infinity . in the literature @xmath22 is sometimes denoted as @xmath25 . we can define the constant coefficient operator @xmath26 as a multiplication operator in fourier space . if @xmath24 we show that @xmath3 is a relatively compact perturbation of @xmath26 , allowing us to define @xmath27 as an unbounded self - adjoint operator on @xmath17 ( see section [ subsec : argugen ] for more details ) . the same construction can be used for complex - valued potentials ( although , of course , the resulting operator will no longer be self - adjoint ) ; this allows us to consider @xmath28 for any @xmath29 . further use of the relative compactness of @xmath3 leads to the following : [ thm : disgspec ] if @xmath24 then @xmath12 is a discrete subset of @xmath30 . [ rem : lambdaspec ] _ standard spectrum . _ the ( usual ) spectrum of the self - adjoint operator @xmath26 can be computed easily by considering it as a multiplication operator in fourier space ; we get @xmath31 while this spectrum is purely absolutely continuous . since @xmath24 is a relatively compact perturbation of @xmath26 the operators @xmath27 and @xmath26 must have the same essential spectrum ( see @xcite ) ; thus @xmath32 the operator @xmath27 may have eigenvalues outside @xmath33 but these must be isolated and of finite multiplicity ( using the fact that we re dealing with a @xmath34-dimensional problem it is not hard to show that these eigenvalues must in fact be simple ; a somewhat restricted form of this result is given in lemma [ lem : simeval ] ) . in common with other dirac operators , @xmath27 possesses a number of elementary symmetries which lead to symmetries for the set @xmath12 . in particular , if @xmath24 then @xmath35 , while @xmath12 is unchanged if we replace @xmath14 with @xmath36 in the definition of @xmath26 . with this last symmetry in mind we shall henceforth assume @xmath37 ; this will enable us to simplify the statement of some results . to obtain estimates for the distribution of points in @xmath12 we impose extra global decay conditions on the potential @xmath3 . let @xmath38 denote the class of real valued locally @xmath17 potentials which satisfy @xmath39 that is , we require @xmath3 to be integrable . equivalently we can define @xmath40 . the class @xmath38 is sometimes denoted as @xmath41 . firstly we consider the number of points of @xmath12 lying inside the disc @xmath42 of radius @xmath43 . [ thm : genvl1upbnd ] suppose @xmath44 . then @xmath45 for any @xmath43 , where @xmath46 is a universal constant ( we can take @xmath47 ) . this result can be generalised ( using a rather different approach ) to deal with potentials @xmath24 which have weaker decay than is required to be @xmath48 ; see theorem [ thm : cfnupperbnd ] . lower bounds which complement the upper bounds given by theorem [ thm : genvl1upbnd ] can also be obtained . restricting our attention to real points we have the following : [ thm : lowerasym ] suppose @xmath44 . then @xmath49)\ge\frac{r}{\pi}\left\lvert\int_{{{\mathbb{r}}}}v(x){{\mathrm{\,d}}}x\right\rvert + o(r)\ ] ] as @xmath50 , while the same estimate holds for @xmath51)$ ] ( by symmetry ) . in particular , @xmath52 contains infinitely many points if @xmath53 . in general the set @xmath12 may contain complex eigenvalues ( see section [ sec : egs ] for some examples of explicit potentials which illustrate various possible behaviours for complex points in @xmath12 ) . note that , even though the operator @xmath27 is self - adjoint ( recall that @xmath3 is real valued ) , it does not follow in general that the corresponding operator pencil should have a purely real spectrum . however , if @xmath3 does not change sign ( as in the example considered in @xcite ) all eigenvalues of the operator pencil are real : [ thm : singsignreal ] if @xmath24 is single - signed then @xmath54 . by symmetry we can write @xmath55 where @xmath56 denotes the sequence of positive points in @xmath12 , arranged in order of increasing size . the bound in theorem [ thm : lowerasym ] can be turned into an asymptotics : [ thm : singsigngvalasym ] suppose @xmath44 is single - signed . then @xmath49)=\frac{r}{\pi}\left\lvert\int_{{{\mathbb{r}}}}v(x){{\mathrm{\,d}}}x\right\rvert + o(r ) = \frac{{\|v\|}_{l^1}}{\pi}\,r+o(r)\ ] ] as @xmath50 . if @xmath3 is non - zero we can equivalently write @xmath57 as @xmath58 . for potentials of variable sign the behaviour of the @xmath10-spectrum may be different , in some cases quite drastically so . for anti - symmetric potentials we have the following : [ thm : oddv0 ] if @xmath24 is anti - symmetric then @xmath59 . note that , the @xmath10-spectrum may still contain an infinite number of complex eigenvalues ; see example [ ex : ex2 ] below . the absence of real points in the @xmath10-spectrum together with theorem [ thm : singsigngvalasym ] shows that the lower bound obtained in theorem [ thm : lowerasym ] is quite sharp . [ rem : translatev ] it is easy to see that translating a potential @xmath3 changes the operator @xmath28 to something which is unitarily equivalent . in particular , theorem [ thm : oddv0 ] also applies to potentials @xmath3 satisfying the condition @xmath60 for some @xmath61 and all @xmath62 . the translation invariance of our problem will also be used to simplify the presentation of some arguments in section [ sec : argu ] . let @xmath63 denote the class of compactly supported real valued functions of ( totally ) bounded variation . clearly @xmath64 while @xmath63 contains compactly supported piecewise constant potentials with a finite number of pieces , as well as compactly supported functions in @xmath65 . we say that a potential _ @xmath66 has no gaps _ if @xmath67 where @xmath68 and @xmath69 denote the lebesgue measure and convex hull of a set @xmath70 respectively . [ thm : vnogapaysm ] suppose @xmath66 has no gaps . then @xmath49)=\frac{r}{\pi}\left\lvert\int_{{\mathbb{r}}}v(x){{\mathrm{\,d}}}x\right\rvert+o(1)\ ] ] as @xmath50 . the same estimate holds for @xmath51)$ ] ( by symmetry ) . [ rem : nogapint0 ] when @xmath71 this result simply states that @xmath52 is finite . our results give information about the asymptotics of the counting function @xmath72)$ ] as @xmath50 . for any @xmath44 the results of section [ sec : basic ] give asymptotic upper and lower bounds of @xmath73 respectively . using theorem [ thm : genvl1upbnd ] we can take @xmath74 , in which case the upper bound is actually uniform for @xmath43 . for an asymptotic upper bound the constant can be reduced to at least @xmath75 in general ( see remark [ rem : otherests ] ) . theorem [ thm : singsigngvalasym ] shows the constant can be reduced further to @xmath76 for single - signed potentials ; in this case the asymptotic upper and lower bounds agree and an asymptotic formula for the points in @xmath12 is obtained . for variable - signed potentials the quantities @xmath77 and @xmath78 differ , leading to differences in the upper and lower bounds in even if we could take @xmath76 . for no - gap potentials @xmath66 theorem [ thm : vnogapaysm ] shows that it is the lower bound that actually gives the leading order term in the asymptotics of @xmath72)$ ] as @xmath50 . the above results may lead to a hypothesis that , in fact , the lower bound always gives the leading order term in the asymptotics of the counting function of the @xmath10-spectrum . however , as we show in the next section , this is not the case . moreover , the precise asymptotic behaviour of @xmath72)$ ] as @xmath50 may depend on the properties of a variable signed potential in a rather subtle way . in particular , it is sensitive to the presence of gaps , that is , intervals where @xmath79 , appearing between components of @xmath80 . even more surprisingly , the leading term of the asymptotics is affected by the arithmetic properties of certain quantities determined by the potential , such as the rationality of the ratio @xmath81 . suppose @xmath66 . @xmath3 has one gap _ if we can write @xmath82 for some non - zero @xmath83 which have no gaps and disjoint supports . for @xmath84 the support of @xmath85 is a closed bounded interval ; write @xmath86 $ ] . without loss of generality we may assume the support of @xmath87 lies to the left of that of @xmath88 . then @xmath89 and the gap is the interval @xmath90 . set @xmath91 for @xmath84 . thus @xmath92 while @xmath93 , with equality iff @xmath87 and @xmath88 are each single - signed . [ thm:1gint0 ] if @xmath94 then @xmath52 contains only finitely many points . [ rem : twogapzerointegral ] this result extends remark [ rem : nogapint0 ] to one gap potentials . however the same result does _ not _ extend to zero integral potentials with two gaps ; see example [ ex : ex4 ] . we now suppose @xmath95 . set @xmath96 then @xmath97 gives a measure of the gap length , while @xmath98 if @xmath99 and @xmath100 if @xmath101 . in particular , if @xmath3 is single - signed then @xmath102 . when @xmath103 we can further define @xmath104.\ ] ] if we fix @xmath100 and allow @xmath105 to vary from @xmath106 to @xmath34 it is easy to check that @xmath107 varies continuously and monotonically from @xmath34 to @xmath108 . if @xmath108 is positive and rational write @xmath109 where @xmath110 are coprime . if @xmath111 and @xmath112 are both odd set @xmath113 and @xmath114 ; if @xmath111 and @xmath112 have opposite parity set @xmath115 and @xmath116 . set @xmath117 we are using @xmath118 to denote the largest integer which does not exceed @xmath119 . [ thm:1ggen ] suppose @xmath120 . if @xmath103 and @xmath121 suppose additionally that @xmath122 . then @xmath49)=\frac{1}{\pi}\,a(\alpha,\beta)\,{\lvert{v_1+v_2}\rvert}\,r+o(r)\ ] ] as @xmath50 . the same estimate holds for @xmath51)$ ] ( by symmetry ) . if @xmath103 and @xmath121 then the bounds @xmath123 give @xmath124 therefore , for any sequence of rational numbers @xmath125 converging to @xmath126 , we have @xmath127 , and hence @xmath128 is continuous at irrational values of @xmath108 . at the same time it is clear that @xmath129 has discontinuities at many rational values of @xmath108 . let us note that continuity at irrational values and discontinuity at rational values of a parameter was observed for other physically meaningful quantities see , for instance , @xcite ( where the mathematical setting is somewhat similar to ours ) , as well as @xcite , @xcite . theorem [ thm:1ggen ] comes almost directly from a result about the zeros of a perturbed trigonometric function . consider the equation @xmath130 where @xmath131 satisfies the decay condition @xmath132 [ thm : coszeros ] let @xmath133 , @xmath134 and @xmath120 . if @xmath103 and @xmath121 let us additionally assume that @xmath135 . also suppose that @xmath131 satisfies and the solutions of form a discrete subset of @xmath1 . then @xmath136:\text{$x$ satisfies \eqref{eq : cospert0}}\bigr\}=\frac1\pi\,a(\alpha,\beta)\,r+o(r)\ ] ] as @xmath50 . note that , @xmath137 in condition is only needed in the case that @xmath103 and @xmath138 . consideration of theorem [ thm : coszeros ] in the case @xmath139 goes back at least as far as @xcite where the irrational case was established ( a somewhat different problem was considered in the rational case ) . using theorem [ thm:1ggen ] it is possible to show that we can obtain an asymptotic formula @xmath140)=\frac{c}{\pi}\,r+o(r)\ ] ] as @xmath50 , where @xmath46 can indeed take any value ( strictly ) between @xmath141 and @xmath142 ; we state this as a separate result . [ thm : mrallasym ] let @xmath143 . then there exists a piecewise constant one gap potential @xmath3 such that @xmath144 , @xmath145 and holds with @xmath146 . if we consider the eigenvalues of @xmath28 as functions of @xmath10 we can view @xmath12 as the set of points at which these curves cross @xmath20 . one could equally consider crossings at any other point @xmath147 belonging to @xmath148 ( the spectral gap of the operator @xmath26 ) . this leads to consideration of the set @xmath149 with some straightforward modifications most of our analysis for @xmath12 can be carried over to @xmath150 for any @xmath151 . we now summarise the changes to the main results . theorem [ thm : disgspec ] holds for @xmath150 . for @xmath24 , @xmath150 is still symmetric under conjugation and unchanged if we replace @xmath14 with @xmath36 ; however , we can not expect @xmath150 to be symmetric about @xmath20 in general ( this symmetry generalises to @xmath152 ) . theorem [ thm : oddv0 ] does not generalise . theorems [ thm : genvl1upbnd ] , [ thm : lowerasym ] , [ thm : singsignreal ] and [ thm : singsigngvalasym ] hold for @xmath150 with two adjustments ; firstly , the constant @xmath46 in theorem [ thm : lowerasym ] may depend on @xmath147 , and secondly , the results for points in @xmath153 no longer follow `` by symmetry '' ( but can be obtained by similar arguments ) . the latter comment also applies to theorem [ thm : vnogapaysm ] , which otherwise holds for @xmath150 in the case that @xmath154 . when @xmath94 we need to impose further conditions on @xmath147 ( to ensure we avoid limiting values of the eigenvalues of @xmath28 as @xmath155 ; cf . @xcite , theorem 8.2(i ) ) . theorem [ thm:1gint0 ] does not admit a straightforward generalisation to the case @xmath156 . a generalisation of theorem [ thm:1ggen ] will require theorem [ thm : coszeros ] to be extended to cover equations of the form @xmath157 , where @xmath158 is an additional parameter ( cf . @xcite for the case @xmath159 , @xmath160 ) . section [ sec : egs ] is devoted to examples . the main arguments , together with a number of auxiliary constructions and results , are collected in section [ sec : argu ] . theorem [ thm : disgspec ] is essentially standard ; its proof appears in section [ subsec : argugen ] . some key ideas from the prfer method are introduced in section [ subsec : boundargu ] . in particular , we re - characterise the set @xmath52 in terms of a quantity @xmath161 , which is closely related to the prfer argument ( see proposition [ prop : gspecchard ] ) . the asymptotic behaviour of @xmath161 is described ( proposition [ prop : dgasym ] ) and leads directly to theorem [ thm : lowerasym ] . theorem [ thm : singsigngvalasym ] follows from a related argument , together with the additional monotonicity of @xmath161 for single - signed @xmath3 ( as described in proposition [ prop : positivedinc ] ) . an alternative approach based on the birman - schwinger principle that could be used in the case of single - signed potentials is discussed in remark [ bs ] . a uniform bound on @xmath161 ( given in proposition [ prop : gendeltavest ] ) leads through several intermediate results to the proof of theorem [ thm : genvl1upbnd ] . derivatives of @xmath161 are considered in sections [ subsec : deriv ] and [ subsec : nogaps ] . the justification of the monotonicity result ( proposition [ prop : positivedinc ] ) appears in section [ subsec : deriv ] , while in section [ subsec : nogaps ] the proof of theorem [ thm : vnogapaysm ] is reduced to some technical estimates ( given in proposition [ prop : intcossinest ] ) . theorem [ thm:1gint0 ] is established in section [ sub : onegap ] while theorem [ thm:1ggen ] is reduced to theorem [ thm : coszeros ] ; theorem [ thm : mrallasym ] is then obtained as a straightforward consequence of the former . for the sake of clarity the proofs of the results in section [ sec : argu ] which require more technical arguments are deferred to section [ sec : tech ] . in section [ subsec : asym ] we consider lemma [ lem:+thetalim ] , section [ subsec : deltav ] deals with propositions [ prop : dgasym ] and [ prop : gendeltavest ] , and in section [ subsec : estphijpsij ] we establish proposition [ prop : intcossinest ] . the last part of the paper is devoted to the proof of theorem [ thm : coszeros ] , which is a variation on a classical theme of independent interest ( cf . @xcite , @xcite , @xcite ) . some preliminary lemmas are established in section [ sec : zprelim ] , section [ sec : zf ] contains the proof of theorem [ thm : coszeros ] in the unperturbed case @xmath139 , while the general case is completed in section [ sec : zpert ] . the authors are grateful to r. frank , s. jitomirskaya , a. laptev , m. portnoi , a. pushnitski , z. rudnick , m. solomyak and t. weidl for useful discussions . the research of i.p . is partially supported by nserc , fqrnt and canada research chairs program . the main purpose of this section is to illustrate the results stated above . we restrict our attention mostly to piecewise constant potentials with compact support ; these allow the easiest analysis and already demonstrate the full range of effects . consider points @xmath162 which partition the real line into @xmath163 finite intervals @xmath164 , @xmath165 , and two semi - infinite intervals @xmath166 and @xmath167 . consider a potential @xmath168 ; \{v_1,\dots , v_m\}\bigr):= \begin{cases } v_j&\text{if $ x\in i_j$ , $ j=1,\dots , m$},\\ 0&\text{if $ x\in i_-\cup i_+$ } , \end{cases}\ ] ] with some given real constants @xmath169 . on each interval , we need to solve the equations @xmath170 with @xmath171 , and then match the solutions to ensure continuity at the points @xmath172 . the following result is straightforward . [ lem : constv ] for a given constant potential @xmath173 such that @xmath174 , the system has the general solution @xmath175 if @xmath176 this solution can be equivalently written as @xmath177 in both cases @xmath178 , @xmath179 are arbitrary complex constants . [ rem : endofinterval ] lemma [ lem : constv ] , or more precisely equation , immediately implies that for any compactly - supported ( not necessarily piecewise - constant ) potential @xmath180 , any eigenfunction @xmath181 satisfies , under the assumption @xmath37 , @xmath182 in order to match the @xmath17 solutions at @xmath183 . let us return to the case of a piecewise constant potential . the solution on each interval @xmath184 , @xmath185 , can be written down using lemma [ lem : constv ] with @xmath186 and @xmath187 , @xmath188 . by remark [ rem : endofinterval ] , we have @xmath189 , and @xmath190 . together with continuity conditions at each @xmath172 , @xmath191 this leads to the homogeneous linear system of @xmath192 equations with respect to @xmath192 unknowns @xmath193 , @xmath188 , @xmath165 . denote the determinant of the corresponding matrix of coefficients by @xmath194 . as we are looking for a non - trivial @xmath17-solution @xmath15 , we have @xmath195 if and only if @xmath196 thus , in each particular case our problem is reduced to constructing @xmath194 and finding its real or complex roots . we visualise the real roots of @xmath194 by simply plotting its graph for real arguments . in the complex case we use the phase plot method ( see @xcite ) in which the value of @xmath197 is plotted using colours from a periodic scale . the roots of @xmath194 are singularities of @xmath198 and appear on the phase plot as points at which all of the colours converge . the colour scale which we use in all such plots is shown in figure [ fig : colorbar ] . .[fig : colorbar ] ] in the following examples it is convenient to set @xmath199 also , we remark that our determinants @xmath194 are defined modulo a real or complex scaling constant , which we choose for convenience of presentation . [ ex : ex1 ] set @xmath200 ; \{1\})$ ] . then @xmath201 as the potential is single - signed , the spectrum @xmath12 is real , as illustrated in figures [ fig : examp1_plot ] and [ fig : examp1_phase ] . against real @xmath10 for the potential @xmath202 ; \{1\})$].[fig : examp1_plot ] ] for complex @xmath10.[fig : examp1_phase ] ] for large ( positive ) values of @xmath10 , the solutions of with @xmath203 are approximately those of @xmath204 , i.e. , @xmath205 matching theorem [ thm : singsigngvalasym ] . [ ex : ex2 ] consider a class of anti - symmetric potentials @xmath206 ; \{-1 , 0,1\})$ ] parametrised by the gap length @xmath207 . then , up to a multiplication by a non - zero constant , @xmath208 for any @xmath209 , the potential @xmath210 is anti - symmetric ; hence the spectrum @xmath211 is purely non - real and @xmath212 does not have any real roots . this is illustrated in figure [ fig : examp2_plot ] for @xmath213 and @xmath214 . against real @xmath10 for the potentials @xmath206 ; \{-1 , 0,1\})$ ] with @xmath213 ( solid black line ) and @xmath214 ( dashed blue line).[fig : examp2_plot ] ] it turns out that the behaviour of complex eigenvalues for the potentials @xmath210 differs substantially for zero and non - zero gaps @xmath209 . by a rather intricate asymptotic analysis of the corresponding transcendental equations ( which in a sense extends theorem [ thm : coszeros ] to complex roots ) we can show that the large eigenvalues with positive real parts are asymptotically located on the curves @xmath215 and on the straight lines @xmath216 figures [ fig : examp2_phase0 ] and [ fig : examp2_phase1 ] illustrate this behaviour of complex eigenvalues . for comparison , we also plot the corresponding curves and ; one can see that the asymptotics is accurate even for the low eigenvalues . for complex @xmath10 . the solid black curves illustrate the asymptotic behaviour of the imaginary parts of the eigenvalues.[fig : examp2_phase0 ] ] for complex @xmath10 . the solid black lines , @xmath214 , illustrate the asymptotic behaviour of the imaginary parts of the eigenvalues.[fig : examp2_phase1 ] ] [ ex : ex3 ] consider the one - gap potentials @xmath217 ; \{-1,0,1\})$ ] parametrised by the gap length @xmath207 and the maximum of the support @xmath218 . for these potentials , @xmath219 and @xmath220 . assume additionally @xmath221 . explicit calculation gives , modulo multiplication by a constant , @xmath222.\end{aligned}\ ] ] the graphs of @xmath223 for real @xmath10 and @xmath213 or @xmath214 are shown in figure [ fig : examp3_plots ] . against real @xmath10 for the potentials @xmath224 ; \{-1,0,1\})$ ] with @xmath213 ( solid black line ) and @xmath214 ( dashed blue line).[fig : examp3_plots ] ] we can expect asymptotics of the form @xmath225)=c_{g , b}\frac{r}{\pi}+o(r),\ ] ] as @xmath50 . for the no - gap potential @xmath226 , theorem [ thm : vnogapaysm ] gives such an asymptotics with @xmath227 . on the hand , @xmath228 has three times as many real roots as @xmath229 ( for sufficiently large @xmath10 ) . this leads to a constant @xmath230 in the asymptotics for the one - gap potential @xmath231 as seen in figure [ fig : examp3_plots ] ; c.f . the discussion in sections [ sec : gaps ] and [ sec : discussion ] . this is just a partial case of a more complicated phenomenon , see theorem [ thm:1ggen ] . set @xmath232 after cancelling some non - zero factors equation with @xmath233 takes the asymptotic form @xmath234 as @xmath235 ( where the first and second derivatives of the @xmath236-term are also @xmath237 ) . introducing the new variable @xmath238 leads to an equation in the form of . the asymptotics for the number of real zeros of can then be obtained from theorem [ thm : coszeros ] . alternatively , we can use theorem [ thm:1ggen ] directly ; both approaches give @xmath239 where @xmath129 is defined in . [ ex : ex4 ] the gap dependence illustrated in the previous example can be made even more dramatic if we consider some special potentials . introduce the symmetric twin gap potentials @xmath240 ; \{-1,0,1,0,-1\}\bigr)\ ] ] parametrised by the gap length @xmath209 . note that @xmath241 and @xmath242 for any @xmath243 . figure [ fig : examp4_plots ] shows the real curves @xmath244 for @xmath245 and @xmath214 . one can see that there are only two real eigenvalues for the former , and an infinite number of real eigenvalues for the latter . against real @xmath10 for the potentials @xmath246 ; \{-1,0,1,0,-1\})$ ] with @xmath245 ( solid black line ) and @xmath214 ( dashed blue line).[fig : examp4_plots ] ] to explain this phenomenon , we once more consider equation , now with @xmath247 . although the explicit expression for the determinant @xmath248 is rather cumbersome , some simplifications lead to the asymptotic form @xmath249 as @xmath250 ( where the derivative of the @xmath236-term is also @xmath237 ) . the asymptotics of the number of zeros of reduces to consideration of a pair of elementary equations for cosine . it is then immediate that the asymptotics of @xmath251)$ ] as @xmath50 changes abruptly between @xmath252 and @xmath253 , depending on whether @xmath254 or @xmath255 , respectively . this shows , as already announced in remark [ rem : twogapzerointegral ] , that unlike no - gap and one - gap potentials , two - gap potentials with zero integral may produce an infinite number of real eigenvalues . [ ex : exportnoi ] using a complicated explicit solution involving special functions , hartmann , robinson and portnoi found that , for the potential @xmath256 and any @xmath37 , the positive part of the spectrum @xmath257 coincides with the set @xmath258 . we treat this potential using the prfer method and plot , for real @xmath10 , the quantity @xmath259 ; by proposition [ prop : gspecchard ] , @xmath260 if and only if @xmath261 ( see section [ subsec : boundargu ] for the definition of @xmath262 and further details ) . the curves in figure [ fig : ex5 ] ( drawn for @xmath263 and @xmath264 ) illustrate the result of @xcite . for @xmath263 ( solid black line ) and @xmath264 ( dashed blue line).[fig : ex5 ] ] in this section we give the arguments for the main theorems based on a series of more technical results ; the proofs for the latter will be deferred to section [ sec : tech ] . the unperturbed operator @xmath26 is an unbounded self - adjoint operator on @xmath17 whose domain is @xmath265 , the sobolev space of ( @xmath266 valued ) functions on @xmath1 ; that is @xmath267 in fact it is straightforward to check that @xmath268 , so @xmath269 is equivalent to @xmath270 . it follows that @xmath26 defines an isomorphism @xmath271 . next we consider multiplication by an element of @xmath22 . firstly note that a norm can be defined on @xmath22 using the expression @xmath272 this norm makes @xmath22 a banach space in which @xmath273 is a dense subset . [ lem : vcptop ] multiplication by a fixed @xmath24 defines a compact map @xmath271 . initially suppose @xmath274 . choose a bounded interval @xmath275 with @xmath276 . we can view multiplication by @xmath3 as a composition @xmath277 where we firstly restrict to @xmath275 , then multiply by @xmath3 and finally extend by @xmath20 . this gives a map @xmath278 , where the last two steps are continuous and the first step is compact ( by the rellich - kondrachov theorem ; see @xcite , for example ) . since @xmath273 is dense in @xmath22 and the set of compact maps is closed , it now suffices to show that multiplication defines a continuous bilinear map @xmath279 . to this end firstly note that the sobolev embedding theorem ( _ ibid . _ ) gives @xmath280 for some constant @xmath46 ( which is independent of @xmath119 ) . thus @xmath281 on the other hand @xmath282 with a similar expression holding for @xmath283 . combining the above then gives @xmath284 for any @xmath24 and @xmath285 . since @xmath286 , lemma [ lem : vcptop ] is equivalent to the statement that ( multiplication by ) @xmath24 is a relatively compact perturbation of @xmath26 . it follows that the sum @xmath287 defines a self - adjoint operator with @xmath288 ( see @xcite ) . although we re interested in real valued potentials it is helpful to consider some basic results for more general complex valued potentials as well . let @xmath289 denote the complex valued version of @xmath22 ( in other words , @xmath290 consists of functions of the form @xmath291 where @xmath292 ) . note that @xmath293 for any @xmath24 and @xmath29 . now lemma [ lem : vcptop ] clearly extends to @xmath290 , so ( multiplication by ) some @xmath294 is still a relatively compact perturbation of @xmath26 . thus the sum @xmath295 defines a closed operator with @xmath296 . although the operator @xmath297 will not be self - adjoint ( unless @xmath298 ) , the essential spectrum is still given by , while any spectrum of @xmath297 in @xmath299 consists of isolated eigenvalues of finite ( algebraic ) multiplicity . we have @xmath300 iff @xmath301 for some non - trivial @xmath285 . in turn this is equivalent to @xmath302 where @xmath303 and @xmath304 ; in other words , @xmath305 should be an eigenvalue of the operator @xmath306 . however @xmath306 is a compact operator by lemma [ lem : vcptop ] , so must have discrete spectrum away from @xmath20 . the result follows . it is helpful to have a more symmetric version of the idea just used in the proof of theorem [ thm : disgspec ] . fix @xmath24 and let @xmath307 be the operator on @xmath17 given as multiplication by @xmath308 ( where , for definiteness , we can set @xmath309 whenever @xmath310 ) . then @xmath311 while @xmath312 define an operator @xmath313 by @xmath314 using similar ideas to those in the proofs of theorem [ thm : disgspec ] and lemma [ lem : vcptop ] we get the following : [ lem : symmspecequiv ] the operator @xmath313 is a compact self - adjoint operator on @xmath17 . furthermore , we have @xmath300 iff @xmath315 . if @xmath3 is single - signed we can choose @xmath316 ( @xmath317 if @xmath318 or @xmath319 if @xmath320 ) . then @xmath300 iff @xmath305 is in the spectrum of the compact self - adjoint operator @xmath321 . this gives a justification of theorem [ thm : singsignreal ] , although a more elementary argument is also possible ( see section [ subsec : symmargu ] ) . [ bs ] lemma [ lem : symmspecequiv ] can be viewed as a birman - schwinger principle for the dirac operator @xmath27 . this wide ranging principle has been used to obtain a number of results related to those presented here , both in the single - sign case where the associated birman - schwinger operator @xmath313 is self - adjoint ( see @xcite ) , and in the variable sign case where we need to consider the non - self - adjoint operator @xmath322 ( see @xcite ) . approaches based on the birman - schwinger principle rely on obtaining spectral information about the operator @xmath313 or @xmath322 . potential sources of information include eigenvalue or singular value estimates ( such as @xcite ) , or pseudo - differential techniques leading to eigenvalue asymptotics ( such as @xcite ) . in section [ subsec : boundargu ] we take a different approach , based on prfer techniques ; this is convenient in our one - dimensional setting , and allows for slightly less restrictive assumptions on the potential ( see remark [ rem : cwandp=1 ] in particular ) . for any @xmath24 note that @xmath323 is a single - signed potential which is also in @xmath22 . using the association with compact operators given by lemma [ lem : symmspecequiv ] we are able to link points in @xmath12 and @xmath324 with the eigenvalues and singular values of a single operator , and thus estimate the former using the latter ( via weyl s inequality ) . let @xmath325 be the positive points in @xmath324 , ordered by size . also let @xmath326 denote the points in @xmath327 ordered so as to have non - decreasing modulus ( and counted according to algebraic multiplicity ) . [ lem : weylineq ] for any @xmath328 we have @xmath329 by symmetry we know that the points in @xmath12 are just @xmath330 , @xmath331 , while the points in @xmath324 are just @xmath332 , @xmath331 . lemma [ lem : symmspecequiv ] now implies @xmath333 , @xmath331 are the non - zero eigenvalues of @xmath322 , while @xmath334 , @xmath331 are the non - zero eigenvalues of @xmath335 ( note that , we can take @xmath336 ) . however @xmath337 so the singular values of @xmath322 are just the eigenvalues of @xmath338 ; that is , @xmath339 , @xmath331 , where each eigenvalue has multiplicity @xmath340 . given @xmath328 we can now use weyl s inequality ( see @xcite ) to compare the largest @xmath341 eigenvalues and singular values of the compact operator @xmath322 ; this gives @xmath342 the result follows . our unperturbed operator is @xmath343 since @xmath3 is real valued we immediately get @xmath344 it follows that @xmath300 iff @xmath345 . on the other hand , the commutator properties of the pauli matrices ( namely @xmath346 if @xmath347 ) give us @xmath348 from the first identity we get @xmath300 iff @xmath349 , while the second shows that @xmath12 is invariant if we replace @xmath14 with @xmath36 in the definition of @xmath26 . the symmetry corresponding to @xmath350 can be used to help study even potentials ( compare with our consideration of anti - symmetric potentials below ) . suppose @xmath351 for some @xmath29 and @xmath285 . then @xmath352 while @xmath353 . if @xmath354 we must therefore have @xmath355 . since @xmath3 is single - signed it follows that @xmath356 , leading to @xmath357 and thus @xmath358 ( recall that @xmath359 is an isomorphism ) . we consider two symmetries of the operator @xmath28 ; define an anti - linear operator @xmath46 and a unitary operator @xmath360 on @xmath17 by @xmath361 these operators map @xmath265 ( isometrically ) onto @xmath265 , and satisfy @xmath362 and @xmath363 . furthermore , can be rewritten as @xmath364 , while @xmath365 and @xmath366 ( as @xmath3 is anti - symmetric ) which leads to @xmath367 . now suppose @xmath368 and choose @xmath369 which satisfies @xmath370 . then @xmath371 however @xmath20 is a simple eigenvalue of the operator @xmath28 by lemma [ lem : simeval ] , so we must have @xmath372 and @xmath373 for some @xmath374 . then @xmath375 so @xmath376 and @xmath377 ( recall that @xmath378 ) . these equations clearly have no solution , so we must have @xmath59 . suppose @xmath379 . we can view our basic equation @xmath370 as the @xmath380 system of first order ordinary differential equations on @xmath1 given by @xmath381 the basic theory for such equations is well established ( see @xcite ; here , and in subsequent references to @xcite , some straightforward modifications of the results are needed in order to cover @xmath382 coefficients ) . in particular , if @xmath383 and @xmath384 , then there exists a unique absolutely continuous solution to on @xmath1 with @xmath385 for @xmath84 . furthermore , for given @xmath62 , this solution depends continuously on @xmath386 , @xmath147 and @xmath3 ( the latter as a function in @xmath387 where @xmath275 is the interval between @xmath388 and @xmath119 ) . a consequence of the uniqueness of solutions is that for any non - trivial solution @xmath15 of we have @xmath389 for all @xmath62 . now suppose @xmath390 . it follows that all coefficients in are real , so we may restrict our attention to solutions which are also real valued . since any non - trivial solution @xmath15 is absolutely continuous and satisfies @xmath389 for all @xmath62 we can define an absolutely continuous function @xmath391 by @xmath392 ( here @xmath393 denotes the unit circle in @xmath30 ) . by lifting to @xmath1 ( the universal cover of @xmath393 ) we can define a further absolutely continuous function @xmath394 so that @xmath395 this function is the prfer argument associated to @xmath15 and is unique up to the addition of a constant in @xmath396 . we note that prfer coordinates are a standard tool for problems of this kind ( see , for example , @xcite ) . a straightforward calculation gives @xmath397 using it follows that @xmath398 however @xmath399 so @xmath400 satisfies the first order non - linear equation @xmath401 conversely , when @xmath379 the differential equation has a unique absolutely continuous solution valid on @xmath1 for a given value of @xmath402 , @xmath383 ( see @xcite ) . if we have one solution @xmath400 of then @xmath403 provides a further solution for any @xmath404 ( note that , for @xmath400 given by the solution @xmath405 corresponds to taking @xmath406 as a solution of ) . now suppose @xmath44 and @xmath15 is a non - trivial solution of . let @xmath400 be given by . the fact that @xmath407 means that , to leading order as @xmath408 , @xmath15 behaves like a solution to with @xmath79 . the corresponding asymptotic behaviour of @xmath400 can be summarised as follows ( see section [ subsec : asym ] for more details ) : [ lem:+thetalim ] the quantity @xmath409 has well defined limits as @xmath408 which satisfy @xmath410 furthermore , upon restriction we have @xmath411 iff @xmath412 for any @xmath390 we can uniquely specify two solutions @xmath413 and @xmath414 to by imposing the boundary conditions @xmath415 lemma [ lem:+thetalim ] shows that @xmath416 correspond to solutions of which are in @xmath17 on @xmath417 . we get an @xmath17 solution on the whole of @xmath1 precisely when these solutions ` match ' at one ( or , equivalently , any ) point of @xmath1 . choosing @xmath20 as the point at which we check , the matching condition is simply that @xmath418 and @xmath419 must differ by a multiple of @xmath420 . define a function @xmath421 by setting @xmath422 we can thus characterise points in @xmath52 as follows : [ prop : gspecchard ] we have @xmath368 iff @xmath423 . we have @xmath424 ( note that @xmath425 are constant functions ) while @xmath426 depends continuously on @xmath10 ( this essentially follows from standard results for the continuous dependence on parameters of solutions of ordinary differential equations ; see @xcite ) . for large @xmath10 we have the following asymptotic behaviour ( the proof is given in section [ subsec : deltav ] ) : [ prop : dgasym ] if @xmath44 then @xmath427 as @xmath428 . together propositions [ prop : gspecchard ] and [ prop : dgasym ] allow us to establish theorem [ thm : lowerasym ] . let @xmath429 denote the closed interval with endpoints @xmath424 and @xmath430 . by the intermediate value theorem @xmath426 takes each value in @xmath431 at least once for some @xmath432 $ ] . from proposition [ prop : gspecchard ] we then get @xmath433 ) & = \#\bigl\{\gamma\in[0,r]:\delta_v(\gamma)\in({{\mathbb{z}}}+1/2)\pi\bigr\ } \nonumber\\ \label{eq : estcross } & \ge\#(i_r\cap({{\mathbb{z}}}+1/2)\pi\bigr ) \ge\frac{{\lvert{i_r}\rvert}}{\pi}-\frac12,\end{aligned}\ ] ] where @xmath434 is the length of @xmath431 . on the other hand , proposition [ prop : dgasym ] gives @xmath435 as @xmath50 . [ schmidt ] for compactly supported potentials , theorem [ thm : lowerasym ] admits a simpler proof , similarly to ( * ? ? ? * theorem 3 ) . the details of this argument have been written down by michael morin ( supported by the nserc undegraduate summer research award , 2011 ) . if @xmath44 is single - signed then @xmath161 is monotonic ( the proof is given in section [ subsec : deriv ] ) : [ prop : positivedinc ] suppose @xmath44 is single - signed and non - trivial . then @xmath161 is strictly increasing if @xmath318 and strictly decreasing if @xmath320 . using this monotonicity we can sharpen the argument given for theorem [ thm : lowerasym ] to establish theorem [ thm : singsigngvalasym ] . if @xmath44 is single - signed it follows from proposition [ prop : positivedinc ] that there is at most one @xmath10 with @xmath436 for any given @xmath404 . thus in the proof of theorem [ thm : lowerasym ] can be modified to give @xmath433 ) & = \#\bigl\{\gamma\in[0,r]:\delta_v(\gamma)\in({{\mathbb{z}}}+1/2)\pi\bigr\}\\ & = \#(i_r\cap({{\mathbb{z}}}+1/2)\pi\bigr ) \le\frac{{\lvert{i_r}\rvert}}{\pi}+\frac12.\end{aligned}\ ] ] the required upper asymptotic bound on @xmath72)$ ] can then be obtained using . to give uniform estimates for @xmath426 we firstly introduce an auxiliary function . for any @xmath437 let @xmath438 denote the largest integer not exceeding @xmath439 ; that is , @xmath440 now define a function @xmath441 by @xmath442 in particular , @xmath443 is strictly increasing , @xmath444 for @xmath445 , @xmath446 for all @xmath437 , and @xmath447 for all @xmath448 ( note that @xmath449 ) . as a general bound on @xmath426 we have the following ( the proof is given in section [ subsec : deltav ] ) : [ prop : gendeltavest ] if @xmath44 and @xmath390 then @xmath450 . this result leads to uniform lower bounds for points in @xmath12 , and in turn helps to justify theorem [ thm : genvl1upbnd ] . we firstly deal with the case when @xmath3 is single - signed ( proposition [ prop : ssvevalupbnd ] ) , and then consider arbitrary potentials ( proposition [ prop : genvevalupbnd ] ) by using lemma [ lem : weylineq ] to reduce this to the single - sign case . [ prop : ssvevalupbnd ] suppose @xmath44 is single - signed and non - trivial . let @xmath56 denote the sequence of positive points in @xmath12 , arranged in order of increasing size . then @xmath451 note that the constant in the bound is only half the asymptotic value ( see theorem [ thm : singsigngvalasym ] ) . suppose @xmath318 ( the case @xmath320 can be treated similarly ) . by propositions [ prop : gspecchard ] and [ prop : positivedinc ] we have @xmath452 for @xmath331 . now if @xmath453 then @xmath454 so @xmath455 by proposition [ prop : gendeltavest ] . however @xmath443 is strictly increasing so we must have @xmath456 . taking @xmath457 now gives the result . [ prop : genvevalupbnd ] suppose @xmath44 is non - trivial and let @xmath326 denote the points in @xmath458 ordered so as to have non - decreasing modulus ( and counted according to algebraic multiplicity ) . then @xmath459 let @xmath325 denote the positive points in @xmath324 , arranged in order of increasing size . noting that @xmath460 is single - signed and non - trivial , proposition [ prop : ssvevalupbnd ] gives @xmath461 for @xmath331 , where @xmath462 . using lemma [ lem : weylineq ] and the ordering on the @xmath463 s we now get @xmath464 for any @xmath328 . if @xmath465 then @xmath466 and there is nothing to prove . now suppose @xmath3 is non - trivial . let @xmath43 , set @xmath467 and suppose @xmath468 . using the symmetry @xmath469 we know that @xmath470 for some @xmath471 . with @xmath326 defined as in proposition [ prop : genvevalupbnd ] it follows that @xmath472 . we then obtain @xmath473 using this result . [ rem : otherests ] various other estimates can obtained from straightforward modifications to the proof of theorem [ thm : genvl1upbnd ] presented above . for example , if @xmath44 is single - signed we can use proposition [ prop : ssvevalupbnd ] in place of proposition [ prop : genvevalupbnd ] to obtain the uniform upper bound @xmath49)\le\frac{2}{\pi}\,{\|v\|}_{l^1}r\ ] ] for any @xmath43 . alternatively , for any @xmath44 we can estimate @xmath474 in the proof of proposition [ prop : genvevalupbnd ] using theorem [ thm : singsigngvalasym ] instead of proposition [ prop : ssvevalupbnd ] ; this leads to the asymptotic bound @xmath475 as @xmath50 . as a direct application of the main result in @xcite we can extend the general upper bound given by theorem [ thm : genvl1upbnd ] to potentials in @xmath476 for @xmath477 . [ thm : cfnupperbnd ] suppose @xmath478 for some @xmath477 . then @xmath479 for any @xmath480 , where @xmath481 is a constant depending only on @xmath111 . [ rem : cwandp=1 ] the main result in @xcite is based on singular value estimates from @xcite . we ca nt extend the argument to cover @xmath482 as it corresponds to an excluded boundary case in @xcite . to study the derivatives of @xmath426 we need to obtain more information about the @xmath10 dependence of solutions to . firstly consider any closed bounded interval @xmath483\subset{{\mathbb{r}}}$ ] and potential @xmath379 on @xmath275 . for each @xmath390 suppose we have a solution @xmath484 of where @xmath485 depends twice differentiably on @xmath10 . standard results for ordinary differential equations ( see @xcite ) then imply @xmath486 is twice differentiable in @xmath10 for each @xmath487 ( in fact @xmath484 will depend analytically on @xmath10 provided @xmath485 does ) , so we can set @xmath488 from we immediately get @xmath489 then @xmath490 , where @xmath491 is any function satisfying @xmath492 . thus @xmath493}}\omega_\gamma(b)-\int_x^b{{\mathrm{e}}}^{2k\psi_{[x , t]}}v(t){{\mathrm{\,d}}}t,\end{aligned}\ ] ] where , for any interval @xmath494 , @xmath495 we need to consider with @xmath496 and @xmath497 when we take @xmath498 . let @xmath499 denote the corresponding derivative in this case . since @xmath500 is constant ( recall ) we would expect @xmath501 . furthermore @xmath502 as @xmath503 , so @xmath504}}\to0 $ ] as @xmath503 . the precise properties that we require are given in the next result ; these can be justified by straightforward if somewhat lengthy arguments . [ prop : dthetadgamma+lim ] the solution @xmath413 to depends on @xmath10 differentiably , while the derivative satisfies @xmath505}}v(x){{\mathrm{\,d}}}x\ ] ] for all @xmath61 . there is a corresponding result for @xmath414 . proposition [ prop : positivedinc ] is now an easy corollary of these results . from we get @xmath506 now suppose @xmath318 ( the case @xmath320 can be handled similarly ) . by proposition [ prop : dthetadgamma+lim ] we have @xmath507}}v(x){{\mathrm{\,d}}}x.\ ] ] since @xmath508 for any ( bounded ) interval @xmath509 the right hand side is non - negative and equal to @xmath20 only if @xmath465 on @xmath510 ( as an @xmath48 function ) . a similar argument shows that @xmath511 is also non - negative and equal to @xmath20 only if @xmath465 on @xmath512 . the result follows . for a potential @xmath379 and interval @xmath513 let @xmath514 denote the total variation of @xmath3 on @xmath275 . we also say that _ @xmath3 has no gaps on @xmath275 _ if @xmath515 to work with no - gap potentials we need estimates for the integrals of @xmath516 and @xmath517 ; to complement @xmath518 ( see ) set @xmath519 for any interval @xmath509 . for large @xmath10 equation suggests @xmath486 should be changing rapidly wherever @xmath520 ; it follows that @xmath516 and @xmath517 should be rapidly oscillating , leading to cancellation in the integrals defining @xmath521 and @xmath518 . this idea lies at the heart of the following result ( the proof is given in section [ subsec : estphijpsij ] ) : [ prop : intcossinest ] let @xmath522 be a closed bounded interval , and suppose a potential @xmath3 satisfies @xmath523 and has no gaps on @xmath275 . also suppose @xmath484 satisfies on @xmath275 . for any sub - interval @xmath494 we have @xmath524 as @xmath525 , uniformly in @xmath526 and possible choices of ( the initial condition for ) the solution @xmath484 . these estimates for @xmath521 and @xmath518 lead directly to the following asymptotic information about the change in the value of @xmath484 across @xmath275 : [ prop : nogapsdeltavi ] let @xmath275 , @xmath3 and @xmath484 be as in proposition [ prop : intcossinest ] . write @xmath483 $ ] . also suppose @xmath527 exists and is bounded in @xmath10 for @xmath528 . then , for @xmath529 , @xmath530 as @xmath525 ; in particular , @xmath531 also exists and is bounded in @xmath10 for @xmath528 . integrating gives @xmath532 so for @xmath533 follows directly from proposition [ prop : intcossinest ] . from we get @xmath534}}\bigr)\omega_\gamma(b)-\int_x^b\bigl(1-{{\mathrm{e}}}^{2k\psi_{[x , t]}}\bigr)v(t){{\mathrm{\,d}}}t\ ] ] for all @xmath487 . by proposition [ prop : intcossinest ] we have @xmath535 and hence @xmath536 as @xmath525 , uniformly for all sub - intervals @xmath494 . setting @xmath537 it follows that @xmath538 is bounded in @xmath10 while @xmath539 as @xmath525 , both uniformly for @xmath487 . with @xmath496 this becomes for @xmath540 . more generally we have that @xmath541 is uniformly bounded for all @xmath10 and @xmath487 , while @xmath542 uniformly for @xmath487 . arguing as for we get @xmath543}}\cos(2\theta_\gamma(x))\,\omega_\gamma^2(x){{\mathrm{\,d}}}x.\ ] ] thus @xmath544}}\bigr)\cos(2\theta_\gamma(x))\,\omega_\gamma^2(x){{\mathrm{\,d}}}x\\ & \qquad\qquad{}+4k\int_a^b\cos(2\theta_\gamma(x))\,\bigl(w^2(x)-\omega_\gamma^2(x)\bigr){{\mathrm{\,d}}}x \;-\;4k\int_a^b\cos(2\theta_\gamma(x))\,w^2(x){{\mathrm{\,d}}}x.\end{aligned}\ ] ] as above @xmath535 and hence @xmath536 as @xmath525 , uniformly for all sub - intervals @xmath494 . combined with and the fact that @xmath545 and @xmath546 are uniformly bounded it follows that the first three terms on the right hand side are @xmath547 as @xmath525 . the following claim deals with the final term and completes the argument . _ claim : we have @xmath548 as @xmath525 . _ firstly note that @xmath549}=\cos(2\theta_\gamma(x ) ) \quad\text{and}\quad \nabla w^2(x)=2w(x)v(x).\ ] ] integrating by parts thus gives @xmath550}w(x)v(x){{\mathrm{\,d}}}x\ ] ] since @xmath551}=0 $ ] . by proposition [ prop : intcossinest ] we have @xmath552 as @xmath525 , uniformly for all sub - intervals @xmath494 . furthermore @xmath538 is uniformly bounded for @xmath10 and @xmath487 while @xmath553)$ ] . it follows that @xmath554}w(x)v(x){{\mathrm{\,d}}}x = o(1)$ ] as @xmath525 , completing the claim . suppose a potential @xmath379 has support contained in the bounded interval @xmath483 $ ] . clearly constant functions taking values in @xmath555 solve outside @xmath275 . the condition ( together with the uniqueness and continuity of @xmath416 ) then gives us @xmath556 for @xmath557 and @xmath558 for @xmath559 ( this can also be seen from the form of the corresponding solutions to ) . when defining @xmath161 in this case it is convenient to choose the left endpoint of @xmath275 as the point at which to check whether @xmath414 and @xmath413 can be ` matched ' ; alternatively , we can keep our current definition of @xmath161 if we simply translate our problem so that @xmath560 ( see remark [ rem : translatev ] ) . making such a choice we get @xmath561 where @xmath562 is constant ( as a function of @xmath10 ) . we will work with @xmath161 in this form for the remainder of the present section . for compactly supported potentials without gaps we can now rephrase the conclusions of proposition [ prop : nogapsdeltavi ] to get the following improved and extended version of proposition [ prop : dgasym ] : [ cor : derivdgasym ] suppose @xmath66 has no gaps . then , for @xmath529 , @xmath563 as @xmath525 . when @xmath53 it follows that @xmath161 is monotonic for sufficiently large @xmath10 . in this case theorem [ thm : vnogapaysm ] can be proved using an argument very similar to that used for theorem [ thm : singsigngvalasym ] . the case @xmath71 can be treated with a separate observation . if @xmath71 corollary [ cor : derivdgasym ] ( for @xmath533 ) enables us to find @xmath564 so that @xmath565 when @xmath566 . then @xmath567 $ ] by proposition [ prop : gspecchard ] . however @xmath12 is a discrete subset of @xmath30 ( theorem [ thm : disgspec ] ) so @xmath568 $ ] contains at most finitely many points . now suppose @xmath53 . by corollary [ cor : derivdgasym ] ( for @xmath540 ) there exists @xmath564 such that @xmath426 is strictly monotonic for all @xmath569 . suppose @xmath570 and let @xmath571 denote the closed interval with endpoints @xmath572 and @xmath430 . arguing as for theorem [ thm : singsigngvalasym ] we then get @xmath573)=\#(i_{s , r}\cap({{\mathbb{z}}}+1/2)\pi\bigr ) = \frac{{\lvert{i_{s , r}}\rvert}}{\pi}+o(1).\end{aligned}\ ] ] however corollary [ cor : derivdgasym ] ( for @xmath533 ) also gives @xmath574 as @xmath50 ( note that , @xmath360 is fixed ) . the fact that @xmath575 $ ] contains at most finitely many points ( see above ) completes the argument . let @xmath66 be a one - gap potential as considered in section [ sec : onegap ] . we can use proposition [ prop : nogapsdeltavi ] to estimate the change in @xmath413 across the intervals @xmath576 $ ] for @xmath84 . information about the change in @xmath413 across the gap @xmath90 will be obtained from the next result . [ lem : gaptheta ] suppose @xmath577 on some interval @xmath578 and set @xmath579 . then @xmath580 let @xmath581 , the zero set of @xmath582 . values in @xmath583 give constant solutions to @xmath577 . for such solutions @xmath584 and @xmath585 , so both sides of are zero . now suppose @xmath586 for some @xmath587 . using the uniqueness and continuity of solutions to the equation @xmath577 it follows that @xmath409 must remain within the same connected component of @xmath588 for all @xmath487 . in particular @xmath589 . now set @xmath590 then @xmath591 so @xmath592 hence @xmath593 . the second expression for @xmath594 then leads to @xmath595 the first part of the expression on the left hand side is just @xmath596 . as in the discussion proceeding corollary [ cor : derivdgasym ] we observe that @xmath556 for @xmath597 and @xmath558 for @xmath598 ( note that @xmath3 has support contained in @xmath599 $ ] ) . we shall also define @xmath161 by choosing @xmath600 as the point at which to check whether @xmath414 and @xmath413 can be ` matched ' . it follows that @xmath601 now set @xmath602 for @xmath84 . then @xmath603 since @xmath465 on @xmath90 lemma [ lem : gaptheta ] then gives @xmath604\sin(\delta_v)\nonumber\\ \label{eq : genrelgapd1d2v } & \qquad{}=\bigl[\sin(\delta_1+\delta_2)+\alpha\sin(\delta_1-\delta_2)\bigr]\cos(\delta_v).\end{aligned}\ ] ] [ lem : altspecchar1gap ] we have @xmath368 iff @xmath605 if @xmath368 we get @xmath606 and @xmath607 from proposition [ prop : gspecchard ] , so follows from . now suppose holds . then gives either @xmath606 , in which case @xmath368 by proposition [ prop : gspecchard ] , or @xmath608 however and imply @xmath609 contradicting the fact that @xmath610 . before giving the proofs of the first two results in section [ sec : onegap ] we note that if @xmath209 satisfies and @xmath611 then it is straightforward to check that @xmath612 also satisfies . by proposition [ prop : nogapsdeltavi ] applied to @xmath85 on the interval @xmath576 $ ] , @xmath84 , we have @xmath613 for some functions @xmath614 and @xmath615 which satisfy . using the observation proceeding the proof we can then write @xmath616 for some @xmath617 which also satisfies . by lemma [ lem : altspecchar1gap ] we thus have @xmath368 iff @xmath618 since @xmath12 is discrete ( theorem [ thm : disgspec ] ) the solutions of ( in @xmath10 ) form a discrete subset of @xmath1 . if @xmath619 then reduces to @xmath620 . however @xmath621 and @xmath622 as @xmath525 , so we can we can choose @xmath360 such that @xmath623 for all @xmath569 . then @xmath624 $ ] ( recall that @xmath12 is symmetric about @xmath20 ) . the discreteness of @xmath12 then limits @xmath52 to at most finitely many points , establishing theorem [ thm:1gint0 ] . now suppose @xmath625 . writing @xmath626 , then gives @xmath49)=\#\bigl\{x\in[0,{\lvert{v_1+v_2}\rvert}r]:\cos(x)+\alpha\cos(\beta x)+\phi(x)=0\bigr\},\ ] ] where @xmath627 which clearly satisfies . theorem [ thm:1ggen ] now follows directly from theorem [ thm : coszeros ] . since @xmath628 we can choose @xmath629 so that @xmath630 and @xmath631 is irrational . set @xmath632 , @xmath633 , @xmath634 and @xmath635 then @xmath636 ; thus we can choose @xmath637 so that @xmath638 . now set @xmath639 and consider the potentials @xmath640;\{v_1\ } ) \quad\text{and}\quad v_2(x)=w\bigl(x;[g , g+1,g+2];\{v_2+v_0,-v_0\}\bigr)\ ] ] ( see for notation ) . then @xmath641 is a one gap potential , with gap from @xmath20 to @xmath209 . since @xmath103 and @xmath108 is irrational theorem [ thm:1ggen ] shows that holds with @xmath642 . furthermore @xmath643 while @xmath644 . we return to viewing our basic equation @xmath370 as the system of ordinary differential equations . when @xmath79 we have the exponential solutions @xmath645 ( see lemma [ lem : constv ] ) . when @xmath24 ( or , more generally , @xmath3 belongs to the locally @xmath48 version of @xmath22 ) we can find solutions of with similar asymptotic properties as @xmath408 ( see ( * ? ? ? * chapter x ) ) . in particular , there are non - trivial solutions @xmath646 and @xmath647 which satisfy @xmath648 since @xmath649 @xmath650 and @xmath651 have different asymptotic behaviour as @xmath652 ( the growth of @xmath653 as @xmath652 is roughly like @xmath654 ) ; it follows that these solutions must be linearly independent . a similar discussion applies to @xmath655 and @xmath656 . [ lem : simeval ] if @xmath24 then either @xmath657 or @xmath20 is a simple eigenvalue of @xmath27 . we have @xmath658 iff @xmath20 is an isolated eigenvalue of @xmath27 ( see remark [ rem : lambdaspec ] ) . now suppose @xmath15 is an eigenfunction corresponding to @xmath20 . then @xmath15 satisfies ( with @xmath659 ) . since @xmath660 and @xmath661 are linearly independent solutions of this equation we must have @xmath662 for some constants @xmath663 . restricting to the interval @xmath510 we have @xmath664 while @xmath665 . it follows that @xmath666 , and so @xmath15 is a multiple of @xmath661 . this must also be true for any other eigenfunction corresponding to @xmath20 , so any two such eigenfunctions are linearly dependent . using a similar argument we can also get @xmath667 for some constant @xmath668 , showing that @xmath661 and @xmath655 are linearly dependent . in fact this is an alternative characterisation of when @xmath20 is an eigenvalue of @xmath27 . when @xmath44 solutions to have well defined leading order asymptotics as @xmath408 ; these asymptotics are solutions to the same equation with @xmath79 , so must be linear combinations of the exponential functions given in ( see ( * ? ? ? * chapter x ) ) . in particular , we can choose @xmath646 and @xmath647 so that [ eq : inftyasylim ] @xmath669 while @xmath670 furthermore @xmath661 and @xmath655 are uniquely determined by these asymptotic conditions . ( the solutions @xmath660 and @xmath656 are however only determined up to the addition of a multiple of @xmath661 and @xmath655 respectively . ) we consider the case @xmath652 ; @xmath671 can be handled similarly . since @xmath660 and @xmath661 are linearly independent we can write @xmath662 for some constants @xmath663 ( which ca nt both be @xmath20 ) . now by @xmath672 however @xmath673 so ( for @xmath652 ) follows . on the other hand , @xmath674 iff @xmath666 , leading to the second part of the result . propositions [ prop : gendeltavest ] and [ prop : dgasym ] both follow almost directly from the following estimate : [ lem : tailest ] let @xmath44 and suppose @xmath400 solves with @xmath675 . for any @xmath62 we then have @xmath676 a similar result holds on @xmath677 $ ] when @xmath678 . the basic idea is that if @xmath409 increases on an interval @xmath679 $ ] crossing a range of values where @xmath680 is non - positive then we must have @xmath681 we can then add the contributions from each such crossing . let @xmath404 and suppose @xmath682 $ ] for all @xmath119 in some interval @xmath679\subset{{\mathbb{r}}}$ ] . then @xmath683 so @xmath684 , and hence @xmath685 this estimate continues to hold with the obvious interpretation when @xmath686 . now let @xmath62 and suppose @xmath687 . choose @xmath688 so that @xmath689 $ ] . using the continuity of @xmath400 , and the assumption that @xmath675 , we can now choose a sequence of points @xmath690 such that * for @xmath691 and @xmath692 $ ] we have @xmath693 $ ] . * for @xmath691 we have @xmath694 and @xmath695 , with the exception that @xmath696 if @xmath697 $ ] . applying we then get @xmath698 if @xmath699 $ ] then each term in the sum on the left of is @xmath700 so @xmath701 it follows that @xmath702 on the other hand @xmath703 so @xmath704 alternatively suppose @xmath697 $ ] so @xmath696 . then the term in the sum on the left of is @xmath700 for @xmath705 , so @xmath706 leading to @xmath707 furthermore @xmath708 using again gives @xmath709 a similar argument can be used to deal with the case @xmath710 ( we need to consider intervals where @xmath409 decreases across the range @xmath711 $ ] ) . by lemma [ lem : tailest ] we get @xmath712 the equivalent estimate on @xmath713 $ ] gives @xmath714 the result now follows from and the fact that @xmath447 for any @xmath448 . recalling we can write @xmath715 where @xmath716 . now suppose @xmath717 . since @xmath413 satisfies we get @xmath718 so @xmath719 on the other hand lemma [ lem : tailest ] gives us @xmath720 therefore @xmath721 now choose @xmath722 for each @xmath10 so that @xmath723 and @xmath724 as @xmath428 ( we can take @xmath725 with @xmath726 , for example ) . then @xmath727 ( since @xmath728 ) so @xmath729 as @xmath428 . a similar estimate can be obtained for @xmath730 . it is easiest to deal with the potential @xmath3 in pieces where it is single - signed and bounded away from @xmath20 ; the next result is the key to identifying these pieces and sets up some of our notation . [ lem : intervals ] suppose @xmath66 has no gaps and set @xmath731 . for each @xmath732 there exists a finite collection of disjoint closed intervals @xmath733 , @xmath734 , such that * for each @xmath734 @xmath3 has constant sign on @xmath735 and @xmath736 for all @xmath737 . * setting @xmath738 we have @xmath739 as @xmath740 . * @xmath741 , where @xmath742 is the total variation of @xmath3 . we would ideally like @xmath743 to be @xmath744 , so the union of the @xmath735 s would be @xmath745 there are however several technical issues associated with this choice ; * we are not assuming that @xmath3 is continuous so may not be closed ( or even particularly well behaved ) . * even if @xmath3 is continuous the number of intervals in @xmath744 may be uncontrollable ( even infinite ) ; we need a useful bound on this quantity . the technicalities in the following argument arise from the need to deal with these issues . set @xmath746 ( so @xmath747 is the ` @xmath748-neighbourhood ' of @xmath749 , while @xmath750 is the ` @xmath748-neighbourhood ' of @xmath751 ) . since @xmath747 is an open subset of @xmath1 it consists of a countable union of disjoint open intervals ; let @xmath752 be the union of those intervals which intersect @xmath753 . if @xmath754 is a maximal interval in @xmath755 it follows that we can find @xmath756 with @xmath757 . furthermore @xmath526 must also be a maximal interval in @xmath747 so , if @xmath526 is bounded , its endpoints satisfy @xmath758 . thus @xmath759 and so @xmath760 . if @xmath526 is a half - infinite interval a similar argument shows that @xmath761 . now let @xmath762 and @xmath763 denote the number of semi - infinite and bounded maximal intervals in @xmath755 ( we re presently allowing @xmath764 ; if @xmath765 set @xmath766 , @xmath767 ) . then @xmath768 in particular , @xmath763 must be finite . however @xmath3 has compact support , so @xmath755 must be unbounded both above and below . since @xmath755 consists of a finite collection of intervals , it must therefore contain semi - infinite intervals at either end ; that is , @xmath766 . the set @xmath769 is then the union of @xmath770 closed bounded intervals ; write @xmath771 where @xmath772 is some indexing set with @xmath773 . it is straightforward to check that we have @xmath774 for any @xmath775 . we can similarly define @xmath776 , @xmath777 , @xmath735 for @xmath778 and @xmath779 . set @xmath780 . property ( i ) is immediate , while ( iii ) holds since @xmath781 now @xmath782 . if @xmath783 a straightforward check gives us @xmath784 so @xmath785 and hence @xmath786 . since @xmath787 for all @xmath732 and @xmath788 , property ( ii ) will now follow if we can show @xmath789 ( see @xcite , for example ) . for each @xmath790 let @xmath791 suppose @xmath792 are distinct points in @xmath793 and let @xmath794 . from the definition of @xmath793 we can find @xmath795 with @xmath796 and @xmath797 for @xmath798 . it follows that @xmath799 taking @xmath800 gives @xmath801 . hence @xmath793 is finite ( with @xmath802 ) . clearly we also have @xmath803 if @xmath804 . similar properties hold for @xmath805 . it follows that the set @xmath806 is countable ( it is contained in a countable union of finite sets ) . however @xmath807 so @xmath808 the no gap condition on @xmath3 and the countability of @xmath809 now imply @xmath789 . to justify proposition [ prop : intcossinest ] we start by considering the cancellations over each period of @xmath810 or @xmath811 ( lemma [ lem : piint ] ) and deal with any incomplete periods ( lemma [ lem : endint ] ) . in both cases we work on an interval @xmath812 $ ] where @xmath813 , so @xmath400 is invertible . making the substitution @xmath814 we get @xmath815{{\mathrm{\,d}}}x,\ ] ] so @xmath816}{{\mathrm{\,d}}}u\ ] ] for any @xmath817 ( we will take either @xmath818 or @xmath819 ) . [ lem : piint ] suppose @xmath400 satisfies on an interval @xmath812 $ ] where @xmath774 with @xmath820 . if @xmath821 then @xmath822 note that we get a better estimate for the @xmath811 integral ; the extra term in the estimate for the @xmath810 integral is needed to cope with the fact that this integral is non - zero even when @xmath3 is constant . since @xmath821 we can define @xmath823 to be the unique bijection with @xmath824 for all @xmath825 ; @xmath826 is piecewise affine with at most one jump ( @xmath826 will have no jumps iff @xmath827 ) . using we can then write @xmath828}{{\mathrm{\,d}}}u = \psi_++\psi_-\ ] ] where @xmath829}{{\mathrm{\,d}}}u\ ] ] with @xmath830 , and @xmath831}{{\mathrm{\,d}}}u = -\int_0^{\pi}\frac{\sin(u)}{2[\gamma v(\xi_-(u))-k\cos(u)]}{{\mathrm{\,d}}}u\ ] ] with @xmath832 ; @xmath833 and @xmath834 are bounded piecewise continuous functions @xmath835\to{{\mathbb{r}}}$ ] with ranges contained in @xmath812 $ ] ( in fact the range of @xmath836 is just the set of @xmath756 where @xmath837 ) . we now seek bounds on @xmath838 using ( constant ) bounds on @xmath3 . set @xmath839 and @xmath840 so @xmath841 and @xmath842 for all @xmath756 . thus @xmath843,\ ] ] so @xmath844}{{\mathrm{\,d}}}u \le\pm\psi_\pm\le\int_0^\pi\frac{\sin(u)}{2[\gamma m\pm k\cos(u)]}{{\mathrm{\,d}}}u.\ ] ] the integrals appearing in these bounds can be calculated explicitly , leading to @xmath845 hence @xmath846\nonumber\\ & = \frac{1}{2k}\log\left(1 + 2k\frac{\gamma(m - m)}{(\gamma m - k)(\gamma m+k)}\right)\nonumber\\ \label{eq : branchptest } & \le\frac{\gamma(m - m)}{(\gamma m - k)(\gamma m+k)}\end{aligned}\ ] ] ( note that , @xmath847 for any @xmath848 ) . since @xmath849 and @xmath850 the required estimate for @xmath518 now follows . in a similar manner we can write @xmath851 where @xmath852}{{\mathrm{\,d}}}u\ ] ] for some bounded piecewise continuous functions @xmath853\to{{\mathbb{r}}}$ ] whose ranges are contained in @xmath812 $ ] ( the range of @xmath854 is just the set of @xmath756 where @xmath855 ) . for @xmath856 $ ] we have @xmath857 and @xmath858 so @xmath859}{{\mathrm{\,d}}}u \le\pm\phi_\pm \le\int_{-\pi/2}^{\pi/2}\frac{\cos(u)}{2[\gamma m - k\cos(u)]}{{\mathrm{\,d}}}u.\ ] ] now , for any @xmath860 , @xmath861 ( recall that @xmath862 while @xmath863 ) ; hence @xmath864 putting these estimates together gives @xmath865}{{\mathrm{\,d}}}u-\int_{-\pi/2}^{\pi/2}\frac{\cos(u)}{2[\gamma m+k\cos(u)]}{{\mathrm{\,d}}}u\nonumber\\ & \le\frac{k}{(\gamma m - k)(\gamma m+k)}\int_{-\pi/2}^{\pi/2}\cos^2(u){{\mathrm{\,d}}}u + \frac{\gamma(m - m)}{2(\gamma m - k)(\gamma m+k)}\int_{-\pi/2}^{\pi/2}\cos(u){{\mathrm{\,d}}}u\nonumber\\ \label{eq : cos1stest } & = \frac{k\pi}{2(\gamma m - k)(\gamma m+k)}+\frac{\gamma(m - m)}{(\gamma m - k)(\gamma m+k)}.\end{aligned}\ ] ] the second term can be estimated as for . on the other hand , implies @xmath866 on @xmath526 , so @xmath867 the required estimate for the first term in follows . [ lem : endint ] suppose @xmath400 satisfies on an interval @xmath812 $ ] where @xmath774 with @xmath820 . if @xmath868 then @xmath869 for any @xmath870 $ ] we have @xmath871 ( note that @xmath872 ) . for either @xmath818 or @xmath819 now leads to the estimate @xmath873 where the middle step follows since @xmath874 . the previous lemmas can be combined in a straightforward way to deal with more general intervals : [ lem : oscillsinint ] suppose @xmath400 satisfies on an interval @xmath875 $ ] where @xmath774 with @xmath820 . then @xmath876 a similar result holds in the case that @xmath877 for all @xmath756 . since @xmath400 is absolutely continuous ( as is any solution of when @xmath379 ) and @xmath878 we can choose @xmath879 and points @xmath880 such that @xmath881 for @xmath882 and @xmath883 . set @xmath884 $ ] for @xmath882 and @xmath885 $ ] so @xmath886 have disjoint interiors while @xmath887 . now @xmath888 using lemmas [ lem : piint ] and [ lem : endint ] . the @xmath518 estimate now follows from the fact that @xmath889 . a similar argument leads to the @xmath521 estimate . we can now combine the previous result with lemma [ lem : intervals ] to deal with arbitrary sub - intervals of @xmath731 : [ prop : unifbndiest ] suppose @xmath66 has no gaps let @xmath732 and consider the notation of lemma [ lem : intervals ] . if @xmath400 satisfies on @xmath275 and @xmath820 then for any sub - interval @xmath494 we have @xmath890 set @xmath891 for @xmath734 , and @xmath892 . in particular @xmath893 by lemma [ lem : intervals](iii ) , while @xmath894 so @xmath895 now @xmath896 using the modulus of the final term is clearly bounded by @xmath897 . on the other hand , by lemma [ lem : intervals](i ) @xmath3 has constant sign on @xmath898 and satisfies @xmath736 for all @xmath899 . lemma [ lem : oscillsinint ] thus gives @xmath900 however the @xmath901 for @xmath902 are disjoint subintervals of @xmath494 , so @xmath903 together with we then get @xmath904 the estimate for @xmath518 follows . since @xmath905 a similar argument leads to the estimate for @xmath521 . choose @xmath906 for each @xmath907 so that @xmath908 and @xmath909 as @xmath525 ( we can take @xmath910 with @xmath911 , for example ) . letting @xmath525 it follows that @xmath912 and @xmath913 ( from lemma [ lem : intervals](ii ) ) ; both limits are independent of @xmath526 . on the other hand , @xmath914 ( since @xmath494 ) so we also have @xmath915 at a rate that can be bounded uniformly in @xmath526 . the result now follows directly from the estimates in proposition [ prop : unifbndiest ] . this section is devoted to the proof of theorem [ thm : coszeros ] . for notational convenience define a function @xmath916 by @xmath917 for any function @xmath918 we also set @xmath919 ; thus becomes @xmath920 . the case @xmath921 is straightforward ; an elementary argument shows that @xmath922 is a `` small '' perturbation of @xmath923 leading to a one - to - one association between points in the corresponding zero sets ( lemma [ lem : zintab<1 ] ) . the case @xmath103 is dealt with in two main steps ; firstly the result is obtained directly when @xmath139 ( section [ sec : zf ] ) and secondly we show that the addition of @xmath131 can not change the leading order asymptotic of the number of zeros ( section [ sec : zpert ] ) . in both steps the arguments for @xmath121 and @xmath138 are unified only in the initial stages . when @xmath121 @xmath924 is periodic and an exact count of the number of zeros can be made . in order to deal with the perturbation @xmath131 we simply need to avoid cases where @xmath924 has tangential zeros ; this leads to the extra condition @xmath122 in this case ( see lemma [ lem : tangzsbrat ] ) . since we are then only dealing with the perturbation of transversal zeros we do not require @xmath137 in condition ; we will establish the result using the weaker decay condition @xmath925 when @xmath138 @xmath924 is no longer periodic but we can appeal to ergodicity to determine the asymptotic distribution of zeros . however dealing with the perturbation @xmath131 is more subtle in this case as we must consider points where @xmath924 comes arbitrarily close to having a tangential zero . the number of such points is limited ( corollary [ cor : diststp ] ) while condition ensures that the addition of @xmath131 will alter the number of zeros by at most @xmath340 near each such point ( corollary [ cor : dzistp ] ) . let @xmath926 denote the counting function given by @xmath927 for any interval @xmath513 ; if @xmath43 we ll abuse notation slightly and write @xmath928 for @xmath929)$ ] . we need to determine the limit of @xmath930 as @xmath50 . to do this it will be convenient to work with sequences of increasing values of @xmath931 ; the next result is straightforward ( note that @xmath928 is an non - decreasing function of @xmath931 ) . [ lem : numzrrseqlim ] the quantity @xmath930 has a limit as @xmath50 iff the quantity @xmath932 has a limit as @xmath58 for some ( equivalently , any ) positive increasing sequence @xmath933 with @xmath934 and @xmath935 as @xmath58 . when the limits exist they are equal . [ lem : genpertz1 ] suppose @xmath938 satisfy @xmath939 on an interval @xmath275 where @xmath940 does nt change sign ( that is , either @xmath941 or @xmath942 ) . then @xmath943 can have at most one zero on @xmath275 . assume @xmath941 ( the case @xmath942 can be handled similarly ) . now suppose @xmath943 has ( at least ) two zeros on @xmath275 . then ( at least ) one of these zeros , say @xmath388 , satisfies @xmath944 , so @xmath945 this leads to the contradiction @xmath946 . [ lem : genpertz2 ] let @xmath938 and suppose @xmath947 $ ] is a closed interval with @xmath948 and @xmath949 for @xmath950 . also suppose @xmath939 on @xmath275 . then @xmath943 and @xmath209 have the same number of zeros on @xmath275 . furthermore the endpoints of @xmath275 ca nt be zeros of either function . since @xmath949 for @xmath950 , @xmath209 can have at most one zero on @xmath275 . also @xmath941 or @xmath942 on @xmath275 ( by continuity ) , so @xmath943 has at most one zero on @xmath275 by lemma [ lem : genpertz1 ] . if @xmath955 ( equivalently @xmath956 ) then @xmath209 ( respectively @xmath943 ) either has no zeros on @xmath275 or a single zero @xmath587 which is also a turning point . it follows that @xmath957 ( respectively @xmath958 ) which leads to a contradiction since @xmath959 on @xmath275 ( respectively @xmath960 ) . hence neither @xmath209 nor @xmath943 have any zeros on @xmath275 when @xmath955 . [ lem : zintab<1 ] suppose @xmath961 and @xmath131 satisfies . then there exists @xmath328 such that @xmath922 has exactly one zero in @xmath962 $ ] for any @xmath963 ; furthermore this zero can not occur at an endpoint of the interval . set @xmath964 and @xmath965 . now @xmath966 our assumptions on @xmath131 then allow us to find @xmath328 such that @xmath967 for all @xmath968 . if @xmath963 then lemma [ lem : genpertz2 ] ( with @xmath969 so @xmath970 ) shows that @xmath810 and @xmath971 have the same number of zeros in @xmath962 $ ] and any zeros lie in the interior . the result follows . throughout this section we shall assume @xmath103 ( although several of the results can be extended to cover other cases ) . since @xmath972 it follows that @xmath100 . define @xmath973 by @xmath974 the complementary angles satisfy @xmath975 if we fix @xmath100 and vary @xmath105 from @xmath106 to @xmath34 it is easy to check that @xmath976 increases from @xmath20 to @xmath700 and @xmath977 decreases from @xmath700 to @xmath20 . also note that @xmath978 ( recall ) . the aim of this section is to establish theorem [ thm : coszeros ] in the case that @xmath139 . for any @xmath404 set @xmath979 ; in particular @xmath980 for any @xmath328 . for any @xmath981 let @xmath982 clearly @xmath983 is @xmath984-periodic in @xmath953 while @xmath985 so the inclusion / exclusion of the possibility @xmath986 or @xmath987 does not alter the definition of @xmath988 . set @xmath997 ( recall and ) and define an open interval by @xmath998 in particular @xmath999 for any open interval @xmath275 set @xmath1000 ( so @xmath1001 is @xmath34 on @xmath275 , takes the value @xmath1002 at the end points of @xmath275 , and is @xmath20 elsewhere ) . set @xmath1005 and @xmath1006 . now suppose @xmath1007 for some @xmath1008 and @xmath981 . firstly observe that @xmath1009 so @xmath1010 . define @xmath1011 and @xmath1012 by @xmath1013 [ these functions correspond to the two basic branches of the inverse of @xmath810 ; the remaining branches can be obtained by adding multiples of @xmath984 . ] also define @xmath1014 and @xmath1015 by @xmath1016 for @xmath1017 . now is equivalent to the existence of unique @xmath1017 and @xmath404 such that @xmath1018 . in turn , this is equivalent to @xmath1019 ( note that , if @xmath1020 the we must take @xmath1021 ) . we can determine @xmath983 using if we know the ranges of @xmath1022 and @xmath1023 , together with the multiplicity of covering . _ range of @xmath1022 : _ the function @xmath1024 is monotonically decreasing while @xmath1025 so @xmath1022 is also monotonically decreasing on @xmath1026 . thus @xmath1027 where @xmath1028 = \bigl[-\beta\bigl(\frac{\pi}2+\zeta\bigr),\,-\beta\bigl(\frac{\pi}2-\zeta\bigr)+\pi\bigr].\ ] ] the multiplicity of covering is 1 . _ range of @xmath1023 : _ the turning points of @xmath1023 ( on @xmath1029 ) satisfy @xmath1030 this gives precisely two turning points , at @xmath1031 . furthermore @xmath1023 is monotonically increasing on @xmath1032 and @xmath1033 , and monotonically decreasing on @xmath1034 $ ] . now @xmath1035 so @xmath1036 hence @xmath1037\\ & = i_+^-\cup i_+^+\cup{\overline}{j},\end{aligned}\ ] ] where @xmath1038 each interval has a multiplicity of 1 . to complete the proof note that the definition of @xmath988 and give @xmath1039 now @xmath1040 and @xmath1041 are disjoint sets with union @xmath1042 it follows that @xmath1043 where the last step uses the identity @xmath1044 which holds whenever @xmath1045 . the result follows . ergodicity can now be used in the case @xmath138 . a convenient ergodic theorem gives us @xmath1046 whenever @xmath138 and @xmath1047 is a @xmath984-periodic riemann integrable function ( this is a version of weyl equidistribution ; see @xcite for example ) . combine with lemmas [ lem : numzjnumt ] and [ lem : numzrrseqlim ] to get @xmath1048 since @xmath138 and @xmath988 is a @xmath984-periodic piecewise constant function and lemma [ lem : altexpnumt ] then give @xmath1049 the result now follows from . for @xmath328 lemma [ lem : numzjnumt ] gives @xmath1051\\ & = n\sum_{k=0}^{q-1}\left[{\mathsf{m}}\bigl(2\pi k\,\frac{p}{q}\bigr)+{\mathsf{m}}\bigl(-2\pi(k+1)\,\frac{p}{q}\bigr)\right]\end{aligned}\ ] ] since @xmath988 is @xmath984-periodic . now the mappings @xmath1052 give bijections on @xmath1053 ( since @xmath111 and @xmath112 are coprime ) . together with lemma [ lem : numzrrseqlim ] and we then get @xmath1054 on the other hand , lemma [ lem : altexpnumt ] gives @xmath1055 with @xmath1056 . let @xmath404 . then @xmath1057 we get @xmath1058 iff @xmath1059 is equal to one of the endpoints , and @xmath1060 iff @xmath1059 lies beyond the given range . to ensure we miss the endpoints we require @xmath1061 ( left endpoint ) and @xmath1062 ( right endpoint ) . if @xmath1063 is even these conditions are equivalent ; otherwise they combine as the requirement @xmath1064 . we will now assume this condition is satisfied . from we then get @xmath1065 ( since @xmath1066 for any @xmath1067 ) . _ case @xmath111 , @xmath112 are both odd . _ then @xmath1068 so @xmath1069 lemma [ lem : numzrrseqlimbrat ] now gives @xmath1070 the right hand side is just @xmath1071 since @xmath113 , @xmath114 in this case . _ case @xmath111 , @xmath112 have opposite parity . _ then @xmath1072 so @xmath1073 ( since @xmath1074 whenever @xmath1075 ) . lemma [ lem : numzrrseqlimbrat ] now gives @xmath1076 since @xmath115 , @xmath116 in this case , the right hand side becomes @xmath1071 ( note that , the condition @xmath1064 becomes @xmath122 ) . consider the set of non - negative turning points of @xmath924 , @xmath1077 since @xmath817 is an analytic function @xmath1078 is a discrete subset of @xmath1 . list the points of @xmath1078 in increasing order as @xmath1079 ( note that @xmath1080 ) . for each @xmath1081 set @xmath1082 $ ] . in particular , @xmath1098 solving and as linear equations for @xmath1099 and @xmath1100 leads to @xmath1101 ( recall that @xmath100 ) . using then gives @xmath1102 the estimates now imply @xmath1103 where @xmath1104 are positive constants . taking @xmath1105 we have thus established the following . it follows that we can find @xmath1109 so that @xmath1110 ( we can choose @xmath1111 to be anything in @xmath1112 $ ] ) . now set @xmath1113 then @xmath1114 is open ( as @xmath1115 is continuous ) and @xmath1116 for all @xmath1117 ( by ) . further useful properties are as follows . * if @xmath1118 for some @xmath1117 then @xmath1119 . * @xmath275 contains a unique point of @xmath1078 . * if @xmath1120 satisfies @xmath1121 on @xmath275 then @xmath922 can have at most two zeros on @xmath275 . for part ( ii ) write @xmath1126 . then @xmath1127 so @xmath1128 for some @xmath487 and hence @xmath1119 by part ( i ) ( note that , @xmath1129 so we ca nt have @xmath1130 ) . if there were distinct points @xmath1131 then we could find @xmath388 between @xmath1132 and @xmath1133 ( and hence in @xmath275 ) with @xmath1134 , contradicting the fact that @xmath1135 . suppose @xmath1137 so @xmath1139 and @xmath1140 . in particular @xmath923 and @xmath1141 have opposite signs , as do @xmath1142 and @xmath1143 . it follows that @xmath119 and @xmath1144 lie in diametrically opposite quadrants . from ( with @xmath1145 ) we get @xmath1146 hence @xmath1147 since @xmath1148 this can be combined with the earlier observation to give one of four possibilities ; @xmath1149 comparing the expressions for @xmath119 and @xmath1144 we can thus find integers @xmath1150 of opposite parity such that @xmath1151 . then @xmath1152 however @xmath1153 so @xmath1154 now @xmath1155 and @xmath1156 have the same parity , as do @xmath1157 and @xmath1059 . therefore @xmath1158 and hence @xmath1138 . suppose @xmath131 satisfies . choose a decreasing function @xmath1160 so that @xmath1161 for all @xmath119 and @xmath1162 as @xmath1163 . set @xmath1164 these are the turning points of @xmath924 which are ` small ' in some sense ( relative to @xmath131 ) and can cause changes in the number of zeros when @xmath131 is added to @xmath924 . choose @xmath1165 so that @xmath1166 ( which is possible since @xmath1162 as @xmath1163 ) . now suppose @xmath1167 for some @xmath1168 . then @xmath1169 so @xmath1170 . let @xmath1171 denote the maximal connected component of @xmath1114 which contains @xmath1172 . if @xmath1173 for some @xmath1168 set @xmath1174 . for any @xmath1175 let @xmath1176 . firstly note that @xmath1177 is non - empty ( as otherwise we would have @xmath1178 , implying that @xmath1114 has a connected component containing the distinct elements @xmath1179 of @xmath1078 ) . also @xmath1177 is an interval ( removal of @xmath1180 and @xmath1171 could only split the interval @xmath1181 if either @xmath1182 or @xmath1183 which , in turn , is only possible if @xmath1184 or @xmath1174 ) . [ lem : minkn ] let @xmath1175 and suppose @xmath275 is a closed and bounded sub - interval of @xmath1181 with @xmath1185 for some @xmath487 . then the minimum of @xmath1186 on @xmath275 occurs at an endpoint . suppose the minimum of @xmath1186 on @xmath275 occurs at @xmath388 which is an interior point of @xmath275 . then @xmath388 is also in the interior of @xmath1181 and hence @xmath1187 . on the other hand , we must have @xmath1188 and @xmath1189 , so @xmath1190 by lemma [ lem : propsseng](i ) . set @xmath1193 $ ] and suppose @xmath1194 for some @xmath1192 . since @xmath1195 we get @xmath1196 . lemma [ lem : minkn ] then shows that the minimum of @xmath1186 on @xmath1177 must occur at either @xmath952 or @xmath953 . if @xmath1198 while @xmath1199 if @xmath1200 . however @xmath1111 is not the minimum value of @xmath1186 on @xmath1177 , while having @xmath1201 as the minimum value would imply @xmath1202 leading to the contradiction @xmath1198 . a similar argument shows that the minimum value of @xmath1186 on @xmath1177 ca nt occur at @xmath953 . if @xmath1081 then @xmath1203 for any @xmath1204 so @xmath924 can have at most 1 zero on @xmath1181 ; that is , @xmath1205 . since @xmath1161 for all @xmath119 we immediately get the following corollary of lemmas [ lem : genpertz1 ] , [ lem : genpertz2 ] and [ lem : enf > sig ] . [ [ proof - of - theorem - thmcoszeros - when - alphabeta1-betainmathbbq ] ] proof of theorem [ thm : coszeros ] when @xmath103 , @xmath121 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ using corollary [ cor : bratengunifnz ] we can choose @xmath1213 so that @xmath1214 for all @xmath119 . so @xmath1207 for any @xmath1216 . corollary [ cor : easyintcomp ] then gives @xmath1217)={\mathsf{n}_{0}}([t_m , t_m])$ ] for any @xmath1218 . on the other hand , @xmath1219 and @xmath1211 are discrete subsets of @xmath1 so @xmath1220 and @xmath1221 are both finite . thus @xmath1222 as @xmath1223 . then @xmath1224 with the help of lemmas [ lem : numzrrseqlim ] and [ lem : basictplem ] . let @xmath1228 with @xmath1229 . now @xmath1230 so @xmath1231 . also @xmath1232 so we can find @xmath1233 with @xmath1134 . then the total variation of @xmath1093 between @xmath952 and @xmath953 is at least @xmath1234 . however @xmath1235 for all @xmath119 ; thus @xmath1236 . we have @xmath1246 for all @xmath1059 and @xmath1247 as @xmath58 . from it follows that @xmath1248 as @xmath58 . hence @xmath1249 as @xmath58 ( recall and for the definitions of @xmath1250 and @xmath977 ) . however , @xmath1239 for all @xmath1059 , while @xmath1251 and @xmath1252 so ( modulo @xmath984 ) @xmath1253 must tend to a quadrant diametrically opposite @xmath1254 . hence @xmath1255+\pi{{\mathbb{z}}}$ ] as @xmath58 . comparing with the previous expressions we then get @xmath1256 as @xmath58 ( note that @xmath1148 ) . finally note that lemma [ lem : minsep ] gives @xmath1257 for all @xmath1059 , so we can replace the final @xmath1258 with @xmath1259 . suppose @xmath1261 for some @xmath46 . then we can find @xmath1262 $ ] and a sub - sequence @xmath1263 such that @xmath1264 as @xmath1265 . lemma [ lem : limdiffs+n ] then gives @xmath1266 and @xmath1267 for some @xmath110 , so @xmath1268 . let @xmath732 and choose @xmath1271 so that @xmath1272 for all @xmath1273 . then , for all @xmath1274 , @xmath1275 . hence @xmath1276 whenever @xmath1277 . thus @xmath1278 taking @xmath800 completes the result . [ [ proof - of - theorem - thmcoszeros - when - alphabeta1-betanotinmathbbq ] ] proof of theorem [ thm : coszeros ] when @xmath103 , @xmath138 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ if @xmath1218 then @xmath1283=\bigcup_{m < n\le m}{j_{n } } ' = \bigcup_{m < n\le m}{\widetilde{j}_{n}}\ \cup\bigcup_{m < n < m}{k_{n}}\ \cup{k_{m}}'\cup{k_{m}}',\ ] ] where @xmath1284 for @xmath1285 , @xmath1286 , @xmath1287 and @xmath1288 $ ] . furthermore the intervals in the first covering are disjoint while those in the second covering can only overlap at points @xmath1289 ; for such points @xmath1290 so @xmath1172 is not zero of @xmath922 . therefore @xmath1291)=\sum_{m < n\le m}{\mathsf{n}_{0}}({j_{n}}')\ ] ] and @xmath1292)=\sum_{m < n\le m}{\mathsf{n}_{0}}({\widetilde{j}_{n}})+\sum_{m < n < m}{\mathsf{n}_{\phi}}({k_{n } } ) \ + { \mathsf{n}_{\phi}}({k_{m}}')+{\mathsf{n}_{\phi}}({k_{m}}').\ ] ] now set @xmath1293).\ ] ] by corollary [ cor : dzistp ] @xmath1294 by corollary [ cor : easyintcomp ] ( and the discussion proceeding it ) @xmath1295 if @xmath1207 , while @xmath1296 in general . since @xmath1297 we then get @xmath1298 combining the above estimates now gives @xmath1299)-{\mathsf{n}_{0}}([t_m , t_m])}\bigr\rvert}\le4{\mathsf{k}_{m , m}}.\ ] ] however @xmath1300)$ ] so corollary [ cor : diststp ] ( together with lemma [ lem : basictplem ] ) implies @xmath1299)-{\mathsf{n}_{0}}([t_m , t_m])}\bigr\rvert}=o(t_m)\ ] ] as @xmath1223 . on the other hand , @xmath1219 and @xmath1211 are discrete subsets of @xmath1 so @xmath1220 and @xmath1221 are both finite . thus @xmath1301 as @xmath1223 and so @xmath1224 with the help of lemmas [ lem : numzrrseqlim ] and [ lem : basictplem ] . [ sec : zlimit ] it is instructive to look at the limiting cases in theorem [ thm : coszeros ] . when @xmath1302 we have @xmath1303 the zeros of this function occur precisely when @xmath1304 . if @xmath1305 for some @xmath110 with opposite parity then all zeros of @xmath924 are simple and @xmath1306 the same formula holds for arbitrary @xmath108 if we count zeros with multiplicity . this agrees with theorem [ thm : coszeros ] and the limiting behaviour of @xmath107 as @xmath1307 . at the same time , theorem [ thm : coszeros ] does not extend in a straightforward manner to the case @xmath1308 . this can be seen by taking @xmath1309 , @xmath1310 ; then @xmath1311 although the zeros of this function are precisely the points @xmath1312 for @xmath404 , we also have @xmath1313 it is then straightforward to construct a perturbation @xmath131 satisfying so that @xmath919 has arbitrarily many zeros close to @xmath1312 for each @xmath404 . m. s. birman , m. z. solomyak , _ spectral asymptotics of pseudodifferential operators with anisotropic homogeneous symbols _ , i , vestnik leningrad . univ . mat . astronom . * 13 * , 1321 ( 1977 ) ; ii , vestnik leningrad . univ . mat . astronom . * 13 * , 510 ( 1979 ) ( russian ) .

