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MINUTE OF MOURN FOR AYLAN KURDI AND OTHERS DI Media [email protected] People across the world will be taking a moment of prayer´-or-silence to remember Aylan Kurdi, his brother, his mother and other refugees who have lost their lives attempting to reach Europe. Details Minutes of silence´-or-prayer to be held worldwide to honour the victims of the humanitarian tragedy unfolding on the shores of Europe and elsewhere. Those paying their respects will be thinking particularly of Aylan Kurdi, his brother Galip Kurdi, their mother Rehan Kurdi and their loved-ones. Time: 4 September 2015 at 8 PM CET7 GMT2 PM ET10 PM Kobane time DI Media Committee said the decision to organise a moment of silence´-or-prayer was taken after requests poured in to DI President, Dr Widad Akrawi, on twitter and other social networks. What can be saidWords disappear as pain and grief take holdTears come rushing and there is no solace What has become of usWe have become blind to the fact that Aylan was our sonMillions of children and youth across the world who suffer unspeakable injustices are all our childrenUntil we realize this there will be no peace We never knew AylanSo why do we cry?Because he is part of usPart of us that died Dear Aylan Wherever you areHave no doubtLike the sunWe will riseTo reclaim our humanity In loving peace Gal Emotional Statement by Mr. Zar Ali khan Afridi, DI representative in Pakistan and executive -dir-ector of Society for Rights and Development Aylan my sweet child. You are not dead. You are ing. You have gone to heaven. My God when I look at you my own son who is of same age just comes and stands before me. I have same sentiments for your brother who is not seen here but I have same feeling for him too. Your Mom who is also no more with you here but she is with you both in heaven I have same sentiments for her as well. Today all day long and to night I have lost no moment to forget what happened with you. You made me speechless like million of people. I am unable to share your picture of with my wife´-or-child who is of your same age. I am sure my wife will be half dead if she sees you. My child more and more. Your is a slap on the face of humanity in general and so called Arab and Muslim Ummah if any in particular. I can not do any thing more except shedding few tears for you all three. Pl accept my flowers wreath for you and your brother and sweet Mom. The more I see you the more I lose my heart. Child we as adult human beings are very much ashamed before you for not protecting you. You’re lying in such an innocent posture does ask us question which we are unable to answer. My toddler you better go to heaven to be sheltered from brutalities of the terrorists. Background The two boys: Aylan Kurdi (three-year-old) and Galip Kurdi (five-year-old) were refugees from Kobane trying to resettle in Canada. When their family lost hope of a new life in Vancouver, they attempted to reach the Greek island of Kos. Their journey ended when their boat overturned due to high waves, leaving their lifeless bodies along with that of their mother Rehan and those of eight other refugees washed up on a Turkish beach of the Bodrum peninsula Wednesday. Their father survived and his only wish now is to return to Kobane with his dead wife and children to bury them. This family’s tragedy encapsulates the challenges refugees are facing to flee armed conflicts in their countries. According to the UN refugee agency, Wednesday’s dead were part of a grim toll of nearly 2,500 people who have died this summer attempting to cross the Mediterranean to Europe. It is estimated that around 205,000 refugees have entered Greece this year alone. Key Messages on behalf of Defend International DI President, Dr. Widad Akrawi, today expressed condolences on behalf of Defend International to the families and friends of victims. Dr. Akrawi stated: “Our heartfelt sympathy goes to the families and friends of those who have died and all refugees and their loved ones. Our thoughts are with them as they mourn the passing of those they loved.” Dr. Akrawi thanked volunteers and humanitarian workers worldwide for their outstanding efforts in aiding desperate refugees. She called on the international community to share equitably the responsibility for protecting, assisting and hosting refugees in accordance with principles of international solidarity and human rights.

Q: mysql CREATE TRIGGER after insert on Update column with count it gives error. I don't understand why. CREATE TRIGGER `estatecat_piece` AFTER INSERT ON `estate` FOR EACH ROW BEGIN UPDATE estate_category set piece = (Select count(*) from estate where estate.estatecat_id=new.estatecat_id); ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '' at line 1 -EDIT- agian error... mysql> DELIMITER ; CREATE TRIGGER `estatecat_piece` AFTER INSERT ON `estate` FOR EACH ROW BEGIN UPDATE estate_category set piece = (Select count(*) from estate where estate.estatecat_id=new.estatecat_id); END; DELIMITER ; mysql> mysql> show triggers; Empty set (0,00 sec) _ LAST ATTEMPT'S ERROR _ mysql> DELIMETER $$ -> CREATE TRIGGER estatecat_piece -> AFTER INSERT ON estate FOR EACH ROW -> BEGIN -> UPDATE estate_category set piece = (Select count(*) from estate where estate.estatecat_id=new.estatecat_id) where estatecat_id=new.estatecat_id; ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'DELIMETER $$ CREATE TRIGGER estatecat_piece AFTER INSERT ON estate FOR EACH ROW ' at line 1 A: The immediate issue with your first statement is that it has BEGIN without a corresponding END. In this case, END should be at the very end of the CREATE TRIGGER statement. Once you add the END keyword, the statement becomes technically correct, but you will have trouble executing it in MySQL. The reason is that semicolons, while being standard statement delimiters in SQL, are also treated by MySQL in a special way. MySQL splits the input text at semicolons and sends each part of the text to the server separately. The server thus receives incomplete, syntactically incorrect pieces and returns an error. See here for more details: Defining Stored Programs So, to prevent MySQL from doing that, you need to instruct it to use a different symbol as a delimiter – that is what the DELIMITER command is for. Consequently, your second attempt should be something like this: DELIMITER $$ CREATE TRIGGER `estatecat_piece` AFTER INSERT ON `estate` FOR EACH ROW BEGIN UPDATE estate_category set piece = (Select count(*) from estate where estate.estatecat_id=new.estatecat_id); END$$ DELIMITER ; The first DELIMITER command tells MySQL to parse the input text until $$ is encountered from that point on. Your CREATE TRIGGER should, therefore, end with the $$ symbol so that MySQL can consume it in its entirety and send the whole statement to the server. Finally, the second DELIMITER command restores the standard delimiter for MySQL to resume normal processing of your commands. There is also a simpler solution, but it works only in cases similar to yours. The trigger body in your case consists of a single statement. That allows you to omit the keywords BEGIN and END from your statement and, as a result, avoid using the DELIMITER command at all: CREATE TRIGGER `estatecat_piece` AFTER INSERT ON `estate` FOR EACH ROW UPDATE estate_category set piece = (Select count(*) from estate where estate.estatecat_id=new.estatecat_id); The above trigger will work exactly the same. On a different note, your UPDATE statement may have a flaw: as currently written, it will update the piece column in every row with the same row count – that of the category matching the inserted row. If the table has multiple rows, each for a different category, you probably need to introduce a filter on new.estatecat_id to your UPDATE statement, similar to the filter in the subquery, in order to update only the corresponding piece value: UPDATE estate_category SET piece = ( SELECT COUNT(*) FROM estate WHERE estate.estatecat_id=new.estatecat_id ) WHERE ... /* specify the necessary column name */ = new.estatecat_id ;

Q: When is my date of birth? ___4,_4,_4 This is my real date of birth, because it looks unique, I try to do a simple operation, and I get a number 222. In fact it is able to solved without looking at the hint, but I'm trying to make this puzzle easy. Hint: ??+?4+,?4+,?4 = 141 When is my date of birth? And how is the number 222 obtained from the calculation results? The main purpose of this puzzle is not just for someone to answer it, but I hope someone can also improve what is needed A: From the hint: We start from $??+?4+?4+?4 = 141$, or in better notation $AB+C4+D4+E4 = 141$. Taking everything modulo 10, we get $B+12\equiv1$, so $B=9$. Since $D4$ is a month, we must have $D=0$ (there is no 14th month). Assuming you're not from the distant past or future (e.g. born in the 10th or 30th century), we must have $A=1$. Now the equation is $19+C4+04+E4=141$, so $C+E=11$. We also know that $E$ must be $0$ or $1$ or $2$, so the only option is $C=9,E=2$. So your date of birth is 1994/04/24 or 24 April 1994. If you want feedback, I would say that this isn't doable without the hint. Certainly not uniquely solvable, when you don't specify what types of operations are allowed. Following this site's generic advice on formation-of-numbers questions, I'd advise you to restrict the possible operations which are permitted to be used in getting from the birthdate to 222. E.g. is it just $+,-,\times,\div$? Are $\sqrt{},!,\lfloor\,\rfloor, \exp$ also allowed? You need to have a clear finite list, otherwise there are too many thinking-outside-the-box possibilities.

Ultrasonic scanners for detecting blood flow based on the Doppler effect are well known. Such systems operate by actuating an ultrasonic transducer array to transmit ultrasonic waves into a body and receiving ultrasonic echoes backscattered from the body. In the measurement of blood flow characteristics, returning ultrasonic waves are compared to a frequency reference to determine the frequency shift imparted to the returning waves by flowing scatterers such as blood cells. This frequency shift, i.e., phase shift, translates into the velocity of the blood flow. The blood velocity is calculated by measuring the phase shift from firing to firing at a specific range gate. The change or shift in backscattered frequency increases when blood flows toward the transducer and decreases when blood flows away from the transducer. Color flow images are produced by superimposing a color image of the velocity of moving material, such as blood, over a black and white anatomical B-mode image. Typically, color flow mode displays hundreds of adjacent sample volumes simultaneously, all laid over a B-mode image and color-coded to represent each sample volume's velocity. In standard color flow processing, a high pass filter, known as a wall filter, is applied to the data before a color flow estimate is made. The purpose of this filter is to remove signal components produced by tissue surrounding the blood flow of interest. If these signal components are not removed, the resulting velocity estimate will be a combination of the velocities from the blood flow and the surrounding, non-flowing tissue. The backscatter component from non-flowing tissue is many times larger than that from blood, so the velocity estimate will most likely be more representative of the non-flowing tissue, rather than the blood flow. In order to obtain the flow velocity, the non-flowing tissue signal must be filtered out. In a conventional ultrasound imaging system operating in the color flow mode, an ultrasound transducer array is activated to transmit a series of multi-cycle (typically 4-8 cycles) tone bursts which are focused at a common transmit focal position with common transmit characteristics. These tone bursts are fired at a pulse repetition frequency (PRF) that is typically in the kilohertz range. A series of transmit firings focused at a common transmit focal position with common transmit characteristics is referred to as a "packet". Each transmit beam propagates through the object being scanned and is reflected by ultrasound scatterers such as blood cells. The return signals are detected by the elements of the transducer array and formed into a receive beam by a beamformer. For example, the traditional color firing sequence is a series of firings (e.g., tone bursts) along a common position, producing the respective receive signals: EQU F.sub.1 F.sub.2 F.sub.3 F.sub.4 . . . F.sub.N where F.sub.i is the receive signal for the i-th firing and N is the number of firings in a packet. These receive signals are loaded into a corner turner memory, and a high pass filter (wall filter) is applied to each downrange position across firings, i.e., in "slow time". In the simplest case of a (1, -1) wall filter, each range point is filtered to produce the respective difference signals: EQU (F.sub.1 -F.sub.2) (F.sub.2 -F.sub.3) (F.sub.3 -F.sub.4) . . . (FN.sub.N-1 -F.sub.N) and these differences are supplied to a color flow velocity estimator. One of the advantages of Doppler ultrasound is that it can provide noninvasive and quantitative measurements of blood flow in vessels. Given the angle .theta. between the insonifying beam and the flow axis, the magnitude of the velocity vector can be determined by the standard Doppler equation: EQU .nu.=c.function..sub.d /(2.function..sub.0 cos .theta.) (1) where c is the speed of sound in blood, .function..sub.0 is the transmit frequency and .function..sub.d is the motion-induced Doppler frequency shift in the backscattered ultrasound. A conventional ultrasound imaging system collects B-mode or color flow mode images in a cine memory on a continuous basis. The cine memory provides resident digital image storage for single image review and multiple image loop review, and various control functions. The region of interest displayed during single-image cine replay is that used during the image acquisition. If an ultrasound probe is swept over an area of interest, two-dimensional images may be accumulated to form a three-dimensional data volume. The data in this volume may be manipulated in a number of ways, including volume rendering and surface projections. In particular, three-dimensional images of power and velocity data have been formed by projecting the maximum pixel values onto an imaging plane. In this process, noise is introduced due to inherent error in estimating the velocity of power level because of a multiplicity of small scatterers present in most body fluids (e.g., red cells in blood). Noise present in the velocity and power signals causes errors in selection of the maximum value and affects uniformity within the projected image and sharpness of edges. Thus, there is need for a method for improving the uniformity and edge sharpness of three-dimensional images of velocity and power data.

Low-overhead rendering with Vulkan on Android - sam42 http://android-developers.blogspot.com/2015/08/low-overhead-rendering-with-vulkan.html ====== gulpahum It's great that Google Android will support Vulkan. Now, the support list seems to be: Android, Windows, SteamOS, Tizen, and many Linux distributions including Ubuntu and Red Hat. [1] It's sad that it doesn't include Apple, most likely because they have now their Metal API. [1] [http://venturebeat.com/2015/08/10/khronos-wins-support- from-...](http://venturebeat.com/2015/08/10/khronos-wins-support-from-google- android-for-its-vulkan-graphics-api/) EDIT: here's another list of hardware vendors: AMD, ARM, Intel, Imagination, NVIDIA, Qualcomm, Samsung. [https://www.khronos.org/news/press/khronos-expands-scope- of-...](https://www.khronos.org/news/press/khronos-expands-scope-of-3d-open- standard-ecosystem) ------ sgrove I'd love to see a WebVulkan [0], as wrestling with WebGL's setup is really a slog to get it to work predictably in the way you want. WebGL is making progress via extensions with Uniform Buffers, instanced geometry, etc., but as most people end up using e.g. Three.js, it seems like exposing a sane, more fine-grained API would help everyone. [0] Knowing full-well that WebVulkan naturally won't magically solve any performance issues, and seems to be a very different beast [https://twitter.com/Tojiro/status/628660898756825089](https://twitter.com/Tojiro/status/628660898756825089) ~~~ gulpahum I think WebVulkan would be great with WebAssembly! The nice thing about those technologies is that they are low-level APIs, which means less rooms for bugs. WebGL, HTML, DOM, and most other web technologies suffer from not being consistent and they are full of bugs. How many graphics cards have been blacklisted from WebGL because the drivers don't have the required features or have too many bugs? [1][2] [1] [https://www.khronos.org/webgl/wiki/BlacklistsAndWhitelists](https://www.khronos.org/webgl/wiki/BlacklistsAndWhitelists) [2] [https://wiki.mozilla.org/Blocklisting/Blocked_Graphics_Drive...](https://wiki.mozilla.org/Blocklisting/Blocked_Graphics_Drivers) ------ StavrosK Can someone knowledgeable tell me if Vulkan is a good API? I've heard that OpenGL is a bit of a mess (maybe DirectX is too?), did they get it right this time? ~~~ flippinburgers Vulkan is still in development. I don't believe anything about the api is published yet. ~~~ caligastia But you can check out the SPIR-V IR spec which is almost finished: [https://www.khronos.org/registry/spir-v/](https://www.khronos.org/registry/spir-v/) Not only the Vulkan API but new programming languages will target this IR, so far it appears to be an innovative architecture for concurrent software, that integrates graphics and compute, not a bolt-on like OpenCL.

Q: Is nesting ARM Thumb2 "IT" instructions well defined? If I have an ARM Thumb 2 instruction stream that looks like the following: itt NZ mov r1,r2 it MI mov r3,r4 The IT block of the first IT instruction contains mov and a second it. Is this sequence allowable, or is it undefined behavior? A: An IT block must not contain another IT instruction. The result of your code is unpredictable.

Q: Vertical scroll Scintilla Textbox during Text Changed event Setting a Scintilla.Net textbox with a string and scrolling to last line doesn't work. This Q & A How make autoscroll in Scintilla? has the answer but it wont work at the same time as setting the text. Bare bones repro: private void button1_Click(object sender, EventArgs e) { string s = RandomString(400); scintilla1.Text = s + " " + s + " " + s + " " + s + " " + s; scintilla1.Scrolling.ScrollBy(0, 10000); //<-doesn't work (but does work eg in a Button2_click) } private static Random random = new Random((int)DateTime.Now.Ticks); private string RandomString(int size) { StringBuilder builder = new StringBuilder(); char ch; for (int i = 0; i < size; i++) { ch = Convert.ToChar(Convert.ToInt32(Math.Floor(26 * random.NextDouble() + 65))); builder.Append(ch); } return builder.ToString(); } Does anyone know how to scroll vertically down to end line after setting the text? A: Well you can try to put Refresh() after adding the text; scintilla1.Text = s + " " + s + " " + s + " " + s + " " + s; scintilla1.Refresh(); for this case i found out that you will need to Refresh() twice depend on the length of the string you put on the textbox.

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27 March 2007 Those Wordy Samuelses Strike Again My father, Jon Samuels, has recently published an essay at the PublicEducation.org site. In it he draws upon the observations of early America made by Alexis de Tocqueville, who suggested that the new nation's prosperity could be attributed in considerable part to its disdain for class strictures, its support for free movement within the country, and its acceptance of broad public education: Writing today, de Tocqueville might note the erosion of our public schools and the roles played in that by racism, failed discipline, missing parents, rote teaching and testing gone berserk. But, he would be confident in our defense of public education. He would argue that it was not within the American character to shrink in the face of challenge. He would expect that we would tax ourselves sufficiently to provide for the common educational good. He would not be surprised when we raised the station of our teachers. He would anticipate our solution of the dropout problem and our reinstitution of discipline and mutual respect in our schools. He would expect that we would use tests surgically to expand an improved curriculum. He concludes: I do not support any “choice” that would further impoverish our public school system, that, however unintentional, could result in a few fleeing the problems that affect the many, that could create educational slums to warehouse an overwhelmingly poor and minority population. That would not be the America that enthralled de Tocqueville . . . . I am sure that those who disagree with me are acting out of the courage of their convictions. I would ask, however, that they also have the courage of the consequences of their convictions. When it comes to public education concerns, I suspect that there's some daylight between our respective positions, but I respect his willingness, as a board member of Public Education Partners, a local education foundation in Aiken, South Carolina, to tackle difficult issues that have stymied many, many others. After years as a career military officer and a successful businessman, I'm proud that he's brought his considerable skills to bear on a topic of such pressing public concern. Unsilent Partners About Me I am presently corporate counsel for Accela, Inc., a software company headquartered in San Ramon, California and am a member of both the Oregon and California State Bars. More detailed professional information is available at my LinkedIn profile. I have been blogging at Infamy or Praise since early 2005. From 2006 to 2009, I served as a "Sherpa" at Blawg Review, the weekly carnival of legal blogging; I have also hosted (or co-hosted) six editions of Blawg Review, the first four of which were awarded a "Blawg Review of the Year" award. I formerly was a co-blogger at Unsilent Partners. I'm on Twitter as "colinsamuels". I am the author of "Humanizing the Profession: Lawyers Find Their Public Voices Through Blogging" (11 Nexus L. J. 89 (2006)) and a contributing author to "Blogging and Other Social Media" (Gower Publishing Limited, 2008) and "Legal Profession: Modern Approach" (The Icfai University Press, 2008). None of the foregoing blogging, tweeting, or personal writing necessarily represents the views of my employer; responsibility for these is entirely mine.

Ripple-like intraocular lens damage from a neodymium:YAG laser. We report a case of accidental intraocular lens (IOL) damage during a neodymium:YAG laser capsulotomy. After a single pulse of 0.9 mJ of laser energy, a large area of ripple-like opacity with more than 10 concentric circles surrounding a small hole in a 2.0 diopter IOL was noted. The opacity extended more than one fourth of the IOL diameter and caused a significant visual effect.

Comments on: Helen Thomas Sees Lack of Courage in Obamahttp://www.conservativedailynews.com/2011/06/helen-thomas-sees-lack-of-courage-in-obama/ The best conservative political news, analysis and opinion articles written by a collection of citizen journalists. Covering a range of important topics in blogs, op-ed, and news posts, these upstanding patriots are bringing back American exceptionalism with every entry..Mon, 02 Mar 2015 18:01:47 +0000hourly1http://wordpress.org/?v=4.1.1By: eileen fleminghttp://www.conservativedailynews.com/2011/06/helen-thomas-sees-lack-of-courage-in-obama/comment-page-1/#comment-5120 Mon, 27 Jun 2011 13:48:06 +0000http://conservativedailynews.com/?p=13656#comment-5120I spent the evening of 20 May 2011 with Ms. Thomas and some of our conversation follows: During my conversation with Ms. Thomas I filled her in on my distress over Amy Goodman’s failure to follow up on her 2004 interview with Mordechai Vanunu which resulted in his being sentenced to 6 months in jail in 2007 and then enduring 78 days back in solitary in 2010, just because he dared to speak to foreign media after he was released from 18 years in jail for telling the truth and providing the photographic proof of Israel’s WMD Program. In April 2007, I had lunch with Amy Goodman-not because we have ever been friends, but only because I had once been a generous donor to Democracy NOW! was I invited to have lunch with Amy. I accepted the invitation only so I could fill Amy in on the fact that her 2004 interview with Vanunu was major testimony against him in his FREEDOM of SPEECH trial-which began the same day Hamas was democratically elected on 25 January 2006- and also to ask her to follow up asap! Amy acted interested and jotted down notes in her Blackberry, but she didn’t bother to call Vanunu until July 2007 after he was sentenced to 6 more months in jail essentially for speaking to foreign media in 2004! Vanunu refused to speak to Amy because she –like all THE MEDIA-hadn’t done anything to raise awareness about Israel’s continuing persecution of him and to this day Vanunu is still waiting for his inalienable right to leave Tel Aviv and fly to freedom. After I filled Ms. Thomas in on my anger with Amy she replied, “She used to be better.” I then brought up Ms. Thomas’s first and last question to President Obama regarding Middle East nuclear weapons when he blew her off claiming he didn’t want to ‘speculate’ and her ‘peers’ remained mute, although the State Department has reams of documentation about Israel’s WMD. Ms. Thomas replied, “They have no conscience.” I also claim their lack of integrity borders on treason! I was not a reporter when I met Vanunu for the first time in June 2005, but I knew I had to become one when he told me: “Did you know that President Kennedy tried to stop Israel from building atomic weapons? In 1963, he forced Prime Minister Ben Guirion to admit the Dimona was not a textile plant, as the sign outside proclaimed, but a nuclear plant. The Prime Minister said, ‘The nuclear reactor is only for peace.’ “Kennedy insisted on an open internal inspection. He wrote letters demanding that Ben Guirion open up the Dimona for inspection. “The French were responsible for the actual building of the Dimona. The Germans gave the money; they were feeling guilty for the Holocaust, and tried to pay their way out. Everything inside was written in French, when I was there, almost twenty years ago. Back then, the Dimona descended seven floors underground. “In 1955, Perez and Guirion met with the French to agree they would get a nuclear reactor if they fought against Egypt to control the Sinai and Suez Canal. That was the war of 1956. Eisenhower demanded that Israel leave the Sinai, but the reactor plant deal continued on. “When Johnson became president, he made an agreement with Israel that two senators would come every year to inspect. Before the senators would visit, the Israelis would build a wall to block the underground elevators and stairways. From 1963 to ’69, the senators came, but they never knew about the wall that hid the rest of the Dimona from them. “Nixon stopped the inspections and agreed to ignore the situation. As a result, Israel increased production. In 1986, there were over two hundred bombs. Today, they may have enough plutonium for ten bombs a year.” After cheese cake for desert I asked Ms. Thomas what she would advise anyone who wanted to go into the field of journalism and she stated: “Go for it! It’s the greatest profession in the world because you are always learning and you are aware of the world, so you just might be able to affect change. “You cannot have a democracy without an informed people. “Information is everything; it enlarges your intellect and that guides you. “The job is to follow the truth and report where it leads you! “Right and wrong is not relative. Empathy is fine but kindness and sympathy do not change the facts and conscience is everything! “Leaders are suppose to do the right thing and we should back up the president when he does the right thing; but drop him when he doesn’t. “The WHY is the most important question-not that something happened- but WHY did it happen? “Somewhere along the way America lost its soul. “People have to rise up but Americans have become so passive and power overwhelmingly abusive.”

MASKS OFF: Roberto and Elizabeth Goizueta of Brookline at the Save Venice Masquerade Gala at Locke-Ober in downtown Boston on October 27. photograph by Bill Brett | November 18, 2012 GOOD CAUSE: Geoff Why of Watertown, Janelle Chan of Boston, and Nick Chau of Newton at a fund-raiser for the Asian Task Force Against Domestic Violence held at the State Room in Boston. on October 26. photograph by Bill Brett | November 18, 2012 PHYSICS OF PUMPKINS: Students gathered to witness the Boston University Physics Department’s annual pumpkin drop on October 26. SEE YOURSELF ON THIS PAGE. E-mail party and event photos to [email protected].

Apollo (storeship) The Apollo is a historic storeship that is buried at a location in downtown San Francisco, California. It was listed on the National Register of Historic Places in 1991. Parts of the ship have been uncovered, most recently in 1921 and 1925. Photographs from the 1921 uncovering exist. The 1925 excavation revealed coins from 1797, 1825, and 1840, a gold nugget, and assorted navigational pieces. One of numerous buried ships within San Francisco, it is an archeological site, listed at least partially for its potential to yield information in the future. References Category:Financial District, San Francisco Category:National Register of Historic Places in San Francisco Category:History of San Francisco Category:Shipwrecks on the National Register of Historic Places in California

Secret Worlds with Michael Arbuthnot Next Episode Air Date When will be Secret Worlds with Michael Arbuthnot next episode air date? Is Secret Worlds with Michael Arbuthnot renewed or cancelled? Where to countdown Secret Worlds with Michael Arbuthnot air dates? Is Secret Worlds with Michael Arbuthnot worth watching? Next Episode of Secret Worlds with Michael Arbuthnot is Take your countdown whenever you go About EpisoDate.com is your TV show guide to Countdown Secret Worlds with Michael Arbuthnot Episode Air Dates and to stay in touch with Secret Worlds with Michael Arbuthnot next episode Air Date and your others favorite TV Shows. Add the shows you like to a "Watchlist" and let the site take it from there.

StrCpy $MUI_FINISHPAGE_SHOWREADME_TEXT_STRING "Vis versjonsmerknader" StrCpy $ConfirmEndProcess_MESSAGEBOX_TEXT "Fant ${APPLICATION_EXECUTABLE}-prosess(er) som må stoppes.$\nVil du at installasjonsprogrammet skal stoppe dem for deg?" StrCpy $ConfirmEndProcess_KILLING_PROCESSES_TEXT "Terminerer ${APPLICATION_EXECUTABLE}-prosesser." StrCpy $ConfirmEndProcess_KILL_NOT_FOUND_TEXT "Fant ikke prosess som skulle termineres!" StrCpy $PageReinstall_NEW_Field_1 "En eldre versjon av ${APPLICATION_NAME} er installert på systemet ditt. Det anbefales at du avinstallerer den versjonen før installering av ny versjon. Velg hva du vil gjøre og klikk Neste for å fortsette." StrCpy $PageReinstall_NEW_Field_2 "Avinstaller før installering" StrCpy $PageReinstall_NEW_Field_3 "Ikke avinstaller" StrCpy $PageReinstall_NEW_MUI_HEADER_TEXT_TITLE "Allerede installert" StrCpy $PageReinstall_NEW_MUI_HEADER_TEXT_SUBTITLE "Velg hvordan du vil installere ${APPLICATION_NAME}." StrCpy $PageReinstall_OLD_Field_1 "En nyere versjon av ${APPLICATION_NAME} er allerede installert! Det anbefales ikke at du installerer en eldre versjon. Hvis du virkelig ønsker å installere denne eldre versjonen, er det bedre å avinstallere gjeldende versjon først. Velg hva du vil gjøre og klikk Neste for å fortsette." StrCpy $PageReinstall_SAME_Field_1 "${APPLICATION_NAME} ${VERSION} er installert allerede.$\n$\nVelg hva du ønsker å gjøre og klikk Neste for å fortsette." StrCpy $PageReinstall_SAME_Field_2 "Legg til/installer komponenter på nytt" StrCpy $PageReinstall_SAME_Field_3 "Avinstaller ${APPLICATION_NAME}" StrCpy $UNINSTALLER_APPDATA_TITLE "Avinstaller ${APPLICATION_NAME}" StrCpy $PageReinstall_SAME_MUI_HEADER_TEXT_SUBTITLE "Velg hva slags vedlikehold som skal utføres." StrCpy $SEC_APPLICATION_DETAILS "Installerer ${APPLICATION_NAME} grunnleggende." StrCpy $OPTION_SECTION_SC_SHELL_EXT_SECTION "Integrering med Windows Utforsker" StrCpy $OPTION_SECTION_SC_SHELL_EXT_DetailPrint "Installerer integrering med Windows Utforsker" StrCpy $OPTION_SECTION_SC_START_MENU_SECTION "Snarvei i Start-menyen" StrCpy $OPTION_SECTION_SC_START_MENU_DetailPrint "Legger til snarvei for ${APPLICATION_NAME} i Start-menyen." StrCpy $OPTION_SECTION_SC_DESKTOP_SECTION "Snarvei på skrivebordet" StrCpy $OPTION_SECTION_SC_DESKTOP_DetailPrint "Oppretter snarveier på skrivebordet" StrCpy $OPTION_SECTION_SC_QUICK_LAUNCH_SECTION "Snarvei i Hurtigstart" StrCpy $OPTION_SECTION_SC_QUICK_LAUNCH_DetailPrint "Oppretter snarvei i Hurtigstart" StrCpy $OPTION_SECTION_SC_APPLICATION_Desc "${APPLICATION_NAME} grunnleggende." StrCpy $OPTION_SECTION_SC_START_MENU_Desc "${APPLICATION_NAME}-snarvei." StrCpy $OPTION_SECTION_SC_DESKTOP_Desc "Skrivebordssnarvei for ${APPLICATION_NAME}." StrCpy $OPTION_SECTION_SC_QUICK_LAUNCH_Desc "Hurtigstart-snarvei for ${APPLICATION_NAME}." StrCpy $UNINSTALLER_FILE_Detail "Skriver Avinstallasjonsprogram." StrCpy $UNINSTALLER_REGISTRY_Detail "Skriver registernøkler for installasjonsprogrammet" StrCpy $UNINSTALLER_FINISHED_Detail "Ferdig" StrCpy $UNINSTALL_MESSAGEBOX "Det ser ikke ut som ${APPLICATION_NAME} er installert i mappe '$INSTDIR'.$\n$\nFortsett likevel (ikke anbefalt)?" StrCpy $UNINSTALL_ABORT "Avinstallering avbrutt av bruker" StrCpy $INIT_NO_QUICK_LAUNCH "Hurtigstart-snarvei (I/T)" StrCpy $INIT_NO_DESKTOP "Snarvei på skrivebordet (skriver over eksisterende)" StrCpy $UAC_ERROR_ELEVATE "Klarte ikke å heve tilgangsnivå. Feil: " StrCpy $UAC_INSTALLER_REQUIRE_ADMIN "Dette installasjonsprogrammet krever administrasjonstilgang. Prøv igjen" StrCpy $INIT_INSTALLER_RUNNING "Installasjonsprogrammet kjører allerede." StrCpy $UAC_UNINSTALLER_REQUIRE_ADMIN "Avinstallasjonsprogrammet krever administrasjonstilgang. Prøv igjen" StrCpy $UAC_ERROR_LOGON_SERVICE "Påloggingstjenesten kjører ikke, avbryter!" StrCpy $INIT_UNINSTALLER_RUNNING "Avinstallasjonsprogrammet kjører allerede." StrCpy $SectionGroup_Shortcuts "Snarveier"

Q: Time conversion Not working properly? I am using the ionic time picker in my project. When I select the time picker it passes a value to the controller. For example when I select 09:00pm, the console shows 79200. If I select 07:00pm the console shows 68400. I want to convert the value to 12 hrs format. I have followed some steps, but it's not working for me. My code: var a = new Date($scope.timePickerObject12Hour.inputEpochTime*1000); console.log(a); var b = moment.utc(a).format("HH:mm"); console.log(b) $scope.timePickerObject12Hour.inputEpochTime = val; console.log(val); //var yourDateObject = new Date(); var selectedTime = new Date(); var amPmHour = $filter('date')(selectedTime, 'hh'); console.log(amPmHour); $scope.time = $filter('date')(new Date(val*1000), 'hh:mma'); console.log($scope.time); console.log('Selected epoch is : ', val, 'and the time is ', selectedTime.getUTCHours(), ':', selectedTime.getUTCMinutes(), 'in UTC'); I tried the code above, but nothing is working. Below i have added my origional code: $scope.timePickerObject12Hour.inputEpochTime = val; console.log(val); console.log('Selected epoch is : ', val, 'and the time is ', selectedTime.getUTCHours(), ':', selectedTime.getUTCMinutes(), 'in UTC'); on the first console.log i am getting 68400, for second console log I am getting 68400 and the time is 19:00 in UTC. How to convert 12 hr format for the selected time? A: I assume you want the result as a string. Here is a simple implementation with moment.js: var secs = 68400; console.log(moment().startOf('day').add(secs, 'seconds').format("h:mm a")); Will output "7:00 pm" See in plunker http://plnkr.co/edit/D0ai2PpEhnuJkTYblW29?p=preview

Addressing mediapersons here, he said the BJP was even willing for the preponement of elections in case the Congress party felt that it would not be feasible to hold elections at higher altitudes of the state in December. Mr Dhumal said the government's request of postponing of elections on the plea that the school education board had decided to hold examinations from December two to 12 only reflected the ''perturbed mindset'' of the Congress leadership. Examination dates could always be changed to suit the interests of the students and the people of the state, he said. The BJP leader the party had lodged a complaint with the EC for getting a few deputy commissioners, SPs and some other key state government officials, who were working as stooges of the ruling party, transferred. The party was keeping an eye on the officers who were over enthusiastically involved in preparing the Congress manifesto or working towards the postponment of elections, he said. He cautioned administrativr officers to ensure that free and fair polls in the state and desist from carrying out the agenda of the Congress. Former minister Parveen Sharma and Kutlehar legislator Virender Kanwar were also present during the conference.

Are caregivers adherent to their own medications? To explore caregiver adherence to chronic medications and predictors of appropriate medication use. Descriptive, nonexperimental, cross-sectional study. United States in May 2009. 2,000 adults randomly selected from a large national consumer panel. Web-based survey of community pharmacy patients. Self-reported medication adherence. 21% of those invited (3,775) responded to the survey invitation. Of the 2,000 individuals who were eligible to participate, 38% described themselves as caregivers. Among caregivers, 45% agreed that they were more likely to forget their own medications than medications for their caregivees. Caregivers were 10% more likely to forget to take their medications, 11% more likely to stop taking medications if they felt well, and 13% more likely to forget to refill their medications than noncare-givers (P < 0.001 for all). In fully adjusted models, caregivers had 36% greater odds (95% CI 0.52-0.79) of reporting that they were nonadherent compared with noncare-givers and increased medication use among caregivees was associated with worse adherence among caregivers (P < 0.05). Medication nonadherence was common in this population, and caregivers were more likely to report poor medication adherence than noncaregivers. Considering that caregivers often engage health professionals, physicians and pharmacists may choose to screen for caregiving status. Pharmacists are uniquely positioned to intervene to enhance appropriate medication adherence.

Irish Barista Champion Well done to Karl of Coffee Angel for beating the other 11 entrants in yesterdays finals in Dublin. I think Karl was expected to do well, and good on him for edging out the rest of the competition and making it to Bern. Great to see someone from a very independent establishment do so well, and hopefully it’ll be great for his business.

Oregon State has never been shy when it comes to recruiting players from all over the country. Athletes from Florida, Texas, Oklahoma, Ohio and Illinois have all made their way to Corvallis in recent years as the Beavers continually look to uncover gems. Last week Coach Mike Riley personally offered a speedy Midwest running back who is excited about what the Beavers bring to the table. St. Louis (Mo.) DeSmet running back Malcolm Agnew is a shifty 5-foot-9, 180 pound back who's highlight reel is impressive. The question on many minds though is 'how did Oregon State find him?'

1. Field of the Invention The present invention relates to a vacuum pump with a dust collecting function for use when a vessel for a process, in which various processes of productions by reaction or melting and crystallization processes are carried out under a reduced pressure atmosphere evacuated by a vacuum pump, is used. The process may be a process of epitaxial growth for producing monocrystalline film of silicon, in which an amount of dust is produced when the reaction process or a melting and crystallization process take place and the produced dust flows into the vacuum pump together with the existing gas. 2. Description of the Related Arts In general, the process of productions by reaction and the melting and crystallization processes in a vessel for processing under a reduced pressure are carried out in vacuum. Therefore, the specific gravity of the gas which flows into a vacuum pump is very small. When the gas, together with the dust, flows into the vacuum pump, the gas flows appropriately but has less ability to convey the dust, and therefore a greater portion of the dust is accumulated in the vacuum pump. In prior arts, the increased amount of the accumulated dust prevents the satisfactory running of the vacuum pump to cause difficulty in continuing the running of the vacuum pump so that frequent operations to remove the dust in the vacuum pump are needed. Also, there is a problem that, if the sizes of grains of the dust which flows together with the gas into the vacuum pump are large, the internal structures of the vacuum pump, such as rotors, collect the grains of the dust to which can lead to a failure or a stoppage of the vacuum pump. To prevent dust from flowing into the vacuum pump attempts have been made to separate the dust by providing filters or the like between the vacuum pump and the dust producing device. There is a problem, however, in that the dust causes blocking of the through-paths in the filter which are then greatly reduced. The effective evacuation performance of the vacuum pump for the process of production by reaction and the melting and crystallization in the vessel for processing prevent the reaction process and the melting and crystallization in the vessel for processing from continuing. It is possible to provide a dust separator for separating dust utilizing the flow of gas, such as a cyclone type separator, between the vacuum pump and the vessel for processing. However, in this case, to reduce the loss of the pressure by the cyclone type separator, if the cross-sectional area of the gas flow in the separator is increased, no sufficient gas flow velocity is obtained so that the satisfactory separation of the dust cannot be realized in the cyclone type separator. Since the process is carried out under high degree of vacuum in the vessel for processing, the amount of the flow of the gas entering into the vessel, coming out from the vessel and being sent to the vacuum pump is relatively small. Therefore, the ability of the vacuum pump to transfer the dust to discharge the dust is low, and accordingly the dust tends to be accumulated in the vacuum pump to lead to a stoppage of the vacuum pump. Since the dust is discharged together with the gas from the vacuum pump, a large amount of dust flows into the exhaust gas processing system. Therefore, there is a problem that the exhaust gas processing system is quickly contaminated and this prevents the functioning of the system.

Q: How do I calculate the intersection between two cosine functions? $f(x) = A_1 \cdot \cos\left(B_1 \cdot (x + C_1)\right) + D_1$ $g(x) = A_2 \cdot \cos\left(B_2 \cdot (x + C_2)\right) + D_2$ Is it possible at all to solve this analytically? I can start doing this but I get stuck half way. $A_1 \cdot \cos\left(B_1 \cdot (x + C_1)\right) + D_1 = A_2 \cdot \cos\left(B_2 \cdot (x + C_2)\right) + D_2$ $\Longleftrightarrow A_1 \cdot \cos\left(B_1 \cdot (x + C_1)\right) - A_2 \cdot \cos\left(B_2 \cdot (x + C_2)\right) = D_2 - D_1$ I'm not sure how to use arccosine on this expression. Therefore I'm asking for help to solve this. Thanks in advance! A: Substituting $\xi:=B_1(x+C_1)$ brings it to the fundamental form $$ \cos (\xi) = p\cos (a\xi+b)+q$$ with $p=\frac{A_2}{A_1}$, $q=\frac{D_2-D_1}{A_1}$, $a=\frac{A_2}{B_1}$ and $b=\frac{C_2-C_1}{B_1}$. As far as I know, this form cannot be solved analytically in general.

Crystallization of a polymorphic hydrate system. Nitrofurantoin can form two monohydrates, which have the same chemical composition and molar ratio of water, but differ in the crystal arrangements. The two monohydrates (hydrates I and II) could be produced independently via evaporative crystallization, where supersaturation and solvent composition were both found to have an effect. Hydrate I showed much slower crystallization than hydrate II. During cooling crystallization, the nucleation and growth of hydrate II was again dominant, consuming all supersaturation and leading to no hydrate I formation. Seeding of hydrate I during cooling crystallization was also applied, but the hydrate I seeds were not able to initiate its nucleation rather than dissolving into crystallizing solution. Although solubility tests revealed that hydrate II is more stable than hydrate I due to its lower solubility (110 +/- 4 and 131 +/- 12 microg/mL for hydrates II and I, respectively), this difference is rather small. Therefore, the small free energy difference between the two hydrates, together with the slow crystallization of hydrate I, both lead to a hindrance of hydrate I formation. Furthermore, the crystal structure of hydrate II demonstrated a higher H-bonding extent than hydrate I, suggesting its more favorable crystallization. This is in good agreement with experimental results.

William Faulkner (cricketer) William George Faulkner (born 5 May 1923) is a former English first-class cricketer. While serving in the Royal Air Force, Faulkner made a single appearance in first-class cricket for the Royal Air Force against Worcestershire at Worcester in 1946. Batting twice in the match, he was dismissed for 5 runs by Peter Jackson in the Royal Air Force first-innings, while in their second-innings he was dismissed by Leonard Blunt for 18 runs. With his right-arm fast-medium bowling, he bowled 24 wicketless overs. References External links Category:1923 births Category:Living people Category:People from Bromley-by-Bow Category:Royal Air Force airmen Category:English cricketers Category:Royal Air Force cricketers

MPTP-Induced pallidal lesions in rhesus monkeys. Dopamine neurons in the substantia nigra of the midbrain are the primary neuronal population affected by 1-methyl-4-phenyl-1,2,3, 6-tetrahydropyridine (MPTP) toxicity, which produces the pathological and behavioral features of Parkinson's disease in nonhuman primates and man. We have identified another injury site in magnetic resonance imaging (MRI) brain scans in 13 of 37 rhesus monkeys taken 10-12 months after administration of this neurotoxin via the right carotid artery. Focal lesions, ranging in volume from 6.75 to 60 mm3 in the rostral globus pallidus region, were seen on the right side of the brain in these 13 animals in addition to the midbrain effects. While no significant differences were seen between globus pallidus lesioned and nonlesioned animals in the severity of MPTP-induced parkinsonian symptoms, the response to levodopa was muted in pallidal-lesioned animals. To confirm the role of neurotoxicity in producing the lesions, brain scans from an additional 12 monkeys were evaluated during the acute period following exposure to either MPTP (n = 6) or saline (n = 6). Focal lesions in the rostral globus pallidus were seen as early as 2-4 h following a carotid artery infusion in two of six MPTP recipients, but no evidence of injury was seen in saline recipients. The globus pallidus includes important components of the neural circuitry regulating motor functions. The present results indicate that in addition to midbrain dopamine neurons, a focal region of the rostral globus pallidus is selectively vulnerable to MPTP toxicity.

Send this card and so much more! Start your 7 day free trial today! ecard verse: Friends are golden rays of sunlight when we need warmth... the cool comfort of shade when we need rest... the silver path of moon glow when we feel lost and need to find our way in this world. The gift of your friendship is more precious to me than any words could say. Friends are golden rays of sunlight when we need warmth... the cool comfort of shade when we need rest... the silver path of moon glow when we feel lost and need to find our way in this world. The gift o...

Big Brother 14 is just around the corner and the search for your next cast is in full swing. Not only is the casting website open for submissions, open casting calls are starting to come in. If you want to be a part of the Big Brother family, you can take the first step at one of the open casting calls below.

Rachael Maskell Rachael Helen Maskell (born 5 July 1972) is a British Labour Co-operative politician serving in Jeremy Corbyn’s Shadow Cabinet since 2020 as Shadow Employment Rights Secretary, succeeding Laura Pidcock, and previously from 2016 to 2017 as Shadow Environment Secretary. She was a Junior Transport Minister under Andy McDonald from 2017 to 2020. She is the Member of Parliament (MP) for the constituency of York Central after retaining the seat for her party at the 2015, 2017, and 2019 general elections. Education She graduated from the University of East Anglia with a degree in physiotherapy in 1994. Background Maskell became politically active at an early age. When she was a child, her uncle campaigned for the abolition of the death penalty, in addition to serving as an advisor to the Wilson government and as an academic. The Yorker, a York-based student publication, states: "[he] preferred to live and work amongst his community rather than be without. [H]is approach to politics was her inspiration as a child". Career Maskell worked as a care-worker and physiotherapist in the National Health Service for 20 years. Maskell has also been a trade-union official. Maskell used her maiden speech to advocate for a new mental health hospital in York to replace the ageing Bootham Park. Speaking of the vision of "late member for Ebbw Vale" Aneurin Bevan, she said that "the growing social and financial inequalities manifest themselves in health inequality, and access to vital services is delayed and even denied as a direct result of the £3 billion structural reorganisation that the previous Government introduced." On Wednesday 8 July 2015, Rachael Maskell was one of four Labour MPs elected to the Health Select Committee. Maskell voted against the Welfare Bill in the House of Commons on 20 July 2015. Maskell made a statement saying "I have a duty to protect our vulnerable people. I could not stand by and let the most vicious Tory attacks on some of the poorest in our city go unchallenged." In September 2015, during the European refugee crisis, Maskell called on the UK to open its doors to refugees; she said "we can all have a bit more compassion. If it was the other way round and we were in that desperate situation, we would expect somebody to show compassion to us." Speaking as 20,000 refugees arrived in Munich in one weekend, and as the German Government gets ready to receive 800,000 refugees in 2015; Maskell said that the UK Government must do more. She questioned David Cameron in the House of Commons asking "what criteria has the Prime Minister used to arrive at a figure of just six refugees per constituency per year?" She is quoted as saying "20,000 is not enough and 30,000 is not enough' and that "We will keep going until we hit our saturation point because what does it matter if we have to wait another week for a hospital visit? Or if our class sizes, are slightly bigger? Or if, our city is slightly fuller? What does it matter, if things are slightly more challenging? If we have to pay a little bit more in to the system?"; in a statement on the crisis, she urged local authorities to help in every way they can and use every space they had to offer to aid people fleeing war in Syria and Northern Iraq, she said "we are in the midst of a humanitarian crisis that is getting worse, I am incensed that Turkey is hosting over one and a half million refugees and our government says we will open our borders to no more than six men, women and children a year in each constituency." Maskell spoke in the Trade-Union Bill 2nd Reading debate on 14 September 2015. She referred the house to her Register of Interests as a member of Unite the Union declared "I am a proud trade-unionist" – she subsequently voted against the Bill. Following a period working part of the Shadow Defence Team under Shadow Secretary of State for Defence Maria Eagle, Maskell was appointed Shadow Environment, Food and Rural Affairs Secretary as part of the Labour Party's post-Brexit reshuffle. Maskell resigned from her position ahead of the vote on the second reading in the House of Commons European Union (Notification of Withdrawal) Bill 2017 which triggers Article 50 which carried a three-line whip imposed on Labour MPs. She returned to the Labour front bench on 3 July 2017 as Shadow Rail Minister. On 5 March 2019, she joined a dozen other Labour MPs on Westminster Bridge, next to the Houses of Parliament, in a protest against Brexit under the banner 'Love Socialism Hate Brexit'. She was one of 5 Labour MPs to vote against the extension of abortion rights to Northern Ireland, and is a vice chair of the All-Party parliamentary Pro-life Group. During votes on the same bill, she also abstained on extending same-sex marriage to Northern Ireland. Maskell endorsed Clive Lewis in the 2020 Labour Party leadership election. In January 2020, Maskell was returned to the Shadow Cabinet as Shadow Employment Rights Secretary, replacing Laura Pidcock who lost her seat in the 2019 general election. Personal life Maskell is a keen cyclist and rode the trip to Labour Conference 2015 in Brighton from Parliament in aid of the British Heart Foundation. References External links |- Category:1972 births Category:Living people Category:21st-century British women politicians Category:Alumni of the University of East Anglia Category:Female members of the Parliament of the United Kingdom for English constituencies Category:Labour Co-operative MPs for English constituencies Category:Politics of York Category:UK MPs 2015–2017 Category:UK MPs 2017–2019 Category:UK MPs 2019–

Neurotrophic effects of Cerebrolysin in animal models of excitotoxicity. Excitotoxicity might play an important role in neurodegenerative disorders such as Alzheimer's disease. In the mouse brain, kainic acid (KA) lesioning results in neurodegeneration patterns similar to those found in human disease. For this study, two sets of experiments were performed in order to determine if Cerebrolysin ameliorates the alterations associated with KA administration. In the first set of experiments, mice received intraperitoneal KA injections followed by Cerebrolysin administration, while in the second, mice were pretreated with Cerebrolysin for 4 weeks and then challenged with KA. Behavioral testing in the water maze and assessment of neuronal structure by laser scanning confocal microscopy showed a significant protection against KA lesions in mice pretreated with Cerebrolysin. In contrast, mice that received Cerebrolysin after KA injections did not show significant improvement. This study supports the contention that Cerebrolysin might have a neuroprotective effect in vivo against excitotoxicity.

(Closed) Sometimes it makes sense After freaking out for months about things with career and relationship, last night was a moment of clarity. My job that I had loved dearly moved out of state 3 months ago, and I chose to go back to another less fullfilling position at my company instead of following the job I loved. I did so because of Mr. Tri… He had stated that he wouldn’t EVER move to this location, so I knew that I would have to choose . Pay etc wasn’t a factor in this choice so…it was basically me choosing between career and relationship. I chose relationship. Let me preface this with the fact that I have done this before in a previous relationship that literally blew up on me and sent my life into a complete tailspin and overhaul, so doing this scared me a ton. For the last 3 months I have been questioning my move a lot… wondering if Mr Tri felt the same way about me as I did him. Half worrying that I was replaying mistakes in my head. But last night all of the little blocks aligned to make sense of a lot of mixed emotions and worries… all thanks to Mr Tri’s cousin Mr Tri has been consumed by $$ for about the last 6 months, and I couldn’t quite figure it out, was it a sense of accomplishment was it a feeling of being good enough, I just didn’t get it. He’s been crazy about his debt and his career to the point of annoying on occasion. But now I know why Last night while at a concert ( his bday present from me) his cousin asked me what the deal was with us and when we were going to get engaged… I danced around the question and decided to use it as ammo for questions later. I needed to put my worries to rest once and for all… they were eating at me… So last night I got some guts and told him what his cousin asked, and I got the answer of when I have enough money, followed by a joking comment in regards to the fact that he would have to propose with a lifesaver right now… Although I’d be happy with that or a twist tie, I will wait happily… I know tha the wants to marry me and right now, that is enough.

