title: Cerebral atrophy

text: As previously mentioned, chronic alcoholism is known to be associated with significant brain damage. The pronounced shrinkage in the frontal lobes and cerebellum of alcoholics correlates with serious impairments in executive and psychomotor functions. However, longitudinal studies suggest that some of these brain damages are partially reversible with abstinence"." In response to drinking cessation, bodies of gray and white matter including the cerebral cortex, the limbic system (amygdala, hippocampus, thalamus), the cerebellum, and the brainstem all showed a general increase in brain volume. Similarly, ventricular enlargement—which reflects atrophy of surrounding brain regions—is also reduced in abstinent alcoholics. Following extended sobriety, the volume of the lateral and third ventricles was decreased, and abstainers showed an improvement in working memory and balance. Finally, evidence for the recovery of brain volume with continued sobriety is supported by the improvement in neuropsychological performance. Compared to the control participants, abstinent alcoholic patients scored significantly better on tests measuring cognitive, sensory, and motor functions including abstract reasoning, memory, visuospatial ability, and gait and balance. That being said, while short-term abstinence suffices to produce structural and functional recovery, some alcohol-induced brain changes may persist even after long-term sobriety.


title: Chinese constellations

text: Traditional Chinese astronomy has a system of dividing the celestial sphere into asterisms or constellations, known as "officials" (Chinese "xīng guān").


title: Chinese constellations

text: The Song dynasty (13th-century) Suzhou planisphere shows a total of 283 asterisms, comprising a total of 1,565 individual stars.


title: Chinese constellations

text: The asterisms are divided into four groups, the Twenty-Eight Mansions (, "Èrshíbā Xiù") along the ecliptic, and the Three Enclosures of the northern sky.


title: Chinese constellations

text: The southern sky was added as a fifth group in the late Ming Dynasty based on European star charts, comprising an additional 23 asterisms.


title: Chinese constellations

text: The Three Enclosures (, "Sān Yuán") include the Purple Forbidden Enclosure, which is centered on the north celestial pole and includes those stars which could be seen year-round, while the other two straddle the celestial equator.


title: Chinese constellations

text: The Twenty-Eight Mansions form an ecliptic coordinate system used for those stars visible (from China) but not during the whole year, based on the movement of the moon over a lunar month.


title: Chinese constellations

text: The Chinese system developed independently from the Greco-Roman system since at least the 5th century BC, although there may have been earlier mutual influence, suggested by parallels to ancient Babylonian astronomy.


title: Chinese constellations

text: The system of twenty-eight lunar mansions is very similar (although not identical) to the Indian "Nakshatra" system, and it is not currently known if there was mutual influence in the history of the Chinese and Indian systems.


title: Chinese constellations

text: The oldest extant Chinese star maps date to the Tang dynasty. Notable among them are the 8th-century "Treatise on Astrology of the Kaiyuan Era" and "Dunhuang Star Chart.


title: Chinese constellations

text: It contains collections of earlier Chinese astronomers (Shi Shen, Gan De and Wu Xian) as well as of Indian astronomy (which had reached China in the early centuries AD).


title: Chinese constellations

text: Gan De was a Warring States era (5th century BC) astronomer who according to the testimony of the Dunhuang Star Chart


title: Chinese constellations

text: enumerated 810 stars in 138 asterisms. The Dunhuang Star Chart itself has 1,585 stars grouped into 257 asterisms.


title: Chinese constellations

text: The number of asterisms, or of stars grouped into asterisms, never became fixed, but remained in the same order of magnitude (for the purpose of comparison, the star catalogue compiled by Ptolemy in the 2nd century had 1,022 stars in 48 constellations).


title: Chinese constellations

text: The 13th-century Suzhou star chart has 1,565 stars in 283 asterisms, the 14th-century Korean Cheonsang Yeolcha Bunyajido has 1,467 stars in 264 asterisms, and the celestial globe made by Flemish Jesuit Ferdinand Verbiest for the Kangxi Emperor in 1673 has 1,876 stars in 282 asterisms.


title: Chinese constellations

text: The southern sky was unknown to the ancient Chinese and is consequently not included in the traditional system. With European contact in the 16th century, Xu Guangqi , an astronomer of the late Ming Dynasty, introduced another 23 asterisms based on European star charts. The "Southern Sky" () asterisms are now also treated as part of the traditional Chinese system.


title: Chinese constellations

text: The character originally had a more complicated form: , a phono-semantic character () whose semantic portion, , originally depicting three twinkling stars (three instances of the "sun" radical ).


title: Chinese constellations

text: The modern Chinese term for "constellation", referring to those as defined by the IAU system, is ('). The older term (') is used only in describing constellations of the traditional system. The character means "public official" (hence the English translation "officials" for the Chinese asterisms), but it is historically a variant glyph of


title: Chinese constellations

text: The Three Enclosures are the Purple Forbidden enclosure (, "Zǐ Wēi Yuán"), the Supreme Palace enclosure (, "Tài Wēi Yuán") and the Heavenly Market enclosure (, "Tiān Shì Yuán").


title: Chinese constellations

text: The Purple Forbidden Enclosure occupies the northernmost area of the night sky. From the viewpoint of the ancient Chinese, the Purple Forbidden Enclosure lies in the middle of the sky and is circled by all the other stars.


title: Chinese constellations

text: It covers the Greek constellations Ursa Minor, Draco, Camelopardalis, Cepheus, Cassiopeia, Auriga, Boötes,


title: Chinese constellations

text: The Heavenly Market Enclosure covers the Greek constellations Serpens, Ophiuchus, Aquila and Corona Borealis,


title: Chinese constellations

text: The Three Enclosures are each enclosed by two "wall" asterisms, designated "yuán" "low wall, fence; enclosure" (not to be confused with the lunar mansion ""Wall" ):


title: Chinese constellations

text: The Twenty-Eight Mansions are grouped into Four Symbols, each associated with a compass direction and containing seven mansions. The names and determinative stars are:


title: Chinese constellations

text: The sky around the south celestial pole was unknown to ancient Chinese. Therefore, it was not included in the Three Enclosures and Twenty-Eight Mansions system. However, by the end of the Ming Dynasty, Xu Guangqi introduced another 23 asterisms based on the knowledge of European star charts. These asterisms were since incorporated into the traditional Chinese star maps.


title: Chinese constellations

text: Ancient Chinese astronomers designated names to the visible stars systematically, roughly more than one thousand years before Johann Bayer did it in a similar way. Basically, every star is assigned to an asterism. Then a number is given to the individual stars in this asterism. Therefore, a star is designated as "Asterism name" + "Number". The numbering of the stars in an asterism, however, is not based on the apparent magnitude of this star, but rather its position in the asterism. The Bayer system uses this Chinese method occasionally, most notably with the stars in the Big Dipper, which are all about the same magnitude; in turn, the stars of the Big Dipper, in Chinese, are numbered in Chinese astronomy in the same order as with the Bayer designations, with Dubhe first in both cases.


title: Chinese constellations

text: For example, Altair is named in Chinese. is the name of the asterism (literally the Drum at the River). is the number designation (two). Therefore, it literally means "the Second Star of the Drum at the River". (Bayer might have called Altair "Beta Tympani Flumine" if he had been cataloguing Chinese constellations.)


title: Chinese constellations

text: Some stars also have traditional names, often related to mythology or astrology. For example, Altair is more commonly known as or (the Star of the Cowherd) in Chinese, after the mythological story of the Cowherd and Weaver Girl.


title: Chinese constellations

text: These designations are still used in modern Chinese astronomy. All stars for which the traditional names are used in English are routinely translated by their traditional Chinese designations, rather than translations of their catalogue names.


title: Chinese constellations

text: Each linked article provides a list of the (traditional) Chinese names of the stars within each (modern) constellation.


title: Education in Scotland

text: Education in Scotland is overseen by the Scottish Government and its executive agency Education Scotland. Education in Scotland has a history of universal provision of public education, and the Scottish education system is distinctly different from those in the other countries of the United Kingdom. The Scotland Act 1998 gives the Scottish Parliament legislative control over all education matters, and the Education (Scotland) Act 1980 is the principal legislation governing education in Scotland. Traditionally, the Scottish system at secondary school level has emphasised breadth across a range of subjects, while the English, Welsh and Northern Irish systems have emphasised greater depth of education over a smaller range of subjects.


title: Education in Scotland

text: Following this, Scottish universities generally have courses a year longer (typically 4 years) than their counterparts elsewhere in the UK, though it is often possible for students to take more advanced specialised exams and join the courses at the second year. One unique aspect is that the ancient universities of Scotland issue a Master of Arts as the first degree in humanities. State schools are owned and operated by the local authorities which act as "Education Authorities", and the compulsory phase is divided into primary school and secondary school (often called high school). Schools are supported in delivering learning and teaching by Education Scotland (formerly Learning and Teaching Scotland). There are also private schools across the country, although the distribution is uneven with such schools in 22 of the 32 Local Authority areas. At September 2011 the total pupil population in Scotland was 702,104, of which 31,425 pupils, or 4.5%, were being educated in independent schools.


title: Education in Scotland

text: Qualifications at the secondary school and post-secondary (further education) level are provided by the Scottish Qualifications Authority, which is the national awarding and accrediting body in Scotland, and delivered through various schools, colleges and other centres. Political responsibility for education at all levels is vested in the Scottish Parliament and the Learning Directorate. Inspections and audits of educational standards are conducted by three bodies: Care Inspectorate inspects care standards in pre-school provision; Education Scotland (formerly Her Majesty's Inspectorate of Education) for pre-school, primary, education, further and community education; with the Scottish office of the Quality Assurance Agency for Higher Education (QAA Scotland) responsible for higher education.


title: Education in Scotland

text: In 2014, research by the Office for National Statistics found that Scotland was the most highly educated country in Europe and among the most well-educated in the world in terms of tertiary education attainment, above countries like Finland, Ireland and Luxembourg, with roughly 40% of Scots aged 16–64 educated to NVQ level 4 and above.


