Tara Westover (born September 27, 1986) is an American memoirist, essayist and historian. Her memoir Educated (2018) debuted at No. 1 on The New York Times bestseller list and was a finalist for a number of national awards, including the LA Times Book Prize, PEN America's Jean Stein Book Award, and two awards from the National Book Critics Circle Award. The New York Times ranked Educated as one of the 10 Best Books of 2018. Westover was chosen by Time magazine as one of the 100 most influential people of 2019.

Early life and education
Westover was the youngest of seven children born in Clifton, Idaho (population 259) to Mormon survivalist parents. She has five older brothers and an older sister. Her parents were suspicious of doctors, hospitals, public schools, and the federal government. Westover was born at home, delivered by a midwife, and was never taken to a doctor or nurse. She was not registered for a birth certificate until she was nine years old. Their father resisted getting formal medical treatment for any of the family. Even when seriously injured, the children were treated only by their mother, who had studied herbalism and other methods of alternative healing.

All the siblings were loosely homeschooled by their mother. Westover has said an older brother taught her to read, and she studied the scriptures of the Church of Jesus Christ of Latter-day Saints. But she never attended a lecture, wrote an essay, or took an exam. There were few textbooks in their house.

As a teenager, Westover began to want to enter the larger world and attend college. She purchased textbooks and studied independently in order to score well on the ACT Exam. She gained admission to Brigham Young University and was awarded a scholarship, although she had no high school diploma. After a difficult first year, in which Westover struggled to adjust to academia and the wider society there, she became more successful and graduated with honors in 2008.

She then earned a Master's degree from the University of Cambridge at Trinity College as a Gates Cambridge Scholar, and was a visiting fellow at Harvard University in 2010. She returned to Trinity College, Cambridge, where she earned a doctorate in intellectual history in 2014. Her thesis is entitled "The Family, Morality and Social Science in Anglo-American Cooperative Thought, 1813–1890".

In 2009, while a graduate student at Cambridge, Westover told her parents that for many years (since age 15), she had been physically and psychologically abused by an older brother. Her parents denied her account and suggested that Westover was under the influence of Satan. The family split over these events. Westover wrote about the estrangement, and her unusual path to and through university education in her 2018 memoir, Educated.

Career
Westover was Fall 2019 A.M. Rosenthal Writer in Residence at the Shorenstein Center at Harvard Kennedy School. She was selected as a Senior Research Fellow at Harvard Kennedy School at Harvard University for Spring 2020.

Westover has written for The New York Times and BBC News.<ref name="bbc/53078330">{{cite news |last1=Westover |first1=Tara |title=Rethink: Tara Westover says Build a world where we can be one people' |url=https://www.bbc.com/news/world-53078330 |access-date=9 November 2022 |work=BBC News |date=24 June 2020}}</ref>

Works
Educated: A Memoir

In 2018, Penguin Random House published Westover's Educated: A Memoir, which tells the story of her struggle to reconcile her desire for education and autonomy with her family's rigid ideology and isolated life. The coming-of-age story was a No. 1 New York Times bestseller, and was positively reviewed by the New York Times, The Atlantic Monthly, USA Today, Vogue, and The Economist, among others.

, Educated has spent two years in hardcover on the New York Times bestseller list and is being translated into 45 languages. The book was voted the No. 1 Library Reads pick by American librarians, and in August 2019, it had been checked out more frequently than any other book through all New York Public Library's 88 branches. As of December 2020, Educated has sold more than 8 million copies.

Through their attorney, the family has disputed some elements of Westover's book, including her suggestion that her father may have bipolar disorder and that her mother may have suffered a brain injury that resulted in reduced motor skills.

 Awards and recognition
Westover's book earned her several awards, and other recognition.

 Named the Book of the Year by the American Booksellers Association
 Finalist for the John Leonard Prize from the National Book Critics Circle
 Finalist for the Autobiography Award from the National Book Critics Circle
 Finalist for the LA Times Book Prize in Biography
 Finalist for PEN/America's Jean Stein Award
 Finalist for the American Booksellers Association Audiobook of the Year Award
 Finalist for Barnes & Noble's Discover Great Writers Award
 One of the New York Times' 10 Best Books of 2018
 Long-listed for the Carnegie Medal of Excellence
 Winner of the Goodreads Choice Award for Autobiography
 Winner of the Audie Award for Autobiography/Memoir
 Alex Award from the American Library Association
 Named an 'Amazing Audiobook for Young Adults' by the American Library Association
 Amazon Editors' pick for the Best Book of 2018
 Apple's Best Memoir of the Year
 Audible's Best Memoir of the Year
 Hudson Group Best Book of the Year
 President Barack Obama's pick for summer reading and his Favorite Books of the Year list
 Bill Gates's Holiday Reading list
 Westover chosen by Time Magazine as one of the 100 most influential people of 2019
 Educated named one of the Best Books of the year by The Washington Post, Oprah Magazine, Time, NPR, Good Morning America, The San Francisco Chronicle, The Guardian, The Economist, The Financial Times, The New York Post, The Skimm, Bloomberg, Real Simple, Town & Country, Bustle, Publishers Weekly, The Library Journal, Book Riot, and the New York Public Library.
 Featured speaker, Seattle Arts & Lectures, 2019
 New York Historical Society Women in Public Life Award
 James Joyce Award
 Evans Handcart Award

 Personal life
Westover lives in London.

References

External links

Tara Westover, After Words,'' C-SPAN

21st-century American memoirists
American women memoirists
21st-century American women writers
21st-century American historians
American women historians
Survivalism in the United States
Alumni of Trinity College, Cambridge
Brigham Young University alumni
Writers from Idaho
1986 births
Living people
Memoirists from Idaho

Tara Westover


The mass murders in Tykocin occurred on 25 August 1941, during World War II, where the local Jewish population of Tykocin (Poland) was killed by German Einsatzkommando.

Background
The town of Tykocin was conquered by Nazi Germany during the Soviet and German invasion of Poland pursuant to their secret agreement known as the Molotov–Ribbentrop Pact. At the end of September 1939, the area was transferred by the Nazis to the Soviet Union in accordance with the German–Soviet Boundary Treaty. In June 1941, the town was taken by the Germans in Operation Barbarossa.

The Germans initially bypassed the town; local Poles affiliated with the National Democracy (Endecja) movement who prior to the war had organized boycotts of Jews prior to the war engaged in systematic looting of the Jewish homes in the town.

According to the testimony of survivor Menachem Turek, the Germans installed Jan Fibich, a local ethnic German, as mayor. Fibich, aided by Edmund Wiśniewski, prepared a list of alleged Jewish communists, which included almost all of Jewish youth.

Massacre

On the morning of 24 August, the Germans announced that Jews should report the next day, to the town square. At the time there were approximately 1,400 Jews in Tykocin. On 25 August the Jews were rounded up in the square by the Germans with help from Polish police. In order to placate the crowd the Germans told the Jews that they were going to be transported to Białystok Ghetto. The men were marched to a nearby village and from there in trucks to the pits in Łopuchowo forest, and murdered. The women and infirm were driven by truck to the pits and murdered. The old, infirm, and other people who did not show up on 25 August, some 700 in total, were driven to the pits on 26 August and shot.

In a West German investigation, a Jewish witness identified SS-Obersturmführer Hermann Schaper, who commanded SS Einsatzkommando, as the man directing the shootings.

Some 150 Jews managed to escape the massacre, however most were handed over to the Germans. Some reached Białystok Ghetto, and shared the fate of the Jews there.

Commemoration
At the site of the massacre in the forest there are four monuments. The first, a communist era Polish monument, contains no reference to Jews. The second and third were erected by American Jews. The fourth, erected due to the efforts of Abraham Kapice, is in the shape of the Star of David and inscribed in Hebrew so that Israeli school children will be able to read it.

See also
 Jedwabne pogrom
 Wąsosz pogrom

References

1941 in Poland
Holocaust massacres and pogroms in Poland
August 1941 events
Mass murder in 1941
1941 in Judaism

Mass murders in Tykocin


Jane de Almeida, born in Para de Minas, Brazil, is a researcher, director, artist, curator and theoretician.

Biography
Raised in Minas Gerais de Almeida started to study psychology and cinematography in Belo Horizonte. Currently she is based in São Paulo, Brazil.

de Almeida works belong in the following categories: experimental film, video art, contemporary art and computer art.

de Almeida is an interdisciplinary researcher, professor and independent curator. She has published several articles and book chapters such as "On Elephants, Telescopes, Microscopes, Cartography, Aliens, and Computers: Notes on Scalability in Alexander Kluge's Works" In: Stichwort: Kooperation. Keiner ist alleine schlau genug (Alexander Kluge-Jahrbuch, Verlag, 2017), "The dot and the line" for A companion to Contemporary Drawing (Wiley, 2020) and organized the books CineGrid: cinematic futures (Cinusp, 2017) and Harun Farocki: Programming the Visible (bilingual, Cinusp, 2018) with articles by Thomas Elsaesser, Erika Balsom, Alfredo Suppia, Harun Farocki, Patricia Moran among others. She curated the first 4K films exhibition in Brazil at the FILE (Electronic Language International Festival) and organized the first transmission from Latin America to the US (UCSD) and Japan (Keio University) of a 4k film over a 10 Gbit/s photonic network at FILE 2009 Transcontinental. Currently she coordinates the Advanced Visualization Working Group (Content) for the Brazilian National Education and Research Network (RNP). Jane is the director of the short films 2014k (4k 3D, 2010, 10 mins) screened at Casa Brasil during the FIFA Soccer World Cup in Johannesburg and San Diego), StereoEssays: Five or Six Essays in Search of a Narrative (4k 3D, 2011, 16 min), which has been exhibited in venues such as the Maison de L'Amérique Latine in Paris, CineGrid in San Diego, the Sesc Film Festival of Arts in São Paulo and the Tecnofagias Art Exhibition (in loop for 2 months) at the Tomie Ohtake Institute for Contemporary Art. She has also directed the short films Openmouthed (4k, 2014, 3 mins), The Diving (4k, 2014, 2 mins) and Pixel Race (4k, 2015, 9 mins), which were screened at CineGrid in San Diego and Tokyo. She was co-scriptwriter for the films 500 Souls (2004, with several national and international awards) and Invenção de Limite (awarded with the Hubert Bals Fund). She directed the film-essay LOGA - Mars Projections about the planet Mars and the 3D city-symphony film StereoEssays São Paulo. Jane holds a Ph.D. in Communication and Semiotics.

de Almeida followed her artistic career using a large variety of film materials, forms and techniques: installation, film and video.