"Here's a little mental virus for you: "For reasons that are obscure to me, but not unimaginable, some of my friends call it 'Duck Machine' instead of 'Deus ex Machina'. Among these friends we call it Harry Potter and the Duck Machine, a delightful image. We used to laugh that Star Trek endings so often employed the Duck Machine, that we imagined this ending written into the script for Star Trek episodes:

1.. Introduction ================ Heart rate has been an important factor in indicating patients' health for quite a long time. As people are paying more and more attention on their health, long-term heart rate monitoring is of more importance to everyone as it's a valuable indicator for early diagnosis of dozens of diseases. Furthermore, long-term heart rate monitoring is also essential for sports enthusiasts and professional athletes. According to these requirements, it is necessary to design and fabricate a device which is suitable for long-term heart rate monitoring and free from external disturbance. The wearing comfort, the reliability and the cost become three key issues for long-term heart rate monitoring for daily use. Several conventional methods have already been developed to measure heart rate, most of which are based on electrocardiograms (ECGs) \[[@b1-sensors-15-03224]\], photoplethysmography (PPG) \[[@b2-sensors-15-03224]\], and the piezoelectric effect \[[@b3-sensors-15-03224]--[@b5-sensors-15-03224]\]. Other principles in heart rate measurement have also been verified by researchers \[[@b6-sensors-15-03224]--[@b8-sensors-15-03224]\]. Among these methods for heart rate monitoring, ECG is the most widely used. It is the standard diagnosis technique for heart disease in hospitals but the specialized equipment needed is clearly not suitable for household applications. Household heart rate monitors based on ECG technique have also been commercialized, but chest strap transmitters are usually needed, which is not appropriate for long-term use. Strapless wrist band ECG heart rate monitors have been developed these days. However, the contradiction between reliable electric connection and the comfort of wearing still has not been settled in a satisfactory way. Techniques for PPG require hard photoelectric modules which are tightly attached to the tissue with a certain penetration depth, for instance, the fingers. For the reasons above, these two kinds of heard rate monitor system are not appropriate for long-term ordinary daily use because of the inconvenience in user experience, especially at night. Monitors based on piezoelectric pressure sensor also have the similar limits. 2.. System Design ================= In this work, a comfort, reliable heart rate monitor for long-term household use is proposed. Unlike the previous ECG, PPG and piezoelectric devices, a flexible pressure sensor with the capability of measuring heart rate by sensing the pulsation of the artery is used in the system. This solution is adopted based on the following considerations. Since the sensor of the monitoring system is the only component which needs to inevitably be in contact with the human skin, trying to have a flexible sensor is crucial in realizing a comfortable, simple heart rate monitor. In this work, a robust, low-cost novel flexible pressure sensor has been proposed and fabricated. The polymer-based flexible sensor has no hard components which it can ensure its comfort and fitness for wearing all day in any situation. Furthermore, to distinguish the tiny pressure changes caused by the artery pulse, the flexible pressure sensor's sensitivity needs to be improved. Based on previous works in this area, a highly sensitive structure is proposed. The conventional structure with one piezoresistive layer is replaced by a novel structure with two piezoresistive layers. The contact interface of the two layers is modified with micro structures. These microstructures are realized with modern soft lithography technology and are treated as the key features for the sensor's high sensitivity. In addition to that, for the specific morphology of the surface microstructures utilized, the pressure sensor device also has a perfect linearity performance. However, due to the high sensitivity of the pressure sensor, noises may be induced by the wearer's muscle movements. This inevitable daily movement can cause pressure changes between the wearer's skin and the device. Such noises can easily make the monitor fail when heart rate counting. In order to solve this problem while maintaining a relatively low cost in signal processing, an Analog Signal Processing (ASP) system is proposed to process the signal and extract the heart rate information from it. The whole system is composed of a sensor subsystem and the ASP subsystem. The sensor subsystem is an elastic belt with the flexible pressure sensor attached on it. The tightness of the belt can be tuned in order to provide a proper pressure for measurement. The system also includes an ASP subsystem to process the pressure signals, a counter, an indicator, and a timing circuit which is used to stop the measurement. 2.1.. Flexible Pressure Sensor ------------------------------ To realize the characteristic of flexibility in addition to the pressure sensing capability, a flexible piezoresistive carbon black/silicone rubber nanocomposite is adopted as the functional material \[[@b9-sensors-15-03224]--[@b12-sensors-15-03224]\]. For its stretchable, flexible properties and piezoresistive effect, this nanocomposite material has already been used in tactile sensors for robots to provide contact or grasping force feedback \[[@b13-sensors-15-03224],[@b14-sensors-15-03224]\]. They are also some other sensors for mechanics that adopt the material for their piezoresistive properties and energy absorbing capabilities in preventing mechanical collisions \[[@b15-sensors-15-03224],[@b16-sensors-15-03224]\]. In addition to that, all other materials used in device are flexible. [Figure 1](#f1-sensors-15-03224){ref-type="fig"} shows a simple schematic diagram demonstrating the assembly and packaging steps used in fabricating the device. Two layers of surface-modified piezoresistive polymer nanocomposite films are placed face-to face inside the device as the pressure sensing layer. These polymer films are packaged by another two layer of patterned Flexible Copper Clad Laminate (FCCL) films which act either as the package material or as the electrode of the device. To isolate this device from external moisture and contamination, another layer of PI bond-ply is used as the adhesion layer to ensure these four layers of material a good firm bond. These bond-ply layers have also been previously patterned by a laser cutting machine to save the space for the pressure sensing layer. The scale of the device's sensing part is 15 × 30 mm^2^. Since the human artery pulse in the wrist is weak and the excited pressure variation is not easy to sense, the flexible device' sensitivity needs to be further improved. Several previous efforts have been made to promote the devices' sensitivity in this research area \[[@b17-sensors-15-03224]--[@b23-sensors-15-03224]\]. A pressure sensor with record sensitivity with highly sensitive material with hollow polymer sphere in it has been proposed by Bao's group \[[@b17-sensors-15-03224]\]. Another type of research mainly utilizea tiny features' very sensitive contact state to realize high sensitivity \[[@b18-sensors-15-03224],[@b19-sensors-15-03224]\]. They usually have polymer-based micrometer scale pyramid structures to make the device electrically sensitive to external pressure loading. Devices of this type usually have a very sensitive electric response at the beginning when an array of unique pyramids gets contact to the opponent electrode. However, as the pressure goes higher, device's response become dull as the pyramidal surface get saturated, as shown in [Figure 2b](#f2-sensors-15-03224){ref-type="fig"}. A certain degree of pre-pressure needs to be maintained between the sensor and the human skin in order to ensure effective contact state and signal acquisition and the wrist artery pulse induced pressure varies (range \< 3 kPa) based on this pre-pressure bias. Furthermore, the pre-pressure also changes with the differences between users when they fasten on the wrist belt. Consequently, the real effective span for the heart rate measurements will be around 8--18 kPa. Several previous works on flexible pressure sensors have reported sensitivity high enough for heart rate measurement. However, these high sensitivities only exist within a limited range around 0 Pa. As shown in [Figure 2b](#f2-sensors-15-03224){ref-type="fig"}, the slope of the device response decreases as pressure goes higher, like the sensitivity. When the pressure reaches the effective range, devices becomes so dull that it can't respond to the artery pulse. As to the proposed novel device with full-scale high sensitivity ([Figure 2a](#f2-sensors-15-03224){ref-type="fig"}), artery pulse-induced pressure variation will make it respond intensively compared with previous ones. To have this full-scale sensitive pressure response, a new flexible pressure sensing device have been proposed in this work. The surface of the nanocomposite film has been modified with micrometer scale bump structures randomly distributed on surface with certain variation in height and lateral size. [Figure 2c](#f2-sensors-15-03224){ref-type="fig"}--d shows the SEM photos of the microbumps from the top view and side view, respectively. Unlike the typical pyramid structures of the same size, the distributed tiny structures' size makes them gradually touch with the opponent conductive surface along the whole pressure loading process so as to have a full scale high sensitivity. By surface profile measurement, the overall surface obeys the Gaussian Random distribution. By numerical simulation with MATLAB, the device response is expected to be linear. Furthermore, the micrometer scale piezoresistive bumps on the surface are very sensitive to external pressure loading as the pressures are concentrated on these tiny structures. Large deformations of these piezoresistive structures lead to dramatic conductance variations of the device. Besides that, for the distributed bump size, the conducting paths are established gradually. The capability in conductance variation is even higher. Based on above statement, the device sensitivity is expected to be higher. The devices' sensing capabilities were tested using a device test platform composed of a micropositioner, force gauge and the electric measurement part. All three of these parts are connected to a computer and controlled by a Labview software routine. Then, the device is tested for 100 cycles and the test results are plotted in [Figure 3](#f3-sensors-15-03224){ref-type="fig"}. The device responds linearly to the external pressure with the sensitivity around 13.4 kPa^−1^. A certain degree of hysteresis has been observed and the relative hysteresis does not exceed 9% over the full measurement scale. The device also shows an extraordinary stability and repeatability. [Figure 4](#f4-sensors-15-03224){ref-type="fig"} shows the statistical distribution of the measured conductance result at five different pressure levels. The temperature dependence of the fabricated device has also been tested, as shown in Supplementary file. However, as the readout circuit mechanism mentioned below, the temperature variation will not have an obvious influence on the system's performance. 2.2.. Materials and Methods --------------------------- The piezoresistive polymer is prepared with the 107 silicone rubber (hydroxyl end-blocked dimethylsiloxane) and the super conductive carbon black (HG-3F: average diameter-12 nm) with the weight ratio of 100:8. An extra amount of *n*-hexane solvent is added into the mixture to promote the dispersion of carbon black particles in the silicone rubber. A subsequent process of 10 h ultrasonic treatment along with the fast stirring is carry out to ensure the carbon black's sufficient dispersion. Before using, a proper amount of curing agent is added into the mixture (carbon grease) with a certain degree of stirring and ultrasonic treatment. Then, the carbon grease is spun coated on the GRD surface mould with the spin speed of 1000 rpm. After about 48 h of curing process under room temperature, the piezeresistive film on the mould is peeled off by hand and tailored to the proper shape and size to match the device design. 2.3.. The Signal Processing Circuit ----------------------------------- To make full use of the piezoresistive pressure sensor, an operational amplifier (op-amp) other than a Wheastone bridge \[[@b24-sensors-15-03224]\] is used to transform the variation of the resistance into a voltage signal. This system is designed with the following principles. Firstly, it uses basic low-cost analog electronic components to lower the over-all cost. Secondly, it is designed to reduce noises and interferences caused by different sources. High-frequency noise is induced by the electromagnetic interference of the environment. The movement of human body, either intended or not, can also cause significant pressure changes in the sensor. This will result in undesired dc-drift of the signal which can be obviously observed before ASP circuits. Finally, after reducing the noises, the system converts the signal into a level signal, which is transferred into a low-cost digital counter. The flow chart of the ASP system is shown in [Figure 5](#f5-sensors-15-03224){ref-type="fig"}. The first op-amp transforms the pressure on the sensor into signal A. Each beat of the heart causes a short time of pressure change on the sensor, which leads to the change of resistance. This results in the variation of signal A. Signal A mainly contains heart rate information and high frequency noise and dc-drift. High frequency noise is introduced by the electromagnetic interference, and dc-drift is caused by human motion. Here the signal processing system is used to remove these two types of interference and extract heart rate information. An analog signal processing system is introduced, first two low pass filter with different cutoff frequency is used to process signal A. Low pass filter 1 generates signal B1. This filter is designed to filter noise with frequency much higher than the heart rate frequency (about 1--2 Hz) in order to reduce noise while preserving the heart rate information. This filter assures that B1 maintains the dc-drift and heart rate information. Low pass filter 2 generates signal B2 by removing the high frequency signal and add a voltage bias to signal A in order to compare with signal B2. It has a low cutoff frequency to only preserve the dc-drift of the original signal. Comparator 1 compare signal B1 with B2 and generate signal C. These series of processes make sure that signal C contains most of the heart rate information while staying nearly undisturbed by dc-drift. However, signal C still has too many glitches and cannot be used to count heart rate directly. Low pass filter 3 is used to reduce the glitches of signal C and generates signal D. Comparator 2 is introduced in order to compare signal D with a constant voltage. Signal E is generated as a result of the comparison of signal D and the constant voltage. Finally E only contains heart rate information and is used to count heart rate. 3.. Integration and Test ======================== The schematic of the device and the test setup in this experiment is shown in [Figure 6](#f6-sensors-15-03224){ref-type="fig"}. The whole system consists of an elastic belt which is used to attach the sensor onto the wearer's wrist, the flexible pressure sensor and a module which contains the ASP system and the counter. This module is used to indicate the heart rate, and power input. The artery's pulsation is transmitted to the human skin, normally this pressure change can be easily sensed if a fingertip is put onto a human's wrist. Under this application situation, an elastic belt is used to fasten the pressure sensor on the wrist above the artery, so that the pressure sensor can be firmly attached to the wrist while sensing the pressure change. The elastic belt and the pressure sensor are both flexible, which ensures that the heart rate monitor is comfortable to wear. The change of the applied pressure will cause the resistance change of the pressure sensor. An amplifier is used to convert the change of the resistance into a voltage signal. Then the voltage signal is processed by the ASP subsystem in the module, as discussed previously. The ASP subsystem generates a level signal which contains heart rate information. Finally, this level signal is transmitted into the counter directly to measure the heart rate. The power input is used to power up the whole system. 4.. Results =========== The heart rate monitor was tested on several researchers. An oscilloscope is used to capture the wave generated by the ASP subsystem while it is processing the signal. The waveform corresponding to the signal in [Figure 5](#f5-sensors-15-03224){ref-type="fig"} is shown in [Figure 7](#f7-sensors-15-03224){ref-type="fig"}. Signal A shows the voltage signal which is converted from the change of the resistance of the pressure sensor. There are eight small concave shapes on the waveform which indicate eight pulses, however this subtle heart rate signal cannot be used to count heart rate directly. B2 is the output of the low pass filter 2 with dc bias. This indicates that the dc-drift of the original signal is quite large, and even larger than pulse itself. However, testing results reveal that our ASP system can successfully remove the interference of the dc-drift. B1 is the result of low pass filter 1. Signal C is the compare result of B1 and B2. D is the output of the low pass filter 3. E is the result of the comparator 2, it is compressed proportionately and put into the counter. This result shows the monitor has good immunity to high level dc drift. Several tests have been made to confirm the reliability of the monitor, see [Table 1](#t1-sensors-15-03224){ref-type="table"}. Reference results are obtained from a commercial electronic sphygmomanometer (HEM-7052, OMRON, Kyoto, Japan). The average error is less than 3%. 5.. Conclusions =============== A flexible, low-cost, small heart rate monitor comfortable enough for full-day wear is demonstrated. It is based on the pressure changes on the skin caused by the artery pulse. A sensitive flexible pressure sensor is used to sense the pressure change and an effective ASP system is used to extract heart rate information from the signal. This heart rate sensor has also been tested on several testees, and the results shows that this sensor is highly precise. The ASP system also shows its effectiveness in reducing the noise. Our work shows that based on this novel flexible pressure sensor and ASP system, a new way for heart rate monitoring can be realized. This work shows the possibility of full-day long-term heart rate monitoring. Supplementary Material ====================== This work was supported by National Natural Science Foundation (61434001), 973 Program (2015CB352100), National Key Project of Science and Technology (2011ZX02403-002), and Special Fund for Agroscientic Research in the Public Interest (201303107) of China. Y. Shu and C. Li conceived the project and contributed equally to this work. Y. Shu conducted the design, fabrication and tesing of the flexible device. C. Li mainly focused on the design, fabrication of the circuit. Z. Wang, W. Mi, Y. Li conducted the test of the system and analysed the data. Y. Shu and C. Li wrote the manuscript. T. Ren supervised the project. All authors discussed the results and commented on the paper. The authors declare no conflict of interest. {#f1-sensors-15-03224} {#f2-sensors-15-03224} {#f3-sensors-15-03224} {#f4-sensors-15-03224} {#f5-sensors-15-03224} {#f6-sensors-15-03224} {ref-type="fig"}.](sensors-15-03224f7){#f7-sensors-15-03224} ###### Result of the heart rate sensor and commercial electronic sphygmomanometer. **Measurement Equipment** **Heart Rate Sensor** **Electronic Phygmomanometer** --------------------------- ----------------------- -------------------------------- Normal 66 64 68 66 70 70 After exercise 90 96 [^1]: These authors contributed equally to this work. [^2]: Academic Editor: Vittorio M.N. Passaro

We have cloned a 9.5-kbp fragment of an oncogene present in a human fibrosarcoma cell line (HT-1080). The cloned fragment is present in all tested HT-1080-derived transformants, and is different from another fragment of the same oncogene (14 kbp) previously isolated. When both fragments are put together, the construction shows a molecular structure similar to that of the N-ras oncogene present in human neuroblastoma cell lines.

Introduction {#s1} ============ The intestinal mucosa is a critical effector site for elimination of enteric pathogens. *Toxoplasma gondii*, a ubiquitous protozoan parasite, is a prime example of such a pathogen. Mammals are infected with *T. gondii* primarily by the ingestion of tissue cysts from undercooked meat or oocysts excreted in the feces of felines, which are the sole definitive hosts. Upon infection, the parasite induces a potent Th1 immune response that is characterized by high levels of IL-12 and IFN-γ [@ppat.1003706-Denkers1], [@ppat.1003706-Dupont1]. Initial IL-12 production is largely the result of MyD88-dependent Toll-like receptor (TLR) signaling in dendritic cells, and the parasite profilin molecule has been identified as a ligand for TLR11 and TLR12 [@ppat.1003706-Scanga1]--[@ppat.1003706-Sukhumavasi1]. IL-12 activates natural killer (NK) cells to initiate IFN-γ production and promotes T-cell differentiation towards a Th1 program. Ultimately IFN-γ is the critical cytokine involved in controlling *Toxoplasma*. While *in vitro* experiments suggest that macrophages activated by this cytokine acquire anti-*Toxoplasma* activity through upregulation of immunity-related GTPase (IRG) molecules that mediate destruction of the parasitophorous vacuole [@ppat.1003706-Zhao1]--[@ppat.1003706-Khaminets1], the *in vivo* function of IFN-γ is less clear. Inflammatory monocytes are an important component of defense against microbial pathogens, including *Toxoplasma* [@ppat.1003706-Dunay1]. These cells express high levels of Ly6C/G (Gr-1) and are recruited from the bone marrow via chemokine (C-C motif) receptor 2 (CCR2) [@ppat.1003706-Geissmann1]. During *Listeria monocytogenes* infection, inflammatory monocytes are recruited from the bone marrow to the spleen and liver where they differentiate into TNF-α- and nitric oxide (NO)-producing DCs (Tip-DCs). There they are essential for bacterial clearance and mouse survival [@ppat.1003706-Shi1], [@ppat.1003706-Serbina1]. Likewise, CCR2-dependent inflammatory monocytes are recruited to the lung during *Mycobacteria tuberculosis* infection where they protect mice from disease by recruiting and activating T cells and by producing NO [@ppat.1003706-Peters1], [@ppat.1003706-Peters2]. Mucosal defense against *T. gondii* has also recently been shown to require CCR2-dependent inflammatory monocytes [@ppat.1003706-Dunay1]. Upon recruitment to the small intestine, these cells control the parasite either indirectly by production of IL-12 and TNF-α or directly through production of NO and IRG proteins [@ppat.1003706-Yarovinsky1]--[@ppat.1003706-Andrade1], [@ppat.1003706-Zhao1], [@ppat.1003706-Taylor1], [@ppat.1003706-Dunay1], [@ppat.1003706-Ling1]. While CCR2 enables recruitment of inflammatory monocytes to sites of infection, the factors that coordinate their activation and acquisition of effector function are not known. CXCR3 is a Th1-associated chemokine receptor, and cells expressing this receptor respond to the IFN-γ-inducible chemokines CXCL9, 10, and 11 [@ppat.1003706-Groom1]. The receptor is expressed predominantly by T cells and NK cells and is rapidly upregulated upon cell activation. There is evidence that CXCR3 expression enables T-cell entry into sites of infection, although the outcome of recruitment varies among pathogens. In the case of *Leishmania major*, recruitment is protective as CXCR3-expressing T cells are required for the resolution of cutaneous lesions [@ppat.1003706-Rosas1]. However, in the case of *Plasmodium berghei* ANKA, CXCR3 is pathogenic because it allows entry of proinflammatory cells into the CNS, resulting in cerebral malaria [@ppat.1003706-Campanella1]. Here we determined the role of CXCR3 in the intestinal immune response to *Toxoplasma*. We found that loss of CXCR3 negatively affected host survival against oral infection. This was associated with diminished recruitment of CD4^+^ T cells to the lamina propria (LP), decreased T cell IFN-γ secretion, impaired inflammatory monocyte effector function, and inability to control the parasite in the intestinal mucosa. Reconstitution with CXCR3-competent CD4^+^ T cells restored inflammatory monocyte function, resulting in improved survival against the parasite. Protective effects of adoptively transferred CD4^+^ T lymphocytes depended upon their ability to produce IFN-γ, but occurred independently of CD4 expression of CD40L. Our data show that CXCR3 enables Th1 recruitment to the intestinal LP, where these cells instruct activation of CCR2-dependent inflammatory monocytes, in turn controlling infection. These results establish CXCR3 as a major determinant orchestrating communication between effectors of innate and adaptive immunity, enabling effective host defense against infection. Results {#s2} ======= CXCR3 and its ligands CXCL9 and CXCL10 are upregulated during acute toxoplasmosis {#s2a} --------------------------------------------------------------------------------- Because CXCR3 and its chemokine ligands are strongly associated with Th1 responses, we asked whether this proinflammatory axis was induced during *Toxoplasma* infection in the intestinal mucosa. Accordingly, mice were orally inoculated with cysts, and relative levels of CXCR3, CXCL9 and CXCL10 mRNA expression were measured over the course of acute infection. We found strong upregulation of CXCR3 and its specific chemokine ligands as early as Day 4 post-infection in both the ileum and mesenteric lymph nodes (MLN) ([Fig. 1A](#ppat-1003706-g001){ref-type="fig"}). Overall, peak CXCR3 mRNA levels were attained by Day 6 post-inoculation. {#ppat-1003706-g001} In order to examine CXCR3 expression in more detail, we utilized *Cxcr3* eGFP reporter (CIBER) mice, a bicistronic reporter strain in which cells expressing CXCR3 also express eGFP [@ppat.1003706-Oghumu1]. We found a large increase in CXCR3 populations of both CD4^+^ and CD8^+^ T lymphocytes in MLN, spleen (SPL) and LP compartments following infection ([Fig. 1B](#ppat-1003706-g001){ref-type="fig"}). In general, CXCR3 upregulation was most pronounced in the CD4^+^ population. For example, in the MLN there was a 6-fold increase in CD4^+^CXCR3^+^ cells but only a 2-fold increase in CD8^+^CXCR3^+^ lymphocytes. NK cells are also known to express CXCR3 and are an important source of early IFN-γ during *T. gondii* infection [@ppat.1003706-Qin1], [@ppat.1003706-Sher1]. However, while CXCR3-GFP expression was relatively high on naïve NK cells, the GFP expression was in fact reduced during infection, suggesting lack of a role for CXCR3^+^ NK cells during intestinal infection ([Fig. S1](#ppat.1003706.s001){ref-type="supplementary-material"}). We next examined expression of the activation marker CD27 on GFP^+^ and GFP^−^ T lymphocytes in infected mice. CD27 was significantly lower in CXCR3^−^GFP^−^ cells, suggesting an altered maturation state of the CXCR3^−^ T cells ([Fig. S2A and B](#ppat.1003706.s002){ref-type="supplementary-material"}). Likewise, there was a lower percentage of CD27^+^ cells amongst CXCR3-GFP^−^ CD8^+^ T lymphocytes, although the decreases in expression were not as striking as with the CD4^+^ lymphocytes ([Fig. S2C and D](#ppat.1003706.s002){ref-type="supplementary-material"}). *Cxcr3^−/−^* mice are increased in susceptibility and are prone to severe intestinal damage following *T. gondii infection* {#s2b} --------------------------------------------------------------------------------------------------------------------------- To further examine the role of CXCR3 during *T. gondii* infection, mice deficient in CXCR3 were orally inoculated with low virulence ME49 cysts, and the outcome of infection was monitored. While all wild-type (WT) mice survived acute infection with 30 cysts, *Cxcr3^−/−^* animals displayed increased susceptibility with nearly 75% of mice dying by 2 weeks post-infection ([Fig. 2A](#ppat-1003706-g002){ref-type="fig"}). When the cyst dose was increased to 50, all CXCR3 knockout (KO) mice rapidly succumbed to infection, but some WT mice also died ([Fig. 2B](#ppat-1003706-g002){ref-type="fig"}). Interestingly, when WT and KO mice were infected by intraperitoneal injection, lack of CXCR3 did not affect survival, indicating that the effect of CXCR3 is specific to the mucosal response ([Fig. S3A](#ppat.1003706.s003){ref-type="supplementary-material"}). To further examine the overall response in orally infected mice, we examined the gross appearance of the small intestine of WT and *Cxcr3^−/−^* mice after 30-cyst infection. The small intestines of the KO mice were strikingly damaged as demonstrated by massive hemorrhage compared to WT ([Fig. 2C](#ppat-1003706-g002){ref-type="fig"}). Consistent with intestinal shortening associated with increased damage [@ppat.1003706-Heimesaat1]--[@ppat.1003706-Ueno1], the length of the small intestine was reduced in the KO mice during infection ([Fig. 2D](#ppat-1003706-g002){ref-type="fig"}). Increased damage was further confirmed by H&E staining of small intestinal sections. WT mice displayed minor villus blunting accompanied by moderate to severe inflammatory cell recruitment in the submucosa ([Fig. 2E and G](#ppat-1003706-g002){ref-type="fig"}). In contrast, *Cxcr3^−/−^* mice displayed severe villus blunting, fusion, epithelial necrosis, sloughing of villus tips, and vascular congestion and hemorrhage ([Fig. 2F and H](#ppat-1003706-g002){ref-type="fig"}). Blind scoring of H&E sections revealed a significant decrease in inflammation scores in the absence of CXCR3 ([Fig. 2I](#ppat-1003706-g002){ref-type="fig"}), but when parameters of intestinal damage were quantitated, *Cxcr3^−/−^* mice scored significantly higher than WT counterparts ([Fig. 2J](#ppat-1003706-g002){ref-type="fig"}). This damage was infection-dependent as intestines from non-infected WT and *Cxcr3^−/−^* mice both had normal architecture with few inflammatory cells ([Fig. S3B](#ppat.1003706.s003){ref-type="supplementary-material"}). Increased epithelial damage in the absence of CXCR3 was further verified by loss of epithelial surface-associated Muc1 compared to infected WT animals, suggesting epithelial cell sloughing ([Fig. S3C](#ppat.1003706.s003){ref-type="supplementary-material"}). Despite the overall decreased inflammatory score, *Cxcr3^−/−^* mice consistently displayed an influx of neutrophils into the LP compartment compared to WT mice, suggesting a role for these cells in causing damage, as argued by others [@ppat.1003706-Shi1], [@ppat.1003706-Serbina1], [@ppat.1003706-Dunay2] ([Fig. S3D and E](#ppat.1003706.s003){ref-type="supplementary-material"}). {#ppat-1003706-g002} *Cxcr3^−/−^* mice are unable to control parasite replication in the small intestine {#s2c} ----------------------------------------------------------------------------------- Genetic knockout of cytokines such as IFN-γ results in susceptibility to *T. gondii* through the inability to control parasite replication, whereas the deletion of anti-inflammatory mediators such as IL-10 results in susceptibility due to cytokine pathology [@ppat.1003706-SchartonKersten1], [@ppat.1003706-Gazzinelli1]. Based on decreased inflammation scores, we hypothesized that the *Cxcr3^−/−^* mice were more likely to be succumbing from uncontrolled parasite replication rather than immune-mediated damage. To examine this, intestinal tissues were stained for parasite antigen by immunohistochemistry. Sections from WT mice displayed minimal parasite infiltration within the LP ([Fig. 3A](#ppat-1003706-g003){ref-type="fig"}). Conversely, *Cxcr3^−/−^* mice contained numerous large foci of parasite throughout the length of the small intestine that often coincided with areas of severe damage ([Fig. 3B](#ppat-1003706-g003){ref-type="fig"}). Surprisingly, this difference was restricted to the LP and submucosa of the small intestine because Peyer\'s patches (PP) in WT and *Cxcr3^−/−^* mice contained similar levels of parasite antigen ([Fig. 3C and D](#ppat-1003706-g003){ref-type="fig"}). Differences in parasite burden between WT and *Cxcr3^−/−^* mice in the MLN, spleen, and lung were also indiscernible by IHC analysis (data not shown). These results were further confirmed by quantitative PCR. Thus, while lung, liver, spleen, MLN and PP contained similar levels of parasite genomes regardless of CXCR3 expression, there was an approximately 50-fold increase in parasite levels in the absence of CXCR3 in intestinal tissues ([Fig. 3E](#ppat-1003706-g003){ref-type="fig"}). These data suggest that increased susceptibility to *Toxoplasma* in *Cxcr3^−/−^* mice was due to a localized inability to control parasite replication within the LP of the small intestine. {#ppat-1003706-g003} CD4^+^ T cells are recruited to the small intestine via CXCR3 {#s2d} ------------------------------------------------------------- The dominant effector cells required for elimination of *T. gondii* following oral infection are inflammatory monocytes. These cells express Ly6C/G (Gr-1), produce TNF-α, IL-12, and are likely to kill parasites via activation of IFN-γ-inducible p47 GTPases that assemble at the parasitophorous vacuole membrane and mediate its destruction [@ppat.1003706-Zhao1], [@ppat.1003706-Dunay1]. Consistent with others [@ppat.1003706-Dunay1], we observed these cells in the LP of infected mice ([Fig. 4A](#ppat-1003706-g004){ref-type="fig"}). Inflammatory monocytes are dependent upon CCR2 for exit from the bone marrow, but we wondered whether CXCR3 might be involved in recruiting these cells to the LP in response to *T. gondii*. Therefore, we examined CXCR3-GFP expression by intestinal inflammatory monocytes during infection. Inflammatory monocytes in the small intestinal LP of infected reporter mice did not express any GFP as compared to inflammatory monocytes isolated from infected *Cxcr3^−/−^* mice ([Fig. 4B](#ppat-1003706-g004){ref-type="fig"}). In stark contrast, approximately 50% of LP CD4^+^ T cells expressed high levels of GFP ([Fig. 4C](#ppat-1003706-g004){ref-type="fig"}). Furthermore, *Cxcr3^−/−^* mice displayed unaltered total numbers of LP inflammatory monocytes compared to wild-type controls (defined as CD11b^+^Ly6C^+^Ly6G^−^) ([Fig. 4D](#ppat-1003706-g004){ref-type="fig"}). We next assessed the kinetics by which CD4^+^ T cells and inflammatory monocytes were recruited to the lamina propria during infection. Between days 4 and 7 of infection, there was a significant increase in the total numbers of CD4^+^CXCR3^−^GFP^+^ T cells and inflammatory monocytes ([Fig. 4E](#ppat-1003706-g004){ref-type="fig"}). However, the total number of CD4^+^CXCR3^−^GFP^−^ cells remained unchanged, further indicating that infection promotes the recruitment of CD4^+^CXCR3^+^ T cells ([Fig. 4E](#ppat-1003706-g004){ref-type="fig"}). Few NK cells were observed in the lamina propria, but there was a small increase in their number during infection. This was attributable to an increase in CXCR3^−^ NK cells (data not shown). Consistent with these results, there was an influx of CD4^+^ T cells in WT small intestines that was diminished in *Cxcr3^−/−^* mice ([Fig. 4F--H](#ppat-1003706-g004){ref-type="fig"}). These findings demonstrate that CD4^+^ T cells fail to effectively traffic to the intestinal compartment in the absence of CXCR3, but the presence of LP inflammatory monocytes does not require this chemokine receptor. {#ppat-1003706-g004} Lamina propria CD4^+^ T cells display impaired IFN-γ production {#s2e} --------------------------------------------------------------- We next asked if expression of CXCR3 affected the ability of T cells to secrete the Th1 cytokine IFN-γ. Initial experiments on bulk populations of splenocytes and mesenteric lymph node (MLN) cells from Day-11 infected WT and KO revealed no differences in the amount of IFN-γ, TNF-α or IL-10 produced during *in vitro* culture ([Fig. S4](#ppat.1003706.s004){ref-type="supplementary-material"}). To specifically examine functional outcomes in intestinal cells, WT and *Cxcr3^−/−^* lamina propria leukocytes were harvested 4 and 6 days post-oral infection, stimulated *ex vivo*, and IFN-γ production was examined by flow cytometry. CD4^+^ T cells from both WT and *Cxcr3^−/−^* displayed enhanced IFN-γ production over time. However, in the absence of CXCR3, CD4^+^ T cells produced significantly less IFN-γ compared to WT cells at both examined time points ([Fig. 5A--E](#ppat-1003706-g005){ref-type="fig"}). This was confirmed by measuring IFN-γ from the supernatants of Day-6 WT and *Cxcr3^−/−^* intestinal biopsy cultures, where IFN-γ was lower in the absence of CXCR3 ([Fig. 5F](#ppat-1003706-g005){ref-type="fig"}). This effect was specific to the CD4^+^ T cell subset, as IFN-γ production by lamina propria CD8^+^ T cells and NK cells was unchanged between WT and knockout animals ([Fig. S5A](#ppat.1003706.s005){ref-type="supplementary-material"}--F). Further confirming that this loss of IFN-γ production was specific to CD4^+^ T lymphocytes in the small intestine, and consistent with the bulk splenocyte culture experiments, splenocytes isolated from infected WT and *Cxcr3^−/−^* mice secreted equivalent levels of IFN-γ upon *ex vivo* stimulation with PMA and ionomycin ([Fig. S5G](#ppat.1003706.s005){ref-type="supplementary-material"}--I). Together, these results indicate an intestine-specific defect in presence of CD4^+^ Th1 cells in the absence of CXCR3 as measured by the capacity to produce IFN-γ. {#ppat-1003706-g005} Inflammatory monocyte responses in the intestinal mucosa are defective in the absence of CXCR3 {#s2f} ---------------------------------------------------------------------------------------------- Although IFN-γ, IL-10, and TNF-α responses remained intact in the MLN and spleen late during infection of CXCR3-deficient mice, a significant decrease in IL-12 production was observed in the MLN ([Fig. 6A](#ppat-1003706-g006){ref-type="fig"}) and spleen ([Fig. 6B](#ppat-1003706-g006){ref-type="fig"}) of *Cxcr3^−/−^* mice. Defective IL-12 responses in the CXCR3 KO strain were infection dependent, because parasite antigen stimulated equivalent amounts of IL-12 in noninfected WT and KO splenocytes ([Fig. 6C](#ppat-1003706-g006){ref-type="fig"}). This response, known to derive from resident splenic CD8α^+^ DC [@ppat.1003706-Mashayekhi1], may account for equivalent Th1 priming in secondary lymphoid organs, despite lower IL-12 levels during late acute infection. {#ppat-1003706-g006} Since IL-12 is also a characteristic cytokine of inflammatory monocytes, we investigated the impact of CXCR3 deletion on intestinal inflammatory monocyte function. Indeed, *in vitro* culture of intestinal biopsy samples revealed decreased production of IL-12 ([Fig. 6D](#ppat-1003706-g006){ref-type="fig"}). To further identify the source of the defective IL-12, we examined the production of IL-12 from inflammatory monocytes. While the total numbers of LP inflammatory monocytes were equivalent in WT and CXCR3 KO mice ([Fig. 4B](#ppat-1003706-g004){ref-type="fig"}), the population of CD11b^+^Gr-1^+^ cells co-expressing IL-12 and TNF-α was dependent upon CXCR3 ([Fig. 6E and F](#ppat-1003706-g006){ref-type="fig"}). Further confirming impaired inflammatory monocyte function, iNOS expression was significantly decreased in inflammatory monocytes ([Fig. 6G and H](#ppat-1003706-g006){ref-type="fig"}). These findings strongly suggest that inflammatory monocytes are functionally impaired in the absence of CXCR3. Interestingly, neutrophils in the LP of KO mice produced significantly higher levels of TNF-α compared to WT neutrophils ([Figure S6A and B](#ppat.1003706.s006){ref-type="supplementary-material"}). Adoptive transfer of WT CD4^+^ T lymphocytes rescues inflammatory monocyte function and restores resistance in *Cxcr3^−/−^* mice {#s2g} -------------------------------------------------------------------------------------------------------------------------------- Given the data so far, we hypothesized that CD4^+^ T cells were unable to effectively home to the small intestine and prime inflammatory monocyte function in the absence of CXCR3, resulting in susceptibility to *Toxoplasma*. We therefore tested whether reconstitution with CXCR3-competent CD4^+^ T cells would allow *Cxcr3^−/−^* mice to overcome susceptibility and restore inflammatory monocyte function. Accordingly, CD4^+^ T cells from naïve WT spleens were enriched to 90--95% purity by magnetic bead separation ([Fig. 7A](#ppat-1003706-g007){ref-type="fig"}) and injected i.v. into *Cxcr3^−/−^* recipients. Mice were orally challenged with *T. gondii* 24 hours post-adoptive transfer, and survival was monitored. Knockout mice that did not receive WT cells began to die 10 days post-challenge, while all KO mice that received CD4^+^ T cells and all WT controls survived the acute phase of infection ([Fig. 7B](#ppat-1003706-g007){ref-type="fig"}). To confirm that the CD4-dependent survival was not an artifact of the transfer, *Cxcr3^−/−^* CD4^+^ T cells were adoptively transferred into KO recipients. The knockout cells were unable to protect against susceptibility, demonstrating that protection is dependent on CXCR3 expression by CD4^+^ T cells ([Fig. S7A](#ppat.1003706.s007){ref-type="supplementary-material"}). {#ppat-1003706-g007} To assess the functional impact of WT CD4 adoptive transfer, parasite burden and cytokine production in the LP were assessed by flow cytometry in WT, *Cxcr3^−/−^*, and *Cxcr3^−/−^* +CD4 mice. While *Cxcr3^−/−^* mice had a clear increase in *Toxoplasma* infected cells relative to WT, upon adoptive transfer of WT CD4^+^ T cells, parasite levels were reduced to WT ([Fig. 7C](#ppat-1003706-g007){ref-type="fig"}). Likewise, expression of IL-12/TNF-α by inflammatory monocytes was significantly reduced in KO mice, but these cytokines returned to WT levels upon transfer of WT CD4^+^ T cells ([Fig. 7D](#ppat-1003706-g007){ref-type="fig"} and [Fig. S7B](#ppat.1003706.s007){ref-type="supplementary-material"}). In addition to cytokine responses, intestinal damage was also alleviated by adoptive transfer of WT CD4^+^ T cells, as the intestinal lengths of the transferred mice were restored to WT ([Fig. 7E](#ppat-1003706-g007){ref-type="fig"}). Possibly as a result of improved monocyte function and parasite clearance, neutrophil levels and neutrophil TNF-α secretion were also restored to WT levels following the transfer of WT CD4^+^ T cells ([Fig. S7C and D](#ppat.1003706.s007){ref-type="supplementary-material"}). CD4+ T-cell rescue is dependent on IFN-γ but independent of CD40L {#s2h} ----------------------------------------------------------------- To identify the mechanism behind the rescue of *Cxcr3^−/−^* susceptibility by WT CD4^+^ T cells, we performed adoptive transfer experiments utilizing T cells derived from knockout animals. Inasmuch as CXCR3 is a Th1 chemokine receptor, we began by asking whether reversal of susceptibility was dependent on CD4-derived IFN-γ Therefore, CD4^+^ T cells were isolated from *Ifnγ* mice and adoptively transferred into CXCR3-deficient recipients. Unlike IFN-γ-competent CD4^+^ T cells ([Fig. 7B](#ppat-1003706-g007){ref-type="fig"} and [Fig. 8B](#ppat-1003706-g008){ref-type="fig"}), transfer of IFN-γ KO CD4^+^ T lymphocytes failed to provide significant protection ([Fig. 8A](#ppat-1003706-g008){ref-type="fig"}). It has been shown that CD40L contributes to inflammatory responses in the intestinal mucosa during oral *Toxoplasma* infection [@ppat.1003706-Li1]. Therefore, we performed the adoptive transfer using *Cd40l^−/−^* CD4^+^ T cells and assessed survival. As expected, CXCR3-deficient animals were highly susceptible to infection. However, *Cxcr3^−/−^* mice receiving *Cd40l^−/−^* CD4^+^ T cells survived the infection, indicating that CD40L does not mediate CXCR3^+^CD4^+^-dependent protection ([Fig. 8B](#ppat-1003706-g008){ref-type="fig"}). {ref-type="fig"} legend (WT: n = 10; KO: n = 11; *Ifn*-γ*^−/−^*: n = 11; *CD40L^−/−^*: n = 5).](ppat.1003706.g008){#ppat-1003706-g008} Discussion {#s3} ========== Effective control of pathogens such as *T. gondii* requires the coordinated action of cells of innate and adaptive immunity. Orchestration of the response is governed by an underlying network of chemokines and chemokine receptor-expressing cells in both the hematopoietic and non-hematopoietic compartments. In this study, we demonstrate a central role for chemokine receptor CXCR3 in empowering Th1 trafficking to the small intestine, in turn enabling inflammatory monocyte activation and concomitant control of infection. While the importance of IFN-γ-secreting CD4^+^ T cells in resistance to *Toxoplasma* is well known to researchers in the field [@ppat.1003706-SchartonKersten1], [@ppat.1003706-Gazzinelli2], [@ppat.1003706-Suzuki1], and while the importance of anti-microbial inflammatory monocytes has recently become clear in the context of *Toxoplasma* and other infections [@ppat.1003706-Dunay1], the present study is the first to reveal the functional link between CXCR3^+^ T-cell effectors, IFN-γ and inflammatory monocyte activation in tissues of the intestinal mucosa. Although Th1 effectors depend upon CXCR3 to reach the site of infection, inflammatory monocytes require chemokine receptor CCR2 for optimal trafficking. In the latter case, inflammatory monocytes fail to exit the bone marrow in *Ccr2^−/−^* mice, resulting in a decreased level of this population in the periphery, in turn resulting in inability to control *T. gondii* infection [@ppat.1003706-Dunay1]. Monocytes have also been suggested to promote the systemic dissemination of *T. gondii* to the brain [@ppat.1003706-Courret1]. While brain parasite loads were not examined in this study, it is unlikely that altered parasite shuttling is a mechanism by which the knockout animals are succumbing to *Toxoplasma* because peripheral parasite loads were not affected by absence of CXCR3 ([Fig. 3B](#ppat-1003706-g003){ref-type="fig"}). Our data argue that the basis for increased parasites specifically in the intestine is the result of defective regional control by inflammatory monocytes that lack CXCR3-dependent activation signals. Recent data indicate that inflammatory monocyte expression of CCR1 enables a response to IL-15-dependent CCL3-secreting innate lymphoid cells, resulting in CCR1-dependent recruitment to the intestinal mucosa of *Toxoplasma* infected mice [@ppat.1003706-Schulthess1]. Taking these data and ours collectively, we propose that CXCR3, CCR2 and CCR1 act together as a control axis of innate and acquired immunity in intestinal immunity, ensuring coordinated recruitment of inflammatory monocytes and Th1 effectors to inflamed tissues. It was recently demonstrated that NK cell-derived IFN-γ controls the differentiation of circulating monocytes into inflammatory dendritic cells during i. p. *T. gondii* infection, and is thus required for an optimal IL-12 response [@ppat.1003706-Goldszmid1]. In our model we did not see a dependence on CXCR3 for NK cell recruitment, as NK cells appeared to lose CXCR3-GFP expression over the course of infection ([Fig. S1](#ppat.1003706.s001){ref-type="supplementary-material"}), and production of NK cell IFN-γ was equivalent in WT and KO mice ([Fig. S5D](#ppat.1003706.s005){ref-type="supplementary-material"}--F). This difference may be attributable to the alternative routes of infection used, as our model incorporates the intestinal response, while the i.p. route bypasses the intestinal mucosa. Consistent with this idea, absence of CXCR3 did not affect the ability of mice to survive i. p. infection ([Fig. S3A](#ppat.1003706.s003){ref-type="supplementary-material"}). While our study focuses on the early response to *Toxoplasma* infection in the intestinal mucosa, others have examined the role of CXCR3 and its ligands in additional tissues and at different stages of infection. Antibody-mediated depletion of CXCL10, a major CXCR3 ligand, increases susceptibility and blocks influx and expansion of T cells in the liver and spleen that accompanies *T. gondii* infection [@ppat.1003706-Khan1]. Additionally, a study of ocular toxoplasmosis revealed that T cells infiltrating the eye during infection express CXCR3 and produce IFN-γ. Depletion of CXCL10 in this model reduced the number of infiltrating T lymphocytes during chronic infection, resulting in increased parasite replication and ocular damage [@ppat.1003706-Norose1]. Recently, CXCL10 was shown to impact CD8^+^ T-cell mobility in the brain of chronically infected mice, enhancing their ability to control the parasite by increasing contact with infected cells [@ppat.1003706-Harris1]. Our results for the first time highlight the importance of CXCR3 and its impact on CCR2-dependent monocytes in the initial protective response to the parasite in the intestine. It has been shown that TGF-β production by intestinal IEL protects against *T. gondii*-induced damage by down-modulating inflammation [@ppat.1003706-BuzoniGatel1]. While we did not examine intraepithelial lymphocytes (IEL) in this study, it is possible that CXCR3 expression could also affect trafficking and function of this cell type, thereby contributing to resistance in this model. Future studies will allow us to determine whether CXCR3-expressing IEL play a role in immunity during intestinal *T. gondii* infection. CXCR3 has also been assessed for its role in immunity to other protozoan pathogens, including *Leishmania* and *Plasmodium*. Interestingly, the function of CXCR3 differs depending upon the parasite, the route of infection and the site examined. For example, *Cxcr3^−/−^* mice exhibit impaired IFN-γ production and increased lesion development during cutaneous *L. major* infection, but the knockout mice are not more susceptible to hepatic *L. donovani* infection [@ppat.1003706-Rosas1], [@ppat.1003706-Barbi1]. Furthermore, CXCR3 and its chemokines promote cerebral inflammation and mortality during experimental malaria infection [@ppat.1003706-Campanella1], [@ppat.1003706-Nie1]. Overall, CXCR3 and its chemokine ligands function as double-edged swords, inasmuch as they make an important contribution to protective immunity, but when dysregulated they are the cause of deleterious immunopathology. In addition to its role in cell recruitment, CXCR3 has recently been suggested to be important for priming CD4^+^ T cells in the lymph node to become Th1 cells by promoting long-lasting interactions between T cells and CXCL10-expressing dendritic cells. In the absence of CXCR3, T cells fail to fully differentiate into IFN-γ-producing cells and are defective during subsequent lymphocytic choriomeningitis virus (LCMV) infection [@ppat.1003706-Groom2]. We found no evidence for defective Th1 responses in secondary lymphoid organs during *Toxoplasma* infection of *Cxcr3^−/−^* mice, a result that is supported by similar findings during *L. major* infection [@ppat.1003706-Rosas1]. However, our results are consistent with impaired recruitment of Th1 cells in the absence of CXCR3, as lamina propria CD4^+^ T cells from *Cxcr3^−/−^* mice exhibited defective IFN-γ production. We conclude that the function of CXCR3 in promoting Th1 differentiation versus, or in addition to, homing to inflammatory sites is likely to be a context-dependent phenomenon. Although we found no differences in T-cell activation in CXCR3 negative T cells of reporter mice or in CXCR3 KO animals, as measured by expression of CD25, CD69 and CD44 (data not shown), we observed a consistent decrease in CD27 expression amongst CXCR3-negative T cells of reporter mice. Overall levels of CD27 expression were also lower in T cells from *Cxcr3^−/−^* mice (data not shown). CD27 is a member of the TNF receptor super family that has been implicated as a T-cell costimulatory molecule [@ppat.1003706-Hendriks1]. CD27 expression is thought to characterize naïve or memory T cells, whereas loss of CD27 represents terminal differentiation [@ppat.1003706-Hamann1]. Accordingly, it is possible that in addition to controlling T-cell recruitment to sites of infection, *Cxcr3^−/−^* T cells may undergo terminal differentiation and, possibly, premature Th1 effector death in tissues prior to mediating IFN-γ dependent inflammatory monocyte activation. This is consistent with studies showing that CD27^low^ cells are more susceptible to apoptosis and that accumulation of influenza-specific T lymphocytes was impaired in the lungs of *Cd27^−/−^* mice during infection [@ppat.1003706-Hendriks1], [@ppat.1003706-Kapina1]. In our study, CD27 expression was not rescued by adoptive transfer of WT CD4^+^ T cells (data not shown), which may suggest that increasing the T-cell pool allows the system to cross a certain threshold of T-cell levels in order to activate inflammatory monocytes without reversing CD27 expression. In the absence of CXCR3, we found that lamina propria neutrophil levels were increased during infection, as was their activation status as measured by TNF-α expression. Furthermore, adoptive transfer of WT CD4^+^ T lymphocytes into the KO strain reversed increased levels of PMN as well as their production of TNF-α. Because this inflammatory cytokine has been linked to intestinal damage during *Toxoplasma* infection [@ppat.1003706-Liesenfeld1], it seems likely that CXCR3-dependent effects on neutrophils are likely to be secondary to loss of inflammatory monocyte function. In this scenario, defects in monocyte-mediated parasite killing would result in damage to the intestinal mucosa. Translocation of luminal gut flora, known to contribute to emergence of parasite-induced intestinal lesions [@ppat.1003706-Heimesaat2]--[@ppat.1003706-Egan1], would in turn be expected to result in local neutrophil recruitment. Indeed, based on neutrophil depletion studies it has been suggested that these cells mediate damage to the intestinal mucosa during *T. gondii* infection [@ppat.1003706-Dunay2]. The cellular and molecular basis for this effect is not at present known, but both the IL-17/IL-23 axis and CXCL8 have been shown to promote neutrophil accumulation in infected tissues suggesting involvement of one or both of these mediators [@ppat.1003706-DelRio1]--[@ppat.1003706-Murphy1]. The results of this study extend our understanding of immunity in the intestinal mucosa, which has become increasingly important as inflammatory bowel diseases (IBD), such as ulcerative colitis and Crohn\'s disease, become more common in developed regions of the world. In this regard, abnormally high levels of CXCR3 are associated with dysregulated intestinal responses in human IBD patients, underscoring the potential hazards of unbalanced inflammatory responses [@ppat.1003706-Papadakis1]--[@ppat.1003706-Schroepf1]. While CXCR3 can be pathogenic by recruiting effector cells to otherwise healthy tissue, as in IBD or cerebral malaria, we show here that CXCR3-expressing T cells play an essential protective role in host defense by enabling defense against pathogenic organisms. Antibodies against CXCL10 have been suggested as potential therapeutic agents against IBD [@ppat.1003706-Nishimura1], [@ppat.1003706-Singh1]. The results from this study, however, highlight the possible harm of inhibiting CXCR3-expressing cells into sites of inflammation during infection with an enteric pathogen. As the first study to demonstrate a protective role for CXCR3^+^CD4^+^ T cells in the intestinal immune response, we have shown here that failure to appropriately recruit these T cells results in impaired inflammatory monocyte activation, accumulation of intestinal parasites, and subsequent recruitment of potentially pathogenic TNF-α-secreting neutrophils. Our results reveal CXCR3 as a critical chemokine receptor of the adaptive immune system that ensures appropriate placement of T cells in inflamed tissue, enabling inflammatory monocytes of innate immunity to acquire effector functions and mediate effective host defense. Materials and Methods {#s4} ===================== Ethics statement {#s4a} ---------------- All experiments in this study were performed strictly according to the recommendations of the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. The protocols were approved by the Institutional Animal Care and Use Committee at Cornell University (permit number 1995--0057). All efforts were made to minimize animal suffering during the course of these studies. Mice and infections {#s4b} ------------------- Female Swiss Webster mice (6--8 weeks of age) were purchased from the Jackson Laboratory (Bar Harbor, ME). *Cxcr3^−/−^* and *Cxcr3* eGFP knock-in reporter mice [@ppat.1003706-Oghumu1] were established as breeding colonies in the Transgenic Mouse Facility at the Cornell University College of Veterinary Medicine. The CXCR3 internal ribosomal entry site bicistronic eGFP reporter (CIBER) mice were generated as described [@ppat.1003706-Oghumu1]. This strain possesses a functional CXCR3 receptor, and all CXCR3 positive cells also express intracellular eGFP. Mouse infections were initiated by oral inoculation of cysts of the type II *T. gondii* ME49 strain. Cysts were isolated from chronically infected Swiss Webster mice by homogenization of whole brain in sterile PBS. Unless stated otherwise, mice were infected at 8--12 weeks of age with 30 cysts. Tissue staining and immunofluorescence microscopy {#s4c} ------------------------------------------------- Intestines were excised, flushed with 10% neutral-buffered formaldehyde, and embedded in paraffin for sectioning. Sections were stained for hematoxylin and eosin for assessment of pathological changes. Sections were also stained for parasite antigen by immunohistochemistry at the Cornell Animal Health Diagnostic Center. Frozen sections were obtained by embedding 1 cm lengths of intestine in OCT. Sections of 6--8 µm were cut on a cryostat, fixed in ice-cold acetone, and blocked with PBS containing 2× casein and goat serum. To examine T-cell infiltration, sections were incubated with rat anti-CD4 antibody (GK1.5) (ATCC, Manassas, VA) or rat IgG at 4°C overnight followed by goat anti-rat Alexa-647 secondary antibody (Life Technologies, Grand Island, NY). Sections were then mounted in DAPI-Prolong antifade (Life Technologies) and imaged by confocal microscopy. ImageJ software was used to analyze fluorescence of independent channels. Cell isolation {#s4d} -------------- Spleens and mesenteric lymph nodes were excised, crushed between sterile slides, and passed through a 70-µm filter (BD, Franklin Lakes, NJ). Red blood cells from splenocyte suspensions were lysed with ACK lysis buffer (Life Technologies). For LP leukocyte isolation, the small intestine was removed, cleaned of mesentery, flushed with sterile PBS, and cleared of Peyer\'s patches. The intestine was opened longitudinally and the mucosal layer was scraped with a blunt scalpel to remove epithelial cells. The tissue was cut into 5 mm sections and vigorously washed with Dulbecco\'s modified Eagle\'s media (Cellgro, Manassas, VA) and 5 mM EDTA (Life Technologies). Cells were liberated from the intestinal tissue by digestion with 10 mg/ml collagenase (Sigma, St. Louis, MO) at 37°C and subsequently passed through a 70-µm filter. Cytokine measurement {#s4e} -------------------- Secretion of IFN-γα, TNF-α, and IL-10 was assayed by ELISA (eBioscience, San Diego, CA) following manufacturer\'s instructions in the presence of soluble tachyzoite antigen (STAg) prepared as previously described [@ppat.1003706-Denkers2]. IL-12p40 was quantitated using an in-house ELISA [@ppat.1003706-Butcher1]. For ileum biopsy cultures, 1 cm intestinal sections were flushed with PBS, opened longitudinally, and cultured overnight in complete Dulbecco\'s modified Eagle\'s media supplemented with 10% bovine growth serum (Hyclone), 0.05 mM β-mercaptoethanol (Sigma), 1 mM sodium pyruvate, 0.1 mM nonessential amino acids, 10,000 U/ml penicillin, 10,000 µg/ml streptomycin, and 30 mM HEPES (reagents from Life Technologies). Supernatants were collected and assayed for cytokine by ELISA. Measurement of mRNA by quantitative PCR {#s4f} --------------------------------------- RNA was isolated from MLN and intestinal tissue from mice over a time course of infection. Tissue was initially disrupted with a tissue homogenizer and subjected to RNA isolation following manufacturer\'s instructions (Tissue RNA Kit, Omega Biotek, Norcross, GA). RNA was converted to cDNA (Quantas Biosciences, Gaithersburg, MD) and assayed for gene expression by SYBR green technology (Quanta Biosciences). Primers were designed to span exons by Integrated DNA Technologies. GAPDH was used as a housekeeping gene. Gene expression from each timepoint was normalized to uninfected control samples. Flow cytometry {#s4g} -------------- Single cell suspensions were pelleted and resuspended with primary antibodies (BioLegend, San Diego, CA: anti-CD4 PerCP, anti-CD8α APC-Cy7, anti-CD45 Alexa-488, anti-CD11b APC-Cy7, anti-CD11b APC, anti-Ly6G FITC; eBioscience, San Diego, CA: anti-CD25 PE, anti-CD45 APC or FITC, anti-CD69 PE, anti-Ly6C/G APC; BD Biosciences, San Jose, CA: anti-Ly6G PE-Cy7, anti-Ly6C V420, anti-CD45 PE, anti-Ly6C/G PerCP, anti-CD44 APC) in ice-cold FACS buffer (1% bovine serum albumin/0.01% NaN~3~ in PBS) for 30 min. For IFN-γ staining, cells were incubated for 6 hrs with Brefeldin-A (eBioscience; 10 ug/ml), PMA (Sigma; 10 ng/ml), and ionomycin (Sigma; 1 ug/ml), then fixed with 4**%** paraformaldehyde and subsequently incubated with primary antibodies resuspended in the FoxP3/transcription factor buffer staining set (eBioscience). For IL-12 and TNF-α staining, cells were incubated for 6 hrs with Brefeldin-A only (eBioscience). Intracellular staining experiments used 10^6^ cells. Antibodies used for intracellular staining included anti-IFN-γ PE-Cy7, anti-TNF-α PE-Cy7 (Biolegend); anti-IL-12 PE, anti-TNF-α APC (BD Biosciences), and anti-*Toxoplasma* p30 (Argene, Shirley, NY). Cell fluorescence was measured using a FACS Canto (BD Biosciences). Data was analyzed using FlowJo software (FlowJo, Ashland, OR). Quantitative PCR for parasite burden {#s4h} ------------------------------------ DNA was isolated from whole intestinal tissue using a Tissue DNA kit following manufacturer\'s instructions (Omega Biotek, Norcross, GA). DNA was amplified by quantitative PCR as described previously using primers against the *T. gondii* B1 gene and the host argininosuccinate lyase (ASL) gene [@ppat.1003706-Butcher2]. Ten-fold serial dilutions of genome copy standard curves were created using known quantities of host (splenocytes) and parasite (tachyzoites) cells based on DNA quantity, Avogadro\'s number, and genome size. To quantify parasite burden, the generated values for host and parasite genome copies from the DNA preparations were expressed as a ratio of parasite (B1) to host (ASL) genomes. Adoptive transfer {#s4i} ----------------- Splenocytes from naïve mice were harvested and subjected to CD4 positive selection by magnetic bead sorting following manufacturer\'s instructions (Stem Cell Technologies, Vancouver, British Columbia). Cells were purified to ∼90--95% purity and were transferred by intravenous retro-orbital injection into *Cxcr3^−/−^* recipients at 5×10^6^ CD4^+^ cells per mouse. Twenty-four hours post transfer, mice were challenged with 30 cysts of the *T. gondii* ME49 strain. In some experiments mice were left to assess survival following cell transfer. In other experiments intestinal tissue was collected at day 9 post-infection for intracellular cytokine analysis. Pathology scoring {#s4j} ----------------- Swiss rolls of the intestines were histopathologically scored by an investigator that was double-blinded to sample identity. Intestines were scored on an ascending 0--4 scale as previously described [@ppat.1003706-Egan1], [@ppat.1003706-Johnson1]. Briefly, scores of 0 were normal, scores of 1 indicated mild focal lesions, scores of 2 indicated moderate focal lesions, scores of 3 indicated moderate multifocal lesions, and scores of 4 indicated severe multifocal lesions. Histopathological features scored included: inflammation of the intestinal submucosa (lamina propria), inflammation extending throughout all histological layers of the intestine (transmural inflammation), sloughing of intestinal epithelium, intestinal villus fusion and blunting, and necrosis of villi. Sections of complete small intestines from 13 KO and 14 WT infected mice were scored. The data are plotted as mean scores of individual mice. Statistics {#s4k} ---------- Differences between groups were analyzed using student\'s *t*-test. Differences between 3 or more groups were analyzed using one-way Anova with Newman-Keuls post-test. P-values less than 0.05 are considered significant and are designated by \* p\<0.05, \*\* p\<0.01, or \*\*\* p\<0.001. Pathology scores were analyzed using the Mann-Whitney *t*-test. Supporting Information {#s5} ====================== ###### **CXCR3-GFP expression on NK cells decreases during infection.** Lamina propria and mesenteric lymph node (MLN) leukocytes were isolated from noninfected (NI) and Day 7-infected (INF) CIBER reporter mice, and CXCR3-GFP expression was measured on NK1.1^+^ cells. Numbers in each panel indicate the percent of NK1.1^+^ cells falling within the CXCR3-eGFP positive quadrant. (TIF) ###### Click here for additional data file. ###### **CXCR3-GFP^+^ and CXCR3-GFP^−^ fractions of CD4^+^ T cells differentially express activation markers.** Splenocytes (n = 4), MLN (n = 5), and Peyer\'s patch (n = 2) cells were isolated from Day 11-infected CIBER reporter mice and stained for surface markers CD27 as well as CD4 (A and B) and CD8 (C and D). Representative mice are shown in A and C. Bar graphs (B and D) represent averages of multiple mice, and significance is represented by \* p\<0.05, and \*\*\* p\<0.001. (TIF) ###### Click here for additional data file. ###### ***Cxcr3^−/−^*** **mice are more susceptible to oral infection with** ***Toxoplasma*** **.** (A) WT and KO mice (n = 5 per group) were infected by i.p. injection of 30 ME49 cysts, and survival was monitored. (B) Small intestines of naïve WT and KO mice (n = 3 per strain) were harvested, fixed in formaldehyde, embedded in paraffin, and sections were stained with H&E. (C) Frozen sections of Day 10 WT and *Cxcr3^−/−^* intestines were stained for Muc1 followed by anti-rabbit Alexa-488 (red). Sections were counter-stained with DAPI (blue). (D) Lamina propria leukocytes from Day 9-orally infected WT and *Cxcr3^−/−^* mice were stained for neutrophil markers Ly6C/G (Gr-1) and Ly6G (1A8). (E) Neutrophil levels were assessed in individual mice (n = 5 per group). The graph shows mean +/− SEM (\*\* p\<0.01). (TIF) ###### Click here for additional data file. ###### **Cytokine responses in WT and KO mice.** Splenocytes (A, C and E) and MLN (B, D and F) were harvested from Day 11-infected WT and *Cxcr3^−/−^* mice and cultured in the presence of soluble tachyzoite antigen (STAg) for 72 hr. Supernatants were collected, and IFN-γ (A and B), TNF-α (C and D), and IL-10 (E and F) were measured by ELISA. (TIF) ###### Click here for additional data file. ###### **T cell and NK cell production of IFN-γ in the presence and absence of CXCR3.** Lamina propria leukocytes were isolated from WT (A) and *Cxcr3^−/−^* (B) mice 6 days post-infection, cultured for 6 hr in the presence of PMA, ionomycin, and Brefeldin-A, and stained for CD8 and IFN-γ. (C) Means and standard errors of individual mice. Lamina propria leukocytes were isolated from WT (D) and *Cxcr3^−/−^* (E) mice, cultured in the presence of PMA, ionomycin, and Brefeldin-A and stained for NK1.1 and IFN-γ. (F) Mean and standard error of individual mice (WT: n = 9; KO: n = 6). Splenocytes were harvested from WT (G) and *Cxcr3^−/−^* (H) Day 7-infected mice, cultured in the presence of PMA, ionomycin, and Brefeldin-A, and stained for CD4 and IFN-γ. (I) Mean and standard error of individual mice (WT: n = 2; KO: n = 2). (TIF) ###### Click here for additional data file. ###### **Lamina propria neutrophils secrete elevated TNF-α in the absence of CXCR3.** Lamina propria leukocytes were harvested from WT and *Cxcr3^−/−^* mice and cultured in the presence of Brefeldin-A for 6 hr. Cells were then stained for neutrophil markers CD11b, Ly6C/G (Gr-1), and Ly6G (1A8), fixed, permeabilized, and intracellularly stained for TNF-α. Cytokine production was assessed by flow cytometry (A). Shown are the mean +/− SEM of individual mice (B) (n = 5 per group, \*\* p\<0.01). (TIF) ###### Click here for additional data file. ###### **Adoptive transfer of CXCR3^+^CD4^+^ T cells into** ***Cxcr3^−/−^*** **recipients protects against oral** ***Toxoplasma*** **infection.** (A) Splenic CD4^+^ T cells were isolated from naive *Cxcr3^−/−^* mice, and 5×10^6^ cells were adoptively transferred intravenously into *Cxcr3^−/−^* recipients. Mice were orally challenged 24 hr later with 30 ME49 cysts and assessed for survival (n = 5 mice per group). (B) Lamina propria leukocytes were harvested from infected WT and *Cxcr3^−/−^* mice and cultured in the presence of Brefeldin-A for 6 hr. Cells were surface stained for CD11b, Ly6C/G (Gr-1), and Ly6G to identify inflammatory monocytes. Cells were then fixed, permeabilized, and intracellularly stained for IL-12 and TNF-α. Cytokine production by inflammatory monocytes was analyzed by flow cytometry. Shown are representative FACS plots of individual mice. (C) Lamina propria leukocytes were surface stained for CD11b, Ly6C/G (Gr-1), and Ly6G (1A8) to identify neutrophils. (D) Cells were then fixed, permeabilized, and intracellularly stained for TNF-α. Cytokine production by neutrophils was analyzed by flow cytometry. Shown are the mean +/− SEM of individual mice (n = 5 mice per group; \* p\<0.05, \*\* p\<0.01). (TIF) ###### Click here for additional data file. We thank M. Hossain and A. Lee for expert technical assistance and B. Butcher for useful discussions. [^1]: The authors have declared that no competing interests exist. [^2]: Conceived and designed the experiments: SBC EYD. Performed the experiments: SBC CEE. Analyzed the data: SBC KJM CEE ARS EYD. Contributed reagents/materials/analysis tools: SO ARS. Wrote the paper: SBC EYD. [^3]: Current address: Center for Comparative Medicine and Research, Dartmouth College, Lebanon, New Hampshire, United States of America [^4]: Current address: Department of Surgery, Division of Pediatric Surgery, Children\'s Hospital of Pittsburgh of UPMC and the University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America

Atlantis Rail Summer 2013 Photo Contest Winners! We have our winners for the Atlantis Rail Summer 2013 Photo Contest! Click on any photo to enlarge. The next contest has already begun, CLICK HERE to read the rules and enter! All entries receive a FREE Rail Care Kit! FIRST Place - $500, Deborah Paine, Inc. - Truro, MA SunRail™ Nautilus System with custom fascia mount brackets Deborah Paine transformed this Cape Cod cottage into an upscale summer getaway. They chose the SunRail™ Nautilus cable railing system with custom fascia mount brackets to achieve a modern look. The decking adds drama by using a mixture of large slate and glass blocks. The hardware that makes up this railing system is made from grade 316 stainless steel to offer maximum corrosion resistance and durability, making it perfect for this oceanfront application. SECOND Place - $250, Brang Construction - Boca Raton, FL Brang Construction constructed multiple railing systems at the Gumbo Limbo Nature Center in Boca Raton, Florida. These systems were built around 4 salt water tanks that house different South Florida marine habitats. The 2 shallow tanks that feature mangroves and near shore reefs are surrounded by our SunRail™ Nautilus cable railing system. The 2 deeper tanks containing a tropical coral reef and artificial reef/shipwreck are encompassed by the SunRail™ Mariner baluster railing system. Custom gates were also constructed for workers to access the tanks. THIRD Place - $100, David - York, PA RailEasy™ Nautilus System for backyard deck This homeowner chose our RailEasy™ Nautilus cable railing system for his new deck. This system features 2" diameter polished stainless steel handrails with horizontal cable infill. The handrails are attached to the posts using straight and adjustable sidemounts. Due to the length between posts, cable stabilizer kits were installed to minimize cable deflection and stay code compliant. This stabilizer features a 1" diameter stainless tube pre-drilled to let cables pass through at 3" on-center. The next contest has already begun, CLICK HERE to read the rules and enter! A WORD FROM OUR CUSTOMERS “Now that the railing is completed, it has greatly exceeded our expectations and gives an outstanding presence to our pool area. The safety factor is just a side benefit from the aesthetic value we have received.” About Atlantis Rail Atlantis Rail specializes in cable railing but we also provide glass railing, vertical balusters and ADA handicap access rails. Our cable railing and stainless steel railing products are designed for professional results but friendly to the do-it-yourself enthusiast. All our products are made from stainless steel to last in tough environments.Find us on Google+ Training Center The Atlantis Rail Training Center was built to provide training, information and and tools to market, sell and support Atlantis Rail products for our mutual success. The Training Center includes our exclusive AIA Continuing Education Course and Sales Consultant Training modules.

