title: Graham Bonnet

text: Bonnet then quit to do advert jingles. He appeared in the 1974 British comedy film, "Three for All" as lead singer of 'Billy Beethoven', a fictional band, along with several notable UK comedy personalities and his then partner Adrienne Posta, although his character's lines were limited to only two words.


title: Graham Bonnet

text: In 1977, he released an eponymous album, which was certified gold in Australia. The single, "It's All Over Now, Baby Blue", a cover version of the Bob Dylan song, also reached Number 3 in Australia in November 1977, and the following year the single "Warm Ride", written by the Bee Gees, a leftover from the "Saturday Night Fever" sessions, reached number two there in August.


title: Graham Bonnet

text: In 1979, Bonnet was approached to join UK glam rock band Sweet to replace Brian Connolly. However, he was chosen by Ritchie Blackmore to replace Ronnie James Dio as the vocalist of hard rock band Rainbow. This was something of a musical departure for Bonnet, who had previously identified himself more as an R&B singer. Bonnet would later credit his time in Rainbow and his collaboration with Blackmore, in particular, as fundamentally changing his musical outlook to a more hard rock focus. He sang on the "Down to Earth" LP, which would become his most successful album. It spawned two hit singles in 1979 and 1980: "Since You Been Gone" and "All Night Long". During Bonnet's time in the band, Rainbow also headlined the inaugural Monsters of Rock festival at Donington Park, Castle Donington.


title: Graham Bonnet

text: Bonnet's time with Rainbow was short and he left to resume his solo career, releasing the "Line-Up" album in 1981, handled by producer John Eden. Following on from his time in Rainbow, the album had a markedly more rock-based sound than his previous solo recordings, whilst retaining some of his former R&B influences. For the recording of "Line Up" Bonnet enlisted several well-known rock musicians including Whitesnake guitarist Mick Moody, Whitesnake and Rainbow drummer Cozy Powell, Deep Purple and Whitesnake keyboard player Jon Lord, and Status Quo guitarists Francis Rossi and Rick Parfitt. The album reached No. 62 in the UK Albums Chart. The album's lead single, "Night Games", reached No. 6 in the UK Singles Chart, with the follow-up single, "Liar", reaching No. 51. Around this time Bonnet sang on an advertisement for Levi's jeans (the song was entitled "These Eyes"), although his version has never been released.


title: Graham Bonnet

text: Tempted by an offer from ex-UFO guitarist Michael Schenker, Bonnet continued his progression to a heavier musical style and joined the Michael Schenker Group (MSG) for the "Assault Attack" album. However, he was fired from the group after a single concert, at Sheffield Polytechnic (now called Sheffield Hallam University), when he drunkenly exposed himself on stage.


title: Graham Bonnet

text: Upon leaving MSG, Bonnet decided to form his own band, drawing inspiration from his days in Rainbow. In 1983, he co-founded Alcatrazz, with Gary Shea (bass), and Jimmy Waldo (keyboards) of the band New England, former Alice Cooper drummer Jan Uvena, and Swedish guitarist Yngwie Malmsteen. The band's debut album, "No Parole from Rock N' Roll", featured a distinctly heavy metal sound, with Bonnet describing the material as the heaviest that he had recorded to date. The band enjoyed moderate success in the United States, and major success in Japan.


title: Graham Bonnet

text: The band released three studio albums ("No Parole from Rock N' Roll", "Disturbing the Peace", with guitarist Steve Vai replacing Malmsteen, and "Dangerous Games" with Danny Johnson on guitar). Alcatrazz also released a live album, "Live Sentence", with material from Yngwie Malmsteen's period in the band. For the "Dangerous Games" LP, Alcatrazz recorded a remake of Bonnet's hit song "Only One Woman" from his first band The Marbles. In 1987, Alcatrazz appeared on the second series of the BBC TV programme "Rock School", with Bonnet providing singing tips. The programme also included clips of Alcatrazz in rehearsal. Later that year, Alcatrazz disbanded, and Bonnet returned to his solo career. In 2009, Bonnet reformed Alcatrazz with three new musicians. Bonnet did not consult with his former bandmates Uvena and Waldo about re-forming the original line-up, and in response they also re-grouped as a separate version of Alcatrazz. Both bands have maintained official pages on MySpace.com.


title: Graham Bonnet

text: Bonnet later reformed his version of the band as "Alcatrazz featuring Graham Bonnet" with guitarist Howie Simon (Jeff Scott Soto Band, Talisman), drummer Glen Sobel (Impellitteri, Beautiful Creatures, Tony MacAlpine), and bassist Tim Luce and toured Japan in May and June 2007—sharing the headline with another ex-Rainbow vocalist, Joe Lynn Turner. Howie Simon revealed in a 2010 interview that it was his suggestion to bring back the Alcatrazz name. They also headlined the BerkRock festival in Berkovitsa, Bulgaria, in July 2008 and have played various West Coast US dates including support slots for Y&T. Alcatrazz continued to perform live occasionally until 2014.


title: Graham Bonnet

text: In March 2017, three-fifths of the original lineup (Bonnet, Waldo and Shea) reunited for three shows in Japan, which also included Conrado Pesinato and Mark Benquechea on guitar and drums respectively. The performances were recorded for the live album/DVD "Parole Denied – Tokyo 2017", which was released on 7 December 2018.


title: Graham Bonnet

text: In February 2019, Bonnet confirmed that he had once again resurrected Alcatrazz, with a new lineup featuring himself, Waldo, Benquechea, Beth-Ami Heavenstone, as well as new guitarist Joe Stump. Heavenstone thus briefly became Alcatrazz's first female member, having played bass in The Graham Bonnet Band, where she was Waldo's bandmate. This lineup planned to record a new album together, which would also include contributions from Chris Impellitteri, Bob Kulick, Dario Mollo and former Alcatrazz guitarist Steve Vai. Shea returned to Alcatrazz in January 2020 to replace Heavenstone.


title: Graham Bonnet

text: Bonnet's post-Alcatrazz projects have all been short-lived and included Blackthorne (working with ex-Balance guitarist Bob Kulick, brother of Kiss guitarist Bruce Kulick), backing vocals for the Danish heavy metal band Pretty Maids' "Future World" and numerous session work for Forcefield, appearing on "To Oz and Back" and "Let The Wild Run Free". In 1988, Bonnet joined Impellitteri, for their album "Stand in Line".


title: Graham Bonnet

text: An appearance on Eddie Hardin and Pete York's musical adaptation of "Wind in The Willows", performed live in Germany in 1991, saw Bonnet sing on around six of the songs alongside fellow musicians Jon Lord, Don Airey and Ray Fenwick amongst others. Fenwick and Airey also featured heavily on Bonnet's 1991 solo album "Here Comes The Night" which includes several covers as well as songs credited to his then wife Jo Eime, and another remake of the Marbles' "Only One Woman".


title: Graham Bonnet

text: In 1997, he released "Underground", a new solo album, which helped re-establish him with his fan base in Japan. 1999's "The Day I Went Mad" featured guitarist Slash, Def Leppard guitarist Vivian Campbell, Bruce Kulick plus guitarist, Mario Parga.


title: Graham Bonnet

text: Bonnet contributed lead vocals to the Japanese heavy metal band Anthem's 2000 release "Heavy Metal Anthem", which had reworks of classic Anthem tracks. Bonnet rejoined Impellitteri in 2000 for their "System X" album. Meanwhile, his 1999 Japanese solo album got a UK release in September 2001.


title: Graham Bonnet

text: At the back end of 2001, Bonnet went on a solo UK tour. His band included keyboard player Don Airey, bassist Chris Childs and drummer Harry James of Thunder and guitarist Dario Mollo.


title: Graham Bonnet

text: In early 2004, Bonnet joined Italian guitarist Dario Mollo's new project Elektric Zoo, touring Europe during April. Maintaining the Italian connection, the singer also participated in Matteo Filippini's project, Moonstone, featuring on the track "Not Dead Yet".


title: Graham Bonnet

text: In 2006, Bonnet contributed vocals to the "Welcome to America" album by Taz Taylor Band. The band toured the UK in 2007 and Europe in 2008.


title: Graham Bonnet

text: He also appeared in the "Countdown Spectacular" concert series in Australia between August and September 2007. He sang two songs, "Warm Ride" and "It's All Over Now, Baby Blue".


title: Graham Bonnet

text: A press release dated 6 November 2008 reported that Bonnet would be contributing vocals for a highlights CD with the metal opera project, Lyraka. The album "Lyraka Volume 1" was released on 2 November 2010. It was announced on 17 November 2010, that Bonnet would also be featured on "Lyraka Volume 2".


title: Graham Bonnet

text: Bonnet currently resides in Los Angeles, California, from where he continues to record and tour extensively. Bonnet toured the UK with Rainbow tribute band Catch the Rainbow starting in March 2014.


title: Graham Bonnet

text: He collaborated in the Stardust Reverie Project, a supergroup featuring Zak Stevens and Lynn Meredith among others. Their first album "Ancient Rites of the Moon" was released in April 2014. He contributed on vocals in one track of the second Stardust Reverie album "Proclamation of Shadows", which came out in March 2015.


title: Graham Bonnet

text: In 2015, Bonnet formed The Graham Bonnet Band, and toured the UK and Europe, playing songs from throughout his career including Alcatrazz and Rainbow. The band released a two-song E.P. titled "My Kingdom Come", (the song "My Kingdom Come", written by Russ Ballard) and announced work on a new studio album to be recorded featuring new compositions and a bonus disc consisting of re-recordings of a number of songs from Bonnet's career. The final line-up of The Graham Bonnet Band was: Graham Bonnet, vocals; Conrad Pesinato, guitars; Beth-Ami Heavenstone, bass; Mark Zonder (Ex-Fates Warning), drums. The band resumed touring towards the end of 2016.


title: Graham Bonnet

text: On 4 November 2016, The Graham Bonnet Band released their debut album, "The Book". Reviews were positive, with the Real Gone website calling the album "surprisingly good" and also stating that some of the tracks "exceeded expectations by some distance". Heavenstone later joined Bonnet in a refounded Alcatrazz (see above).