title: Education in Scotland

text: Children start primary school aged between 4½ and 5½ depending on when the child's birthday falls. Scottish school policy places all those born between March of a given year and February of the following year in the same year group. Children born between March and August start school in August at between 5 and 5½ years old, and those born between September and February start school in the previous August at between age 4½ and 4 years 11 months years old. The Scottish system is the most flexible in the UK, however, as parents of children born between September and December can decide to defer for 1 year (but may or may not receive a funded nursery place in the deferral year), whilst children born between January and February can opt to hold their child back a year and let them start school the following August, with guaranteed nursery funding. This usually allows those not ready for formal education to have an extra year at an early years centre (formerly known as nursery).


title: Education in Scotland

text: Pupils remain at primary school for seven years. Then aged eleven or twelve, they start secondary school for a compulsory four years with the following two years being optional. In Scotland, pupils sit National 4/5 exams (previously Standard Grade or Intermediate exams) at the age of fifteen/sixteen, normally for between 6 and eight subjects including compulsory exams in English and Mathematics. A Science subject (Physics, Biology or Chemistry) and a Social Subject (Geography, History or Modern Studies) were also compulsory, but this was changed in accordance with the new curriculum. It is now required by the Scottish Parliament for students to have two hours of physical education a week; each school may vary these compulsory combinations. The school leaving age is generally sixteen (after completion of National 4/5s), after which students may choose to remain at school and study for Higher and/or Advanced Higher exams.


title: Education in Scotland

text: A small number of students at certain private, independent schools may follow the English system and study towards GCSE instead of National 4/5s (Standard Grades), and towards A and AS-Levels instead of (or alongside) Higher Grade and Advanced Higher exams. The International Baccalaureate has also been introduced in some independent schools.


title: Education in Scotland

text: The table below lists rough equivalences with the year system in the rest of the United Kingdom (For England and Wales, the equivalence given is for children born before 1 September; the equivalence for those born from September to February [December for deferred pupils] is given in brackets):


title: Education in Scotland

text: Government funded schools are free for children aged 5–19. In many cases, this applies to children of international post-graduate students, and other immigrants.


title: Education in Scotland

text: The age ranges specify the youngest age for a child entering that year and the oldest age for a child leaving that year. Playgroup can be described as a daycare centre for toddlers, then children may go on to attend an early years centre as soon as they have passed their third birthday, and progress to Primary 1 in the August of the year in which they turn five.


title: Education in Scotland

text: In general, the cut-off point for ages is the end of February, so all children must be of a certain age on 1 March to begin class in August.


title: Education in Scotland

text: All parents of children born between September and February (i.e. still 4 years old on the school start date) are entitled to defer entry to Primary School if they believe their child is not ready for school.


title: Education in Scotland

text: Only children whose birthdays fall in January or February will be considered for funding for a subsequent year at an early years centre, unless there are special circumstances.


title: Education in Scotland

text: Children may leave school once they reach their statutory school leaving date; this is dependent on date of birth. For children born between 1 March and 30 September, this date is 31 May of their 4th year of secondary school. For children born between 1 October and 28 February, the last day of June is the first date they may leave school if they have a placement at college and the school have signed the health & safety forms.


title: Education in Scotland

text: Which high school the children go to depends on the area where they live, known as the "catchment area", which has a specific high school that takes children who live in that area.


title: Education in Scotland

text: Parents can also apply for a placement request if they would like their child to attend a school outside their catchment area and a panel will decide if the child is the most worthy (out of all placing requests) to take one of the spaces left after all children from the catchment area have been taken.


title: Education in Scotland

text: The table below lists list the numbers of children, schools and teachers in all publicly funded schools:


title: Education in Scotland

text: Home education is also legal in Scotland. Parents wishing to home educate do not need the permission of the Local Authority unless the children are already registered at a school. There are no exact numbers available for children being educated at home in Scotland.


title: Education in Scotland

text: Within the Scottish Government, the Cabinet Secretary for Education and Skills has overall responsibility for education provision in Scotland. The Cabinet Secretary is assisted by three junior ministers, currently the Minister for Childcare and Early Years, the Minister for Further Education, Higher Education and Science and the Minister for Employability and Training.


title: Education in Scotland

text: All educational qualifications in Scotland are part of the Scottish Credit and Qualifications Framework, ranging between Scottish Qualifications Authority qualifications, Scottish Vocational Qualifications and higher education qualifications.


title: Education in Scotland

text: The vast majority of Scottish pupils take Scottish Qualifications Certificate qualifications provided by the Scottish Qualifications Authority (SQA). Generally, most pupils take National 4/5s (previously Standard Grades, but some schools offered Intermediates instead) in S3-S4, and Highers in S5. The number of National 4/5 qualifications a pupil enters can vary drastically depending on the individual, with the most common number of National 5s taken, per pupil, in 2017 being 6, however some may choose to undertake as few as one or two, up to eight or nine. For those who wish to remain at school for the final year (S6), more Highers and Advanced Highers (formerly CSYS) in S6 can be taken. Previous qualifications Intermediate 1 and Intermediate 2 – were intended to be roughly equivalent to General and Credit Level Standard Grades respectively.


title: Education in Scotland

text: Pupils can go to university at the end of S5, as Highers provide the entry requirements for Scottish universities where degrees are normally four years long; however, recently it is more common for students to remain until S6, taking further Highers and/or taking Advanced Highers. The majority of English universities, the most popular choice for Scottish students who wish to study university degrees outside of Scotland, require Advanced Higher qualification levels as these are deemed by the English universities to be most similar to A-levels.


title: Education in Scotland

text: Secondary education is provided by secondary schools throughout Scotland, both in the state and independent sector. The vast majority of schools in the state sector are administered directly by the local Education Authority, which is synonymous with the 32 councils used for local government.


title: Education in Scotland

text: There is not a set name for secondary schools in Scotland, but whatever they might be called, with just a few specific exceptions in mainly rural or island authorities, state secondary schools in Scotland are fully comprehensive and non-selective. Amongst the state-run secondary schools:


title: Education in Scotland

text: Other schools include The Community School of Auchterarder, Auchterarder, Perth and Kinross; The Nicolson Institute, Stornoway, Western Isles; North Walls Community School on Hoy, Orkney Islands and Wester Hailes Education Centre, Wester Hailes, Edinburgh. All of these are, equally, fully comprehensive non-selective schools, differing only in designation from all other state secondary schools in Scotland.


title: Education in Scotland

text: In 2003, work began on an education reform programme, to produce a new "Curriculum for Excellence" that would replace existing guidance on the school curriculum. Curriculum for Excellence was launched in Scottish secondary schools from school session 2012–2013.


title: Education in Scotland

text: In 2017, new reforms were introduced moving control over curriculum and schools more towards head teachers and parents.


title: Education in Scotland

text: The majority of schools are non-denominational, and include the parish schools, pioneered by the Church of Scotland and other Protestant Churches, which became state schools in 1872. Religious education is taught in non-denominational schools and in denominational schools. Of over 2,500 schools in Scotland, there are 366 state schools which are Roman Catholic, three Episcopalian and one Jewish. The Education (Scotland) Act 1918 brought Roman Catholic schools within the State education system, ensuring the promotion of a Roman Catholic ethos within such schools.


title: Education in Scotland

text: In 2015, the Scottish Government launched the Scottish Attainment Challenge which aims to achieve equity in educational outcomes throughout Scotland. The Scottish Government envisages equity being achieved by ensuring every child has the same opportunity to succeed, with a particular focus on closing the poverty-related attainment gap. It is underpinned by national Scottish educational policies such as Curriculum for Excellence, Getting it Right for Every Child (GIRFEC) as well as the National Improvement Framework. The attainment challenge focuses and accelerates targeted improvement activity in literacy, numeracy and health and wellbeing in specific areas of Scotland, known as "challenge authorities" (those councils with a higher percentage of children growing up in poverty and deprivation). At a cost of £750 million to the Scottish Government through the Attainment Scotland Fund, the challenge is a targeted initiative focused on supporting pupils in the local authorities of Scotland with the highest concentrations of deprivation. Currently, the nine 'Challenge Authorities' are Glasgow City Council, Dundee City Council, Inverclyde, West Dunbartonshire, North Ayrshire, Clackmannanshire, North Lanarkshire, East Ayrshire and Renfrewshire.


title: Education in Scotland

text: On 1 February 2017 the share each primary and secondary school will receive for the academic year 2017–2018 from the Scottish Government's £120 million Pupil Equity Funding was announced by the Deputy First Minister and Cabinet Secretary for Education and Skills John Swinney. This funding is provided through the Attainment Scotland Fund and allocated directly to schools, targeted at those children most affected by the poverty related attainment gap.


title: Education in Scotland

text: The SNP-led government launched the Scottish Survey of Literacy and Numeracy in 2011. The survey showed a sustained decline in basic literacy and numeracy among school pupils over six years. It was then scrapped by the government and its measures of literacy were replaced in part with a system based on teacher judgements. The teacher judgement data from December 2018 indicated that 70% of pupils achieved the expected literacy level by the end of primary school.


title: Education in Scotland

text: The government withdrew Scotland from the Progress in International Reading Literacy Study in 2010, making international comparisons of literacy difficult. It remains part of the Programme for International Student Assessment, which shows that Scotland's international standing in reading and mathematics (as well as science) in schools fell between the first decade of the century and 2018.


title: Education in Scotland

text: The Scottish Survey of Adult Literacies in 2009 reported that 26.7% of adults in Scotland "may face occasional challenges and constrained opportunities due to their literacies difficulties, but will generally cope with their day-to-day lives". Of that group, 3.6% "face serious challenges in their literacies practices".


title: Education in Scotland

text: Music education is available at several levels. Formal music education begins at 4½ years and can progress as high as postgraduate studies. Music education can take place within a Scottish Music school; through a music service or privately.


title: Education in Scotland

text: Some schools in Scotland provide education given in the Scottish Gaelic language. They are mainly located in the main cities of Scotland and in areas with higher amounts of Gaelic speakers. Gaelic medium education is becoming increasingly popular throughout Scotland, and the number of pupils who are in Gaelic medium education at primary school level has risen from 24 in 1985, to 2500 in the 2012–13 school year.


title: Education in Scotland

text: Further education is provided through a network of further education colleges available to people having reached the end of compulsory education at 16. In the early 2010s, colleges were merged to form larger, regional institutions.