we study the spectrum of a one - dimensional dirac operator pencil , with a coupling constant in front of the potential considered as the spectral parameter . motivated by recent investigations of graphene waveguides , we focus on the values of the coupling constant for which the kernel of the dirac operator contains a square integrable function . in physics literature such a function is called a confined zero mode . several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained . in particular , we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential . surprisingly , it also depends on the arithmetic properties of certain quantities determined by the potential . we further observe that variable sign potentials may produce complex eigenvalues of the operator pencil . some examples and numerical calculations illustrating these phenomena are presented .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Trade Adjustment Assistance Improvements Act of 1999''. SEC. 2. AUTHORIZATION OF CONSOLIDATED TRADE ADJUSTMENT ASSISTANCE. (a) Authorization of Appropriations.-- (1) In general.--Section 245 of the Trade Act of 1974 (19 U.S.C. 2317) is amended to read as follows: ``SEC. 245. AUTHORIZATION OF APPROPRIATIONS. ``There are authorized to be appropriated to the Department of Labor for each of the fiscal years 1999 through 2001 such sums as may be necessary to carry out the purposes of this chapter.''. (2) Temporary extension of nafta assistance.--Section 250(d)(2) of such Act (19 U.S.C. 2331(d)(2)) is amended by striking ``June 30, 1999, shall not exceed $15,000,000'' and inserting ``September 30, 1999, shall not exceed $30,000,000''. (b) Repeal of NAFTA Transitional Adjustment Assistance Program.-- (1) In general.--Subchapter D of chapter 2 of title II of such Act (19 U.S.C. 2331) is hereby repealed. (2) Conforming amendments.--(A) Section 249A of such Act (19 U.S.C. 2322) is hereby repealed. (B) The table of contents of such Act is amended-- (i) by striking the item relating to section 249A; and (ii) by striking the items relating to subchapter D of chapter 2 of title II. (c) Termination.--Section 285 of such Act (19 U.S.C. 2271 note) is amended-- (1) by amending subsection (c)(1) to read as follows: ``(c)(1) Except as provided in paragraph (2), no assistance, vouchers, allowances, or other payments may be provided under chapter 2, and no technical assistance may be provided under chapter 3, after September 30, 2001.''; and (2) in subsection (c)(2), by striking ``June 30, 1999,'' and inserting ``September 30, 1999,''. (d) Effective Date.-- (1) Subsections (a) and (c).--The amendments made by subsections (a) and (c) take effect on-- (A) July 1, 1999; or (B) the date of enactment of this Act, whichever is earlier. (2) Subsection (b).--The amendments made by subsection (b) take effect on-- (A) October 1, 1999; or (B) 90 days after the date of enactment of this Act, whichever is later. SEC. 3. FILING OF PETITIONS AND PROVISION OF RAPID RESPONSE ASSISTANCE; EXPEDITED REVIEW OF PETITIONS BY SECRETARY OF LABOR. (a) Filing of Petitions and Provision of Rapid Response Assistance.--Section 221(a) of the Trade Act of 1974 (19 U.S.C. 2271(a)) is amended to read as follows: ``(a)(1) A petition for certification of eligibility to apply for adjustment assistance for a group of workers under this chapter may be filed with the Governor of the State in which such workers' firm or subdivision is located by any of the following: ``(A) The group of workers (including workers in an agricultural firm or subdivision of any agricultural firm). ``(B) The certified or recognized union or other duly authorized representative of such workers. ``(C) Employers of such workers, one-stop operators or one- stop partners (as defined in section 101 of the Workforce Investment Act of 1998 (29 U.S.C. 2801)), or State employment agencies, on behalf of such workers. ``(2) Upon receipt of a petition filed under paragraph (1), the Governor shall-- ``(A) immediately transmit the petition to the Secretary of Labor (hereinafter in this chapter referred to as the `Secretary'); ``(B) ensure that rapid response assistance and basic readjustment services authorized under other Federal laws are made available to the workers covered by the petition to the extent authorized under such laws; and ``(C) assist the Secretary in the review of the petition by verifying such information and providing such other assistance as the Secretary may request. ``(3) Upon receipt of the petition, the Secretary shall promptly publish notice in the Federal Register that the Secretary has received the petition and initiated an investigation.''. (b) Expedited Review of Petitions by Secretary of Labor.--Section 223(a) of such Act (19 U.S.C. 2273(a)) is amended in the first sentence by striking ``60 days'' and inserting ``40 days''. SEC. 4. ADDITION OF SHIFT IN PRODUCTION AS BASIS FOR ELIGIBILITY FOR TRADE ADJUSTMENT ASSISTANCE. Section 222(a) of the Trade Act of 1974 (19 U.S.C. 2272(a)) is amended to read as follows: ``(a) A group of workers (including workers in any agricultural firm or subdivision of an agricultural firm) shall be certified by the Secretary as eligible to apply for adjustment assistance under this chapter pursuant to a petition filed under section 221 if the Secretary determines that-- ``(1) a significant number or proportion of the workers in such workers' firm or an appropriate subdivision of the firm have become totally or partially separated, or are threatened to become totally or partially separated; and ``(2)(A)(i) the sales or production, or both, of such firm or subdivision have decreased absolutely; ``(ii) imports of articles like or directly competitive with articles produced by such firm or subdivision have increased; and ``(iii) the increase in imports described in clause (ii) contributed importantly to such workers' separation or threat of separation and to the decline in the sales or production of such firm or subdivision; or ``(B) there has been a shift in production by such workers' firm or subdivision to a foreign country of articles like or directly competitive with articles which are produced by such firm or subdivision.''. SEC. 5. INFORMATION ON CERTAIN CERTIFICATIONS. Section 223 of the Trade Act of 1974 (19 U.S.C. 2273) is amended by adding at the end the following subsection: ``(e) The Secretary shall collect and maintain information-- ``(1) identifying the countries to which firms have shifted production resulting in certifications under section 222(a)(2)(B), including the number of such certifications relating to each country; and ``(2) to the extent feasible, identifying the countries from which imports of articles have resulted in certifications under section 222(a)(2)(A), including the number of such certifications relating to each country.''. SEC. 6. ENROLLMENT IN TRAINING REQUIREMENT. Section 231(a)(5)(A) of the Trade Act of 1974 (19 U.S.C. 2291(a)(5)(A)) is amended-- (1) by inserting ``(i)'' after ``(A)''; (2) by adding ``and'' after the comma at the end; and (3) by adding at the end the following: ``(ii) the enrollment required under clause (i) occurs no later than the latest of-- ``(I) the last day of the 16th week after the worker's most recent total separation from adversely affected employment which meets the requirements of paragraphs (1) and (2); ``(II) the last day of the 8th week after the week in which the Secretary issues a certification covering the worker; or ``(III) 45 days after the later of the dates specified in subclause (I) or (II), if the Secretary determines there are extenuating circumstances that justify an extension in the enrollment period;''. SEC. 7. WAIVERS OF TRAINING REQUIREMENTS. (a) In General.--Section 231(c) of the Trade Act of 1974 (19 U.S.C. 2291(c)) is amended to read as follows: ``(c)(1) The Secretary may issue a written statement to a worker waiving the enrollment in the training requirement described in subsection (a)(5)(A) if the Secretary determines that such training requirement is not feasible or appropriate for the worker, as indicated by 1 or more of the following: ``(A) The worker has been notified that the worker will be recalled by the firm from which the qualifying separation occurred. ``(B) The worker has marketable skills as determined pursuant to an assessment of the worker, which may include the profiling system under section 303(j) of the Social Security Act (42 U.S.C. 503(j)), carried out in accordance with guidelines issued by the Secretary. ``(C) The worker is within 2 years of meeting all requirements for entitlement to old-age insurance benefits under title II of the Social Security Act (42 U.S.C. 401 et seq.) (except for application therefor). ``(D) The worker is unable to participate in training due to the health of the worker, except that a waiver under this subparagraph shall not be construed to exempt a worker from requirements relating to the availability for work, active search for work, or refusal to accept work under Federal or State unemployment compensation laws. ``(E) The first available enrollment date for the approved training of the worker is within 45 days after the date of the determination made under this paragraph, or, if later, there are extenuating circumstances for the delay in enrollment, as determined pursuant to guidelines issued by the Secretary. ``(F) There are insufficient funds available for training under this chapter, taking into account the limitation under section 236(a)(2)(A). ``(G) The duration of training appropriate for the individual to obtain suitable employment exceeds the individual's maximum entitlement to basic and additional trade readjustment allowances and, in addition, financial support available through other Federal or State programs, including title III of the Job Training Partnership Act (29 U.S.C. 1651 et seq.) or chapter 5 of subtitle B of title I of the Workforce Investment Act of 1998, that would enable the individual to complete a suitable training program cannot be assured. ``(2) The Secretary shall specify the duration of the waiver under paragraph (1) and shall periodically review the waiver to determine whether the basis for issuing the waiver remains applicable. If at any time the Secretary determines such basis is no longer applicable to the worker, the Secretary shall revoke the waiver. ``(3) Pursuant to the agreement under section 239, the Secretary may authorize the State or State agency to carry out activities described in paragraph (1) (except for the determination under subparagraphs (F) and (G) of paragraph (1)). Such agreement shall include a requirement that the State or State agency submit to the Secretary the written statements provided pursuant to paragraph (1) and a statement of the reasons for the waiver. ``(4) The Secretary shall submit an annual report to the Committee on Finance of the Senate and the Committee on Ways and Means of the House of Representatives identifying the number of workers who received waivers and the average duration of such waivers issued under this subsection during the preceding year.''. (b) Conforming Amendment.--Section 231(a)(5)(C) of such Act (19 U.S.C. 2291(a)(5)(C)) is amended by striking ``certified''. SEC. 8. PROVISION OF TRADE READJUSTMENT ALLOWANCES DURING BREAKS IN TRAINING. Section 233(f) of the Trade Act of 1974 (19 U.S.C. 2293(f)) is amended in the matter preceding paragraph (1) by striking ``14 days'' and inserting ``30 days''. SEC. 9. INCREASE IN ANNUAL TOTAL AMOUNT OF PAYMENTS FOR TRAINING. Section 236(a)(2)(A) of the Trade Act of 1974 (19 U.S.C. 2296(a)(2)(A)) is amended by striking ``$80,000,000'' and all that follows through $70,000,000 and inserting ``$150,000,000''. SEC. 10. ELIMINATION OF QUARTERLY REPORT. (a) In General.--Section 236(d) of the Trade Act of 1974 (19 U.S.C. 2296(d)) is amended by striking the last sentence. (b) Effective Date.--The amendment made by this section takes effect on October 1, 1999. SEC. 11. COORDINATION WITH ONE-STOP DELIVERY SYSTEMS, THE JOB TRAINING PARTNERSHIP ACT, AND THE WORKFORCE INVESTMENT ACT OF 1998. (a) Coordination With One-Stop Delivery Systems.--Section 235 of the Trade Act of 1974 (19 U.S.C. 2295) is amended by inserting ``, including the services provided through one-stop delivery systems described in section 134(c) of the Workforce Investment Act of 1998 (19 U.S.C. 2864(c))'' before the period at the end of the first sentence. (b) Coordination With Job Training Partnership Act and Workforce Investment Act of 1998.--Section 239(e) such Act (19 U.S.C. 2311(e)) is amended-- (1) in the first sentence, by striking ``or title I of the Workforce Investment Act of 1998'' and inserting ``or under the provisions relating to dislocated worker employment and training activities set forth in chapter 5 of subtitle B of title I of the Workforce Investment Act of 1998 (29 U.S.C. 2861 et seq.), as the case may be,''; and (2) by inserting after the first sentence the following: ``Such coordination shall include use of common reporting systems and elements, including common elements relating to participant data and performance outcomes (including employment, retention of employment, and wages).''. SEC. 12. SUPPORTIVE SERVICES. (a) In General.--Part II of subchapter B of chapter 2 of title II of the Trade Act of 1974 (19 U.S.C. 2295 et seq.) is amended by adding at the end the following: ``SEC. 238A. SUPPORTIVE SERVICES. ``(a) Application.--Any adversely affected worker covered by a certification under subchapter A of this chapter may file an application with the Secretary for the provision of supportive services, including transportation, child and dependent care, and other similar services. ``(b) Conditions.--The Secretary may approve an application filed under subsection (a) and provide supportive services to an adversely affected worker only if the Secretary determines that-- ``(1) the provision of such services is necessary to enable the worker to participate in or complete training; and ``(2) the provision of such services is consistent with the provision of supportive services to participants under the program of employment and training assistance for dislocated workers carried out under title III of the Job Training Partnership Act (29 U.S.C. 1651 et seq.), as in effect on the date of enactment of the Trade Adjustment Assistance Reform Act of 1999, or under the provisions relating to dislocated worker employment and training activities set forth in chapter 5 of subtitle B of title I of the Workforce Investment Act of 1998 (29 U.S.C. 2861 et seq.), as the case may be.''. (b) Conforming Amendment.--The table of contents of such Act is amended by inserting after the item relating to section 238 the following: ``Sec. 238A. Supportive services.''. SEC. 13. ADDITIONAL CONFORMING AMENDMENTS. (a) Section 225.--Section 225(b) of the Trade Act of 1974 (19 U.S.C. 2275(b)) is amended in each of paragraphs (1) and (2) by striking ``or subchapter D''. (b) Section 240.--Section 240(a) of such Act (19 U.S.C. 2312(a)) is amended by striking ``subchapter B of''. SEC. 14. AVAILABILITY OF CONTINGENCY FUNDS. (a) In General.--Section 245 of the Trade Act of 1974 (19 U.S.C. 2317), as amended by section 2, is amended-- (1) by striking ``There are authorized'' and inserting ``(a) In General.--There are authorized''; and (2) by adding at the end the following: ``(b) Contingency Funds.--Subject to the limitation contained in section 236(a)(2), if in any fiscal year the funds available to carry out the programs under this chapter are exhausted, there shall be made available from funds in the Treasury not otherwise appropriated amounts sufficient to carry out such programs for the remainder of the fiscal year.''. (b) Effective Date.--The amendments made by this section take effect on-- (1) July 1, 1999; or (2) the date of enactment of this Act, whichever is earlier. SEC. 15. REAUTHORIZATION OF ADJUSTMENT ASSISTANCE FOR FIRMS. (a) In General.--Section 256(b) of the Trade Act of 1974 (19 U.S.C. 2346(b)) is amended by striking ``for the period beginning October 1, 1998, and ending June 30, 1999'' and inserting ``for each of fiscal years 1999 through 2001''. (b) Effective Date.--The amendment made by this section takes effect on-- (1) July 1, 1999; or (2) the date of enactment of this Act, whichever is earlier. SEC. 16. EFFECTIVE DATE; TRANSITION PROVISION. (a) Effective Date.--Except as otherwise provided in this Act, this Act and the amendments made by this Act take effect on-- (1) October 1, 1999; or (2) 90 days after the date of enactment of this Act, whichever is later. (b) Transition.--The Secretary of Labor may promulgate such rules as the Secretary determines to be necessary to provide for the implementation of the amendments made by this Act.

Trade Adjustment Assistance Reform Act of 1999 - Amends the Trade Act of 1974 to authorize appropriations to the Department of Labor for FY 1999 through 2001 for trade adjustment assistance (TAA) for workers. (Sec. 2) Extends, temporarily, through September 30, 1999, the North American Free Trade (NAFTA) Transitional Adjustment Assistance Program. Repeals the NAFTA Transitional Adjustment Assistance Program (effectively eliminating TAA for workers under such program). (Sec. 3) Revises requirements for the filing of petitions for TAA for a group of workers adversely affected by imports. Authorizes employers of such workers, one-stop operators or one-stop partners, or State employment agencies to file on their behalf with the Governor of the State (currently, with the Secretary of Labor) a petition for certification of eligibility for such assistance. Requires the Governor to: (1) transmit the petition to the Secretary immediately; (2) ensure that rapid response assistance and basic readjustment services are made available to the workers; and (3) assist the Secretary in the review of the petition. Requires the Secretary to review such petitions for certification of eligibility within 40 days (currently, 60 days) of its filing. (Sec. 4) Adds as a factor in the Secretary's determination of the eligibility of a group of workers for TAA any shift in production by such workers' firm to a foreign country of articles like or directly competitive with articles produced by such firm. (Sec. 5) Directs the Secretary to collect and maintain certain information with respect to certifications of TAA. (Sec. 6) Revises enrollment in training requirements with respect to the payment of TAA to adversely affected workers to set forth certain time periods during which such enrollment must occur. Authorizes the Secretary to issue a statement to a worker waiving the enrollment in training requirements if it is determined that such training requirement is not feasible or appropriate for the worker, based on specified factors. (Sec. 8) Increases from 14 to 30 the number of days an adversely affected worker may have a scheduled break in a training program and still be treated as participating in the program for purposes of TAA eligibility. (Sec. 9) Increases the total annual amount of payments for worker training from $80 million to $150 million for any fiscal year. (Sec. 11) Authorizes the Secretary to secure for adversely affected workers certain employment services, including services provided through one-stop delivery systems. Provides for the coordination of employment services for adversely affected workers under the Job Training Partnership Act and the Workforce Investment Act of 1998. (Sec. 12) Authorizes an adversely affected worker to file an application with the Secretary for the provision of supportive services, including transportation, child and dependent care, and other similar services. Sets forth specified conditions with respect to such services. (Sec. 14) Makes unappropriated Treasury funds available in any fiscal year that TAA funds become exhausted. (Sec. 15) Authorizes appropriations to the Department of Labor for FY 1999 through 2001 for TAA for firms.

a major component of the adaptive immune response to infection is the generation of protective and long - lasting humoral immunity , but factors governing selection of the particular antigens recognized are unclear . it is not uncommon for viruses encoding a small number of proteins to generate antibodies against each encoded protein . but for infectious agents containing hundreds or thousands of proteins only a subset of the proteome is recognized and little is known about the extent or the characterisitics of this subset of antigens . methods for making a complete empirical accounting of the immunoproteome have limitations , particularly when the genome of the organism is large . here we describe a b. melitensis proteome microarray that enables this problem to be directly addressed by applying an unbiased systems biology approach to identify immunodominant and serodiagnostic antigens and to classify the reactive antigens based on functional and physical properties . protein microarrays can be used with relative ease to probe the entire proteome of different infectious microorganisms including bacteria , viruses and parasites . this approach permits assessing the repertoire of antibodies produced in response to infections or vaccinations from large collections of individual patient sera , and can be used to perform large - scale sero - epidemiological and sero - surveillance analyses not possible with other technologies , while consuming small quantities ( < 2 l ) of each serum sample . probing large numbers of patient specimens empowers the statistical tests resulting in more reliable conclusions while correcting for false discovery required for multiple comparison testing inherent in microarray analysis . moreover , microarrays can display all proteins of an infectious agent and may allow for identification of novel antigens , otherwise undetectable by methods like 2-d gels that are highly biased by microbial protein expression patterns . brucella melitensis , the most virulent species infecting humans , also infects goats , sheep and cattle , in central and south america , the middle east , east asia , and some southern european countries . consumption of animal products , direct animal contact and inhalation of aerosolized bacteria in the laboratory setting ( indicating the potential for air - borne spread via a bioterrorism - type attack ) are well - recognized routes of infection . the current knowledge of protein antigens recognized by humans and reservoir animals is based on limited numbers of studies on brucella melitensis and brucella abortus . we recently constructed a pilot proteome array consisting of 1406 b. melitensis proteins and observed marked differences in immune responses between humans and goats.(5 ) here we have expanded our previous study to the full proteome microarray consisting of 3046 b. melitensis proteins , by including expression of newly cloned 1640 bm genes . in addition to developing a better classifier capable of predicting disease based on serological response , more importantly , this study allows an estimate of the extent of immune reactivity against the whole proteome , and prediction of proteomic features that may dictate immune recognition for other yet uncharacterized gram - negative bacteria . human sera were obtained from patients enrolled in a prospective clinical study of brucellosis in lima , peru . the human subjects part of the study was approved by the humans research protections committee of the university of california san diego , the comite de tica of universidad peruana cayetano heredia , lima , peru and the comite de tica of asociacin benfica prisma , lima , peru , all of whom have maintained federal wide assurances with the united states department of health and human services . all patients provided written informed consent prior to enrollment in the study , and signed consent forms have been stored in locked files in study offices at upch and ab prisma , lima , peru . forty- two patients were confirmed to have acute brucellosis by positive culture , positive rose bengal test and by tube agglutination tests titers 1/160 . eighteen patients presenting with brucellosis - compatible syndromes were culture negative and rose bengal positive , and treated according to standard antibiotic therapy within 2 days of serum sampling . additional control patient samples included 13 sera from rose bengal - negative patients , 44 samples from ambulatory healthy controls from north lima where brucellosis occasionally affects patients , and sera from humans in the u.s . where brucellosis is not found . approximately 10 g of autoclaved pellet of b. melitensis 16 m were used to isolate lps using the hot phenol - water method.(32 ) the purified lps was treated with rnase , dnase and proteinase - k , and the hot phenol - water treament was repeated . b. melitensis lps obtained from both upper phenol saturated aqueous layer ( aqueous phase ) and lower water saturated phenol layer ( phenol phase ) were pooled . the lps from e. coli 055:b5 and b. melitensis 16 m were analyzed on a gradient 412% tris - glycine sodium dodecyl sulfate ( sds ) polyacrylamide gel ( invitrogen corp . , the presence of lps in the gels was detected with a periodic acid silver stain(33 ) and protein using coomassie blue stain . b. melitensis lps was quantified using a colorimetric assay to measure 2-keto-3-deoxyoctonate ( kdo ) concentration.(34)e . all orfs from brucella melitensis 16 m genomic dna were identified using genbank nc_003317 and nc_003318 , and 1640 orfs that were absent from pilot chip were amplified and cloned using a high - throughput pcr and recombination cloning method described previously.(5 ) microarrays and immunostrips were fabricated and probed as described before.(5 ) plasmids were expressed at 24 c for 16 h in in vitro transcription / translation e. coli reactions ( expressway maxi kits from invitrogen ) , according to the manufacturer s instructions . for microarrays , 10 l of reaction was mixed with 3.3 l 0.2% tween 20 to give a final concentration of 0.05% tween 20 , and printed onto nitrocellulose coated glass fast slides ( whatman ) using an omni grid 100 microarray printer ( genomic solutions ) . for immunostrips , b. melitensis lps was printed at 0.01 mg / ml . all antigens were printed on optitran ba - s 85 0.45 m nitrocellulose membrane ( whatman ) using biojet dispenser ( biodot ) at 1 l / cm , and cut into 3 mm strips . human sera samples were diluted to 1:200 with 10 mg / ml e. coli lysate ( mclab ) . microarray slides were incubated in biotin - conjugated secondary antibody ( jackson immunoresearch ) diluted 1/200 in blocking buffer , and detected by incubation with streptavidin - conjugated surelight p-3 ( columbia biosciences ) . microarray slides were scanned and analyzed using a perkin - elmer scanarray express ht microarray scanner . human sera were diluted to 1/200 in 5% bsa solution containing 20% e. coli lysate ( mclab ) . strips were then incubated in alkaline phosphatase conjugated donkey antihuman immunoglobulin ( anti - igg , fc fragment - specific , jackson immunoresearch ) secondary antibody , diluted to 1/2000 , and reactive bands were visualized by incubating with 1-step nitro - blue tetrazolium chloride/5-bromo-4-chloro-3-indolyphosphate p - toluidine salt ( nbt / bcip ) developing buffer ( thermo fisher scientific ) . immunostrips were scanned with hewlett - packard document scanner , and were quantified using image j software . the mass spectrometry data set characterization of host and pathogen proteins affected by brucella abortus infection was from caprion proteomics studies of b abortus , downloadable from pathogen portal web site hosted by proteomics resource center at http://www.pathogenportal.org/portal/portal/pathport/home . samples were processed for intact bacteria or cell envelope preparations from exponentially growing bacteria according to the caprion protocol 24401 and 24302 , as described before . briefly , to process intact bacteria for ms analysis , 50 l aliquots of 20 g protein samples were denatured in 50 mm ammonium bicarbonate ( sigma - aldrich , st . after sonication , samples were centrifuged at 2000 g for 1 min and a 950 l cold ( 20 c ) chloroform / methanol solution ( 2:1 v / v ) were added . samples were vortex mixed and incubated at 20 c for 2 h. subsequently , 100 l cold ( 20 c ) methanol was added and samples were clarified by centrifugation at 21 000 g for 10 min at 4 c . the supernatants were dried under vacuum , resuspended in 100 mm ammonium bicarbonate containing 8 m urea and 1% ( w / v ) of acid - labile surfactant ( als ; waters , milford , ma ) and sonicated for 10 min . after centrifugation for 20 s at 2000 g , samples were incubated for 1 h at ambient temperature . a volume of 450 l of 100 mm ammonium bicarbonate containing 5% ( v / v ) of acetonitrile was added . lys - c ( wako , richmond , va ) was added to yield a 1:50 enzyme to protein ratio . trypsin ( promega , madison , wi ) was then added at a 1:50 enzyme to protein ratio and samples were incubated for an additional 16 h. following proteolysis , tcep ( pierce , rockford , il ) was added to a final concentration of 10 mm and samples were incubated for 30 min at ambient temperature and then lyophilized . to cleave the acid labile surfactant n hcl and 100 l of water were added into each sample with subsequent incubation for another half hour at ambient temperature . to process cell envelope for ms analysis , supernatants of exponentially growing b. abortus strains were clarified , centrifuged at 100 000 g for 6 h at 4 c , pellets resuspended in double distilled water . the sample was sonicated , and 50 mm ammonium bicarbonate containing 2% acid - labile surfactant and 8 m urea were added . the sample was vortex mixed for 1 h. a sample of 50 l of the om suspension was added to a final volume of 1 ml of a chloroform / methanol solution ( 2:1 v / v ) . the sample was vortex mixed and incubated at 20 c for 2 h. subsequently , 100 l of cold methanol ( 20 c ) was added , and the sample was cleared by centrifugation for 10 min at 21 000 g. the supernatant was dried under vacuum and resuspended in 4 m urea ; 50 mm ammonium bicarbonate ph 8.0 . the samples were then diluted 4:1 with 50 mm ammonium bicarbonate buffer ph 8.0 , and trypsin was added at a 1:25 protein ratio for an additional 16 h. following proteolysis , the samples were distributed into 96-well plates for mass spectrometry analysis . peptide digests were analyzed by liquid chromatography coupled to mass spectrometry ( lc - ms ) as described . ms system consisted of a caplc ( waters , milford , ma ) with a cooled autosampler and a qtof ultima ( waters , milford , ma ) controlled by masslynx version 4.0 software . the peptide concentrations were normalized and the samples were injected into a reversed - phase column ( jupiter c18 , phenomenex , torrance , ca ) for hplc separation . ms spectra to mascot software ( matrixscience , boston , ma ) for searching against the national center for biotechnology information protein database ( ncbi ) . numbers of different peptides for each identified protein were counted and listed in table s4 ( supporting information ) . data analysis was performed using the r ( http://www.r-project.org ) and sas ( http://www.sas.com/ ) statistical software . it has been noted in literature that data derived from microarray platforms is heteroskedatic . to stabilize the variance , the vsn normalization method implemented as part of the bioconductor suite ( www.bioconductor.org ) in addition to removing heteroskedacity , this procedure corrects for nonspecific noise effects by finding maximum likelihood shifting and scaling parameters for each array such that control probe variance is minimized . this calibration has been shown to be effective on a number of platforms.(42 ) differentially reactive proteins between groups were determined using a bayes regularized t test adapted from cyber - t for protein arrays , which has been shown to be more effective than other differential expression techniques.(44 ) to account for multiple comparison conditions , the benjamini and hochberg ( bh ) method was used to control the false discovery rate.(45 ) after benjamini and hochberg correction , p - value smaller than 0.05 was considered significant , and the corresponding protein was considered differentially reactive and serodiagnostic . multiplex classifiers were constructed using linear and nonlinear support vector machines ( svms ) using the e1071 r package . plots of receiver operating characteristic ( roc ) curves were made with the rocr r package . sensitivity specificity and area under the curve ( auc ) were determined from the resulting roc curves . principle component analysis ( pca ) to visually reduce and summarize signal intensity variance among the subjects was conducted in jmp software ( www.jmp.com ) . hierarchical clustering was used to group sera samples into subsets , such that those within each cluster ( subset ) are more closely related to one another than samples assigned to other clusters . clustering is based on the degree of similarity between the protein intensity for each individual . mev v4.6 ( tm4microarray software suite , www.tm4.org ) was used to perform the clustering analysis . tmhmm v2.0 was utilized for transmembrane domains prediction(46 ) ( http://www.cbs.dtu.dk/services/tmhmm/ ) , signalp v3.0 for signal peptide prediction(47 ) ( http://www.cbs.dtu.dk/services/signalp/ ) , psortb v3.0 . pi / mw tool from swiss institute of bioinformatics was used to determine isolectric point ( http://ca.expasy.org/tools/pi_tool.html ) . p value for enrichment statistical analysis was calculated using fisher s exact test in the r environment . the 3198 predicted orfs of b. melitensis ( bm ) 16 m were subjected to amplification from genomic dna , and 1406 orfs were cloned and printed on pilot chip.(5 ) in this study , another 1640 orfs were successfully cloned using our high throughput recombination method . about one - fourth of the cloned genes were sequenced and > 99% of sequenced clones had the correct sequence . all 3046 bm orfs cloned in pxt7 vector ( > 95% of proteome ) were expressed under t7 promoter in the e. coli in vitro transcription / translation system , and printed on microarrays . over 98% of protein spots bm protein arrays were probed with sera from acute brucellosis patients in lima , peru obtained within 13 weeks of the onset of symptoms , and sera from bm culture - positive humans ( figure s1b , supporting information ) showed robust reactivity against a collection of antigens compared to unexposed individuals . among the 3046 antigens tested , 1464 antigens reacted with at least one culture positive individual , accounting for 48% of the proteome ( figure 1 ) . within this immunoproteome , , with mean reactivity greater than the mean of the no dna controls plus 2.5 standard deviations among culture positive individuals ( figure 2 , figure s2 and table s1 , supporting information ) . of these , 33 protein antigens were serodiagnostic , and were significantly differentially reactive between nave and culture positive patients from peru ( benjamini and hochberg adjusted cyber - t p - value < 0.05 ) . most of these antigens also reacted strongly with sera from brucellosis cases that were culture negative but positive for the rose bengal diagnostic test . an unbiased hierarchical clustering analysis segregated most of the individual specimens into two groups , with a few infected cases with weak reactivity sporadically clustered among samples diagnosed as uninfected ( figure s2 , supporting information ) . we also identified 90 cross - reactive antigens that reacted similarly among all human samples , whether from nave individuals or individuals diagnosed to be infected . the raised bars of any color represent 1464 reactive proteins , which define the immunoproteome ( approximately 48% of the proteome ) . there are 538 antigens reactive in 1 sample , 648 antigens reactive in 25 samples , 143 antigens reactive in 69 samples and 135 antigens reactive in 1042 samples . bmei0536 and bmei1079 reacted in all 42 bm culture positive samples . all serodiagnostic antigens except bmei0503 reacted in 1042 samples ; bmei0503 reacted in 9 samples . discovery of new human serodiagnostic antigens by probing the full b. melitensis proteome arrays with a collection of b. melitensis peruvian nave and culture positive human sera . the mean sera reactivity of the 3046 antigens was compared between the culture positive and peruvian naive groups . antigens with benjamini hochberg corrected p - value less than 0.05 ( serodiagnostic ) are organized to the left and cross - reactive ( bh_p > 0.05 ) antigens to the right . shown are the 33 serodiagnostic protein antigens , bm lps , and a subset of cross - reactive antigens . we performed unsupervised principal component analysis and showed that the 33 serodiagnostic antigens clearly separated the peruvian naive from culture positive groups ( figure 3a ) . to further determine the accuracy of distinguishing brucellosis cases from controls , cross - validation receiver operating characteristic ( roc ) curves and area under the curve ( auc ) the top four orfs , bmei0536 ( bp26 ) , bmei0805 ( hypothetical protein ) , bmei1330 ( protease do ) , and bmei 1890 ( transporter ) , as wells as bm lps , all have an individual antigen auc greater than 0.90 ( table s1 , supporting information ) . three of the antigens were identified previously on microarrays.(5 ) antigen bp26 ( bmei0536 ; auc 0.991 ; bh p - value < 1 10 ) gave the best single antigen discrimination with 95% sensitivity and specificity rate . variability and mean value of accuracy from this model has been shown in the auc boxplot . the top 5 antigens all produced sensitivity and specificity over 96% ( figure 3c ) . with the top 3 antigens , this classifier yielded a highest sensitivity and specificity rate of 98.6 and 98.6% , respectively . altogether 33 protein antigens plus lps produced sensitivity and specificity over 93% ( a ) unsupervised principal component analysis of the signal intensity for samples from peruvian naives and culture positive groups revealed that these two groups could be segregated on the basis of 33 selected serodianosis protein antigens and 2 bm lps ( at 0.1 mg / ml or 0.01 mg / ml ) . the serodiagnostic antigens were ranked by single antigen auc . ( b ) cross - validation auc boxplot with variance and mean value and ( c ) cross - validation roc graphs show classifiers with increasing number of human serodiagnostic antigens . with the top 3 antigens , this classifier yielded a highest sensitivity and specificity rate of 98.6% and 98.6% , respectively . all 33 antigens plus bm lps also produced sensitivity and specificity over 93% . eighteen serodiagnostic proteins and bm lps the individual strips were probed with 31 different randomly selected culture positive sera and 31 peruvian naive sera . brucellosis patients reacted strongly against the serodiagnostic antigens with variable signal intensities among the patients . the roc curve ( figure 4b ) shows that this immunostrip test yielded a high auc of 0.97 , with sensitivity rate of 96.7% and specificity rate of 96.7% . ( a ) eineteen serodiagnostic antigens and bm lps at 0.01 mg / ml were printed onto nitrocellulose membrane in adjacent stripes using a biodot jet dispenser as described in materials and methods . strips were probed with culture positive or peruvian naive sera diluted 1/200 followed by alkaline phosphatase conjugated secondary antibody and enzyme substrate . weak reactivity in the nave healthy controls ( b ) cross - validation roc curve was generated and sensitivity and specificity of immunostrips test is 96% and 96% , respectively . serological tests are routinely used to diagnose brucellosis . while the qualitative agglutination test ( rose bengal ) is 90% sensitive for screening for acute / subacute brucellosis , quantitative agglutination testing ( e.g. , tube agglutination test ( tat ) ) with titer typically greater than 1/160 used as a more precise diagnostic criterion , can also be used to diagnose relapse . often blood cultures are negative at the time of initial presentation or relapse , possibly because of low levels of bacteremia or antecedent use of antibiotics . without being able to ascertain whether the sera used in this study were obtained from patients who might have taken antibiotics prior to blood cultures , we queried our data set to determine whether sera from blood culture - positive , rose bengal positive brucellosis patients ( gold standard diagnosis ) vs blood culture - negative , rose bengal positive ( tat not done ) subjects ( presumptive positive , unconfirmed ) recognized different proteins on the protein microarrays . sera from blood culture - negative , rose bengal positive subjects reacted with 10 b. melitensis antigens much more strongly than blood culture - positive , rose bengal positive individuals ( figure s3 , supporting information ) . this unique set of 10 antigens was distinct from the 33 antigens that distinguish culture positive cases from peruvian naves . these results indicate that protein microarray analysis was able to delineate distinct antibody profiles in blood culture positive and negative patients , which has the potential to identify antigens capable of differentiating active acute / subacute brucellosis from previously exposed patients . these findings may suggest novel biological interactions between bacteria and host that need to be further explored because culture negativity / rose bengal seropositivity might be associated with some biological difference between human hosts , perhaps an immune response that might lower bacterial loads to levels difficult to culture from blood . alternatively , it is possible that antibiotic use might lead to an altered host immune response to killed bacteria that no longer would subvert the host immune responses ( typical of intracellular pathogens such as brucella ) . to better understand the determinants of antigenicity in bacteria , we performed a functional enrichment analysis of the serodominant and serodiagnostic antigens identified in this study . a total of 543 proteins are unassociated with cogs , and 39 proteins are associated with cogs but have not been assigned to a category , shown as some proteins have multiple cog assignments so there are 3,291 cogs in total for 3046 proteins on chip . proteins with predicted cog- u function , involved in intracellular trafficking and secretion , were 6.2- fold enriched in serodiagnostic antigens and 4.3- fold enriched in serodominant antigens . proteins in the cog - m category , cell envelope biogenesis and outer membrane , were 2-fold enriched in serodominant antigens ( p - value 0.01 ) . proteins in cog - n category , cell motility and secretion , were 3.5-fold enriched in serodominant antigens ( p = 0.027 ) . proteins with predicted cog - o function , posttranslational modification , protein turnover , chaperones , were also significantly enriched at 3.0-fold in serodominant antigens . there was only 1 serodominant antigen out of 176 cog - k category proteins , predicted to be involved in transcription and identified as serodominant , which was 0.1- fold enrichment and significantly underrepresented with p value of 0.014 ( figure 5a , table s3a , supporting information ) . overview of an enrichment analysis of bm proteome classified with cogs and computational predictions categories . the size of each slice represents the number of proteins assigned to each cog category . proteins classified with cogs - u , m , n , o categories are significantly overrepresented in serodominant antigens and shown in extracted red . cog - k proteins are significantly underrepresented in serodominant antigens are shown in extracted black . cog categories with < 5 proteins were not included in the figure ( cogs - b , w ) . significant over- and under - representations are shown in extracted red or black , respectively . numbers of serodominant antigens within these categories / number of total proteins within these categories are in parentheses in the legend . results of the complete cog analysis and computational predictions are in table s3 ( supporting information ) . ( c ) correlation between enrichment fold and peptide numbers detected by mass spectrometry . as peptide numbers for serdiagnostic antigens in contrast , enrichment fold for cross - reactive antigens decreases as peptide numbers for cross - reactive antigens increase . as shown in figure 5b and table s3b ( supporting information ) , proteins with 1 transmembrane domain were significantly enriched in serodominant , serodiagnostic and cross - reactive antigens groups , with enrichment fold at 4.3 , 5.0 , and 4.0 , respectively . interestingly , proteins with more than 1 transmembrane domain were also significantly underrepresented among the serodominant and cross - reactive antigens . proteins with predicted signal peptides ( signalp score > 0.7 ) were significantly enriched in all three groups at a range of 2.8- to 3.6-fold . conversely , proteins without signal peptides ( signalp score < 0.7 ) were significantly underrepresented . psortb predicted 4 serodiagnostic and 5 serodominant outermembrane antigens , resulting in 11.5- and 3.9-fold enrichment , respectively . however , psortb cytoplasmic proteins were 0.5- to 0.7-fold underrepresented in serodominant and serodiagnostic antigens groups . we also found that proteins with isoelectric points lower than 5 were 1.7- to 2.0-fold enriched in serodominant and cross - reactive antigen groups , whereas , proteins with pi = 9 to 14 were 0.6- and 0.5-fold underrepresented in these two groups . another potential feature that could account for protein antigenicity is the level of in vivo expression ; proteins expressed at a high level in vivo would be expected more likely to be seen by the immune system than proteins expressed at a low level . to test this hypothesis , we compared the group of antigenic b. melitensis proteins with an existing data set of expressed protein peptide data from a very closely related species , b. abortus . in this study , cytosolic proteins and cell envelope proteins from b. abortus in the log phase of in vitro growth , were extracted and subjected to lc mass spectrometry ( ms ) analysis as described in materials and methods . the number of different peptides identified for each protein was listed in table s4 ( supporting information ) . two - hundred forty proteins were exclusively expressed in the cytosol of b. abortus with 1 to12 detected peptides , and 53 proteins exclusively expressed in the cell envelope of b. abortus with 1 to 15 detected peptides , and 80 overlapping proteins expressed in both conditions . of these , 356 proteins were printed on our proteome chip . not surprisingly , expression was a significant enriching feature with 5.2-fold enrichment among serodiagnostic antigens ( p - value 1.87 10 ) , and 2.9-fold in serodominant antigens ( p - value 5.28 10 ) ( table 1 ) . interestingly , the fold enrichment was directly proportional to the number of peptides detected ( figure 5c ) . there was 8.4- fold enrichment of serodiagnostic antigens in proteins detected with more than 1 peptide ( p - value 3.56 10 ) , 16.2- fold in proteins detected with 5 or more peptides ( p - value 1.30 10 ) , 23.1- fold enrichment in proteins detected with 7 or more peptides ( p - value 1.90 10 ) , and 20.5-fold enrichment in proteins detected with 9 or more peptides ( p - value 3.91 10 ) . conversely , proteins that were not identified by ms were significantly underrepresented at 0.4-fold among the serodiagnostic and 0.8-fold among serodominant antigens . the data suggests that protein expression level is an important factor contributing to antigenicity of protein antigens . this was also supported by data in other experimental systems from different research groups.(55 ) significant enrichment or underrepresentation for certain features are underlined and bold . there are a total of 10 enriching features that fall into 3 categories : ( i ) functionally annotated cogs u , m , n and o , ( ii ) computationally predicted features ( tmhmm = 1 , signalp > 0.7 , psort outermembrane , psort periplasmic , and pi < 5 ) , and ( iii ) ms evidence of expression . the venn diagrams summarize the number of enriched proteins found in each of these 3 categories , showing overlap among the proteins found in each category ( figure 6 ) . there are 338 proteins in the enriched cog categories , 696 computationally predicted proteins , and 356 proteins that were positive by ms ( table 2 ) . accounting for the overlap between categories , 1128 proteins in all enriched categories represented 37% of the proteome . cogs accounted for 30% of the serodiagnostic hits , the computationally predicted features accounted for 61% of the hits , and ms positive proteins contained 61% of the hits . all together the three categories account for 37% of the proteome and include 91% of the serodiagnostic antigens . but there is only 1 unique serodiagnostic cog antigen that is not represented in either the computationally predicted or ms+ categories ( bmei1060 , table s1 , supporting information ) . so by combining the pool of computationally predicted and ms+ proteins representing 30% of the proteome , 88% of the serodiagnostic antigens can be predicted . enriching features are classified into three categories : ( 1 ) cogs - umno , for proteins assigned to one or more of these four cogs ; ( 2 ) computational predictions with enriching features , for proteins predicted to have one or more of the following features , that is , tmhmm = 1 , signalp > 0.7 , psort outermembrane , psort periplasmic , or pi < 5 , and ( 3 ) protein expression as detected by peptide presence in mass spectrometry . separately shown are numbers of antigens with enriching features , including all such 1128 antigens on chip , 99 serodominant , and 30 serodiagnostic antigens . numbers of antigens having more than one category of enriching features are also presented in the overlapping region of such categories . enriching features are classified into three categories : ( 1 ) cogs - umno , for proteins assigned to one or more of these four cogs ; ( 2 ) computational predictions with enriching features , for proteins predicted to have one or more of the following features , i.e. , tmhmm = 1 , signalp > 0.7 , psort outermembrane , psort periplasmic , or pi < 5 ; and ( 3 ) protein expression as detected by mass spectrometry . today with increasing efficiency , accuracy and speed we access completed genome sequences from thousands of infectious microorganisms . however , systems- level studies to understand the complete network of antibody responses have not been widely performed . this work was motivated by the disturbing lack of a detailed scientific understanding of the antibody responses to infectious diseases . we have been taking a systems biology approach to account for all of the antibodies that develop after exposure to infectious microorganisms and to identify specific antibody signatures associated with each disease , in order to understand the molecular basis for antigen selection by the immune system and to predict serodiagnostic and vaccine antigens targets . our previous study identified a set of serodiagnostic antigens from a randomly selected half of the b. melitensis proteome . however , an important difference between the present study and this previous report is that analysis of the complete proteome not only has allowed us to delineate additional serodiagnostic antigens but , more fundamentally , also provided the basis for a rigorous , comprehensive and quantitative determination of basic biological characteristics of the entire set of the serodominant antigens on a genomic level . the current standard serological screening assay , an agglutination test that uses tinted , killed bacteria as antigen ( rose bengal ) is based primarily on identification of antibodies to lps in patient serum . in the present microarray study , we confirmed lps reactivity ( with purified lps spotted onto the microarray ) , and identified novel protein antigens . although antibody responses against all 33 protein antigens used together can predict disease with 92% accuracy , using the serological responses against the top 3 individual antigens together improves accuracy to > 98% for diagnosis of acute human brucellosis . one limitation is that the humans studied here only had acute or subacute brucellosis - fever but not focal or chronic disease . future studies are needed to assess suspected cases that are agglutination test negative , for example chronic neurobrucellosis or focal disease such as orchitis or vertebral osteomyelitis . eleven of the 33 serodiagnostic antigens identified in this study were also identified on the pilot array(5 ) ( table s1 , supporting information ) . our findings are in good agreement with published studies that identified well characterized antigens from other brucella spp , including bp26 ( bmei0536 ) , htra / degp ( bmei1330),(28 ) omp16 ( bmei0340),(29 ) the chaperonin groel protein ( bmeii1048 ) and omp 10 ( bmeii0017 ) . in addition to the well characterized antigens , we also identified 21 novel serodiagnostic antigens on the current array , including top antigen hypothetical protein bmei0805 . two pyruvate dehydrogenase complex molecules and the associated acetyl coa hydrolase , which together form a large multimeric structure consisting of 60 subunits , are also differentially recognized ; this large enzyme complex is found in most bacteria and is frequently a target of immune recognition for other infections . protein microarrays enable enrichment analyses to identify proteomic features that are enriched in the immunodominant antigen set , and development of protein antigenicity prediction tools based on enriched features . the prediction tools then can be applied on a high - throughput scale to existing or new proteomes to identify key antigenic proteins that may have serodiagnostic or protective characteristics . the proteomic features fall into 3 categories : ( i ) cog annotations , ( ii ) computationally predicted proteomic features , and ( iii ) proteins with ms evidence of expression in viable organisms . no single proteomic feature or category of features is sufficient to identify all these signature antigens . our data suggests that cloning of 37% of genome with these enriching features would reveal more than 90% of serodiagnostic antigens . we have classified the reactive immunodominant antigens for numerous agents and have consistently found these features predict antigenicity . these results describe the relationship between antigenicity and in vivo expression of individual proteins . in our study , we utilized the expression of proteins quantified by ms of a closely related strain , b. abortus during in vitro growth . we found that mass spec positive antigens were significantly enriched among serodiagnostic antigens but not among the cross- reactive antigens . this validates the classification of the serodiagnostic antigens being derived from actively replicating organisms , and validates the classification of cross - reactive antigens being derived from previous exposure to nonbrucellosis infections . although the number of peptides observed per protein has been applied to estimating protein abundance , we are aware that mass spectra of cultured organisms may not reflect the expression during infection in vivo . first , nutrients are not limiting in log phase growth in vitro , whereas in vivo , brucella is likely to be within a nutrient - limited intracellular environment.(63 ) second , the ms method may not be particularly quantitative , especially for membrane proteins . our protein array technology is also able to provide strong evidence of the comprehensive set of proteins expressed in vivo within a mammalian host by b. melitensis , by virtue of their exposure to the host immune system . the expression and abundance of proteins during in vivo growth merits further examination by other novel technologies , such as measurement of transcript abundance from rna - seq ( deep sequencing ) technique.(64 ) the b. melitensis immunoproteome comprises 1464 antigens that are significantly reactive in at least one of the individuals in this study . answers to questions of why and how the immune system focuses on 4% of the potential target antigens are not yet apparent from this work . one might expect that an immune response against a larger collection of antigens could result in a more effective immune response attack against the infectious agent . but antibody responses against thousands of antigens from hundreds of clinical infections could accumulate during a lifetime , leading to cross reactivity against autologous antigens and autoimmune chaos . the observation that dozens of organism- specific antibody responses develop after b. melitensis infection is consistent with similar observations from other infectious agents , and has implications for subunit vaccine discovery and development . mimicking the natural response to infection could be considered a viable strategy for vaccine development but most subunit vaccines aim to derive protection from immunization with only a single antigen . attenuated or killed whole organism vaccines produce an antibody reactivity profile against dozens of antigens more similar to natural infection.(6 ) this systematic genome scale analysis of human antibody responses against b. melitensis proteins provides a top hit list of antigens worthy of assessing for improved diagnostics , and furthermore , enables development of a predictive model of proteomic features that determine whether a protein is antigenic and produces antibodies that confer protection . this systems biology approach provides an empirical basis for understanding the breadth and specificity of the immune response to b. melitensis and a new framework for comparing the humoral responses against other organisms .

a complete understanding of the factors that determine selection of antigens recognized by the humoral immune response following infectious agent challenge is lacking . here we illustrate a systems biology approach to identify the antibody signature associated with brucella melitensis ( bm ) infection in humans and predict proteomic features of serodiagnostic antigens . by taking advantage of a full proteome microarray expressing previously cloned 1406 and newly cloned 1640 bm genes , we were able to identify 122 immunodominant antigens and 33 serodiagnostic antigens . the reactive antigens were then classified according to annotated functional features ( cogs ) , computationally predicted features ( e.g. , subcellular localization , physical properties ) , and protein expression estimated by mass spectrometry ( ms ) . enrichment analyses indicated that membrane association and secretion were significant enriching features of the reactive antigens , as were proteins predicted to have a signal peptide , a single transmembrane domain , and outer membrane or periplasmic location . these features accounted for 67% of the serodiagnostic antigens . an overlay of the seroreactive antigen set with proteomic data sets generated by ms identified an additional 24% , suggesting that protein expression in bacteria is an additional determinant in the induction of brucella - specific antibodies . this analysis indicates that one - third of the proteome contains enriching features that account for 91% of the antigens recognized , and after b. melitensis infection the immune system develops significant antibody titers against 10% of the proteins with these enriching features . this systems biology approach provides an empirical basis for understanding the breadth and specificity of the immune response to b. melitensis and a new framework for comparing the humoral responses against other microorganisms .

the angular correlation function of galaxies has been used to characterize the large - scale distribution of galaxies for over 2 decades . if the number density on the sky at angular position @xmath4 is @xmath5 , then @xmath0 is defined as @xmath6 the 3-dimensional unit vectors @xmath4 and @xmath7 are used to define the angular separation @xmath8 as @xmath9 , and @xmath10 is the mean galaxy number density on the sky . the observed galaxy distribution is well described by a power law @xmath11 , with slope @xmath12 . since @xmath0 is a projection on the sky of the 3-dimensional auto - correlation function @xmath13 , the above power law for @xmath0 has been associated with a power law for @xmath14 with slope @xmath15 which is close to the observed value in the nearby galaxy distribution . measurements of @xmath0 are difficult to interpret as it involves a projection of the galaxy distribution out to redshifts of order 1 ( e.g. for a sample with limiting @xmath3 magnitude of about 24.5 ) . thus the effects of evolution of large scale structure due to gravitational clustering as well as galaxy evolution need to be understood to interpret @xmath0 . recently villumsen ( 1996 ) has considered the effect on @xmath0 of gravitational lensing by large - scale structure along the line of sight ( gunn 1967 ) . lensing increases the area of a given patch on the sky , thus diluting the number density . on the other hand , galaxies too faint to be included in a sample of given limiting magnitude are brightened due to lensing and may therefore be included in the sample . the net effect , known as magnification bias , can go either way : it can lead to an enhancement or suppression of the observed number density of galaxies , depending on the slope of the number - magnitude relation . variations in the number density which are correlated over some angular separation alter @xmath0 . villumsen ( 1996 ) showed how the linear evolution of density fluctuations along the line of sight can be used to compute the change in @xmath0 due to magnification bias . the deflections of neighbouring photon trajectories due to lensing by large scale structure are very small , hence the calculation can be done in the limit of weak lensing . in this paper we compute @xmath0 for different cosmological models taking into account the effects of nonlinear gravitational evolution and gravitational lensing . since @xmath0 is a 2-point statistic , even in the fully nonlinear regime it is determined completely by the 3-dimensional power spectrum . we use extensions of the proposal of hamilton et al . ( 1991 ) to include the nonlinear evolution of the power spectrum into the calculation of @xmath0 . we also include the dependence on the cosmological parameters @xmath16 and @xmath17 . in section 2 the formalism for computing @xmath0 is presented . section 2.1 discusses the effects of the cosmological model via the growth of density perturbations and the distance - redshift relation . results for cdm - like power spectra for different values of @xmath16 and @xmath17 are presented in section 3 . we explore ways to isolate the effect of the lensing contribution to @xmath0 in section 4 and conclude in section 5 . the effect of magnification bias due to weak gravitatinal lensing on the galaxy angular correlation function @xmath0 has been derived in villumsen ( 1996 ) . written in terms of the time - dependent power spectrum instead of the present day one , which makes it applicable to nonlinear power spectra , @xmath0 is given by @xmath18 ^ 2 \nonumber \\ & & \times \int_0^\infty dk\ , k\ , { p(\chi , k)\over a^2(\chi)}\ , j_0\left[k r(\chi)\theta\right]\ , . \label{wfull}\end{aligned}\ ] ] in this section the physical meaning of the various terms in the above equation and the notation used will be clarified . we have used the notation of jain & seljak ( 1997 ) , where @xmath19 is the radial comoving distance , @xmath20 that to the horizon , @xmath21 is the comoving angular diameter distance , @xmath22 the normalized radial distribution of galaxies in the sample , and @xmath23 from the expression for the unperturbed line element @xmath24 @xmath25 being conformal time , it follows that @xmath26 where @xmath27 is the spatial curvature . note that for a delta - function distribution of galaxies , @xmath28 , @xmath29 reduces to @xmath30 . this notation is related to the one of villumsen ( 1996 ) through @xmath31 , @xmath32 , @xmath33 and @xmath34 . first we shall briefly describe the effect of magnification bias on @xmath0 . gravitational lensing of a galaxy by dark matter concentrations between us and the galaxy increases the area of the galaxy image while conserving surface brightness . this results in a magnification @xmath35 which is given by the ratio of lensed to unlensed area of the image . the amplitude of @xmath35 depends on the convergence @xmath36 , which is the surface mass density divided by the critical density , and the shear @xmath37 through ( young 1981 ) = [ mugen ] in the limit of weak lensing , @xmath38 , applicable to lensing by large - scale structure , the above expression reduces to = 1 + 2[mu ] this magnification has two effects . since the lensed area is increased due to deflection of the light rays , the number density of galaxies decreases inversely proportional to @xmath35 . there is a competing effect , however . in a flux limited survey , magnification brings some faint galaxies above the flux limit , which would not otherwise have been detectable , thus increasing the number density of galaxies . which of the effects wins depends on the reservoir of faint galaxies available , which can be quantified by the slope @xmath39 of the true number counts @xmath40 for a magnitude limit @xmath41 , s= . the two effects change the galaxy numbers by ( e.g. broadhurst , taylor & peacock 1995 ) n^(m)=n_0(m ) ^2.5s-1 which reduces to n^(m)=n_0(m)[np ] in the weak lensing limit . in addition , the number density of galaxies is changed by @xmath42 due to intrinsic clustering . let @xmath10 denote the average number density of galaxies . at a given position in the sky @xmath43 , the number density is thus changed to n()=|n ( 1 + n ( ) + 5(s-0.4 ) ( ) ) . [ nth ] now we further assume that galaxies trace the underlying dark matter distribution so that the 3-dimensional galaxy overdensity is , _ g(x ) = b ( x ) , where @xmath44 is the dark matter overdensity and the bias @xmath45 is the proportionality factor . in this linear bias model , the perturbed , projected number density is given by ( villumsen 1996 ) n()= b _ 0^_h d w ( ) ( r ( ) ) . [ ndelta ] whereas the convergence @xmath36 is given by ( villumsen 1996 ) ( ) = _ 0^_h d g ( ) . [ kappa ] the angular correlation function @xmath0 as defined in equation [ wthav ] involves the expectation value @xmath46 . since both @xmath42 due to intrinsic clustering , and @xmath36 are related to @xmath47 according to eqs . [ ndelta ] and [ kappa ] , intrinsic dark matter correlations will induce correlations among galaxies . there are three distinct effects : correlations among the galaxies tracing correlated dark matter densities , described by @xmath48 ; among background galaxies being lensed by correlated dark matter concentrations , described by @xmath49 ; and finally among background galaxies and the foreground galaxies tracing the correlated dark matter concentrations , which are responsible for the lensing of the background galaxies , described by the term @xmath50 . the expressions for @xmath51 , @xmath52 and @xmath53 from the above equations are inserted into eq . [ wthav ] . expressing @xmath44 in terms of its fourier transform @xmath54 and performing the ensemble average @xmath55 then introduces the power spectrum @xmath56 . one finally obtains the result of eq . [ wfull ] ( villumsen 1996 ) by evaluating the integrals , under the further assumption of @xmath57 , and using the plane - parallel approximation that only fourier modes with wave vectors nearly perpendicular to the line of sight @xmath43 contribute to the integral . in the previous paragraphs we discussed the origin of the three terms in the angular correlation function , obtained by multiplying out the squared bracket in eq . [ wfull ] . we can write them schematically as , @xmath58 the third term @xmath59 is proportional to the correlation function @xmath60 of galaxy image ellipticities ( villumsen 1996 ) , _ ll ( ) = ( 2.5s-1)^2 c_pp ( ) , the dependence of this term on @xmath61 and @xmath62 is discussed in detail in jain & seljak ( 1997 ) ( see also bernardeau et al . 1997 ; kaiser 1996 ) . with the assumption of constant linear bias , we can factor out the constants involving bias , @xmath39 and @xmath16 , and write @xmath0 as @xmath63 \ ; . \label{wtilde}\end{aligned}\ ] ] besides the explicit @xmath61 dependence , @xmath0 depends on @xmath61 and @xmath62 mainly through the evolution of the power spectrum and the dependence of @xmath21 on @xmath16 and @xmath17 . in the linear regime the power spectrum depends on the linear growing mode of density perturbations @xmath64 and the normalization @xmath65 as , p(,k ) ^2 . the linear growing mode is well approximated by ( carroll , press & turner 1992 ) @xmath66^{-1 } \ ; , \end{aligned}\ ] ] where we have defined , following mo , jing & boerner ( 1997 ) , the time dependent fractions of density in matter and vacuum energy , @xmath67 and @xmath68 in terms of the present - day values @xmath61 and @xmath62 , ( a)= and ( a)= . the spatial geometry also differs in different models , leading to a dependence of the angular distance @xmath21 on @xmath61 and @xmath62 according to eq . these effects are contained in the terms @xmath69 , @xmath70 and @xmath71 in eq . [ wtilde ] . on small scales ( high-@xmath72 ) the growth of the power spectrum is significantly affected by nonlinear gravitational clustering . the nonlinear power spectrum is obtained from the linear one through the fitting formulae of jain , mo & white ( 1995 ) for @xmath73 , and from those of peacock & dodds ( 1996 ) for the open and @xmath74 dominated models . these fitting formulae are based on the idea of relating the nonlinear power spectrum at scale @xmath72 to the linear power spectrum at a larger scale @xmath75 , where the relation @xmath76 depends on the power spectrum itself ( hamilton et al . 1991 ) . they have been calibrated from and tested extensively against n - body simulations . for the linear power spectrum we take a cdm - like spectrum ( bardeen et al . 1986 ) with shape parameter @xmath77 , which provides a reasonable fit to the observed galaxy power spectrum . with this choice of the linear power spectrum , we use the fitting formulae for the fully nonlinear power spectrum as a function of @xmath78 and @xmath72 to evaluate equation [ wfull ] for @xmath0 . having specified the shape of the mass power spectrum , we need to set the global cosmological parameters @xmath16 and @xmath17 . the normalization of the power spectrum in turn will depend on these parameters . the four different cosmological models we consider include : a flat universe with @xmath79 , an open model with @xmath80 , and a flat @xmath74 dominated model , with @xmath80 and @xmath81 . these three models are normalized to cluster abundances , which give the approximate relation ( white et al . 1993 ; viana & liddle 1996 ; eke , cole & frenk 1996 ; pen 1996 ) : @xmath82 ( for @xmath80 , we use @xmath83 , which is slightly lower than given by the above relation . ) our fourth model is a flat universe , @xmath73 , with a higher normalization of @xmath84 . while the cosmological model is specified above , the galaxy population still needs to be described in terms of its redshift distribution , the number count slope @xmath39 and the bias parameter @xmath45 . we model the redshift distribution of galaxies by @xmath85 } \exp(-(z / z_0)^{\beta})\ ; , \label{nz}\ ] ] for @xmath86 , which agrees reasonably well with the redshift distribution estimated for the hubble deep field from photometric redshifts ( mobasher et al . , 1996 ) . @xmath22 is related to the redshift distribution by @xmath87 , where the expressions for the hubble constant @xmath88 and the radial comoving distance @xmath89 depend on the background cosmology . the mean redshift is given by @xmath90 for a flat model with @xmath79 , we obtain the @xmath3 magnitude limit corresponding to a given mean redshift by interpolation of a set of estimated values from charlot ( 1996 ) . in this section we consider red and blue galaxy populations , with number count slopes @xmath91 and @xmath92 respectively , and a fixed bias @xmath93 for both samples . in the next section we will consider the more realistic case of a relative bias for the different colour samples , since red galaxies are more strongly clustered . figure [ wtheta1 ] shows @xmath0 for the @xmath73 , @xmath84 model . the linear and nonlinear predictions , shown by the solid and dashed curve , are compared with a power law shape with slope @xmath94 . these curves are for @xmath95 , for which the lensing term drops out , and therefore show the contribution of the clustering term to @xmath0 . the effect of nonlinear evolution enhances @xmath0 for @xmath96 , while it slightly suppresses @xmath0 for @xmath97 . on larger scales the linear and nonlinear curves coincide . it is interesting that the nonlinear @xmath0 is much closer to the observed power law than the linear curve which reflects the curvature of the cdm power spectrum . at large angles , @xmath98 the @xmath0 curve starts to deviate from the power law shape . for the open and @xmath2 dominated models , the results are similar , with the nonlinear contribution being larger than the @xmath73 model . in fig . [ wtheta ] we show how lensing affects @xmath0 in the flat @xmath79 cosmological model , for three values of the number count slope @xmath99 , @xmath100 , and @xmath95 . the mean redshift is @xmath101 , corresponding to an @xmath3 magnitude limit of about @xmath102 . the @xmath95 curve represents the intrinsic clustering as in the previous figure . for @xmath103 , the amplitude of @xmath0 is increased due to lensing , and for @xmath104 it is decreased . magnification bias hardly changes the shape of @xmath0 since the three curves are nearly parallel to each other . in fig . [ wintrinsic ] we show the dependence of @xmath0 on mean redshift of the sample . the contribution due to intrinsic clustering is shown for the four cosmological models , i.e. setting @xmath95 . three values of @xmath8 are shown , ranging from @xmath105 , where nonlinear effects are important , to @xmath106 where nonlinear effects become unimportant . at @xmath105 , the models with low @xmath61 have higher amplitudes than the models with @xmath73 . this is because in the former models the growth of perturbations is slowed down at late times ; when normalizing to present - day cluster abundances , this implies a higher normalization at earlier times compared to the @xmath73 models . this in turn means that nonlinear effects become important earlier on , and lead to a greater effect of nonlinear clustering by today . at large mean redshifts , however , the amplitude for the @xmath74model dips below the @xmath73 , @xmath84 model . here a competing geometrical effect starts to come in : at a given redshift a physical volume element is larger if @xmath107 than in the absence of a cosmological constant , and therefore the intrinsic clustering is decreased . for @xmath106 , this geometrical effect in the @xmath74model is more noticeable and starts to be seen at lower mean redshifts because competing nonlinear effects are unimportant . in fig . [ wauto2 ] we plot @xmath108 as a function of mean redshift for three values of @xmath39 , as in fig . [ wtheta ] , and for all four cosmological models . for the @xmath79 models , we also give the @xmath3 magnitude limits inferred from charlot ( 1996 ) on the top axis of the plot , corresponding to the mean redshifts shown on the bottom axis . these values are given as an orientation only , since the relation between @xmath3 magnitude and mean redshift is not exactly linear , and depends on the model of galaxy evolution used to derive it . we can understand these results better by looking at the three terms of @xmath0 in eqs . [ wterms ] and [ wtilde ] separately . at low mean redshifts , the intrinsic clustering term @xmath109 dominates , but it decreases with redshift . at low @xmath110 the cross - term @xmath111 is much smaller than the intrinsic term , but it is approximately constant with redshift ; @xmath112 is even smaller than the cross - term due to the small lensing depth at small mean redshift , but it increases with @xmath113 . as the mean redshift of the sample increases , @xmath109 drops , and the cross - term starts to become noticeable . the cross - term contains the factor @xmath114 , so that for @xmath115 , @xmath0 is increased with respect to the intrinsic contribution due to lensing , and for @xmath116 it is decreased . also , the redshift at which this happens is larger for smaller @xmath16 and @xmath117 . at still larger @xmath110 , @xmath112 has increased sufficiently to become noticeable as well . since @xmath118 is always positive , its effect goes in the same direction as that of the cross - term for @xmath119 . but for @xmath116 , its effect is in the opposite direction to that of the cross - term , so that the decrease due to @xmath111 is partly compensated . the flat model with the higher normalization @xmath84 shows a stronger lensing signal than the one with the lower @xmath120 , because the bias factor @xmath93 is smaller , which increases the lensing contribution from the cross - term @xmath121 relative to the intrinsic clustering term @xmath122 . in the open or @xmath74 model , as compared to the flat model , the change in growth rate of perturbations and the spatial geometry affect the intrinsic clustering part of @xmath0 as discussed above . the geometric effect for @xmath107 , which decreases the intrinsic clustering , is the opposite of the lensing part . since the volume element is larger , the optical depth to lensing is larger , and lensing is more effective . this explains why the amplitudes for red and blue samples deviate more strongly than in the @xmath73 case in spite of the extra factor of @xmath61 in front of the cross - term @xmath123 . for the open model also this geometric effect is present , and compensates for some of the decrease due to the @xmath61-prefactor , but it is weaker than in the @xmath2 model . the results presented so far for @xmath0 include the contribution from intrinsic clustering and from lensing . it is interesting to consider measurable statistics that are more sensitive to the lensing contribution ; in this section we show that the ratio of @xmath0 for red and blue samples is one such example . we assume the presence of a population of blue galaxies with a number count slope @xmath92 out to @xmath124 , and also of a population of red galaxies with a slope of @xmath91 . a sample with such a slope may be obtained by defining color selected subsamples @xcite , using the fact that the number count slope is a decreasing function of @xmath125 color @xcite . since red and blue galaxy samples are observed to have a relative bias at present , with red galaxies being more strongly clustered ( they are more likely to be found in the centers of clusters ) than blue ones , in this section we consider a bias factor for the red sample @xmath126 which is larger than the bias @xmath127 of the blue sample . we assume the individual biases to be constant in time , and we neglect possible physical evolution of the spatial correlation function ( besides the one due to gravitational evolution ) . in the absence of lensing , and assuming one has selected samples with the same redshift distribution , the ratio of @xmath0 of the blue and red samples would be equal to the ratio of their relative biases squared , @xmath128 however , lensing changes this relationship . in the regime where the cross - term dominates the third term , the lensing contribution increases @xmath0 for the blue , and decreases it for the red sample . in fig . [ wratio ] we plot @xmath129 , which ought to be equal to @xmath101 in the absence of lensing , versus mean redshift for @xmath130 , and a relative bias of two of the red and blue samples . the four curves show the results for the different cosmological models considered ( see section 2 ) . we can see that there is only little variation with angle as expected from the results of fig . [ wtheta ] . for intermediate mean redshifts @xmath131 we can neglect the @xmath112term , and expand in the small quantity @xmath132 to see the dependence on bias factors and number count slope , @xmath133 \frac{\tilde{w}_{gl}(\theta)}{\tilde{w}_{gg}(\theta ) } \right)\nonumber \\ & & \times \left ( \frac{b_b}{b_r}\right)^2 \ ; .\end{aligned}\ ] ] for @xmath134 , @xmath112 can no longer be neglected . as discussed in the previous section , this term has the effect of compensating some of the decrease in amplitude of @xmath0 due to the cross - term for the red sample , and the exact redshift at which this happens depends on @xmath16 and @xmath135 . this effect is responsible for the flattening off of the ratio seen in fig . [ wratio ] . at still larger redshifts , ( not plotted here ) , the ratio would decrease again . as discussed in section 3 , for the open and @xmath74dominated models , both the growth rate of perturbations and the spatial geometry are different from the @xmath73 model . by taking the ratio of two correlation functions , the effect of the growth rate cancels out , so that we are left with the effect of the different geometries on the three terms . for the @xmath74dominated model the geometrical effect is largest , so that in spite of the factor of @xmath61 in the cross - term , the ratio is larger than for the flat model normalized to @xmath120 . it even attains a value comparable to the @xmath73 model with the higher normalization of @xmath84 . recall that a larger @xmath65 favors the lensing contribution over the intrinsic clustering since the bias factor @xmath93 is smaller , and @xmath121 whereas @xmath122 . for the open model the geometrical effect is not as important , and the ratio is below that for the flat case . we have quantified the effect of gravitational lensing by large - scale structure on the angular correlation function of galaxies @xmath0 , for different cosmological models , on angular scales ranging from @xmath136 to @xmath137 . we have taken into account nonlinear gravitational clustering which affects both the intrinsic clustering and lensing contributions to @xmath0 . we find that the ratio of the angular correlation function for red and blue galaxy samples , normalized by the inverse of the relative bias of the two samples , deviates from the value of @xmath101 expected in the absence of lensing at sufficiently large mean redshifts of the sample . for a mean redshift of 1.3 of the sample , this ratio rises to about @xmath138 for the model with @xmath73 and @xmath84 , and continues to rise , flattening off , until it reaches @xmath139 by a mean redshift of 2 . at @xmath140 it rises to about @xmath141 for the model with @xmath73 and @xmath120 , and to about @xmath142 for the open model . in the @xmath74dominated model , the ratio reaches a value of about @xmath143 at @xmath140 , and continues to rise to a value of about @xmath144 at a mean redshift of 2 . these values are at @xmath136 angular separation ; for larger angles they differ somewhat , but not to a great extent as shown in fig . [ wratio ] . the largest uncertainty in the application of this result is due to the assumption of two populations with different number count slopes but the same redshift distribution with @xmath145 . the effect of magnification bias on the angular correlation function could be used in future surveys , such as the eso imaging survey ( renzini et al . 1996 ) , to detect weak lensing by large - scale structure and constrain the cosmological parameters @xmath61 and @xmath62 . the eso imaging survey aims to detect about 200 - 300 galaxies with redshifts between @xmath101 and @xmath146 in a field of 25 arcminutes squared , and a similar number with redshifts larger than @xmath146 in a field ten times larger . one problem with trying to detect the effect of magnification bias on @xmath0 is that unknown physical evolution of the galaxies can modify the intrinsic clustering and introduce uncertainties which may be larger than the lensing signal . the presence of bias evolution would introduce further uncertainties . in future work , we plan to study the cross - correlation of two galaxy samples with different mean redshifts and non - overlapping redshift distributions ( moessner & jain 1997 ) . in this way we hope to minimize the importance of uncertainties due to intrinsic clustering and the exact form of the redshift distribution , and propose a measurable statistic that is dominated by the lensing contribution . we would like to thank matthias bartelmann , teresa brainerd , peter schneider , uro seljak and simon white for useful discussions .