title: Graham Bonnet

text: In 2016, Bonnet joined Michael Schenker and fellow former MSG singers Gary Barden and Robin McAuley in Michael Schenker Fest, initially for a tour of Japan. This resulted in a CD/DVD "Live – Tokyo International Forum Hall". Later tours of Europe and Japan followed. In 2017, with the addition of Temple of Rock singer Doogie White (another former Rainbow vocalist), Michael Schenker Fest recorded the album Resurrection featuring vocal contributions from all 4 singers. This line-up toured the US and Europe in 2018.


title: Graham Bonnet

text: Bonnet was extensively interviewed for 2 books by author Greg Prato: 2016's "The Other Side of Rainbow" and 2017's "Shredders!: The Oral History Of Speed Guitar (And More)".


title: Jin Goo

text: Jin Goo (born July 20, 1980) is a South Korean actor. He won Best Supporting Actor at the Grand Bell Awards and Blue Dragon Film Awards for his role in Bong Joon-ho's 2009 noir thriller "Mother". He is also known for his role in the critically and commercially successful series "Descendants of the Sun".


title: Jin Goo

text: Jin Goo made his television debut in the 2003 gambling drama "All In", as the younger version of the protagonist character played by Lee Byung-hun. They reunited onscreen in Kim Jee-woon's film noir "A Bittersweet Life", and Jin would later join Lee when he established his own management agency, BH Entertainment.


title: Jin Goo

text: In 2005, Jin starred in the one-episode drama "Saya, Saya" ("Bird, Bird"), adapted from the novel written by Shin Kyung-sook about a mother and son who are both deaf. It won the top award in the TV movie/miniseries category of Prix Italia, and the jury praised it as "a magical, moving and poetic story about the power of love with high quality performances."


title: Jin Goo

text: After a guest appearance as a Korean language teacher on the webisodes of Japanese drama "Joshi Deka!", Jin returned to Korean television in 2008's "Spotlight", a glimpse into the lives of broadcast news reporters covering the city beat. To prepare for his role, Jin followed a cub reporter for a day, and realized they didn't have time to bathe or even wash their faces.


title: Jin Goo

text: Though he appeared in little-seen mystery romance "The ESP Couple", Jin would become known for playing strong moody characters, such as a low-ranking thug in Yoo Ha's "A Dirty Carnival", and a serial killer in "Truck". For his portrayal of a secretive doctor in arthouse horror film "Epitaph", Jin received a Best New Actor trophy from the Golden Cinematography Awards.


title: Jin Goo

text: Jin's breakthrough would be his critically acclaimed supporting turn in 2009's "Mother". His performance in the Bong Joon-ho thriller earned him recognition from the Grand Bell Awards, the University Film Festival of Korea, and the Blue Dragon Film Awards.


title: Jin Goo

text: In 2010, Jin shed his hardboiled image to play a down-to-earth, aspiring chef in "". He said the film was a great pleasure to make since cooking is a hobby of his, though emulating a professional chef meant undergoing "200 hours of chopping radishes" in order to perfect the motion. He added that after the filming, he was able to make kimchi with his mother, which proved to be a memorable experience.


title: Jin Goo

text: 2011 was a busy year for Jin. Besides appearing in conspiracy thriller "Moby Dick", he had a starring role as one of three desperate Joseon soldiers in "The Showdown". He also made his stage debut as Nathan in a Korean production of the musical "Guys and Dolls".


title: Jin Goo

text: He next starred in "26 Years", based on Kang Full's manhwa about a plot to assassinate the man responsible for the Gwangju Massacre. Jin had been attached to the project since pre-production began in 2008, but investors backed out due to the politically controversial content. Online donations from thousands of private individuals enabled filming to resume in 2012. Jin was the only holdover from the original cast; initially cast as the young policeman, he now played the more central role of the gangster.


title: Jin Goo

text: In 2013, he played the titular character in TV series "Ad Genius Lee Tae-baek", a success story about a man who comes up to Seoul from the countryside armed with nothing but a high school diploma and a gift for drawing, and through sheer hard work, fights his way to become the best ad man and art director in the business.


title: Jin Goo

text: Supporting roles followed in thriller "The Target", period blockbuster "", and nostalgic musical drama "C'est Si Bon". In 2015, Jin starred in "Northern Limit Line", a naval thriller about the Second Battle of Yeonpyeong.


title: Jin Goo

text: 2016 was a remarkable year for Jin Goo. He was cast as an elite special forces soldier in "Descendants of the Sun", a romantic melodrama written by Kim Eun-sook. The drama was a critical and commercial success in Asia, and led to a surge in popularity for Jin. Later in the year, Jin starred in MBC's melodrama "Night Light".


title: Jin Goo

text: In 2017, Jin starred in the action film "One Line", where he played a legendary swindler that joins with a student (Im Si-wan) to rob a bank. He then starred in JTBC's action melodrama "Untouchable".


title: Jin Goo

text: In 2019, Jin starred in the legal drama "Legal High", a remake of the Japanese television series of the same name.


title: Jin Goo

text: Jin married his girlfriend on September 21, 2014. The couple welcomed a baby boy in June 2015. They welcomed their second child, a baby girl, in November 2016.


title: Everton Soares

text: Everton Sousa Soares (born 22 March 1996), usually known as just Everton () or Everton "Cebolinha" ("Jimmy Five" in Portuguese), is a Brazilian professional footballer who plays as a forward for Campeonato Brasileiro Série A club Flamengo and the Brazil national team.


title: Everton Soares

text: Everton was born in Maracanaú, Ceará, and joined Grêmio's youth setup in 2012, from Fortaleza. Initially on loan, he signed a permanent contract in October 2013, whilst also being linked to Manchester City in the process.


title: Everton Soares

text: Promoted to the main squad by Enderson Moreira ahead of the 2014 season, Everton made his first team debut on 19 January of that year, coming on as a second-half substitute for Yuri Mamute in a 1–0 Campeonato Gaúcho away loss against São José-PA. His first goal came on four days later, as he scored the first goal in a 2–1 home win against Lajeadense.


title: Everton Soares

text: Everton made his Série A debut on 20 April 2014, replacing Pará in a 1–0 away loss against Athletico Paranaense. Rarely used during the tournament, he started to feature more regularly during the 2015 campaign, scoring his first goal in the top tier on 6 September in a 2–1 home success over Goiás.


title: Everton Soares

text: On 15 August 2016, Everton renewed his contract with Grêmio until 2020. On 23 November, in the first leg of the 2016 Copa do Brasil Finals, he came on as a late substitute for Douglas and scored the 3rd goal in a 3–1 away win against Atlético Mineiro; he was a starter in the second leg, a 1–1 home draw which granted the title to Grêmio.


title: Everton Soares

text: Everton played his 100th match for Grêmio on 9 March 2017, after coming on for Pedro Rocha in a 2–0 Copa Libertadores away win against Zamora FC.


title: Everton Soares

text: On 17 August 2018, Everton was called up by coach Tite for friendly matches against United States, and El Salvador. Thus, Everton was in the first list of Brazil after the 2018 FIFA World Cup.


title: Everton Soares

text: In May 2019, he was included in Brazil's 23-man squad for the 2019 Copa América on home soil. He scored his first ever international goal in Brazil's opening game of the tournament, netting the final goal in a 3–0 win against Bolivia on 15 June. Seven days later, Everton scored his second international goal against Peru, in Brazil's final group stage match, firing in a shot at the near post from outside the box; the match ended in a 5–0 victory to Brazil, which enabled the hosts to advance to the quarter-finals of the tournament.


title: Everton Soares

text: In the 2019 Copa América Final on 7 July, at the Maracanã Stadium, Everton scored the opening goal in an eventual 3–1 win over Peru, and was named Man of the Match; he also finished the tournament as the top scorer with 3 goals, alongside Peru's Paolo Guerrero, but won the Golden Boot Award due to having played fewer minutes than the Peruvian throughout the tournament.


title: Everton Soares

text: Everton Soares was not drafted to play the 2022 World Cup in Qatar, however, he still hopes to be drafted for the 2026 World Cup based on his performance in Flamengo.


title: Everton Soares

text: Everton got the nickname "Cebola" (Onion in Portuguese) from his Grêmio teammate Pará, however, with the arrival of Uruguayan new transfer Cristian Rodríguez, who's also known as "Cebolla", Everton came to be called "Cebolinha" in reference to the cartoon character Jimmy Five ("Cebolinha" in Brazil), of Monica's Gang.


title: Extreme poverty

text: Extreme poverty, deep poverty, abject poverty, absolute poverty, destitution, or penury, is the most severe type of poverty, defined by the United Nations (UN) as "a condition characterized by severe deprivation of basic human needs, including food, safe drinking water, sanitation facilities, health, shelter, education and information. It depends not only on income but also on access to services" (UN 1995 report of the World Summit for Social Development). Historically, other definitions have been proposed within the United Nations.


title: Extreme poverty

text: In 2018, extreme poverty mainly refers to an income below the international poverty line of $1.90 per day (in 2011 prices, $ in dollars), set by the World Bank. In October 2017, the World Bank updated the international poverty line, a global absolute minimum, to $1.90 a day. This is the equivalent of $1.00 a day in 1996 US prices, hence the widely used expression "living on less than a dollar a day". The vast majority of those in extreme poverty reside in South Asia and Sub-Saharan Africa. As of 2018, it is estimated that the country with the most people living in extreme poverty is Nigeria, at 86 million.


title: Extreme poverty

text: The percentage of the global population living in absolute poverty fell from over 80% in 1800 to under 20% by 2015. According to UN estimates, roughly 734 million people or 10% remained under those conditions. The number had previously been measured as 1.9 billion in 1990, and 1.2 billion in 2008. Despite the significant number of individuals still below the international poverty line, these figures represent significant progress for the international community, as they reflect a decrease of more than one billion people over 15 years.


title: Extreme poverty

text: In public opinion surveys around the globe, people surveyed tend to think that extreme poverty has not decreased.


title: Extreme poverty

text: The reduction of extreme poverty and hunger was the first Millennium Development Goal (MDG1), as set by the United Nations in 2000. Specifically, the target was to reduce the extreme poverty rate by half by 2015, a goal that was met five years ahead of schedule. In the Sustainable Development Goals, which succeeded the MDGs, the goal is to end extreme poverty in all its forms everywhere. With this declaration the international community, including the UN and the World Bank have adopted the target of ending extreme poverty by 2030.