Research and teaching
de Almeida has taught at numerous universities and cultural centers, among others at the University of California, San Diego in San Diego, at the São Paulo Museum of Art and at Pontifícia Universidade Católica de São Paulo, in São Paulo, Brazil. Jane de Almeida was artist in residence at the Arthur C. Clarke Center for Human Imagination, Visiting Fellow in the Department of History of Art and Architecture at Harvard University (2005), visiting scholar in the Department of Philosophy at Boston College (1999), guest researcher at Medialab-Prado (2006), visiting scholar in the Department of Communication and lecturer in the Visual Arts Department at University of California, San Diego (2007/2008/2018).

Curatorial activities
de Almeida curated art exhibitions and film festivals for art spaces, galleries and museums such as Off the Radar at University of California, San Diego Visual Arts Gallery, Harun Farocki: Programming the Visible at Paço das Artes, In the Beginning all was Black about Aldo Tambellini's work, Ulla, Ulla, Martians! at Casanova Gallery, the Dziga Vertov Group, Alexander Kluge: the fifth act, Metacinemas and Aisthesis at Centro Cultural Banco do Brasil, accompanied with catalogs or comprehensive books.

Selected bibliography

 Passages on Brazilian scientific cinema. Public Understanding of Science, 26(5), 579–595.
 Apontamentos sobre o Cinema Científico: Arlindo Machado. Significação: Revista De Cultura Audiovisual, 49(57), 41-60.
 The dot and the line. Drawing amongst computers. In: A Companion to Contemporary Drawing. London, Wiley, 2020.
 Harun Farocki: programming the visible. São Paulo, CINUSP, 2018.
 On Elephants, Telescopes, Microscopes, Cartography, Aliens, and Computers: Notes on Scalability in Alexander Kluge's Works. In: Stichwort: Kooperation. Keiner ist alleine schlau genug (Alexander Kluge-Jahrbuch, Verlag, 2017).
 CineGrid: cinematic futures. São Paulo, CINUSP, 2017.
 Interview with Yve-Alain Bois
 Interview with Jean-Pierre Gorin
 Alexander Kluge: o quinto ato. São Paulo, CosacNaify, 2007.
 Dziga Vertov Group. São Paulo, witz edições, 2005.

Films

 Loga - Mars Projections
 StereoEssays Rio de Janeiro
 StereoEssays São Paulo
 Openmouthed (4k, 2014, 3 mins)
 The Diving (4k, 2014, 2 mins)
 Pixel Race (4k, 2015, 9 mins)
 500 Souls (scriptwriter)

Decorations and awards
 1994: Hubert Bals Fund

External links
 Website of Jane de Almeida
 Jane de Almeida at University of California
 Laboratory of Scientific Image at UNICAMP
 Laboratory of Cinematic Arts and Visualization
 In the Beginning all was Black exhibition about Aldo Tambellini's works
 Ulla, Ulla, Ulla, Ulla! Martians, Aliens, Intergalactics and Humans exhibition article by Bruce Sterling for Wired (magazine).
 Jane de Almeida at Itaú Cultural Encyclopedia

1964 births
Living people
People from Minas Gerais
 University of California, San Diego faculty
 Brazilian people of Portuguese-Jewish descent
Harvard University alumni
Brazilian film directors
Brazilian experimental filmmakers

Jane de Almeida


Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean or expected value). A low standard deviation means that most of the numbers are close to the average, while a high standard deviation means that the numbers are more spread out.

The reported margin of error is usually twice the standard deviation. Scientists commonly report the standard deviation of numbers from the average number in experiments. They often decide that only differences bigger than two or three times the standard deviation are important. Standard deviation is also useful in money, where the standard deviation on interest earned shows how different one person's interest earned might be from the average.

Many times, only a sample, or part of a group can be measured.  Then a number close to the standard deviation for the whole group can be found by a slightly different equation called the sample standard deviation, explained below. In which case, the standard deviation of the whole group is represented by the Greek letter , and that of the sample by .

Basic example
Consider a group having the following eight numbers:

These eight numbers have the average (mean) of 5:

To calculate the population standard deviation, first find the difference of each number in the list from the mean. Then square the result of each difference:

Next, find the average of these values (sum divided by the number of numbers).  Last, take the square root:

The answer is the population standard deviation. The formula is only true if the eight numbers we started with are the whole group. If they are only a part of the group picked at random, then we can obtain an unbiased estimate of what the population standard deviation is by dividing by  instead of  in the bottom (denominator) of the formula above. Then the answer is the (bias-corrected) sample standard deviation. This is called the Bessel's Correction. We often use this correction because the sample variance, i.e., the square of the sample standard deviation, is an unbiased estimator of the population variance, in other words, the expected value or long-run average of the sample variance equals the population (true) variance. However, it is not the case that the sample standard deviation is an unbiased estimator of the population standard deviation. Although Bessel's correction is an unbiased estimate of the variance, this estimate does have a higher mean square error than the biased estimate, or in other words, the biased estimate (that is, dividing by n rather than n-1) is on average closer to the true value.

More examples
Here is a slightly harder, real-life example: The average height for grown men in the United States is 70", with a standard deviation of 3". A standard deviation of 3" means that most men (about 68%, assuming a normal distribution) have a height between 3" taller and 3" shorter than the average (67"–73") — one standard deviation. Almost all men (about 95%) have a height between 6" taller and 6" shorter than the average (64"–76") — two standard deviations. Three standard deviations include all the numbers for 99.7% of the sample population being studied. This is true if the distribution is normal (bell-shaped).

If the standard deviation were zero, then all men would be exactly 70" tall. If the standard deviation were 20", then some men would be much taller or much shorter than the average, with a typical range of about 50"–90".

For another example, each of the three groups {0, 0, 14, 14}, {0, 6, 8, 14} and {6, 6, 8, 8} has an average (mean) of 7. But their standard deviations are 7, 5, and 1. The third group has a much smaller standard deviation than the other two because its numbers are all close to 7. In general, the standard deviation tells us how far from the average the rest of the numbers tend to be, and it will have the same units as the numbers themselves. If, for example, the group {0, 6, 8, 14} is the ages of a group of four brothers in years, the average is 7 years and the standard deviation is 5 years.

Standard deviation may serve as a measure of uncertainty. In science, for example, the standard deviation of a group of repeated measurements helps scientists know how sure they are of the average number. When deciding whether measurements from an experiment agree with a prediction, the standard deviation of those measurements is very important. If the average number from the experiments is too far away from the predicted number (with the distance measured in standard deviations), then the theory being tested may not be right. For more information, see prediction interval.

Application examples
Understanding the standard deviation of a set of values allows us to know how large a difference from the "average" (mean) is expected.

Weather
As a simple example, consider the average daily high temperatures for two cities, one inland and one near the ocean. It is helpful to understand that the range of daily high temperatures for cities near the ocean is smaller than for cities inland. These two cities may each have the same average daily high temperature. However, the standard deviation of the daily high temperature for the coastal city will be less than that of the inland city .

Sports
Another way of seeing it is to consider sports teams. In any sport, there will be teams that are good at some things and not at others. The teams that are ranked highest will not show a lot of differences in abilities. They do well in most categories. The lower the standard deviation of their ability in each category, the more balanced and consistent they are. Teams with a higher standard deviation, however, will be less predictable. A team that is usually bad in most categories will have a low standard deviation. A team that is usually good in most categories will also have a low standard deviation. However, a team with a high standard deviation might be the type of team that scores many points (strong offense) but also lets the other team score many points (weak defense).

Trying to know ahead of time which teams will win may include looking at the standard deviations of the various team "statistics." Numbers that are different from expected can match strengths vs. weaknesses to show what reasons may be most important in knowing which team will win.

In racing, the time a driver takes to finish each lap around the track is measured. A driver with a low standard deviation of lap times is more consistent than a driver with a higher standard deviation. This information can be used to help understand how a driver can reduce the time to finish a lap.

Money
In money, standard deviation may mean the risk that a price will go up or down (stocks, bonds, property, etc.). It can also mean the risk that a group of prices will go up or down (actively managed mutual funds, index mutual funds, or ETFs). Risk is one reason to make decisions about what to buy. Risk is a number people can use to know how much money they may earn or lose. As risk gets larger, the return on an investment can be more than expected (the "plus" standard deviation). However, an investment can also lose more money than expected (the "minus" standard deviation).

For example, a person had to choose between two stocks. Stock A over the past 20 years had an average return of 10 percent, with a standard deviation of 20 percentage points (pp). Stock B over the past 20 years had an average return of 12 percent but a higher standard deviation of 30 pp. Thinking about the risk, the person may decide that Stock A is the safer choice. Even though they may not make as much money, they probably will not lose much money either. The person may think that Stock B's 2 point higher average is not worth the additional 10 pp standard deviation (greater risk or uncertainty of the expected return).

Rules for normally distributed numbers

Most math equations for standard deviation assume that the numbers are normally distributed. This means that the numbers are spread out in a certain way on both sides of the average value. The normal distribution is also called a Gaussian distribution because it was discovered by Carl Friedrich Gauss. It is often called the bell curve because the numbers spread out to make the shape of a bell on a graph.

Numbers are not normally distributed if they are grouped on one side or the other side of the average value. Numbers can be spread out and still be normally distributed. The standard deviation tells how widely the numbers are spread out.

Relationship between the average (mean) and standard deviation
The average (mean) and the standard deviation of a set of data are usually written together. Then a person can understand what the average number is and how widely other numbers in the group are spread out.

The way a group of numbers is spread out can also be given by the coefficient of variation (CV), which is the standard deviation divided by the average. It is a dimensionless number. Coefficient of variation is often multiplied by 100% and written as a percentage.

History
The term standard deviation was first used in writing by Karl Pearson in 1894, after he used it in lectures. It was as a replacement for earlier names for the same idea: for example, Gauss used mean error.