MIT Blackjack Team “The first year I played, we returned 154 percent to our investors. That’s after paying off expenses. You try and do that on Wall Street.” – Jeff Ma, member of the MIT Blackjack Team. How did a bunch of college kids from the Massachusetts Institute of Technology (MIT) and Harvard University become the most feared blackjack team on earth in the 1980’s and ’90’s? Individual players on that blackjack card counting squad routinely made $100,000 to $180,000 per session in profits, and Las Vegas treated them like royalty. That is, until they found out these fresh faced blackjack bandits were using an intricate card counting system and confederates to uncover the most favorable circumstances for a big bet. While blackjack card counting itself by using your brain is not illegal, the MIT team which has been the subject of films like the documentary “Breaking Vegas” and the more recent Hollywood production “21” sometimes went above and beyond simply using great math skills, and paid the price. But not until after winning tens of millions of dollars at blackjack and bringing Vegas to its knees. And if you think the claims above made by Jeff Ma of 154% returns are a little outlandish, they actually started off much better than that. Bill Kaplan is a 1980 Harvard MBA graduate who had run a very successful blackjack team out of Las Vegas in the late 1970’s, and in 1977 used a blackjack card counting strategy to generate a 35X rate of return over a nine-month period (that’s turning $1,000 into $36,000 in 9 months). In 1980, Kaplan headed up a team of MIT and Harvard students that hit Las Vegas using formal management procedures and approaching a blackjack card counting and betting system as a business. On August 1, 1980 that original MIT team began with a stake of $89,000, with player names like Massar, Jonathan, Goose, and Big Dave doubling the original stakes in less than 10 weeks. An investor prospectus had estimated profits of $170 per hour, and actual play delivered realized profits of $162.50 per hour. Mostly undergraduates, the MIT team, as it came to be known, earned across-the-board an average of over $80 an hour while investors enjoyed annualized profits of 250%. All this while Las Vegas showered the young players with free rooms, lavish suites and other Sin City comps. Andy Bloch, now a professional poker player that holds two electrical engineering degrees from MIT and a Juris Doctorate from Harvard Law School, was one of the MIT blackjack members. He has claimed “tens of millions” of dollars won by his fellow teammates and subsequent team members, and it is hard to argue with that estimate. And all those millions started to draw attention. Henry Houh, at the time a grad student at MIT, noticed his office-mate lugging around thousands of dollars of casino chips at work. Saddled with massive debt, he eagerly joined the card counting team, stating, “It was great fun.” With plenty of “crazy stories” of partying and staying in $1,000 a night suites complements of Las Vegas casinos, Houh also said that the MIT blackjack team was the reason it took him 13 years to finish school. But these brilliant blackjack brains did not simply decide to get together and then hit Las Vegas. The mysterious Mister M and Kaplan put potential blackjack team candidates through grueling training sessions. A fully trained card counter then had to undergo a “trial by fire” final exam by playing through 8 six-deck shoes without mistakes, all while being lambasted with loud noises, music and other distractions typical to the average casino. Players learned to stagger their betting patterns as to disguise the fact that they were counting cards and waiting for the perfect scenario. They would then make a massive bet when they had an extreme advantage, and while losses naturally occurred, the profits were far greater. Advanced techniques like ace tracking and shuffle tracking were also employed, but John Chang, an MIT undergraduate that joined the team in late 1980, stated that the most consistent profits came from straight blackjack card counting. Playing throughout the ’80s, and growing to as many as 35 players in 1984, a full 22 different partnerships composed MIT blackjack teams from 1979 through 1989. A total of 70 people played at one time or another in some capacity, either as card counters, “Big Players”, or in other supporting roles. Many times a player would count cards at a blackjack table while placing small bets without wavering his play. When the table was right for the picking, that player would signal someone sitting at a nearby bar or appearing to simply be watching, and that Big Player would swoop into the table for a single large bet, collect and leave. Incredibly enough, every single MIT blackjack team was successful during that tenure, paying in some cases over 300% per year to investors. In 1992 and ’93, MIT blackjack team members Bill Kaplan, J.P. Massar and John Chang formed Strategic Investments as a limited partnership to run the blackjack card counting enterprise. Through the early and mid-90s, the MIT team grew to nearly 80 players, with 30 players playing simultaneously at different casinos around the world. While blackjack teams consistently come and go, the MIT blackjack card counting team of the 1980s and ’90s will always live on in memory as one of the most brash and successful blackjack teams of all-time.

Q: Loading assemblies and its dependencies My application dynamically loads assemblies at runtime from specific subfolders. These assemblies are compiled with dependencies to other assemblies. The runtime trys to load these from the application directory. But I want to put them into the modules directory. Is there a way to tell the runtime that the dlls are in a seperate subfolder? A: One nice approach I've used lately is to add an event handler for the AppDomain's AssemblyResolve event. AppDomain currentDomain = AppDomain.CurrentDomain; currentDomain.AssemblyResolve += new ResolveEventHandler(MyResolveEventHandler); Then in the event handler method you can load the assembly that was attempted to be resolved using one of the Assembly.Load, Assembly.LoadFrom overrides and return it from the method. EDIT: Based on your additional information I think using the technique above, specifically resolving the references to an assembly yourself is the only real approach that is going to work without restructuring your app. What it gives you is that the location of each and every assembly that the CLR fails to resolve can be determined and loaded by your code at runtime... I've used this in similar situations for both pluggable architectures and for an assembly reference integrity scanning tool. A: You can use the <probing> element in a manifest file to tell the Runtime to look in different directories for its assembly files. http://msdn.microsoft.com/en-us/library/823z9h8w.aspx e.g.: <configuration> <runtime> <assemblyBinding xmlns="urn:schemas-microsoft-com:asm.v1"> <probing privatePath="bin;bin2\subbin;bin3"/> </assemblyBinding> </runtime> </configuration>

<a class="{% if not nav_item.is_link %}reference internal{% endif %}{% if nav_item.active%} current{%endif%}" href="{% if not nav_item.is_section %}{{ nav_item.url|url }}{% else %}#{% endif %}">{{ nav_item.title }}</a> {%- set navlevel = navlevel + 1 %} {%- if navlevel <= config.theme.navigation_depth and ((nav_item.is_page and nav_item.toc.items and (not config.theme.titles_only and (nav_item == page or not config.theme.collapse_navigation))) or (nav_item.is_section and nav_item.children)) %} <ul{% if nav_item.active %} class="current"{% endif %}> {%- if nav_item.is_page %} {#- Skip first level of toc which is page title. #} {%- set toc_item = nav_item.toc.items[0] %} {%- include 'toc.html' %} {%- elif nav_item.is_section %} {%- for nav_item in nav_item.children %} <li class="toctree-l{{ navlevel }}{% if nav_item.active%} current{%endif%}"> {%- include 'nav.html' %} </li> {%- endfor %} {%- endif %} </ul> {%- endif %} {%- set navlevel = navlevel - 1 %}

Networks, Movements and Technopolitics in Latin America Networks, Movements and Technopolitics in Latin America Critical Analysis and Current Challenges Caballero, Francisco Sierra, Gravante, Tommaso (Eds.) Networks, Movements and Technopolitics in Latin America About this book: This edited collection presents original and compelling research about contemporary experiences of Latin American movements and politics in several countries. The book proposes a theoretical framework that conceptualises different mediation processes that emerge between cyberdemocracy and the emancipation practices of new social movements. Additionally, this volume presents some Latin American practices and experiences that are autonomously and by using self-management–creating other identities and social spaces on the margins of and against the neoliberal system through the use of digital technology. This book will be of great interest to scholars of media and social movements studies as well as of contemporary politics. About the authors: Francisco Sierra Caballero is President of Unión Latina de Economía Política de la Información, la Comunicación y la Cultura (ULEPICC) and Coordinator of Technopolitics Consortium of European Unión. He is also Professor of Communication Theory and Director of the Interdisciplinary Group of Studies in Communication, Politics and Social Change (COMPOLITICAS) at the University of Seville, Spain. Tommaso Gravante is Postdoctoral Fellow at the Center for Interdisciplinary Research in the Sciences and Humanities (CEIICH) at the National Autonomous University of Mexico.

Order filed October 6, 2016 In The Fourteenth Court of Appeals ____________ NO. 14-15-00634-CV ____________ POWELL DORFAYE, ET AL, Appellant V. BRECKENRIDGE AT CITY VIEW APARTMENTS, Appellee On Appeal from the County Civil Court at Law No. 2 Harris County, Texas Trial Court Cause No. 1064270 ORDER On August 12, 2015, this court abated this appeal because appellant petitioned for voluntary bankruptcy in the United States Bankruptcy Court for the Southern District of Texas, under cause number 15-33972. See Tex. R. App. P. 8.2. Through the Public Access to Court Electronic Records (PACER) system, the court has learned that the bankruptcy case was closed on October 21, 2015. The parties failed to advise this court of the bankruptcy court action.  Unless within 20 days of the date of this order, any party to the appeal files a motion demonstrating good cause to retain this appeal, this appeal will be reinstated and dismissed for want of prosecution. PER CURIAM 

David-Weill David-Weill is a surname. Notable people with the surname include: David David-Weill (1871-1952), French-American banker Jean David-Weill (1898-1972), French epigrapher Michel David-Weill (born 1932), French investment banker Pierre David-Weill (1900-1975), French investment banker See also David (surname) Weil (surname) Category:Compound surnames Category:French-language surnames Category:Jewish surnames

Q: error in ajax and json array I'm going to develop an interactive map (google maps).The coordinates parse via ajax from json,but i get error JSON Format {"Level":[{"route":[{"lat":39.105251,"lgn":26.551727}, {"lat":39.105247125,"lgn":26.551774625}...],"balls": [{"lat":39.105239375,"lgn":26.551869875},{"lat":39.10524325,"lgn":26.55182225}]}, {"route":[{........},{.....}...],"balls":[{........},{.....}...]}]} AJAX REQUEST $.ajax({ type: "GET", url: "getcoordp?q=2", dataType: "json", cache: false, contentType: "application/json", success: function(data) { $.each(data.Level, function(i,Level){ $.each(data.route, function(index, route) { alert(data.lat) }); }); } }); ERROR Uncaught TypeError: Cannot read property 'length' of undefined any help? A: Replace below $.each(data.route, function(index, route)... With $.each(Level.route, function(index, route) { alert(route.lat) }); This will fix your issue.

Neoadjuvant chemotherapy with cisplatin, ifosfamide and 5-fluorouracil in the treatment of locally advanced cervical cancer. The objective of this study was to evaluate clinical and histological response, resectability, and survival in patients with cervical epidermoid carcinoma stage IB2 to IIIB with the use of neoadjuvant chemotherapy followed by radical surgery and/or radiation therapy. Between September 1989 and February 1996, 53 patients were admitted to this study. They were given three cycles of cisplatin 30 mg/m2/day, 5-fluorouracil 500 mg/m2/day, ifosfamide 2000 mg/m2/day i.v., and mesna 400 mg/m2/day i.v. at hour 0 and 400 mg/m2 at hours 4 and 8 during three days every 21-28 days. We evaluated 47 patients. Global clinical response obtained was 85% {95% (CI), 75-97%, CR in 14 patients (30%) and PR in 26 patients (55%)}. Twenty-three patients underwent surgery. Six patients (13%) had a complete histological response. Median follow-up was 42 months (5-96). In resected patients, with a median follow-up of 57 months (5-96), the estimated five-year disease-free survival was 78%. Global survival estimated to 60 months was 83% for stage IB2, 70% for IIB, and 20% for IIIB. This mode of therapy offers a new option to improve survival in locally advanced cervical cancer. Randomized trials are required in order to establish a definitive role for this therapeutic strategy.

Associative network based on cyclodextrin polymer: a model system for drug delivery. Associative networks have been elaborated by mixing in aqueous media a cyclodextrin polymer to a dextran bearing adamantyl groups. The two polymers interact mainly via inclusion complexes between adamantyl groups and cyclodextrin cavities, as evidenced by the high complexation constants determined by isothermal titration microcalorimetry (approximately 10(4) L mol(-1)). Additional interaction mechanisms participating in the strength of the network, mainly hydrogen bonding and electrostatic interactions, are sensitive to the pH and ionic strength of the medium, as shown by pH-dependent rheological properties. The loading and release of an apolar model drug, benzophenone, has been studied at two pH values and different cyclodextrin polymer content. Slow releases have been obtained (10-12 days) with slower kinetics at pH 2 than at pH 7. Analysis of the experiments at pH 7 shows that drug release is controlled both by diffusion in the network and by inclusion complex interactions with cyclodextrin cavities.

Q: Top down car game (game-maker) I'm new to programming on game-maker and programming in general. This is probably very easy but i'm unsure of how to go about things. I am programming a simple top-down car game in which the car drives (forward) by it's self and is steered with the left and right mouse buttons. I attempted to get the car to drive on it's own with: speed = 3 This, although making the car go forward, stopped the steering from working somehow and now the car rotates instead of actually turning around the corner. How can i get the car to drive on it's own and still be able to turn the car? A: You should not change image_angle, but direction instead. Image_angle is juste what you see, direction is the real physics direction. Replace the code in your link by : direction = direction + 2; image_angle = direction; Like this, you turn the car, and then align the image on the car orientation.

Q: Inserting Related MySQL Data with AUTO_INCREMENT I'm looking at a database that has 3 tables into which I have to insert data: resource id (AUTO_INCREMENT) name resource_item id (AUTO_INCREMENT) name resource_id (FK ref resource.id) resource_item_business_function id (AUTO_INCREMENT) business_function_name resource_item_id What I'm struggling with is the fact that this must be scripted. I'm only inserting 1 resource record so I can script the insert into the resource table easily enough. I have ~20 resource_item records to insert for that resource and I can even do that easily enough using the LAST_INSERT_ID() function. The question is...how do I insert into resource_item_business_function? I have no idea how to insert the proper resource_item_id into each resource_item_business_function record. Any thoughts would be much appreciated. A: You would need to use LAST_INSERT_ID() after each insert into resource_item. So your final script could look something like this: SET AUTOCOMMIT=0; SET @RESOURCE_ID=0; INSERT INTO resource ( NULL, "Some Name"); SELECT LAST_INSERT_ID() INTO @RESOURCE_ID; INSERT INTO resource_item ( NULL, "Some Name", RESOURCE_ID ); INSERT INTO resource_item_business_function ( NULL, "Some Name", LAST_INSERT_ID() ); ...etc... INSERT INTO resource_item ( NULL, "Some Name", RESOURCE_ID ); INSERT INTO resource_item_business_function ( NULL, "Some Name", LAST_INSERT_ID() ); COMMIT;

Q: Google Calendar API server to server Rails I want insert events in my calendar after some user's actions. That's why I'm want use server-to-server authorization with Google API. I wrote next code: require 'google/apis/calendar_v3' require 'googleauth' require 'google/api_client/client_secrets' require 'google/api_client' Initialize the client client = Google::Apis::CalendarV3::CalendarService.new load and decrypt private key key = G.load_from_pkcs12('google_secrets.json', 'notasecret') generate request body for authorization client.authorization = Signet::OAuth2::Client.new( :token_credential_uri => 'https://accounts.google.com/o/oauth2/token', :audience => 'https://accounts.google.com/o/oauth2/token', :scope => 'https://www.googleapis.com/auth/calendar', :issuer => '....', :signing_key => key) fetch access token client.authorization.fetch_access_token! # load API definition service = client.discovered_api('calendar', 'v3') # there is a place for variable "event" declaration client.execute(:api_method => service.event.insert, :parameters => { '....' => 'primary' }, :event => event) But when I try to use that code, i recive next answer: cannot load such file -- google/api_client (LoadError) I'm understand that maybe I must use previous version of gem google-api-client(<0.9) for get rid of that error. But don't know how i must make insert event with syntax of < 0.9 google api version. A: I found solution. Use for it api v.0.8.2 and see next page: Rails + Google Calendar API events not created

This is one of those “more bang for your buck” meetings. At the September 17 meeting we will have two programs. 1:30-2:45 – Panel on writing mysteries, Rae Cuda and Louse Pelzl 3:00-4:00 – Mike Klaassen presentation “Warped Time: How You Can Manipulate Time in Fiction” –

Gornja Borina Gornja Borina is a village in the municipality of Loznica, Serbia. According to the 2002 census, the village has a population of 188 people. References Category:Populated places in Mačva District

Q: More than one tab bar in an app? I have developed an app that has work successfully for the last 4 months using iOS 4.3 and under. Since iOS 5 however the tightening of view hierarchy has left my app dead in the water. The app starts with a tab bar as its main view with 5 tabs. When the user selects a row on a tableview on the first tab it pushes onto another tabbar with 3 tabs which gives specific information about that selection. This structure worked fine but obviously broke when testing on iOS 5. My question is: Is it bad design to utilize 2 or more tab bars in one application? I don't mean "bad design" in the grand scheme of things because that is subjective. I mean in a practical sense where it is specifically forbidden or not recommended. A: have a look at this: iOs Human Interface Guideline Yes, I think that it's not recommended. For example: Use a tab bar to give users access to different perspectives on the same set of data or different subtasks related to the overall function of your app. When you use a tab bar, follow these guidelines: Don’t use a tab bar to give users controls that act on elements in the current mode or screen. If you need to provide controls for your users, use a toolbar instead (for usage guidelines, see “Toolbar”). In general, use a tab bar to organize information at the application level. A tab bar is well-suited for use in the main app view because it’s a good way to flatten your information hierarchy and provide access to several peer information categories or modes at one time.

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The immune system has the peculiar ability to respond to foreign substances (or antigens) by producing antibody molecules that bind to these antigens with extremely high affinity and a remarkable degree of specificity. In order to achieve this high level of affinity, B cells – the cells that produce antibodies – must undergo a series of steps that culminate in the generation of an anatomical structure known as the germinal center (GC). Within this structure, B cells introduce random mutations into their antibody genes and, in a process reminiscent of Darwinian evolution, B cells that have acquired affinity-enhancing mutations proliferate, and are eventually directed to differentiate into antibody-producing plasma cells or memory cells that can re-expand upon future contact with the same antigen. A germinal center reaction in a lymph node of an immunized mouse. It is within this structure that B cells mutate their antibody genes, in a process that ultimately leads to the generation of high-affinity antibodies. It is this process that allows vaccines to work, and that makes us immune to catching certain diseases more than once. On the flip side, failures in the GC reaction can result in the production of high- affinity antibodies against innocuous substances or even components of one’s own body – leading to allergies and autoimmune diseases such as lupus and rheumatoid arthritis. Furthermore, when misplaced the mutations introduced during the GC reaction can cause genetic lesions that may ultimately lead to lymphomas and other malignancies. In the Victora lab, we combine a number of cutting-edge techniques – from the development of novel mouse models to intravital multiphoton microscopy – to shed light on the intricacies of the GC reaction and its regulation. For example, using multiphoton-based geotagging of GC cells in a newly developed photoactivatable mouse, we have been able to define the cellular and molecular characteristics of different subpopulations of GC B cells, as well as their dynamic behavior and its relationship to selection. The characteristics we defined in mice are now being used in human studies to better understand the events leading to B cell lymphoma. We believe that unveiling the molecular mechanisms of the GC reaction will be essential if we wish to design better vaccines, develop treatments for allergies and autoimmune diseases, and dissect the molecular basis of lymphomagenesis.

Evaluation of two minimally invasive techniques for electroencephalogram recording in wild or freely behaving animals. Insight into the function of sleep may be gained by studying animals in the ecological context in which sleep evolved. Until recently, technological constraints prevented electroencephalogram (EEG) studies of animals sleeping in the wild. However, the recent development of a small recorder (Neurologger 2) that animals can carry on their head permitted the first recordings of sleep in nature. To facilitate sleep studies in the field and to improve the welfare of experimental animals, herein, we test the feasibility of using minimally invasive surface and subcutaneous electrodes to record the EEG in barn owls. The EEG and behaviour of four adult owls in captivity and of four chicks in a nest box in the field were recorded. We scored a 24-h period for each adult bird for wakefulness, slow-wave sleep (SWS), and rapid-eye movement (REM) sleep using 4 s epochs. Although the quality and stability of the EEG signals recorded via subcutaneous electrodes were higher when compared to surface electrodes, the owls' state was readily identifiable using either electrode type. On average, the four adult owls spent 13.28 h awake, 9.64 h in SWS, and 1.05 h in REM sleep. We demonstrate that minimally invasive methods can be used to measure EEG-defined wakefulness, SWS, and REM sleep in owls and probably other animals.

Pages Monday, January 30, 2012 Comfort and superficial peace "It is true that God may have called you to be exactly where you are. But, it is absolutely vital to grasp that he didn’t call you there so you could settle in and live your life in comfort and superficial peace."--Francis Chan No comments: In Its Time I am a wife, a mother and a saved-by-grace writer who is learning to rest in the truth that He makes everything beautiful in its time. I write about the One whose timing and ways and plans I do not understand, but who gives joy in the midst of waiting and brings beauty out of ashes.

Our individual data points can not be publicly deposited as supporting information due to ethical restrictions imposed by Nagoya University International Bioethics Committee, since the data contains the sensitive personal information. Information regarding our data can be requested at the following e-mail address: Kazunori Hashimoto (e-mail: <[email protected]>). Introduction {#sec001} ============ Exposure to arsenic (As) via drinking water is a health risk for humans \[[@pone.0198743.ref001]--[@pone.0198743.ref003]\]. Previous studies showed that exposure of humans to As was associated with cancer of the bladder, kidney, skin, prostate, lung and liver \[[@pone.0198743.ref004]\] and with cardiovascular disease \[[@pone.0198743.ref005]\]. It was also shown that exposure to As was associated with neurological diseases including cognitive impairment in children \[[@pone.0198743.ref006], [@pone.0198743.ref007]\] and adults \[[@pone.0198743.ref008]\] and with diabetes mellitus \[[@pone.0198743.ref009]--[@pone.0198743.ref012]\]. Levels of toxic elements in noninvasive biological samples including nails, hair and urine have been determined to investigate associations with hearing loss in humans \[[@pone.0198743.ref013], [@pone.0198743.ref014]\]. A univariate analysis showed a significant correlation of As levels in fingernails with amplitude of distortion product otoacoustic emission (DPOAE) at 2 kHz, which reflects activity levels of outer hair cells, in 30 subjects aged 9--78 years residing in the gold mining community of Bonanza, Nicaragua \[[@pone.0198743.ref015]\]. Thus, it is possible that As in nails is a reliable index for As-mediated hearing loss in humans. However, there is no direct evidence showing correlations between As levels in toenails and hearing levels. In our previous study using pure tone audiometry (PTA), an association of oral exposure to As via drinking water with hearing loss in young people was shown by multivariate analysis with adjustments for confounders including age, smoking, sex and BMI \[[@pone.0198743.ref016]\]. However, multivariate analysis has not been performed to demonstrate the association of As levels in nails with hearing loss in humans, although age and smoking are known to be strong factors affecting hearing levels in humans \[[@pone.0198743.ref014], [@pone.0198743.ref017]--[@pone.0198743.ref019]\]. In experimental studies, oral exposure to As has been shown to cause several health risks including carcinogenesis \[[@pone.0198743.ref020]\] and cardiovascular diseases \[[@pone.0198743.ref021]\]. Levels of toxic elements in inner ears, which are known to be the sensory organ for hearing, have been determined to demonstrate the correlation with hearing loss \[[@pone.0198743.ref022], [@pone.0198743.ref023]\]. Exposure of guniea pigs to As at 200 mg/L via intraperitoneal injection for 2 months resulted in morphological impairments of the inner ear \[[@pone.0198743.ref024]\]. Our previous study has showed that exposure of young mice to As via drinking water caused accumulation of As in inner ears, resulting in hearing loss \[[@pone.0198743.ref016]\]. However, it is not clear whether there is a correlation between As levels in inner ears and nails in mice. In this study, we epidemiologically and experimentally investigated whether As levels in nails are reliable as non-invasive indexes for As-mediated hearing loss in humans and whether As levels in nails are associated with As levels in inner ears in mice. Materials and methods {#sec002} ===================== Epidemiological study {#sec003} --------------------- We obtained information on age, sex, smoking history, weight and height in 145 healthy subjects aged from 12 to 55 years by self-reported questionnaires in Bangladesh as previously described \[[@pone.0198743.ref014]\]. We obtained informed consent in written form from all of the subjects. For subjects aged 12 to 18 years, we obtained consent in written form from their parents. The subjects were only Bangladeshi people who lived mainly in rural areas. The subjects living in one area drink tap water and the rest of the subjects living in another area drink tube well water contaminated with As. The subjects included students, housewives and businessmen. The subjects did not have portable music players with earphones and had no occupational exposure to wielding fumes. None of the subjects had a habit of drinking alcohol. We excluded only subjects who had a history of ear diseases or illness at the time of the survey. We calculated body mass index (BMI) by diving weight (kg) by the square of height (m^2^) and used definitions of underweight (\< 18.5 kg/m^2^), normal weight (18.5--24.9 kg/m^2^) and overweight (≥ 25 kg/m^2^) set by the WHO \[[@pone.0198743.ref025]\]. We set the mean value of age (29.6 years) of the subjects in this study as the cut-off value for age. We collected 0.1--2 cm samples of toenails from each subject by using a ceramic nail clipper. We also collected urine samples from each subject and stored the samples in 50 ml sterile tubes at -80°C until measurements. We determined the hearing levels at 1, 4 and 8 kHz in addition to 12 kHz of the participants by PTA, since hearing level at 12 kHz was shown to be sensitive to environmental stresses \[[@pone.0198743.ref014], [@pone.0198743.ref017], [@pone.0198743.ref026]\]. We used an iPod with earphone-type headphones (Panasonic RP-HJE150) in a soundproof room as described previously \[[@pone.0198743.ref027], [@pone.0198743.ref028]\]. We output pure tones at each frequency to a subject until the subject recognized the sound. We stood behind the subject and provided the subject with an initial stimulus of 5 decibels (dB) and then increased the sound level by 5 dB step-by-step. The subject raised their hand when they recognized the sound. We evaluated the sound level recognized by each subjects as hearing threshold. Pure tones at each frequency from the earphones in the soundproof room were verified by using a noise level meter (Type 6224 with an FFT analyzer, ACO CO., LTD, Japan). The epidemiological study was approved by Nagoya University International Bioethics Committee following the regulations of the Japanese government (approval number: 2013--0070) and the Faculty of Biological Science, University of Dhaka (Ref. no. 5509/Bio.Sc). Experimental study {#sec004} ------------------ Hairless mice having the C57BL/6J background (1 month old, female, body weight of 10--15 g) were procured from Hoshino Laboratory Animal, Inc. Three or four mice were housed in a cage under super pathogen-free (SPF) conditions with a standard temperature of 23 ± 2°C and a 12-h light/dark cycle. The mice were fed a standard rodent chow (Clea Rodent Diet CE-2). Neither randomization nor blinding investigation were used in this animal study. In brief, we exposed mice (n = 7) to 22.5 mg/L of sodium arsenite (NaAsO~2~, Sigma-Aldrich) dissolved in distilled water for 2 months via drinking water and changed the drinking water every week as previously described \[[@pone.0198743.ref016]\]. The exposure dose was based on the As exposure for mice at 10 and 100 ppm via drinking water in a previous study \[[@pone.0198743.ref029]\]. The control group (n = 6) was given just distilled water. After exposure for 2 months, mice were anesthetized with isoflurane and sacrificed by decapitation. Nails and inner ears were collected and kept in a 1.5 ml tube. For the collection of inner ears, we first identified temporal bones at the bottom of the skull and then carefully removed the cranial nerves and tissues using standard forceps. The inner ears were dislodged by pushing down on the posterior semicircular canal with the thumb of a hand and fixing the tip region of the otic bone capsule with standard forceps. After carefully removing extra tissues adhered to the inner ears, we used the inner ears for ashing. The experimental study was approved by the Institutional Animal Care and Use Committee in Nagoya University (approval number: 28251) and followed the Japanese Government Regulations for Animal Experiments. Measurement of As levels in biological samples {#sec005} ---------------------------------------------- As levels in biological samples including toenails and urine were measured by inductively coupled plasma mass spectrometry (ICP-MS; Agilent 7500cx) as described previously \[[@pone.0198743.ref014], [@pone.0198743.ref022], [@pone.0198743.ref023]\]. In brief, toenails were washed with detergent water. One or two drops of acetone were added and then the samples were kept at room temperature until starting the ashing. Samples were ashed by incubation in 3 ml of HNO~3~ at room temperature overnight followed by incubation at 80°C for 3 hours. Samples were further incubated in 1--1.5 ml of H~2~O~2~ at 80°C for 3 hours. After cooling, Milli-Q water was added to the samples to adjust the final volume to 5 ml. In the case of urine, 4 ml of urine was incubated in 1 ml of HNO~3~ at room temperature overnight followed by incubation at 80°C for 24--72 hours. After cooling, the ashed urine samples were centrifuged at 2,000 rpm (= 269 g) for 1 min and Milli-Q water was added to the samples to adjust the final volume to 5 ml. Levels of As in urine were normalized by specific gravity using the following formula: SG-corrected concentration = raw hormone concentration × \[(SG~target~− 1.0)/(SG~sample~---1)\], where SG~target~ is a population mean SG \[[@pone.0198743.ref030]\]. In this study, the mean SG was 1.012 for the subjects. In the case of murine samples, nails were rinsed with Milli-Q water 3 times and air-dried at room temperature. Ashing of the samples was then performed with the same protocol as that described above. Levels of As in biological samples were determined by ICP-MS. Statistical analysis for epidemiological study {#sec006} ---------------------------------------------- All statistical analyses were performed by JMP software (version 11.0.0). In univariate analysis, the Mann-Whitney *U* test and Steel-Dwass test were used to detect significant differences in hearing levels between the groups because the hearing levels were discontinuous variables. In multivariate analysis, binary logistic regression analysis was performed with adjustments for age, sex, smoking and BMI as confounding factors. We used the method in a previous study \[[@pone.0198743.ref026]\] to categorize subjects with an auditory threshold higher than the cut-off value at each frequency as hearing loss. We set hearing thresholds \[1 kHz (≥ 7 dB), 4 kHz (≥ 10 dB), 8 kHz (≥ 24 dB), and 12 kHz (≥ 45 dB)\] with the mean values of hearing levels at each frequency to divide the subjects into two groups. In this study, values of p \< 0.05 were considered statistically significant. Statistical analysis for experimental study {#sec007} ------------------------------------------- In our experimental study, Spearman's correlation coefficients were used to evaluate the association between As levels in inner ears and those in nails. Values of p \< 0.05 were considered statistically significant. Results {#sec008} ======= Characteristics of the study participants {#sec009} ----------------------------------------- [Table 1](#pone.0198743.t001){ref-type="table"} shows the characteristics of the subjects, which were described in our previous report \[[@pone.0198743.ref014]\]. The hearing thresholds in the older group (≥ 29.6 years old, n = 68) were significantly higher than those in the younger group (\< 29.6 years old, n = 77) at 1 kHz (p = 0.0098), 4 kHz, 8 kHz and 12 kHz (p \< 0.0001) ([Table 2](#pone.0198743.t002){ref-type="table"}). The hearing thresholds in females (n = 76) were significantly higher than those in males (n = 69) at 4 kHz (p = 0.0257), 8 kHz (p = 0.0004) and 12 kHz (p = 0.0066) ([Table 2](#pone.0198743.t002){ref-type="table"}). No significant differences were found in hearing thresholds among the three BMI groups ([Table 2](#pone.0198743.t002){ref-type="table"}). Smokers (n = 31) had higher hearing thresholds than those in non-smokers (n = 114) at 1 kHz (p = 0.0057), 4 kHz (p \< 0.0001), 8 kHz (p = 0.0002) and 12 kHz (p \< 0.0001) ([Table 2](#pone.0198743.t002){ref-type="table"}). 10.1371/journal.pone.0198743.t001 ###### Characteristics of the study participants. {#pone.0198743.t001g} ------------------------------------------------------------------ Characteristics mean ± SD Variables Participants\ \[n (%)\] ----------------- ------------- ------------------ --------------- Age 29.6 ± 11.0 \< 29.6 77 ≥ 29.6 68 Sex Male 69 Female 76 Smoking history No 114 Yes 31 BMI 22.0 ± 3.4 \< 18.5 23 18.5 ≤ BMI \< 25 94 ≥ 25 28 ------------------------------------------------------------------ 10.1371/journal.pone.0198743.t002 ###### Associations between hearing levels and confounding factors including age, BMI, sex and smoking. {#pone.0198743.t002g} Hearing levels (mean ± SD) ------------------ ---------------------------- --------------- --------------- --------------- Age \< 29.6 6.10 ± 3.50 7.01 ± 4.39 19.29 ± 9.79 35.39 ± 15.64 ≥ 29.6 7.43 ± 4.69 13.31 ± 9.60 29.93 ± 12.53 56.69 ± 22.15 p value 0.0098 p \< 0.0001 p \< 0.0001 p \< 0.0001 Sex Male 6.59 ± 3.88 8.84 ± 6.81 21.23 ± 12.08 40.94 ± 21.61 Female 6.84 ± 4.38 10.99 ± 8.76 27.04 ± 11.98 49.41 ± 21.13 p value 0.7697 0.0257 0.0004 0.0066 Smoking No 6.40 ± 3.85 8.42 ± 5.70 22.06 ± 10.56 40.70 ± 18.38 Yes 7.90 ± 4.96 15.65 ± 11.74 32.42 ± 14.94 62.58 ± 24.49 p value 0.0057 p \< 0.0001 0.0002 p \< 0.0001 BMI \< 18.5 6.52 ± 4.38 7.17 ± 3.64 19.78 ± 5.93 42.17 ± 16.91 18.5 ≤ BMI \< 25 6.49 ± 3.35 10.05 ± 6.66 24.26 ± 12.11 44.95 ± 21.61 ≥ 25 7.68 ± 6.01 11.96 ± 12.72 28.04 ± 15.65 49.46 ± 25.40 p value 0.6148 0.1797 0.1346 0.6595 Association between As levels in biological samples and hearing levels by univariate analysis {#sec010} --------------------------------------------------------------------------------------------- Concentrations of As (mean ± SD) in toenails and urine were 1.38 ± 1.17 μg/g and 90.27 ± 103.04 μg/L, respectively ([Table 3](#pone.0198743.t003){ref-type="table"}). In this study, we set the cut-off values based on the receiver operating characteristic (ROC) curve and the highest Youden index \[[@pone.0198743.ref031]\]. We categorized the subjects into two groups at 0.60 μg/g in toenails and 76.12 μg/L in urine ([Table 3](#pone.0198743.t003){ref-type="table"}). The mean ages of subjects in the high and low As groups were 31 years and 27 years, respectively. We found that hearing thresholds were significantly higher in the high As group in toenails (n = 97) at 4 kHz (mean = 10.48 dB; p = 0.0023), 8 kHz (mean = 26.71 dB; p \< 0.0001) and 12 kHz (mean = 51.64 dB; p \< 0.0001) than those in the low As group (n = 48) at 4 kHz (mean = 9.44 dB), 8 kHz (mean = 21.81 dB) and 12 kHz (mean = 39.03 dB) ([Fig 1A](#pone.0198743.g001){ref-type="fig"}). We also found that the group with high As levels in urine (n = 73) had significantly higher hearing thresholds at 4 kHz (mean = 10.41 dB; p = 0.0200), 8 kHz (mean = 25.96 dB; p = 0.0104) and 12 kHz (mean = 50.07 dB; p = 0.0015) than those in the low As group (n = 72) at 4 kHz (mean = 9.51 dB), 8 kHz (mean = 22.57 dB) and 12 kHz (mean = 40.63 dB) ([Fig 1B](#pone.0198743.g001){ref-type="fig"}). {#pone.0198743.g001} 10.1371/journal.pone.0198743.t003 ###### As levels in biological samples from humans. {#pone.0198743.t003g} Mean ± SD Range Cut-off value ----------------- ---------------- -------------- --------------- Toenails (μg/g) 1.38 ± 1.17 0.06--6.22 0.60 Urine (μg/L) 90.27 ± 103.04 4.17--1013.5 76.12 Association between hearing thresholds and As levels in biological samples {#sec011} -------------------------------------------------------------------------- We next performed logistic regression analysis with adjustments for age, sex, smoking history and BMI to determine the risk of hearing loss in subjects with high As in biological samples ([Table 4](#pone.0198743.t004){ref-type="table"}). In this study, we followed the method used in a previous study \[[@pone.0198743.ref016]\] to define subjects with hearing loss as subjects with hearing thresholds more than the cut-off values at each frequency. Levels of As in toenails were significantly associated with hearing loss at 4 kHz \[odds ratio (OR) = 4.27; 95% confidence interval (CI): 1.56, 12.70\], 8 kHz (OR = 3.91; 95% CI: 1.50, 10.77) and 12 kHz (OR = 5.58; 95% CI: 2.21, 15.07) ([Table 4](#pone.0198743.t004){ref-type="table"}). No significant correlations were found between As levels in urine and hearing loss at any frequency ([Table 4](#pone.0198743.t004){ref-type="table"}). We further shifted the cut-off values of the independent variables dichotomizing As levels in biological samples to verify the models. We found that the significance of ORs in toenails remained when the cut-off values in toenails were shifted from 0.30 to 0.70 μg/g, while As levels in urinary samples did not show significant ORs even when the cut-off values were shifted from 10 to 380 μg/L. 10.1371/journal.pone.0198743.t004 ###### Adjusted ORs (95% CI) for hearing loss and As levels in biological samples (n = 145)[^a^](#t004fn002){ref-type="table-fn"}. {#pone.0198743.t004g} -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 kHz\ 4 kHz\ 8 kHz\ 12 kHz\ (≥ 7 dB) (≥ 10 dB) (≥ 24 dB) (≥ 45 dB) -------------------- -------------- ---------------------------------------------- ---------------------------------------------- ---------------------------------------------- **As in toenails** Low Reference Reference Reference Reference High 1.28\ 4.27[\*\*](#t004fn003){ref-type="table-fn"}\ 3.91[\*\*](#t004fn003){ref-type="table-fn"}\ 4.15[\*\*](#t004fn003){ref-type="table-fn"}\ (0.43--3.83) (1.51--12.05) (1.47--10.38) (1.55--11.09) **As in urine** Low Reference Reference Reference Reference High 0.69\ 1.89\ 1.48\ 1.15\ (0.29--1.63) (0.83--4.29) (0.65--3.34) (0.52--2.56) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- OR, odds ratio; CI, confidence interval. References mean 1.00. ^a^Adjusted for age, sex, smoking history and BMI. \*\**p* \< 0.01. Mice orally exposed to As showed an association between As levels in inner ear and nails {#sec012} ---------------------------------------------------------------------------------------- We finally performed an experimental study to determine the correlation between As levels in nails and inner ears in mice. After exposure of mice to As via drinking water for 2 months, we measured As levels in nails and inner ears from the exposed group and the control group. We found that there was a significant correlation (r = 0.8113, p = 0.0014) between As levels in inner ears and nails ([Fig 2](#pone.0198743.g002){ref-type="fig"}). {#pone.0198743.g002} Discussion {#sec013} ========== As level in toenails is a possible biomarker associated with hearing loss {#sec014} ------------------------------------------------------------------------- In our epidemiological study, As levels in toenails were shown to be significantly correlated with hearing loss at 4, 8 and 12 kHz in humans by multivariate analysis with adjustments for age, sex, smoking and BMI. Our experimental study also showed that As level in nails is a reliable index to assess As level in inner ears. Thus, the results of our combined study suggest that As level in toenails is a possible biomarker associated with hearing loss at 4, 8 and 12 kHz in humans. Association between chronic exposure to As and hearing loss {#sec015} ----------------------------------------------------------- The levels of an element in nails and hair are indexes reflecting chronic exposure status, while those in blood and urine samples are regarded as indexes of acute exposure \[[@pone.0198743.ref032], [@pone.0198743.ref033]\]. In our multivariate analysis, As levels in urine were not significantly correlated with hearing loss. Correspondingly, previous studies in which multivariate analyses with adjustments for age, sex and smoking were performed showed that As levels in urine were not associated with hearing loss \[[@pone.0198743.ref034]--[@pone.0198743.ref036]\]. Therefore, our results suggest that chronic exposure to As, but not acute exposure, is required for hearing loss in humans. In this study, we determined associations between As levels in biological samples and hearing levels in Bangladeshi only. Previous studies showed that races are associated with hearing levels \[[@pone.0198743.ref037], [@pone.0198743.ref038]\]. Thus, further study is needed to verify the associations between As levels in toenails and hearing loss in other countries. Association between As levels in hair and hearing loss at 12 kHz {#sec016} ---------------------------------------------------------------- The association between As levels in hair and hearing loss in humans aged 12--55 years was also analyzed in this study ([S1 Table](#pone.0198743.s002){ref-type="supplementary-material"}). As levels in hair were significantly associated with hearing loss at 12 kHz (OR = 2.94; 95% CI: 1.20, 7.20) but not with hearing loss at 4 or 8 kHz ([S1 Table](#pone.0198743.s002){ref-type="supplementary-material"}). Thus, our multivariate analysis showed that the significant association of As levels in hair with hearing loss was limited to an extra-high frequency (12 kHz), which is not necessary for daily communication in humans. A previous study showed that children living in an As-polluted area had hearing losses at 125, 250, 500, 1,000 and 8,000 Hz \[[@pone.0198743.ref039]\]. The As level in hair was 3.26 μg/g (mean value) in the previous study, while the As level in hair was 0.50 μg/g (mean value) in this study, about 6.5-times lower than that in the previous study. Therefore, it is possible that different levels of As in hair are associated with hearing loss at different frequencies. Relative contributions of As in toenails and confounders to hearing loss {#sec017} ------------------------------------------------------------------------ Age and smoking are known to be strong confounders for hearing loss. In this study, multivariate analysis showed that age was significantly associated with hearing loss at 4 kHz (OR = 4.25; 95% CI: 1.83, 9.89), 8 kHz (OR = 4.37; 95% CI: 1.84, 10.39) and 12 kHz (OR = 3.31; 95% CI: 1.46, 14.51). Smoking also had significant associations with hearing loss at 4 kHz (OR = 3.78; 95% CI: 1.17, 12.15) and 12 kHz (OR = 4.49; 95% CI: 1.39, 14.51). We then used the McFadden's Pseudo *R*^*2*^ values \[[@pone.0198743.ref040]\] to determine the relative contributions (%) of As in toenails and the other confounders including age to hearing loss at each frequency in the multivariate analysis ([S2 Table](#pone.0198743.s003){ref-type="supplementary-material"}). The relative contribution of As in toenails (17.33%) to hearing loss at 12 kHz was higher than the relative contributions of age (16.53%) and smoking (13.78%), while the relative contributions of age to hearing loss (20.75% at 4 kHz and 20.41% at 8 kHz) were higher than those of As in toenails (14.54% at 4 kHz and 13.70% at 8 kHz), smoking (9.44% at 4 kHz) and sex (12.09% at 8 kHz). Thus, our multivariate analysis suggests that As level in toenails is the largest contributor to hearing loss at 12 kHz among the confounders including age and smoking, while As level in toenails is the second-largest contributor after age to hearing loss at 4 and 8 kHz. On the other hand, hearing levels in males are generally known to be worse than those in females \[[@pone.0198743.ref041]\]. In this study, hearing thresholds in females were significantly higher than those in males. As levels in toenails (mean ± SD) in females (1.58 ± 1.00 μg/g) were significantly higher than those in males (1.17 ± 1.30 μg/g; p \< 0.0001). Therefore, it is possible that there is an association between higher As levels in females and higher hearing thresholds than those in males. It would be worthwhile to investigate the reason for the gender difference in As levels. Possible route of exposure to As for the subjects in this study {#sec018} --------------------------------------------------------------- The major route of exposure to As in the subjects in this study is not clear, but in our experimental study in which mice were orally exposed to As, there was a correlation between As levels in nails and inner ears. In our epidemiological study, we found a significant correlation (r = 0.5826; p \< 0.0001) between As levels in toenails and duration of drinking tube well water ([S1 Fig](#pone.0198743.s005){ref-type="supplementary-material"}). Therefore, it is likely that the route of exposure to As for the subjects in this study was drinking well water. Tube well water polluted with As is known to contain other elements. In our previous studies, barium was detected at a level similar to that of As in well drinking water in Bangladesh \[[@pone.0198743.ref042]\] and was to be associated with hearing loss in humans \[[@pone.0198743.ref014]\]. In this study, significant correlations between As levels in toenails and hearing loss remained in multivariate analysis adjusted with barium in addition to the confounders ([S3 Table](#pone.0198743.s004){ref-type="supplementary-material"}). Thus, the results suggest that As level in toenails is independently associated with hearing loss at 4, 8 and 12 kHz in humans. Further study is needed to investigate the association between hearing loss and As levels in well water worldwide, since more than 137 million people drink tube well water polluted by As worldwide \[[@pone.0198743.ref043]\]. Study limitations {#sec019} ----------------- This pilot study has several limitations. First, we used an ipod with headphones as the screening method for the field work in Bangladesh, since there is no clinical audiometer in rural areas. In addition, we did not perform otoscopy and tympanometry to check middle-ear problems. Second, our cross-sectional analysis was useful for determining the association between As levels in biological samples and hearing loss, but a the causal relationship could not be established. Cohort studies will be needed to determine the causality. Third, there was no information about noise background, though the subjects lived in rural areas and did not have portable music players with earphones. Fourth, the sample size of the pilot study in Bangladesh was small. Additional study is needed to analyze the association between As and hearing loss with consideration of the above limitations in larger sample sizes in other areas. Conclusion {#sec020} ---------- In conclusion, our combined experimental study and epidemiological study showed that As levels in nails were significantly associated with hearing loss in humans and that As levels in nails were significantly associated with those in inner ears in mice. Our epidemiological study also suggests the possible thresholds of As ranging from 0.30 μg/g to 0.70 μg/g in toenails that increase the risk for hearing loss in humans. Exposure to As is a worldwide health risk for humans. Our study provides new information that As level in toenails is a reliable index to predict As-mediated hearing loss in humans living in As-polluted areas. Supporting information {#sec021} ====================== ###### Determination of As levels in hair samples. (DOC) ###### Click here for additional data file. ###### Adjusted ORs (95% CI) for hearing loss and As levels in hair samples (n = 145)^a^. (DOC) ###### Click here for additional data file. ###### Hearing loss on McFadden's pseudo *R*^*2*^ for each factor. (DOC) ###### Click here for additional data file. ###### Adjusted ORs (95% CI) for hearing loss and As levels in biological samples (n = 145)^a^. (DOC) ###### Click here for additional data file. ###### Correlation between As levels in toenails and duration of drinking tube well water. Correlation between As levels in toenails and duration of drinking tube well water (years) was determined by spearman correlation coefficients. (TIF) ###### Click here for additional data file. We would like to thank the laboratory member for their helpful discussion. [^1]: **Competing Interests:**The authors have declared that no competing interests exist.

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Q: How to change background Color on external element drop based on it's id: Fullcalendar? I am trying to change background Color of the external element on drop. So how to do that? My code is following and I wanted to do something like if I drop red then red color of element on drop. If I drop green then...... so basically, based on it's id it change the color of element. As if you see then when you drop anything on week calendar, it's by default color is getting blue but it should transform to red as you are dropping red for ex. Any help will be really useful thanks guys Here is my code: jsFiddle link http://jsfiddle.net/jimil/8hqe3wxd/2/ A: My suggestion would be to add a data-attribute to the draggable components, not rely on their class (since theres more in their class than just the color) and then when building the little dragged components in the external events section, set a color attribute (either red, orange, purple or the actual css color) http://jsfiddle.net/8hqe3wxd/4/ in the fiddle, observe i added data attributes to the html: <div class='fc-event orange' id="1" data-color="orange">Orange</div> <div class='fc-event red' id="2" data-color="red">Red</div> <div class='fc-event purple' id="3" data-color="purple">Purple</div> and added a line to the external events config color: $(this).data('color') this is storing what color you want each draggable to be, and setting that color when building the little calendar element. hopefully this is what you want

Isolation of two distinct activator proteins for lipoprotein lipase from ovine plasma. Two distinct activator proteins for lipoprotein lipase (LPL) have been isolated in approximately equal amounts from ovine plasma. These low molecular weight proteins were readily separated from each other on the basis of size and charge. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis indicated proteins of Mr about 8000 and 5000, with pI in urea-containing gels of about 5.1 and 4.8 respectively. Each of the ovine activator proteins was as effective as human apolipoprotein C-II (apo C-II) in activating LPL, with 1 microgram/ml giving near to maximum activation, and in lowering the apparent Km of LPL for triolein substrate. As the ratio of activator to triolein increased from 0.16 to 5.2 (micrograms/mg) the apparent Km fell from about 0.5 to 0.18 mM. Whereas human apo C-II and the two ovine activators were equally effective in stimulating the hydrolysis of triolein, differences were observed between the human and ovine activators when p-nitrophenylbutyrate was used as substrate. Unlike human apo C-II, which produced significant inhibition of p-nitrophenylbutyrate hydrolysis, the ovine activators were without effect. This suggests that the interaction between the ovine activators and LPL is different from that of human apo C-II.

