title: Steve Smith (cricketer)

text: Following the T20I series', Australia played Pakistan and New Zealand at home in two and three match Test series respectively. In contrast to the preceding Ashes tour, Smith made little contribution with the bat throughout the test series against Pakistan, scoring 4 and 36 in the first and second matches respectively. Despite this, Australia went on to win the Test series 2–0, winning both matches by an innings margin. During the second test match of the series at Adelaide, Smith overtook Donald Bradman as the 11th highest run scorer for Australia in tests. Smith also became the fastest test batsman to score 7,000 test runs in his 126th innings, bettering the 73-year-old record of Walter Hammond (130 innings).


title: Steve Smith (cricketer)

text: In the first day-night Test match at Perth against New Zealand, Smith struggled, scoring 43 and 16, and was dismissed both innings to the short-pitched bowling of fast-bowler Neil Wagner. Australia went on to win the first Test by 296 runs. In the second test at Melbourne, Smith continued to find form when he scored 85 in the first innings before he was again dismissed by Neil Wagner, denying Smith of a record fifth consecutive Test century at the MCG. Although Australia bowled New Zealand out for 148 and progressively built on their large first innings lead, Smith was dismissed for 7 in the second innings, giving Neil Wagner his 200th Test wicket and fourth consecutive dismissal of Smith in the series. Despite this, Australia comfortably won the match by 247 runs and retained the Trans-Tasman Trophy. On Day 1 of the Melbourne test, Smith also went past Greg Chappell's tally of 7,110 moving into 10th position as highest run-scorer for Australia in Tests. The 3rd Test saw Smith reach the half-century mark again, reaching 63 from 182 balls, taking 45 minutes to get off the mark. Australia won the match by 279 runs, completing a clean sweep of the Test series.


title: Steve Smith (cricketer)

text: In a similar vein to Bodyline devised by England in the 1930s to disrupt Bradman's scoring, which was largely employed by Harold Larwood, New Zealand devised a set of tactics to curb Smith's scoring. It involved left-arm fast-medium bowler Neil Wagner pitching short to Smith attempting to get him out caught on the leg side. The plan enjoyed good results, with Wagner dismissing Smith all four times in Perth and Melbourne, however Colin de Grandhomme claimed Smith's wicket in the Test at Sydney. Smith himself said after the first Test, "The pink one's a little bit different - it just sort of comes off the wicket at different paces ... I couldn't quite time the ball where I wanted to at certain times but no doubt I'm going to get a little bit (of short-pitch bowling) in Melbourne, I dare say, on probably a different wicket. We'll see how we go." Despite Smith scoring 214 runs from 5 innings at an average of 42.80, and atypically for Smith a low strike rate of 34.13—who just three months earlier in the 2019 Ashes scored at a rate of 64.71 per 100 balls—Australia managed to win all three Tests by a margin of over 200 runs, largely thanks to Labuschagne's batting.


title: Steve Smith (cricketer)

text: Australia travelled to India to play three ODI matches between 14 and 19 January 2020. Smith was not required in the first match. In the second match, Smith came in at 1/20 and looked set to reach another hundred, but was dismissed for 98 as he played on to his stumps off Kuldeep Yadav. In the 3rd match, Smith made 131 off 132 balls as Australia reached a total of 286 from the 50 overs. However, Smith's hundred was in vain as India chased down the target in the 48th over, India winning the series 2–1.


title: Steve Smith (cricketer)

text: Australia travelled to South Africa to play a 3 ODI matches and 3 T20I matches between 21 February and 7 March 2020. The first match of the T20I series in Johannesburg saw Smith topscore with 45, helping Australia to a total of 196 winning by 107 runs. Australia was sent in to bat in the 3rd match at Cape Town, making 193 runs from their 20 overs, Smith remaining not out on 30 from 15 balls. South Africa was bowled out for 96, Australia winning by 97 runs, and winning the T20I series 2–1.


title: Steve Smith (cricketer)

text: Smith topscored in the first ODI match with 76, but the rest of the team could only manage 134 between them, getting bowled out in the 46th over for 217. Smith failed to make any significant scores for the remaining games as Australia lost the ODI series 0–3.


title: Steve Smith (cricketer)

text: New Zealand returned to Australia after the Test series, with games scheduled to be held on 13, 15 and 20 March 2020. The first match was won by Australia, with a winning margin of 71 runs; Smith getting bowled for 14 by Santner. However, due to the COVID-19 pandemic, the 2nd and 3rd matches were cancelled without a ball being bowled due to travel restrictions.


title: Steve Smith (cricketer)

text: On 16 July 2020, Smith was named in a 26-man preliminary squad of players to begin training ahead of a possible tour to England following the COVID-19 pandemic. On 14 August 2020, Cricket Australia confirmed that the fixtures would be taking place, with Smith included in the touring party.


title: Steve Smith (cricketer)

text: Smith's scoring was unremarkable in the 3 T20I matches. Between the last T20I match and first ODI match, Smith was struck on the head at training, and subsequently missed the first two ODIs. Smith was still feeling the effects before the 3rd ODI, and was left out again, missing all three matches in the series.


title: Steve Smith (cricketer)

text: India's tour began with a 3-match ODI series. In the first match in Sydney, Smith came to the wicket after a large opening partnership, and put on a 108-run partnership with Aaron Finch. Smith brought up his hundred off 62 deliveries, the third fastest by an Australian and finished with 105 runs off 66 balls. Smith made a second century in the second match at Sydney, again requiring only 62 deliveries. He was dismissed on 104 from 64 deliveries. Smith and Labuschagne put on a 136-run partnership. Australia won the match by 51 runs, and Smith was again awarded Player of the Match for his performance. Australia won the series 2–1. Smith was awarded Player of the Series for his efforts.


title: Steve Smith (cricketer)

text: Following the ODI series was a 3-match T20I series. Smith made a respectable 46 in the second match, but his scores in the other matches were unremarkable. Australia lost the series 1–2.


title: Steve Smith (cricketer)

text: In November 2020, Smith was nominated for the Sir Garfield Sobers Award for ICC Male Cricketer of the Decade, and the award for Test cricketer of the decade.


title: Steve Smith (cricketer)

text: Smith's poor form for his standards continued as he scored 1 and 1* in the opening Test of the Border-Gavaskar trophy in Adelaide, Australia winning the match after bowling India out for 36, their lowest total in Tests. Smith scored 0 and 8 at Melbourne as India won by 8 wickets in contrast to his previous seven Tests at the ground where he had averaged 113.50. Since the 2019 Ashes, Smith had averaged 26.40. Ex-Australian captain Ian Chappell noted "He doesn't look as comfortable at the crease because India have given him things to think about" and "In trying to avoid one way of getting out, you can create another one, and I think that's happened a bit with Smith."


title: Steve Smith (cricketer)

text: Smith was able to break his 14-innings century drought since the 2019 Ashes at his home ground in Sydney with a 226-ball 131 in the first innings. He followed that up with a 167-ball 81 in the third innings, helping to set India a target of 407 in the fourth innings. The match ended in a draw as the series was poised 1 all.


title: Steve Smith (cricketer)

text: In the fourth and final match of the series at the Gabba, Smith made 36 in the first innings and topscored for Australia with 55 in the third innings. Australia set India a target of 328 to win. India took the game into the 5th day as they chased the target with three wickets remaining as Australia lost the series 1–2.


title: Steve Smith (cricketer)

text: Smith was ruled out of the tours to West Indies and Bangladesh with an elbow injury in his left arm — a recurrence of an injury that prohibited him from playing domestic cricket for a month during February and March in 2021. National selection panel chair Trevor Hohns said of the injury - "I can't tell you how long or how serious it is but it's something that he's had before, and it definitely flared up again whilst playing in the IPL ... How long it'll take to get it completely right, I can't tell you that at the moment … the main thing from our point of view with Steven is to make sure he is fit for the T20 World Cup and of course the Ashes next season." In August 2021, Smith was named in Australia's squad for the 2021 ICC Men's T20 World Cup.


title: Steve Smith (cricketer)

text: Smith played a "floating position" in Australia's win in the T20 World Cup. He scored 69 runs at a strike rate of 97.18.


title: Steve Smith (cricketer)

text: In November 2021, following Tim Paine's resignation from the Test captaincy amid allegations of improper conduct in 2017, Pat Cummins was promoted to captain of the Test side, as Smith returned to a leadership position with the vice captaincy. In the first Test in Brisbane, Smith fell to 'a lazy shot' to Mark Wood for 12.


title: Steve Smith (cricketer)

text: Smith captained Australia for the second Test in Adelaide, when Cummins was ruled out for the match after he was deemed to be a close contact of someone with COVID-19. Smith passed 50 in the first innings, but was trapped leg before wicket on 93 to James Anderson to a ball that kept low. In the second innings, Smith survived multiple chances (including a first-ball drop by Buttler) but was out on 6, gloved down the leg side to Robinson. Smith had also picked up his first test wicket in 6 years, dismissing Jack Leach, who was caught by David Warner.


title: Steve Smith (cricketer)

text: After the Test, Smith said "It brought back some old memories in a way and I had fun out there, but it's Patty's team. I'm the vice-captain and I will help him any way I can. That's my job. Hopefully we can keep the momentum going into what should be an amazing Boxing Day Test."


title: Steve Smith (cricketer)

text: Australia toured Pakistan in 2022 to play three tests, three ODIs and a one off T20I. Smith played during the three tests, but did not play in the ODIs and T20Is. This tour was the Australia's first tour of Pakistan since 1998. Smith performed well against Pakistan, averaging 56.50 in 4 innings and achieving a top score of 78, but did not manage to fully take advantage of the "dead" and "benign" pitch at the Rawalpindi Cricket Stadium during the first test, unlike his Pakistani contemporaries. During the series, Smith had also become the fastest man to reach 8,000 test runs, achieving it in 151 innings, one less than the previous title holder, Kumar Sangakkara and three innings faster than Sachin Tendulkar. Smith was also the first person to achieve this feat with a batting average over 60, reaching 8,000 test runs with a 60.1 average at the time.