the angular correlation function @xmath0 of faint galaxies is affected both by nonlinear gravitational evolution and by magnification bias due to gravitational lensing . we compute the resulting @xmath0 for different cosmological models and show how its shape and redshift evolution depend on @xmath1 and @xmath2 . for galaxies at redshift greater than 1 ( @xmath3 magnitude fainter than about 24 ) , magnification bias can significantly enhance or suppress @xmath0 , depending on the slope of the number - magnitude relation . we show for example how it changes the ratio of @xmath0 for two galaxy samples with different number - count slopes . galaxies : clustering - cosmology : observations - gravitational lensing - large scale structure of the universe

phase - change materials based on chalcogenide alloys are attracting an increasing interest worldwide due to their ability to undergo reversible and fast transitions between the amorphous and crystalline phases upon heating @xcite . this property is exploited in rewriteable optical media ( cd , dvd , blu - ray discs ) and electronic nonvolatile memories ( nvm ) , which are based on the strong optical and electronic contrast between the two phases @xcite . the material of choice for nvm applications is the ternary compound ge@xmath0sb@xmath0te@xmath1 ( gst ) . however , the related binary alloy gete has also been thoroughly investigated because of its higher crystallization temperature and better data retention at high temperature with respect to gst . in the last few years atomistic simulations based on density functional theory ( dft ) have provided useful insights into the properties of phase change materials @xcite . however , several key issues such as the thermal conductivity at the nanoscale , the crystallization dynamics , and the properties of the crystalline / amorphous interface , just to name a few , are presently beyond the reach of ab initio simulations due to the high computational costs . the development of reliable classical interatomic potentials is a possible route to overcome the limitations in system size and time scale of ab initio molecular dynamics . however , traditional approaches based on the fitting of comparably simple functional forms for the interatomic potentials are very challenging due to the complexity of the chemical bonding in the crystalline and amorphous phases revealed by the ab initio simulations . a possible solution has been proposed recently by behler and parrinello @xcite , who developed high - dimensional interatomic potentials with close to ab initio accuracy employing artificial neural networks ( nn ) . to date , potentials of this type have been reported for silicon @xcite , carbon @xcite , sodium @xcite , zinc oxide @xcite and copper @xcite by fitting large ab initio databases . here we describe the development of a classical interatomic potential for the bulk phases of gete employing this nn technique . the potential is validated by comparing results on the structural and dynamical properties of liquid , amorphous and crystalline gete derived from nn - based simulations with the ab initio data obtained in our previous work @xcite . artificial neural networks constitute a class of algorithms inspired by the properties of biological neural networks , which are widely applied in many different fields ranging from weather forecasting to robotics @xcite . in the last few years , nn have also been used as a tool to construct interatomic potentials @xcite to this aim , the nn are exploited as a non - linear technique that allows fitting any real - valued function to arbitrary accuracy , without any previous knowledge about the functional form of the underlying problem @xcite . in our case , this function is the potential energy surface ( pes ) of the atomistic system and the goal of the nn is to construct a functional relation between the energy and the atomic configuration . given a number of atomic configurations , for which the ab initio energies are known , the nn parameters are adjusted to reproduce these energies in the training process . overfitting , i.e. , obtaining a good fit of the training data , but performing less accurately when making predictions is controlled by testing the performance of the nn for an independent test set not used in the fitting . once trained , the nn performs an interpolation to construct the potential energy for new atomic configurations at a low computational load , which allows performing long molecular dynamics runs for large systems . the nn methodology overcomes many problems associated with classical potentials . first and foremost , nn completely obviate the problem of guessing a complicated functional form of the interatomic potential . this form is determined automatically by the nn . moreover , the entire training procedure is fully automated so that nn can be readily extended to new regions of the pes . finally , the accurate mapping of ab initio energies ensures that all properties determined by the topology of the pes are described with an accuracy comparable with that of first principles calculations . nn have been successfully used to interpolate the pes of simple chemical systems like small molecules @xcite and molecule - surface interactions @xcite . until recently , the main limitation of most nn approaches has been the small number of degrees of freedom that could be described , which confined their application to very small systems . this limitation has been overcome by behler and parrinello who introduced a nn potential , in which the total energy is expressed as a sum of atomic energy contributions depending on the local environments @xcite . in this approach the energy contribution of each atom is evaluated using an individual nn instead of using one nn for the total energy of the system . the local environment of a given atom is described by a set of local parameters called symmetry functions , which include radial and angular many - body terms and depend on the positions of all neighbors within a specified cutoff radius @xcite . the use of symmetry functions instead of cartesian coordinates as nn inputs and the partitioning of the total energy into atomic contributions ensures that all quantities computed with the nn potential , such as energies , analytical forces , and stress tensor are invariant to translations , rotations , and atoms exchange . furthermore , once the fit is obtained , the nn potential can be applied to systems containing an arbitrary number of atoms . the validity of this approach has been demonstrated by reproducing the high - pressure phase diagram of silicon , carbon , and sodium @xcite . this scheme has been recently extended to binary systems by including long range coulomb interaction between environment dependent ionic charges @xcite . in the case of gete , we are faced with the problem of developing a potential suitable to describe both the semiconducting crystalline and amorphous phases as well as the metallic liquid . as a first step toward the development of a nn potential for gete , we neglect long - range coulomb interactions for atoms being separated by a larger distance than the cutoff radius of the symmetry functions . the resulting `` short - ranged '' nn potential just consists of atomic energy contributions arising from the local chemical environments , but it is important to note that also short - ranged electrostatic interactions are fully taken into account implicitly . more details of the employed method can be found elsewhere @xcite . the resulting potential will not be able to describe the dielectric response and lo - to splitting of crystalline gete in its ferroelectric phase , but it will be suitable to reproduce structural properties of the liquid , amorphous and crystalline phases and the dynamical properties of the disordered phases . to generate the nn potential , we fitted the total energies of about 30.000 configurations of 64- , 96- and 216-atom supercells computed by dft . we started with a relatively small dataset of about 5.000 structures , where we considered crystalline configurations , snapshots of the liquid phase and of the amorphous phase generated by quenching from the melt at ambient conditions and at different pressures up to 50 gpa . we also considered mixed crystalline / amorphous models generated by partially crystallizing the amorphous phase by means of the metadynamics technique @xcite . all these configurations were generated within ab initio molecular dynamics simulations at different temperatures ( up to 3000 k ) with the code cp2k @xcite . this first dataset was then expanded by adding randomly distorted structures of the initial dataset at slightly different pressures and temperatures and models with slight deviations from the perfect stoichiometry . the refinement of the potential was achieved by inserting in the data set the ab initio energy of configurations generated by molecular dynamics simulations ( see below ) using the not yet refined nn potential . total energy convergence has to be strictly guaranteed for every point of the dataset to make the nn input fully consistent . therefore , we had to perform brillouin zone ( bz ) integration over a dense @xmath2 monkhorst - pack ( mp ) @xcite mesh for the 64-atom cell and employing meshes of a corresponding k - point density for the larger systems . the ab initio energies were calculated using the quantum - espresso package @xcite . the perdew - burke - ernzerhof ( pbe ) @xcite exchange - correlation functional and norm conserving pseudopotentials were employed , considering only the outermost @xmath3 and @xmath4 electrons in the valence shell . the kohn - sham orbitals were expanded in a plane waves basis up to a kinetic energy cutoff of 40 ry . these settings ensure convergence of the total energy to 2 mev / atom . the best nn fit we found employs three hidden layers with 20 nodes each . sigmoidal activation functions were used in the nodes of the hidden layers , while a linear function was used for the output node . details concerning the architecture of the nn can be found elsewhere @xcite . the local environment of each atom is defined by the value of 159 symmetry functions ( see ref . @xcite for details ) defined in terms of the positions of all neighbors within a distance cutoff of 6.88 . the generation of the nn potential and the calculation of the forces for the md simulations were performed with the nn code runner @xcite . we used the tinker @xcite code as md driver . the time step for the md runs was set to 0.2 fs , and constant temperature simulations were performed using the berendsen thermostat @xcite . the results of the fitting process of the nn potential are summarized in fig . the root mean square error ( rmse ) for the energy is 5.01 and 5.60 mev / atom for the training and the test set , respectively , while the rmses of the forces are 0.46 and 0.47 ev / , for the two sets . among all structures considered , only a negligible fraction shows noticeable absolute errors , up to 25.8 mev / atom and 11.2 ev / @xmath5 for energies and forces ( see fig . [ fig1 ] insets ) . we have found that these configurations correspond to high - energy structures that are not visited in md simulations carried out in the present work . the equilibrium geometry of the trigonal phase of crystalline gete ( @xmath6 space group ) was obtained by optimizing all structural parameters consisting of the lattice parameter @xmath7 , the trigonal angle @xmath8 and the internal parameter @xmath9 that assigns the positions of the two atoms in the unit cell , namely ge at ( @xmath9,@xmath9,@xmath9 ) and te at ( -@xmath9,-@xmath9,-@xmath9 ) @xcite . the residual anisotropy in the stress tensor at the optimized lattice parameter at each volume is below 0.02 kbar . the energy versus volume data were fitted with a murnaghan equation of state @xcite . the theoretical structural parameters of the trigonal phase of gete at equilibrium are compared in tab . [ tab1 ] with experimental data @xcite and dft results obtained with a @xmath10 mp k - point mesh in the bz integration . dft data are similar to those reported previously @xcite . the length of the short and long ge - te bonds are also given . the structure of trigonal gete can be seen as a distorted rocksalt geometry with an elongation of the cube diagonal along the [ 111 ] direction and an off - center displacement of the inner te atom along the [ 111 ] direction , which moves to a distance @xmath11 from the ge atom at the vertex as shown in fig . [ fig2]a . the energy gained by the off - center displacement is analyzed by varying the distance @xmath11 at fixed lattice parameters @xmath7 and @xmath8 . the resulting energy as a function of @xmath11 is reported in fig . [ fig2]b for the nn and the dft calculations . we note that the dft values were not included in the training set but were recalculated for investigating the quality of the nn potential only . the double well potential identifies the two possible ferroelectric configurations while the maximum corresponds to a paraelectric configuration . .structural parameters of the trigonal phase of crystalline gete from nn and dft calculations and from the experimental data of ref . . the lengths of the short and long bonds are also given . [ cols="^,^,^,^",options="header " , ] the structural properties of a - gete and a - gst have been elucidated recently by ab initio simulations @xcite . in these systems ge and te atoms are mostly four - coordinated and three - coordinated , respectively . te atoms are in a defective octahedral - like environment , which resembles the local environment of the corresponding crystalline phases . the majority of ge atoms are in a defective octahedral environment too , but about one quarter of ge atoms are in a tetrahedral - like geometry . the presence of homopolar ge - ge ( and , in the case of gst , ge - sb ) bonds favors the tetrahedral coordination . in the following , we compare the structural properties of models of amorphous gete generated by nn and ab initio simulations . the nn amorphous phase was generated by quenching the molten sample from 1150 k to room temperature in 100 ps . average properties are obtained from a nve simulation 40 ps long at an average temperature of 300 k. doubling or even tripling the quenching time ( up to 300 ps ) does not introduce sizable changes in the structural and vibrational properties of our nn model of amorphous gete . structural properties are described in figs . [ fig6]-[fig8 ] . the partial pair correlation functions of our nn models are compared with ab initio data in fig . [ fig6 ] . by decreasing the system size from 4096-atom to 1728-atom one obtains essentially the same results . by using instead a small 216-atom cell fluctuations in properties related to ge - ge homopolar bonds are found by looking at ten different independent models . the quantities averaged over ten models are reported hereafter and are very close to those of the larger models . the fluctuations among the different 216-atom models can be appreciated in figs . s1-s2-s3 of the additional material ( epaps @xcite ) . the distribution of coordination numbers and their average values are reported in fig . [ fig6bis ] and table [ tab5 ] for nn and ab initio @xcite simulations . bond angles distribution functions are reported in fig . [ fig7 ] . are used . ] the agreement between nn and dft data is overall very good . the largest discrepancy is on the height of the first peak of the ge - ge pair correlation function . however , this misfit is partially due to fluctuations in the number of ge - ge bonds in the still small 216-atom cell ( cf . figs . s1-s2 in epaps @xcite ) . in fact , by generating ten different 216-atom models with the nn potential we observed sizable fluctuations in the average ge - ge coordination number ranging from 0.6 to 0.9 . a more compelling comparison would require the availability of several independent ab initio models of a - gete . another discrepancy with the dft results is the presence of a small peak at around 60@xmath12 in the angle distribution function due to a very small fraction of three membered rings ( see below ) . following our previous works @xcite , we quantified the fraction of ge atoms in a tetrahedral geometry by computing the local order parameter @xmath13 where the sum runs over the pairs of atoms bonded to a central atom @xmath14 . @xmath15 for the ideal tetrahedral geometry , @xmath16 for the six - coordinated octahedral site , and @xmath17 for a four - coordinated defective octahedral site . the distribution of the local order parameter @xmath18 for ge atoms is reported in fig . [ fig8 ] for different coordination numbers . the @xmath18 distribution for 4-coordinated ge is bimodal with peaks corresponding to defective octahedra and tetrahedra . in contrast , the @xmath18-distribution for te does not show any signature of the tetrahedral geometry ( cf . [ fig8 ] ) . we estimated the fraction of tetrahedral ge atoms by integrating the @xmath18-distribution of 4-coordinated ge from 0.8 to 1 . this procedure was demonstrated to provide reliable values for the fraction of tetrahedral ge from the analysis of the wannier functions that allow a direct identification of the tetrahedral geometry in terms of the electronic structure @xcite . in fact , ge in tetrahedral sites has four bonding sp@xmath19-like wannier functions , while ge in defective octahedra has three p - like bonding wannier functions and one s - like lone pair . the fraction of tetrahedral ge atoms for the ten 216-atom nn models , for the large 4096-atom model and for the ab initio 216-atom model of ref . is given in fig . [ fig9 ] . by chance the ab initio value is very close to the value obtained by averaging over the ten 216-atom nn models while the fraction of tetrahedral ge in the large 4096-atom cell is 24 @xmath20 , a value very close to the average over the ten small cells and also to the result obtained for a 1728-atom model ( 22 @xmath20 ) . the concentration of tetrahedra depends on the fraction of ge - ge homopolar bonds , which is the property more affected by finite size effects in the small 216-atom cell . turning now to the medium range order , we report in fig . [ fig10 ] the distribution of ring lengths computed according to ref . for the large and small nn models and for the small dft model of ref . . the amorphous phases of gete and gst have been shown to display a large concentration of nanocavities @xcite . the distribution of the volume of nanocavities computed according to the definition of ref . and the algorithm of ref . is compared in fig . [ fig10bis ] for the nn and dft models . the same scheme for the calculation of nanocavities was applied in our previous works on different phase change materials @xcite . these comparisons show that the agreement between nn and dft results is very good for the medium range order as well . we also optimized the density of the amorphous model at zero temperature by interpolating the energy - volume points with a murnaghan equation of state . we obtained an equilibrium density of 0.03351 atoms @xmath21 to be compared with the value of 0.03156 atoms @xmath21 resulting from the ab initio equation of state of a 216-atom cell with the bz integration restricted to the @xmath22-point @xcite . the experimental equilibrium density @xcite of a - gete is 0.03327 atoms @xmath21 . the nn and ab initio bulk moduli of a - gete are 17 gpa and 14 gpa , respectively . concerning the vibrational properties , the phonon density of states of amorphous gete from nn and ab initio simulations are compared in fig . [ fig11 ] . phonon frequencies are computed by diagonalizing the dynamical matrix obtained in turn from the variation of atomic forces due to finite atomic displacements 0.02 large . only phonons with the periodicity of our supercells ( @xmath22-point phonons ) were considered . ab initio phonons are computed in a 216-atom cell @xcite while nn phonons are obtained from the 4096-atom and 216-atom cells . projections on the different type of atoms ( te , ge in tetrahedral and defective octahedral geometries ) are also shown . in an amorphous material , phonons display localization properties , which depend on frequency . to address this issue and following our previous ab initio works @xcite , we computed the inverse participation ratio ( @xmath23 ) of the @xmath14-th vibrational mode defined as @xmath24 here @xmath25 are phonon eigenvectors and the sum over @xmath26 runs over the @xmath27 atoms in the unit cell with masses @xmath28 . according to this definition , the value of @xmath23 varies from @xmath29 for a completely delocalized phonon , to one for a mode completely localized on a single atom . the values of @xmath23 for the nn and ab initio models of a - gete are reported in fig . [ fig12 ] . the nn potential reproduces the strong localization on tetrahedra of phonons above 200 @xmath30 . the overall shape and frequency range of the phonon dos is reasonably reproduced by the nn potential . a discrepancy is present in the relative height of the two main structures at 50 @xmath30 and 150 @xmath30 , which , however , might be partially due to the still small size of the 216-atom cell . actually the dos of the different 216-atom models generated by the nn potentials are all very similar , but somehow different from the large 4096-atom cell due to a size effect in summary , a nn potential for the phase change material gete has been created and tested to reproduce the properties of crystalline , liquid and amorphous phases . the nn potential has been validated by comparing the results on structural and dynamical properties of the bulk phases of gete with our previous data from dft calculations @xcite . the development of a classical potential with close to ab initio accuracy represents a breakthrough in the simulation of phase change materials , as it will allow addressing several key issues on the properties of this class of materials that are presently beyond the reach of ab initio simulations . the study of thermal conductivity in the amorphous phase @xcite and the dynamics of homogeneous and heterogeneous crystallization are few examples of useful follow - on developments of this work , which promises to improve our microscopic understanding of the operation of phase change memories . we thankfully acknowledge the computational resources by deisa consortium under projects netphase , by cscs ( manno , switzerland ) and by the iscra initiative at cineca . this work has been partially supported by regione lombardia and cilea consortium through a lisa initiative ( laboratory for interdisciplinary advanced simulation ) 2011 grant [ link : http://lisa.cilea.it ] , by the cariplo foundation through project monads and by murst through the program prin08 . jb thanks the dfg for financial support ( emmy noether program ) . m. wuttig and n. yamada , nat . mater . * 6 * , 824 ( 2007 ) . a. pirovano , a. l. lacaita , a. benvenuti , f. pellizzer , and r. bez , ieee trans . dev . * 51 * , 452 ( 2004 ) . a.l . lacaita and d.j . wouters , phys . a * 205 * , 2281 ( 2008 ) . d. lencer , m. salinga , and m. wuttig , adv . mat . * 23 * , 2030 ( 2011 ) . s. raoux , w. welnic , and d. ielmini , chem . rev . * 110 * , 240 ( 2010 ) . s. caravati , m. bernasconi , t. d. khne , m. krack , and m. parrinello , appl . lett . * 91 * , 171906 ( 2007 ) . s. caravati , m. bernasconi , t. d. khne , m. krack , and m. parrinello , j. phys . cond . mat . 255501 ( 2009 ) ; 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gete is a prototypical phase change material of high interest for applications in optical and electronic non - volatile memories . we present an interatomic potential for the bulk phases of gete , which is created using a neural network ( nn ) representation of the potential - energy surface obtained from reference calculations based on density functional theory . it is demonstrated that the nn potential provides a close to ab initio quality description of a number of properties of liquid , crystalline and amorphous gete . the availability of a reliable classical potential allows addressing a number of issues of interest for the technological applications of phase change materials , which are presently beyond the capability of first principles molecular dynamics simulations .

twenty years ago ( 1992 ) , a landmark institute of medicine ( iom ) report entitled emerging infections : microbial threats to health in the united states underscored the important but often underappreciated concept of emerging infectious diseases ( eids ) ( 1 ) . although the iom report was influential in thrusting the issue of eids squarely into scientific and public discourse , the awareness that diseases periodically emerge and reemerge actually goes back millennia ( 2 , 3 ) . for example , ancient greek , roman , and persian writers documented the emergence of many new epidemics . during and after the 14th - century black death pandemic of bubonic / pneumonic plague , european city officials quarantined arriving ships to prevent its importation and set up quarantine stations to isolate and care for patients . in 1685 , the scientist robert boyle presciently observed that there are ever new forms of epidemic diseases appearing among [ them ] the emergent variety of exotick and hurtful ( 4 , 5 ) . by the mid-19th century , the discovery of microbes as causative agents of infectious diseases led to the development of preventive countermeasures such as passive immunotherapy , vaccines , and drugs against infective agents ( 6 ) . these advances spurred optimistic predictions that infections would soon be conquered ( 7 ) , and physicians and public health workers began to lose sight of the possibility of the emergence of new and previously unrecognized infectious diseases . to a large extent , it was the shock of the recognition of hiv / aids in the early 1980s , followed by the iom report of 1992 , that rekindled awareness of , and interest in , eids . two decades after the iom report , it is appropriate to ask what has been learned about eids , where have we succeeded or failed in our efforts to fight them , and what challenges remain . as predicted in 1992 ( 1 ) , previously unrecognized infectious diseases have continued to emerge , including variable creutzfeldt - jakob disease / bovine spongiform encephalopathy ( vcjd / bse ) , severe acute respiratory syndrome ( sars ) , and 2009 pandemic h1n1 influenza , and others have reemerged , e.g. , disease caused by multiple - drug - resistant staphylococcus aureus ( mrsa ) , multiple - drug - resistant and extensively drug - resistant ( mdr and xdr ) tuberculosis , cholera , and dengue . the recent eid with the greatest global impact has been hiv / aids . over the past 3 decades , humankind has witnessed the unexpected emergence of , and then the relentless devastation resulting from , one of history s deadliest pandemics ( 8) . at the same time , modern research tools have helped us to understand how , where , and when hiv emerged ; to understand its pathogenesis and natural history ; and to develop life - saving treatment and prevention modalities that have put the control of the hiv / aids pandemic within reach . surely , future generations will look back on the era of hiv / aids as one of the most remarkable periods in the history of human disease , in which civilization was challenged by a devastating pandemic eid and aggressively addressed it from a scientific and global health standpoint , leading to the real possibility of effective control in a relatively timely manner . the term eid and the concepts of newly emerging and reemerging infectious diseases have recently become much more widely appreciated . the 1992 iom report led to rapid and heightened awareness of this issue in the scientific , public health , medical , and lay communities . for example , both the united states centers for disease control and prevention ( cdc ) and the national institute of allergy and infectious diseases of the national institutes of health released eid research and response plans ( 9 , 10 ) . in 1995 , the cdc established an eid - oriented scientific journal , emerging infectious diseases . now in its 18th year , the journal has published nearly 10,000 articles and has become standard reading for many in the disciplines of microbiology , clinical infectious diseases , public health , and allied medical fields . other microbiology and general medical journals emphasizing eids have been established , e.g. , plos pathogens , or expanded their coverage of eids , e.g. , the journal of infectious diseases and vaccine , while mbio and other journals published by the american society for microbiology ( asm ) have remained leaders in publishing important eid - related research . for example , promed was launched in 1994 as a grass roots effort by the federation of american scientists and has been continued by the international society for infectious diseases . today , promed s 60,000-plus subscribers from 185 countries can read openly , online , and in real time about virtually all important eids occurring anywhere in the world . this creates immediate awareness of epidemics not only for scientists but also for the public and the media . promed has made it extremely difficult for cautious governments to suppress outbreak information and has greatly enhanced the capacity of public health systems to control infectious disease outbreaks ( 11 ) . cdc has expanded the mmwr ( morbidity and mortality weekly report ) , which is now abstracted in medical journals such as the journal of the american medical association , so that every week practitioners around the world can get the latest information about eids . it has become clear that the five or six eids emerging annually ( on average ) over the past 8 decades have disproportionately emerged from perturbed ecological niches , especially those in tropical areas with vector - borne enzootic diseases ( 12 , 13 ) . since 1992 , high - throughput genetics techniques have led to the sequencing of thousands of microorganisms , their vectors , and many of their hosts . genomics and proteomics have helped in the discovery of new infectious diseases and in acquiring a better understanding of the pathogenesis of existing ones ; have substantially improved surveillance , diagnosis , and drug and vaccine design ; and promise to help elucidate host susceptibility factors and host responses to treatment of infections . for example , by 2003 , the genomes of the human species , the mosquito anopheles gambiae , and the malaria parasite plasmodium falciparum all had been sequenced , representing the first time that all the major actors in the drama of an important emerging / reemerging infectious disease had been characterized at the molecular genetic level ( 12 , 14 ) . these breakthroughs are important additions to our continuing efforts to control malaria , which have had recent successes but still require new countermeasures . these genomic data are contributing to vaccine and drug development and are elucidating the pathogenesis of and human resistance and susceptibility to malaria ( 14 ) . genomics techniques , like pcr and high - throughput deep and whole - genome sequencing , that now greatly facilitate the discovery of eids ( e.g. , the etiologic agents of hantavirus pulmonary syndrome and kaposi sarcoma ) also reveal previously unimagined genomic diversity among microbes . this diversity includes complex and evolving viral quasispecies and microbes that have undergone considerable interbacterial horizontal gene transfer , creating new phenotypic properties of virulence and drug resistance . given these and other advances in science and technology , it is now possible to perceive , as dawkins argued decades ago ( 15 ) , that the evolution and natural selection of human diseases are not simply a struggle between microbes and hosts . rather , it is fought out at a more basic level of gene - to - gene competition , pitting the genomes of microbes against those of their hosts ( many of whose genomes contain genetic evidence of past microbial encounters ) . dawkins contended that the visible evidence of genomic survival is an organism s expressed phenotype , its survival machine , which is akin to a simple virus being protected by its external protein coat ; however , dawkins proposed that we should think of natural selection as operating at the level of the gene , not the organism it encodes . specifically , our gut flora represents a complex external organ system comprising at least three different enterotypes that have coevolved with us over millennia and appear to affect our health , including by preventing and modifying infection ( 16 , 17 ) . indeed , fecal transplantation is now a novel treatment for clostridium difficile colitis ( a potentially fatal eid ) ( 18 ) . infants who start life with or develop reduced flora ( e.g. , via pre- or postnatal antibiotics ) may be at increased risk of ids and eids . variations in the microbiome may also affect the occurrence of certain chronic diseases , allergies , and malnutrition ( 19 ) . in this newer view , humans are not just static victims of virulent microbes but hubs of gene flow in which pathogens not only seek to survive environmental barriers and natural and acquired immunity but also compete with other microbes on the playing field that we think of as us . additional conceptual advances in eids include the realization that many chronic diseases have a direct or indirect infectious basis , e.g. , cervical , hepatic , and gastric cancers ; gastroduodenal ulcers ; hemolytic - uremic syndrome ; and possibly some types of tics and obsessive - compulsive disorders ( 6 , 12 ) . we also have become aware of the critical role of microbial coinfections in the pathogenesis of certain infectious diseases ( e.g. , hiv and numerous opportunistic infections ; influenza and measles in association with secondary bacterial pneumonias ) and of nutrition , e.g. , the link between vitamin a and measles ( 20 , 21 ) . the one - health concept , which emphasizes understanding and studying the unity of human and animal infectious diseases ( 22 ) , reflects growing awareness that the majority of human eids , probably more than 60 per cent ( 11 ) , are of animal origin ( zoonotic ) , a realization that has implications not only for disease surveillance but also for understanding pathogenesis and controlling disease . for example , hiv / aids , influenza , lyme disease , tuberculosis , measles , plague , smallpox , and possibly even leprosy are directly or primarily of animal origin . viral host switching , in some cases associated with rapid and complicated microbial comutations ( 23 ) , has become an important research topic ( 23 , 24 ) for both newer eids , such as sars , and reemerging ones , such as influenza . the processes by which animal - adapted microorganisms leave their hosts and adapt to new species , such as humans , are largely unknown and represent an important challenge in the study of eids . moreover , host - switching is not just a one - way street from other animals to humans . for example , ebola virus , a devastating disease for humans , has decimated african gorilla populations ; in the united states , suburban expansion associated with deforestation has driven raccoons into the suburbs , increasing rabies transmission to and from them ; and a human strain of staphylococcus aureus has adapted to chickens , spread globally , and developed new mutations enhancing avian virulence ( 25 , 26 ) . these examples remind us that ecosystem dynamism in which humans play a critical role is a key variable in eid occurrence and prevention ( 6 , 12 ) . since 1992 , enormous strides have also been made in understanding the history of eids , most notably by genetic sequencing of historically preserved microbial dna and rna . perhaps the most significant example is the 1918 pandemic influenza virus , which caused the deadliest single disease event in recorded human history ( 27 ) . although that pandemic occurred 15 years before influenza viruses were first identified , recent sequencing efforts from rna in preserved tissues allowed full reconstruction of the 1918 pandemic viral genome , leading to a remarkable body of ongoing research and a greater understanding of how influenza viruses continue to emerge among humans and other animal species ( 27 , 28 ) . of the several thousand microorganisms already sequenced , those of historical importance include smallpox virus strains , the plague bacillus ( yersinia pestis ) ( 29 ) , and ancient tuberculosis organisms . strikingly , paleovirus oncogenes have even been resurrected and studied in infectivity assays to find the original cellular receptors to which they had become adapted millions of years ago ( 30 ) . both traditional historical research and study of phylogenetic trees derived from gene sequencing of modern organisms have added significantly to these efforts , leading , for example , to the discovery that the initial jump of what became known as hiv from nonhuman primates to humans probably occurred nearly a century ago with multiple independent host - switching events that ultimately led to the pandemic that was first recognized in 1981 ( 31 ) . understanding the history and evolution of emerging microbes allows us to predict more accurately what their potential pandemic impact will be , and to understand how we can best prevent and control them . it is now becoming accepted that disease eradication has a legitimate place in the armamentarium of responses to eids ( 6 ) . smallpox , a devastating reemerging disease for millennia , was eradicated in 1980 , and the epizootic morbillivirus ( measles - related ) disease rinderpest was eradicated in 2011 ( 32 , 33 ) . with dracunculiasis and polio disease close to eradication , with measles on the path to eradication , and with significant strides in controlling such diseases as hepatitis b and even malaria and hiv infection being made , it is now possible to realistically consider eradication as an ultimate means of controlling certain eids . even though antibiotic resistance has accelerated alarmingly , new generations of antibiotics have kept pace ( albeit , barely ) , and vaccines against some of the most important diseases have been developed or improved , such as those against haemophilus influenzae type b , pneumococci , and cancer - causing human papillomavirus strains . the development of antivirals and antiviral combination therapies has led to a historic breakthrough in helping to control hiv / aids ( 12 ) and major strides in curing chronic hepatitis c virus infection . future directions in research and drug development likely will include better antibacterial and antiviral combination therapies as well as the development and use of more narrow - spectrum drugs against infective agents , which are less likely to cause polymicrobial resistance . in the 20 years since the iom report on eids , hiv infection was considered a death sentence for most patients . in 2012 , after the tragedy of more than 35 million aids deaths , persons treated early with combination antiretroviral therapy , although not cured of their viral infection , can expect to live normal life spans with only a low risk of transmitting infection to others . in 1992 , at least a million children died annually of measles . in 2012 , fewer than 100,000 are expected to die , and measles eradication based upon an already - available effective vaccine is a realistic near - term goal . in 1992 , it was possible to enter villages in many developing countries to monitor poliovirus circulation by conducting childhood lameness surveys . in 2012 , most lame individuals are adults whose children are largely free of the threat of polio and probably will live to see it eradicated ( poliovirus type 2 has already been extinguished ) . despite extraordinary progress during the past 2 decades , infectious diseases still kill 15 million people each year ( 6 ) , and new and deadly diseases continue to emerge and reemerge . the perpetual nature of the emergence of infectious diseases poses a continuing challenge , which is volatile and ever - changing . this challenge includes a need for constant surveillance and prompt , efficient diagnosis ; a need to develop and deploy new vaccines and drugs to combat new diseases ; and a need for ongoing research not only in developing countermeasures but also in understanding the basic biology of new organisms and our susceptibilities to them . the future is ever uncertain , because unimagined new diseases surely lie in wait , ready to emerge unexpectedly ; however , our ability to detect and identify them , our armamentarium of treatment and prevention options , our capacity to undertake and maintain basic and applied research , and our commitment to eradicating certain eids have never been greater . we have made far - reaching advances in the past 20 years since the original iom report , and scientists are guardedly optimistic that further breakthroughs lie ahead .

abstracttwenty years ago ( 1992 ) , a landmark institute of medicine report entitled emerging infections : microbial threats to health in the united states underscored the important but often underappreciated concept of emerging infectious diseases ( eids ) . a review of the progress made and setbacks experienced over the past 2 decades suggests that even though many new diseases have emerged , such as sars ( severe acute respiratory syndrome ) and the 2009 pandemic influenza , significant advances have occurred in eid control , prevention , and treatment . among many elements of the increase in the capacity to control eids are genomics - associated advances in microbial detection and treatment , improved disease surveillance , and greater awareness of eids and the complicated variables that underlie emergence . in looking back over the past 20 years , it is apparent that we are in a time of great change in which both the challenge of eids and our responses to them are being transformed . recent advances support guarded optimism that further breakthroughs lie ahead .

FILE PHOTO: Tesla Motors CEO Elon Musk speaks during the National Governors Association Summer Meeting in Providence, Rhode Island, U.S., July 15, 2017. REUTERS/Brian Snyder/File Photo (Reuters) - Tesla Inc (TSLA.O) Chief Executive Elon Musk said the tweet that cost him and the company $20 million in fines each by the U.S. Securities and Exchange Commision was “Worth It”. The tweet, sent late Friday evening less than an hour before Musk tweeted that he would take a break from Twitter “for a few days,” was in response to a question from a Twitter follower. The SEC in September charged Musk, 47, with misleading investors with tweets on Aug. 7 that said he was considering taking Tesla private at $420 a share and had secured funding. The tweets had no basis in fact, and the ensuing market chaos hurt investors, regulators claimed. Tesla Inc and Elon Musk have agreed to pay $20 million each to financial regulators and the billionaire will step down as the company’s chairman but remain as chief executive, under a settlement. Under the settlement agreement, Tesla needs to appoint an independent chairman by Nov. 13. ||||| Photo: Chris Carlson (AP) It’s arguably unfathomable that any human being slapped with a $20 million fine for a bad tweet would ever consider returning to the platform, much less continue to fire off word salad at all hours of the day and night. In the face of any logical explanation, however, one such man seemingly continues to insist that he is not owned. Tweeting Friday evening in a thread about “criticism” and “like” ratios on Twitter’s platform, Tesla CEO Elon Musk appeared to claim that his disastrous “420” tweet in August about taking the electric car company private was “worth” the tens of millions of dollars in fines regulators levied on him in response. Advertisement Why? The likes. Earlier this month, a judge officially approved Tesla’s settlement with the Securities and Exchange Commission after it argued that Musk made “false and misleading” statements in regards to going private. In the settlement, Musk and Tesla agreed to each pay a fine of $20 million, with Musk also forced to step down as Tesla’s chairman for at least three years. Tesla was also required to rein in Musk’s communications with investors. Advertisement This was a mere weeks ago. Remarkably, Musk later tweeted that he was going to sign “off Twitter for a few days,” which honestly doesn’t seem like such a bad long-term plan either. In fact, maybe we should all log off. ||||| Tweet with a location You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more

– Elon Musk apparently has no regrets about a tweet that set him and Tesla back each $20 million. In a tweet late Friday—just before tweeting that he would be taking a break from Twitter—Musk responded to a question about his ill-fated tweet claiming he would take the company private, which resulted in $40 million in SEC fines and him stepping down as company chairman, reports Reuters. "Worth It," he tweeted. Given that the ink is barely dry on the SEC fines, Gizmodo thinks that Musk's plan to take a break from "(firing) off word salad at all hours of the day and night" for a while "doesn’t seem like such a bad long-term plan."

A federal appeals court on Thursday blocked a judge's order requiring changes to a New York Police Department stop-and-search tactic that has been widely criticized by rights advocates as targeting black and Hispanic men. The stops reached an all-time high in 2011 of 684,330. FILE- In this Friday, May 17, 2013, file photo, U.S. District Court Judge Shira Scheindlin is interviewed in her federal court chambers, in New York. On Thursday, Oct. 31, 2013, a New York federal appeals... (Associated Press) FILE - In this Aug. 13, 2013 file photo, police officers walk through the Brownsville Houses the Brownsville section of Brooklyn, New York. A federal appeals court on Thursday, Oct. 31, 2013, blocked... (Associated Press) FILE - In this Aug. 13, 2013 file photo, police officers take a report from a woman who had her phone stolen in the Brownsville section of Brooklyn, New York. A federal appeals court on Thursday, Oct.... (Associated Press) The 2nd U.S. Circuit Court of Appeals also took the unusual step of removing Judge Shira Scheindlin from the case, saying interviews she gave during the trial responding to criticism of the court called her impartiality into question. Scheindlin ruled in August that the city violated the Constitution in the way it carried out its program of stopping and questioning people. She ruled that police in America's largest city violated the civil rights of tens of thousands of people by wrongly targeting black and Hispanic men. The issue has attracted national interest. Students at Brown University in Rhode Island this week shouted down Police Commissioner Ray Kelly when he tried to give a speech about the so-called stop-and-frisk practice there. Scheindlin also appointed an outside monitor to oversee major changes and ordered a pilot program to test body-worn cameras in some areas where most stops occur. She noted she wasn't ending the practice, which is constitutional, but was reforming the way the NYPD implemented its stops. The city appealed her findings and her orders to change the program. The appeals court said her rulings will be stayed pending the outcome of the city's appeal. The front-runner in next week's mayoral election, Democratic candidate Bill de Blasio, said he was "extremely disappointed" in Thursday's decision. The Center for Constitutional Rights, which represented plaintiffs in the case, said it was shocked that the appeals court "cast aspersions" on the judge's professional conduct and reassigned the case. Stop-and-frisk has been around for decades in some form, but recorded stops increased dramatically under the administration of current Mayor Michael Bloomberg. A lawsuit was filed in 2004 by four men and became a class action case. The city has said police officers are afraid to stop and frisk people now and the number of stop-and-frisks has dropped dramatically. Opponents of changes to the stop-and-frisk program say they would lower police morale but not crime. About 5 million stops have been made in New York in the past decade, with frisks, or searches, occurring about half the time. To make a stop, police must have reasonable suspicion that a crime is about to occur or has occurred. Only about 10 percent of the stops result in arrests or summonses, and weapons are found about 2 percent of the time. ___ Associated Press writer Larry Neumeister contributed. ||||| An appeals court delivered a stinging rebuke Thursday to Manhattan federal Judge Shira Scheindlin — unanimously booting her from cases involving stop-and-frisk, calling into question her impartiality and saying she “ran afoul” of judicial ethics. In a ruling that put a series of NYPD reforms she mandated on hold, a three-judge panel at the US Second Circuit Court of Appeals said Scheindlin violated the Code of Conduct for United States Judges by failing to “avoid impropriety and the appearance of impropriety in all activities” and by failing to disqualify herself “in a proceeding in which the judge’s impartiality might reasonably be questioned.” The judges faulted Scheindlin for granting a series of media interviews in May while overseeing a nonjury trial over the NYPD’s use of the tactic, which she later ruled unconstitutional. At the time, an editorial in The Post blasted Scheindlin for making public comments “that skate so close to the issues involved.” “From the start of this trial, she hasn’t been shy about letting the city know how dubious she is about police judgment,” it read. In their ruling, the three judges also said “the appearance of impartiality surrounding this litigation was compromised” when Scheindlin invited lawyers to file suit against stop-and-frisk and steer it to her through what the appellate judges called an “improper application of the court’s ‘related-case rule’ ” in a 2007 proceeding over the NYPD’s since-disbanded Street Crime Unit. “What I am trying to say — I am sure I am going to get in trouble for saying it — for $65 you can bring that lawsuit,” she said from the bench in that case according to Thursday’s ruling. “And as I said before, I would accept it as a related case, which the plaintiff has the power to ­designate.” The order by Judges José Cabranes and Barrington Parker — both generally regarded as liberal — and Judge John Walker Jr. also stayed a series of reforms that Scheindlin ordered to the stop-and-frisk program until after a pending appeal by the city is ­resolved. Among them is the ­appointment of a federal panel to monitor the NYPD. Experts on judicial ethics said it was a rare move by the higher court. “I’m shocked,” said Hofstra University law professor Monroe Freedman. “It’s not a common thing. It’s ordinarily reserved for extreme cases.” Indiana University law professor Charles Geyh said the order could expose Scheindlin to disciplinary action, such as a censure. “They’re citing core provisions of the Code of Conduct here,” Geyh said. “This almost seems like an invitation to do it.” In a statement, Scheindlin wrote, “I said I would take the case [involving the Street Crime Unit] as related because the plaintiffs charged that the city had violated my order.” She also maintained that quotes attributed to her about stop-and-frisk were actually taken from statements she made in court. City Corporation Counsel Michael Cardozo praised the ruling, saying stop-and-frisk “will now receive a fresh and independent look both by the appeals court and then, if necessary, by a different trial-court judge.” The New York Civil Liberties Union vowed to appeal the order. “There is overwhelming evidence that the stop-and-frisk regime is unconstitutional and out of control — just ask any black or brown New Yorker,” said executive director Donna Lieberman. Baher Azmy of the Center for Constitutional Rights, whose lawyers helped spearhead the plaintiffs’ case, said his group remained “optimistic about genuine reform finally occurring.”

– Supporters of the NYPD's controversial stop-and-frisk strategy have reason to cheer tonight after a new appeals court ruling. The federal court rebuked the judge who declared the policy to be unconstitutional in August and ordered that the reforms she put in place be suspended, reports the New York Post. The court also, in what the New York Times calls "strikingly personal terms," removed Judge Shira Scheindlin from the case. Essentially, the appeals court found her to be biased from the get-go against stop-and-frisk and declared that she "ran afoul" of the code of conduct for judges. (Interviews she gave during the trial didn't help, reports AP.) One thing the court did not do, however, was rule on whether it considered stop-and-frisk to be unconstitutional. That won't be decided until next year, but now Scheindlin's changes won't go into effect in the interim. Among other things, she ordered an independent monitor to oversee the program to make sure that the civil liberties of minorities were protected, and she began a pilot program to have officers wear body cameras to record their stops. Those and another changes are now suspended.

since the 1930 s , the linear rayleigh - ritz ( rr ) variational method @xcite has been the primary tool for determining the low energy part of the spectrum of quantum systems . in this approach , the trial function is expanded into a finite set of basis functions , and the coefficients of the expansion are determined by the variational principle . the approximations provided by the eigenvalues of the rr matrix are upper bounds that approach the exact energies monotonically from above on increasing the number of included functions of the basis @xcite . however , the matrix elements are given by integrals and the number of the basis functions required to obtain accurate results grows exponentially with the number of degrees of freedom , which renders the method computationally prohibitive for complex systems . there are basically two strategies to reduce the computational cost of the method : choosing the basis functions in a sophisticated way or using approximations in calculating the hamiltonian matrix elements . among various implementations of the first strategy the introduction of nonlinear parameters into the functions of the basis is one of the most effective @xcite . the adjustable parameters may be fixed so as to improve the convergence for a particular state @xcite or a group of states @xcite . an example of the second strategy is the collocation method where the matrix elements are approximated by @xmath0point quadratures . the recently published paper on `` variational collocation for systems of coupled anharmonic oscillators '' @xcite combines both strategies mentioned above , demonstrating that by introducing adjustable parameters the convergence of the collocation method may be improved . however , it should be remembered that in contrast to the rr method , the collocation method does not have a variational character . discretization in the collocation approach introduces approximation in the hamiltonian matrix , as a consequence of which the results do not represent upper bounds to the exact bound - state energies . introducing the adjustable parameters does not change this fact ; therefore the method proposed by amore and fernandez should be termed optimized rather than variational . to illustrate the similarities and differences between optimization in the rr and collocation methods , we consider the example of the pullen - edmonds hamiltonian @xmath1 that has been studied in ref . the parameter @xmath2 represents the coupling between the two degrees of freedom . amore and fernandez observed that introducing a rotation parameter , the convergence of the collocation method may be improved further . the optimal rotation angle has been found to be close to @xmath3 , which corresponds to the hamiltonian @xmath4 hamiltonians ( [ eq : hdim2 ] ) and ( [ eq : hdim2rot ] ) have the same spectrum but the speed of convergence of the collocation method turns to be considerably higher in case of the application to the rotated one ( [ eq : hdim2rot ] ) . below we consider the application of the rr method to both hamiltonians using basis functions @xmath5 constructed as tensor products of the functions @xmath6 from a basis in one - dimensional ( 1d ) space that depends on an arbitrary parameter @xmath7 . the @xmath8th order approximations are obtained with the use of @xmath8 even - parity 1d functions , which corresponds to diagonalization of the rr matrix of dimension @xmath9 . optimization is performed by choosing the value of @xmath7 so as to make the trace of that matrix stationary at each order of approximation @xcite . in our procedure , we take the advantage of symbolic calculation in the mathematica package by performing the numerical algebra exactly in terms of the ratio of integers , which allows determination of the eigenvalues to arbitrary accuracy . first we calculate the accurate values of ground - state energy of the coupled oscillators through the optimized rr method , using the basis of trigonometric functions @xmath10 , \label{trig}\ ] ] which are eigenfunctions of the infinite potential well of a half - width @xmath11 that is taken as a nonlinear parameter . the same basis has been used by amore and fernandez in their collocation approach @xcite . in table @xmath12 , we compare the approximations to the ground - state energy @xmath13 and @xmath14 for the hamiltonian ( [ eq : hdim2 ] ) and ( [ eq : hdim2rot ] ) , respectively , for different values of @xmath8 . the optimal value of the nonlinear parameter @xmath15 that renders the trace of the given order rr matrix stationary is also shown . the underlined digits are those that coincide with the exact result . we observe that both the series of approximations converge monotonically from above to the exact value with increasing @xmath8 , but the convergence for the hamiltonian ( [ eq : hdim2rot ] ) is much quicker . this is similarly true at other couplings as can be seen in table [ eq : tablcomp ] , where the results obtained with @xmath16 are compared for different values of @xmath2 . we conclude that the same rotation that speeds up the convergence of the collocation method improves also the convergence of the rr method . [ ! .rr approximations to the ground - state energy of hamiltonians ( [ eq : hdim2 ] ) and ( [ eq : hdim2rot ] ) with @xmath17 obtained using @xmath8 functions from the trigonometric basis with optimized quarter period @xmath15 . the underlined digits are those that coincide with the exact result . [ cols="^,^,^,^,^",options="header " , ] in this paper , we studied the convergence of the optimized rr method for the ground - state energy of the coupled anharmonic oscillators using two basis sets : trigonometric functions and harmonic oscillator eigenfunctions . the comparison of the effectiveness of the methods with that of the optimized collocation method @xcite is summarized in figure [ eq : p_nr1 ] by plotting the precision achieved in the computation performed with mathematica ver . the precision calculated as a difference between the approximate and exact result @xmath18 is shown in a log - log plot as a function of cpu time . an important observation is that the rotation that has been shown to improve the convergence of the collocation method @xcite accelerates also the convergence of both variants of the rr method . it is seen that far greater accuracy in the ground - state energy is obtained by using the rotated hamiltonian ( [ eq : hdim2rot ] ) than by increasing the size of the basis . the optimized rr method is more effective with the harmonic oscillator basis than with the trigonometric one , but in both cases the convergence is quicker than that of the optimized collocation approach . this is opposed to the common understanding that the computational cost of the collocation method is less then that of the rr method @xcite . our results show that the rr method with an appropriately optimized basis offers a similar accuracy to the optimized collocation method with much lower computational cost . another important advantage of the rr method is its variational character , which allows us to state that the lower the achieved result , the closer it is to the exact one . discretization in the collocation approach facilitates calculation of the hamiltonian matrix but destroys the variational behavior . normally the monotonic convergence from above is recovered when the number of grid point is sufficiently large but this is not automatically granted . for instance we observe that the approximations obtained by the collocation method from the rotated hamiltonian ( [ eq : hdim2rot ] ) in table 4 of @xcite are below the accurate ground - state energies ( @xcite and our table [ eq : tabocomp ] ) and they decrease with increasing @xmath8 , which suggests that they do not converge to the proper result . this is a warning that when using the collocation method one has to be very cautious about deriving accurate results . 9 reed m and simmons b 1978__methods of modern mathematical physics , vol.4 _ _ ( academic , new york ) p.82 hylleraas e a , zeit.phys._54_ 347 ( 1929 ) cencek w , komasa j , and rychlewski j , in _ handbook on parallel and distributed processing _ ( springer , berlin , 2000 ) , p. 505 . okopiska a 1987 _ phys.rev.d _ * 36 * 1273 amore p and fernndez f m 2010 _ phys.scr . _ * 81 * 045011 arias de saavendra f and buendia e 1991 _ j.phys.a:math.gen . _ * 24 * l1209 yang w and peet a c , 1988 _ chem . _ * 153 * 98 .

for a system of coupled anharmonic oscillators we compare the convergence rate of the variational collocation approach presented recently by amore and fernndez ( 2010 phys.scr.81 045011 ) with the one obtained using the optimized rayleigh - ritz ( rr ) method . the monotonic convergence of the rr method allows us to obtain more accurate results at a lower computational cost .

directed assembly of gold nanorods through the use of dithiolated molecular linkers is one of the most efficient methodologies for the morphologically controlled tip - to - tip assembly of this type of anisotropic nanocrystals . however , in a direct analogy to molecular polymerization synthesis , this process is characterized by difficulties in chain - growth control over nanoparticle oligomers . in particular , it is nearly impossible to favor the formation of one type of oligomer , making the methodology hard to use for actual applications in nanoplasmonics . we propose here a light - controlled synthetic procedure that allows obtaining selected plasmonic oligomers in high yield and with reaction times in the scale of minutes by irradiation with low fluence near - infrared ( nir ) femtosecond laser pulses . selective inhibition of the formation of gold nanorod n - mers ( trimers ) with a longitudinal localized surface plasmon in resonance with a 800 nm ti : sapphire laser , allowed efficient trapping of the ( n 1)-mers ( dimers ) by hot spot mediated photothermal decomposition of the interparticle molecular linkers . laser irradiation at higher energies produced near - field enhancement at the interparticle gaps , which is large enough to melt gold nanorod tips , offering a new pathway toward tip - to - tip welding of gold nanorod oligomers with a plasmonic response at the nir . thorough optical and electron microscopy characterization indicates that plasmonic oligomers can be selectively trapped and welded , which has been analyzed in terms of a model that predicts with reasonable accuracy the relative concentrations of the main plasmonic species .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Restoring the Value of Every American in Environmental Decisions Act''. SEC. 2. VALUATION OF STATISTICAL LIFE IN ENVIRONMENTAL PROTECTION AGENCY DECISIONMAKING. (a) Findings.--Congress finds that-- (1) using a dollar value to establish the worth of a human life as the basis of making decisions about whether to take actions to protect humans from dying from environmental pollution has been controversial, because that practice-- (A) offends many deeply held religious, moral, and ethical beliefs of people in the United States; (B) fails to sufficiently consider the long- standing use of credible and accepted alternative decisionmaking tools, such as-- (i) health-based protections that use the latest science to understand and address serious health threats, including safeguards that seek to protect vulnerable individuals (such as pregnant women, infants, children, and the elderly); (ii) technology-forcing standards that promote increased research and development in effective, cutting-edge technologies that can save lives by cutting costs while-- (I) reducing the use of dangerous materials; (II) preventing or reducing the release of those materials into the environment; or (III) creating new and safer systems or materials; (iii) right-to-know safeguards that-- (I) inform families, communities, workers, and others about known or potential threats; (II) enable those individuals and communities to make decisions about safety based on the information; and (III) encourage emitters and users of toxic chemicals to reduce the emission and use of those chemicals; and (C) fails to promote the development and improvement of other desirable methods of decisionmaking; (2) decisionmaking by the Environmental Protection Agency usually involves policy decisions and legal standards, such as health-based protections, technology-forcing standards, or right-to-know safeguards, rather than monetized values of life and illnesses; (3) Federal agencies should continue to consider the nonquantifiable benefits of agency actions, regardless of whether the number of deaths or illnesses resulting from those actions can be quantified or expressed in monetary terms; (4)(A) there is a great difference between a voluntarily accepted risk and an involuntarily imposed risk; and (B) that difference renders the use of a value of statistical life based on measures of voluntarily accepted risks questionable as applied to involuntarily imposed risks; and (5) as of the date of enactment of this Act, applicable value of statistical life methodologies do not represent the full value of a human life, including (among other issues) the concepts that-- (A) an individual may value another life more than one's own, for example the lives of family members or children; (B) infants, children, and many other individuals do not have the ability to decide the appropriate value of avoiding death; (C) many studies of statistical life methodologies are based on a small subset of the population that may be willing to accept a higher risk of death or illness for less compensation than other members of society; and (D) differing economic situations or negotiating positions may falsely skew statistical life methodology estimates downward. (b) Value of Statistical Life.-- (1) Requirement.--To the extent that the Administrator of the Environmental Protection Agency (referred to in this Act as the ``Administrator'') uses in decisionmaking any value of statistical life, including the life of pregnant women, infants, children, and the elderly, the Administrator-- (A) shall not reduce that value below the highest value of statistical life used in a decisionmaking of the Administrator before the date of enactment of this Act; and (B) shall increase that value not less frequently than once each calendar year, by adjusting the value to reflect-- (i) the average annual total compensation of individuals, including income and benefits; (ii) the average capital that may be liquidated upon the death of an individual; and (iii) the value of nonpaid activities, including the relevant activities described in the American Time Survey Results published by the Bureau of Labor Statistics of the Department of Labor. (2) Prohibition.--The Administrator shall not decrease the value of statistical life used in a decisionmaking by the Administrator based on age, income, race, illness, disability, date of death, or any other personal attribute or relativistic analysis of the value of life. (3) Transparency requirement.--The Administrator shall-- (A) ensure that the process of the Administrator for establishing a value of statistical life under this subsection is conducted in a manner that is open to the public, including by-- (i) providing public notice and an opportunity to comment for a period of at least 60 days on any proposed revision of a value of a statistical life; (ii) explaining the process to the public using common, understandable terms; and (iii) for each significant study upon which the Administrator relies, providing-- (I) a short description of the methodological strengths and weaknesses of the study; and (II) a description of the injury, illness, death, or other event used as a basis for the study; and (B) provide to the Committee on Environment and Public Works of the Senate and the Committee on Energy and Commerce of the House of Representatives, concurrently with the public notice described in subparagraph (A)(i), any proposed revision of a value of a statistical life. (c) Effect of Section.--Nothing in this section-- (1) expresses on behalf of Congress any endorsement of any-- (A) use of value of statistical life analysis as a decisionmaking criterion; (B) cost-benefit analysis; (C) regulatory decisionmaking threshold; or (D) single process of agency decisionmaking; (2) creates a duty to make or revise any standard under any other applicable law; or (3) affects any substantive standard for promulgating regulations under any other applicable law.

Restoring the Value of Every American in Environmental Decisions Act - Requires the Administrator of the Environmental Protection Agency (EPA), when using in decisionmaking any value of statistical life, including the life of pregnant women, infants, children, and the elderly, to: (1) not reduce that value below the highest value of statistical life used in a decisionmaking before the enactment of this Act; and (2) increase that value at least once each year, by adjusting the value to reflect the average annual total compensation of individuals, the average capital that may be liquidated upon the death of an individual, and the value of nonpaid activities, including the relevant activities described in the American Time Survey Results published by the Bureau of Labor Statistics of the Department of Labor. Prohibits the Administrator from decreasing the value of statistical life based on age, income, race, illness, disability, date of death, or any other personal attribute or relativistic analysis of the value of life. Requires the Administrator to: (1) ensure that the process for establishing a value of statistical life is open to the public; and (2) provide to specified congressional committees, concurrently with public notice, any proposed revision of a value of a statistical life. Declares that nothing in this Act: (1) expresses on behalf of Congress an endorsement of any use of value of statistical life analysis as a decisionmaking criterion, cost-benefit analysis, regulatory decisionmaking threshold, or single process of agency decisionmaking; (2) creates a duty to make or revise any standard under any other law; or (3) affects any substantive standard for promulgating regulations under any other law.

measurements of the ground state properties of the most basic element of the constituents of stable matter , namely , the proton , have intrigued physicists since the sixties until now . the structure of the proton in fact plays an important role in atomic physics where experiments have reached very high precision . finite size effects ( fse ) due to the proton structure can be theoretically included using different methods , with one of them being the breit equation @xcite which is a typical example of how one derives coordinate potentials from quantum field theory @xcite . using such a method where one evaluates the elastic electron - proton amplitude expanded in powers of @xmath1 , corrections to the energy levels of the hydrogen atom due to the finite size of the proton have been evaluated @xcite . the fse are included through the elastic electromagnetic form factors obtained from electron proton scattering cross sections @xcite . the electromagnetic form factors as such are an essential part of the description of the properties of the nucleon as they incorporate the probability for a nucleon to absorb a virtual photon of four momentum squared @xmath4 and probe its interior . in the non - relativistic limit , the fourier transforms of the form factors in the breit frame ( defined by @xmath5 ) describe the charge distribution @xmath6 and magnetization current distribution @xmath7 in the nucleon respectively @xcite . an experimental determination of the form factors ( and hence the proton charge density distribution ) from electron proton scattering can thus enable one to determine the charge radius of the proton . on the other hand , the unprecedented precision of the experimental results in the hydrogen atom also allows one to probe the static properties of one of the components of the hydrogen atom , namely , the proton . the size of the proton for example , can be extracted from precise measurements of the difference in the energy levels or lamb shifts in the hydrogen atom . such an extraction performed on the muonic hydrogen atom led to the surprising finding that the extracted value of @xmath8 fm was much smaller than the world average codata value of @xmath9 fm @xcite . this so - called proton puzzle " was later reinforced @xcite with the precise value of @xmath10 fm obtained from muonic hydrogen spectroscopy . apart from some determinations from standard hydrogen atom spectroscopy , the codata value largely depends on the extraction of the radius from electron proton scattering experiments . the shrunk proton gave rise to explanations ranging from the charge density being poorly constrained by data @xcite to those involving large extra dimensions and non - identical protons @xcite . in an attempt to resolve the discrepancy between the proton radius from muonic hydrogen spectroscopy and electron proton scattering data , we re - examine the connection of the electromagnetic form factors to the nucleon properties . we present a new approach to relate the form factors in momentum space to their coordinate space counter parts ( the charge and magnetization densities ) through a fourier transform of the type @xmath11 . the standard non - relativistic expression is obtained when @xmath12 , where @xmath13 is the well known sachs form factor @xcite . the relativistic corrections for @xmath14 are incorporated by evaluating @xmath15 in the form @xmath16 $ ] using the higher order breit equation which we derive in this work . since such a relation is still valid only in the breit frame ( i.e. @xmath17 ) , a lorentz boost must be applied to @xmath15 before extracting the mean radius from @xmath18 . we find that the inclusion of the two effects ( lorentz boost and use of the higher order breit equation ) brings the radius extracted from electron proton scattering quite close to that determined from the muonic hydrogen lamb shift @xcite , thus partly resolving the proton radius puzzle . the relativistic corrections to the non - relativistic @xmath14 are obtained by extending the standard breit equation @xcite ( which involves an expansion of the amplitude to order 1/c@xmath19 ) @xcite to higher orders . the proton electric potential @xmath20 in this equation is used to find the density @xmath6 via the poisson equation , @xmath21 . the hyperfine interaction terms in the breit equation are shown to be related to the magnetization density @xmath7 . in what follows , we shall see that an interesting outcome of the calculation is that the charge form factor @xmath22 appearing in the fourier transform , depends on the magnetic form factor @xmath23 and @xmath24 appearing in the fourier transform of the magnetization density , @xmath7 , depends on @xmath13 . in order to make the approach clear let us begin with the standard breit equation for the hamiltonian h@xmath25 @xcite which results from the @xmath1 expansion of the elastic electron proton transition matrix element m@xmath26 . this amplitude can be written as , m@xmath27 , where @xmath28 are two component spinors . in the diagonal case , @xmath29 , @xmath30 and we write m@xmath31 , where we used @xmath32 = { \bm \xi}$ ] with @xmath33 being the spin density matrix . let us now rearrange terms from the breit hamiltonian h@xmath25 such that , h@xmath34 , where , @xmath35 . @xmath36 is the potential part remaining after separating all the @xmath37 operator dependent and differential operator @xmath38 dependent terms . here @xmath39 is either @xmath40 or @xmath41 . in addition , we choose @xmath36 not to contain the electron mass as the electric proton potential should not depend on the probe . these restrictions allow @xmath36 to be interpreted as a proton electric potential in momentum space . for the standard breit equation at lowest order in @xmath1 , with form factors , this indeed leads to @xcite , @xmath42\ , = 4 \pi e \ , \biggl [ { g_e({\bm q}^{2})\over { \bm q}^{2 } } \biggr ] .\ ] ] where @xmath40 is the positive charge of the proton . the fourier transform of @xmath36 is then the electric potential @xmath43 . the laplacian of @xmath20 , namely , @xmath44 taken together with @xmath45 then brings us to the standard definition of the proton charge density @xmath46 . applying similar restrictions to the magnetic field in the second term in h@xmath25 , i.e. , the magnetic field of the proton @xmath47 should not contain any electron mass or operator @xmath38 dependence , the terms which remain ( apart from the coulomb term ) are those corresponding to the hyperfine interaction . the hyperfine interaction potential with form factors @xcite is given as , @xmath48 g_m({\bm q}^2 ) \nonumber \\ & = & \ , { \bf \mu}_e \cdot { \bf b}({\bm q})\ , , \end{aligned}\ ] ] with @xmath49 as defined earlier . the magnetic field of the proton is thus , @xmath50 g_m({\bm q}^2)\ , .\ ] ] taking the fourier transform of @xmath51 and using the static maxwell equation @xmath52 , we can identify @xmath53 thus implying @xmath54 with @xmath55 which defines the proton magnetization distribution @xmath56 . in the diagonal case , by the replacement of @xmath57 by the polarization vector @xmath58 , we can conclude that polarized protons will have a magnetic field of the form , @xmath59 , where , @xmath60 . all the conclusions drawn above and derived at the lowest order in the relativistic expansion are , of course , valid if we include relativistic corrections . the procedure to obtain the breit potential at higher orders using the electron proton scattering amplitude is exactly the same as that described in @xcite except that the proton and electron wave functions which were written in @xcite using the non - relativistic approximation with corrections up to order @xmath1 are now replaced by those containing relativistic corrections up to order @xmath61 . this is done by using the foldy wouthuysen transformation @xcite , @xmath62 , where @xmath63 @xmath64 , @xmath65 , @xmath66 and @xmath67 , @xmath68 the usual dirac matrices . it then follows that @xcite @xmath69 \psi_{\!_d}$ ] , where , @xmath70 contains both the positive and negative energy solutions . the upper and lower components @xmath71 and @xmath72 of @xmath70 can be shown to be related to the dirac upper and lower components @xmath73 and @xmath74 respectively as @xcite @xmath75 the relativistic energy @xmath76 of the particle includes also its rest energy @xmath77 which must be excluded in arriving at a non - relativistic approximation . we must therefore replace @xmath78 ( fw or d ) by @xmath79 defined as @xmath80 . this leads to a relation between the upper and lower components @xmath81 and @xmath82 of @xmath79 @xcite which is given by , @xmath83^{-1 } \ , \mbox{\boldmath $ \sigma$ } \cdot { \bf p}\ , \phi,\ ] ] where @xmath84 is the energy eigenvalue in the schrdinger equation . identifying the upper component @xmath85 of @xmath70 with the non - relativistic schrdinger spinor @xmath86 , we get , @xmath87 . finally , expanding @xmath88 and replacing for @xmath81 in terms of @xmath86 in @xmath82 , we obtain the spinor to be used in the calculation of the amplitude @xmath89 as @xmath90 with @xmath91 and @xmath92 , @xmath93 , @xmath94 and @xmath95 . the above spinor should be contrasted with @xmath96 used to obtain the standard breit equation @xcite . ( [ spinoreq2 ] ) and the vertices @xmath97 and @xmath98 , the amplitude @xmath99 and hence the breit equation with form factors is evaluated just as in @xcite . note that the energy transfer at the vertices is chosen to be zero , i.e. , @xmath100 is replaced by @xmath101 . formally , this is achieved by going to the breit frame . this is in keeping with the quasistatic approach wherein we are going to relate the proton potential obtained from the breit equation to the charge density via the poisson equation . the higher order breit equation with form factors thus obtained is very lengthy and will be given elsewhere . the present work deals with the parts relevant for obtaining the relativistic corrections to the charge and magnetization densities . the proton electric potential @xmath102 with relativistic corrections is obtained from the higher order breit equation in the same manner as explained before for the standard breit equation . dropping all terms involving the spin and momentum operators as well as those containing the electron mass , what remains in the higher order breit equation is @xmath103 \biggr \ } . \end{aligned}\ ] ] the above equation can be rewritten as @xmath104 , such that the proton electric potential , @xmath105 and @xmath106 . the magnetic form factor @xmath24 including corrections is obtained by examining the hyperfine interaction terms as mentioned before , however , in the higher order breit equation . noting that the terms of order @xmath61 and higher are of decreasing importance and due to the alternating sign in ( [ newpot1 ] ) , the first four terms in the curly bracket in ( [ newpot1 ] ) can be approximated as @xmath107^{-1/2}$ ] . the expressions for @xmath108 can thus be summarized in an expansion effectively as , @xmath109 with @xmath110 and @xmath111 . it is interesting that @xmath15 and @xmath24 depend on both the @xmath112 and @xmath113 sachs form factors and have relativistic corrections of a similar form with the same exponents @xmath114 and @xmath115 . note also that the exponent @xmath116 in the first terms is approximate ( in contrast to the exact @xmath107^{-1/2}$ ] in @xcite ) . at order @xmath1 , the expression for @xmath117 is independent of @xmath113 as in @xcite , however , the magnetic form factor at order @xmath1 reduces to @xmath118 and contains apart from the darwin term @xmath119 , a term dependent on @xmath112 . since we chose the energy transfer in the evaluation of the electron - proton scattering amplitude , @xmath120 , the above form factors are similar to those usually given in the so - called breit frame . an additional important relativistic correction arises due to the lorentz contraction of the spatial distributions in the breit frame @xcite . the latter has been discussed at length in the first reference of @xcite where the author proposes the use of the fourier transform of @xmath121^{\lambda_{e , m}}$ ] , rather than the fourier transform of @xmath122 in order to determine the density distributions of the nucleon . with @xmath123 being model dependent constants , they eventually appear as parameters in the determination of the proton radius and other moments . the author in the first reference in @xcite fitted the form factor data to obtain @xmath124 in agreement with some @xcite while in contrast with other predictions @xcite of @xmath125 and @xmath126 based on soliton and cluster models . the standard way of defining the @xmath127 moment of the charge and magnetization distribution in literature @xcite follows from a consideration of the fourier transforms of the sachs form factors in the breit frame . it makes sense to dwell a little bit on the basics of the definition of the second moment , i.e. , @xmath128 starting with the fourier transform of @xmath129 , namely , @xmath130 we can readily show that @xmath131\nonumber \\ & = & { 1 \over 2 \pi^2 } \ , \biggl [ \int_0^{\infty } r^2 \rho(r ) dr - { { \bm q}^2 \over 6 } \int_0^{\infty } r^4 \ , \rho(r ) dr \ , + \ , ... \ , \biggr ] \end{aligned}\ ] ] leads to the standard result @xmath132 eq . ( [ newx1 ] ) is equivalent to writing @xmath133 where @xmath134 is the @xmath127 moment of the electric or magnetic distribution . neither ( [ newx0 ] ) nor ( [ newx1 ] ) are relativistic invariants . the form factor @xmath135 which depends on the four momentum transfer is an invariant and sometimes one finds in the literature the expansion @xmath136 with @xmath137 being the four - momentum transfer . this is then followed by an expression of the first moment proportional to @xmath138 taken at @xmath139 . this in turn might lead to the confusing conclusion that the proton radius is a lorentz invariant . to resolve the confusion let us first note that we would get the same result by writing @xmath140 and taking the derivative with respect to @xmath141 evaluated at @xmath142 which agrees with ( [ newx2 ] ) and , of course , ( [ newx0 ] ) . therefore , we would face a paradox here : by using ( [ newx3 ] ) and its derivative with respect to the four momentum squared @xmath143 , it seems like we have found a lorentz invariant quantity and this is equivalent to a lorentz non - invariant result ( up to the minus sign which is absorbed into the definition ) . the resolution of the paradox lies in the meaning of the condition , @xmath139 . with @xmath144 , it either means that @xmath145 ( in which case we have a real photon ) or @xmath146 . it is impossible to exchange a real photon in the t - channel exchange diagram in elastic electron - proton scattering and hence we have to drop the first possibility . the second choice is , however , equivalent to first choosing the frame ( @xmath147 implies that we have chosen the breit frame again ) and then @xmath142 is necessary to extract the taylor coefficient ( the radius ) . in short , even if @xmath138 is invariant , the condition @xmath148 makes the radius defined using @xmath138 at @xmath149 , a lorentz non - invariant quantity ( as the condition forces one to choose @xmath150 ) . if @xmath6 and @xmath7 ( defined by @xmath151 and @xmath152 ) , receive relativistic corrections as given in ( [ finalresult ] ) , so will the corresponding radii . hence , the proton moments including the relativistic corrections and the lorentz boost are defined here as : @xmath153 and @xmath154 ( with @xmath155^ { \lambda_{\!_{e}}}$ ] ) . replacing from ( [ finalresult ] ) for @xmath156 leads to @xmath157 the magnetic radius with relativistic and lorentz boost corrections is given by , @xmath158\end{aligned}\ ] ] the relativistic corrections alone ( giving @xmath159 and @xmath160 in table i ) arising from ( [ finalresult ] ) can be found by setting @xmath161 . comparison of the proton radius values extracted from the muonic hydrogen lamb shift @xcite , codata values @xcite and some recent analyses @xcite of @xmath162 scattering data . the hydrogen spectroscopy average is from @xcite.,width=340,height=340 ] .corrections to the proton charge radius @xmath163 in fm . the fourth moments @xmath164 of the proton charge distribution with corrections ( up to order 1/c@xmath19 and 1/c@xmath165 ) are given in the brackets ( in fm@xmath165 ) . the first column gives the usual uncorrected values obtained from @xmath167 scattering , the second column shows the increase in values due to relativistic corrections , the third and fourth the reduction due to lorentz boost and finally the last two columns display the effects of both corrections together . [ cols= " < , < , < , < , < , < , < " , ] the effect of the lorentz boost in general is to reduce the radius and the fourth moment of the proton charge as compared to that obtained from @xmath168 in the breit frame . the relativistic corrections introduced with the use of @xmath15 obtained from the higher order breit potential , in general , increase the radius of the proton . however , a fortuitous combination of the two effects , brings the proton radius closer to @xmath10 fm obtained from precise lamb shift measurements @xcite . for a lorentz boost with @xmath169 such an agreement is favoured by fit ii in @xcite which gives @xmath170 fm and @xmath171 fm obtained from the bump - tail parametrization ( with parameters from table ii in @xcite ) . indeed , if we apply the lorentz boost with @xmath172 to the central value of the radius @xmath2 fm deduced recently by bernauer et al . @xcite we obtain @xmath173 fm which is once again close to the muonic hydrogen spectroscopy result @xcite . this is demonstrated in figure 1 . the reason for applying only the lorentz boost and not the entire relativistic corrections is the following : bernauer et al . include in their analysis , the feshbach correction " which as stated above eq.(20 ) in @xcite is in agreement with the coulomb correction of rosenfelder @xcite at @xmath174 . this correction of rosenfelder is similar to the relativistic corrections of the present paper upto order @xmath1 ( compare eq.(7 ) of @xcite with the first term in eq.([finalresult ] ) of the present work ) . it would lead to a double counting if we would apply the relativistic correction of our work to the radius of bernauer et al . and hence we apply only the lorentz boost . though we do not show explicitly , similar corrections would also shift the other radii in fig.1 , extracted from @xmath167 scattering , to lower values . the proton magnetic radius , @xmath175 fm @xcite , with relativistic and lorentz boost corrections changes to @xmath176 fm . finally , we must emphasize that the proton is characterized fully by all its moments and not just the radius . the corrections in eqs ( [ finalresult ] ) introduce a significant change in @xmath177 too . finally , in passing we mention that the proton structure corrections as such are also dependent on the theoretical formalism used to calculate them . we refer the reader to ref . @xcite for a detailed discussion of the proton structure corrections using different formalisms . the relations between charge / magnetization densities and the electromagnetic form factors are necessarily of a non - relativistic nature . in other words , relativistic corrections can be computed and the standard relation between the sachs form factors ( @xmath13 and @xmath23 ) and the densities is valid only at the lowest order of the non - relativistic expansion . to compute the relativistic corrections in a consistent way we employed the higher order breit equation in which , for instance , terms independent of the probe , spin and momentum operators should correspond to the proton electric potential in momentum space . using the poisson equation , this potential gives us the relativistically modified charge density . a similar procedure can be found for the magnetization density . both results are valid in the breit frame . hence using a lorentz transformation suggested in the literature , we can bring them to the rest frame of the proton and calculate the modified moments of the proton charge and magnetization densities . an interesting outcome of the manipulations , i.e. , including relativistic corrections and the lorentz transformation is that the proton radius from @xmath178 scattering experiments comes closer to the result obtained from muonic hydrogen spectroscopy . a free spin @xmath179 particle is described by a four component wave function satisfying the dirac equation . it is however , often desirable to convert this equation to a two component equation of the pauli type . methods attempting to do this however encounter difficulties if one wishes to go beyond the lowest order in the @xmath180 expansion . a method proposed by foldy and wouthuysen @xcite however overcomes these difficulties . their treatment involves a unitary transformation which block diagonalizes the dirac hamiltonian and eventually splits the dirac equation into two uncoupled equations of the pauli type , describing particles in positive- and negative - energy states , respectively . since the procedure to carry out the foldy - wouthuysen transformation is given below eq . ( [ foldy1 ] ) in the main text , here we only write the intermediate steps for obtaining the coefficients in eq . ( [ spinoreq2 ] ) . we start with @xmath87 as given below eq . ( [ spinoreq ] ) and expanding @xmath88 , we obtain , @xmath181 \ , w \,.\ ] ] this is the upper component given in eq . ( [ spinoreq2 ] ) . replacing the above @xmath81 in eq . ( [ spinoreq ] ) namely , @xmath182 ^{-1 } \ , \mbox{\boldmath $ \sigma$ } \cdot { \bf p}\ , \phi , \nonumber \\ & = & { \mbox{\boldmath $ \sigma$ } \cdot { \bf p } \over 2 m c } \biggl ( 1 - { e_s \over 2 m c^2 } + { e_s^2 \over 4 m^2 c^4 } - { e_s^3 \over 8 m^3 c^6 } + .... \biggr ) \ , \phi \ , , \nonumber\end{aligned}\ ] ] using the fact that @xmath183 where , @xmath184 and replacing accordingly for every @xmath185 by @xmath186 w$ ] , we get @xmath187 \ , \biggl [ 1 - { p^2 \over 8 m^2 c^2 } + { 11\over 128 } { p^4 \over m^4 c^4 } \ , ... \ , \biggr ] \ , w \nonumber \\ & = & \biggl [ 1 - { 3 \over 8}{p^2 \over m^2 c^2 } + { 31\over 128 } { p^4 \over m^4 c^4 } \ , ... \ , \biggr ] \ , { \mbox{\boldmath $ \sigma$ } \cdot { \bf p } \over 2 m c}\,w \,.\end{aligned}\ ] ] this is the lower component in eq . ( [ spinoreq2 ] ) . we investigated another method @xcite to obtain such an expansion and it was gratifying to find the same coefficients as above . if we begin again with eq . ( [ spinoreq ] ) as the starting point and perform an expansion for @xmath82 after noting that @xmath84 is the total energy with rest energy subtracted , @xmath82 can be rewritten as , @xmath188\ , \phi.\ ] ] now noting that the density @xmath189 \ , \biggl [ \mbox{\boldmath $ \sigma$ } \cdot ( { \bf p } a \phi ) \biggr ] \ ] ] where @xmath190 is basically the operator in square brackets in ( [ chiagain ] ) . this @xmath33 obviously differs from the schrdinger expression . in order to find the wave equation corresponding to the schrdinger equation , we must replace @xmath81 by another function @xmath191 , for which the time independent integral would be of the form @xmath192 as it should be for the schrdinger equation . hence , to obtain the required transformation , we write the condition @xmath193 \ , [ \mbox{\boldmath $ \sigma$ } \cdot ( { \bf p } a \phi ) ] \biggr \ } \ , d^3 x\ , .\ ] ] integrating the second term by parts and after some lengthy but straightforward algebra , we find that the following expression for @xmath81 , satisfies the relation in ( [ condition ] ) . @xmath194 \ , \phi_{sch } \,,\ ] ] this is however the same as eq . 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the proton charge and magnetization density distributions can be related to the well known sachs electromagnetic form factors @xmath0 through fourier transforms , only in the breit frame . the breit frame however moves with relativistic velocities in the lab and a lorentz boost must be applied to the form factors before extracting the static properties of the proton from the corresponding densities . apart from this , the fourier transform relating the densities and form factors is inherently a non - relativistic expression . we show that the relativistic corrections to it can be obtained by extending the standard breit equation to higher orders in its @xmath1 expansion . we find that the inclusion of the above corrections reduces the size of the proton determined from electron proton scattering data . indeed the central value of the latest proton radius of @xmath2 fm as determined from e - p scattering changes to @xmath3 fm after applying corrections .