For the most part, the Broncos are finished with phase one of free agency. Getting a newly restructured/reduced contract with pass-rushing defensive end Elvis Dumervil is their final piece of business before owner Pat Bowlen, president Joe Ellis, front-office boss John Elway and coach John Fox take off Sunday for the NFL owners meetings in Scottsdale, Ariz. Otherwise, the Broncos as they stand now are pretty much tapped out of salary-cap room, according to two NFL sources. They are roughly $50,000 to $52,000 below league-imposed $123 million payroll limit. This is not a surprise given their furious attack on the open market through the first two days. Add in the re-signings of special-teams standout David Bruton and starting defensive tackle Kevin Vickerson, plus the franchise tag placed on starting left tackle Ryan Clady, and the Broncos have made $63.5 million worth of financial commitments to eight free-agent players. Those eight players will be paid a collective $30 million this year. The Broncos are likely to use the draft to select a running back, probably within the first three rounds. Maybe even in the first round. They wanted to add a safety to compete with Rahim Moore, Mike Adams and Quinton Carter. Maybe later. They will have to pick up a No. 3 and No. 4 quarterback by training camp. This team is solid at the first two spots with Peyton Manning, who will turn 37 in 10 days, and Brock Osweiler, who is barely 22. Otherwise, the Broncos want to make sure they are not left with a gaping hole opposite Von Miller at right end. Dumervil is scheduled to make $12 million this year, after he made $14 million in each of the past two years. The Broncos want him to take a pay cut to a salary more in line with the adjusted pass-rusher market. Paul Kruger's new deal averaged $8 million a year. He has only 15 ½ sacks in his career. Dumervil had 17 in 2009 alone. Yet, Cliff Avril had 20 ½ sacks the past two seasons, the number Dumervil has had. He got $7.5 million a year. There is a case that can be argued for both sides. The Broncos are willing to add back some of their proposed reduction in the form of guaranteed dollars in the later years of Dumervil's contract. His current deal calls for an non-guaranteed $10 million in 2014 and $8 million in 2015. In some ways, the Broncos and Dumervil's agent Marty Magid are not far apart. In other ways, they are not close. The Broncos have a backup plan if they can't work out a deal with Dumervil by Friday, the day before his $12 million salary would become fully guaranteed. Dwight Freeney is one possibility, but there are other defensive-end candidates the Broncos would consider. Missy Franklin, Jenny Simpson, Adeline Gray and three other Colorado women could be big players at the 2016 Rio OlympicsWhen people ask Missy Franklin for her thoughts about the Summer Olympics that will begin a year from Wednesday in Rio de Janeiro, she hangs a warning label on her answer.

Perimeter growth of a branched structure: application to crackle sounds in the lung. We study an invasion percolation process on Cayley trees and find that the dynamics of perimeter growth is strongly dependent on the nature of the invasion process, as well as on the underlying tree structure. We apply this process to model the inflation of the lung in the airway tree, where crackling sounds are generated when airways open. We define the perimeter as the interface between the closed and opened regions of the lung. In this context we find that the distribution of time intervals between consecutive openings is a power law with an exponent beta approximately 2. We generalize the binary structure of the lung to a Cayley tree with a coordination number Z between 2 and 4. For Z=4, beta remains close to 2, while for a chain, Z=2 and beta=1, exactly. We also find a mean field solution of the model.

Q: itextsharp: java to vb.net i am trying to change the font on a pdftable and i have this hint in java but need some help to put it into vb.net PdfPTable table = new PdfPTable(3); table.AddCell("Cell 1"); PdfPCell cell = new PdfPCell(new Phrase("Cell 2", new Font(Font.HELVETICA, 8f, Font.NORMAL, Color.YELLOW))); A: Imports iTextSharp.text Imports iTextSharp.text.pdf Module Module1 Sub Main() Dim table As New PdfPTable(3) table.AddCell("Cell 1") Dim f As New Font(Font.HELVETICA, 8.0F, Font.NORMAL, Color.YELLOW) Dim ph As New Phrase("Cell 2", f) Dim cell As New PdfPCell(ph) End Sub End Module

252 N.J. Super. 660 (1991) 600 A.2d 525 THELMA LAUTENSLAGER, PLAINTIFFS, v. SUPERMARKETS GENERAL CORPORATION, DEFENDANT. Superior Court of New Jersey, Law Division Union County. Decided June 28, 1991. *661 Patricia Breuninger (Breuninger, Hansen & Casale, Esqs.), for plaintiff. Hal R. Crane, Corporate Counsel for Supermarkets General Corporation. OPINION MENZA, J.S.C. Defendant moves for partial summary judgment. The question presented is which statute of limitations is applicable to a NJLAD case based on employment discrimination. On May 11, 1989, the plaintiff filed a complaint alleging a continuing pattern of employment discrimination on the part of her current employer, Supermarkets General Corporation. Specifically, the plaintiff contends that she was denied promotional opportunities from 1979 to the present, and that positions for which she was equally qualified were given to younger, usually male employees. Count One of the Complaint alleges violations of the New Jersey Laws Against Discrimination (NJLAD), N.J.S.A. 10:5-1 et seq. The defendant moves for a partial dismissal of the plaintiff's claims on the grounds that the two-year statute of limitations governing personal injury actions controls the NJLAD claim. The defendant contends, therefore, that all claims of discrimination that relate to events prior to May 11, 1987, are time barred by application of the statute. The plaintiff argues that the two-year statute is inapplicable to her claims, and that N.J.S.A. 2A:14-1, which provides a six-year statute for actions sounding in property rights, is the most befitting for discrimination claims. The NJLAD statute does not specify a statute of limitations period of limitations for actions involving employment discrimination. The limitation of actions statutes provide: *662 Every action at law for trespass to real property, for any tortious injury to real or personal property, for taking, detaining, or converting personal property, for replevin of goods or chattels, for any tortious injury to the rights of another not stated in sections 2A:14-2 and 2A:14-3 of this Title, or for recovery upon a contractual claim or liability, express or implied, not under seal, or upon an account other than one which concerns the trade or merchandise between merchant and merchant, their factors, agents and servants shall be commenced within 6 years next after the cause of any such action shall have accrued. (N.J.S.A. 2A:14-1). Every action at law for an injury to the person caused by the wrongful act, neglect or default of any person within this state shall be commenced within 2 years next after the cause of any such action shall have accrued. (N.J.S.A. 2A:14-2). In Leese v. Doe, 182 N.J. Super. 318, 440 A.2d 1166 (Law Div. 1981), the court addressed the question of which statute of limitations was applicable to the NJLAD claims based on sex discrimination. The court held that the plaintiff's employment discrimination claim was governed by the six year statute of limitations set forth in N.J.S.A. 2A:14-1. In doing so, the court analogized the NJLAD claim to a claim brought under its federal counterpart, 42 U.S.C. § 1981 and cited as authority for its holding the case of Davis v. United States Steel Supply, 581 F.2d 335 (3rd Cir.1978). The Davis case held that a petitioner's § 1981 complaint was one which sounded in property rights, and was therefore actionable under Pennsylvania's six-year statute. The Davis court said: Plaintiff's complaint cites incidents of abuse and of personal property damage, but not of bodily injury. The gravamen of the complaint does not concern Mrs. Davis' interest in personal security, but rather involves unlawful interference with her rights as an employee. Mrs. Davis implicitly asserts a right to good faith efforts by an employer to correct instances of co-worker racial harassment and a right not to be discharged for complaining of such incidents. Essentially, Mrs. Davis complains that U.S. Steel Supply demeaned her and fired her because of her race. (Id. at p. 338). In Skadegaard v. Farrell, 578 F. Supp. 1209 (D.N.J. 1984), the court, also relying on Davis, held that the six year statute was applicable to a NJLAD case based on sexual harassment. The court said: *663 The relief sought by plaintiff is the key to characterization of a cause of action for statute of limitation purposes, and as in Davis, [i]n terms of legal relief, plaintiff's complaint does not seek damages for bodily injury.' (Id. at p. 1214). The Davis case, the premise for the Leese and Skadegaard cases, was reversed by the United States Supreme Court in Goodman v. Lukens Steel, 482 U.S. 656, 107 S.Ct. 2617, 96 L.Ed.2d 572 (1987). In that case, which involved racial discrimination, the Supreme Court held that federal courts should select the most applicable state statute of limitations for § 1981 claims, and that the applicable state statute should be the one governing personal injury claims. The court said: Section 1981 has a much broader focus than contractual rights ... [It] asserts in effect that competence and capacity to contract shall not depend on race. It is thus part of a federal law barring racial discrimination, which, as the court of appeals said, is a fundamental injury to the individual rights of a person ... The Court of Appeals was correct in selecting the Pennsylvania 2-year limitation period governing personal injury actions. (Id. at 661-662, 107 S.Ct. at 2620-2621). In White v. Johnson & Johnson, 712 F. Supp. 33 (D.N.J. 1989), the District Court applying Goodman rejected Leese and Skadegaard, and held that the two year statute was applicable. The court said: The New Jersey Supreme Court has not yet ruled on the appropriate statute of limitations in an action under NJLAD. (citation omitted). In the absence of an authoritative pronouncement from the state's highest court, the task of a federal court is to predict how that court would rule.' (citation omitted). ........ The only New Jersey state case cited by the parties that has addressed the issue is Leese v. Doe, 182 N.J. Super. 318, 321, 440 A.2d 1166, 1168 (Law Div. 1981), which ruled that the six-year statute pertaining to claims for injury to property governs NJLAD claims ... Importantly, however, both Leese and one of the federal cases following it based their holding on the Third Circuit case that was overruled by Goodman in the § 1981 context, namely, Davis v. United States Steel Supply, 581 F.2d 335 (3d Cir.1989). ........ Although it [NJLAD] has wide-ranging economic consequences, it is fundamentally aimed at eliminating the injury that racial discrimination causes to the person of the aggrieved. ........ *664 The Court can only assume that if the issue were before the highest court of New Jersey, that court would do as the Superior Court did in Leese and look to federal law for guidance, but would find the current federal guidance (in contrast to what existed at the time of Leese), to favor application of the personal injury statute of limitations to NJLAD claims. Thus, the Court agrees with defendants the New Jersey Supreme Court would most likely apply the two-year limitations period of N.J.S.A. § 2A:14-1 [sic][1] to NJLAD claims. (Id. at 37-38). Although there are no New Jersey decisions which have specifically addressed the question, it appears that the New Jersey courts do apply the six year statute of limitations. In Nolan v. Otis Elevator Co., 197 N.J. Super. 468, 485 A.2d 312 (App.Div. 1984), rev'd on other grounds, 102 N.J. 30, 505 A.2d 580 (1986), cert. den., 479 U.S. 820, 107 S.Ct. 84, 93 L.Ed.2d 38 (1986), a case decided before Goodman, the Supreme Court, in reversing the Appellate Division held that the federal age discrimination in employment act preempted a state court action which was brought under NJLAD after the expiration of the statute of limitations governing the federal act. Although the Supreme Court did not specifically state the statute of limitations applicable to NJLAD claims, the Appellate Division did do so but did it in dicta and without explanation. The court said: Defendant contends here that the action is barred by the time limitations expressed in the New Jersey Law Against Discrimination and the statute of limitations, N.J.S.A. 2A:14-2. ........ ... [W]e conclude that the applicable time limitation is that stated in N.J.S.A. 2A:14-1 "6 years next after the cause of action shall have accrued. (197 N.J. Super. p. 473-474, 485 A.2d 312). And in Fisher v. Quaker Oats, 233 N.J. Super. 319, 559 A.2d 1 (App.Div. 1989), the court, in the first sentence of its opinion, framed the issue in the case by stating, "On this appeal, we must determine whether the 6 year period permitted for the filing of an age discrimination complaint under our Law Against Discrimination ... has been preempted by the shorter limitation period of the federal Age *665 Discrimination in Employment Act." (At 320, 559 A.2d 1, citing the Nolan case as authority). No explanation was thereafter offered by the court as to the reason why the six year statute of limitation was applicable to NJLAD. The quandary then is this: the Leese case, a law division case, and the Skadegaard case, a federal district court case, each of which held that the six year statute was applicable, was based on a federal circuit court case subsequently reversed by the Supreme Court. The White case also a federal district court case, concluded that the two year statute is applicable and two appellate division cases have stated in dicta, and without explanation, that the six year statute is applicable. It would seem that the best way for this Court to determine which statute of limitations is applicable to NJLAD is through an evolutionary analysis of N.J.S.A. 2A:14-1 and N.J.S.A. 2A:14-2. The history of New Jersey's statutes of limitations was detailed by the Supreme Court in the case of Earl v. Winne, 14 N.J. 119, 101 A.2d 535 (1953). This history is as follows: As of February 7, 1779, New Jersey has an "Act for the Limitation of Actions," consisting of 17 subsections. The first two sections of that act are relevant to this inquiry. The first section was the six-year limitation period. Among other things, it explicitly governed "all actions of account and upon the case, except actions for slander ..." The second section, a four-year statute, covered trespass actions involving direct physical harm such as "assault, menace, battery, wounding and imprisonment ..." A third section applied a two-year statute to "actions upon the case for words," presumably a reference to libel. In 1874, the statute was revised. The revised statute retained the six-year statute for all actions ... upon the case, and the four-year statute for trespass vi et armis. *666 In 1896, the legislature again revised the statute adopting a new section which retained the two-year limitation for "action upon the case for words," i.e., libel, but added to the two-year statute "all actions for injuries to the person caused by wrongful act, neglect or default of any person ... The phrase "injuries to persons" was meant to embrace only direct physical injury torts such as "assault, menace, battery, wounding, ..." etc. That new section, the precursor of New Jersey's current two-year statute impliedly repealed Section Two, the four-year statute for trespass vi et armis. It did not repeal the applicability of the six-year statute to actions on the case. In a 1934 revision, the six-year statute continued to apply to all "actions in the nature of actions upon the case," and was designated R.S. 2:24-1. The two-year statute that originally specified "menace, assault, mayhem, etc.," was replaced by the language of the 1896 revision referring to "injuries to the person" and libel and slander were given a one-year statute in Section Three, now designated R.S. 2:24-3. In a "recent revision" referred to but not identified by date in Earl, section One of the Act was rewritten and the phrase "any tortious injury to the rights of another" was substituted for specific common law references to "action on the case." See Earl v. Winne, 14 N.J. 119, 129-32, 101 A.2d 535). The historical analysis makes it clear that the words in the current statute, N.J.S.A. 2A:14-1 (formerly R.S. 2:24-1), "any tortious injury to the rights of another," means all actions "in the nature of actions on the case", whereas, the phrase "injuries to persons," contained in N.J.S.A. 2A:14-2, (formerly R.S. 2:24-2 refers to actions in trespass vi et armis. How is a NJLAD case to be characterized? Is it an action in the nature of an action on the case or is it one characteristic of a trespass vi et armis? An action on the case, in Black's Law Dictionary, 51 (4th Ed. 1968), is defined as: *667 It is founded on the common law or upon acts of Parliament, and lies generally to recover damages for torts not committed with force, actual or implied' or having been occasioned by force where the matter affected was not tangible, or the injury was not immediate but consequential, or where the interest in the property only in reversion, in all of which cases trespass is not sustainable ... In the progress of judicial contestation it was discovered that there was a mass of tortious wrongs unattended by direct and immediate force, or where the force, though direct, was not expended on an existing right of present enjoyment. A trespass is defined as: An unlawful act committed with violence, actual or implied, causing injury to the person, property or relative rights of another. ........ In practice a form of action, at the common law, which lies for redress in the shape of money damages for any unlawful injury done to the plaintiff, in respect either to his person, property or rights, by the immediate force a violence of the defendant. (Id. at 1674). In Osborne v. Butcher, 26 N.J.L. 308 (1857), the New Jersey Supreme Court commented on the distinction between the two common law actions. In that case, the plaintiff filed an action of trespass vi et armis against the defendant for obstructing a road used by the plaintiff for egress from his farm. In holding that the action was properly brought as an action on the case, the court stated: The gravamen is the obstruction of a by-road, and thereby depriving the plaintiff of its use. The obstructing and blocking up of the road may have been direct, immediate, willful, and forcible, but that was not to, or upon the land of the plaintiff or to his possession; it was not direct and immediate to him. The injury to him was the depriving him of the use of the by-road by reason of such obstruction. It was indirect and consequential, and therefore the subject of an action on the case, and not of trespass. (Id. at 309-10). And in H.J. Jaegar Research Laboratories v. Radio Corporation of America, 90 F.2d 826, 827 (Cir.1937), the court, in characterizing a cause of action under the Sherman Anti-Trust Act as one similar to an action on the case, said: ... the Acts of New Jersey ... follow the British statute of James I in limiting actions of case to six years. That action was created to meet a recognized need in the administration of justice, namely, a special form of action for particular cases where the ancient form of action did not provide a remedy. ........ *668 `Actions of the case are founded on common law or upon acts of Parliament, and lie generally to recover damages for torts not committed by force, actual or implied;' ... (Id. at 827). (quoting 1 Chit.Pl. 133 and 142). Historically, therefore, an action of trespass was proper for injury caused by a direct application of force, while an action on the case governed injuries which were indirect and consequential. The language of the current statutes of limitations is derivative of the common law limitation period. N.J.S.A. 2A:14-2 was intended by the legislature to cover claims of actual, physical injury such as negligence, assault and battery, and actions for trespass vi et armis. N.J.S.A. 2A:14-1 was intended to cover indirect injuries, actions on the case. Thus, in Earl v. Winne, supra, the court held that since the tort of false imprisonment involved "immediate wrongs accompanied by force to the person," and the torts of abuse of process and malicious prosecution involved only indirect action against the person, the former tort was covered by the two-year statute, while the latter torts were covered by the six-year statute. And in Canessa v. Kislak, Inc., 97 N.J. Super. 327, 235 A.2d 62 (Law Div. 1967), the court held that the six-year statute of limitations is applicable to a claim for the tort of "invasion of privacy" involving the appropriation of one's name and likeness. The court reasoned that the two year statute of limitations set forth in N.J.S.A. 2A:14-2 only governs those claims involving direct physical injury and since an invasion of privacy is not an immediate physical affront, but rather a deprivation of a property right, and therefore an indirect tort, it is governed by the six year statute of limitations. Id. at 351, 235 A.2d 62. Employment discrimination is an offensive, personal violation resulting in deprivation of one's right to equal employment opportunity. It is not a direct personal injury in the traditional sense but rather an indirect one such as that suffered by the farmer in Osborne v. Butcher whose driveway was wrongfully obstructed. The farmer's injury is that he cannot gain access to his house. The employee's injury is the deprivation of the *669 right to employment. Both are indirect injuries; as such, both are in the nature of "actions on the case." Under the circumstances, this Court is of the opinion that NJLAD claims are characteristic of common law actions on the case. They are therefore governed by the six year statute of limitations: N.J.S.A. 2A:14-1. Defendant's motion for summary judgment is denied. NOTES [1] See N.J.S.A. 2A:14-2.

I'm not exactly sue how the whole familiar movement thing goes, but we have always played that if you move the familiar can move along with you. But now I am getting zephyr boots and I wanted to know if my floating weapon familiar can fly along with me. Also I have a winged shield, will hat float up with me also? if your fam is on passive mode it is part of you can goes where u go. But if it is active it only moves when you move it via a move action (so moves instead of you) and it moves based on its move speed and type. That doens't make any sense. If a familiar can't be more than so many squares from you that would mean you would have to walk only every other round, essentially half speed in order for it to keep up. It may not make sense but it's the rules. There is a feat that specifically allows your active familiar to move when you take a move action named Active Familiar. There is also another feat that lets you move your familiar with a minor action 1/turn, Quick Familiar. So without those, either you move, or your familiar moves, but not both. On a side note, "keeping up" isn't really a concern because for overland movement you can just put it in passive mode to stay with you, and in combat it's unlikely for the range to be an issue.