title: Extreme poverty

text: In July 1993, Leandro Despouy, the then UN Special Rapporteur on extreme poverty and human rights made use of a definition he adapted from a 1987 report to the French Economic and Social Council by Fr. Joseph Wresinski, founder of the International Movement ATD Fourth World, distinguishing "lack of basic security" (poverty) and "chronic poverty" (extreme poverty), linking the eradication of extreme poverty by allowing people currently experiencing it a real opportunity to exercise all their human rights:


title: Extreme poverty

text: "The lack of basic security connotes the absence of one or more factors enabling individuals and families to assume basic responsibilities and to enjoy fundamental rights. The situation may become widespread and result in more serious and permanent consequences. The lack of basic security leads to chronic poverty when it simultaneously affects several aspects of people’s lives, when it is prolonged and when it severely compromises people’s chances of regaining their rights and of reassuming their responsibilities in the foreseeable future."


title: Extreme poverty

text: This definition was mentioned previously, in June 1989, in the preliminary report on the realization of economic, social and cultural rights by the UN Special Rapporteur Danilo Türk. It is still in use today, among others, in the current UN Guiding Principles on Extreme Poverty and Human Rights adopted by the UN Human Rights Council in September 2012


title: Extreme poverty

text: Extreme poverty is defined by the international community as living below $1.90 a day, as measured in 2011 international prices (equivalent to $2.12 in 2018). This number, also known as the international poverty line, is periodically updated to account for inflation and differences in the cost of living; it was originally defined at $1.00 a day in 1996. The updates are made according to new price data to portray the costs of basic food, health services, clothing, and shelter around the world as accurately as possible. The latest revision was made in 2015 when the World Bank increased the line to international- $1.90.


title: Extreme poverty

text: Because many of the world's poorest people do not have a monetary income, the poverty measurement is based on the monetary value of a person's "consumption". Otherwise the poverty measurement would be missing the home production of subsistence farmers that consume largely their own production.


title: Extreme poverty

text: The $1.90/day extreme poverty line remains the most widely used metric as it highlights the reality of those in the most severe conditions. Although widely used by most international organizations, it has come under scrutiny due to a variety of factors. For example, it does not account for how far below the line people are, referred to as the depth of poverty. For this purpose, the same institutions publish data on the poverty gap.


title: Extreme poverty

text: The international poverty line is designed to stay constant over time, to allow comparisons between different years. It is therefore a measure of absolute poverty and is not measuring relative poverty. It is also not designed to capture how people view their own financial situation (known as the socially subjective poverty line). Moreover, the calculation of the poverty line relies on information about consumer prices to calculate purchasing power parity, which are very hard to measure and are necessarily debatable. As with all other metrics, there may also be missing data from the poorest and most fragile countries.


title: Extreme poverty

text: Several alternative instruments for measuring extreme poverty have been suggested which incorporate other factors such as malnutrition and lack of access to a basic education. The Multidimensional Poverty Index (MPI), based on the Alkire-Foster Method, is published by the Oxford Poverty & Human Development Initiative (OPHI): it measures deprivation in basic needs and can be broken down to reflect both the incidence and the intensity of poverty. For example, under conventional measures, in both Ethiopia and Uzbekistan about 40% of the population is considered extremely poor, but based on the MPI, 90% of Ethiopians but only 2% of Uzbeks are in multidimensional poverty.


title: Extreme poverty

text: The MPI is useful for development officials to determine the most likely causes of poverty within a region, using the M0 measure of the method (which is calculated by multiplying the fraction of people in poverty by the fraction of dimensions they are deprived in). For example, in the Gaza Strip of Palestine, using the M0 measure of the Alkire-Foster method reveals that poverty in the region is primarily caused by a lack of access to electricity, lack of access to drinking water, and widespread overcrowding. In contrast, data from the Chhukha District of Bhutan reveals that income is a much larger contributor to poverty as opposed to other dimensions within the region. However, the MPI only presents data from 105 countries, so it cannot be used for global measurements.


title: Extreme poverty

text: Using the World Bank definition of $1.90/day, , roughly 710 million people remained in extreme poverty (or roughly 1 in 10 people worldwide). Nearly half of them live in India and China, with more than 85% living in just 20 countries. Since the mid-1990s, there has been a steady decline in both the worldwide poverty rate and the total number of extreme poor. In 1990, the percentage of the global population living in extreme poverty was 43%, but in 2011, that percentage had dropped down to 21%. This halving of the extreme poverty rate falls in line with the first Millennium Development Goal (MDG1) proposed by former UN Secretary-General Kofi Annan, who called on the international community at the turn of the century to reduce the percentage of people in extreme poverty by half by 2015.


title: Extreme poverty

text: This reduction in extreme poverty took place most notably in China, Indonesia, India, Pakistan and Vietnam. These five countries accounted for the alleviation of 715 million people out of extreme poverty between 1990 and 2010 – more than the global net total of roughly 700 million. This statistical oddity can be explained by the fact that the number of people living in extreme poverty in Sub-Saharan Africa rose from 290 million to 414 million over the same period. However, there have been many positive signs for extensive, global poverty reduction as well. Since 1999, the total number of extreme poor has declined by an average of 50 million per year. Moreover, in 2005, for the first time in recorded history, poverty rates began to fall in every region of the world, including Africa.


title: Extreme poverty

text: As aforementioned, the number of people living in extreme poverty has reduced from 1.9 billion to 766 million over the span of the last decades. If we remain on our current trajectory, many economists predict we could reach global zero by 2030–2035, thus ending extreme poverty. Global zero entails a world in which fewer than 3% of the global population lives in extreme poverty (projected under most optimistic scenarios to be fewer than 200 million people). This zero figure is set at 3% in recognition of the fact that some amount of frictional (temporary) poverty will continue to exist, whether it is caused by political conflict or unexpected economic fluctuations, at least for the foreseeable future. However, the Brookings Institution notes that any projection about poverty more than a few years into the future runs the risk of being highly uncertain. This is because changes in consumption and distribution throughout the developing world over the next two decades could result in monumental shifts in global poverty, for better or worse.


title: Extreme poverty

text: Others are more pessimistic about this possibility, predicting a range of 193 million to 660 million people still living in extreme poverty by 2035. Additionally, some believe the rate of poverty reduction will slow down in the developing world, especially in Africa, and as such it will take closer to five decades to reach global zero. Despite these reservations, several prominent international and national organizations, including the UN, the World Bank and the United States Federal Government (via USAID), have set a target of reaching global zero by the end of 2030.


title: Extreme poverty

text: There are a variety of factors that may reinforce or instigate the existence of extreme poverty, such as weak institutions, cycles of violence and a low level of growth. Recent World Bank research shows that some countries can get caught in a "fragility trap", in which self-reinforcing factors prevent the poorest nations from emerging from low-level equilibrium in the long run. Moreover, most of the reduction in extreme poverty over the past twenty years has taken place in countries that have not experienced a civil conflict or have had governing institutions with a strong capacity to actually govern. Thus, to end extreme poverty, it is also important to focus on the interrelated problems of fragility and conflict.


title: Extreme poverty

text: USAID defines fragility as a government's lack of both legitimacy (the perception the government is adequate at doing its job) and effectiveness (how good the government is at maintaining law and order, in an equitable manner). As fragile nations are unable to equitably and effectively perform the functions of a state, these countries are much more prone to violent unrest and mass inequality. Additionally, in countries with high levels of inequality (a common problem in countries with inadequate governing institutions), much higher growth rates are needed to reduce the rate of poverty when compared with other nations. Additionally, if China and India are removed from the equation, up to 70% of the world's poor live in fragile states by some definitions of fragility. Some analysts project that extreme poverty will be increasingly concentrated in fragile, low-income states like Haiti, Yemen and the Central African Republic. However, some academics, such as Andy Sumner, say that extreme poverty will be increasingly concentrated in middle-income countries, creating a paradox where the world's poor do not actually live in the poorest countries.


title: Extreme poverty

text: To help low-income earners, fragile states make the transition towards peace and prosperity, the New Deal for Engagement in Fragile States, endorsed by roughly forty countries and multilateral institutions, was created in 2011. This represents an important step towards redressing the problem of fragility as it was originally articulated by self-identified fragile states who called on the international community to not only "do things differently", but to also "do different things".


title: Extreme poverty

text: Civil conflict also remains a prime cause for the perpetuation of poverty throughout the developing world. Armed conflict can have severe effects on economic growth for many reasons such as the destruction of assets, destruction of livelihoods, creation of unwanted mass migration, and diversion of public resources towards war. Significantly, a country that experienced major violence during 1981–2005 had extreme poverty rates 21 percentage points higher than a country with no violence. On average, each civil conflict will cost a country roughly 30 years of GDP growth. Therefore, a renewed commitment from the international community to address the deteriorating situation in highly fragile states is necessary to both prevent the mass loss of life, but to also prevent the vicious cycle of extreme poverty.


title: Extreme poverty

text: Population trends and dynamics (e.g. population growth) can also have a large impact on prospects for poverty reduction. According to the United Nations, "in addition to improving general health and well-being, analysis shows that meeting the reproductive health and contraceptive needs of all women in the developing world more than pays for itself").


title: Extreme poverty

text: In 2013, a prevalent finding in a report by the World Bank was that extreme poverty is most prevalent in low-income countries. In these countries, the World Bank found that progress in poverty reduction is the slowest, the poor live under the worst conditions, and the most affected persons are children age 12 and under.


title: Extreme poverty

text: In September 2000, world leaders gathered at the Millennium Summit held in New York, launching the United Nations Millennium Project suggested by then UN Secretary-General Kofi Annan. Prior to the launch of the conference, the office of Secretary-General Annan released a report entitled "We The Peoples: The Role of the United Nations in the 21st Century". In this document, now widely known as the Millennium Report, Kofi Annan called on the international community to reduce the proportion of people in extreme poverty by half by 2015, a target that would affect over 1 billion people. Citing the close correlation between economic growth and the reduction of poverty in poor countries, Annan urged international leaders to indiscriminately target the problem of extreme poverty across every region. In charge of managing the project was Jeffrey Sachs, a noted development economist, who in 2005 released a plan for action called "Investing in Development: A Practical Plan to Achieve the Millennium Development Goals". Thomas Pogge criticized the 2000 Millennium Declaration for being less ambitious than a previous declaration from the World Food Summit due to using 1990 as the benchmark rather than 1996.