Related pages
 Accuracy and precision
 Sample size
 Standard error
 Variance

References

Other websites
 A simple way to understand Standard Deviation
 Standard Deviation – an explanation without maths
 Standard Deviation, an elementary introduction
 Standard Deviation, a simpler explanation for writers and journalists

Statistics

Standard deviation


A Girl in the Street, Two Coaches in the Background (F13, JH179) is an oil painting by Vincent van Gogh.  It is one of his very early works, painted in The Hague in August 1882, at a time when his brother Theo was encouraging him to paint landscapes in colour, rather than drawing figures.  It is an early work to bear his "Vincent" signature, suggesting he was happy with the effect.

Description
The work in an evening scene of a young blonde woman, with straw hat, dark jacket and skirt, and white apron, carrying a basket as she walks along a dirt road past two horse-drawn carriages which are waiting beside some trees, with some buildings visible beyond. It was probably painted en plein air, quickly, one evening, when Van Gogh stopped on a walk around the city with his easel seeking artistic inspiration.

It measures .  It was bought by Arthur Hahnloser before 1913, and is still in the private collection at the  in Winterthur.

See also
Paintings of Children (Van Gogh series)
List of works by Vincent van Gogh

References

External links

Paintings by Vincent van Gogh
Paintings of the Netherlands by Vincent van Gogh
1882 paintings
Horses in art


Matt's Scooter (1985 – June 30, 2014) was a Standardbred pacer and sire who was named Harness Horse of the Year in 1989. Matt's Scooter competed as a pacer in harness racing, winning the Meadowlands Pace, Prix d'Été, Confederation Cup, Messenger Stakes, American National Stakes, Breeders Crown, Driscoll Series, Mohawk Gold Cup, he was named Pacer of the Year in 1988 and 1989, and Harness Horse of the Year in 1989 by the United States Harness Association.

Background
Matt's Scooter was a bay ridgeling bred by Max Gerson of New York. He was sired by Direct Scooter out of Ellen's Glory by Meadow Skipper. As a yearling, he was bought for $17,500 by Gordon and Illa Rumpel of Calgary, and Charles Juravinski. He was trained by Harry Poulton at his base near Lake Scugog, Ontario.

Racing career
As  two-year-old, Matt's Scooter was given a relatively light campaign winning three of his nine races. He was not an easy horse to handle: Poulton described him as "always bucking, kicking or doing something... he wanted to do everything 100 miles an hour".

In 1988, despite being ineligible for the Cane Pace and the Little Brown Jug, Matt's Scooter earned $1.78 million winning eleven of his twenty two races. His major victories included the Meadowlands Pace and the Messenger Stakes.

In Autumn 1988, he paced a mile in 1:48.2 at the Red Mile in Lexington, Kentucky, lowering the world record previously held by Niatross, by four-fifths of a second.

As a four-year-old he won 23 of his thirty races and earned $1.14 million.

Honors and awards
Matt's Scooter was named Pacer of the Year and best three-year-old in 1988. In the following year, he was again named best pacer and was awarded the title of Harness Horse of the Year. Matt's Scooter was inducted into the Canadian Horse Racing Hall of Fame and the United States Horse Racing Hall of Fame in 2006.

Retirement and stud career
He was retired from racing after 4 years, and stood as a breeding stallion for Perretti Farms in Cream Ridge, New Jersey. He was pensioned from stud duty in 2011. Bob Marks of Perretti Farms said "His libido is willing, but with his hind suspensory, we're afraid he could hurt himself".

Matt's Scooter was euthanised at Mid-Atlantic Equine Clinic in Ringoes, New Jersey on June 30, 2014.

Pedigree

References

1985 racehorse births
2014 racehorse deaths
American Standardbred racehorses
American Champion harness horses
Harness Horse of the Year winners
Harness racing in Canada
Harness racing in the United States
Canadian Horse Racing Hall of Fame inductees
United States Harness Racing Hall of Fame inductees
Messenger Stakes winners

Matt's Scooter


Brunsbüttel is a town of the district of Dithmarschen, in Schleswig-Holstein, Germany. It is the location of the western entrance to the Kiel Canal, the busiest artificial waterway in the world. As of 31 December 2018, 12,554 people lived there.

Other websites

 Official website

Towns in Schleswig-Holstein

Brunsbüttel


Education in France is organized in a highly centralized manner, with many subdivisions. It is divided into the three stages of primary education (enseignement primaire), secondary education (enseignement secondaire), and higher education (enseignement supérieur). The main age that a child starts school in France is age two and since 2022, education is obligatory from the age of three. Two year olds do not start primary school, they start preschool. Then, by the age of six, a child in France starts primary school and soon moves onto higher and higher grade levels until they graduate.

In French higher education, the following degrees are recognized by the Bologna Process (EU recognition): Licence and Licence Professionnelle (bachelor's degrees), and the comparably named Master and Doctorat degrees.

The Programme for International Student Assessment coordinated by the OECD in 2018 ranked the overall knowledge and skills of French 15-year-olds as 26th in the world in reading literacy,  mathematics, and science, below the OECD average of 493. The average OECD performance of French 15-year-olds in science and mathematics has declined, with the share of low performers in reading, mathematics and science developing a sharp upward trend. France's share of top performers in mathematics and science has also declined.

France's performance in mathematics and science at the middle school level was ranked 23 in the 1995 Trends in International Math and Science Study. In 2019, France ranked 21 in the TIMSS Science general ranking.

History

Napoleon began the French university and secondary educational systems. Guizot started the elementary system. Intense battles took place over whether the Catholic Church should play a dominant role. The modern era of French education begins at the end of the 19th century. Jules Ferry, a Minister of Public Instruction in 1841, is widely credited for creating the modern school (l'école républicaine) by requiring all children between the ages of 6 and 12, both boys and girls, to attend. He also made public instruction mandatory, free of charge, and secular (laïque). With those laws, known as French Lubbers, Jules Ferry laws, and several others, the Third Republic repealed most of the Falloux Laws of 1850–1851, which gave an important role to the clergy.

The French curriculum predominantly emphasized the works of French writers of European descent. Ferry and others considered literature the glue of French identity. The ethnic and cultural demographics of the student body did not factor in to the quest to transmit a "common culture" to the students.

Like literature, history education is seen as critical to shaping the identity of young people and the integration of immigrants to French identity. Ferry's views continue to exert influence today. Ministry reports have confirmed that the rule of schools in promoting "common culture" is only made more critical by the rising levels of student diversity. According to the ministry, history education in France has, over the course of one century made possible "the integration of children of Italians, Poles, Africans and Portuguese".

Governance

All educational programmes in France are regulated by the Ministry of National Education, Youth and Community Life (officially called Ministère de l'Éducation nationale, de la Jeunesse et de la Vie associative). The head of the ministry is the Minister of National Education.

All teachers in public primary and secondary schools are state civil servants, making the ministère the largest employer in the country. Professors and researchers in France's universities are also employed by the state.

At the primary and secondary levels, the curriculum is the same for all French students in any given grade, which includes public, semi-public and subsidised institutions. However, there exist specialised sections and a variety of options that students can choose. The reference for all French educators is the Bulletin officiel de l'éducation nationale, de l'enseignement supérieur et de la recherche (B.O.), which lists all current programmes and teaching directives. It is amended many times every year.

Schooling in France is not mandatory (although instruction is). Since French law mandates only education, and not necessarily attendance at a school, families may provide teaching themselves, provided that they comply with the educational standards laid down in law and monitored by the State.

School year

In Metropolitan France, the school year runs from early September to early July. The school calendar is standardized throughout the country and is the sole domain of the ministry.

In May, schools need time to organize exams (for example, the baccalauréat). Outside Metropolitan France, the school calendar is set by the local recteur.

Major holiday breaks are as follows:
All Saints (la Toussaint), two weeks (since 2012) around the end of October and the beginning of November;
Christmas (Noël), two weeks around Christmas Day and New Year's Day;
winter (hiver), two weeks starting in mid-February;
spring (printemps) or Easter (Pâques), two weeks starting in mid April;
summer (été), two months starting in early July. (mid-June for high school students).

Primary school

Most parents start sending their children to preschool (maternelle) when they turn 3. Some even start earlier at age 2 in toute petite section ("TPS"). The first two years of preschool (TPS and petite section "PS") are introductions to community living; children learn how to become students and are introduced to their first notions of arithmetic, begin to recognize letters, develop oral language, etc. The last two years of preschool, moyenne section and grande section, are more school-like; pupils are introduced to reading, writing and more mathematics.

A preschool can be stand-alone (mostly true in towns and cities) or be affiliated to an elementary school (mostly in villages). As in other educational systems, primary school students in France usually have a single teacher (or two) who teaches the entire curriculum, without specialist teachers.

After kindergarten, the young students move on to the école élémentaire (elementary school). In the first 3 years of elementary school, they learn to write, develop their reading skills and get some basics in subjects such as French, mathematics, science and the arts, to name a few. The French word for a teacher at the primary school level is professeur or professeure des écoles (previously called instituteur, or its feminine form institutrice).

Children stay in elementary school for 5 years until they are 10–11 years-old. The grades are named: CP (cours préparatoire), CE1 (cours élémentaire 1), CE2 (cours élémentaire 2), CM1 (cours moyen 1) and CM2 (cours moyen 2).

Middle school and high school

The compulsory middle and high school subjects cover French language and literature, history and geography, foreign languages, arts and crafts, musical education, civics, mathematics, physics, chemistry, natural sciences, technology, and PE. The curriculum is set by the Ministry of National Education and applies to most collèges in France and also to AEFE-dependent institutions. Académies and individual schools have little freedom in the State curriculum.

Class sizes vary from school to school, but usually range from 20 to 35 pupils.

After primary school, two educational stages follow:
collège (middle school), for children during their first four years of secondary education from the age of 11 to 14.
 lycée (high school), which provides a three-year course of further secondary education for children between the ages of 15 and 18. Pupils are prepared for the baccalauréat (baccalaureate, colloquially known as le bac) or the CAP (Certificat d'aptitude professionnelle). The baccalauréat can lead to higher education studies or directly to professional life (there are three main types of baccalauréat: the baccalauréat général, the baccalauréat technologique, and the baccalauréat professionnel).
 CFA (centre de formation des apprentis, apprentice learning center), which provides vocational degrees: le Certificat d'aptitude professionnelle.