It’s hard to get into the world of the Internet of Things (IoT) without eventually talking about Digital Twins. I was first exposed to the concept of Digital Twins when working with GE. Great concept. But are Digital Twins only relevant to physical machines such as wind turbines, jet engines, and locomotives? What can we learn about the concept of digital twins that we can apply more broadly – to other physical entities (like contracts and agreements) and even humans? What Is a Digital Twin?A Digital Twin is a digital representation of an industrial asset that enables companies to better understand and predict the performance of their machines, find new revenue streams, and change the way their business operates[1]. GE uses the concept of Digital Twins to create a digital replica of their physical product (e.g., wind turbine, jet engine, locomotive) that captures the asset’s detailed history (from design to build to maintenance to retirement/salvage) that can be mined to provide actionable insights into the product’s operations, maintenance and performance. The Digital Twin concept seems to work for any entity around which there is ongoing activity or “life”; that is, there is a continuous flow of new information about that entity that can constantly update the condition or “state” of that entity. The Digital Twin concept is so powerful that it would be a shame to not apply the concept beyond just physical products. So let’s try to apply the Digital Twin concept to another type of common physical entity – contracts or agreements. Applying Digital Twins to ContractsMany contracts and agreements have a life of their own; they are not just static entities. Many contracts (e.g., warranties, health insurance, automobile insurance, car rental agreements, construction contracts, apartment rental agreements, leasing agreements, personal loans, line of credit, maintenance contracts) once established, have a stream of ongoing interactions, changes, enhancements, additions, enforcements and filings. In fact, the very process of establishing a contract can constitute many interactions with exchanges of information (negotiations) that shape the coverage, agreement, responsibilities and expectations of the contract. Let’s take a simple home insurance contract. Once the contract is established, there is a steady stream of interactions and enhancements to that contract including: Payments Addendums Claims filings Changes in terms and conditions Changes in coverage Changes in deductibles Each of these engagements changes the nature of the contract including its value and potential liabilities. The insurance contract looks like a Digital Twin of the physical property for which it insures given the cumulative history of the interactions with and around that contract. Expanding upon the house insurance contract as a living entity, the insurance company might want to gather other data about the property in order to increase the value of the contract while reducing the contract’s risks, liabilities and obligations. Other data sources that the insurance company might want to integrate with the house insurance contract could include: Changes in the value of the home (as measured by Zillow and others) Changes in the value of the nearby homes Changes in local crime Changes in local traffic Changes in the credentials and quality of local schools Quality of nearby parks Changes in zoning (the value and liabilities of a house could change if someone constructs a mall nearby) Changes in utilities (a house with lots of grass might not be as attractive as the price of water starts to increase) If the goal of the insurance company holding the home insurance policy is to 1) maximize the value of that policy while 2) reducing any potential costs, liabilities and obligations, then creating a Digital Twin via a home insurance contract seems like a smart economic move. Applying Digital Twins to Humans“Big Data is not about big data; it’s about getting down to the individual!” One of the keys to data monetization is to understand the behaviors and tendencies of each individual including consumers, students, teachers, patients, doctors, nurses, engineers, technicians, agents, brokers, store managers, baristas, clerks, and athletes. In order to better serve your customers, you need to capture and quantify each individual customer’s preferences, behaviors, tendencies, inclinations, interests, passions, associations and affiliations in the form of actionable insights (such as propensity scores). See Figure 3. Figure 3: Big Data About Insights at Level of the Individual These actionable insights can be captured in an Analytic Profile for re-use across a number of use cases including customer acquisition, retention, cross-sell/up-selling, fraud reduction, money laundering, advocacy development and likelihood to recommend (see Figure 3). SummaryGE uses the concept of Digital Twins to create a digital replica of a physical product that captures the asset’s detailed history (from design to build to maintenance to retirement/salvage) that can be mined to provide actionable insights into the product’s operations, maintenance and performance. That same Digital Twins concept can be applied to contracts and agreements in order to increase the value of those contracts while minimizing any potential risks and liabilities. And the Digital Twins concept can also be applied to humans in order to better monetize the individual human (customers) across the organization’s value creation process. As a CTO within Dell EMC’s 2,000+ person consulting organization, he works with organizations to identify where and how to start their big data journeys. He’s written white papers, is an avid blogger and is a frequent speaker on the use of Big Data and data science to power an organization’s key business initiatives. He is a University of San Francisco School of Management (SOM) Executive Fellow where he teaches the “Big Data MBA” course. Bill also just completed a research paper on “Determining The Economic Value of Data”. Onalytica recently ranked Bill as #4 Big Data Influencer worldwide. Bill has over three decades of experience in data warehousing, BI and analytics. Bill authored the Vision Workshop methodology that links an organization’s strategic business initiatives with their supporting data and analytic requirements. Bill serves on the City of San Jose’s Technology Innovation Board, and on the faculties of The Data Warehouse Institute and Strata. Previously, Bill was vice president of Analytics at Yahoo where he was responsible for the development of Yahoo’s Advertiser and Website analytics products, including the delivery of “actionable insights” through a holistic user experience. Before that, Bill oversaw the Analytic Applications business unit at Business Objects, including the development, marketing and sales of their industry-defining analytic applications. Bill holds a Masters Business Administration from University of Iowa and a Bachelor of Science degree in Mathematics, Computer Science and Business Administration from Coe College. Artificial intelligence (AI) is the intelligence of machines and the branch of computer science which aims to create it. Major AI textbooks define the field as "the study and design of intelligent agents," where an intelligent agent is a system that perceives its environment and takes actions which maximize its chances of success. John McCarthy, who coined the term in 1956,defines it as "the science and engineering of making intelligent machines." The field was founded on the claim that a central property of human beings, intelligence—the sapience of Homo sapiens—can be so precisely described that it can be simulated by a machine. Cloud Expo Cloud Computing & All That It Touches In One Location Cloud Computing - Big Data - Internet of Things SDDC - WebRTC - DevOps Cloud computing is become a norm within enterprise IT. The competition among public cloud providers is red hot, private cloud continues to grab increasing shares of IT budgets, and hybrid cloud strategies are beginning to conquer the enterprise IT world. Big Data is driving dramatic leaps in resource requirements and capabilities, and now the Internet of Things promises an exponential leap in the size of the Internet and Worldwide Web. The world of SDX now encompasses Software-Defined Data Centers (SDDCs) as the technology world prepares for the Zettabyte Age. 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--- abstract: 'This paper is to prove the asymptotic normality of a statistic for detecting the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size $n$ tends to infinity and the number of covariates $p$ is either fixed or tends to infinity. Moreover our approach indicates that its asymptotic normality holds even without homoscedasticity.' address: - 'KLASMOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, P.R.C., 130024.' - 'School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371' - 'KLASMOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, P.R.C., 130024.' author: - Zhidong Bai - Guangming Pan - Yanqing Yin title: 'Homoscedasticity tests for both low and high-dimensional fixed design regressions' --- [ emptyifnotempty[@addto@macro]{} @addto@macro]{} [^1] [ emptyifnotempty[@addto@macro]{} @addto@macro]{} [^2] [ emptyifnotempty[Corresponding author]{}[@addto@macro]{} @addto@macro]{} [^3] Introduction ============ A brief review of homoscedasticity test --------------------------------------- Consider the classical multivariate linear regression model of $p$ covariates $$\begin{aligned} y_i={\mathbf}x_i{\mathbf}\beta+{\mathbf}\varepsilon_i,\ \ \ \ \ i=1,2,\cdots,n,\end{aligned}$$ where $y_i$ is the response variable, ${\mathbf}x_i=(x_{i,1},x_{i,2},\cdots,x_{i,p})$ is the $p$-dimensional covariates, $\beta={\left(}\beta_1,\beta_2,\cdots,\beta_p{\right)}'$ is the $p$ dimensional regression coefficient vector and $\varepsilon_i$ is the independent random errors obey the same distribution with zero mean and variance $\sigma_i^2$. In most applications of the linear regression models the homoscedasticity is a very important assumption. Without it, the loss in efficiency in using ordinary least squares (OLS) may be substantial and even worse, the biases in estimated standard errors may lead to invalid inferences. Thus, it is very important to examine the homoscedasticity. Formally, we need to test the hypothesis $$\label{a1} H_0: \ \sigma_1^2=\sigma_2^2=\cdots=\sigma_n^2=\sigma^2,$$ where $\sigma^2$ is a positive constant. In the literature there are a lot of work considering this hypothesis test when the dimension $p$ is fixed. Indeed, many popular tests have been proposed. For example Breusch and Pagan [@breusch1979simple] and White [@white1980heteroskedasticity] proposed statistics to investigate the relationship between the estimated errors and the covariates in economics. While in statistics, Dette and Munk [@dette1998estimating], Glejser [@glejser1969new], Harrison and McCabe [@harrison1979test], Cook and Weisberg [@cook1983diagnostics], Azzalini and Bowman[@azzalini1993use] proposed nonparametric statistics to conduct the hypothesis. One may refer to Li and Yao [@li2015homoscedasticity] for more details in this regard. The development of computer science makes it possible for people to collect and deal with high-dimensional data. As a consequence, high-dimensional linear regression problems are becoming more and more common due to widely available covariates. Note that the above mentioned tests are all developed under the low-dimensional framework when the dimension $p$ is fixed and the sample size $n$ tends to infinity. In Li and Yao’s paper, they proposed two test statistics in the high dimensional setting by using the regression residuals. The first statistic uses the idea of likelihood ratio and the second one uses the idea that “the departure of a sequence of numbers from a constant can be efficiently assessed by its coefficient of variation", which is closely related to John’s idea [@john1971some]. By assuming that the distribution of the covariates is ${\mathbf}N({\mathbf}0, {\mathbf}I_p)$ and that the error obey the normal distribution, the “coefficient of variation" statistic turns out to be a function of residuals. But its asymptotic distribution missed some part as indicated from the proof of Lemma 1 in [@li2015homoscedasticity] even in the random design. The aim of this paper is to establish central limit theorem for the “coefficient of variation" statistic without assuming randomness of the covariates by using the information in the projection matrix (the hat matrix). This ensures that the test works when the design matrix is both fixed and random. More importantly we prove that the asymptotic normality of this statistics holds even without homoscedasticity. That assures a high power of this test. The structure of this paper is as follows. Section 2 is to give our main theorem and some simulation results, as well as two real data analysis. Some calculations and the proof of the asymptotic normality are presented in Section 3. Main Theorem, Simulation Results and Real Data Analysis ======================================================= The Main Theorem ---------------- Suppose that the parameter vector $\beta$ is estimated by the OLS estimator $$\hat{ {\beta}}={\left(}{\mathbf}X'{\mathbf}X{\right)}^{-1}{\mathbf}X'{\mathbf}Y.$$ Denote the residuals by $$\hat{{\mathbf}\varepsilon}={\left(}\hat{{\mathbf}\varepsilon_1},\hat{{\mathbf}\varepsilon_2},\cdots,\hat{{\mathbf}\varepsilon_n}{\right)}'={\mathbf}Y-{\mathbf}X\hat \beta={\mathbf}P\varepsilon,$$ with ${\mathbf}P=(p_{ij})_{n\times n}={\mathbf}I_n-{\mathbf}X({\mathbf}X'{\mathbf}X)^{-1}{\mathbf}X'$ and $\varepsilon={\left(}\varepsilon_1,\varepsilon_2,\cdots,\varepsilon_n{\right)}'$. Let ${\mathbf}D$ be an $n\times n$ diagonal matrix with its $i$-th diagonal entry being $\sigma_i$, set ${\mathbf}A=(a_{ij})_{n\times n}={\mathbf}P{\mathbf}D$ and let $\xi={\left(}\xi_1,\xi_2,\cdots,\xi_n{\right)}'$ stand for a standard $n$ dimensional random vector whose entries obey the same distribution with $\varepsilon$. It follows that the distribution of $\hat \varepsilon$ is the same as that of ${\mathbf}A\xi$. In the following, we use ${{\rm Diag}}{\left(}{\mathbf}B{\right)}={\left(}b_{1,1},b_{2,2},\cdots,b_{n,n}{\right)}'$ to stand for the vector formed by the diagonal entries of ${\mathbf}B$ and ${{\rm Diag}}'{\left(}{\mathbf}B{\right)}$ as its transpose, use ${\mathbf}D_{{\mathbf}B}$ stand for the diagonal matrix of ${\mathbf}B$, and use ${\mathbf}1$ stand for the vector ${\left(}1,1,\cdots,1{\right)}'$. Consider the following statistic $$\label{a2} {\mathbf}T=\frac{\sum_{i=1}^n{\left(}\hat{\varepsilon_i}^2-\frac{1}{n}\sum_{i=1}^n\hat{\varepsilon_i}^2{\right)}^2}{\frac{1}{n}{\left(}\sum_{i=1}^n\hat{\varepsilon_i}^2{\right)}^2}.$$ We below use ${\mathbf}A {\circ}{\mathbf}B$ to denote the Hadamard product of two matrices ${\mathbf}A$ and ${\mathbf}B$ and use ${\mathbf}A ^{{\circ}k}$ to denote the Hadamard product of k ${\mathbf}A$. \[th1\] Under the condition that the distribution of $\varepsilon_1$ is symmetric, ${{\rm E}}|\varepsilon_1|^8\leq \infty$ and $p/n\to y\in [0,1)$ as $n\to \infty$, we have $$\frac{{\mathbf}T-a}{\sqrt b}\stackrel{d}{\longrightarrow}{\mathbf}N(0,1)$$ where $a$, $b$ are determined by $n$, $p$ and ${\mathbf}A$. Under $H_0$, we further have $$a={\left(}\frac{n{\left(}3{{\rm tr}}{\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}+\nu_4{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)^2{\right)}}{{\left(}{\left(}n-p{\right)}^2+2{\left(}n-p{\right)}+\nu_4{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P){\right)}}-1{\right)},\ b=\Delta'\Theta\Delta,$$ where $$\Delta'=(\frac{n}{{\left(}{\left(}n-p{\right)}^2+2{\left(}n-p{\right)}+\nu_4{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P){\right)}},-\frac{n^2{\left(}3{{\rm tr}}{\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}+\nu_4{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)^2{\right)}}{{{\left(}{\left(}n-p{\right)}^2+2{\left(}n-p{\right)}+\nu_4{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P){\right)}}^2})$$ and $$\Theta=\left( \begin{array}{cc} \Theta_{11} & \Theta_{12} \\ \Theta_{21} & \Theta_{22} \\ \end{array} \right),$$ where $$\begin{aligned} \Theta_{11}=&72{{\rm Diag}}'({\mathbf}P) {\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}{{\rm Diag}}({\mathbf}P)+24{{\rm tr}}{\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}^2\\\notag &+\nu_4{\left(}96{{\rm tr}}{\mathbf}P {\mathbf}{D_P} {\mathbf}P {\mathbf}P^{{\circ}3}+72{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)^3+36{{\rm Diag}}'({\mathbf}P) {\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}^2{{\rm Diag}}({\mathbf}P) {\right)}\\\notag &+\nu^2_4{\left(}18{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)^4+16{{\rm tr}}({\mathbf}P^{{\circ}3}{\mathbf}P)^2){\right)}\\\notag &+\nu_6{\left(}12{{\rm tr}}{\left(}{\left(}{\mathbf}P{\mathbf}D_{{\mathbf}P}{\mathbf}P {\right)}{\circ}{\left(}{\mathbf}P^{{\circ}2}{\mathbf}P^{{\circ}2}{\right)}{\right)}+16{{\rm tr}}{\mathbf}P {\mathbf}P^{{\circ}3}{\mathbf}P^{{\circ}3}{\right)}+\nu_8{\mathbf}1'({\mathbf}P^{{\circ}4}{\mathbf}P^{{\circ}4}){\mathbf}1,\end{aligned}$$ $$\begin{aligned} \Theta_{22}=\frac{8{\left(}n-p{\right)}^3+4\nu_4{\left(}n-p{\right)}^2{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)}{n^2},\end{aligned}$$ $$\begin{aligned} &\Theta_{12}=\Theta_{21}\\\notag =&\frac{{\left(}n-p{\right)}}{n}{\left(}24{{\rm tr}}{\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}+16\nu_4{{\rm tr}}({\mathbf}P {\mathbf}P^{{\circ}3})+12\nu_4{{\rm tr}}{\left(}{\left(}{\mathbf}P{\mathbf}D_{{\mathbf}p}{\mathbf}P{\right)}{\circ}{\mathbf}P{\right)}+2\nu_6[{{\rm Diag}}({\mathbf}P)'({\mathbf}P^{{\circ}4}){\mathbf}1]{\right)},\end{aligned}$$ $\nu_4=M_4-3$ , $\nu_6=M_6-15 M_4+30$ and $\nu_8=M_8-28 M_6-35M_4^2+420M_4-630$ are the corresponding cumulants of random variable $\varepsilon_1$. The existence of the 8-th moment is necessary because it determines the asymptotic variance of the statistic. The explicit expressions of $a$ and $b$ are given in Theorem \[th1\] under $H_0$. However the explicit expressions of $a$ and $b$ are quite complicated under $H_1$. Nevertheless one may obtain them from (\[e1\])-(\[e2\]) and (\[t10\])-(\[ct12\]) below. In Li and Yao’s paper, under the condition that the distribution of $\varepsilon$ is normal, they also did some simulations when the design matrices are non-Gaussian. Specifically speaking, they also investigated the test when the entries of design matrices are drawn from gamma distribution $G(2,2)$ and uniform distribution $U(0,1)$ respectively. There is no significant difference in terms of size and power between these two non-normal designs and the normal design. This seems that the proposed test is robust against the form of the distribution of the design matrix. But according to our main theorem, it is not always the case. In our main theorem, one can find that when the error $\varepsilon$ obey the normal distribution, under $H_0$ and given $p$ and $n$, the expectation of the statistics is only determined by ${{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)$. We conduct some simulations to investigate the influence of the distribution of the design matrix on this term when $n=1000$ and $p=200$. The simulation results are presented in table \[table1\]. $N(0,1)$ $G(2,2)$ $U(0,1)$ $F(1,2)$ $exp(N(5,3))/100$ ------------------------------------------- ---------- ---------- ---------- ---------- ------------------- ${{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)$ 640.3 640.7 640.2 712.5 708.3 : The value of ${{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)$ corresponding to different design distributions[]{data-label="table1"} It suggests that even if the entries of the design matrix are drawn from some common distribution, the expectation of the statistics may deviate far from that of the normal case. This will cause a wrong test result. Moreover, even in the normal case, our result is more accurate since we do not use any approximate value in the mean of the statistic $T$. Let’s take an example to explain why this test works. For convenient, suppose that $\varepsilon_1$ obey the normal distribution. From the calculation in Section \[exp\] we know that the expectation of the statistic ${\mathbf}T$ defined in (\[a2\]) can be represented as $${{\rm E}}{\mathbf}T=\frac{3n\sum_{i=1}^np_{ii}^2\sigma_i^4}{(\sum_{i=1}^np_{ii}\sigma_i^2)^2}-1+o(1).$$ Now assume that $p_{ii}=\frac{n-p}{n}$ for all $i=1,\cdots,n$. Moreover, without loss of generality, suppose that $\sigma_1=\cdots=\sigma_n=1$ under $H_0$ so that we get ${{\rm E}}{\mathbf}T\to 2$ as $n \to \infty$. However, when $\sigma_1=\cdots=\sigma_{[n/2]}=1$ and $\sigma_{[n/2]+1}=\cdots=\sigma_{n}=2$, one may obtain ${{\rm E}}{\mathbf}T\to 3.08$ as $n\to \infty$. Since ${\rm Var}({\mathbf}T)=O(n^{-1})$ this ensures a high power as long as $n$ is large enough. Some simulation results ----------------------- We next conduct some simulation results to investigate the performance of our test statistics. Firstly, we consider the condition when the random error obey the normal distribution. Table \[table2\] shows the empirical size compared with Li and Yao’s result in [@li2015homoscedasticity] under four different design distributions. We use $``{\rm CVT}"$ and $``{\rm FCVT}"$ to represent their test and our test respectively. The entries of design matrices are $i.i.d$ random samples generated from $N(0,1)$, $t(1)$ ($t$ distribution with freedom degree 1), $F(3,2)$ ($F$ distribution with parameters 3 and 2) and logarithmic normal distribution respectively. The sample size $n$ is 512 and the dimension of covariates varies from 4 to 384. We also follow [@dette1998testing] and consider the following two models: Model 1 : $y_i={\mathbf}x_i{\mathbf}\beta+{\mathbf}\varepsilon_i(1+{\mathbf}x_i {\mathbf}h),\ \ \ \ \ i=1,2,\cdots,n$,\ where ${\mathbf}h=(1,{\mathbf}0_{(p-1)})$, Model 2 : $y_i={\mathbf}x_i{\mathbf}\beta+{\mathbf}\varepsilon_i(1+{\mathbf}x_i {\mathbf}h),\ \ \ \ \ i=1,2,\cdots,n $\ where ${\mathbf}h=({\mathbf}1_{(p/2)},{\mathbf}0_{(p/2)})$. Tables \[table3\] and \[table4\] show the empirical power compared with Li and Yao’s results under four different regressors distributions mentioned above. Then, we consider the condition that the random error obey the two-point distribution. Specifically speaking, we suppose $P(\varepsilon_1=-1)=P(\varepsilon_1=1)=1/2$. Since Li and Yao’s result is unapplicable in this situation, Table \[table5\] just shows the empirical size and empirical power under Model 2 of our test under four different regressors distributions mentioned above. According to the simulation result, it is showed that when $p/n\to [0,1)$ as $n\to \infty$, our test always has good size and power under all regressors distributions. N(0,1) t(1) $F(3,2)$ $e^{(N(5,3))}$ ----- -------- -------- -------- -------- ---------- -------- ---------------- -------- -- -- p FCVT CVT FCVT CVT FCVT CVT FCVT CVT 4 0.0582 0.0531 0.0600 0.0603 0.0594 0.0597 0.0590 0.0594 16 0.0621 0.0567 0.0585 0.0805 0.0585 0.0824 0.0595 0.0803 64 0.0574 0.0515 0.0605 0.2245 0.0586 0.2312 0.0578 0.2348 128 0.0597 0.0551 0.0597 0.5586 0.0568 0.5779 0.0590 0.5934 256 0.0551 0.0515 0.0620 0.9868 0.0576 0.9908 0.0595 0.9933 384 0.0580 0.0556 0.0595 1.0000 0.0600 1.0000 0.0600 1.0000 : empirical size under different distributions[]{data-label="table2"} N(0,1) t(1) $F(3,2)$ $e^{(N(5,3))}$ ----- -------- -------- -------- -------- ---------- -------- ---------------- -------- -- -- p FCVT CVT FCVT CVT FCVT CVT FCVT CVT 4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 64 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 128 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 256 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 384 0.8113 0.8072 0.9875 1.0000 0.9876 1.0000 0.9905 1.0000 : empirical power under model 1[]{data-label="table3"} N(0,1) t(1) $F(3,2)$ $e^{(N(5,3))}$ ----- -------- -------- -------- -------- ---------- -------- ---------------- -------- -- -- p FCVT CVT FCVT CVT FCVT CVT FCVT CVT 4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 64 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 128 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 256 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 384 0.9066 0.9034 0.9799 1.0000 0.9445 1.0000 0.8883 1.0000 : empirical power under model 2[]{data-label="table4"} N(0,1) t(1) $F(3,2)$ $e^{(N(5,3))}$ ----- -------- -------- -------- -------- ---------- -------- ---------------- -------- -- -- p Size Power Size Power Size Power Size Power 4 0.0695 1.0000 0.0726 1.0000 0.0726 1.0000 0.0664 1.0000 16 0.0695 1.0000 0.0638 1.0000 0.0706 1.0000 0.0556 1.0000 64 0.0646 1.0000 0.0606 1.0000 0.0649 1.0000 0.0622 1.0000 128 0.0617 1.0000 0.0705 1.0000 0.0597 1.0000 0.0630 1.0000 256 0.0684 1.0000 0.0685 1.0000 0.0608 1.0000 0.0649 1.0000 384 0.0610 0.8529 0.0748 1.0000 0.0758 1.0000 0.0742 1.0000 : empirical size and power under different distributions[]{data-label="table5"} Two Real Rata Analysis ---------------------- ### The Death Rate Data Set In [@mcdonald1973instabilities], the authors fitted a multiple linear regression of the total age adjusted mortality rate on 15 other variables (the average annual precipitation, the average January temperature, the average July temperature, the size of the population older than 65, the number of members per household, the number of years of schooling for persons over 22, the number of households with fully equipped kitchens, the population per square mile, the size of the nonwhite population, the number of office workers, the number of families with an income less than \$3000, the hydrocarbon pollution index, the nitric oxide pollution index, the sulfur dioxide pollution index and the degree of atmospheric moisture). The number of observations is 60. To investigate whether the homoscedasticity assumption in this models is justified, we applied our test and got a p-value of 0.4994, which strongly supported the assumption of constant variability in this model since we use the one side test. The data set is available at <http://people.sc.fsu.edu/~jburkardt/datasets/regression/regression.html>. ### The 30-Year Conventional Mortgage Rate Data Set The 30-Year Conventional Mortgage Rate data [@Mortgage] contains the economic data information of USA from 01/04/1980 to 02/04/2000 on a weekly basis (1049 samples). The goal is to predict the 30-Year Conventional Mortgage Rate by other 15 features . We used a multiple linear regression to fit this data set and got a good result. The adjusted R-squared is 0.9986, the P value of the overall F-test is 0. Our homoscedasticity test reported a p-value 0.4439. Proof Of The Main Theorem ========================= This section is to prove the main theorem. The first step is to establish the asymptotic normality of ${\mathbf}T_1$, ${\mathbf}T_2$ and $\alpha{\mathbf}T_1+\beta{\mathbf}T_2$ with $\alpha^2+\beta^2 \neq 0$ by the moment convergence theorem. Next we will calculate the expectations, variances and covariance of the statistics ${\mathbf}T_1=\sum_{i=1}^n\hat{\varepsilon_i}^4$ and ${\mathbf}T_2=\frac{1}{n}{\left(}\sum_{i=1}^n\hat{\varepsilon_i}^2{\right)}^2$. The main theorem then follows by the delta method. Note that without loss of generality, under $H_0$, we can assume that $\sigma=1$. The asymptotic normality of the statistics. {#clt} ------------------------------------------- We start by giving a definition in Graph Theory. A graph ${\mathbf}G={\left(}{\mathbf}V,{\mathbf}E,{\mathbf}F{\right)}$ is called two-edge connected, if removing any one edge from $G$, the resulting subgraph is still connected. The next lemma is a fundamental theorem for Graph-Associated Multiple Matrices without the proof. For the details of this theorem, one can refer to the section ${\mathbf}A.4.2$ in [@bai2010spectral]. \[lm2\] Suppose that ${\mathbf}G={\left(}{\mathbf}V,{\mathbf}E, {\mathbf}F{\right)}$ is a two-edge connected graph with $t$ vertices and $k$ edges. Each vertex $i$ corresponds to an integer $m_i \geq 2$ and each edge $e_j$ corresponds to a matrix ${\mathbf}T^{(j)}={\left(}t_{\alpha,\beta}^{(j)}{\right)},\ j=1,\cdots,k$, with consistent dimensions, that is, if $F(e_j)=(f_i(e_j),f_e(e_j))=(g,h),$ then the matrix ${\mathbf}T^{{\left(}j{\right)}}$ has dimensions $m_g\times m_h$. Define ${\mathbf}v=(v_1,v_2,\cdots,v_t)$ and $$\begin{aligned} T'=\sum_{{\mathbf}v}\prod_{j=1}^kt_{v_{f_i(e_j)},v_{f_e(e_j)}}^{(j)}, \end{aligned}$$ where the summation $\sum_{{\mathbf}v}$ is taken for $v_i=1,2,\cdots, m_i, \ i=1,2,\cdots,t.$ Then for any $i\leq t$, we have $$|T'|\leq m_i\prod_{j=1}^k\|{\mathbf}T^{(j)}\|.$$ Let $\mathcal{T}=({\mathbf}T^{(1)},\cdots,{\mathbf}T^{(k)})$ and define $G(\mathcal{T})=(G,\mathcal{T})$ as a Graph-Associated Multiple Matrices. Write $T'=sum(G(\mathcal{T}))$, which is referred to as the summation of the corresponding Graph-Associated Multiple Matrices. We also need the following truncation lemma \[lm3\] Suppose that $\xi_n={\left(}\xi_1,\cdots,\xi_n{\right)}$ is an i.i.d sequence with ${{\rm E}}|\xi_1|^r \leq \infty$, then there exists a sequence of positive numbers $(\eta_1,\cdots,\eta_n)$ satisfy that as $n \to \infty$, $\eta_n \to 0$ and $$P(\xi_n\neq\widehat \xi_n,\ {\rm i.o.})=0,$$ where $\widehat \xi_n={\left(}\xi_1 I(|\xi_1|\leq \eta_n n^{1/r}),\cdots,\xi_n I(|\xi_n|\leq \eta_n n^{1/r}){\right)}.$ And the convergence rate of $\eta_n$ can be slower than any preassigned rate. ${{\rm E}}|\xi_1|^r \leq \infty$ indicated that for any $\epsilon>0$, we have $$\sum_{m=1}^\infty 2^{2m}P(|\xi_1|\geq\epsilon2^{2m/r})\leq \infty.$$ Then there exists a sequence of positive numbers $\epsilon=(\epsilon_1,\cdots,\epsilon_m)$ such that $$\sum_{m=1}^\infty 2^{2m}P(|\xi_1|\geq\epsilon_m2^{2m/r})\leq \infty,$$ and $\epsilon_m \to 0$ as $m \to 0$. And the convergence rate of $\epsilon_m$ can be slower than any preassigned rate. Now, define $\delta_n=2^{1/r}\epsilon_m$ for $2^{2m-1}\leq n\leq 2^{2m}$, we have as $n\to \infty$ $$\begin{aligned} P(\xi_n\neq\widehat \xi_n,\ {\rm i.o.})\leq &\lim_{k\to \infty}\sum_{m=k}^{\infty}P\Big(\bigcup_{2^{2m-1}\leq n\leq 2^{2m}}\bigcup_{i=1}^n{\left(}|\xi_i|\geq\eta_nn^{1/r}{\right)}\Big)\\\notag \leq&\lim_{k\to \infty}\sum_{m=k}^{\infty}P\Big(\bigcup_{2^{2m-1}\leq n\leq 2^{2m}}\bigcup_{i=1}^{2^{2m}}{\left(}|\xi_i|\geq\epsilon_m 2^{1/r}2^{\frac{{\left(}2m-1{\right)}}{r}}{\right)}\Big)\\\notag \leq&\lim_{k\to \infty}\sum_{m=k}^{\infty}P\Big(\bigcup_{2^{2m-1}\leq n\leq 2^{2m}}\bigcup_{i=1}^{2^{2m}}{\left(}|\xi_i|\geq\epsilon_m 2^{{2m}/{r}}{\right)}\Big)\\\notag =&\lim_{k\to \infty}\sum_{m=k}^{\infty}P\Big(\bigcup_{i=1}^{2^{2m}}{\left(}|\xi_i|\geq\epsilon_m 2^{{2m}/{r}}{\right)}\Big)\\\notag \leq&\lim_{k\to \infty}\sum_{m=k}^{\infty}2^{2m}P\Big(|\xi_1|\geq\epsilon_m 2^{{2m}/{r}}\Big)=0.\end{aligned}$$ We note that the truncation will neither change the symmetry of the distribution of $\xi_1$ nor change the order of the variance of ${\mathbf}T$. Now, we come to the proof of the asymptotic normality of the statistics. We below give the proof of the asymptotic normality of $\alpha{\mathbf}T_1+\beta{\mathbf}T_2$ , where $\alpha^2+\beta^2\neq 0$. The asymptotic normality of either ${\mathbf}T_1$ or ${\mathbf}T_2$ is a result of setting $\alpha=0$ or $\beta=0$ respectively. Denote $\mu_1={{\rm E}}{\mathbf}T_1={{\rm E}}\sum_{i=1}^n\hat \varepsilon_i^4$, $\mu_2={{\rm E}}{\mathbf}T_2={{\rm E}}n^{-1}{\left(}\sum_{i=1}^n\hat \varepsilon_i^2{\right)}^2$ and $S=\sqrt{{\rm {Var}}{\left(}\alpha {\mathbf}T_1+\beta{\mathbf}T_2{\right)}}$. Below is devote to calculating the moments of ${\mathbf}T_0=\frac{\alpha {\mathbf}T_1+\beta {\mathbf}T_2-{\left(}\alpha \mu_1+\beta \mu_2{\right)}}{S}=\frac{\alpha {\left(}{\mathbf}T_1-\mu_1{\right)}+\beta {\left(}{\mathbf}T_2-\mu_2{\right)}}{S}$. Note that by Lemma \[lm3\], we can assume that $\xi_1$ is truncated at $\eta_n n^{1/8}$. Then we have for large enough $n$ and $l>4$, $$M_{2l}\leq \eta_n M_8{\sqrt n}^{2l/4-1}.$$ Let’s take a look at the random variable $$\begin{aligned} &\alpha T_1+\beta T_2=\alpha \sum_{i=1}^n{\left(}\sum_{j=1}^n a_{ij}\xi_j{\right)}^4+(n^{-1})\beta {\left(}\sum_{i=1}^n{\left(}\sum_{j=1}^n a_{ij}\xi_j{\right)}^2{\right)}^2\\\notag =&\alpha \sum_{i,j_1,\cdots,j_4} a_{i,j_1}a_{i,j_2}a_{i,j_3}a_{i,j_4}\xi_{j_1}\xi_{j_2}\xi_{j_3}\xi_{j_4}+(n^{-1})\beta\sum_{i_1,i_2,j_1,\cdots,j_4} a_{i_1,j_1}a_{i_1,j_2}a_{i_2,j_3}a_{i_2,j_4}\xi_{j_1}\xi_{j_2}\xi_{j_3}\xi_{j_4}\\\notag =&\alpha \sum_{i,j_1,\cdots,j_4} a_{i,j_1}a_{i,j_2}a_{i,j_3}a_{i,j_4}\xi_{j_1}\xi_{j_2}\xi_{j_3}\xi_{j_4}+(n^{-1})\beta\sum_{u_1,u_2,v_1,\cdots,v_4} a_{u_1,v_1}a_{u_1,v_2}a_{u_2,v_3}a_{u_2,v_4}\xi_{v_1}\xi_{v_2}\xi_{v_3}\xi_{v_4}.\end{aligned}$$ We next construct two type of graphs for the last two sums. For given integers $i,j_1,j_2,j_3,j_4\in [1,n]$, draw a graph as follows: draw two parallel lines, called the $I$-line and the $J$-line respectively; plot $i$ on the $I$-line and $j_1,j_2,j_3$ and $j_4$ on the $J$-line; finally, we draw four edges from $i$ to $j_t$, $t=1,2,3,4$ marked with $\textcircled{1}$. Each edge $(i,j_t)$ represents the random variable $a_{i,j_t}\xi_{j_t}$ and the graph $G_1(i,{\mathbf}j)$ represents $\prod_{\rho=1}^{4}a_{i,j_\rho}\xi_{j_\rho}$. For any given integer $k_1$, we draw $k_1$ such graphs between the $I$-line and the $J$-line denoted by $G_1(\tau)=G_1(i_\tau,{\mathbf}j_\tau)$, and write $G_{(1,k_1)}=\cup_{\tau} G_1(\tau)$. For given integers $u_1,u_2,v_1,v_2,v_3,v_4\in [1,n]$, draw a graph as follows: plot $u_1$ and $u_2$ on the $I$-line and $v_1,v_2,v_3$ and $v_4$ on the $J$-line; then, we draw two edges from $u_1$ to $v_1$ and $v_2$ marked with $\textcircled{2}$ , draw two edges from $u_2$ to $v_3$ and $v_4$ marked with $\textcircled{2}$. Each edge $(u_l,v_t)$ represents the random variable $a_{u_l,v_t}\xi_{v_t}$ and the graph $G_2({\mathbf}u,{\mathbf}v)$ represents $a_{u_1,v_1}a_{u_1,v_2}a_{u_2,v_3}a_{u_2,v_4}$. For any given integer $k_2$, we draw $k_2$ such graphs between the $I$-line and the $J$-line denoted by $G_2(\psi)=G_2({\mathbf}u_\psi,{\mathbf}v_\psi)$, and write $G_{(2,k_2)}=\cup_{\psi} G_2(\psi)$, $G_{k}=G_{(1,k_1)}\cup G_{(2,k_2)}$. Then the $k$-th order moment of ${\mathbf}T_0$ is $$\begin{aligned} M_k'=&S^{-k}\sum_{k_1+k_2=k}{k\choose k_1}\alpha^{k_1}\beta^{k_2}\sum_{\substack{\{i_1,{\mathbf}j_1,\cdots,i_{k_1},{\mathbf}j_{k_1}\} \\ \{{\mathbf}u_1,{\mathbf}v_1,\cdots,{\mathbf}u_{k_2},{\mathbf}v_{k_2}\}}}\\ &n^{-k_2}{{\rm E}}\Big[\prod_{\tau=1}^{k_1}[G_1(i_\tau,{\mathbf}j_\tau)-{{\rm E}}(G_1(i_\tau,{\mathbf}j_\tau))]\prod_{\phi=1}^{k_2}[G_2({\mathbf}u_\psi,{\mathbf}v_\psi)-{{\rm E}}(G_2({\mathbf}u_\psi,{\mathbf}v_\psi))]\Big].\end{aligned}$$ We first consider a graph $G_k$ for the given set of integers $k_1,k_2$, $i_1, {\mathbf}j_1,\cdots,i_{k_1},{\mathbf}j_{k_1}$ and ${\mathbf}u_1,{\mathbf}v_1,\cdots,{\mathbf}u_{k_2},{\mathbf}v_{k_2}$. We have the following simple observations: Firstly, if $G_k$ contains a $j$ vertex of odd degree, then the term is zero because odd-ordered moments of random variable $\xi_j$ are 0. Secondly, if there is a subgraph $G_1(\tau)$ or $G_2(\psi)$ that does not have an $j$ vertex coinciding with any $j$ vertices of other subgraphs, the term is also 0 because $G_1(\tau)$ or $G_2(\psi)$ is independent of the remainder subgraphs. Then, upon these two observations, we split the summation of non-zero terms in $M_k'$ into a sum of partial sums in accordance of isomorphic classes (two graphs are called isomorphic if one can be obtained from the other by a permutation of $(1,2,\cdots,n)$, and all the graphs are classified into isomorphic classes. For convenience, we shall choose one graph from an isomorphic class as the canonical graph of that class). That is, we may write $$\begin{aligned} M_k'=&S^{-k}\sum_{k_1+k_2=k}{k\choose k_1}\alpha^{k_1}\beta^{k_2}n^{-k_2}\sum_{G_k'}M_{G_k'},\end{aligned}$$ where $$M_{G_k'}=\sum_{G_k\in G_k'}{{\rm E}}G_k.$$ Here $G_k'$ is a canonical graph and $\sum_{G_k\in G_k'}$ denotes the summation for all graphs $G_k$ isomorphic to $G_k'$. In that follows, we need the fact that the variances of ${\mathbf}T_1$ and ${\mathbf}T_2$ and their covariance are all of order n. This will be proved in Section \[var\]. Since all of the vertices in the non-zero canonical graphs have even degrees, every connected component of them is a circle, of course a two-edge connected graph. For a given isomorphic class with canonical graph $G_k'$, denote by $c_{G_k'}$ the number of connected components of the canonical graph $G_k'$. For every connected component $G_0$ that has $l$ non-coincident $J$-vertices with degrees $d_1,\cdots,d_l$, let $d'=\max\{d_1-8,\cdots,d_l-8,0\}$, denote $\mathcal{T}=(\underbrace{{\mathbf}A,\cdots,{\mathbf}A}_{\sum_{t=1}^l d_t})$ and define $G_0(\mathcal{T})=(G_0,\mathcal{T})$ as a Graph-Associated Multiple Matrices. By Lemma \[lm2\] we then conclude that the contribution of this canonical class is at most ${\left(}\prod_{t=1}^l M_{d_t}{\right)}sum(G(\mathcal{T}))=O(\eta_n^{d'}n\sqrt n^{d'/4})$. Noticing that $\eta_n \to 0$, if $c_{G_k'}$ is less than $k/2+k_2$, then the contribution of this canonical class is negligible because $S^k\asymp n^{k/2}$ and $M_{G_k'}$ in $M_k'$ has a factor of $n^{-k_2}$. However one can see that $c_{G_k'}$ is at most $[k/2]+k_2$ for every ${G_k'}$ by the argument above and noticing that every $G_2(\bullet)$ has two $i$ vertices. Therefore, $M_k'\to 0$ if $k$ is odd. Now we consider the limit of $M_k'$ when $k=2s$. We shall say that [*the given set of integers $i_1, {\mathbf}j_1,\cdots,i_{k_1},{\mathbf}j_{k_1}$ and ${\mathbf}u_1,{\mathbf}v_1,\cdots,{\mathbf}u_{k_2},{\mathbf}v_{k_2}$ (or equivalent the graph $G_k$) satisfies the condition $c(s_1,s_2,s_3)$ if in the graph $G_k$ plotted by this set of integers there are $2s_1$ $G_1{{\left(}\bullet{\right)}}$ connected pairwisely, $2s_2$ $G_2{{\left(}\bullet{\right)}}$ connected pairwisely and $s_3$ $G_1{{\left(}\bullet{\right)}}$ connected with $s_3$ $G_2{{\left(}\bullet{\right)}}$, where $2s_1+s_3=k_1$, $2s_2+s_3=k_2$ and $s_1+s_2+s_3=s$, say $G_1{{\left(}2\tau-1{\right)}}$ connects $G_1{{\left(}2\tau{\right)}}$, $\tau=1,2,\cdots,s_1$, $G_2{{\left(}2\psi-1{\right)}}$ connects $G_1{{\left(}2\psi{\right)}}$, $\psi=1,2,\cdots,s_2$ and $G_1{{\left(}2s_1+\varphi{\right)}}$ connects $G_2{{\left(}2s_2+\varphi{\right)}}$, $\varphi=1,2,\cdots,s_3$, and there are no other connections between subgraphs.*]{} Then, for any $G_k$ satisfying $c(s_1,s_2,s_3)$, we have $$\begin{aligned} {{\rm E}}G_k=&\prod_{\tau=1}^{s_1}{{\rm E}}[(G_1{{\left(}2\tau-1{\right)}}-{{\rm E}}(G_1{{\left(}2\tau-1{\right)}}))(G_1{{\left(}2\tau{\right)}}-{{\rm E}}(G_1{\left(}{2\tau}{\right)}))]\times\\\notag &\prod_{\psi=1}^{s_2}{{\rm E}}[(G_2{{\left(}2\psi-1{\right)}}-{{\rm E}}(G_2{{\left(}2\psi-1{\right)}}))(G_2{{\left(}2\psi{\right)}}-{{\rm E}}(G_2{\left(}{2\psi}{\right)}))]\times\\\notag &\prod_{\varphi=1}^{s_3}{{\rm E}}[(G_1{{\left(}2s_1+\varphi{\right)}}-{{\rm E}}(G_1{{\left(}2s_1+\varphi{\right)}}))(G_2{{\left(}2s_2+\varphi{\right)}}-{{\rm E}}(G_2{\left(}{2s_2+\varphi}{\right)}))].\end{aligned}$$ Now, we compare $$\begin{aligned} &n^{-k_2}\sum_{G_k\in c(s_1,s_2,s_3)} {{\rm E}}G_k\\\notag =&n^{-k_2}\sum_{G_k\in c(s_1,s_2,s_3)}\prod_{\tau=1}^{s_1}{{\rm E}}[(G_1{{\left(}2\tau-1{\right)}}-{{\rm E}}(G_1{{\left(}2\tau-1{\right)}}))(G_1{{\left(}2\tau{\right)}}-{{\rm E}}(G_1{\left(}{2\tau}{\right)}))]\times\\\notag &\prod_{\psi=1}^{s_2}{{\rm E}}[(G_2{{\left(}2\psi-1{\right)}}-{{\rm E}}(G_2{{\left(}2\psi-1{\right)}}))(G_2{{\left(}2\psi{\right)}}-{{\rm E}}(G_2{\left(}{2\psi}{\right)}))]\times \\\notag &\prod_{\varphi=1}^{s_3}{{\rm E}}[(G_1{{\left(}2s_1+\varphi{\right)}}-{{\rm E}}(G_1{{\left(}2s_1+\varphi{\right)}}))(G_2{{\left(}2s_2+\varphi{\right)}}-{{\rm E}}(G_2{\left(}{2s_2+\varphi}{\right)}))], \end{aligned}$$ with $$\begin{aligned} &{\left(}{{\rm E}}{\left(}{\mathbf}T_1-\mu_1{\right)}^2{\right)}^{s_1}{\left(}{{\rm E}}{\left(}{\mathbf}T_2-\mu_2{\right)}^2{\right)}^{s_2}{\left(}{{\rm E}}{\left(}{\mathbf}T_1-\mu_1{\right)}{\left(}{\mathbf}T_2-\mu_2{\right)}{\right)}^{s_3}\\\notag =&n^{-k_2}\sum_{G_k}\prod_{\tau=1}^{s_1}{{\rm E}}[(G_1{{\left(}2\tau-1{\right)}}-{{\rm E}}(G_1{{\left(}2\tau-1{\right)}}))(G_1{{\left(}2\tau{\right)}}-{{\rm E}}(G_1{\left(}{2\tau}{\right)}))]\times\\\notag &\prod_{\psi=1}^{s_2}{{\rm E}}[(G_2{{\left(}2\psi-1{\right)}}-{{\rm E}}(G_2{{\left(}2\psi-1{\right)}}))(G_2{{\left(}2\psi{\right)}}-{{\rm E}}(G_2{\left(}{2\psi}{\right)}))]\times \\\notag &\prod_{\varphi=1}^{s_3}{{\rm E}}[(G_1{{\left(}2s_1+\varphi{\right)}}-{{\rm E}}(G_1{{\left(}2s_1+\varphi{\right)}}))(G_2{{\left(}2s_2+\varphi{\right)}}-{{\rm E}}(G_2{\left(}{2s_2+\varphi}{\right)}))],\end{aligned}$$ where $\sum_{G_k\in c(s_1,s_2,s_3)}$ stands for the summation running over all graph $G_k$ satisfying the condition $c(s_1,s_2,s_3)$. If $G_k$ satisfies the two observations mentioned before, then ${{\rm E}}G_k=0$, which does not appear in both expressions; if $G_k$ satisfies the condition $c(s_1,s_2,s_3)$, then the two expressions both contain ${{\rm E}}G_k$. Therefore, the second expression contains more terms that $G_k$ have more connections among subgraphs than the condition $c(s_1,s_2,s_3)$. Therefore, by Lemma \[lm2\], $${\left(}{{\rm E}}{\left(}{\mathbf}T_1-\mu_1{\right)}^2{\right)}^{s_1}{\left(}{{\rm E}}{\left(}{\mathbf}T_2-\mu_2{\right)}^2{\right)}^{s_2}{\left(}{{\rm E}}{\left(}{\mathbf}T_1-\mu_1{\right)}{\left(}{\mathbf}T_2-\mu_2{\right)}{\right)}^{s_3}=n^{-k_2}\sum_{G_k\in c(s_1,s_2,s_3)} {{\rm E}}G_k+o(S^k). \label{map1}$$ If $G_k\in G_k'$ with $c_{G_k'}=s+k_2$, for any nonnegative integers $s_1,s_2,s_3$ satisfying $k_1=2s_1+s_3$, $k_2=2s_2+s_3$ and $s_1+s_2+s_3=s$, we have ${k_1\choose s_3}{k_2 \choose s_3}(2s_1-1)!!(2s_2-1)!!s_3!$ ways to pairing the subgraphs satisfying the condition $c(s_1,s_2,s_3)$. By (\[map1\]), we then have $$\begin{aligned} &&\sum_{c_{G_k'}=s+k_2}n^{-k_2}{{\rm E}}G_k+o(S^k)\\ &=&\sum_{s_1+s_2+s_3=s\atop 2s_1+s_3=k_1, 2s_2+s_3=k_2}{k_1\choose s_3}{k_2 \choose s_3}(2s_1-1)!!(2s_2-1)!!s_3! (Var({\mathbf}T_1))^{s_1}(Var({\mathbf}T_2))^{s_2}(Cov({\mathbf}T_1,{\mathbf}T_2))^{s_3}\end{aligned}$$ It follows that $$\begin{aligned} M_k'=&S^{-k}\sum_{k_1+k_2=k}{k\choose k_1}\alpha^{k_1}\beta^{k_2}n^{-k_2}\sum_{c_{G_k'}=s+k_2}{{\rm E}}G_k+o(1)\\ =&\Big(S^{-2s}\sum_{k_1=0}^{2s}\sum_{s_3=0}^{\min\{k_1,k_2\}}{2s\choose k_1}{k_1 \choose s_3}{k_2 \choose s_3}{\left(}2s_1-1{\right)}!!{\left(}2s_2-1{\right)}!!s_3!\\ &{\left(}\alpha^2Var({\mathbf}T_1){\right)}^{s_1}{\left(}\beta^2Var({\mathbf}T_2){\right)}^{s_2}{\left(}\alpha\beta Cov({\mathbf}T_1,{\mathbf}T_2){\right)}^{s_3}\Big)+o(1)\\ =&\Big(S^{-2s}\sum_{s_1+s_2+s_3=s}{2s\choose 2s_1+s_3}{2s_1+s_3 \choose s_3}{2s_2+s_3 \choose s_3}{\left(}2s_1-1{\right)}!!{\left(}2s_2-1{\right)}!!s_3!\\ &{\left(}\alpha^2Var({\mathbf}T_1){\right)}^{s_1}{\left(}\beta^2Var({\mathbf}T_2){\right)}^{s_2}{\left(}\alpha\beta Cov({\mathbf}T_1,{\mathbf}T_2){\right)}^{s_3}\Big)+o(1)\\ =&\Big(S^{-2s}\sum_{s_1+s_2+s_3=s}\frac{(2s)!(2s_1+s_3)!(2s_2+s_3)!}{{\left(}2s_1+s_3{\right)}!(2s_2+s_3)!s_3!(2s_1)!s_3!(2s_2)!}{\left(}2s_1-1{\right)}!!{\left(}2s_2-1{\right)}!!s_3!\\ &{\left(}\alpha^2Var({\mathbf}T_1){\right)}^{s_1}{\left(}\beta^2Var({\mathbf}T_2){\right)}^{s_2}{\left(}\alpha\beta Cov({\mathbf}T_1,{\mathbf}T_2){\right)}^{s_3}\Big)+o(1)\\ =&\Big(S^{-2s}\sum_{s_1+s_2+s_3=s}(2s-1)!!\frac{s!}{s_1!s_2!s_3!}\\ &{\left(}\alpha^2Var({\mathbf}T_1){\right)}^{s_1}{\left(}\beta^2Var({\mathbf}T_2){\right)}^{s_2}{\left(}2\alpha\beta Cov({\mathbf}T_1,{\mathbf}T_2){\right)}^{s_3}\Big)+o(1),\end{aligned}$$ which implies that $$M'_{2s}\to (2s-1)!!.$$ Combining the arguments above and the moment convergence theorem we conclude that $$\frac{{\mathbf}T_1-{{\rm E}}{\mathbf}T_1}{\sqrt{{\rm Var}{\mathbf}T_1}}\stackrel{d}{\rightarrow} {\rm N}{\left(}0,1{\right)},\ \frac{{\mathbf}T_2-{{\rm E}}{\mathbf}T_2}{\sqrt{{\rm Var}{\mathbf}T_2}}\stackrel{d}{\rightarrow} {\rm N}{\left(}0,1{\right)}, \ \frac{ {\left(}\alpha {\mathbf}T_1+\beta {\mathbf}T_2{\right)}-{{\rm E}}{\left(}\alpha {\mathbf}T_1+\beta {\mathbf}T_2{\right)}}{\sqrt{{\rm Var}{\left(}\alpha {\mathbf}T_1+\beta {\mathbf}T_2{\right)}}}\stackrel{d}{\rightarrow} {\rm N}{\left(}0,1{\right)},$$ where $\alpha^2+\beta^2\neq 0.$ Let $$\Sigma=\left( \begin{array}{cc} {\rm {Var}}({\mathbf}T_1) & \rm {Cov}({\mathbf}T_1,{\mathbf}T_2) \\ \rm {Cov}({\mathbf}T_1,{\mathbf}T_2) & \rm {Var}({\mathbf}T_2) \\ \end{array} \right) .$$ We conclude that $\Sigma^{-1/2}{\left(}{\mathbf}T_1-{{\rm E}}{\mathbf}T_1,{\mathbf}T_2-{{\rm E}}{\mathbf}T_2{\right)}'$ is asymptotic two dimensional gaussian vector. The expectation {#exp} --------------- In the following let ${\mathbf}B={\mathbf}A{\mathbf}A'$. Recall that $${\mathbf}{T_1}=\sum_{i=1}^n\widehat{\varepsilon_i}^4=\sum_{i=1}^n{\left(}\sum_{j=1}^n a_{i,j}\xi_j{\right)}^4=\sum_{i=1}^n\sum_{j_1,j_2,j_3,j_4}a_{i,j_1}a_{i,j_2}a_{i,j_3}a_{i,j_4}\xi_{j_1}\xi_{j_2}\xi_{j_3}\xi_{j_4},$$ $${\mathbf}T_2=n^{-1}{\left(}\sum_{i=1}^n{\left(}\sum_{j=1}^n a_{i,j}\xi_j{\right)}^2{\right)}^2 =n^{-1}\sum_{i_1,i_2}\sum_{j_1,j_2,j_3,j_4}a_{i_1,j_1}a_{i_1,j_2}a_{i_2,j_3}a_{i_2,j_4}\xi_{j_1}\xi_{j_2}\xi_{j_3}\xi_{j_4}.$$ Since all odd moments of $\xi_1,\cdots,\xi_n$ are 0, we know that ${{\rm E}}{\mathbf}T_1$ and ${{\rm E}}{\mathbf}T_2$ are only affected by terms whose multiplicities of distinct values in the sequence $(j_1,\cdots,j_4)$ are all even. We need to evaluate the mixed moment ${{\rm E}}{\left(}{\mathbf}T_1^{\gamma}{\mathbf}T_2^{\omega}{\right)}$. For simplifying notations particularly in Section \[var\] we introduce the following notations $$\begin{aligned} &\Omega_{\{\omega_1,\omega_2,\cdots,\omega_s\}}^{{\left(}\gamma_1,\gamma_2,\cdots,\gamma_t{\right)}}[\underbrace{{\left(}\phi_{1,1},\cdots,\phi_{1,s}{\right)},{\left(}\phi_{2,1},\cdots,\phi_{2,s}{\right)}, \cdots,{\left(}\phi_{t,1},\cdots,\phi_{t,s}{\right)}}_{t \ groups}]_0 \\ =&\sum_{i_1,\cdots,i_{t},j_1\neq\cdots\neq j_{s}}\prod_{\tau=1,\cdots, t}\prod_{\rho=1,\cdots, s} a_{i_{\tau},j_{\rho}}^{\phi_{\tau,\rho}},\end{aligned}$$ where $i_1,\cdots,i_{t}$ and $j_1,\cdots,j_{s}$ run over $1,\cdots,n$ and are subject to the restrictions that $j_1,\cdots,j_s$ are distinct; $\sum_{l=1}^t \gamma_l=\sum_{l=1}^s \omega_l=\theta,$ and for any $k=1,\cdots, s$, $\sum_{l=1}^t \phi_{l,k}=\theta$. Intuitively, $t$ is the number of distinct $i$-indices and $s$ that of distinct $j$’s; $\gamma_\tau$ is the multiplicity of the index $i_\tau$ and $\omega_\rho=\sum_{l=1}^t\phi_{l,\rho}$ that of $j_\rho$; $\phi_{\tau,\rho}$ the multiplicity of the factor $a_{i_\tau,j_\rho}$; and $\theta=4(\gamma+\omega)$. Define $$\begin{aligned} &\Omega_{\{\omega_1,\omega_2,\cdots,\omega_s\}}^{{\left(}\gamma_1,\gamma_2,\cdots,\gamma_t{\right)}}[\underbrace{{\left(}\phi_{1,1},\cdots,\phi_{1,s}{\right)},{\left(}\phi_{2,1},\cdots,\phi_{2,s}{\right)}, \cdots,{\left(}\phi_{t,1},\cdots,\phi_{t,s}{\right)}}_{t \ groups}] \\ =&\sum_{i_1,\cdots,i_{t},j_1,\cdots, j_{s}}\prod_{\tau=1,\cdots, t}\prod_{\rho=1,\cdots, s} a_{i_{\tau},j_{\rho}}^{\phi_{\tau,\rho}}.\end{aligned}$$ The definition above is similar to that of $$\Omega_{\{\omega_1,\omega_2,\cdots,\omega_s\}}^{{\left(}\gamma_1,\gamma_2,\cdots,\gamma_t{\right)}}[\underbrace{{\left(}\phi_{1,1},\cdots,\phi_{1,s}{\right)},{\left(}\phi_{2,1},\cdots,\phi_{2,s}{\right)}, \cdots,{\left(}\phi_{t,1},\cdots,\phi_{t,s}{\right)}}_{t \ groups}]_0$$ without the restriction that the indices $j_1,\cdots,j_s$ are distinct from each other. To help understand these notations we demonstrate some examples as follows. $$\begin{aligned} \Omega_{\{2,2,2,2\}}^{(4,4)}[(2,2,0,0),(0,0,2,2)]=\sum_{i_1,i_2,j_1,\cdots,j_4}a_{i_1,j_1}^2a_{i_1,j_2}^2a_{i_2,j_3}^2a_{i_2,j_3}^2,\end{aligned}$$ $$\begin{aligned} \Omega_{\{2,2,2,2\}}^{(4,4)}[(2,1,1,0),(0,1,1,2)]=\sum_{i_1,i_2,j_1,\cdots,j_4}a_{i_1,j_1}^2a_{i_1,j_2}a_{i_1,j_3}a_{i_2,j_2}a_{i_2,j_3}a_{i_2,j_4}^2,\end{aligned}$$ $$\begin{aligned} \Omega_{\{2,2,2,2\}}^{(4,4)}[(2,2,0,0),(0,0,2,2)]_0=\sum_{i_1,i_2,j_1\neq\cdots\neq j_4}a_{i_1,j_1}^2a_{i_1,j_2}^2a_{i_2,j_3}^2a_{i_2,j_3}^2,\end{aligned}$$ $$\begin{aligned} \Omega_{\{2,2,2,2\}}^{(4,4)}[(2,1,1,0),(0,1,1,2)]_0=\sum_{i_1,i_2,j_1\neq\cdots\neq j_4}a_{i_1,j_1}^2a_{i_1,j_2}a_{i_1,j_3}a_{i_2,j_2}a_{i_2,j_3}a_{i_2,j_4}^2.\end{aligned}$$ We further use $M_k$ to denote the $k$-th order moment of the error random variable. We also use ${\mathbf}C_{n}^k$ to denote the combinatorial number $n \choose k$. We then obtain $$\begin{aligned} \label{e1} &{{\rm E}}{\mathbf}T_1={{\rm E}}\sum_{i=1}^n\sum_{j_1,j_2,j_3,j_4}a_{i,j_1}a_{i,j_2}a_{i,j_3}a_{i,j_4}\xi_{j_1}\xi_{j_2}\xi_{j_3}\xi_{j_4}\\\notag =&M_4\Omega_{\{4\}}^{(4)}+M_2^2{\Omega_{\{2,2\}}^{(4)}}_0=M_4\Omega_{\{4\}}^{(4)}+\frac{{\mathbf}C_4^2}{2!}{\Omega_{\{2,2\}}^{(4)}}[{\left(}2,0{\right)},{\left(}0,2{\right)}]_0\\\notag =&M_4\Omega_{\{4\}}^{(4)}+\frac{{\mathbf}C_4^2}{2!}{\left(}{\Omega_{\{2,2\}}^{(4)}}[{\left(}2,0{\right)},{\left(}0,2{\right)}]-\Omega_{\{4\}}^{(4)}{\right)}\\\notag =&\frac{{\mathbf}C_4^2}{2!}{\Omega_{\{2,2\}}^{(4)}}[{\left(}2,0{\right)},{\left(}0,2{\right)}]+\nu_4 \Omega_{\{4\}}^{(4)} =3\sum_i{\left(}\sum_{j}a_{i,j}^2{\right)}^2+\nu_4\sum_{ij}a_{ij}^4\\\notag =&3\sum_ib_{i,i}^2+\nu_4\sum_{ij}a_{ij}^4=3{{\rm tr}}{\left(}{\mathbf}B{\circ}{\mathbf}B{\right)}+\nu_4{{\rm tr}}({\mathbf}A{\circ}{\mathbf}A)'({\mathbf}A{\circ}{\mathbf}A),\end{aligned}$$ where $\nu_4=M_4-3$ and $$\begin{aligned} \label{e2} &{{\rm E}}{\mathbf}T_2=n^{-1}{{\rm E}}\sum_{i_1,i_2}\sum_{j_1,j_2,j_3,j_4}a_{i_1,j_1}a_{i_1,j_2}a_{i_2,j_3}a_{i_2,j_4}\xi_{j_1}\xi_{j_2}\xi_{j_3}\xi_{j_4}\\\notag =&n^{-1}{\left(}M_4\Omega_{\{4\}}^{(2,2)}+M_2^2{\Omega_{\{2,2\}}^{(2,2)}}_0{\right)}\\\notag =&n^{-1}{\left(}M_4\Omega_{\{4\}}^{(2,2)}+{\left(}{\Omega_{\{2,2\}}^{(2,2)}}[{\left(}2,0{\right)},{\left(}0,2{\right)}]_0+2\Omega_{\{2,2\}}^{(2,2)}[{\left(}1,1{\right)},{\left(}1,1{\right)}]_0{\right)}{\right)}\\\notag =&n^{-1}{\left(}M_4\Omega_{\{4\}}^{(2,2)}+{\left(}{\Omega_{\{2,2\}}^{(2,2)}}[{\left(}2,0{\right)},{\left(}0,2{\right)}]+2\Omega_{\{2,2\}}^{(2,2)}[{\left(}1,1{\right)},{\left(}1,1{\right)}]{\right)}-3\Omega_{\{4\}}^{(2,2)}{\right)}\\\notag =&n^{-1}{\left(}\sum_{i_1,i_2,j_1,j_2}a_{i_1,j_1}^2a_{i_2,j_2}^2+2\sum_{i_1,i_2,j_1,j_2}a_{i_1,j_1}a_{i_1,j_2}a_{i_2,j_1}a_{i_2,j_2} +\nu_4\sum_{i_1,i_2,j}a_{i_1j}^2a_{i_2j}^2{\right)}\\\notag =&n^{-1}{\left(}{\left(}\sum_{i,j}a_{i,j}^2{\right)}^2+2\sum_{i_1,i_2}{\left(}\sum_{j}a_{i_1,j}a_{i_2,j}{\right)}^2+\nu_4\sum_{i_1,i_2,j}a_{i_1j}^2a_{i_2j}^2{\right)}\\\notag =&n^{-1}{\left(}{\left(}\sum_{i,j}a_{i,j}^2{\right)}^2+2\sum_{i_1,i_2}b_{i_1,i_2}^2+\nu_4\sum_{j=1}^nb_{jj}^2{\right)}\\ \notag =&n^{-1}{\left(}{\left(}{{\rm tr}}{\mathbf}B{\right)}^2+2{{\rm tr}}{\mathbf}B^2+\nu_4{{\rm tr}}({\mathbf}B{\circ}{\mathbf}B){\right)}.\end{aligned}$$ The variances and covariance {#var} ---------------------------- We are now in the position to calculate the variances of ${\mathbf}T_1$, ${\mathbf}T_2$ and their covariance. First, we have $$\begin{aligned} \label{t10} &{\rm Var}( {\mathbf}T_1)={{\rm E}}{\left(}\sum_{i}\widehat{\varepsilon_i}^4-{{\rm E}}{\left(}\sum_{i}\widehat{\varepsilon_i}^4{\right)}{\right)}^2\\\notag =&\sum_{i_1,i_2,j_1,\cdots,j_8}[{{\rm E}}G(i_1,{\mathbf}j_1)G(i_2,{\mathbf}j_2)-{{\rm E}}G(i_1,{\mathbf}j_1){{\rm E}}G(i_2,{\mathbf}j_2)]\\\notag =&\Bigg(\Omega_{\{8\}}^{(4,4)}+\Omega_{\{2,6\}_0}^{(4,4)}+\Omega_{\{4,4\}_0}^{(4,4)}+\Omega_{\{2,2,4\}_0}^{(4,4)}+\Omega_{\{2,2,2,2\}_0}^{(4,4)}\Bigg),\\\notag\end{aligned}$$ where the first term comes from the graphs in which the 8 $J$-vertices coincide together; the second term comes from the graphs in which there are 6 $J$-vertices coincident and another two coincident and so on. Because $G(i_1,{\mathbf}j_1)$ and $G(i_2,{\mathbf}j_2)$ have to connected each other, thus, we have $$\begin{aligned} \label{t11} &\Omega_{\{2,2,2,2\}_0}^{(4,4)}\\\notag=&\frac{{\mathbf}C_4^2{\mathbf}C_4^2{\mathbf}C_2^1{\mathbf}C_2^1}{2!}\Omega_{\{2,2,2,2\}}^{(4,4)}[(2,1,1,0),(0,1,1,2)]_0+{{\mathbf}C_4^1{\mathbf}C_3^1{\mathbf}C_2^1}\Omega_{\{2,2,2,2\}}^{(4,4)}[(1,1,1,1),(1,1,1,1)]_0\\\notag =&72\Big(\Omega_{\{2,2,2,2\}}^{(4,4)}[(2,1,1,0),(0,1,1,2)]-4\Omega_{\{2,2,4\}}^{(4,4)}[(2,1,1),(0,1,3)]_0-\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]_0\\\notag &-\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]_0-2\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]_0-\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]_0\\\notag &-2\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]_0-2\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)]_0-\Omega_{\{8\}}^{(4,4)}\Big)\\\notag &+24\Big(\Omega_{\{2,2,2,2\}}^{(4,4)}[(1,1,1,1),(1,1,1,1)]-6\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]_0-3\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]_0\\\notag &-4\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]_0-\Omega_{\{8\}}^{(4,4)}\Big).\\\notag =&72\Big(\Omega_{\{2,2,2,2\}}^{(4,4)}[(2,1,1,0),(0,1,1,2)]-4\Omega_{\{2,2,4\}}^{(4,4)}[(2,1,1),(0,1,3)]-\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]\\\notag &-\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]+2\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]_0+\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]_0\\\notag &+4\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]_0+4\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)]_0+5\Omega_{\{8\}}^{(4,4)}\Big)\\\notag &+24\Big(\Omega_{\{2,2,2,2\}}^{(4,4)}[(1,1,1,1),(1,1,1,1)]-6\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]+3\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]_0\\\notag &+8\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]_0+5\Omega_{\{8\}}^{(4,4)}\Big).\\\notag =&72\Big(\Omega_{\{2,2,2,2\}}^{(4,4)}[(2,1,1,0),(0,1,1,2)]-4\Omega_{\{2,2,4\}}^{(4,4)}[(2,1,1),(0,1,3)]-\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]\\\notag &-\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]+2\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]+\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]\\\notag &+4\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]+4\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)]-6\Omega_{\{8\}}^{(4,4)}\Big)\\\notag &+24\Big(\Omega_{\{2,2,2,2\}}^{(4,4)}[(1,1,1,1),(1,1,1,1)]-6\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]+3\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]\\\notag &+8\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]-6\Omega_{\{8\}}^{(4,4)}\Big).\end{aligned}$$ Likewise we have $$\begin{aligned} \label{t12} &{\Omega_{\{2,2,4\}}^{(4,4)}}_0\\\notag =&{{\mathbf}C_2^1{\mathbf}C_4^3{\mathbf}C_4^1{\mathbf}C_3^1}M_4\Omega_{\{2,2,4\}}^{(4,4)}[(1,2,1),(1,0,3)]_0\\\notag &+\frac{{\mathbf}C_4^2{\mathbf}C_4^2{\mathbf}C_2^1{\mathbf}C_2^1}{2!}M_4\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]_0+{{\mathbf}C_4^2{\mathbf}C_4^2}(M_4-1)\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]_0\\\notag =&96M_4\Omega_{\{2,2,4\}}^{(4,4)}[(1,2,1),(1,0,3)]_0\\\notag &+72M_4\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]_0+36(M_4-1)\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]_0,\\\ \notag =&96M_4\Omega_{\{2,2,4\}}^{(4,4)}[(1,2,1),(1,0,3)]\\\notag &+72M_4\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]+36(M_4-1)\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]\\\ \notag &-96M_4\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]_0-(108 M_4-36)\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]_0\\\notag &-240M_4\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]_0-(168M_4-72)\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)]_0-(204M_4-36)\Omega_{\{8\}}^{(4,4)}\\\notag =&96M_4\Omega_{\{2,2,4\}}^{(4,4)}[(1,2,1),(1,0,3)]\\\notag &+72M_4\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]+36(M_4-1)\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]\\\ \notag &-96M_4\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]-(108 M_4-36)\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]\\\notag &-240M_4\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]-(168M_4-72)\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)]+(408M_4-72)\Omega_{\{8\}}^{(4,4)}\end{aligned}$$ $$\begin{aligned} \label{t13} \Omega_{\{4,4\}_0}^{(4,4)}=&{{\mathbf}C_2^1{\mathbf}C_4^1{\mathbf}C_4^3}M_4^2\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]_0 +\frac{{\mathbf}C_4^2{\mathbf}C_4^2}{2!}(M_4^2-1)\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]_0\\\notag =&16M_4^2\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]+18(M_4^2-1)\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]\\\notag &-(34M_4^2-18)\Omega_{\{8\}}^{(4,4)},\end{aligned}$$ $$\begin{aligned} \label{t14} \Omega_{\{2,6\}_0}^{(4,4)}=&{\mathbf}C_2^1{\mathbf}C_4^2(M_6-M_4)\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)]_0+{\mathbf}C_4^1{\mathbf}C_4^1M_6\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]_0\\\notag =&12(M_6-M_4)\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)]+16M_6\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]\\\notag & -(28 M_6-12 M_4)\Omega_{\{8\}}^{(4,4)}.\end{aligned}$$ and $$\begin{aligned} \label{t15} \Omega_{\{8\}_0}^{(4,4)}=&(M_8-M_4^2)\Omega_{\{8\}}^{(4,4)}[(4),(4)].\end{aligned}$$ Combining (\[t10\]), (\[t11\]), (\[t12\]), (\[t13\]), (\[t14\]) and (\[t15\]), we obtain $$\begin{aligned} \label{vt1} &{\rm Var}( {\mathbf}T_1)=72\Omega_{\{2,2,2,2\}}^{(4,4)}[(2,1,1,0),(0,1,1,2)]+24\Omega_{\{2,2,2,2\}}^{(4,4)}[(1,1,1,1),(1,1,1,1)]\\\notag &+96(M_4-3)\Omega_{\{2,2,4\}}^{(4,4)}[(2,1,1),(0,1,3)] +36(M_4-3)\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]\\\notag &+72(M_4-3)\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]+16(M_4^2-6M_4+9)\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]\\\notag &+18(M_4^2-6M_4+9)\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]+16(M_6-15M_4+30)\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]\\\notag &+12(M_6-15M_4+30)\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)] +(M_8-28M_6-35M_4^2+420M_4-630)\Omega_{\{8\}}^{(4,4)}[(4),(4)],\end{aligned}$$ where $$\begin{aligned} &\Omega_{\{2,2,2,2\}}^{(4,4)}[(2,1,1,0),(0,1,1,2)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}^2a_{i_1,j_2}a_{i_1,j_3}a_{i_2,j_2}a_{i_2,j_3}a_{i_2,j_4}^2\\\notag &={{\rm Diag}}'({\mathbf}B) {\left(}{\mathbf}B{\circ}{\mathbf}B{\right)}{{\rm Diag}}({\mathbf}B),\end{aligned}$$ $$\begin{aligned} &\Omega_{\{2,2,2,2\}}^{(4,4)}[(1,1,1,1),(1,1,1,1)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}a_{i_1,j_2}a_{i_1,j_3}a_{i_1,j_4}a_{i_2,j_1}a_{i_2,j_2}a_{i_2,j_3}a_{i_2,j_4}\\\notag &={{\rm tr}}{\left(}{\mathbf}B{\circ}{\mathbf}B{\right)}^2,\end{aligned}$$ $$\begin{aligned} &\Omega_{\{2,2,4\}}^{(4,4)}[(2,1,1),(0,1,3)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}^2a_{i_1,j_2}a_{i_1,j_3}a_{i_2,j_2}a_{i_2,j_3}^3={{\rm tr}}{\mathbf}B {\mathbf}{D_B} {\mathbf}A {\mathbf}A'^{{\circ}3},\end{aligned}$$ $$\begin{aligned} &\Omega_{\{2,2,4\}}^{(4,4)}[(2,0,2),(0,2,2)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}^2a_{i_1,j_3}^2a_{i_2,j_2}^2a_{i_2,j_3}^2\\\notag &={{\rm Diag}}'({\mathbf}B) {\left(}{\mathbf}A{\circ}{\mathbf}A{\right)}{\left(}{\mathbf}A{\circ}{\mathbf}A{\right)}'{{\rm Diag}}({\mathbf}B) ,\end{aligned}$$ $$\begin{aligned} &\Omega_{\{2,2,4\}}^{(4,4)}[(1,1,2),(1,1,2)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}a_{i_1,j_2}a_{i_1,j_3}^2a_{i_2,j_1}a_{i_2,j_2}a_{i_2,j_3}^2\\\notag &={{\rm tr}}{\left(}{\left(}{\mathbf}B{\circ}{\mathbf}B{\right)}{\left(}{\mathbf}A{\circ}{\mathbf}A{\right)}{\left(}{\mathbf}A{\circ}{\mathbf}A{\right)}'{\right)},\end{aligned}$$ $$\begin{aligned} &\Omega_{\{4,4\}}^{(4,4)}[(3,1),(1,3)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}^3a_{i_1,j_2}a_{i_2,j_1}a_{i_2,j_2}^3={{\rm tr}}{\left(}{\left(}{\mathbf}A^{{\circ}3}{\mathbf}A'{\right)}{\left(}{\mathbf}A^{{\circ}3}{\mathbf}A'{\right)}'{\right)},\end{aligned}$$ $$\begin{aligned} &\Omega_{\{4,4\}}^{(4,4)}[(2,2),(2,2)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}^2a_{i_1,j_2}^2a_{i_2,j_1}^2a_{i_2,j_2}^2={{\rm tr}}{\left(}{\left(}{\mathbf}A {\circ}{\mathbf}A{\right)}{\left(}{\mathbf}A {\circ}{\mathbf}A{\right)}'{\right)}^2 ,\end{aligned}$$ $$\begin{aligned} &\Omega_{\{2,6\}}^{(4,4)}[(1,3),(1,3)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}a_{i_1,j_2}^3a_{i_2,j_1}a_{i_2,j_2}^3={{\rm tr}}{\left(}{\mathbf}B {\mathbf}A^{{\circ}3} {\mathbf}A'^{{\circ}3}{\right)},\end{aligned}$$ $$\begin{aligned} &\Omega_{\{2,6\}}^{(4,4)}[(2,2),(0,4)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}^2a_{i_1,j_2}^2a_{i_2,j_2}^4={{\rm tr}}{\left(}{\left(}{\mathbf}A' {\mathbf}D_{{\mathbf}B}{\mathbf}A {\right)}{\circ}{\left(}{\mathbf}A'^{{\circ}2}{\mathbf}A^{{\circ}2}{\right)}{\right)},\end{aligned}$$ and $$\begin{aligned} &\Omega_{\{8\}}^{(4,4)}[(4),(4)]=\sum_{i_1,\cdots,i_2,j_1,\cdots, j_4}a_{i_1,j_1}^42a_{i_2,j_1}^4={\mathbf}1'{\mathbf}A^{{\circ}4}{\mathbf}A'^{{\circ}4}{\mathbf}1,\end{aligned}$$ Using the same procedure, we have $$\begin{aligned} &{\rm Var}({\mathbf}T_2)=n^{-2}{\left(}{{\rm E}}{\left(}\sum_{i}\widehat{\varepsilon_i}^2{\right)}^4-{{\rm E}}^2{\left(}\sum_{i}\widehat{\varepsilon_i}^2{\right)}^2{\right)}\\\notag =&n^{-2}\sum_{i_1,\cdots,i_4,j_1,\cdots,j_8}a_{i_1,j_1}a_{i_1,j_2}a_{i_2,j_3}a_{i_2,j_4}a_{i_3,j_5}a_{i_3,j_6}a_{i_4,j_7}a_{i_4,j_8} {\left(}{{\rm E}}\prod_{t=1}^8\xi_{j_t}-{{\rm E}}\prod_{t=1}^4\xi_{j_t}{{\rm E}}\prod_{t=5}^8\xi_{j_t}{\right)}\\\notag =&n^{-2}(P_{2,1}+P_{2,2})+O(1),\end{aligned}$$ where $$\begin{aligned} P_{2,1}= {\mathbf}C_2^1{\mathbf}C_2^1{\mathbf}C_2^1\sum_{i_1,\cdots,i_4,j_1,\cdots, j_4}a^2_{i_1,j_1}a_{i_2,j_2}a_{i_3,j_2}a_{i_2,j_3}a_{i_3,j_3}a_{i_4,j_4}^2 =8{\left(}{{\rm tr}}{\mathbf}B{\right)}^2{{\rm tr}}{\mathbf}B^2,\end{aligned}$$ $$\begin{aligned} P_{2,2}=\nu_4{\mathbf}C_2^1{\mathbf}C_2^1\sum_{i_1,\cdots,i_4,j_1,j_2, j_3}a^2_{i_1,j_1}a^2_{i_2,j_2}a^2_{i_3,j_2}a_{i_4,j_3}^2 =4\nu_4{{\rm tr}}({\mathbf}B'{\circ}{\mathbf}B'){\left(}{{\rm tr}}{\mathbf}B{\right)}^2,\end{aligned}$$ Similarly, we have $$\begin{aligned} &{\rm Cov}({\mathbf}T_1,{\mathbf}T_2)=n^{-1}{\left(}{{\rm E}}{\left(}\sum_{i}\widehat{\varepsilon_i}^2{\right)}^2\sum_{i}\widehat{\varepsilon_i}^4-{{\rm E}}{\left(}\sum_{i}\widehat{\varepsilon_i}^2{\right)}^2\sum_{i}\widehat{\varepsilon_i}^4{\right)}\\\notag =&n^{-1}\sum_{i_1,\cdots,i_3,j_1,\cdots,j_8}a_{i_1,j_1}a_{i_1,j_2}a_{i_2,j_3}a_{i_2,j_4}a_{i_3,j_5}a_{i_3,j_6}a_{i_3,j_7}a_{i_3,j_8} {\left(}{{\rm E}}\prod_{t=1}^8\xi_{j_t}-{{\rm E}}\prod_{t=1}^4\xi_{j_t}{{\rm E}}\prod_{t=5}^8\xi_{j_t}{\right)}\\ =&n^{-1}(P_{3.1}+P_{3,2}+P_{3,3}+P_{3,4})+O(1),\end{aligned}$$ where $$\begin{aligned} P_{3,1}={\mathbf}C_4^2{\mathbf}C_2^1{\mathbf}C_2^1\sum_{i_1,\cdots,i_3,j_1,\cdots, j_4}a_{i_1,j_1}^2a_{i_2,j_2}a_{i_2,j_3}a_{i_3,j_2}a_{i_3,j_3}a_{i_3,j_4}^2 =24{{\rm tr}}{\left(}{\mathbf}B^2{\circ}{\mathbf}B{\right)}{{\rm tr}}{\mathbf}B,\end{aligned}$$ $$\begin{aligned} P_{3,2}=\nu_4{\mathbf}C_4^1{\mathbf}C_2^1{\mathbf}C_2^1\sum_{i_1,\cdots,i_3,j_1,\cdots, j_3}a_{i_1,j_1}^2a_{i_2,j_2}a_{i_3,j_2}a_{i_2,j_3}a_{i_3,j_3}^3 =16\nu_4{{\rm tr}}({\mathbf}B{\mathbf}A {\mathbf}A'^{{\circ}3}){{\rm tr}}{\mathbf}B,\end{aligned}$$ $$\begin{aligned} P_{3,3}=\nu_4{\mathbf}C_4^2{\mathbf}C_2^1\sum_{i_1,\cdots,i_3,j_1,\cdots, j_3}a_{i_1,j_1}^2a^2_{i_2,j_2}a^2_{i_3,j_2}a_{i_3,j_3}^2 =12\nu_4{{\rm tr}}{\left(}{\left(}{\mathbf}A'{\mathbf}D_{{\mathbf}B}{\mathbf}A{\right)}{\circ}{\left(}{\mathbf}A'{\mathbf}A{\right)}{\right)}{{\rm tr}}{\mathbf}B,\end{aligned}$$ $$\begin{aligned} \label{ct12} P_{3,3}=\nu_6{\mathbf}C_2^1\sum_{i_1,i_2,i_3,j_1, j_2}a_{i_1,j_1}^2a^2_{i_2,j_2}a^4_{i_3,j_2} =2\nu_6[{{\rm Diag}}({\mathbf}A'{\mathbf}A)'({\mathbf}A'^{{\circ}4}){\mathbf}1]{{\rm tr}}{\mathbf}B,\end{aligned}$$ We would like to point out that we do not need the assumption that $H_0$ holds up to now. From now on, in order to simplify the above formulas we assume $H_0$ holds. Summarizing the calculations above, we obtain under $H_0$ $$\begin{aligned} {{\rm E}}{\mathbf}T_1=3\sum_ib_{i,i}^2+\nu_4\sum_{ij}a_{ij}^4=3{{\rm tr}}{\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}+\nu_4{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)^2,\end{aligned}$$ $$\begin{aligned} \label{e2} {{\rm E}}{\mathbf}T_2=n^{-1}{\left(}{\left(}n-p{\right)}^2+2{\left(}n-p{\right)}+\nu_4{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P){\right)},\end{aligned}$$ $$\begin{aligned} {\rm Var}{\mathbf}T_1=&72{{\rm Diag}}'({\mathbf}P) {\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}{{\rm Diag}}({\mathbf}P)+24{{\rm tr}}{\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}^2\\\notag &+\nu_4{\left(}96{{\rm tr}}{\mathbf}P {\mathbf}{D_P} {\mathbf}P {\mathbf}P^{{\circ}3}+72{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)^3+36{{\rm Diag}}'({\mathbf}P) {\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}^2{{\rm Diag}}({\mathbf}P) {\right)}\\\notag &+\nu^2_4{\left(}18{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)^4+16{{\rm tr}}({\mathbf}P^{{\circ}3}{\mathbf}P)^2){\right)}\\\notag &+\nu_6{\left(}12{{\rm tr}}{\left(}{\left(}{\mathbf}P{\mathbf}D_{{\mathbf}P}{\mathbf}P {\right)}{\circ}{\left(}{\mathbf}P^{{\circ}2}{\mathbf}P^{{\circ}2}{\right)}{\right)}+16{{\rm tr}}{\mathbf}P {\mathbf}P^{{\circ}3}{\mathbf}P^{{\circ}3}{\right)}+\nu_8{\mathbf}1'({\mathbf}P^{{\circ}4}{\mathbf}P^{{\circ}4}){\mathbf}1,\end{aligned}$$ $$\begin{aligned} {\rm Var}({\mathbf}T_2)=\frac{8{\left(}n-p{\right)}^3+4\nu_4{\left(}n-p{\right)}^2{{\rm tr}}({\mathbf}P{\circ}{\mathbf}P)}{n^2}+O(1),\end{aligned}$$ and $$\begin{aligned} &{\rm Cov}({\mathbf}T_1,{\mathbf}T_2)\\\notag =&\frac{{\left(}n-p{\right)}}{n}{\left(}24{{\rm tr}}{\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}+16\nu_4{{\rm tr}}({\mathbf}P {\mathbf}P^{{\circ}3})+12\nu_4{{\rm tr}}{\left(}{\left(}{\mathbf}P{\mathbf}D_{{\mathbf}p}{\mathbf}P{\right)}{\circ}{\mathbf}P{\right)}+2\nu_6[{{\rm Diag}}({\mathbf}P)'({\mathbf}P^{{\circ}4}){\mathbf}1]{\right)}.\end{aligned}$$ The proof of the main theorem ----------------------------- Define a function $f(x,y)=\frac{x}{y}-1$. One may verify that $f_x(x,y)=\frac{1}{y},$ $f_y(x,y)=-\frac{x}{y^2}$, where $f_x(x,y)$ and $f_y(x,y)$ are the first order partial derivative. Since ${\mathbf}T=\frac{{\mathbf}T_1}{{\mathbf}T_2}-1,$ using the delta method, we have under $H_0$, $${{\rm E}}{\mathbf}T=f({{\rm E}}{\mathbf}T_1,{{\rm E}}{\mathbf}T_2)={\left(}\frac{3n{{\rm tr}}{\left(}{\mathbf}P{\circ}{\mathbf}P{\right)}}{(n-p)^2+2{\left(}n-p{\right)}}-1{\right)},$$ $$\begin{aligned} {\rm {Var}} {\mathbf}T=(f_x({{\rm E}}{\mathbf}T_1,{{\rm E}}{\mathbf}T_2),f_y({{\rm E}}{\mathbf}T_1,{{\rm E}}{\mathbf}T_2))\Sigma(f_x({{\rm E}}{\mathbf}T_1,{{\rm E}}{\mathbf}T_2),f_y({{\rm E}}{\mathbf}T_1,{{\rm E}}{\mathbf}T_2))'.\end{aligned}$$ The proof of the main theorem is complete. [10]{} Adelchi Azzalini and Adrian Bowman. On the use of nonparametric regression for checking linear relationships. , pages 549–557, 1993. Zhidong Bai and Jack W Silverstein. , volume 20. Springer, 2010. Trevor S Breusch and Adrian R Pagan. A simple test for heteroscedasticity and random coefficient variation. , pages 1287–1294, 1979. R Dennis Cook and Sanford Weisberg. Diagnostics for heteroscedasticity in regression. , 70(1):1–10, 1983. Holger Dette and Axel Munk. Testing heteroscedasticity in nonparametric regression. , 60(4):693–708, 1998. Holger Dette, Axel Munk, and Thorsten Wagner. Estimating the variance in nonparametric regression—what is a reasonable choice? , 60(4):751–764, 1998. Herbert Glejser. A new test for heteroskedasticity. , 64(325):316–323, 1969. Michael J Harrison and Brendan PM McCabe. A test for heteroscedasticity based on ordinary least squares residuals. , 74(366a):494–499, 1979. S John. Some optimal multivariate tests. , 58(1):123–127, 1971. Zhaoyuan Li and Jianfeng Yao. Homoscedasticity tests valid in both low and high-dimensional regressions. , 2015. Gary C McDonald and Richard C Schwing. Instabilities of regression estimates relating air pollution to mortality. , 15(3):463–481, 1973. Halbert White. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. , pages 817–838, 1980. H.Altay Guvenir and I.Uysal. Bilkent University Function Approximation Repository. , 2000 [^1]: Zhidong Bai is partially supported by a grant NSF China 11571067 [^2]: G. M. Pan was partially supported by a MOE Tier 2 grant 2014-T2-2-060 and by a MOE Tier 1 Grant RG25/14 at the Nanyang Technological University, Singapore. [^3]: Yanqing Yin was partially supported by a project of China Scholarship Council

Amazon Deals New at Amazon Thursday, July 14, 2016 “It’s a simple idea that looks really wacky,” Jordan admits. “But it does have a sound basis in animal behavior theory.” The question is whether lions can be fooled by this same trick. Jordan suspects that they can, especially since lions tend to stalk their prey, and only pounce when an unsuspecting antelope or cow lets down its guard. “Lions are supreme ambush predators—they rely on stealth,” Jordan says in the video. “When seen, they lose this element of surprise and abandon their hunt.” In theory, farmers could protect their cattle by, you guessed it, painting eyes on the cows’ butts so that even when their backs are turned, they appear to be staring at the lions. With their butts. At least one small-scale study has already shown promising results. Dr Jordan’s idea of painting eyes onto cattle rumps came about after two lionesses were killed near the village in Botswana where he was based. While watching a lion hunt an impala, he noticed something interesting: “Lions are ambush hunters, so they creep up on their prey, get close and jump on them unseen. But in this case, the impala noticed the lion. And when the lion realized it had been spotted, it gave up on the hunt,” he says. In nature, being ‘seen’ can deter predation. For example, patterns resembling eyes on butterfly wings are known to deter birds. In India, woodcutters in the forest have long worn masks on the back of their heads to ward-off man-eating tigers. Jordan’s idea was to “hijack this mechanism” of psychological trickery. Last year, he collaborated with the BPCT and a local farmer to trial the innovative strategy, which he’s dubbed “iCow”.