title: Extreme poverty

text: Overall, there has been significant progress towards reducing extreme poverty, with the MDG1 target of reducing extreme poverty rates by half being met five years early, representing 700 million people being lifted out of extreme poverty from 1990 to 2010, with 1.2 billion people still remaining under those conditions. The notable exception to this trend was in Sub-Saharan Africa, the only region where the number of people living in extreme poverty rose from 290 million in 1990 to 414 million in 2010, comprising more than a third of those living in extreme poverty worldwide.


title: Extreme poverty

text: The 2005 World Summit, held in September which was organized to measure international progress towards fulfilling the Millennium Development Goals (MDGs). Notably, the conference brought together more than 170 Heads of State. While world leaders at the summit were encouraged by the reduction of poverty in some nations, they were concerned by the uneven decline of poverty within and among different regions of the globe. However, at the end of the summit, the conference attendees reaffirmed the UN's commitment to achieve the MDGs by 2015 and urged all supranational, national and non-governmental organizations to follow suit.


title: Extreme poverty

text: As the expiration of the Millennium Development Goals approached in 2015, the UN convened a panel to advise on a Post-2015 Development Agenda, which led to a new set of 17 goals for 2030 titled the Sustainable Development Goals (SDGs). The first goal (SDG 1) is to "End poverty in all its forms everywhere."


title: Extreme poverty

text: The HLP report, entitled A New Global Partnership: Eradicate Poverty and Transform Economies Through Sustainable Development, was published in May 2013. In the report, the HLP wrote that:


title: Extreme poverty

text: Therefore, the report determined that a central goal of the Post-Millennium Development agenda is to eradicate extreme poverty by 2030. However, the report also emphasized that the MDGs were not enough on their own, as they did not "focus on the devastating effects of conflict and violence on development ... the importance to development of good governance and institution ... nor the need for inclusive growth..." Consequently, there now exists synergy between the policy position papers put forward by the United States (through USAID), the World Bank and the UN itself in terms of viewing fragility and a lack of good governance as exacerbating extreme poverty. However, in a departure from the views of other organizations, the commission also proposed that the UN focus not only on extreme poverty (a line drawn at $1.25), but also on a higher target, such as $2. The report notes this change could be made to reflect the fact that escaping extreme poverty is only a first step.


title: Extreme poverty

text: In addition to the UN, a host of other supranational and national actors such as the European Union and the African Union have published their own positions or recommendations on what should be incorporated in the Post-2015 agenda. The European Commission's communication, published in A decent Life for all: from vision to collective action, affirmed the UN's commitment to "eradicate extreme poverty in our lifetime and put the world on a sustainable path to ensure a decent life for all by 2030". A unique vision of the report was the commission's environmental focus (in addition to a plethora of other goals such as combating hunger and gender inequality). Specifically, the Commission argued, "long-term poverty reduction ... requires inclusive and sustainable growth. Growth should create decent jobs, take place with resource efficiency and within planetary boundaries, and should support efforts to mitigate climate change." The African Union's report, entitled Common African Position (CAP) on the Post-2015 Development Agenda, likewise encouraged the international community to focus on eradicating the twin problems of poverty and exclusion in our lifetime. Moreover, the CAP pledged that "no person – regardless of ethnicity, gender, geography, disability, race or other status – is denied universal human rights and basic economic opportunities".


title: Extreme poverty

text: The UN least developed country (LDC) conferences were a series of summits organized by the UN to promote the substantial and even development of the world's least developed countries.


title: Extreme poverty

text: The first UN LDC Conference was held between 1 and 14 September 1981, in Paris, the first UN LDC Conference was organized to finalize the UN's "Substantial New Programme of Action" for the 1980s in Least Developed Countries. This program, which was unanimously adopted by the conference attendees, argued for internal reforms in LDCs (meant to encourage economic growth) to be complemented by strong international measures. However, despite the major economic and policy reforms initiated many of these LDCs, in addition to strong international aid, the economic situation of these countries worsened as a whole in the 1980s. This prompted the organization of a 2nd UN LDC conference almost a decade later.


title: Extreme poverty

text: The second UN LDC Conference was held between 3 and 14 September 1990, once again in Paris, the second UN LDC Conference was convened to measure the progress made by the LDCs towards fulfilling their development goals during the 1980s. Recognizing the problems that plagued the LDCs over the past decade, the conference formulated a new set of national and international policies to accelerate the growth rates of the poorest nations. These new principles were embodied in the "Paris Declaration and Programme of Action for the Least Developed Countries for the 1990s".


title: Extreme poverty

text: The fourth UN LDC Conference was the most recent conference. It was held in May 2011 in Istanbul, recognized that the nature of development had fundamentally changed since the 1st conference held almost 30 years earlier. In the 21st century, the capital flow into emerging economies has increasingly become dominated by foreign direct investment and remittances, as opposed to bilateral and multilateral assistance. Moreover, since the 1980s, significant structural changes have taken place on the international stage. With the creation of the G-20 conference of the largest economic powers, including many nations in the Global South, formerly undeveloped nations are now able to have a much larger say in international relations. Furthermore, the conference recognized that in the midst of a deep global recession, coupled with multiple crises (energy, climate, food, etc.), the international community would have fewer resources to aid the LDCs. Thus, the UN considered the participation of a wide range of stakeholders (not least the LDCs themselves), crucial to the formulation of the conference.


title: Extreme poverty

text: In 2013, the Board of Governors of the World Bank Group (WBG) set two overriding goals for the WBG to commit itself to in the future. First, to end extreme poverty by 2030, an objective that echoes the sentiments of the UN and the Obama administration. Additionally, the WBG set an interim target of reducing extreme poverty to below 9% by 2020. Second, to focus on growth among the bottom 40% of people, as opposed to standard GDP growth. This commitment ensures that the growth of the developing world lifts people out of poverty, rather than exacerbating inequality.


title: Extreme poverty

text: As the World Bank's primary focus is on delivering economic growth to enable equitable prosperity, its developments programs are primarily commercial-based in nature, as opposed to the UN. Since the World Bank recognizes better jobs will result in higher income, and thus less poverty, the WBG seeks to support employment training initiatives, small business development programs and strong labor protection laws. However, since much of the growth in the developing world has been inequitable, the World Bank has also begun teaming with client states to map out trends in inequality and to propose public policy changes that can level the playing field.


title: Extreme poverty

text: Moreover, the World Bank engages in a variety of nutritional, transfer payments and transport-based initiatives. Children who experience under-nutrition from conception to two years of age have a much higher risk of physical and mental disability. Thus, they are often trapped in poverty and are unable to make a full contribution to the social and economic development of their communities as adults. The WBG estimates that as much as 3% of GDP can be lost as a result of under-nutrition among the poorest nations. To combat undernutrition, the WBG has partnered with UNICEF and the WHO to ensure all small children are fully fed. The WBG also offers conditional cash transfers to poor households who meet certain requirements such as maintaining children's healthcare or ensuring school attendance. Finally, the WBG understands investment in public transportation and better roads is key to breaking rural isolation, improving access to healthcare and providing better job opportunities for the World's poor.


title: Extreme poverty

text: The UN Office for the Coordination of Humanitarian Affairs (OCHA) works to synchronize the disparate international, national and non-governmental efforts to contest poverty. OCHA seeks to prevent "confusion" in relief operations and to ensure that the humanitarian response to disaster situations has greater accountability and predictability. To do so, OCHA has begun deploying Humanitarian Coordinators and Country Teams to provide a solid architecture for the international community to work through.


title: Extreme poverty

text: The United Nation's Children's Fund (UNICEF) was created by the UN to provide food, clothing and healthcare to European children facing famine and disease in the immediate aftermath of World War II. After the UN General Assembly extended UNICEF's mandate indefinitely in 1953, it actively worked to help children in extreme poverty in more than 190 countries and territories to overcome the obstacles that poverty, violence, disease and discrimination place in a child's path. Its current focus areas are 1) Child survival & development 2) Basic education & gender equality 3) Children and HIV/AIDS and 4) Child protection.


title: Extreme poverty

text: The UN Refugee Agency (UNHCR) is mandated to lead and coordinate international action to protect refugees worldwide. Its primary purpose is to safeguard the rights of refugees by ensuring anyone can exercise the right to seek asylum in another state, with the option to return home voluntarily, integrate locally or resettle in a third country. The UNHCR operates in over 125 countries, helping approximately 33.9 million persons.


title: Extreme poverty

text: The World Food Programme (WFP) is the largest agency dedicated to fighting hunger worldwide. On average, the WFP brings food assistance to more than 90 million people in 75 countries. The WFP not only strives to prevent hunger in the present, but also in the future by developing stronger communities which will make food even more secure on their own. The WFP has a range of expertise from Food Security Analysis, Nutrition, Food Procurement and Logistics.


title: Extreme poverty

text: The World Health Organization (WHO) is responsible for providing leadership on global health matters, shaping the health research agenda, articulating evidence-based policy decisions and combating diseases that are induced from poverty, such as HIV/AIDS, malaria and tuberculosis. Moreover, the WHO deals with pressing issues ranging from managing water safety, to dealing with maternal and newborn health.


title: Extreme poverty

text: The US Agency for International Development (USAID) is the lead US government agency dedicated to ending extreme poverty. Currently the largest bilateral donor in the world, the United States channels the majority of its development assistance through USAID and the US Department of State. In President Obama's 2013 State of the Union address, he declared, "So the United States will join with our allies to eradicate such extreme poverty in the next two decades ... which is within our reach." In response to Obama's call to action, USAID has made ending extreme poverty central to its mission statement. Under its New Model of Development, USAID seeks to eradicate extreme poverty through the use of innovation in science and technology, by putting a greater emphasis on evidence based decision-making, and through leveraging the ingenuity of the private sector and global citizens.


title: Extreme poverty

text: A major initiative of the Obama Administration is Power Africa, which aims to bring energy to 20 million people in Sub-Saharan Africa. By reaching out to its international partners, whether commercial or public, the US has leveraged over $14 billion in outside commitments after investing only US$7 billion of its own. To ensure that Power Africa reaches the region's poorest, the initiative engages in a transaction based approach to create systematic change. This includes expanding access to electricity to more than 20,000 additional households which already live without power.