Add a location to your Tweets When you tweet with a location, Twitter stores that location. You can switch location on/off before each Tweet and always have the option to delete your location history. Learn more ||||| A 31-year-old climber, Alex Honnold, on June 3, 2017, became the first person to scale the 3,000-foot El Capitan in Yosemite National Park, Calif., shown in a 2015 file photo, without a rope or safety gear, according to National Geographic. (Photo: Ben Margot, AP) Alex Honnold, a celebrated 31-year-old rock climber, on Saturday became the first person to scale Yosemite's El Capitan, a nearly 3,000-foot granite wall, without using ropes or other safety gear, according to National Geographic. After his standard breakfast of oats, flax, chia seeds and blueberries, Honnold started the ropeless ascent — known as free soloing — at the first light of dawn, 5:32 a.m., and pulled himself over a rocky lip to the summit, a sandy ledge, 3 hours and 56 minutes later. This exclusive photo was taken moments after renowned rock climber @AlexHonnold scaled El Capitan in Yosemite https://t.co/P9EEUcaLbypic.twitter.com/jHIlq32JCM — National Geographic (@NatGeo) June 3, 2017 The climb, which National Geographic said may be the greatest feat of pure rock climbing in the history of the sport, was captured by a team of filmmakers, led by Jimmy Chin, one of Honnold’s longtime climbing partners, and Elizabeth Chai Vasarhelyi, for an upcoming National Geographic Documentary Films feature. It was his second attempt to crack El Capitan. In November, Honnold made his first free-solo run at the granite behemoth, but quit after less than an hour because he said conditions did not feel right. National Geographic said he had been training for the climb for a year at locations in the United States, China, Europe and Morocco, but kept it a secret from all but a small circle of friends and fellow climbers. Honnold’s climbs are “so remarkable that it defies belief,” CBS correspondent Lara Logan said in a 2015 profile by CBS' 60 Minutes. According to his website, Honnold "maintains his simple 'dirtbag-climber' existence, living out of his van and traveling the world in search of the next great vertical adventure." Read or Share this story: https://usat.ly/2rDIN4X ||||| This story was originally published on June 4, 2017. It was updated with additional photos on October 3, 2018. YOSEMITE NATIONAL PARK, CALIFORNIA—Renowned rock climber Alex Honnold on Saturday became the first person to scale the iconic nearly 3,000-foot granite wall known as El Capitan without using ropes or other safety gear, completing what may be the greatest feat of pure rock climbing in the history of the sport. He ascended the peak in 3 hours, 56 minutes, taking the final moderate pitch at a near run. At 9:28 a.m. PDT, under a blue sky and few wisps of cloud, he pulled his body over the rocky lip of summit and stood on a sandy ledge the size of a child’s bedroom. View Images Rock climber Alex Honnold training on Freerider for the first ever rope-free climb of El Capitan in Yosemite National Park. He completed the feat on Saturday, June 3, 2017. The historic event was documented for an upcoming National Geographic feature film and magazine story. Photograph by Jimmy Chin, National Geographic Watch Alex Honnold's journey toward his rope-free climb of the world's most famous rock wall—Yosemite National Park's El Capitan—in Free Solo, a stunning, intimate, unfliching film by E. Chai Vasarhelyi and Jimmy Chin. Find the film in theaters starting September 28, 2018. Honnold began his historic rope-less climb—a style known as “free soloing”—in the pink light of dawn at 5:32 a.m. He had spent the night in the customized van that serves as his mobile base camp, risen in the dark, dressed in his favorite red t-shirt and cutoff nylon pants, and eaten his standard breakfast of oats, flax, chia seeds, and blueberries, before driving to El Capitan Meadow. FREE SOLO: ALEX HONNOLD'S EPIC ROPE-FREE CLIMB Watch the trailer for Free Solo, a stunning, intimate, and vertigo-inducing film about rock climber Alex Honnold's journey to climbing the world’s most famous rock wall—El Capitan in Yosemite National Park—without a rope or safety gear. He parked the van and hiked up the boulder-strewn path to the base of the cliff. There, he pulled on a pair of sticky soled climbing shoes, fastened a small bag of chalk around his waist to keep his hands dry, found his first toehold, and began inching his way up toward climbing history. For more than a year, Honnold has been training for the climb at locations in the United States, China, Europe, and Morocco. A small circle of friends and fellow climbers who knew about the project had been sworn to secrecy. A team of filmmakers, led by Jimmy Chin, one of Honnold’s longtime climbing partners, and Elizabeth Chai Vasarhelyi, captured the ascent for an upcoming National Geographic Documentary Films feature. This past November, Honnold made his first attempt at the free solo, but backed off after less than an hour of climbing because conditions did not feel right. THE MOON LANDING OF FREE-SOLOING Trained in a climbing gym in Sacramento, Honnold, 31, burst onto the international scene in 2008 with two high-risk, rope-free ascents—the northwest face of Yosemite’s Half Dome and the Moonlight Buttress in Utah’s Zion National Park. Those free solos astonished the climbing world and set new benchmarks in much the same way that Roger Bannister redefined distance running when he broke the four-minute mile in 1954. “What Alex did on Moonlight Buttress defied everything that we are trained, and brought up and genetically engineered to think,” said Peter Mortimer, a climber who has made numerous films with Honnold. “It’s the most unnatural place for a human to be.” View Images Rock climber Alex Honnold stands atop El Capitan after nearly four hours of climbing alone, without ropes or any other equipment or safety gear. Photograph by Jimmy Chin But those pioneering climbs pale in comparison to El Capitan. It’s hard to overstate the physical and mental difficulties of a free solo ascent of the peak, which is considered by many to be the epicenter of the rock climbing world. It is a vertical expanse stretching more than a half mile up—higher than the world’s tallest building, the Burj Khalifa in Dubai. From the meadow at the foot of El Capitan, climbers on the peak’s upper reaches are practically invisible to the naked eye. “This is the ‘moon landing’ of free soloing,” said Tommy Caldwell, who made his own history in 2015 with his ascent of the Dawn Wall, El Capitan’s most difficult climb, on which he and his partner Kevin Jorgeson used ropes and other equipment only for safety, not to aid their progress. (What Caldwell and Jorgeson did is called free climbing, which means climbers use no gear to help them move up the mountain and are attached to ropes only to catch them if they fall. Free soloing is when a climber is alone and uses no ropes or any other equipment that aids or protects him as he climbs, leaving no margin of error.) Pull Quote With free-soloing, obviously I know that I’m in danger, but feeling fearful while I’m up there is not helping me in any way. Climbers have been speculating for years about a possible free solo of El Capitan, but there have only been two other people who have publicly said they seriously considered it. One was Michael Reardon, a free soloist who drowned in 2007 after being swept from a ledge below a sea cliff in Ireland. The other was Dean Potter, who died in a base jumping accident in Yosemite in 2015. John Bachar, the greatest free soloist of the 1970s, who died while climbing un-roped in 2009 at age 52, never considered it. When Bachar was in his prime, El Capitan had still never been free climbed. Peter Croft, 58, who completed the landmark free solo of the 1980s—Yosemite’s 1,000-foot Astroman—never seriously contemplated El Capitan, but he knew somebody would eventually do it. “It was always the obvious next step,” says Croft. “But after this, I really don’t see what’s next. This is the big classic jump.” By the end of 2014, Honnold had achieved international fame for his exploits. He had been featured on the covers of National Geographic, New York Times Magazine, Outside, and 60 Minutes had profiled him. He had a slew of corporate sponsors, had co-written a best-selling memoir, and started a nonprofit foundation to improve the lives of needy communities around the world. But he felt like he had not yet made the mark he hoped to on climbing history. In January 2015, when Caldwell and Jorgeson summited the Dawn Wall, a project they had spent years studying and training for, Honnold was there to meet them. Jorgeson told a reporter, “I think everyone has their own secret Dawn Wall to complete one day.” What’s my Dawn Wall? Honnold asked himself. But he already knew the answer. For years he’d been thinking about what it would take to free solo El Capitan. AN ABILITY TO CONTROL FEAR The route Honnold chose to reach the top of El Capitan, known as Freerider, is one of the most prized big wall climbs in Yosemite. The route has 30 sections—or pitches—and is so difficult that even in the last few years, it was newsworthy when a climber was able to summit using ropes for safety. It is a zigzagging odyssey that traces several spidery networks of cracks and fissures, some gaping, others barely a knuckle wide. Along the way, Honnold squeezed his body into narrow chimneys, tiptoed across ledges the width of matchboxes, and in some places, dangled in the open air by his fingertips. Freerider tests nearly every aspect of a climber’s physical abilities—strength of fingers, forearms, toes, and abdomen, as well as flexibility and endurance. Environmental factors, like sun, wind, and the potential for sudden rainstorms, are also factors that Honnold had to carefully calculate. But the true test for Honnold was whether he could maintain his composure alone on a cliff face hundreds or thousands of feet up while executing intricate climbing sequences where positioning a foot slightly too low or high could mean the difference between life and death. Elite climbers have pointed to Honnold’s unique ability to remain calm and analytical in such dangerous situations, a skill that Honnold has slowly developed over the 20 years he has been climbing. Some of his poise can be attributed to his detailed preparation. He is obsessive about his training, which includes hour-long sessions every other day hanging by his fingertips and doing one- and two-armed pullups on a specially-made apparatus that he bolted into the doorway of his van. He also spends hours perfecting, rehearsing, and memorizing exact sequences of hand and foot placements for every key pitch. He is an inveterate note-taker, logging his workouts and evaluating his performance on every climb in a detailed journal. YOSEMITE NATIONAL PARK CALIF. Freerider route El Capitan El Capitan Summit Soloing Freerider 2,750 ft above valley floor End of Freerider route With his successful ascent of Freerider, Alex Honnold is the first person to ever free solo a major route on El Capitan, a major rock formation in Yosemite National Park. The Freerider route extends almost 3,000 feet from the base of El Capitan in Yosemite Valley. Freerider (section) The Round Table Location of ‘crux’, or critical, move The Block 2,000 ft Teflon Corner El Cap Spire 1,500 ft The Ear The Heart 1,000 ft Hollow Flake Mammoth Terraces Lung Ledge Heart Ledges Half Dollar Freerider, rated a 5.13a on the Yosemite Decimal System and consisting of 30 pitches, is a variation of the Salathé Wall. With Alex Honnold’s ropeless ascent, this is now the first major route on El Cap to ever be free soloed. 500 ft Triangle Ledge Beginning of Freerider route 0 ft Lauren C. Tierney, NG STAFF; Charles Preppernau Locator Map Art: Clay Wadman SOURCES: Mark SynNott; Antoine Guerin, Battista Matasci, Michel Jaboyedoff, and Marc-Henri Derron, University of Lausanne. El Capitan summit Soloing Freerider 2,750 ft above valley floor End of Freerider route With his successful ascent of Freerider, Alex Honnold is the first person to ever free solo a major route on El Capitan, a major rock formation in Yosemite National Park. The Freerider route extends almost 3,000 feet from the base of El Capitan in Yosemite Valley. 2,500 ft YOSEMITE NATIONAL PARK Freerider (section) CALIF. A move that involves small holds far apart, followed by an airy traverse, all without rest. Freerider route The Round Table El Capitan Location of ‘crux’, or critical, move The Block 2,000 ft “The Boulder Problem”, the crux of the entire climb, involves a small hold 1/8” wide, followed by a karate kick move. Teflon Corner El Cap Spire Difficult traverse into the “Monster Offwidth” 1,500 ft The Ear The Heart 1,000 ft Hollow Flake Traverse and downclimb into the Hollow Flake Mammoth Terraces Lung Ledge Thin slab moves on blank face between Heart and Lung Ledge Heart Ledges Half Dollar Freerider, rated a 5.13a on the Yosemite Decimal System and consisting of 30 pitches, is a variation of the Salathé Wall. Royal Robbins, Chuck Pratt, and Tom Frost made the first ascent of the Salathé Wall in 1961. The Salathé route was first free climbed by Todd Skinner and Paul Piana in 1988, and Alex and Thomas Huber established Freerider in 1998. With Alex Honnold’s ropeless ascent of Freerider, this is now the first major route on El Cap to be free soloed. 500 ft Very thin, smooth, hold- less slab moves at end of pitch Triangle Ledge Difficult move turning a roof Beginning of Freerider route 0 ft Lauren C. Tierney, NG STAFF; Charles Preppernau Locator Map Art: Clay Wadman SOURCES: Mark SynNott; Antoine Guerin, Battista Matasci, Michel Jaboyedoff, and Marc-Henri Derron, University of Lausanne. There are other climbers in Honnold’s league physically, but no one else has matched his mental ability to control fear. His tolerance for scary situations is so remarkable that neuroscientists have studied the parts of his brain related to fear to see how they might differ from the norm. Honnold sees it in more pragmatic terms. “With free-soloing, obviously I know that I’m in danger, but feeling fearful while I’m up there is not helping me in any way,” he said. “It’s only hindering my performance, so I just set it aside and leave it be.” On Freerider, one of the most daunting physical and mental challenges Honnold faced was two pitches of steep, undulating expanse of rock about 600 feet up. Polished smooth by glaciers over the millennia, the granite here offers no holds, forcing a climber to basically walk up it with his feet only. Honnold used a delicate technique called “smearing,” which involves pressing his rubber shoes against the rock to create just enough grip to support his weight on the incline. He had to keep his weight perfectly balanced and maintain enough forward momentum to avoid sliding off. “It’s like walking up glass,” Honnold said. Over Memorial Day weekend, Honnold made a practice run up Freerider with Caldwell. The pair reached the top in a little over five and half hours, breaking their own speed record in the process. “Alex was on fire,” said Caldwell. “I’ve never seen him climbing so well.” A few days before this week’s climb, Honnold hiked to the top of El Capitan and rappelled Freerider to make sure that a recent rainstorm had not washed off the marks he had made with dabs of chalk to highlight the route’s key holds. He found it dry and in perfect condition. Now all that was left was to rest and prepare mentally for the climb of his life. “Years ago, when I first mentally mapped out what it would mean to free solo Freerider, there were half a dozen of pitches where I was like, ‘Oh that’s a scary move and that’s a really scary sequence, and that little slab, and that traverse,’” Honnold said. “There were so many little sections where I thought ‘Ughh—cringe.’ But in the years since, I’ve pushed my comfort zone and made it bigger and bigger until these objectives that seemed totally crazy eventually fell within the realm of the possible.” On Saturday, the possible finally became reality. After trusting his skill and endurance over hundreds of handholds and footholds and controlling his fear for just under four hours, Honnold pulled his body over the last ledges. Chin along with his assistant Sam Crossley and cameraman Cheyne Lempe had rappelled down with their cameras from the top to follow Honnold as he climbed the upper half of the wall, even using jumars—a type of mechanical winch—to hoist themselves up, the two had struggled to keep up with him. ||||| Alex Honnold has free-soloed El Capitan, completing a ropeless ascent of the legendary California cliff in just under four hours on Saturday morning, making the summit in time for breakfast. The 31-year-old rock climber is the first to achieve the feat and indeed was regarded as the only climber capable of attempting it. After completing the climb, Honnold tweeted: “So stoked to realize a life dream today”, including a photo of himself ascending along a wide crack near the top of the route. “This is the ‘moon landing’ of free-soloing,” fellow climber Tommy Caldwell told National Geographic, which filmed the ascent for a documentary and first carried the news on its website. Caldwell won fame outside the climbing world for his 2015 ascent with Kevin Jorgeson of El Capitan’s Dawn Wall route, setting a new standard of difficulty on the Yosemite valley cliff. Free-soloing is the practice of climbing without a harness or rope, leaving zero margin for error. The route Honnold climbed, known as Freerider, is 2,900ft tall and near the top of the ratings system for difficulty, at 5.12d (6b UK). At multiple points on the route, Honnold was obliged to make off-balance moves on widely spaced holds the width of raisins, with hundreds, and then thousands, of feet of air beneath him. Honnold’s preparation for the exploit was the subject of rumor even as it was written off as impossibly daunting and risky. The Sacramento native, who has repeatedly shocked the climbing world with ropeless ascents of forbidding routes, had been discreetly training for the route for more than a year. Honnold backed off of an earlier attempt at a free-solo, last November, after judging conditions to be suboptimal. He most recently climbed the route with a rope, and Caldwell as partner, on a Monday late last month. “Alex was on fire,” Caldwell told National Geographic of the ascent. “I’ve never seen him climbing so well.” Describing his preparations, Honnold said he had expanded his “comfort zone” until he was ready to commit to the route. “Years ago, when I first mentally mapped out what it would mean to free-solo Freerider, there were half a dozen of pitches where I was like: ‘Oh, that’s a scary move and that’s a really scary sequence, and that little slab, and that traverse,’” Honnold told National Geographic. “There were so many little sections where I thought ‘Ugh – cringe.’ But in the years since, I’ve pushed my comfort zone and made it bigger and bigger until these objectives that seemed totally crazy eventually fell within the realm of the possible.” Honnold’s historic ascent began with the first hint of dawn at 5.32am on Saturday. He reached the top three hours and 56 minutes later, at 9.28am. Most roped ascents of El Capitan take hours, days, or longer. The route was first ascended by a climber pulling only on stone – as opposed to pulling on gear drilled or cantilevered into the stone – in 1995, by the German climber Alex Huber. Huber wore a harness and was attached to ropes that would have caught him had he fallen. For much of its length, Freerider follows the Salathe Wall route, which was established in 1961 by the wall-climbing pioneer Royal Robbins, who died in March. Honnold grew up in Sacramento and began climbing in the local training gym at age 11. He dropped out of the University of California at Berkeley, where he had been studying engineering, at age 19, to commit to his climbing career. His previous exploits have been widely documented. One of his corporate sponsors, North Face, produced a 2014 film of his free-solo of the 2,500ft El Sendero Luminoso in Mexico. A National Geographic film crew captured Honnold’s revolutionary 2011 free-solo of the north-west face of Half Dome, in Yosemite, including a hair-raising moment of truth near the top in which Honnold struggled, uncharacteristically, to keep his cool. As his stature in the climbing world and beyond has grown over the last decade, Honnold has maintained an itinerant lifestyle, living in a converted van and traveling the world. His training for Freerider took him to Europe, Morocco and China, according to National Geographic. The climbers who trained with him were sworn to secrecy about the project. ||||| This story was originally published on June 4, 2017. It was updated with additional photos on October 3, 2018. Writer and climber Mark Synnott took Alex Honnold on his first international climbing expedition to Low’s Gully in Borneo back in 2009, and subsequent trips to Chad, Oman, and Newfoundland. Over the years they’ve kept up a running dialogue about the finer points of climbing and debated the dangers of free soloing—climbing alone, without ropes or other safety gear. It seems fitting that in the first moments after Honnold had become the first person to free solo Yosemite’s El Capitan, the greatest pure feat of rock climbing in history, that he’d sit down with his old friend at the Manure Pile, a popular climbing spot at the foot of El Capitan. He ate an apple, listened to the birds, and described the experience of a lifetime. Watch Alex Honnold's journey toward his rope-free climb of the world's most famous rock wall—Yosemite National Park's El Capitan—in Free Solo, a stunning, intimate, unfliching film by E. Chai Vasarhelyi and Jimmy Chin. Find the film in theaters starting September 28, 2018. You just had the best day of your life. Or you’re having the best day of your life. Honestly, I think this is the most satisfied I’ve ever been. It was exactly what I hoped for. I felt so good. It went pretty much perfectly. Did the mountain look scary this morning? I don’t think the mountain looked that scary this morning. Everything felt the same. I didn't have much of a backpack, and the climbing just felt amazing. Not dragging 60 meters of rope behind you for the whole mountain, I felt so much more energetic and fresh. How did you feel at the start? Not perfect. Maybe I didn't drink enough yesterday. I kind of had a headache when I went to bed. I didn't feel that stressed because in a way I had already committed to autopilot and just put everything aside. FREE SOLO: ALEX HONNOLD'S EPIC ROPE-FREE CLIMB Watch the trailer for Free Solo, a stunning, intimate, and vertigo-inducing film about rock climber Alex Honnold's journey to climbing the world’s most famous rock wall—El Capitan in Yosemite National Park—without a rope or safety gear. Walking to the base, it was still quite dark. I started slightly earlier than I had been because I wanted to make sure I was the first (climber) at the base. I saw a bear running away on the walk in. I think I flushed him. So tell me about your state of mind. Pull Quote I knew exactly what to do the whole way. A lot of the handholds feel like old friends. At the bottom I was slightly nervous. I mean it’s a freaking big wall above you. It’s like—it’s something. And then on the Freeblast (glass-smooth slabs of granite without handholds), I was slightly tense, but felt really good. Has it sunk in yet? Honestly even now I feel like I could go do another lap right now. I feel so amped. Another lap on the cliff? Yikes! I feel so good. Are you going to climb more? Probably not. But today is hang-boarding day. I’ll have to hang board in a bit. (Editor’s note: climbers regularly practice dangling from fingertip holds on a hang board to improve their grip strength.) So it’s still just game on? I think so. I mean I still want to climb hard things someday. I mean you don’t just retire as soon as you get down. (Laughing) That’s the quote of the day so far. I think you’re good. Noooo. There were a few groups on route. Did you talk to anyone? I passed five people asleep on the Heart and Lung ledges, but I didn’t really chat with anyone. Did they wake up? (Laughing) Nobody really said anything. Everybody kept it super chill. I was watching through a telescope. At Heart Ledge it looked like you were trying to get a water bottle you’d stashed without waking anyone up. Pull Quote It felt much less scary than a lot of other solos I’ve done. I woke up one guy and he sort of said, “Oh, hey.” Then when I went by, I think he discreetly woke up his buddies because when I looked down they were all three standing there like ‘what the f***’? It looked like one person was wearing a unicorn costume? What costume? I didn’t pay attention. What was it like at the top? We ended up on top exchanging hugs for a while. We were all pretty freaking stoked. What’d you do yesterday? I went bouldering in the morning a little bit because I wanted to break in my shoes a little, and then I went hiking with my mom and some of her friends. Then I watched the last Hobbit movie and just vegged. You didn’t even take a rest day before you free-soloed El Cap? That’s part of the plan. You don’t want to be coming off bed rest. You want to be coming off light exercise. Because physically (the climb) is not that hard to execute. It’s more you have to be in exactly the right (mental) place, so I was trying to create the right place. How was your sleep last night? Oh, I slept like a baby. I woke up at around 2:30 or 3:30, like, ‘Let’s do this!’ And then looked at the clock and was like, ‘oh,’ and then went back to sleep and then woke up around 4:30. When you’re 70, you’re going to come into Yosemite with your grandkids, and they’re going to see El Capitan. And you’re going to say? Kids, that thing takes about four hours to climb by yourself—after years of effort. (laughs) Which parts are going to stick in your mind when you’re 70? The Monster was one of the best because you feel completely safe and, without a harness on, it felt really easy there. I bet that’s the fastest the Monster has ever been climbed. I was in there like ‘this is so cruiser’, having a great time. And from the round table to the summit it was celebratory climbing. It was like taking a victory lap. I was karate chopping hand jams, just flying up. Was there ever a moment of doubt? Not any real moments of doubt. The Freeblast was still engaging for sure. And the first roof (at the start of the third pitch), I’m always a little bit tense there because you’re just starting up the route. And the Boulder Problem was the crux. That was the main thing probably. Did you think about anything other than rock climbing while you were going up the wall? During all the easy terrain, in the middle, through the Monster and up to the Spire, I was thinking about random stuff—the whole village of people who have supported me on this. I got an email from (friend and climbing partner Conrad Anker) this morning. So I was thinking about Conrad and his whole ethos of ‘be kind, be good, be happy’. And I was also thinking in terms of life goals. This has been my biggest life goal for years. And the other one is to climb 9a—to sport climb real hard. (Editor’s note: 9a refers to one of the highest rated, most physically demanding levels of sport climbing.) So I’m halfway up the wall and thinking it’s time to focus on 9a. It’s so exciting to work on something hard. So you already have a new goal? It’s been a strategy the whole time I’ve worked on El Cap is to look past it, so that it’s not just all this one moment. To think about what’s beyond, what other stuff I’m excited about. So this just feels like a semi-normal day. Otherwise you’re kind of setting yourself up for a major letdown? You don’t want to put that much pressure on yourself where everything in my life focuses on this one moment. This has been my big focus for years and my big dream for years, but I would like to climb at my physical limits and step away from adventure for a little while. And you do that with a rope. I’m pretty stoked to not be focusing on free solo projects for a while. I talked to free solo pioneer Peter Croft about it. He was one of your heroes when you were a kid. There’s nothing else as far as he’s concerned. He said El Cap was the final step. That’s how I’ve always felt about it, but who knows in a couple years? Do you think you’ll ever get really keen on really gnarly alpine climbing? I really doubt it. I haven’t so far. Pull Quote The whole pursuit of this dream has allowed me to live my best life, that makes me hopefully the best version of me. What else do you have on your agenda? Is there any personal stuff? I don’t know. I guess having a family. Does your mom know you free soloed El Cap? I haven’t talked to her yet. I don’t even think she knows what this whole project is about, you know? I feel weird about it. I’ll call her in a bit. Though I don’t even know what to tell her. ‘Hey, by the way…’ She might think I’d already done it. She’s really bad at differentiating between free climbing and free soloing. So how do you think this whole project was for Jimmy Chin and his crew filming you? It was better for me not to think at all about anyone else’s experiences except for my own. I’m sure this is ultra-stressful for everybody else involved, but for me it was a big enough challenge to even walk to the base and put my shoes on. Because you look up and go, ‘that’s a f***ing big wall.’ It’s like, pretty crazy. So the crew didn’t project any of their stress? No, everybody kept it ultra-chill. I think this is pretty much the best crew we could have. View Images Rock climber Alex Honnold sits atop Yosemite's iconic El Capitan after nearly four hours of climbing alone, without ropes or any other equipment or safety gear. Photograph by Jimmy Chin I trusted everybody going into the project. And then certainly after a year and a half, you really trust everybody. Do you have any notion of how big a deal this is and what you’ve done? That’s always the funny thing. It doesn’t feel that big a deal when you finally do it, because you put so much effort in. I mean the whole point is to make it feel not that crazy. Do you feel the world kind of needed something cool like this, at this moment in time? What the world needs is for the U.S. to stay in the Paris Accords. There’s some bigger issues. But I think it’s always cool for somebody to work on something difficult and achieve their dream. Hopefully people can draw inspiration from this. What are you going to do this afternoon? I’m probably going to hang board. You’re going to go do a hang board workout? I mean, in a bit, yeah. I mean I want to eat some lunch, I want to get in the shade and then I’m probably going to hang board in a bit. I am perfectly warmed up, I just did four hours’ light exercise, you know? The whole pursuit of this dream has allowed me to live my best life, that makes me hopefully the best version of me. Just because I’ve achieved a dream doesn’t mean that I just give up on the best version of me. I want to be the guy that trains and stays fit and motivated. Just because you finish a big route doesn’t mean that you just quit. A normal person would probably take the afternoon off after they free-soloed El Cap. But I’ve been trying to hang board every other day, and it’s the other day. Do you feel now that you’ve free soloed El Cap you could do it again? If I had a reason I could probably go climb El Cap again, no problem. It seems slightly less daunting. That mental hurdle has been cleared. If someone offered me $250,000 tomorrow, I’d be like f*** yeah. I would just go and do it tomorrow. I think we’re good Alex. You don’t need to do it again. Because it is dangerous, right? It felt much less scary than a lot of other solos I’ve done. Which ones? Probably all of them. Because I put so much work into this one. I was so dialed. Well, that's kind of awesome. SEE FIRST VIDEO OF MOST DANGEROUS ROPE-FREE CLIMB EVER (ALEX HONNOLD) June 6, 2017 - These hair-raising moments are the first video footage from renowned rock climber Alex Honnold's ascent of the 3,000-foot wall of El Capitan—without a rope. On June 3rd, Honnold became the first person ever to free solo climb this famous rock face at Yosemite National Park, California. The video was shot by Jimmy Chin (who also photographed the climb) for an upcoming documentary by National Geographic. There was no uncertainty on this. I knew exactly what to do the whole way. A lot of the handholds feel like old friends.

– A California rock climber has become the first person to conquer Yosemite's El Capitan without using ropes, USA Today reports. Alex Honnold, 31, scaled the nearly 3,000-foot peak on Saturday going free solo, meaning he didn't use ropes, harness, or other safety equipment. "This is the ‘moon landing’ of free-soloing," fellow climber Tommy Caldwell tells National Geographic. It's a particularly daunting prospect since the Guardian notes the granite peak is ranked as among the most difficult, with some hand-holds the width of raisins. After stunning the climbing world with other rope-free feats, Honnold had quietly trained for his latest exploit for more than a year. After spending the night in his van, Honnold pulled on a red T-shirt, nylon pants, and sticky-soled climbing shoes. With chalk to keep his hands dry tucked in a bag around his waist, Honnold set off at 5:32am. He made the summit three hours and 56 minutes later. "So stoked to realize a life dream today :)" he tweeted. Caldwell and a National Geographic crew were along for the climb, which they filmed for a documentary. "Alex was on fire," Caldwell tells the mag, which called the feat the greatest in the history of pure rock climbing. Honnold had ditched an earlier bid to climb El Capitan in November, saying it didn't feel right. This time around, Honnold confesses he was "slightly nervous" at the bottom. "I mean it’s a freaking big wall above you." But as he began his ascent, he adds, "the climbing just felt amazing." (Tense moments when a 1,500-pound rock pinned this climber.)

Sage Stallone White Powder Found In Bedroom White Powder Found In Sage Stallone's Bedroom Exclusive Details Authorities found baggies of white powder in the room wheredied ... TMZ has learned.Our law enforcement sources confirm detectives found "several little baggies in the bedroom." One law enforcement source says the powder is being tested and suggests it could be cocaine or crushed Vicodin.We're told there were no obvious signs of white powder on Sage's body when he was found.As we first reported, authorities found "huge" empty prescription bottles in Sage's bedroom. A law enforcement source has now elaborated, telling TMZ they found "more than 60 gigantic bottles, like the ones in pharmacies."Authorities know the bottles contained Hydrocodone -- generic Vicodin.Investigators are baffled at the quantity of the bottles and are trying to figure out where Sage may have gotten them. They say it's possible he got them online, but they're also looking at several doctors. ||||| Sylvester Stallone Calls In Famed P.I. To Investigate Sage's Death Sylvester Stallone Calls In Famed P.I. Scott Ross to Investigate Sage's Death EXCLUSIVE has called in a private investigator to figure out how his son Sage died and what lead up to the tragedy ... TMZ has learned.We've learned famed P.I.-- who was the lead investigator in themolestation case and thebattery case -- met Tuesday at Stallone's home with Sly, his brother Frank, and an official from the L.A. County Coroner's Office. Sources tell us they discussed's death and the status of the investigation.We're told Sly wants Ross to figure out what happened to his son -- and he's not ruling out foul play, even though he has no evidence of that. Sly also wants to know about Sage's final weeks ... whether he was using drugs or consuming alcohol. The actor also wants to know what, if anything, was troubling his son.Ross has a long history working for the Stallone family ... we're told Sly wants someone he knows and trusts to provide him with answers about his son's death.Calls to Ross were not returned. ||||| Members of the Westboro Baptist Church have been called to picket actor Sage Stallone's funeral on account of his "adulterous dad," Sylvester Stallone. After it was announced that the 36-year-old actor had died on July 13, Margie Phelps, daughter of Westboro leader Fred Phelps, tweeted to her 5,600 followers, urging them to picket Stallone's funeral. "Thrice-married rebel taught his son to mock God. ‪#picketfuneral‬," Phelps first tweeted on July 13. The Westboro Baptist Church, infamous for its organized pickets at military funerals as part of its anti-gay agenda, is apparently targeting Sage because of his father's previous relationships. "Adulterous dad brought wrath of God on son. ‪#BloodOnDadsHands‬ ‪#picketfuneral‬ ‪#woe‬," Phelps tweeted, adding, "Tell @TheSlyStallone to mourn for his sins, not pimp out son's dead body to more proud sin!" Sylvester Stallone has been married three times and Sage was his first child with his first wife, Sasha Czack, to whom he was married from 1975 to 1985, according to MTV. Sylvester has asked that his family's privacy be respected during this difficult time. "When a parent loses a child there is no greater pain," he said in a statement released to TMZ. "Therefore I am imploring people to respect my talented son's memory and feel compassion for his loving mother Sasha." Sage Stallone was found dead in his Los Angeles home on Friday, July 13. The Los Angeles Times reported Sunday that the Los Angeles County coroner's office confirmed the autopsy had been completed, but toxicology results and a cause of death are still pending.

– Sylvester Stallone has hired a private investigator to look into son Sage's death, TMZ reports. Scott Ross was involved in the investigations into the Chris Brown/Rihanna assault and the Michael Jackson molestation case, and he will look into Sage's final weeks and his cause of death. The New York Post adds that Sage Stallone had extensive dental surgery two weeks before he died, and that his mother begged him not to go through with it. "I’ve heard about people dying having multiple procedures done to your mouth. Do not have more than one tooth [pulled]," Sasha Czack says, adding that Sage was on painkillers following the procedure. TMZ reports that a white powder, which could be cocaine or crushed Vicodin, was found in the room where Sage died. And in case Stallone doesn't have enough grief to deal with in the mysterious death of his 36-year-old son, the Westboro Baptist Church has decided to pile on. The group, famous for protesting soldier funerals as part of its anti-gay movement, plans to picket Sage Stallone's funeral to protest his famous dad's love life. "Thrice-married rebel taught his son to mock God. #picketfuneral," tweeted Margie Phelps, daughter of controversial preacher Fred Phelps. "Adulterous dad brought wrath of God on son," she tweeted later, according to the Huffington Post.

People react after a statue of Soviet state founder Vladimir Lenin was toppled by protesters during a rally organized by pro-Ukraine supporters in the center of the eastern Ukrainian town of Kharkiv. (Reuters) In an incident reflecting growing Ukrainian anger toward the Kremlin, anti-Russian protesters pulled down a massive Vladimir Lenin statue in Ukraine's second-largest city late Sunday. To many Ukrainians, Lenin is a symbol of the Soviet Union and Russia's aggressive support for the separatist rebels in eastern Ukraine. Despite the 1991 breakup of the Soviet Union which resulted in the split between Russia and Ukraine, hundreds of monuments to the founder of modern Russia survived the transition. Over the last months, however, many have been toppled: This map – based on accounts of activists -- shows the massive demolition of Ukrainian Lenin monuments in 2014 alone. "To many Ukrainians, Lenin represents not only the communist regime, but also radical separation from Europe and Western civilization more broadly," Steven Fish, a Russian studies professor at University of California Berkeley, told the Los Angeles Times last December after a statue had been toppled in Kiev. Other scholars view the toppling in a more modern light. Sasha Senderovich, assistant professor of Russian Studies at the University of Colorado Boulder who wrote a New York Times op-ed on this issue last December, considers Sunday's event not to be connected to Lenin specifically. "At this point, after Putin's assault on Ukraine's territorial integrity, the statue has become more symbolic of Russia's continued attempt to exercise imperial dominance over Ukraine rather than solely the historical legacy of the Soviet Union," he told The Post on Monday. Kharkiv is considered one of the most vulnerable cities in the east if the pro-Russian rebellion were to spread. Previous attempts to pull down the statue failed because pro-Russian activists intervened, according to The Post's Michael Birnbaum. These pictures show that Sunday's incident was clearly organized and must have been noticed. First, protesters cut the Lenin statue's legs. Then, they pulled the statue down. In fact, the recent toppling of the Lenin statue is just the latest in a series of attacks on hundreds of others that have been toppled in Ukraine over the last months as tensions with Russia have grown. Here is an alternative chronology of Ukraine's crisis, told through toppled Lenin statues. A measurement of anger Tearing down the iconic Lenin monuments rapidly gained momentum when it became clear that Ukrainian President Viktor Yanukovych had lost power over his country. On Feb. 20, Kiev witnessed its worst day of violence in 70 years, with snipers targeting and killing protesters. On Feb. 22, Yanukovych disappeared, protesters stormed presidential buildings and opposition leader Yulia Tymoshenko was freed from jail. Data gathered by Ukrainian activists and visualized by The Washington Post show that more than 90 Lenin statues were toppled that day alone. The activists uploaded pictures, dates and locations of the toppled statues on a platform called Leninopad and the individual contributions could not be independently verified. How the 'statue war' spread The visualizations below are based on the same data. Until Feb. 21 (the day before Yanukovych disappeared), the incidents appear to have largely been limited to the surrounding areas of Kiev where the pro-Western supporters had been in an overwhelming majority. Map: Gene Thorp/ Lazaro Gamio, The Washington Post. Data: Leninopad. Then, however, the number of toppled Lenin statues quickly increased and spread throughout the country. The statues which were toppled earlier are shown in grey in the map below. It is important to note that not all defaced monuments in Crimea and the east are included in this map, because the activists did not provide a sufficient amount of date for some of them. However, there appears to be a general lack of incidents both in the east (where the Ukrainian Russian speakers are predominantly located), as well as in the west. The latter observation is surprising because the western areas are the ones which are least supportive of Russia. One possible explanation could be that Lenin statues in the west had been removed much earlier: Back in June 2009, pro-Western Ukrainian President Viktor Yushchenko had called upon his supporters to erase communist symbols from the country. Map: Gene Thorp/ Lazaro Gamio, The Washington Post. Data: Leninopad. This map shows more recent incidents until August, but it is not clear whether the activists kept track of the toppling of Lenin statues during this time frame in the same manner as they did in February and March. Map: Gene Thorp/ Lazaro Gamio, The Washington Post. Data: Leninopad. Our maps only include Lenin statues toppled in 2014. However, they have been a target for much longer, as part of a larger fight between pro-Russian activists and nationalists. Last August 2013, Russian news agency RIA Novosti specified that at least 12 Lenin statues had been pulled down or defaced since 2009, calling the incidents a "statue war." According to The Atlantic, an advertisement video for the Euro 2012 soccer championships in Kharkiv erased a Lenin statue from a shot -- it appears to have been the very same statue which was pulled down Sunday evening and is unlikely to be the last such incident. In a Facebook post, Ukraine's Interior Minister Arsen Avakov wrote on Monday: “Lenin? Let him fall down. As long as nobody suffers under his weight. As long as this bloody Communist idol does not take more victims with it when it goes." ||||| Most of the massive statue of Soviet leader Vladimir Lenin that a crowd in Kharkiv toppled last week still lies where it landed in the city’s central Freedom Square. And no wonder. The statue - reputed to be the largest in Ukraine - is 8.5m tall, and weighs several tonnes. But in recent days, body parts have begun appearing for sale. A nose here, an ear there, plus hints that there are more if collectors want them. One seller in Kharkiv recently showed the Lenin statue’s nose – 36cm wide, 36cm long and about 25cm high – to RFE/RL’s Ukraine Service and other media in the city. Wearing a ski mask and identifying himself only as “Oleksiy”, he said he was ready to sell the nose to anyone who will make a sizeable contribution to Ukrainian volunteers fighting pro-Russian separatists in eastern Ukraine. “If there is anyone who says, ‘I am ready, let’s say, to provide a battalion of soldiers with winter underwear and uniforms,’ then we will give him [the nose],” he said. “That is, if no one says, better yet, that he’s ready to provide two battalions with the things I have mentioned.” Oleksiy says he got the nose when the statue hit the ground face first. The nose – including bridge, both nostrils, and moustache beneath – split off, and he and his companions lugged it away. Facebook Twitter Pinterest An unidentified protester holds the cut off nose of the statue of Vladimir Lenin after it was toppled. Photograph: Sergei Kozlov/EPA At the same time Oleksiy is trying to sell the nose, another seller is offering one of Lenin’s ears. The ear is up for auction on Facebook by Aleksandr Makarenko, a Ukrainian from Kharkiv who says he, too, is raising money for Ukrainian forces. “The money collected will go toward a thermal camera for the Kharkiv-1 battalion,” he wrote on his Facebook page. “Make me an offer. The ear weighs close to 35 kilograms. You can hear Donbas through it.” Whether those selling pieces of Lenin can do so without fear of prosecution is an open question. When the crowd pulled down the statue on the night of 28 September, sawing through one of Lenin’s legs and using cables to pull him off his pedestal, the city’s police looked on impassively. Chanting “glory to Ukraine” and waving Ukrainian flags, the crowd toppled with impunity a symbol of the Soviet Union that had towered over Freedom Square since 1967. But the day after the statue was toppled, Kharkiv Mayor Gennady Kernes gave an angry press conference in which he branded the crowd’s actions “illegal” and vowed to put Lenin up again. “We will restore it on Liberty Square on the same podium,” he said. “If there is no way to restore it, then we will make [a new one] from scratch.” He also said he was ordering the police to hunt down those who had “barbarically destroyed” city property. As Kharkiv’s mayor, Kernes has straddled the pro-Kiev and pro-Russian camps in his city in a risky balancing act that already has nearly cost him his life. On 28 April he was shot in the back by an unknown gunman as he was jogging and now uses a wheelchair.

– Lenin must be thrilled with this: Not only did protesters in Ukraine tear down a huge statue of him, they're using old-fashioned capitalism to make some money off it. The 28-foot-tall statue came down last weekend in the eastern city of Kharkiv, and now pieces of it are going up for auction, reports the Guardian. Interested in the former Soviet leader's nose, with mustache still attached? An anti-Russian fighter named Olesky awaits your bid. How about an ear? See Aleksandr Makarenko's Facebook page for details. The catch in both examples: Proceeds will go to Ukrainian troops fighting pro-Russian forces. “If there is anyone who says, ‘I am ready, let’s say, to provide a battalion of soldiers with winter underwear and uniforms,’ then we will give him [the nose],” says Olesky. “That is, if no one says, better yet, that he’s ready to provide two battalions with the things I have mentioned.” The ear, meanwhile, will pay for a "thermal camera" for the troops. As the Washington Post explains in both story and graphics, a huge number of Lenin monuments have come down in Ukraine in this year alone, even if there's disagreement about the exact symbolism involved.

in a striking contribution @xcite , nualart and peccati discovered a few years ago that the fourth moment of homogeneous polynomial chaos on wiener space characterizes convergence toward the gaussian distribution . specifically , and in a simplified ( finite dimensional ) setting , let @xmath0 , @xmath1 , be defined by @xmath2 where @xmath3 are real numbers vanishing on diagonals and symmetric in the indices . assume by homogeneity that @xmath4 where @xmath5 is the standard gaussian measure on @xmath6 . such a function @xmath7 will be called homogeneous of degree @xmath8 . let now @xmath9 on @xmath10 , @xmath11 , @xmath12 , be a sequence of such homogeneous polynomials of fixed degree @xmath8 . the main theorem of nualart and peccati @xcite expresses that the sequence of distributions of the @xmath9 s converges toward the standard gaussian distribution @xmath13 on the real line if and only if @xmath14 ( 3 being the fourth moment of the standard normal ) . the result actually holds for homogeneous chaos on the infinite dimensional wiener space , and the equivalence is further described in terms of convergence of contractions . the proof of @xcite relies on multiplication formulas for homogeneous chaos and the use of stochastic calculus . since @xcite was published , numerous improvements and developments on this theme have been considered ; cf . , for example , @xcite@xmath15 an introduction to some of these developments ( with emphasis on multiplication formulas ) is the recent monograph @xcite by peccati and taqqu . in particular , the work by nualart and ortiz - latorre @xcite introduces a technological breakthrough with a new proof only based on malliavin calculus and the use of integration by parts on wiener space . in this work , the convergence of @xmath16 to a gaussian distribution [ and thus also ( [ equ2 ] ) ] is also shown to be equivalent to the fact that @xmath17 where @xmath18 is the variance with respect to @xmath19 . based upon this observation , recent work by nourdin and peccati @xcite develops the tool of the so - called stein method ( cf . , e.g. , @xcite ) in order to quantify the convergence toward the gaussian distribution . relying also on multiplication formulas and the use of integration by parts on wiener space , one key step in the investigation @xcite is expressed by the following inequality : for a given homogeneous function @xmath7 of degree @xmath8 on @xmath6 normalized in @xmath20 , @xmath21 where @xmath22 only depends on @xmath8 . in particular , the proximity of @xmath23 to 3 controls the variance of @xmath24 . now , stein s method for homogeneous chaos on wiener space as developed in @xcite expresses that @xmath25 where @xmath26 stands for some appropriate distance between the law @xmath27 of @xmath7 and @xmath13 , so that @xmath24 being close to a constant forces the distribution of @xmath7 to be close to a gaussian distribution . the conjunction of ( [ equ4 ] ) and ( [ equ5 ] ) thus describes how the fourth moment condition controls convergence to a gaussian . the primary motivation of this work is to understand what structure of a functional @xmath7 allows for the preceding results , in particular thus the control by the fourth moment of the distance to the gaussian distribution . in the process of this investigation , we will revisit the preceding results and conclusions in the setting of a symmetric markov operator , including , as a particular example , the ornstein uhlenbeck operator @xmath28 , corresponding to the wiener space setting . in order to achieve this goal , observe that the homogeneous polynomial @xmath7 of ( [ equ1 ] ) is an eigenfunction with eigenvalue @xmath8 of the ornstein uhlenbeck operator , that is , @xmath29 . we shall therefore try to understand what is necessary for an eigenfunction @xmath7 of a markov operator in order to satisfy an inequality such as ( [ equ4 ] ) . this investigation leads us to define a notion of chaos eigenfunction with respect to such a markov operator with pure point spectrum consisting of a countable sequence of eigenvalues , the homogeneous polynomial @xmath7 of ( [ equ1 ] ) being one example with respect to the ornstein uhlenbeck operator . the main achievement of this work is then the formulation of an explicit condition on the sequence of eigenvalues under which a chaos eigenfunction satisfies an inequality such as ( [ equ4 ] ) . the basic data will thus be a markov operator @xmath30 on some state space @xmath31 with invariant and reversible probability measure @xmath32 and symmetric bilinear carr du champ operator @xmath33,\ ] ] acting on functions @xmath34 in a suitable domain @xmath35 . for simplicity , we often write @xmath36 which is always nonnegative . by invariance and symmetry of @xmath32 with respect to @xmath30 , the definition of the carr du champ operator @xmath37 yields the integration by parts formula @xmath38 in particular @xmath39 since @xmath40 by the markov property . the operator @xmath30 is said , in addition , to be a diffusion operator if , for every smooth function @xmath41 , and every @xmath42 , @xmath43 alternatively , @xmath37 is a derivation in the sense that @xmath44 . we refer to the lecture notes @xcite , chapter 2 , by bakry for an introduction to this abstract framework of markov and carr du champ operators and a discussion of some of the examples emphasized below . additional general references include @xcite for further probabilistic interpretations and @xcite for constructions in terms of dirichlet forms ; see also @xcite and the forthcoming @xcite . one prototype example of a markov diffusion operator is the ornstein uhlenbeck operator acting on say the algebra @xmath45 of polynomial functions @xmath46 on @xmath47 as @xmath48 , with invariant and reversible probability measure the gaussian distribution @xmath49 and carr du champ @xmath50 . one could consider its infinite dimensional extension on wiener space ( cf . @xcite and @xcite , chapter 1 ) , but for simplicity in the exposition we stick here on the finite dimensional case as a reference example . the preceding general setting also includes discrete examples , such as the two - point space and its products . namely , on @xmath51 , let @xmath52 where @xmath53 , @xmath54 , @xmath55 . @xmath30 is invariant and symmetric with respect to the uniform measure @xmath32 on @xmath56 with carr du champ @xmath57 , but is not a diffusion operator . these two examples actually entail a crucial chaos structure in the sense that the generators @xmath30 may be diagonalized in a sequence of orthogonal polynomials ( hermite polynomials in the gaussian case , walsh polynomials in the cube example ) ; see , for example , @xcite , chapter 1 , @xcite , chapter 1 , @xcite , chapter 2 , @xcite , chapter 5 . more precisely , setting for @xmath58 , @xmath59 , @xmath60 , with @xmath61 the sequence of orthonormal hermite polynomials on the real line , any function @xmath62 in @xmath63 may be written as @xmath64 where @xmath65 is the scalar product in @xmath20 and where the second sum runs over all @xmath66 with @xmath67 . an element @xmath68 with @xmath69 is an eigenfunction of the ornstein uhlenbeck operator with @xmath70 and the spectrum of the operator @xmath71 thus consists of the sequence of the nonnegative integers . for fixed @xmath72 , linear combinations @xmath73 define generic eigenfunctions ( chaos ) of @xmath71 with eigenvalue @xmath8 , the homogeneous function @xmath7 of ( [ equ1 ] ) being one example . similarly , if @xmath74 , @xmath75 where the second sum runs over all subsets @xmath76 of @xmath77 with @xmath8 elements and @xmath78 are the so - called walsh polynomials . for the discrete operator @xmath79 , @xmath80 if @xmath81 . the spectrum of @xmath71 is thus equal to @xmath82 , and linear combinations @xmath83 describe the family of eigenfunctions ( chaos ) of @xmath71 with eigenvalue @xmath8 . a further example is poisson space . in dimension one , let @xmath32 be the poisson law on @xmath82 with parameter @xmath84 . for a function @xmath85 with finite support say , let @xmath86 for every @xmath87 [ @xmath88 . the poisson operator may then be defined as @xmath89 , . it is not a diffusion . the associated carr du champ operator is given by , @xmath87 . the operator @xmath90 has a spectrum given by the sequence of the integers and is diagonalized along the charlier orthogonal polynomials . multi - dimensional poisson models are similar . laplacians @xmath91 on ( compact ) riemannian manifolds , and acting on families of smooth functions , also enter this framework . these laplacians are diffusion operators and , in the compact case , have again a spectrum consisting of a countable sequence of eigenvalues ; cf . , for example , @xcite . this work will analyze properties of eigenfunctions of such markov operators @xmath30 , that is , functions @xmath92 ( in the domain of @xmath30 ) such that @xmath93 for some @xmath94 . ( we emphasize that @xmath7 and @xmath95 are thus rather eigenfunction and eigenvalue of @xmath71 which is nonnegative . ) the ultimate goal of this work is to find conditions on such an eigenfunction @xmath7 of a diffusion operator @xmath30 in order that the analog of ( [ equ4 ] ) holds , and that the fourth moment condition then ensures the proximity with the gaussian distribution . we outline here the various steps of the investigation . the first step will be to show ( following @xcite in the ornstein uhlenbeck setting ) that stein s method applied to an eigenfunction @xmath7 indicates that it has a gaussian distribution if ( and only if ) its carr du champ @xmath96 is constant ; see proposition [ proposition1 ] below . more precisely , in accordance with ( [ equ5 ] ) , for suitable families of functions @xmath97 , and whenever @xmath98 , @xmath99 where @xmath100 is the variance with respect to @xmath32 . on the basis of this result , the fourth moment condition appears quite naturally by the integration by parts formula since ( assuming the necessary domain and integrability conditions ) @xmath101 moreover , @xmath102 , so that , still assuming by homogeneity that @xmath98 , @xmath103 this identity is the first indication that the proximity of @xmath104 with 3 actually amounts to the proximity of @xmath96 with its constant mean value @xmath95 . the next step in the investigation , the main result of this note , describes a chaos structure of an eigenfunction @xmath7 of a markov operator @xmath30 ( not necessarily diffusive ) with spectrum consisting in a sequence @xmath105 of eigenvalues in order that whenever @xmath7 is such a chaos with eigenvalue @xmath106 normalized in @xmath107 , @xmath108 for some finite constant @xmath109 only depending on @xmath110 . the relations ( [ equ8 ] ) , ( [ equ9 ] ) and ( [ equ10 ] ) together therefore describe how the fourth moment condition@xmath111 ensures that @xmath112 is close to constant and thus that the distribution of @xmath7 is close to gaussian . this family of inequalities may then be used to describe convergence to a gaussian distribution of a sequence of such chaos eigenfunctions . the abstract chaos structure underlying these results is defined by means of the iterated gradients of the markov operator @xmath30 and is shown to easily cover the examples of wiener , walsh or poisson chaos . for example , the chaos structure of the homogeneous polynomial @xmath7 of ( [ equ6 ] ) actually amounts to the fact that @xmath113 . the proof of ( [ equ10 ] ) will proceed by a standard and direct algebraic @xmath37-calculus on eigenfunctions involving the iterated gradients of the operator @xmath30 and avoiding any type of multiplication formulas for chaos . turning to the content of this note , section [ sec2 ] briefly presents stein s method applied to an eigenfunction of a markov diffusion operator . the next section discusses the iterated gradients and the associated @xmath37-calculus on eigenfunctions , of fundamental use in the investigation . section [ sec4 ] introduces the notion of chaos of a markov operator with pure point spectrum and presents the aforementioned main result ( [ equ10 ] ) , proved in section [ sec6 ] . the last section briefly describes analogous conclusions for convergence to gamma distributions covering recent results of @xcite . it should be carefully emphasized that the present exposition develops more the algebraic and spectral descriptions of the problem under investigation [ and concentrates on a proof of ( [ equ10 ] ) ] rather than the analytic issues on domains and classes of functions involved in the analysis . in particular , we work with families of functions in the domain of the markov operator and its carr du champ and with eigenfunctions assumed to satisfy all the necessary domain and integrability conditions required to develop integration by parts and the associated @xmath37-calculus . these properties are classically and easily satisfied for the main examples in mind , the gaussian case , the discrete cube or the setting of the laplace operator on a compact riemannian manifold . note , however , that the extension from the finite dimensional gaussian setting to the infinite dimensional one requires basic analysis on wiener space as presented , for example , in the first chapter of @xcite ( see also @xcite ) in order to fully justify the domain issues and the various conclusions . these aspects , carefully developed in the aforementioned references , are not discussed here . further conditions ensuring the validity of the results presented here might be developed in broader contexts . we start our investigation with a brief exposition of stein s lemma applied to eigenfunctions of a diffusion operator . we refer to @xcite and the references therein for general introductions on stein s method . the results below are mere adaptations of the investigation @xcite by nourdin and peccati in wiener space to which we refer for further details . throughout this section , @xmath30 is thus a diffusion operator with invariant and reversible measure @xmath32 and carr du champ @xmath37 as described in the . all the necessary domain and integrability conditions on the eigenfunctions under investigation are implicitly assumed , and are satisfied for the main ornstein uhlenbeck example ; cf . @xcite . we first illustrate , at a qualitative level , stein s method in this abstract context . given a measurable map @xmath114 , say that @xmath30 commutes to @xmath7 if there exists a markov operator @xmath115 on the real line such that for every @xmath41 ( in the domain of @xmath116 and such that @xmath117 is in the domain of @xmath30 ) @xmath118 in this case , the image measure @xmath119 of @xmath32 by @xmath7 is the invariant measure of @xmath115 . one model factorization operator @xmath116 on @xmath120 is the ornstein uhlenbeck operator @xmath121 with invariant measure the standard gaussian distribution @xmath122 . let then @xmath123 be an eigenfunction of @xmath71 with eigenvalue . the observation here , at the root of stein s argument , is that whenever @xmath124 is ( @xmath32-almost everywhere ) constant , then @xmath30 commutes to @xmath7 through the ornstein uhlenbeck operator @xmath116 , and thus the distribution @xmath119 of @xmath7 is gaussian . namely , note first that by integration by parts , @xmath125 so that if @xmath37 is constant and @xmath7 is normalized in @xmath126 , then @xmath127 . then , for @xmath41 smooth enough , by the chain rule formula for the diffusion operator @xmath30 , @xmath128 hence , if @xmath127 , @xmath129 so that @xmath30 commutes to @xmath7 , and thus @xmath119 is the invariant measure of the ornstein uhlenbeck operator @xmath116 characterized as the gaussian distribution @xmath130 . for an eigenfunction @xmath7 , @xmath131 constant thus forces the distribution of @xmath7 to be gaussian . now , as such , this observation is not of much use and to describe convergence to normal as for sequences of homogeneous polynomials in the , it should be suitably quantified in the form of inequality ( [ equ8 ] ) in order to express that the proximity of @xmath37 with a constant value forces the distribution of @xmath7 to be close to gaussian . this is the content of the classical stein lemma as described in the next statement . [ proposition1 ] let @xmath123 be an eigenfunction of @xmath71 with eigenvalue @xmath94 and set @xmath131 . denote by @xmath119 the distribution of @xmath7 . given integrable with respect to @xmath119 and @xmath13 , let @xmath132 be a smooth solution of the associated stein equation @xmath133 . then , @xmath134 where @xmath135 . in particular , if @xmath136 , @xmath137 since @xmath119 is the distribution of @xmath7 under @xmath32 , and by the stein equation , @xmath138 \,d\mu.\ ] ] now @xmath139 so that @xmath140 and hence , after integration by parts with respect to the operator @xmath30 and the use of the diffusion property , @xmath141 \,d\mu.\ ] ] together with the cauchy schwarz inequality , @xmath142 ^ 2 \,d\mu\biggr)^{1/2},\ ] ] which amounts to ( [ equ11 ] ) . if @xmath143 , then @xmath144 and thus @xmath145 . the proof of proposition [ proposition1 ] is complete . proposition [ proposition1 ] is thus investigated in @xcite for wiener chaos . as is discussed there ( lemma 1.2 and theorem 3.1 ) , the constant @xmath146 in ( [ equ11 ] ) of proposition [ proposition1 ] can be uniformly bounded inside specific classes of functions . for instance , @xmath147 when @xmath148 is the characteristic function of a borel set ( corresponding to the total variation distance ) and @xmath149 when @xmath148 is the characteristic function of a half - line ( corresponding to the kolmogorov distance ) . for the further purposes , observe , as is classical ( cf . @xcite ) , that stein s strategy may be developed similarly for the laguerre operator on the positive half - line @xmath150 , @xmath151 , with invariant measure the gamma distribution @xmath152 . let @xmath123 be an eigenfunction of @xmath71 with eigenvalue @xmath94 and @xmath131 . as above , for every @xmath41 smooth enough , setting @xmath153 , @xmath154 in this case , if @xmath155 , @xmath156 so that @xmath157 is the invariant measure of @xmath158 characterized as the gamma distribution @xmath159 . for this example of the laguerre operator , the criterion for an eigenfunction @xmath7 to have a gamma distribution is thus that @xmath160 . on the basis of this qualitative description of stein s method for the laguerre operator , the next statement illustrates the analog of proposition [ proposition1 ] for this model . [ proposition2 ] let @xmath123 be an eigenfunction of @xmath71 with eigenvalue @xmath94 , and set @xmath131 . let @xmath161 and denote by @xmath162 the distribution of @xmath163 . given @xmath41 integrable with respect to @xmath162 and @xmath164 , let @xmath132 be a smooth solution of the associated stein equation @xmath165 . then , @xmath166 where @xmath135 . in particular , if @xmath167 , @xmath168 set again @xmath169 . start as in the proof of proposition [ proposition1 ] , namely @xmath170 \,d\mu.\end{aligned}\ ] ] since @xmath139 , and thus @xmath171 , @xmath172 after integration by parts with respect to the operator @xmath30 and the use of the diffusion property , @xmath173 \,d\mu.\ ] ] the conclusion follows similarly from the cauchy schwarz inequality . proposition [ proposition2 ] is similarly investigated in @xcite in the context of stein s method on wiener space . again the the constant @xmath146 in ( [ equ12 ] ) may be bounded only in terms of @xmath174 inside specific classes of functions ; cf . @xcite , lemma 1.3 and theorem 3.11 . analogs of stein s lemma in the context of the preceding statements have been investigated on discrete poisson or bernoulli spaces in @xcite . in those examples , the control of the variance of @xmath37 is not enough to ensure proximity to a gaussian distribution and has to be supplemented by various additional conditions . this section presents the family of the iterated gradients of a markov operator and the basic ( algebraic ) @xmath37-calculus on eigenfunctions at the root of the investigation . given a symmetric markov operator @xmath30 as above ( not necessarily a diffusion operator ) , recall following @xcite , the iterated gradients @xmath175 , @xmath176 , associated to @xmath30 defined according to the rule defining @xmath177 as @xmath178\ ] ] for functions @xmath179 in a suitable class @xmath45 . by extension , @xmath180 . for simplicity , set @xmath181 . note that in general @xmath182 for @xmath183 is not necessarily nonnegative . the @xmath184 operator has been introduced first by bakry and mery @xcite to describe curvature properties of markov operators and to provide a simple criterion to ensure spectral gap and functional inequalities ; cf . @xcite , chapter 6 , @xcite and @xcite . this criterion will be used in proposition [ proposition4 ] below . the iterated gradients @xmath175 have been exploited in @xcite toward variance and entropy expansions . the following elementary lemma will be of constant use throughout this note and concentrates on the significant properties of the iterated gradients of a given eigenfunction . recall that we assume the necessary domain and integrability conditions to justify the relevant identities . [ lemma3 ] let @xmath7 be an eigenfunction of @xmath90 with eigenvalue @xmath95 . set @xmath185 , @xmath186 . then , for every @xmath186 , @xmath187 furthermore , for every @xmath188 , @xmath189 in particular , by selecting @xmath190 , for every @xmath186 , @xmath191 equality ( [ equ13 ] ) is an immediate consequence of the definition of @xmath175 and the eigenfunction property @xmath192 the conclusion follows by iteration . recalling the notation @xmath185 , multiply the preceding identity by @xmath193 and integrate with respect to @xmath32 to get , by symmetry , @xmath194 changing the role of @xmath195 and @xmath196 , by symmetry again , @xmath197 and the identity ( [ equ14 ] ) follows . the proof of the lemma is complete . the following statement is a first illustration of the method developed next . it expresses a kind of rigidity result under the geometric @xmath184 curvature condition mentioned previously . [ proposition4 ] assume that the operator @xmath30 is of curvature @xmath198 in the sense of bakry mery @xcite ( @xcite , chapter 6 ) , that is , @xmath199 for every . if @xmath7 is an eigenfunction of @xmath71 with eigenvalue @xmath200 , then @xmath112 is ( @xmath32-almost everywhere ) constant . in case @xmath30 is a diffusion operator , the distribution of @xmath7 is gaussian . it might be useful to recall ( @xcite , chapter 6 , @xcite ) that under the curvature condition of the statement , @xmath201 for every nonzero eigenvalue @xmath95 of @xmath71 . in particular , @xmath30 is ergodic in the sense that if @xmath202 , then @xmath46 is constant ( @xmath32-almost everywhere ) . it is also worthwhile mentioning that for the model space consisting of the ornstein uhlenbeck diffusion operator @xmath28 with invariant measure @xmath203 , @xmath204 and the eigenfunctions with eigenvalue 1 are the linear functions @xmath205 whose distributions are of course gaussian . since gaussian wiener chaos of order larger than or equal to 2 do not contain any nonzero gaussian variable @xcite and @xcite , proposition [ proposition4 ] thus expresses a kind of rigidity property in the sense that if @xmath7 is a nonzero eigenfunction of the ornstein uhlenbeck operator @xmath30 with eigenvalue @xmath95 , then @xmath7 is gaussian if and only if @xmath112 is constant , and if and only if @xmath206 . the proof of proposition [ proposition4 ] is rather straigthforward . write as before @xmath207 , @xmath186 . by lemma [ lemma3 ] [ formula ( [ equ13 ] ) ] , @xmath208 . therefore , under the curvature condition @xmath209 , @xmath210 . but then @xmath211 so that @xmath124 is ( @xmath32-almost everywhere ) constant . the final assertion of the statement then follows from stein s lemma ( proposition [ proposition1 ] ) . this section is devoted to the main conclusions of this work . we are thus given , on a state space @xmath212 , a markov operator @xmath30 with symmetric and invariant probability measure @xmath32 and carr du champ @xmath37 ( acting on a suitable algebra of functions @xmath45 ) . assume in addition that @xmath30 has a pure point spectrum consisting of a countable sequence of eigenvalues ( more precisely , @xmath110 is the spectrum of @xmath71 ) ( cf . @xcite ) . since @xmath213 , @xmath30 is ergodic [ in the sense that if @xmath202 , then @xmath46 is constant ] . given the spectrum @xmath214 , define for every @xmath215 the polynomial of degree @xmath8 in the real variable @xmath216 , @xmath217 ( @xmath218 . define then the bilinear form ( acting on @xmath219 ) @xmath220 the following main definition introduces the notion of chaos associated to @xmath30 and its spectrum @xmath110 . [ definition5 ] an eigenfunction @xmath7 of @xmath90 with eigenvalue @xmath106 ( @xmath221 ) is said to be a chaos of degree @xmath222 relative to @xmath110 if @xmath223 ( @xmath32-almost everywhere ) . we call @xmath7 a chaos eigenfunction ( with eigenvalue @xmath106 ) . motivation for the preceding definition is provided by the ornstein uhlenbeck operator with spectrum @xmath224 . namely , it is easily shown in this case ( see @xcite , section 2 ) that @xmath225 . any eigenfunction @xmath7 as in ( [ equ6 ] ) is such that @xmath226 is constant and @xmath227 leading thus to definition [ definition5 ] . in the infinite dimensional setting of an abstract wiener space @xmath228 with separable hilbert space @xmath229 , referring to @xcite , chapter 1 , for notation and terminology , the ornstein uhlenbeck operator @xmath30 has domain @xmath230 and @xmath231 for any @xmath232 where @xmath233 is the derivative operator ( use as in the finite dimensional case the commutation @xmath234 = d$ ] and the chain rule formula @xcite , proposition 1.4.5 ) . now , if @xmath235 denotes the projection of @xmath7 ( in @xmath236 ) on the @xmath8th wiener chaos , @xmath237 and @xmath238 so that @xmath239 thus defines a @xmath8-chaos in the sense of definition [ definition5 ] . for example , in case @xmath240 where @xmath27 is a @xmath241-finite atomless measure on a measurable space @xmath242 , the elements @xmath235 may be represented as multiple stochastic integrals @xmath243 of symmetric functions @xmath244 on @xmath245 with respect to the white noise @xmath246 and @xmath247 the discrete operator @xmath52 on the cube @xmath248 and the poisson operator are further instances entering this definition with again @xmath249 ( see @xcite , section 2 ) . on the cube @xmath248 , for example , @xmath250 where the sum is over distinct @xmath251 and thus any @xmath123 of the form ( [ equ7 ] ) is a @xmath8-chaos ( @xmath252 ) . there are of course examples of eigenfunctions which are not chaos . for instance , the laguerre operator on the positive half - line @xmath253 , @xmath151 , has spectrum equal to @xmath82 ( with eigenvectors the laguerre orthogonal polynomials with respect to the gamma distribution @xmath164 ) , but the eigenfunction @xmath254 with eigenvalue 1 is not a @xmath255-chaos as @xmath256 . according to the preceding examples , another possible definition of @xmath8-chaos would have been that @xmath257 is constant . ( if @xmath7 is normalized in @xmath107 , then ( @xcite , page 443 ) , @xmath258 hence @xmath259 . ) now , it is easily checked [ using ( [ equ13 ] ) of lemma [ lemma3 ] ] that if @xmath7 is an eigenfunction of @xmath90 with eigenvalue @xmath106 , then @xmath260 . in particular therefore , if @xmath261 is constant , then . conversely , if @xmath262 , by ergodicity , @xmath261 is constant . it will turn out more simple in the proofs of the main results to use the first definition of chaos [ as @xmath262 ] . the following statements are the main results of this work . recall the polynomials @xmath264 and set , for @xmath222 , @xmath265 , @xmath266 = \sum_{i=2}^{k+1 } { 1\over i ! } q_{k+1}^{(i ) } ( 0 ) x^{i-2}\ ] ] and @xmath267 thus , for example , @xmath268 , @xmath269 and @xmath270 , @xmath271 , @xmath272 and @xmath273 . set furthermore @xmath274 the following theorem puts forward the fundamental identity at the root of this work . [ theorem6 ] in the preceding setting , let @xmath7 be a @xmath8-chaos eigenfunction with eigenvalue @xmath106 , @xmath222 . set @xmath124 . then @xmath275 [ corollary7 ] in the preceding setting , let @xmath7 be a @xmath8-chaos eigenfunction with eigenvalue @xmath106 , @xmath222 . set @xmath124 . if @xmath276 then @xmath277 in particular , if @xmath7 is normalized in @xmath278 , then @xmath279 and thus @xmath280 under the additional diffusion hypothesis on @xmath30 , according to ( [ equ9 ] ) , inequality ( [ equ19 ] ) of corollary [ corollary7 ] may be expressed equivalently as @xmath281 in particular , if @xmath282 , then @xmath124 is constant and by stein s lemma ( proposition [ proposition1 ] ) , the distribution of @xmath7 is gaussian . the next statement describes a fundamental instance for which the spectral condition ( [ equ17 ] ) in corollary [ corollary7 ] is fulfilled . [ theorem8 ] the spectral condition ( [ equ17 ] ) in corollary [ corollary7 ] , @xmath283 is satisfied when @xmath284 . as a consequence of this result , the conclusions of corollary [ corollary7 ] apply to the examples of the ornstein uhlenbeck , bernoulli and poisson operators . as such , some of the main conclusions of @xcite are covered by the preceding general statement , and in particular the initial result of @xcite , namely that if @xmath285 is a sequence of homogeneous gaussian chaos , normalized in @xmath286 , @xmath287 , then @xmath285 converges to a gaussian distribution as soon as @xmath288 . for discrete models as the cube or the poisson space , the picture is less satisfactory . for instance on the cube @xmath289 , @xmath287 , if @xmath290 , @xmath11 , is a sequence of walsh chaos of degree @xmath8 normalized in @xmath107 for the uniform measure @xmath32 , and if @xmath291 , then as an application of corollary [ corollary7 ] , @xmath292 in @xmath107 . now @xmath112 being constant in this case is not always discriminative [ as shown by the example of @xmath293 and further conditions have to be imposed on the sequence @xmath285 to ensure convergence toward a gaussian distribution . this analysis has been recently achieved in @xcite . similar additional conditions have been studied on poisson spaces in @xcite . the input of corollary [ corollary7 ] on convergence of chaos in these discrete examples is that it reduces the convergence @xmath294 in @xmath107 by the weaker condition @xmath295 . before turning to the general proofs of theorem [ theorem6 ] and corollary [ corollary7 ] , and to get a better feeling about these statements , we discuss in this section the particular values @xmath296 and @xmath297 . recall that we write for simplicity @xmath185 , @xmath298 , for an eigenfunction @xmath7 . when @xmath296 , that is , @xmath299 , multiplying this identity by @xmath300 and integrating with respect to @xmath32 , it follows thanks to lemma [ lemma3 ] [ formula ( [ equ15 ] ) ] that @xmath301 now here @xmath269 , and thus @xmath302 , so that both the fundamental identity ( [ equ16 ] ) and the spectral condition ( [ equ17 ] ) are automatically satisfied . when @xmath303 , start from @xmath304 . multiplying by @xmath300 and integrating , it follows similarly thanks to lemma [ lemma3 ] [ formula ( [ equ15 ] ) ] that @xmath305 by ( [ equ13 ] ) of lemma [ lemma3 ] , @xmath306 so that @xmath307 here @xmath272 and @xmath308 so that the fundamental identity ( [ equ16 ] ) holds , and the spectral condition ( [ equ17 ] ) amounts to @xmath309 for every @xmath310 . one observation on which we will come back in the next section is that , in the case @xmath303 , only the inequality @xmath311 is used in order to reach the conclusions of corollary [ corollary7 ] . a further observation is that for chaos of order 1 or 2 , the spectral condition ( [ equ17 ] ) is fulfilled for any sequence of eigenvalues @xmath312 this is clearly not the case when @xmath313 . in this section , we establish theorem [ theorem6 ] , corollary [ corollary7 ] and theorem [ theorem8 ] . let thus @xmath7 be a @xmath8-chaos with eigenvalue @xmath106 . ( if necessary , we may assume that @xmath313 according to the preceding section . ) write as usual @xmath175 for @xmath314 , @xmath315 . as in the preceding section for chaos of order 1 or 2 , start as a first step from the chaos hypothesis @xmath316 . multiply this identity by @xmath300 and integrate with respect to @xmath32 . by definition of @xmath317 and ( [ equ15 ] ) of lemma [ lemma3 ] , @xmath318 now , by ( [ equ13 ] ) of lemma [ lemma3 ] , @xmath319 recalling the definition of the polynomial @xmath320 , note that @xmath321 hence @xmath322 now @xmath323 so that @xmath324 the fundamental identity ( [ equ16 ] ) of theorem [ theorem6 ] then follows from ( [ equ21 ] ) together with the fact that @xmath325 and @xmath326 the proof is complete . corollary [ corollary7 ] is deduced from theorem [ theorem6 ] through the following classical and elementary property , consequence of the point spectrum hypothesis . [ lemma9 ] if @xmath327 is a polynomial , @xmath328 for every @xmath329 [ in the @xmath107-domain of @xmath330 if ( and only if ) @xmath331 for every @xmath310 . for each @xmath310 , denote by @xmath332 the eigenspace associated to the eigenvalue @xmath333 so that @xmath334 since @xmath335 is the spectrum of @xmath30 . decompose then @xmath329 in @xmath107 as @xmath336 with @xmath337 , @xmath11 , so that @xmath338 and @xmath339 from which conclusion follows . as mentioned for chaos of order 2 , when @xmath8 is even , only the inequality @xmath340 is used in order to reach the conclusions of corollary [ corollary7 ] . we next turn to the proof of theorem [ theorem8 ] , checking the spectral condition ( [ equ17 ] ) @xmath341 , @xmath342 , for @xmath284 . since in this case @xmath343 , we have to show that @xmath344 \geq(k-1 ) ! .\ ] ] when @xmath345 , the expression on the left - hand side is equal to @xmath346 so that the conclusion holds in this case . when @xmath347 , we need to show that @xmath348 \geq ( k-1 ) ! .\ ] ] assume first that @xmath349 . then @xmath350 hence @xmath348 \geq k!,\ ] ] which answers this case . we turn to the case where @xmath351 for which it is necessary to check that @xmath352 it is enough to assume that @xmath195 is odd , @xmath353 , @xmath354 . then @xmath355 therefore , the inequality to establish amounts to @xmath356 which is trivially satisfied . the claims thus holds in this case too . theorem [ theorem8 ] is therefore established . in this last section , we briefly address the analogs of theorem [ theorem6 ] and corollary [ corollary7 ] in the context of convergence to gamma distributions on the basis of the corresponding stein characterization of proposition [ proposition2 ] . the main conclusion is obtained by a simple variation on the fundamental identity ( [ equ16 ] ) of theorem [ theorem6 ] . in particular , the analysis covers the recent results of @xcite ( see also @xcite ) in the context of wiener chaos . the framework is the one of the preceding sections , with a markov operator @xmath30 with spectrum @xmath357 and invariant and reversible probability measure @xmath32 and carr du champ @xmath37 . recall @xmath358 , @xmath359 , and the polynomials @xmath360 and @xmath361 of theorem [ theorem6 ] . the following theorem addresses approximation of a @xmath8-chaos @xmath7 by a gamma distribution via the control of @xmath362 as emphasized in proposition [ proposition2 ] . as announced , the proof is an easy modification on the fundamental identity ( [ equ16 ] ) of theorem [ theorem6 ] . [ theorem10 ] let @xmath7 be a @xmath8-chaos with eigenvalue @xmath363 , @xmath359 , such that @xmath364 . set @xmath124 . under the spectral condition ( [ equ17])@xmath365 for every @xmath310 , it holds @xmath366 where @xmath367 in the diffusion case , @xmath368 so that the conclusion of the theorem reads @xmath369 consider now the example where @xmath370 for which we know from theorem [ theorem8 ] that the spectral condition ( [ equ17 ] ) holds . the inequality of theorem [ theorem10 ] takes a nicer form when @xmath371 is even . indeed in this case @xmath372 so that @xmath373 in particular in the diffusion case , @xmath374 this inequality ( [ equ22 ] ) then ensures , through stein s lemma ( proposition [ proposition2 ] ) , that if @xmath285 is a sequence of @xmath8-chaos such that @xmath375 for every @xmath195 and @xmath376 then @xmath377 converges in distribution to the gamma distribution with parameter @xmath174 , that is the main result of @xcite . proof of theorem [ theorem10 ] let thus @xmath7 be a @xmath8-chaos with @xmath378 , hence @xmath379 . set @xmath380 ( so @xmath381 ) . it is immediately checked that @xmath382 and , for every @xmath383 , @xmath384 therefore , the fundamental identity ( [ equ16 ] ) of theorem [ theorem6 ] takes the form , after a little algebra , @xmath385 under the spectral condition ( [ equ17 ] ) @xmath386 for every @xmath310 , @xmath387 which amounts to the statement of the theorem . the proof is complete . the author is grateful to one of the referees for the numerous and constructive comments that led to an improved exposition of this work .

we analyze from the viewpoint of an abstract markov operator recent results by nualart and peccati , and nourdin and peccati , on the fourth moment as a condition on a wiener chaos to have a distribution close to gaussian . in particular , we are led to introduce a notion of chaos associated to a markov operator through its iterated gradients and present conditions on the ( pure ) point spectrum for a sequence of chaos eigenfunctions to converge to a gaussian distribution . convergence to gamma distributions may be examined similarly . . .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Corporate Patriot Enforcement Act of 2002''. SEC. 2. PREVENTION OF CORPORATE EXPATRIATION TO AVOID UNITED STATES INCOME TAX. (a) In General.--Paragraph (4) of section 7701(a) of the Internal Revenue Code of 1986 (defining domestic) is amended to read as follows: ``(4) Domestic.-- ``(A) In general.--Except as provided in subparagraph (B), the term `domestic' when applied to a corporation or partnership means created or organized in the United States or under the law of the United States or of any State unless, in the case of a partnership, the Secretary provides otherwise by regulations. ``(B) Certain corporations treated as domestic.-- ``(i) In general.--The acquiring corporation in a corporate expatriation transaction shall be treated as a domestic corporation. ``(ii) Corporate expatriation transaction.--For purposes of this subparagraph, the term `corporate expatriation transaction' means any transaction if-- ``(I) a nominally foreign corporation (referred to in this subparagraph as the `acquiring corporation') acquires, as a result of such transaction, directly or indirectly substantially all of the properties held directly or indirectly by a domestic corporation, and ``(II) immediately after the transaction, more than 80 percent of the stock (by vote or value) of the acquiring corporation is held by former shareholders of the domestic corporation by reason of holding stock in the domestic corporation. ``(iii) Lower stock ownership requirement in certain cases.--Subclause (II) of clause (ii) shall be applied by substituting `50 percent' for `80 percent' with respect to any nominally foreign corporation if-- ``(I) such corporation does not have substantial business activities (when compared to the total business activities of the expanded affiliated group) in the foreign country in which or under the law of which the corporation is created or organized, and ``(II) the stock of the corporation is publicly traded and the principal market for the public trading of such stock is in the United States. ``(iv) Partnership transactions.--The term `corporate expatriation transaction' includes any transaction if-- ``(I) a nominally foreign corporation (referred to in this subparagraph as the `acquiring corporation') acquires, as a result of such transaction, directly or indirectly properties constituting a trade or business of a domestic partnership, ``(II) immediately after the transaction, more than 80 percent of the stock (by vote or value) of the acquiring corporation is held by former partners of the domestic partnership (determined without regard to stock of the acquiring corporation which is sold in a public offering related to the transaction), and ``(III) the acquiring corporation meets the requirements of subclauses (I) and (II) of clause (iii). ``(v) Special rules.--For purposes of this subparagraph-- ``(I) a series of related transactions shall be treated as 1 transaction, and ``(II) stock held by members of the expanded affiliated group which includes the acquiring corporation shall not be taken into account in determining ownership. ``(vi) Other definitions.--For purposes of this subparagraph-- ``(I) Nominally foreign corporation.--The term `nominally foreign corporation' means any corporation which would (but for this subparagraph) be treated as a foreign corporation. ``(II) Expanded affiliated group.-- The term `expanded affiliated group' means an affiliated group (as defined in section 1504(a) without regard to section 1504(b)).'' (b) Effective Dates.-- (1) In general.--The amendment made by this section shall apply to corporate expatriation transactions completed after September 11, 2001. (2) Special rule.--The amendment made by this section shall also apply to corporate expatriation transactions completed on or before September 11, 2001, but only with respect to taxable years of the acquiring corporation beginning after December 31, 2003.

Corporate Patriot Enforcement Act of 2002 - Amends the Internal Revenue Code by determining that acquiring corporations in"corporate expatriation transactions" shall be considered domestic corporations. Defines a "corporate expatriation transaction" as, with certain exceptions, one in which a "nominally foreign corporation" acquires substantially all of the properties held by a domestic corporation and in which, immediately after the transaction, more than 80 percent of the stock of the acquiring corporation is held by former shareholders of the domestic corporation. Lowers the 80 percent threshold to 50 percent when the acquiring "nominally foreign corporation" lacks substantial business activities in the foreign country in which it was created and organized compared to the total activities of the "expanded affiliated group" and the stock is publicly traded, with the principal market of trading being the United States. Defines the terms "nominally foreign corporation" and "expanded affiliated group."Applies similar rules to partnership transactions.Establishes that a series of related transactions relevant to the Act shall be handled as a single transaction.

SECTION 1. SHORT TITLE. This Act may be cited as the ``Protecting Jobs in Your State Act of 2010''. SEC. 2. PROHIBITION ON USE OF CERTAIN STIMULUS AND DISASTER RELIEF FUNDS FOR BUSINESS RELOCATION INCENTIVES. (a) In General.--A State or a political subdivision of a State may not use any funds described in subsection (b) as an incentive for a business-- (1) to relocate a plant, facility, or other operation, in whole or in part, from one State to another; or (2) to expand such an operation in a State in a manner that will result in a reduction in such an operation in another State. (b) Funds Described.--The funds described in this subsection are the following: (1) Funds made available under any of the following: (A) The American Recovery and Reinvestment Act of 2009 (Public Law 111-5) or any amendment made by such Act. (B) The Hiring Incentives to Restore Employment Act (Public Law 111-147) or any amendment made by such Act. (C) Public Law 111-226 (relating to education jobs and Medicaid payments to States) or any amendment made by such Public Law. (D) The Small Business Jobs Act of 2010 (H.R. 5297, as enacted into law) or any amendment made by such Act. (E) The Robert T. Stafford Disaster Relief and Emergency Assistance Act (42 U.S.C. 5211 et seq.). (2) Funds for disaster relief administered by the Secretary of Homeland Security. (c) Enforcement.-- (1) Petition.-- (A) By political subdivision of state to governor.--A political subdivision of a State may submit to the Governor of such State a petition stating that the political subdivision has been adversely affected by a violation of subsection (a) and requesting that the Governor submit to the Secretary of Commerce a petition for an investigation of whether a violation has occurred. (B) By governor to secretary of commerce.--A Governor who receives a petition under subparagraph (A) may submit to the Secretary of Commerce a petition for an investigation of whether a violation of subsection (a) has occurred. (2) Investigation by secretary of commerce.--Upon receiving a petition from a Governor under paragraph (1)(B), the Secretary of Commerce shall conduct an investigation to determine whether a violation of subsection (a) has occurred. (3) Results of investigation; referral to secretary of the treasury.--If the Secretary of Commerce determines under paragraph (2) that a violation of subsection (a) has occurred, the State that committed the violation (or in the case of a violation by a political subdivision of a State, the State of which such political subdivision is a part) shall be liable to the United States for the amount of funds used in violation of such subsection. The Secretary of Commerce shall inform the Secretary of the Treasury that the United States has a claim against such State. (4) Collection by secretary of the treasury.--If the Secretary of the Treasury is informed under paragraph (3) that the United States has a claim against a State, the Secretary shall take such action as is necessary to collect on such claim. (5) Prohibition on receipt of certain funds until repayment made.--A State that is determined to be liable to the United States under paragraph (3) shall not receive any funds described in subsection (b) during the period beginning on the date of the determination of liability and ending on the date on which the State fully repays to the United States the amount of funds used in violation of subsection (a). (6) Rule of construction.--Nothing in this subsection shall be construed to limit the authority or responsibility of any other Federal official to enforce subsection (a) under other Federal law. (d) GAO Report.--Biannually during the 5-year period that ends on the date that is 5 years after the date of the enactment of this Act, the Comptroller General of the United States shall submit to the Committee on Energy and Commerce of the House of Representatives and the Committee on Commerce, Science, and Transportation of the Senate a report on the impact of the preceding provisions of this section. Such a report shall include, for the period covered by the report-- (1) a statement of the number of petitions received by the Secretary of Commerce under subsection (c)(1)(B) and a summary of the disposition of such petitions, including a list of the instances in which the Secretary found violations of subsection (a); (2) a list of any claims of the United States described in subsection (c)(3) that arose, were outstanding, or were collected in whole or in part; and (3) a list of any funds that were withheld under subsection (c)(5). (e) State Defined.--In this section, the term ``State'' includes the District of Columbia, the Commonwealth of Puerto Rico, Guam, the United States Virgin Islands, American Samoa, and the Commonwealth of the Northern Mariana Islands. (f) Effective Date.--This section shall apply with respect to funds obligated by a State or a political subdivision of a State after the date of the enactment of this Act.

Protecting Jobs in Your State Act of 2010 - Prohibits a state or a political subdivision from using funds made available under the American Recovery and Reinvestment Act of 2009 (ARRA), the Hiring Incentives to Restore Employment Act, Public Law 111-226 (relating to education jobs and Medicaid payments to states), the Small Business Jobs Act of 2010, or the Robert T. Stafford Disaster Relief and Emergency Assistance Act, or funds for disaster relief administered by the Secretary of Homeland Security (DHS), as an incentive for a business to: (1) relocate a plant, facility, or other operation from one state to another; or (2) expand an operation in a state in a manner that will result in a reduction in such an operation in another state. Authorizes a political subdivision to submit to the state governor a petition stating that it has been adversely affected by a violation of such prohibition and requesting that the governor submit to the Secretary of Commerce a petition for an investigation. Provides that if the Secretary determines that a violation has occurred, the state in which such a violation was committed shall be liable to the United States for the amount of funds involved. Prohibits such a state from receiving any other funds under such Acts until it fully repays such amount to the United States. Directs the Comptroller General, biannually during the period that ends five years after this Act's enactment, to submit to specified committees a report on the impact of such provisions, including: (1) a statement of the number of petitions received by the Secretary of Commerce and a summary of the disposition of such petitions; (2) a list of U.S. claims that arose, were outstanding, or were collected; and (3) a list of any funds withheld.