Private schools

Primary and secondary private schools in France are divided into two categories:
Private schools which respect the State curriculum (known as "under contract') are private, fee-paying institutions where pupils study the same national curriculum as those in public schools. Teachers in private schools are recruited in the same way and have roughly the same status as their equivalents in public schools. They are also employed directly by the State, but they are not permanently assigned and may not return to a public school position. The great majority of private schools in France are "under contract".Private schools without contract employ their teachers directly and may teach their own curriculum; the State, however, still monitors their educational standards. Most of these schools provide religious instruction in parallel with a broad curriculum.

International education
As of January 2015, the International Schools Consultancy (ISC) listed France as having 105 international schools. ISC defines an 'international school' in the following terms: "ISC includes an international school if the school delivers a curriculum to any combination of pre-school, primary or secondary students, wholly or partly in English outside an English-speaking country, or if a school in a country where English is one of the official languages, offers an English-medium curriculum other than the country's national curriculum and is international in its orientation." That definition is used by publications including The Economist.

France has its own international school regulator, the AEFE (Agence pour l'enseignement français à l'étranger).

 Higher education

Higher education in France is organized in three levels, which correspond to those of other European countries, facilitating international mobility: the Licence and Licence Professionnelle (bachelor's degrees), and the Master's and Doctorat degrees. The Licence and the Master are organized in semesters: 6 for the Licence and 4 for the Master. Those levels of study include various "parcours" or paths based on UE (Unités d'enseignement or Modules), each worth a defined number of European credits (ECTS). A student accumulates those credits, which are generally transferable between paths. A licence is awarded once 180 ECTS have been obtained; a master is awarded once 120 additional credits have been obtained.

Licence and master's degrees are offered within specific domaines and carry a specific mention. Spécialités, which are either research-oriented or professionally oriented during the second year of the Master. There are also professional licences whose objective is immediate job integration. It is possible to return to school later by continuing education or to validate professional experience (through VAE, Validation des Acquis de l'Expérience).

Higher education in France is divided between grandes écoles and public universities. The grandes écoles admit the graduates of the level Baccalauréat + 2 years of validated study (or sometimes directly after the Baccalauréat) whereas universities admit all graduates of the Baccalauréat.

Higher education in France was reshaped by the student revolts of May 1968.  During the 1960s, French public universities responded to a massive explosion in the number of students (280,000 in 1962-63 to 500,000 in 1967-68) by stuffing approximately one-third of their students into hastily developed campus annexes (roughly equivalent to American satellite campuses) which lacked decent amenities, resident professors, academic traditions, or the dignity of university status.  With so many students ripe for radicalization after being forced to study in such miserable conditions, change was necessary and inevitable. Rather than expand already-overwhelmed parent campuses, it was decided to split off the annexes as new universities.

This is why a striking trait of French higher education, compared with other countries, is the small size and multiplicity of establishments, each specialised in a more-or-less broad spectrum of areas. A middle-sized French city, such as Grenoble or Nancy, may have 2 or 3 universities (focused on science, sociological studies, engineering, etc.) as well as a number of other establishments specialised in higher education. In Paris and its suburbs, there are currently 11 universities (there were 13 from 1970 to 2017), none of which is specialised in one area or another, plus many smaller institutions that are highly specialised. It is not uncommon for graduate teaching programmes (master's degrees, the course part of doctorate programmes etc.) to be operated in common by several institutions, allowing the institutions to present a larger variety of courses.

In engineering schools and the professional degrees of universities, a large share of the teaching staff is often made up of non-permanent professors; instead, part-time professors are hired to teach one specific subject. Part-time professors are generally hired from neighbouring universities, research institutes or industries.

Another original feature of the French higher education system is that a large share of the scientific research is carried out by research establishments such as CNRS or INSERM, which are not formally part of the universities. However, in most cases, the research units of those establishments are located inside universities (or other higher education establishments) and jointly operated by the research establishment and the university.

In 2021, 1.65 million students are enrolled in French higher education institutions (61% in licence, 35% in master, 4% in doctorat).

Tuition costs
Higher education is mostly funded by the State which leads to very low tuition fees. For citizens of the EU, EEA, Switzerland or Quebec, the annual fees range from 170 to 380 euros per year depending on the level (licence, master, doctorat). One can therefore get a master's degree (in 5 years) for about €750–3,500. For other international students, these fees range from 2,770 to 3,770 euros. Students from low-income families can apply for scholarships, paying nominal sums for tuition or textbooks, and can receive a monthly stipend of up to €450 per month.

The tuition in public engineering schools is comparable to universities but a little higher (around €700). However, it can reach €7,000 a year for private engineering schools. Private business schools typically charge up to €12,000 a year for Bachelor programmes and up to €24,000 for Master programmes, while some elite institutions may charge €40,000 and more.

Health insurance for students is free until the age of 20 and so only the costs of living and books must be added. After the age of 20, health insurance for students costs €200 a year and covers most of the medical expenses.

Some public schools have other ways of gaining money. Some do not receive funds for class trips and other extra activities and so those schools may ask for a small entrance fee for new students.

Universities in France

The public universities in France are named after the major cities near which they are located, followed by a numeral if there are several. Paris, for example, has 13 universities, labelled Paris I to XIII. Some of them are in Paris itself, some in the suburbs. In addition, most of the universities have taken a more informal name that is usually that of a famous person or a particular place. Sometimes, it is also a way to honor a famous alumnus, for example the science university in Strasbourg is known as "Université Louis-Pasteur" while its official name is "Université Strasbourg I" (however, since 2009, the three universities of Strasbourg have been merged).

The French system has undergone a reform, the Bologna process, which aims at creating European standards for university studies, most notably a similar time-frame everywhere, with three years devoted to the bachelor's degree ("licence" in French), two for the Master's, and three for the doctorate. French universities have also adopted the ECTS credit system (for example, a licence is worth 180 credits). The traditional curriculum based on end of semester examinations tends to remain in place in some universities. That double standard has added complexity to a system. It is difficult to change a major during undergraduate studies without losing a semester or even a whole year. Students usually also have few course selection options once they enroll in a particular diploma.

France also hosts rare catholic universities recognized by the State, the largest one being Lille Catholic University, as well branch colleges of foreign universities. They include Baruch College, the University of London Institute in Paris, Parsons Paris School of Art and Design and the American University of Paris.

There are about 4,000 Master programmes offered in the French university system (listed at trouvermonmaster.gouv.fr), and 17,000 undergraduate programmes (offered by Parcoursup).

Grandes écoles

The grandes écoles of France are elite higher-education establishments. They are generally focused on a single subject area (e.g., engineering or business), have a small size (typically between 100 and 300 graduates per year), and are highly selective. They are widely regarded as prestigious, and most of France's scientists and executives have graduated from a grande école.

National rankings are published every year by various magazines.L'Étudiant, Palmarès des écoles d'ingénieurs.L'Usine nouvelle, Palmarès des écoles d'ingénieurs. While the rankings slightly vary from year to year, the top grandes écoles have been very stable for decades:

 science and engineering: Écoles normales supérieures, École polytechnique, Mines ParisTech, Télécom Paris, ISAE-Supaéro, Ponts Paristech,  Ecole Nationale de l'Aviation Civile and CentraleSupélec;
 humanities: three Écoles normales supérieures, École des Chartes and CELSA – Sorbonne;
 business: HEC Paris, NEOMA Business School, ESSEC Business School, ESCP Europe, INSEAD, EMLyon, Audencia, Grenoble École de Management, INSEEC and EDHEC;
 administration and political sciences: ENA and Sciences Po.

Preparatory classes (CPGEs)

Preparatory classes (in French "classes préparatoires aux grandes écoles" or CPGE), widely known as prépas, are courses whose main goal is to prepare students for enrollment in a grande école. Admission to CPGEs is based on academic performance during the last two years of high school, called Première and Terminale. Only 5% of a given cohort is admitted to a prépa. CPGEs are usually located within high schools but are a part of tertiary education, which means that to be admitted, each student must have already successfully passed their Baccalauréat (or equivalent). Most CPGE receive applications from hundreds of applicants every year in April and May, and then selects students based on their own criteria. A few mainly private CPGEs, accounting for 10% of CPGEs, also have an interview process and ' or expect student participation in local community initiatives.

The ratio of CPGE students who fail to enter any grande école is lower in scientific and business CPGEs than in humanities CPGEs.

Some preparatory classes are widely considered "elite", being extremely selective, and recruiting only the best students from each high school, if not the best student from each high school. These CPGEs practically guarantee their students a place in one of the top "grandes écoles". Among them are the Lycée Louis-Le-Grand, the Lycée Henri-IV, the Lycée Stanislas and the Lycée privé Sainte-Geneviève.

Scientific CPGEs
The oldest CPGEs are the science ones, which can be accessed only with a bac in science Bacheliers. Science CPGE are called TSI ("Technology and Engineering Science"), MPSI ("Mathematics, Physics and Engineering Science"), PCSI ("Physics, Chemistry, and Engineering Science") or PTSI ("Physics, Technology, and Engineering Science") in the first year, MP ("Mathematics and Physics"), PSI ("Physics and Engineering Science"), PC ("Physics and Chemistry") or PT ("Physics and Technology") in the second year and BCPST ("Biology, Chemistry, Physics, Life and Earth Sciences").

The first year of a CPGE is widely known as "Math Sup", or Hypotaupe, (Sup for "Classe de Mathématiques Supérieures", superior in French, meaning post-high school), and second year as "Math Spé", or Taupe, (Spés standing for "Classe de Mathématiques Spéciales", special in French). The students of these classes are known as Taupins. Both the first and second year programmes include as much as twelve hours of mathematics teaching per week, ten hours of physics, two hours of philosophy, two to four hours of (one or two) foreign languages and four to six hours of options: chemistry, SI (Engineering Industrial Science) or Theoretical Computer Science (including some programming using the Pascal or CaML programming languages, as a practical work). There are also several hours of homework, which can double the class-based workload. A well-known joke among CPGE students is that they become moles for two years, sometimes three, hence the nicknames taupe and taupin (taupe being the French word for a mole).