title: Steve Smith (cricketer)

text: In 2022, Australia toured Sri Lanka for 3 T20Is, 5 ODIs and 2 tests. Smith did not play during the first T20I, but played in the second and third, where he scored 5 runs in the second match and 37 runs off of 27 balls and remained not out in the third match. Smith finished the T20I series with a 42.0 batting average, with a high score of 37. Smith played during the first two ODI matches, but was unable to play during the last three due to a quad injury. He scored 53 runs off 60 balls during the first match and scored 28 runs off of 35 balls during the second match. He finished the ODI series with an average of 40.50, a high score of 53 and scored 81 runs in 2 innings.


title: Steve Smith (cricketer)

text: Smith played during both of the tests, and scored 6 runs off of 11 balls before being run out by Niroshan Dickwella. This mix up had caused Smith to lose his temper against his batting partner at the time, Usman Khawaja, where he was visibly irritated. However, Smith states that there is no lingering fallout between the two of them. Smith did not bat during the second innings, as Australia bowled Sri Lanka out for 212 and 113, and had a target of 5 runs, winning the match by 10 wickets. During the second test, Smith scored 145 runs off of 272 balls and remained not out. This was his first century since January 2021; a time span of 547 days, as well as being his 28th Test century. During the second innings however, Smith was dismissed for 0 and Australia collapsed, as Sri Lanka beat Australia by an innings and 39 runs. During the second innings, Smith had reviewed the original "out" decision by the umpire, only to confirm the umpire's decision. This review was called "comical" and "appalling" by multiple news sources. Smith finished the test series with 151 runs from 3 innings, an average of 75.50 and with a high score of 145*. He was the second highest run scorer during the series, behind Sri Lankan batsman, Dinesh Chandimal.


title: Steve Smith (cricketer)

text: In October 2022, Smith was named in the Australian ODI squad for the three-match home ODI series. He scored 195 runs including two half centuries in 3 matches at an average of 97.50 as Australia won the series in a 3–0 whitewash.


title: Steve Smith (cricketer)

text: In the first Test in Perth, Smith scored 200 not out from 311 deliveries, his fourth double-century in his Test career. Smith said after his innings: "I think from the first one-dayer against England, where I sort of implemented the work that I've been doing, it felt really good straightaway." He went on to say "I suppose the reason for my slight change in technique is because I was unhappy with where I was at with my batting ... But I think now with the way I'm able to play and the way teams have bowled against me, I've had to adapt a bit and where I'm at with my body and my hands I feel like I'm opening up the whole ground as opposed to probably just behind square on the leg side, and I'm able to hit the ball in different areas, which I probably was able to hit previously. So I feel in a good place."


title: Steve Smith (cricketer)

text: Smith is a right-handed batsman with a technique that has attracted attention for its unorthodoxy. He moves around frequently in the crease, especially during bowlers' run-up, and ends up with the toes of his feet outside off stump against right-handers, controls the bat with his bottom hand (that is, the hand closest to the blade of the bat), and is capable of playing unconventional cricket shots like the reverse sweep. Playing in a club match in January 2010, right-handed Smith took guard left-handed and hit a six. Due to his unorthodox style, Smith was initially labelled as a limited-overs batsman who might struggle in the longer form of the game, especially early in his career when he was vulnerable outside off stump. However, Smith compensates for his unique technique with outstanding hand-eye co-ordination, focus, and his footwork, especially to spin bowlers, is exemplary. Smith spontaneously experimented with his technique during the Perth Test match in the 2013–14 Ashes, during which he decided to take a "prelim movement back and across" to counter short-pitched bowling. This change took his batting average from 33 in 2013 to 64.95 in 2019. As of 2021, it is 61.80. At the time of delivery, Smith's stumps are fully covered, making bowled dismissals unlikely. This position also allows him to play to either the on or off side with ease.


title: Steve Smith (cricketer)

text: Much of the credit for Smith's success can also be attributed to batting coach Trent Woodhill, who coached Smith as a junior and noted his abundant talent. He has also defended Smith's unique batting style, and has long argued that in Australia, many naturally talented cricketers who may not necessarily have an orthodox technique are let down by over-coaching; in the years between leaving school and his elevation into international cricket, Smith had his technique picked apart by a number of well-intentioned coaches. Since re-establishing his working relationship with Woodhill, Smith appears to have regained calm and confidence in his cricket, which has since produced results over the last few seasons. Smith is also known for his concentration, being able to bat for long periods of time, even through a whole day's play.


title: Steve Smith (cricketer)

text: As a bowler, however, after his quick rise up the batting order (until he became captain, and settled in at 4), the comparisons to Shane Warne never gathered momentum. He was an able option as a leg spinner early in his career, but was under-used because he was described as a very defensive bowler.


title: Steve Smith (cricketer)

text: When he was captain for Australia, he had been initially tagged as the second "Captain Grumpy" since Allan Border early in his captaincy reign, having to warn Mitchell Starc for unsportsmanlike behaviour, and being highly critical of the team's bowling and fielding despite beating New Zealand by over 200 runs in 2015. Later, in 2017–2018, he publicly criticised Glenn Maxwell's training regimen when Maxwell was dropped from the Australian ODI squad. He was also criticised for having too much influence over team selections.


title: Steve Smith (cricketer)

text: Smith is consistently rated as one of the top-ranked Test batsmen in the world, according to the ICC Player Rankings.


title: Steve Smith (cricketer)

text: , Smith has made a total of 45 first-class centuries, 13 List A centuries and one T20 century. Of these, 29 of his first-class centuries were scored in Test matches and 12 of his List A centuries scored in One Day Internationals. His best bowling figures of seven wickets for the cost of 64 runs (7/64) were taken for New South Wales against South Australia in the Sheffield Shield.


title: Steve Smith (cricketer)

text: , a 2020 Australian English-language TV documentary, produced as an Original for Amazon Prime Video. The documentary was also co-produced by Cricket Australia. The documentary revolves around the Infamous ball-tampering scandal at Cape Town in March 2018 and how Australia rebuild their reputation after the scandal. Smith's redemption and his dominating batting display in the 2019 Ashes after the scandal was one of the key point of the series.


title: Climate

text: Climate is the long-term weather pattern in an area, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years. Some of the meteorological variables that are commonly measured are temperature, humidity, atmospheric pressure, wind, and precipitation. In a broader sense, climate is the state of the components of the climate system, including the atmosphere, hydrosphere, cryosphere, lithosphere and biosphere and the interactions between them. The climate of a location is affected by its latitude/longitude, terrain, altitude, land use and nearby water bodies and their currents.


title: Climate

text: Climates can be classified according to the average and typical variables, most commonly temperature and precipitation. The most widely used classification scheme was the Köppen climate classification. The Thornthwaite system, in use since 1948, incorporates evapotranspiration along with temperature and precipitation information and is used in studying biological diversity and how climate change affects it. Finally, the Bergeron and Spatial Synoptic Classification systems focus on the origin of air masses that define the climate of a region.


title: Climate

text: Paleoclimatology is the study of ancient climates. Paleoclimatologists seek to explain climate variations for all parts of the Earth during any given geologic period, beginning with the time of the Earth's formation. Since very few direct observations of climate were available before the 19th century, paleoclimates are inferred from proxy variables. They include non-biotic evidence—such as sediments found in lake beds and ice cores—and biotic evidence—such as tree rings and coral. Climate models are mathematical models of past, present, and future climates. Climate change may occur over long and short timescales from various factors. Recent warming is discussed in global warming, which results in redistributions. For example, "a 3 °C [5 °F] change in mean annual temperature corresponds to a shift in isotherms of approximately in latitude (in the temperate zone) or in elevation. Therefore, species are expected to move upwards in elevation or towards the poles in latitude in response to shifting climate zones."


title: Climate

text: Climate () is commonly defined as the weather averaged over a long period. The standard averaging period is 30 years, but other periods may be used depending on the purpose. Climate also includes statistics other than the average, such as the magnitudes of day-to-day or year-to-year variations. The Intergovernmental Panel on Climate Change (IPCC) 2001 glossary definition is as follows:


title: Climate

text: The World Meteorological Organization (WMO) describes "climate normals" as "reference points used by climatologists to compare current climatological trends to that of the past or what is considered typical. A climate normal is defined as the arithmetic average of a climate element (e.g. temperature) over a 30-year period. A 30-year period is used as it is long enough to filter out any interannual variation or anomalies such as El Niño–Southern Oscillation, but also short enough to be able to show longer climatic trends."


title: Climate

text: The WMO originated from the International Meteorological Organization which set up a technical commission for climatology in 1929. At its 1934 Wiesbaden meeting the technical commission designated the thirty-year period from 1901 to 1930 as the reference time frame for climatological standard normals. In 1982 the WMO agreed to update climate normals, and these were subsequently completed on the basis of climate data from 1 January 1961 to 31 December 1990. The 1961-1990 climate normals serve as the baseline reference period. The next set of climate normals to be published by WMO is from 1991 to 2010. Aside from collecting from the most common atmospheric variables (air temperature, pressure, precipitation and wind), other variables such as humidity, visibility, cloud amount, solar radiation, soil temperature, pan evaporation rate, days with thunder and days with hail are also collected to measure change in climate conditions.


title: Climate

text: The difference between climate and weather is usefully summarized by the popular phrase "Climate is what you expect, weather is what you get." Over historical time spans, there are a number of nearly constant variables that determine climate, including latitude, altitude, proportion of land to water, and proximity to oceans and mountains. All of these variables change only over periods of millions of years due to processes such as plate tectonics. Other climate determinants are more dynamic: the thermohaline circulation of the ocean leads to a warming of the northern Atlantic Ocean compared to other ocean basins. Other ocean currents redistribute heat between land and water on a more regional scale. The density and type of vegetation coverage affects solar heat absorption, water retention, and rainfall on a regional level. Alterations in the quantity of atmospheric greenhouse gases determines the amount of solar energy retained by the planet, leading to global warming or global cooling. The variables which determine climate are numerous and the interactions complex, but there is general agreement that the broad outlines are understood, at least insofar as the determinants of historical climate change are concerned.


title: Climate

text: Climate classifications are systems that categorize the world's climates. A climate classification may correlate closely with a biome classification, as climate is a major influence on life in a region. One of the most used is the Köppen climate classification scheme first developed in 1899.