title: Extreme poverty

text: In terms of specific programming, USAID works in a variety of fields from preventing hunger, reducing HIV/AIDS, providing general health assistance and democracy assistance, as well as dealing with gender issues. To deal with food security, which affects roughly 842 million people (who go to bed hungry each night), USAID coordinates the Feed the Future Initiative (FtF). FtF aims to reduce poverty and under-nutrition each by 20% over five years. Because of the President's Emergency Plan for AIDS Relief (PEPFAR) and a variety of congruent actors, the incidence of AIDS and HIV, which used to ravage Africa, reduced in scope and intensity. Through PEPFAR, the United States has ensured over five million people have received life-saving antiviral drugs, a significant proportion of the eight million people receiving treatment in relatively poor nations.


title: Extreme poverty

text: In terms of general health assistance, USAID has worked to reduce maternal mortality by 30%, under-five child mortality by 35%, and has accomplished a host of other goals. USAID also supports the gamut of democratic initiatives, from promoting human rights and accountable, fair governance, to supporting free and fair elections and the rule of law. In pursuit of these goals, USAID has increased global political participation by training more than 9,800 domestic election observers and providing civic education to more than 6.5 million people. Since 2012, the Agency has begun integrating critical gender perspectives across all aspects of its programming to ensure all USAID initiatives work to eliminate gender disparities. To do so, USAID seeks to increase the capability of women and girls to realize their rights and determine their own life outcomes. Moreover, USAID supports additional programs to improve women's access to capital and markets, builds theirs skills in agriculture, and supports women's desire to own businesses.


title: Extreme poverty

text: Other major government development agencies with annual aid programmes of more than $10 billion include: GIZ (Germany), FCDO (United Kingdom), JICA (Japan), European Union and AFD (France).


title: Extreme poverty

text: A multitude of non-governmental organizations operate in the field of extreme poverty, actively working to alleviate the poorest of the poor of their deprivation. To name but a few notable organizations: Save the Children, the Overseas Development Institute, Concern Worldwide, ONE, Trickle Up and Oxfam have all done a considerable amount of work in extreme poverty.


title: Extreme poverty

text: Save the Children is the leading international organization dedicated to helping the world's indigent children. In 2013, Save the Children reached over 143 million children through their work, including over 52 million children directly. Save the Children also recently released their own report titled "Getting to Zero", in which they argued the international community could feasibly do more than lift the world's poor above $1.25/day.


title: Extreme poverty

text: The Overseas Development Institute (ODI) is a UK based think tank on international development and humanitarian issues. ODI is dedicated to alleviating the suffering of the world's poor by providing high-quality research and practical policy advice to the World's development officials. ODI also recently released a paper entitled, "The Chronic Poverty Report 2014–2015: The road to zero extreme poverty", in which its authors assert that though the international communities' goal of ending extreme poverty by 2030 is laudable, much more targeted resources will be necessary to reach said target. The report states that "To eradicate extreme poverty, massive global investment is required in social assistance, education and pro-poorest economic growth".


title: Extreme poverty

text: Concern Worldwide is an international humanitarian organization whose mission is to end extreme poverty by influencing decision makers at all levels of government (from local to international). Concern has also produced a report on extreme poverty in which they explain their own conception of extreme poverty from a NGO's standpoint. In this paper, named "How Concern Understands Extreme Poverty", the report's creators write that extreme poverty entails more than just living under $1.25/day, it also includes having a small number of assets and being vulnerable to severe negative shocks (whether natural or man made).


title: Extreme poverty

text: ONE, the organization co-founded by Bono, is a non-profit organization funded almost entirely by foundations, individual philanthropists and corporations. ONE's goals include raising public awareness and working with political leaders to fight preventable diseases, increase government accountability and increase investment in nutrition. Finally, trickleUp is a micro-enterprise development program targeted at those living on under $1.25/day, which provides the indigent with resources to build a sustainable livelihood through both direct financing and considerable training efforts.


title: Extreme poverty

text: Oxfam is a non-governmental organization that works prominently in Africa; their mission is to improve local community organizations and it works to reduce impediments to the development of the country. Oxfam helps families suffering from poverty receive food and healthcare to survive. There are many children in Africa experiencing growth stunting, and this is one example of an issue that Oxfam targets and aims to resolve.


title: Extreme poverty

text: Cash transfers appear to be an effective intervention for reducing extreme poverty, while at the same time improving health and education outcomes.<ref name="doi10.1002/14651858.CD011135.pub2"></ref> <ref name="doi10.1002/14651858.CD011135.pub3"></ref>


title: Kernel (linear algebra)

text: In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the linear subspace of the domain of the map which is mapped to the zero vector. That is, given a linear map between two vector spaces and , the kernel of is the vector space of all elements of such that , where denotes the zero vector in , or more symbolically:


title: Kernel (linear algebra)

text: In the linear map formula_2 two elements of have the same image in if and only if their difference lies in the kernel of , that is,


title: Kernel (linear algebra)

text: where the term refers the dimension of the image of , formula_6 while "" refers to the dimension of the kernel of , formula_7


title: Kernel (linear algebra)

text: When is an inner product space, the quotient formula_10 can be identified with the orthogonal complement in of formula_11 This is the generalization to linear operators of the row space, or coimage, of a matrix.


title: Kernel (linear algebra)

text: The notion of kernel also makes sense for homomorphisms of modules, which are generalizations of vector spaces where the scalars are elements of a ring, rather than a field. The domain of the mapping is a module, with the kernel constituting a submodule. Here, the concepts of rank and nullity do not necessarily apply.


title: Kernel (linear algebra)

text: If "V" and "W" are topological vector spaces such that "W" is finite-dimensional, then a linear operator "L": "V" → "W" is continuous if and only if the kernel of "L" is a closed subspace of "V".


title: Kernel (linear algebra)

text: Consider a linear map represented as a "m" × "n" matrix "A" with coefficients in a field "K" (typically formula_12 or formula_13), that is operating on column vectors x with "n" components over "K".


title: Kernel (linear algebra)

text: The kernel of this linear map is the set of solutions to the equation , where 0 is understood as the zero vector. The dimension of the kernel of "A" is called the nullity of "A". In set-builder notation,


title: Kernel (linear algebra)

text: The kernel of a matrix "A" over a field "K" is a linear subspace of K. That is, the kernel of "A", the set Null("A"), has the following three properties:


title: Kernel (linear algebra)

text: Here, a, ... , a denote the rows of the matrix "A". It follows that x is in the kernel of "A", if and only if x is orthogonal (or perpendicular) to each of the row vectors of "A" (since orthogonality is defined as having a dot product of 0).


title: Kernel (linear algebra)

text: The row space, or coimage, of a matrix "A" is the span of the row vectors of "A". By the above reasoning, the kernel of "A" is the orthogonal complement to the row space. That is, a vector x lies in the kernel of "A", if and only if it is perpendicular to every vector in the row space of "A".


title: Kernel (linear algebra)

text: The dimension of the row space of "A" is called the rank of "A", and the dimension of the kernel of "A" is called the nullity of "A". These quantities are related by the rank–nullity theorem


title: Kernel (linear algebra)

text: The left null space, or cokernel, of a matrix "A" consists of all column vectors x such that x"A" = 0, where T denotes the transpose of a matrix. The left null space of "A" is the same as the kernel of "A". The left null space of "A" is the orthogonal complement to the column space of "A", and is dual to the cokernel of the associated linear transformation. The kernel, the row space, the column space, and the left null space of "A" are the four fundamental subspaces associated to the matrix "A".


title: Kernel (linear algebra)

text: It follows that any solution to the equation "Ax = b can be expressed as the sum of a fixed solution v and an arbitrary element of the kernel. That is, the solution set to the equation "Ax = b is


title: Kernel (linear algebra)

text: Geometrically, this says that the solution set to "A"x = b is the translation of the kernel of "A" by the vector v. See also Fredholm alternative and flat (geometry).


title: Kernel (linear algebra)

text: The following is a simple illustration of the computation of the kernel of a matrix (see , below for methods better suited to more complex calculations). The illustration also touches on the row space and its relation to the kernel.


title: Kernel (linear algebra)

text: The kernel of "A" is precisely the solution set to these equations (in this case, a line through the origin in R). Here, since the vector (−1,−26,16) constitutes a basis of the kernel of "A". The nullity of "A" is 1.


title: Kernel (linear algebra)

text: which illustrates that vectors in the kernel of "A" are orthogonal to each of the row vectors of "A".


title: Kernel (linear algebra)

text: These two (linearly independent) row vectors span the row space of "A"—a plane orthogonal to the vector (−1,−26,16).


title: Kernel (linear algebra)

text: With the rank 2 of "A", the nullity 1 of "A", and the dimension 3 of "A", we have an illustration of the rank-nullity theorem.


title: Kernel (linear algebra)

text: For this purpose, given an "m" × "n" matrix "A", we construct first the row augmented matrix formula_35 where is the "n" × "n" identity matrix.


title: Kernel (linear algebra)

text: Computing its column echelon form by Gaussian elimination (or any other suitable method), we get a matrix formula_36 A basis of the kernel of "A" consists in the non-zero columns of "C" such that the corresponding column of "B" is a zero column.


title: Kernel (linear algebra)

text: In fact, the computation may be stopped as soon as the upper matrix is in column echelon form: the remainder of the computation consists in changing the basis of the vector space generated by the columns whose upper part is zero.


title: Kernel (linear algebra)

text: Proof that the method computes the kernel: Since column operations correspond to post-multiplication by invertible matrices, the fact that formula_41 reduces to formula_42 means that there exists an invertible matrix formula_43 such that formula_44 with formula_45 in column echelon form. Thus formula_46 formula_47 and formula_48 A column vector formula_49 belongs to the kernel of formula_50 (that is formula_51) if and only formula_52 where formula_53 As formula_45 is in column echelon form, formula_55 if and only if the nonzero entries of formula_56 correspond to the zero columns of formula_57 By multiplying by formula_58, one may deduce that this is the case if and only if formula_59 is a linear combination of the corresponding columns of formula_60


title: Kernel (linear algebra)

text: If the coefficients of the matrix are exactly given numbers, the column echelon form of the matrix may be computed by Bareiss algorithm more efficiently than with Gaussian elimination. It is even more efficient to use modular arithmetic and Chinese remainder theorem, which reduces the problem to several similar ones over finite fields (this avoids the overhead induced by the non-linearity of the computational complexity of integer multiplication).