Eduard Spelterini Eduard Spelterini (June 2, 1852 – June 16, 1931) was a Swiss pioneer of ballooning and of aerial photography. Early life Spelterini was born in Bazenheid in the Toggenburg area in Switzerland as Eduard Schweizer. His father, Sigmund Schweizer, was an innkeeper. When he was eight years old, the family reportedly moved to northern Italy, to a place near the Swiss-Italian border in the province of Como. Eduard is said to have attended the schools in Lugano. At the age of eighteen, Eduard allegedly went first to Milan and then to Paris to be trained as an opera singer. During this time, he chose the name "Spelterini", because to him it sound fancier than "Schweizer". His singing career was cut short by a severe case of pneumonia. In any case, Spelterini turned up in the mid-1870s in Paris, and in 1877 he was licensed by the Académie d'Aérostation météorologique de France as a ballon pilot. Ascents around the world In the 1880s, after having successfully made 17 ascents by himself, Spelterini began to offer commercial rides with passengers. In 1887, he had his first own balloon made by the Surcouf company in Paris, a gas balloon with a volume of 1,500 cubic meters, which he named "Urania". The first voyage with this ballon was on October 5, 1887, starting in Vienna. Subsequently, Spelterini moved to the United Kingdom, where he performed together with an American aerial acrobat going by the name of Leona Dare who would perform acrobatic acts suspended under the basket of Spelterini's balloon during the flights. The spectacle, but also Spelterini's often taking journalists for a ride for free ensured them favourable publicity. Together, they toured eastwards through Europe until Moscow, where they parted. Spelterini turned southwards, making ascents in Bucharest, Saloniki, and Athens, before moving to Cairo. After his ascents in spring 1890 over the pyramids of Giza he continued touring, first to Naples, then to Istanbul. In 1891, Spelterini returned to Switzerland. By that time, he was famous for his ballooning adventures. On July 26, 1891, Spelterini made his first ascent in Switzerland, starting at the Heimplatz in Zurich. The initial skepticism of the people vanished quickly, and his starts soon attracted crowds wherever he turned up: Zurich, Winterthur, St. Gall, Interlaken, Vevey, ... His endeavours also caught the attention of scientists. On various occasions, Spelterini made ascents with scientists solely for the purpose of conducting experiments: with physicists to study the atmosphere, with physicians to study human blood cells at low atmospheric pressure, with geologists to study the earth from above. Geologist Albert Heim had once proposed to Spelterini to try crossing the Alps by balloon. But he needed a larger balloon for such an endeavour. With the help of sponsors, he was able to buy the "Wega", twice as large as "Urania" with a volume of 3,260 cubic meters. With it, Heim and Spelterini planned to travel from Sion in the Valais across Uri into the Grisons. But the winds decided otherwise. Despite unfavourable wind conditions, they started on October 3, 1898. The winds drove the balloon across Les Diablerets and then further westwards, across Lake Neuchatel and the Jura Mountains, until they descended near Besançon in France. Much of the trip was made at altitudes between 5000 and 6000 meters above sea level. In the following years, Spelterini crossed the Alps numerous times with his balloons, in all directions. In 1904, he spent several months in Egypt, and in 1911, he even travelled to South Africa, yet he returned each time to Switzerland. Aerial photography Around 1893, Spelterini had begun to take a camera aboard his balloon and started to take pictures on his flights. It was certainly not easy to photograph with this equipment, weighing between 40 and 60 kilograms, and with a minimum exposure time of 1/30th of a second. But Spelterini brought back stunning photographs of the landscape seen from above that won awards repeatedly at aeronautical expositions in Milan, Paris, Brussels, or Frankfurt. For Albert Heim his photos provided whole new insights about the relief of the Alps. Spelterini presented his photos in slide shows wherever he went, from Stockholm to Cape Town, fascinating his audiences and winning the general acclaim of the press, who reviewed his presentations favorably. Decline of ballooning The outbreak of World War I put an end to Spelterini's travels. Borders were closed, and Spelterini's balloons remained grounded. He retired as an independent gentleman to Coppet near Geneva with his wife Emma (née Karpf), whom he had married on January 28, 1914 in the church of St Martin-in-the-Fields in London. But although he was well off financially, his savings diminished in the war years, and what was left of it was eaten up by the post-war inflation. The airplane had surpassed ballooning, nobody cared anymore about his pre-war exploits, and Spelterini was all but forgotten. In 1922, he hired out as a showman at the Tivoli Gardens in Copenhagen, posing for photos and taking people for short rides in a captive balloon. He detested it. Disappointed, he retired to Zipf near Vöcklabruck in Austria, where he had bought a small house and lived from the sale of the eggs of his 300 chickens. In 1926, he tried a last time to revive his old ballooning adventures. With the financial help of some friends, he started from Zurich in a rented balloon. But he fell unconscious during the voyage; his passengers just barely managed to crash-land the balloon in Vorarlberg. Spelterini returned to Zipf, where he died impoverished and largely unknown in 1931. References Further reading Capus, A.: "Geschenke des Himmels", p. 36-50 in Das Magazin 38/2007. In German. Degen, H.R.: "Eduard Spelterini (1852–1931)", p. 39-57 in Schweizer Flugtechniker und Ballonpioniere, Verein für wirtschaftshistorische Studien, Meilen. . In German. Heim, A.: Die Fahrt der "Wega" über Alpen und Jura am 3. Oktober 1898, Verlag B. Schwabe, Basel 1899. In German. Kramer, Th., Stadler, H. (eds.): Edurad Spelterini – Fotografien des Ballonpioniers, Scheidegger & Spiess, 2007. . In German & English. Spelterini, E.: Über den Wolken/Par dessus les nuages, Brunner & Co, Zürich 1928, with an introduction by A. Heim. In German & French. Category:19th-century Swiss photographers Category:Aerial photographers Category:1852 births Category:1931 deaths Category:Aviation pioneers Category:People from Toggenburg Category:20th-century Swiss photographers Category:Swiss balloonists

“If the police are once again made to do political work, the leadership will doubtless fail again. The police institution must be larger than the government or any other entity,” Riyaz advised the hundreds of serving officers in attendance. Riyaz – appointed after the controversial transfer of power in February 2012 – stated that his plans to move into a political career are in order to build trust in this area too. “The police must not be seen to be an institution that just protects the government. The police is an institution that serves all citizens and implements lawful orders and norms. We have to be answerable to the government. We have to be accountable to the parliament”. Riyaz stated that, when he had assumed responsibilities of the police commissioner on the night of February 8, 2012, the police leadership of the time had “failed and hence, people’s perceptions of the police had completely changed”. He asserted that one of his first objectives after assuming the post was to ensure that the police was freed from all external influences and went back to working independently and professionally. Riyaz further stated that police had remained steadfast in the face of wrongful allegations and perceptions of their work, while emphasizing that during his time as commissioner he had “never made a decision or issued an order with the intention of inflicting harm or harassment to any specific individual”. “When Amnesty International released a report with false statements against us, I personally made a phone call to their president. In response to every one of these statements, we sent a statement clarifying the truth of the matter.” “When I first took up the post, I was reluctant to even claim my pay as there was so much murder being committed. However, due to the work done unitedly, god willing we haven’t seen a major death this year,” Riyaz said. February, 2012 Riyaz spoke in detail about his role in the controversial transfer of power on February 7, 2012. The retired commissioner – who had at the time been relieved of his duties as a police officer – stated on Monday night that he had gone there on the day with “good intentions because [he] could not bear to sit home and watch the situation the police and soldiers were in”. He added that he had contacted both the current Defence Minister Mohamed Nazim and former Deputy Minister of Home Affairs Mohamed Fayaz via phone prior to going there. Stating that he had prioritized national interest above all, Riyaz claimed that he had accepted the post of police commissioner because his country needed him. “Police were desiring a leadership that would not issue unlawful orders. Many asked me why I was going back to this institution, including my wife. But I decided that I cannot turn my back to the nation at the time it needed me most.” Riyaz ended his speech by “seeking forgiveness from any police officer of citizen I may have inconvenienced during my time as commissioner of police”. “Although I am leaving behind life as a police officer and entering politics, I will always defend this institution. There is no institution I can love as much as I do the police.” He added that Vice Presidentv Dr Mohamed Jameel Ahmed had been the first to advise him to enter the political arena. Appreciation from the state “The happiest day that I have come across so far is the day when a new president was elected on November 16, the second round of the presidential election. What made me happiest about it is that we were assured that a government has been established which will not undermine or disrespect important state institutions like the police, the military, the judiciary and other entities,” he said. “And that this is a government which will protect the religious unity of this nation and ensure that expensive state assets are not sold out to foreign companies,” he continued. “The fact that Maldivian citizens voted in a Jumhooree Party and Progressive Party of Maldives government proves that the events that happened on February 7 [2012] was not a coup d’etat,” he stated. Other speakers at the event, including Vice President Jameel, Home Minister Umar Naseer and current Police Commissioner Hussain Waheed commended Riyaz for his work. Home Minister Umar described Riyaz as an assertive and sharp-minded officer who had brought commendable development to the institution. Current Commissioner of Police Hussain Waheed stated that Riyaz had stood up to defend the police institution even when faced with “immense pressure, criticism and threats against [police officers’] families”. “Even as police were referred to with various hateful names, and even some officers’ lives were taken, our brother Riyaz was working tirelessly in our defence.” There used to be an old British Sit Com, 'It ain't half hot mum', the theme tune was, 'the boys to entertain you'. A bit like The Maldives now, all very entertaining, except of course if you support the MDP.

Q: What is wrong with this definition of a discrete random variable? (note regarding notation for function application: I sometimes write $f(x)$ as $f.x$, to simplify brackets) I begin by defining the key pieces of the random variable definition, in a way that is more detailed than necessary, for the sake of pedagogy. A "random variable" isn't random or a variable. It is a surjective function between a sample space $S$ and a set of real values in a set $V \subset \mathbb{R}$. Let $X$ be some such function. Even though $X$ is surjective and thus does not necessarily have an inverse, we will still be interested in the co-function: $\tilde{X}: V \rightarrow A \subset S$, which maps a value in $V$ to some subset of elements in $S$ in this way: $$\tilde{X}.v = \bigcup\{A \subset S: X.A = v\}$$ Recall that a probability function $P$ over $S$ maps subsets of $S$ to a real numbers in $U$, where $U$ is such that $U \subset [0, 1]$, and $\sum U = 1$. This means that $P.\tilde{X}: V \rightarrow A \subset S \rightarrow U$ is a probability function on the set $V$, governed by the structure of $P$ on $S$. The function $p_X = P.\tilde{X}$ is called the "mass" function if $S$ is finite in size. Let $S = \{A, B, C\}$, and let $V = \{1, 2\}$. Let $P$ be a probability function over $S$ such that $P(A) = P(B) = P(C) = 1/3$. Let $X$ be a random variable such that $X: R \subseteq S \rightarrow V$, such that: $X.\{A, B\} = 1 = X.\{B, C\}$ and $X.\{A, C\} = 2$. Let $p_X$ be the probability mass function for the RV $X$. How will $p_X$ be defined? Note that $p_X = P.\tilde{X}$. So we first need to construct $\tilde{X}$. There is two values in $V$: \begin{align} &\tilde{X}.1 = \bigcup \{E \subset S : X.E = 1\} = \{A, B\} \cup \{B, C\} = \{A, B, C\} \\ &\tilde{X}.2 = \bigcup \{E \subset S : X.E = 2\} = \{A, C\} \end{align} So: \begin{align} &p_{X}.1 = P.\tilde{X}.1 = P.\{A, B, C\} = 1 \\ &p_{X}.2 = P.\tilde{X}.2 = P.\{A, C\} = 2/3 \end{align} What is the sum of $p_{X}$ over all the values it can take? \begin{align} \sum_{y \in V} p_{X}.y = p_{X}.1 + p_{X}.2 = 1 + 2/3 = 5/3 \end{align} Shouldn't the sum of $p_X$ over all its values sum to $1$ though? What am I doing wrong? A closer reading of my textbook suggests the following: 1) a random variable is simply any function from a sample space, to a subset of the real numbers. 2) a random variable is a discrete random variable if for a set of finite or countably infinite values $\{k_1, k_2, \dots\}$, where $\{k_i\} \subset \mathbb{R}$, we have that $\sum_{i} P.\tilde{X}.k_i = 1$. What is a random variable for which an appropriate $\{k_i\}$ satisfying point 2 has not been defined called? This is what I constructed in the first part of the question. An easy way to fix the problem would be to renormalize $P.\tilde{X}.v$ by what it sums to be: $$ P.\tilde{X}.1 = 1/(5/3) = 3/5, \; P.\tilde{X}.2 = 2/3/(5/3) = 2/5$$ What would such renormalization be called? A: your mistake is your definition of X. As it is a function from S, you need to set X for each element of S and not for subsets of S. Ie you need to define $X.A, X.B, X.C$ (and not $X.\{A,C\}$, $X.\{A,B\}$ or $X.\{B,C\}$) so the sum of probabilities will be consistent.

Q: Reshaping a tensor with more than one uknown diemnsions I need to be able to reshape a tensor only on its last axis: (None, 4) --> (None, 2, 2), which at time of execution can have instances like these: (128, 10, 4) --> (128, 10, 2, 2) (128, 4) --> (128, 2, 2) Is there a straight forward solution or I need to iterate on the first axes (by excluding the last one), and considering the case that it can be None? A: You can do that like this: my_tensor = ... new_shape = tf.concat([tf.shape(my_tensor)[:-1], [2, 2]], axis=0) my_tensor_reshaped = tf.reshape(my_tensor, new_shape)

--- abstract: 'In this article we relate word and subgroup growth to certain functions that arise in the quantification of residual finiteness. One consequence of this endeavor is a pair of results that equate the nilpotency of a finitely generated group with the asymptotic behavior of these functions. The second half of this article investigates the asymptotic behavior of two of these functions. Our main result in this arena resolves a question of Bogopolski from the Kourovka notebook concerning lower bounds of one of these functions for nonabelian free groups.' author: - 'K. Bou-Rabee[^1]  and D. B. McReynolds[^2]' title: | **Asymptotic growth and\ least common multiples in groups** --- 1991 MSC classes: 20F32, 20E26 .05in keywords: *free groups, hyperbolic groups, residual finiteness, subgroup growth, word growth.* Introduction ============ The goals of the present article are to examine the interplay between word and subgroup growth, and to quantify residual finiteness, a topic motivated and described by the first author in [@Bou]. These two goals have an intimate relationship that will be illustrated throughout this article. Our focus begins with the interplay between word and subgroup growth. Recall that for a fixed finite generating set $X$ of $\Gamma$ with associated word metric ${\left\vert \left\vert \cdot\right\vert\right\vert}_X$, word growth investigates the asymptotic behavior of the function $$\operatorname{w}_{\Gamma,X}(n) = {\left\vert{\left\{\gamma \in \Gamma~:~ {\left\vert \left\vert \gamma\right\vert\right\vert}_X \leq n\right\}}\right\vert},$$ while subgroup growth investigates the asymptotic behavior of the function $$\operatorname{s}_\Gamma(n) = {\left\vert{\left\{\Delta \lhd \Gamma~:~ [\Gamma:\Delta]\leq n\right\}}\right\vert}.$$ To study the interaction between word and subgroup growth we propose the first of a pair of questions: **Question 1.** *What is the smallest integer $\operatorname{F}_{\Gamma,X}(n)$ such that for every word $\gamma$ in $\Gamma$ of word length at most $n$, there exists a finite index normal subgroup of index at most $\operatorname{F}_{\Gamma,X}(n)$ that fails to contain $\gamma$?* To see that the asymptotic behavior of $\operatorname{F}_{\Gamma,X}(n)$ measures the interplay between word and subgroup growth, we note the following inequality (see Section \[Preliminary\] for a simple proof): $$\label{BasicInequality} \log (\operatorname{w}_{\Gamma,X}(n)) \leq \operatorname{s}_\Gamma(\operatorname{F}_{\Gamma,X}(2n))\log (\operatorname{F}_{\Gamma,X}(2n)).$$ Our first result, which relies on Inequality (\[BasicInequality\]), is the following. \[DivisibilityLogGrowth\] If $\Gamma$ is a finitely generated linear group, then the following are equivalent: - $\operatorname{F}_{\Gamma,X}(n) \leq (\log(n))^r$ for some $r$. - $\Gamma$ is virtually nilpotent. For finitely generated linear groups that is not virtually nilpotent, Theorem \[DivisibilityLogGrowth\] implies $\operatorname{F}_{\Gamma,X}(n) \nleq (\log(n))^r$ for any $r >0$. For this class of groups, we can improve this lower bound. Precisely, we have the following result—see Section \[Preliminary\] for the definition of $\preceq$. \[basiclowerbound\] Let $\Gamma$ be a group that contains a nonabelian free group of rank $m$. Then $$n^{1/3} \preceq \operatorname{F}_{\Gamma,X}(n).$$ The motivation for the proof of Theorem \[basiclowerbound\] comes from the study of $\operatorname{F}_{{\ensuremath{{\ensuremath{\mathbf{Z}}}}},X}(n)$, where the Prime Number Theorem and least common multiples provide lower and upper bounds for $\operatorname{F}_{{\ensuremath{{\ensuremath{\mathbf{Z}}}}},X}(n)$. In Section \[FreeGroupGrowth\], we extend this approach by generalizing least common multiples to finitely generated groups (a similar approach was also taken in the article of Hadad [@Hadad]). Indeed with this analogy, Theorem \[basiclowerbound\] and the upper bound of $n^3$ established in [@Bou], [@Rivin] can be viewed as a weak Prime Number Theorem for free groups since the Prime Number Theorem yields $\operatorname{F}_{\ensuremath{{\ensuremath{\mathbf{Z}}}}}(n) \simeq \log(n)$. Recently, Kassabov–Matucci [@KM] improved the lower bound of $n^{1/3}$ to $n^{2/3}$. A reasonable guess is that $\operatorname{F}_{F_m,X}(n) \simeq n$, though presently neither the upper or lower bound is known. We refer the reader to [@KM] for additional questions and conjectures. There are other natural ways to measure the interplay between word and subgroup growth. Let $B_{\Gamma,X}(n)$ denote $n$–ball in $\Gamma$ for the word metric associated to the generating set $X$. Our second measurement is motivated by the following question—in the statement, $B_{\Gamma,X}(n)$ is the metric $n$–ball with respect to the word metric ${\left\vert \left\vert \cdot\right\vert\right\vert}_X$: **Question 2.** *What is the cardinality $\operatorname{G}_{\Gamma,X}(n)$ of the smallest finite group $Q$ such that there exists a surjective homomorphism ${\varphi}{\ensuremath{\colon}}\Gamma \to Q$ with the property that ${\varphi}$ restricted to $B_{\Gamma,X}(n)$ is injective?* We call $\operatorname{G}_{\Gamma,X}(n)$ the *residual girth function* and relate $\operatorname{G}_{\Gamma,X}(n)$ to $\operatorname{F}_{\Gamma,X}$ and $\operatorname{w}_{\Gamma,X}(n)$ for a class of groups containing non-elementary hyperbolic groups; Hadad [@Hadad] studied group laws on finite groups of Lie type, a problem that is related to residual girth and the girth of a Cayley graph for a finite group. Specifically, we obtain the following inequality (see Section \[FreeGroupGrowth\] for a precise description of the class of groups for which this inequality holds): $$\label{BasicGirthEquation} \operatorname{G}_{\Gamma,X}(n/2) \leq \operatorname{F}_{\Gamma,X}{\left( 6n(\operatorname{w}_{\Gamma,X}(n))^{2} \right) }.$$ Our next result shows that residual girth functions enjoy the same growth dichotomy as word and subgroup growth—see [@gromov] and [@lubsegal-2003]. \[GirthPolynomialGrowth\] If $\Gamma$ is a finitely generated group then the following are equivalent. - $\operatorname{G}_{\Gamma,X}(n) \leq n^r$ for some $r$. - $\Gamma$ is virtually nilpotent. The asymptotic growth of $\operatorname{F}_{\Gamma,X}(n)$, $\operatorname{G}_{\Gamma,X}(n)$, and related functions arise in quantifying residual finiteness, a topic introduced in [@Bou] (see also the recent articles of the authors [@BM], Hadad [@Hadad], Kassabov–Mattucci [@KM], and Rivin [@Rivin]). Quantifying residual finiteness amounts to the study of so-called divisibility functions. Given a finitely generated, residually finite group $\Gamma$, we define the *divisibility function* $\operatorname{D}_\Gamma{\ensuremath{\colon}}\Gamma^\bullet {\longrightarrow}{\ensuremath{{\ensuremath{\mathbf{N}}}}}$ by $$\operatorname{D}_\Gamma(\gamma) = \min {\left\{[\Gamma:\Delta] ~:~ \gamma \notin \Delta\right\}}.$$ The associated *normal divisibility function* for normal, finite index subgroups is defined in an identical way and will be denoted by $\operatorname{D}_{\Gamma}^\lhd$. It is a simple matter to see that $\operatorname{F}_{\Gamma,X}(n)$ is the maximum value of $\operatorname{D}_{\Gamma}^\lhd$ over all non-trivial elements in $B_{\Gamma,X}(n)$. We will denote the associated maximum of $\operatorname{D}_\Gamma$ over this set by $\max \operatorname{D}_\Gamma (n)$. The rest of the introduction is devoted to a question of Oleg Bogopolski, which concerns $\max \operatorname{D}_{\Gamma,X}(n)$. It was established in [@Bou] that $\log(n) \preceq \max \operatorname{D}_{\Gamma,X}(n)$ for any finitely generated group with an element of infinite order (this was also shown by [@Rivin]). For a nonabelian free group $F_m$ of rank $m$, Bogopolski asked whether $\max \operatorname{D}_{F_m,X}(n) \simeq \log(n)$ (see Problem 15.35 in the Kourovka notebook [@TheBook]). Our next result answers Bogopolski’s question in the negative—we again refer the reader to Section \[Preliminary\] for the definition of $\preceq$. \[toughlowerbound\] If $m>1$, then $\max \operatorname{D}_{F_m,X}(n) \npreceq \log(n)$. We prove Theorem \[toughlowerbound\] in Section \[toughlowerboundSection\] using results from Section \[FreeGroupGrowth\]. The first part of the proof of Theorem \[toughlowerbound\] utilizes the material established for the derivation of Theorem \[basiclowerbound\]. The second part of the proof of Theorem \[toughlowerbound\] is topological in nature, and involves a careful study of finite covers of the figure eight. It is also worth noting that our proof only barely exceeds the proposed upper bound of $\log(n)$. In particular, at present we cannot rule out the upper bound $(\log(n))^2$. In addition, to our knowledge the current best upper bound is $n/2 + 2$, a result established recently by Buskin [@Bus]. In comparison to our other results, Theorem \[toughlowerbound\] is the most difficult to prove and is also the most surprising. Consequently, the reader should view Theorem \[toughlowerbound\] as our main result. #### **Acknowledgements.** Foremost, we are extremely grateful to Benson Farb for his inspiration, comments, and guidance. We would like to thank Oleg Bogopolski, Emmanuel Breuillard, Jason Deblois, Jordan Ellenberg, Tsachik Gelander, Uzy Hadad, Frédéric Haglund, Ilya Kapovich, Martin Kassabov, Larsen Louder, Justin Malestein, Francesco Matucci, and Igor Rivin for several useful conversations and their interest in this article. Finally, we extend thanks to Tom Church, Blair Davey, and Alex Wright for reading over earlier drafts of this paper. The second author was partially supported by an NSF postdoctoral fellowship. Divisibility and girth functions {#Preliminary} ================================ In this introductory section, we lay out some of the basic results we require in the sequel. For some of this material, we refer the reader to [@Bou Section 1]. #### **Notation.** Throughout, $\Gamma$ will denote a finitely generated group, $X$ a fixed finite generating set for $\Gamma$, and ${\left\vert \left\vert \cdot\right\vert\right\vert}_X$ will denote the word metric. For $\gamma \in \Gamma$, ${\left< \gamma \right>}$ will denote the cyclic subgroup generated by $\gamma$ and $\overline{{\left< \gamma \right>}}$ the normal closure of ${\left< \gamma \right>}$. For any subset $S \subset \Gamma$ we set $S^\bullet = S-1$. #### **1. Function comparison and basic facts**. For a pair of functions $f_1,f_2{\ensuremath{\colon}}{\ensuremath{{\ensuremath{\mathbf{N}}}}}\to {\ensuremath{{\ensuremath{\mathbf{N}}}}}$, by $f_1 \preceq f_2$, we mean that there exists a constant $C$ such that $f_1(n) \leq Cf_2(Cn)$ for all $n$. In the event that $f_1 \preceq f_2$ and $f_2 \preceq f_1$, we will write $f_1 \simeq f_2$. This notion of comparison is well suited to the functions studied in this paper. We summarize some of the basic results from [@Bou] for completeness. \[DivisibilityAsymptoticLemma\] Let $\Gamma$ be a finitely generated group. - If $X,Y$ are finite generating sets for $\Gamma$ then $\operatorname{F}_{\Gamma,X} \simeq \operatorname{F}_{\Gamma,Y}$. - If $\Delta$ is a finitely generated subgroup of $\Gamma$ and $X,Y$ are finite generating sets for $\Gamma,\Delta$ respectively, then $\operatorname{F}_{\Delta,Y} \preceq \operatorname{F}_{\Gamma,X}$. - If $\Delta$ is a finite index subgroup of $\Gamma$ with $X,Y$ as in (b), then $\operatorname{F}_{\Gamma,X} \preceq (\operatorname{F}_{\Delta,Y})^{[\Gamma:\Delta]}$. We also have a version of Lemma \[DivisibilityAsymptoticLemma\] for residual girth functions. \[GirthAsymptoticLemma\] Let $\Gamma$ be a finitely generated group. - If $X,Y$ are finite generating sets for $\Gamma$, then $\operatorname{G}_{\Gamma,X} \simeq \operatorname{G}_{\Gamma,Y}$. - If $\Delta$ is a finitely generated subgroup of $\Gamma$ and $X,Y$ are finite generating sets for $\Gamma,\Delta$ respectively, then $\operatorname{G}_{\Delta,Y} \preceq \operatorname{G}_{\Gamma,X}$. - If $\Delta$ is a finite index subgroup of $\Gamma$ with $X,Y$ as in (b), then $\operatorname{G}_{\Gamma,X} \preceq (\operatorname{G}_{\Delta,Y})^{[\Gamma:\Delta]}$. As the proof of Lemma \[GirthAsymptoticLemma\] is straightforward, we have opted to omit it for sake of brevity. As a consequence of Lemmas \[DivisibilityAsymptoticLemma\] and \[GirthAsymptoticLemma\], we occasionally suppress the dependence of the generating set in our notation. #### **2. The basic inequality.** We now derive (\[BasicInequality\]) from the introduction. For the reader’s convenience, recall (\[BasicInequality\]) is $$\log (\operatorname{w}_{\Gamma,X}(n)) \leq \operatorname{s}_\Gamma(\operatorname{F}_{\Gamma,X}(2n))\log (\operatorname{F}_{\Gamma,X}(2n)).$$ We may assume that $\Gamma$ is residually finite as otherwise $\operatorname{F}_\Gamma(n)$ is eventually infinite for sufficiently large $n$ and the inequality is trivial. By definition, for each word $\gamma \in B_{\Gamma,X}^\bullet(2n)$, there exists a finite index, normal subgroup $\Delta_\gamma$ in $\Gamma$ such that $\gamma \notin \Delta_\gamma$ and $[\Gamma:\Delta_\gamma] \leq \operatorname{F}_{\Gamma,X}(2n)$. Setting $\Omega_{\operatorname{F}_{\Gamma,X}(2n)}(\Gamma)$ to be the intersection of all finite index, normal subgroup of index at most $\operatorname{F}_{\Gamma,X}(2n)$, we assert that $B_{\Gamma,X}(n)$ injects into quotient $\Gamma/\Omega_{\operatorname{F}_{\Gamma,X}(2n)}(\Gamma)$. Indeed, if two elements $\gamma_1,\gamma_2 \in B_{\Gamma,X}(n)$ had the same image, the element $\gamma_1\gamma_2^{-1}$ would reside in $\Omega_{\operatorname{F}_{\Gamma,X}(2n)}(\Gamma)$. However, by construction, every element of word length at most $2n$ has nontrivial image. In particular, we see that $$\begin{aligned} \operatorname{w}_{\Gamma,X}(n) &= {\left\vertB_{\Gamma,X}(n)\right\vert} \leq {\left\vert\Gamma/\Omega_{\operatorname{F}_{\Gamma,X}(2n)}(\Gamma)\right\vert} \\ & \leq \prod_{\scriptsize{\begin{matrix} \Delta \lhd \Gamma \\ [\Gamma:\Delta]\leq \operatorname{F}_{\Gamma,X}(2n)\end{matrix}}} {\left\vert\Gamma/\Delta\right\vert} \\ &\leq \prod_{\scriptsize{\begin{matrix} \Delta \lhd \Gamma \\ [\Gamma:\Delta]\leq \operatorname{F}_{\Gamma,X}(2n)\end{matrix}}} \operatorname{F}_{\Gamma,X}(2n) \\ &\leq (\operatorname{F}_{\Gamma,X}(2n))^{\operatorname{s}_\Gamma(\operatorname{F}_{\Gamma,X}(2n))}.\end{aligned}$$ Taking the log of both sides, we obtain $$\log(\operatorname{w}_{\Gamma,X}(n)) \leq \operatorname{s}_\Gamma(\operatorname{F}_{\Gamma,X}(2n))\log(\operatorname{F}_{\Gamma,X}(2n)).$$ In fact, the proof of (\[BasicInequality\]) yields the following. Let $\Gamma$ be a finitely generated, residually finite group. Then $$\log (\operatorname{G}_{\Gamma,X}(n)) \leq \operatorname{s}_\Gamma(\operatorname{F}_{\Gamma,X}(2n)) \log(\operatorname{F}_{\Gamma,X}(2n)).$$ #### **3. An application of (\[BasicInequality\]).** We now derive the following as an application of (\[BasicInequality\]). \[BasicInequalityMainProp\] Let $\Gamma$ be a finitely generated, residually finite group. If there exists $\alpha > 1$ such that $\alpha^n \preceq \operatorname{w}_{\Gamma,X}(n)$, then $\operatorname{F}_{\Gamma,X}(n) \npreceq (\log n)^r$ for any $r \in {\ensuremath{{\ensuremath{\mathbf{R}}}}}$. Assume on the contrary that there exists $r \in {\ensuremath{{\ensuremath{\mathbf{R}}}}}$ such that $\operatorname{F}_{\Gamma,X} \preceq (\log(n))^r$. In terms of $\preceq$ notation, inequality (\[BasicInequality\]) becomes: $$\log(\operatorname{w}_{\Gamma, X} (n)) \preceq s_\Gamma (\operatorname{F}_{\Gamma, X}(n)) \log(\operatorname{F}_{\Gamma, X}(n)).$$ Taking the log of both sides, we obtain $$\log\log(\operatorname{w}_{\Gamma, X} (n)) \preceq \log(\operatorname{s}_\Gamma (\operatorname{F}_{\Gamma, X}(n)))+ \log(\log(\operatorname{F}_{\Gamma, X}(n))).$$ This inequality, in tandem with the assumptions $$\begin{aligned} \alpha^n &\preceq \operatorname{w}_{\Gamma,X}(n), \\ \operatorname{F}_{\Gamma,X}(n) &\preceq (\log(n))^r,\end{aligned}$$ and $\log(\operatorname{s}_\Gamma(n)) \preceq (\log(n))^2$ (see [@lubsegal-2003 Corollary 2.8]) gives $$\log(n) \preceq (\log\log(n))^2 + \log\log\log(n),$$ which is impossible. With Proposition \[BasicInequalityMainProp\], we can now prove Theorem \[DivisibilityLogGrowth\]. For the direct implication, we assume that $\Gamma$ is a finitely generated linear group with $\operatorname{F}_\Gamma \preceq (\log n)^r$ for some $r$. According to the Tits’ alternative, either $\Gamma$ is virtually solvable or $\Gamma$ contains a nonabelian free subgroup. In the latter case, $\Gamma$ visibly has exponential word growth and thus we derive a contradiction via Proposition \[BasicInequalityMainProp\]. In the case $\Gamma$ is virtually solvable, $\Gamma$ must also have exponential word growth unless $\Gamma$ is virtually nilpotent (see [@harpe-2000 Theorem VII.27]). This in tandem with Proposition \[BasicInequalityMainProp\] implies $\Gamma$ is virtually nilpotent. For the reverse implication, let $\Gamma$ be a finitely generated, virtually nilpotent group with finite index, nilpotent subgroup $\Gamma_0$. According to Theorem 0.2 in [@Bou], $\operatorname{F}_{\Gamma_0} \preceq (\log n)^r$ for some $r$. Combining this with Lemma \[DivisibilityAsymptoticLemma\] (c) yields $\operatorname{F}_\Gamma \preceq (\log n)^{r[\Gamma:\Gamma_0]}$. In the next two sections, we will prove Theorem \[basiclowerbound\]. In particular, for finitely generated linear groups that are not virtually solvable, we obtain an even better lower bound for $\operatorname{F}_{\Gamma,X}(n)$ than can be obtained using (\[BasicInequality\]). Namely, $n^{1/3} \preceq \operatorname{F}_{\Gamma,X}(n)$ for such groups. The class of non-nilpotent, virtually solvable groups splits into two classes depending on whether the rank of the group is finite or not. This is not the standard notion of rank but instead $$\textrm{rk}(\Gamma) = \max{\left\{ r(\Delta)~:~ \Delta \text{ is a finitely generated subgroup of } \Gamma\right\}},$$ where $$r(\Delta) = \min{\left\{{\left\vertY\right\vert}~:~Y \text{ is a generating set for }\Delta\right\}}.$$ The class of virtually solvable groups with finite rank is known to have polynomial subgroup growth (see [@lubsegal-2003 Chapter 5]) and thus have a polynomial upper bound on normal subgroup growth. Using this upper bound with (\[BasicInequality\]) yields our next result. If $\Gamma$ is virtually solvable, finite rank, and not nilpotent, then $n^{1/d} \preceq \operatorname{F}_{\Gamma,X}(n)$ for some $d \in {\ensuremath{{\ensuremath{\mathbf{N}}}}}$. For a non-nilpotent, virtually solvable group of finite rank, we have the inequalities: $$\begin{aligned} \alpha^n &\preceq \operatorname{w}_{\Gamma,X}(n) \\ \operatorname{s}_{\Gamma,X}(n) &\preceq n^m.\end{aligned}$$ Setting $d=2m$ and assuming $\operatorname{F}_{\Gamma,X}(n) \preceq n^{1/d}$, inequality (\[BasicInequality\]) yields the impossible inequality $$n \simeq \log(\alpha^n) \preceq \log(\operatorname{w}_{\Gamma,X}(n)) \preceq \operatorname{s}_\Gamma(\operatorname{F}_{\Gamma,X}(n))\log(\operatorname{F}_{\Gamma,X}(n)) \preceq (n^{1/d})^m \log(n^{1/d}) \simeq \sqrt{n}\log(n).$$ Virtually solvable group $\Gamma$ with infinite $\textrm{rk}(\Gamma)$ cannot be handled in this way as there exist examples with $c^{n^{1/d}} \preceq \operatorname{s}_{\Gamma,X}(n)$ with $c>1$ and $d \in {\ensuremath{{\ensuremath{\mathbf{N}}}}}$. Least common multiples ====================== Let $\Gamma$ be a finitely generated group and $S {\subset}\Gamma^\bullet$ a finite subset. Associated to $S$ is the subgroup $L_S$ given by $$L_S = {\bigcap}_{\gamma \in S} \overline{{\left< \gamma \right>}}.$$ We define the *least common multiple of $S$* to be the set $$\operatorname{LCM}_{\Gamma,X}(S) = {\left\{\delta \in L_S^\bullet~:~ {\left\vert \left\vert \delta\right\vert\right\vert}_X \leq {\left\vert \left\vert \eta\right\vert\right\vert}_X \text{ for all }\eta \in L_S^\bullet\right\}}.$$ That is, $\operatorname{LCM}_{\Gamma,X}(S)$ is the set of nontrivial words in $L_S$ of minimal length in a fixed generating set $X$ of $\Gamma$. Finally, we set $$\operatorname{lcm}_{\Gamma,X}(S) = \begin{cases} {\left\vert \left\vert \delta\right\vert\right\vert}_X& \text{ if there exists }\delta \in \operatorname{LCM}_{\Gamma,X}(S), \\ 0 & \text{ if }\operatorname{LCM}_{\Gamma,X}(S) = \emptyset. \end{cases}$$ The following basic lemma shows the importance of least common multiples in the study of both $\operatorname{F}_\Gamma$ and $\operatorname{G}_\Gamma$. \[WordLengthForLCM\] Let $S {\subset}\Gamma^\bullet$ be a finite set and $\delta \in \Gamma^\bullet$ have the following property: For any homomorphism ${\varphi}{\ensuremath{\colon}}\Gamma \to Q$, if $\ker {\varphi}\cap S \ne {\emptyset}$, then $\delta \in \ker {\varphi}$. Then $\operatorname{lcm}_{\Gamma,X}(S) \leq {\left\vert \left\vert \delta\right\vert\right\vert}_X$. To prove this, for each $\gamma \in S$, note that ${\varphi}_\gamma{\ensuremath{\colon}}\Gamma \to \Gamma/\overline{{\left< \gamma \right>}}$ is homomorphism for which $\ker {\varphi}_\gamma \cap S \ne {\emptyset}$. By assumption, $\delta \in \ker {\varphi}_\gamma$ and thus in $\overline{{\left< \gamma \right>}}$ for each $\gamma \in S$. Therefore, $\delta \in L_S$ and the claim now follows from the definition of $\operatorname{lcm}_{\Gamma,X}(S)$. Lower bounds for free groups {#FreeGroupGrowth} ============================ In this section, using least common multiples, we will prove Theorem \[basiclowerbound\]. #### **1. Construct short least common multiples.** We begin with the following proposition. \[FreeCandidateLemma\] Let $\gamma_1,\dots,\gamma_n \in F_m^\bullet$ and ${\left\vert \left\vert \gamma_j\right\vert\right\vert}_X \leq d$ for all $j$. Then $$\operatorname{lcm}_{F_m,X}(\gamma_1,\dots,\gamma_n) \leq 6dn^2.$$ In the proof below, the reader will see that the important fact that we utilize is the following. For a pair of non-trivial elements $\gamma_1,\gamma_2$ in a nonabelian free group, we can conjugate $\gamma_1$ by a generator $\mu \in X$ to ensure that $\mu^{-1}\gamma_1\mu$ and $\gamma_2$ do not commute. This fact will be used repeatedly. Let $k$ be the smallest natural number such that $n \leq 2^k$ (the inequality $2^k \leq 2n$ also holds). We will construct an element $\gamma$ in $L_{{\left\{\gamma_1,\dots,\gamma_n\right\}}}$ such that $${\left\vert \left\vert \gamma\right\vert\right\vert}_X \leq 6d4^k.$$ By Lemma \[WordLengthForLCM\], this implies the inequality asserted in the statement of the proposition. To this end, we augment the set ${\left\{\gamma_1,\dots,\gamma_n\right\}}$ by adding enough additional elements $\mu \in X$ such that our new set has precisely $2^k$ elements that we label ${\left\{\gamma_1,\dots,\gamma_{2^k}\right\}}$. Note that it does not matter if the elements we add to the set are distinct. For each pair $\gamma_{2i-1},\gamma_{2i}$, we replace $\gamma_{2i}$ by a conjugate $\mu_i\gamma_{2i}\mu_i^{-1}$ for $\mu_i \in X$ such that $[\gamma_{2i-1},\mu_i^{-1}\gamma_{2i}\mu_i]\ne 1$ and in an abuse of notation, continue to denote this by $\gamma_{2i}$. We define a new set of elements ${\left\{\gamma_i^{(1)}\right\}}$ by setting $\gamma_i^{(1)} = [\gamma_{2i-1},\gamma_{2i}]$. Note that ${\left\vert \left\vert \gamma_i^{(1)}\right\vert\right\vert}_X \leq 4(d+2)$. We have $2^{k-1}$ elements in this new set and we repeat the above, again replacing $\gamma_{2i}^{(1)}$ with a conjugate by $\mu_i^{(1)}\in X$ if necessary to ensure that $\gamma_{2i-1}^{(1)}$ and $\gamma_{2i}^{(1)}$ do not commute. This yields $2^{k-2}$ non-trivial elements $\gamma_i^{(2)}=[\gamma_{2i-1}^{(1)},\gamma_{2i}^{(1)}]$ with ${\left\vert \left\vert \gamma_i^{(2)}\right\vert\right\vert}_X \leq 4(4(d+2)+2)$. Continuing this inductively, at the $k$–stage we obtain an element $\gamma_1^{(k)} \in L_S$ such that $${\left\vert \left\vert \gamma_1^{(k)}\right\vert\right\vert}_X \leq 4^kd + a_k,$$ where $a_k$ is defined inductively by $a_0=0$ and $$a_j = 4(a_{j-1}+2).$$ The assertion $$a_j = 2{\left( \sum_{\ell=1}^j 4^\ell \right) },$$ is validated with an inductive proof. Thus, we have $${\left\vert \left\vert \gamma_1^{(k)}\right\vert\right\vert}_X \leq 4^kd+a_k \leq 3{\left( 4^kd + 4^k \right) } \leq 6d(4^k).$$ An immediate corollary of Proposition \[FreeCandidateLemma\] is the following. \[PrimeNumberTheorem\] $$\operatorname{lcm}_{F_m,X}(B_{F^m,X}^\bullet(n)) \leq 6n(\operatorname{w}_{F_m,X}(n))^2.$$ #### **2. Proof of Theorem \[basiclowerbound\].** We now give a short proof of Theorem \[basiclowerbound\]. We begin with the following proposition. \[freelowerbound\] Let $\Gamma$ be a nonabelian free group of rank $m$. Then $n^{1/3} \preceq \operatorname{F}_{\Gamma,X}(n)$. For $x \in X$, set $$S = {\left\{x,x^2,\dots,x^{n}\right\}}.$$ By Proposition \[FreeCandidateLemma\], if $\delta \in \operatorname{LCM}_{F_m,X}(S)$, then $${\left\vert \left\vert \delta\right\vert\right\vert}_X \leq 6n^3.$$ On the other hand, if ${\varphi}{\ensuremath{\colon}}F_m \to Q$ is a surjective homomorphism with ${\varphi}(\delta) \ne 1$, the restriction of ${\varphi}$ to $S$ is injective. In particular, $$\operatorname{D}_{F_m,X}^\lhd(\delta) \geq n.$$ In total, this shows that $n^{1/3} \preceq \operatorname{F}_{F_m,X}$. We now prove Theorem \[basiclowerbound\]. Let $\Gamma$ be a finitely generated group with finite generating set $X$. By assumption, $\Gamma$ contains a nonabelian free group $\Delta$. By passing to a subgroup, we may assume that $\Delta$ is finitely generated with free generating set $Y$. According to Lemma \[DivisibilityAsymptoticLemma\] (b), we know that $\operatorname{F}_{\Delta,Y}(n) \preceq \operatorname{F}_{\Gamma,X}(n)$. By Proposition \[freelowerbound\], we also have $n^{1/3} \preceq \operatorname{F}_{\Delta,Y}(n)$. The marriage of these two facts yields Theorem \[basiclowerbound\]. #### **3. The basic girth inequality.** We are now ready to prove (\[BasicGirthEquation\]) for free groups. Again, for the reader’s convenience, recall that (\[BasicGirthEquation\]) is $$\operatorname{G}_{F_m,X}(n/2) \leq \operatorname{F}_{F_m,X}(n/2){\left( 6n (\operatorname{w}_{F_m,X}(n))^{2} \right) }.$$ Let $\delta \in \operatorname{LCM}(B_{F_m,X}^\bullet(n))$ and let $Q$ be a finite group of order $\operatorname{D}_{F_m,X}^\lhd(\delta)$ such that there exists a homomorphism ${\varphi}{\ensuremath{\colon}}F_m \to Q$ with ${\varphi}(\delta)\ne 1$. Since $\delta \in L_{B_{F_m,X}(n)}$, for each $\gamma$ in $B_{F_m,X}^\bullet(n)$, we also know that ${\varphi}(\gamma) \ne 1$. In particular, it must be that ${\varphi}$ restricted to $B_{F_m,X}^\bullet(n/2)$ is injective. The definitions of $\operatorname{G}_{F_m,X}$ and $\operatorname{F}_{F_m,X}$ with Corollary \[PrimeNumberTheorem\] yields $$\operatorname{G}_{F_m,X}(n/2) \leq \operatorname{D}^\lhd_{F_m,X}(\delta) \leq \operatorname{F}_{F_m,X}({\left\vert \left\vert \delta\right\vert\right\vert}_X)\leq \operatorname{F}_{F_m,X}(6n(\operatorname{w}_{F_m,X}(n))^2),$$ and thus the desired inequality. #### **4. Proof of Theorem \[GirthPolynomialGrowth\].** We are also ready to prove Theorem \[GirthPolynomialGrowth\]. We must show that a finitely generated group $\Gamma$ is virtually nilpotent if and only if $\operatorname{G}_{\Gamma,X}$ has at most polynomial growth. If $\operatorname{G}_{\Gamma,X}$ is bounded above by a polynomial in $n$, as $\operatorname{w}_{\Gamma,X} \leq \operatorname{G}_{\Gamma,X}$, it must be that $\operatorname{w}_{\Gamma,X}$ is bounded above by a polynomial in $n$. Hence, by Gromov’s Polynomial Growth Theorem, $G$ is virtually nilpotent. Suppose now that $\Gamma$ is virtually nilpotent and set $\Gamma_{\textrm{Fitt}}$ to be the Fitting subgroup of $\Gamma$. It is well known (see [@Dek]) that $\Gamma_{\textrm{Fitt}}$ is torsion free and finite index in $\Gamma$. By Lemma \[GirthAsymptoticLemma\] (c), we may assume that $\Gamma$ is torsion free. In this case, $\Gamma$ admits a faithful, linear representation $\psi$ into ${\ensuremath{\mathbf{U}}}(d,{\ensuremath{{\ensuremath{\mathbf{Z}}}}})$, the group of upper triangular, unipotent matrices with integer coefficients in $\operatorname{GL}(d,{\ensuremath{{\ensuremath{\mathbf{Z}}}}})$ (see [@Dek]). Under this injective homomorphism, the elements in $B_{\Gamma,X}(n)$ have matrix entries with norm bounded above by $Cn^k$, where $C$ and $k$ only depends on $\Gamma$. Specifically, we have $${\left\vert(\psi(\gamma))_{i,j}\right\vert} \leq C{\left\vert \left\vert \gamma\right\vert\right\vert}_X^k.$$ This is a consequence of the Hausdorff–Baker–Campbell formula (see [@Dek]). Let $r$ be the reduction homomorphism $$r {\ensuremath{\colon}}{\ensuremath{\mathbf{U}}}(d,{\ensuremath{{\ensuremath{\mathbf{Z}}}}}) {\longrightarrow}{\ensuremath{\mathbf{U}}}(d,{\ensuremath{{\ensuremath{\mathbf{Z}}}}}/ 2Cn^k {\ensuremath{{\ensuremath{\mathbf{Z}}}}})$$ defined by reducing matrix coefficients modulo $2 Cn^k$. By selection, the restriction of $r$ to $B_{\Gamma,X}^\bullet(n)$ is injective. So we have $$\label{CardinalityInequality} {\left\vertr(\psi(\Gamma))\right\vert} \leq {\left\vert{\ensuremath{\mathbf{U}}}(d,{\ensuremath{{\ensuremath{\mathbf{Z}}}}}/ 2Cn^k {\ensuremath{{\ensuremath{\mathbf{Z}}}}})\right\vert} \leq (2Cn^k)^{d^2}.$$ This inequality gives $$\operatorname{G}_{\Gamma,X}(n) \leq (2Cn^k)^{d^2} = C_1n^{kd^2}.$$ Therefore, $\operatorname{G}_{\Gamma,X}(n)$ is bounded above by a polynomial function in $n$ as claimed. #### **5. Generalities.** The results and methods for the free group in this section can be generalized. Specifically, we require the following two properties: - $\Gamma$ has an element of infinite order. - For all non-trivial $\gamma_1,\gamma_2 \in \Gamma$, there exists $\mu_{1,2} \in X$ such that $[\gamma_1,\mu_{1,2}\gamma_2\mu_{1,2}^{-1}]\ne 1$. With this, we can state a general result established with an identical method taken for the free group. Let $\Gamma$ be finitely generated group that satisfies (i) and (ii). Then - $\operatorname{G}_{\Gamma,X}(n/2) \leq \operatorname{F}_{\Gamma,X}(n/2){\left( 6n (\operatorname{w}_{\Gamma,X}(n))^{2} \right) }$. - $n^{1/3} \preceq \operatorname{F}_{\Gamma,X}$. The proof of Theorem \[toughlowerbound\] {#toughlowerboundSection} ======================================== In this section we prove Theorem \[toughlowerbound\]. For sake of clarity, before commencing with the proof, we outline the basic strategy. We will proceed via contradiction, assuming that $\max \operatorname{D}_{F_m}(n) \preceq \log n$. We will apply this assumption to a family of test elements $\delta_n$ derived from least common multiples of certain simple sets $S(n)$ to produce a family of finite index subgroups $\Delta_n$ in $F_m$. Employing the Prime Number Theorem, we will obtain upper bounds (see (\[LinearBound\]) below) for the indices $[F_m:\Delta_n]$. Using covering space theory and a simple albeit involved inductive argument, we will derive the needed contradiction by showing the impossibility of these bounds. The remainder of this section is devoted to the details. Our goal is to show $\max \operatorname{D}_{F_m}(n) \npreceq \log(n)$ for $m \geq 2$. By Lemma 1.1 in [@Bou], it suffices to show this for $m=2$. To that end, set $\Gamma = F_2$ with free generating set $X={\left\{x,y\right\}}$, and $$S(n) = {\left\{x,x^2,\dots,x^{\operatorname{lcm}(1,\dots,n)}\right\}}.$$ We proceed by contradiction, assuming that $\max \operatorname{D}_\Gamma(n) \preceq \log(n)$. By definition, there exists a constant $C>0$ such that $\max \operatorname{D}_\Gamma(n) \leq C\log(Cn)$ for all $n$. For any $\delta_n \in \operatorname{LCM}_{\Gamma,X}(S(n))$, this implies that there exists a finite index subgroup $\Delta_n < \Gamma$ such that $\delta_n \notin \Delta_n$ and $$[\Gamma:\Delta_n] \leq C\log(C{\left\vert \left\vert \delta_n\right\vert\right\vert}_X).$$ According to Proposition \[FreeCandidateLemma\], we also know that $${\left\vert \left\vert \delta_n\right\vert\right\vert}_X \leq D(\operatorname{lcm}(1,\dots,n))^3.$$ In tandem, this yields $$[\Gamma:\Delta_n] \leq C\log(CD(\operatorname{lcm}(1,\dots,n))^3).$$ By the Prime Number Theorem, we have $$\lim_{n \to {\infty}} \frac{\log(\operatorname{lcm}(1,\dots,n))}{n} = 1.$$ Therefore, there exists $N>0$ such that for all $n \geq N$ $$\frac{n}{2} \leq \log(\operatorname{lcm}(1,\dots,n)) \leq \frac{3n}{2}.$$ Combining this with the above, we see that there exists a constant $M>0$ such that for all $n\geq N$, $$\label{LinearBound} [\Gamma:\Delta_n] \leq C\log(CD) + \frac{9Cn}{2} \leq Mn.$$ Our task now is to show (\[LinearBound\]) cannot hold. In order to achieve the desired contradiction, we use covering space theory. With that goal in mind, let $S^1 \vee S^1$ be the wedge product of two circles and recall that we can realize $\Gamma$ as $\pi_1(S^1 \vee S^1,*)$ by identifying $x,y$ with generators for the fundamental groups of the respective pair of circles. Here, $*$ serves as both the base point and the identifying point for the wedge product. According to covering space theory, associated to the conjugacy class $[\Delta_n]$ of $\Delta_n$ in $\Gamma$, is a finite cover $Z_n$ of $S^1 \vee S^1$ of covering degree $[\Gamma:\Delta_n]$ (unique up to covering isomorphisms). Associated to a conjugacy class $[\gamma]$ in $\Gamma$ is a closed curve $c_\gamma$ on $S^1 \vee S^1$. The distinct lifts of $c_\gamma$ to $Z_n$ correspond to the distinct $\Delta_n$–conjugacy classes of $\gamma$ in $\Gamma$. The condition that $\gamma \notin \Delta_n$ implies that at least one such lift cannot be a closed loop. Removing the edges of $Z_n$ associated to the lifts of the closed curve associated to $[y]$, we get a disjoint union of topological circles, each of which is a union of edges associated to the lifts of the loop associated to $[x]$. We call these circles $x$–cycles and say the length of an $x$–cycle is the total number of edges of the cycle. The sum of the lengths over all the distinct $x$–cycles is precisely $[\Gamma:\Delta_n]$. For an element of the form $x^\ell$, each lift of the associated curve $c_{x^\ell}$ is contained on an $x$–cycle. Using elements of the form $x^\ell$, we will produce enough sufficiently long $x$–cycles in order to contradict (\[LinearBound\]). We begin with the element $x^{\operatorname{lcm}(1,\dots,m)}$ for $1 \leq m \leq n$. This will serve as both the base case for an inductive proof and will allow us to introduce some needed notation. By construction, some $\Gamma$–conjugate of $x^{\operatorname{lcm}(1,\dots,m)}$ is not contained in $\Delta_n$. Indeed, $x^\ell$ for any $1 \leq \ell \leq \operatorname{lcm}(1,\dots,n)$ is never contained in the intersection of all conjugates of $\Delta_n$. Setting $c_m$ to be the curve associated to $x^{\operatorname{lcm}(1,\dots,m)}$, this implies that there exists a lift of $c_m$ that is not closed in $Z_n$. Setting $C_n^{(1)}$ to be the $x$–cycle containing this lift, we see that the length of $C_n^{(1)}$ must be at least $m$. Otherwise, some power $x^\ell$ for $1 \leq \ell \leq m$ would have a closed lift for this base point and this would force this lift of $c_m$ to be closed. Setting $k_{n,m}^{(1)}$ to be the associated length, we see that $m \leq k_{n,m}^{(1)} \leq Mn$ when $n \geq N$. Using the above as the base case, we claim the following: **Claim.** *For each positive integer $i$, there exists a positive integer $N_i \geq N$ such that for all $n \geq 8N_i$, there exists disjoint $x$–cycles $C_n^{(1)},\dots,C_n^{(i)}$ in $Z_n$ with respective lengths $k_n^{(1)},\dots,k_n^{(i)}$ such that $k_n^{(j)} \geq n/8$ for all $1 \leq j \leq i$.* That this claim implies the desired contradiction is clear. Indeed, if the claim holds, we have $$\frac{ni}{8} \leq \sum_{j=1}^i k_n^{(j)} \leq [\Gamma:\Delta_n]$$ for all positive integers $i$ and all $n \geq N_i$. Taking $i > 8M$ yields an immediate contradiction of (\[LinearBound\]). Thus, we are reduced to proving the claim. For the base case $i=1$, we can take $N_1=N$ and $m=n$ in the above argument and thus produce an $x$–cycle of length $k_n^{(1)}$ with $n \leq k_n^{(1)}$ for any $n \geq N_1$. Proceeding by induction on $i$, we assuming the claim holds for $i$. Specifically, there exists $N_i \geq N$ such that for all $n \geq 8N_i$, there exists disjoint $x$–cycles $C_n^{(1)},\dots,C_n^{(i)}$ in $Z_n$ with lengths $k_n^{(j)} \geq n/8$. By increasing $N_i$ to some $N_{i+1}$, we need to produce a new $x$–cycle $C_n^{(i+1)}$ in $Z_n$ of length $k_n^{(i+1)} \geq n/8$ for all $n \geq 8N_{i+1}$. For this, set $$\ell_{n,m} = \operatorname{lcm}(1,\dots,m)\prod_{j=1}^i k_n^{(j)}.$$ By construction, the lift of the closed curve associated to $x^{\ell_{n,m}}$ to each cycle $C_n^{(j)}$ is closed. Consequently, any lift of the curve associated to $x^{\ell_{n,m}}$ that is not closed must necessarily reside on an $x$–cycle that is disjoint from the previous $i$ cycles $C_n^{(1)},\dots, C_n^{(i)}$. In addition, we must ensure that this new $x$–cycle has length at least $n/8$. To guarantee that the curve associated to $x^{\ell_{n,m}}$ has a lift that is not closed, it is sufficient to have the inequality $$\label{NonClosedLift} \ell_{n,m} \leq \operatorname{lcm}(1,\dots,n).$$ In addition, if $m\geq n/8$, then the length of $x$–cycle containing this lift must be at least $n/8$. We focus first on arranging (\[NonClosedLift\]). For this, since $k_n^{(j)} \leq Mn$ for all $j$, (\[NonClosedLift\]) holds if $$(Mn)^i\operatorname{lcm}(1,\dots,m) \leq \operatorname{lcm}(1,\dots,n).$$ This, in turn, is equivalent to $$\log(\operatorname{lcm}(1,\dots,m)) \leq \log(\operatorname{lcm}(1,\dots,n)) - i\log(Mn).$$ Set $N_{i+1}$ to be the smallest positive integer such that $$\frac{n}{8} - i\log(Mn) > 0$$ for all $n \geq 8N_{i+1}$. Taking $n>8N_{i+1}$ and $n/8 \leq m \leq n/4$, we see that $$\begin{aligned} \log(\operatorname{lcm}(1,\dots,m)) &\leq \frac{3m}{2} \\ &\leq \frac{3n}{8} \\ &\leq \frac{3n}{8} + {\left( \frac{n}{8}-i\log(Mn) \right) } \\ &= \frac{n}{2} - i\log(Mn) \\ &\leq \log(\operatorname{lcm}(1,\dots,n)) - i\log(Mn).\end{aligned}$$ In particular, we produce a new $x$–cycle $C_n^{(i+1)}$ of length $k_n^{(i+1)}\geq n/8$ for all $n \geq N_{i+1}$. Having proven the claim, our proof of Theorem \[toughlowerbound\] is complete. Just as in Theorem \[basiclowerbound\], Theorem \[toughlowerbound\] can be extended to any finitely generated group that contains a nonabelian free subgroup. Let $\Gamma$ be a finitely generated group that contains a nonabelian free subgroup. Then $$\max \operatorname{D}_{\Gamma,X}(n) \npreceq \log(n).$$ [9]{} K. Bou-Rabee, *Quantifying residual finiteness*, J. Algebra, [**323**]{} (2010), 729–737. K. Bou-Rabee and D. B. McReynolds, *Bertrand’s postulate and subgroup growth*, to appear in J. Algebra. N. V. Buskin, *Economical separability in free groups*, Siberian Mathematical Journal, **50** (2009), 603–-608. K. Dekimpe, *Almost-Bieberbach groups: Affine and polynomial structures*, Springer-Verlag, 1996. M. Gromov with an appendix by J. Tits, *Groups of polynomial growth and expanding maps*, Publ. Math. Inst. Hautes Étud. Sci., **53** (1981), 53–78. P. de La Harpe, *Topics in Geometric Group Theory*, Chicago Lectures in Mathematics, Chicago 2000. U. Hadad, *On the Shortest Identity in Finite Simple Groups of Lie Type*, preprint. M. Kassabov and F. Matucci, *Bounding residual finiteness in free groups*, preprint. A. Lubotzky and D. Segal, *Subgroup growth*, Birkhäuser, 2003. V. D. Mazurov and E. I. Khukhro, editors, *The Kourovka notebook*, Russian Academy of Sciences Siberian Division Institute of Mathematics, Novosibirsk, sixteenth edition, 2006. Unsolved problems in group theory, Including archive of solved problems. I. Rivin, *Geodesics with one self-intersection, and other stories*, preprint. Department of Mathematics\ University of Chicago\ Chicago, IL 60637, USA\ email: [[email protected]]{}, [[email protected]]{}\ [^1]: University of Chicago, Chicago, IL 60637. E-mail: [^2]: University of Chicago, Chicago, IL 60637. E-mail:

[Surgical treatments of nonconfluent pulmonary arteries with congenital cardiac defects]. Pulmonary artery angioplasty or reconstruction was performed in seven patients with nonconfluent pulmonary arteries and congenital cardiac defects. Age of these patients were ranged from 6 months to 41 years old. Five of them had pulmonary truncal atresia and complex cardiac anomalies. Two of these five patients demonstrated nonconfluent pulmonary arteries due to deformities at ductal insertion of pulmonary arteries. Three patients had had previous systemic to pulmonary artery shunt operations which caused pulmonary artery distortions. Other two patients had intrapulmonary arterial obstructions due to pulmonary artery thrombosis. Patch pulmonary artery plasty was carried out in three patients, dilatation of severe stenotic pulmonary artery was done in one patient simultaneously with pulmonary valvotomy. Central shunt operation was added in one patient with the pulmonary artery which was unable to be reconstructed. Last two patients underwent intrapulmonary artery reconstruction with the rolled pericardial graft. Hospital death occurred in one patient with unproperly increased pulmonary blood flow by central shunt. Average follow-up period of these six survivors after operation was 1.4 +/- 0.8 years. As definite repairs, two patients had Fontan operation, two patients had right ventricle to pulmonary artery reconstruction. And remaining two patients are still to be followed until sufficient growth of pulmonary artery suitable for Fontan operation.