The expert says there are too many people in shark territory. NBC 7's Liberty Zabala reports. (Published Sunday, April 30, 2017) A shark attacked a woman as she swam in the waters off San Onofre State Beach in North San Diego County Saturday evening. The attack happened shortly after 6 p.m. in a well-known surf spot nearby called Church, north of the power plant near Basilone Road. The location is near Camp Pendleton. Hunter Robinson, who along with his friends helped rescue the woman, said she was bitten once from her hip to her leg. "Somebody just yelled 'shark', you know, and like 'shark! My friend got bit!' got us kind of, he was just yelling it on the beach," Robinson told NBC 7. Camp Pendleton officials confirmed a shark bite victim had been airlifted to a local hospital around 6:30 p.m. Robinson said that when they found the woman in the water, her friends had her on her surfboard and they were trying to get her onto the sand. But a low tide and plenty of rocks were hampering their efforts. "The back of her leg was really badly bit, you know, just to the bone, from above her knee to above to her butt, it was bad," Robinson recalled. "It was a real bite, yeah. I'll never forget it, ever. It was like full what you would imagine in a shark bite." Good Samaritans rushed to help the woman, pulling her ashore. One of the man had first aid training and used a surf leash to help slow down the bleeding. The woman's rescuers said almost all the muscle in her leg was missing by the time they got her to the shore. The victim, believed to be in her 30s, reportedly told her rescuers she was having trouble breathing. Robinson said he is aware there are sharks in the area, but said he has never witnessed anything like this up close. The woman has not been identified. San Onofre State Beach is closed for swimmers and surfers until 4:30 a.m. Monday, when lifeguards plan to re-evaluate the waters. A GoFundMe page has been set up for the woman. No other information was available. ||||| San Onofre State Beach remains closed after a woman was attacked by a shark in the area Saturday afternoon. (Photo by Laylan Connelly, Orange County Register/SCNG) San Onofre State Beach remains closed after a woman was attacked by a shark in the area Saturday afternoon. (Photo by Laylan Connelly, Orange County Register/SCNG) Sound The gallery will resume in seconds San Onofre State Beach remains closed after a woman was attacked by a shark in the area Saturday afternoon. (Photo by Laylan Connelly, Orange County Register/SCNG) Four friends jumped into action Saturday when a woman was being brought out of the water after a shark attack at San Onofre State Beach. From left to right are Grant Parker, Wade Nevitt, Hunter Robinson and Thomas Williams. (Photo courtesy of Thomas Williams) A view of San Onofre State Beach with the Church surf break pictured at bottom. The shark attack occurred at this vicinity. (Photo courtesy of Tom Cozad) Even as the words “shark attack�? pierced the calm air at the remote beach, it took a moment for Thomas Williams to realize what was happening. But then he saw the woman being carried out of the water on a surfboard, then the blood. And in that split second, Williams’ training kicked in. Williams, a 29-year-old from San Clemente who recently passed his EMT training test, and a handful of others jumped into action when a woman was attacked by a shark at San Onofre State Beach Saturday evening. “It was definitely to the point, her hamstring was gone,�? said Williams a few hours after the attack late Saturday. “If she didn’t receive immediate care, it was life-threatening.�? “All of the back of her leg was kind of missing.�? The shark attack happened at 6:24 p.m. The victim – identified by friends and news outlets as Leeanne Ericson – was airlifted from San Onofre by Mercy Air-5 to Scripps Memorial Hospital in La Jolla, according to Camp Pendleton spokesperson Sgt. Asia Sorenson. The extent of the victim’s injuries is unknown. The San Onofre, San Clemente state beaches and San Clemente city beach were closed through Sunday and expected to remain closed through Monday. . Lifeguards will re-evaluate opening beaches on Tuesday morning. Water off Camp Pendleton will be closed until Wednesday. On Sunday morning, a sign at the kiosk entering San Onofre surf beach warned of the ocean closure, and a ranger said the area from south of trails to T-street was closed for the day, though many surfers were still out in the water at nearby Lower Trestles, one of the area’s best surf spots, just north of where the attack occurred. In the area near the shark attack incident, military guards were stopping people from entering, only allowing people in the campsite access to the sand. Bright red signs reading “Shark Warning Keep Out … Water activity prohibited in this area” lined the sand. Dave Flynn, spokesperson for Scripps Memorial Hospital, said he could not confirm the shark attack and could not give out any information on a patient’s status because of privacy laws. State Parks aide Travis Lara said four people were in the water at the surf spot called “Church,�? also referred casually by surfers as “Churches,” just north of the San Onofre surf beach and the Southern California Edison nuclear power plant, in front of Camp Pendleton campgrounds. The beach, popular with Orange County surfers, is in northern San Diego County. A female, who was wearing swim fins and wading in the water, was bit on her “glute and down her thigh,�? he said. The beach along San Onofre is rocky, so it was no easy task for two surfers who put the woman on a surfboard, trying to navigate the slippery boulders that line the water’s edge while quickly getting her to shore. That’s when Williams, Hunter Robinson, Grant Parker and Wade Nevitt rushed over to help. Robinson, a longtime surfer, suggested using a surf leash as a tourniquet to stop the bleeding. Williams did a quick assessment of the situation: She was conscious and talking. He asked her questions, like if she knew her age, and she was able to answer. Blood, while there was a lot of it, was not squirting out – which means an artery was not hit. That was a good thing. “If the artery had been hit, it’s a lot harder to control,�? he said. “She was not calm, of course,�? he said. “But she was coherent.�? Then, he used the surf leash, to help stop the bleeding. The injury to her leg was on the right side. “I wrapped it around and held it until we got on shore where a couple of friends applied towels for direct pressure.�? He said Camp Pendleton medics showed up on the scene. “I’m glad to see the training I received, after I took in the initial panic of what was going on, that I could kind of assess the situation so I could respond accordingly,�? he said. “If any one of us weren’t there it would have been so much worse.�? News spread as beachgoers attempted to get to San Onofre but were instructed to stay out of the water after the attack. Beachgoer Amber Booth, of San Clemente, was headed to San Onofre to watch the sunset with her family when the ranger told her the ocean water was closed because of the shark attack. Booth, who surfs San Onofre often, said the news made her worry about her daughter, Angelina, 8, who boogie boards often in the area. “There’s so many kids in the water at San O,�? she said. “You don’t really want to think about it when you’re out in the water.�? There have been two videos that have surfaced lately of sharks breaching out of the water near surfers, one at Lower Trestles and another at Upper Trestles, both just north of the attack site. A video surfaced last week of an estimated 16-foot great white feasting on a dead whale off the Dana Point coastline. Nearby, Trails at San Onofre State Beach is known to have resident great white sharks who have lived there for years – some locals dubbed them “Fluffy and Bumper.” And though the area is known as a nursing ground for great whites during spring months, experts and long-time lifeguards say there’s been an uptick in shark activity, especially closer to shore, in recent years in the Orange County area. Chris Lowe, director of the Shark Lab at California State University, Long Beach believes El Nino could have kept sharks around the area in recent years, and his team has tagged several great white sharks that were living in the Surfside Beach area two years ago. Earlier this year, several great white sharks were caught and released from the Huntington Beach area, two from the pier and one from shore in Sunset Beach. Just a few weeks ago, an area of San Clemente beach near the pier was under shark advisory when a shark was spotted by lifeguard trainees in the shorebreak. The latest attack comes nearly one year after swimmer Maria Korcsmaros was attacked off Corona del Mar last Memorial Day. Based on her bite marks, which spanned across her chest, down her hip and over her shoulder, experts estimate the shark was at least 10-feet in length. Shark expert Lowe said while it’s unknown what kind of shark attacked, there’s likely only two shark species in that area that could have caused the injury: a great white or a seven-gill shark. “Those are the only two species I can think of that are capable of inflicting that kind of wound,�? Lowe wrote via e-mail. Williams is eager to hear if the victim is healing. “We all just want to make sure she’s doing OK. We just want to hear some update on whether she’s stable or alive,�? he said. “We just want to know if she’s alright.�? Williams, who just took up surfing recently, said he and his friends planned on surfing San Onofre surf beach but changed their minds to go on the base instead. They brought their surfboards, but with strong winds whipping, they decided to hang out on the sand instead. “We all kind of talked about it, everything kind of happens for a reason,�? he said. “We were just thankful there was enough people there at the right time.�? When asked if the incident would keep him out of the ocean, he said he’s still willing to take his chances out in the water. “The probability of it happening is pretty slim,�? he said. “I don’t think it deters anything. I think it’s the risk you take when you get into any kind of environment.�?

– An unidentified woman was attacked by a shark Saturday while swimming at “Churches,” a popular surf spot in Orange County, California. Two surfers towed the victim in on their board, reports the Orange County Register, traversing slippery rocks before safely pulling her ashore. Several surfers on the scene administered first aid to the victim before she was airlifted to a nearby hospital. “Her hamstring was gone,” says 29-year-old Thomas Williams, who recently completed EMT training and used a surf leash as a tourniquet. "If she didn’t receive immediate care, it was life-threatening.” The victim’s current condition is unknown, while San Onofre beach remains closed through Monday morning. She is believed to be in her 30s, reports NBC San Diego.

more than 60% of adult females in the united states have abdominal obesity , a condition that independently predicts mortality , major morbidities , and metabolic risk factors in women . recent data suggest that waist circumference and the prevalence of abdominal obesity continue to increase . women may be at greater risk for abdominal obesity due to weight gain following pregnancy and/or hormonal fluctuations at menopause , which shift body fat distribution from peripheral regions to the abdomen . current expert guidelines recommend initiating weight loss treatment in women whose waist circumference is > 88 cm ( or bmi 25 to 29.9 kg / m ) and who have two or more comorbidities , such as type 2 diabetes , cardiovascular disease ( cvd ) , hypertension , or dyslipidemia . although abdominal fat decreases with weight loss , there is no consensus on an appropriate evidence - based preventive and treatment nutrition model to control abdominal obesity , and dietary interventions to sustain long - term weight loss ( > 1 year ) have not been identified . many investigations of abdominal obesity measures and diet have focused on single - nutrients ( e.g. , alcohol , fat , protein ) ; however , identification of the isolated nutritional effects is confounded in observational research by the coexistence of dietary factors in the foods we eat . examination of the total diet and nutrient intake patterns of individuals may provide better measures of diet exposure , helping identify individuals who may benefit from targeted nutritional risk interventions [ 9 , 10 ] . few studies have evaluated overall dietary quality using composite dietary indices / scores in relation to abdominal adiposity , [ 1016 ] and the majority are cross - sectional investigations [ 1115 ] . further , none of the existing composite dietary quality indices / scores are based on a specific evidence basis for the most consistent dietary determinants of abdominal or peripheral obesity . the concept of a disease - specific dietary quality index is unique and important since general indices without disease - specificity have not been predictive of all major chronic diseases in women [ 17 , 18 ] . a dietary quality index / score that combines specific dietary determinants of obesity may be more helpful than existing approaches in identifying diet - obesity associations and may offer new insights into nutritional risk assessment , preventive intervention and treatment for abdominal obesity risk reduction . a nutrient - based approach , such as this , is appropriate because nutrient targeting influences patterns of food intake [ 9 , 19 , 20 ] , and the core of all us population - based dietary guidelines and nutrition policy for maintaining health focus on achieving optimal nutrient intake with both nutrient and food - based messages . this investigation prospectively examined the relationship between dietary quality and development of abdominal obesity in women , which has not been adequately addressed in current literature . we evaluated the ability of a novel obesity - specific nutritional risk score ( onrs ) to predict development of abdominal obesity over 12 years in healthy women . the framingham study is a longitudinal population - based investigation that began in 1948 to study the progression of cvd . briefly , cohort members were 5209 men and women , aged 28 to 62 years , from the town of framingham , ma . in 1971 , 5124 adult children and their spouses of the original cohort were invited to participate in the framingham offspring - spouse study ( fos ) . this second - generation cohort ( 2483 men and 2641 women ) participated in clinical examinations every 4 years , on average . each clinical visit , conducted according to a standardized protocol , consists of an updated , detailed medical history and a complete physical exam with laboratory and noninvasive diagnostic testing . of the 1956 women who attended the third examination ( exam 3 , 19841988 ) , only 1265 ( 65% ) of those 1265 women , 288 were not abdominally obese ( waist circumference 88 cm ) , aged 30 to 69 years , and presented without cvd ( including coronary heart disease and stroke ) , cancer , diabetes or metabolic syndrome ( mets ) risk factors at baseline ( exam 4 , 19881992 ) , and comprise the sample for these analyses . waist circumference was first assessed at exam 4 ; therefore , evaluation of baseline characteristics and covariates , except physical activity ( exam 2 ) , also come from this exam . diet exposure is exam 3 , not exam 4 , for these analyses because this is the collection time point for the 3-day dietary records ; this approach is consistent with other published fos research . follow - up was assessed through exam 7 ( 19982001 ) for a total of 12 years . all protocols were approved by the human subjects institutional review board of the boston university medical campus and boston medical center . diet was assessed from 3-day dietary records completed at the exam 3 clinic visit according to standardized research protocols [ 22 , 23 ] . participants were instructed by a registered dietitian to record all foods consumed over 2 weekdays and 1 weekend day without deviation in their current eating behavior . to quantify portion sizes , nutrient intake calculations were performed using the minnesota nutrition data system software ( version 2.6 ; food database 6a ; nutrient database 23 ; nutrition coordinating center , university of minnesota , minneapolis , mn ) . we previously validated our approach to composite nutrient risk score assessment in this cohort and we used this approach to construct the obesity - specific nutritional risk score ( onrs ) . the new onrs is based on dietary factors that have been shown to either promote or protect - against general obesity [ 2427 ] . potential components of the nutritional risk score were identified by reviewing existing dietary composite indices [ 9 , 28 , 29 ] , as well as the extensive literature on diet and obesity in human studies . we selected eleven components to include in the onrs : total energy ( kj ) , energy density ( kj / g ) , carbohydrate ( % energy ) , protein ( % energy ) , total , monounsaturated , polyunsaturated , and saturated fats ( % energy ) , fiber ( g/4184 kj ) , calcium ( mg/4184 kj ) , and alcohol ( % energy ) . the methodology used to calculate the onrs is similar to that of our previously validated framingham nutritional risk score as described in the original validation of dietary patterns in the fos cohort . ranking of individual nutrients in the score is based on the number of women in the sample where each nutrient is ranked from 1 ( low risk ) to 288 ( high risk ) for every woman with completed 3-day dietary records . ranks are assigned so that a woman with a desirable nutrient intake level ( protective nutrients ) receives a lower rank while a woman with an undesirable nutrient intake level ( risk - promoting nutrients ) receives a higher rank . energy , energy density , alcohol , and total , saturated , monounsaturated , and polyunsaturated fat intakes were ranked low to high , whereas protein , carbohydrate , fiber , and calcium intakes were ranked high to low . the mean ranks of each individual nutrient are used to calculate the overall nutritional risk score of each woman . monounsaturated and polyunsaturated fats were ranked as risk - promoting nutrients in contrast to some reports suggesting that they may be protective [ 30 , 31 ] . this was done because the majority of monounsaturated fat consumed by fos women in this time - frame was derived from animal sources with higher saturated fat content rather than plant sources , and the polyunsaturated fat levels contained partially hydrogenated margarine rather than marine or plant oils . the main outcome was development of abdominal obesity at any time point during follow - up . abdominal obesity was defined according to the recommended waist circumference level for women ( > 88 cm ) . waist circumference was measured at clinic visits at the umbilicus with participants standing and the tape measure parallel to the floor , according to standard protocol . metabolic and anthropometric measurements are routinely collected at clinic visits according to validated methods [ 32 , 33 ] : systolic and diastolic blood pressure ( duplicate measurements ) , fasting lipids [ total cholesterol , high density lipoprotein ( hdl ) , low density lipoprotein ( ldl ) , and triglycerides ] , fasting glucose , and bmi ( height and weight ) . the national cholesterol education program 's adult treatment panel iii cutoffs were used to evaluate each woman 's mets risk factors . women were considered to be free of mets risk factors according to the following criteria : glucose < 110 mg / dl , blood pressure < 130/<85 mmhg , triglycerides < 150 mg / dl , hdl > 50 mg / dl , and waist circumference 88 cm . selected socio - demographic and behavioral characteristics self - reported dietary behavior was evaluated using the framingham food habit questionnaire and included adherence to a modified diet ( currently on a diet ) and usual weight pattern described as stable ( 5 pounds ) or fluctuating ( 10 pounds ) body weight . other self - reported characteristics included age , smoking status , physical activity , parity , menopausal status , and use of hormone replacement therapy . physical activity was assessed using a standardized questionnaire at exam 2 ( 19791983 ) and not at exam 3 ; these values were used in the analyses consistent with published framingham protocols . age - adjusted mean levels of baseline characteristics and nutrient intakes were computed for each nutritional risk score tertile . the glm procedure in sas ( analysis of covariance ) was used to compute age - adjusted means for continuous variables . logistic regression ( sas procedure logistic ) was used to compute age - adjusted proportions for dichotomous variables . bonferroni 's correction was used to adjust for multiple comparisons in analyses of baseline characteristics and nutrient intakes . the primary research goal was to examine the association between dietary quality , assessed by the onrs , and development of abdominal obesity . stepwise multiple logistic regression was used to evaluate other variables that were related to abdominal obesity . after the stepwise regression , we constructed a final model to establish that the variables did not attenuate the onrs - abdominal obesity relationship . the final , fixed model included the following variables : age ( continuous ) , physical activity ( continuous ) , menopausal status ( yes / no ) and smoking status ( never , former , or current smokers ) . metabolic , anthropometric , and demographic variables that did not differ at baseline according to nutritional risk score tertile were not identified as confounders and were thus not added to the model . odds ratios ( ors ) were calculated for each nutritional risk score tertile of the onrs with the lowest tertile as the referent group . the p - value for trend was determined using the tertile groups of the onrs in a continuous form . secondary analyses adjusting for age , physical activity , menopausal status , and smoking status , were conducted to determine the relationship of individual nutrient risk score components to abdominal obesity . intakes of each index component were ranked low to high and categorized into tertiles , and ors were calculated for each intake tertile with the lowest tertile as the referent group . the p - value for trend was determined using the tertile groups of intake for each individual nutrient in a continuous form . all analyses were performed using sas software ( version 9.1 ; 2003 , sas institute , cary , nc ) . at baseline , women with higher dietary quality ( i.e. , lowest nutritional risk tertile ) were significantly older and smoked less during their lifetimes ( table 1 ) . their metabolic profiles reflect the health status of this disease - free cohort at baseline ; their blood pressure , total cholesterol , ldl , hdl , triglyceride , and blood glucose levels were within normal ranges . relative to women with higher dietary quality ( i.e. , lowest nutritional risk tertile ) , women with the poorest dietary quality ( i.e. , highest nutritional risk tertile ) had lower intakes of fiber , calcium , protein , and carbohydrate , higher energy - dense diets , and higher intakes of total energy , alcohol and total , saturated , polyunsaturated , and monounsaturated fats . the overall incidence of abdominal obesity over 12 years was ~52% ( n = 149 ; table 3 ) . the onrs was directly related to abdominal obesity ( p for trend = .048 ) . in multiple logistic regression analyses adjusted for age , physical activity , menopause , and smoking status , women in the highest nutritional risk tertile were 1.87 ( 95% ci , 1.01 , 3.47 ) times more likely to become abdominally obese compared to those in the lowest tertile of nutritional risk . in secondary analyses that explored all onrs nutrients individually , carbohydrate intake was inversely associated , while monounsaturated fat intake was positively associated , with development of abdominal obesity ( p for trend < .05 ) . in multiple logistic regression analyses adjusted for age , physical activity , menopause , and smoking status , compared to the lowest tertile of intake , odds of becoming abdominally obese were lower in the highest tertile of carbohydrate intake ( or 0.50 ; 95% ci , 0.27 , 0.92 ) and higher in the highest tertile of monounsaturated fat intake ( or 1.91 ; 95% ci , 1.04 , 3.52 ) . we evaluated dietary quality and its relationship to abdominal obesity using an 11-nutrient obesity - specific composite dietary risk index / score developed in the fos . the onrs predicted development of abdominal obesity over 12 years in women , aged 30 to 69 years , who were free of disease and mets risk factors at baseline . women with eating habits of poorest dietary quality ( i.e. , highest nutritional risk ) consumed diets that were significantly lower in protein , carbohydrate , fiber , and calcium , and higher in total calories , energy - density , total fat , and alcohol . our longitudinal findings support those of cross - sectional studies investigating the association of a priori dietary quality indices / scores and abdominal adiposity [ 1113 , 15 ] . for example , fogli - cawley et al . found that adults in the highest quartile of the 2005 dietary guidelines adherence index ( dgai ) had the lowest waist circumference compared to those in the lowest quartile ( 90 cm versus 96 cm ; p for trend across 2005 dgai quintiles < .001 ) . the 2005-dgai uses 20 criteria , each with a maximum value of 1 , reflecting key dietary recommendations in the 2005 dietary guidelines for americans . these results are also consistent with earlier research using the framingham nutritional risk score ( fnrs ) , a 19-nutrient cvd - oriented nutritional risk index , which also predicted abdominal obesity in fos women . compared to women with higher dietary quality ( i.e. , lowest nutritional risk ) , those with poorer dietary quality ( i.e. , highest nutritional risk ) had more than a twofold risk of developing abdominal obesity ( or 2.3 ; 95% ci , 1.2 , 4.3 ) . an advantage of the onrs , however , is that it incorporates new foci of research , such as energy density and evidence - based predictors of obesity - related outcomes ( e.g. , carbohydrate , protein , fat , fiber , calcium , and total calories ) . synergistic mechanisms among nutrients in the onrs may be modulating metabolic pathways that may lead to excess abdominal fat . the lower fat and energy - density combined with higher fiber and protein intakes in women consuming a higher quality diet may reduce circulating levels of glucose and free - fatty acids , which may prevent insulin resistance and/or high insulin levels , leading to decreased visceral fat storage [ 3739 ] . the role of diet in abdominal fat accumulation , however , is not clearly established . the findings of single - nutrient analyses by halkjaer et al . did not show total energy or macronutrient intake as a predictor of five - year changes in waist circumference in adults . to our knowledge , we are among the first to prospectively examine development of abdominal obesity and nutrient intake patterns using an obesity - specific dietary quality index / score with a specific energy density component and other evidence - based predictors of obesity . the results of these analyses suggest that overall dietary quality influences abdominal adiposity independent of age , physical activity , smoking , and menopausal status . composite dietary quality appears more informative than the single nutrient approach in determining risk of abdominal obesity . while the onrs can not be directly applied as is , dietary quality and intakes of the nutrients that comprise the score could become a new focus as these results are translated into public policy and assessment , prevention and treatment recommendations for abdominal obesity . specifically , future translational research would assess nutrient - related risk using the onrs combined with an evaluation of established dietary patterns to identify food- and nutrient - based targets for preventive intervention to help control abdominal weight gain . as this type of translational research progresses , we could then encourage that nutrition interventions be guided by use of both a composite nutrient index and dietary pattern approach . in a recent randomized controlled clinical trial , a calorie - reduced diet modeled on the dietary approaches to stop hypertension ( dash ) protocol resulted in a significantly greater weight loss and reduction in waist circumferences in overweight and obese women after 6 months ( 14 kg , p = .03 and 5 cm , p = .04 , resp . ) than the control group ( + 1 kg , ns and 1 cm , ns , resp . ) . the dash diet plan emphasizes fruits , vegetables , low - fat dairy , whole grains , poultry , fish , and nuts and is higher in calcium and magnesium and lower in total and saturated fat . it is important to note that longer term efficacy of this dietary protocol was not determined and that this protocol may be difficult for some individuals to follow for extended periods , particularly if it requires major changes in habitual eating behavior and is not compatible with personal preferences and tastes . a dietary quality approach that targets obesity - specific nutrients , as demonstrated by the onrs , combined with approaches that are informed by habitual eating patterns offers an alternative methodology . this current research suggests that opportunities exist for a new intervention paradigm that promotes improved nutrient quality while retaining the beneficial aspects of the individual 's established eating pattern . although our results suggest that higher intakes of polyunsaturated and monounsaturated fats may increase a woman 's risk of abdominal weight gain , it is important to emphasize that the food sources of monounsaturated and polyunsaturated fats consumed by fos women in the mid-1980s baseline time - frame were not derived from protective plant sources , but rather animal sources high in saturated fat and partially hydrogenated margarines potentially high in trans fat , respectively . the increased risk of abdominal obesity associated with saturated and trans fat has been demonstrated in animal and human [ 43 , 44 ] investigations . further , current clinical trial literature has demonstrated a protective effect of monounsaturated and polyunsaturated fats derived from plant oils on central fat distribution [ 45 , 46 ] . if the onrs were to be applied to more recent dietary data , it would seem important to alter the scoring of these fat subtypes to reflect current diets . in addition , given that the scoring system is based on ranking within a study population , direct application of the onrs is not advised at this time . future translational research needs to determine an optimal method of ranking individuals in other populations . before we would advocate a direct translation of this index , we would wish to conduct a formal translational research study similar to one we conducted with fos food - based dietary patterns developed from cluster analyses [ 9 , 47 ] . translational research of this nature was beyond the scope of the present study but the importance of carrying out such analytical research seems supported by our present findings . the major strength of this study is the longitudinal design with long duration of follow - up and direct measurement of the outcome variable ( i.e. , waist circumference ) , as opposed to self - report . additionally , the onrs is nutrient - based , which is consistent with the foundation of the dietary guidelines for americans for determining adequacy of intake and overall dietary quality . other strengths include calculation of dietary quality using energy - adjusted index components and consideration of a wide range of potential confounders in stepwise analyses with the final fixed model adjusted for age , physical activity , smoking , and menopausal status . in addition , our methodology of including only components associated with obesity in the onrs potentially increased the diagnostic accuracy of the index . this is a methodological strength in dietary quality index construction that has recently been noted by kourlaba and panagiotakos . and although our scoring system approach , in which components of the onrs are weighted equally , is consistent with other dietary quality indices [ 28 , 29 ] , ongoing work is required to refine the use and construction of such indices . our outcome was development of abdominal obesity ; therefore , it was critical to exclude women with abdominal obesity and those with related risk factors at baseline . the fact that fewer than 25% of women in the fos cohort met the inclusion criteria underscores the high prevalence of abdominal obesity and related metabolic risk factors . despite the smaller number of women included in this investigation , we were able to demonstrate the predictive validity between a lower quality diet and abdominal obesity . another limitation is the use of 3-day dietary records which may introduce error as they have been reported to underestimate intake and are subject to reporting bias . we attempted to partially correct for energy misreporting in that all nutrients are energy - adjusted in the index using the nutrient - density method ( i.e. , % kcal or unit of nutrient/4184 kj ) as discussed in a recent systematic review . nonetheless , it is our view that in this lean sample of women at baseline , energy mis - reporting ( notably over - reporting ) would likely have attenuated the results and led to a failure to detect a relationship between dietary quality and abdominal obesity . while it is also true that we can not assess nutritional risk over time , intakes in the fos cohort we also note the potential for bias in our sample since of the 1956 women who attended exam 3 , only 1265 completed a 3-day dietary record . previously , we have compared women who completed the 3-day dietary records to those who did not . women who completed the records were older ( ~49 years versus ~47 years ) , had lower bmis ( 25 versus 26 ) , and were more likely to be nonsmokers . further , these results may not be generalizable to women outside of the fos as 98% of these women are white and eating patterns and nutrient intakes may differ by ethnicity . we further recognize the importance of socio - economic status ; however , information on this and other potential confounders was not available for these analyses . in conclusion , we identified a relationship between dietary quality assessed using an obesity - specific dietary quality index / score and accumulation of central body fat . an energy - adjusted , nutrient - based risk score , like the onrs , identifies important components of nutritional risk assessment for abdominal obesity prevention in women and suggests that new opportunities exist for preventive nutrition intervention paradigms that target specific improvements in dietary quality in the context of the individual 's nutrient intake pattern . as future research moves to a translational model , the nutrient components of interest can be translated into targeted food sources , which can be used to guide improvements by establishing guidelines for the counseling process and optimal approaches to dietary interventions . strategies of this nature are crucial in planning and implementing programs for abdominal and peripheral obesity risk reduction and individualized treatment recommendations .

background . links between dietary quality and abdominal obesity are poorly understood . objective . to examine the association between an obesity - specific dietary quality index and abdominal obesity risk in women . methods . over 12 years , we followed 288 framingham offspring / spouse study women , aged 3069 years , without metabolic syndrome risk factors , cardiovascular disease , cancer , or diabetes at baseline . an 11-nutrient obesity - specific dietary quality index was derived using mean ranks of nutrient intakes from 3-day dietary records . abdominal obesity ( waist circumference > 88 cm ) was assessed during follow - up . results . using multiple logistic regression , women with poorer dietary quality were more likely to develop abdominal obesity compared to those with higher dietary quality ( or 1.87 ; 95% ci , 1.01 , 3.47 ; p for trend = .048 ) independent of age , physical activity , smoking , and menopausal status . conclusions . an obesity - specific dietary quality index predicted abdominal obesity in women , suggesting targets for dietary quality assessment , intervention , and treatment to address abdominal adiposity .

TOKYO — Ordinarily, Fordham University Law School in New York does not publicize an incoming student who is about to matriculate. But Kei Komuro is no ordinary student. He is the fiancé of Princess Mako, the eldest grandchild of Japan’s Emperor Akihito, head of the world’s oldest monarchy. Or is he? On Thursday, in response to a request by Japan’s Imperial Household Agency, which oversees the ceremonial functions and protocols of the royal family, Fordham removed a phrase from a news release that had trumpeted Mr. Komuro, a paralegal in Tokyo, as the “fiancé of Princess Mako of Japan.” As demonstrated by the recent wedding of Prince Harry of Britain and Meghan Markle, a biracial, divorced American, any commoner who marries into a royal family is subjected to intense scrutiny. ||||| Kei Komuro, a paralegal at the Okuno & Partners law firm in Japan who is engaged to be married to Japan’s Princess Mako, will attend Fordham Law School starting in August. He has received the Michael M. Martin Scholarship. The Martin Scholarship is a merit scholarship covering the full cost of tuition from Fordham Law based on his strong academic and other credentials. The Martin Scholarship is not a loan and does not need to be repaid. He will enter the law school’s one-year LL.M. program and then hopes to continue for two more years to receive a J.D. The law school’s LL.M. program is structured on two interdependent principles: globalization and specialization. The eight LL.M. degrees offer the opportunity to specialize in fields that are evolving as the law, economy, technology, and times demand. This spring, 181 students were enrolled in the LL.M. program, six of them from Japan. More information about the LL.M. program is here.

– One word in a press release put out by Fordham University Law School in New York has attracted international attention—attention strong enough to get Fordham to tweak the release. The egregious word? "Fiancé." It was written in reference to Kei Komuro, who is set to begin studying for his master's degree in law on a full scholarship next month. He's also engaged to marry Japan's Princess Mako. The press release identified him as her "fiancé," and the word choice apparently rankled Japan's Imperial Household Agency, which handles royal protocol. The New York Times reports a rep for the agency told reporters Komuro "does not have the status of being engaged and therefore is not a fiancé." The university explained the removal (you can see the updated release here) was done "out of respect" for the agency's protocol and traditions, one of which is the Nosai no Gi—a royal engagement ceremony that was supposed to occur on March 4. It was postponed after the agency in February announced the 26-year-olds' wedding wouldn't occur in November as planned, with the Japan Times reporting at the time that a "lack of preparation" and "immaturity" were cited as the reasons for the delay to 2020, though tabloids have speculated that alleged financial troubles on the part of Komuro's mother played a part. The Japan Times used the word "fiancé" in its own report on Komuro's university plans, noting that after the one-year program, he hopes to continue for two more years in order to secure a degree that would allow him to practice law in the US. (Mako will lose her royal status after the wedding.)

SECTION 1. SHORT TITLE. This Act may be cited as the ``Stem Cell Research for Patient Benefit Act of 2001''. SEC. 2. IMPLEMENTATION OF NATIONAL INSTITUTES OF HEALTH GUIDELINES FOR RESEARCH USING HUMAN PLURIPOTENT STEM CELLS. The Director of the National Institutes of Health shall conduct or support research using human pluripotent stem cells from embryos and fetal tissue in accordance with the National Institutes of Health Guidelines for Research Using Human Pluripotent Stem Cells, as published in the Federal Register on August 25, 2000 (65 FR 51976), and corrected on November 21, 2000 (65 FR 69951). SEC. 3. STUDY ON STEM CELLS BY THE NATIONAL INSTITUTES OF HEALTH. (a) In General.--The Director of the National Institutes of Health shall conduct a study on the following: (1) The current state of knowledge about the following: (A) Biological properties of stem cells obtained from embryos, fetal tissues, and adult tissues. (B) Biological differences among stem cells obtained from embryos, fetal tissues, and adult tissues and the significance of these differences for research and medicine. (C) Ability of stem cells to generate tissues, including neurons and heart, kidney, blood, and liver tissues, and the potential clinical uses of these tissues. (2) Emerging stem cell applications. (3) The effectiveness of the guidelines referred to in section 2. (b) Report.--Not later than 5 years after the date of the enactment of this Act, the Director of the National Institutes of Health shall submit a report describing the findings and conclusions of the study to the Committee on Energy and Commerce of the House of Representatives and the Committee on Health, Education, Labor, and Pensions of the Senate. SEC. 4. STUDY ON THERAPIES ADDRESSING IMMUNOLOGICAL REJECTION OF STEM CELLS AND DIFFERENTIATED CELLS AND TISSUE DERIVED FROM STEM CELLS. (a) In General.--The Secretary of Health and Human Services (in this section referred to as the ``Secretary'') shall seek to enter into an agreement with the Institute of Medicine under which the Institute, taking into consideration the results of the study authorized by section 3, will conduct a study to-- (1) assess the current state of knowledge about therapies, including somatic cell nuclear transfer and therapies using pharmaceuticals, that may be used to address immunological rejection of stem cells and differentiated cells and tissue derived from stem cells; (2) compare the potential therapeutic value of such therapies; and (3) identify safeguards that could be implemented to prevent the use of human embryos created by somatic cell nuclear transfer for purposes other than the development of therapies for diseases. (b) Other Entities.--If the Institute of Medicine declines to conduct the study described in subsection (a), the Secretary shall enter into an agreement with another appropriate public or nonprofit private entity to conduct the study. (c) Report.--The Secretary shall ensure that, not later than 2 years after the date of the enactment of this Act, the study to be conducted under subsection (a) is completed and a report describing the findings and conclusions of the study is submitted to the Committee on Energy and Commerce of the House of Representatives and the Committee on Health, Education, Labor, and Pensions of the Senate. SEC. 5. BIOMEDICAL ADVISORY COMMISSION. (a) Establishment.--There is established a commission to be known as the Biomedical Advisory Commission (in this section referred to as the ``Commission''). (b) Duties.-- (1) Study.--The Commission shall conduct studies on the following: (A) Bioethical issues arising from research on human biology and applications of such research. (B) Emerging biomedical research, including the ethical, social, legal, and regulatory issues concerning such research and its clinical applications. (2) Recommendations.--Based on the results of the study, the Commission shall formulate such recommendations as it considers appropriate with the goal of realizing the development of effective therapies as quickly as possible, taking into account the relevant ethical, social, legal, and regulatory considerations. (c) Membership.-- (1) Appointment.--The Commission shall be composed of 13 members as follows: (A) 1 member appointed by the President. (B) 3 members appointed by the Speaker of the House of Representatives. (C) 3 members appointed by the minority leader of the House of Representatives. (D) 3 members appointed by the majority leader of the Senate. (E) 3 members appointed by the minority leader of the Senate. (2) Qualifications.--The members appointed under subparagraphs (B), (C), (D), and (E) of paragraph (1) shall include representatives from the legal, ethical, scientific, medical, patient, religious, and industry communities. (3) Consultation.--All appointments under paragraph (1) shall be made in consultation with members of the communities referred to in paragraph (2). (4) Chairperson.--The Chairperson of the Commission shall be elected by a majority from among the members of the Commission. (5) Terms.--Each member of the Commission shall be appointed for a term of 3 years and may be reappointed. (6) Vacancies.--A vacancy in the Commission shall be filled in the manner in which the original appointment was made. (d) Meetings.--The Commission shall meet-- (1) at the call of the Chairperson; and (2) at least 2 times but not more than 4 times each calendar year. (e) Compensation and Expenses.-- (1) Compensation.--Subject to paragraph (2), each member of the Commission shall be compensated at a rate equal to the daily equivalent of the annual rate of basic pay prescribed for level III of the Executive Schedule under section 5314 of title 5, United States Code, for each day (including travel time) during which such member is engaged in the performance of the duties of the Commission. (2) Prohibition of compensation of federal employees.-- Members of the Commission who are full-time officers or employees of the United States or Members of Congress may not receive additional pay, allowances, or benefits by reason of their service on the Commission. (3) Travel expenses.--Each member of the Commission shall receive travel expenses, including per diem in lieu of subsistence, in accordance with applicable provisions under subchapter I of chapter 57 of title 5, United States Code, while away from the member's home or regular place of business in the performance of services for the Commission. (f) Executive Director and Staff.-- (1) Executive director.-- (A) Appointment.--The Commission shall have an Executive Director who shall be appointed by the Secretary of Health and Human Services. (B) Pay.--The Executive Director shall be paid at a rate not to exceed the rate payable for level V of the Executive Schedule under section 5316 of title 5, United States Code. (2) Staff.-- (A) Appointment.--The Executive Director may appoint such additional personnel as the Executive Director sees fit. (B) Pay.--The staff of the Commission shall be paid in accordance with the provisions of chapter 51 and subchapter III of chapter 53 of title 5, United States Code, relating to classification and General Schedule pay rates. (3) Applicability of certain civil service laws.--The Executive Director and staff of the Commission shall be appointed subject to the provisions of title 5, United States Code, governing appointments in the competitive service. (g) Hearings and Sessions.--The Commission may, for the purpose of carrying out this section, hold hearings, sit and act at times and places, take testimony, and receive evidence as the Commission considers appropriate. (h) Obtaining Official Data.--The Commission may secure directly from any department or agency of the United States information (other than information required by any Federal statute to be kept confidential by such department or agency) necessary for the Commission to carry out its duties under this section. Upon request of the Commission, the head of that department or agency shall furnish such nonconfidential information to the Commission. (i) Administrative Support Services.--Upon the request of the Commission, the Administrator of General Services shall provide to the Commission, on a reimbursable basis, the administrative support services necessary for the Commission to carry out its responsibilities under this Act. (j) Contracts.--To the extent or in the amounts provided in advance in appropriations Acts, the Commission may contract with and compensate government and private agencies or persons for supplies and services. (k) Reports.--The Commission may submit to the Congress and the President such reports as the Congress requests or the Commission considers appropriate. (l) Termination.--The Commission terminates 30 days after the date that is 6 years after the date of the enactment of this Act.

Stem Cell Research for Patient Benefit Act 2001 - Requires the Director of the National Institutes of Health to: (1) conduct or support research using human pluripotent stem cells from embryos and fetal tissue in accordance with the National Institutes of Health Guidelines for Research Using Human Pluripotent Stem Cells; and (2) study and report to specified congressional committees on stem cells and the effectiveness of such guidelines.Requires the Secretary of Health and Human Services to enter into an agreement with: (1) the Institute of Medicine under which the Institute shall assess the current state of knowledge about therapies, including somatic cell nuclear transfer and therapies using pharmaceuticals, that may be used to address immunological rejection of stem cells and differentiated cells and tissue derived from stem cells; and (2) another appropriate public or nonprofit private entity to conduct such assessment if the Institute declines.Establishes the Biomedical Advisory Commission to study: (1) bioethical issues arising from research on human biology and applications of such research; and (2) emerging biomedical research, including the ethical, social, legal, and regulatory issues concerning such research and its clinical applications.

These crawls are part of an effort to archive pages as they are created and archive the pages that they refer to. That way, as the pages that are referenced are changed or taken from the web, a link to the version that was live when the page was written will be preserved.Then the Internet Archive hopes that references to these archived pages will be put in place of a link that would be otherwise be broken, or a companion link to allow people to see what was originally intended by a page's authors.The goal is to fix all broken links on the web . Crawls of supported "No More 404" sites. ||||| CAMDEN -- The death of a 20-year-old Pennsylvania man who died days after he was allegedly struck in the head repeatedly by Camden City police nearly a decade ago has been ruled a homicide, according to Philly.com. Brett Katzenmoyer was arrested outside the venue now called the BB&T Pavilion on Aug. 18, 2007 and suffered a concussion, a broken nose, bruising on his torso and other injuries, according to a lawsuit filed by his mother that's since been settled for $750,000. He was unresponsive four days later, suffering from heart and renal failure, and died in a hospital, the suit says. According to Philly.com, his death was originally ruled a homicide by then-coroner Robert Satriale, but changed to undetermined after tests revealed morphine and sleeping pills in his system that were not prescribed. But Chester County Coroner Gordon R. Eck told the news site that he changed the manner of death back to homicide after being urged to re-examine the case by Katzenmoyer's mother, Ginger Katzenmoyer, of Phoenixville, Pennsylvania. The officers named in the suit as Katzenmoyer's assailants are former Camden City police officers John McArdle and Ronald Lattanzio. Philly.com reported that they were never disciplined and they do not work for the county force that now polices the city. In the civil case, the city refuted claims that the officers used excessive force or contributed to Katzenmoyer's death. Philly.com reported he was arrested after police received a report he had hit a woman he did not know on the chest. The site reported he refused to be cuffed and was taken to the ground during his arrest. A friend of his who was also taken into custody reported seeing multiple officers hit him in the head with batons. He was taken to Virtua hospital in Camden, where police say he tried to grab McArdle's gun while he was strapped down to a board -- something the security guard testified never happened, according to Philly.com. The guard reportedly said he saw McArdle punch Katzenmoyer in the face multiple times as Katzenmoyer screamed and threatened to sue them. He was also pepper sprayed, according to the lawsuit. He was transferred to a different hospital and released the next day with percocet for the pain from his injuries. He went to a Pennsylvania hospital the following day, suffering from headaches, facial tremors and blood leaking from his ears, according to the suit. A CT scan found nothing wrong. His mother found him unresponsive Aug. 22, and he was given Narcan in the ambulance. Emergency responders and hospital staff resuscitated him multiple times but he died the following day. The lawsuit says he died from cardiac issues but also had signs of renal failure and oxygen deprivation in his brain. Ginger Katzenmoyer told Philly.com she plans to ask the Camden County prosecutor's office to reopen the investigation into the actions that caused her son's death, according to the new ruling from the coroner. The prosecutor's office told the news site it has not received any new information from the coroner and so it can't comment on what will happen with the case. Rebecca Everett may be reached at [email protected]. Follow her on Twitter @rebeccajeverett. Find NJ.com on Facebook.

– Ten years after Brett Katzenmoyer died following a "violent struggle" with New Jersey police, a county coroner has classified the 20-year-old's death as a homicide, the Philadelphia Inquirer reports. Katzenmoyer was drinking beer with friends outside an OAR concert in 2007 in Camden when a woman told police officers Katzenmoyer hit her in the chest. In a police report, officers Ronald Lattanzio and John McArdle say Katzenmoyer refused to put his hands behind his back and swung at them. After subduing Katzenmoyer, the officers took him to a hospital. A hospital security guard says Katzenmoyer was threatening to sue the officers, and McArdle hit him repeatedly in the face to "shut him up." The guard says McArdle also “beat [Katzenmoyer] in the face, from the nose to the eye" while the 20-year-old was restrained. Katzenmoyer suffered a concussion, broken nose, and more, NJ.com reports. He was sent home from the hospital but died days later from heart and renal failure. The coroner at the time ruled a cause of death "could not be determined" because Katzenmoyer had morphine and sleeping pills in his system. His family has been fighting that ruling for years, getting the new county coroner, Gordon Eck, to re-examine the case. On Thursday, Eck changed the cause of death to "homicide." Katzenmoyer's mother says she's "just grateful that someone finally ... did the right thing." She plans to ask the prosecutor's office to reopen the investigation. Katzenmoyer's family received a $750,000 settlement from the city in 2013, but the officers were never disciplined.

A number of US supermarket chains pledged on Wednesday not to sell genetically modified salmon, in a sign of growing public concern about engineered foods on the dinner table. The US Food and Drug Administration (FDA) is in the final stages of deciding whether to allow GM salmon on to the market. If approved, AquaBounty Technology's salmon would be the first genetically engineered animal to enter the food supply. The company combined genes from two species of salmon with a pouter eel to produce a fish it says it can bring to market twice as fast as conventional salmon. The GM salmon is the first in some 30 other species of genetically engineered fish under development, including tilapia. Researchers are also working to bring GM cows, chickens and pigs to market. However, those plans could be blocked by Wednesday's commitment not to sell genetically engineered seafood from national grocery chainsincluding Trader Joe's, Aldi and Whole Foods, as well as regional retailers. Between them, the chains control about 2,000 outlets – a fraction of supermarkets across the country. But campaigners said they represent a growing segment of the population that is concerned about GM food, and willing to pay higher prices for healthier foods. Eric Hoffman, a campaigner for Friends of the Earth, said in a statement: "Now it's time for other food retailers, including Walmart, Costco and Safeway, to follow suit and let their customers know they will not be selling unlabelled, poorly studied genetically engineered seafood." Trudy Bialic from PCC Natural Markets, a chain of health food stores in Washington state, said: "We won't sell genetically engineered fish because we don't believe it is sustainable or healthy." There was no immediate response from AquaBounty, a struggling biotechnology firm which has spent nearly 20 years trying to bring the fish to market. The company has hit a number of financial crisis points over the past few years, relying on research grants and investors to stay in operation. Last year the company turned to a former Soviet oligarch, Georgian billionaire and former economics minister Kakha Bendukidze, for a bailout. As the FDA review process enters its final stages, campaign groups have are pushing retailers not to stock the product and tapping into growing awareness in America about GM foods. Voters in California and other states have been pushing for labels on GM foods. Meanwhile, the Whole Foods chain announced earlier this month it would begin labelling foods containing GM corn and soybean by 2018. Critics of GM salmon say the FDA has not conducted proper oversight of the fish, which are raised from eggs hatched in a facility in Prince Edward Island, Canada, and grown to maturity in tanks in a remote area of Panama, to ensure they can not escape into the wild. They say there is insufficient data to back up AquaBounty's claims its salmon can grow to maturity twice as fast as wild salmon. They also dispute the company's claims that there is no increased risk to people with allergies. Those concerns were amplified by the FDA's preliminary finding that there was no need to label GM salmon. Patty Lovera of the campaign group Food and Water Watch said it was not clear what effect the supermarkets' move would have on the FDA's decision, which is supposed to be focused on science. But she said she hoped the growing public opposition to GM salmon – even before its approval – would push retailers to think twice about stocking the fish or more than 30 other varieties of GM seafood currently under development. "It reinforces that there is no demand or no need for this product, so why does the FDA need to approve it?" she said. "If this many stores are willing to say 'no' ahead of time, I think that is a pretty strong signal that there is not a lot of demand." ||||| Latest news: On heels of Canada's approval, more retailers say no to GMO salmon Health Canada’s approval of GMO salmon denounced Major grocery stores and restaurants say “no” to GMO salmon Despite FDA’s irresponsible approval of GMO salmon, nearly 80 grocery retailers with more than 11,000 stores have now made commitments to not sell the GMO salmon, including Albertsons, Safeway, Costco, Kroger, Target, Trader Joe’s, Aldi and Whole Foods, along with restaurant chains including Red Lobster and Legal Sea Foods. Do you want to eat genetically engineered salmon? Three quarters of Americans surveyed in a New York Times poll said they would not eat genetically engineered fish, and 93 percent wanted GMO foods to be labeled. Polls show that 80 percent of Americans who regularly eat fish say sustainable practices are "important" or "very important" to them. Nearly 2 million people -- including scientists, fishermen, business owners and consumers -- have written to the FDA in opposition to the approval of genetically engineered salmon and in response to AquaBounty's revised draft environmental assessment in 2013. Despite this outcry and robust scientific studies suggesting environmental and health risks, the FDA approved the GMO salmon. This is the first genetically engineered animal in the U.S. food supply and the FDA has said it will require it to be labeled, leaving consumers in the dark about what we are eating. At least 35 species of genetically engineered fish are in development and the approval of genetically engineered salmon will set a precedent that could open the floodgates for other genetically engineered animals (including cows, chickens and pigs) to enter our food system. To avoid confusion in the marketplace, and ensure the consumer’s right to know, we are asking grocery stores, seafood restaurants, chefs and seafood companies to demonstrate their commitment to sustainably produced seafood and consumer choice by joining our Pledge for GE-Free Seafood, a commitment to not knowingly purchase or sell genetically engineered salmon or other genetically engineered seafood should it come to market. Learn more about the risks to health, the environment and the fish industry posed by genetically engineered salmon here. Nearly 80 major food retailers with more than 11,000 stores nationwide have already taken the Pledge for GE-Free Seafood or otherwise committed to not purchase or sell genetically engineered salmon, or any products containing genetically engineered salmon or seafood. Learn more: Read more about the problems with genetically engineered fish in our issue brief. Read the letter we sent to grocery stores asking them to sign the pledge. FAQs about genetically engineered fish. Read the letter from the Golden Gate Salmon Association thanking grocery stores for not selling GE seafood. Learn more about our additional genetic engineering campaign efforts. Press releases:

– A cadre of major US supermarket chains say they want no part of the genetically modified salmon the FDA is currently considering approving, or any other frankenfish the food industry might devise. The FDA is in the final stages of approving a fast-growing fish from AquaBounty Technology that combines two species of salmon and a pouter eel. But yesterday about a dozen supermarket chains, including Trader Joe's, Aldi, and Whole Foods, announced that they wouldn't carry the fish even if it's approved, the Guardian reports. Together, the groups that have signed onto the Friends of the Earth's campaign control roughly 2,000 stores nationwide. "Now it's time for other food retailers, including Walmart, Costco, and Safeway, to follow suit and let their customers know they will not be selling unlabelled, poorly studied genetically engineered seafood," a campaigner from the group said. The FDA's preliminary finding indicated that the fish was fully safe, though critics say it hasn't been sufficiently tested.

UPDATE: On August 20th, Blake Meahl, guitarist and founding member of Huntress, announced a public memorial will be held for his partner and bandmate Jill Janus at the Rainbow Bar and Grill in West Hollywood this Friday (August 24) at 9 p.m. Guests are asked to say "We are here for Jill" at the door to gain entrance. "Since Jill's departure, the amount of outreach and support from friends, fans and family has been absolutely incredible," Meahl stated on his personal Facebook page. "Let's get together and celebrate her life and the importance that we still have each other." Jill Janus, frontwoman of the occult-themed heavy-metal group Huntress, has taken her own life, Blabbermouth reports. She was 43 years old. Casey Wood, Janus's longtime friend and former bandmate, shared the news via Facebook; Huntress' former manager, Jackie Kajzer a.k.a. Full Metal Jackie, confirmed the story to Loudwire. The band also shared a statement and a call for people experiencing suicidal thoughts to reach out for help. "It is with crushed hearts that we announce that Jill Janus — frontwoman for the California heavy metal band Huntress — passed away on Tuesday, August 14," the post on the Huntress Facebook page reads. "A long-time sufferer of mental illness, she took her own life outside of Portland, Oregon. Janus spoke publicly about these challenges in hopes of guiding others to address and overcome their mental illness. "Janus was a truly special creative involved with numerous musical projects including her role as vocalist for female metal/hard rock cover bands TheStarbreakers and Chelsea Girls. In addition, Janus was co-composer and creator of an upcoming rock opera with Trans-Siberian Orchestra's Angus Clark and had a decade-long career as NYC DJ Penelope Tuesdae. Her musical career began in childhood. "Beyond her accomplishments in the music world and her advocacy for mental health issues, she was a beautiful person passionate about her family, animal rescue and the world of natural medicine. She will be missed more than she could have ever known. "If you or someone you know might be at risk of suicide, Call 1-800-273-8255 to reach the National Suicide Prevention Lifeline. It provides free and confidential support 24 hours a day, seven days a week for people in suicidal crisis or distress." Janus formed Huntress in 2009 in LA. The group released three albums, 2012's Spell Eater, 2013's Starbound Beast and 2015's Static, and toured on Ozzfest 2016. As well as for her powerhouse operatic vocals, the singer was known for her courageous openness about her struggles with mental illness, including bipolar disorder and schizophrenia, a battle she first talked about publicly in a 2015 interview with Revolver. "I was diagnosed with bipolar disorder first, when I was 20. I started to show signs of it when I was 13, though, and I struggled with it through high school," she revealed. "But it started to get dangerous in my early teens. ... I was suicidal constantly. I was very suicidal early on in my life. Then in my mid-twenties, it shifted to full-blown mania, where I can't really remember much of my twenties." Looking ahead to a hysterectomy that she would have in July that year, she closed the interview by saying, "I know I'll survive. I've survived much worse." R.I.P. If you are experiencing suicidal thoughts, contact the National Suicide Prevention Lifeline at 1-800-273-8255 (TALK) or go to SpeakingOfSuicide.com/resources for a list of resources. ||||| Jill Janus, the lead singer of the rock bank Huntress, died by suicide on Aug. 14. She was 43. Janus’ band confirmed the news on their Facebook page on Thursday in which they wrote she “took her own life outside of Portland, Oregon.” “It is with crushed hearts that we announce that Jill Janus — frontwoman for the California heavy metal band Huntress — passed away on Tuesday, August. 14,” the band wrote. “A long-time sufferer of mental illness, she took her own life outside of Portland, Oregon.” “Janus spoke publicly about these challenges in hopes of guiding others to address and overcome their mental illness,” the post continued. The band celebrated Janus’ talent as well as her collaborations with female hard rock cover bands such as The Starbreakers and Chelsea Girls. Janus also worked as a “co-composer and creator of an upcoming rock opera with Trans-Siberian Orchestra’s Angus Clark and had a decade-long career as NYC DJ Penelope Tuesdae.” “Beyond her accomplishments in the music world and her advocacy for mental health issues, she was a beautiful person passionate about her family, animal rescue and the world of natural medicine,” the band wrote. “She will be missed more than she could have ever known.” Several of Janus’ friends mourned the singer’s death on social media, including Lizzy Hale of Halestorm. Hale shared a photo of herself with Janus on Instagram in which she also wrote about the Huntress singer’s “struggles with mental health and addiction.” “It is with a heavy heart that we say goodbye to one of our peers. Jill Janus, has died today. Jill was very open about her struggles with mental health and addiction,” Hale wrote. “Now, more than ever, spanning across Every age group, the suicide rate is extremely high.” “I’d like to take a moment to state again how important it is to talk about mental health, and remind all of you out there battling demons that you are not alone,” she wrote. “I have to navigate my own dark labyrinth and I turn to music and writing for my lifeline. I want to encourage you to keep searching for Your lifeline, something that makes You happy.” “It doesn’t matter if no one gets it but you…that’s ok! We need to Stop trying to live up to expectations that society places in front of us to make us feel Unworthy of love, beauty and success,” she continued. “We need to stop comparing ourselves to others. We need to stop trying to be ‘normal.’ And we need to stop being quiet about our mental wellbeing. Asking for help doesn’t mean your broken,” Hale added. “And if you don’t know how to ask for help that’s ok too, those of us who have a shoulder will let you lean on it!” She also had a special message to Janus. “To Jill, My sister of scream, I hope wherever you are you have found the peace that you couldn’t here,” Hale wrote. “My deepest sympathy’s go out to Jill’s Family and her band Huntress during this time.” Janus’ former Huntress bandmate, Casey Wood, also shared his grief on social media with a touching post on Facebook. “I’m in shock and can’t stop crying. My ex-band mate singer has left the world. She was the biggest sweetheart and I hope that her Legacy lives on as it should!” He wrote. “You were supposed to be on your way back here Jill Janus. I love you I miss you, and my door is still open for you always. Rest in peace my sister.” Janus sang for Huntress since the band’s creation in 2009. In an interview with Revolver magazine (and obtained by Loudwire) in July 2015, she opened up about her numerous struggles with mental health, revealing she had Bipolar disorder — a diagnosis she received when she was 20. “I started to show signs of it when I was 13, though, and I struggled with it through high school,” she said at the time. “It started to get dangerous in my early teens. By the time I was 20 and living in Manhattan, it was very, very difficult for me.” Jill Janus with Huntress in concert Chelsea Lauren/WireImage She continued, “That’s when I was admitted into a mental health facility and was diagnosed bipolar with schizoaffective disorder, which progressed into schizophrenia and dissociative disorder.” Janus revealed she’d always struggled with suicidal thoughts, describing herself as “very suicidal” in her early years, which turned into “full-blown mania” which resulted in her losing some memories. “I lost my long-term memory and can’t remember names, faces, or even places,” she said. Janus was also diagnosed with cancer in 2015. “When we were on tour with Amon Amarth, I started to bleed heavily between my periods,” she recalled. “I had a procedure, and my doctor found early stages of cancer in my uterus.” According to Loudwire, Janus had a hysterectomy in June 2015. If you or someone you know is considering suicide, please contact the National Suicide Prevention Lifeline at 1-800-273-TALK (8255), text “help” to the Crisis Text Line at 741-741 or go to suicidepreventionlifeline.org. ||||| While Los Angeles-based metal band Huntress have been riding high on the success of their first two albums and subsequent tours with Amon Amarth , Lamb of God and DragonForce , among others, frontwoman Jill Janus has been battling demons few people know about. In an interview with Revolver , Janus opens up about her battle with various mental illnesses that have plagued her for many years. The singer suffers from bipolar disorder, schizophrenia, and dissociative identity disorder, a condition previously known as multiple personality disorder. She also divulges that she has battled cancer, as well. In the personal and revealing interview, Janus explains she was diagnosed with bipolar disorder when she was 20. “I started to show signs of it when I was 13, though, and I struggled with it through high school," Janus says. “It started to get dangerous in my early teens. By the time I was 20 and living in Manhattan, it was very, very difficult for me. That’s when I was admitted into a mental health facility and was diagnosed bipolar with schizoaffective disorder, which progressed into schizophrenia and dissociative identity disorder.” Janus said that she was “very suicidal" early in her life, which turned into “full-blown mania” resulting in vast memory loss. “I lost my long-term memory and can’t remember names, faces, or even places. We’ll be at a venue on tour [guitarist] and Blake [Meahl] will be like, ‘We’ve played here two times before,’ but I’ll have no recollection.” The singer also explained her struggle with dissociative identity disorder. “My friends started to notice that I was developing these other personalities, almost as protection. I was slowly not wanting to be who I was. That started to come into play at the age of 18 when I was going to music school in Manhattan.” She adds that she took on a persona named ‘Penelope Tuesdae,’ which helped encouraged her to go out and enjoy the nightlife as well as conceal her life as an opera singer. She says, “I really wanted to split the two lives. ‘Penelope Tuesdae’ started to take on a life of her own.” Janus’ mental health issues reached a boiling point once Huntress finished recording their upcoming third album. The singer had to be hospitalized so she didn’t hurt herself or someone around her. “Once a Huntress album is done, it’s almost like I slip into a postpartum depression. Being bipolar and schizophrenic, I have to be hospitalized.” Janus added, “I spent some time in the hospital so I could be re-evaluated and medicated properly. I’ve been prescribed new meds, so I’m feeling more stable.” As if all these psychiatric issues weren't enough, Janus was also recently diagnosed with cancer. “When we were on tour with Amon Amarth, I started to bleed heavily between my periods. I had a procedure, and my doctor found early stages of cancer in my uterus.” The singer had a hysterectomy in June and is on the mend. Janus concluded, “I know I’ll survive. I’ve survived much worse.” Huntress will release their third album, Static , on Sept. 25, via Napalm Records. Fans can pre-order the effort here . The band will take part in the Motorhead Motorboat Cruise this fall. The ship sets sail from Sept. 28-Oct. 2. Check out all their tour dates at this location . For anyone with thoughts of suicide, Janus recommends: The National Suicide Prevention Lifeline at 1-800-273-8255, To Write Love on Her Arms , and SuicidePreventionLifeline.org . To read the full interview with Jill Janus, fans can pick up the August/September issue of Revolver magazine, which will arrive on newsstands on July 21. To order the issue, click here .

– The California heavy metal band Huntress shared the news with "crushed hearts": Frontwoman Jill Janus died Tuesday at age 43. "A long-time sufferer of mental illness, she took her own life outside of Portland, Oregon," the band wrote on Facebook. It added that "Janus spoke publicly about these challenges in hopes of guiding others to address and overcome their mental illness." People elaborates, citing a July 2015 interview with Revolver magazine in which she spoke—apparently for the first time publicly—of her diagnosis of bipolar disorder at age 20. "I started to show signs of it when I was 13, though, and I struggled with it through high school. It started to get dangerous in my early teens. By the time I was 20 and living in Manhattan, it was very, very difficult for me." "That’s when I was admitted into a mental health facility and was diagnosed bipolar with schizoaffective disorder, which progressed into schizophrenia and dissociative disorder." The struggles didn't end there. She noted that after completing the band's third album, which dropped a few months after the interview ran, she had to be hospitalized. "... I spent some time in the hospital so I could be re-evaluated and medicated properly." She also had a hysterectomy in June 2015 following the discovery of cancer in her uterus. Revolver describes her legacy as a two-part one: She'll be remembered for "her powerhouse operatic vocals" as well as "her courageous openness."

SECTION 1. SHORT TITLE. This Act may be cited as the ``Fiscal Year 2010 Federal Aviation Administration Extension Act, Part II''. SEC. 2. EXTENSION OF TAXES FUNDING AIRPORT AND AIRWAY TRUST FUND. (a) Fuel Taxes.--Subparagraph (B) of section 4081(d)(2) of the Internal Revenue Code of 1986 is amended by striking ``December 31, 2009'' and inserting ``March 31, 2010''. (b) Ticket Taxes.-- (1) Persons.--Clause (ii) of section 4261(j)(1)(A) of the Internal Revenue Code of 1986 is amended by striking ``December 31, 2009'' and inserting ``March 31, 2010''. (2) Property.--Clause (ii) of section 4271(d)(1)(A) of such Code is amended by striking ``December 31, 2009'' and inserting ``March 31, 2010''. (c) Effective Date.--The amendments made by this section shall take effect on January 1, 2010. SEC. 3. EXTENSION OF AIRPORT AND AIRWAY TRUST FUND EXPENDITURE AUTHORITY. (a) In General.--Paragraph (1) of section 9502(d) of the Internal Revenue Code of 1986 is amended-- (1) by striking ``January 1, 2010'' and inserting ``April 1, 2010''; and (2) by inserting ``or the Fiscal Year 2010 Federal Aviation Administration Extension Act, Part II'' before the semicolon at the end of subparagraph (A). (b) Conforming Amendment.--Paragraph (2) of section 9502(e) of such Code is amended by striking ``January 1, 2010'' and inserting ``April 1, 2010''. (c) Effective Date.--The amendments made by this section shall take effect on January 1, 2010. SEC. 4. EXTENSION OF AIRPORT IMPROVEMENT PROGRAM. (a) Authorization of Appropriations.-- (1) In general.--Section 48103(7) of title 49, United States Code, is amended to read as follows: ``(7) $2,000,000,000 for the 6-month period beginning on October 1, 2009.''. (2) Obligation of amounts.--Sums made available pursuant to the amendment made by paragraph (1) may be obligated at any time through September 30, 2010, and shall remain available until expended. (3) Program implementation.--For purposes of calculating funding apportionments and meeting other requirements under sections 47114, 47115, 47116, and 47117 of title 49, United States Code, for the 6-month period beginning on October 1, 2009, the Administrator of the Federal Aviation Administration shall-- (A) first calculate funding apportionments on an annualized basis as if the total amount available under section 48103 of such title for fiscal year 2010 were $4,000,000,000; and (B) then reduce by 50 percent-- (i) all funding apportionments calculated under subparagraph (A); and (ii) amounts available pursuant to sections 47117(b) and 47117(f)(2) of such title. (b) Project Grant Authority.--Section 47104(c) of such title is amended by striking ``December 31, 2009,'' and inserting ``March 31, 2010,''. SEC. 5. EXTENSION OF EXPIRING AUTHORITIES. (a) Section 40117(l)(7) of title 49, United States Code, is amended by striking ``January 1, 2010.'' and inserting ``April 1, 2010.''. (b) Section 44302(f)(1) of such title is amended-- (1) by striking ``December 31, 2009,'' and inserting ``March 31, 2010,''; and (2) by striking ``March 31, 2010,'' and inserting ``June 30, 2010,''. (c) Section 44303(b) of such title is amended by striking ``March 31, 2010,'' and inserting ``June 30, 2010,''. (d) Section 47107(s)(3) of such title is amended by striking ``January 1, 2010.'' and inserting ``April 1, 2010.''. (e) Section 47115(j) of such title is amended by striking ``January 1, 2010,'' and inserting ``April 1, 2010,''. (f) Section 47141(f) of such title is amended by striking ``December 31, 2009.'' and inserting ``March 31, 2010.''. (g) Section 49108 of such title is amended by striking ``December 31, 2009,'' and inserting ``March 31, 2010,''. (h) Section 161 of the Vision 100--Century of Aviation Reauthorization Act (49 U.S.C. 47109 note) is amended by striking ``January 1, 2010,'' and inserting ``April 1, 2010,''. (i) Section 186(d) of such Act (117 Stat. 2518) is amended by striking ``January 1, 2010,'' and inserting ``April 1, 2010,''. (j) The amendments made by this section shall take effect on January 1, 2010. SEC. 6. FEDERAL AVIATION ADMINISTRATION OPERATIONS. Section 106(k)(1)(F) of title 49, United States Code, is amended to read as follows: ``(F) $4,676,574,750 for the 6-month period beginning on October 1, 2009.''. SEC. 7. AIR NAVIGATION FACILITIES AND EQUIPMENT. Section 48101(a)(6) of title 49, United States Code, is amended to read as follows: ``(6) $1,466,888,500 for the 6-month period beginning on October 1, 2009.''. SEC. 8. RESEARCH, ENGINEERING, AND DEVELOPMENT. Section 48102(a)(14) of title 49, United States Code, is amended to read as follows: ``(14) $92,500,000 for the 6-month period beginning on October 1, 2009.''. Speaker of the House of Representatives. Vice President of the United States and President of the Senate.

Fiscal Year 2010 Federal Aviation Administration Extension Act, Part II - Amends the Internal Revenue Code to extend through March 31, 2010: (1) excise taxes on aviation fuels and air transportation of persons and property; and (2) the expenditure authority for the Airport and Airway Trust Fund. Authorizes appropriations for the six-month period from October 1, 2009, through March 31, 2010, for airport improvement program (AIP) projects, including project grant authority. Sets forth a formula for calculating the apportionment of AIP funding. Extends through March 31, 2010, various airport development projects, including: (1) the pilot program for passenger facility fees at nonhub airports; (2) small airport grants for airports located in the Marshall Islands, Micronesia, and Palau; (3) the temporary increase to 95% in the government share of certain AIP project costs; and (4) the funding of Midway Island airport development. Extends through March 31, 2010, state and local land use compatibility projects under the AIP program. Extends through March 31, 2010, the authority of the Metropolitan Washington Airports Authority to apply for an airport development grant and impose a passenger facility fee. Extends through March 31 2010, Department of Transportation (DOT) insurance coverage for domestic and foreign-flag air carriers. Allows further extension through June 30, 2010. Extends through June 30, 2010, air carrier liability limits for injuries to passengers resulting from acts of terrorism. Extends through March 31, 2010, certain competitive access assurance requirements for large or medium hub airport sponsors applying for AIP grants. Extends for the six-month period beginning October 1, 2009, the authorization of appropriations for: (1) Federal Aviation Administration (FAA) operations; (2) air navigation facilities and equipment; and (3) research, engineering, and development.