title: Education in Scotland

text: Colleges offer a wide range of vocational qualifications to young people and older adults, including vocational, competency-based qualifications (previously known as SVQs), Higher National Certificates and Higher National Diplomas. In Scotland, FE college students receiving certain qualifications - frequently HNC and HND qualifications in a relevant subject - can apply for entry at a later stage at university.


title: Education in Scotland

text: Further education colleges also provide support to apprenticeship programmes, which are coordinated by the public body Skills Development Scotland.


title: Education in Scotland

text: There are fifteen universities in Scotland and three other institutions of higher education which have the authority to award academic degrees. The oldest is St. Andrews, which was founded in 1413. Three other "ancient universities", Glasgow, Aberdeen and Edinburgh, date from before 1600. The University of the Highlands and Islands (UHI) gained full university status in 2011, having been created through the federation of 13 colleges and research institutions across the Highlands and Islands, a process that began in 2001.


title: Education in Scotland

text: All Scottish universities have the power to award degrees at all levels: undergraduate, taught postgraduate, and doctoral. Education in Scotland is controlled by the Scottish Government under the terms of the Scotland Act 1998. The minister responsible for higher education is the Cabinet Secretary for Education and Skills, currently John Swinney MSP of the Scottish National Party. University status in Scotland and throughout the United Kingdom today is conferred by the Privy Council which takes advice from the Quality Assurance Agency for Higher Education.


title: Education in Scotland

text: All Scottish universities are public universities and funded by the Scottish Government (through its Scottish Funding Council) and financial support is provided for Scottish-domiciled students by the Student Awards Agency for Scotland. Students ordinarily resident in Scotland or the European Union do not pay tuition fees for their first undergraduate degree, but tuition fees are charged for those from the rest of the United Kingdom. All students are required to pay tuition fees for postgraduate education (e.g. MSc, PhD), except in certain priority areas funded by the Scottish Government, or if another source of funding can be found (e.g. research council studentship for a PhD). A representative body called Universities Scotland works to promote Scotland's universities, as well as six other higher education institutions.


title: Education in Scotland

text: The university sector in Scotland had a total income of £3.5 billion in 2014/15 with the Scottish Government giving approximately £623 million in funding for individual university student support. The Scottish Funding Council contributing £1.1 billion of public money to the fifteen universities, this was a six per cent reduction since 2010/11.


title: Education in Scotland

text: In 2014–15, approximately 232,570 students studied at universities or institutes of higher education in Scotland, of which 56% were female and 44% male, with 66% being domiciled in Scotland, 12% from the rest of the United Kingdom, 9% from the EU and the remaining 13% being international students. Of all these, approximately 76% were studying for their first degree (i.e. undergraduate level) and 24% for a taught postgraduate degree (primarily a master's degree) or a doctoral research degree (primarily PhD). The remainder were mostly on other programmes such as Higher National Diploma. 16,000 students were studying in Scotland with The Open University via distance-learning, and the Open University teaches 40 per cent of Scotland's part-time undergraduates.


title: Education in Scotland

text: In the 2019 QS World University Rankings, three Scottish universities are among the top 100 worldwide: University of Edinburgh (at 18), University of Glasgow (at 69), University of St. Andrews (at 97). Other high ranked universities are the University of Aberdeen (at 172), University of Strathclyde (at 268), University of Dundee (at 272), Heriot-Watt University (at 302) and University of Stirling (at 417).


title: Action (firearms)

text: In firearms terminology, an action is the functional mechanism of a breech-loading firearm that handles (loads, locks, fires, extracts and ejects) the ammunition cartridges, or the method by which that mechanism works. Actions are technically not present on muzzleloaders, as all those are single-shot firearms with a closed off breech with the powder and projectile manually loaded from the muzzle. Instead, the muzzleloader ignition mechanism is referred to as the "lock" (e.g. matchlock, flintlock, caplock).


title: Action (firearms)

text: Actions can be categorized in several ways, including single action versus double action, break action versus bolt action, and others. The term action can also include short, long, and magnum if it is in reference to the length of the rifle's receiver and the length of the bolt. The short action rifle usually can accommodate a cartridge length of or smaller. The long action rifle can accommodate a cartridge of , and the magnum action rifle can accommodate cartridges of .


title: Action (firearms)

text: Single-shot actions operate only to ignite a cartridge that is separately set up ("in battery") for firing, and are incapable of moving the cartridge by itself. As the name implies, all single-shot long and short arms (unless multi-barreled) can only hold one round of ammunition and need to be manually reloaded after every firing. Historically, these are the earliest cartridge firearm actions to be invented.


title: Action (firearms)

text: The dropping block are actions wherein the breechblock lowers or "drops" into the receiver to open the breech, usually actuated by an underlever. There are two principal types of dropping block: the tilting block and the falling block.


title: Action (firearms)

text: In a tilting block or pivoting block action, the breechblock is hinged on a pin mounted at the rear. When the lever is operated, the block tilts down and forward, exposing the chamber. The best-known pivoting block designs are the Peabody, the Peabody–Martini, and Ballard actions.


title: Action (firearms)

text: The original Peabody rifles, manufactured by the Providence Tool Company, used a manually cocked side-hammer. Swiss gunsmith Friedrich Martini developed a pivoting block action by modifying the Peabody, that incorporated a hammerless striker which was cocked by the operating lever with the same single, efficient motion that also pivoted the block. The 1871 Martini–Henry which replaced the "trapdoor" Snider–Enfield was the standard British Army rifle of the later Victorian era, and the Martini is also a popular action for civilian rifles.


title: Action (firearms)

text: Charles H. Ballard's self-cocking tilting-block action was produced by the Marlin Firearms Company from 1875, and earned a superlative reputation among long-range "Creedmoor" target shooters. Surviving Marlin Ballards are today highly prized by collectors, especially those mounted in the elaborate Swiss-style Schützen stocks of the day.


title: Action (firearms)

text: A falling block action (also known as a sliding block action) is a single-shot firearm action in which a solid metal breechblock slides vertically in grooves cut into the breech of the firearm and actuated by a lever. Examples of firearms using the falling block action are the Sharps rifle and Ruger No. 1.


title: Action (firearms)

text: In a rolling block action the breechblock takes the form of a part-cylinder, with a pivot pin through its axis. The operator rotates or "rolls" the block to open and close the breech; it is a simple, rugged and reliable design. Rolling blocks are most often associated with firearms made by Remington in the later 19th century; in the Remington action the hammer serves to lock the breech closed at the moment of firing, and the block in turn prevents the hammer from falling with the breech open.


title: Action (firearms)

text: The hinged block used in the earliest metallic-cartridge breechloaders designed for general military issue began as conversions of muzzle-loading rifle-muskets. The upper rear portion of the barrel was filed or milled away and replaced by a hinged breechblock which opened upward to permit loading. An internal angled firing pin allowed the re-use of the rifle's existing side-hammer. The Allin action made by Springfield Arsenal in the US hinged forward; the Snider–Enfield used by the British opened to the side. Whereas the British quickly replaced the Snider with a dropping-block Peabody-style Martini action, the US Army felt the trapdoor action to be adequate and followed its muzzleloader conversions with the new-production Springfield Model 1873, which was the principal longarm used as a weapon in the Indian Wars and was still in service with some units in the Spanish–American War.


title: Action (firearms)

text: A break action is a type of firearm where the barrel(s) are hinged and can be "broken open" to expose the breech. Multi-barrel break action firearms are usually subdivided into over-and-under or side-by-side configurations for two barrel configurations or "combination gun" when mixed rifle and shotgun barrels are used.


title: Action (firearms)

text: Although bolt-action guns are usually associated with fixed or detachable box magazines, in fact the first general-issue military breechloader was a single-shot bolt action: the paper-cartridge Prussian needle gun of 1841. France countered in 1866 with its superior Chassepot rifle, also a paper-cartridge bolt action. The first metallic-cartridge bolt actions in general military service were the Berdan Type II introduced by Russia in 1870, the Mauser Model 1871, and a modified Chassepot, the Gras rifle of 1874; all these were single-shots.


title: Action (firearms)

text: Single-shot bolt actions in .22 caliber were also widely manufactured as inexpensive "boys' guns" in the earlier 20th century; and there have been a few single-shot bolt-action shotguns, usually in .410 bore.


title: Action (firearms)

text: The eccentric screw action first seen on the M1867 Werndl–Holub and later on the Magnum Research Lone Eagle pistol, the breech closure is a rotating drum with the same axis, but offset from the bore. When locked, a firing pin aligns with the primer and the breech is otherwise solid. When rotated open, a slot in the drum is exposed for extraction and feeding of a new round. Though first used on the Werndl-Holub, this action is commonly known as a cannon breech due to its association with the French 75mm Model of 1897 cannon. The French M1897 was, itself, based on William Hubbell's .


title: Action (firearms)

text: Repeating actions are characterized by reciprocating/rotating components that can move cartridges in and out of battery from an ammunition-holding device (magazine, cylinder or belt), which allows the gun to hold multiple rounds and shoot repeatedly before needing a manual ammunition reload.


title: Action (firearms)

text: A revolver is a multi-chamber (but single-barrelled) firearm that houses cartridges in a rotary cylinder which indexes each round into alignment with the bore (with the help of a forcing cone) prior to each shot. Revolvers are most often handguns; however, examples of revolving rifles, shotguns and cannons have been made. The cylinder is most often rotated via linkage to a manually manipulated external hammer, although some revolvers are "double-action" and can use the manual pull of the trigger to drive both the cylinder rotation and hammer cocking.


title: Action (firearms)

text: In bolt-action firearms, the opening and closing of the breech is operated by direct manual manipulation of the bolt via a protruding bolt handle. Most bolt-actions utilize a rotating bolt ("turn-pull") design, where the bolt handle must be rotated upwards for unlocking before the bolt can be pulled back to opening the breech and eject any spent cartridge, and must be rotated back down for locking after the bolt closes the breech. The three predominant rotating bolt-action systems are the Mauser, Lee–Enfield and Mosin–Nagant systems, with the Mauser system emerging as the modern mainstream.