Business CPGEs
There are also CPGEs that are focused on economics (who prepare the admission in business schools). They are known as prépa EC (short for Economiques et Commerciales) and are divided into two parts: prépa ECS, which focuses more on mathematics, generally for those who graduated the scientific baccalauréat, and prépa ECE, which focuses more on economics, for those who were in the economics section in high school.

Humanities CPGEs (Hypokhâgne and Khâgne)
The literary and humanities CPGEs have also their own nicknames, Hypokhâgne for the first year and Khâgne for the second year. The students are called the khâgneux. Those classes prepare for schools such as the three Écoles normales supérieures, the École des Chartes, and sometimes Sciences Po.

There are two kinds of Khâgnes. The Khâgne de Lettres is the most common, and focuses on philosophy, French literature, history and languages. The Khâgne de Lettres et Sciences Sociales (Literature and Social Sciences), otherwise called Khâgne B/L, also includes mathematics and socio-economic sciences in addition to those literary subjects.

The students of Hypokhâgne and Khâgne (the humanities CPGE) are simultaneously enrolled in universities, and can go back to university in case of failure or if they feel unable to pass the highly competitive entrance examinations for the Écoles normales supérieures.

Colles
The amount of work required of the students is high. In addition to class time and homework, students spend several hours each week completing oral exams called colles (sometimes written 'khôlles' to look like a Greek word, that way of writing being initially a khâgneuxs joke since khâgneux study Ancient Greek). The colles are unique to French academic education in CPGEs.

In scientific and business CPGEs, colles consist of oral examinations twice a week, in French, foreign languages (usually English, German, or Spanish), maths, physics, philosophy, or geopolitics—depending on the type of CPGE. Students, usually in groups of three or four, spend an hour facing a professor alone in a room, answering questions and solving problems.

In humanities CPGEs, colles are usually taken every quarter in every subject. Students have one hour to prepare a short presentation that takes the form of a French-style dissertation (a methodologically codified essay, typically structured in 3 parts: thesis, counter-thesis, and synthesis) in history, philosophy, etc. on a given topic, or the form of a commentaire composé (a methodologically codified form of literary criticism) in literature and foreign languages. In Ancient Greek or Latin, they involve a translation and a commentary. The student then has 20 minutes to present his/her work to the teacher, who finally asks some questions on the presentation and on the corresponding topic.Colles are regarded as very stressful, particularly due to the high standards expected by the teachers, and the subsequent harshness that may be directed at students who do not perform adequately. But they are important insofar as they prepare the students, from the very first year, for the oral part of the highly competitive examinations, which are reserved for the happy few who pass the written part.

Recruitment of teachers
Decades ago, primary school teachers were educated in Écoles normales and secondary teachers recruited through the "Agrégation" examination. The situation has been diversified by the introduction in the 1950s of the CAPES examination for secondary teachers and in the 1990s by the institution of "Instituts universitaires de formation des maitres" (IUFM), which have been renamed Écoles supérieures du professorat et de l'éducation (ESPE) in 2013 and then Instituts Nationaux supérieurs du professorat et de l'éducation (INSPE) in 2019.

Precisely, school teachers are divided between :
 Primary school and kindergarten teachers (Professeurs des écoles), educated in an INSPE, have usually a "master" (Bac+5). Their weekly service is about 28 hours a week.
 Certified teachers (Professeurs certifiés), educated in both a University and an INSPE, have a "master" (Bac+5) and must pass a competitive exam called Certificat d'aptitude au professorat de l'enseignement du second degré (CAPES) in a specific domain. Their rank usually determines their geographic assignment for the first years of their careers. The majority of them are teaching in collège (middle school).
 Agrégés teachers (Professeurs agrégés) are recruited through a different competitive exam called Agrégation, of much higher level in each domain. They could either be certified teachers or external holders of at least a "master" (Bac+5) in the domain. In the latter case they must attend an additional formation in teaching in an INSPE. Agrégés teachers have a higher salary rate and reduced weekly service. The majority of them are teaching in lycée (high school).

University teachers are recruited by special commissions, and are divided between:

 "teachers-researchers" (enseignants-chercheurs), with at least a doctorate: they teach classes and conduct research in their field of expertise with a full tenure. They are either Maître de conférences (Senior lecturers), or Professeurs (Professors). A Maître de conférence must publish a reviewed work named Habilitation à diriger des recherches (HDR) (professorial thesis) in order to be allowed to become the director of studies for PhD students. The HDR is in turn necessary to be appointed as Professeur. The net pay (all insurances included) is from 2,300 to 8,800 (with extra duties) euros per month. Net salaries of over 4,000 euros per month (2011 level) are however very unusual, and limited to the small minority of teacher-researchers who have held the grade of first class full professor for at least seven years, which is rare. The maximum possible net salary for second-class full professors and chief senior lecturers (maître de conférence hors classe), the end of career status for most full-time teacher-researchers in French universities, is 3,760 euros a month (2011), and only a few of the group ever reach that level.
 Secondary school teachers who have been permanently assigned away from their original school position to teach in a university. They are not required to conduct any research but teach twice as many hours as the "teachers-researchers". They are called PRAG (professeurs agrégés) and PRCE (professeurs certifiés). Their weekly service is 15 or 18 hours. The net pay is from 1,400 to 3,900 euros per month.
 CPGE teachers are usually "agrégés" or "chaire sup", assigned by the Inspection générale according to their qualifications and competitive exam rank as well as other factors. Their weekly service is about 9 hours a week, 25 or 33 weeks a year. Net pay : from 2,000 to 7,500 euro (extra hours)
France did a great activity of supplying training for their people, via way of means of the 1800s, France had approximately 350 eight-yr faculties and six-yr faculties. Also in the course of the 1800s, they furnished classical training to approximately 50,000 to younger guys from a long time of 10-20. Getting greater specific, the very best increase charge of training in France became in the course of the 1821-1837 whilst towns welcomed new colleges. The increase charge slowed in the course of 1837–1867 because the authorities reached thinly populated rural areas. Then, via way of means of 1867-1906, the emphasis became on deepening the first-rate of colleges and teaching. Camille Sée added secondary colleges for ladies in 1880, which became a vital pass due to the fact he furnished secondary faculty stage of training to ladies. There have been 36 such colleges in France in 1896.

Religion
Religious instruction is not given by public schools (except for 6- to 18-year-old students in Alsace-Moselle under the Concordat of 1801). Laïcité (secularism) is one of the main precepts of the French Republic.

In a March 2004 ruling, the French government banned all "conspicuous religious symbols" from schools and other public institutions with the intent of preventing proselytisation and to foster a sense of tolerance among ethnic groups. Some religious groups showed their opposition, saying the law hindered the freedom of religion as protected by the French constitution.

Statistics
The French Republic has 67 million inhabitants, living in the 13 regions of metropolitan France and four overseas departments (2.7 million). Despite the fact that the population is growing (up 0.4% a year), the proportion of young people under 25 is falling. There are now fewer than 19 million young people in Metropolitan France, or 32% of the total population, compared with 40% in the 1970s and 35% at the time of the 1990 census. France is seeing a slow aging of the population, however, that is less marked than in other neighbouring countries (such as Germany and Italy), especially as the annual number of births is currently increasing slightly.

Eighteen million pupils and students, a quarter of the population, are in the education system, over 2.9 million of whom are in higher education. In 2000, the French Education Minister reported that only 39 out of 75,000 state schools were "seriously violent" and some 300 were "somewhat violent".

See also
 Trouvermonmaster.gouv.fr, a Web portal listing all the masters available in France
 Parcoursup, a Web portal listing all the undergraduate programmes available in France
 Academic grading in France
 Agency for French Teaching Abroad (Agence pour l'enseignement français à l'étranger)
 Campus France (Agency for the promotion of French Higher Education)
 Conférence des Grandes écoles (CGE)
 Conference of the Directors of French Engineering Schools (Conférence des directeurs des écoles françaises d'ingénieurs'' (CDEFI))
 Homeschooling in France
 Open access in France
 Nursery schools of France

References

Further reading

External links
 Eurydice France, Eurydice: Portal for European education systems
 French Ministry of National Education, Higher Education and Research (English)
 School Education in France, Eduscol: the French portal for Education players (English)
 Education in France, a webdossier by the German Education Server (English)
 Understand the French School System in 5 min (English & French)

Education in France


In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix. The LU decomposition was introduced by the Polish astronomer Tadeusz Banachiewicz in 1938. To quote: "It appears that Gauss and Doolittle applied the method
[of elimination] only to symmetric equations. More recent authors, for example, Aitken, Banachiewicz, Dwyer, and Crout … have emphasized the use of the method, or variations of it, in connection with non-symmetric problems … Banachiewicz … saw the point … that the basic problem is really one of matrix factorization, or "decomposition" as he called it."
It's also referred to as LR decomposition (factors into left and right triangular matrices).

Definitions

Let A be a square matrix. An LU factorization refers to the factorization of A, with proper row and/or column orderings or permutations, into two factors – a lower triangular matrix L and an upper triangular matrix U:

In the lower triangular matrix all elements above the diagonal are zero, in the upper triangular matrix, all the elements below the diagonal are zero. For example, for a 3 × 3 matrix A, its LU decomposition looks like this:

Without a proper ordering or permutations in the matrix, the factorization may fail to materialize. For example, it is easy to verify (by expanding the matrix multiplication) that . If , then at least one of  and  has to be zero, which implies that either L or U is singular. This is impossible if A is nonsingular (invertible). This is a procedural problem. It can be removed by simply reordering the rows of A so that the first element of the permuted matrix is nonzero. The same problem in subsequent factorization steps can be removed the same way; see the basic procedure below.

LU factorization with partial pivoting

It turns out that a proper permutation in rows (or columns) is sufficient for LU factorization. LU factorization with partial pivoting (LUP) refers often to LU factorization with row permutations only:

where L and U are again lower and upper triangular matrices, and P is a permutation matrix, which, when left-multiplied to A, reorders the rows of A. It turns out that all square matrices can be factorized in this form, and the factorization is numerically stable in practice. This makes LUP decomposition a useful technique in practice.