let @xmath5 be a @xmath1-adic field , i.e. , a finite extension of @xmath6 . let @xmath7 be an integer and @xmath8 a central division algebra over @xmath5 such that @xmath9 . the famous local jacquet - langlands correspondence gives a natural bijective correspondence between irreducible discrete series representations of @xmath10 and irreducible smooth representations of @xmath11 . let us recall its precise statement . write @xmath12 for the set of isomorphism classes of irreducible smooth representations of @xmath11 . we denote by @xmath13 the set of isomorphism classes of irreducible discrete series representations of @xmath10 . for @xmath14 ( resp . @xmath15 ) , we denote the character of @xmath16 ( resp . @xmath17 ) by @xmath18 ( resp . @xmath19 ) . here @xmath18 is a locally constant function on @xmath11 , and @xmath19 is a locally integrable function on @xmath10 which is locally constant on @xmath20 , the set of regular elements of @xmath10 . the precise statement of the local jacquet - langlands correspondence is the following : [ thm : ljlc ] there exists a unique bijection @xmath21 satisfying the following character relation : for every regular element @xmath22 of @xmath11 , @xmath23 , where @xmath24 is an arbitrary element of @xmath10 whose minimal polynomial is the same as that of @xmath22 . the original proof of this theorem , due to deligne - kazhdan - vigneras @xcite and rogawski @xcite , was accomplished by using a global automorphic method . in some cases , more explicit local studies can be found in @xcite , @xcite , @xcite , which are based on the theory of types . however , apart from the case of @xmath25 , a purely local proof of theorem [ thm : ljlc ] seems not to be known yet ( ( * ? ? ? * a comment after theorem 2 ) ) . in this article , under the assumption that the invariant of @xmath8 is @xmath2 , we will give a geometric approach to construct the bijection @xmath26 above . let @xmath27 be the grothendieck group of finite - dimensional smooth representations of @xmath11 , and @xmath28 the grothendieck group of finite length smooth representations of @xmath10 `` modulo induced representations '' ( for a precise definition , see @xcite ) . it is known that the classes of elements of @xmath12 ( resp . @xmath13 ) form a basis of @xmath27 ( resp . @xmath28 ) . put @xmath29 and @xmath30 . the main theorems of this article are the following : [ thm : main - intro ] we can construct the following two homomorphisms geometrically : @xmath31 these two maps are inverse to each other , and satisfy the character relations @xmath32 for every regular @xmath33 . [ thm : jl - intro ] if @xmath4 is prime , then @xmath26 induces a bijection @xmath34 theorem [ thm : jl - intro ] provides a purely local proof of theorem [ thm : ljlc ] in the case above . in particular , the local jacquet - langlands correspondence for @xmath35 and @xmath36 are fully recovered . the geometric object we use is the drinfeld tower for @xmath10 . it is a tower of rigid spaces over ( a disjoint union of ) the @xmath37-dimensional drinfeld upper half space @xmath38 , where @xmath39 runs through hyperplanes of @xmath40 defined over @xmath5 ( for more detailed explanation , see section [ sec : drinfeld - tower ] ) . thanks to extensive studies by many people ( @xcite , @xcite , @xcite , @xcite ) , it is now well - known that the local jacquet - langlands correspondence is realized in the @xmath3-adic cohomology @xmath41 of the drinfeld tower . the methods in the works cited above are again global and automorphic . however , there is also a purely local study of the cohomology due to faltings @xcite . he began with an irreducible smooth representation @xmath16 of @xmath11 , and investigated the @xmath16-isotypic part @xmath42 $ ] of @xmath41 by means of the lefschetz trace formula . by this method , he succeeded to observe that the character relation in theorem [ thm : ljlc ] appears naturally in @xmath42 $ ] . by using this result , we can give the map @xmath26 in theorem [ thm : main - intro ] . to construct the inverse map @xmath43 , we need to consider the opposite direction ; we begin with an irreducible discrete series representation @xmath17 of @xmath10 and investigate the `` @xmath17-isotypic part '' of @xmath41 . more precisely , we should consider the alternating sum of the extension groups @xmath44 , since @xmath17 is neither projective nor injective in general . to study it , we apply the method introduced in @xcite ; namely , we use local harmonic analysis , such as transfer of orbital integrals . furthermore , to prove theorem [ thm : jl - intro ] , the non - cuspidality result obtained in @xcite plays a crucial role . since our approach is entirely geometric , it is natural to expect that a similar argument may give interesting consequences for the mod-@xmath3 jacquet - langlands correspondence ( @xcite ) . the author also expects that our strategy can be extended to other rapoport - zink spaces , especially the rapoport - zink space for @xmath45 . he hopes to deal with these problems in future works . we sketch the outline of this paper . in section [ sec : drinfeld - tower ] , we recall the definition of the drinfeld tower and results in @xcite . we use the framework of @xcite to deal with finitely generated representations systematically . in section [ sec : harmonic - analysis ] , we study the alternating sum of the extention groups @xmath44 by means of local harmonic analysis . in section [ sec : faltings - isom ] , we apply another deep result of faltings on the comparison of the lubin - tate tower and the drinfeld tower . it provides a very important finiteness result on @xmath41 . under this finiteness , results in section [ sec : drinfeld - tower ] and section [ sec : harmonic - analysis ] can be written in a very simple form . after short preliminaries on representation theory in section [ sec : rep - theory ] , finally in section [ sec : ljlc ] , we construct the maps @xmath26 and @xmath43 in theorem [ thm : main - intro ] by using the @xmath3-adic cohomology of the drinfeld tower , and investigate their properties . * * acknowledgment**the author would like to thank matthias strauch for very helpful discussions . he is also grateful to tetsushi ito and sug woo shin for their valuable comments . * notation*for a totally disconnected locally compact group @xmath39 , let @xmath46 be the set of isomorphism classes of irreducible smooth representations of @xmath39 . we denote the grothendieck group of finitely generated ( resp . finite length ) smooth @xmath39-representations by @xmath47 ( resp . @xmath48 ) . put @xmath49 . for a finite - dimensional smooth representation @xmath50 of @xmath39 , write @xmath51 for the character of @xmath50 . it is a locally constant function on @xmath39 . if moreover a haar measure on @xmath39 is fixed , we denote by @xmath52 the hecke algebra of @xmath39 , namely , the abelian group of locally constant compactly supported functions on @xmath39 with convolution product . put @xmath53=\mathcal{h}(h)_h$ ] ( the @xmath39-coinvariant quotient ) . let @xmath5 be a @xmath1-adic field and @xmath54 its ring of integers . we denote the normalized valuation of @xmath5 by @xmath55 and the cardinality of the residue field of @xmath54 by @xmath56 . fix a uniformizer @xmath57 of @xmath54 . denote the completion of the maximal unramified extension of @xmath54 by @xmath58 and the fraction field of @xmath58 by @xmath59 . throughout this paper , we fix an integer @xmath7 . let @xmath8 be the central division algebra over @xmath5 with invariant @xmath2 , and @xmath60 its maximal order . fix a uniformizer @xmath61 such that @xmath62 . for simplicity , put @xmath63 . we denote by @xmath64 ( resp . @xmath65 ) the set of regular ( resp . regular elliptic ) elements of @xmath66 . write @xmath67 for the center of @xmath66 . we apply these notations to other groups . for example , we write @xmath68 for the set of regular elements of @xmath11 . as in theorem [ thm : ljlc ] , for @xmath69 , let @xmath24 be an element of @xmath65 whose minimal polynomial is the same as that of @xmath22 . such an element always exists , and is unique up to conjugacy . moreover , @xmath70 induces a bijection between conjugacy classes in @xmath68 and those in @xmath65 . therefore , to @xmath71 we can attach an element @xmath72 whose minimal polynomial is the same as that of @xmath73 . for a smooth @xmath66-representation @xmath17 of finite length , we denote by @xmath19 the distribution character of @xmath17 . it is a locally integrable function on @xmath66 which is locally constant on @xmath64 . we identify @xmath74 with @xmath67 and @xmath75 . then , we can consider the quotient groups @xmath76 and @xmath77 under a discrete subgroup @xmath78 of @xmath74 . we regard @xmath79 ( resp . @xmath80 ) as a subset of @xmath12 ( resp . @xmath81 ) . similarly , @xmath82 ( resp . @xmath83 ) is regarded as a submodule of @xmath27 ( resp . @xmath84 ) . write @xmath85 for the set of isomorphism classes of irreducible discrete series representations of @xmath66 . put @xmath86 . fix haar measures on @xmath66 and @xmath11 . we endow @xmath78 with the counting measure and consider the quotient measures on @xmath76 and @xmath77 . for @xmath87 and @xmath88 , put @xmath89 ( the orbital integral ) . it is well - known that this integral converges . similarly , for @xmath90 and @xmath33 , put @xmath91 . for a field @xmath92 , we denote its algebraic closure by @xmath93 . let @xmath3 be a prime which is invertible in @xmath54 . we fix an isomorphism @xmath94 and identify them . every representation is considered over @xmath95 . let us briefly recall the definition of the drinfeld tower . for more detailed description , see @xcite , @xcite , ( * ? ? ? * chapter 3 ) . first of all , fix a special formal @xmath60-module @xmath96 of @xmath97-height @xmath98 over @xmath99 . it is well - known that such @xmath96 is unique up to @xmath60-isogeny . we denote by @xmath100 the category of @xmath58-schemes on which @xmath57 is locally nilpotent . consider the functor @xmath101 from @xmath100 to the category of sets that maps @xmath102 to the set of isomorphism classes of pairs @xmath103 consisting of * a special formal @xmath60-module @xmath104 over @xmath102 , * and an @xmath60-quasi - isogeny @xmath105 , where we put @xmath106 . then @xmath101 is represented by a formal scheme locally of finite type over @xmath58 . we denote the formal scheme by @xmath101 again , and the rigid generic fiber of @xmath101 by @xmath107 . it is known that @xmath107 is the disjoint union of countable copies of the @xmath37-dimensional drinfeld upper half space . for an integer @xmath108 , let @xmath109 be the rigid space classifying @xmath110-level structures on the universal formal @xmath60-module over @xmath111 . it is a finite tale galois covering of @xmath111 with galois group @xmath112 . the projective system @xmath113 is called the drinfeld tower . we can define a natural right action of @xmath63 on each @xmath109 because @xmath66 is isomorphic to the group of self @xmath60-quasi - isogenies of @xmath96 . on the other hand , @xmath11 also acts naturally on @xmath109 on the right , since @xmath114 is a normal subgroup of @xmath11 . since @xmath115 is too large ( it has infinitely many connected components ) , we take the quotient @xmath116 of @xmath109 by @xmath117 . put @xmath118 these are smooth representations of @xmath119 . unless @xmath120 , @xmath121 . [ prop : fin - gen ] the representation @xmath122 is finitely generated as a @xmath66-module . moreover , there exist compact open subgroups @xmath123 of @xmath76 , @xmath124 and finite - dimensional smooth representations @xmath125 of @xmath126 for each @xmath127 such that the following holds : @xmath128=\sum_{\nu=1}^n \varepsilon_\nu [ \operatorname{c - ind}_{k_\nu}^{g/\varpi^\z}\sigma_{m,\nu}]\quad \text{in $ k(g/\varpi^\z\times d^\times/\varpi^\z)$.}\ ] ] we only give a sketch of a proof , since it seems to be well - known ( ( * ? ? ? * proposition 4.4.13 ) ) . it is known that @xmath129 has an open covering @xmath130 consisting of quasi - compact open subsets , indexed by the set @xmath131 of vertices of the bruhat - tits building of @xmath132 . this covering satisfies the following properties : * for @xmath133 , @xmath134 . * for each @xmath135 , there exist only finitely many @xmath136 satisfying @xmath137 . * for each @xmath135 , @xmath138 is a compact open subgroup of @xmath76 . for a finite subset @xmath139 , put @xmath140 for an integer @xmath141 , set @xmath142 . then , by the three properties above , we have the following : * for each @xmath141 , the set of @xmath76-orbits in @xmath143 is finite . * we have @xmath144 for sufficiently large @xmath145 . * for every finite subset @xmath139 , @xmath146 is a compact open subgroup of @xmath76 . take a system of representatives @xmath147 of @xmath148 and put @xmath149 . let @xmath150 be the covering obtained as the inverse image of @xmath151 . for a finite subset @xmath152 , put @xmath153 . then we have the ech spectral sequence @xmath154 put @xmath155 it is a finite - dimensional smooth representation of @xmath156 and vanishes for @xmath157 ( ( * ? ? ? * propositon 5.5.1 , proposition 6.3.2 ) ) . we can easily observe that @xmath158 is isomorphic to @xmath159 as a @xmath119-representation . therefore @xmath158 is a finitely generated @xmath76-representation , and vanishes for all but finitely many @xmath160 . hence @xmath122 is finitely generated as a @xmath66-module ( ( * ? ? ? * remarque 3.12 ) ) . moreover , in @xmath161 we have @xmath162=\sum_{r , s}(-1)^{-r+s}e_1^{-r , s}=\sum_{r , s}\sum_{i=1}^{n_r}(-1)^{-r+s}\operatorname{c - ind}_{k_{r , i}}^{g/\varpi^\z } v^s_{m , r , i}.\ ] ] this concludes the proof . we denote by @xmath163 the image of @xmath164 $ ] under the rank map @xmath165 ( @xcite ) . for @xmath33 , we define @xmath166 by @xmath167 using the expression of @xmath164 $ ] in proposition [ prop : fin - gen ] , we can give more explicit description of @xmath163 and @xmath168 : [ prop : eta - cind ] for @xmath108 and @xmath33 , define @xmath169 and @xmath170 by @xmath171 where @xmath172 denotes the contragredient , and @xmath173 ( resp . @xmath174 ) is regarded as a function on @xmath119 ( resp . @xmath76 ) by setting @xmath175 for @xmath176 . then , the image of @xmath177 ( resp . @xmath178 ) in @xmath179 ( resp . @xmath180 ) coincides with @xmath163 ( resp . @xmath168 ) . the assertion for @xmath178 immediately follows from that for @xmath177 . thus it suffices to prove the following : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ let @xmath181 be a compact open subgroup of @xmath76 . for every finite - dimensional smooth representation @xmath50 of @xmath182 , the image of @xmath183 in @xmath179 coincides with @xmath184)$ ] . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ since the image of @xmath185 $ ] under the rank map @xmath186 is @xmath187 , this claim follows from the commutative diagram below ( ( * ? ? ? * proof of theorem 1.6 ) ) : @xmath188 ^ -{\operatorname{rk}}\ar[d]_-{\operatorname{c - ind}_k^{g/\varpi^\z } } & \overline{\mathcal{h}}(k\times d^\times/\varpi^\z)\ar[d]^-{\text{\rm extention by $ 0$}}\\ k(g/\varpi^\z\times d^\times/\varpi^\z)\ar[r]^-{\operatorname{rk } } & \overline{\mathcal{h}}(g/\varpi^\z\times d^\times/\varpi^\z)\lefteqn{. } } \ ] ] in @xcite , faltings investigated the function @xmath177 above by means of the lefschetz trace formula . his results can be summarized in the following theorem . [ thm : ltf ] let @xmath189 and @xmath33 . 1 . if @xmath73 is elliptic , then we have @xmath190 2 . if @xmath73 is not elliptic , then we have @xmath191 , where @xmath192 denotes the centralizer of @xmath73 . let us briefly recall the proof in @xcite . we use the notation in the proof of proposition [ prop : fin - gen ] . first consider the case where @xmath73 is elliptic . then , we can find a finite subset @xmath193 such that @xmath194 and @xmath195 for @xmath196 . put @xmath197 . then @xmath198 is quasi - compact smooth and @xmath199 has no fixed point on the boundary of @xmath198 . therefore we can apply the lefschetz trace formula for this endomorphism ( for a general theory of the lefschetz trace formula for rigid spaces , see @xcite ) . noting that every fixed point of @xmath200 lies in @xmath198 , we obtain the following equality : @xmath201 by the ech spectral sequence , we can easily show that the left hand side is equal to @xmath202 . the right hand side can be computed by using the period map , as in @xcite . the result is @xmath203 it is slightly different from ( * ? ? ? * theorem 1 ) , because our @xmath204 is the disjoint union of @xmath4 copies of @xmath205 considered in @xcite . rather , it is compatible with ( * ? ? ? * theorem 2.6.8 ) . this concludes the proof of i ) . to prove ii ) , apply the same argument to @xmath206 , where @xmath207 is a sufficiently small discrete torsion - free cocompact subgroup of @xmath192 . [ cor : in - k0 ] for @xmath208 , @xmath209 is a finitely generated @xmath76-representation by ( * ? ? ? * lemma 5.2 ) . the image of @xmath210 $ ] under the map @xmath211 coincides with @xmath212 . recall that for @xmath213 the locally constant function @xmath214 on @xmath65 is given by @xmath215 ( @xcite ) . take a sufficiently large integer @xmath108 so that @xmath216 is trivial . then we have @xmath217 . it is easy to see that the following diagram is commutative : @xmath218 ^ -{\operatorname{rk}}\ar[d]_-{\hom_{d^\times}(\rho,- ) } & \overline{\mathcal{h}}(g/\varpi^\z\times d^\times/\varpi^\z)\ar[d]^-{(*)}\\ k(g/\varpi^\z)\ar[r]^-{\operatorname{rk } } & \overline{\mathcal{h}}(g/\varpi^\z)\lefteqn { , } } \ ] ] where @xmath219 is given by @xmath220 therefore , the image of @xmath221 $ ] under @xmath222 can be calculated as follows : @xmath223 this completes the proof . in this section , we use theorem [ thm : ltf ] to investigate the virtual @xmath11-representation @xmath224 . in the lubin - tate case , a similar study is carried out in @xcite . for @xmath108 , denote by @xmath225 the image of @xmath114 in @xmath77 . [ lem : ext - invariant ] for a smooth representation @xmath226 of @xmath119 and a smooth representation @xmath17 of @xmath76 , we have @xmath227 . here @xmath228 is taken in the category of smooth @xmath76-representations . first we prove that there exist a smooth @xmath119-representation @xmath229 which is projective as a @xmath76-representation and a @xmath119-equivariant surjection @xmath230 . take a @xmath76-equivariant surjection @xmath231 from a projective @xmath76-representation @xmath232 . put @xmath233 . then @xmath229 is a smooth @xmath119-representation which is projective as a @xmath76-representation , and a surjection @xmath230 is naturally induced . therefore , we can take a @xmath119-equivariant resolution @xmath234 of @xmath226 such that @xmath235 is projective as a smooth @xmath76-representation . since @xmath236 is a direct summand of @xmath235 as a @xmath76-representation , @xmath236 is also projective . thus @xmath237 gives a projective resolution of @xmath238 . hence we have @xmath239 as desired . [ cor : ext - invariant - dr ] for every @xmath108 and @xmath240 , we have @xmath241 it is finite - dimensional and vanishes if @xmath242 . in particular , @xmath243 is an admissible representation of @xmath77 and vanishes if @xmath242 , where @xmath244 denotes the set of @xmath77-smooth vectors . lemma [ lem : ext - invariant ] tells us that @xmath245 by proposition [ prop : fin - gen ] and ( * ? ? ? * corollary ii.3.3 ) , it is finite - dimensional and vanishes if @xmath242 . later ( corollary [ cor : bernstein ] ) we will prove that @xmath246 is in fact a finite - dimensional smooth @xmath11-representation . the character of @xmath247 can be computed by @xmath168 introduced in the previous section : [ prop : ext - char ] for every @xmath240 and @xmath248 , we have @xmath249 first note that @xmath250 induces a homomorphism @xmath251 of abelian groups . therefore , by proposition [ prop : fin - gen ] and proposition [ prop : eta - cind ] , we have only to show the following : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ let @xmath181 be a compact open subgroup of @xmath76 . for every finite - dimensional smooth representation @xmath50 of @xmath182 and @xmath33 , we have @xmath252 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ since @xmath253 is a projective @xmath76-representation , @xmath254 for @xmath255 . take an open normal subgroup @xmath256 such that @xmath257 is trivial . then the left hand side can be computed as follows : @xmath258 this completes the proof . [ lem : fix - orb - int ] for every @xmath71 , @xmath33 and an integer @xmath108 , we have @xmath259 where @xmath260 denotes the characteristic function of @xmath261 . by theorem [ thm : ltf ] i ) , we obtain @xmath262 next recall the definition of a transfer of a test function . for @xmath263 and @xmath264 , we say that @xmath265 is a transfer of @xmath266 if @xmath267 for every @xmath71 . we know that if @xmath263 is supported on @xmath65 , then it has a transfer @xmath264 ( ( * ? ? ? * lemma 3.2 ) ) . the following lemma is obvious : [ lem : phi - pi ] assume that @xmath263 is supported on @xmath65 and let @xmath264 be its transfer . put @xmath268 then @xmath269 , @xmath270 and @xmath271 for every @xmath71 . [ thm : dr - pi ] assume that @xmath263 is supported on @xmath65 and let @xmath264 be its transfer . then , for every @xmath272 we have @xmath273 let @xmath274 and @xmath275 be as in the previous lemma . then clearly we have @xmath276 thus we may replace @xmath266 and @xmath265 by @xmath274 and @xmath275 , respectively . take @xmath108 such that @xmath275 is @xmath225-invariant , and write @xmath277 where @xmath278 is a finite subset of @xmath77 and @xmath279 . by corollary [ cor : ext - invariant - dr ] and proposition [ prop : ext - char ] , we have @xmath280 by theorem [ thm : ltf ] ii ) and weyl s integral formula ( ( * ? ? ? * theorem f ) ) , we have @xmath281 where @xmath282 runs through conjugacy classes of elliptic maximal tori of @xmath66 , @xmath283 denotes the rational weyl group of @xmath282 and @xmath284 denotes the weyl denominator ( @xcite ) . the measure @xmath285 on @xmath286 is normalized so that the volume of @xmath286 is one . lemma [ lem : fix - orb - int ] and lemma [ lem : phi - pi ] tell us that @xmath287 for every @xmath288 . by weyl s integral formula again , we have @xmath289 as desired . here we freely use the notation in ( * ? ? ? * section 2 ) . we need the following deep theorem due to faltings ( @xcite , see also @xcite for more detailed exposition ) : [ thm : faltings ] we have a @xmath290-equivariant isomorphism @xmath291 for every @xmath292 . note that the proof of faltings theorem does not require automorphic method . it gives the following very important finiteness result on @xmath293 . [ cor : dr - adm ] the @xmath66-representation @xmath293 is admissible . put @xmath294 . since @xmath295 is finite - dimensional , @xmath296 is an admissible representation of @xmath66 . thus , by theorem [ thm : faltings ] , @xmath293 is also an admissible representation of @xmath66 . [ cor : bernstein ] for every @xmath272 and integers @xmath297 , @xmath298 is a finite - dimensional smooth representation of @xmath11 . moreover , @xmath299 if @xmath242 . let @xmath300 be the cuspidal support of @xmath17 , and @xmath301 be the @xmath300-component of @xmath293 . clearly we have @xmath302 . let us observe that @xmath301 is a finitely generated @xmath66-representation . since @xmath301 is an admissible @xmath66-representation by corollary [ cor : dr - adm ] , it is @xmath303-admissible , where @xmath303 denotes the bernstein center of @xmath66 ( @xcite ) . therefore , ( * ? ? ? * corollaire 3.10 ) tells us that @xmath301 is finitely generated . in particular , there exists a compact open subgroup @xmath304 which acts on @xmath301 trivially . therefore , by ( * ? ? ? * corollary ii.3.3 ) , @xmath305 is finite - dimensional and vanishes if @xmath242 . the natural action of @xmath11 on @xmath305 is smooth , since the action of @xmath306 is trivial . this completes the proof . for @xmath240 , put @xmath307=\sum_{i , j\ge 0}(-1)^{i+j}\ext_{g/\varpi^\z}^j(h^i_{{\mathrm{dr}}},\pi)\quad \text{in $ r(d^\times/\varpi^\z)$.}\ ] ] we can consider the character @xmath308}$ ] of @xmath309 $ ] . theorem [ thm : dr - pi ] can be written in the following way : [ thm : char - rel - g ] for every @xmath240 and @xmath69 , we have @xmath310}(h)=n\theta_\pi(g_h).\ ] ] theorem [ thm : dr - pi ] says that @xmath311)=(-1)^{n-1}n\tr(\varphi;\pi)$ ] . we can use exactly the same method as in the proof of ( * ? ? ? * theorem 4.3 ) . the following is another consequence of theorem [ thm : faltings ] : [ cor : dr - rho ] for every @xmath208 , @xmath312=\hom_{d^\times}(h^i_{{\mathrm{dr}}},\rho)^{\mathrm{sm}}$ ] is a smooth @xmath66-representation of finite length . moreover @xmath312 $ ] is isomorphic to @xmath313 . by proposition [ prop : fin - gen ] , corollary [ cor : dr - adm ] and ( * ? ? ? * lemma 5.2 ) , @xmath312 $ ] is a smooth @xmath66-representation of finite length . in the proof of ( * lemma 5.2 ) , a @xmath66-equivariant injection @xmath312\hooklongrightarrow \hom_{d^\times}(\rho , h^i_{{\mathrm{dr}}})^\vee$ ] is constructed . it is easy to see that it is actually an isomorphism . for @xmath208 , put @xmath314=\sum_{i}(-1)^ih^i_{{\mathrm{dr}}}[\rho]\quad \text{in $ r(g/\varpi^\z)$.}\ ] ] we can consider the character @xmath315}$ ] of @xmath316 $ ] . corollary [ cor : in - k0 ] can be written in the following way : [ thm : char - rel - d ] for every @xmath208 and @xmath69 , we have @xmath317}(g_h)=n\theta_\rho(h).\ ] ] we denote the natural homomorphism @xmath318 by @xmath319 . by ( * lemma 3.7 ) , the composite of @xmath320 coincides with @xmath321 ( it was originally proved in ( * ? ? ? * theorem iii.4.23 ) ) . therefore , by corollary [ cor : in - k0 ] and corollary [ cor : dr - rho ] we have @xmath322}(g)=\bigl((\vee\circ \operatorname{rk}\circ\mathrm{ep})(h_{{\mathrm{dr}}[\rho]})\bigr)(g)=n\theta_\rho(h_g)\ ] ] for every @xmath71 . hence @xmath315}(g_h)=n\theta_\rho(h)$ ] for every @xmath323 , as desired . the proof of ( * ? ? ? * theorem iii.4.23 ) seems to use ( * ? ? ? * theorem 0 ) , whose proof relies on global technique . however , theorem [ thm : faltings ] and ( * ? ? ? * theorem 4.3 ) give an alternative proof of theorem [ thm : char - rel - d ] , which does not involve any global argument . for locally constant class functions @xmath324 , @xmath325 on @xmath326 , put @xmath327 where @xmath282 runs through conjugacy classes of elliptic maximal tori of @xmath66 . other notations are also the same as in the proof of theorem [ thm : dr - pi ] . for locally constant functions @xmath328 , @xmath329 on @xmath77 , put @xmath330 where the measure @xmath331 is normalized so that the volume of the compact group @xmath77 is one . these two pairings are compatible , in the sense of the following lemma : [ lem : inner - prod ] let @xmath324 , @xmath325 be locally constant class functions on @xmath326 , and @xmath328 , @xmath329 locally constant class functions on @xmath77 . assume that @xmath332 for every @xmath69 . then , we have @xmath333 clear from weyl s integral formula for @xmath11 . the following orthogonality relation of characters is very important for our work . [ prop : orthogonality ] for @xmath334 , we have @xmath335 let @xmath336 , @xmath337 be the central characters of @xmath338 , @xmath339 , respectively . then they are unitary , since @xmath340 is compact . if @xmath341 , then the lemma follows immediately from ( * ? ? ? * lemma 5.3 ) . otherwise , @xmath342 as desired . the proof of ( * ? * theorem 5.3 ) ( for example , ( * ? ? ? * a.4 ) ) seems to need a global argument , such as howe s conjecture due to clozel . however , at least if @xmath4 is prime , we can give a purely local proof of proposition [ prop : orthogonality ] as follows . here we use freely the notation which will be introduced in the next section . note that , if @xmath4 is prime , then any irreducible discrete series representation of @xmath66 is either a twisted steinberg representation or supercuspidal ( ( * ? ? ? * theorem 9.3 ) ) . first assume that both @xmath338 and @xmath339 are twisted steinberg representations , and write @xmath343 and @xmath344 , where @xmath345 and @xmath346 are characters of @xmath340 . then , by lemma [ lem : inner - prod ] and lemma [ lem : steinberg ] , we have @xmath347 since @xmath348 implies @xmath349 ( their characters are different ) , we have the orthogonality relation in this case . next assume that @xmath339 is supercuspidal . then , by ( * ? ? ? * a.3.e , a.3.g ) , we can find a matrix coefficient @xmath350 of @xmath339 satisfying the following : * @xmath351 for @xmath71 and @xmath352 for @xmath353 . * @xmath354 and @xmath355 for @xmath356 with @xmath357 . by ( a ) and weyl s integral formula , we have @xmath358 therefore ( b ) gives the desired orthogonality relation . let @xmath359 be the submodule of @xmath84 generated by the image of parabolically induced representations ( @xcite ) and put @xmath360 . it is known that @xmath361 is a free @xmath362-module with a basis @xmath363\mid \pi\in\operatorname{\mathbf{disc}}(g)\}$ ] ( ( * ? ? ? * lemme 2.1.4 ) ) . we regard @xmath364 as a subset of @xmath361 . recall that the character of a parabolically induced representation vanishes on @xmath65 . therefore , @xmath365 induces a map @xmath366 . moreover , we denote by @xmath367 the image of @xmath83 in @xmath361 . it is easy to see that @xmath363\mid \pi\in\operatorname{\mathbf{disc}}(g/\varpi^\z)\}$ ] gives a basis of @xmath367 . set @xmath368 and @xmath369 . let @xmath229 be a proper parabolic subgroup of @xmath66 with levi factor @xmath372 and @xmath50 an irreducible smooth representation of @xmath372 on which @xmath373 acts trivially . by theorem [ thm : char - rel - g ] , the character of @xmath374 on @xmath375 is given by @xmath376 . since @xmath68 is dense in @xmath11 , it vanishes for every @xmath33 . thus @xmath377 by linear independence of characters . since the kernel of @xmath378 is generated by such representations as @xmath379 , we conclude the proof . we define two homomorphisms @xmath380 by @xmath381,\qquad \operatorname{\mathit{lj}}(\pi)=\frac{(-1)^{n-1}}{n}h_{{\mathrm{dr}}}[\pi]\ ] ] for @xmath208 and @xmath240 . the latter map is well - defined by the previous lemma . 1 . we have the character relations @xmath382 for every @xmath208 , @xmath240 and @xmath323 . 2 . for every @xmath383 and @xmath384 , we have @xmath385 3 . two maps @xmath26 and @xmath43 are inverse to each other . the map @xmath26 is compatible with character twists . namely , for a character @xmath386 of @xmath74 which is trivial on @xmath387 , we have @xmath388 . the same holds for @xmath43 . 5 . the map @xmath26 preserves central characters . namely , for @xmath389 , write @xmath390 $ ] . then , every @xmath17 with @xmath391 has the same central character as @xmath16 . the same holds for @xmath43 . prove iii ) . for @xmath392 , write @xmath393 $ ] . then , by ii ) and proposition [ prop : orthogonality ] we have @xmath394 therefore , @xmath395 if @xmath396 , and @xmath397 otherwise . in other words , @xmath398 . thus we have @xmath399 . similarly we can prove that @xmath400 . for iv ) , it suffices to show that @xmath43 is compatible with character twists . let @xmath240 and @xmath386 be a character of @xmath74 which is trivial on @xmath387 . then , for every @xmath69 , we have @xmath401 since @xmath68 is dense in @xmath11 , we have @xmath402 . by linear independence of characters , we conclude that @xmath403 . finally we prove v ) . write @xmath390 $ ] . by proposition [ prop : orthogonality ] , @xmath404 . assume that the central character of @xmath405 is different from that of @xmath16 . then , we have @xmath406 in the same way as in the proof of proposition [ prop : orthogonality ] . therefore @xmath26 preserves central characters . by this result and ii ) , we have @xmath407 unless @xmath16 and @xmath17 have the same central character . this means that the coefficient of @xmath389 in @xmath408 is zero unless the central character of @xmath16 is the same as that of @xmath17 . namely , @xmath43 preserves central characters . there exists a unique extension of @xmath26 to a homomorphism from @xmath409 to @xmath410 which is compatible with character twists . similarly , we have a unique extension of @xmath43 to a homomorphism @xmath411 which is compatible with character twists . we denote them by @xmath26 and @xmath43 again . these are inverse to each other , satisfy the same character relations as in proposition [ prop : jl - lj - properties ] i ) , and preserve central characters . for @xmath14 , let @xmath412 be its central character . take @xmath413 such that @xmath414 , and consider the character @xmath415 of @xmath74 . then @xmath416 . extend @xmath26 to @xmath417 by @xmath418 by proposition [ prop : jl - lj - properties ] iv ) , it is independent of the choice of @xmath419 . moreover , we can easily observe that it is the unique extension of the original @xmath26 which is compatible with character twists . similarly , we can uniquely extend @xmath43 to a map @xmath411 compatible with character twists . by using proposition [ prop : jl - lj - properties ] v ) , we can easily check that the extended @xmath26 and @xmath43 are inverse to each other . the remaining parts are also immediate consequences of proposition [ prop : jl - lj - properties ] i ) , v ) . 1 . let @xmath420 be a homomorphism satisfying the character relation @xmath421 for every @xmath69 . then we have @xmath422 . 2 . let @xmath423 be a homomorphism satisfying the character relation @xmath424 for every @xmath69 . then we have @xmath425 . to prove i ) , it suffices to show that @xmath426 . by the character relation , we have @xmath427 for every @xmath428 and @xmath323 . thus we can conclude that @xmath429 by linear independence of characters for @xmath11 . for ii ) , prove @xmath430 by a similar argument . [ thm : main ] we can construct the following two homomorphisms geometrically : @xmath431 these two maps are inverse to each other , and satisfy the character relations @xmath32 for every @xmath323 . they are characterized by these character relations . moreover , @xmath26 and @xmath43 are compatible with character twists , and preserve central characters . let @xmath432 be the borel subgroup consisting of upper triangular matrices . recall that the steinberg representation @xmath433 is the unique irreducible quotient of the unnormalized induction @xmath434 from the trivial character @xmath435 on @xmath436 . for a character @xmath386 of @xmath74 , put @xmath437 . a representation of the form @xmath438 is called a twisted steinberg representation . it is an irreducible discrete series representation of @xmath66 . the following lemma is very well - known : we may assume that @xmath272 . since @xmath17 is injective in the category of smooth @xmath76-representations , @xmath447 unless @xmath448 . by theorem [ thm : faltings ] and ( * theorem 3.7 ) , we have @xmath449 unless @xmath450 . therefore we have @xmath451 $ ] . this concludes the proof . first we shall prove ( a ) . if @xmath16 is a character , then it follows from corollary [ cor : steinberg ] . assume that @xmath16 is not a character , and write @xmath390 $ ] . then , @xmath457 unless @xmath17 is supercuspidal . indeed , if @xmath458 , then @xmath17 is a twisted steinberg representation @xmath438 , for @xmath4 is prime ( ( * ? ? ? * theorem 9.3 ) ) . by proposition [ prop : orthogonality ] , proposition [ prop : jl - lj - properties ] ii ) and corollary [ cor : steinberg ] , we have @xmath459 since @xmath460 , there exists at least one @xmath461 satisfying @xmath391 . let us observe that such @xmath17 is unique . assume that there exist @xmath462 such that @xmath463 and @xmath464 are non - zero . then , we have @xmath465 , and similarly @xmath466 . in other words , if we write @xmath467,\quad \operatorname{\mathit{lj}}(\pi')=\sum_{\varrho\in\operatorname{\mathbf{irr}}(d^\times/\varpi^\z)}b'_\varrho[\varrho],\ ] ] then @xmath468 and @xmath469 are non - zero . on the other hand , proposition [ prop : non - cusp ] tells us that @xmath470 and @xmath471 for every @xmath472 . thus , by proposition [ prop : jl - lj - properties ] ii ) , we conclude that @xmath473 which is equivalent to @xmath474 by proposition [ prop : orthogonality ] . now we have @xmath475 $ ] for some @xmath476 . moreover , the argument above tells us that @xmath477 . by proposition [ prop : orthogonality ] and proposition [ prop : jl - lj - properties ] ii ) , we have @xmath478 hence we conclude that @xmath479 and @xmath480 . next prove ( b ) . write @xmath481 $ ] . then , since @xmath26 and @xmath43 are inverse to each other , we have @xmath482 , and thus @xmath483 by ( a ) and proposition [ prop : orthogonality ] , there exists @xmath389 such that @xmath484 . then @xmath485 , as desired . boutot and h. carayol , _ uniformisation @xmath1-adique des courbes de shimura : les thormes de erednik et de drinfeld _ , astrisque ( 1991 ) , no . 196 - 197 , 7 , 45158 ( 1992 ) , courbes modulaires et courbes de shimura ( orsay , 1987/1988 ) . p. deligne , d. kazhdan , and m .- f . vignras , _ reprsentations des algbres centrales simples @xmath1-adiques _ , representations of reductive groups over a local field , travaux en cours , hermann , paris , 1984 , pp . 33117 . l. fargues , _ cohomologie des espaces de modules de groupes @xmath1-divisibles et correspondances de langlands locales _ , astrisque ( 2004 ) , no . 291 , 1199 , varits de shimura , espaces de rapoport - zink et correspondances de langlands locales . g. henniart , _ correspondance de jacquet - langlands explicite . i. le cas modr de degr premier _ , sminaire de thorie des nombres , paris , 199091 , progr . 108 , birkhuser boston , boston , ma , 1993 , pp . 85114 . m. harris and r. taylor , _ the geometry and cohomology of some simple shimura varieties _ , annals of mathematics studies , vol . 151 , princeton university press , princeton , nj , 2001 , with an appendix by vladimir g. berkovich .

in this paper , we give a purely geometric approach to the local jacquet - langlands correspondence for @xmath0 over a @xmath1-adic field , under the assumption that the invariant of the division algebra is @xmath2 . we use the @xmath3-adic tale cohomology of the drinfeld tower to construct the correspondence at the level of the grothendieck groups with rational coefficients . moreover , assuming that @xmath4 is prime , we prove that this correspondence preserves irreducible representations . this gives a purely local proof of the local jacquet - langlands correspondence in this case . we need neither a global automorphic technique nor detailed classification of supercuspidal representations of @xmath0 . faculty of mathematics , kyushu university , 744 motooka , nishi - ku , fukuoka , 8190395 japan e - mail address : ` [email protected] ` 2010 _ mathematics subject classification_. primary : 22e50 ; secondary : 11f70 , 14g35 .

transmissible spongiform encephalopathies ( tse ) are fatal , infectious , neurodegenerative diseases . they include bovine spongiform encephalopathies ( bse ) in cattle , scrapie in sheep and creutzfeldt - jakob disease ( cjd ) in human @xcite . the infectious agents responsible for disease transmission , known as prions , present some unusual biological properties ( as a high resistance to inactivation by heat or radiation ) . according to the protein - only hypothesis " , prions may consist in a misfolded protein ( called prpsc ) , without any nucleic acid . this hypothesis suggests that prpsc replicates in a self - propagating process , by converting the normal form of prp ( called prpc ) into prpsc @xcite . many evidences are in favour of an autocatalytic replication of prpsc , as the generation of infectivity from recombinant proteins @xcite or the use of in vitro prpsc conversion systems , such as the protein misfolding cyclic amplification ( pmca ) technique @xcite . however , the precise mechanism of conversion remains unclear . moreover , prion infectious agent can exist under different strains , characterized by their incubation period and their lesion profile in brains @xcite . in the framework of the protein - only hypothesis , it is supposed that strain diversity is supported by various conformation states of prpsc , that leads to various biological and biochemical properties @xcite . a critical challenge of prion biology consists in elucidating the mechanism of conversion of prpc into prpsc , and therefore how a diversity of strains may exist in the same host ( expressing the same prp molecule ) . to investigate the conversion of prpc in prpsc , many relevant mathematical modeling of prion replication have been proposed @xcite . major aim of these modelling is to demonstrate that essential features of prion disease can be explained by purely physico - chemical mechanisms , as supposed by the protein - only hypothesis . in addition , mathematical modeling allows to study the effect of every elementary process in a separate manner @xcite , what is difficult to do experimentally . the early proposed model is the heterodimer one . it is based on the conformational change of prpc into prpsc after the formation of a heterodimeric complex ( prpc + prpsc @xmath0 prpc*prpsc @xmath0 prpsc*prpsc @xmath0 2 prpsc ) . this model does not take into account the aggregation of prpsc , and thereby fails to explain the association between infectivity and aggregated prp . some other mechanisms have been proposed , which are interested in prp aggregation @xcite . based on fibrilar aggregation , the model which seems by now broadly accepted is the one of nucleated polymerization @xcite . in this approach , prpsc is considered to be a polymeric form of prpc . polymers can lengthen by addition of prpc monomers , and they can replicate by splitting into smaller fragments . it is worth noting that deterministic @xcite as well as stochastic @xcite simulations of this model lead to an unimodal size distribution of prp aggregates , which seems to be quite insensitive to small variations of parameters @xcite . greer et al . @xcite recently improved the model and include a mean saturation effect by the whole population of polymers onto the lenghtening process ( called general incidence ) , and polymer joining ( through a smoluchowski coagulation equation ) . in these models , each aggregate has the same behaviour , regardless to its size . however , recent experimental analysis of relation between infectivity and size distribution of prpsc aggregates ( for prpsc purified from infected brain @xcite or for prpsc produced by pmca @xcite ) contradicts this uniform behaviour of prpsc aggregates . in addition , silveira et al . shows that bimodal distribution of the polymer size is more likely to occur within the real process @xcite . the goal of this present study is to better understand the unexpected experimental size distribution of prion aggregates in brain , and to investigate the potential implication of this size distribution in the strain phenomenon . to do so , we generalize masel and coauthors model so as to take into account aggregate size - dependent parameters . the paper is organized as follows : in section [ sec : model ] we recall and review the model of masel _ et al . _ and its continuous version @xcite which is going to be used . we introduce our main improvement , namely a size - dependent lenghtening factor related to nonuniform infectivity rate ; and we discuss the eigenvalue problem which is a key tool to analyze the model . in section [ sec : bimodal ] we investigate heuristically and numerically the formation of a bimodal distribution of polymers . in section [ sec : stability ] we prove the stability of the zero steady state in the disease free regime ( generalizing partially a result in @xcite ) . finally , in section [ sec : timescales ] we study numerically the influence of different parameters on the dynamics of our model , in a prion strain perspective . the following set of coupled differential equations has been introduced by masel et al . @xcite in order to model the polymerization ( aggregation , fragmentation ) process involved in infectious prion self - replication . it describes the dynamics of the quantity of prpc , @xmath1 , coupled with the evolution of aggregates of prpsc which have size @xmath2 , @xmath3 , @xmath4 the index @xmath5 denotes the minimal size of prpsc polymers . the quantity @xmath6 is the total amount of prion aggregates . the constant parameters @xmath7 are respectively the basal synthesis rate of prpc , the degradation rate of prpc , the conversion rate of prpc into prpsc ( autocatalytic process following the mass action law ) , the fragmentation coefficient and the degradation rate of prpsc . analysis is simpler in the framework of continuous size of prions because analytical tools can serve to find simpler formulations . accordingly , greer _ introduce a continuous version of where the variable @xmath8 denotes the size of aggregates and replaces the index @xmath9 . asymptotic derivations of continuous models from discrete models can be found in @xcite . the continuous model reads , with possibly nonconstant coefficients , @xmath10 + 2 \int_0^{x_0}x \int_{x}^{\infty } \beta(y ) \kappa(x , y)\ , u(y , t ) \ , dy \ , dx , \vspace{.2cm}\\ \dfrac{\partial}{\partial t } u(x , t ) & = \displaystyle - v(t ) \frac{\partial}{\partial x } \big(\tau(x ) u(x , t)\big ) - [ \mu(x ) + \beta(x ) ] u(x , t ) + 2 \int_{x}^{\infty } \beta(y ) \kappa ( x , y ) \ , u(y , t ) \ , dy , \vspace{.2cm}\\ u(x_0,t ) & = 0 , \end{array } \right.\ ] ] together with appropriate initial conditions . this is a well established family of models used for describing aggregation , fragmentation and possibly coagulation in polymers and also size structured cell dynamics with finite resources @xcite . well - posedness , in the class of weak solutions , can be found in @xcite . the transport term @xmath11 accounts for the growth in size of polymers : their size grows with the speed @xmath12 , proportional to the available prpc molecules @xmath1 , with an aggregation ability depending on the size of the polymer ( a conceivable hypothesis being that their size confers them a peculiar geometry affecting the autocatalytic process ) . the fragmentation rate , for a polymer of size @xmath13 , is @xmath14 . the repartition of the two fragments of ( smaller ) sizes @xmath15 and @xmath16 is given by @xmath17 . it should thus satisfy the two usual laws @xcite expressing that the number of fragments increases but with constant total molecular mass ( recall the factor @xmath18 in the right hand side of ( [ eq : greer ] ) ) @xmath19 as usual for size - structured population models @xcite , this model may incorporate a minimal size of infectious prpres aggregates @xmath20 , whose value remains unknown . experimentally , no monomer of prpsc has been isolated yet . in addition , small aggregates have been shown not to be infectious @xcite ( even - though they have to enter the actual modeling ) and thus the assumption of a critical size of nucleation @xmath21 has been used . however , the continuous model holds under the assumption that the monomer size can be neglected as opposed to possibly numerous large polymers ( such that @xmath22 ) . therefore we keep @xmath21 in the following but we sometimes neglect it in order to simplify the presentation . [ [ assumptions - on - the - coefficients . ] ] assumptions on the coefficients . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + in its entire generality , model is rather difficult to attack even though some qualitative behaviors can be described as in section [ sec : stability ] . we aim to reduce the complexity of this system in order to extract some relevant information as the bimodal distribution motivated by the recent work of siveira et al . a simple choice for the coefficients is as follows @xcite : the fragmentation rate is taken proportional to the fragment size and the degradation rate does not depend of the size , that is @xmath23 and the probability distribution of fragments of size @xmath15 is chosen to be uniform with respect to the length of the splitted polymers of size @xmath13 : @xmath24 last , but not least , the transition rate @xmath25 may also be assumed to be constant : @xmath26 in this situation the possible time asymptotic behaviors have been completely classified @xcite as well as the stable distribution of aggregates ( see figure [ fig : bimodal](left ) and the paragraph " constant coefficients at the end of this section ) . when referring to the model of greer _ et al . _ with a constant rate @xmath27 , we will denote it by the constant coefficients case . with this respect , the main purpose of our work is to take into account different shapes for the function @xmath25 in order to fit the recent experimental data . also we perform a stability analysis which does not assume particular coefficients as in ( [ as : cc1][as : cc3 ] ) . at this stage of knowledge of the biochemical process , the available microscopic experimental data are insufficient to investigate different fragmentation laws in details . indeed , we are not able to dissociate the three elementary processes ( degradation / sequestration , splitting and polymerization ) implicated in prion replication . we have made the choice of varying the rate of infection @xmath25 as a first step , whereas silveira et al . clearly indicate that large polymers are more stable than small ones ( this could be assumed as a reduced degradation rate or a reduced fragmentation factor for large sizes ) . the system ( [ eq : greer ] ) keeps an important biochemical property , that is the prion molecules are properly transfered from one configuration to another ( inducing no loss of mass during fragmentation or polymerization ) . this enhances the following macroscopic law involving the total quantity of polymers @xmath28 and the mean length of aggregates @xmath29 : @xmath30 in fact equation ( [ eq : greer ] ) yields , @xmath31 within our formalism , and the latter represents a bell - shaped converting rate being @xmath25 in model . _ abscissa = fraction number ; ordinate = prp ( in ng ) for the solid line , and relative specific infectivity ( in arbitrary units ) for the dotted line_. note that the scale of the polymer size @xmath15 in this graph is not likely to be linear . however we can hardly evaluate the precise scale because of the limitation of measurement experiments . ] [ [ stationary - polymer - distribution . ] ] stationary polymer distribution . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + contrary to the one - peak distribution of infectious prion proteins depicted in figure [ fig : bimodal](left ) under the constant coefficients assumptions ( [ as : cc1][as : cc3 ] ) , experiments indicate that this distribution is rather bimodal ( figure [ fig : silveira ] ) . it comes out that bimodal configurations could be the result of a non - constant converting factor @xmath25 ( having a bell shape for instance ) . as we are interested mainly in long - time dynamics resulting in a balance between polymerization and fragmentation , we will often stress out the so - called stable size distributions ( see @xcite ) that are the stable steady states of system ( [ eq : greer ] ) , i.e. satisfying @xmath32 = \lambda + 2 \int_0^{x_0}x \int_{x}^{\infty } \beta ( y ) \kappa(x , y ) \ , u_\infty(y ) \ , dy \ , dx , \vspace{.2cm}\\ \displaystyle v_\infty \frac{\partial}{\partial x } \big(\tau(x ) u_\infty(x)\big ) + [ \mu(x ) + \beta ( x ) ] u_\infty(x ) = 2 \int_{x}^{\infty } \beta ( y ) \kappa(x , y)\ , u_\infty(y ) \ , dy \ , \end{array } \right.\ ] ] with sufficient decay conditions at infinity . there are in general two steady states , the first one corresponds to healthy cells , and we refer to it as the zero steady state : @xmath33 a second possible steady state , denoted by @xmath34 , corresponds to the infection regime , and can be understood as follows . for a given @xmath35 , the fragmentation equation has a dominant eigenvalue @xmath36 ( growth rate ) , associated to a nonnegative eigenvector . in other words there is a unique solution to @xmath37 { \mathcal u } ( v;x ) - 2 \int_{x}^{\infty } \beta(y ) \kappa ( x , y ) \ , { \mathcal u } ( v;y ) \ , dy=\lambda(v ) \ ; { \mathcal u } ( v;x ) , \vspace{.2cm}\\ { \mathcal u } ( v;x_0 ) = 0 , \quad { \mathcal u } ( v;x ) \ge 0 , \quad \int { \mathcal u } ( v;x)\ , dx = 1 \ . \end{array } \right.\ ] ] such solutions have been shown to exist , and the integrability condition implies a much faster decay at infinity , see @xcite . intermediate asymptotics of and particularly early stages of the infection ( exponential phase ) are also considered in the sequel ( section [ sec : timescales ] ) . interestingly , the distribution shape corresponding to the exponential phase ( figure [ fig : eigenvalue](left , full line ) ) matches quantitatively with the experimental data of figure [ fig : silveira ] . indeed we observe that large polymers are prevalent , corresponding to a level of prpc close to the healthy state @xmath38 ( see also section [ sec : timescales ] ) . the equilibrium distribution @xmath39 arises as an eigenvector associated to the eigenvalue @xmath40 . in fact , this characterizes both the ground level of prpc , @xmath41 , and the shape of the polymer distribution @xmath42 , up to a constant factor ( the total number of polymers ) . this missing factor is determined thanks to the first equation of as we show it later . interestingly enough , the value @xmath41 does not depend on the differential equation driving @xmath1 . in particular it does not depend on @xmath43 and @xmath44 . the decay condition at infinity ensures that the following integrations by parts can be justified ( we assume @xmath45 below for the sake of simplicity ) . integrating successively against @xmath46 and @xmath15 , and using ( [ as : kappa ] ) , gives respectively @xmath47 and @xmath48 as a direct consequence we obtain @xmath49 \mathcal u(v;x)\ , dx \frac{- v\int \tau(x)\mathcal u(v;x)\ , dx + \int x \mu(x ) \mathcal u(v;x)\ , dx } { \int x\mathcal u(v;x)\ , dx}.\ ] ] [ [ macroscopic - non - zero - steady - state . ] ] macroscopic ( non zero ) steady state . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + back to , the steady state of interest , if it exists , is given according to the rule @xmath50 where @xmath51 denotes the total number of polymers . there do not always exist non - trivial steady states . to see it , consider again the case @xmath52 . then , according to the first equation of system , we have @xmath53= \lambda \ , \ ] ] or , equivalently @xmath54 this points out a constraint for the non trivial steady state @xmath55 to exist , namely it is required that @xmath56 we tackle in this issue the nonlinear ( in)stability of the trivial steady state @xmath57 in section [ sec : stability ] for general coefficients . in particular , we show that stability of the trivial steady state when @xmath58 follows directly from the property that @xmath59 [ [ constant - coefficients . ] ] constant coefficients . + + + + + + + + + + + + + + + + + + + + + + the case of constant coefficients ( [ as : cc1][as : cc3 ] ) has been completely understood by greer _ we have the opportunity to recall their results under the viewpoint of the eigenvalue @xmath60 in ( [ eq : frag ] ) . this eigenvalue can be explicitly computed from which yields @xmath61 eliminating the quantity @xmath62 , we obtain @xmath63 notice that it is a decreasing function of @xmath35 ( this property is in fact crucial in the subsequent analysis ) . we also point out for further use the following consequence for the non - zero steady state : @xmath64 following the constraint , a non trivial steady state exists if and only if @xmath65 . still from @xcite , we know that it is globally asymtotically stable . on the contrary , when it does not exist , the zero steady state is globally asymptotically stable . recent experimental data obtained in @xcite suggest that prpsc aggregates have different infectious abilities , according to their size ( see figure [ fig : silveira ] ) . although infectious ability actually seems to be a competition between the three processes involved in the model ( namely fragmentation , polymerization and degradation ) one simple way to improve the model compared to @xcite is to introduce a single variable coefficient . results from @xcite show different in vitro abilities to convert prpc into prpsc , arguing in favour of a non - constant polymerization rate . therefore , in this section we consider the system ( [ eq : stst ] ) with the choice @xmath66 , @xmath67 and @xmath68 given by ( [ def : kappa ] ) , and a non - constant polymerization rate @xmath69 . we study , by means of numerical experiments and analytical methods , how bimodal fragment distributions may occur . [ [ direct - numerical - simulations . ] ] direct numerical simulations . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + our first observation is that a reasonable bell shaped converting factor @xmath25 induces a bimodal stationary distribution ( see figure [ fig : eigenvalue ] for instance ) . this is supported by various simulations of the model ( [ eq : stst ] ) . this numerical result leads to investigate analytically which conditions are needed for a bimodal distribution to appear . this is our next step . [ [ a - differential - equation - formulation . ] ] a differential equation formulation . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + as a first step , we present a simpler differential formulation of the stationary problem ( [ eq : stst ] ) , where we strongly use our particular choice of coefficients ( all are constants except @xmath25 ) . differentiating equation ( [ eq : stst ] ) , we find the following second order differential equation @xmath70 this differential equation is complemented by the boundary conditions @xmath71 recall also the additional relation derived from ( [ eq : stst ] ) , after testing against @xmath15 , @xmath72 the equation is reminiscent of the standard one - dimensional fokker - planck equation . in fact , if we drop the last term of order 0 , it becomes @xmath73 that is , a inhomogeneous diffusion with an effective potential given by @xmath74 . hence the contribution of a non constant @xmath25 might rise a double well potential on @xmath75 , and thus be responsible for the formation of a two - peaked solution . this holds , by perturbation analysis , at least for @xmath76 small . but we can give a more accurate estimate . [ [ condition - for - a - bimodal - equilibrium - distribution . ] ] condition for a bimodal equilibrium distribution . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + we now give a necessary condition for a bimodal distribution . we evaluate the derivatives in the microscopic equilibrium equation , @xmath77 a bimodal length distribution @xmath39 has a critical point where it is convex and therefore we are looking for a point @xmath78 such that @xmath79 and @xmath80 . a necessary condition on @xmath25 for the existence of such a point is therefore @xmath81 the above condition is indeed intricated because @xmath41 itself depends on @xmath25 . but it gives a first insight of the desirable conditions , meaning that a peak which is concave enough is required . as we will see it below , this condition is not sufficient . the locus of this strongly concave peak is also important [ [ locus - of - the - peak - of - taux - heuristics . ] ] locus of the peak of @xmath25 : heuristics . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + for coefficients like @xmath66 and @xmath82 , we know from , that the center of mass at the equilibrium configuration has the value @xmath83 . departing with @xmath27 constant , the unimodal distribution is split into a bimodal one under the action of @xmath25 . the further is the peak of the bell - like function @xmath25 from @xmath83 , the weaker is the splitting effect on the unimodal distribution . this is in accordance with numerical results ( see figure [ fig : heuristic ] ) . we have seen previously that there are two possible steady states , setting the alternative between a disease free and an infected system and depending upon the prion production and degradation rates @xmath43 , @xmath44 . for constant coefficients , greer _ _ @xcite could study their stability using that the system can be reduced to a differential system on @xmath84 ( see section [ sec : model ] ) . here , we investigate the same question for general coefficients . our main assumption is some monotonicity of the eigenvalue in problem ( [ eq : frag ] ) , which we have checked for constant coefficients , see formula ( [ eq : eigenvaccc ] ) . we choose @xmath45 throughout this section . we first tackle the stability of the disease - free steady state . recall the notation @xmath86 for the zero steady state from ( [ eq : zerostst ] ) . assume that @xmath87 defined in ( [ eq : frag ] ) is decreasing and that @xmath85 , where @xmath41 is defined by @xmath88 according to ( [ eq : stabless ] ) . then , in equation ( [ eq : greer ] ) , the zero steady state @xmath89 , @xmath90 is locally nonlinearly stable . [ lm : stab1 ] we recall that in the case at hand ( @xmath85 ) , there does not exist a non - zero steady state because ( [ as : stst ] ) can not be fulfilled with @xmath91 . we give in the subsection [ sec : ex ] below a class of coefficients for which we can compute the eigenvalue @xmath87 and it is indeed decreasing . the eigenvalue @xmath87 is assumed to be a decreasing function of @xmath35 . so , the condition @xmath85 ensures that @xmath92 . we consider a perturbation of the ground state @xmath93 and @xmath94 ( note that @xmath95 is nonnegative , whereas @xmath96 has no sign ) . the nonlinear system for this perturbation writes @xmath97 - \overline v \int_{0}^{\infty } \tau(x ) \widetilde u(x , t ) \ ; dx , \vspace{.2cm}\\ \dfrac{\partial}{\partial t } \widetilde u(x , t ) & = & \displaystyle - \overline v \frac{\partial}{\partial x } \big(\tau(x ) \widetilde u(x , t)\big)- \widetilde v(t ) \frac{\partial}{\partial x } \big(\tau(x ) \widetilde u(x , t)\big ) - [ \mu(x ) + \beta ( x ) ] \widetilde u(x , t ) \vspace{.2cm}\\ & & \qquad + \displaystyle2 \int_{x}^{\infty}\ , \beta(y ) \kappa(x , y ) \widetilde u(y , t ) \ , dy . \end{array } \right.\ ] ] following the duality method in @xcite , we introduce the adjoint eigenvector for the eigenvalue @xmath98 , namely @xmath99 given by the equation @xmath100\overline \varphi(x ) = 2 \int_{0}^{x}\beta(x ) \kappa(y , x ) \overline \varphi(y ) \ , dy + \lambda(\overline v ) \overline \varphi(x)\ .\ ] ] we now introduce constants @xmath101 such that @xmath102 this is possible because @xmath103 grows linearly at infinity according to general abstract properties proved in @xcite . see again subsection [ sec : ex ] for examples . we test the adjoint equation against the equation on @xmath104 in and obtain @xmath105 on the other hand , multiplying the first differential equation in by the sign of @xmath96 , we get : @xmath106+\overline v \int_{0}^{\infty } \tau(x ) \widetilde u(x , t ) \ ; dx\ , .\ ] ] we obtain , choosing @xmath107 large enough such that @xmath108 , @xmath109 from this differential equation we conclude that , when @xmath110 is initially small enough , then the right hand side is negative . therefore it decays for all times with the asymptotic exponential rate @xmath111 we can also state the following variant of theorem [ lm : stab1 ] additionally to the hypotheses of theorem [ lm : stab1 ] , assume that @xmath112 for some constant @xmath113 and @xmath114 is small enough compared to @xmath115 . then , in equation ( [ eq : greer ] ) , the zero steady state @xmath116 , @xmath90 is globally nonlinearly stable . [ lm : stab2 ] by opposition to those of theorem [ lm : stab1 ] , the assumptions of this theorem are difficult to check directly because the coefficients are intricated here . they mean that we are close to the constant coefficients case because @xmath117 in this case and we can choose @xmath118 . with these additional assumptions , we may keep one negative term in the last computation and arrive to @xmath119 this last inequality will hold if we can find @xmath120 such that @xmath121 , which is precisely our smallness assumption . then we have exponential decay of the solution . the same kind of method allows for another type of results initiated in @xcite , namely that solutions can not go extinct when another steady state exists . again we choose @xmath52 in this subsection . we have , recalling that @xmath103 is defined in ( [ eq : adjoint ] ) , the assume that @xmath87 defined in ( [ eq : frag ] ) is decreasing , that for some constant @xmath123 , @xmath124 , that @xmath125 and that @xmath126 . then , in equation ( [ eq : greer ] ) , the zero steady state @xmath89 , @xmath90 is locally unstable . [ lm : unstab1 ] following the proof of theorem [ lm : stab1 ] , we have on the one hand @xmath127 therefore we have @xmath128 for all @xmath129 . on the other hand , we can again combine the equations ( [ eq : adjoint ] ) for @xmath130 and the equation on @xmath131 in ( [ eq : greer ] ) , to obtain @xmath132 we define the quantity ( sum of two positive terms ) @xmath133 as a consequence of the above calculations and of the hypothesis @xmath134 , we have therefore , @xmath135 \int_0^\infty u(x , t ) \overline \varphi(x)\ , dx \ , , \end{aligned}\ ] ] for some constants @xmath136 . indeed , in this case when @xmath137 , we know that @xmath138 . we can conclude from this inequality that @xmath139 is unstable . indeed , whenever @xmath140 becomes small enough , then @xmath141 becomes also small enough so that @xmath140 increases and the solution gets away from @xmath139 . in order to clarify the assumptions and properties stated before , we give a class of coefficients in equation ( [ eq : greer ] ) where the different eigenelements can be explicitly computed . in each case we will see that @xmath142 s a decreasing function of @xmath35 , and that ( [ as : stab ] ) reduces to the fact that @xmath25 is bounded . + we first recall from @xcite , the case @xmath143 , @xmath144 and @xmath145 constant . we obtain the solution to ( [ eq : adjointp ] ) below , @xmath146 the eigenlements are usually difficult to evaluate in the direct problem ( [ eq : frag ] ) but can be easily computed in the adjoint equation , recall ( [ eq : adjoint ] ) , @xmath147 \varphi(x ) = 2 \int_{0}^{x}\beta(x ) \kappa(y , x ) \varphi(y ) \ , dy + \lambda ( v ) \varphi(x)\ .\ ] ] indeed , searching for an affine solution @xmath148 , we find , using the structure properties of @xmath149 in ( [ as : kappa ] ) , @xmath150 hence a more general class where one can compute @xmath36 is when @xmath151 , and @xmath27 , @xmath152 are constant . we arrive at @xmath153 therefore we obtain @xmath154 and @xmath155 as in section [ sec : model ] . observe that @xmath36 is a decreasing function of @xmath35 as used in theorem [ lm : stab1 ] . we leave to the reader to check that @xmath36 is also decreasing when @xmath156 , @xmath157 and @xmath152 is constant . indeed solving the two equations for @xmath148 , we find @xmath158 and thus @xmath159 solves @xmath160 this last constraint comes from the condition @xmath161 . + more generally , notice that it always holds true that @xmath162 to prove it , we just multiply ( [ eq : frag ] ) by @xmath15 and integrate . notice that the problem is then degenerate and the eigenfunction is singular at @xmath163 . on the other hand , still for the same reason , if @xmath164 , we have @xmath165 and then there is at least one non - zero steady state . as we highlighted previously , recent experimental work by weber et al @xcite and by silveira et al @xcite suggests that prpsc aggregates are differentially infectious with respect to their size . the former also shows that the prpsc size distribution in a whole infected brain is bimodal rather than unimodal . based on the nucleated polymerization model for prion growth , we have shown that bimodal stationary distribution can occur for a size - dependent conversion rate . however , during the time course of incubation period and clinical stage of prion diseases , prpsc accumulation seems to follow an exponential dynamic until the death . apart from hemizygote mice ( prp+ /0 ) , no steady state of prpsc accumulation was observed in the brain during all the disease @xcite . consequently , we focus in this section on the dynamic of prpsc accumulation in the early stages of the infection named exponential phase. our approach is based both on the eigenvalue problem and on direct numerical simulations of the temporal dynamics . [ [ numerics . ] ] numerics . + + + + + + + + + parameters of the nucleated polymerization model for prion growth have been estimated for the constant parameters model from experimental data and are available in the literature @xcite . the parameter values used in the sequel have been quoted from rubenstein et al . @xcite . unless explicitly mentioned , they are : @xmath166 per day , @xmath167 per day , @xmath168 per day , and @xmath169 per day . the conversion function @xmath25 is the sum of a basal rate @xmath170 and a gaussian bell centered on @xmath171 : @xmath172 with a magnitude @xmath173 to be chosen by several orders of magnitude above @xmath27 ( from biological evidence on different specific converting activities in @xcite ) . the simulations assume an initial prpc population @xmath174 ( corresponding to the healthy steady state ) and an initial prpsc population given by @xmath175 , which is a small perturbation of the zero steady state indeed . [ [ dynamics - of - prpsc - accumulation - and - eigenvalue - problem . ] ] dynamics of prpsc accumulation and eigenvalue problem . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + the eigenvalue problem can be used to measure the dynamics of prpsc aggregates accumulation during the exponential growth . we assume below that @xmath176 , that @xmath36 is a decreasing function and that instability of the healthy state holds true ( see section [ sec : stability ] ) . the practical choice of coefficients is mentioned above . assuming that @xmath1 remains close enough to @xmath98 ( this is exponential growth phase in a linear regime ) , then the polymerization behaves following a linear problem . actually the second equation in is decoupled from the first one at the first order of approximation . the dominant eigenvalue @xmath177 thus measures the exponential growth of the prpsc total population ( see @xcite for a mathematical formulation of this fact using the generalized relative entropy ) . as a by - product , we also learn that the renormalized distribution tends to align along the eigenvector @xmath178 . one noticeable difference with the stationary case studied in section [ sec : model ] is that the center of mass of @xmath178 is translated to the right as opposed to @xmath179 ( for which it is @xmath83 ) , according to : @xmath180 observe that for the parameters picked up in the literature , the difference is significant ( approximately 500% ) . + + if @xmath181 denotes the total population of prpsc , then it evolves eventually as @xmath182 from the ground healthy state @xcite in the exponential phase . here the initial condition @xmath183 accounts for the inoculation dose . therefore @xmath184 grows linearly in time as a first approximation . if we define mathematically the incubation time as a threshold in that macroscopic amount of prpsc @xcite , we rederive the logarithmic relationship between incubation time and inoculation dose in the linear regime : @xmath185 moreover , the relationship stresses out the importance of measuring the dependence of @xmath186 with respect to the parameters of the model . following figure [ fig : eigenvalue ] we suggest to evaluate the influence of the tightness of the transconformation peak . closely looking at figure [ fig : eigenvalue](right ) we indeed notice that the growth rate @xmath177 ( right limit of the graph ) is slightly larger for the model with constant rate @xmath187 ( solid line ) . several transconformation rates @xmath25 being the same basal rate @xmath27 combined with a more and more concentrated gaussian bell are tested and the corresponding growth rate in the exponential phase @xmath177 are computed numerically ( figure [ fig : vp ] ) . interestingly , the results exhibit a best compromise around @xmath188 ( intermediate concentrations of the peak ) . however , this does not correspond to a bimodal distribution for the polymerization profile . thus , according to this model the optimal conditions for prpsc accumulation in the exponential expansion phase are not those which lead to a bimodal size - distribution of prpsc aggregates as observed by silveira et al . @xcite . [ [ prion - strain - mechanisms . ] ] prion strain mechanisms . + + + + + + + + + + + + + + + + + + + + + + + + it is a challenging problem to investigate the prion strain phenomenon under the light of model which provides informations on the possible microscopic distributions of prpsc polymers . the prion strain phenomenon is supported by the fact that prion infected animals may develop several distinct pathologies , whose clinical and neuropathological outcomes can be maintained through several passages in rodents models of prion diseases . each prion strain transmitted in the same congenic host exhibits stable incubation period , clinical expression , lesions profile and infectious properties . these phenotypic features can be used to differentiate between different prion strains @xcite . among them , the most commonly used is the incubation period . for most prion strains within the same host , incubation period is determined by the rate and pattern of prpsc accumulation . for our purpose however it will be reduced to the time for the total amount of prpsc to reach a certain threshold . we therefore study by mean of direct numerical simulations how parameters influence the dynamics of prpsc accumulation . the values used for these numerical tests are mentioned above . the locus and the thightness of the transconformation rate are qualitatively compatible with a bimodal distribution of prpsc polymers in the exponential growth phase ( see figure [ fig : htau ] and figure [ fig : betavar ] , b ) , as well as in the equilibrium phase ( data not shown ) . for the experiments depicted in figure [ fig : htau ] and figure [ fig : betavar ] , varying parameters acts upon the kinetics of prpsc accumulation as follows . the higher the transconformation or the fragmentation rates are , the faster prpsc accumulates , and thus , the shorter the incubation time seems to be . in particular this implies that a fast strain could be either instable ( i.e. can be easily broken ) or able to fix and transconform prpc with great efficiency ( or both ) . interestingly , our simulations also predict changes in the microscopic size - distribution of prpsc aggregates , whose profiles are specific of the given parameters . . transconformation rate is given by @xmath189 . three values for @xmath190 have been tested : @xmath191 ( solid line ) , @xmath192 ( dashed line ) and @xmath193 ( dotted line ) . ( a ) size distribution of @xmath194 ( abscissa = prpsc aggregates size ; ordinate = rate @xmath194 ) ( b ) time evolution of total prpsc . the arrow represents time t = 96 days ( abscissa = time ( in day ) ; ordinate = rate @xmath194 ( per day ) ( c ) normalized prpsc aggregates size distribution at t = 96 days , corresponding to the exponential growth of prpsc . the distributions are normalized by the total number of prpsc aggregates ( abscissa = prpsc aggregates size ; ordinate = prpsc aggregates number ) . , title="fig : " ] . transconformation rate is given by @xmath189 . three values for @xmath190 have been tested : @xmath191 ( solid line ) , @xmath192 ( dashed line ) and @xmath193 ( dotted line ) . ( a ) size distribution of @xmath194 ( abscissa = prpsc aggregates size ; ordinate = rate @xmath194 ) ( b ) time evolution of total prpsc . the arrow represents time t = 96 days ( abscissa = time ( in day ) ; ordinate = rate @xmath194 ( per day ) ( c ) normalized prpsc aggregates size distribution at t = 96 days , corresponding to the exponential growth of prpsc . the distributions are normalized by the total number of prpsc aggregates ( abscissa = prpsc aggregates size ; ordinate = prpsc aggregates number ) . , title="fig : " ] . transconformation rate is given by @xmath189 . three values for @xmath190 have been tested : @xmath191 ( solid line ) , @xmath192 ( dashed line ) and @xmath193 ( dotted line ) . ( a ) size distribution of @xmath194 ( abscissa = prpsc aggregates size ; ordinate = rate @xmath194 ) ( b ) time evolution of total prpsc . the arrow represents time t = 96 days ( abscissa = time ( in day ) ; ordinate = rate @xmath194 ( per day ) ( c ) normalized prpsc aggregates size distribution at t = 96 days , corresponding to the exponential growth of prpsc . the distributions are normalized by the total number of prpsc aggregates ( abscissa = prpsc aggregates size ; ordinate = prpsc aggregates number ) . , title="fig : " ] have been tested : @xmath195 ( solid line ) , @xmath196 ( dashed line ) and @xmath197 ( dotted line ) . ( a ) , ( b ) and ( c ) : same as figure [ fig : htau],title="fig : " ] have been tested : @xmath195 ( solid line ) , @xmath196 ( dashed line ) and @xmath197 ( dotted line ) . ( a ) , ( b ) and ( c ) : same as figure [ fig : htau],title="fig : " ] have been tested : @xmath195 ( solid line ) , @xmath196 ( dashed line ) and @xmath197 ( dotted line ) . ( a ) , ( b ) and ( c ) : same as figure [ fig : htau],title="fig : " ] our motivation for this work is to better understand the unexpected bimodal size distribution of prions , observed by silveira et al @xcite . based on the nucleated polymerization model of prion fibril growth describing the dynamics of prpc monomeres and prpsc aggregates , we take into account aggregate - size dependent parameters , expanding thus a previous study @xcite . we have shown numerically that bimodal stationary distribution can occur in the case of a non - uniform conversion rate from prpc into prpsc . it is worth noticing that experimental distribution of prp may not correspond to a steady state of the system since the biological process is dramatically stopped with the animal death . therefore the considerations about the stationary distribution might be not biologically relevant . nevertheless we also observe bimodal distribution generically along the temporal dynamics , a new feature in comparison to @xcite . for further modifications concerning model we suggest to take into account saturation in the fragmentation rate for large fibrils , as noticed in @xcite . theoretical analysis of the model gives necessary criterion on the parameters for a bimodal distribution to occur in the stationary phase . numerical analysis of the eigenvalue problem shows in addition that parameters which lead to a bimodal distribution of prpsc are not the most favourable for prpsc accumulation in the exponential phase , see figure [ fig : vp ] . it suggests that infectious ability concentrated on a restricted range of prpsc aggregate sizes ( 14 to 28 molecules @xcite ) does not consist in a replicative advantage for prion at the molecular level . therefore , this restriction could be caused by a physico - chemical constraint , carried out by the host metabolism or by the prion aggregate itself . this could eventually be due to the prpsc aggregate shape , since the most infectious intermediate aggregates have been found to be spherical or ellipsoidal whereas the others form fibrilar structures @xcite . however , understanding the precise nature of the constraint would help to identify new therapeutic targets . furthermore , we investigate the implications of varying the fragmentation and transconformation rates notably in the biological perspectives of the prion strain phenomenon . prion strains have been initially distinguished by incubation periods and lesion profiles in congenic mice @xcite . nowadays , a large body of literature suggests that differences between prion strains lie in the diversity of structures of prpsc aggregates that can be stably and faithfully propagated @xcite . however , it remains poorly understood how these changes in the conformation of prpsc aggregates can account for their physiopathological effects @xcite . among the attempted biochemical characterisation of prion strains , a relationship was found between the relative stability values of prpsc aggregates @xcite or level of aggregation @xcite and incubation times , indicating that less stable prions are more infectious , as judged by their shorter incubation times . this is presumably because unstable prions fragment more easily , giving rise to smaller aggregates of prpsc that are more infectious than larger ones ( represented by an increased transconformation rate in the mathematical model ) . our model agrees with these observations , since increasing the fragmentation rate @xmath198 leads to a faster prpsc accumulation . more interestingly , our model enables to explore quickly the influence of every elementary mechanism involved in prion replication . whereas changing parameters leads to similar effects on prpsc accumulation kinetics , the resulting size - distribution variations are indeed different . the achievement of experimental size - distribution of prpsc aggregates for many prion strains , as obtained by silveira et al @xcite for 263k prion strain , could therefore allow to better understand the mechanisms involved in prion strain phenomenon , by comparing the experimental distribution and the predicted ones . one limit to our approach is that prion strains are not only characterized by a precise incubation time but also by a specific cellular tropism . it would be of interest to introduce some mathematical formalism taking into account cell heterogenity in the brain and the resulting local influences . in addition , transmission of prion diseases between different mammalian species is almost systematically less efficient than within a single species . this obstruction has been termed species barriers . early studies argue that barrier resides in prp primary structure difference between donor and recipient species @xcite . however , this issue has been called into question notably by bse strain capability . indeed , different strains propagated in the same host may thus have completely different barriers to another species . consequently , transmission barrier appears to depend on prion strain specificities @xcite . this is supported by our model . indeed , we learn that the renormalized bimodal distribution of prpsc aggregates tends to align along the eigenvector associated to the dominant eigenvalue @xmath186 ( solid line in figure [ fig : eigenvalue](left ) ) @xcite . in our analysis , we assumed implicitely that the distribution of polymers is initially proportional to this eigenvector ( which depends upon the the parameters of the model , and thus on the strain - host relationship ) . otherwise there is some delay for the microscopic distribution to reach the good shape which slows down the process of prion accumulation . this might account for the strain adaptation mechanism , where primary inoculation is associated with more prolonged incubation period than subsequent passages in the same type of hosts @xcite . according to these observations and the experimental ones , it should be very interesting to study experimentally the distribution of aggregates and infectivity between strains which are able or not to cross many species barriers . the distributions of prpsc aggregates could be used to evaluate the influence of fragmentation , transconformation rate or infectivity distribution on the strenght of prion strain in crossing species barriers . these data could give a new signature of prion strain . meanwhile the elucidation of structural basis of prion strains , strenght barrier species discrimination by these prion strain signature could be useful to predict the potential transmissibility of prion strain to human , notably for recent atypical scrapie strain , bovine amyloidic spongiform encephalopathy ( base ) strain and chronic wasting disease strain @xcite . thus , our model could be used to investigate essential features of prion strains . the next step of our work is to approximate faithfully the inverse problem in order to obtain the size dependence of the transconformation rate from the distribution of prpsc . we therefore would be able to determine the most infectious compartment for several prion strains . this knowledge is a critical step for experimental approaches of prion infectivity investigation , like pmca . pmca goal is to quickly synthetize in vitro large amounts of prpsc starting with minute amounts of prions . the yield of this technique is very sensitive to experimental procedures . then size distribution of infectivity could help to optimize strain specific pmca protocols , notably by adaptating sonication steps to fall into the most infectious size compartment of prpsc aggregates . finally , we have analyse the stability of the steady states in a general framework . the difficulty arising here is that we can not reduce the study to a set of ordinary differential equations , as it is the case in @xcite . under general assumptions on the coefficients , compatible with bimodal distributions , the asymptotic stability of the healthy state ( i.e. no prion aggregates ) is established when the prpc is low . we also prove that this healthy state is unstable when the prpc production rate is high enough . this is in accordance with the asymptotic stability of the non - zero steady state for constant coefficients proved in @xcite , even though a perfect dichotomy between the two results is left open in the general case . biologically , these results can be interpreted as the propensity of prpsc aggregates to give rise to prion disease depends on the amount of prpc . in the more general context of understanding why some amyloids are infectious and others are not , it therefore could be useful to investigate the amount of amyloidogenic precursors . this work has been achieved during a visit of do within the dease project ( marie curie early stage training multi site ( mest ) of the eu , mest - ct-2005 - 021122 ) . + we would like to sincerely thank j. silveira , a. hughson and b. caughey for their experimental data about prp distribution . we are also grateful to m. doumic for fruitful discussions . this work would not have been achieved without the help of h. zaag . r. rubenstein , p.c . gray , t.j . cleland , m.s . piltch , w.s . hlavacek , r.m . roberts , j. ambrosiano and j .- i . kim , _ dynamics of the nucleated polymerization model of prion replication _ , biophys . chem . * 125 * , 360367 ( 2007 ) . greer , p. van den driessche , l. wang and g.f . webb , _ effects of general incidence and polymer joining on nucleated polymerization in a model of prion proliferation _ , to appear in siam j. appl . math . p. weber , a. giese , n. piening , g. mitteregger , a. thomzig , m. beekes and h.a . kretzschmar , _ cell - free formation of misfolded prion protein with authentic prion infectivity _ , proc . usa * * , 257261 ( 2006 ) . g. legname , h - o.b . nguyen , d. peretz , f.e . cohen , s.j . dearmond and s.b . prusiner , _ continuum of prion protein structures enciphers a multitude of prion isolate - specified phenotypes _ , usa * 103 * , 1910510 ( 2006 ) . sigurdson , k.p.r nilsson , s. hornemann , g. manco , m. polymenidou , p. schwarz , m. leclerc , p. hammarstrom , k. wuthrich and a. aguzzi , _ prion strain discrimination using luminescent conjugated polymers _ , nat . methods * 4 * , 1023 - 1030 ( 2007 ) . prusiner , m. scott , d. foster , k .- pan , d. groth , s .- l . yang , d. serban , g.a . carlson , p.c . hoppe , d. westaway and s.j . dearmond , _ transgenic studies implicate interactions between homologous prp isoforms in scrapie prion replication _ , cell * 63 * , 673386 ( 1990 ) . m. bruce , a. chree , i. mcconnell , j. foster , g. pearson and h. fraser , _ transmission of bovine spongiform encephalopathy and scrapie to mice : strain variation and the species barrier _ , phil . b , * 343 * , 405411 ( 1994 ) . j. collinge , m.s . palmer , k.c . sidle , a.f . hill , i. gowland , j. meads , e. asante , r. bradley , l.j . doey and p.l . lantos , _ unaltered susceptibility to bse in transgenic mice expressing human prion protein _ , nature * 378 * , 779783 ( 1995 ) .

we consider a model for the polymerization ( fragmentation ) process involved in infectious prion self - replication and study both its dynamics and non - zero steady state . we address several issues . firstly , we give conditions leading to size repartitions of prpsc aggregates that exhibit bimodal distributions , as indicated by recent experimental studies of prion aggregates distribution @xcite . this is achieved by a choice of coefficients in the model that are not constant , thus extending a previous study of the nucleated polymerization model @xcite . surprisingly , conditions for bimodality do not seem to be the most favourable for prion replication . secondly , we show stability results for this steady state for general coefficients where reduction to a system of differential equations is not possible . we use a duality method based on recent ideas developed for population models . these results underline the potential influence of the amyloid precursor production rate in promoting amyloidogenic diseases . finally , we numerically investigate the influence of different parameters of the model on prpsc accumulation kinetics , in the aim to study specific features of prion strains . this study suggests that prpsc aggregate size distribution could be a signature of a strain in a given host and a constraint during the adaption mechanism of the species barrier overcoming , that open experimental perspectives for prion strain investigation .

proposed a subclassification of t2 rcc into pt2a and pt2b according to tumor diameter with a cutoff of 10 cm . based on their reports , the 7th edition of tnm classification , threshold value between t1 and t2 rcc was divided into t2a ( up to 10 cm ) and t2b ( more than 10 cm ) . reported that local control may be achieved in surgical management of contemporary patients with rcc of 4 cm or less either by radical or nephron sparing surgery , and , in addition , local recurrence rate after nephron sparing surgery was 012% . the rate decreases to 0% to 3% for microscopically organ confined disease and 0% to 5% for small renal tumors . it is well known that renal cell carcinoma with a diameter of more than 10 cm has high potential to cause distant metastasis and generally recommended surgical procedure is radical nephrectomy . previously , we reported that systemic symptoms of rcc have a strong significant relationship with the expression of matrix metalloproteinase 9 ( mmp-9 ) . it is well known that both mmps ( matrix metalloproteinases ) and timps ( tissue inhibitors of metalloproteinases ) play an important role in the progression of rcc . however , there are no reports examining the relationships among tumor diameter and mmps and timps . to clarify what kind of clinicopathological feature is necessary for extension of the tumor diameter , we studied localized rcc patients . between january 1988 and december 2003 , a total of 237 patients had underwent radical nephrectomy for localized renal cell carcinoma at nihon university itabashi or surugadai hospital . patients consisted of 176 males and 61 females , mean age of 60 ( 3383 ) and 58 ( 2582 ) , respectively . all patients underwent preoperative chest and abdominal contrast enhanced ct , and bone scan if required . tumors were classified as pt1a , pt1b , pt2a , and pt2b in 94 ( 40% ) , 74 ( 31% ) , 43(18% ) , and 26 ( 11% ) cases , respectively . the nuclear grade of rcc was determined using the criteria proposed by fuhrman et al . . since several studies found no significant difference in survival results between patients with grade 1 versus 2 tumors and those with grade 3 versus 4 tumors , a total of 237 patients were divided into two groups according to nuclear grade : a low nuclear grade group ( grades 1 and 2 , 190 patients ) and a high nuclear grade group ( grades 3 and 4 , 47 patients ) . microvessel invasion ( mvi ) was defined as a tumor infiltration locally through the intact vessel wall including the endothelium , leading to free extension of cancer cells into the lumen . we applied immunohistochemistry on the cut surface of tumor with no necrosis nor intratumoral hemorrhage . the immunohistochemical study for mmp-2 , mmp-9 , timp-1 , timp-2 , and mt - mmp-1 was performed by methods we previously reported . for evaluation of immunohistochemical staining , staining intensities of 2 + and 3 + were considered strong expressions of each protein ( figure 1 ) . cancer - specific survival ( css ) was defined as the interval from initial surgery to death and was calculated by the method of kaplan and meier . cox multivariate analysis was performed to determine any independent predictive values . to determine the relationships between t categories and 8 pathological features of rcc ( histopathological type , nuclear grade , mvi , mmp-2 , mmp-9 , timp-1 , timp-2 , and mt - mmp-1 ) , we compared the quantitative results using a multiple logistic regression analysis . all analyses were performed using jmp4.0 ( sas institute , cory , nc , usa ) . the study using these specimens was performed under the approval of nihon university school of medicine ethics board ( irb number 106 - 1 ) . among the tumors , 194 ( 82% ) were conventional clear cell carcinomas , 42 ( 17% ) were papillary carcinomas , and 1 ( 0.3% ) was a chromophobe carcinoma . tumors were classified as pt1a , pt1b , pt2a , and pt2b in 94 ( 40% ) , 74 ( 31% ) , 43 ( 18% ) , and 26 ( 11% ) cases , respectively . the median tumor diameter was 50 mm ( 15250 mm ) . among a total of 237 patients , 190 were classified as having a low nuclear grade ( grades 1 and 2 ) , whereas 47 as having a high nuclear grade ( grades 3 and 4 ) . the cancer - specific 10-year survival rates were 88.8% , 69.5% , 80.3% , and 50.0% for pt1a , pt1b , pt2a , and pt2b , respectively ( figure 2 , p < 0.001 ) . with respect to the cancer - specific mortality , the univariate analysis showed no significance for pt1a versus pt2a and timp-1 and timp-2 as a determinant factor , while the remaining 8 factors were significant factors of postoperative specific mortality of 247 patients ( table 1 ) . by the multivariate analysis of clinicopathological factors , nuclear grade , timp-2 , and mt - mmp-1 were independent prognostic factors ( risk ratio 1.50 , p = 0.037 , risk ratio 1.12 , p = 0.02 , and risk ratio 1.84 , p = 0.045 , resp . ) ( table 1 ) . we compared the clinicopathological factors in three categories : pt1a versus pt1b , all pt1 versus pt2a , and all pt1 + pt2a versus pt2b . by the cox multivariate analysis ( table 2 ) , among the pt1a versus pt1b group , timp-1 was an independent factor ( risk ratio 3.30 , p = 0.010 ) . for pt1 versus pt2a , both nuclear grade ( risk ratio 5.15 , p = 0.0015 ) and mvi ( risk ratio 3.08 , p = 0.002 ) were independent factors . for the remaining pt1 + pt2a versus pt2b , both nuclear grade ( risk ratio 3.39 , p = 0.020 ) and mvi ( risk ratio 2.91 , p = 0.018 ) were significant factors . once mmps are stimulated , they are susceptible to prohibition by the general serum proteinase inhibitor 2-macroglobulin and by a family of specific tissue inhibitors ( timps ) . on the other hand , timps have been frequently reported that they may be multifunctional , because of additional effects on cell growth and apoptosis . previously , we reported that high expression levels of mmp-9 were associated with poor prognosis of rcc . basically , timps are known to inhibit mmp activity by forming a complex with active mmps and are believed to be specific for enzymes of this family , such as timp-1 with mmp-9 and timp-2 with mmp-2 . members of the timp family have also been associated with cancer . in several cases , mmp-9 has a significant relationship with high nuclear grade rcc and was found to be an independent prognosticator by multivariate analysis . furthermore , nuclear grade and timp-2 were independent prognostic factors among the incidental rcc patients . with regard to mvi , ishimura reported that mvi is not a significant prognostic factor in localized rcc patients ; on the other hand , it is the only significant prognostic factor of disease free recurrence after radical operation for patients with pt1 and pt2 disease . additionally , dall'oglio et al . showed a significant relationship between mvi and clinical stage . in 95 tumors below 4 cm in diameter , mvi was detected in 11 ( 12% ) , while in 74 tumors of 4.17 cm , mvi was detected in 20 ( 27% ) , and in 61 of over 7 cm , 28 ( 48% ) had mvi . previously we reported that cancer - specific 5-year survival was 45.0% for patients with high nuclear grade tumor ( grade 3.4 ) and zhang et al . reported a significant correlation between tumor size and nuclear grade . by their report , tumor diameters of g1 , g2 , and g3 tumors were significantly different ( 3.27 1.46 cm , 4.87 2.23 cm , and 7.39 3.11 cm , p < 0.05 ) . in conclusion , higher expression of timp-1 is necessary for advancement of tumor diameter from pt1a to pt1b , and a process of tumor diameter extension beyond pt1 category needs the presence of mvi and high nuclear grade .

objectives . to clarify what kind of pathological factor is necessary for the extension of tumor diameter in localized rcc , we studied localized rcc patients . methods . we retrospectively reviewed medical records of 237 rcc patients in our institute who underwent nephrectomy . we performed immune histological analysis of mmp-2 , mmp-9 , timp-1 , timp-2 , and mt - mmp-1 for all samples . results . among the clinicopathological factors , multivariate analysis revealed nuclear grade ; timp-2 and mt - mmp-1 were independent prognostic factors of localized rcc ( risk ratio 1.50 , p = 0.037 , risk ratio 1.12 , p = 0.008 , and risk ratio 1.84 , p = 0.045 , resp . ) . by the multiple logistic regression analysis among pt1a versus pt1b , timp-1 was an independent factor ( risk ratio 3.30 , p = 0.010 ) whereas all pt1 versus pt2a and all pt1 + pt2a versus pt2b high nuclear grade ( risk ratio 5.15 , p = 0.0015 ) and micro vessel invasion ( mvi , risk ratio 3.08 , p = 0.002 ) were independent factors . for all pt1 + pt2a versus pt2b , nuclear grade ( risk ratio 3.39 , p = 0.020 ) and mvi ( risk ratio 2.91 , p = 0.018 ) were independent factors . conclusion . higher expression of timp-1 is necessary for advancement tumor diameter from pt1a to pt1b , and a process of tumor diameter extension beyond pt1 and pt2a category needs presence of mvi and high nuclear grade .

The current issue of Newsweek has a photo of President Obama with a rainbow-colored halo superimposed over his head and the title “The First Gay President.” Nonsense. Obama is not the first gay president. He is the first female president. Dana Milbank writes about political theater in the nation’s capital. He joined the Post as a political reporter in 2000. View Archive Consider his activities on Monday: He sat down to tape a session with the ladies of ABC’s “The View” — his fourth appearance on the talk show by women and for (mostly) women. He accepted an award from Barnard College and gave the commencement speech to graduates of the women’s school. Heck, he even appeared in public wearing a gown. Obama was still early in his address when he acknowledged that his praise for the young generation of women is “a cheap applause line when you’re giving a commencement at Barnard.” But Obama was being modest. He didn’t deliver a cheap applause line. He delivered an entire speech full of them. His reelection campaign has been working for months to exploit the considerable gender gap, which puts him far ahead of likely GOP rival Mitt Romney among women. But Monday’s activities veered into pandering, as Obama brazenly flaunted his feminine mystique. He speculated that “Congress would get a lot more done” if more women were there. He speculated that, although no women signed the Constitution, “we can assume that there were founding mothers whispering smarter things in the ears of the founding fathers.” He announced that “more and more women are out-earning their husbands. You’re more than half of our college graduates and master’s graduates and PhDs.” He told them that they are “poised to make this the century where women shape not only their own destiny but the destiny of this nation and of this world.” And they can look good doing it! “You can be stylish and powerful, too,” he said. “That’s Michelle’s advice.” The first lady, the couple’s two daughters, and the president’s mother and mother-in-law had recurring roles as “strong, remarkable women” in the speech. There were some ironies in the appearance. When the White House asked Barnard for the commencement speaking role, the college dumped its original speaker, Jill Abramson. In addition to being an actual woman, Abramson is the first of her sex to become executive editor of the New York Times. Obama made no mention of Abramson, but he did mention that he knows the past three Barnard commencement speakers, including Hillary Rodham Clinton, whose presidential aspirations Obama dashed. Obama was moved to paraphrase an old adage: “Keep your friends close and your Barnard commencement speakers even closer.” In making the appearance on the Ivy League campus in Manhattan, Obama risked confirming that he is the coastal elitist he’s often accused of being. On that score, it perhaps didn’t help that he shared the stage with fellow honoree Evan Wolfson, founder of Freedom to Marry. The president nodded as Wolfson was hailed for fighting the Boy Scouts’ ban on gay scoutmasters. Barnard President Debora Spar, bestowing a medal on Obama, lauded his support of same-sex marriage and his furthering of “a whole lot smarter world.” More helpful to Obama’s theme was Spar’s praise of his appointment of a “long list of gifted and remarkable women leaders.” Obama had a list of his own — an itemization of the various things he has done for women, from signing the Lilly Ledbetter Fair Pay Act to his appointment of Susan Rice as ambassador to the United Nations. He said that his labor secretary was told by her high school guidance counselor that she “should think about becoming a secretary. . . . And, lo and behold, Hilda Solis did end up becoming a secretary.” The young women applauded and cheered lines about “equal pay for equal work,” controlling “decisions about your own health” and many others. “We are better off when women are treated fairly and equally in every aspect of American life,” Obama told them, urging them to “fight for a seat at the head of the table.” Obama made a fair and at times inspirational argument, but the tone seemed more suited to campaign than campus, particularly when he, toward the end, lifted lines from his stump speech. “If you’re willing to reach up and close that gap between what America is and what America should be,” he said, raising his voice, “I want you to know that I will be right there with you.” The president departed — he had to get to Barbara, Whoopi, Joy, Elisabeth and Sherri — but not before sharing hugs and kisses with the other women onstage. [email protected] ||||| The current issue of Newsweek has a photo of President Obama with a rainbow-colored halo superimposed over his head and the title “The First Gay President.” Nonsense. Obama is not the first gay president. He is the first female president. Consider his activities on Monday: He sat down to tape a session with the ladies of ABC’s “The View” — his fourth appearance on the talk show by women and for (mostly) women. He accepted an award from Barnard College and gave the commencement speech to graduates of the women’s school. Heck, he even appeared in public wearing a gown. Obama was still early in his address when he acknowledged that his praise for the young generation of women is “a cheap applause line when you’re giving a commencement at Barnard.” But Obama was being modest. He didn’t deliver a cheap applause line. He delivered an entire speech full of them. His reelection campaign has been working for months to exploit the considerable gender gap, which puts him far ahead of likely GOP rival Mitt Romney among women. But Monday’s activities veered into pandering, as Obama brazenly flaunted his feminine mystique. He speculated that “Congress would get a lot more done” if more women were there. He speculated that, although no women signed the Constitution, “we can assume that there were founding mothers whispering smarter things in the ears of the founding fathers.” He announced that “more and more women are out-earning their husbands. You’re more than half of our college graduates and master’s graduates and PhDs.” He told them that they are “poised to make this the century where women shape not only their own destiny but the destiny of this nation and of this world.” And they can look good doing it! “You can be stylish and powerful, too,” he said. “That’s Michelle’s advice.” The first lady, the couple’s two daughters, and the president’s mother and mother-in-law had recurring roles as “strong, remarkable women” in the speech. There were some ironies in the appearance. When the White House asked Barnard for the commencement speaking role, the college dumped its original speaker, Jill Abramson. In addition to being an actual woman, Abramson is the first of her sex to become executive editor of the New York Times. Obama made no mention of Abramson, but he did mention that he knows the past three Barnard commencement speakers, including Hillary Rodham Clinton, whose presidential aspirations Obama dashed. Obama was moved to paraphrase an old adage: “Keep your friends close and your Barnard commencement speakers even closer.” In making the appearance on the Ivy League campus in Manhattan, Obama risked confirming that he is the coastal elitist he’s often accused of being. On that score, it perhaps didn’t help that he shared the stage with fellow honoree Evan Wolfson, founder of Freedom to Marry. The president nodded as Wolfson was hailed for fighting the Boy Scouts’ ban on gay scoutmasters. Barnard President Debora Spar, bestowing a medal on Obama, lauded his support of same-sex marriage and his furthering of “a whole lot smarter world.” More helpful to Obama’s theme was Spar’s praise of his appointment of a “long list of gifted and remarkable women leaders.” Obama had a list of his own — an itemization of the various things he has done for women, from signing the Lilly Ledbetter Fair Pay Act to his appointment of Susan Rice as ambassador to the United Nations. He said that his labor secretary was told by her high school guidance counselor that she “should think about becoming a secretary. . . . And, lo and behold, Hilda Solis did end up becoming a secretary.” The young women applauded and cheered lines about “equal pay for equal work,” controlling “decisions about your own health” and many others. “We are better off when women are treated fairly and equally in every aspect of American life,” Obama told them, urging them to “fight for a seat at the head of the table.” Obama made a fair and at times inspirational argument, but the tone seemed more suited to campaign than campus, particularly when he, toward the end, lifted lines from his stump speech. “If you’re willing to reach up and close that gap between what America is and what America should be,” he said, raising his voice, “I want you to know that I will be right there with you.” The president departed — he had to get to Barbara, Whoopi, Joy, Elisabeth and Sherri — but not before sharing hugs and kisses with the other women onstage. [email protected]

– Good news, Barack Obama. You may not be the first black president (that would be Bill Clinton), but you are the first gay one, and apparently the first woman, too. That's how Dana Milbank of the Washington Post is interpreting yesterday's schedule. Eager to exploit his advantage over Mitt Romney with the fairer sex, Obama made his fourth appearance on The View, then gave the commencement speech at the all-female Barnard College. "Heck, he even appeared in public wearing a gown," Milbank quips. Obama praised a generation of young women, acknowledging that it was "a cheap applause line" at Barnard. "But Obama was being modest. He didn't deliver a cheap applause line. He delivered an entire speech full of them." He said Congress would get more done with more women legislators, speculated that "founding mothers" were "whispering smarter things" in the founding fathers' ears, and so on. In Milbank's eyes it "veered into pandering, as Obama brazenly flaunted his feminine mystique." Click for Milbank's full column. (Milbank, incidentally, isn't the first columnist, or even the first Post columnist, to call Obama a woman—Kathleen Parker did it two years ago, and then defended herself thusly).