title: Action (firearms)

text: There are also straight-pull bolt-action systems that uses complex bolt head designs to facilitate locking instead of needing to rotate the bolt handle every time.


title: Action (firearms)

text: In the Mauser-style turn-bolt action, the bolt handle must be rotated upward, pull rearward, pushed forward, and finally rotated back downward into lock. In a straight-pull action, the bolt can be cycled without rotating, hence reducing the required range of motion by the shooter from four movements to two, with the goal of increasing the rate of fire. The Ross and Schmidt–Rubin rifles load via stripper clips, albeit of an unusual paperboard and steel design in the Schmidt–Rubin rifle, while the Mannlicher uses en-bloc clips. The Schmidt–Rubin series, which culminated in the K31, are also known for being among the most accurate military service rifles ever made. Yet another variant of the straight-pull bolt action, of which the M1895 Lee Navy is an example, is a camming action in which pulling the bolt handle causes the bolt to rock, freeing a stud from the receiver and unlocking the bolt.


title: Action (firearms)

text: In 1993 the German Blaser company introduced the Blaser R93, a new straight-pull action where locking is achieved by a series of concentric "claws" that protrude/retract from the bolthead, a design that is referred to as "Radialbundverschluss" ("radial connection"). As of 2017 the Rifle Shooter magazine listed its successor Blaser R8 as one of the three most popular straight pull rifles together with Merkel Helix and Browning Maral. Some other notable modern straight pull rifles are made by Chapuis, Heym, Lynx, Rößler, Strasser, and Steel Action.


title: Action (firearms)

text: In the sport of biathlon, because shooting speed is an important performance factor and semi-automatic guns are illegal for race use, straight-pull actions are quite common, and are used almost exclusively on the Biathlon World Cup. The first company to make the straight-pull action for .22 caliber was J. G. Anschütz; the action is specifically the straight-pull ball bearing-lock action, which features spring-loaded ball bearings on the side of the bolt which lock into a groove inside the bolt's housing. With the new design came a new dry-fire method; instead of the bolt being turned up slightly, the action is locked back to catch the firing pin.


title: Action (firearms)

text: In pump action or slide action firearms, a sliding grip at the fore-end beneath the barrel is manually operated by the user to eject and chamber a new round. Pump actions are predominantly found in shotguns. An example of firearms using the pump action are the Remington 870 and Winchester Model 1897.


title: Action (firearms)

text: The lever-action firearms use a linked lever to eject and chamber cartridges. An example of firearms using lever action are the Winchester Repeating Rifle, the Henry rifle and the Marlin Model 1894.


title: Action (firearms)

text: The bolt release or lever release action is a hybrid repeating action that uses the physical manipulation of a bolt release lever/button to complete the cartridge chambering process. However, unlike the lever action (which demands the shooter's hand to actually provide the force needed for cycling the action), bolt release firearms eject the used cartridge automatically without involving the lever, usually via blowback or gas operation, and often uses a spring-assisted mechanism to chamber the next round. However, after moving rearwards the bolt is stopped by a bolt catch and will not move back into battery position and chamber the new round, until the user manually disengage the catch by depressing a release lever/button. Due to the fact that the action cannot complete its loading cycle without manual input from the user, it is technically a manually operated action rather than a self-loading one.


title: Action (firearms)

text: Whilst the basic principle can be traced back to other self-ejecting rifles, such as the single-shot Harrington & Richardson Model 755 rifle, this action has since been popularized in the United Kingdom by Southern Gun Company, who manufacture with "Manually Actuated Release System" (MARS) action rifles/pistol-caliber carbines in .223, .308, 9mm and .45 ACP calibers, as the interrupted mechanism complies with The Firearms (Amendment) Act 1988 which bans possession of self-loading centrefire rifles. The French company Verney-Carron makes and exports the "Speedline" hunting rifle and the "Véloce" shotgun, which has caused some moral concern in the mainstream media in Australia due to lobbying by the Greens and anti-gun groups such as Gun Control Australia, with David Shoebridge quoting the term "semi-semi-automatic". Similarly, Savage Arms has introduced the A17R and A22R rimfire rifles (both modified from its new A-series rifles, with a bolt release lever in front of the trigger guard), aiming at the Australian market, but law enforcement agencies such as the Northern Territory Police has attempted to unilaterally defining these rifles as "linear repeating firearms with assisted ejection" and reclassify them as semi-automatic, and hence prohibited without at least a Category C license, which is off-limit to most urban and rural residents who do not own farms. In 2020, CZ also introduced CZ 515, a bolt-release modified version of the CZ 512, to the Australian market via its importer Winchester Australia. The Turkish manufacturer Pardus Arms also produces the 12 gauge-caliber BRS17 shotgun, which uses a bolt release button on the back of the receiver to chamber rounds before firing.


title: Action (firearms)

text: The blowback operation is a system in which semi-automatic and fully automatic firearms operate through the energy created by combustion in the chamber and bore acting directly on the bolt face through the cartridge. In blowback operation the bolt is not locked to the chamber, relying only on spring pressure and inertia from the weight of the bolt to keep the action from opening too quickly. Blowback operation is used for low-powered cartridges due to the weight of the bolt required.


title: Action (firearms)

text: Delayed blowback actions use some mechanism to slow down rearward travel of the bolt, allowing this action to handle more powerful ammunition and/or reduced weight of the bolt.


title: Action (firearms)

text: The blow-forward operation uses a fixed breech and moving barrel that is forced forward relative to the breech by the friction of the projectile against the bore as well as the breech recoiling away from the barrel. The barrel is spring loaded and returns automatically to chamber a fresh round from the magazine. Examples of this action are the Steyr Mannlicher M1894, Hino Komuro M1908 Pistol and the Schwarzlose Model 1908.


title: Action (firearms)

text: The recoil operation is a type of locked-breech action used in semi-automatic and fully automatic firearms. It also uses energy from the combustion in the chamber acting directly on the bolt through the cartridge head, but in this case the firearm has a reciprocating barrel and breech assembly, combined with a bolt that locks to the breech. The breech remains locked as the bolt and barrel travel rearward together for some distance, allowing pressure in the chamber to drop to a safe level before the breech is opened.


title: Action (firearms)

text: The gas operation is a system of operation mechanism used to provide energy to semi-automatic and fully automatic firearms. In gas-operation, a portion of high pressure gas from the cartridge being fired is tapped through a hole in the barrel and diverted to operate the action. There are three basic types: long stroke gas piston (where the gas piston goes the same distance as the operating stroke of the action parts, and is often attached to the action parts), short stroke gas piston (where the gas piston travels a shorter distance than the operating stroke of the action parts), and direct impingement (AKA "direct gas", "gas impingement", where there is no piston, and the gas acts directly on the action parts). A fourth type, now considered obsolete and ineffective, are those systems based on the Bang rifle that utilize a muzzle cap to capture gas after the bullet has left the barrel. While this system is successful in boosting the operating power of recoil operated guns, it is insufficient and too susceptible to fouling for use as the primary operating system.


title: Acura RL

text: The Acura RL is a mid-size luxury car that was manufactured by the Acura division of Honda for the 1996–2012 model years over two generations. The RL was the flagship of the marque, having succeeded the Acura Legend, and was replaced in 2013 by the Acura RLX. All models of the Legend, RL and RLX lines have been adapted from the Japanese domestic market Honda Legend. The model name "RL" is an abbreviation for "Refined Luxury."


title: Acura RL

text: The first-generation Acura RL was a rebadged version of the third-generation Honda Legend, and was first introduced to the North American market in 1996, to replace the second-generation Acura Legend. The second-generation Acura RL was a rebadged version of the fourth-generation Honda Legend, introduced to the North American market in September 2004, as a 2005 model. This iteration of the RL received an extensive mid-generational facelift for the 2009 model year, and a further update for 2011. The third-generation debuted for the 2014 model year as the Acura RLX.


title: Acura RL

text: In 1996, Acura introduced the Acura 3.5RL, known internally as "KA9," to replace the Legend. Acura dropped the Legend name when market research showed that consumers referred to Acura products by their model names, "Legend" and "Integra," and did not necessarily associate the names with Honda's "Acura" brand.


title: Acura RL

text: The 3.5RL's longitudinally mounted V6 engine had its center-line mounted in-line with the car's axis, and not transversely (i.e., 90 degrees offset from the vehicle axis) like most other front-wheel-drive cars. This longitudinal placement allowed for a smaller turning radius and easy in-town maneuverability, as well as 56/44 front/rear weight distribution.


title: Acura RL

text: In late 1998, the 1999 3.5RL received a front and rear facelift with integrated foglights, revised bumpers and hood, as well as driver and front passenger side airbags. The suspension and chassis were stiffened, and new alloy wheels were offered.


title: Acura RL

text: In 1999, a larger navigation system screen was added for the 2000 model year. Along with that larger screen came the conversion to easy-to-replace DVD map databases. In 2001, the 2002 model year 3.5RL received painted lower trim and mudflaps along with redesigned alloys and a newer, sportier suspension setup. The revised engine produced and of torque. More insulation was added in the engine compartment for 2002. In 2004, RL's received clear turn signal lenses in the rear lights, another new alloy wheel design, and various interior upgrades including new color schemes. For model year 2004, the 3.5RL offered as standard equipment a revised navigation system and integrated satellite radio in addition to a redesigned center console and chrome door lock pulls. The 2004 3.5RL was the first production saloon car to offer satellite radio as standard equipment.


title: Acura RL

text: The 1996–2004 3.5RL's engine was the last in the Acura lineup not to use Honda's variable valve timing system (VTEC), This 3.5 L 90-degree V6 engine was internally designated as the C35A, and was the last of the Honda C engine V6 engines used in Honda and Acura lineups, being replaced by the newer Honda J engine 60-degree V6 engines. The 2004 RL was also the last Acura to use the numeric designation (i.e., 3.5) for its engine displacement.