LU factorization with full pivoting

An LU factorization with full pivoting involves both row and column permutations:

where L, U and P are defined as before, and Q is a permutation matrix that reorders the columns of A.

Lower-diagonal-upper (LDU) decomposition

A Lower-diagonal-upper (LDU) decomposition is a decomposition of the form

where D is a diagonal matrix, and L and U are unitriangular matrices, meaning that all the entries on the diagonals of L and U are one.

Rectangular matrices
Above we required that A be a square matrix, but these decompositions can all be generalized to rectangular matrices as well. In that case, L and D are square matrices both of which have the same number of rows as A, and U has exactly the same dimensions as A. Upper triangular should be interpreted as having only zero entries below the main diagonal, which starts at the upper left corner. Similarly, the more precise term for U is that it is the "row echelon form" of the matrix A.

Example

We factor the following 2-by-2 matrix:

One way to find the LU decomposition of this simple matrix would be to simply solve the linear equations by inspection. Expanding the matrix multiplication gives

This system of equations is underdetermined. In this case any two non-zero elements of L and U matrices are parameters of the solution and can be set arbitrarily to any non-zero value. Therefore, to find the unique LU decomposition, it is necessary to put some restriction on L and U matrices. For example, we can conveniently require the lower triangular matrix L to be a unit triangular matrix (i.e. set all the entries of its main diagonal to ones). Then the system of equations has the following solution:

Substituting these values into the LU decomposition above yields

Existence and uniqueness

Square matrices

Any square matrix  admits LUP and PLU factorizations. If  is invertible, then it admits an LU (or LDU) factorization if and only if all its leading principal minors are nonzero (for example
does not admit an LU or LDU factorization). If  is a singular matrix of rank , then it admits an LU factorization if the first  leading principal minors are nonzero, although the converse is not true.

If a square, invertible matrix has an LDU (factorization with all diagonal entries of L and U equal to 1), then the factorization is unique. In that case, the LU factorization is also unique if we require that the diagonal of  (or ) consists of ones.

In general, any square matrix  could have one of the following:
 a unique LU factorization (as mentioned above);
 infinitely many LU factorizations if two or more of any first (n−1) columns are linearly dependent or any of the first (n−1) columns are 0;
 no LU factorization if the first (n−1) columns are non-zero and linearly independent and at least one leading principal minor is zero.

In Case 3, one can approximate an LU factorization by changing a diagonal entry   to   to avoid a zero leading principal minor.

Symmetric positive-definite matrices

If A is a symmetric (or Hermitian, if A is complex) positive-definite matrix, we can arrange matters so that U is the conjugate transpose of L. That is, we can write A as

This decomposition is called the Cholesky decomposition. The Cholesky decomposition always exists and is unique — provided the matrix is positive definite. Furthermore, computing the Cholesky decomposition is more efficient and numerically more stable than computing some other LU decompositions.

General matrices

For a (not necessarily invertible) matrix over any field, the exact necessary and sufficient conditions under which it has an LU factorization are known. The conditions are expressed in terms of the ranks of certain submatrices. The Gaussian elimination algorithm for obtaining LU decomposition has also been extended to this most general case.

Algorithms

Closed formula

When an LDU factorization exists and is unique, there is a closed (explicit) formula for the elements of L, D, and U in terms of ratios of determinants of certain submatrices of the original matrix A. In particular, , and for ,  is the ratio of the -th principal submatrix to the -th principal submatrix. Computation of the determinants is computationally expensive, so this explicit formula is not used in practice.

Using Gaussian elimination
The following algorithm is essentially a modified form of Gaussian elimination. Computing an LU decomposition using this algorithm requires  floating-point operations, ignoring lower-order terms. Partial pivoting adds only a quadratic term; this is not the case for full pivoting.

Generalized explanation

Notation
Given an N × N matrix , define  as the original, unmodified version of the matrix .  The parenthetical superscript (e.g., ) of the matrix  is the version of the matrix. The matrix  is the  matrix in which the elements below the main diagonal have already been eliminated to 0 through Gaussian elimination for the first  columns.

Below is a matrix to observe to help us remember the notation (where each  represents any real number in the matrix):

Procedure
During this process, we gradually modify the matrix  using row operations until it becomes the matrix  in which all the elements below the main diagonal are equal to zero. During this, we will simultaneously create two separate matrices  and , such that .

We define the final permutation matrix  as the identity matrix which has all the same rows swapped in the same order as the  matrix while it transforms into the matrix . For our matrix , we may start by swapping rows to provide the desired conditions for the n-th column. For example, we might swap rows to perform partial pivoting, or we might do it to set the pivot element  on the main diagonal to a non-zero number so that we can complete the Gaussian elimination.

For our matrix , we want to set every element below  to zero (where  is the element in the n-th column of the main diagonal). We will denote each element below  as  (where ). To set  to zero, we set  for each row . For this operation, . Once we have performed the row operations for the first  columns, we have obtained an upper triangular matrix  which is denoted by .

We can also create the lower triangular matrix denoted as , by directly inputting the previously calculated values of  via the formula below.

Example
If we are given the matrixwe will choose to implement partial pivoting and thus swap the first and second row so that our matrix  and the first iteration of our  matrix respectively becomeOnce we have swapped the rows, we can eliminate the elements below the main diagonal on the first column by performing such that,Once these rows have been subtracted, we have derived from  the matrix Because we are implementing partial pivoting, we swap the second and third rows of our derived matrix and the current version of our  matrix respectively to obtainNow, we eliminate the elements below the main diagonal on the second column by performing  such that . Because no non-zero elements exist below the main diagonal in our current iteration of  after this row subtraction, this row subtraction derives our final  matrix (denoted as ) and final  matrix:Now we can obtain our final  matrix:Now these matrices have a relation such that .

Relations when no rows are swapped
If we did not swap rows at all during this process, we can perform the row operations simultaneously for each column  by setting  where  is the N × N identity matrix with its n-th column replaced by the transposed vector  In other words, the lower triangular matrix

Performing all the row operations for the first  columns using the  formula is equivalent to finding the decomposition

Denote  so that .

Now let's compute the sequence of . We know that  has the following formula.

If there are two lower triangular matrices with 1s in the main diagonal, and neither have a non-zero item below the main diagonal in the same column as the other, then we can include all non-zero items at their same location in the product of the two matrices. For example:

Finally, multiply  together and generate the fused matrix denoted as  (as previously mentioned). Using the matrix , we obtain

It is clear that in order for this algorithm to work, one needs to have  at each step (see the definition of ). If this assumption fails at some point, one needs to interchange n-th row with another row below it before continuing. This is why an LU decomposition in general looks like .

LU Crout decomposition
Note that the decomposition obtained through this procedure is a Doolittle decomposition: the main diagonal of L is composed solely of 1s. If one would proceed by removing elements above the main diagonal by adding multiples of the columns (instead of removing elements below the diagonal by adding multiples of the rows), we would obtain a Crout decomposition, where the main diagonal of U is of 1s.

Another (equivalent) way of producing a Crout decomposition of a given matrix A is to obtain a Doolittle decomposition of the transpose of A. Indeed, if  is the LU-decomposition obtained through the algorithm presented in this section, then by taking  and , we have that  is a Crout decomposition.

Through recursion

Cormen et al. describe a recursive algorithm for LUP decomposition.

Given a matrix A, let P1 be a permutation matrix such that

 ,

where , if there is a nonzero entry in the first column of A; or take P1 as the identity matrix otherwise. Now let , if ; or  otherwise. We have

Now we can recursively find an LUP decomposition . Let . Therefore

which is an LUP decomposition of A.

Randomized algorithm
It is possible to find a low rank approximation to an LU decomposition using a randomized algorithm. Given an input matrix  and a desired low rank , the randomized LU returns permutation matrices  and lower/upper trapezoidal matrices  of size  and  respectively, such that with high probability , where  is a constant that depends on the parameters of the algorithm and  is the -th singular value of the input matrix .

Theoretical complexity
If two matrices of order n can be multiplied in time M(n), where M(n) ≥ na for some a > 2, then an LU decomposition can be computed in time O(M(n)). This means, for example, that an O(n2.376) algorithm exists based on the Coppersmith–Winograd algorithm.

Sparse-matrix decomposition
Special algorithms have been developed for factorizing large sparse matrices. These algorithms attempt to find sparse factors L and U. Ideally, the cost of computation is determined by the number of nonzero entries, rather than by the size of the matrix.

These algorithms use the freedom to exchange rows and columns to minimize fill-in (entries that change from an initial zero to a non-zero value during the execution of an algorithm).

General treatment of orderings that minimize fill-in can be addressed using graph theory.

Applications

Solving linear equations
Given a system of linear equations in matrix form

we want to solve the equation for x, given A and b. Suppose we have already obtained the LUP decomposition of A such that , so .

In this case the solution is done in two logical steps:
 First, we solve the equation  for y.
 Second, we solve the equation  for x.

In both cases we are dealing with triangular matrices (L and U), which can be solved directly by forward and backward substitution without using the Gaussian elimination process (however we do need this process or equivalent to compute the LU decomposition itself).

The above procedure can be repeatedly applied to solve the equation multiple times for different b. In this case it is faster (and more convenient) to do an LU decomposition of the matrix A once and then solve the triangular matrices for the different b, rather than using Gaussian elimination each time. The matrices L and U could be thought to have "encoded" the Gaussian elimination process.

The cost of solving a system of linear equations is approximately  floating-point operations if the matrix  has size . This makes it twice as fast as algorithms based on QR decomposition, which costs about  floating-point operations when Householder reflections are used. For this reason, LU decomposition is usually preferred.

Inverting a matrix
When solving systems of equations, b is usually treated as a vector with a length equal to the height of matrix A. In matrix inversion however, instead of vector b, we have matrix B, where B is an n-by-p matrix, so that we are trying to find a matrix X (also a n-by-p matrix):

We can use the same algorithm presented earlier to solve for each column of matrix X. Now suppose that B is the identity matrix of size n. It would follow that the result X must be the inverse of A.

Computing the determinant
Given the LUP decomposition  of a square matrix A, the determinant of A can be computed straightforwardly as

The second equation follows from the fact that the determinant of a triangular matrix is simply the product of its diagonal entries, and that the determinant of a permutation matrix is equal to (−1)S where S is the number of row exchanges in the decomposition.