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1928 Salvadoran legislative election Legislative elections were held in El Salvador in January 1928. The result was a victory for the National Democratic Party, which won all 42 seats. Results References Category:1928 elections in Central America Category:Elections in El Salvador Category:1928 in El Salvador

Q: Change view frame in landscape using autolayout in storyboard I am very new to AutoLayout. I have one problem. I need to change the frame of any UIView when moving form portrait to landscape mode. For example: If I have one UILabel with frame (100,100,100,30) in portrait mode. And I want to change its frame to (400,400,100,30) if rotate iPad to landscape mode. I want to do this using storyboard and auto layout. I want to avoid coding for this. A: I try this one : First check Use AutoLayout Move your mouse point to UILabel and drag right side with Ctrl Key and select Trailing space to container Move your mouse point to UILabel and drag left side with Ctrl Key and select Leading space to container This is your output : Check it. :)

Q: AVAudioRecorder shows time delay for recording sound in IOS 5 I am using AVAudioRecorder to record sound in 'wav' format. My code works fine for ios 4 and recording is done perfectly. But in case of ios 5, a time delay of 3-4 seconds occur in 2 out of 10 attempts for recording sound. I also used : [audioRecorder prepareToRecord] function in order to start the recording without delay. Is there any bug in my code or somrthing else... Please guide me.. My code is: AVAudioSession *audioSession = [AVAudioSession sharedInstance]; [audioSession setCategory:AVAudioSessionCategoryRecord error:nil]; NSMutableDictionary *recordSettings = [[NSMutableDictionary alloc] initWithCapacity:10]; [recordSettings setObject:[NSNumber numberWithInt: kAudioFormatLinearPCM] forKey: AVFormatIDKey]; [recordSettings setObject:[NSNumber numberWithFloat:44100.0] forKey: AVSampleRateKey]; [recordSettings setObject:[NSNumber numberWithInt:2] forKey:AVNumberOfChannelsKey]; [recordSettings setObject:[NSNumber numberWithInt:16] forKey:AVLinearPCMBitDepthKey]; [recordSettings setObject:[NSNumber numberWithBool:NO] forKey:AVLinearPCMIsBigEndianKey]; [recordSettings setObject:[NSNumber numberWithBool:NO] forKey:AVLinearPCMIsFloatKey]; NSArray *paths = NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES); NSString *recDir = [paths objectAtIndex:0]; NSURL *url = [NSURL fileURLWithPath:[NSString stringWithFormat:@"%@/audio%d.wav", recDir,nextCount]]; NSError *error = nil; audioRecorder = [[ AVAudioRecorder alloc] initWithURL:url settings:recordSettings error:&error]; audioRecorder.delegate=self; if(!audioRecorder){ NSLog(@"recorder: %@ %d %@", [error domain], [error code], [[error userInfo] description]); UIAlertView *alert = [[UIAlertView alloc] initWithTitle: @"Warning" message: [error localizedDescription] delegate: nil cancelButtonTitle:@"OK" otherButtonTitles:nil]; [alert show]; [alert release]; return; } [audioRecorder prepareToRecord]; audioRecorder.meteringEnabled = YES; BOOL audioHWAvailable = audioSession.inputIsAvailable; if (! audioHWAvailable) { UIAlertView *cantRecordAlert = [[UIAlertView alloc] initWithTitle: @"Warning" message: @"Audio input hardware not available" delegate: nil cancelButtonTitle:@"OK" otherButtonTitles:nil]; [cantRecordAlert show]; [cantRecordAlert release]; return; } [audioRecorder prepareToRecord]; [audioRecorder recordForDuration:(NSTimeInterval) 25]; [recordSettings release]; } else { [recordButton setBackgroundImage:[UIImage imageNamed:@"record.png"] forState:UIControlStateNormal]; self.recordBtn=NO; [audioRecorder stop]; AVAudioSession *audioSession = [AVAudioSession sharedInstance]; [audioSession setCategory:AVAudioSessionCategoryPlayback error:nil]; } A: The problem was with AVAudioSession. Every time when i record the video, i create a session for recording: AVAudioSession *audioSession = [AVAudioSession sharedInstance]; [audioSession setCategory:AVAudioSessionCategoryRecord error:nil]; and this was the problem sometimes session takes time to start and recording was delayed by 3-4sec. So, i created the session in viewdidload and make it global and the problem was resolved. Thanks to the suggestion by hotpaw2 on a similar kind of link...

[Sentinel node biopsy using dye methods]. At first, sentinel node identification was performed using dyes such as isosulfan blue dye and patent blue dye. Although dye localization is a simple and cheap method, this procedure requires training and the success rate and accuracy are not very good. It is considered that the addition of a radiocolloid injection is needed for sentinel node biopsy in melanoma and breast cancer. For gastrointestinal tract malignancies, good results were reported in several feasibility studies. However, the validity of sentinel node biopsy for those malignancies depends on the results of a large ongoing clinical trial.

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1. Field of the Invention This invention relates to continuous thickeners, clarifiers and similar gravititational settling devices for separating feed slurries or pulps into clarified liquid and sludge and is particularly concerned with a method and device for controlling the operation or design of such settling devices. 2. Description of the Prior Art Continuous thickeners, clarifiers and similar gravitational settling devices are widely used in the chemical and metallurgical industries for the removal of liquids from slurries, metallurgical pulps, sewage and other liquid-solid suspensions. Such devices generally include a circular tank having a cylindrical center feedwell which extends downwardly into the vessel and is open at the bottom. The incoming slurry or pulp passes through a feed pipe or launder into the upper part of this central feedwell and is introduced into the surrounding liquid through the bottom of the feedwell in a manner designed to create a minimum of turbulence. This makes it possible to contain the bulk of the solids near the center of the unit. On leaving the feedwell, the liquid entering with the pulp or slurry tends to move outwardly in a radial direction and flow upwardly toward a peripheral overflow launder. The solids suspended in the slurry or pulp settle downwardly through the slow-moving liquid and accumulate on the bottom of the unit. These solids are compacted as they accumulate and are slowly moved toward a bottom sludge discharge opening by means of slowly rotating rakes suspended a short distance above the bottom. The rakes aid in compacting the sludge and reduce its liquid content. During the normal operation of a thickener, decanter, clarifier or similar continuous gravity settling device of the type referred to above, a series of relatively well-defined, vertically-spaced zones exist within the settler. The uppermost of these zones comprises a layer of clear liquid from which most of the solids have settled out. Below this is an intermediate layer containing suspended solid particles which is generally referred to as the settling zone. The interface between the clear solution and the settling zone may be referred to as the upper boundary or slime level. At the bottom of the unit is a layer of settled sludge. Such a system is a dynamic one characterized by the movement of liquid and solid particles between the above zones. The levels of the three zones may vary considerably, depending upon the feed stream, operating conditions and other variables. To achieve maximum capacity with such a settling unit, it has generally been thought that the upper boundary should be maintained as close to the top of the unit as possible and that only a relatively thin layer of clarified solution be maintained above the floc layer. It is conventional to add flocculants or coagulants to thickeners, decanters, clarifiers and similar settling devices to increase their capacity. These materials cause the suspended particles in the slurry or pulp to flocculate or agglomerate and thus settle more rapidly. The amount of flocculant or the like which is required at any particular moment depends in part upon the slurry or pulp feed rate, the solids content of the feed, the solids size range and distribution, the densities of the solid particles, and the temperature and other operating conditions. Under constant conditions, the amount of flocculant needed to achieve maximum capacity in a particular gravity settling unit is generally determined by trial and error. However, in actual practice the conditions may change due to variations in the amount and compositions of the solid suspended in the feed stream and other variables over which the operator of the unit may have relatively little or no control. Adjustments of the amount of flocculant added to the system is therefore necessary to compensate for the variations and maintain the desired capacity and degree of separation while at the same time keeping operating costs within acceptable bounds by eliminating overflocculation, and its related problems in downstream operations such as in the final polishing filtration. It has been common practice to use the upper boundary of the settling zone within a settler as a measure of the settler's performance and to monitor this level as a means for determining the need for changes in the flocculant rate. In general, the higher the upper boundary, the more flocculant that is needed. This location of the upper boundary has generally been done manually by means of measuring sticks lowered into the vessel near the outer edge of the unit. Vacuum tubes, depth samplers, ultrasonic probes may also be used. The upper boundary is, however, not a direct measure of the settling characteristics of solids in the pulp or slurry and instead is the result of the combination of variables, including flocculant type and flow rate, solids feed rate, solids and liquid characteristics, mixing etc. There is normally a long time lag between the changes in the rate of addition of flocculant and corresponding changes in the upper boundary and hence the operator must estimate the amount of change in the rate of addition of flocculant which will be needed to produce a desired change in upper boundary. If he overestimates or underestimates the change in rate required, the unit may become unstable and eventually have to be shut down to avoid overloading or the carryover of solids. The upper boundary therefore provides at best a visible means for assessing the state of the thickener or clarifier operation and, if it increases progressively, it may serve as an delayed warning that the capacity of the settler has been exceeded. Attempts have also been made to control the operation of a settler by sampling the incoming feed slurry to the feedwell at regular intervals downstream of the point at which flocculant is added to the feed slurry. The samples thus collected are passed to a laboratory sized gravity separation vessel where representative settling can take place. By sensing the interface level between the liquid and solid phases in the separation vessel and adjusting the rate of flocculant addition to the feed stream in accordance with variations in the level of the interface during operation of the system, it was hoped that the rate of addition of flocculant could be controlled automatically and that the flocculant consumption could be thereby substantially reduced. However, attempts to develop such a system in the past were abandoned because none was capable of providing reliable data necessary for the control and operation of a full size commercial settler. One example of sampling equipment for measuring sedimentation rate is that described in Parker et al U.S. Pat. No. 4,318,296, issued Mar. 9, 1982. This system includes a sampling chamber for a sample to be tested, Elmer means for controlling a control means to stop the feed of suspension to the sampling chamber and means for retaining the height of the sample at a preselected level in the sampling chamber during a settling period. It also includes detector means for detecting when a boundary level defined by the settling solids in the sample in the sampling chamber reaches a further preselected level. The timer means determines the period of time elapsing between the stare of the settling period when the height of the sample is at the preselected level and the time when the detector means detects that the boundary level has reached the further preselected level. Another control system is described in Valheim, "Flocculant Optimization Cuts Chemical Costs and Boosts Performance"; Process Control in Engineering; August 1990, pp. 34-35. That system measures continuously the concentration of suspended solids in the total flow of incoming slurry, the flow raze of the slurry and the turbidity of the material leaving the full size industrial settling unit. The turbidity is the control parameter for the flocculant dosage system. In Eisenlauer et al "Z. Wasser Abwasser Forsch." 16, (1983) pp. 9-15 there is described a process for the control of flocculant to a settler which involves adding a varying amount of flocculant to a side stream of the suspension to be treated, and passing this mixture through a flow-through cell where the particle size distribution of the flocs is measured by a laser light scattering. This information determines the concentration at which flocculation begins, and the size and strength of the flocs. Other control attempts have been made directly to full size settling devices such as that described in Chandler, U.S. Pat. No. 4,040,954, issued Aug. 9, 1977. This describes a process for controlling the settling rate by measuring continuously the turbidity of the suspension at a selected height in the full size settling vessel. The position corresponds to the upper limit of cloudy liquor or floc layer above the bottom layer of mud in a state of hindered settlement. This is done by measuring the light transmittance through a continuous sample withdrawn from the settling vessel, using a light beam from a light source directed through a curtain of liquor. When the turbidity is higher than the desired set point, indicating that the interface is going higher, the amount of flocculant is increased. It is the object of the present invention to provide an improved testing system for measuring the settling characteristics of slurries and flocculant samples and using the results to either control a full size continuous industrial gravity settler or to construct such a full size settler.

Conventionally, in the field of handicraft such as patchworking, various tools for facilitating the making of handicraft have been proposed. For instance, Patent Document 1 given below discloses a pattern set for facilitating the work of cutting cloth in making a patchwork. Patent Document 1: JP-A-2004-169238 A yo-yo quilt is known as one of patchwork quilts which has excellent decoration effect. A yo-yo quilt is made using e.g. a plurality of circular quilt parts (yo-yos). To make a yo-yo quilt, a plurality of yo-yos are first formed. A yo-yo is formed by folding back the edge of circular cloth, sewing the cloth along folded edge and then pulling and knotting the thread tightly. As shown in FIG. 19 of the present application, the yo-yo made in this way has a circular shape formed with gathers on the front side. By connecting a plurality of such yo-yos by sewing the respective edges together or sewing the connected yo-yos onto cloth as the base, a yo-yo quilt is completed. Yo-yo quilts require a large number of yo-yos depending on the design, and to make a large number of yo-yos may be a burden. Further, to make a large number of yo-yos of uniform size and gathers requires experiences and skills.

Pension Zandvoort About us Welcome to pension zandvoort in the Netherlands (europe)We offer several beautiful rooms against attractive prices.The beautifull rooms are in the centre of zandvoort and only 100 meters of the beach.The distance to Amsterdam is 28 km, haarlem 8 km, schiphol(airport) 16 km.It is a pleasure to relax at the beach and in the evening to the casino and afterwards to the sparkling nightlife. The prices of the rooms:25 euro till 30 euro pppn We have completely furnished rooms with a waterboiler, coffeemachine and with the usual equipment of the kitchen. All rooms are equiped with a color tv(cable), refrigerator, safe and including towels.Unfortunately pets are not allowed. Mail or call us for more information and the availability.We will respond your request in 36 hours.

Esthetic rehabilitation of anterior discolored teeth with lithium disilicate all-ceramic restorations. The esthetic treatment of darkened anterior teeth represents a great challenge to dentists, because dental materials ideally should match the natural teeth. The optical behavior of the final restoration is determined by the color of the underlying tooth structure, the color of the luting agent, and the thickness and opacity of the ceramic material used. This article reports a case in which veneers and full crowns made of heat-pressed, lithium disilicate glass-ceramic were used for the esthetic rehabilitation of anterior discolored teeth. The patient was referred for treatment with defective anterior composite resin restorations, provisional acrylic resin crowns, darkening of the gingival margins, and uneven gingival contours. The multidisciplinary treatment plan included dental bleaching, periodontal plastic surgery to create gingival symmetry, and indirect all-ceramic restorations using high-opacity lithium disilicate glass-ceramic ingots. The treatment was successful and an excellent esthetic result was achieved.

Pharmacokinetics and Indications: Stanozolol is a synthetic anabolic steroid approved by FDA for human use. It is derived from testosterone. Stanozolol has large oral bioavailability because it survives through liver metabolism and therefore available in tablet form. It does not produce estrogen as end product. Stanozolol is popular in female bodybuilders because of its large anabolic effect and weak androgenic effects; however virilisation and masculinization are most common side effects. Stanozolol is banned from use in sports competitions by IAAF and many other sporting bodies. Stanozolol is popular in bodybuilders because of its anabolic effects also because it tends to retain lean body mass without any water retention and weight gain. Stanazolol is also thought to be a fat burning drug, however there is very little evidence supporting this. It is used by bodybuilders for anabolic effects to enhance the masculine appearance. Clinically it has been used to treat anemia and hereditary angioedema in humans with remarkable success and is very popular among most of the physicians. In veterinary it has been used in weak animals to increase body mass, improve blood counts and appetite. Stanozolol has also been used in horse racing to give a metabolic assist during the preparation of the competition. Stanozolol is normally presented as 5 mg tablets. The dosage is 10-25 mg/day with optimal results at 50 mg/day. Possible Side Effects: The effects of this drug are not permanent and only last as long as one keeps taking it in regular dosage. As soon as the intake stops body mass decreases rapidly. Possible side effects of Stanozolol are insomnia, depression, jaundice which can be serious, nausea and vomiting, gynocomastia, male pattern baldness and deepening of voice.

Learner Support Support you can expect from AOT Our focus is to provide the real-world skills and knowledge that you need to advance your career, fulfil your goals and achieve success in the workplace. No matter what course you choose, here at AOT you will receive the assistance and support that will help make your study time convenient, manageable and worthwhile. The benefit of studying with us is that you don’t have to schedule your time to attend face-to-face classroom sessions. You can study at times convenient to you in your own home or anywhere that suits your learning style. To support you in your study we provide: Personal course induction A Learner Support Officer will personally take you through the sauceLMS and your course. Live chat Trainer support available whilst you are studying 7am – 9pm AEST (Mon to Fri). Contact us form Contact us at any time using the Contact us form found within your course to create support tickets. Mentoring sessions You can book an appointment with your personal trainer to discuss the learning material, assessment expectations, or assessment feedback. Virtual classroom sessions This can be booked with your trainer for specific assessments. Help and Support A section on your sauceLMS dashboard with useful links including FAQs.

Residue analysis of 500 high priority pesticides: better by GC-MS or LC-MS/MS? This overview evaluates the capabilities of mass spectrometry (MS) in combination with gas chromatography (GC) and liquid chromatography (LC) for the determination of a multitude of pesticides. The selection of pesticides for this assessment is based on the status of production, the existence of regulations on maximum residue levels in food, and the frequency of residue detection. GC-MS with electron impact (EI) ionization and the combination of LC with tandem mass spectrometers (LC-MS/MS) using electrospray ionization (ESI) are identified as techniques most often applied in multi-residue methods for pesticides at present. Therefore, applicability and sensitivity obtained with GC-EI-MS and LC-ESI-MS/MS is individually compared for each of the selected pesticides. Only for one substance class only, the organochlorine pesticides, GC-MS achieves better performance. For all other classes of pesticides, the assessment shows a wider scope and better sensitivity if detection is based on LC-MS.

P-51D Mustang American fighters old and new will come together in the skies over RIAT 2018 during a USAF Heritage Flight display. This will see the present-day F-35A Raptor flown by Cap Andrew 'Dojo' Olson, from Luke Air Force Base, Nevada, accompanying a P-51D Mustang piloted by a USAF Heritage Flight Foundation pilot.

Diagnosis of Benign and Malignant Breast Lesions on DCE-MRI by Using Radiomics and Deep Learning With Consideration of Peritumor Tissue. Computer-aided methods have been widely applied to diagnose lesions detected on breast MRI, but fully-automatic diagnosis using deep learning is rarely reported. To evaluate the diagnostic accuracy of mass lesions using region of interest (ROI)-based, radiomics and deep-learning methods, by taking peritumor tissues into consideration. Retrospective. In all, 133 patients with histologically confirmed 91 malignant and 62 benign mass lesions for training (74 patients with 48 malignant and 26 benign lesions for testing). 3T, using the volume imaging for breast assessment (VIBRANT) dynamic contrast-enhanced (DCE) sequence. 3D tumor segmentation was done automatically by using fuzzy-C-means algorithm with connected-component labeling. A total of 99 texture and histogram parameters were calculated for each case, and 15 were selected using random forest to build a radiomics model. Deep learning was implemented using ResNet50, evaluated with 10-fold crossvalidation. The tumor alone, smallest bounding box, and 1.2, 1.5, 2.0 times enlarged boxes were used as inputs. The malignancy probability was calculated using each model, and the threshold of 0.5 was used to make a diagnosis. In the training dataset, the diagnostic accuracy was 76% using three ROI-based parameters, 84% using the radiomics model, and 86% using ROI + radiomics model. In deep learning using the per-slice basis, the area under the receiver operating characteristic (ROC) was comparable for tumor alone, smallest and 1.2 times box (AUC = 0.97-0.99), which were significantly higher than 1.5 and 2.0 times box (AUC = 0.86 and 0.71, respectively). For per-lesion diagnosis, the highest accuracy of 91% was achieved when using the smallest bounding box, and that decreased to 84% for tumor alone and 1.2 times box, and further to 73% for 1.5 times box and 69% for 2.0 times box. In the independent testing dataset, the per-lesion diagnostic accuracy was also the highest when using the smallest bounding box, 89%. Deep learning using ResNet50 achieved a high diagnostic accuracy. Using the smallest bounding box containing proximal peritumor tissue as input had higher accuracy compared to using tumor alone or larger boxes. 3 Technical Efficacy: Stage 2.

Norms Matter The calls for Donald Trump to releasehis tax returns beganearly during the campaign and never really let up. It was easy to assume he eventually would make good on his promises to turn them over. Every president since Jimmy Carter had released his taxes; Trump would have to do the same, right? What we’ve learned since then, of course, is that Trump didn’t have to reveal anything. The Constitution doesn’t require disclosure; plenty of federal officials need to submit their tax returns to the Senate, but not the president. It’s just a norm. Story Continued Below One of the crucial lessons of the past year, turns out, is just how much of American politics is governed not by written law, but by norms like these. For instance, the president isn’t required to divest himself of his businesses, but previous occupants of the White House have followed this tradition. Carter even put his peanut farm into a blind trust to avoid conflicts of interest. By contrast, Trump handed the reins to his sons, maintaining the rights to directly extract profits from the trust that controls his business empire. It’s not illegal, but before this year, it was a line no modern president had crossed. Social scientists have long understood the importance of norms—the unwritten rules and conventions that shape political behavior—but our political system has largely taken them for granted. As a result, we have been slow to recognize how vulnerable these informal constraints on power are to someone who refuses to follow rules that everyone else respects. Trump’s assault on norms started during the campaign, when he encouraged violence among his supporters, attacked the ethnicity of a federal judge (a double norm violation) and called for the imprisonment of his opponent. Once he was elected, many observers assumed this pattern would cease: Surely there are constraints on this kind of behavior from the president. There aren’t—or, at least, there are few formal ones. Many of Trump’s statements and behavior have no precedent in recent history, but they aren’t illegal. He openly admitted to firing James Comey as FBI director because of Comey’s investigation into Russian influence in Trump’s campaign—probably a legal act, but a violation of long-respected norms against political influence in the Justice Department. Similarly, Trump continues to visit and promote his businesses while in office, which would be prohibited for a Cabinet secretary, but is legal for the president. White House jobs for his children? Directly attacking the press? Railing about politics to military service members under his command? These were red lines so strong that they seemed to have the force of law, but no longer. We normally count on politicians to restrain themselves out of fear of public consequences. But as Trump’s election showed, the polarization and partisanship of our era has weakened those guardrails. Democrats are sounding the alarm, but members of his own party have remained largely silent. Violating norms is part of Trump’s appeal to his core supporters. As a result, these violations are frequently dismissed as just another case of partisan disagreement. Boundaries on presidential behavior that both parties have previously respected are blurring, making further abuses all too easy to imagine. Directly attacking the press? Railing about politics to military service members? These were red lines so strong that they seemed to have the force of law, but no longer. Internal checks, too, have withered. The Office of Government Ethics previously relied on voluntary compliance from officials who served under past presidents, including both Barack Obama and George W. Bush. Under Trump, however, this norm, too, has been breached with little cost to the president or his appointees. Walter Shaub, the head of OGE, recently stepped down, frustrated at his ineffectiveness during the Trump administration. Shaub told the New Yorker, “To have OGE criticize you would have been a career-ender in the olden days—now it’s just lost in the noise.” What happens when norms are shattered like this? One response is to write them into law. After Watergate, Congress created an independent special prosecutor role to guard against interference in investigations of the executive branch, and strengthened campaign finance regulations in response to abuses during the 1972 election. Similarly, after Franklin D. Roosevelt broke George Washington’s precedent of serving only two terms, the Constitution was amended to formally limit the length of a presidency. After Trump, Congress could well take similar steps like requiring presidential tax disclosures, strengthening conflict-of-interest protections and increasing independent legal authority over the executive branch. Such laws will never be sufficient, however. As political scientists have long known, there is no way to formally prohibit every type of bad behavior in advance. Who could have anticipated that it might be necessary to criminalize collusion with a hostile foreign power on the release of hacked emails? Ultimately, our country must therefore also rebuild respect for the informal rules of our political system. The fact that presidents have long separated business and politics voluntarily was a measure of how seriously they—and we—took the public trust. These conventions of behavior were virtually invisible to us precisely because so many public officials dutifully followed them, until now. As we have seen, these norms might be a fragile bulwark against a demagogue, but they also reflect a commitment to a set of shared rules and values that is an important indicator of the health of our politics. Without that commitment, preserving our freedoms will become a much more difficult and dangerous task.

Beijing - Artprice's Chairman, thierry Ehrmann, and its senior executives have just returned from several days of intense work at Artron's headquarters in Beijing where discussions focused on accelerating and implementing, as quickly as possible, all the agreed strategic and commercial initiatives that will inevitably generate very positive results in terms of turnover and the expansion of Artprice's client base... not to mention shareholder value. Artron and its Chairman Mr. Wan Jie gave the Artprice team an exceptionally respectful, warm and loyal welcome and introduced Artprice to China's top-level institutional leaders, the country's principal Art Market players and all of Artron's 3,500 employees. These face-to-face introductions are an essential step in Artprice's bid to fructify the enormous potential of the Chinese market in a fast and optimal manner. In 2018, China accounted for 45% of global online transactions, generating 12 times more online transactions than the United States. China has a huge advantage over the West because it is building its market economy directly on the Internet (Source GEAB / LEAP 2020). Speaking in front of his senior executives and top management, Mr. Wan Jie – at the head of his Artron empire and probably the most powerful player in China's Art Market – reiterated his unfailing personal friendship and loyalty vis-à-vis Artprice's founder-Chairman, thierry Ehrmann. This fact deserves emphasis as Chinese custom usually prohibits such ‘departures' from accepted business protocol. As China has become the global Art Market's leading marketplace over the past decade – Artprice had been the first to report it in 2009 –, it naturally represents a fascinating new market for Artprice. China has grand ambitions: As the French language business weekly Challenges headlined last week: “China, the giant that wants to dominate the World”. China is still accelerating with its “Made in China 2025” plan and its “New Silk Roads”. As a global company, Artprice made a point to successfully enter the Chinese market, now the last great ‘eldorado' for any group whose market is global. According to Artprice's founding Chairman, thierry Ehrmann, “I appreciated the emergence of China's global power, its insatiable appetite and its desire for leadership a long time ago! Over the past nine years, Artprice has translated hundreds of millions of data from its proprietary databases into Mandarin. However, observant visitors to our famous head offices (L'Organe Museum of Contemporary Art at the “Abode of Chaos” [dixit The New York Times]) over the past 30 years will have noticed thousands of artworks – including my own sculptures and paintings – directly or indirectly referring to the ancient culture and history of China.” “Unlike many, I am not surprised to see China gradually becoming the world's leading economic power. Artprice has decided to enter the Chinese market through the front door with a humility that has clearly been lacking in many Western listed companies. Any other strategy would have been a fatal mistake. I therefore wish to reiterate my thanks to Wan Jie, Artron's Chairman, and all his colleagues for making this open and proper strategy possible after 9 years of close collaboration!” Thanks to Artron's expert advice, Artprice fully complies with the specifications of China's “Great Electronic Wall” and its terms and conditions: Law CL97 (1997) as well as its “Golden Shield” protocol (1998). In order to comply with law CL97, Artprice spent two years rewriting all its databank code in order to eliminate all US and European corporate source code containing cookies, tags, metadata, backdoor elements (amongst other elements). Since Monday morning, Artprice is one of the very few Western companies to possess a WeChat profile reserved for companies operating under Chinese law. WeChat is used by more than 1.8 billion Chinese Internet users around the world. The statistics concerning China are eye-watering: a population of over 1.4 billion people, 5 times that of the United States, a GDP growth of 6.5% this year and, regarding specifically Artprice, a colossal art market with a massive pool of living artists (1 million in China versus 120,000 for the USA and Europe combined) and an almost infinite number of artworks. China's art market is animated by tens of millions of art buyers, professionals and collectors, many of whom are Artron customers and therefore, going forward, potential customers for Artprice. The title of Artron's press release: “Artron and Artprice team up to create the art ‘silk road'”, (the ‘silk road' notion is massively used by the Chinese State) makes perfect sense. The New Silk Road is part of China's soft power strategy (OBOR for One Belt, One Road) to conquer the world economically. China had initiated the project. According to the IMF, the World Bank and the CIA World Factbook, China is the world's leading economic power in terms of GDP-PPP in 2017. According to CNN, this project encompasses 68 countries representing 4.8 billion people and 62% of global GDP. Artron is a very powerful company and, for those interested in Art or the Art Market, Artron is completely unavoidable in China. Artron is not only the world's leading publisher of Fine Art books and auction catalogues (with more than 400 million books/catalogues printed); it is also a major scientific laboratory – with premises in Beijing, Shanghai and Shenzhen – and a technical and scientific knowledge base that easily rivals that of Silicon Valley. Its scanning processes in virtual reality, augmented reality and mixed reality have reached the very highest level of global sophistication and the company's scientific and cultural innovation has been rewarded with more than 800 prizes and awards for excellence. Artron.Net is the most respected brand in the Chinese art world. It has more than 3 million professional members in the arts sector and an average of 15 million daily visits, making it the world's leading art website. It is the first choice for art professionals, investors / collectors and art lovers. Founded in 1993, the Artron Art Group is celebrating its 25th anniversary this year. The involvement of Artron and its Chairman Mr. Wan Jie in Art in China is completely uncontested. Mr. Wan Jie is a ‘protector' of Beijing's famous 798 Factory which enjoys global visibility and was visited by Artprice staff. He is also Vice-Chairman and Founder of the Institute of the famous Forbidden City, where he and thierry Ehrmann visited government offices that are closed to the public during the recent trip to Beijing. The was also an opportunity for Artprice's Chairman thierry Ehrmann to see first-hand Mr. Wan Jie's involvement and support for the protection and diffusion of ancient masterpieces of Chinese art in the Imperial Granaries. These superb works have been “returned to the people” thanks to Artron's scientific breakthroughs and ultra high-speed Internet which allows these masterpieces of humanity to be contemplated in a virtual reality context, with the support of the Chinese State. During the trip, the Artprice team met some of China's world-renowned artists including Fang Lijun (born in 1963) ranked 623/700,000 in 2018 and Zhang Xiaogang (born in 1958) ranked 121/700,000 artists in 2018 in Artprice's global ranking. Artprice's press agency, ArtMarketInsight, together with Artron's editors, have decided to post around thirty daily dispatches in both Chinese and English aimed at combining information about the Chinese art market with information about the Western art market. Our various meetings and visits in Beijing left no doubt in our minds as to the power of China, the extraordinary wealth and depth of its history (over 4,000 years), and the country's incredible advance over the West in terms of technology… a vision and an understanding of China that completely disqualifies the ignorant visions of the Chinese Empire that can still be found in the West to this day. A geo-cultural analysis is not interested in the percentage of GDP spent on arms, but rather in the depth of the countries' respective histories and the relative strengths and weaknesses of the protagonist civilizations. Among its numerous manifestations, China's ‘soft power' is also focused on the Art Market. In this context, Artron's alliance with Artprice is part of Xi Jinping's “BRI” (belt and road initiative) launched in 2013 (aka the “Silk Road” in Europe). According to CNN, this project encompasses 68 countries representing 4.8 billion people and 62% of global GDP with an investment of close to $8 trillion. It is therefore a great honour for Artprice to have been chosen by Artron and its Chairman Mr. Wan Jie. Artron appreciates the work conducted by Artprice and has validated its place as World Leader in Art Market Information. That is why Artprice subscriptions will be distributed in China, with a huge potential for new customers. Artprice's data will contribute to the fluidity of the Chinese and, more broadly, the Asian Art Market, in a context where ‘Greater Asia' will account for 70% of the global Art Market by 2019. According to Artron, Artprice's econometric expertise associated with Artron's proprietary data will not only provide an extraordinary boost to the fluidity of China's Art Market (throughout its numerous provinces and autonomous regions), it will also greatly enhance and facilitate the work conducted by the country's tax, administrative and customs authorities. According to Artron and its Chairman Mr. Wan Jie, the only legitimate way to approach this colossal mission was to team up with a recognised and globally authoritative third-party certifier like Artprice, as World Leader in Art Market Information. Never mentioned in the press or identified by economists or sociologists, this massive new market that Artprice is entering is typical of the kind of domestic market that only a central player in China's Art Market could have been aware of. China's Provincial-level administrative divisions are the highest level administrative divisions in the People's Republic of China. There are 34 such divisions, classified as 23 provinces, 4 municipalities, 5 autonomous regions, and 2 Special Administrative Regions. Artprice subscriptions sold exclusively by Artron in China will therefore reach directly into the heart of the need identified by Artron within China's domestic market. Similarly, Artprice will be accessible via Artron.Net's home page and all the Chinese social networks where Artron is omnipresent. Artron's Chairman Mr. Wan Jie has already introduced Artprice to some very promising commercial contacts including the Chairman of China Guardian, China's first publicly-traded Chinese auction house. China Guardian needs high-end Artprice subscriptions for its VIP customers as well as Artprice's monthly analyses for its internal operations. Thanks to Artron's unique technology in the field of scanning parchments, manuscripts and collection catalogues from the previous century, Artprice will finally be able to offer all its customers extremely high value-added data such as the hundreds of thousands of handwritten notes by Hippolyte Mireur and the various pre-17th century documentary collections that Artprice owns, which are too fragile to be scanned using Western scanning devices. With this major breakthrough, Artprice will further strengthen its position as World Leader in Art Market Information. In the context of this extraordinary alliance with Artron and the massive potential for new customers in China, Artprice is anticipating a major boost to its 2019 sales and profits. For the launch and marketing of its services and databases in China, Artprice will benefit from all of Artron's logistical resources in terms of communication, via the Internet, as well as the physical world, thanks to its power, its reputation and its innumerable electronic and/or commercial networks throughout Greater Asia. In this context, Artprice, with the assistance of Artron, has just translated 125 million data into the Chinese currency, the Renmimbi (RMB). Naturally the primary objective of this translation process is to facilitate the purchase of its data by its new Chinese clientele, presented by Artron. This captive clientele is accustomed to using Alipay and WeChat (1.8 billion users), two Chinese instant payment platforms (QR Code in kiosk mode debiting the Chinese customer on behalf of Artprice) that are mandatory for Chinese buyers. Numerous synergies have already been identified from our joint working sessions and the merging of Artprice/Artron teams with the similar functions. Given the extent of strategic, financial and economic involvement with Artron, Artprice has decided to appoint a Chief Executive responsible for its Chinese and Greater Asia operations, who will reside in Beijing and work closely with Artron's teams. The objective of this strategy is to accelerate the numerous initiatives recently engendered by Artprice's and Artron's contractual and promissory agreements. This informed decision has been carefully deliberated and enjoys unanimous support within the Group. This appointment will, notably, make it easier to coordinate Artron's and Artprice's joint initiatives. Artron's goals are both transparent and unambiguous: In Mr. Wan Jie's own words: “The founders and Chairmen of the two companies, thierry Ehrmann and myself – with our enthusiasm for art – will create a Silk Road linking the Chinese and Western art markets on the principle of mutual respect and cooperation”. “The two parties will build a global, diversified and professional exchange platform in the art market that will ultimately promote the sustainable development of the global art market.” As this platform develops, Artprice's Standardised Marketplace® will host millions of works by Chinese artists, provided by Artron, generating a massive increase in the number of artworks available online. Artmarket.com, .net and .org therefore represent a decisive advantage in our quest to capture and drive the Global Art Market's development on the Internet. According to a bailiff's report established by the Estelle PONS - Sarah MERGUI licensed court bailiff partnership in Lyon, Artmarket.com is the top result out of 1.82 billion results on Google.com (all languages combined) and therefore represents the best possible vector for Artprice to promote the works of 1 million Chinese artists and their tens of millions of works (already hosted by Artron) in the Western art market. In view of the radical change in scope anticipated, Artprice is naturally moving towards an IPO of its subsidiary artmarket.com, its Standardized Marketplace®, on a Chinese stock exchange (Shanghai, Hong Kong, Shenzhen ...) and not on an Anglo-Saxon exchange as originally planned. According to thierry Ehrmann, “In 2019 Artprice will begin a new chapter alongside Artron that will trigger tremendous value for the global Art Market and our loyal shareholders. I am particularly pleased that my long-term strategy based on China's rapid economic emergence will generate such positive results.” “Today I am 56; when I first visited China I was 25. Since then I have spent 30 years patiently studying the Middle Kingdom. Beyond this satisfaction, I have had the immense pleasure of knowing Mr. Wan Jie, a founding Chairman with whom I share the same vision regarding the democratization and promotion of art in the world. In short… Artprice's long march is about to reach its objectives for its shareholders and for the global art market.” Artron will soon be publishing a documentary-report explaining all the meetings, discussions and agreements between the Artprice and Artron teams in Beijing. It will allow Western viewers to see images of Artron's ultra-sophisticated scientific processes and appreciate the economic power of Artron in Greater Asia. About the Artron Group: “Artron Art Group (Artron), a comprehensive cultural industrial group founded in 1993, is committed to inheriting, enhancing and spreading art value. Based on abundant art data, Artron provides art industry and art fans with professional service and experience of quality products by integrated application of IT, advanced digital science and innovative crafts and materials. Having produced more than 60,000 books and auction catalogues, Artron is the world's largest art book printer with a total print volume of 300 million a year. It has more than 3 million professional members in the arts sector and an average of 15 million daily visits, making it the world's leading art website. Founded in 1993, the Artron Art Group is celebrating its 25th anniversary this year. It is the first choice for art professionals, investors, collectors and art fans in general wishing to discover and/or participate in the art world or the art market. Founded in 1993, Artron Art Group is celebrating its 25th anniversary this year.” According to the Artron Group and its founder-Chairman Mr. Wan Jie “After 7 years of cooperation, Artron and Artprice have optimised their cooperation regarding the Chinese and Western art markets. The founders and Chairmen of both companies, Mr. Wan Jie and Mr. Thierry Ehrmann, with their enthusiasm for art, will create a Silk Road linking the Chinese and Western art markets on the principle of respect and mutual cooperation. The two groups will build a global, diversified and professional exchange platform in the Art Market, which will ultimately promote the sustainable development of the Global Art Market. Artprice is the global leader in art price and art index databanks. It has over 30 million indices and auction results covering more than 700,000 artists. Artprice Images® gives unlimited access to the largest Art Market resource in the world: a library of 126 million images or prints of artworks from the year 1700 to the present day, along with comments by Artprice's art historians. 12 Oct. 2018: Artprice and Artron have just created an “Art Media Mogul”: Artprice permanently enriches its databanks with information from 6,300 auctioneers and it publishes a constant flow of art market trends for the world's principal news agencies and approximately 7,200 international press publications. For its 4,500,000 members, Artprice gives access to the world's leading Standardised Marketplace for buying and selling art. Artprice is preparing its blockchain for the Art Market. It is BPI-labelled (scientific national French label)Artprice's Global Art Market Annual Report for 2017 published last March 2018: https://www.artprice.com/artprice-reports/the-art-market-in-2017

Q: Color every second row of the table I need to color every second row in my table. I would love it to look like on the attached image Any ideas how to do this? A: EVEN AND ODD RULES One way to improve the readability of large tables is to color alternating rows. For example, the table below has a light gray background for the even rows and white for the odd ones. The rules for that are extremely simple: Css: tr:nth-child(even) {background: #CCC} tr:nth-child(odd) {background: #FFF} Check here google 1st result