title: Acura RL

text: The new-generation car, known internally as "KB1," was launched in late 2004 for the 2005 model year. Without the rumored V8 engine, it featured an all-wheel drive system marketed by Acura as "Super Handling-All Wheel Drive" (SH-AWD). It integrated active differentials with the all-wheel-drive system and traction control to improve handling, similar to the "ATTS" system featured on the 1997 Honda Prelude "SH". At the time of its introduction, the Acura RL's SH-AWD was the first all-wheel-drive system to vary the distribution of power not only from front to back, but also side to side in the rear using a technique called torque vectoring. The RL can direct up to 70% of available torque to the rear wheels, and up to 100% of that available rear torque can be directed to just one wheel. In combination with a specially designed planetary gear-set which can over-drive the rear wheels at up to 5% greater speed than the front wheels, the torque directed to one wheel, or torque vectoring, can have a steering effect. As the car speeds around a curve, torque vectored to the outside rear wheel will push the rear end around the curve faster, just as paddling the outside oar of a row boat faster than the inside oar will cause the row boat to turn, to minimize the understeer common in front-heavy vehicles.


title: Acura RL

text: The first-generation RL was powered by a 225 hp (168 kW) 90-degree C-series V6 non-VTEC engine. The second-generation RL uses a newer design 60-degree J-series 3.5 L V6 SOHC VTEC engine delivering ; this was later revised to due to new SAE testing procedures. To give the car a more sporty feel, the car featured drive-by-wire throttle control and a five-speed sequential sport shifting automatic transmission with shift paddles mounted on the steering wheel. As with the first-generation Acura RL, the second-generation Acura RL used premium unleaded fuel rated at 91 (R+M)/2 octane.


title: Acura RL

text: A first for the RL was the use of aluminum 4-piston front brake calipers over 12.6-inch cast-iron ventilated front rotors. These multi-piston calipers derived from racing applications, are extremely rigid. In the rear, 12.2-inch cast-iron ventilated discs attached to their hub with lightweight aluminum collets and were gripped by one-piston aluminum brake calipers. The RL was equipped with unique five-spoke 17-inch alloy wheels and Michelin Pilot HX MXM 4 245/50-R-17 98V all season grand touring tires. These wheels were one inch larger in diameter, and the tires 20 mm wider in section, than those found on the first-generation Acura RL.


title: Acura RL

text: New features on the 2005 RL included a keyless entry system which allowed the driver to both lock and unlock the car by touching the door handle, without having to use the remote control, and a keyless start system. A new 260 watt, ten speaker Bose DVD-Audio 5.1 sound system equalized for the RL cabin featured several Bose technologies. Bose AudioPilot is a noise compensation technology which analyzes background environmental cabin noise and uses an algorithm based on cabin acoustics to boost certain portions of the musical signal so that it may be heard more clearly above environmental sound "clutter" without any apparent change in volume. Bose Centerpoint processes stereo and matrix surround sound recordings to allow play through the 5.1 sound system even though the source may only be a stereo sound track. Bose Active Noise Cancellation (ANC) rounded out the suite. Always on, whether the stereo was on or not, ANC took input from two microphones placed in the cabin to analyze drivetrain-related low-frequency sound waves entering the cabin. The ANC sent information to the sound system to create a precisely shaped and timed reverse-phased audio signal from the door speakers and the subwoofer. The result was a dramatic reduction in engine and exhaust noise.


title: Acura RL

text: XM Satellite Radio, integrated Bluetooth hands-free technology for wireless phone use, voice recognition technology with over 560 voice commands to control navigation system and displays, wireless phone, audio system, heating and ventilation controls rounded out the cabin's technological features. Heating and air conditioning systems were tied into a solar sensor and GPS positioning so that cabin temperature remained constant in a mixed sun and shade situation. Based on sun position and cabin orientation, the system could automatically send additional cooling air to the sunny side of the car to keep that occupant comfortable, while not freezing out the occupant on the shady side.


title: Acura RL

text: The Alpine Electronics DVD-based navigation system was integrated with an 8-inch LCD display and a multi-use Interface Dial, which could move up, down, left and right like a mouse, turn like a knob, scroll through preset menus, and click when pushed to act as a selector button. Unlike many in-car navigation systems, the Alpine DVD-based navigation unit allowed the driver to change destinations and routes "on the fly" while driving, rather than being locked out unless the car was in Park. The tightly integrated voice recognition system worked with the navigation system and could recognize spoken city and street names. Also unique at the time was two-way communication via AcuraLink satellite communication. Using a facility of XM Radio service, the system could send a variety of messages to the car, including service appointment reminders (appointments first made via Internet) or important messages such as recall notices. The use of OnStar was carried over from the previous generation RL. Use of digital/analog trimode (two digital bands and one analog band) technology allowed the 2005 RL OnStar technology to survive the planned 2007 phase-out of the analog OnStar to fully digital OnStar service.


title: Acura RL

text: Other new RL features included the Active Front Lighting System, in which the high intensity discharge headlamps swiveled in concert with the steering up to twenty degrees, for improved night cornering vision. Light emitting diodes (LED) replaced traditional incandescent bulbs in the tail and brake lights, the turn signals integrated in the side mirror housings, and many interior cabin lights.


title: Acura RL

text: The 2005 RL was also the first Honda vehicle to use the "Advanced Compatibility Engineering" (ACE) body structure, which has since proliferated throughout every newly introduced Honda and Acura vehicle design. The ACE structure features extensive use of high-tensile steel and lightweight aluminum components in a front-mounted polygonal main frame, designed to engage vehicles of differing size and weight in a frontal collision and spread the forces through multiple structural pathways, while preventing or minimizing cabin deformation. In practical terms, this means in an SUV versus ACE structure car collision, there is a greater chance that the ACE body structure will engage with the SUV's frame and dissipate collision forces around the passenger compartment. In more conventional non-ACE car structures, the SUV frame has a much greater chance of missing or over-riding the conventional car's major structural components and a greater chance of deforming the passenger compartment.


title: Acura RL

text: The 2005 RL car structure used aluminum alloy in the hood, front fenders, trunk lid and frame, front and rear subframes, suspension arms, front knuckles and bumper beams. Magnesium was used in the intake manifold, and the two-piece center drive shaft was made of a carbon reinforced composite. The new RL featured extensive aerodynamic design treatment including details such as flush side glass, plus underbody covers and diffusers to reduce lift, resulting in a very low drag coefficient of 0.29.


title: Acura RL

text: For 2006, the Acura RL was also offered in a second trim level, the optional 'Technology Package' which included three new features: adaptive cruise control (ACC), Collision Mitigation Braking System, and Michelin PAX System run-flat tires on unique PAX 235 mm x 460 mm A ("A" for asymmetric) aluminum alloy wheels with unique 245-680R460A Michelin Pilot HX MXM 4 all-season Grand Touring type radials designed for the Michelin PAX System. The metric sized, run-flat Michelin PAX System wheels and tires are equivalent to 18" x 9" wheels and 245/45-R18 conventional tires. The previously standard color-matched mud guards were removed in 2006. All 2006 models had a slight change to the navigation system that allowed the installation of an optional rearview camera. MSRP increased by $200 over the equivalent 2005 model.


title: Acura RL

text: For 2007, the Acura RL was offered in three trim levels, detailed in the table below: a "standard" or "base" package, a newly defined "Technology Package," and the highest level trim, the "Technology Package with CMBS/PAX."


title: Acura RL

text: Base model cars were well equipped, but deleted certain features such as the navigation system and Adaptive Front Lighting System (AFS), and substituted plastic simulated wood for the dashboard maple wood trim.


title: Acura RL

text: Technology Package cars were essentially the same as the 2005 and 2006 standard models, coming with navigation and AFS, while adding as standard equipment a rear backup camera and a 3.5 mm stereo input jack for Apple iPod and other MP3-type devices.


title: Acura RL

text: The Technology Package plus CMBS/PAX trim level had no 2005 equivalent, though it was most similar to the 2006 Technology Package that had also included ACC/CMBS and PAX technologies. While the label "CMBS/PAX" might appear to indicate ACC was dropped as a feature, in reality, ACC was an extension of the CMBS system, and so was included.


title: Acura RL

text: As noted above, the MP3 audio player feature (usable for any device with a 3.5 mm headphone jack) was added to all trim levels. An integrated rearview camera was added to the top two trim levels. An integrated rearview camera could be added to the non-navigation Base model as a dealer installed option. The Base model optional rearview camera was installed in the same manner and position as on the 2006 models, mounted dead center in the trunk trim, with the trunk release button displaced to the right of center (passenger side). The difference was subtle, but the factory rearview camera installation on the Technology Package and the Technology Package with CMBS/PAX is to the left side (driver's side) of the center-mounted trunk release.


title: Acura RL

text: In 2005 and 2006, all models came standard with "genuine curly maple wood dashboard trim." With the introduction of three trim levels, the genuine curly maple wood dashboard trim now only appeared on the two higher level cars: the Technology Package and the Technology Package with CMBS/PAX. OnStar was deleted as a feature from all trim levels. Colors were added and deleted. MSRP increased by $100 from the roughly equivalent 2006 trims.


title: Acura RL

text: The 2008 Acura RL continued unchanged in the U.S. market from the 2007 model, with three trim levels. Colors were added and deleted. MSRP increased $500 for each trim:


title: Acura RL

text: In Canada, the 2008 Acura RL was available in two different models, Base and Elite Package. The Elite Package added Collision Mitigation Braking System (CMBS), Active Front Lighting System (AFS), Adaptive Cruise Control (ACC), heated and cooled ventilated front seats, and burled maple wood trim.


title: Acura RL

text: For the 2005–2008 models, Acura offered an A-Spec package for the RL. The dealer-installed package consisted of a body kit, badging, revised suspension and different wheels. The package was first announced at a late 2004 Specialty Equipment Market Association (SEMA) trade show in Las Vegas. The A-Spec package for sale was distinctly different from the Acura RL A-Spec Concept Vehicle announced and shown as a striking dark red one-of-a-kind custom creation in early 2005 at the Detroit Auto Show.


title: Acura RL

text: The performance part of the package included the A-Spec sport suspension and A-Spec 18-inch alloy wheels, which allowed the use of more sports-oriented lower profile tires.