title: Climate

text: There are several ways to classify climates into similar regimes. Originally, climes were defined in Ancient Greece to describe the weather depending upon a location's latitude. Modern climate classification methods can be broadly divided into "genetic" methods, which focus on the causes of climate, and "empiric" methods, which focus on the effects of climate. Examples of genetic classification include methods based on the relative frequency of different air mass types or locations within synoptic weather disturbances. Examples of empiric classifications include climate zones defined by plant hardiness, evapotranspiration, or more generally the Köppen climate classification which was originally designed to identify the climates associated with certain biomes. A common shortcoming of these classification schemes is that they produce distinct boundaries between the zones they define, rather than the gradual transition of climate properties more common in nature.


title: Climate

text: Paleoclimatology is the study of past climate over a great period of the Earth's history. It uses evidence with different time scales (from decades to millennia) from ice sheets, tree rings, sediments, pollen, coral, and rocks to determine the past state of the climate. It demonstrates periods of stability and periods of change and can indicate whether changes follow patterns such as regular cycles.


title: Climate

text: Details of the modern climate record are known through the taking of measurements from such weather instruments as thermometers, barometers, and anemometers during the past few centuries. The instruments used to study weather over the modern time scale, their observation frequency, their known error, their immediate environment, and their exposure have changed over the years, which must be considered when studying the climate of centuries past. Long-term modern climate records skew towards population centres and affluent countries. Since the 1960s, the launch of satellites allow records to be gathered on a global scale, including areas with little to no human presence, such as the Arctic region and oceans.


title: Climate

text: Climate variability is the term to describe variations in the mean state and other characteristics of climate (such as chances or possibility of extreme weather, etc.) "on all spatial and temporal scales beyond that of individual weather events." Some of the variability does not appear to be caused systematically and occurs at random times. Such variability is called "random variability" or "noise". On the other hand, periodic variability occurs relatively regularly and in distinct modes of variability or climate patterns.


title: Climate

text: There are close correlations between Earth's climate oscillations and astronomical factors (barycenter changes, solar variation, cosmic ray flux, cloud albedo feedback, Milankovic cycles), and modes of heat distribution between the ocean-atmosphere climate system. In some cases, current, historical and paleoclimatological natural oscillations may be masked by significant volcanic eruptions, impact events, irregularities in climate proxy data, positive feedback processes or anthropogenic emissions of substances such as greenhouse gases.


title: Climate

text: Over the years, the definitions of "climate variability" and the related term "climate change" have shifted. While the term "climate change" now implies change that is both long-term and of human causation, in the 1960s the word climate change was used for what we now describe as climate variability, that is, climatic inconsistencies and anomalies.


title: Climate

text: Climate change is the variation in global or regional climates over time. It reflects changes in the variability or average state of the atmosphere over time scales ranging from decades to millions of years. These changes can be caused by processes internal to the Earth, external forces (e.g. variations in sunlight intensity) or, more recently, human activities.


title: Climate

text: In recent usage, especially in the context of environmental policy, the term "climate change" often refers only to changes in modern climate, including the rise in average surface temperature known as global warming. In some cases, the term is also used with a presumption of human causation, as in the United Nations Framework Convention on Climate Change (UNFCCC). The UNFCCC uses "climate variability" for non-human caused variations.


title: Climate

text: Earth has undergone periodic climate shifts in the past, including four major ice ages. These consisting of glacial periods where conditions are colder than normal, separated by interglacial periods. The accumulation of snow and ice during a glacial period increases the surface albedo, reflecting more of the Sun's energy into space and maintaining a lower atmospheric temperature. Increases in greenhouse gases, such as by volcanic activity, can increase the global temperature and produce an interglacial period. Suggested causes of ice age periods include the positions of the continents, variations in the Earth's orbit, changes in the solar output, and volcanism. However, these naturally-caused changes in climate occur on a much slower time scale than the present rate of change which is caused by the emission of greenhouse gases by human activities.


title: Climate

text: Climate models use quantitative methods to simulate the interactions and transfer of radiative energy between the atmosphere, oceans, land surface and ice through a series of physics equations. They are used for a variety of purposes; from the study of the dynamics of the weather and climate system, to projections of future climate. All climate models balance, or very nearly balance, incoming energy as short wave (including visible) electromagnetic radiation to the Earth with outgoing energy as long wave (infrared) electromagnetic radiation from the earth. Any imbalance results in a change in the average temperature of the earth.


title: Climate

text: Climate models are available on different resolutions ranging from >100 km to 1 km. High resolutions in global climate models are computational very demanding and only few global datasets exists. Global climate models can be dynamically or statistically downscaled to regional climate models to analyze impacts of climate change on a local scale. Examples are ICON or mechanistically downscaled data such as CHELSA (Climatologies at high resolution for the earth's land surface areas).


title: Climate

text: The most talked-about applications of these models in recent years have been their use to infer the consequences of increasing greenhouse gases in the atmosphere, primarily carbon dioxide (see greenhouse gas). These models predict an upward trend in the global mean surface temperature, with the most rapid increase in temperature being projected for the higher latitudes of the Northern Hemisphere.


title: Jack Irons

text: Jack Steven Irons (born July 18, 1962) is an American drummer. He is the founding drummer of the rock band Red Hot Chili Peppers and is a former member of Pearl Jam and Eleven.


title: Jack Irons

text: Alongside his work with Red Hot Chili Peppers and Pearl Jam, Irons has been a member of Eleven, The Wallflowers and Mark Lanegan Band. He has worked with Joe Strummer and The Latino Rockabilly War, Redd Kross, Raging Slab, Spinnerette and The Les Claypool Frog Brigade. In 1995 Irons and the other members of Pearl Jam recorded and toured the "Mirror Ball" album with Neil Young. Irons has released two solo albums, "Attention Dimension" (2004) and "No Heads Are Better Than One" (2010).


title: Jack Irons

text: Irons was inducted into the Rock and Roll Hall of Fame as a member of the Red Hot Chili Peppers in 2012. Irons, along with former drummer Cliff Martinez, joined the band onstage for the first time in 24 years for a performance of their 1991 hit "Give It Away". Irons was an opening act in 2017 for the Chili Peppers on The Getaway World Tour.


title: Jack Irons

text: Jack Irons was born and raised in Los Angeles. He is from a Jewish background. Irons grew up using his family's cutlery as drumsticks, playing along to whatever was on the radio. He talked his parents into buying him a drum set, and took a drum class. Irons attended Bancroft Jr. High School in Hollywood, where he met future bandmates Michael "Flea" Balzary and Hillel Slovak. He then went on to attend Fairfax High School in Los Angeles alongside Balzary and Slovak, as well as future bandmates Anthony Kiedis and Alain Johannes. He and Slovak were both fans of Kiss, and they formed a tribute act. Irons was influenced by Jack DeJohnette, Stewart Copeland, and Keith Moon.


title: Jack Irons

text: As teenagers, Irons, Johannes, Slovak, and schoolmate Todd Strassman formed the band Chain Reaction in 1976. After its first gig, the band renamed itself Anthym. Slovak, dissatisfied with Strassman's bass playing, taught friend Michael "Flea" Balzary to play then replaced Strassman with Flea. After graduating high school, the band changed its name to What Is This? after a question often asked by people who heard the band play. Flea soon departed to play bass in the prominent Los Angeles punk band Fear. What Is This? continued, performing many shows along the California coast.


title: Jack Irons

text: In 1983, Flea formed a "one-off" band, Tony Flow and the Miraculously Majestic Masters of Mayhem, with Kiedis, Slovak and Irons. Their performance was a hit and, after deciding to continue past the single concert, they changed their name to Red Hot Chili Peppers, quickly gaining popularity around Los Angeles. After six months, they earned a record deal with EMI and prepared to record its first album. Since What Is This? had signed a record deal two weeks earlier and Slovak and Irons considered the Red Hot Chili Peppers a side project, they quit. With What Is This?, Irons recorded 1984's "Squeezed (EP)", 1985's "3 Out of 5 Live" EP, and a full-length self-titled album that same year. The band broke up following the album's recording as Slovak became frustrated with the band and rejoined the Red Hot Chili Peppers. In the meantime, Irons played on several recordings by Walk the Moon, a duo made up of Johannes and Natasha Shneider. In 1986, after learning that drummer Cliff Martinez had resigned, Irons returned to the Red Hot Chili Peppers.


title: Jack Irons

text: Irons played drums on the Red Hot Chili Peppers' first demo tape and their third album, 1987's "The Uplift Mofo Party Plan". When Slovak died of a heroin overdose on June 25, 1988, Irons again quit the band because he did not want to be part of a group where his friends were dying. In 2006, Irons said Slovak's death had been such a huge shock that he had been suffering from depression ever since.


title: Jack Irons

text: On August 12, 2012, Irons and Martinez performed "Give It Away" with the Red Hot Chili Peppers at a Los Angeles concert. In 2017, Irons was an opening act for several dates on "The Getaway World Tour".


title: Jack Irons

text: After Irons left Red Hot Chili Peppers, he went to a psychiatric hospital to receive treatment. After a brief stint with Joe Strummer's backing band the Latino Rockabilly War, Irons teamed up with Johannes and Shneider in 1990 to form Eleven. With Eleven, Irons recorded the albums "Awake in a Dream" (1991) and "Eleven" (1993). Midway through the recording of Eleven's third album, "Thunk" (1995), Irons departed to drum with Pearl Jam, and Matt Cameron of Soundgarden played drums on the album's remaining four tracks. Irons returned to the band once again in 2002 prior to the recording of the band's fifth album, "Howling Book" (2003). Shneider died on July 2, 2008, following a battle with cancer. Prior to Shneider's death, the band was working on a sixth album due for release in the fall of 2008.


title: Jack Irons

text: Bassist Jeff Ament and guitarist Stone Gossard invited Irons to join Mookie Blaylock, the band that would become Pearl Jam, in 1990, when the band was first forming and still looking for a singer and a drummer. Although he did not join the band at that time because he was committed to his own band, Eleven, he did pass on a cassette of the band's work to a singer and local musician in San Diego named Eddie Vedder. Irons had formed a friendship with Vedder after meeting him through the Southern California music scene and would play basketball with him. Vedder subsequently joined the band. Irons also called the Red Hot Chili Peppers in 1991 and asked the band to allow Vedder's new group to open for the band on its forthcoming "Blood Sugar Sex Magik" tour.