In the case of LU decomposition with full pivoting,  also equals the right-hand side of the above equation, if we let S be the total number of row and column exchanges.

The same method readily applies to LU decomposition by setting P equal to the identity matrix.

Code examples

C code example
/* INPUT: A - array of pointers to rows of a square matrix having dimension N
 *        Tol - small tolerance number to detect failure when the matrix is near degenerate
 * OUTPUT: Matrix A is changed, it contains a copy of both matrices L-E and U as A=(L-E)+U such that P*A=L*U.
 *        The permutation matrix is not stored as a matrix, but in an integer vector P of size N+1
 *        containing column indexes where the permutation matrix has "1". The last element P[N]=S+N,
 *        where S is the number of row exchanges needed for determinant computation, det(P)=(-1)^S
 */
int LUPDecompose(double **A, int N, double Tol, int *P) {

    int i, j, k, imax;
    double maxA, *ptr, absA;

    for (i = 0; i <= N; i++)
        P[i] = i; //Unit permutation matrix, P[N] initialized with N

    for (i = 0; i < N; i++) {
        maxA = 0.0;
        imax = i;

        for (k = i; k < N; k++)
            if ((absA = fabs(A[k][i])) > maxA) {
                maxA = absA;
                imax = k;
            }

        if (maxA < Tol) return 0; //failure, matrix is degenerate

        if (imax != i) {
            //pivoting P
            j = P[i];
            P[i] = P[imax];
            P[imax] = j;

            //pivoting rows of A
            ptr = A[i];
            A[i] = A[imax];
            A[imax] = ptr;

            //counting pivots starting from N (for determinant)
            P[N]++;
        }

        for (j = i + 1; j < N; j++) {
            A[j][i] /= A[i][i];

            for (k = i + 1; k < N; k++)
                A[j][k] -= A[j][i] * A[i][k];
        }
    }

    return 1;  //decomposition done
}

/* INPUT: A,P filled in LUPDecompose; b - rhs vector; N - dimension
 * OUTPUT: x - solution vector of A*x=b
 */
void LUPSolve(double **A, int *P, double *b, int N, double *x) {

    for (int i = 0; i < N; i++) {
        x[i] = b[P[i]];

        for (int k = 0; k < i; k++)
            x[i] -= A[i][k] * x[k];
    }

    for (int i = N - 1; i >= 0; i--) {
        for (int k = i + 1; k < N; k++)
            x[i] -= A[i][k] * x[k];

        x[i] /= A[i][i];
    }
}

/* INPUT: A,P filled in LUPDecompose; N - dimension
 * OUTPUT: IA is the inverse of the initial matrix
 */
void LUPInvert(double **A, int *P, int N, double **IA) {

    for (int j = 0; j < N; j++) {
        for (int i = 0; i < N; i++) {
            IA[i][j] = P[i] == j ? 1.0 : 0.0;

            for (int k = 0; k < i; k++)
                IA[i][j] -= A[i][k] * IA[k][j];
        }

        for (int i = N - 1; i >= 0; i--) {
            for (int k = i + 1; k < N; k++)
                IA[i][j] -= A[i][k] * IA[k][j];

            IA[i][j] /= A[i][i];
        }
    }
}

/* INPUT: A,P filled in LUPDecompose; N - dimension.
 * OUTPUT: Function returns the determinant of the initial matrix
 */
double LUPDeterminant(double **A, int *P, int N) {

    double det = A[0][0];

    for (int i = 1; i < N; i++)
        det *= A[i][i];

    return (P[N] - N) % 2 == 0 ? det : -det;
}

C# code example
public class SystemOfLinearEquations
{
    public double[] SolveUsingLU(double[,] matrix, double[] rightPart, int n)
    {
        // decomposition of matrix
        double[,] lu = new double[n, n];
        double sum = 0;
        for (int i = 0; i < n; i++)
        {
            for (int j = i; j < n; j++)
            {
                sum = 0;
                for (int k = 0; k < i; k++)
                    sum += lu[i, k] * lu[k, j];
                lu[i, j] = matrix[i, j] - sum;
            }
            for (int j = i + 1; j < n; j++)
            {
                sum = 0;
                for (int k = 0; k < i; k++)
                    sum += lu[j, k] * lu[k, i];
                lu[j, i] = (1 / lu[i, i]) * (matrix[j, i] - sum);
            }
        }

        // lu = L+U-I
        // find solution of Ly = b
        double[] y = new double[n];
        for (int i = 0; i < n; i++)
        {
            sum = 0;
            for (int k = 0; k < i; k++)
                sum += lu[i, k] * y[k];
            y[i] = rightPart[i] - sum;
        }
        // find solution of Ux = y
        double[] x = new double[n];
        for (int i = n - 1; i >= 0; i--)
        {
            sum = 0;
            for (int k = i + 1; k < n; k++)
                sum += lu[i, k] * x[k];
            x[i] = (1 / lu[i, i]) * (y[i] - sum);
        }
        return x;
    }
}

MATLAB code example
function LU = LUDecompDoolittle(A)
    n = length(A);
    LU = A;
    % decomposition of matrix, Doolittle's Method
    for i = 1:1:n
        for j = 1:(i - 1)
            LU(i,j) = (LU(i,j) - LU(i,1:(j - 1))*LU(1:(j - 1),j)) / LU(j,j);
        end
        j = i:n;
        LU(i,j) = LU(i,j) - LU(i,1:(i - 1))*LU(1:(i - 1),j);
    end
    %LU = L+U-I
end

function x = SolveLinearSystem(LU, B)
    n = length(LU);
    y = zeros(size(B));
    % find solution of Ly = B
    for i = 1:n
        y(i,:) = B(i,:) - LU(i,1:i)*y(1:i,:);
    end
    % find solution of Ux = y
    x = zeros(size(B));
    for i = n:(-1):1
        x(i,:) = (y(i,:) - LU(i,(i + 1):n)*x((i + 1):n,:))/LU(i, i);
    end
end

A = [ 4 3 3; 6 3 3; 3 4 3 ]
LU = LUDecompDoolittle(A)
B = [ 1 2 3; 4 5 6; 7 8 9; 10 11 12 ]'
x = SolveLinearSystem(LU, B)
A * x

See also
Block LU decomposition
Bruhat decomposition
Cholesky decomposition
Crout matrix decomposition
Incomplete LU factorization
LU Reduction
Matrix decomposition
QR decomposition

Notes

References

 .
 .
 .
 . See Section 3.5. N − 1
 .
 .
 .
 .
 .

External links
References
 LU decomposition on MathWorld.
 LU decomposition on Math-Linux.
 LU decomposition at Holistic Numerical Methods Institute
 LU matrix factorization. MATLAB reference.

Computer code
 LAPACK is a collection of FORTRAN subroutines for solving dense linear algebra problems
 ALGLIB includes a partial port of the LAPACK to C++, C#, Delphi, etc.
 C++ code, Prof. J. Loomis, University of Dayton
 C code, Mathematics Source Library
 Rust code
 LU in X10

Online resources
 WebApp descriptively solving systems of linear equations with LU Decomposition
 Matrix Calculator with steps, including LU decomposition,
 LU Decomposition Tool, uni-bonn.de
 LU Decomposition by Ed Pegg, Jr., The Wolfram Demonstrations Project, 2007.

Matrix decompositions
Numerical linear algebra
Articles with example C code
Articles with example C Sharp code

de:Gaußsches Eliminationsverfahren#LR-Zerlegung

LU decomposition


The Chevrolet Avalanche was a four-door sport utility truck. It was sold by General Motors' Chevrolet brand in the United States. The Avalanche was first made in 2002 in Silao, Guanajuato, Mexico and the second generation was first shown at the Chicago Auto Show in February 2006. It was named after the sudden collapse of mountain snowpacks that are known as Avalanches. There have been two generations of the Chevrolet Avalanche with the second one being made in 2007, until it was discontinued in 2020.

Other websites
Chevrolet Avalanche at chevrolet.com

Avalanche
2000s automobiles
2010s automobiles
Pickup trucks

Chevrolet Avalanche


Sigue Sigue Sputnik is a Filipino street gang. They are one of the largest and most well-known gangs, whose influence and territory stretched throughout the slums of Tondo, Manila. They are one of the gangs present in major penitentiaries in Manila including Manila City Jail and New Bilibid Prison.

Origins
High poverty led to many in Tondo, Manila to band and form gangs. The gang was born in the 1960s as part of two branching groups of "Sigue Sigue" hoodlums in Tondo, the other one being Sigue Sigue Commandos, who are the Sputnik's most ardent rival. During the decade, they made turfs of many slums and jails in Manila. Researcher Franklin G. Ashburn described them as "perhaps the most structured and best organized conflict gang in the Manila City Jail at the time".

The motto of the gang was "He who comes to destroy us, will himself be destroyed" which is a direct reference to the Visayan gangs like the Oxo group who the Sputniks felt have "invaded" the Tagalog territory of Manila. Their name was derived from the Russian orbital satellite of the same name because of its "spying' or "all-knowing" capabilities. The Sputniks pride themselves on their knowledge of what was going on both inside and outside of the jail at all times - among friends, enemies, and the police. In addition, the claim was made that Sputnik organization is not confined to the Manila area alone, but that it was well known throughout the entire Philippines. Many murders in both the slums and in the jail of rival gangs were attributed to the Sputniks.

Culture
All full members of the Sputnik gang must undergo an initiation where they must wear a "tatak" (tattoo or brand), considered to be a badge of honor. There was a pride among the Sputniks regarding the tatak that borders on "blood brother" ties. The tatak is usually tattooed on the buttocks of each member and the ones examined by the investigator were found to be works of art. Talent does not go unnoticed in confinement for the Sputniks had one member who was designated as the official artist and he enjoyed a high status position in the group. The Sigue Sigue Sputniks in confinement have an elaborate system of "kautusan" or "regulations" which have come down from the Muntinglupa Prison and to which the members must subscribe while in jail. These "regulations" are known as the "Ten Commandments" of the Sputniks and are as follows:

1. Thou shalt not "squeal".

2. Thou shalt not kill fellow members.

3. Thou shalt not organize another gang.

4. Thou shalt not be selfish.

5. Thou shalt not steal from fellow members.

6. Thou shalt not own your own knife. If you own a knife, the leader must keep it.

7. Thou shalt not tell fairy tales to fellow members.

8. Obey your leader.

9. Love and honor your mark.

10. Be careful.

There is no set punishment for any given offense until the case has been tried before a council of elders and judges. One exception to this rule is in cases involving "squealing" where the punishment is merciless. Although the role definitions of individual Sputnik members were diffuse, even for the leaders, there was one main role that all must play. Every member must at all times "be friendly" with every other member of the gang - a kind of forced practicing "pakikisama". Each must help his fellow member whenever asked to do so, regardless of the situation or the circumstances.