title: Acura RL

text: The A-Spec sport suspension changed out the four spring and damper (shock absorber) strut assemblies. The A-Spec suspension featured lowering springs (approximately 0.75 inch) and revalved dampers. The ride was stiffer, but not overly so, and handling was improved with less body roll, more controlled cornering and enhanced feel. Reportedly Acura chose to make the RL's A-Spec suspension more compliant than the very stiff A-Spec sport suspension upgrade for the Acura TL, in keeping with the two different missions of the cars: luxury for the RL, luxury sport for the TL. Acura RL A-Spec retained the same suspension geometry as the stock Acura RL suspension alignment specifications.


title: Acura RL

text: The other A-Spec performance upgrade was A-Spec 18x8 inch alloy wheels, a 10-spoke lightweight design (about the same weight as the 5-spoke 17x8 inch OEM wheels). Recommended tires were either 245/45-18 sized Michelin Pilot Sport PS2 ultra high-performance summer tires or Michelin Pilot Sport A/S ultra-high-performance all-season tires. Alternatively, less sport-oriented Michelin Pilot HX MXM4 Grand Touring All Season tires were also available in the same size. Typical of Acura optional wheels, the 55 mm offset of the stock 17x8 inch wheels was maintained so that suspension geometry could remain untouched.


title: Acura RL

text: The A-Spec appearance package consisted of a front air dam, side skirts, rear bumper air diffuser and a subtle trunk decklid lip style spoiler, all designed to give the car a more aggressive "aero" look. The parts came pre-painted from the factory to match factory colors. All parts were dealer installable. If the dealer installed the A-Spec parts at the time of purchase, the original new car warranty of four years/50,000 miles would apply. If installed after purchase, the normal one year/12,000 mile parts warranty would apply.


title: Acura RL

text: As of the 2009 mid-model change, A-Spec options were no longer offered. However, Acura moved to a firmer standard suspension for 2009, plus larger and wider 18" x 8" inch standard wheels and lower-profile 245/45-18 size tires. More aggressive "aero" look body work was also standard, and a revised trunk decklid spoiler was made available as a dealer installed option.


title: Acura RL

text: For the 2009 model year, the RL received an extensive mid-model change (MMC), and made its introduction at the Chicago Auto Show on February 6, 2008, billed as "the most extensive Acura MMC ever". The new sedan was designated KB2 in the VIN codes, differentiating it from the 2005–2008 KB1 chassis VIN code. The revised sedan was released on July 1, 2008, to dealerships. The engine is upgraded to 3.7 liters with . While on paper, the engine may seem to be the same unit as shared with the Acura MDX, it is actually a variant that introduces, for the first time ever on an SOHC Honda V6, an implementation of the Honda VTEC variable valve train technology on both intake and exhaust for improved horsepower and torque. Heretofore, all previous SOHC Honda V6 engines with VTEC used the technology on the intake side only. Engine emissions were reduced to meet the stricter U.S. Environmental Protection Agency (EPA) TIER 2 – BIN 5 and California Air Resources Board ULEV-2 standards. Implementation of the SH-AWD was adjusted for earlier intervention and a greater rear-wheel bias for better handling dynamics.


title: Acura RL

text: The MMC RL suspension was upgraded with higher-rate coil springs, larger diameter anti-sway bars and stiffer bushings all around. The MMC RL was equipped with a new larger front anti-sway bar of hollow construction, 30 mm diameter overall with a 6.5 mm wall thickness, and a larger rear solid anti-sway bar, 19 mm in diameter. The pre-MMC models sported a solid 29 mm front and 17 mm rear sway bar.


title: Acura RL

text: Standard 18- x 8-inch seven-spoke alloy wheels with 245/45-18 tires replaced the previous years' 17- x 8-inch five-spoke offerings for not only the Base and Tech package models, but also for the highest trim level, the ACC/CMBS equipped model. Previous years' ACC/CMBS equipped models were equipped with [Michelin PAX System] run-flat tires on 18-inch equivalent (460 mm diameter) five-spoke wheels.


title: Acura RL

text: Inside, the front seats were revised for greater comfort and to allow a slight increase in rear leg room. The passenger front seat received the same full 10-way power control as the driver's seat. Both front seats featured active head restraint systems, and the existing seat-heating feature was supplemented by six levels of cooling ventilation. Controls for heating and air conditioning were simplified, and additional individual vent controls were added for the driver and passenger. The shift gear no longer had a gated sequence, but moved straight fore and aft like the ones in the Acura TSX and Acura TL. Simulated woodgrain trim was added to the steering wheel and the top of the shifter, to emphasize the RL's upscale aspirations compared to its less costly TL and TSX siblings.


title: Acura RL

text: Additional insulation, improved acoustic isolation windshield design, and a new implementation of the Active Noise Cancellation system (ANC) combined to make the 2009 RL's interior quieter in a variety of conditions. Whereas the former ANC was set to cancel out only low frequency boominess from the engine and exhaust, the MMC system, called Active Sound Control, was expanded in its range to cancel some higher frequency road and tire noise as well. Unlike its predecessor ANC, Active Sound Control was now linked to throttle position and engine RPM to provide a quieter cockpit during normal cruising, yet allowed more of the new 3.7 L engine's "muscular sound" to be heard at higher engine speeds and higher velocities.


title: Acura RL

text: An additional microphone as well as some switchable directionality was added to the HFL (Hands Free Link) and Voice Activated Navigation and Convenience controls. When the system was in "accept commands" mode, the new microphone system provided more accurate system "understanding" of the driver's voice. Extraneous sounds, such as other voices in the cabin and wind noise, were better distinguished and filtered out by the dual microphone system. Directionality was removed when an HFL voice call was established, so that all passengers could still participate in a phone call as in the pre-MMC model. The new dual microphone system used real estate in the overhead console that was previously used in the 2005 and 2006 models for OnStar control electronics. The number of voice recognition commands was increased to over 700, up from 560 previously.


title: Acura RL

text: The DVD-based navigation system improved on previous XM satellite-linked traffic flow reporting, adding continuously updated real-time weather reporting and the capability to reroute based on current traffic conditions. The DVD Audio-capable 10-speaker sound system remained, but integration with the audio system was improved with the addition of Bluetooth stereo and a USB port that allowed integration and operation of Apple iPod and other MP3 type devices. Also new was the ability to display iPod or other MP3 device (such as a USB flash memory device) folder and playlist information on the car's 8-inch central navigation display screen.


title: Acura RL

text: New shifter and center console arrangements were added, including a Sport mode. The steering wheel paddle shifters were reprogrammed for faster response, and the paddle shifters could be operated in both Drive and Sport modes. In pre-MMC models, the gear selector had to be put in manual mode for the paddle shifters to operate.


title: Acura RL

text: In exterior length, the 2009 RL grew slightly by . The height grew by a scant , while the width, track and wheelbase remained the same. The front end including the hood, and the rear including the trunkline, were revised, and the headlights and taillights redesigned. One of the most controversial features of the 2009 RL was its "Power Plenum" grille design, the first of three similar designs that was soon joined by the second-generation 2009 Acura TSX and the fourth-generation 2009 Acura TL.


title: Acura RL

text: Curb weights increased for 2009. The MMC Base weighed in at 4083 lbs, the Technology Package model 4085 lbs, and the ACC/CMBS with no PAX weighed 4110. The equivalent 2006 pre-MMC Technology Package had weighed 4012 lbs, and the pre-MMC with ACC/CMBS/PAX weighed 4074 lbs.


title: Acura RL

text: MSRP for the 2009 Acura RL increased by $500 over 2008 model for each of its three trim levels. For 2009, the Michelin PAX Run Flat Tire system was no longer offered in combination with the CMBS/ACC package. ACC was now featured alongside CMBS as part of the package name, after a two-year hiatus. In reality, ACC was always included as a part of the CMBS. Colors were also added and deleted.


title: Acura RL

text: The 2010 Acura RL continued with few changes in the U.S. from the 2009 model, as indicated on the Acura.com website for the RL. Colors were added and deleted once again, and MSRP increased $150 in each trim:


title: Acura RL

text: The 2011 Acura RL added new color combinations and new features: six-speed automatic transmission, power folding mirrors, and rear backup/parking sensors.


title: Acura RL

text: The six-speed automatic transmission, first introduced on the 2010 Acura ZDX, finally replaced the RL's five-speed automatic, long criticized by the press as outdated. The transmission upgrade was credited for an EPA gas mileage improvement to 17/24/20 (City/Highway/Combined) an increase of 2 mpg in highway driving. In addition, 0-60 times were said to decrease by 0.5 seconds, to 6.0 seconds. There have been reports that the 2009 Acura RL Mid Model Change was originally the introduction candidate for the six-speed feature within the Acura lineup, but that the transmission was still undergoing testing and was not yet ready at that time.


title: Acura RL

text: Power folding mirrors had been available in markets other than North America since the 2004 introduction in Japan. Parking/backup sensors had been available in the North American market as a dealer installed option since the second generation Acura RL's introduction in late 2004. A host of other features had also been available since the car's introduction in late 2004, some of which are detailed in the Safety section below.


title: Acura RL

text: The RL exterior was updated for 2011 with a toned-down version of the controversial "power plenum" front grille. Inside, the RL offered a new interior color (Sea Coast), new Dark Burlwood interior trim, and thin-thread stitching on the steering wheel.


title: Acura RL

text: Unique new 18" x 8" diameter 15-spoke aluminum wheels included a new noise quieting technology: a polypropylene "Helmholtz resonator" that encircled the center portion of the inside of the wheel. The resonator served to suppress specific frequencies between 100 and 500 hertz, and in combination with increased floorboard insulation, decreased interior noise by 1.3 dB, or 15%. The Helmholtz resonators in the wheels were touted as a "world's first" for a passenger vehicle. The new wheels appeared to be conventional alloy wheels modified to incorporate an internal noise reduction device. A diagram showed an elastomer-type ring with multiple hollow chambers surrounding the center line of the wheel circumference. This resonator was designed to absorb the resonances generated by rough road surfaces such as highway seams.


title: Acura RL

text: The 2012 Acura RL appears to be a carryover from the 2011 refresh with no substantive changes. Price increases US$1,000. The color Platinum Frost Metallic had been dropped in 2011, but appears to be added back in 2012.