title: Jack Irons

text: Irons became the drummer for Pearl Jam in late 1994 following the firing of drummer Dave Abbruzzese. His first recording with the band was "Hey Foxymophandlemama, That's Me" for "Vitalogy" (1994). Gossard said, "Jack entered the band right at the end of making "Vitalogy". Jack's a breath of fresh air, a family man. Everybody had a strong sense of friendship with him immediately. He was just there to play drums and help out." Irons made his debut with the band at Neil Young's 1994 Bridge School Benefit, but he was not officially announced as the band's new drummer until its 1995 "Self-Pollution" satellite radio broadcast, a four-and-a-half-hour-long "pirate" broadcast out of Seattle, Washington which was available to any radio stations that wanted to carry it. Irons joined the group and played Pearl Jam's live shows supporting the "Vitalogy" album.


title: Jack Irons

text: Irons performed with other members of Pearl Jam on Neil Young's 1995 album, "Mirror Ball", and subsequently toured Europe as part of Young's backing band. With Irons, the band recorded its fourth studio album, "No Code", released in 1996, for which Irons also toured. The band subsequently released "Yield" in 1998. "Do the Evolution" (from "Yield") received a Grammy nomination for Best Hard Rock Performance. As a member of Pearl Jam, Irons brought a unique drumming style to the band, particularly in the way he played his fills and with his use of a trash can lid as a cymbal. Irons co-wrote the music for the "No Code" songs "Who You Are", "In My Tree", "Red Mosquito", and "I'm Open". He also wrote and sang on the Pearl Jam songs "Happy When I'm Crying" (from the 1997 fan club Christmas single), "●" (from "Yield"), and "Whale Song" (from the 1999 "Music for Our Mother Ocean Vol. 3" compilation). He played with Pearl Jam through March 20, 1998. In 1998, prior to Pearl Jam's U.S. Yield Tour, Irons left the band due to dissatisfaction with touring. Pearl Jam's sound engineer Brett Eliason stated, "We went and did Hawaii and Australia with Jack. When we came back, Jack wasn't in a position to carry on. He made that decision more or less by himself. He can be a really great drummer but he had difficulty on tour putting out the energy for the length of shows they were doing. I don't know if he thought they'd put things on hold for him." Vedder said, "I think that him deciding that he wasn't going to be in the band really hurt." Coincidentally, Matt Cameron, from the recently split Soundgarden, replaced him again as he did four years prior on Eleven's "Thunk".


title: Jack Irons

text: On September 7, 2004, Irons released a solo album called "Attention Dimension". Irons started creating his first pieces of drum music in 1994, but it wasn't until fall 1999, about a year after he left Pearl Jam, that he seriously began recording himself for a possible solo album. The album features appearances by former bandmates such as Alain Johannes, Flea, Eddie Vedder, Stone Gossard, Jeff Ament, and Les Claypool. Vedder contributed vocals to a cover of Pink Floyd's "Shine On You Crazy Diamond". Johnny Loftus of Allmusic said, ""Attention Dimension" is the drummer's chance to be in the bright white klieg light."


title: Jack Irons

text: Aside from the aforementioned bands, Irons recorded and toured as a member of Joe Strummer's backing band The Latino Rockabilly War for the album "Earthquake Weather" (1989), and also toured with Redd Kross in support of the band's album "Third Eye" (1990). He appears in Redd Kross' promotional video for the song "Annie's Gone". In 1992, Raging Slab (a band notorious for having over 25 different drummers over the course of the band's 18-year career), complete with Irons on drums, began recording the follow-up to its 1989 RCA Records self-titled debut, with producer Michael Beinhorn at the helm. The entire album was recorded, mixed, and mastered; however when RCA Records executives heard the album, it was rejected. The album, titled "Freeburden", remains unreleased. In 2000, Irons played as part of the initial line-up of Colonel Les Claypool's Fearless Flying Frog Brigade. Irons is featured on the track "Milky Ave" on the album "Ultra Payloaded" (2007) by Perry Farrell's band Satellite Party. Joining him on the album is former bandmate Flea. In 2012 he appeared on former Chili Pepper bandmate, Flea's debut solo EP "Helen Burns". Aside from populat music, Irons has worked as a drumming advisor and teacher for numerous U.S. television projects. Irons appeared on five of the ten songs on "To Be One With You", the debut solo album by former Red Hot Chili Peppers guitarist Josh Klinghoffer who released the album under the name Pluralone. The album was released on November 22, 2019. He then went on to record four songs on Josh's follow-up record, "I Don't Feel Well" released on October 16, 2020.


title: Jack Irons

text: Irons has been diagnosed with bipolar disorder. About being diagnosed, he said "back in my twenties they said, 'When you get to your forties you might be able to turn a corner with this kind of a thing'. And I think that's very accurate. I had to learn to decipher sort of what was real and what was in my head. And that took time."


title: Jack Irons

text: He is married and has two children. His son, Zach Irons, is founder and lead guitarist for Irontom. In September 2015, Zach Irons became lead guitarist for AWOLNATION.


title: Centurion (tank)

text: The Centurion was the primary British Army main battle tank of the post-World War II period. Introduced in 1945, it is widely considered to be one of the most successful post-war tank designs, remaining in production into the 1960s, and seeing combat into the 1980s. The chassis was adapted for several other roles, and these variants have remained in service. It was a very popular tank with good armour, manoeuvrability, and armament.


title: Centurion (tank)

text: Development of the Centurion began in 1943 with manufacture beginning in January 1945. Six prototypes arrived in Belgium less than a month after the war in Europe ended in May 1945. It entered combat with the British Army in the Korean War in 1950 in support of the UN forces. The Centurion later served on the Indian side in the Indo-Pakistani War of 1965, where it fought against US-supplied M47 and M48 Patton tanks, and it served with the Royal Australian Armoured Corps in the Vietnam War.


title: Centurion (tank)

text: Israel's army used Centurions in the 1967 Six-Day War, the 1973 Yom Kippur War, the 1978 South Lebanon conflict, and the 1982 Lebanon War. Centurions modified as armoured personnel carriers were used in Gaza, the West Bank and on the Lebanese border. The Royal Jordanian Land Force used Centurions, first in 1970 to fend off a Syrian incursion within its borders during the Black September events and later in the Golan Heights in 1973. South Africa deployed its Centurions in Angola during the South African Border War.


title: Centurion (tank)

text: The Centurion became one of the most widely used tank designs, equipping dozens of armies around the world, with some in service until the 1990s. In the 2006 Israel–Lebanon conflict the Israel Defense Forces employed modified Centurions as armoured personnel carriers and combat engineering vehicles. The South African National Defence Force still employs over 200 Centurions, which were modernised in the 1980s and 2000s as the (elephant).


title: Centurion (tank)

text: Between 1946 and 1962, 4,423 Centurions were produced, consisting of 13 basic marks and numerous variants. In British Army use it was replaced by the Chieftain and Conqueror tanks.


title: Centurion (tank)

text: In 1943, the Directorate of Tank Design, under Sir Claude Gibb, was asked to produce a new design for a heavy cruiser tank under the General Staff designation A41. After a series of fairly mediocre designs in the A series in the past, and bearing in mind the threat posed by the German 88 mm gun, the War Office demanded a major revision of the design requirements, specifically: increased durability and reliability, the ability to withstand a direct hit from the German 88 mm gun and providing greater protection against mines. Initially in September 1943 the A41 tank was to weigh no more than , the limit for existing Mark I and Mark II transport trailers and for a Bailey bridge of span. The British railway loading gauge required that the width should not exceed and the optimum width was , but, critically, for the new tank this restriction had been lifted by the War Office under pressure from the Department of Tank Design. A high top speed was not important, while agility was to be equal to that of the Comet. A high reverse speed was specified, as during the fighting in southern Italy, Allied tanks were trapped in narrow sunken roads by the German Army. The modified production gearbox had a two-speed reverse, with the higher reverse speed similar to second gear.


title: Centurion (tank)

text: The Department produced a larger hull by replacing the long-travel five-wheel Christie suspension used on the Comet with a six wheel Horstmann suspension, and extending the spacing between the second and third wheels. The Christie suspension, with vertical spring coils between side armour plates, was replaced by a Horstmann suspension with three horizontally sprung, externally mounted two-wheel bogies on each side. The Horstmann design did not offer the same ride quality as the Christie system, but took up less room and was easier to maintain.


title: Centurion (tank)

text: But even before the Outline Specification of the A41 was released in October 1943, these limits were removed and the weight was increased from 40 tons to , because of the need for heavier armour and a wider turret (too wide for the tank to be transported by rail) with a more powerful gun. The new version carried armour equal to the heaviest infantry tanks, while improved suspension and engines provided cross-country performance superior to even the early cruiser tanks. The War Office decided it would be wiser to build new trailers, rather than hamper what appeared to be a superb design. Historian David Fletcher states, "But was Centurion, after all, a Universal Tank? The answer has to be a qualified negative."


title: Centurion (tank)

text: The design mockup, built by AEC Ltd, was viewed in May 1944. Subsequently, twenty pilot models were ordered with various armament combinations: ten with a 17 pounder and a 20 mm Polsten gun (of which half had a Besa machine gun in the turret rear and half an escape door), five with a 17-pounder, a forward Besa machine gun and an escape door, and five with a QF 77 mm gun and a driver-operated hull machine gun.


title: Centurion (tank)

text: Prototypes of the original 40-ton design, the Centurion Mark I, had 76 mm of armour in the front glacis, which was thinner than that on the then current infantry tanks (the Churchill), which had 101 mm or 152 mm on the Churchill Mk VII and VIII being produced at the time. However, the glacis plate was highly sloped, and so the effective thickness of the armour was very high—a design feature shared by other effective designs, such as the German Panther tank and Soviet T-34. The turret was well armoured at 152 mm. The tank was also highly mobile, and easily outperformed the Comet in most tests. The uparmoured Centurion Mark II soon arrived; it had a new 118 mm-thick glacis and the side and rear armour had been increased from 38 mm to 51 mm. Only a handful of Mk I Centurions had been produced when the Mk II replaced it on the production lines. Full production began in November 1945 with an order for 800 on production lines at Leyland Motors, Lancashire the Royal Ordnance Factories ROF Leeds and Royal Arsenal, and Vickers at Elswick. The tank entered service in December 1946 with the 5th Royal Tank Regiment.