title: Kernel (linear algebra)

text: For coefficients in a finite field, Gaussian elimination works well, but for the large matrices that occur in cryptography and Gröbner basis computation, better algorithms are known, which have roughly the same computational complexity, but are faster and behave better with modern computer hardware.


title: Kernel (linear algebra)

text: For matrices whose entries are floating-point numbers, the problem of computing the kernel makes sense only for matrices such that the number of rows is equal to their rank: because of the rounding errors, a floating-point matrix has almost always a full rank, even when it is an approximation of a matrix of a much smaller rank. Even for a full-rank matrix, it is possible to compute its kernel only if it is well conditioned, i.e. it has a low condition number.


title: Kernel (linear algebra)

text: Even for a well conditioned full rank matrix, Gaussian elimination does not behave correctly: it introduces rounding errors that are too large for getting a significant result. As the computation of the kernel of a matrix is a special instance of solving a homogeneous system of linear equations, the kernel may be computed by any of the various algorithms designed to solve homogeneous systems. A state of the art software for this purpose is the Lapack library.


title: Russian entry into World War I

text: The Russian Empire gradually entered World War I during the three days prior to 28th July 1914. This began with Austria-Hungary's declaration of war against Serbia, which was a Russian ally. The Russian Empire sent an ultimatum, via Saint Petersburg, to Vienna, warning Austria-Hungary not to attack Serbia. Following the invasion of Serbia, Russia began to mobilise its reserve army near its border with Austria-Hungary. Consequently, on 31st July, German leadership in Berlin demanded Russian demobilisation. There was no response, which resulted in the German declaration of war on Russia on the same day (1st August 1914). In accordance with its war plan, Germany disregarded Russia and moved first against France, declaring war on 3rd August. Germany sent its main armies through Belgium to surround Paris. The threat to Belgium caused Britain to declare war on Germany on 4th August. The Ottoman Empire soon joined the Central Powers and fought Russia along their border.


title: Russian entry into World War I

text: Historians researching the causes of World War I have emphasised the role of Germany and Austria-Hungary. Scholarly consensus has typically minimised Russian involvement in the outbreak of this mass conflict. Key elements were Russia's defense of Orthodox Serbia, its pan-Slavic roles, its treaty obligations with France, and its concern with protecting its status as a world power. However, historian Sean McMeekin emphasises Russian plans to expand its empire southward and to seize Constantinople (modern-day Istanbul) as an outlet to the Mediterranean Sea.


title: Russian entry into World War I

text: Archduke Franz Ferdinand, the heir to the Austro-Hungarian throne, was assassinated by Bosnian Serbs on 28rh June 1914, due to Austria-Hungary's annexation of the largely Slavic province. Vienna was unable to find evidence that the Serbian state had sponsored this assassination, but one month later, it issued an ultimatum to Serbia, which it assumed would be rejected and thus lead to war. Austria-Hungary deemed Serbia to be deserving of punishment for the assassination. Although Russia had no formal treaty obligation to Serbia, it stressed its desire to control the Balkans and had a long-term perspective toward gaining a military advantage over Germany and Austria-Hungary in the region. Russia had the incentive to delay militarisation and the majority of its leaders wanted to avoid war. However, Russia had yielded French support and feared that a failure to defend Serbia would lead to the loss of Russian credibility, constituting a major political defeat in its goal of controlling the Balkans. Tsar Nicholas II mobilised Russian forces on 30th July 1914 to threaten Austria-Hungary if it invaded Serbia. Christopher Clark believes that the "Russian general mobilisation [of 30th July] was one of the most momentous decisions of the August crisis". The first general mobilisation occurred before the German government declared a state of impending war.


title: Russian entry into World War I

text: Russia's threatening of Germany resulted in military action by German forces, which followed through with its own mobilisation and a declaration of war on 1st August 1914. At the outset of hostilities, Russian forces led offensives against both Germany and Austria-Hungary.


title: Russian entry into World War I

text: Between 1873 and 1887, Russia was allied with Germany and Austria-Hungary in the League of the Three Emperors, and then with Germany in the 1887–1890 Reinsurance Treaty. Both collapsed because of the competing interests of Austria-Hungary and Russia in the Balkans. France took advantage of this, agreeing to the 1894 Franco-Russian Alliance, but Britain viewed Russia with deep suspicion because of the Great Game. In 1800, over separated Russia and British India, but by 1902, it was lessened to with Russian advances into Central Asia. The proximity threatened to bring the two powers into conflict along with the long-held Russian objective of gaining control of the Bosporus Straits, and with it access to the British-dominated Mediterranean Sea.


title: Russian entry into World War I

text: Britain's isolation during the 1899–1902 Second Boer War and defeat in the 1905 Russo-Japanese War led both parties to seek allies. The Anglo-Russian Convention of 1907 settled disputes in Asia and allowed the establishment of the Triple Entente with France, which was largely informal. In 1908, Austria-Hungary annexed the former Ottoman province of Bosnia and Herzegovina, prompting the Russian response of the Balkan League to prevent further Austrian expansion.


title: Russian entry into World War I

text: In the 1912–1913 First Balkan War, Serbia, Bulgaria , and Greece captured most of the remaining Ottoman possessions in Europe. Disputes over their division resulted in the Second Balkan War, in which Bulgaria was comprehensively defeated by its former allies. This defeat turned Bulgaria into a revanchist local power, which fueled a second opportunity to fulfill its national aspirations. This left Serbia as the most important Russian ally in the region.


title: Russian entry into World War I

text: Russia's industrial base and railway network had significantly improved since 1905, although from a relatively low base. In 1913, Nicholas II approved an increase in the Russian Army of over 500,000 men. Although there was no formal alliance between Russia and Serbia, their close bilateral links provided Russia with a route into the crumbling Ottoman Empire, where Germany also had significant interests. Combined with the increase in Russian military strength, both Austria and Germany felt threatened by Serbian expansion. When Austria invaded Serbia on July 28, 1914, Russian Foreign Minister Sergei Sazonov viewed it as an Austro-German conspiracy to end Russian influence in the Balkans.


title: Russian entry into World War I

text: On July 30, Russia declared general mobilization in support of Serbia. The next day, on August 1, Germany declared war on Russia, followed by Austria-Hungary on August 6. Russia and the Entente declared war on the Ottoman Empire in November 1914, after Ottoman warships had bombarded the Black Sea port of Odessa in late October.


title: Russian entry into World War I

text: Most historians agree that generally, Russia's top military leadership was tremendously incompetent. Tsar Nicholas II made all final decisions, but was repeatedly given conflicting advice by his peers, resulting in unsound decision-making throughout his time in power. He set up a deeply flawed organizational structure that proved inadequate for the high pressures and the instant demands of wartime. The British historian David Stevenson, for example, points to the "disastrous consequences of deficient civil-military liaison" in which the civilians and generals were not in contact with each other. The government was entirely unaware of its fatal weaknesses and remained out of touch with public opinion. The Foreign Minister had to warn Nicholas that "unless he yielded to the popular demand and unsheathed the sword on Serbia's behalf, he would run the risk of revolution and the loss of his throne". Nicholas yielded, but nevertheless lost his throne. Stevenson concludes:


title: Russian entry into World War I

text: Foreign Minister Sergei Sazonov was not a powerful figure in the events leading up to Russia's entry into World War 1, nor did he play a consequential role in Russia's decisions following their entry. According to the historian Thomas Otte, "Sazonov felt too insecure to advance his positions against stronger men... Tsar Nicholas II tended to yield rather than to press home his own views... At the critical stages of the July crisis, Sazonov was inconsistent and showed an uncertain grasp of international realities".


title: Russian entry into World War I

text: French Ambassador Maurice Paléologue quickly became influential by repeatedly promising France would go to war alongside Russia, which reflected the position of President Raymond Poincaré.


title: Russian entry into World War I

text: Serious planning for a future war was practically impossible because of the complex rivalries and priorities given to royalty. The main criteria for high command were linkage to the royalty, rather than expertise. The General Staff had expertise but was often outweighed by the elite Imperial Guards, a favorite bastion of the aristocracy that prized throwing parades over planning large-scale military maneuvers. This led to the grand dukes inevitably gaining high command.


title: Russian entry into World War I

text: Russia depended heavily on the French alliance, since a two-front war against Germany was winnable, but not if Russia was alone. The French ambassador, Maurice Paléologue, hated Germany and saw that when war broke out, France and Russia had to be close allies against Germany. His approach agreed with French President Raymond Poincaré. Unconditional French support to Russia was promised in the unfolding crisis with Germany and Austria. Historians debate whether Paléologue exceeded his instructions, but agree that he failed to inform Paris of exactly what was happening, and he did not warn that Russian mobilization might launch a world war.


title: Russian entry into World War I

text: On June 28, 1914, Archduke Franz Ferdinand of Austria was assassinated in Sarajevo, and Tsar Nicholas II vacillated as to Russia's course of action. A relatively-new factor influencing Russian policy was the growth of Pan-Slavism, which identified Russia's duty to all Slavs, especially those who practiced Eastern Orthodox Christianity. The growth of that impulse shifted attention away from the Ottoman Empire and toward the threat posed to the Slavic people by Austria-Hungary. Serbia identified itself as the champion of the Pan-Slavic ideal, and Austria-Hungary planned to destroy Serbia for that reason. Nicholas wanted to defend Serbia, but not to fight a war with Germany. In a series of letters exchanged with Kaiser Wilhelm of Germany (the so-called "Willy and Nicky correspondence"), both cousins proclaimed their desire for peace, and each attempted to get the other to back down. Nicholas desired Russia's mobilization to be only against Austria-Hungary in the hopes of avoiding war with Germany. The Kaiser, however, had pledged to support Austria-Hungary.