title: Acura RL

text: The second-generation 2005 Acura RL appeared on "Car and Driver"'s Ten Best list for 2005. The car also garnered a CNET.com "Editor's Choice" Award for Top Tech Car and has had been reviewed in 2005, 2006, 2007, 2009, and 2011 as well as 2013 for its successor, the RLX. The SH-AWD all-wheel-drive system was lauded by "Popular Science" as one of the best automotive innovations of 2004, and earned the 2005 "Tech Car of the Year" from CNET.com. In a comparison of 2006–2007 model year mid-luxury sedans with all-wheel drive (prices ranging from $60,000 to 65,000 CAD), the RL compared favorably to a Mercedes-Benz E300 4MATIC and a BMW 528xi with xDrive. Subsequent moves by both Audi and BMW to design and market their own versions of torque vectoring all-wheel-drive systems bear out the innovative nature of the SH-AWD design.


title: Acura RL

text: While critically acclaimed, sales did not meet expectations. Despite the mid-generational update in 2009, only 2,043 cars were sold in the U.S., a 55 percent drop from 2008. Among Japanese luxury flagships marketed in America during the first six months of 2010, Acura sold only 872 RLs, compared to 5,650 Lexus LS and 6,602 Infiniti M sedans. Only 379 RLs were sold in North America in 2012.


title: Acura RL

text: Enthusiasts and dealers said that the RL was not competitive because it lacked the full-size dimensions (the back seat was regarded as tight for a car of this size), a V8 engine performance option, and the better handling and balanced rear-wheel drive of its larger rivals in the mid-luxury segment. The 2009 refresh and 2011 update did not keep the RL competitive enough in acceleration or fuel economy, considering that other marques had released new generations of their mid-size luxury sedans, and as the 2009-10 RL retained a five-speed automatic transmission while other rivals had automatics with six or seven gears. Other competitors that were midway through their model cycle, such as the 2004-07 BMW 530i and 2005–08 Audi A6 3.2 FSI (with naturally-aspirated 6-cylinder engines that were less powerful than the Acura RL's 3.5L V6) received updated engines with turbocharging/supercharging; the resulting 2008 BMW 535i and 2009 Audi A6 3.0 TFSI proved more powerful and fuel-efficient than the 2009 Acura RL (with a 3.7L V6). The RL's styling, while generally considered handsome, was not viewed as inspiring or passionate enough to alert buyers to its technological features or stand out in a crowded field, and the 2009 model was criticized for its "power plenum" grille, a bright horizontal pentagon of chrome that formed a shield across the upper center.


title: Acura RL

text: Some have suggested that the Acura RL's failure in the market was due to its initial pricing which was perceived to be out of its bracket. Honda Japan believed that the new RL offered more features and performance than the base version of its luxury competitors (i.e., the base six-cylinder BMW 5 Series), and suggested that it could charge more, though Honda Canada disagreed. The RL's initial MRSP was $69,500 CAD, considerably more than the six-cylinder BMW 525i and close to that of the V8-powered 2005 BMW 545i at $70,000 CAD. At the RL's price point, most consumers expected a V8. Furthermore, they did not perceive the Acura brand as being on par with its German rivals (Audi, BMW, Mercedes-Benz) and expected more value from the Japanese marque, particularly with Acura's more expensive offerings (as opposed to entry-level offerings like the Acura TL which were much more successful in their price brackets). The damage from Honda Japan's alleged hubris was done, perhaps giving the RL an unfavorable image that could not be removed, even though Honda Canada has since reduced the RL's price as well as releasing a decontented trim to hit a lower price point. Although other Japanese manufacturers have had limited success in the mid-luxury market which has been dominated by the Germans, the Lexus GS 350 and Infiniti M35 (which debuted around the same time as the second-generation Acura RL) sold considerably better than the Acura RL as they followed a strategy of undercutting the German executive cars with lower pricing and/or more standard features. Late in its production lifespan the RL also faced competition from the Hyundai Genesis which was less expensive yet similarly refined, while featuring rear wheel drive and an optional V8 engine.


title: Acura RL

text: In 2009, the new generation of the Acura TL was released. The TL's high performance trim features essentially the same engine (but slightly more horsepower, so Acura advertised the TL as its most powerful car), the SH-AWD system, similar dimensions, and many of the RL's other key features for only $44,900 CAD, causing some to question whether it rendered the costlier RL superfluous in Acura's own showrooms. An auto journalist remarked of the RL's successor, the Acura RLX, saying "Making the RLX bigger fixes nothing. The RL's problem, and now the RLX's, is that the car looks and feels like an exalted, compulsively over-equipped Honda Accord".


title: Acura RL

text: In October 2010, the Acura RL was named by "Consumer Reports" as the most reliable new car among luxury sedans, one of five Honda models so honored in their respective categories. The others were the front-wheel-drive version of the Acura TL among upscale sedans, the Honda CR-V small SUV, the Acura RDX small upscale SUV, and the Honda Ridgeline compact pickup truck.


title: Acura RL

text: From 2005 to 2008, Acura RL has been ranked #1 and has achieved the best car safety score (46.4) in Informed for LIFE's "2003–2009 Vehicle risk index SCOREs". For both the 2009 and 2010 model years, the Acura RL received a five-star crash safety ratings from the National Highway Traffic Safety Administration (NHTSA). For the 2009 model year, the Acura RL received a Top Safety Pick designation from the Insurance Institute for Highway Safety (IIHS) earning a "Good" — the highest score possible — on frontal offset, side impact and rear crash protection tests. The "Good" scores continued for all tests conducted on the 2010 model. When a roof strength (rollover) evaluation was added to the battery of tests, the RL was rated only "Marginal" in this category, causing it to lose the Top Safety Pick award.


title: Acura RL

text: From the 2006 model year forward, the Acura RL features an optional precrash system called the Collision Mitigation Braking System (CMBS), which can alert drivers of objects up to 330 feet ahead. If the driver gets dangerously close and does not take evasive action, the RL first provides visible and audible alerts. If the driver does not respond, the electronic pretensioning seatbelt system tugs on the shoulder belts. If the driver still does not react and the collision is deemed unavoidable, the RL retracts and locks seatbelts and brakes hard. Depending on the situation, all three stages may blend together as if one.


title: Acura RL

text: The same CMBS millimeter wave radar was also used to operate the optional Adaptive Cruise Control (ACC) feature. The driver selected a cruise speed and could set a timed following distance of 2.0, 1.5 or 1.0 seconds. When the ACC detected a target at any distance up to 330 feet ahead, the engine throttle would be modulated to keep the timed following distance. If throttle modulation did not provide enough slowing, the car would also apply the brakes to help maintain the chosen distance.


title: Acura RL

text: From 2006 through 2008, Michelin PAX System run-flat tires were also offered as an option. This system allowed the car to run up to at with a flat.


title: Acura RL

text: Michelin PAX System run-flat tires require special equipment to replace them. Such equipment is available only at a limited number of specially certified tire and car dealerships. In April 2008, Michelin announced that it would discontinue its PAX run-flat tires. Unless special equipment is available, the Acura RL's optional run-flat tires are usually fixed by replacing the entire wheel/tire assembly. Unlike Honda dealers, Acura dealers were not required to become PAX certified service centers, which included expensive training and specialized machinery. Acura dealers would generally take a flat tire/wheel assembly off and put a new PAX System on the vehicle, or refer the customer to the nearest PAX certified facility.


title: Acura RL

text: For warranty and safety reasons, it is not recommended that owners of PAX equipped vehicles switch to another type of tire assembly. Both Acura and Michelin have not been forthcoming about how current owners of PAX equipped Acura RLs can address this impasse once the current supply of PAX tires run out. Some hope that the PAX tire supply will not run out and that they will be continued to be produced on a specialty basis, just as the ill-fated Michelin TRX system tires are still produced today.


title: Acura RL

text: Reasons for discontinuing the PAX run-flat system were several, one big reason probably being the class-action suit against Honda and Michelin. Other reasons may have been the difficulty in repair and replacement of PAX tires, which are generally special order and require special mount/demount machinery and training, and the paucity of PAX certified dealers throughout the United States. While RLs have reportedly low incidence of complaints with the premium Michelin Pilot MXM4 all season tires, the opposite was true of the top-of-the-line Honda Odyssey Touring model minivan equipped with Michelin Energy LX4 PAX tires that allegedly did not live up to their promise of long tread life and easy replacement. In addition, during this time, Michelin announced that due to the low general acceptance of the PAX technology throughout the industry, new PAX development would be stopped, although tires would be provided for the foreseeable future. Other PAX equipped vehicles include the world's fastest production car, the Bugatti Veyron EB 16.4, and certain Rolls Royce and Audi vehicles.


title: Acura RL

text: On the safety front, it is also worth noting that the Honda Legend, the name under which the RL is marketed in most of the rest of the world where there is no Acura brand, offers some additional optional safety features. These include Lane Keeping Assistance System (LKAS), Intelligent Night Vision, front bumper mounted cameras to assist in parking and turning, and a standard pop-up hood for pedestrian safety.


title: Acura RL

text: The LKAS can, with the assistance of a front windshield mounted CMOS camera, make small steering adjustments using the car's Electric Power Steering (EPS) system to keep a car in its lane so long as the radius of the turn was more than 220 meters, which was the then-legal minimum in Japan. The LKAS would relinquish control at the slightest steering input by the driver, so the driver retained control at all times.


title: Acura RL

text: The night vision system used a separate heads-up type display reflected from the front lower center windshield. Far infrared technology cameras do not require an infrared light source as near infrared technology cameras do, and the software was able to detect human-like figures, surround the image with a red box and give audible caution tones.


title: Acura RL

text: Bumper-mounted cameras gave the driver a view out at each front corner to assist in parking, and also to see the amount of clearance down the road if the car were in an alley-like situation, where driver vision around the corner would require moving much of the car out into the path of possible oncoming traffic.


title: Acura RL

text: The pop-up hood used a series of sensors that could detect a pedestrian-like object being thrown onto the hood. An actuator popped the hood up at the rear, close to the windshield, 10 cm (4 inches) to help minimize pedestrian injuries, especially head trauma. RL/Legend models in all markets featured energy-absorbing hood and fender supports and deformable windshield wiper pivots to minimize pedestrian injury.


title: Acura RL

text: There have been two recalls on the second-generation Acura RL, based on defects in parts used in both Acura and Honda vehicles.