title: Centurion (tank)

text: Soon after the Centurion's introduction, Royal Ordnance finished work on the 84 mm calibre Ordnance QF 20 pounder tank gun. With this, the Centurion went through another upgrade to mount the 20-pounder. By this point, the usefulness of the 20 mm Polsten had been called into question, it being unnecessarily large for use against troops, so it was replaced with a Besa machine gun in a completely cast turret. The new Centurion Mark III also featured a fully automatic stabilisation system for the gun, allowing it to fire accurately while on the move, dramatically improving battlefield performance. Production of the Mk 3 began in 1948. The Mk 3 was so much more powerful than the Mk 1 and Mk 2, that the earlier designs were removed from service as soon as new Mk 3s arrived, and the older tanks were then either converted into the Centurion armoured recovery vehicle (ARV) Mark 1 for use by the Royal Electrical and Mechanical Engineers or upgraded to Mk 3 standards. Improvements introduced with the Mk 3 included a more powerful version of the engine and a new gun sight and gun stabiliser.


title: Centurion (tank)

text: The 20 pounder gun was used until the Royal Ordnance Factories introduced the 105 mm L7 gun in 1959. All later variants of the Centurion, from Mark 5/2 on, used the L7.


title: Centurion (tank)

text: Design work for the Mk 7 was completed in 1953, with production beginning soon afterwards. One disadvantage of earlier versions was the limited range, initially just on hard roads, hence external auxiliary tanks and then a "monowheel" trailer were used. But the Mk7 had a third fuel tank inside the hull, giving a range of . Additionally, it was found possible to put the Centurion on some European rail routes with their larger loading gauges.


title: Centurion (tank)

text: The Centurion was used as the basis for a range of specialist equipment, including combat engineering variants with a 165 mm demolition gun Armoured Vehicle Royal Engineers (AVRE). It is one of the longest-serving designs of all time, serving as a battle tank for the British and Australian armies from the Korean War (1950–1953) to the Vietnam War (1961–1972), and as an AVRE during Operation Desert Storm in January–February 1991.


title: Centurion (tank)

text: On 14 November 1950, the British Army's 8th King's Royal Irish Hussars, equipped with three squadrons (64 tanks) of Centurion Mk 3, landed in Pusan. The first recorded Centurion kill occurred near Seoul against a North Korean captured Cromwell tank. Operating in sub-zero temperatures, the 8th Hussars learnt the rigors of winter warfare: their tanks had to be parked on straw to prevent the steel tracks from freezing to the ground. Engines had to be started every half-hour, with each gear being engaged in turn to prevent them from being frozen into place. During the Battle of the Imjin River, Centurions won lasting fame when they covered the withdrawal of the 29th Brigade, with the loss of five tanks, most later recovered and repaired. In 1952, Centurions of the 5th Royal Inniskilling Dragoon Guards were also involved in the Second Battle of the Hook where they played a significant role in repelling Chinese attacks. Centurions of the 1st Royal Tank Regiment participated in the Third Battle of the Hook repelling the PLA and also were involved in the Battle of the Samichon River in 1953. In a tribute to the 8th Hussars, General John O'Daniel, commanding the US 1st Corps, stated: "In their Centurions, the 8th Hussars have evolved a new type of tank warfare. They taught us that anywhere a tank can go, is tank country: "even the tops of mountains"." The lack of pintle-mounted machine guns on the turret meant that the Centurion was only able to fire in one direction and so was vulnerable to infantry attacks.


title: Centurion (tank)

text: By early 1952, with the Cold War heating up, NATO needed modern heavy tanks to meet the T-34 versions with the Warsaw Pact countries, and to deter Soviet forces by stationing them with the BAOR in West Germany, where the French had just the light AMX-13, and the Germans had none. America was keen to have Centurions supplied to Denmark and the Netherlands under the Mutual Defence Assistance Program, as production of the M48 Patton would not start until April 1952. A Mk 3 cost £31,000 or £44,000 with ammunition. The Royal Canadian Armoured Corps deployed a regiment of Centurions to Germany to support the Canadian Brigade.


title: Centurion (tank)

text: During the Suez Crisis, British ground commander General Sir Hugh Stockwell believed that methodical and systematic armoured operations centred on the Centurion would be the key to victory.


title: Centurion (tank)

text: The Egyptians destroyed Port Said's Inner Harbour, which forced the British to improvise and use the Fishing Harbour to land their forces. The 2nd Brigade of the Parachute Regiment landed by ship in the harbour. Centurions of the British 6th Royal Tank Regiment were landed and by 12:00 they had reached the French paratroopers. While the British were landing at Port Said, the men of the 2 RPC at Raswa fought off Egyptian counter-attacks featuring SU-100 tank destroyers.


title: Centurion (tank)

text: After establishing themselves in a position in downtown Port Said, 42 Commando headed down the Shari Muhammad Ali, the main north–south road to link up with the French forces at the Raswa bridge and the Inner Basin lock. While doing so, the Marines also took Port Said's gasworks. Meanwhile, 40 Commando supported by the Royal Tank Regiment remained engaged in clearing the downtown of Egyptian snipers. Lieutenant Colonel Norman Tailyour arranged for more reinforcements to be brought in via helicopter.


title: Centurion (tank)

text: In 1967, the Royal Australian Armoured Corps' (RAAC), 1st Armoured Personnel Carrier (APC) Squadron transferred to "A" Squadron, 3rd Cavalry Regiment in South Vietnam. Although they successfully conducted combat operations in their areas of operations, reports from the field stated that their lightly-armoured M113A1 armoured personnel carriers were unable to force their way through dense jungle limiting their offensive actions against enemy forces. The Australian government, under criticism in Parliament, decided to send a squadron of Australian Centurion tanks to South Vietnam. The 20-pdr armed Australian Centurions of 'C' Squadron, 1st Armoured Regiment landed in South Vietnam on 24 February 1968, being headquartered at Nui Dat in III Corps (MR3).


title: Centurion (tank)

text: Colonel Donald Dunstan, later to be governor of South Australia, was the deputy task force commander of the 1st Australian Task Force (1 ATF) in South Vietnam. Dunstan had quite possibly been the last Australian to use tanks and infantry in a combined operation during the Second World War, (as part of the Bougainville campaign), and the first since the war to command Australia's tanks and infantry in combat. When he temporarily took over command during Brigadier Ronald Hughes's absence, he directed that the Centurions be brought up from Nui Dat to reinforce firebases "Coral" and "Balmoral", believing that they were a strong element that were not being used. Besides adding a great deal of firepower, Dunstan stated, he "couldn't see any reason why they [the Centurions] shouldn't be there". His foresight enabled 1 ATF to kill approximately 267 soldiers from the 141st and 165th North Vietnamese Army Regiments during the six-week-long Battle of Coral–Balmoral in May 1968, as well as capturing 11 prisoners, 36 crew-served weapons, 112 small arms, and other miscellaneous enemy weapons.


title: Centurion (tank)

text: After the Battle of Coral-Balmoral, a third Centurion troop, which included two tankdozers, was formed. By September 1968, 'C' Squadron was brought to its full strength of four troops, each equipped with four Centurion tanks. By 1969, 'B' Squadron, 3rd Cavalry; 'A' Squadron, 1st Armoured Regiment; 'B' Squadron, 1st Armoured Regiment; and 'C' Squadron, 1st Armoured Regiment, had all made rotations through South Vietnam. Originally deployed as 26 Centurion tanks, after three and a half years of combat operations, 58 Centurions had served in country; 42 had suffered battle damage with six beyond repair and two crewmen had been killed in action.


title: Centurion (tank)

text: The Centurion crews, after operating for a few weeks in country, soon learned to remove the protective armoured side skirts from both sides of the tank, to prevent the vegetation and mud from building up between the track and the mudguards. Each Centurion in Vietnam normally carried a basic load of 62 rounds of 20 pounder shells, 4,000 rounds of .50 cal and 9,000 rounds of .30 cal machine gun ammunition for the tank commander's machine gun as well as the two coaxial machine guns. They were equipped with petrol engines, which necessitated the use of an extra externally mounted fuel tank, which was attached to the vehicle's rear.


title: Centurion (tank)

text: In 1965, the bulk of India's tank fleet was older M4 Sherman tanks, but India also had Centurion Mk.7 tanks, with the 20 pounder gun, and also AMX-13 and M3 Stuart light tanks. The Centurion Mk.7 at that time was one of the most modern western tanks.


title: Centurion (tank)

text: The offensive of Pakistan's 1st Armoured Division was blunted at the Battle of Asal Uttar on 10 September. Six Pakistani armoured regiments were opposed by three Indian armoured regiments. One of these regiments, 3 Cavalry, fielded 45 Centurion tanks. The Centurion, with its 20-pounder gun and heavy armour, proved to be more than a match for the M47 and M48 Pattons. On the other side, when Pakistani Army armoured division primary composed of M47 Pattons and M48 Pattons, they proved to be only able to penetrate a few of the Centurion tanks, as witnessed in the Battle of Chawinda in the Sialkot sector. A post-war US study of the tank battles in South Asia concluded that the Patton's armour could, in fact, be penetrated by the 20-pounder tank gun (84 mm) of the Centurion (later replaced by the even-more successful L7 105mm gun on the Mk. 7 version which India also possessed) as well as the 75 mm tank gun of the AMX-13 light tank.


title: Centurion (tank)

text: In 1971, at the Battle of Basantar, an armoured division and an armoured brigade of the Pakistani I Corps confronted two armoured brigades of the Indian I Corps, which had Centurion tanks. This resulted in a substantial tank battle, between the American-built tanks of the Pakistani Army and the Indian Army's mixture of Soviet T-55s and British Centurions. Casualties were heavily skewed against the Pakistani force, with 46 tanks destroyed.


title: Centurion (tank)

text: The first country which bought Centurion tanks was Egypt. The first tanks were received in 1950. Israel's formerly British Centurions were first delivered in 1959. Differing varieties of the Centurion were bought by Israel over the years from many different countries or captured in combat. Following their acquisition the Israelis quickly upgraded the tanks with British 105 mm L7 instead of the original 20-pounder main gun and renamed them Sho't ("scourge" or "whip").