title: Russian entry into World War I

text: On July 25, 1914, Nicholas decided to intervene in the Austro-Serbian conflict, a step toward general war. He put the Russian army on "alert" on July 25. Although it was not general mobilization, the German and Austro-Hungarian borders were threatened and looked like military preparation for war. However, the Russian Army had few workable plans and no contingency plans for a partial mobilization. On July 30, 1914, Nicholas took the fateful step of confirming the order for general mobilization, despite being very reluctant.


title: Russian entry into World War I

text: On July 28, Austria-Hungary formally declared war against Serbia. Count Witte told the French Ambassador Maurice Palaeologus that the Russian point of view considered the war to be madness, Slavic solidarity to be simply nonsense and nothing could be hoped by war.


title: Russian entry into World War I

text: On July 30, Russia ordered general mobilization but still maintained that it would not attack if peace talks began. Germany, reacting to the discovery of Russian partial mobilization ordered on July 25, announced its own pre-mobilization posture, the imminent danger of war. Germany told Russia to demobilize within twelve hours. In St. Petersburg, at 7 p.m., the German ultimatum to Russia expired. The German ambassador to Russia met Russian Foreign Minister Sergei Sazonov; asked three times if Russia would reconsider; and delivered the note accepting Russia's war challenge and declaring war on August 1. On August 6, Franz Joseph I of Austria signed the Austro-Hungarian declaration of war against Russia.


title: Russian entry into World War I

text: At the outbreak of war, each of the European powers began to publish selected, and sometimes misleading, compendia of diplomatic correspondence, seeking to establish justification for their own entry into the war and to cast blame on other actors. The first of these color books to appear was the German White Book which appeared on August 4, 1914, the same day as Britain's war declaration. The British Blue Book came out two days later, followed by the Russian Orange Book in mid-August.


title: Russian entry into World War I

text: The outbreak of war on August 1, 1914, found Russia grossly unprepared. The Allies placed their faith in the Russian army. Its pre-war regular strength was 1,400,000, mobilization added 3,100,000 reserves. In every other aspect, however, Russia was unprepared for war. Germany had ten times as much railway track per square kilometer, and Russian soldiers traveled an average of to reach the front, but German soldiers traveled less than a quarter of that distance. Russian heavy industry was not large enough to equip the massive armies that the Tsar could raise, and its reserves of munitions were small. While the German army in 1914 was better equipped than any other man for man, the Russian army was severely short on artillery pieces, shells, motorized transports, and boots.


title: Russian entry into World War I

text: Before the war, Russian planners had completely neglected the critical logistical issue of how the Allies could ship supplies and munitions to Russia. With the Baltic Sea barred by German U-boats and surface ships and the Dardanelles by the guns of Germany's ally, the Ottoman Empire, Russia initially could receive help only via Archangel, which was frozen solid in winter, or via Vladivostok, which was over from the front line. By 1915, a new rail line was begun which gave access to the ice-free port of Murmansk by 1917.


title: Russian entry into World War I

text: The Russian High Command was greatly weakened by the mutual contempt between War Minister Vladimir Sukhomlinov and Grand Duke Nicholas, who commanded the armies in the field. However, an immediate attack was ordered against the German province of East Prussia. The Germans mobilized there with great efficiency and completely defeated the two Russian armies that invaded. The Battle of Tannenberg, where the entire Russian Second Army was annihilated, cast an ominous shadow over the empire's future. The loyal officers lost were the very ones that were needed to protect the dynasty. The Russian armies had some success against both the Austro-Hungarian and the Ottoman Armies, but they were steadily pushed back by the German Army. In September 1914, to relieve pressure on France, the Russians were forced to halt a successful offensive against Austria-Hungary in Galicia to attack German-held Silesia.


title: Russian entry into World War I

text: The main Russian goal was focused on the Balkans and especially taking control of Constantinople (Istanbul). The Ottoman entry into the war opened up new opportunities, but Russia was much too hard-pressed to take advantage of them. Instead, the government incited Britain and France to the action at Gallipoli, which failed badly. Russia then incited a rebellion by the Armenians, who were massacred in one of the great atrocities of the war, the Armenian genocide. The combination of poor preparation and poor planning destroyed the morale of Russian troops and set the stage for the collapse of the entire regime in early 1917.


title: Russian entry into World War I

text: Gradually, a war of attrition set in on the vast Eastern Front; the Russians were facing the combined forces of Germany and Austria-Hungary and suffered staggering losses. General Anton Denikin, retreating from Galicia wrote:


title: Russian entry into World War I

text: Historians on the origin of the First World War have emphasized the role of Germany and Austria-Hungary. The consensus of scholars includes scant mention of Russia and only brief mentions of Russia's defense of Serbia, its pan-Slavic roles, its treaty obligations with France, and its concern for protecting its status as a great power.


title: Russian entry into World War I

text: However, the historian Sean McMeekin has emphasized Russia's aggressive expansionary goal to the south. He argues that for Russia the war was ultimately about the Ottoman Empire and that the Foreign Ministry and Army were planning a war of aggression from at least 1908 and perhaps even 1895. He emphasizes that the immediate goal was to seize Constantinople and an outlet to the Mediterranean by control of the Dardanelles and Bosporus straits. Reviewers have generally been negative of McMeekin revisionist interpretation.


The February 13–17, 2021 North American winter storm, unofficially referred to as "Winter Storm Uri" by the Weather Channel, was a major winter and ice storm that had widespread impacts across the United States, Northern Mexico, and parts of Canada from February 13 to 17. The storm started out in the Pacific Northwest and quickly moved into the Southern United States, before moving on to the Midwestern and Northeastern United States a couple of days later.


title: February 13–17, 2021 North American winter storm

text: The storm resulted in the National Weather Service issuing various winter weather alerts impacting over 170 million Americans. Over 9.9 million people in the U.S. and Mexico experienced blackouts, many due to a major power crisis in Texas, which became the largest in the U.S. since the Northeast blackout of 2003. The storm contributed to a severe cold wave that affected most of North America. The storm also brought severe destructive weather to Southeastern United States, including several tornadoes. On February 16, there were at least 20 direct fatalities and 13 indirect fatalities attributed to the storm; by January 2, 2022, the death toll had risen to at least 290, including 276 people in the United States and 14 people in Mexico. The system is estimated to have cost over $196.5 billion (2021 USD) in damages, including at least $195 billion in the United States and over $1.5 billion in Mexico, making it the costliest winter storm on record, as well as the costliest natural disaster recorded in the United States. It is also the deadliest winter storm in North America since the 1993 Storm of the Century, which killed 318 people.


text: On February 13, a frontal storm developed off the coast of the Pacific Northwest and moved ashore, before moving southeastward, with the storm becoming disorganized in the process. During this time, the storm reached a minimum pressure of over the Rocky Mountains. On the same day, The Weather Channel gave the storm the unofficial name "Winter Storm Uri", due to the expected impacts from the storm; the Federal Communications Commission later adopted the name in their reports after February 17. From February 12 to 13, a trough dipped southward from Northern California into northern Mexico, which channeled moisture from Texas towards the storm, as the system moved southeastward. Over the next couple of days, the storm began to develop as it entered the Southern United States and moved into Texas. From February 13 to 14, a second, much larger trough developed over Central United States, aided by a southward shift from the polar vortex, while the winter storm moved into Texas. The trough became fully developed by February 15, channeling significant amounts of moisture into the winter storm and also contributing to a historic cold wave that affected most of the Central and Eastern United States. Winds in the jet stream reached 170 mph (275 km/h) around the trough. On February 15, the system developed a new surface low off the coast of the Florida Panhandle, as the storm turned northeastward and expanded in size.


text: On February 16, the storm developed another low-pressure center to the north as the system grew more organized, while moving towards the northeast. Later that day, the storm broke in half, with the newer storm moving northward into Quebec, while the original system moved off the East Coast of the U.S. By the time the winter storm exited the U.S. late on February 16, the combined snowfall from the multiple winter storms within the past month had left nearly 75% of the contiguous United States covered by snow, which was the largest amount of snow cover seen in the United States since early 2003. On February 17, the storm's secondary low dissipated as the system approached landfall on Newfoundland, intensifying in the process. At 12:00 UTC that day, the storm's central pressure reached , as the center of the storm moved over Newfoundland. On the same day, the storm was given the name "Belrem" by the Free University of Berlin. The storm continued to strengthen as it moved across the North Atlantic, with the storm's central pressure dropping to by February 19. On February 20, the storm developed a second-low pressure area and gradually began to weaken, as it moved northwestward towards Iceland. Afterward, the storm turned westward and moved across southern Greenland on February 22, weakening even further as it did so. The storm then stalled south of Greenland, while continuing to weaken, before dissipating on February 24.


text: On February 14, the expected impacts from the storm resulted in over 170 million Americans being placed under various winter weather alerts across the United States, which saw the largest portion of the country covered by winter weather alerts in 15 years. Over 120 million of those people were placed under winter storm warnings or ice storm warnings by the National Weather Service. The winter storm caused power grids to fail across the U.S., causing blackouts for over 5.2 million homes and businesses, the vast majority of which were in the state of Texas, which became one of the largest blackout events in modern U.S. history, the largest one since the Northeast blackout of 2003. The storm left at least 276 people dead across the United States, with 246 of them in Texas. The initial death toll had been estimated at 70 before it was later revised upward, after more information was collected. A BuzzFeed study in May 2021 estimated that the winter storm may have killed a total of 702 people in Texas, which would add hundreds of deaths to the official death toll if verified. The system was estimated by NOAA to have cost $21 billion in damage in the United States, making it the costliest winter storm in U.S. history. Austin County and Travis County officials estimated that the winter storm caused at least $195 billion in damage in Texas, making the winter storm the single-costliest natural disaster in the history of Texas and the United States as a whole. Some insurance firms had estimated a damage total as high as $195–295 billion.


text: The winter storm was the second of the two snowstorms that swept through the region within a one-week period. of snow in Seattle, Washington compounded the previous storm. This was the largest two-day snowfall recorded in Seattle since 1972.


text: The Portland metro area was hit very hard by the storm, which brought a mix of snow and ice to the region. of snow fell at Portland International Airport on February 12–13, the most snow to fall over this city in a two-day period since 1968. Over 270,000 people were left without power in the region. Governor Kate Brown declared a state of emergency. Four people were killed in Oregon, due to Carbon monoxide poisoning.