Introduction {#s1} ============ Some of the most diverse and bizarre organelle genomes of all eukaryotes come from the Volvocales, which is a large order of predominantly freshwater green algae, belonging to chlorophycean class of the Chlorophyta. Volvocalean mitochondrial and plastid DNAs (mtDNAs and ptDNAs) show an impressive array of architectures, nucleotide landscapes, and coding compositions ([Table 1](#pone-0057177-t001){ref-type="table"})-- and see Leliaert et al. [@pone.0057177-Leliaert1] and Lee and Hua [@pone.0057177-Lee1] for additional compilations. Moreover, certain volvocalean species, particularly those within the "*Reinhardtinia* clade" *sensu* Nakada et al. [@pone.0057177-Nakada1], have proven to be excellent systems for testing contemporary hypotheses on the evolution of organelle genome expansion and linearization [@pone.0057177-Smith1], [@pone.0057177-Michaelis1], [@pone.0057177-Smith2]. 10.1371/journal.pone.0057177.t001 ###### Completely sequenced organelle genomes from volvocalean green algae. {#pone-0057177-t001-1} Species Clade (lineage) Organelle genome architecture -------------------------------- ---------------------------- ------------------------------- -------- ---- -------- ---- ------ ------------------- MITOCHONDRIAL DNA * Chlamydomonas* *reinhardtii* *Reinhardtinia*(volvocine) Linear 16--19 55 67--82 7 0--3 EU306617--23 * Chlamydomonas* *moewusii* *Xenovolvoxa* Circular 23 65 54 7 9 AF008237 * Chlorogonium* *elongatum* *Caudivolvoxa* Circular 23 62 53 7 6 Y13643--4,Y07814 * Dunaliella salina* *Caudivolvoxa* Circular 28 66 42 7 18 GQ250045 * Gonium pectorale* *Reinhardtinia*(volvocine) Circular 16 61 73 7 1 AP012493 * Polytomella capuana* *Reinhardtinia* Linear 13 43 82 7 0 EF645804 * Polytomella parva* *Reinhardtinia* Linear 16 59 66 7 0 AY062933-4 * Polytomella* sp.SAG 63--10 *Reinhardtinia* Linear 16 58 66 7 0 GU108480-1 * Volvox carteri* *Reinhardtinia*(volvocine) Circular 35 66 \<40 7 3 EU760701,GU084821 PLASTID DNA * Chlamydomonas* *reinhardtii* *Reinhardtinia*(volvocine) Circular 204 66 44 66 7 FJ423446 * Dunaliella salina* *Caudivolvoxa* Circular 269 68 35 66 \>35 GQ250046 * Gonium pectorale* *Reinhardtinia*(volvocine) Circular 223 70 44 66 3 AP012494 * Volvox carteri* *Reinhardtinia*(volvocine) Circular 525 57 \<20 66 9 GU084820 Note: Values rounded to whole numbers. Clade names are based on Nakada et al. [@pone.0057177-Nakada1]. Percent coding includes all annotated protein-, rRNA-, and tRNA-coding regions as well as non-standard ORFs, such as the *rtl* gene in the *C. reinhardtii* mtDNA. Gene number includes standard protein-coding genes, but does not include intronic or nonstandard ORFs, like *rtl*. Duplicate genes and introns were counted only once. Genome statistics for *P. parva* and *P. piriformis* are based on the concatenation of the two mitochondrial chromosomes; those for *V. carteri* should be considered as approximations as the mtDNA and ptDNA contain assembly gaps due to unresolved repeats. For *C. reinhardtii*, the mitochondrial genome size, intron number, and coding content can vary because of optional introns. Most of our understanding of volvocalean mitochondrial and plastid genomes is limited to unicellular species, such as the model organisms *Chlamydomonas reinhardtii* and *C. globosa* (previously misidentified as *C. incerta*; see Nakada et al. [@pone.0057177-Nakada2]) [@pone.0057177-Michaelis1], [@pone.0057177-Popescu1], the colorless and wall-less *Polytomella capuana*, *P. parva*, and *P. piriformis* [@pone.0057177-Smith2], [@pone.0057177-Fan1], [@pone.0057177-Smith3], and the halotolerant β-carotene-rich *Dunaliella salina* [@pone.0057177-Smith4]. Surprisingly little is known about the organelle genomes of colonial and multicellular volvocaleans, which are found within the volvocine lineage of the *Reinhardtinia* clade ([Figure S1](#pone.0057177.s001){ref-type="supplementary-material"}). Volvocine algae are preeminent models for studying the evolution of multicellularity [@pone.0057177-Kirk1], [@pone.0057177-Sachs1], and span the gamut of cellular complexity, from simple 4-celled species (e.g., *Tetrabaena*), to 8-64-celled colonial forms (e.g., *Gonium*), all the way to highly complex spheroidal taxa, with more than 500 cells (e.g., *Volvox*) [@pone.0057177-Nozaki1], [@pone.0057177-Herron1]. It is estimated that multicellular volvocine species last shared a common unicellular ancestor ∼200 million years ago [@pone.0057177-Herron1]. Of the 8 different volvocalean algae for which complete mtDNA and/or ptDNA sequences are available [@pone.0057177-Smith4], only one is multicellular: *Volvox carteri*, which is comprised of ∼4,000 cells. The organelle genomes of this species are distended with repetitive noncoding DNA, and similar palindromic repeats are located in both the mitochondrial and plastid compartments [@pone.0057177-Smith5]. Moreover, the *V. carteri* ptDNA, at ∼525 kb, is among the largest plastomes ever observed (from any eukaryote) [@pone.0057177-Smith1], dwarfing that of *C. reinhardtii*, which is 204 kb [@pone.0057177-Maul1]. Although smaller than its plastid counterpart, the ∼35 kb mtDNA of *V. carteri* is still larger than any the other completely sequenced volvocalean mitochondrial genome. It is hypothesized that the expanded organelle genomes of *V. carteri* are a consequence of a low organelle mutation rate and/or a small effective population size [@pone.0057177-Smith1]. The *V. carteri* mtDNA assembles as a circular molecule, contrasting the linear (or linear fragmented) architectures of all other well-studied *Reinhardtinia*-clade mitochondrial genomes, including those of *C. reinhardtii*, *Polytomella* spp., and the multicellular *Pandorina morum* [@pone.0057177-Michaelis1], [@pone.0057177-Smith4], [@pone.0057177-Moore1]. These linear mtDNAs have evolved complex terminal structures [@pone.0057177-Michaelis1], [@pone.0057177-Smith3], called mitochondrial telomeres, which form long palindromic repeats at the genome ends. The origin and number of times that linear mitochondrial chromosomes have evolved within the *Reinhardtinia* is unknown, but it has been argued that they arose only once [@pone.0057177-Smith1]. If true, this would imply that in a recent ancestor of *V. carteri*, the mtDNA reverted from a linear to a circular form. To learn about organelle genome architecture within multicellular volvocine algae and to gain insight into ptDNA expansion and the origin of linear mtDNAs, we sequenced the mitochondrial and plastid genomes of *Gonium pectorale*--an 8- or 16-celled freshwater colonial alga, occupying a phylogenetic position closer to that of *V. carteri* than *C. reinhardtii* within the volvocine line [@pone.0057177-Nozaki1], [@pone.0057177-Herron1], [@pone.0057177-Nozaki2] ([Figure S1](#pone.0057177.s001){ref-type="supplementary-material"}). Materials and Methods {#s2} ===================== The organelle genomes described here come from *Gonium pectorale* K3-F3-4 (mating type *minus*), which was one of the F3 backcross strains to K41 (mating type *plus*) (originating from K41×K32 \[F1 strains of Kaneko3×Kaneko4\]) [@pone.0057177-Hamaji1], [@pone.0057177-Mogi1] and is available as NIES-2863 from the Microbial Culture Collection at National Institute for Environmental Studies, Tsukuba, Japan (<http://mcc.nies.go.jp/>). *G. pectorale* was grown in 200--300 mL VTAC medium [@pone.0057177-Nozaki3], [@pone.0057177-Kasai1] at 20°C on a 14∶10 h light-dark cycle, under cool-white fluorescent lamps (165--175 µmol m^−2^ s^−1^ intensity). Total DNA was extracted based on the protocol of Miller et al. [@pone.0057177-Miller1]. Sequencing libraries were prepared from *G. pectorale* K3-F3-4 genomic DNA using the GS FLX Titanium Rapid Library Preparation Kit (F. Hoffmann-La Roche, Basel, Switzerland) and the TruSeq DNA Sample Prep Kit (Illumina Inc., San Diego, CA, USA), and were run on a GS FLX (F. Hoffmann-La Roche) and a MiSeq sequencer (Illumina Inc.), respectively. The GS FLX reads were assembled with Newbler v2.6. A fosmid library (23,424 clones) was constructed from *G. pectorale* K3-F3-4 genomic DNA using fosmid vector pKS300, which was developed in-house. End sequencing of the fosmid library and the BAC library of *G. pectorale* Kaneko3 (18,048 clones, Genome Institute (CUGI), Clemson Univ., Clemson, SC, USA) was carried out using a BigDye terminator kit ver3 (Life Technologies, Carlsbad, California, USA) and was run on automated ABI 3730 capillary sequencers (Life Technologies). The GS FLX contig sequences, which were derived from mitochondrial and chloroplast genomes, and the BAC/fosmid end-sequences were assembled using the Phrap/Consed systems. Gap closing and re-sequencing of low-quality regions in the assembly were performed by shotgun sequencing of the corresponding BAC/fosmid clones, PCR, primer walking, and direct sequencing of fosmid clones. The MiSeq sequence reads were mapped against the assembly sequences using the BWA program [@pone.0057177-Li1] after passing through the quality filter. The errors on each GS FLX assembly sequence were also corrected. The assembling delineated one circular mtDNA and two ptDNA isoforms (A and B), a common feature of plastid genomes with inverted repeats [@pone.0057177-Stein1], [@pone.0057177-Harris1] ([Figure S2](#pone.0057177.s002){ref-type="supplementary-material"}). The annotated *G. pectorale* mtDNA and ptDNA (isoform A) sequences are deposited in the DDBJ database under accession numbers AP012493 and AP012494, respectively. Phylogenetic analyses were performed under maximum likelihood (ML) using RAxML [@pone.0057177-Stamatakis1] and PhyML 3.0 [@pone.0057177-Guindon1] with 100 bootstrap replicates. Maximum parsimony (MP) bootstrap analyses (based on 10 random replications of the full heuristic search with the tree bisection--reconnection branch-swapping algorithm) were performed in PAUP 4.0b10 [@pone.0057177-Swofford1] with 1,000 replications. MtDNA protein phylogeny was based on the deduced *nad5*, *cox1*, and *cob* amino acid sequences ([Table S1](#pone.0057177.s010){ref-type="supplementary-material"}), which were aligned using Clustal X [@pone.0057177-Thompson1]. Intron phylogenies were based on the deduced and aligned amino acid sequences of the *nad5* and *psaB* intronic open reading frames (ORFs), which gave data matrices of 205 and 256 amino acids with 9 and 14 operational taxonomic units (OTUs), respectively ([Tables S2](#pone.0057177.s011){ref-type="supplementary-material"}, [S3](#pone.0057177.s012){ref-type="supplementary-material"}). Intron secondary structure maps were constructed as previously described [@pone.0057177-Nozaki4]. Results and Discussion {#s3} ====================== The *Gonium pectorale* mtDNA: A Compact Circular Mapping Chromosome {#s3a} ------------------------------------------------------------------- The mitochondrial genome of *G. pectorale* has a conservative architecture: it is small (16 kb), circular-mapping, AT rich (61%), compact (73% coding), contains very few repeats, and has only a single intron ([Figure 1](#pone-0057177-g001){ref-type="fig"}, [Table 1](#pone-0057177-t001){ref-type="table"}, [Figure S3](#pone.0057177.s003){ref-type="supplementary-material"}). It lacks the eccentricities that often characterize the mtDNAs of other volvocalean species, such as a high GC content (e.g., *P. capuana*), a linear or linear-fragmented conformation (e.g., *P. parva*), a large intron density (e.g., *D. salina*), non-standard genes (e.g., *C. reinhardtii*), and/or a bloated repeat-rich structure (e.g., *V. carteri*) [@pone.0057177-Smith4]. The *G. pectorale* mtDNA is gene poor, encoding 7 proteins, 2 rRNAs, and 3 unique tRNAs, representing methionine, glutamine, and tryptophan ([Figure 1](#pone-0057177-g001){ref-type="fig"}). Two copies of *trnM* were identified adjacent to one another in the genome. Both have similar sequences and cloverleaf structures, and appear to have a role in elongation rather than initiation, as suggested for the *trnM* of other volvocalean algae. When ignoring non-standard genes and duplicate tRNAs, the *G. pectorale* mitochondrial gene repertoire mirrors those from all other available volvocalean algae, with the exception of *Polytomella* species, which lack *trnW* and *trnQ*. The *G. pectorale* mitochondrial large and small subunit (LSU and SSU) rRNA genes, like those from other available *Reinhardtinia* algae, are fragmented and scrambled throughout the genome into 8 and 4 coding modules, respectively. In *V. carteri* the eighth LSU module has been invaded by palindromic repeats, splitting it into two segments (L8a and L8b) [@pone.0057177-Smith5]; in *G. pectorale*, however, the L8 module is intact. {#pone-0057177-g001} The sole intron of the *G. pectorale* mtDNA, located in *nad5*, is of group ID affiliation [@pone.0057177-Michel1] ([Figure S3](#pone.0057177.s003){ref-type="supplementary-material"}) and encodes a putative intronic endonuclease. Other volvocaleans contain a *nad5* group I intron (with the same insertion site), but none are from the *Reinhardtinia* clade. Our phylogenetic analyses of various volvocalean intronic ORFs ([Figure S4](#pone.0057177.s004){ref-type="supplementary-material"}) suggest that the *G. pectorale nad5* intron either was acquired through horizontal transmission from a volvocalean closely related to *Chlamydomonas moewusii* or *Chlorogonium elongatum* or that it was present in the ancestor of the Volvocales and preserved in *G. pectorale*. Linear mitochondrial chromosomes are widespread throughout the *Reinhardtinia* clade, occurring in all explored taxa [@pone.0057177-Laflamme1], with the exception of *V. carteri*, which has a circular mtDNA map, but rare possible linear forms of the genome have been observed [@pone.0057177-Smith1], [@pone.0057177-Smith5] ([Table 1](#pone-0057177-t001){ref-type="table"}). Our *de novo* and mapping assemblies of the *G. pectorale* mtDNA gave an unambiguous circular-mapping chromosome (see Materials and Methods), and although such a map could represent a circularly permuted, linear-type structure, various features of the *G. pectorale* mitochondrial genome support the idea that it is circular. For instance, all twelve of the *G. pectorale* mtDNA genes have the same transcriptional polarity--a trait that is also found in *V. carteri* and available volvocalean species with circular mitochondrial genomes. Conversely, in all of the sequenced linear mtDNAs from the Volvocales, the genes are divided into two transcriptional polarities, proceeding outward towards the ends of the chromosome [@pone.0057177-Smith2].Furthermore, our Southern blot analysis of the *G. pectorale* mtDNA, cut with restriction enzymes, demonstrates that it is a circular molecule ([Figure S5](#pone.0057177.s005){ref-type="supplementary-material"}). Our evidence for a circular mitochondrial genome in *G. pectorale* raises interesting questions about the origin of linear mtDNAs within the *Reinhardtinia* clade. There is little doubt that the ancestral volvocalean mtDNA was circular, and it is argued that there was a single shift from a circular to a linear mtDNA structure in the ancestor that gave rise to *Reinhardtinia* algae [@pone.0057177-Smith2]. Within the *Reinhardtinia* clade, *V. carteri* and *G. pectorale* belong to a monophyletic colonial or multicellular volvocalean group from which unicellular members are separated [@pone.0057177-Nozaki1], [@pone.0057177-Herron1] ([Figure 2](#pone-0057177-g002){ref-type="fig"}), but the multicellular volvocalean *Pandorina morum* has a linear mtDNA [@pone.0057177-Moore1]. Moreover, *V. carteri* and *P. morum* belong to the monophyletic Volvocaceae from which *G. pectorale* is excluded [@pone.0057177-Nozaki1], [@pone.0057177-Herron1], [@pone.0057177-Nozaki2] ([Figure S1](#pone.0057177.s001){ref-type="supplementary-material"}). Thus, the appearance of circular mitochondrial genome maps in both *V. carteri* and *G. pectorale* suggests that the mtDNAs of these species independently reverted from a linear to a circular conformation in the two separate ancestors of *G. pectorale* and *V. carteri* ([Figure S1](#pone.0057177.s001){ref-type="supplementary-material"}) or alternatively that there were multiple origins of linear mitochondrial genomes in the *Reinhardtinia* clade, in the ancestors of *Polytomella*, *C. reinhardtii*, and *P. morum* ([Figure S1](#pone.0057177.s001){ref-type="supplementary-material"}). Studies of mtDNA structure from other volvocine species, such as *Tetrabaena* and *Yamagishiella*, are needed to further investigate these hypotheses. ![MtDNA protein phylogeny of seven species belonging to *Reinhardtinia* clade and three outgroup species from the Volvocales.\ The tree was constructed under the RAxML (with WAG+I+4G model) method using the concatenated sequences of the deduced *nad5*, *cox1*, and *cob* amino acid sequences. Left, middle, and right bootstrap values (≥50%) obtained using the RAxML, PhyML (with LG+I+4G model), and MP analysis, respectively. The amino acid sequences of the three proteins were aligned by Clustal X [@pone.0057177-Guindon1], and ambiguously aligned and highly variable regions were removed to construct a multiprotein data matrix of 909 amino acids from the 10 operational taxonomic units ([Table S1](#pone.0057177.s010){ref-type="supplementary-material"}).](pone.0057177.g002){#pone-0057177-g002} The *Gonium pectorale* ptDNA Shows Moderate Genome Expansion {#s3b} ------------------------------------------------------------ Volvocalean plastid genomes are big and that of *G. pectorale*, at 222.6 kb, is no exception. Of the approximately 300 complete (or almost complete) ptDNAs in GenBank, as of 1 August 2012, fewer than ten have a length \>200 kb, all but one of which are from chlorophyte green algae, including the volvocaleans *C. reinhardtii* (204 kb), *D. salina* (269 kb) and *V. carteri* (∼525 kb) [@pone.0057177-Smith1], [@pone.0057177-Smith4], [@pone.0057177-Maul1]. The large size of volvocalean ptDNAs is not a product of an inflated gene number, but a consequence of having an abundance of noncoding nucleotides, often represented by repetitive elements and introns. This is also true for the *G. pectorale* ptDNA, which is 56% (∼125 kb) noncoding. Almost all of these noncoding nucleotides are AT rich (average = 71%) and found in intergenic regions. The coding regions also have a high AT content (68%) and encompass a total of 98 unique genes, encoding 67 proteins, 3 rRNAs, 27 tRNAs, and a single misc RNA (*tscA*) ([Figure 3](#pone-0057177-g003){ref-type="fig"}). Six of these genes (*psbA*, *rrnL*, *rrnS*, *rrnF*, *trnA,* and *trnI*) are duplicated, being located in a pair of 14.8 kb inverted repeats, which divide the *G. pectorale* ptDNA into a large (99.6 kb) and a small (93.5 kb) single-copy region ([Figure 3](#pone-0057177-g003){ref-type="fig"}). This gene complement and inverted-repeat arrangement is almost identical to those of *C. reinhardtii* and *V. carteri* ([Figure 3](#pone-0057177-g003){ref-type="fig"}, [Figure S6](#pone.0057177.s006){ref-type="supplementary-material"}). {#pone-0057177-g003} Although some volvocalean algae harbour many ptDNA introns ([Table 1](#pone-0057177-t001){ref-type="table"})--*V. carteri* has 9 and *D. salina* has \>35--*G. pectorale* harbours just three: one located in *psaB*, which appears to be of group IA affiliation [@pone.0057177-Michel1] ([Figure S3](#pone.0057177.s003){ref-type="supplementary-material"}), and encodes a putative endonuclease-like protein, and two short group II introns (117 and 176 bp) found upstream of *psaA* exons 2 and 3 ([Figure 3](#pone-0057177-g003){ref-type="fig"}). Phylogenetic analysis of the *G. pectorale* intron ([Figure S7](#pone.0057177.s007){ref-type="supplementary-material"}) show that it is closely related to the *psaB* group I intron of the chlorophycean (but non-volvocalean) green alga *Stigeoclonium helveticum* [@pone.0057177-Blanger1]; moreover, both introns have the same insertion site within the *psaB* gene. *V. carteri* also has a *psaB* intron, but it is of group II affiliation [@pone.0057177-Smith1]. In fact, there is not a single homologous pair of either group I or group II introns among the *G. pectorale*, *V. carteri*, and *C. reinhardtii* plastid genomes ([Figure S6](#pone.0057177.s006){ref-type="supplementary-material"}), suggesting that rapid horizontal intron transfer and loss occurred within the colonial Volvocales. The *G. pectorale* plastid genome, like its *V. carteri* and *C. reinhardtii* counterparts, contains hundreds of short repetitive elements, distributed throughout the intergenic regions, as demonstrated by the dotplot similarity matrix ([Figure S8](#pone.0057177.s008){ref-type="supplementary-material"}). Many of the *V. carteri* ptDNA repeats are palindromes, and can be folded into hairpin structures [@pone.0057177-Smith5]. The same is true for the *G. pectorale* ptDNA, which contains ∼135 short (13 nt) palindromic repeats (including eight in the coding regions) with the motif: 5′- TCCCCNNNGGGGA-3′ ([Figure S9](#pone.0057177.s009){ref-type="supplementary-material"}). This is fewer repeats than found in the *V. carteri* ptDNA, which contains over a thousand palindromic elements. The *G. pectorale* ptDNA is slightly more expanded (by ∼19 kb) than that of *C. reinhardtii*, but much smaller than those of the unicellular *D. salina* (269 kb, ∼65% noncoding) and the multicellular *V. carteri* (∼525 kb, \>80% noncoding) ([Table 1](#pone-0057177-t001){ref-type="table"}). What has led to such a wide spectrum of ptDNA expansion within the Volvocales? One contemporary--and controversial [@pone.0057177-Daubin1], [@pone.0057177-Sloan1]--hypothesis for the evolution of genome size, called the mutational hazard hypothesis [@pone.0057177-Lynch1], argues that genome expansion is a product of a low effective population size (*N~e~*) (which results in increased random genetic drift) and/or a low mutation rate (μ), which reduces the burden of harbouring excess DNA. The *V. carteri* ptDNA is estimated to have a very low *N~e~*μ [@pone.0057177-Smith1], about twenty times lower than that of the *C. reinhardtii* ptDNA [@pone.0057177-Smith6], which may explain why it is so bloated. We do not know the value of *N~e~*μ for the *G. pectorale* ptDNA--this will require sequencing the plastid genomes of several additional *G. pectorale* isolates. However, given that this species is ∼10 times larger than *C. reinhardtii* (16 cells vs a single cell) and a hundred times smaller than *V. carteri* (16 cells vs 4,000 cells), and that all three of these algae are found in a similar environment (freshwater ponds)--unlike *D. salina*, which is marine--one might expect the effective population size of *G. pectorale* to be similar or marginally smaller than that of *C. reinhardtii*, and much larger than that of *V. carteri*. If true, this may have contributed to *G. pectorale* having a ptDNA architecture comparable to that of *C. reinhardtii* but much different than that of *V. carteri*. Under this hypothesis, it can therefore be predicted that as more volvocine organelle DNAs are sequenced, species with large cell numbers and presumably low effective population sizes will have more bloated genomes than those with small cell numbers and large effective population sizes. Supporting Information {#s4} ====================== ###### Simplified diagram for phylogenetic relationships of selected taxa of the unicellular, colonial and multicellular vovlocaleans. (TIF) ###### Click here for additional data file. ###### Diagrams of possible isoforms of ptDNA of *Gonium pectorale*. A. Two isoforms as found in other ptDNAs with a typical inverted repeat. B. Two additional isoforms that were not rejected based on assembling of our sequence data. (TIF) ###### Click here for additional data file. ###### Secondary structures of group I introns within the *Gonium pectorale* organelle DNAs. A. Mitochondrial *nad5* group ID intron. B. Chloroplast *psaB* group IA intron. (TIF) ###### Click here for additional data file. ###### Phylogeny of *Gonium pactorale nad5* group I intronic ORF. The tree was constructed under the RAxML (with WAG+4G model) method using 8 additional, related amino acid sequences selected based on the topology of the distance tree provided by blastp research of NCBI (<http://www.ncbi.nlm.nih.gov/>). Numbers on the left, middle and right at branches represent bootstrap values (≥50%) obtained using the RAxML, PhyML (with LG+4G model), and MP analysis, respectively. The amino acid sequences were aligned by Clustal X, and ambiguously aligned and highly variable regions were removed to construct a data matrix of 205 amino acids from the 9 operational taxonomic units ([Table S2](#pone.0057177.s011){ref-type="supplementary-material"}). (TIF) ###### Click here for additional data file. ###### Southern blot analysis of *Gonium pectorale* mtDNA with four restriction enzymes that cut the genome once (SacI and StuI) or twice (SacII and EcoRI). Genome map coordinates are based on the *G. pectorale* mtDNA DDBJ accession (AP012493). SacI and StuI digestions each gave single genome-sized bands (∼16 kb), and the SacII and EcoRI reactions each gave two bands. These data are consistent with the *G. pectorale* mtDNA being a circular molecules. Probe DNA was amplified by PCR with two specific primers (Gopec-mito-F 5′-CGGGCAAAGCATAATTAGTGTAG-3′ and Gopec-mito-R 5′-ACGAACAAGAGGAAGACCTAAC-3′). (TIF) ###### Click here for additional data file. ###### Venn diagram comparing the gene repertoires of three volvocalean chloroplast genomes (AP012494, GU084820 and FJ423446). 102 genes (single asterisk) shared by the three genomes include 12 genes distributed in IRA and IRB and *trnI* (cau), which was previously annotated as one of the triplicated *trnM* in *C. reinhardtii* and *V. carteri*. Double asterisks represent one of the duplicated genes in *G. pectorale* and *C. reinhardtii*. Triple asterisks exhibit one of the duplicated genes in *C. reinhardtii*. Note that all intronic ORFs in *G. pectprale* (1^\#^) and *V. carteri* (6^\#^) are unique for each genome and considered "non-coding" in the text. (PDF) ###### Click here for additional data file. ###### Phylogeny of *Gonium pactorale psaB* group I intronic ORF. The tree was constructed under the RAxML (with WAG+4G model) method using 13 additional, related amino acid sequences selected based on the topology of the distance tree provided by blastp research of NCBI (<http://www.ncbi.nlm.nih.gov/>). Numbers on the left, middle and right at branches represent bootstrap values (≥50%) obtained using the RAxML, PhyML (with LG+G model), and MP analysis, respectively. The amino acid sequences were aligned by Clustal X, and ambiguously aligned and highly variable regions were removed to construct a data matrix of 256 amino acids from the 14 operational taxonomic units ([Table S3](#pone.0057177.s012){ref-type="supplementary-material"}). (TIF) ###### Click here for additional data file. ###### Dotplot similarity matrix of the *Gonium pectorale* plastid genome. The X- and Y-axes each represent the *G. pectorale* plastid genome (222.6 kb). Dots in the nucleotide similarity matrix represent regions of sequence similarity. The matrix was generated using JDotter, with a sliding-window size of 50. The inverted repeats are highlighted in red in the matrix. (TIF) ###### Click here for additional data file. ###### Distribution of short (13 nt) palindromic repeats (including seven \[red arrows\] in five coding regions \[blues arrows\]) with the motif: 5′- TCCCCNNNGGGGA-3′ in ptDNA of *Gonium pectorale*. The repeats were examined by using Serial Cloner 2.5 (<http://serialbasics.free.fr/Serial_Cloner.html>). (JPG) ###### Click here for additional data file. ###### Amino acid alignment and origin of the data used for [Figure 2](#pone-0057177-g002){ref-type="fig"}. (DOC) ###### Click here for additional data file. ###### Amino acid alignment and origin of the data used for [Figure S4](#pone.0057177.s004){ref-type="supplementary-material"}. (DOC) ###### Click here for additional data file. ###### Amino acid alignment and origin of the data used for [Figure S7](#pone.0057177.s007){ref-type="supplementary-material"}. (DOC) ###### Click here for additional data file. We thank all the technical staff of the Comparative Genomics lab at National Institute of Genetics for their assistance. [^1]: **Competing Interests:**The authors have declared that no competing interests exist. [^2]: Conceived and designed the experiments: HT DS H. Noguchi AT AF H. Nozaki. Performed the experiments: TH AT MS HKT AF IN TM BO H. Nozaki. Analyzed the data: TH DS H. Noguchi AT AF H. Nozaki. Contributed reagents/materials/analysis tools: TH IN TM BO H. Nozaki. Wrote the paper: TH DS H. Noguchi AT AF H. Nozaki.

Khaleda to address 20-party rally in Gazipur Dec 27 Staff Reporter BNP chairperson Khaleda will go to Gazipur on December 27 to address a rally of her 20-party alliance in the district. The local unit of the 20-party will organize the rally at Bhawal Badre Alam Government College ground, BNP chairperson’s adviser Gazipur City Mayor MA Mannan told. Mannan said they have recently held a meting at BNP standing committee member Hannan Shah’s residence in Dhaka and finalized the rally schedule. The rally will be arranged protesting the ‘growing’ incidents of killing, enforced disappearance, abduction and the current ‘illegal’ government’s repressive acts and misrule, he said. The rally is also meant for drumming up public support in favour of their demand for snap polls under a non-party administration, he added. Mannan said they have already got permission from the college authorities to hold the public meeting. He said Khaleda will give direction to his party men about their upcoming decisive movement from the rally. It will be Khaleda’s 11th rally outside the capital after the January-5 election boycotted by the BNP-led opposition alliance. Earlier, Khaleda went to Rajbari on March 1, Munshiganj on May 28, Joypurhat on June 22, Brahmanbaria on September 23, Jamalpur on September 27, Nilphamari October 23, Natore on November 1, Kishoreganj on November 12, Comilla on November 29, and Narayanganj on December 13 and addressed public rallies there.

Q: what is up with this "modified 2 hours ago by Community" questions in the "active" list When I check the "active" questions, there are often questions included that are considered "active" because there were "modified N hours ago" and the modifying user is "Community". If open the question, I don't see any edit N hours ago, in fact most of the time the last activity was weeks, months or even years ago. Can anyone please clarify what is going on here? Personally I find it very inconvenient to see these long-time-inactive questions in the active stream, as sometimes I don't notice it's an old question until after I answer it :) A: A question without an accepted answer will be "modified" by the system from time to time so that it pops back up and gets looked at again. It will keep looking for an answer until it has an accepted answer. This happens on all the SE sites.

Q: Custom JSON Result in ASP.NET MVC I created custom ActionResult (simplified): public class FastJSONResult : ActionResult { public string JsonData { get; private set; } public FastJSONResult(object data) { JsonData = JSON.Instance.ToJSON(data); } public override void ExecuteResult(ControllerContext context) { HttpResponseBase response = context.HttpContext.Response; response.ContentType = "application/json"; response.Output.Write(JsonData); } } And use it from my WebApi controller: public ActionResult GetReport() { var report = new Report(); return new FastJSONResult(report); } Now the problem is, despite the fact that in FastJSONResult constructor my object serializes perfectly, ExecuteResult never gets called and in response I end up with object like {"JsonData":"{my json object as a string value}"} What am I doing wrong? A: Solved it with custom formatter (simplified to post less code) public class FastJsonFormatter : MediaTypeFormatter { private static JSONParameters _parameters = new JSONParameters() { public FastJsonFormatter() { SupportedMediaTypes.Add(new MediaTypeHeaderValue("application/json")); SupportedEncodings.Add(new UTF8Encoding(false, true)); } public override bool CanReadType(Type type) { return true; } public override bool CanWriteType(Type type) { return true; } public override Task<object> ReadFromStreamAsync(Type type, Stream readStream, HttpContent content, IFormatterLogger formatterLogger) { var task = Task<object>.Factory.StartNew(() => JSON.Instance.ToObject(new StreamReader(readStream).ReadToEnd(), type)); return task; } public override Task WriteToStreamAsync(Type type, object value, Stream writeStream, HttpContent content, TransportContext transportContext) { var task = Task.Factory.StartNew(() => { var json = JSON.Instance.ToJSON(value, _parameters); using (var w = new StreamWriter(writeStream)) w.Write(json); }); return task; } } In WebApiConfig.Register method: config.Formatters.Remove(config.Formatters.JsonFormatter); config.Formatters.Add(new FastJsonFormatter()); And now I receive json object properly:

Introduction {#s1} ============ Mitochondria perform a dual role in the life and death of the cardiomyocyte. When functioning normally they generate the energy required for normal cellular processes and survival. However, in situations of cellular stress such as during acute myocardial ischemia-reperfusion injury (IRI), they can become dysfunctional and be the arbitrators of cardiomyocyte death. Therefore, new treatment strategies which are capable of preventing mitochondrial dysfunction during acute IRI may reduce myocardial injury, preserve cardiac function and improve clinical outcomes in patients with ischemic heart disease. In this regard, the mitochondrial serine-threonine protein kinase, PTEN (phosphatase and tensin homologue on chromosome 10)-induced kinase 1 (PINK1), may provide a novel therapeutic target for cardioprotection [@pone.0062400-Siddall1]. Mutations in the PINK1 gene are responsible for the autosomal recessive PARK6 inherited form of early onset Parkinson disease, a neurodegenerative disorder characterized by the loss of dopaminergic neurons in the substantia nigra [@pone.0062400-Valente1]. Genetic ablation of PINK1 in neurons results in mitochondrial dysfunction characterized by: mitochondrial membrane depolarization [@pone.0062400-WoodKaczmar1], [@pone.0062400-Gandhi1], reduced mitochondrial respiration and ATP levels [@pone.0062400-Park1], increased oxidative stress [@pone.0062400-WoodKaczmar1], [@pone.0062400-Gandhi1], [@pone.0062400-Clark1]--[@pone.0062400-Dagda1], mitochondrial calcium overload [@pone.0062400-Gandhi1], and enhanced susceptibility to mitochondrial permeability transition pore (MPTP) opening [@pone.0062400-Gandhi1]. In contrast, wild-type PINK1 has been reported to protect neurons from mitochondrial dysfunction [@pone.0062400-Valente1], reduce mitochondrial cytochrome C release and caspase 3 and 9 activation [@pone.0062400-Petit1], [@pone.0062400-Wang2], and attenuate apoptotic cell death [@pone.0062400-Valente1], [@pone.0062400-Petit1]. Interestingly, PINK1 protein is highly expressed in the myocardium [@pone.0062400-Unoki1] but its role in the heart, is not clear [@pone.0062400-Siddall1], [@pone.0062400-Siddall2]. Given its beneficial effects on mitochondrial function and neuroprotective properties, we investigated whether PINK1 could also protect the heart against acute IRI. We find that the loss of PINK1 increases the heart\'s vulnerability to ischemia-reperfusion injury and this may be by worsening mitochondrial function. Materials and Methods {#s2} ===================== Animal experiments were conducted in strict accordance with the *Animals* (*Scientific Procedures*) *Act 1986* published by the UK Home Office and the *Guide for the Care and Use of Laboratory Animals* published by the US National Institutes of Health (NIH Publication No. 85--23, revised 1996). Approval has been granted by a local ethics review board at University College London. All efforts were made to minimize suffering. HL-1 Cell Culture and PINK1 Over-expression {#s2a} ------------------------------------------- HL-1 cells are an adherent murine atrial cell line that spontaneously beat in culture (the cells were obtained from Claycomb) [@pone.0062400-Claycomb1]. Cells were cultured in tissue culture flasks pre-coated for 2--3 hrs with 10 µg/ml fibronectin (diluted in 0.02% gelatin). Growth medium (Claycomb media supplemented with 10% FBS, 2 mM L glutamine (Invitrogen, Gibco), 0.1 mM norepinephrine (prepared in 30 mM ascorbic acid), 500 IU penicillin and 500 µg streptomycin (PAA Laboratories)) was changed every 1--2 days and cells were maintained at 37°C in 95%O~2~/5%CO~2~ with 90% humidity. A similar vector expressing PINK1 under the control of the CMV promoter (Addgene plasmid 13315: pcDNA-DEST53 PINK1) from Addgene Inc., Cambridge, MA was used to over-express PINK1. HL-1 cells were seeded onto fibronectin coated glass cover slips and upon reaching 50--60% confluence were transfected for 24 hours using Fugene6 ® (Roche, UK) according to manufacturer's instructions. The pEGFP expression plasmid (Clontech) was included for identification of successfully transfected cells, at a ratio of 1∶2. The vector control group was designated as cells transfected with an empty plasmid expression vector (RcCMV). A similar vector expressing PINK1 under the control of the CMV promoter (Addgene plasmid 13315: pcDNA-DEST53 PINK1) from Addgene Inc., Cambridge, MA was used to over-express PINK1 in a separate set of cells. The pEGFP expression plasmid (Clontech) was included for identification of successfully transfected cells, at a ratio of 1∶2. The transfection efficacy was 60--70% of cells. Culture media containing transfection components was replaced with fresh growth medium and cells were incubated overnight. Unfortunately due to a lack of a specific commercially available PINK1 antibody were not able to demonstrate PINK1 protein expression or localization. Simulated Ischemia-reperfusion Injury in HL-1 Cells Over-expressing PINK1 {#s2b} ------------------------------------------------------------------------- In order to determine the effect of PINK1 over-expression on the susceptibility to simulated ischemia-reperfusion injury (SIRI), HL-1 cells were subjected to a sustained episode of lethal hypoxia and reoxygenation [@pone.0062400-Lim1], [@pone.0062400-Smith1]. Culture medium was removed and replaced with hypoxic buffer (comprising in mM: KH~2~PO~4~ 1.0, NaHCO~3~ 10.0, MgCl~2~.6H~2~O 1.2, NaHEPES 25.0, NaCl 74.0, KCl 16, CaCl~2~ 1.2 and NaLactate 20 at pH 6.2, bubbled with 100% nitrogen) and then placed in an airtight custom-built hypoxic chamber kept at 37°C for 12 hours to simulate ischemia. Following the period of simulated ischemia, the cells were removed from the hypoxic chamber and placed in normoxic Claycomb medium (containing 3 µM propidium iodide) and returned to a tissue culture incubator, to simulate reperfusion. Following 1 hour simulated reperfusion at 37°C, the percentage of GFP-transfected cells stained with propidium iodide was determined using a Nikon Eclipse TE200 fluorescent microscope in order to calculate the percentage cell death in each treatment group. For each treatment group 80 cells were counted, taken from four randomly-selected fields of view. This experiment was repeated on at least four separate occasions giving a total of 320 cells per treatment group. For a time-matched normoxic control group, HL-1 cells were placed in normoxic buffer (comprising in mM: KH~2~PO~4~ 1.0, NaHCO~3~ 10.0, MgCl~2~.6H~2~O 1.2, NaHEPES 25.0, NaCl 98.0, KCl 3, CaCl~2~ 1.2, d-glucose 10.0, Na pyruvate 2.0 at pH 7.4, bubbled with 5% CO~2~/95% O~2~) for the total 13 hours duration of the experiment and the percentage cell death was determined. ROS-induced MPTP Opening in HL-1 Cells Over-expressing PINK1 {#s2c} ------------------------------------------------------------ To determine the effect of PINK1 over-expression on the susceptibility to MPTP opening, a previously validated cell model of MPTP opening was utilized [@pone.0062400-Zorov1]. Confocal laser-stimulation of the fluorophore tetra methyl rhodamine methyl (TMRM), which accumulates into mitochondria, generates reactive oxygen species (ROS) within mitochondria. This cell model can be used to simulate the events occurring at reperfusion, in which the production of ROS results in MPTP opening and the collapse of the mitochondrial membrane potential [@pone.0062400-Zorov1], [@pone.0062400-Davidson1]. The collapse of mitochondrial membrane potential in this cell model has previously been verified as indicating MPTP opening as it coincides with the redistribution of calcein from the mitochondria to the cytosol [@pone.0062400-Hausenloy1]. Culture medium was removed and replaced with Krebs imaging buffer. Cells were then loaded with the 3 µM TMRM for 15 min at 37°C and washed with Krebs imaging buffer. The time taken to induce mitochondrial membrane depolarization is recorded as a measure of susceptibility to MPTP opening. This was defined as the time taken to reach half the maximum TMRM fluorescence intensity. Twenty transfected cells were randomly selected for the induction and detection of MPTP opening from each treatment group, and this was repeated in four independent experiments giving a total of 80 cells per treatment group. As a positive control and in order to confirm that mitochondrial membrane depolarization was indicative of MPTP opening, following TMRM loading, a group of cells were pre-treated for 10 minutes with the MPTP inhibitor, cyclosporin A (0.2 µM) [@pone.0062400-Lim1], [@pone.0062400-Hausenloy2], [@pone.0062400-Davidson2]. The time taken to induce to MPTP opening was recorded. HL-1 cells were visualized using a Leica TCS SP5 CLSM confocal microscope equipped with HCX PL APO 40×/1.25 oil objective lens using the 488-nm of an Argon laser and the 543-nm emission line of a HeNe laser. Time scans were recorded with simultaneous excitation at 488 nm (for GFP) and 543 nm (for TMRM), collecting fluorescence emission at 500--536 nm and 585--680 nm, respectively. For these MPTP experiments, all conditions of the confocal imaging system (laser power, confocal pinhole - set to give an optical slice of 1 micron -- pixel dwell time, and detector sensitivity) were identical to ensure comparability between experiments. Images were analyzed using the LAS AF Version: 2.0.0 Build 1934 software program. PINK1 Knockout Mice {#s2d} ------------------- PINK1 knockout mice were a kind gift from Dr Luis Miguel Martins and Dr Nicoleta Moisoi of the MRC Toxicology Unit at the University of Leicester. These were bred in-house and PINK1+/+, +/− and −/− genotypes were generated. Genotyping was performed by extracting DNA from mouse ear biopsies using a Qiagen DNeasy kit with a proteinase K and spin column extraction method (Qiagen, UK) as previously described [@pone.0062400-WoodKaczmar1]. Myocardial Infarction in PINK1 Knockout Mouse Hearts {#s2e} ---------------------------------------------------- Hearts from PINK1+/+, PINK1+/− and PINK1−/− mice (10--15 weeks, 20--30 g) were isolated and perfused using a Langendorff constant pressure system as described previously [@pone.0062400-Siddall1]. Mice were given 500 IU of heparin by intraperitoneal injection before being culled by cervical dislocation. Hearts were rapidly excised and retrogradely perfused via the aorta on a Langendorff-apparatus (AD Instruments, UK) at 100 mmHg, with oxygenated Krebs-Henseleit buffer containing NaCl 118 mM, NaHCO~3~ 24 mM, KCl 4 mM, NaH~2~PO~4~ 1 mM, CaCl~2~ 1.8 mM, MgCl~2~ 1.2 mM and glucose 10 mM. Myocardial temperature was maintained at 37.0±0.5°C. Isolated perfused hearts were subjected to a 30 minute stabilization period followed by 35 minute global normothermic ischemia and 30 minute reperfusion. Infarct size was measured by perfusing a 1% triphenyltetrazolium chloride (TTC) solution retrogradely through the aorta and incubating the hearts at 37.0°C for 10 min before storing at −20.0°C. Subsequently, hearts were sliced (\<1 mm slices), destained in formalin, photographed and planimetered using the NIH Image 1.63 software package (National Institutes of Health, Bethesda, MD, USA). Infarct size was calculated as the percentage of the whole myocardium at risk (I/R%). Isolation of Adult Murine Cardiomyocytes {#s2f} ---------------------------------------- As described previously [@pone.0062400-Lim1] PINK1+/+ and PINK1−/− mice (10--15 weeks, 20--30 g) were injected (i.p) with 500 IU of heparin 30 minutes prior to an 0.01 mg/g i.p injection of anaesthetic, (10 mg/ml Ketamine, 2 mg/ml Xylazine and 0.06 mg/ml Atropine) as a terminal procedure. Hearts were excised and immediately placed in ice cold calcium free perfusion buffer (113 mM NaCl, 4.7 mM KCL, 0.6 mM KH~2~PO~4~, 0.6 mM Na~2~HPO~4~, 1.2 mM MgSO~4~.7H~2~O, 12 mM NaHCO~3~, 10 mM KHCO~3~, 30 mM Taurine, 10 mM HEPES, 11 mM Glucose and 10 mM 2,3-Butanedione monoxime). Within 3 minutes the heart was secured to a 22 gauge cannula via the aorta and attached to a perfusion apparatus. The heart was retrogradely perfused at 3 ml/min, with pre-warmed (37.0°C) oxygenated (95%O~2~/5%CO~2~) calcium-free perfusion buffer for 4 minutes. The heart was then perfused for 10 minutes with pre-warmed oxygenated digestion buffer (220 U/ml of type 2 Collagenase (Worthington, UK) and 55 U/ml Hyaluronidase (Sigma, UK) dissolved in the calcium free perfusion buffer and supplemented with 12.5 µM CaCl~2~). The ventricles were collected in 10 mlof digestion buffer and gently teased apart for additional tissue disruption. The tissue was digested further by incubating the mixture with 95%O~2~/5%CO~2~ in a shaking incubator (180 rpm) at 37°C for 10 minutes. The supernatant was collected and the remaining tissue pellet was incubated with an additional 10 ml digestion buffer followed by 10 minutes incubation with 95%O~2~/5%CO~2~ in a shaking incubator at 37°C. Under sterile conditions each ventricular cell suspension was transferred to a fresh tube and 5% FBS was added. The cells were centrifuged at 600 relative centrifugal force (RCF) for 3 minutes to separate the larger, cardiomyocyte pellet. The smaller fibroblasts and remaining connective tissue in the supernatant were discarded. The cardiomyocyte pellet was re-suspended in a low calcium buffer, which consisted of the calcium free perfusion buffer supplemented with 12.5 µM CaCl~2~. Small volumes of calcium were re-introduced to the cardiomyocyte suspension every 4 minutes to gradually reach a final concentration of 1 mM. The cells were then centrifuged at 600 RCF for 3 min and re-suspended in 1--2 ml of plating media (Medium-199)(Sigma, UK) supplemented with 2 mg/ml bovine serum albumin, 0.66 mg/ml creatine, 0.66 mg/ml taurine, 0.32 mg/ml carnitine, 50 U/ml penicillin, 5 µg/ml streptomycin and 25 µM blebbistatin (Calbiochem, Nottingham, UK). The cell suspension was then added to a glass cover slip, 22 mm diameter (VWR, Lutterworth, UK) pre-coated with laminin (1 mg/ml) to aid cell adhesion. Cells were left to adhere for 1 hr at 37°C, 95%O~2~/5%CO~2~ and 90% humidity. Finally, each cover slip was washed with plating media and the adhered cardiomyocytes were incubated with 1 ml of fresh plating media without blebbistatin. Measuring Mitochondrial Membrane Potential in PINK1−/− Cardiomyocytes {#s2g} --------------------------------------------------------------------- Primary adult cardiomyocytes were isolated from the myocardium of PINK1+/+ and −/− mice, as described above and loaded with 50 nM TMRM diluted in imaging buffer (which consisted of low calcium perfusion buffer without BDM and supplemented with 10 mM HEPES and 1.2 mM CaCl~2~ at pH 7.4) for 30 minutes. This was used to measure the mitochondrial membrane potential [@pone.0062400-Gandhi1], [@pone.0062400-Davidson1]. The isolated cardiomyocytes were mounted onto the confocal apparatus. The HeNe laser (543 nm) used to excite the TMRM was set to 2% power to prevent bleaching. Images were captured and the fluorescent intensity of each cell was recorded using the Leica application suite for Advanced Fluorescence (LAS AF Leica TCS SP5). Measuring Oxygen Consumption in Intact Cardiomyocytes and Isolated Mitochondria {#s2h} ------------------------------------------------------------------------------- To measure respiration rate in intact cells, approximately 2 × 10^6^ cells were suspended in HBSS in a Clark-type oxygen electrode thermostatically maintained at 37°C. The oxygen electrode was calibrated with air-saturated water, assuming 406 nmol O atoms/ml at 37°C. Oxygen consumption was measured over time with addition of oligomycin (final concentration 2 µg/ml) and 1 µM FCCP. To measure respiratory control ratio, intact mitochondria were isolated from hearts of WT and PINK1 KO mice by a method of differential centrifugation [@pone.0062400-Rosca1] and resuspended in medium containing 135 mM KCl, 10 mM NaCl, 20 mM HEPES, 0.5 mM KH~2~PO~4~, 1 mM MgCl~2~, 5 mM EGTA at pH 7.1. Oxygen consumption was measured in a Clark-type oxygen electrode thermostatically maintained at 25°C. Glutamate (5 mM) and malate (5 mM) were added to measure Complex I-linked respiration, succinate (5 mM) with rotenone (5 µM) were added to measure Complex II-linked respiration. All data were obtained using an Oxygraph Plus system with Chart recording software. Measuring Time to Contracture in PINK1−/− Cardiomyocytes {#s2i} -------------------------------------------------------- Primary adult cardiomyocytes were isolated from PINK1+/+ and −/− hearts, as described above, and, while imaging the cells, 10 µM carbonyl cyanide m-chlorophenyl hydrazone (CCCP) was added to the imaging buffer. In the presence of this uncoupling agent, the F~0~F~1~ATPase runs in "reverse" mode, consuming ATP in order to pump protons out of the mitochondria and maintain the membrane potential. When ATP decreases to a threshold level, adult cardiomyocytes undergo rigor contracture. The time to contracture can therefore be used as an indirect measure of basal levels of ATP or the activity of F~0~F~1~ATPase [@pone.0062400-Li1]--[@pone.0062400-Kaminishi1]. Sequential images of cells incubated with CCCP were taken at intervals of one minute using a standard light microscope affixed with a SPOT camera (Diagnostics Instruments, USA) connected to SPOT imaging software version 4.6 (Diagnostic Instruments, USA). The time to contracture was recorded and compared in the isolated PINK1+/+ and −/− cardiomyocytes. Measuring ROS during SIRI in PINK1−/− Cardiomyocytes {#s2j} ---------------------------------------------------- The generation of ROS following SIRI was investigated in isolated adult cardiomyocytes isolated from PINK1+/+ and PINK1−/− mouse hearts. Cardiomyocytes were subjected to 45 min simulated ischemia followed by 30 min re-oxygenation (SIRI) in the presence of 2 µM dihydroethidium (DHE, Molecular Probes, Invitrogen, UK), which is oxidized in the presence of superoxide to become fluorescent [@pone.0062400-Robinson1]. The fluorescence intensity, reflecting ROS levels, using SPOT imaging software version 4.6 (Diagnostic Instruments, USA) and NIH-Image, values were normalized to PINK1+/+ normoxic control. Statistical Analysis {#s2k} -------------------- Values are mean ± SEM. Data were analyzed using either the Student\'s *t*-test or one-way analysis of variance (ANOVA), followed by Bonferroni's multiple comparison post hoc test. P\<0.05 was considered significant. Results {#s3} ======= PINK1 Over-expression Protects HL-1 Cells against SIRI {#s3a} ------------------------------------------------------ PINK1 over-expression significantly reduced HL-1 cardiac cell death following SIRI: 49.0±2.4% in the vector control to 29.0±5.2% with PINK1 ([Figure 1](#pone-0062400-g001){ref-type="fig"}; P\<0.05). The proportion of dead cells in the time-matched normoxic control conditions was \<5.0% and this was not significantly altered by transgene expression. {#pone-0062400-g001} PINK1 Over-expression in HL-1 Cells Decreases Susceptibility to MPTP Opening {#s3b} ---------------------------------------------------------------------------- PINK1 over-expression in HL-1 cells delayed the time to MPTP opening by 1.3±0.3 fold when compared to control values (P\<0.01; [Figure 2](#pone-0062400-g002){ref-type="fig"}). The delay in MPTP opening was similar to that conferred by the known MPTP inhibitor, CsA (1.4±0.1 fold;P\<0.05; [Figure 2](#pone-0062400-g002){ref-type="fig"}). {#pone-0062400-g002} Myocardial Infarct Size is Increased in PINK1 Knockout Mice {#s3c} ----------------------------------------------------------- PINK1−/− mice developed significantly larger myocardial infarcts following an episode of sustained ischemia-reperfusion injury compared to PINK1+/+ mice, with PINK1+/− mice sustaining an intermediate sized infarct (25.1±2.0% in PINK1+/+ hearts versus 38.9±3.4% in PINK1+/− hearts; P\<0.01) and (25.1±2.0% in PINK1+/+ hearts versus 51.5±4.3% in PINK1−/− hearts (P\<0.001)(see [Figure 3](#pone-0062400-g003){ref-type="fig"}). {#pone-0062400-g003} Mitochondrial Membrane Potential and Time to Contracture in PINK1−/− Cardiomyocytes {#s3d} ----------------------------------------------------------------------------------- Since PINK1 has been implicated in mitochondrial function we evaluated mitochondrial membrane potential in primary adult cardiomyocytes under basal conditions. This was found to be lower in PINK1−/− cardiomyocytes compared to PINK1+/+ cardiomyocytes ([Figure 4](#pone-0062400-g004){ref-type="fig"}), as evidenced by decreased TMRM fluorescence (In arbitrary units: 12.1±2.8 in PINK1−/− cardiomyocytes versus 17.9±2.6 in PINK1+/+ cardiomyocytes; P\<0.05; [Figure 5](#pone-0062400-g005){ref-type="fig"}). {#pone-0062400-g004} {#pone-0062400-g005} Oxygen Consumption in Isolated Intact Cardiomyocytes {#s3e} ---------------------------------------------------- The basal oxygen consumption rate was significantly reduced in the PINK1 KO cardiomyocytes (0.48±0.04 nmol/O~2~/min/10^6^ cells, N = 4 experiments; [Figure 6](#pone-0062400-g006){ref-type="fig"}) compared to control cells (0.81±0.01 nmol O/min/10^6^ cells, N = 4 experiments, P\<0.001). Oligomycin (2 µg/ml) inhibited the respiration coupled to oxidative phosphorylation in control cells (to 0.11±0.01 nmol O/min/10^6^ cells, P\<0.05) but significantly less in PINK1 KO cardiomyocytes (0.37±0.03 nmol O~2~/min/10^6^ cells, compared to basal 0.48±0.04 nmol/O~2~/min/10^6^ cells; P\<0.001; [Figure 6](#pone-0062400-g006){ref-type="fig"}). 1 µM FCCP accelerated respiration to maximal levels in control cells, but to a lesser extent in PINK1 KO cardiomyocytes (4.2±0.19 vs. 3.4±0.03 nmol/O~2~/min/10^6^ cells; P\<0.001; [Figure 6](#pone-0062400-g006){ref-type="fig"}). This data suggest a generalised impairment of respiration in PINK1 KO heart cells. To identify the mechanism underlying the impaired mitochondrial respiration we investigated isolated mitochondria. {#pone-0062400-g006} Oxygen Consumption in Isolated Mitochondria {#s3f} ------------------------------------------- We evaluated the effect of PINK1 deficiency on oxygen consumption in isolated mitochondria. Compared to WT, oxygen consumption in PINK1 deficient mitochondria in the presence of the substrate of Complex I (5 mM Malate/5 mM Glutamate) was not significantly different (N = 6 experiments; [Figure 7a,c](#pone-0062400-g007){ref-type="fig"}). Application of Complex II substrate (succinate in the presence of rotenone; N = 6 experiments; [Figure 7b,c](#pone-0062400-g007){ref-type="fig"}) activated oxygen consumption equally in PINK1-KO and WT heart mitochondria. The respiratory control ratio (RCR), the ratio of state 3 (ADP-stimulated) to state 4 respiration (no ADP present), is an indication of the degree of coupling of the mitochondrial respiratory chain activity to oxidative phosphorylation. The RCR was unchanged in PINK1 KO, when compared to WT mitochondria. {#pone-0062400-g007} Time to Uncoupler-induced Hypercontracture {#s3g} ------------------------------------------ The time taken to hypercontracture following the administration of mitochondrial uncoupler, CCCP was recorded in cardiomyocytes. This time was significantly decreased in PINK1−/− cardiomyocytes (22.8±1.8 min in PINK1+/+ cells to 13.3±1.6 min in PINK1−/− cells; P\<0.01; [Figure 7](#pone-0062400-g007){ref-type="fig"}) indicating either a significantly lower basal level of cellular ATP or decreased function of the F~0~F~1~ATPase. However, it must be important to bear in mind that this is an indirect measure of cellular ATP levels. Oxidative Stress Post-SIRI is Increased in PINK1−/− Mice {#s3h} -------------------------------------------------------- At baseline, there was no significant difference in oxidative stress in isolated PINK1+/+ and PINK1−/− cardiomyocytes ([Figure 8](#pone-0062400-g008){ref-type="fig"}). However, following SIRI, the PINK1−/− cardiomyocytes exhibited a significantly greater level of superoxide production when compared to PINK1+/+ cardiomyocytes (145±12% in PINK1+/+ cardiomyocytes compared to 216±27% in PINK1−/− cardiomyocytes following SIRI (P\<0.05; [Figure 9](#pone-0062400-g009){ref-type="fig"}). {#pone-0062400-g008} {#pone-0062400-g009} Discussion {#s4} ========== The major findings of the current study are as follows: (1) Over-expressing PINK1 in the HL-1 cardiac cell line delayed the time taken to induce MPTP opening and reduced cell death following SIRI; (2) Mice lacking PINK1 sustained larger myocardial infarcts compared to wild type littermates (PINK1+/+), suggesting that the absence of PINK1 in the heart makes it more vulnerable to IRI. Interestingly, mice heterozygous for PINK1 sustained myocardial infarcts which were intermediate in size; (3) The increased susceptibility to IRI of PINK1−/− mice may be due to impaired mitochondrial function, as evidenced by a lower mitochondrial potential under basal conditions, impaired mitochondrial respiration, increased susceptibility to rigor contracture, and enhanced oxidative stress production during SIRI. Our study suggests a role for mitochondrial PINK1 as a target for cardioprotection in the heart. This mitochondrial protein appears to be required for endogenous protection against SIRI, as its genetic ablation resulted in an enhanced susceptibility to myocardial infarction, a response which was graded according to whether one or both PINK1 alleles were knocked-out. Our data suggests that the loss of PINK1 increases the heart\'s vulnerability to ischemia-reperfusion injury by worsening mitochondrial function. Its absence was associated with mitochondrial membrane depolarization, impaired mitochondrial respiration, increased susceptibility to rigor contracture, and more oxidative stress production during SIRI. In contrast, the over-expression of PINK1 was able to prevent the opening of the MPTP in the HL-1 cardiac cell line. A minor limitation of our study is that we did not investigate whether MPTP opening susceptibility was increased in adult cardiomyocytes deficient in PINK1. A recently published experimental study has also reported detrimental effects on mitochondrial function and cardiomyocyte homeostasis in mice lacking PINK1, but the effects of PINK1 on susceptibility to IRI was not explored in that study [@pone.0062400-Billia1]. Furthermore, these authors reported cardiac hypertrophy and cardiac fibrosis from 2 months of age [@pone.0062400-Billia1]. Despite many studies implicating PINK1 as a neuroprotective mitochondrial protein kinase, there have been a limited number of studies investigating the protective effect of PINK1 against ischemic neuronal injury. Shan and co-workers [@pone.0062400-Shan1] have reported that PINK1 can protect neonatal rat cortical neurons against simulated ischemia. Emerging studies have suggested that a functional impairment in activity of complex I of the electron transport chain underlies the mitochondrial dysfunction central to Parkinson's disease [@pone.0062400-Gandhi1], [@pone.0062400-Morais1]. The involvement of complex I inhibition in the pathogenesis of Parkinson's disease has long been appreciated with reduced complex I activity noted in patients with Parkinson's disease [@pone.0062400-Schapira1], and the use of complex I inhibitors such as rotenone to reproduce robust animal models of Parkinson's disease [@pone.0062400-Betarbet1]. Complex I inhibition may also explain some of the other known features of Parkinson's mitochondrial dysfunction including mitochondrial membrane depolarization [@pone.0062400-WoodKaczmar1], [@pone.0062400-Gandhi1], [@pone.0062400-Morais1], increase production of oxidative stress from complex I [@pone.0062400-WoodKaczmar1], [@pone.0062400-Gandhi1], [@pone.0062400-Clark1]--[@pone.0062400-Dagda1], reduced mitochondrial respiration and ATP depletion [@pone.0062400-Park1] and predisposition to MPTP opening [@pone.0062400-Gandhi1]. Interestingly, in our studies, we found that in isolated PINK1 deficient mitochondria there were no changes in the rate of mitochondrial respiration in the presence of substrates for Complex I and Complex II. Furthermore, PINK1 deficiency had no effect on uncoupling of oxidative phosphorylation as the respiratory control ratio remained unchanged. These findings are in agreement with experimental data, which have been performed in other cell types [@pone.0062400-Gandhi1], [@pone.0062400-Yao1]. However, in intact cardiomyocytes, PINK1 deficiency did significantly depress oxygen consumption, suggesting that the absence of PINK1 does not impair respiratory complex function but affects the delivery of substrates to the mitochondria (such as inhibition of glycolysis or the TCA cycle or inhibition of glucose uptake) [@pone.0062400-Gandhi1]. The MPTP is a non-selective high-conductance channel of the inner mitochondrial membrane whose opening results in cell death by uncoupling oxidative phosphorylation [@pone.0062400-Hausenloy2], [@pone.0062400-Halestrap1], [@pone.0062400-Di1]. In the absence of PINK1, a number of factors can result in an increased susceptibility to MPTP opening including mitochondrial membrane depolarization [@pone.0062400-Morais1], reduced mitochondrial calcium retention [@pone.0062400-Gandhi1], increased oxidative stress [@pone.0062400-WoodKaczmar1], [@pone.0062400-Gandhi1], [@pone.0062400-Clark1]--[@pone.0062400-Dagda1] particularly from complex I inhibition [@pone.0062400-Batandier1]. Of course there may be other beneficial effects on mitochondrial function which may explain the cardioprotective effects of PINK1. PINK1 has been reported to phosphorylate TNF receptor-associated protein 1 (TRAP1), a mitochondrial chaperone protein, which protects against oxidative stress-induced apoptotic cell death [@pone.0062400-Pridgeon1]. It has been proposed that PINK1 promotes the translocation of Parkin (an E3 ubiquitin ligase) to dysfunctional mitochondria, where outer mitochondrial membrane Mitofusins are ubiquinated, to provide a signal for mitophagy (the autophagic removal of dysfunctional mitochondria) [@pone.0062400-Poole1], [@pone.0062400-Ziviani1]. Changes in mitochondrial morphology can impact on a variety of cellular functions including metabolism, development and more recently cardioprotection [@pone.0062400-Ong1]. However, the effect of PINK1 on mitochondrial morphology has been variable and inconclusive [@pone.0062400-Bueler1]. Whether any of these other effects of PINK1 on mitochondrial function occur in the heart remains to be determined. Conclusions {#s4a} ----------- In conclusion, our data suggests that the loss of PINK1 increases the heart\'s vulnerability to ischemia-reperfusion injury, which may be due, in part, to worsened mitochondrial function. The mechanism underlying its cardioprotective effect appears to be mediated at the level of the mitochondria with improved mitochondrial function, less oxidative stress, and reduced susceptibility to MPTP opening. Therefore, the discovery of novel pharmacological activators of PINK1 may provide a novel therapeutic strategy for cardioprotection. Furthermore, its importance for endogenous cardioprotection lends further support to the importance of mitochondria in cardioprotection. We thank Luis Miguel Martins and Nicoleta Moisoi from the MRC Toxicology Unit, University of Leicester for donating the PINK1 knockout mice. For assistance in breeding the PINK1 knockout mice we would like to thank Abdul Mokit from the Biological Service Unit, University College London. [^1]: **Competing Interests:**The authors have declared that no competing interests exist. [^2]: Conceived and designed the experiments: HKS DMY SBO UAM NB ARH PRA MHRL ED SMD MMM DJH. Performed the experiments: HKS SBO UAM NB ARH PRA MHRL ED SMD DJH. Analyzed the data: HKS DMY SBO UAM NB ARH PRA MHRL ED SMD MMM DJH. Contributed reagents/materials/analysis tools: HKS DMY SBO UAM NB ARH PRA MHRL ED SMD MMM DJH. Wrote the paper: HKS DMY SBO UAM NB ARH PRA MHRL ED SMD MMM DJH.

TEHRAN (Press Shia Agency) – Israel protested to Jordan on Sunday after the spokeswoman for the government in Amman was photographed stepping on the Israeli flag during a meeting with trade unionists. – World news – Jumana Ghunaimat, Jordan’s minister for media affairs and communications and the government spokeswoman, on Thursday walked over an Israeli flag painted on the floor of the headquarters of Jordan’s professional unions in Amman, Reuters reported on Sunday. She was on her way to attend a meeting between Jordanian Prime Minister Omar al Razzaz and union representatives. Razzaz, however, entered the building through a rear door, avoiding having to walk over the flag. Israel’s Foreign Ministry issued a statement on Sunday deploring what it called the flag “desecration”, and said it had summoned acting Jordanian ambassador Mohammed Hmaid for a reprimand and that the Israeli embassy in Amman had also issued a “sharp protest”. The flag was painted on the floor of the building several years ago to encourage passers by to tread on it, a mark of disrespect, unions said at the time. Despite the neighbors’ 1994 peace deal and commercial and security ties, many Jordanians resent Israel and identify with the Palestinian struggle against it. Jordan’s Foreign Ministry spokesman Majed al-Qatarneh confirmed in a statement issued via state media that the Israeli embassy in Amman had asked for clarifications over the incident and that Israel had called in the Jordanian charge d’affaires in Tel Aviv to “discuss” the matter. Qatarneh said that Jordan respects its peace treaty with Israel and that Ghunaimat had entered a private building by its main entrance to attend an official meeting.

News Straub Farms The Straub family has decided to retire from farming after 50 years. This auction will feature several late model pieces of farm equipment. The auction will take place on October 12th at 11:00am. This will be an excellent opportunity to purchase some newer, well maintained equipment. This auction will take place in Milan, Michigan, just north of Dundee. For questions on this auction, please contact Chuck Ranney at [email protected]

Ginifer Ginifer may refer to: Ginifer railway station, in Melbourne, Australia Jack Ginifer (1927–1982), Australian politician

The role of stigma in the quality of life of older adults with severe mental illness. Stigma and discrimination against older people with mental illness is a seriously neglected problem. (1) To investigate whether stigmatisation of older adults with mental disorder is associated with the type of residential institution they live in or the type of disorder they suffer and (2) to assess the role of stigma experiences in their quality of life. A cross-sectional study was carried out of 131 older adults with severe mental illness, recruited in 18 elder care homes operating supported living programmes and in eight psychiatric hospitals throughout the Netherlands. Stigmatisation was assessed with an 11-item questionnaire on stigma experiences associated with mental illness. Quality of life was assessed with the Manchester Short Assessment of Quality of Life (MANSA). To better ascertain the role of stigma, we also assessed in comparison the relationship of social participation to quality of life. Some 57% of the respondents had experienced stigmatisation. No association emerged between residential type or disorder type and the extent of stigma experiences. Stigmatisation did show a negative association with quality of life, a connection stronger than that between social participation and quality of life. A feeling of belonging, as contrasted with being excluded, is at least as important for the quality of life of older people with severe mental illness as their actual participation in the community.

Networx: Black mold: Get it out of your house Laura Firszt More Content Now Thursday Sep 13, 2018 at 9:31 AMSep 13, 2018 at 9:31 AM Eew! Black mold! A mold-infested house not only looks and smells terrible; it may also be a serious threat to your family’s health. Find out how black mold can grow in your home and how to get rid of it. What is black mold? First of all, mold is a multi-celled, thready fungus. The more than 100,000 species of mold in existence come in a veritable rainbow of colors, including white, green, yellow, blue, and pink mold. "Black mold" can refer to a large variety of mold types, although it most commonly describes the highly toxigenic (toxin-producing) Stachybotrys — which actually tends to be blackish-green in hue. Many other types of black-colored mold are quite harmless. Black mold in house health risks If you’ve got black mold in your house, health risks include exacerbated breathing difficulties for household members with asthma or other respiratory problems, and an increased possibility of infection for immune-compromised people. Milder negative reactions include coughing, wheezing, and hay fever-like symptoms. Conditions such as extreme fatigue, impaired concentration, headaches, skin rashes, and digestive upsets have also been reported. How does black mold grow? Stachybotrys tends to grow in houses and other buildings which are damp due to any of several causes: leakage, poor sealing around openings such as windows and doors, inadequate ventilation, or flooding (post-Hurricane Katrina, many New Orleans homes were infested with black mold). Black mold thrives on a combination of moisture, warmth, and cellulose-based food sources like wood and drywall. Mold testing With black mold in the house, you may be tempted to call a commercial mold testing service or to purchase a DIY mold testing kit. However, the procedure for removal for any type of mold is the same, so you might prefer to spend your time and money actually getting rid of the fungus, rather than pinpointing exactly which variety you have. Nevertheless, mold testing could be useful in some cases — notably when you suspect there may be mold in your home (usually due to an acrid smell) but can’t spot any. How do you get rid of black mold (or most other types of mold)? Start by finding and removing the source of excessive moisture. Next, equip yourself with non-porous gloves, breathing mask, goggles, and protective clothing to protect against the mold. Now it’s decision-making time. You’ll have to choose what may be cleaned (hard surfaces like walls and floors, as well as machine-washable textiles such as curtains and some area rugs) and what will have to be discarded (paper and cardboard, even treasured family albums — sigh! — in addition to badly molded fabric items, including upholstered furniture and wall-to-wall carpet). Scrub hard surfaces thoroughly with soap and warm water. Launder washables with your usual detergent on a high setting, adding a commercial mold-removing agent if desired. Dry well, with the help of fans or outdoors in the sun where feasible. Unfortunately, some grayish stains may remain even after cleaning. How to prevent mold Worried about how to prevent mold? Good news: The prevention process involves just three simple steps. And it’s a lot easier (not to mention less emotionally wrenching) than dealing with the aftereffects of a major black mold infestation. — Avoid any "moisture traps." For example, don’t leave wet towels or shower curtains crumpled up in the bathroom — spread them to dry. In a damp basement, avoid carpet and choose tile or concrete flooring instead.