title: Centurion (tank)

text: When the Six-Day War broke out in 1967, the Israel Defense Forces (IDF) had 293 Centurion / Sho't tanks that were ready for combat out of a total of 385 tanks. In Sinai, Egypt had 30 Centurion tanks. All 30 Egyptian tanks were destroyed or captured by Israel during the conflict. Israel also captured about 30 Jordanian Centurion tanks from a total of 90 in Jordanian service. 25 tanks were abandoned in Hebron by the 10th Jordanian Independent Tank Regiment.


title: Centurion (tank)

text: All Sho't tanks were upgraded with the more efficient Continental AVDS-1790-2A diesel engine (also used in the M48 and the M60 tanks) and an Allison CD850-6 transmission from 1970 to 1974. The upgraded version were named Sho't Kal Alef and were followed by three additional sub-variants called Bet, Gimel and Dalet according to the upgrades added. The upgrades included thicker armour, new turret rotating mechanism, new gun stabiliser, improved ammunition layout with more rounds and increased fuel capacity. A modern fire control system, an improved fire extinguisher system, better electrical system and brakes, and the capability of installing reactive armour completed the modifications. They had American radios and either the original 7.62 mm calibre MG on the commander's cupola or a 12.7 mm calibre HMG. The Sho't Kal could be distinguished from the Centurion by its raised rear deck, to accommodate the bigger engine.


title: Centurion (tank)

text: The Sho't Kal version of Centurion earned its legendary status during the Battle of "The Valley of Tears" on the Golan Heights in the 1973 Yom Kippur War. 105 Sho't Kal tanks of the 7th Armoured Brigade and 20 Sho't tanks of the 188th Brigade defeated the advance of some 500 Syrian T-55s and T-62s and the Sho't Kal became emblematic of Israeli armour's prowess. During the entire war, 1,063 Israeli tanks were disabled (more than half of them Centurions), about 600 of which were completely destroyed or captured. Some 35 Israeli Centurions were captured by Egypt, dozens more were captured by Syria, Iraq and four by Jordan. On the other hand, 2,250 Arab tanks were disabled (including 33 Jordanian Centurions, 18 of them destroyed), 1,274 of them were completely destroyed or captured (643 tanks were lost in the north and 631 were lost in the south). After the war, to replace Israeli losses, the United States delivered 200 M60 and M48 tanks and the United Kingdom delivered 400 Centurion tanks to Israel.


title: Centurion (tank)

text: Sho't Kal tanks with Blazer reactive armour package were used in the 1982 invasion of Lebanon. During the war, 21 Centurion tanks were knocked out, 8 of them were destroyed.


title: Centurion (tank)

text: The Israelis started to retire the Sho't Kal during the 1980s and they were completely retired during the 1990s. Most of them were converted to Nagmasho't, Nagmachon, and Nakpadon (heavy armoured personnel carriers or Infantry Fighting Vehicles) and Puma armoured engineering vehicles.


title: Centurion (tank)

text: During Operation Desert Storm in 1991, 12 FV4003 Centurion Mk5 AVREs were deployed with 32 Armoured Engineer Regiment as part of British operations during the campaign. Three were lost in training in two separate incidents involving vehicle fires and detonation of munitions. One AVRE was destroyed on 5 February 1991 and two were destroyed in a second incident the next day. Four minor injuries were sustained. No AVRES saw action during the operation.


title: Centurion (tank)

text: Fifty Centurions were purchased by Jordan between 1954 and 1956 and by 1967 about 90 Centurions were in service. The Jordanian Army used its Centurion tanks in the Six-Day War. In 1967, the 10th Independent Tank Regiment was equipped with 44 Centurion Mk.V tanks armed with 20pdr guns, but was initially deployed on East Bank. Later, the unit was moved urgently to the Hebron area, in West Bank, in order to link with the supposed Egyptian advance. Some Centurion tanks were destroyed and about 30 captured by the Israeli Army. Israelis entering Hebron captured 25 Jordanian Centurion tanks. The Royal Guards Brigade had one regiment that was also equipped with Centurions.


title: Centurion (tank)

text: In September 1970 (Black September) Jordan used Centurions of the 40th Armoured Brigade against invading Syrian T-55 tanks. Jordan lost 75 to 90 tanks out of 200 involved. Most of them were destroyed by Syrian tank fire at ar-Ramtha. But some of them were destroyed by the PLO in Amman.


title: Centurion (tank)

text: In 1972, Centurion tanks were reequipped with 105 mm guns. During the Yom Kippur War, the Jordanian 40th Armoured Brigade was deployed in the Golan front to support Syrian troops and show King Hussein's concern for Arab solidarity. The 40th Armoured Brigade moved northward towards Sheikh Meskin, but its counterattack was uncoordinated and largely ineffective as the Israelis were in prepared defensive positions.


title: Centurion (tank)

text: In 1982–1985, 293 surviving Centurions of the Jordanian Army were refitted with the diesel engine and transmission of the M60A1 tank in place of the original Meteor petrol engine, Belgian SABCA computerised fire-control system, which incorporated a laser range-finder and passive night sight for the gunner, Cadillac Gage electro-hydraulic turret drive and stabilisation system and a new Teledyne Continental hydropneumatic suspension in place of the Horstmann units. These upgraded vehicles were called the Tariq. After retirement from service with the arrival of ex-British Challenger tanks in the late 1990s, several Tariqs were converted into heavy APCs.


title: Centurion (tank)

text: South Africa ordered 203 Centurion Mk 3 tanks from the United Kingdom in 1953. The South African Centurions entered service between 1955 and 1958, and included about 17 armoured recovery vehicles. South Africa's major strategic priorities at the time revolved around assisting the British Armed Forces and other member states of the Commonwealth of Nations during a conventional war in the Middle East or Anglophone Africa. The Centurions were procured specifically because they were compatible with Commonwealth tank tactics and pre-existing British armoured formations.


title: Centurion (tank)

text: Following South Africa's withdrawal from the Commonwealth in 1961, its priorities shifted toward internal security and diversifying national arms procurement outside traditional suppliers such as the United Kingdom. To that end, 100 Centurion Mk 3s and 10 Centurion-based recovery vehicles were sold off to Switzerland in 1961. The remaining Centurions were largely relegated to reserve roles as a result of maintenance problems compounded by parts shortages and a tendency to overheat in the hot African climate. In 1972, the South African Army retrofitted some of its Centurions with the engines and transmission of American-made M48 Patton tanks in an attempt to improve technical performance. The upgraded Centurions were designated "Skokiaan" and proved unpopular due to their high fuel consumption and poor operating range.


title: Centurion (tank)

text: Tanks reentered the mainstream of South African military doctrine in 1975, following Operation Savannah, which saw the lightly armoured South African forces in Angola threatened by large formations of Soviet tanks supplied to the People's Armed Forces for the Liberation of Angola (FAPLA) and their Cuban allies. Operation Savannah was followed by further modifications and trials under Project "Semel", and the South African government was obliged to finance the creation of a new private sector enterprise, the Olifant Manufacturing Company (OMC), to refurbish the Centurions. During this period South Africa managed to restore its tank fleet to its original size by purchasing a number of surplus Centurion hulls from Jordan and India. The passage of United Nations Security Council Resolution 418, which imposed a mandatory arms embargo on the country, forced South Africa to purchase the hulls without turrets or armament. OMC upgraded each Centurion with a 29-litre Continental turbocharged diesel engine and a new transmission adopted from the M60 Patton. The refurbished Centurions were also armed with a South African variant of the Royal Ordnance L7 105 mm main gun. They were accepted into service with the South African Armoured Corps as the Olifant Mk1A in 1985.


title: Centurion (tank)

text: South African expeditionary forces clashed with FAPLA T-54/55 tanks during Operation Askari in late 1983 and early 1984; however, due to the enormous logistical commitment needed to keep the Olifants operational so far from conventional repair facilities, they were not deployed. At length the South African mechanised infantry, bolstered by Eland and Ratel-90 armoured car squadrons, succeeded in destroying the tanks on their own, although severe delays were encountered due to their lack of adequate anti-tank weaponry. Morale also suffered when inexperienced armoured car crews were ordered to take on the Angolan T-54/55s in their vulnerable vehicles. Criticism in this regard led to the deployment of a single squadron of thirteen Olifant Mk1As to the Angolan border, where they were attached to the 61 Mechanised Battalion Group. Following the Lusaka Accords, which effectively ensured a ceasefire between South Africa and Angola, these Olifants were placed into storage and the tank crews rotated out.


title: Centurion (tank)

text: The collapse of the Lusaka Accords and the subsequent launch of Operation Moduler in late 1987 led to the Olifant squadron being reactivated on the direct orders of South African State President P.W. Botha. On 9 November 1987 the Olifants destroyed two Angolan T-55s during a heated nine-minute skirmish. This marked the first occasion South African tanks had been sent into battle since World War II. Throughout Operation Moduler, South African forces typically dispersed into an "arrowhead" formation, with Olifants in the lead, Ratel-90 armoured cars on the flanks, and the remainder of the mechanised infantry to the rear and centre. Three Olifants were abandoned in a minefield during Operation Packer and subsequently captured by FAPLA, while another two were damaged beyond immediate repair by mines but successfully recovered. A number of others suffered varying degrees of track and suspension damage due to mines or Angolan tank fire, but were able to keep moving after field repairs.


title: Centurion (tank)

text: In the early 1990s, the Olifant Mk1A was superseded by the Olifant Mk1B, which incorporated major improvements in armour protection, a slightly more powerful engine, a double armoured floor for protection against mines, and a torsion bar suspension.


title: Centurion (tank)

text: At the end of the Second World War, it was clear that the mix of tanks in service with the Swedish Armed Forces was not just obsolete but also presented a large logistical problem. Kungliga Arméförvaltningens Tygavdelning (KAFT, the weapons bureau of the army administrative service) conducted a study that concluded that the most cost-effective alternative would be to purchase the newly developed Centurion Mk 3, which, while quite modern, was judged to also have upgrade potential for future requirements. A purchase request was sent to Great Britain, but the reply was that no deliveries could be made before the needs of the British Army had been satisfied, which was deemed to take between five and 15 years. Thus, in 1951, the vehicle bureau of KAFT was set to develop a Swedish alternative project, E M I L. Parallel with this, negotiations were initiated with France about buying the AMX-13.