text: The storm brought heavy snow and bitterly cold temperatures to Colorado and New Mexico. Snow amounts in Colorado ranged from a few inches in the north to over in the San Juan Mountains in northern New Mexico and southern Colorado. In New Mexico, the storm system brought a combination of heavy snow, strong winds, and bitterly cold temperatures. On February 14th, a Blizzard Warning was issued for the Albuquerque metro area due to strong winds exceeding 50 mph, cold temperatures, and blowing snow. Meanwhile, Winter Storm Warnings were issued for much of the rest of New Mexico. Up to two feet of snow fell in the mountains of northern and central New Mexico. Snow amounts in the Albuquerque metro area ranged from . Interstate 40 through the Albuquerque metro area was closed for several hours due to numerous motor vehicle crashes caused by the icy conditions. Southern New Mexico received up to two inches of snow accumulation, with locally higher amounts in the mountains.


text: With the threat of icing, the Texas Department of Transportation (TxDOT) pre-treated roadways, using a brine-salt mix, across six Southeast Texas counties. For the first time on record, the National Weather Service (through its 13 regional offices serving Texas and adjoining portions of Oklahoma, New Mexico, Arkansas and Louisiana) issued Winter Storm Warnings for all 254 counties in the state. In addition, Houston saw their first ever wind chill warning, as wind chills dipped to .


text: On February 14–15, the storm dropped prolific amounts of snow across Texas and Oklahoma. As a result of the winter storm and a concurrent cold wave, power grids—unable to sustain the higher-than-normal energy and heating demand from residential and business customers—failed across the Texas Interconnection; at the peak of the outages, at least 4.5 million Texas residents were left without electricity. Two of the electricity reliability commissions servicing the Southern U.S., the Southwest Power Pool (SPP) and the Electric Reliability Council of Texas (ERCOT), ordered rolling blackouts for 14 states amid the frigid temperatures, in an attempt to manage the strain on the power grid and prevent widespread, long-duration blackouts. The controlled outages were initiated after the Southwest Power Pool declared Level 3 Emergency Energy Alerts on both February 15 and 16; the SPP and ERCOT faced criticism by government officials and residents in the region for the limited advanced notice of the outages, and for not outlining the specific areas serviced by SPP partner utilities that would be affected.


text: At one point during the rolling outages, over 4.2 million people across the south-central states were left without power, with over 3.5 million of them in Texas alone. The rolling blackouts led to calls by Governor Greg Abbott for the Texas Legislature to conduct investigations into preparations and decisions undertaken by ERCOT in advance of the storm. Some of the blackouts were initiated as several cities throughout the Central and Southern Plains experienced record overnight low temperatures: on February 16 alone, daily record lows were broken in Oklahoma City (, the city's coldest temperature since 1899 and its second-coldest on record), Dallas (, the city's coldest temperature since 1930 and its second-coldest on record), Houston (, the city's coldest temperature since 1989), San Antonio (, the city's coldest temperature since 1989) and Little Rock (, the city's coldest temperature since 1989), with all-time low temperatures being set in Fayetteville, Arkansas () and Hastings, Nebraska ().


text: Rolling blackouts, longer-duration power outages and ice accretion caused by the precipitation and unusually cold temperatures (for the region's climate) caused widespread disruptions to water distribution systems across the Southern Plains. Water line breaks occurred in many areas, and power disruptions impacted water treatment plants in parts of the region that forced several cities—including Houston, San Antonio, Fort Worth, Abilene, Austin, Killeen and Arlington, Texas; and Shreveport, Louisiana—to enact residential boil-water orders (i.e., to boil drinking water for one minute in order kill bacteria and other pathogens); By February 18, more than 13 million people in Texas lived in areas covered by boil-water advisories. In cases where residents had no energy sources to heat water, purchasing bottled water was advised; in Houston, this led to shortages of bottled water in grocery stores. In addition, pipe bursts caused significant damage to numerous residences in the Dallas area and other areas of North Texas.


text: After consulting Dallas Mayor Eric Johnson, two NHL games between the Nashville Predators and the Dallas Stars that were scheduled for the evenings of February 15 and 16 at American Airlines Center were postponed. In contrast, the Oklahoma City Thunder opted to hold their February 16 home game against the Portland Trail Blazers as scheduled, even as most other buildings in Downtown Oklahoma City decided to turn off lighting and electrical equipment overnight to reduce strain on the city's power grid; the NBA team stated that Chesapeake Energy Arena would take steps to conserve power while the game was being played, including turning off concourse lighting, video panels, exterior signage and most outdoor lighting.


text: Due to the deregulated electricity market and the spike in demand, since February 10, wholesale electricity prices have gone up in some places by 10,000 percent. As a result, some Texans are receiving exceptionally expensive electric bills as high as $450 for one day of use. On February 17, U.S. Senator Ted Cruz (R-TX) stirred controversy when he was filmed boarding an airplane to Cancún, Mexico with his family. He returned to Houston the following day, and admitted he had scheduled the vacation to avoid freezing conditions inside their home.


text: In Oklahoma, winter storm warnings were issued for all 77 counties in the state ahead of the storm by National Weather Service offices in Norman, Tulsa, Amarillo and Shreveport. Governor Kevin Stitt also issued a statewide winter weather State of Emergency on February 12, as the state was already dealing with effects from minor winter weather events and prolonged sub-freezing temperatures from the days prior. Widespread areas of were recorded throughout the state with locally higher amounts in some areas. Roosevelt saw of snow, the highest total measured in the state during the event.


text: The heavy, blowing snow caused massive travel issues across the state on February 14. By 5:20 p.m. CST that day, the Oklahoma Highway Patrol had responded to 56 non-injury collisions, 24 injury collisions, and 116 motorist assists. A fiery crash involving multiple vehicles, including two semi-trucks, shut down the Turner Turnpike near Hiwassee Road in northeastern Oklahoma County, with westbound traffic being diverted to the Kickapoo Turnpike and eastbound traffic being diverted to I-35. Another vehicle collision on I-35 near Braman caused one fatality. The record cold temperatures during the event also caused a dam at Lake Overholser to completely freeze over.


text: By February 16, the storm had killed at least 17 people across the South. By February 18, the death toll rose to at least 47. At least 10 people in Texas died in weather-related incidents since February 14, including a mother and a child due to carbon monoxide poisoning. By January 2, 2022, the Texas State Government revised the official death toll in Texas to 246. Nine other people in the South, outside of Texas, have died as a result of the system or through indirect storm-related incidents. According to a BuzzFeed study in May 2021, based on the excess mortalities in Texas in February 2021, the actual death toll of the winter storm may range from 426 to 978 in Texas, with a mean estimate of 702, which would add hundreds of deaths to the official death toll, if verified. The official death toll was modified in December 2021 with the Texas Department of State Health Services announcing a death toll of 246.


text: The storm was also partially responsible for a nationwide chicken shortage, due to the freezing temperatures, widespread power and water outages that lasted days.


text: Chicago along with other cities in northern Illinois received up to of snow along with winds up to . Indianapolis, Indiana received about 7 inches of snow as well as Detroit, Michigan also had 7 inches of snow. Toledo, Ohio received of snow, the third-highest two-day snowfall record, and the highest since 1912. Other Northern Ohio cities received up to of snow while cities in the central part received up to of snow like in Columbus, Ohio.


text: A severe weather outbreak struck the Southeastern United States on February 15, with large hail, damaging winds, and six tornadoes affecting five states. An EF2 tornado destroyed two homes and damaged trees near Damascus, Georgia, injuring five people. A more destructive high-end EF3 tornado struck the Ocean Ridge Plantation neighborhood near Sunset Beach, North Carolina, causing major damage to many homes, some of which were leveled or swept away, before moving into rural areas and damaging or snapping hundreds of trees. This tornado killed three and injured 10.


text: The tornado touched down at the north edge of Sunset Beach, just north of the border with South Carolina, damaging numerous pine trees and limbs at EF0 intensity as it crossed NC 179, before rapidly intensifying to EF2 strength as it neared NC 904. The storm was not tornado-warned immediately and a warning wasn't issued until after the tornado touched down and began causing damage. As the tornado crossed the road, a large metal building was destroyed and a number of RVs were overturned. Still rapidly strengthening, the tornado entered Grissettown and struck the Ocean Ridge Plantation subdivision at its peak intensity of high-end EF3. A community garden center and two homes were leveled at this location, one of which was swept completely away. This home was well-constructed, but built on a block foundation, and vehicles parked at the site were moved only short distances. Dozens of other nearby homes were damaged, some of which sustained loss of roofs and exterior walls. Many large trees were snapped and denuded in the subdivision, and a car was overturned. All three fatalities occurred in the Ocean Ridge Plantation subdivision. The tornado then abruptly weakened, but reached its maximum width as it crossed U.S. 17 between Grissettown and Cool Run as it exited Ocean Ridge Plantation at EF1 strength, rolling a double-wide mobile home on the north side of the highway. As the tornado continued northeast, it reintensifed to EF2 strength, causing major damage to several homes and snapping hundreds of trees. It then inflicted a continuous path of tree damage through forest and swamp land, crossing NC 130 and NC 211. The tornado finally lifted east of NC 211. It was the deadliest single tornado in Southeastern North Carolina since an F3 touched down on November 16, 2006, and the first deadly tornado in Brunswick County. With this tornado causing 3 deaths, this became the 6th year in a row to see a tornadic fatality in February.


text: The winter storm strained the power grids in northern Mexico, leading to cascading blackouts for 4.7 million homes and businesses in Mexico. Temperatures as low as were recorded, as shortages of natural gas led to blackouts in Nuevo León, Coahuila, Tamaulipas, and Chihuahua along the border with Texas. At least 14 people died in Ciudad Juárez, Chihuahua; Río Bravo and Matamoros, Tamaulipas; and Monterrey, Nuevo León; due to the winter storm. President Andrés Manuel López Obrador (AMLO) said on February 17 that Mexico would increase the use of oil and coal to produce electricity, as well as purchase three shiploads of natural gas to deal with power shortages. He also warned that periodic local outages would continue through February 21. Local authorities mentioned that no hospitals had been left without electricity at any time. The storm was estimated to have caused over $1.5 billion (2021 USD) in damages in Mexico.