title: Acura RL

text: In December 2007, certain 2005–2008 model Acura RLs were subject to a safety recall for the power steering hose. Prolonged high under-hood temperatures may cause the power steering hose to deteriorate prematurely and may cause the hose to crack and leak power steering oil. Oil leaking onto a hot catalytic converter will generate smoke and possibly lead to an under-hood fire. Affected vehicles were to be inspected and repaired, as applicable, at no charge. Reportedly, this recall extended to both 2005–2008 Acura RL and 2004–2008 Acura TL models.


title: Acura RL

text: In December 2010, certain 2005–2007 model Acura RLs were subject to a safety recall for potential leaking of the brake master cylinder seal. A seal in the brake master cylinder may be susceptible to damage following the use of brake fluid other than the recommended Acura or (Honda) Genuine DOT3 brake fluid. If the seal is damaged, it can result in a brake fluid leak under certain conditions. If a leak should occur, the driver might see a low brake fluid indicator light or a BRAKE FLUID LOW or CHECK BRAKE SYSTEM message. If the driver continues to drive the vehicle after receiving this message without refilling the brake fluid reservoir, it could result in a brake pedal that feels soft or spongy, and may eventually affect braking performance, increasing the risk of a crash. Affected vehicles were to be inspected and repaired, as applicable, at no charge. Reportedly, this recall applied to both 2005–2007 Acura RL and 2005–2007 Honda Odyssey models.


title: Acura RL

text: In April 2012, the Acura RLX concept was introduced by Honda, and the production model debuted at the Los Angeles Auto Show. The initial available trim of the RLX will be front-wheel drive; later the all-wheel drive version will be released featuring a 377-horsepower hybrid engine mated to a seven-speed dual-clutch transmission.


title: Set cover problem

text: The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972.


title: Set cover problem

text: Given a set of elements (called the universe) and a collection of sets whose union equals the universe, the set cover problem is to identify the smallest sub-collection of whose union equals the universe. For example, consider the universe and the collection of sets Clearly the union of is . However, we can cover all of the elements with the following, smaller number of sets:


title: Set cover problem

text: More formally, given a universe formula_1 and a family formula_2 of subsets of formula_1, a "cover" is a subfamily formula_4 of sets whose union is formula_1. In the set covering decision problem, the input is a pair formula_6 and an integer formula_7; the question is whether there is a set covering of size formula_7 or less. In the set covering optimization problem, the input is a pair formula_6, and the task is to find a set covering that uses the fewest sets.


title: Set cover problem

text: The decision version of set covering is NP-complete, and the optimization/search version of set cover is NP-hard. It is a problem "whose study has led to the development of fundamental techniques for the entire field" of approximation algorithms. If each set is assigned a cost, it becomes a "weighted" set cover problem.


title: Set cover problem

text: The integrality gap of this ILP is at most formula_10, so its relaxation gives a factor-formula_10 approximation algorithm for the minimum set cover problem (where formula_12 is the size of the universe).


title: Set cover problem

text: In weighted set cover, the sets are assigned weights. Denote the weight of set formula_13 by formula_14. Then the integer linear program describing weighted set cover is identical to the one given above, except that the objective function to minimize is formula_15.


title: Set cover problem

text: Set covering is equivalent to the hitting set problem. That is seen by observing that an instance of set covering can


title: Set cover problem

text: be viewed as an arbitrary bipartite graph, with the universe represented by vertices on the left, the sets represented by vertices on the


title: Set cover problem

text: right, and edges representing the inclusion of elements in sets. The task is then to find a minimum cardinality subset of right-vertices which covers all of the left-vertices, which is precisely the Hitting set problem.


title: Set cover problem

text: There is a greedy algorithm for polynomial time approximation of set covering that chooses sets according to one rule: at each stage, choose the set that contains the largest number of uncovered elements. This method can be implemented in time linear in the sum of sizes of the input sets, using a bucket queue to prioritize the sets. It achieves an approximation ratio of formula_16, where formula_17 is the size of the set to be covered. In other words, it finds a covering that may be formula_18 times as large as the minimum one, where formula_18 is the formula_20-th harmonic number:


title: Set cover problem

text: This greedy algorithm actually achieves an approximation ratio of formula_22 where formula_23 is the maximum cardinality set of formula_24. For formula_25dense instances, however, there exists a formula_26-approximation algorithm for every formula_27.


title: Set cover problem

text: There is a standard example on which the greedy algorithm achieves an approximation ratio of formula_28.


title: Set cover problem

text: The universe consists of formula_29 elements. The set system consists of formula_7 pairwise disjoint sets


title: Set cover problem

text: each of which contains half of the elements from each formula_34. On this input, the greedy algorithm takes the sets


title: Set cover problem

text: Inapproximability results show that the greedy algorithm is essentially the best-possible polynomial time approximation algorithm for set cover up to lower order terms


title: Set cover problem

text: (see Inapproximability results below), under plausible complexity assumptions. A tighter analysis for the greedy algorithm shows that the approximation ratio is exactly formula_39.


title: Set cover problem

text: If each element occurs in at most sets, then a solution can be found in polynomial time that approximates the optimum to within a factor of using LP relaxation.


title: Set cover problem

text: If the constraint formula_40 is replaced by formula_41 for all in formula_2 in the integer linear program shown above, then it becomes a (non-integer) linear program . The algorithm can be described as follows:


title: Set cover problem

text: When formula_43 refers to the size of the universe, showed that set covering cannot be approximated in polynomial time to within a factor of formula_44, unless NP has quasi-polynomial time algorithms. Feige (1998) improved this lower bound to formula_45 under the same assumptions, which essentially matches the approximation ratio achieved by the greedy algorithm. established a lower bound


title: Set cover problem

text: of formula_46, where formula_47 is a certain constant, under the weaker assumption that Pformula_48NP.


title: Set cover problem

text: A similar result with a higher value of formula_47 was recently proved by . showed optimal inapproximability by proving that it cannot be approximated to formula_50 unless Pformula_51NP.


title: Set cover problem

text: Relaxing the integer linear program for weighted set cover stated above, one may use randomized rounding to get an formula_52-factor approximation. Non weighted set cover can be adapted to the weighted case.


title: Argyll Robertson pupil

text: Argyll Robertson pupils (AR pupils) are bilateral small pupils that reduce in size on a near object (i.e., they accommodate), but do "not" constrict when exposed to bright light (i.e., they do not react). They are a highly specific sign of neurosyphilis; however, Argyll Robertson pupils may also be a sign of diabetic neuropathy. In general, pupils that accommodate but do not react are said to show light-near dissociation (i.e., it is the absence of a miotic reaction to light, both direct and consensual, with the preservation of a miotic reaction to near stimulus (accommodation/convergence).


title: Argyll Robertson pupil

text: AR pupils are extremely uncommon in the developed world. There is continued interest in the underlying pathophysiology, but the scarcity of cases makes ongoing research difficult.


title: Argyll Robertson pupil

text: The two different types of near response are caused by different underlying disease processes. "Adie's pupil" is caused by damage to "peripheral" pathways to the pupil (parasympathetic neurons in the ciliary ganglion that cause pupillary constriction to bright light "and" with near vision). The pathophysiologic mechanism which produces an Argyll Robertson pupil is unclear, but is believed to be the result of bilateral damage to the pretectal nuclei in the midbrain. Studies have failed to demonstrate a focal localising lesion. Research has implicated the rostral midbrain in the vicinity of the cerebral aqueduct of the third ventricle as the most likely region of damage. A lesion in this area would involve efferent pupillary fibres on the dorsal aspect of the Edinger-Westphal nucleus (associated with the response to light) while sparing the fibres associated with the response to near, which lie slightly more ventrally.


title: Argyll Robertson pupil

text: The exact relationship between syphilis and the two types of pupils ("AR pupils" and "tonic pupils") is not known at the present time. The older literature on AR pupils did not report the details of pupillary constriction (brisk vs. tonic) that are necessary to distinguish AR pupils from tonic pupils. Tonic pupils can occur in neurosyphilis. It is not known whether neurosyphilis itself (infection by "Treponema pallidum") can cause tonic pupils, or whether tonic pupils in syphilis simply reflect a coexisting peripheral neuropathy.


title: Argyll Robertson pupil

text: A third cause of light-near dissociation is Parinaud syndrome, also called dorsal midbrain syndrome. This uncommon syndrome involves vertical gaze palsy associated with pupils that “accommodate but do not react." The causes of Parinaud syndrome include brain tumors (pinealomas), multiple sclerosis and brainstem infarction.


title: Argyll Robertson pupil

text: Due to the lack of detail in the older literature and the scarcity of AR pupils at the present time, it is not known whether syphilis can cause Parinaud syndrome. It is not known whether AR pupils are any different from the pupils seen in other dorsal midbrain lesions.


title: Argyll Robertson pupil

text: There is no definite treatment, but, because syphilis may be an underlying cause, it should be treated.


title: Argyll Robertson pupil

text: However, because this sign is associated with neurosyphilis, it should be treated with crystalline penicillin 24 mU intravenous per day for 10 to 14 days. If the patient is allergic to penicillin, they should undergo desensitization and then be treated.


title: Argyll Robertson pupil

text: Argyll Robertson pupils were named after Douglas Argyll Robertson (1837–1909), a Scottish ophthalmologist and surgeon who described the condition in the mid-1860s in the context of neurosyphilis.


title: Argyll Robertson pupil

text: In the early 20th century, William John Adie described a second type of pupil that could "accommodate but not react". Adie's tonic pupil is usually associated with a benign peripheral neuropathy (Adie syndrome), not with syphilis.


title: Argyll Robertson pupil

text: When penicillin became widely available in the 1940s, the prevalence of AR pupils (which develop only after decades of untreated infection) decreased dramatically. AR pupils are now quite rare. A patient whose pupil “accommodates but does not react” almost always has a tonic pupil, not an AR pupil.


title: Argyll Robertson pupil

text: In the 1950s, Loewenfeld distinguished between the two types of pupils by carefully observing the exact way in which the pupils constrict with near vision. The near response in "AR pupils" is brisk and immediate. The near response in "tonic pupils" is slow and prolonged.