title: Centurion (tank)

text: The British stance altered in early December 1952, due to the economic necessity of increasing exports to earn scarce foreign currency. Britain offered to sell the desired Centurions immediately. Minister of Defence Torsten Nilsson arbitrarily placed an order of 80 Mk 3, with Swedish Army designation "Stridsvagn 81" (Strv 81), around new year 1952/1953, with the first delivery in April 1953. In 1955, Sweden ordered a batch of 160 Centurion Mk 5 (also designated Strv 81), followed by a batch of 110 Centurion Mk 10 around 1960 (designated Strv 101). The Centurions, together with the Stridsvagn 103, formed the backbone of the Swedish armoured brigades for several decades. The Mk 3 and the Mk 5 were upgraded with a 105 mm gun in the 1960s, becoming Strv 102.


title: Centurion (tank)

text: Between 1983 and 1987, the Centurions had a midlife renovation and modification (REMO) done, which included among other things night vision equipment, targeting systems, laser range finders, improved gun stabilisation, thermal sleeves on the barrel and exhaust pipes and reactive armour developed by the Swedish FFV Ordnance. Around 80 Strv 102 were upgraded with Continental diesel engines and Allison gearboxes in the early 1980s, becoming Strv 104.


title: Centurion (tank)

text: The Swedish Army gradually phased out its Centurions and Strv 103 during the 1990s as a consequence of comparative tests of the T-72, Leclerc, M1A1 and Leopard 2. They were replaced with the Stridsvagn 121 and Stridsvagn 122.


title: Centurion (tank)

text: An Australian Army Mk 3 Centurion Type K, Army Registration Number 169041, was involved in a small nuclear test at Emu Field in Australia in 1953 as part of Operation Totem 1. Built as number 39/190 at the Royal Ordnance Factory, Barnbow in 1951 it was assigned the British Army number 06 BA 16 and supplied to the Australian Commonwealth Government under Contract 2843 in 1952.


title: Centurion (tank)

text: It was placed less than from the 9.1 kt blast with its turret facing the epicentre, left with the engine running and a full ammunition load. Examination after detonation found that it had been pushed away from the blast point by about , pushed slightly left and that its engine had stopped working, but only because it had run out of fuel. Antennae were missing, lights and periscopes were heavily sandblasted, the cloth mantlet cover was incinerated, and the armoured side plates had been blown off and carried up to from the tank. It could still be driven from the site. Had the tank been manned, the crew would most likely have been killed by the shock wave.


title: Centurion (tank)

text: 169041, subsequently nicknamed "The Atomic Tank", was used in the Vietnam War. In May 1969, during a firefight, 169041 (call sign 24C) was hit by a rocket-propelled grenade (RPG). The turret crew were all wounded by fragmentation as the RPG hollow charge jet entered the lower left side of the fighting compartment, travelled diagonally across the floor and lodged in the rear right corner. Trooper Carter was evacuated, while the others remained on duty and the tank remained battleworthy.


title: Centurion (tank)

text: "The Atomic Tank" is now located at Robertson Barracks in Palmerston, Northern Territory. Although other tanks were subjected to nuclear tests, 169041 is the only one known to have withstood a blast and to have later fought in a war.


title: Centurion (tank)

text: The designations follows the pattern of main gun calibre in centimetres followed by the service order number. Hence the Strv 81 is read as the first tank with an 8 cm gun, while the Strv 101 is the first tank with a 10 cm gun that was accepted into service.


title: Least squares

text: The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation.


title: Least squares

text: The most important application is in data fitting. When the problem has substantial uncertainties in the independent variable (the "x" variable), then simple regression and least-squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares.


title: Least squares

text: Least squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. The nonlinear problem is usually solved by iterative refinement; at each iteration the system is approximated by a linear one, and thus the core calculation is similar in both cases.


title: Least squares

text: Polynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent variable and the deviations from the fitted curve.


title: Least squares

text: When the observations come from an exponential family with identity as its natural sufficient statistics and mild-conditions are satisfied (e.g. for normal, exponential, Poisson and binomial distributions), standardized least-squares estimates and maximum-likelihood estimates are identical. The method of least squares can also be derived as a method of moments estimator.


title: Least squares

text: The following discussion is mostly presented in terms of linear functions but the use of least squares is valid and practical for more general families of functions. Also, by iteratively applying local quadratic approximation to the likelihood (through the Fisher information), the least-squares method may be used to fit a generalized linear model.


title: Least squares

text: The least-squares method was officially discovered and published by Adrien-Marie Legendre (1805), though it is usually also co-credited to Carl Friedrich Gauss (1795) who contributed significant theoretical advances to the method and may have previously used it in his work.


title: Least squares

text: The method of least squares grew out of the fields of astronomy and geodesy, as scientists and mathematicians sought to provide solutions to the challenges of navigating the Earth's oceans during the Age of Discovery. The accurate description of the behavior of celestial bodies was the key to enabling ships to sail in open seas, where sailors could no longer rely on land sightings for navigation.


title: Least squares

text: The method was the culmination of several advances that took place during the course of the eighteenth century:


title: Least squares

text: The first clear and concise exposition of the method of least squares was published by Legendre in 1805. The technique is described as an algebraic procedure for fitting linear equations to data and Legendre demonstrates the new method by analyzing the same data as Laplace for the shape of the earth. Within ten years after Legendre's publication, the method of least squares had been adopted as a standard tool in astronomy and geodesy in France, Italy, and Prussia, which constitutes an extraordinarily rapid acceptance of a scientific technique.


title: Least squares

text: In 1809 Carl Friedrich Gauss published his method of calculating the orbits of celestial bodies. In that work he claimed to have been in possession of the method of least squares since 1795. This naturally led to a priority dispute with Legendre. However, to Gauss's credit, he went beyond Legendre and succeeded in connecting the method of least squares with the principles of probability and to the normal distribution. He had managed to complete Laplace's program of specifying a mathematical form of the probability density for the observations, depending on a finite number of unknown parameters, and define a method of estimation that minimizes the error of estimation. Gauss showed that the arithmetic mean is indeed the best estimate of the location parameter by changing both the probability density and the method of estimation. He then turned the problem around by asking what form the density should have and what method of estimation should be used to get the arithmetic mean as estimate of the location parameter. In this attempt, he invented the normal distribution.


title: Least squares

text: An early demonstration of the strength of Gauss's method came when it was used to predict the future location of the newly discovered asteroid Ceres. On 1 January 1801, the Italian astronomer Giuseppe Piazzi discovered Ceres and was able to track its path for 40 days before it was lost in the glare of the sun. Based on these data, astronomers desired to determine the location of Ceres after it emerged from behind the sun without solving Kepler's complicated nonlinear equations of planetary motion. The only predictions that successfully allowed Hungarian astronomer Franz Xaver von Zach to relocate Ceres were those performed by the 24-year-old Gauss using least-squares analysis.


title: Least squares

text: In 1810, after reading Gauss's work, Laplace, after proving the central limit theorem, used it to give a large sample justification for the method of least squares and the normal distribution. In 1822, Gauss was able to state that the least-squares approach to regression analysis is optimal in the sense that in a linear model where the errors have a mean of zero, are uncorrelated, and have equal variances, the best linear unbiased estimator of the coefficients is the least-squares estimator. This result is known as the Gauss–Markov theorem.


title: Least squares

text: The idea of least-squares analysis was also independently formulated by the American Robert Adrain in 1808. In the next two centuries workers in the theory of errors and in statistics found many different ways of implementing least squares.


title: Least squares

text: The objective consists of adjusting the parameters of a model function to best fit a data set. A simple data set consists of "n" points (data pairs) formula_1, "i" = 1, …, "n", where formula_2 is an independent variable and formula_3 is a dependent variable whose value is found by observation. The model function has the form formula_4, where "m" adjustable parameters are held in the vector formula_5. The goal is to find the parameter values for the model that "best" fits the data. The fit of a model to a data point is measured by its residual, defined as the difference between the observed value of the dependent variable and the value predicted by the model:


title: Least squares

text: The least-squares method finds the optimal parameter values by minimizing the sum of squared residuals, formula_7:


title: Least squares

text: In the simplest case formula_9 and the result of the least-squares method is the arithmetic mean of the input data.


title: Least squares

text: An example of a model in two dimensions is that of the straight line. Denoting the y-intercept as formula_10 and the slope as formula_11, the model function is given by formula_12. See linear least squares for a fully worked out example of this model.


title: Least squares

text: A data point may consist of more than one independent variable. For example, when fitting a plane to a set of height measurements, the plane is a function of two independent variables, "x" and "z", say. In the most general case there may be one or more independent variables and one or more dependent variables at each data point.


title: Least squares

text: To the right is a residual plot illustrating random fluctuations about formula_13, indicating that a linear modelformula_14 is appropriate. formula_15 is an independent, random variable.


title: Least squares

text: If the residual points had some sort of a shape and were not randomly fluctuating, a linear model would not be appropriate. For example, if the residual plot had a parabolic shape as seen to the right, a parabolic modelformula_16 would be appropriate for the data. The residuals for a parabolic model can be calculated via formula_17.


title: Least squares

text: This regression formulation considers only observational errors in the dependent variable (but the alternative total least squares regression can account for errors in both variables). There are two rather different contexts with different implications:


title: Least squares

text: The minimum of the sum of squares is found by setting the gradient to zero. Since the model contains "m" parameters, there are "m" gradient equations:


title: Least squares

text: The gradient equations apply to all least squares problems. Each particular problem requires particular expressions for the model and its partial derivatives.


title: Least squares

text: A regression model is a linear one when the model comprises a linear combination of the parameters, i.e.,


title: Least squares

text: Letting formula_24 and putting the independent and dependent variables in matrices formula_25 and formula_26, respectively, we can compute the least squares in the following way. Note that formula_27 is the set of all data.


title: Least squares

text: There is, in some cases, a closed-form solution to a non-linear least squares problem – but in general there is not. In the case of no closed-form solution, numerical algorithms are used to find the value of the parameters formula_33 that minimizes the objective. Most algorithms involve choosing initial values for the parameters. Then, the parameters are refined iteratively, that is, the values are obtained by successive approximation:


title: Least squares

text: where a superscript "k" is an iteration number, and the vector of increments formula_35 is called the shift vector. In some commonly used algorithms, at each iteration the model may be linearized by approximation to a first-order Taylor series expansion about formula_36:


title: Least squares

text: The Jacobian J is a function of constants, the independent variable "and" the parameters, so it changes from one iteration to the next. The residuals are given by


title: Least squares

text: To minimize the sum of squares of formula_39, the gradient equation is set to zero and solved for formula_40:


title: Least squares

text: These differences must be considered whenever the solution to a nonlinear least squares problem is being sought.