SECTION 1. SHORT TITLE. This Act may be cited as the ``Caregiver Tax Relief Act of 2008''. SEC. 2. CREDIT FOR TAXPAYERS WITH LONG-TERM CARE NEEDS. (a) In General.--Subpart C of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 (relating to refundable personal credits) is amended by inserting after section 35 the following new section: ``SEC. 35A. CREDIT FOR TAXPAYERS WITH LONG-TERM CARE NEEDS. ``(a) Allowance of Credit.-- ``(1) In general.--There shall be allowed as a credit against the tax imposed by this chapter for the taxable year an amount equal to the applicable credit amount multiplied by the number of applicable individuals with respect to whom the taxpayer is an eligible caregiver for the taxable year. ``(2) Applicable credit amount.--For purposes of paragraph (1), the applicable credit amount shall be $2,500. ``(b) Limitation Based on Adjusted Gross Income.-- ``(1) In general.--The amount of the credit allowable under subsection (a) shall be reduced (but not below zero) by $100 for each $1,000 (or fraction thereof) by which the taxpayer's modified adjusted gross income exceeds the threshold amount. For purposes of the preceding sentence, the term `modified adjusted gross income' means adjusted gross income increased by any amount excluded from gross income under section 911, 931, or 933. ``(2) Threshold amount.--For purposes of paragraph (1), the term `threshold amount' means-- ``(A) $150,000 in the case of a joint return, and ``(B) $75,000 in any other case. ``(3) Indexing.--In the case of any taxable year beginning in a calendar year after 2009, each dollar amount contained in paragraph (2) shall be increased by an amount equal to the product of-- ``(A) such dollar amount; and ``(B) the medical care cost adjustment determined under section 213(d)(10)(B)(ii) for the calendar year in which the taxable year begins, determined by substituting `2008' for `1996' in subclause (II) thereof. If any increase determined under the preceding sentence is not a multiple of $50, such increase shall be rounded to the next lowest multiple of $50. ``(c) Definitions.--For purposes of this section: ``(1) Applicable individual.-- ``(A) In general.--The term `applicable individual' means, with respect to any taxable year, any individual who has been certified, before the due date for filing the return of tax for the taxable year (without extensions), by a physician (as defined in section 1861(r)(1) of the Social Security Act) as being an individual with long-term care needs described in subparagraph (B) for a period-- ``(i) which is at least 180 consecutive days, and ``(ii) a portion of which occurs within the taxable year. Such term shall not include any individual otherwise meeting the requirements of the preceding sentence unless within the 39\1/2\ month period ending on such due date (or such other period as the Secretary prescribes) a physician (as so defined) has certified that such individual meets such requirements. ``(B) Individuals with long-term care needs.--An individual is described in this subparagraph if the individual meets any of the following requirements: ``(i) The individual is at least 18 years of age and-- ``(I) is unable to perform (without substantial assistance from another individual) at least 3 activities of daily living (as defined in section 7702B(c)(2)(B)) due to a loss of functional capacity, or ``(II) requires substantial supervision to protect such individual from threats to health and safety due to severe cognitive impairment and is unable to perform at least 1 activity of daily living (as so defined) or to the extent provided in regulations prescribed by the Secretary (in consultation with the Secretary of Health and Human Services), is unable to engage in age appropriate activities. ``(ii) The individual is at least 6 but not 18 years of age and-- ``(I) is unable to perform (without substantial assistance from another individual) at least 3 activities of daily living (as defined in section 7702B(c)(2)(B)) due to a loss of functional capacity, ``(II) requires substantial supervision to protect such individual from threats to health and safety due to severe cognitive impairment and is unable to perform at least 1 activity of daily living (as so defined) or to the extent provided in regulations prescribed by the Secretary (in consultation with the Secretary of Health and Human Services), is unable to engage in age appropriate activities, ``(III) has a level of disability similar to the level of disability described in subclause (I) (as determined under regulations promulgated by the Secretary), or ``(IV) has a complex medical condition (as defined by the Secretary) that requires medical management and coordination of care. ``(iii) The individual is at least 2 but not 6 years of age and-- ``(I) is unable due to a loss of functional capacity to perform (without substantial assistance from another individual) at least 2 of the following activities: eating, transferring, or mobility, ``(II) has a level of disability similar to the level of disability described in subclause (I) (as determined under regulations promulgated by the Secretary), or ``(III) has a complex medical condition (as defined by the Secretary) that requires medical management and coordination of care. ``(iv) The individual is under 2 years of age and-- ``(I) requires specific durable medical equipment by reason of a severe health condition or requires a skilled practitioner trained to address the individual's condition to be available if the individual's parents or guardians are absent, ``(II) has a level of disability similar to the level of disability described in subclause (I) (as determined under regulations promulgated by the Secretary), or ``(III) has a complex medical condition (as defined by the Secretary) that requires medical management and coordination of care. ``(v) The individual has 5 or more chronic conditions (as defined in subparagraph (C)) and is unable to perform (without substantial assistance from another individual) at least 1 activity of daily living (as so defined) due to a loss of functional capacity. ``(C) Chronic condition.--For purposes of this paragraph, the term `chronic condition' means a condition that lasts for at least 6 consecutive months and requires ongoing medical care. ``(2) Eligible caregiver.-- ``(A) In general.--A taxpayer shall be treated as an eligible caregiver for any taxable year with respect to each of the following individuals: ``(i) The taxpayer. ``(ii) The taxpayer's spouse. ``(iii) An individual who is a qualifying child (as defined in section 152(c)) or a qualifying relative (as defined in section 152(d)) with respect to whom the taxpayer is allowed a deduction under section 151(c) for the taxable year. ``(iv) An individual who would be a qualifying relative described in clause (iii) for the taxable year if section 152(d)(1)(B) were applied by substituting for the exemption amount an amount equal to the sum of the exemption amount, the standard deduction under section 63(c)(2)(C), and any additional standard deduction under section 63(c)(3) which would be applicable to the individual if clause (iii) applied. ``(v) An individual who would be a qualifying relative described in clause (iii) for the taxable year if-- ``(I) the requirements of clause (iv) are met with respect to the individual; and ``(II) the requirements of subparagraph (B) are met with respect to the individual in lieu of the support test of section 152(d)(1)(C). ``(B) Residency test.--The requirements of this subparagraph are met if an individual has as his principal place of abode the home of the taxpayer and-- ``(i) in the case of an individual who is an ancestor or descendant of the taxpayer or the taxpayer's spouse, is a member of the taxpayer's household for over half the taxable year, or ``(ii) in the case of any other individual, is a member of the taxpayer's household for the entire taxable year. ``(C) Special rules where more than 1 eligible caregiver.-- ``(i) In general.--If more than 1 individual is an eligible caregiver with respect to the same applicable individual for taxable years ending with or within the same calendar year, a taxpayer shall be treated as the eligible caregiver if each such individual (other than the taxpayer) files a written declaration (in such form and manner as the Secretary may prescribe) that such individual will not claim such applicable individual for the credit under this section. ``(ii) No agreement.--If each individual required under clause (i) to file a written declaration under clause (i) does not do so, the individual with the highest modified adjusted gross income (as defined in section 32(c)(5) (as in effect on the day before the enactment of the Economic Growth and Tax Relief Reconciliation Act of 2001)) shall be treated as the eligible caregiver. ``(iii) Married individuals filing separately.--In the case of married individuals filing separately, the determination under this subparagraph as to whether the husband or wife is the eligible caregiver shall be made under the rules of clause (ii) (whether or not one of them has filed a written declaration under clause (i)). ``(d) Identification Requirement.--No credit shall be allowed under this section to a taxpayer with respect to any applicable individual unless the taxpayer includes the name and taxpayer identification number of such individual, and the identification number of the physician certifying such individual, on the return of tax for the taxable year. ``(e) Taxable Year Must Be Full Taxable Year.--Except in the case of a taxable year closed by reason of the death of the taxpayer, no credit shall be allowable under this section in the case of a taxable year covering a period of less than 12 months. ``(f) Citizens or Nationals of Other Countries.-- ``(1) In general.--The terms `applicable individual' and `eligible caregiver' do not include an individual who is not a citizen or national of the United States unless such individual is a resident alien (as defined in section 7702(b)). ``(2) Exception for adopted child.--Paragraph (1) shall not exclude any child of a taxpayer (within the meaning of section 151(f)(1)(B)) if-- ``(A) for the taxable year of the taxpayer, the child has the same principal place of abode as the taxpayer and is a member of the taxpayer's household, and ``(B) the taxpayer is a citizen, national, or resident alien of the United States.''. (b) Conforming Amendments.-- (1) Section 6213(g)(2) of such Code is amended by striking ``and'' at the end of subparagraph (L)(ii), by striking the period at the end of subparagraph (M) and inserting ``, and'', and by inserting after subparagraph (M) the following new subparagraph: ``(N) an omission of a correct TIN or physician identification required under section 35A(d) (relating to credit for taxpayers with long-term care needs) to be included on a return.''. (2) The table of sections for subpart C of part IV of subchapter A of chapter 1 of such Code is amended by inserting after the item relating to section 35 the following new item: ``Sec. 35A. Credit for taxpayers with long-term care needs.''. (c) Effective Date.--The amendments made by this section shall apply to taxable years beginning after December 31, 2008.

Caregiver Tax Relief Act of 2008 - Amends the Internal Revenue Code to allow caregivers of family members or dependents with long-term care needs a refundable income-based tax credit of $2,500 for each such family member or dependent.

inclusion criteria were all psychiatric patients planned to undergo ect , willing / fit to give consent , and without any medical / neurological comorbidity . patients with a past history of psychiatric illness , coexisting medical / central nervous system illness , while on medication affecting cognition ( other than psychotropic medication ) , and unwilling for the study were excluded . sociodemographic pro forma was administered to assess the demographic , family , clinical , and social domains of participants . in addition , becks depression inventory ( bdi ) and brief psychiatric rating scale ( bprs ) were used to measure the severity of depression and psychosis , respectively . retest reliability ( pearson r = 0.93 ) and an internal consistency of = 0.91 . bprs is a 16-item rating scale to measure positive symptoms , general psychopathology , and affective symptoms . trail making test was used to assess nonmemory cognition in processing speed and executive functioning . trail making test has two parts : a and b. a is used primarily to examine cognitive processing speed . b , in which the subject alternates between numbers and letters , is used to examine executive functioning . patients were evaluated clinically , started on psychopharmacological treatment , and decision to administer ect was taken purely on clinical indications for the same . common indications were suicidal ideation , catatonic features , lack of self - care , etc . as it was a clinical research , the choice of medication was made entirely on clinical requirement and psychiatrist preference . all subjects received twice weekly , modified , bi - temporal ect by brief pulse machine . the entire anesthetic procedure was supervised by an anesthetist and ect administration by a psychiatrist . thiopentone , atropine , and succinyl choline were used during all ect procedures in the recommended dosage . seizure of adequate duration was produced under anesthesia and vital parameters were monitored till resumption of full consciousness . assessment of severity of illness and performance on trail - making test was done at baseline , after a course of ect , and after 4 weeks of ect . the resultant means and standard deviations ( sds ) at the three points in time were compared statistically . mean years of schooling was more than 12 years ( median - 12 years ) . about 81% of the subjects had diagnosis of depression and the rest were had nonaffective psychotic disorders . mean score on depression severity on bdi was 31.32 ( sd - 2.33 ) ; which is severe . score of psychosis on bprs was also higher ( 90.71 , sd - 2.81 ) . scores on depression and psychosis improved statistically over the course of treatment [ table 1 ] . there was an improvement in both the trail - making tests over the course of treatment at all points in trail - making test a. in trail - making test b , though there was statistical improvement in score from the baseline to after a course of ect , the same did not show any statistical change thereon [ table 2 ] . effects of electroconvulsive therapy on disease profile from baseline to four weeks of treatment effects on electroconvulsive therapy on nonmemory cognition across from baseline to four weeks of electroconvulsive therapy our study showed that there was an improvement in nonmemory cognition . processing speed and executive functioning improved over the course of treatment from before the ect procedure to that of after the procedure . this could be due to effects of ect , effects of other prescribed drugs , due to improvement of illness which might have caused temporary cognitive impairment , or a natural course in the process of the mental illness . a randomized study using a sham control while controlling the confounding factors would bring out those factors which are responsible for these changes in nonmemory cognition in a more specific manner . the above finding negates the notion and clears the ambiguity that the ect affects the nonmemory cognition in an adverse manner . argued that as ect affects both frontal and temporal lobe , it is expected that the cognitive effects of the same would also encompass both memory and the nonmemory components . deficits in executive functions and other related nonmemory cognition have been found by the earlier researchers in this field . however , no long - term controlled studies have been done to find out whether the nonmemory cognitive functions normalizes or not and if so when . getz et al . noted that the objective function of the individual improved after the ect even though the individual persisted with subjective complaints of impairment . studied the effect of sine and pulse waveforms on the aspects of memory and nonmemory cognition on an average of 8.2 days after the last ect . aspects of nonmemory cognitions such as processing speed and executive functions improved over the course of treatment from before ect to after ect . a control population without ect or with sham ect would have brought more clarity and is recommended . all patients were included in this study irrespective of the type of drugs they were on . however , as ect is not the first line of treatment ; it is not possible to have drug - naive population in clinical research . clinical indication for ect was as per the treating psychiatrist and there was no standardization done in this direction . an empirical study keeping the above limitations in mind will add further merit to the subject . this study being purely an observation one limits the specificity of finding . a control population without ect or with sham ect would have brought more clarity and is recommended . all patients were included in this study irrespective of the type of drugs they were on . however , as ect is not the first line of treatment ; it is not possible to have drug - naive population in clinical research . clinical indication for ect was as per the treating psychiatrist and there was no standardization done in this direction . an empirical study keeping the above limitations in mind will add further merit to the subject .

introduction : possibility of cognitive side effects has made electroconvulsive therapy ( ect ) questionable . variable deficits have been debated in memory cognition . pattern of changes in nonmemory cognition pre- and post - ect is not clear.methodology:forty patients undergoing ect were studied on nonmemory cognitive parameters before ect , after a course of ect , and after 4 weeks of last . ect.results:nonmemory cognition improved during the course of ect and over 4 weeks of ect.conclusions:ect does not affect the nonmemory cognition adversely .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Raechel and Jacqueline Houck Safe Rental Car Act of 2012''. SEC. 2. APPLICATION OF MOTOR VEHICLE SAFETY STANDARDS TO CAR RENTAL COMPANIES. (a) Covered Rental Vehicle and Rental Company Defined.--Section 30102(a) of title 49, United States Code, is amended-- (1) by redesignating paragraphs (1) through (11) as paragraphs (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), and (13), respectively; (2) by inserting before paragraph (2) (as so redesignated) the following: ``(1) `covered rental vehicle' means a motor vehicle that-- ``(A) is rated at 26,000 pounds gross vehicle weight or less; ``(B) is rented without a driver for an initial term of less than 4 months; and ``(C) is part of a motor vehicle fleet of 5 or more motor vehicles that is used for rental purposes by a rental company.''; and (3) by inserting after paragraph (10) (as so redesignated) the following: ``(11) `rental company' means a person who-- ``(A) is engaged in the business of renting covered rental vehicles; and ``(B) uses for rental purposes a motor vehicle fleet of 5 or more covered rental vehicles.''. (b) Notification by Rental Companies to Renters.-- (1) In general.--Section 30119 of such title is amended by adding at the end the following: ``(g) Notification by Rental Company to Renter.--A rental company that receives a notification required under section 30118 of this title that includes the vehicle identification number of a covered rental vehicle during a period in which the vehicle is rented shall, as soon as practicable, contact the renter of the vehicle and any authorized driver of the vehicle for whom the rental company has immediate contact information to inform the renter and authorized driver of the defect or noncompliance.''. (2) Regulations.--The Secretary of Transportation may not begin any process to promulgate regulations under subsection (g) of such section, as added by paragraph (1), until the date that is 3 years after the date of the enactment of this Act. (c) Limitation on Sales, Leases, or Rentals by Rental Companies.-- Section 30120(i) of such title is amended-- (1) in paragraph (1)-- (A) in the matter preceding subparagraph (A)-- (i) by inserting ``, or the manufacturer has provided to a rental company notification about a covered rental vehicle (including the vehicle identification number for such vehicle) in the company's possession at the time of notification,'' after ``time of notification''; and (ii) by striking ``the dealer may sell or lease'' and inserting ``the dealer or rental company may sell, lease, or rent''; and (B) in subparagraph (A), by striking ``under the sale or lease'' and inserting ``under the sale, lease, or rental agreement''; (2) in paragraph (2), by inserting ``or rental company'' after ``a dealer''; and (3) in the subsection heading by striking ``or Lease'' and inserting ``, Lease, or Rental''. (d) Prohibition on Making Safety Devices and Elements Inoperative.--Section 30122(b) of such title is amended by inserting ``rental company,'' after ``dealer,'' both places it appears. (e) Inspections, Investigations, and Records.-- (1) Matters that can be inspected and impoundment.-- Subsection (c)(2) of section 30166 of such title is amended by striking ``or dealer'' both places it appears and inserting ``dealer, or rental company''. (2) Records and making reports.--Subsection (e) of such section is amended by striking ``or dealer'' each place it appears and inserting ``dealer, or rental company''. (3) Providing copies of communications about defects and noncompliance.--Subsection (f) of such section is amended by inserting ``rental companies or other'' after ``dealers or to''. (f) Research Authority.--The Secretary of Transportation may conduct a study of the effectiveness of the amendments made by this section and of other activities of rental companies (as defined in section 30102(a) of title 49, United States Code, as added by subsection (a)(2)) related to their use and disposition of motor vehicles that are the subject of a notification required under section 30118 of title 49, United States Code. (g) Effective Date.--The amendments made by this section shall take effect on the date that is 60 days after the date of enactment of this Act.

Raechel and Jacqueline Houck Safe Rental Car Act of 2012 - Requires a rental company that receives a Secretary of Transportation (DOT) ordered notification from the manufacturer of a covered rental vehicle of equipment defect, or noncompliance with federal motor vehicle safety standards, during the vehicle rental period to contact the renter and any authorized driver of the vehicle about the defect or noncompliance. Covers a rental vehicle: (1) rated at 26,000 pounds gross vehicle weight or less, (2) rented without a driver for an initial term of under 4 months, and (3) that is part of a motor vehicle fleet of 5 or more motor vehicles used for rental purposes by a rental company. Authorizes a rental company that receives notification of a defect or the noncompliance of a new vehicle or new replacement vehicle equipment in the company's possession to rent such vehicle or equipment only if the defect or noncompliance is remedied. Prohibits a rental company from knowingly making inoperable any safety devices or elements of design installed on or in a compliant motor vehicle or vehicle equipment unless the company reasonably believes such vehicle or equipment will not be used when the devices or elements are inoperable. Authorizes the Secretary, upon request, to inspect records of a rental company with respect to a safety investigation. Authorizes the Secretary to require a rental company to keep records or make reports for purposes of compliance with federal motor vehicle safety orders or regulations. Authorizes the Secretary to study the effectiveness of the amendments made by this Act and of other activities of rental companies.

radio - frequency ( rf ) spectroscopy is widely applied to many experiments on atoms or molecules , for which an exquisite energy resolution can be achieved . this is due to the magnetic coupling nature of the rf transition and the associated long coherence time of the systems . in recent experiments on ultracold weakly - bound molecules , rf spectroscopy also allows a precise determination of the molecular binding energy @xcite and the pairing gap in a degenerate fermi gas @xcite . in the latter case , the high energy resolution reveals the fermionic nature of the pairing in the bardeen - cooper - schrieffer ( bcs ) regime . in this article we investigate theoretically the radio - frequency excitation spectrum of ultracold molecules . previous experimental work in this regime shows that molecules are dissociated upon receiving the rf photons @xcite . the associated bound - free excitation lineshape is characteristically broader and highly asymmetric compared to that for atoms . here , we provide an intuitive picture to model and derive a simple analytic formula for the excitation rates and the lineshapes . we show that much information regarding cold collision properties can be extracted from the lineshape . in particular , the spectrum is very sensitive to tuning a feshbach resonance in the final state scattering continuum , where the rf spectra will evolve into two components : a bound - bound transition to the newly formed molecular state and a remaining weaker bound - free transition . our analytic results provide excellent fits to both the numerical calculations and the experimental measurements from the innsbruck group @xcite . we argue that radio - frequency spectroscopy on cold molecules has several advantages in probing ultracold collision properties over the conventional collision measurements . these include a high energy resolution , the flexibility to probe different channels and its insensitivity to the sample density and temperature . in this paper , we first introduce our model and derive the lineshape ( sec . we then compare our results to the numerical calculation ( sec . iii ) and discuss the spectral feature ( sec . iv ) . finally , we compare our results to the experimental data ( sec . we consider a weakly - bound molecule in the state @xmath0 . the bound state consists of two atoms with binding energy @xmath1 relative to the dissociation continuum @xmath2 @xcite . here @xmath3 is planck s constant , @xmath4 is the reduced mass of the two atoms , @xmath5 is the scattering length in the scattering channel @xmath2 and @xmath6 is the interaction range of the van der waal potential , which varies with interatomic separation @xmath7 as @xmath8 : @xmath9 for weakly - bound molecules , we assume @xmath10 . the molecule is initially at rest and a radio - frequency photon with energy @xmath11 couples the molecule to a different channel @xmath12 , characterized by the scattering length @xmath13 . for @xmath14 , the final state is a continuum and the excited molecule dissociates ; for @xmath15 , a stable bound state @xmath16 is also available in the final state channel and the molecule can either dissociate or be driven to the bound state @xmath16 . in the following , we assume that both scattering channels are in the threshold regime ( @xmath5 , @xmath17 ) . atoms , bound or unbound , then have the same internal wavefunction . we also assume the relative energy of the continuum threshold to be @xmath18 . first , we consider the bound - free transition . energy conservation gives @xmath19 where @xmath20 is the kinetic energy of the outgoing wave and @xmath21 is the associated wavenumber . for @xmath22 , the transition is forbidden . for @xmath23 , the bound - free transition rate from the initial state @xmath0 to the final state @xmath24 is given by the fermi s golden rule : @xmath25 where @xmath26 is the bound - free franck - condon factor per unit energy , @xmath27 is the rf interaction for the rf rabi frequency @xmath28 , @xmath29 is the bound molecular wavefunction in channel @xmath2 , and @xmath30 is the energy - normalized s - wave scattering wavefunction in channel @xmath12 @xcite . we can evaluate the bound - free franck - condon factor @xmath31 based on the asymptotic behavior of the wavefunctions . @xmath32 where @xmath33 is the scattering phase shift in channel a. combining eqs . ( [ ffk ] ) , ( [ psikr ] ) and ( [ phimr ] ) , we have @xmath34 since @xmath35 , we can use the low energy expansion of the scattering phase shift @xcite , @xmath36 where the effective range @xmath37 depends on the scattering length @xmath13 and the interaction range @xmath6 . the explicit form of @xmath37 for a van der waals potential is given in ref . @xcite in the limit @xmath38 : @xmath39 by taking the leading term in the expansion in eq . ( [ kcotd ] ) and expressing @xmath40 and @xmath41 , we derive a simple and very useful form of the lineshape , @xmath42 in the limit @xmath43 , where @xmath44 , we have @xmath45 , which is the wigner threshold regime . the transition rate peaks between @xmath46 for @xmath47 and @xmath48 for @xmath49 and decreases to higher @xmath50 . for very large @xmath51 , eq . ( [ kcotd ] ) is no longer valid . a few extreme situations including @xmath52 , where @xmath53 vanishes and @xmath54 , where the wigner threshold law fails , will be discussed in later sections . the integrated rf line strength @xmath55 is given by @xmath56 the unit franck - condon factor for @xmath14 means that within the approximations we made , the molecular wavefunction @xmath29 is fully expanded by the scattering states @xmath24 . for @xmath15 , we have @xmath57 , which implies there are additional outgoing channels . this is because the additional bound - bound transition process is opened for @xmath15 . for positive scattering length in the outgoing channel @xmath58 , a weakly - bound molecular state @xmath0 exists . bound - bound transitions are allowed . from energy conservation , we have @xmath59 effectively , @xmath60 . the bound - bound franck - condon factor @xmath61 can be calculated similar to eqs . ( [ gfk ] ) and ( [ ffk ] ) . @xmath62 where we have used the molecular wavefunction in eq . ( [ phimr ] ) for both @xmath0 and @xmath16 states and have introduced the @xmath63-function to provide energy normalization analogous to that of @xmath64 . the bound - bound line strength is then @xmath65 . note that sum of the bound - bound and bound - free integrated line strengths is identically one for @xmath15 , as expected from the wavefunction projection theorem : @xmath66 we check the validity of the above analytic formulas by comparing them to a numerical calculation . we choose fermionic @xmath67li atoms as our model system , for which the interaction parameters are precisely known by fitting various cold atom and molecule measurements to a multichannel quantum scattering calculation @xcite . the energy structure and the scattering lengths in the two relevant channels @xmath68 and @xmath69 are shown in fig . [ fig1 ] . here , @xmath70 refers to the state with one atom in state @xmath71 and one in @xmath72 , and @xmath73 refers to the lowest @xmath74th internal state in the @xmath67li atom ground state manifold . li@xmath75 in the @xmath76 and @xmath70 channels ( dotted lines ) . all energies are referenced to the @xmath70 scattering threshold . in these two channels , feshbach couplings induce the formation of molecules ( solid lines ) below 69.1mt and 83.5mt , respectively . arrows show the bound - bound and bound - free transitions based on molecules in the @xmath70 channel . the lower figure shows the scattering lengths in the two channels.,width=264 ] to calculate the scattering phase shifts , we construct a reduced single - channel hamiltonian to describe the @xmath76 continuum . the phase shifts from this model are nearly indistinguishable from those from the full multichannel calculations in this range of @xmath77-fields . the van der waals interaction is set to @xmath78a.u . @xcite , yielding an interaction range of @xmath79 . the scattering lengths are set to match the values from the multi - channel calculation . the resulting scattering phase shifts from the calculation are compared with the effective range expansion given in eq . ( [ kcotd ] ) ( see fig . [ fig2 ] ) . here , the scattering parameters are based on the @xmath76 scattering states at 72.0mt with a scattering length of @xmath80 . the result shows the expected behavior that @xmath81 provides an excellent fit at low scattering energy @xmath82 k and the effective range correction works up to @xmath83mk . here @xmath84 is boltzman s constant . ) with ( solid line ) and without ( dashed line ) the effective range correction . the scattering parameters are based on @xmath67li in the @xmath76 channel near 72.0mt with @xmath85.,width=264 ] we also compare the franck - condon factors obtained from the numerical calculation and from eq . ( [ ffkfinal ] ) . the numerical calculation is based on an initial bound state in the @xmath70 channel and the final state @xmath76 continuum , described by the reduced hamiltonian . we show the calculations at two magnetic fields of 72.0mt and 68.0mt , where the scattering parameters are set according to the multichannel calculations . the results show that eq . ( [ ffkfinal ] ) provides an excellent fit to the full bound - free spectra , see fig . [ fig3 ] . ) ( solid line at 72.0mt and dotted line at 68.0mt ) . the parameters are @xmath86k and @xmath87 at 68.0mt ; @xmath88k and @xmath80 at 72.0mt.,width=264 ] the appearance of the bound - bound transition for only @xmath15 seems to suggest a distinct behavior in rf excitation near the feshbach resonance where the scattering length changes sign . in this section , we show that the evolution of the rf spectrum is actually continuous when a @xmath77-field is tuned through the resonance position . we use eq . ( [ ffkfinal ] ) andeq . ( [ fbk ] ) to show the bound - free and bound - bound spectra in the vicinity of a feshbach resonance . . for the bound - free transition , the franck - condon factor is plotted as a function of @xmath89 . curves of different @xmath90 are offset and shown in the order of that near a feshbach resonance in the @xmath12 channel . ( dotted line for the resonance condition ) for @xmath15 , the locations of the bound - bound transitions are indicated by the sharp peaks . notably , bound - free transition vanishes at @xmath91.,width=264 ] figure [ fig4 ] shows a continuous change near a feshbach resonance from a bound - free lineshape for @xmath14 to a combination of bound - bound and bound - free transitions for @xmath15 . when the scattering length approaches negative infinity , the linewidth of the bound - free lineshape approaches zero as @xmath92 and `` evolves '' into the bound - bound delta function . remarkably , for @xmath15 , the bound - free transition is much weaker . at @xmath91 , the bound - free transition is fully suppressed , @xmath93 . the vanishing bound - free transition for @xmath94 can be understood by the wavefunction overlap given in eq . ( [ ffk ] ) . as a positive scattering length @xmath13 indicate a zero in wavefunction near @xmath95 , the sign change of the scattering wavefunction results in a cancellation in the overlap . alternatively , we may consider the transition amplitude to the continuum @xmath12 is exactly cancelled by the feshbach coupling between molecular state @xmath16 and the continuum @xmath12 . this interference effect results in the fano - like profile of the peak transition rate near a feshbach resonance @xcite ( see fig . [ fig5 ] ) . on the other hand , the bound - bound franck - condon factor approaches one when @xmath94 , since both molecular wavefunction are identical for @xmath96 . the peak bound - free transition rates therefore shows a strong asymmetry with respect to the sign of the scattering length , shown in fig . [ fig5 ] . . the peak franck - condon factors with @xmath97 are calculated for different @xmath98 based on eq . ( [ ffkfinal ] ) . near the feshbach resonance , @xmath98 approaches zero.,width=264 ] based on the above features , the rf spectroscopy does provides a new strategy to extract various important scattering parameters . in particular , while cold collision measurements are generally insensitive to the sign of the scattering length , our rf excitation spectroscopy is drastically different for the two cases and provides a new tool to probe the scattering properties . to compare with the experimental result , we take @xmath67li as a model system and calculate the rf spectra . the experimental spectra are obtained from the li group in innsbruck @xcite . adopting the convention used in ref.@xcite , we define the rf offset energy as @xmath99 . using eq . ( [ ffkfinal ] ) , we can rewrite the franck - condon factors as @xmath100 we compare the theoretical curves with the experiment in fig . an integration bandwidth of 1khz is assumed . when the magnetic field approaches 69.1mt from high values , the molecular binding energy @xmath101 in the @xmath70 channel increases ( see fig . [ fig1 ] ) . this dependence is shown in fig . [ fig6 ] as the whole excitation line moves toward higher frequency . at the same time , the lineshape becomes sharper due to the feshbach resonance in @xmath76 channel at 69.1mt . below 69.1mt , we expect both bound - free and bound - bound transitions are allowed . at 68.4mt , these two components coexist , but can not be clearly distinguished due to the small binding energy of @xmath102khz , lower than the experimental resolution of @xmath103khz . at 67.6mt and 66.1mt , the bound - free transitions are strongly suppressed . the bound - bound transition then shows up as the dominant component in the spectra . the excellent agreement between the experiment and the calculation over a large range of magnetic fields is remarkable . this result strongly suggests that the rf molecular spectroscopy can be used for a precision determination of the atomic interaction parameters @xcite . li@xmath75 molecule at different magnetic field values . theoretical curves are based on eq . ( [ expfcf1 ] ) and eq . ( [ expfcf2 ] ) with the binding energies and scattering lengths obtained from the multichannel calculation . to shown both the bound - free and bound - bound spectra , an integration bandwidth of 1khz is assumed . rf - induced loss on the molecular population at 76.4mt ( solid squares ) , 72.0mt ( open squares ) , 69.5mt ( solid circles ) , 68.4mt ( open circles ) , 67.6mt ( solid diamonds ) and 66.1mt ( open diamonds ) are re - scaled . experiment data are from the grimm s group in innsbruck.,width=264 ] we model and evaluate the radio - frequency excitation rates on weakly - bound ultracold molecules in the threshold regime . we derive a simple and analytic form of the bound - free and bound - bound spectral profiles which provide an excellent fit to both the numerical calculation and the recent rf measurements on li@xmath75 molecules . an interesting case is studied when a feshbach resonance occurs in the outgoing channel . we show that the bound - free spectra in the absence of a bound state smoothly evolves into a combination of bound - bound and bound - free spectra when the bound state formed near a feshbach resonance . the bound - free transition rate strongly depends on the sign of the scattering length and shows a fano - like structure near the resonance . we like to point out that the rf spectroscopy based on weakly - bound molecules can be an excellent tool to determine the long - range interaction properties with high precision . from the excitation spectra , the molecular binding energies , the atomic scattering lengths and their signs , and the scattering phase shifts can be determined . furthermore , in contrast to conventional cold collision measurements , rf transitions on molecules are insensitive to the sample density and temperature , can probe different scattering channels by tuning the rf frequency to different states , and can be implemented instantly without thermalization . finally , rf transitions between molecular states may also provide a new avenue to transfer the molecular population to low - lying molecular states . we thank r. grimm s li group in innsbruck for providing the experimental data and stimulating discussions . julienne would like to thank the office of naval research for partial support . c.c . is a lise - meitner research fellow of the austrian science fund . c. regal , d. jin , phys . * 90 * , 230404 ( 2003 ) ; c. a. regal , c. ticknor , j. l. bohn , d. s. jin , nature * 424*. c. chin , m. bartenstein , a. altmeyer , s. riedl , s. jochim , , j. hecker denschlag , and r. grimm , cond - mat/0405632 , published online jul . 22 , 2004 ( science express ) . m. bartenstein , a. altmeyer , s. riedl , r. geursen , s. jochim , c. chin , j. hecker denschlag , r. grimm , a. simoni , e. tiesinga , c. j. williams , and p. s. julienne , in preparation . gribakin and v.v . flambaum , phys . a * 48 * , 546 ( 1993 ) . n. f. mott and h.s.w . massey , _ the theory of atomic collisions _ , ( clarendon press , oxford ) 1965 . b. gao , phys . rev . a , * 62 * , 050702(r ) ( 2000 ) . julienne and f.h . mies , phys . a * 30 * , 831 ( 1984 ) . u. fano , phys . rev . * 124 * , 1866 ( 1961 ) z.c . yan , j.f . babb , a. dalgarno , and g.w.f . drake , phys . a * 54 * , 2824 ( 1996 ) .

we show that radio - frequency spectroscopy on weakly - bound molecules is a powerful and sensitive tool to probe molecular energy structure as well as atomic scattering properties . an analytic expression of the rf excitation lineshape is derived , which in general contains a bound - free component and a bound - bound component . in particular , we show that the bound - free process strongly depends on the sign of the scattering length in the outgoing channel and acquires a fano - type profile near a feshbach resonance . the derived lineshapes provide an excellent fit to both the numerical calculation and the experimental measurements .

the hypercp collaboration recently observed three events for the rare decay mode @xmath7 with dimuon invariant masses narrowly clustered around 214.3mev @xcite . it is possible to account for these events within the standard model ( sm ) when long - distance contributions are properly included @xcite . however , the probability that the three events have the same dimuon mass , given the sm predictions , is less than one percent . this result has prompted several studies investigating the consequences of a new state with this mass @xcite . in particular , it was pointed out that the flavor - changing coupling of the new state to @xmath8 has to be ( dominantly ) of a pseudoscalar or axial - vector nature to explain why it has not been seen in @xmath9 . this would still allow the new particle to be observed in the other rare modes @xmath10 and @xmath11 . predictions for the new particle s contributing to these modes , consistent with existing constraints , were made in refs . these predictions indicate that there could be evidence for the particle in the data already taken by the ktev collaboration , specifically in the mode @xmath12 currently being studied @xcite . beyond the above - mentioned theoretical analyses , to explore the possible consequences of the hypercp result in greater detail one has to incorporate some model dependence . to this end , various ideas have been proposed in the literature @xcite . specifically , we have demonstrated that a light pseudoscalar higgs boson in the next - to - minimal supersymmetric standard model ( nmssm ) , the @xmath0 , could be identified as the possible new particle responsible for the hypercp events while satisfying all constraints from kaon and @xmath13-meson decays @xcite . now , it is long known that kaon decays involving a light higgs boson , such as in the nmssm , receive two types of contributions that can be of comparable size : two - quark contributions in which the flavor change occurs in one - loop processes involving the light @xmath0 , and four - quark contributions in which the flavor change occurs via a tree - level standard - model @xmath14 exchange with the light @xmath0 radiated off one of the light quarks @xcite . not too long ago , we showed that the same situation occurs in the case of light higgs production in hyperon decays @xcite . in this paper we revisit the modes @xmath15 and @xmath5 in order to present a complete prediction within the model suggested in ref . @xcite , plus the possible modifications recently pointed out in ref . this differs from the model - independent studies of refs . @xcite in two important ways . within the nmssm , we can identify the effective scalar and pseudoscalar couplings of the model - independent studies with specific one - loop processes . here we consider not only the chargino - mediated diagrams of refs . @xcite , but also the gluino- and neutralino - mediated diagrams discussed in ref . @xcite . in addition , we include the four - quark contributions which are missing in refs . these four - quark contributions were shown in ref . @xcite to be essential to evade the bounds arising from the nonobservation of the @xmath0 in @xmath9 modes @xcite . following our earlier work @xcite , we will here assume that @xmath16 , additional processes where such a light @xmath0 would appear have been recently studied in the literature : collider signatures for a light @xmath17 @xcite , @xmath13-meson decays @xcite , and radiative quarkonium decays @xcite . the latter are especially useful because , being flavor conserving , they are independent of the specifics of the one - loop flavor - changing couplings and follow directly from the tree - level couplings of the @xmath0 to down - type quarks . finally , in this paper we also consider the modes @xmath3 which , like radiative quarkonium decays , are flavor diagonal and only sensitive to the tree - level couplings of the @xmath0 . the prediction for these modes is , therefore , much less model - dependent . we find a rate two orders of magnitude larger than the corresponding sm rate , that could be probed at da@xmath4ne . in this section , we briefly review some features of the nmssm that are relevant to our study . the model is an extension of the minimal supersymmetric standard model ( mssm ) and provides a solution to the so - called @xmath18-problem of the mssm @xcite . in the nmssm , there is a gauge - singlet higgs field @xmath19 in addition to the two higgs fields @xmath20 and @xmath21 responsible for the up- and down - type quark masses in the mssm . as a result , the physical spectrum of the extended model has two additional neutral higgs bosons : one a scalar and the other a pseudoscalar . we follow the specific model described in ref . @xcite , with suitable modifications . the superpotential of the model is given by @xmath22 where @xmath23 , @xmath24 , @xmath25 , @xmath26 , and @xmath27 represent the usual quark and lepton fields , @xmath28 are the yukawa couplings , and @xmath29 and @xmath30 are dimensionless parameters . the soft - supersymmetry - breaking term in the higgs potential is @xmath31 and the resulting higgs potential has a global @xmath32 symmetry in the limit that the parameters @xmath33 @xcite . the nmssm has two physical @xmath34-odd higgs bosons which are linear combinations of the pseudoscalar components in @xmath35 , @xmath36 , and @xmath19 in the model mix , with the @xmath0 being the lighter mass - eigenstate with mass given by @xmath37 in the large-@xmath38 limit , where @xmath39 is the vacuum expectation value of @xmath19 and @xmath38 is the ratio of vacuum expectation values ( vevs ) of the two higgs doublets . if the @xmath32 symmetry is broken slightly , the mass of @xmath17 becomes naturally small , with values as low as @xmath40100mev phenomenologically allowed @xcite . in the large-@xmath38 limit , the @xmath0 is mostly the singlet pseudoscalar and couples to sm fields through mixing . also in the large-@xmath38 limit , its couplings to fermions are suppressed by a factor of @xmath38 with respect to those of the @xmath41 in the mssm @xcite . in particular , this makes the tree - level couplings to up - type quarks negligible . the tree - level couplings to down - type quarks and charged leptons can be described in terms of one parameter , @xmath42 where the parameter @xmath43 involves both the different higgs vevs and soft - supersymmetry - breaking parameters , @xmath44 with @xmath45gev being the electroweak scale and @xmath46 . requiring the mass of the heavier pseudoscalar not to exceed 500gev , ref . @xcite finds a lower bound @xmath47 for @xmath48 . at the same time , the contribution of @xmath0 to the muon anomalous magnetic moment results in an upper bound @xmath49 @xcite . as shown in ref . @xcite , this scenario leads to four - quark contributions that easily reproduce the hypercp result . unfortunately , they are also in conflict with the nonobservation of the @xmath0 in @xmath9 @xcite . to satisfy these bounds , it is necessary to include contributions from one - loop flavor - changing diagrams in the nmssm , which depend in a complicated way on the many parameters of the model . we can describe them in terms of an effective lagrangian for the @xmath50 couplings as @xmath51 where the parameters @xmath52 are generally independent . in ref . @xcite , we followed ref . @xcite to consider only chargino - mediated one - loop diagrams in the large-@xmath38 limit . furthermore , we selected the supersymmetric parameters so as to suppress the @xmath53 transition and in this way satisfy the nonobservation of @xmath0 in @xmath13 decay @xcite . this scenario led to @xmath54 with @xmath55 @xcite . more recently , ref . @xcite has pointed out a different scenario in which @xmath56 also receive contributions from gluino- and neutralino- mediated one - loop diagrams . although the gluino - mediated contributions are suppressed by a factor of @xmath38 compared to the chargino contributions , the former are proportional to the strong coupling @xmath57 , compensating for the suppression factor , and hence can be as important as the latter . moreover , in some regions of the parameter space the neutralino - mediated contributions could be comparable to the gluino - mediated ones @xcite . if all the different contributions are similar in size , then @xmath56 can become effectively independent . this opens up the possibility of satisfying the kaon bounds without the four - quark contributions by having @xmath58 , which results in an effective @xmath50 coupling that is mostly pseudoscalar . the hypercp observation can then be explained as in the model - independent analysis of refs . however , to have @xmath58 requires some sort of fine tuning . furthermore , the four - quark contributions may not necessarily be negligible . in our analysis , we will thus keep @xmath59 and @xmath60 independent and constrain them with data . also , we will assume that @xmath34 is conserved and hence @xmath56 are real . to evaluate hadronic amplitudes induced by the @xmath62 interactions , we employ chiral perturbation theory ( @xmath63pt ) . thus , the leading - order chiral realization of @xmath64 above is @xmath65 in eq . ( [ la ] ) in appendix [ lags ] , which also contains other relevant chiral lagrangians . from @xmath65 and the chiral strong lagrangian @xmath66 in eq . ( [ ls ] ) , we derive the leading - order diagrams shown in fig . [ 2qdiag ] for @xmath67 and @xmath5 . the resulting amplitudes are @xmath68 @xmath69 @xmath70 where @xmath71 . the same lagrangians also yield @xmath72 @xmath73 previously derived in refs . hence we also adopt @xmath74 . ( 90,90)(-45,-40 ) ( -33,0)[]@xmath75 ( -25,0)(25,0 ) ( 0,-20)(0,20 ) ( 0,25)[]@xmath76 ( 0,-24)[]@xmath76 ( 32,0)[]@xmath0 ( 0,0)(4,4 ) ( 2,90)(-1,-40 ) ( 0,-30)[](a ) ( 120,90)(-50,-40 ) ( -33,0)[]@xmath75 ( -25,0)(55,0 ) ( 0,-20)(0,20 ) ( 0,25)[]@xmath76 ( 0,-24)[]@xmath76 ( 15,6)[]@xmath77 ( 62,0)[]@xmath0 ( 30,0)(4,4 ) ( 0,0)2 ( 150,90)(-80,-30 ) ( -38,0)[]@xmath78 ( -30,0)(30,0 ) ( 0,0)(0,40 ) ( 7,10)[]@xmath79 ( 0,45)[]@xmath0 ( 38,0)[]@xmath80 ( 0,20)(4,4 ) ( 0,0)2 ( 0,-20)[](b ) from @xmath81 given in appendix [ lags ] , we obtain the leading - order diagrams shown in figs . [ 4qdiag ] and [ 4qdiag ] for @xmath67 and @xmath5 . the resulting amplitudes are @xmath82 @xmath83 @xmath84 where the expressions for @xmath85 and @xmath86 have been collected in appendix [ mi ] , and @xmath87 is related in @xmath63pt to the dominant @xmath88-wave amplitude for @xmath89 by @xmath90 . hence the @xmath89 data yields @xmath91 . we note that the @xmath92 contributions to @xmath93 cancel completely , which is expected due to the fact that the @xmath92 terms in @xmath94 could be rotated away if the baryonic part were absent @xcite . we also note that the @xmath92 contribution to @xmath89 appears only at next - to - leading order . ( 80,90)(-40,-50 ) ( -26,0)[]@xmath75 ( -20,0)(20,0 ) ( 0,-20)(0,20 ) ( 0,24)[]@xmath76 ( 0,-24)[]@xmath76 ( 26,0)[]@xmath0 ( 0,0)(4,4)blackblack ( 110,90)(-40,-50 ) ( -26,0)[]@xmath75 ( -20,0)(50,0 ) ( 0,0)2 ( 0,-20)(0,20 ) ( 0,24)[]@xmath76 ( 0,-24)[]@xmath76 ( 15,5)[]@xmath75 ( 56,0)[]@xmath0 ( 30,0)(4,4)blackblack ( 80,90)(-40,-50 ) ( -26,0)[]@xmath75 ( -20,0)(20,0 ) ( 0,0)2 ( 0,-20)2 ( 0,-40)(0,20 ) ( 0,24)[]@xmath76 ( 0,-44)[]@xmath76 ( 5,-10)[]@xmath75 ( 26,0)[]@xmath0 ( 0,-20)(4,4)blackblack ( 110,90)(-40,-50 ) ( -26,0)[]@xmath75 ( -20,0)(50,0 ) ( 15,5)[]@xmath95 ( 0,-40)(0,20 ) ( 0,24)[]@xmath76 ( 0,-44)[]@xmath76 ( 5,-10)[]@xmath75 ( 56,0)[]@xmath0 ( 0,-20)(4,4)blackblack ( 0,0)2 ( 0,-20)2 ( 30,0)2 ( 110,90)(-40,-50 ) ( -26,0)[]@xmath75 ( -20,0)(50,0 ) ( 15,5)[]@xmath95 ( 30,-20)(30,20 ) ( 30,24)[]@xmath76 ( 30,-24)[]@xmath76 ( 56,0)[]@xmath0 ( 0,0)(4,4)blackblack ( 30,0)2 + ( 120,70)(-40,-35 ) ( -26,0)[]@xmath75 ( -20,0)(50,0 ) ( 0,-20)(0,20 ) ( 0,24)[]@xmath76 ( 0,-24)[]@xmath76 ( 15,5)[]@xmath95 ( 56,0)[]@xmath0 ( 0,0)(4,4)blackblack ( 30,0)2 ( 150,70)(-40,-35 ) ( -26,0)[]@xmath75 ( -20,0)(80,0 ) ( 15,5)[]@xmath75 ( 0,-20)(0,20 ) ( 0,24)[]@xmath76 ( 0,-24)[]@xmath76 ( 45,5)[]@xmath95 ( 0,0)2 ( 86,0)[]@xmath0 ( 30,0)(4,4)blackblack ( 60,0)2 ( 150,70)(-40,-35 ) ( -26,0)[]@xmath75 ( -20,0)(80,0 ) ( 30,-20)(30,20 ) ( 30,24)[]@xmath76 ( 30,-24)[]@xmath76 ( 15,5)[]@xmath95 ( 45,5)[]@xmath95 ( 30,0)2 ( 86,0)[]@xmath0 ( 0,0)(4,4)blackblack ( 60,0)2 ( 110,80)(-40,-15 ) ( -38,0)[]@xmath78 ( -30,0)(70,0 ) ( 40,0)(40,40 ) ( 45,10)[]@xmath95 ( 40,45)[]@xmath0 ( 20,5)[]@xmath96 ( 78,0)[]@xmath80 ( 0,0)(4,4)blackblack ( 40,0)2 ( 40,20)2 for @xmath97 and @xmath98 , the four - quark amplitudes were previously calculated in ref . @xcite . for @xmath99 , they can be rewritten as should be corrected to @xmath100 . this error , however , did not occur in our computation . ] @xmath101 \gamma_8^*\ , l_d^ { } \,\,,\end{aligned}\ ] ] @xmath102 \gamma_8^*\ , l_d^ { } \,\,,\end{aligned}\ ] ] @xmath103 where @xmath104 and @xmath105 , up to an overall sign , extracted from @xmath106 data . in this section we present numerical results for the different modes including all contributions to the respective amplitudes . we begin by determining the region in the @xmath107@xmath108@xmath109 parameter space that is allowed by both the @xmath110 and @xmath111 constraints . we show this in fig . [ bounds(k->pia ) ] . notice that only small values of @xmath59@xmath108@xmath60 are allowed . this corresponds to the conclusion of the analyses of refs . @xcite that the effective @xmath62 scalar coupling is severely constrained by these decay modes . that case , without the four - quark contributions , corresponds to @xmath112 in this plot . the inclusion of the four - quark contributions does not change this conclusion , but simply shifts the allowed region due to the interplay between the two- and four - quark contributions . regions in the @xmath107@xmath108@xmath109 parameter space allowed by @xmath110 ( shaded , blue ) and @xmath113 ( lightly shaded , green ) . the overlap ( dark , red ) band covers points that satisfy both constraints . , width=288 ] for definiteness , we select @xmath114 as in ref . @xcite and study the allowed region in the @xmath107@xmath108@xmath115@xmath116@xmath117 parameter space . we display in fig . [ hypercp ] the lightly shaded ( yellow ) region that reproduces the hypercp result for @xmath118 ( at the one - sigma level combining statistical and systematic errors in quadrature ) . the darkly shaded ( red ) vertical band covers the region that satisfies the constraints from the nonobservation of @xmath0 in @xmath9 modes . for @xmath119 , these ( yellow and red ) areas would both be centered at the origin . the ( black ) overlap between these regions is the allowed parameter space that we use for our predictions . also displayed on the vertical band is an unshaded ( white ) thin area corresponding to the @xmath54 scenario of ref . @xcite . regions in the @xmath107@xmath108@xmath115@xmath116@xmath117 parameter space reproducing the hypercp result for @xmath118 ( lightly shaded , yellow ) and respecting the @xmath9 bounds ( darkly shaded , red ) for @xmath120 . the overlap ( black ) areas cover points satisfying both the hyperon and kaon constraints . the unshaded ( white ) region on the vertical band corresponds to the special case discussed in ref . @xcite.,width=288 ] with these results , we show in fig . [ predictions ] the predicted branching ratios ( solid curves ) for @xmath121 and @xmath122 as functions of @xmath123@xmath116@xmath124 for @xmath114 and @xmath125 . the range of each of these predictions over the allowed values of @xmath123@xmath116@xmath124 is larger than that obtained in ref . @xcite , due partly to the presence of the four - quark contributions and partly to the uncertainty in the hypercp measurement . each of the solid curves has a minimum that is not zero , as the two- and four - quark contributions have different kinematical dependences and hence do not cancel in general . the rates for most of the allowed regions are significantly large , but those around the minima may be too small to be observed . for comparison , we also show in fig . [ hypercp ] dotted curves representing the branching ratios obtained from the two - quark contributions alone and vertical ( green ) dashed lines each indicating the narrow range of @xmath123@xmath116@xmath124 found in the scenario of ref . @xcite . predicted branching ratios ( solid curves ) for @xmath121 and @xmath122 with @xmath114 as functions of @xmath123@xmath116@xmath124 . the dotted curves result from the two - quark contributions alone . the shaded ( pink ) bands indicate the allowed ranges of @xmath123@xmath116@xmath124 as determined from fig . [ hypercp ] . each vertical ( green ) dashed line corresponds to the special case discussed in ref . @xcite.,width=480 ] since the values of @xmath126 and @xmath127 in eq . ( [ m4q(s->pa ) ] ) are determined from experiment only up to an overall sign , we should also consider the possibility that the two and four - quark contributions to @xmath118 have a different relative sign . this yields a different allowed range of @xmath59@xmath116@xmath60 , as can be seen in fig . [ hypercp ] . we display the resulting predictions for @xmath2 in fig . [ predictions ] , whose ranges over the allowed regions turn out to be roughly only half as large as those in fig . [ predictions ] , respectively . the same as fig . [ hypercp ] , except that the relative sign between the two- and four - quark contributions to @xmath118 is the opposite . , width=288 ] the same as fig . [ predictions ] , except that the allowed range of @xmath123@xmath116@xmath124 is from fig . [ hypercp ] . , width=480 ] finally , from the results of fig . [ hypercp ] we display the predicted branching ratio ( solid curve ) for @xmath5 in fig . [ omega ] . the range of the prediction over the allowed values of @xmath59@xmath116@xmath60 is again larger than that obtained in ref . @xcite due to the presence of the four - quark contributions as well as to the experimental error . the best limit for this mode currently available was reported by hypercp @xcite , @xmath128 at 90% c.l . , whereas the standard - model prediction is @xmath129 @xcite . therefore , the @xmath5 rate for most of the allowed regions is substantial , but the curve has a zero , around which the rate is too small to be observed . the significant enhancement possible with respect to the sm rate lends support to pursuing a future @xmath78 experiment @xcite . for comparison , we also display in fig . [ omega ] the dotted curve representing the branching ratio obtained from only the two - quark contributions and the vertical ( green ) dashed lines corresponding to the special case of ref . @xcite . in fig . [ omega ] we show the corresponding prediction with the allowed range of @xmath59@xmath116@xmath60 from fig . [ hypercp ] . predicted branching ratio ( solid curve ) for @xmath5 with @xmath114 as function of @xmath123@xmath116@xmath124 . the dotted curve results from the two - quark contributions alone . the shaded ( pink ) bands indicate the allowed ranges of @xmath123@xmath116@xmath124 as determined from fig . [ hypercp ] . the vertical ( green ) dashed line corresponds to the special case of ref . @xcite.,width=288 ] the same as fig . [ omega ] , except that the allowed range of @xmath123@xmath116@xmath124 is from fig . [ hypercp].,width=288 ] these modes are special because they involve only flavor - diagonal interactions . as such , they are not sensitive to the unknown parameters in the flavor sector of the model that give rise to the two - quark amplitudes . the predicted rates follow only from the tree - level diagonal couplings of @xmath0 and in this way they are similar to the radiative quarkonium decays proposed in ref . these @xmath130 decays are also analogous to the @xmath130 decay with a light @xmath34-even higgs boson which was severely constrained by data @xcite . the leading - order amplitude for @xmath3 comes from the two diagrams in fig . [ etadiag ] . it is the same for @xmath131 and @xmath132 , @xmath133 l_d^ { } \,\ , . \nonumber \\\end{aligned}\ ] ] ( 100,70)(-50,-30 ) ( -25,0)[]@xmath130 ( -20,0)(20,0 ) ( 0,-20)(0,20 ) ( 0,25)[]@xmath76 ( 0,-23)[]@xmath76 ( 26,0)[]@xmath0 ( 0,0)2 ( 140,70)(-50,-30 ) ( -25,0)[]@xmath130 ( -20,0)(50,0 ) ( 0,-20)(0,20 ) ( 0,25)[]@xmath76 ( 0,-23)[]@xmath76 ( 15,5)[]@xmath134 ( 56,0)[]@xmath0 ( 0,0)2 ( 30,0)2 for an @xmath130-@xmath135 mixing angle of @xmath136 , we then find @xmath137 allowing the mixing angle to vary between @xmath138 and @xmath139 would result in @xmath140 changes . the rate for the neutral - pion mode is not exactly half the rate for the charged - pion mode because we have used physical masses for the numerical estimate . the best limit currently available on any of these modes comes from the celcius / wasa collaboration . at the 90% c.l . they find @xcite . @xmath141 presently this does not place a stringent bound on the coupling @xmath43 , giving @xmath142 . nevertheless , eq . ( [ etawitha ] ) is a very significant enhancement over the expected standard - model rate , @xmath143 @xcite , and may be accessible to da@xmath4ne @xcite . we have studied several rare decay modes involving a light @xmath34-odd higgs boson in the nmssm . in the analysis , for the flavor - changing modes , we have consistently included the two - quark contributions in which the flavor change occurs in one - loop processes involving the light @xmath0 and the four - quark contributions in which the flavor change occurs via a tree - level standard - model @xmath14 exchange with the light @xmath0 radiated off one of the light quarks . the interplay between these two contributions was crucial to evade the bounds arising from the nonobservation of the @xmath0 in @xmath9 modes in our previous analysis @xcite . for the two - quark contributions , we have considered a somewhat general scenario in which the coefficients @xmath56 are effectively independent . we have started with the large-@xmath38 limit where chargino - mediated one - loop diagrams dominate , but we have also allowed for the possibility of having sizable neutralino- and gluino - mediated one - loop diagrams . in this more general scenario , it would also be possible to evade the @xmath9 bounds even if the four - quark contributions were absent . we have evaluated the rare modes @xmath2 which depend on both the two- and four - quark contributions . we have found that their rates are significant for most of the allowed parameter space . these modes are of immediate interest because they can be studied with ktev data . it is expected that these studies can help confirm or refute the light @xmath0 hypothesis as a candidate to explain the hypercp events in @xmath144 . we have also studied the modes @xmath3 which depend only on the tree - level couplings of the @xmath0 . therefore , the predictions for these modes are much less model - dependent and should be of interest for future experiments at da@xmath4ne . in particular , the @xmath0-mediated contribution to @xmath145 can be much larger than the sm contribution . finally , we have revisited the mode @xmath146 to include both the two- and four - quark contributions . we have found that its decay rate could be substantially enhanced with respect to the @xmath11 rate in the sm . this should give additional motivation for conducting experimental studies on the @xmath78 in the future . the work of x.g.h . was supported in part by nsc and ncts . the work of g.v . was supported in part by doe under contract number de - fg02 - 01er41155 . thanks c .- s . li for useful discussions . thanks cts at ntu for its hospitality during the completion of this work . thanks the cavendish laboratory at the university of cambridge and cern for their hospitality while this work was completed . the lagrangians we have collected here contain not only the baryon- and meson - octet fields , but also the baryon - decuplet fields . since we already derived or used some of the following formulas in refs . @xcite , further details can be found therein . the chiral realization of @xmath64 in eq . ( [ lasd ] ) can be obtained employing the operator matching of ref . thus at leading order @xmath147 \right\rangle + b_0^ { } \left\langle h_{\cal a}^ { } \right\rangle \left\langle\bar{b}{}^{}b^{}\right\rangle \,\,+\,\ , \mbox{$\frac{1}{2}$ } f^2 b_0^ { } \left\langle h_{\cal a}^ { } \right\rangle \nonumber \\ & & + \,\ , c\ , \bar{t}{}^\alpha h_{\cal a}^ { } t_{\alpha}^ { } - c_0^ { } \left\langle h_{\cal a}^ { } \right\rangle \bar{t}{}^\alpha t_{\alpha}^ { } \,\,+\,\ , { \rm h.c . } \,\,,\end{aligned}\ ] ] where @xmath148 , @xmath149mev , and @xmath150 to derive amplitudes , we also need the chiral lagrangian for the strong interactions of the hadrons @xcite . at lowest order in the derivative and @xmath151 expansions , it can be expressed as @xmath152 \bigr ) \right\rangle - m_0^ { } \left\langle \bar{b}^ { } b^ { } \right\rangle % \nonumber \\ & & + \,\ , \,+\ , d \left\langle \bar{b}^ { } \gamma^\mu\gamma_5^ { } \left\ { { \cal a}_\mu^ { } , b^ { } \right\ } \right\rangle + f \left\langle \bar{b}^ { } \gamma^\mu\gamma_5^ { } \left [ { \cal a}_\mu^ { } , b^ { } \right ] \right\rangle \nonumber \\ & & + \,\ , b_d^ { } \left\langle\bar{b}^{}\left\{m_+,b^{}\right\}\right\rangle + b_f^ { } \left\langle\bar{b}^{}\left[m_+,b^{}\right]\right\rangle + b_0^ { } \left\langle m_+ \right\rangle \left\langle \bar{b}^ { } b^ { } \right\rangle \,+\ , \mbox{$\frac{1}{4}$ } f^2 \left\langle \partial^\mu\sigma^\dagger\ , \partial_\mu^{}\sigma \right\rangle + \mbox{$\frac{1}{2}$ } f^2 b_0^ { } \left\langle m_+ \right\rangle \nonumber \\ & & -\,\ , \bar t^\mu\ , { \rm i}\!\not{\!\!\cal d } t_\mu^ { } + m_t^{}\ ; \bar t^\mu t_\mu^ { } + { \cal c } \left ( \bar t^\mu { \cal a}_\mu^ { } b + \bar b { \cal a}_\mu^ { } t^\mu \right ) \,+\ , c\ , \bar t^\mu m_+^ { } t_\mu^ { } - c_0^ { } \left\langle m_+^{}\right\rangle \bar t^\mu t_\mu^ { } \,\,,\end{aligned}\ ] ] where only the relevant terms are displayed and @xmath153 . the leading - order lagrangians relevant to the four - quark interactions involving the @xmath0 can be derived , following the prescription described in refs . @xcite , from @xmath154 above and from the mass term in the leading - order lagrangian for the @xmath155 component of the effective hamiltonian transforming as @xmath156 , namely @xcite @xmath157 \right\rangle \,+\ , \gamma_8^{}f^2 \left\langle h\,\partial_\mu^{}\sigma\ , \partial^\mu \sigma^\dagger \right\rangle + 2\tilde\gamma_8^ { } f^2 b_0^ { } \left\langle h \xi m_+^ { } \xi^\dagger \right\rangle \nonumber \\ & & + \,\ , h_c^{}\ , \bar t^\mu \xi^\dagger h \xi t_\mu^ { } \,\,+\,\ , { \rm h.c . } \,\,,\end{aligned}\ ] ] where @xmath158 . thus we have @xmath159 \bigr\rangle + b_0^{}\ , \bigl\langle \tilde{m}_-^ { } \bigr\rangle \bigl\langle \bar{b}^ { } b^ { } \bigr\rangle \,+\ , \mbox{$\frac{1}{2}$ } f^2 b_0^{}\ , \bigl\langle\tilde{m}_-^{}\bigr\rangle \nonumber \\ & & \;\;+\,\ , c\ , \bar t^\mu \tilde{m}_-^ { } t_\mu^ { } - c_0^{}\ , \bigl\langle \tilde{m}_-^ { } \bigr\rangle\ , \bar t^\mu t_\mu^ { } \bigr ) \frac{{i}a_1 ^ 0}{v } \,\,,\end{aligned}\ ] ] @xmath160 where @xmath161 , with @xmath162 at large @xmath38 . we include the su(3 ) singlet @xmath163 in @xmath81 by replacing @xmath164 with @xmath165 and adding the anomaly - generated term @xmath166 which modifies the @xmath163-@xmath0 mixing generated by @xmath167 . the physical @xmath130 and @xmath168 fields are related to @xmath163 and the su(3 ) octet @xmath169 by @xmath170 and @xmath171 , where @xmath172 and @xmath173 . as in ref . @xcite , we adopt @xmath174mev and @xmath175 . in the case of @xmath177 , for @xmath99 the eight diagrams in fig . [ 4qdiag ] yield , respectively , @xmath178 @xmath179 @xmath180 @xmath181 \frac{\gamma_8^{}\ , m_\pi^2-\tilde\gamma_8^{}\ , m_k^2}{m_k^2-m_\pi^2 } \ , l_d^ { } \,\,,\end{aligned}\ ] ] @xmath182 \bigl(\gamma_8^{}-\tilde\gamma_8^{}\bigr)\ , l_d^ { } \,\,,\end{aligned}\ ] ] @xmath183 \gamma_8^{}\ , l_d^ { } \nonumber \\ & & -\,\ , \frac{\sqrt2\ , m_k^2}{36 f v } \bigl [ 3 b_\pi^ { } \,-\ , b_\eta^{}\ , \bigl(c_\theta^{}-4\sqrt2\ , s_\theta^{}\bigr ) \,-\ , b_{\eta'}^{}\,\bigl(4\sqrt2\,c_\theta^{}+s_\theta^{}\bigr)\bigr ] \tilde\gamma_8^{}\,l_d^{}\,\,,\end{aligned}\ ] ] @xmath184 \bigl(\gamma_8^{}\ , m_{\cal a}^2-\tilde\gamma_8^{}\ , m_k^2\bigr ) l_d^ { } \nonumber \\ & & \times\,\ , \frac{3 m_{{\cal a}\pi^+}^2 - 2 m_k^2 - 3 m_\pi^2-m_{\cal a}^2}{m_k^2-m_{\cal a}^2 } \,\,,\end{aligned}\ ] ] @xmath185 \frac{\bigl(c_\theta^{}+\sqrt8\ , s_\theta^{}\bigr)m_\pi^2}{m_k^2-m_\eta^2 } \nonumber \\ & & \hspace*{5ex } -\,\ , \bigl [ b_\eta^{}\ , \bigl(\sqrt2-c_\theta^ { } s_\theta^{}-\sqrt8\,s_\theta^2\bigr ) + b_{\eta'}^{}\ , \bigl(2+\sqrt8\,c_\theta^ { } s_\theta^{}-s_\theta^2\bigr ) \bigr ] \frac{\bigl(\sqrt8\,c_\theta^{}-s_\theta^{}\bigr ) m_\pi^2}{m_k^2-m_{\eta'}^2 } \biggr\ } \bigl(\gamma_8^{}-\tilde\gamma_8^{}\bigr ) l_d^ { } \,\ , , \nonumber \\\end{aligned}\ ] ] where @xmath71 , @xmath186 @xmath187 @xmath188 in the case of @xmath189 , the diagrams in fig . [ 4qdiag ] yield , for @xmath99 , @xmath190 @xmath191 @xmath192 @xmath193 \frac{\gamma_8^{}\ , m_\pi^2 \,-\ , \tilde\gamma_8^{}\ , m_k^2}{m_k^2-m_\pi^2}\,\ , l_d^ { } \,\,,\end{aligned}\ ] ] @xmath194 \bigl(\gamma_8^{}-\tilde\gamma_8^{}\bigr ) l_d^ { } \,\,,\end{aligned}\ ] ] @xmath195 \gamma_8^{}\ , l_d^ { } \nonumber \\ & & \!\!\ ! \ ! -\,\ , \frac{\sqrt2\ , m_k^2}{36 f v } \bigl [ 9 b_\pi^ { } \,-\ , b_\eta^{}\ , \bigl(c_\theta^{}-4\sqrt2\ , s_\theta^{}\bigr ) \,-\ , b_{\eta'}^{}\ , \bigl(4\sqrt2\ , c_\theta^{}+s_\theta^{}\bigr ) \bigr ] \tilde\gamma_8^{}\ , l_d^{}\end{aligned}\ ] ] @xmath196 \bigl(\gamma_8^{}\ , m_{\cal a}^2-\tilde\gamma_8^{}\ , m_k^2\bigr ) l_d^{}\,\ , \frac{m_{\cal a}^2-m_k^2 - 3 m_{\pi^0\pi^0}^2}{m_k^2-m_{\cal a}^2 } \,\ , , \nonumber \\\end{aligned}\ ] ] @xmath197 \frac{\bigl(c_\theta^{}+\sqrt8\ , s_\theta^{}\bigr ) m_\pi^2}{m_k^2-m_\eta^2 } \nonumber \\ & & \hspace*{5ex } -\,\ , \bigl [ b_\eta^{}\ , \bigl(\sqrt2-c_\theta^ { } s_\theta^{}-\sqrt8\ , s_\theta^2\bigr ) + b_{\eta'}^{}\ , \bigl(2+\sqrt8\,c_\theta^{}\,s_\theta^{}-s_\theta^2 \bigr ) \bigr ] \frac{\bigl(\sqrt8\,c_\theta^{}-s_\theta^{}\bigr ) m_\pi^2}{m_k^2-m_{\eta'}^2 } \biggr\ } \bigl(\gamma_8^{}-\tilde\gamma_8^{}\bigr ) l_d^ { } \,\ , , \nonumber \\\end{aligned}\ ] ] in the expressions for @xmath198 or @xmath199 above , we have kept the terms proportional to @xmath200 in order to check our algebra . as explained in ref . @xcite , the @xmath92 terms in @xmath94 can be rotated away for kaon decay , and we have verified that the @xmath92 terms cancel accordingly in the sum of the contributions . in our numerical evaluation , @xmath92 is thus set to zero . h. park _ et al . _ [ hypercp collaboration ] , phys . lett . * 94 * , 021801 ( 2005 ) [ arxiv : hep - ex/0501014 ] . l. bergstrom , r. safadi , and p. singer , z. phys . c * 37 * , 281 ( 1988 ) . he , j. tandean , and g. valencia , phys . d * 72 * , 074003 ( 2005 ) [ arxiv : hep - ph/0506067 ] . he , j. tandean , and g. valencia , phys . b * 631 * , 100 ( 2005 ) [ arxiv : hep - ph/0509041 ] . deshpande , g. eilam , and j. jiang , phys . b * 632 * , 212 ( 2006 ) [ arxiv : hep - ph/0509081 ] . geng and y.k . hsiao , phys . b * 632 * , 215 ( 2006 ) [ arxiv : hep - ph/0509175 ] . r. tschirhart private communication . gorbunov and v.a . rubakov , phys . d * 73 * , 035002 ( 2006 ) [ arxiv : hep - ph/0509147 ] ; 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we have previously proposed a light pseudoscalar higgs boson in the next - to - minimal supersymmetric standard model ( nmssm ) , the @xmath0 , as a candidate to explain the hypercp observations in @xmath1 . in this paper we calculate the rates for several other rare decay modes that can help confirm or refute this hypothesis . the first modes we evaluate are @xmath2 , which are interesting because they are under study by the ktev collaboration . we next turn to @xmath3 , which are interesting because they are independent of the details of the flavor - changing sector of the nmssm and may be accessible at da@xmath4ne . for completeness , we also evaluate @xmath5 .