Philippine Drug War
The Sigue Sigue Sputnik gang became one of the most embroiled street gangs during the Philippine Drug War. Various cases of violence were conducted by the gang during the war. On January 4, 2017, a Sputnik member by the name of Randy Lizardo shot and killed policeman PO1 Enrico Domingo in Tondo. Domingo, together with other PNP officers, were conducting a buy-bust operation inside Lizardo's home. As the lawmen burst, the gang surprised them out of the curtains with handguns. Domingo was hit in the head and died instantly, while another, PO2 Harley Gacera, was wounded in the shoulder. Lizardo and the gang managed to get away, but he would later be captured as he tried to flee the city nine days later.

On July 27, 2020, big time gang leader Rolando Loyola was captured during Operation Pagtugis led by Regional Intelligence Division, NCRPO; MPD Police Station 4 in Sampaloc, Manila. Loyola was a known leader of a robbery stick-up group. The Sputnik gang was also one of the main combatants during the 2020 New Bilibid Prison riots, one of the largest prison riots in contemporary Philippines. Although the reasons varied for the cause of the riot (investigations either saying it was started when a Sputnik gang member was killed or beheaded, or one of their LGBT members was insulted). Nonetheless, the gang retaliated against an alliance of Sigue Sigue Commando and Abu Sayyaf convicts, who they believed were the ones responsible. During the two month long series of riots, gang members fought with improvised melee weapons, knives, arrows, and allegedly, firearms. The riot was quelled after a combined force of Special Action Force and SWAT members stormed the prison. Thirteen convicts from both sides were killed.

In popular culture
 The gang's name was adopted in the 1980s by British new wave/punk band Sigue Sigue Sputnik.
 Bahala Na vs. Sputnik was a film released in 1995 that told the story of a gang war between the Bahala Na Gang and the Sputniks. The film starred George Estregan Jr. and Chuck Perez.
 Sigue Sigue Sputnik was featured in the Discovery Channel show Inside The Gangsters' Code episode "The Commandos" hosted by Louis Ferrante.
 The gang was also featured in the episode "Man Gets Attacked by Gang In The Filipino Slums" of the series Beyond Human Boundaries by Wonder.

References

See also
 Bahala Na Gang

Organizations established in the 1960s
Philippine drug war
1960s establishments in the Philippines
Street gangs
Gangs in the Philippines

Sigue Sigue Sputnik (gang)


Balfour House is an antebellum mansion located at the corner of Crawford Street and Cherry Street in Vicksburg, Mississippi. Built in 1835, it was the home of Emma Balfour, celebrated diarist of the Siege of Vicksburg. The red-brick, two-story structure features elements of Greek Revival and Federalist styles and is listed on the National Register of Historic Places.

1862 Christmas ball
In a scene reminiscent of the 1815 Duchess of Richmond's Ball prior to the Battle of Waterloo, Balfour House played host to a grand Christmas Ball on the night of December 24, 1862. The guests included many Confederate Army officers and their ladies. Among them was Brig. Gen. Martin Luther Smith, and Lt. Gen. Stephen D. Lee, who decades later published his own recollections of the fateful ball.

As the Christmas Eve revelry progressed, the telegraph office just across the Mississippi River in Louisiana received an urgent message from Major L.L. Daniel at Lake Providence, about 36 miles north.  Telegraph operator Colonel Philip H. Fall took the call.

The weather was cold and stormy, the river was dangerously turbulent and the only available transport across to Vicksburg was a small skiff.  It would mean risking his life, but Colonel Fall felt compelled to deliver the crucial information to General Smith, who he knew would be at the Balfours' Christmas Ball at that moment.

Shortly after midnight, Colonel Fall, exhausted and covered in mud, burst through the door of Balfour House and waded into the crowd of dancers, who gave him a wide berth.  When he saw General Smith he went directly to him and told him what he'd heard from Lake Providence.  Upon hearing the news, Smith announced loudly "This ball is at an end!  The enemy is coming down river.  All non-combatants must leave the city!" The men had only seconds to bid loved-ones good-bye as they rushed away and reported to station.  Later, on December 26, came the Battle of Chickasaw Bayou, the initial battle of the Vicksburg Campaign.

Siege of Vicksburg
During the Siege of Vicksburg, most houses were abandoned in favor of caves dug into hillsides for protection against mortar attacks, but Balfour House remained occupied. Emma Balfour famously refused to leave, and in fact used her home to shelter wounded Confederate soldiers.

With Union forces surrounding Vicksburg on all sides, and the Union Navy occupying the Mississippi River, the feeling of entrapment was palpable.  Emma wrote:  "What is to become of all the living things in this place when the boats commend shelling—God only knows—shut up as in a trap—no ingress or egress—and thousands of women and children...".

Union headquarters
After the surrender of the Confederates, Balfour House served as headquarters of Union Maj. Gen. James B. McPherson.

Notes

References

External links
 — includes images

Buildings and structures in Vicksburg, Mississippi
Houses on the National Register of Historic Places in Mississippi
Houses completed in 1835
Federal architecture in Mississippi
Colonial Revival architecture in Mississippi
Greek Revival houses in Mississippi
Houses in Warren County, Mississippi
National Register of Historic Places in Warren County, Mississippi

Balfour House


A floodplain is the flat area around a river that is covered in times of flood.  A floodplain is a very fertile area due to the rich alluvium (fine sediment) deposited by floodwaters. This makes floodplains a good place for agriculture. A build-up of alluvium on the banks of a river can create levees, which raise the riverbank.

Wetlands
Landforms
Waterways
Flood control

Floodplain


Sdelka!? (Cyrillic: Сделка!?, Russian for "deal") is the Russian version of Deal or No Deal.  It was broadcast on REN TV from April 17 to September 22, 2006, and hosted by Alexei Veselkin.  The prizes available ranged from 3,000,000 Russian rubles (about US$98,000, €69,000 or £61,000) to 1 kopek (smallest Russian unit of currency, less than 1 US cent, euro cent or penny).

The music used was taken from various other Deal or No Deal versions, like Miljoenenjacht (Theme), UK Deal or No Deal and Australian Deal or No Deal (various incidentals).

There are 22 cases held on a podium with 22 players that return each show like on Deal or No Deal UK, but they have briefcases rather than boxes. The show's set is similar to that of the American one, but the set is a lot smaller.

Case Values

External links
Official site

Deal or No Deal
Russian game shows
2006 Russian television series debuts
2006 Russian television series endings
2000s Russian television series

Sdelka


Celypha is a genus of tortrix moths (family Tortricidae). It belongs to the tribe Olethreutini of subfamily Olethreutinae.

The closely related genus Syricoris is sometimes included in Celypha.

Taxonomy

Species
The twenty currently recognized species of Celypha are:

 Celypha anatoliana (Caradja, 1916)
 Celypha argyrata Razowski, 2009
 Celypha atriapex Razowski, 2009
 Celypha aurofasciana
 Celypha capreolana (Herrich-Schäffer, 1851)
 Celypha cespitana
 Celypha conflictana (Kennel, 1901)
 Celypha constructa (Meyrick, 1922)
 Celypha cornigerus (Oku, 1968)
 Celypha ermolenkoi Kostyuk, 1980
 Celypha erythrana (Tengstrom, 1848)
 Celypha flavipalpana (Herrich-Schäffer, 1851)
 Celypha hydrangeana (Kuznetzov, 1969)
 Celypha kostjukorum Budashkin & Dubatolov, 2006
 Celypha kurilensis (Oku, 1965)
 Celypha perfracta Diakonoff, 1983
 Celypha pseudalarixicola Liu & Fang in Jianwen & Liu, 1992
 Celypha rufana
 Celypha rurestrana (Duponchel in Godart, 1842)
 Celypha sapaecola Razowski, 2009
 Celypha sistrata (Meyrick, 1911)
 Celypha striana
 Celypha woodiana (Barrett, 1882)

Synonyms
Obsolete scientific names (junior synonyms and others) for this genus are:
 Celypa (lapsus)
 Celyphoides Obraztsov, 1960
 Cleyphoides (lapsus)
 Euchroma (lapsus, non Solier, 1833: preoccupied)
 Euchromia Stephens, 1829 (non Hübner, [1819]: preoccupied)
 Loxoterma Busck, 1906

Due to the very close relationship between Celypha and the "wastebin genus" Olethreutes, there has been some confusion about the former's synonymy. Celyphoides and Loxoterma are sometimes listed as a synonym of Olethreutes. But the type species of the first is Tortrix flavipalpana (a junior synonym of C. flavipalpana), and that of the second is T. latifasciana (a junior synonym of C. aurofasciana). This makes Celyphoides and Loxoterma junior subjective synonyms of Celypha, at least in its present delimitation.

Celyphoides, meanwhile, was a nomen nudum for 5 years. It was first used by R. Agenjo Cecilia in 1955, but only properly established by N.S. Obraztsov in 1960.

Footnotes

References
  (2009a): Online World Catalogue of the Tortricidae – Genus Celypha account. Version 1.3.1. Retrieved 2009-JAN-20.
  (2009b): Online World Catalogue of the Tortricidae – Celypha species list. Version 1.3.1. Retrieved 2009-JAN-20.
  (2005a): Markku Savela's Lepidoptera and some other life forms – Celypha. Version of 2005-SEP-14. Retrieved 2010-APR-15.
  (2005b): Markku Savela's Lepidoptera and some other life forms – Olethreutes. Version of 2005-SEP-16. Retrieved 2010-APR-15.

Olethreutini
Tortricidae genera
Taxa named by Jacob Hübner

Celypha