title: Least squares

text: Consider a simple example drawn from physics. A spring should obey Hooke's law which states that the extension of a spring is proportional to the force, "F", applied to it.


title: Least squares

text: constitutes the model, where "F" is the independent variable. In order to estimate the force constant, "k", we conduct a series of "n" measurements with different forces to produce a set of data, formula_48, where "y" is a measured spring extension. Each experimental observation will contain some error, formula_49, and so we may specify an empirical model for our observations,


title: Least squares

text: There are many methods we might use to estimate the unknown parameter "k". Since the "n" equations in the "m" variables in our data comprise an overdetermined system with one unknown and "n" equations, we estimate "k" using least squares. The sum of squares to be minimized is


title: Least squares

text: We assume that applying force causes the spring to expand. After having derived the force constant by least squares fitting, we predict the extension from Hooke's law.


title: Least squares

text: In a least squares calculation with unit weights, or in linear regression, the variance on the "j"th parameter,


title: Least squares

text: where the true error variance "σ" is replaced by an estimate, the reduced chi-squared statistic, based on the minimized value of the residual sum of squares (objective function), "S". The denominator, "n" − "m", is the statistical degrees of freedom; see effective degrees of freedom for generalizations. "C" is the precision matrix (i.e., inverse covariance matrix).


title: Least squares

text: If the probability distribution of the parameters is known or an asymptotic approximation is made, confidence limits can be found. Similarly, statistical tests on the residuals can be conducted if the probability distribution of the residuals is known or assumed. We can derive the probability distribution of any linear combination of the dependent variables if the probability distribution of experimental errors is known or assumed. Inferring is easy when assuming that the errors follow a normal distribution, consequently implying that the parameter estimates and residuals will also be normally distributed conditional on the values of the independent variables.


title: Least squares

text: It is necessary to make assumptions about the nature of the experimental errors to test the results statistically. A common assumption is that the errors belong to a normal distribution. The central limit theorem supports the idea that this is a good approximation in many cases.


title: Least squares

text: However, suppose the errors are not normally distributed. In that case, a central limit theorem often nonetheless implies that the parameter estimates will be approximately normally distributed so long as the sample is reasonably large. For this reason, given the important property that the error mean is independent of the independent variables, the distribution of the error term is not an important issue in regression analysis. Specifically, it is not typically important whether the error term follows a normal distribution.


title: Least squares

text: A special case of generalized least squares called weighted least squares occurs when all the off-diagonal entries of "Ω" (the correlation matrix of the residuals) are null; the variances of the observations (along the covariance matrix diagonal) may still be unequal (heteroscedasticity). In simpler terms, heteroscedasticity is when the variance of formula_57 depends on the value of formula_58 which causes the residual plot to create a "fanning out" effect towards larger formula_57 values as seen in the residual plot to the right. On the other hand, homoscedasticity is assuming that the variance of formula_57 and formula_15 is equal.


title: Least squares

text: The first principal component about the mean of a set of points can be represented by that line which most closely approaches the data points (as measured by squared distance of closest approach, i.e. perpendicular to the line). In contrast, linear least squares tries to minimize the distance in the formula_62 direction only. Thus, although the two use a similar error metric, linear least squares is a method that treats one dimension of the data preferentially, while PCA treats all dimensions equally.


title: Least squares

text: Notable statistician Sara van de Geer used Empirical process theory and the Vapnik-Chervonenkis dimension to prove a least-squares estimator can be interpreted as a measure on the space of square-integrable functions.


title: Least squares

text: In some contexts a regularized version of the least squares solution may be preferable. Tikhonov regularization (or ridge regression) adds a constraint that formula_63, the L-norm of the parameter vector, is not greater than a given value to the least squares formulation, leading to a constrained minimization problem. This is equivalent to the unconstrained minimization problem where the objective function is the residual sum of squares plus a penalty term formula_64 and formula_65 is a tuning parameter (this is the Lagrangian form of the constrained minimization problem).


title: Least squares

text: In a Bayesian context, this is equivalent to placing a zero-mean normally distributed prior on the parameter vector.


title: Least squares

text: An alternative regularized version of least squares is "Lasso" (least absolute shrinkage and selection operator), which uses the constraint that formula_66, the L-norm of the parameter vector, is no greater than a given value. (As above, this is equivalent to an unconstrained minimization of the least-squares penalty with formula_67 added.) In a Bayesian context, this is equivalent to placing a zero-mean Laplace prior distribution on the parameter vector. The optimization problem may be solved using quadratic programming or more general convex optimization methods, as well as by specific algorithms such as the least angle regression algorithm.


title: Least squares

text: One of the prime differences between Lasso and ridge regression is that in ridge regression, as the penalty is increased, all parameters are reduced while still remaining non-zero, while in Lasso, increasing the penalty will cause more and more of the parameters to be driven to zero. This is an advantage of Lasso over ridge regression, as driving parameters to zero deselects the features from the regression. Thus, Lasso automatically selects more relevant features and discards the others, whereas Ridge regression never fully discards any features. Some feature selection techniques are developed based on the LASSO including Bolasso which bootstraps samples, and FeaLect which analyzes the regression coefficients corresponding to different values of formula_65 to score all the features.


title: Least squares

text: The L-regularized formulation is useful in some contexts due to its tendency to prefer solutions where more parameters are zero, which gives solutions that depend on fewer variables. For this reason, the Lasso and its variants are fundamental to the field of compressed sensing. An extension of this approach is elastic net regularization.


title: Diana Krall

text: Diana Jean Krall (born November 16, 1964) is a Canadian jazz pianist and singer known for her contralto vocals. She has sold more than 15 million albums worldwide, including over six million in the US. On December 11, 2009, "Billboard" magazine named her the second greatest jazz artist of the decade (2000–2009), establishing her as one of the best-selling artists of her time.


title: Diana Krall

text: Krall is the only jazz singer to have had eight albums debuting at the top of the "Billboard" Jazz Albums. To date, she has won three Grammy Awards and eight Juno Awards. She has also earned nine gold, three platinum, and seven multi-platinum albums.


title: Diana Krall

text: Krall was born on November 16, 1964, in Nanaimo, British Columbia, the daughter of Adella A. ("née" Wende), an elementary school teacher, and Stephen James "Jim" Krall, an accountant. Krall's only sibling, Michelle, is a former member of the Royal Canadian Mounted Police (RCMP). Krall's father played piano at home, and her mother sang in a community choir. Krall began studying piano herself at the age of four and took exams through The Royal Conservatory of Music. In high school, she was a member of a student jazz group; at 15, she began playing professionally in local restaurants. Krall won a scholarship to attend the Berklee College of Music in Boston, where she studied from 1981 to 1983, before spending time in Los Angeles to play jazz. She returned to Canada to record her first album in 1992.


title: Diana Krall

text: Krall recorded her first album, "Stepping Out", for Justin Time Records in 1992; the album was released in 1993. She was accompanied by bassist John Clayton and drummer Jeff Hamilton. It caught the attention of producer Tommy LiPuma, who produced her second album, "Only Trust Your Heart" (1995).


title: Diana Krall

text: Her third album, "" (1996), was nominated for a Grammy and continued for 70 weeks in the "Billboard" jazz charts. "Love Scenes" (1997) quickly became a hit record with the trio of Krall, Russell Malone (guitar), and Christian McBride (bass).


title: Diana Krall

text: In August 2000, Krall partnered with Tony Bennett for a 20-city tour, and in 2008–09 they worked together again for a song on the TV series ""


title: Diana Krall

text: Orchestral arrangements by Johnny Mandel provided the background for her fifth studio album "When I Look in Your Eyes" (1999), her first released through Verve Records. The band mix was kept, following arrangements on "The Look of Love" (2001) created by Claus Ogerman; this record achieved platinum status and reached the top 10 of the "Billboard" 200. The title track from the album, a cover of the "Casino Royale" standard popularized in the late 1960s by Dusty Springfield and Sérgio Mendes, reached number 22 on the adult contemporary chart.


title: Diana Krall

text: In September 2001, Krall began a world tour. Her concert at the Paris Olympia was recorded and released in 2002 as her first live record, "Live in Paris" (issued with a different European title, "A Night In Paris"). The album included covers of Billy Joel's "Just the Way You Are" (a hit on U.S. smooth jazz radio) and Joni Mitchell's "A Case Of You", and was also released as a video album.


title: Diana Krall

text: The 2001 movie "The Score" (US and Germany), starring Robert De Niro and Marlon Brando, featured a recording of Krall's entitled: "I'll Make It Up As I Go." This song accompanies the film's ending credits (chapter 12) and was composed by fellow Canadian, David Foster.


title: Diana Krall

text: After marrying English singer-songwriter Elvis Costello in 2003, Krall worked with him as a lyricist and began to compose her own songs, resulting in the album "The Girl in the Other Room". Released in April 2004, it quickly rose to the top five in the United Kingdom and made the Australian top 40 album charts. She also joined Ray Charles on his "Genius Loves Company" album in 2004 for the song "You Don't Know Me", and her 2004 performance at Bell Centre, Montreal on June 29 was released as her second live CD and DVD, "Live at the Montreal Jazz Festival", released on November 23, 2004.


title: Diana Krall

text: In late May 2007, Krall was featured in a Lexus ad campaign. That year she also sang "Dream a Little Dream of Me" with piano accompaniment by pianist Hank Jones for an "all-star" tribute album "" (2007) produced by Phil Ramone.


title: Diana Krall

text: "Quiet Nights", produced by Krall and Tommy LiPuma, was released on March 31, 2009, and consisted of mainly bossa nova standards.


title: Diana Krall

text: In 2011, Krall went on a private retreat to Sri Lanka. In September 2012, she accompanied Paul McCartney at Capitol Studios in a live performance of his album "Kisses on the Bottom", which was shown live on the internet. On September 13, 2012, Krall performed "Fly Me to the Moon" at astronaut Neil Armstrong's memorial service in Washington, D.C.