much of the analytical technology developed over the past two decades to facilitate genomics , transcriptomics , proteomics and metabolomics has been aimed at helping to elucidate the connections between genes , proteins and metabolites and their physiological consequences . these connections , their processes and outcomes can usually be summarized in pathway diagrams or pathway maps . indeed , pathway maps in textbooks and wall charts have long been used to describe the basics of metabolism . they have also proven to be valuable tools in giving some rhyme and reason to complex and interconnected metabolic processes ( 1 ) . the concept of metabolic pathway mapping has actually proven to be so effective that it has been extended to describe protein signaling , protein dna interactions and many other molecular biological phenomena . perhaps the first molecular pathway resource to gain wide popularity was a paper wall chart developed by dr . gerhard michal , a staff scientist at boehringer mannheim ( now roche applied sciences ) , and published in 1968 ( 2 ) . this richly annotated and compactly illustrated poster depicts most of the known metabolic pathways , metabolites and enzymes associated primarily with eukaryotic metabolism . it has been revised and expanded many times since its first release and has proven to be very popular , with more than 1 million copies now in print . with the development of the world wide web along the growing interest in systems biology ( 3 ) and model organism pathways ( 4 ) , the utility of wall charts has diminished somewhat and a substantial shift has been made to displaying this information through web - accessible pathway charts and pathway databases . over the past decade , a number of superb , web - accessible molecular pathway resources have emerged , including kyoto encyclopedia of genes and genomes ( kegg ) ( 5 ) , the cyc databases ( 6,7 ) , the reactome database ( 8) , wikipathways / genemapp ( 9 ) , the edinburgh human metabolic network ( ehmn ) ( 10 ) , pharmgkb ( 11 ) , the medical biochemistry page ( http://themedicalbiochemistrypage.org/ ) and pathwaycommons ( http://www.pathwaycommons.org ) . several companies have also created beautifully illustrated , freely available pathway databases such as biocarta ( www.biocarta.com ) , cell signal pathways ( www.cellsignal.com ) , sigma - aldrich pathways ( http://www.sigmaaldrich.com/life-science/cell-biology/learning-center/ ) ambion pathways ( http://www.ambion.com ) , calbiochem / merck pathways ( http://www.merckbiosciences.co.uk ) and proteinlounge ( http://www.proteinlounge.com/ ) . a number of commercial pathway databases also exist , such as transpath ( from biobase inc . ) , pathart ( from jubilant biosys inc . ) , metabase ( from genego inc . ) and ingenuity pathways analysis ( ingenuity systems inc . ) , many of which provide impressive numbers of molecular pathway diagrams . almost all of the above - mentioned databases contain a mix of metabolic , cell signaling and disease pathways . a few , such as kegg , the cyc databases and reactome , have a much greater emphasis on small - molecule interactions ( i.e. metabolism ) while most of the company - generated databases place a greater emphasis on protein protein interactions ( i.e. signaling pathways ) . most pathway databases maintain data on a large number of different organisms ( microbes to plants to animals ) , while a small number are very organism specific ( the medical biochemistry page , ecocyc ) . some pathway resources such as kegg and reactome use pathway diagrams that are very generic and highly schematic or simplified , while still others use diagrams that very specific and rich in detail , color and content ( biocarta , proteinlounge , ambion ) . most of these web - based databases support interactive image mapping with hyperlinked information content that can range from very sparse ( most of the open - access company databases ) to moderately detailed ( kegg , reactome , the cyc databases ) . almost all of the databases support some kind of limited text search and a few , such as reactome , pathway commons and the cyc databases , support the mapping of gene , protein and/or metabolite expression data onto pathway diagrams . overall , the quality , coverage and capability of today s molecular pathway databases are quite impressive and they are frequently used in studies relating to proteomics , systems biology , metabolic engineering and metabolomics . however , all is not well in the pathway database field . over the past few years , our group has been actively involved in clinical metabolomics ( 12,13 ) and in developing a number of clinical metabolomics databases , including drugbank ( 14 ) , the hmdb ( 15 ) and the t3db ( http://www.t3db.org ) . in the course of this work , we have used or become very familiar with many of the pathway resources described above . unfortunately , with respect to clinical metabolomics ( i.e. human metabolism , human diseases and drug therapy ) , we have found that none of the pathway databases mentioned above has the depth or breadth of information needed to be truly effective in this particular area of research . this situation is certainly understandable given that most pathway databases were developed before the advent of metabolomics or without the intent of creating a resource specifically for clinical metabolomics . ideally , what is needed for clinical metabolomics is a pathway database that focuses on small molecules only and which provides large numbers ( > 300 ) of detailed , hyperlinked diagrams of human metabolic pathways , metabolic disease pathways , metabolite signaling pathways and drug - action or drug - metabolism pathways . to be truly useful , these pathway diagrams need to include information on the relevant organs , organelles , subcellular compartments , protein cofactors , protein locations , metabolite locations , chemical structures and protein quaternary structures . each small molecule , gene or protein shown in each pathway diagram should hyperlinked to detailed descriptions as well as relevant clinical information and all pathways should be accompanied with overviews describing the corresponding pathway , condition or processes . the database should be easily browsed and must support full text , structure and sequence searching . likewise , gene , metabolite and protein lists or concentration data should be easily mapped to every one of the pathway diagrams . in response to these very specific needs , we have developed just such a database : the small molecule pathway database ( smpdb ) . in particular , smpd consists of more than 350 hand - drawn pathways describing small - molecule metabolism or small - molecule processes that are specific to humans . these pathways fall into four different categories : ( i ) metabolic pathways ; ( ii ) small - molecule disease pathways ; ( iii ) small - molecule drug pathways ; and ( iv ) small - molecule signaling pathways . in determining whether a small - molecule pathway or process is suitable for inclusion in smpdb , the pathway must be found in humans and it must have at least five small molecules ( if it is a metabolic pathway ) or its central feature must be based on the action of at least one small molecule ( if it is a disease , drug or signaling pathway ) . more specifically , in smpdb , disease pathways refer to those pathways describing human disease processes ( cause and effect ) where small - molecule metabolite dysregulation is the primary hallmark of the disease . that is , if significant concentration changes for a small molecule or set of small molecules is commonly used for the diagnosis , prognosis or monitoring of a given disease , then it qualifies for inclusion in smpdb . for example , most inborn errors of metabolism ( i.e. phenylketonuria ) qualify for inclusion into smpdb . likewise diseases such as diabetes , metabolic syndrome , hyperlipidemia , various endocrine disorders as well as several kidney , liver and gastrointestinal disorders would also qualify . on the other hand , most cardiovascular diseases , pulmonary diseases , infectious diseases , cancers and many neuromuscular diseases are defined as those pathways describing either the metabolism or mode of action of small - molecule drugs at a molecular , cellular or physiological level . likewise , signaling pathways in smpdb are defined as those pathways or physiological processes where signaling events are primarily mediated by small - molecule metabolites as opposed to proteins . this would include process such as neural or synaptic transmission , muscle activation , second - messenger signaling and small - molecule endocrine signaling . smpdb signaling pathways would therefore not include most protein- or phosphoprotein - mediated signaling events . an example of a typical smpdb pathway ( bile acid biosynthesis ) is shown in figure 1 . as seen in this figure , all smpdb pathways explicitly include the chemical structure of the major metabolites ( or drugs ) in each pathway . in addition , the cellular locations ( membrane , cytoplasm , extracellular , mitochondrion , nucleus , peroxisome , etc . ) of all metabolites and the enzymes or proteins involved in their processing are explicitly illustrated . likewise , the quaternary structures ( if known ) and cofactors associated with each of the pathway proteins are also shown . if some of the metabolic processes occur primarily in one organ or in the intestinal microflora ( as in bile acid biosynthesis ) , these features are also illustrated . ( i.e. cellular , chemical and physiological ) is one of the more unique and useful features of smpdb . in particular , this kind of information provides both context and clarity to a number of metabolic processes that are highly dependent on certain key organs , organelles or chemical frameworks . this figure illustrates the typical design and layout of an smpdb pathway diagram with the chemical structures , protein quaternary structures , cofactors , cellular locations , cellular structures and key organs all being explicitly shown . this figure illustrates the typical design and layout of an smpdb pathway diagram with the chemical structures , protein quaternary structures , cofactors , cellular locations , cellular structures and key organs all being explicitly shown . the smpdb interface is largely modeled after the interface used for drugbank ( 14 ) and the hmdb ( 15 ) , with a navigation panel for browsing , searching and downloading the database . below the navigation panel is a simple text query box that supports general text queries of the entire textual component of the database . mousing over the browse button allows users to choose between two browsing options , smp - browse and smp - toc . smp - toc is a scrollable hyperlinked table of contents that lists all pathways by name and category . smp - browse is a more comprehensive browsing tool that provides a tabular synopsis of smpdb 's ; content using thumbnail images of the pathway diagrams , textual descriptions of the pathways , as well as lists of the corresponding chemical components and enzyme / protein components . this browse view allows users to casually scroll through the database , select different pathway categories or re - sort its contents . clicking on a given thumbnail image or the smpdb pathway button brings up a full - screen image for the corresponding pathway . once opened the pathway image may be expanded by clicking on the zoom button located at the top and bottom of the image or the magnifying - glass icons in the highlight / analyzer box on the right of the image . a pathway legend link is also available above the zoom button . at the top of each image is pathway synopsis contained in a yellow box , while at the bottom of each image is a list of references . on the right of each pathway image is a gray green highlight / analyzer tool with a list of the key metabolites / drugs and enzymes / proteins found in the pathway . checking on selected items when in the smp - highlight mode will cause the corresponding metabolite or protein in the pathway image to be highlighted with a red box . entering concentration or relative expression values ( arbitrary units ) beside compound or protein names , when in the smp - analyzer mode , will cause the corresponding metabolites or proteins to be highlighted with differing shades of green or red to illustrate increased or decreased concentrations . as with most pathway databases , all of the chemical structures and proteins / enzymes illustrated in smpdb s diagrams are hyperlinked to other online databases or tables . specifically , all metabolites , drugs or proteins shown in the smp - browse tables or in a pathway diagram are linked to hmdb , drugbank or uniprot ( 16 ) , respectively . therefore , clicking on chemical or protein image will open a new browser window with the corresponding drugcard , metabocard or uniprot table being displayed . by hyperlinking to these particular databases , smpdb is able to provide considerably more information about its small molecules and its proteins than any other pathway database . indeed , smpdb s uniprot links provide an average of 40 data fields about each protein , including nomenclature , function , reaction and structural information , while smpdb s drugbank / hmdb links provide an average of 100 data fields about each compound , including detailed descriptions , extensive nomenclature information , comprehensive physico - chemical data , reference nmr and ms spectra as well as extensive information about tissue or biofluid locations and concentrations . smpdb s search menu offers users a choice of searching the database by chemical structure ( chemquery ) , text ( textquery ) , sequence ( sequence search ) or multiple identifiers ( smp - map ) . the chemquery option allows users to draw ( using marvinsketch applet ) or write ( using a smiles string ) a chemical compound and to search smpdb for drugs and metabolites similar or identical to the query compound . the textquery button supports a more sophisticated text search ( partial word matches , case sensitive , data field selection , boolean text searches , misspellings , etc . ) of the text portion of smpdb . the sequence search button allows users to conduct blastp ( protein ) sequence searches of the protein sequences contained in smpdb . the most powerful search option in smpdb is smp - map , which offers both multi - identifier searches as well as omic ( transcriptomic , proteomic or metabolomic ) mapping . through a pull - down menu located at the top of the query textbox omic data ( chemical names , hmdb ids , drugbank ids , kegg ids , gene names , protein names , uniprot ids , genbank ids , agilent ids or affymetrix ids ) , then paste in a list of the identifiers and to have a table generated of appropriately highlighted pathways containing those components . the input lists may be pasted into the search box in a single column ( name or identifiers only ) or a double column ( identifiers + concentration data ) format . the resulting table , like the smp - browse table , displays a thumbnail image of the matching pathways along with the list of matching components ( metabolites , drugs , proteins , etc . ) . the table is ordered by the number of matches and a significance score ( calculated via a hypergeometric function ) , with the pathway having the most matches being at the top . clicking on the thumbnail image or the smpdb pathway button brings up a full - screen image for the corresponding pathway with all the matching components ( metabolites , drugs , proteins , etc . ) concentration data are displayed using a red - to - green gradient - color intensity scheme . highlighting is editable through the smp - highlight / analyzer tool located beside the pathway image . through smp - map , smpdb is able to support pathway elucidation and pathway discovery in a variety of clinical for instance , users may assemble lists of significantly altered metabolites ( or metabolite identifiers ) , genes ( or gene identifiers ) or proteins ( or protein identifiers ) from clinical metabolomic , microarray or proteomic studies . the resulting lists , scores and color - coded pathways can allow the identification or diagnostic confirmation of certain diseases , the association of certain omic signatures with specific pathways or the discovery of pathway and/or disease associations that had not previously been detected . by allowing users to explore each high - scoring pathway individually , smp - map may also allow new biochemical insights to be gained or suggest new confirmatory clinical tests to be performed . in addition to the browse and search options , smpdb also offers background data , citation information , references , links to other databases and statistical information under its users may also download sequence data , structure data and all of the image pathway data ( as powerpoint or jpg ) images by navigating through the each pathway diagram in the smpdb is initially drawn using microsoft powerpoint using a palette of specially drawn icons to facilitate consistent illustration of organs , membranes , organelles , dna , rna , proteins , protein complexes , co - factors and chemical structures . a legend showing all of the standard smpd icons and their meanings is given under the about section in the smpdb menu bar . once drawn , the pathway image is converted to a jpg format and the chemical structures , proteins and co - factors are manually image mapped using the dreamweaver software package . three different - sized jpg images are prepared to facilitate rapid and consistent image zooming . all protein names , metabolite names , drug names , uniprot ids , hmdb ids and drugbank ids associated with each pathway are entered into a mysql database to facilitate searching and hyperlinking . all pathways in the smpdb have been drawn using a standard operating procedure ( sop ) with a checklist of features that each of the pathway artists and pathway annotators were required to follow . about menu . to ensure that the pathways have been knowledgably illustrated , all of the smpdb pathway artists and annotators were required to have degrees in biology , biochemistry or bioinformatics . to check that the pathway illustrations ( especially for metabolic and small molecule signaling pathways ) were as correct and as comprehensive as possible , the smpdb pathway artists and annotators were also required to consult a variety of sources including biochemistry textbooks , the boerhinger manheim wall chart ( 2 ) , omim ( 17 ) , wikipedia , kegg ( 5 ) , humancyc ( 7 ) , reactome ( 8) , the medical biochemistry page , uniprot ( 16 ) , the hmdb ( 15 ) , drugbank ( 14 ) and pharmgkb ( 11 ) . this allowed the annotation team to identify and consolidate pathway nomenclature , key pathway components , critical reactions , cellular compartments and key organs or organelles . inconsistencies and errors were resolved by comparing data from multiple sources or finding review papers that clarified the situation . pathway layouts were also assessed , compared and discussed by smpdb team members prior to manually generating any pathway diagrams . because of the unique rendering requirements and the strict sops for smpdb , no pathway in smpdb could be copied from any other pathway diagram in any other database . because of the dearth of online drug and disease pathways , smpdb s metabolic disease pathways and drug pathways were generated independently of any pathway database . instead , relevant information was gathered from various medical and pharmacology textbooks , relevant encyclopedias , as well as several online databases such as omim ( 17 ) and drugbank ( 14 ) . the same sops for generating the metabolic and metabolite signaling pathways were used for generating smpdb s disease and drug pathways . reference information for every smpdb pathway is provided in the pathway description textbox located below each pathway image . as an additional layer of quality assurance , all of the pathway diagrams in the smpdb have been inspected and corrected by two or more curators having phds in biochemistry or physiology . while there are several well - known metabolic pathway databases ( kegg , humancyc , reactome , biocarta , etc . ) , we have generally found that for the purposes of clinical omics studies , the display formats , query options , information content and pathway coverage in these databases were often insufficient , sometimes incorrect or occasionally absent . in developing smpdb , we not only tried to improve upon these shortcomings but also to build on some of the strengths of existing databases . we also endeavored to add content that is not normally found in other pathway databases . in particular , of the 364 pathways in smpdb , 281 ( or 72% of smpdb s content ) are unique . more specifically , 11/13 metabolite signaling pathways , 4/70 metabolic pathways , 154/168 drug pathways and 112/113 metabolic disease pathways depicted in smpdb are not depicted in any form by kegg , reactome , ehmn , wikipathways , humancyc , biocarta , pharmgkb or any other database . indeed , smpdb is currently the only pathway database that includes significant numbers of metabolic disease pathways ( > 110 ) and drug pathways ( > 160 ) . in addition to providing a large number of novel pathways , smpdb also adds a significant amount of new information content , including more than 30 000 words of original text describing each pathway in the context of human physiology and human biochemistry . furthermore , each drug or metabolite in smpdb is hyperlinked to detailed descriptions of that molecule , including extensive nomenclature information , comprehensive physico - chemical data , thousands of reference nuclear magnetic resonance ( nmr ) and mass spectrometry ( ms ) spectra as well as extensive information about tissue or biofluid locations and concentrations ( 100 data fields per compound ) . in addition to this textual content , smpdb also offers a significant amount of new and useful graphical content , including the depiction of the relevant organs , cellular locations , organelles , membrane boundaries , protein quaternary structures , cofactors and other cellular features in its pathway diagrams . with regard to its interface design in particular , smpdb uses thumbnail images to facilitate pathway viewing and browsing , it uses a scrollable table to display pathways and pathway synopses , and it employs a unique checkbox highlight / analyzer tool to allow users to interactively highlight and color multiple metabolites , drugs and/or proteins on its pathway images . smpdb also uses a graphical structure - searching applet to enable sophisticated drug or metabolite similarity searches . as with some of the more fully developed pathway databases , smpdb also provides protein / metabolite lists for each pathway , it supports advanced text and sequence queries and it allows pathway mapping from protein , gene and metabolite lists . while space does not permit a detailed comparison against all existing pathway databases , it is perhaps instructive to compare smpdb to six of the larger and more established resources : kegg , reactome humancyc , biocarta , ehmn and wikipathways / genmapp . this comparison is summarized in table 1 where we have used a number of general features or criteria to make our assessment . in particular : information provided on pathway entities is defined as providing hyperlinks to pages that give additional detail on protein / drug / metabolite sequences , functions , properties , reactions , structure , concentrations or spectra . supports advanced text search is defined as supporting field - specific searches , wild - card queries , boolean searches , synonym searches , mis - spellings , text sorting or other kinds of complex textual queries beyond simple text matching . component lists available is defined as providing easily accessed , plain text or hyperlinked textual lists of all the genes , proteins , drugs and/or metabolites displayed in the pathway . in addition to the information in table 1 , we have also elaborated on the comparisons for four of the databases ( kegg , humancyc , reactome and biocarta ) in the following paragraphs . table 1.comparison of smpdb to kegg , humancyc , reactome , biocarta , ehmn and wikipathways / genmappfeaturesmpdbkeggreactomehumancycbiocartaehmnwikipathwaysnumber of metabolic pathways7073 ( for humans)64 ( for humans)317 ( total ) , 238 ( conf)557044 ( for humans)number of disease pathways11335302404number of drug action pathways1680331004provides multiple organism pathwaysnoyesyesnoyesnoyeschemical structures shown in diagramsyesnosomeyes ( when zoomed)somenonoprotein 4 structures shown in diagramsyesnononosomenonocell structures shown in pathway diagramsyesnononoyesnonoorgans shown in pathway diagramssomenonononononodescriptions of pathways providedyesnoyesyesyesnosomepathway images are hyperlinkedyesyeslimitedyesyesnonopathway images are zoomableyesnonoyesnoyeslimitedinformation provided on pathway entitiesdetailedmodestlimitedmoderatelimitedlimitedlimitedsupports simple text searchyesyesyesyesnoyesyessupports advanced text searchyesnoyesyesnononosupports sequence searchingyesnonoyesnononosupports graphical chemical structure searchyesnonononononosupports chemical expression mappingyesnoyesyesnononosupports gene / protein expression mappingyesnoyesyesnononodownloadableyesyesyesyesnonoyescomponent lists availableyesnoyesnoproteins onlyyesyesbiopax , cellml or sbml compatiblenopartialyesyesnoyesno comparison of smpdb to kegg , humancyc , reactome , biocarta , ehmn and wikipathways / genmapp kegg , with 330 reference pathways , is considered to be the gold standard for most pathway databases because of its comprehensiveness and its breadth of organism - specific coverage . of kegg s 158 metabolic pathways ( table 1 ) , 73 are relevant to humans or other mammals . interestingly , several key metabolic pathways in mammals are actually missing from kegg ( i.e. the malate - aspartate shuttle , and electron transfer ) . as the pathway diagrams in kegg are designed to be very generic they display no organ data , no cellular structure information , no protein superstructure data , no chemical structure information ( except through hyperlinks ) and no gene or protein names ( only ec numbers ) . while kegg does have 35 disease pathways , most are for cancer , neurological or immune diseases and only three of these relate to small - molecule metabolites or metabolic diseases . kegg s drug pathways are limited to showing only drug development or drug similarity as opposed to drug action or drug mechanism . while kegg does provide very useful annotations ( via hyperlinks ) for the compounds shown in its pathways , it does not provide descriptive summaries of these pathways nor does it support the visual display of gene / protein / metabolite concentrations . as yet , kegg does not provide protein / metabolite lists for each pathway nor does it support graphical structure queries or chemical structure similarity searches . similar to kegg , the reactome database provides 1000s of metabolic and signaling pathway data sets for many model organisms . of these , 64 pathways are associated with human metabolism , three with human diseases and three with drug action or drug metabolism . through its reaction map interface , reactome is able to provide users with low - resolution pathway maps ( similar to the thumbnail images used by the smpdb browser ) that allow users to interactively navigate through the database . like smpdb , reactome provides extensive pathway or reaction descriptions along with hyperlinks to several external databases . unlike smpdb , reactome does not display organ data , cellular compartment data , cellular organelle information , protein complex information or protein / gene names in its pathway diagrams . likewise , reactome has very few disease or drug pathways . on the other hand , reactome , like smpdb skypainter feature allows users to paste in a list of genes or gene identifiers and to the humancyc database contains 349 pathways , including 29 superpathways ( supersets of many of the other 320 pathways in the database ) . two hundred and thirty - eight of these pathways are confirmed , meaning they have evidence glyphs indicating 50% or more of the reactions have some evidence of occurring in humans . all pathways in humancyc can be zoomed - in to display chemical structures , ec numbers and protein names , similar to smpdb . humancyc s metabolic pathways are well referenced and generally well described , although most descriptions are given in the context of bacterial or plant metabolism . the images in humancyc do not display organ data , cellular compartment data , cellular organelle information or protein complex information . currently , humancyc does not have any disease pathways and it provides only three drug pathways . while humancyc does support the visual display of gene / protein / metabolite concentrations using its own omicsviewer , the display is small and sometimes difficult to interpret especially for metabolomics applications . unlike smpdb , humancyc does not provide protein / metabolite lists for each pathway nor does it support chemical structure similarity searches . the biocarta database , with 360 pathways , is probably the most visually sophisticated database of the four pathway databases described here . like smpdb , not only most of its pathways depict cell , protein and chemical structure information , but also all of its pathways are well annotated with very detailed descriptions . biocarta also contains a large number ( > 250 ) of protein signaling pathways and many other macromolecular interaction processes . however , biocarta only has a modest number ( 55 ) of pathways that are devoted to small molecule metabolism and an even smaller number ( < 35 ) of pathways that are devoted to disease or drug action pathways . as biocarta is a community - annotated / generated database , its collection of pathways is somewhat haphazard and largely dependent on community interest . likewise , biocarta s querying and display tools are very limited compared to most other pathway databases . compared to most other pathway databases , smpdb is really a niche database that is specific to just one ( albeit important ) organism namely humans . in this regard , smpdb certainly lacks the breadth of metabolic coverage offered by kegg , reactome or the because smpdb is focused on small molecules , it does not include the key protein signaling pathway information found in other databases , such as kegg , biocarta or transpath . as a consequence , smpdb is not nor will it ever be very useful for those interested in comparative metabolic studies , protein network analysis , metabolic engineering , protein signal transduction or metabolic evolution . because of its narrow focus and restricted mandate , smpdb should not be thought of as a replacement for existing pathway databases . rather , the information in smpdb should be viewed as complementary to what is already out there . while smpdb is essentially a database of small - molecule pathways , it is also a database of scientific artwork . the art , in this case , corresponds to our best understanding and our best efforts at representing the complex chemical and biochemical processes found in humans . as such . certainly , with any illustration or piece or art , there are other ( potentially better ) ways of rendering the process or in capturing its essence . likewise , because art is very much a personal choice , it is likely that the style , layout and color scheme adopted by smpd may not agree with every user . for instance , the display of all chemical structures ( which vary widely in size ) may make some smpdb pathway images a little difficult to interpret . however , because smpdb is primarily designed to serve the metabolomics community , this made chemical structure rendering an essential part of its construction . other aspects , such as the use of a dark blue background ( to represent aqueous conditions ) and thin directional arrows ( to reduce clutter ) , may not appeal to all users . however , the fact that all of smpdb s powerpoint images are downloadable , certainly should allow users to re - render or re - color the pathways to their liking . while considerable effort and many revisions went into developing both the current pathways and standard pathway drawing protocols , smpdb is far from uniform it is worth noting that smpdb was assembled from multiple artists , and this means there will always be some inconsistency in how data are schematically represented and how much detail is displayed in any given figure . again , these issues can be addressed if users provide feedback to smpdb s annotation team or if they choose to download and edit smpdb images on their own . another important limitation to smpdb is the fact that its pathways are not ( yet ) represented in biopax or sbml format ( 18 ) . efforts will be made in the future to convert most smpdb images to sbml and simcell ( 19 ) compatible formats , but it is important to note that smpdb was designed to be more of a human - readable database rather than a machine - readable resource . consequently , most of our computational effort has gone into to providing powerful searching , querying and viewing tools to facilitate user interactivity . we are currently adding two to three new pathways a week and are constantly revising or improving the renderings of existing pathways images based on new data or on user feedback . while the number of metabolic pathways is unlikely to change substantially , it is expected that the total number of disease and metabolic signaling pathways will eventually exceed 200 , and the number of drug action pathways will certainly exceed 400 . in addition , to the planned expansion in size , smpdb s metabolic and disease pathways will be formally linked to the next release of the hmdb , while its drug action pathways will be linked the next release of drugbank . smpdb is also being integrated into a virtual reality cave environment for interactively visualizing and modeling human metabolism ( 20 ) . overall , we believe smpdb is a useful addition to the current collection of pathway databases and we are hopeful that some of its more innovative or useful ideas will eventually find their way into other online pathway databases . the alberta ingenuity fund ( aif ) ; alberta advanced education and technology ( aaet ) ; the canadian institutes for health research ( cihr ) ; genome alberta , a division of genome canada .

the small molecule pathway database ( smpdb ) is an interactive , visual database containing more than 350 small - molecule pathways found in humans . more than 2/3 of these pathways ( > 280 ) are not found in any other pathway database . smpdb is designed specifically to support pathway elucidation and pathway discovery in clinical metabolomics , transcriptomics , proteomics and systems biology . smpdb provides exquisitely detailed , hyperlinked diagrams of human metabolic pathways , metabolic disease pathways , metabolite signaling pathways and drug - action pathways . all smpdb pathways include information on the relevant organs , organelles , subcellular compartments , protein cofactors , protein locations , metabolite locations , chemical structures and protein quaternary structures . each small molecule is hyperlinked to detailed descriptions contained in the human metabolome database ( hmdb ) or drugbank and each protein or enzyme complex is hyperlinked to uniprot . all smpdb pathways are accompanied with detailed descriptions , providing an overview of the pathway , condition or processes depicted in each diagram . the database is easily browsed and supports full text searching . users may query smpdb with lists of metabolite names , drug names , genes / protein names , swissprot ids , genbank ids , affymetrix ids or agilent microarray ids . these queries will produce lists of matching pathways and highlight the matching molecules on each of the pathway diagrams . gene , metabolite and protein concentration data can also be visualized through smpdb s mapping interface . all of smpdb s images , image maps , descriptions and tables are downloadable . smpdb is available at : http://www.smpdb.ca .

$100 Million Bev Hills Mansion Come for the Sale ... Stay for the Sexy Fantasy Chicks! Hot Naked Chicks Plug $100 Million Sale of Famed Opus Mansion EXCLUSIVE Leave it to a Hollywood producer to unload his $100 million mansion with the SEXIEST video sales pitch ever -- complete with semi-naked women ... touching each other. The famed Bev Hills estate known as Opus just hit the market, and this movie trailer-styled reel is sure to have buyers lining up for the 20,500 sq ft, 7 bed, 11 bath palace. Opus was built by mega developer and former movie producer Nile Niami. He also had a hand in the promotional vid for the "Billionaires' Row" property. You might notice the 2 pools, waterfall, champagne vault, home theater and beauty salon -- in between shots of topless women in body paint. It also comes with a 10-car museum pre-stocked with a gold Lamborghini Aventador and Rolls-Royce Dawn. Opus is listed by Drew Fenton of Hilton & Hyland, who also brokered the Playboy Mansion deal. Golden ladies not included. We're pretty sure. ||||| The most expensive home in Beverly Hills has just come on the market with an asking price of $100 million. The property, known simply as Opus, has every amenity a luxury buyer would expect, and several they couldn’t have dreamed up if they tried. Seven bedrooms and eleven bathrooms can be found within the 20,500-square-foot home, which keeps a surprisingly low profile for all it hides. But space is hardly its most impressive feature. Get push notifications with news, features and more. See the full tour. The mansion includes a champagne “vault” designed specifically to hold 170 gilded bottles of Cristal. Though, the listing notes, overflow can be stored in the 944-bottle, glass-enclosed display that surrounds the dining room. Downstairs, the 10-car “museum” comes stocked with a gold Rolls-Royce Dawn and Lamborghini Aventador roadster, should the buyer’s collection be lacking. The cars are included in the asking price. Jim Bartschm/ Two swimming pools, a 20-foot waterfall, a wellness center, and a full-service salon round out the offerings. But listing agent Drew Fenton of Hilton & Hyland doesn’t have to rely on a list of spectacular features to sell this one — it’s making its debut with a full-on theatrical trailer. The safe-for-work version is above. (The not-so-SFW cut can be found here.) Jim Bartsch/courtesy Hilton & Hyland The steamy videos, which show an imagined homeowner writhing around in bed and swimming naked in a pool, are meant to evoke “a modern day Cleopatra complete with golden ladies in waiting” and give potential buyers “a sneak peek into a life where the boundaries are limitless,” according to a release from the firm. ||||| OPUS Beverly Hills’ most expensive property. Interior features of this state of the art dream home include: • Roberto Cavalli flooring • 15-seat curved screen theater with JBL Synthesis Audio • 2 massive bars, one of which has “Winestation” that preserves and dispenses glasses with the exact amount and temperature • Gourmet Show Kitchen w/ iPad controlled Top Brewer coffee machine • State of the Art "Savant" Home Automation and Security • Privacy and protection ensured through a private entrance • Longhi doors in suede and embossed leather • Specially commissioned golden sculpture adorning the large motor court • Separate Catering/Event Kitchen For more information contact Drew Fenton at [email protected]. © 2017 - Drew Fenton - CalBRE# 01317962

– "Come for the sale ... Stay for the sexy fantasy chicks!" That's the way TMZ plugs a bizarre video trying to sell what's being touted as Beverly Hills' most expensive home: a $100 million retreat called Opus, the brainchild of film producer Nile Niami, per People. The 20,500-square-foot residence features seven bedrooms, 11 bathrooms, and a list of other extravagant amenities that People notes "a luxury buyer ... couldn't have dreamed up if they tried." Those add-ons include a champagne vault that can hold 170 bottles of Cristal champagne (there's a 944-bottle overflow area if that's not enough room); a 10-car "museum" that comes already stocked with a Rolls and a Lamborghini that, combined, could be worth close to $800,000 themselves; and more plebeian comforts like a couple of swimming pools, a wellness center, and a salon. But it's the hedonistic, NSFW video that real estate firm Hilton & Hyland is using to promote the fancy digs that's really catching everyone's attention. The three-minute commercial is designed to show hopeful homeowners "a sneak peek into a life where the boundaries are limitless," which in Beverly Hills seems to include writhing, nearly naked gold-coated women enjoying their time in the house with a pretend female homeowner, with the spectacular Los Angeles landscape in full view. To say there are sexual undertones is an understatement—especially when the homeowner breaks open one of those Cristal bottles. "I kept telling the director 'Go darker … go sexier …' and was thrilled to see the results," Niami says, per People. (There's another home in LA that's serious competition.)

in this paper we are concerned with various invariants of graphs related to distance ( girth , diameter ) , expansion properties of the graph ( cheeger constant ) and spectrum of the laplacian ( the first eigenvalue , the tree number ) . the behavior of many of these invariants for random graphs has been extensively studied ( @xcite ) . for regular graphs , the results about weak convergence of graph spectra to the spectrum of the infinite regular tree ( @xcite ) allow to get many results on the asymptotic behavior of spectral invariants ( as the number of vertices increases ) . often when certain bounds are established for the rate of growth of some invariant , one is interested in studying families graphs with ( asymptotically ) the _ best possible _ behavior with respect to a given invariant ( two well - known examples are ramanujan graphs and cages ) . a related problem is to study the graphs which maximize ( or minimize ) a given invariant among all simple connected graphs with @xmath0 vertices and @xmath1 edges ( we denote the set of such graphs by @xmath2 ) , or among @xmath3-regular connected simple graphs with @xmath0 vertices ( we denote the set of such graphs by @xmath4 ) . the sets @xmath2 and @xmath4 are finite , so maximizing a given invariant is a discrete optimization problem . on the other hand , @xmath2 ( respectively , @xmath4 ) is naturally embedded in the complex @xmath5 of all _ weighted _ graphs with @xmath0 vertices and @xmath1 edges ( respectively , the complex @xmath6 of weighted @xmath3-regular graphs with @xmath0 vertices ) ; the edge weights are normalized so that their sum is constant . one can study the extremal problems for weighted analogs of graph invariants ( see e.g. @xcite ) . a natural question then is which _ unweighted _ simple graphs in @xmath2 or @xmath4 ( all weights are equal to @xmath7 ) are local extrema in @xmath5 or @xmath6 for a given invariant . in section [ sec : edges ] we study this question for various graph invariants . in section [ sec : heuristics ] we discuss some heuristics about the structure of graphs which have many spanning trees . in section [ sec : genustree ] we give an upper bound on the rate of growth of the number of spanning trees for @xmath8-regular simple graphs on a fixed surface . in section [ sec : lattice ] we prove a result about the asymptotic properties of certain lattices , associated to graphs by bacher , de la harpe and nagnibeda ( cf . @xcite ) , for sequences of regular graphs . finally , in section [ sec : construct ] we explain how the first @xmath9 cubic cages appear naturally in a sequence of graphs produced from @xmath10 by `` greedy '' edge insertion with respect to the number of spanning trees . in the remainder of this section we review the definitions and some results about the asymptotic behavior of various graph invariants . the _ adjacency _ matrix @xmath11 of a graph @xmath12 is a square matrix of size @xmath0 where @xmath13 is the number of edges joining the vertices @xmath14 and @xmath15 . we always consider loopless graphs , so @xmath16 ; for simple graphs @xmath17 is equal to @xmath18 or @xmath7 . the nearest neighbor _ laplacian _ @xmath19 acts on functions on the set @xmath20 of the vertices of @xmath21 : given @xmath22 , @xmath23 . let @xmath24 be the matrix of @xmath25 of a ( not necessarily simple ) graph @xmath21 ; then @xmath26 is the degree of the vertex @xmath14 , and @xmath27 is the number of the edges joining @xmath14 and @xmath28 ( equal to @xmath18 or @xmath7 for simple graphs ) . for @xmath3-regular graphs @xmath29 . let @xmath11 be the adjacency matrix of a graph @xmath30 , and let its spectrum ( in the decreasing order ) be given by @xmath31 ( the constant function is the eigenfunction with the eigenvalue @xmath3 ) . the last eigenvalue @xmath32 if and only if @xmath21 is bipartite . the spectrum of @xmath25 is @xmath33 ; it satisfies @xmath34 . alon and boppana ( @xcite ) proved that @xmath35 ( cf . @xcite for more precise results ) ; @xmath3-regular graphs all of whose @xmath36 lie inside @xmath37 $ ] are called _ ramanujan _ graphs ( because of the relation to ramanujan conjectures , cf . the first such graphs were constructed in @xcite ; many other constructions followed . an important invariant of @xmath21 is the number @xmath38 of spanning trees of @xmath21 ; it is sometimes called the _ complexity _ of @xmath21 . by kirckhoff s theorem ( @xcite ) , @xmath39 and @xmath38 is equal to the determinant of any cofactor of the matrix @xmath19 and ( it is some times called the _ determinant of laplacian _ ) . mckay proved in @xcite that @xmath40 and that a typical graph @xmath21 in @xmath4 satisfies @xmath41 the above formula also holds for some ramanujan graphs ( @xcite ) . alon in @xcite proved some results concerning @xmath42 namely , he showed that for @xmath43 , @xmath44 and that @xmath45 as @xmath46 . valdes in @xcite determines the @xmath47-connected cubic graphs with the _ minimum _ number of spanning trees . it follows from her results that if the limit in is taken over all @xmath47-connected cubic graphs , the answer is @xmath48 ( this was also proved by a. kostochka in @xcite ) . we begin with girth . it is easy to show that a @xmath3-regular graph ( @xmath43 ) with girth @xmath49 has at least @xmath50 vertices where @xmath51/(k-2),\\ \ ; & \ 2[(k-1)^{g/2 } - 1]/(k-2),\endaligned\right . \qquad \left.\aligned \ ; & g\ odd\\ \ ; & g\ even\endaligned\right.\ ] ] the @xmath3-regular graphs with girth @xmath52 and @xmath50 vertices are called _ moore graphs _ ( sometimes they are also called _ generalized polygons _ for even @xmath53 ) ; these graphs are unique if they exist . for @xmath54 those are complete graphs @xmath55 , for @xmath56 those are complete bipartite graphs @xmath57 . it is proved in ( * ? ? ? 23 ) that for @xmath58 moore graphs only exist if @xmath59 and @xmath60 ( petersen graph ) , @xmath61 ( hoffmann - singleton graph ) , and ( possibly ) @xmath62 ; or if @xmath63 or @xmath64 . @xmath3-regular moore graphs of girth @xmath8 exist if and only if a projective plane with @xmath3 points on the line does @xcite . the @xmath3-regular graphs of girth @xmath52 which have the smallest possible number of vertices are called @xmath65 _ cages _ ( such graphs always exist , cf . ( * ? ? ? 6 ) ) , and the number of their vertices is denoted by @xmath66 . for @xmath43 and @xmath52 such that the corresponding moore graphs exist , those graphs are @xmath65 cages @xmath67 ; if moore graphs do nt exist , @xmath68 . very few cages other than moore graphs are known ( see @xcite , ( * ? ? ? 6 ) and ( * ? ? ? 23 ) for surveys of known results ) . for cubic graphs , @xmath69 is known for @xmath70 ( @xcite ) . for @xmath71 , the @xmath72 is already unknown . the best upper bounds for @xmath66 come from various infinite series of symmetric graphs ( cf . it is known that @xmath73 for all known infinite families of regular graphs , @xmath74 it is sometimes conjectured that the upper bound in is actually an asymptotic result . we next turn to the number of spanning trees . it is easy to see that the complete graph on @xmath0 vertices has the maximum number of trees among all multigraphs with the same number of vertices and edges . in a series of papers ( see e.g. @xcite ) kelmans characterized the graphs , obtained by removing a small number of edges form the complete graph , which have the maximum number of spanning trees among all the graphs with the same number of vertices and edges . cheng ( @xcite ) proved that the complete multipartite regular graphs also have this property ; see also @xcite . we notice that @xmath55 and @xmath57 are , respectively , the unique @xmath75 and @xmath76 cages . one can also check ( see @xcite ) that the petersen graph ( which is the @xmath77 cage ) has the most trees ( @xmath78 ) among all cubic simple graphs with @xmath79 vertices . we conjecture [ conj : moore : trees ] moore graphs have the maximum number of spanning trees among all simple graphs with the same number of vertices and edges . some evidence supporting this conjecture is discussed in section [ sec : construct ] . * acknowledgements . * the authors would like to thank n. alon , p. sarnak , p. seymour and r. wilson for helpful conversations , and a. kelmans for explaining many results in extremal graph theory during his visit to caltech in the spring of 1997 , as well as for suggesting many improvements to the manuscript . the first author would like to thank the institute for advanced study at princeton for their hospitality in the fall of 1997 and in the spring of 1998 . in this chapter we shall discuss several extremal problems for weighted graphs . we will be concerned with finding extrema for various functionals on the _ weighted edge polytope _ @xmath80 ( which is actually a simplex ) defined below . let @xmath21 be a simple connected graph , and let @xmath81 be the set of its edges . then @xmath82 where the ( nonnegative ) real number @xmath83 is called the _ weight _ of @xmath84 ; the corresponding graph is denoted by @xmath85 . the graph @xmath86 is called an _ unweighted graph_. we introduce the following notation : @xmath87 the adjacency matrix of @xmath85 is defined by @xmath88 the _ degree _ @xmath89 of a vertex @xmath14 is defined by @xmath90 the laplacian is defined by @xmath91 the notation for the eigenvalues of @xmath11 and @xmath19 will be the same as for the unweighted graphs . the proof of kirchhoff s theorem extends to weighted graphs ( @xcite ) ; we shall continue to call the determinant @xmath38 of any cofactor of @xmath92 the ( weighted ) tree number of @xmath21 . one can regard @xmath89 as a combinatorial analog of a curvature at @xmath14 . motivated by an analogy with metrics of constant curvature , we define another polytope @xmath93 by @xmath94 where @xmath95 is the degree of @xmath14 in the unweighted graph @xmath21 . we will consider the problem of maximizing or minimizing various functionals over @xmath80 and @xmath96 . some of the functionals ( girth and diameter ) will be linear in @xmath83-s , and so we will be solving a problem in linear programming ( ( * ? ? ? * ch . 7 ) ) . other functionals ( expansion constants ) will not be linear in @xmath83-s on @xmath80 , but will become linear on @xmath96 . we shall be often concerned with the following question : * question : * when is @xmath97 an extremum ( in @xmath80 or @xmath96 ) ? in other words , when is the unweighted graph an extremum for a given functional ? in some cases we are able answer the above question completely . we turn to ths study of the girth and the diameter . we make several definitions : the _ length _ of a path in a weighted graph @xmath21 is the sum of the weights of the edges in the path . the girth @xmath98 is the length of the shortest cycle in @xmath21 . the _ distance _ between two vertices of @xmath21 is the length of the shortest path connecting them ; the _ diameter _ @xmath99 is equal to the largest such distance . we are interested in the points @xmath100 where @xmath101 takes its maximal value and where @xmath102 takes its minimal value on @xmath80 . denote by @xmath103 all the cycles of @xmath21 . then finding the maximum of the girth leads to solving the following problem in linear programming : @xmath104 we assume that any edge on a cycle is visited at most once , so there are finitely many cycles ; we make a similar assumption about the paths in the next definition . similarly , for two vertices @xmath105 of @xmath21 denote by @xmath106 the set of all paths in @xmath21 connecting @xmath107 and @xmath108 ( where @xmath109 ) . finding the minimum of the diameter leads to the following problem : @xmath110 we now fix some @xmath100 and consider the corresponding graph @xmath111 . two vertices @xmath112 of @xmath21 are called _ diametrically opposite _ if @xmath113 . any path connecting two diametrically opposite points which has length @xmath99 is called a _ meridian_. also , any shortest cycle is called a _ systole_. to study how girth changes , we remark that for small weight changes the new systoles will come from among the weighted old systoles . denote the systoles of @xmath21 by @xmath114 , and form the ( @xmath1-by-@xmath115 ) edge cycle incidence matrix @xmath116 . turning to the diameter , we remark that for small weight changes the new meridians will come from among the weighted old meridians . denote the meridians of @xmath21 by @xmath117 and form the ( @xmath1-by-@xmath118 ) edge - meridian incidence matrix @xmath119 . denote by @xmath120 ( respectively , @xmath121 ) the cone formed by all linear combinations of column vectors of @xmath116 ( respectively , @xmath119 ) with nonnegative coefficients . clearly , both @xmath122 and @xmath121 lie inside the first quadrant . [ thm : girdiam ] the graph @xmath21 is a local maximum for girth ( respectively , a local minimum for diameter ) if and only if @xmath123 lies in @xmath120 ( respectively , @xmath121 ) . * proof . * let @xmath124 be the graph in question , and let @xmath125 be another point in @xmath126 . denote by @xmath127 the vector @xmath128 connecting the points in @xmath80 . the graph @xmath124 is a local maximum for the girth if and only if the inequality @xmath129 has no solutions for small enough @xmath127 . by farkas lemma ( ( * ? ? ? 7 ) ) , this condition is equivalent to the condition @xmath130 . similarly , the graph @xmath124 is a local maximum for the girth if and only if the inequality @xmath131 has no solutions for small enough @xmath127 . again by farkas lemma , this is equivalent to the condition @xmath132 . ( 2.5,2.5 ) ( 0,0)(2.5,2.5 ) an obvious sufficient condition for the assumptions of the theorem [ thm : girdiam ] to hold is for every edge to be contained in the same number of systoles ( diameters ) , so that edge - transitive graphs are always satisfy this assumption . another large class of graphs where every edge is contained in the same number of systoles consists of graphs arising from @xmath133-vertex - connected proper triangulations of surfaces ( every edge is contained in exactly two triangles ) . on the other hand , the assumptions of theorem [ thm : girdiam ] are clearly _ not _ satisfied when there is an edge in @xmath21 which is not contained in any systole ( diameter ) . we now turn to cheeger and expansion constants . let @xmath21 be an unweighted graph . given a partition of its vertex set @xmath134 into _ disjoint _ sets @xmath11 and @xmath135 , define @xmath136 to be the set of all edges with one endpoint in @xmath11 and another in @xmath135 . let @xmath137 be the sum of the weights of the edges in @xmath136 , for unweighted graphs . ] and let @xmath138 denote the sum of degrees of all vertices in @xmath11 ( also called the _ volume _ of @xmath11 ) . denotes the number of vertices in @xmath11 , which for regular graphs is proportional to our definition ; our definition allows a straightforward extension to weighted graphs . ] the expansion constant @xmath139 is defined by @xmath140 the _ cheeger constant _ @xmath141 is defined by @xmath142 to prove an analog of theorem [ thm : girdiam ] for the above constants , we find it convenient to maximize cheeger and expansion constants over @xmath143 instead of @xmath126 . the reason is that for @xmath144 the volume @xmath138 does not depend on @xmath145 ( since the degrees are preserved ) , and so @xmath139 and @xmath141 become linear functionals on @xmath143 . let @xmath146 denote the @xmath1-by-@xmath0 edge vertex incidence matrix . the dimension of @xmath96 is equal to @xmath147 . we denote by @xmath148 the cone spanned by linear combination of the column vectors of @xmath149 with nonnegative coefficients . stands for _ normalization _ conditions ; in general , the more conditions we impose , the larger the cone @xmath148 is ; vector @xmath123 should always be in @xmath148 . ] to state the next theorem , we need to define several matrices . given @xmath150 , let @xmath151 be the corresponding graph . an edge cut @xmath152 of @xmath151 is called an _ expansion edge cut _ ( respectively , a _ cheeger edge cut _ ) if it is one of the cuts for which the expansion constant ( respectively , the cheeger constant ) of @xmath21 is attained . let @xmath153 ( respectively , @xmath154 ) be the expansion ( respectively , cheeger ) edge cuts . denote by @xmath155 and @xmath156 the disjoint subsets into which @xmath152 separates @xmath20 . we now define two matrices : an @xmath1-by-@xmath115 _ expansion _ matrix @xmath157 and an @xmath1-by-@xmath118 _ cheeger matrix _ @xmath158 by @xmath159 and by @xmath160 let @xmath161 ( respectively , @xmath122 ) denote the cone formed by linear combinations of column vectors of @xmath162 ( respectively , @xmath163 ) . we are now ready to formulate and prove [ thm : chexpan ] a graph @xmath21 is a local maximum for the expansion constant ( respectively , the cheeger constant ) for degree - preserving edge valuations if and only if @xmath164 ( respectively , @xmath165 ) contains a nonzero vector . * proof * : the proof is similar to that of theorem [ thm : girdiam ] . ( 2.5,2.5 ) ( 0,0)(2.5,2.5 ) we remark that edge - transitive graphs satisfy both assumptions of theorem [ thm : chexpan ] ( for such graphs @xmath166 and @xmath167 ) . also , as in the case of girth and diameter the assumptions are not satisfied if some edge is not contained in any cheeger ( respectively , expansion ) edge cut . by the weighted version of kirckhoff s theorem ( @xcite ) @xmath168 where the sum is taken over the set @xmath169 of the spanning trees of @xmath21 . finding the maximum of @xmath38 on @xmath80 becomes a lagrange multiplier problem with the constraints given by eq . ( [ weight : sum ] ) . the condition for @xmath100 to be a critical point for @xmath38 is @xmath170 the partial derivatives above are given by @xmath171 the ratio @xmath172 is called the _ effective resistance _ of @xmath84 . we have thus proved : [ prop : detcrit ] the graph @xmath151 is a critical point for @xmath38 if and only if the effective resistances of all edges are the same . if an unweighted graph satisfies the assumptions of proposition [ prop : detcrit ] then every edge of this graph is contained in _ the same _ number of spanning trees . such graphs were studied by godsil in @xcite ; he calls these graphs _ equiarboreal_. obviously , all edge - transitive graphs ( the automorphism group acts transitively on the edges ) are equiarboreal . godsil gives several more sufficient conditions for a graph to be equiarboreal ; in particular , any distance - regular graph and any color class in an association scheme is equiarboreal ( the least restrictive condition godsil gives is for a graph to be _ 1-homogeneous _ ) . by an easy counting argument one can show that for an unweighted equiarboreal graph @xmath173 ( this is actually the result of foster , cf . @xcite ) so the necessary condition for a graph to be equiarboreal is @xmath174 we remark that the graphs which have the most spanning trees among the regular graphs with the same number of vertices are not necessarily equiarboreal , and vice versa . for example , the @xmath9-vertex mbius wheel ( cf . section [ sec : construct ] ) which has the most spanning trees among the @xmath9-vertex cubic graphs is not equiarboreal ( cf . also @xcite ) , while the _ cube _ ( which is certainly edge - transitive , hence equiarboreal ) has the _ second biggest _ number of spanning trees among the @xmath9-vertex cubic graphs . we next study the function @xmath38 on @xmath126 . surprisingly , it turns out to be concave , so there is at most one critical point , and if there is one it has to be a global maximum . the eigenspace @xmath175 corresponding to the eigenvalue @xmath176 of @xmath19 on @xmath151 is the same for all @xmath177 in the interior of @xmath80 ( and consists of constant functions ) . let @xmath178 be the operator of projection onto @xmath175 ; its matrix is given by @xmath179 , where @xmath180 is the matrix of @xmath7-s . the eigenvalues of @xmath181 are @xmath182 , hence @xmath183 this result is due to temperley ( @xcite ) . thus it suffices to study the concavity of the positive - definite operator @xmath184 . [ logdet : concave ] the function @xmath38 is concave on ( the interior of ) @xmath80 . the theorem immediately implies if @xmath185 is a critical point of @xmath38 in the interior of @xmath80 , then it is the global maximum for @xmath38 . in particular , the unweighted graph is the global maximum for equiarboreal graphs . * proof of theorem [ logdet : concave ] . * it suffices to prove that the determinant is a concave function on the set of positive definite symmetric matrices . let @xmath186 be such a matrix , and let @xmath187 be a line of symmetric matrices through @xmath186 . then @xmath188 and @xmath189 it suffices to show that the last trace is strictly positive . the matrix @xmath190 is positive definite . conjugate @xmath191 to a diagonal matrix with eigenvalues @xmath192 . then @xmath193 where @xmath194 is the _ hadamard product _ of @xmath191 with itself . by schur product theorem ( ( * ? ? ? * theorem 7.5.3 ) ) , @xmath195 is positive definite , which finishes the proof . ( 2.5,2.5 ) ( 0,0)(2.5,2.5 ) we remark that theorem [ logdet : concave ] can be considered as an analogue of the convexity of the determinant of laplacian in a conformal class of metrics on surfaces of genus greater than or eqaul to one , proved by osgood , phillips and sarnak in @xcite . it would be interesting to characterize graphs @xmath21 where @xmath38 achieves its maximum in the interior of @xmath126 . we introduce some notation which will be used in studying the taylor expansion of the eigenvalues . given two points @xmath196 , let @xmath197 and let @xmath198 be the segment ( call it @xmath199 ) connecting the two points in @xmath80 . the normalization condition reads @xmath200 the basis of all @xmath127-s satisfying is given by vectors @xmath201 for @xmath202 where @xmath203-s are the standard basis vectors . we next turn to studying how the eigenvalues of the laplacian depend on @xmath118 . we look at one parameter family @xmath204 of laplacians on @xmath21 corresponding to the points on @xmath199 . the laplacian is given by the matrix @xmath205 by standard results in perturbation theory ( @xcite ) , there exists an orthonormal basis of the eigenvectors of @xmath186 such that the the eigenvalues and the eigenvectors admit taylor expansions in @xmath118 . let @xmath206 be an eigenvalue of the multiplicity @xmath207 . let @xmath208 be the corresponding ( @xmath209-dimensional ) eigenspace , and let @xmath210 denote the corresponding projection . the condition for the graph @xmath21 to be a critical point for @xmath211 is that the matrix @xmath212 be indefinite for all @xmath135 . we now compute the eigenvalues of @xmath212 for the edge weightings given by with @xmath213 as in . we distinguish between two cases : * edges @xmath214 and @xmath215 are disjoint . * edges @xmath214 and @xmath215 share an endpoint we first consider the case a ) . let @xmath216 be a basis of eigenvectors of @xmath208 . for convenience , we denote @xmath217 by @xmath218 and @xmath219 by @xmath220 . the eigenvalues of @xmath212 are given by the eigenvalues of the linear form @xmath221 defined by @xmath222 it is easy to see that the matrix of @xmath223 is given by @xmath224 the eigenvalue @xmath211 is critical if @xmath225 is indefinite for any choice of @xmath135 . we remark that @xmath225 is a difference of two rank one matrices , @xmath226 where @xmath227 and @xmath228 and so has rank at most two . computing the coefficient @xmath229 of @xmath230 in the characteristic polynomial of @xmath225 , we find that @xmath231 therefore , @xmath232 and is strictly negative unless @xmath177 and @xmath127 are proportional or one of them is zero . now , if @xmath233 then @xmath225 is indefinite ( since it has at most two nonzero eigenvalues ) . if @xmath234 ( and @xmath225 has rank one ) and if @xmath211 is critical then @xmath235 . consider first the case of a simple eigenvalue ( @xmath236 ) . then @xmath211 is critical if @xmath237 for every choice of @xmath135 and therefore @xmath238 or @xmath239 . recalling the definition of @xmath240 and @xmath241 , we see that for the eigenvector @xmath242 @xmath243 of @xmath21 is adjacent to every other edge , we prove an analogue of for the case b ) of adjacent edges ( it was proved before for the case a ) of non - adjacent edges ) . [ eigen : crit ] a simple eigenvalue @xmath211 of the laplacian on @xmath21 is critical if and only if the corresponding eigenvector @xmath22 satisfies @xmath244 we now study the graphs which admit an eigenvector @xmath22 satisfying for some @xmath245 . if @xmath246 then @xmath247 is a multiple of a constant vector and so has eigenvalue zero which is a contradiction . if @xmath248 then it is easy to see that the graph @xmath21 can not have odd cycles and hence is bipartite . namely , let @xmath249 be a cycle . then ( putting @xmath250 ) @xmath251 . but each term in the sum is equal to @xmath252 , and since the number of terms in the sum is odd , they can not add up to @xmath253 we now want to study the unweighted @xmath3-regular graphs which have an eigenvector ( corresponding to an eigenvalue @xmath254 ) satisfying ( without necessarily assuming that @xmath211 is simple ) . we shall rescale the eigenvector so that @xmath255 in . from and it follows that for each vertex @xmath107 the expression @xmath256 can only take one of the values @xmath257 . consider first the vertex @xmath258 where @xmath259 takes its maximal value @xmath260 ( by changing the sign if necessary we can assume that @xmath261 ) . it follows that @xmath247 takes value @xmath262 on all the neighbors of @xmath258 , hence @xmath263 next , consider any neighbor @xmath264 of @xmath107 . the value of @xmath247 at any neighbor of @xmath264 can be either @xmath260 ( let there be @xmath265 such neighbors ; @xmath258 is one of them ) ; or @xmath266 ( it follows that there are @xmath267 such neighbors ) . from it follows that @xmath268 it follows from the last two formulas that @xmath269 where @xmath265 is a positive integer . if @xmath270 , then @xmath271 is the largest eigenvalue of @xmath19 . we next define the _ level _ of a vertex @xmath107 to be equal to @xmath272 if @xmath273 ; we denote the set of all vertices of @xmath21 at level @xmath272 by @xmath274 . it is easy to see that if @xmath275 has @xmath276 neighbors where @xmath247 takes value @xmath277 then @xmath278 it follows that @xmath276 is the same for all @xmath275 . using we see that @xmath279 consider now a `` local minimum '' @xmath280 . then @xmath281 , and we see that @xmath282 let @xmath283 denote the number of vertices in @xmath274 . counting the vertices connecting @xmath274and @xmath284 in two different ways , we see that for all @xmath285 , @xmath286 consider the case @xmath287 . it follows from the previous calculations that @xmath288 and that @xmath289 . accordingly , @xmath290 and latexmath:[\[\label{vertn : dfconst:2 } eigenvector of @xmath19 with @xmath292 satisfying . an obvious example of such a @xmath3-regular graph is the @xmath3-cube , and any such graph has the same number of vertices as a disjoint union of @xmath293 cubes by . start now with such a union , choose the partition of the vertices of each cube into `` levels '' and take two edges @xmath294 and @xmath295 in two different cubes such that @xmath296 are both in level @xmath272 while @xmath297 are both in level @xmath298 . if we perform an edge switch @xmath299 then the number of the connected components of our graph will decrease while the eigenvector @xmath247 will remain an eigenvector with the same eigenvalue . performing sequences of edge switches as described above , we obtain examples of connected graphs satisfying and for any @xmath293 . conversely , it is easy to show that starting from a graph satisfying and and having chosen a partition of its vertices into levels one can obtain @xmath293 disjoint @xmath3-cubes by performing a sequence of edge switches as above . we now want to consider the case when @xmath300 is the lowest eigenvalue of the laplacian . the first remark is that then necessarily @xmath301 , and @xmath302 only if @xmath303 . next , we want to consider `` small '' @xmath3 for which @xmath304 ( the `` ramanujan bound '' ) is less than @xmath47 ( this happens for @xmath305 ) . it then follows from the results of alon ( @xcite ) that the diameter of @xmath21 ( and hence the number of vertices in @xmath21 ) is bounded above . [ mu1:finite ] for @xmath305 there are finitely many @xmath3-regular graphs for which the condition is satisfied for an eigenvector of @xmath306 . we next discuss graphs which have an eigenvector satisfying with the eigenvalue @xmath307 . recall that by @xmath308 . by counting the edges connecting the vertices in two consecutive levels one can show ( as for @xmath292 ) that the number of vertices satisfies @xmath309 has @xmath310 distinct neighbors in @xmath311 , @xmath312 it is easy to construct examples of regular graphs which have eigenvectors with the eigenvalue @xmath313 satisfying ; the construction is similar to that for @xmath292 . we summarize the previous results : [ eigencrit : character ] let @xmath21 be a @xmath3-regular graph which has an eigenvector of @xmath19 with an eigenvalue @xmath211 satisfying . then @xmath21 is bipartite , @xmath314 is an even integer dividing @xmath315 , the number of vertices of @xmath21 is divisible by @xmath316 , and for @xmath317 there exist such graphs with @xmath318 vertices . here we shall give some heuristic arguments concerning some properties that graphs with many spanning trees are expected to have . one such property is having large girth ; the sequences of cubic graphs described in section [ sec : construct ] seem to support that expectation . we shall give some heuristic arguments in its support . we start with the following formula from @xcite for the number @xmath38 of spanning trees of a @xmath3-regular graph @xmath21 with @xmath0 vertices : @xmath319 where @xmath320 is a function depending on the valency @xmath3 only ( and hence _ the same _ for all @xmath3-regular graphs ) , while @xmath321 is the number of walks which are not _ totally reducible _ ( i.e. which do nt `` come '' from the infinite tree @xmath322 ) . in particular , @xmath323 for @xmath324 . the coefficients @xmath325 in the sum in are always negative for small @xmath118 , so each nonzero term in the sum _ decreases _ the value of the expression in brackets in . heuristically then , the more @xmath321-s are equal to zero , the larger the expression in brackets is in and so the larger is the limit which is @xmath38 . now , if we want to compare @xmath38 for different graphs in @xmath4 those with larger girth @xmath98 have more @xmath321-s equal to zero and therefore are the natural candidates for large values of @xmath38 , and even more so moore graphs , since they are the unique graphs in @xmath4 having the largest girth . of course , we have only looked at the first nonzero term in the infinite series , but we remark that the subsequent @xmath321-s get multiplied by @xmath326 which is exponentially decreasing in @xmath115 . this seems to give at least a partial heuristic explanation of the cages appearing in section [ sec : construct ] . it also seems reasonable to conjecture that graphs with higher connectivity have more spanning trees . indeed , one can show that if an edge @xmath327 is a bridge in a one - connected graph @xmath328 and if @xmath329 ( say ) is two - connected , then one can make an edge switch in @xmath21 which will increase the number of spanning trees ( cf . @xcite for the discussion of operations on graphs increasing their number of spanning trees ) . however , it seems to be more difficult to prove that for a two - connected graph there exists an edge switch which simultaneously increases the number of spanning trees . we believe this to be true in essentially all cases , however . in this section we shall give an upper bound for the number of spanning trees for @xmath8-regular graphs on a fixed surface @xmath195 which is strictly smaller than the mckay s bound for general @xmath8-regular graphs . let @xmath21 be a @xmath3-regular simple graph on @xmath0 vertices embedded in an orientable surface @xmath330 of genus @xmath52 . let @xmath331 denote the number of vertices , edges and faces of @xmath21 . by euler s formula , @xmath332 ( the inequality becomes an equality if all faces are simply - connected ) . it follows easily that if infinitely many simple @xmath3-regular graphs can be embedded in a fixed surface @xmath195 , then @xmath333 . we denote by @xmath334 the set of all simple @xmath3-regular graphs embeddable on the orientable surface @xmath330 . mckay proves in @xcite that for a random @xmath3-regular graph on @xmath0 vertices , @xmath335 as @xmath336 . we now state the main result of this section : [ thm:6sur ] let @xmath334 be as above . then @xmath337 to prove the theorem we first establish a proposition estimating the ratio of the tree number of @xmath21 to the tree number of its dual graph @xmath338 . we next remark that the dual of a @xmath8-regular graph on @xmath0 vertices is `` roughly '' a @xmath339-regular graph on @xmath340 vertices ; an application of mckay s theorem finishes the proof . [ tree : ratio ] let @xmath341 be a sequence of simple graphs on an orientable surface @xmath195 of genus @xmath52 such that their maximal degrees are bounded . let @xmath38 and @xmath342 be the corresponding numbers of spanning trees , and let @xmath343 be the number of vertices of @xmath274 . then @xmath344 * proof . * we first define a mapping from the spanning trees of @xmath274 into ( subsets of ) the spanning trees of @xmath345 as follows : take a spanning tree @xmath346 of @xmath274 , and consider the complement @xmath347 of @xmath346 in @xmath274 . it is easy to see ( @xcite ) that @xmath195 is connected , spans @xmath345 and that one can get a spanning tree of @xmath345 by removing at most @xmath348 edges of @xmath195 . we denote by @xmath349 the set of all spanning trees of @xmath345 which can be obtained from @xmath346 by the above procedure . by reversing the construction , it is easy to see that the mapping @xmath350 is onto . let @xmath351 , and let the maximal degree be bounded above by @xmath352 . let @xmath346 be a spanning tree of @xmath274 , and let @xmath353 . then @xmath354 and so @xmath355 adding the inequalities for all @xmath346 proves one of the bounds in . the other inequality is proved similarly . we remark that the constants in depend on @xmath352 , @xmath3 and @xmath52 only . ( 2.5,2.5 ) ( 0,0)(2.5,2.5 ) consider now a simple @xmath8-regular graph @xmath21 ( embedded on a surface @xmath330 ) with @xmath0 vertices and @xmath356 edges , and let @xmath338 be the dual graph ( of genus @xmath357 ) . @xmath338 has @xmath358 edges and at least @xmath359 vertices ; moreover , since @xmath21 is simple , every face of @xmath21 has at least three sides , so the minimal degree of @xmath338 is at least three . it is easy to see that @xmath338 can be obtained from a ( possibly disconnected ) graph @xmath329 of maximal degree at most @xmath339 with at most @xmath360 vertices by adding @xmath361 `` new '' edges between the vertices of @xmath329 . * proof of theorem [ thm:6sur ] . * let @xmath21 be a graph in @xmath362 . by proposition [ tree : ratio ] , it suffices to estimate @xmath342 . consider a spanning tree @xmath346 of @xmath338 containing @xmath363 of the `` new '' edges @xmath364 , where @xmath365 . removing the @xmath363 edges from @xmath346 produces a spanning forest of @xmath329 with @xmath366 components . it suffices to establish the estimate for @xmath363-component spanning forests of @xmath329 for each @xmath363 separately . for @xmath367 the estimate follows easily from mckay s estimate for cubic graphs on at most @xmath360 vertices . to establish the estimate for @xmath368 , we first remark that the number of the connected components of @xmath329 is at most @xmath369 ; let @xmath370 be denote these components , and let @xmath371 have @xmath372 vertices , where @xmath373 . each component @xmath374 is a graph of maximal degree at most @xmath339 . let @xmath225 be an @xmath363-component spanning forest of @xmath329 . let @xmath375 be a spanning forest of @xmath371 with @xmath376 components , where @xmath377 . @xmath378 can be obtained from a spanning tree of @xmath152 by removing @xmath376 edges from the tree . each tree has @xmath379 edges , so one can get at most @xmath380 spanning forests by removing @xmath376 edges from it , so the total number of such forests is at most @xmath381 multiplying the inequalities for all @xmath371-s we estimate the number of @xmath363-component spanning trees of @xmath329 by @xmath382 now , let a sequence @xmath383 be a sequence of @xmath8-regular graphs on @xmath330 , and let @xmath343 . taking the @xmath283-th root in and letting @xmath343 shows that it suffices to prove that @xmath384 where the subscript @xmath272 refers to the graph @xmath274 . in order to arrive at a contradiction , we shall assume that there exists a sequence of graphs @xmath274 on @xmath330 such that the limit in is strictly greater than @xmath385 . passing to a subsequence if necessary we may assume that the number @xmath386 of components of @xmath387 is actually constant and equal to @xmath209 . we shall order the components @xmath388 so that @xmath389-s are non - decreasing . passing once again to a subsequence if necessary , we may assume that there exists a nonnegative number @xmath390 and a sequence @xmath391 such that @xmath392 for @xmath393 , and @xmath394 for @xmath395 . now applying mckay s bound for each @xmath395 ( with @xmath396 ) and estimating each of the first @xmath115 terms in by an absolute constant leads easily to a contradiction , finishing the proof of theorem [ thm:6sur ] . ( 2.5,2.5 ) ( 0,0)(2.5,2.5 ) the bound proved in theorem [ thm:6sur ] is not optimal . we define the optimal bound for @xmath305 : @xmath397 it follows from the proof of theorem [ thm:6sur ] that for @xmath398 , @xmath399 it follows that the limit in does not depend on @xmath52 ( as long as @xmath334 is not empty for large @xmath0 , which can happen for small @xmath52 ) . accordingly , we define @xmath400 to be stands for _ surface_. ] the limit @xmath401 achieved in for some fixed @xmath402 and @xmath305 . noga alon has informed the authors that he can show that @xmath403 ( where @xmath404 is defined in ) . it follows from the proof of theorem [ thm:6sur ] that @xmath405 . one can actually show by a similar argument that @xmath406 we make a conjecture about the graphs that achieve the limit in for @xmath407 : [ conj : surftree ] the limit @xmath408 ( respectively , @xmath409 ) is achieved by quotients of the hexagonal lattice ( respectively , the square lattice ) in @xmath410 . it would follow from conjecture [ conj : surftree ] ( cf . @xcite ) that @xmath411 here @xmath21 is catalan s constant . the exponent @xmath412 in is equal to the toplogical entropy @xmath413 of the _ essential spanning forest process _ on the nearest neighbor graph on @xmath414 ( @xcite ) . the integral above is equal to the _ mahler measure _ of the polynomial @xmath415 ; it is equal to @xmath416 where @xmath417 is the dirichlet @xmath418-function associated to the quadratic extension @xmath419 ( cf . it would be interesting to find candidates for achieving @xmath420 . in this section we want to establish an analog for graphs of a result of buser and sarnak ( @xcite ) about the rate of growth of the minimal norm of a period matrix of a riemann surface . they have shown that as the genus of a surface increases , the minimal norm grows at most logarithmically in the genus . bacher , de la harpe and nagnibeda in their work ( @xcite ) defined two lattices associated to any unweighted graph , _ the lattice of integral flows _ @xmath421 and _ the lattice of integral coboundaries _ @xmath422 . the quotient @xmath423 is a finite abelian group called a _ jacobian _ of a graph ( in an analogy to jacobians of riemann surfaces ) . we shall now consider @xmath3-regular graphs for some fixed @xmath43 . let @xmath424 ; the dimension of @xmath425 is equal to @xmath426 . the determinant of @xmath425 is equal to the tree number @xmath38 , and the ( unnormalized ) minimal norm @xmath427 of @xmath425 is equal to the girth of @xmath21 . we rescale @xmath421 so that the volume of its fundamental domain is equal to @xmath7 ; the ( normalized ) minimal norm @xmath428 is given by @xmath429 from and we conclude that for every @xmath430 , @xmath431 for @xmath0 large enough . we want to study the behavior of @xmath428 when @xmath3 is fixed and @xmath336 . using the known results about the behavior of the girth , we conclude : [ jacobian : rate ] the minimal norm @xmath428 of the jacobian of a @xmath3-regular graph @xmath424 satisfies @xmath432 this establishes an analogue of the results of buser and sarnak . it is known ( @xcite ) that every @xmath339-connected cubic graph may be constructed from a tetrahedron by a sequence of _ edge insertions _ : given a cubic graph on @xmath340 vertices , choose a pair of edges , subdivide them by putting a single vertex in the middle , and connect the two subdivision vertices to get a cubic graph on @xmath360 vertices . so , every @xmath339-connected cubic graph @xmath21 may be constructed from the tetrahedron provided we know the `` history , '' i.e. the sequence in which insertions were applied to successive pairs of edges . clearly , that `` history '' is not unique . however , one may hope that if @xmath21 is an extremal graph , among all its histories there exist ones with some nice properties . below we shall give some examples when that is indeed the case . the first example is the following sequence @xmath195 : starting from a tetrahedron , insert edges in such a way that the number of spanning trees is maximized after each application . when the number of vertices is small , one may find the graphs in @xmath195 from the table of graphs in @xcite . the @xmath8-vertex graph is @xmath433 , the @xmath9-vertex graph is a mbius ladder ( an @xmath9-cycle with the pairs of `` opposite '' vertices connected , cf . @xcite ) ; it has @xmath434 trees . the @xmath79-vertex graph is the petersen graph @xmath80 ( @xmath78 trees ) , and the @xmath64-vertex graph is obtained from @xmath80 by applying @xmath11 to a pair of edges at distance @xmath47 from each other ( this is graph # 84 in @xcite ; it has @xmath435 spanning trees ) . the last graph also appears in @xcite . from the table of graphs in @xcite one can check that the graphs in the sequence have the most trees among the cubic graphs with the same number of vertices . the rest of the graphs in the sequence @xmath195 are shown in the appendix ; they were obtained by a computer program . it is remarkable that the sequence contains all @xmath436-cages for @xmath437 . namely , the @xmath438-vertex graph in @xmath195 is the heawood graph , the @xmath439-vertex one is the mcgee graph , and the @xmath440-vertex one is the tutte - coxeter graph ( cf . @xcite or ( * ? ? ? 6 ) ) . unfortunately , the graphs in @xmath195 with @xmath441 or more vertices seem to be less interesting . the first few graphs in the sequence appear in @xcite ( but without the reference to the tree number ) ; however , the inclusion of the @xmath64-vertex graph in the sequence and the graphs with @xmath442 or more vertices appear to be new . the authors hope that similar constructions may lead to discovery of new extremal graphs . one can use operations similar to the edge insertion to increase the number of vertices and construct sequences of @xmath3-regular graphs by maximizing a certain invariant . ] edge insertion has its disadvantages : for example , certain cages of even girth have the property that every two edges are contained in a common shortest cycle ( @xcite ) ; inserting an edge will then certainly decrease the girth . so , one might try adding several new vertices and edges simultaneously . for cubic graphs , one can try subdividing several edges of an `` old '' graph ( with one , two or more points on an edge ) to get an _ even _ number of `` new '' vertices of valence @xmath47 , then choosing a perfect matching for the new vertices and connecting pairs of these vertices according to the perfect matching to get a new cubic graph . several cubic cages can be obtained by taking uniform subdivisions of smaller graphs and inserting edges : * the petersen graph can be constructed from a tetrahedron by subdividing its @xmath8 edges ; * the heawood graph can be obtained from the unique loopless two - vertex cubic graph ( @xmath443 ) by putting 4 new vertices on each of its @xmath339 edges ; * the tutte graph can be obtained from @xmath444 by subdividing each of its @xmath445 edges . this section describes a sequence of cubic graphs generated ( by a computer ) from the tetrahedron by edge insertion where at each stage the insertion was chosen so that the number of spanning trees of he new graph was the maximal possible . the first six graphs are shown in figure 1 ; the endpoints of the new edge inserted into a cubic graph on @xmath340 vertices were numbered @xmath446 and @xmath360 . in figure 4 we show how to construct petersen and heawood graphs by edge insertions into the tetrahedron and the graph @xmath443 respectively . the vertices of @xmath10 and @xmath443 are shown in black . in figure 5 we show how to construct the tutte graph by edge insertions into @xmath444 . the vertices and the edges of @xmath444 are shown in black ; the vertices of the two copies of @xmath433 are marked @xmath11 and @xmath135 respectively .

in this paper we are concerned with various graph invariants ( girth , diameter , expansion constants , eigenvalues of the laplacian , tree number ) and their analogs for weighted graphs weighing the graph changes a combinatorial problem to one in analysis . we study both weighted and unweighted graphs which are extremal for these invariants . in the unweighted case we concentrate on finding extrema among all ( usually ) regular graphs with the same number of vertices ; we also study the relationships between such graphs . [ section ] [ theorem]proposition [ theorem]lemma [ theorem]corollary [ theorem]corollary [ theorem]definition [ theorem]question [ theorem]remark [ theorem]claim [ theorem]note [ theorem]conjecture

the unexpected measurement of ultraviolet light in the metal rich populations of bulges and spheroids was one of the early important discoveries in space astronomy @xcite . initial suggestions that the ultraviolet rising flux ( or uvx ) was caused by low level star formation or nuclear activity gave way to the current view , that evolved stars are responsible for the uvx . while not arising from recent star formation , the stellar population responsible for the uvx in early type galaxies has eluded convincing identification among the resolved stars in globular clusters and other nearby populations . early theoretical work aimed at solving the mystery ( e.g. , @xcite ) favors evolved stars as the source , with helium burning stars being both luminous enough , and sufficiently long lived , to be plausible candidates . recent observations of nearby galaxies support this view . modeling integrated spectra of nearby uvx galaxies , @xcite argue against post - agb stars as the dominant contributor . direct imaging of m32 @xcite finds fewer than expected luminous uv stars ( and a striking lack of post - agb stars ) firming support for the extreme horizontal branch ( ehb ) hypothesis . recent reviews considering the problem of the uvx are given in @xcite , @xcite , and @xcite . one of the core observational results is the correlation of the uv rising flux with metallicity and velocity dispersion ( @xcite;bbbfl ) . bbbfl show that the nuclear populations of 24 early - type galaxies with optical spectra indicating no signs of agn or star formation exhibit a strong correlation between uvx ( in the form of a @xmath3 color ) and the lick @xmath2 metallicity index , a result which strongly influenced theoretical efforts to explain the uvx . the discovery of very blue horizontal branch stars in the metal rich globular clusters ngc 6388 and 6441 @xcite shows that uv bright stars are present even in some old metal rich populations . the presence of a correlation between uvx and independent measurable parameters not only gives a clue to the source of the uvx , but also could be exploited to gain insight into the evolution of the uvx with lookback time . if the source of the uvx is hot horizontal branch stars , theoretical models ( e.g. @xcite ) expect a rapid decline as a function of lookback time , because only within the last few gyr have the masses of old turnoff stars been low enough that the helium burning progeny of rgb tip stars would have envelopes thin enough to make the stars uv bright . to make possible the study of the uvx in large samples , or distant galaxies , we seek correlations in properties measurable from integrated light . recent observations have begun to weaken the assertion of a strong primary correlation between uvx and metallicity . @xcite use the film - based imaging of the _ ultraviolet imaging telescope _ @xcite to find far - uv color gradients in early - type galaxies , in the sense of redder colors in the optically bluer , outer parts of ellipticals . however , this study finds a range in color gradients and no clear trend with the lick @xmath2 index . @xcite form a color using @xmath4 as measured from the balloon - borne _ foca _ mission @xcite and plot this against the @xmath2 index for early - type galaxies . they find no correlation between @xmath4 and @xmath2 for the early - type galaxies in their sample . however , they do not spectroscopically screen against galaxies with agn and weak star formation and , most significantly , the uvx dominates _ blueward _ of 2000 , in the satellite ultraviolet . the successful launch of the _ galaxy evolution explorer _ has made possible the construction of a significantly larger sample of early - type galaxies with which to probe the behavior of uvx than was possible for bbbfl . the observations above the atmosphere permit measurement of the uvx in the optimal window where it is most prominent , from @xmath5 . the satellite and its operations are described in this volume @xcite . in this _ letter _ we explore the relationship between the uvx ( in the form of integrated light @xmath1 and metallicity ) for a sample of galaxies considerably more distant than was considered in bbbfl , but nonetheless early - type galaxies in the relatively local universe @xmath6 . we use the @xmath1 color as the best proxy for the @xmath3 color of bbbfl , given that sdss @xmath7 is generally measured with higher s / n and has a smaller k - correction than sdss @xmath8 . we aim to combine galex and sdss data for a sample of early - type galaxies with no optical signs of star formation , nuclear activity , or disturbed morphology . we require that the galaxies have sdss spectra with high enough s / n to assure neither detectable @xmath9 nor k+a type spectra will enter this sample . these `` quiescent '' early - type ( qe ) galaxies are selected based on morphology and spectroscopy . we begin by selecting candidates from the sdss dr1 spectroscopic sample that are consistent with early - type morphology and basic spectral shape . we draw our sample from objects photometrically classified as galaxies , and use essentially the same criteria used by @xcite : a ) @xmath10 , the high ratio of radii capturing 90 and 50% of the petrosian flux ( also known as concentration ) ensures that most early - type galaxies are selected ( but with sizable late - type contamination ) ; b ) @xmath11 selects objects whose likelihood of a devaucouleurs ( @xmath12 ) profile in @xmath7-band is 3% higher than the exponential profile ; c ) @xmath13 ( spectral template fitting coefficient obtained from principal component analysis of spectra ) additionally ensures that objects with spectra inconsistent with early - type galaxies are not selected ( note that eclass corresponds to negative @xmath14 in @xcite ) . finally , we ask that spectra have s / n @xmath15 in @xmath7-band . unlike @xcite we do not require that the zwarning flag not be set , nor do we impose a redshift cut at this stage . these criteria yield 54950 candidates , or some 40% of all dr1 galaxies with spectra . for these galaxies we retrieve dereddened petrosian magnitudes and their errors , velocity dispersion measurements , and various other parameters . for these galaxies , we measure lick @xmath16 and d4000 indices ( using the @xcite definition ) , using a special purpose analysis pipeline ( see @xcite for details ) . also , by measuring the residual nebular emission lines left from the subtraction of a stellar continuum model @xcite we can classify these galaxies using a bpt plot @xcite into star - forming galaxies ( 3% ) , star - forming galaxies with weak s / n features ( 13% ) , galaxies that show both star forming and agn features ( composites , 8% ) , and agns ( 19% ) . the remainder comprises galaxies with @xmath17 in h@xmath18 , i.e. no measurable lines permitting classification in any of the above categories . this is our core sample of `` quiescent '' early - type galaxies . they represent 57% of our sample ( yet just 30% of the full dr1 are quiescent early - type galaxies ) . galex images the sky in the far and near uv ( 1530 and 2310 ) in two modes : all - sky imaging survey ( ais , @xmath19 ) and medium - deep imaging survey ( mis , @xmath20 ) . each circular field covers 1.1 sq.deg . @xcite have performed sdss dr1/galex matching of objects in galex internal release ( ir 0.2 ) catalog , consisting of 649 ais and 94 mis fields , of which 117 and 91 overlap ( not always entirely ) with sdss dr1 . we include an additional field ( not in ir0.2 ) on the cluster of galaxies abell 2670 @xmath21 . thus our total overlap with sdss dr1 is @xmath22 sq . deg . , or some 10% of dr1 spectroscopic footprint . we use @xmath23 and @xmath24 magnitudes and errors derived in an elliptical aperture . we cross - correlate our 54950 early - type candidates from dr1 with galex objects having sdss spectroscopic counterparts ( 10357 objects ) and obtain 2174 objects in common . we discard 120 galaxies with @xmath25 because of our compromised ability to classify them , and due to the 2 gyr lookback time . we also exclude 24 objects not classified spectroscopically as galaxies . this leaves us with 2038 galaxies with acceptable sdss and galex data , with morphology and basic spectral shape consistent with early - type galaxies , and with @xmath0 . we then subject this sample to further scrutiny using the bpt classification outlined above . now the star forming ( sf ) galaxies constitute 6% , low - s / n sf 17% , composites 15% , agns 27% , and the remaining , quiescent early - types ( qe ) , 35% of the sample . since galex is sensitive to uv light from young stars and nuclear activity , it is not surprising that the quiescent galaxies have fallen in proportion with respect to sdss - only sample . although we initially select all of these five classes as early - type candidates , many of the non - qe galaxies ( especially sf ) are obviously late - types . their inclusion in the candidate list is often times due to the presence of a dominant bulge , with a relatively faint disk . in our analysis we will primarily be concerned with galaxies that exhibit fuv flux . of our 2038 galaxies , only one - half ( 1032 ) have detectable ( @xmath26 ) fuv flux . it is these galaxies that are plotted in figure 1 . however , in this fuv - selected sample , qe comprise only 18% , or 189 objects . these optically `` old red and dead '' galaxies are the focus of our study . since , as we have seen , relying on just the morphological criteria is unreliable , and further considering that the fiber spectra ( in contrast to the integral fluxes ) sample only the central @xmath27 of a galaxy , we have visually inspected sdss images of these 189 galaxies . as a result of this , we find 17 objects that show hints of a structure : bars , weak spiral arms , or rings . while their classification as true early type galaxies is in doubt , the colors of these objects are no bluer , nor their spectra suspect , compared to our main qe sample . we remove these objects from our final sample of 172 quiescent e / s0s with a detectable far - uv flux . roughly 1/2 of these galaxies lie closer than @xmath28 and the other half at @xmath29 . we visually inspected the spectra of the 172 qe galaxies , and find that they are homogeneous with no abnormalities consistent with the presence of a late burst of star formation not accompanied by @xmath9 emission . the s / n of the qe sample spectra is @xmath30 ( rms ) ; we are confident that we did not miss any significant emission . the lowest s / n quartile of our sample has fuv@xmath31 , while the highest s / n quartile has fuv@xmath32 . we attribute this difference to bright red nearby galaxies which drop out of the sample at @xmath33 . we first consider the uv - optical properties of the full sample of sdss dr1 galaxies with early - type morphology , spectra with s / n@xmath15 , and detections in the fuv band ( figure 1 ) . these plots show a weak correlation between @xmath2 and @xmath1 , but in the sense that more metal rich galaxies are redder , opposite the trend of bbbfl . notably , galaxies with even weak spectroscopic signatures of star formation tend to have the bluest fuv colors and uniformly lower @xmath2 , and even lower d4000 ( not shown ) . the distribution of the agn and especially of star forming galaxies look similar in this plane , and clearly differs from that of the qe galaxies in the lowest panel , which mostly have @xmath34 , and very few galaxies with @xmath35 . averging @xmath2 for galaxies with @xmath36 , we find 0.16 for the star forming , 0.22 for the agn , and 0.24 for the qe . figure 2 concerns only possible correlations within the qe sample , now separated by redshift . we also identify members of abell 2670 which has also been investigated by @xcite to study the evolution of the uv rising flux . a rich cluster of galaxies with a large population of ellipticals , one might expect the galaxies in abell 2670 to be more uniform in their age of formation , and less affected by residual star formation , than are the field galaxies . we see no tendency to recover the bbbfl trends among the abell 2670 sample . the a2670 members appear to be uniformly more red than the field , both for the @xmath37 and @xmath29 subsets . in addition to @xmath2 , we consider the metallicity sensitive d4000 index ( the continuum drop below the ca hk lines is due to a large increase in metal lines , and is a metallicity sensitive index ) and with velocity dispersion ( mass ) . we find a weak correlation between @xmath1 and metallicity or mass , but in the opposite sense to that of bbbfl : more massive , metal rich galaxies have redder @xmath1 color . concerned by this failure to reproduce the bbbfl trends , we checked that the mg@xmath38 and d4000 correlate as expected , and that @xmath39 and @xmath2 correlate . we inspect visually each fuv detection and find a handful of cases where the uv emision is extended , even for galaxies in the qe sample ; removal of these from our sample has no effect . early type galaxies with @xmath40 are classified as residual star forming galaxies by @xcite in their study of the uv color - magnitude relation . they argue that such a strong uvx is inconsistent with that found in local samples ( e.g. bbbfl ) . we assert that our spectroscopic pre - selection and observed behavior in the d4000 and mg@xmath38 vs @xmath1 plots qualifies these as true uvx candidates . even if such galaxies were excised from the sample , our conclusions remain unaffected . the @xmath37 sample of qe galaxies appears to be redder in @xmath1 color than the @xmath29 sample . we have considered whether this could be due to a k correction by convolving the sdss and galex bandpasses with the appropriate quiescent evolving red metal rich population , constructed from the @xcite models . the k correction ( single burst population formed 13 gyr ago ) alone will cause an evolution of 0.3 mag to @xmath28 and 0.5 mag to @xmath41 ( a single burst stellar population formed at @xmath42 is already @xmath43 gyr old at @xmath41 ) . the difference in the color distribution may be related to rapid evolution of the uvx ( as is evidently also seen in @xcite ) . we will consider this and other issues in greater detail , later . however , we emphasize that we do not recover the bbbfl trends even for the lowest redshift subset of our data . surprising in light of their spectroscopic uniformity is the 5 mag range of @xmath44 . while half of our initial sample of early type galaxies was not detected in fuv , we verified that the bright end of our sample is sufficiently well detected in the fuv that the red limit is physical and not due to the reddest galaxies being undetected . the @xmath45 color may signal changes in the character of the underlying stellar population responsible for the uv upturn . figure 3 suggests that galaxies with the reddest @xmath1 ( weakest uvx ) also have redder @xmath45 colors . note that the qe galaxies are bluer than sf in @xmath45 : only 3% of the sf lack an nuv detection , while 16% of the qe galaxies lack nuv . in light of our absence of a correlation between uvx and metallicity , it becomes difficult to invoke helium abundance ( entering through @xmath46 ) as the primary controlling parameter in the strength of the uvx . the wide variation in color and lack of correlation with an obvious physical property might reflect small variations in star formation history which affect the age distribution of the old stars , or with uvx arising from a rare population fed by stochastic mass loss on the first ascent of the red giant branch . the lookback time in our sample is not negligble . for the concordance cosmology of @xmath47 , @xmath48 , and @xmath49 , the lookback time at @xmath28 is 1.3 gyr and reaches 2.4 gyr at @xmath41 . small differences in the formation time of our qe sample could correspond to observed diffferences of 1 - 2 gyr in age . well populated blue horizontal branches are found only in globular clusters with the age of the galactic halo . this observation is reflected in theoretical models ( e.g. @xcite ) which predict that the fuv flux should fade by 2 - 4 mag within the 2.4 gyr lookback time spanned by this sample . _ galex _ continues its surveys , and we plan to exploit the overlap between these and the sdss dr2 , resulting in a large jump in sample size . normal science operations with _ galex _ did not begin until august 2003 , however , observations of the virgo cluster have now been obtained and we expect to be able to reproduce more closely the measurements of bbbfl both for nuclear and integrated light , for nearby early - type galaxies . the origin of the uv rising flux and its systematic behavior with physical properties remains a complicated and challenging problem , some 30 years after its discovery using the first orbiting ultraviolet telescope . galex ( galaxy evolution explorer ) is a nasa small explorer , launched in april 2003 . we gratefully acknowledge nasa s support for construction , operation , and science analysis for the galex mission , developed in cooperation with the centre national detudes spatiales of france and the korean ministry of science and technology . we also acknowledge use of data from the sloan digital sky survey . the authors thank t. brown and a. renzini for valuable comments . jb acknowledges the support of an esa postdoctoral fellowship .

we present ultraviolet photometry for a sample of morphologically early - type galaxies selected by matching the sloan digital sky survey data release 1 with the _ galex _ medium and all - sky imaging surveys . we obtain a working sample of 1032 early - type galaxies with _ galex _ fuv detections , sdss spectroscopy , and @xmath0 . using the sdss spectra to identify galaxies with even weak star formation or evidence of agn , and further removing galaxies with any evidence of non early - type morphology , we derive a final sample of 172 red quiescent early - type galaxies . we find that the @xmath1 color has a full range of 5 mag . plotting against the @xmath1 color the metallicity sensitive lick @xmath2 and d4000 indices , and the stellar velocity dispersion , we find no correlation between our measurement of uv rising flux , and any parameter sensitive to metallicity .