OpenLLM-France/wikimedia huggingface dataset:
# Chain rule for Kolmogorov complexity

The chain rule for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states:
    $H(X,Y)=H(X)+H(Y|X)$
That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X. This follows immediately from the definitions of conditional and joint entropy, and the fact from probability theory that the joint probability is the product of the marginal and conditional probability:
    $P(X,Y)=P(X)P(Y|X)$
    $\Rightarrow \log P(X,Y)=\log P(X)+\log P(Y|X)$
The equivalent statement for Kolmogorov complexity does not hold exactly; it is true only up to a logarithmic term:
    $K(x,y)=K(x)+K(y|x)+O(\log(K(x,y)))$
(An exact version, KP(x, y) = KP(x) + KP(y|x$^∗$) + O(1), holds for the prefix complexity KP, where x$^∗$ is a shortest program for x.)
It states that the shortest program printing X and Y is obtained by concatenating a shortest program printing X with a program printing Y given X, plus at most a logarithmic factor. The results implies that algorithmic mutual information, an analogue of mutual information for Kolmogorov complexity is symmetric: ⁠$I(x:y)=I(y:x)+O(\log K(x,y))$⁠ for all x,y.

## Proof

The ≤ direction is obvious: we can write a program to produce x and y by concatenating a program to produce x, a program to produce y given access to x, and (whence the log term) the length of one of the programs, so that we know where to separate the two programs for x and y|x (log(K(x, y)) upper-bounds this length).
For the ≥ direction, it suffices to show that for all k,l such that ⁠$k+l=K(x,y)$⁠ we have that either
    $K(x|k,l)\leq k+O(1)$
or
    $K(y|x,k,l)\leq l+O(1)$.
Consider the list (a$_1$,b$_1$), (a$_2$,b$_2$), ..., (a$_e$,b$_e$) of all pairs ⁠$(a,b)$⁠ produced by programs of length exactly ⁠$K(x,y)$⁠ [hence ⁠$K(a,b)\leq K(x,y)$⁠]. Note that this list
* contains the pair ⁠$(x,y)$⁠,
* can be enumerated given k and l (by running all programs of length ⁠$K(x,y)$⁠ in parallel),
* has at most 2$^{K(x,y)}$ elements (because there are at most 2$^n$ programs of length n).
First, suppose that x appears less than 2$^l$ times as first element. We can specify y given x,k,l by enumerating (a$_1$,b$_1$), (a$_2$,b$_2$), ... and then selecting ⁠$(x,y)$⁠ in the sub-list of pairs ⁠$(x,b)$⁠. By assumption, the index of ⁠$(x,y)$⁠ in this sub-list is less than 2$^l$ and hence, there is a program for y given x,k,l of length ⁠$l+O(1)$⁠. Now, suppose that x appears at least 2$^l$ times as first element. This can happen for at most 2$^{K(x,y)−l}$ = 2$^k$ different strings. These strings can be enumerated given k,l and hence x can be specified by its index in this enumeration. The corresponding program for x has size ⁠$k+O(1)$⁠. Theorem proved.
# Terry Morrow

Terry Morrow (born October 22, 1963) is a Minnesota politician and former member of the Minnesota House of Representatives. A member of the Minnesota Democratic–Farmer–Labor Party (DFL), he represented District 23A, which included portions of Nicollet and Sibley counties.

## Minnesota House of Representatives

He was first elected in 2006, and was re-elected in 2008, 2010. In 2012, he was re-elected to the newly drawn District 19A seat, but resigned before the beginning of the new legislative session.
Morrow served as an assistant majority leader during the 2009–2010 biennium. He is a former member of the House Agriculture, Rural Economies & Veterans Affairs Committee; the House State and Local Government Operations Reform, Technology & Elections Committee; and of the Finance subcommittees for the Transportation and Transit Policy and Oversight Division; and the Transportation Finance and Policy Division. On November 16, 2010, incoming Minority Leader Paul Thissen announced that he would be one of four Minority Whips during the 2011–2012 legislative session.
On December 19, 2012, Morrow announced he will be stepping down at the end of his current term to join the National Conference of Commissioners on Uniform State Laws as its legislative director.

## Personal life

Morrow was a communication studies professor (1995-2013) at Gustavus Adolphus College in Saint Peter, Minnesota, where he also resides. Prior to running for the House, Morrow served on the Saint Peter School Board for several years.
# Roz Peterson

Roz Peterson is an American politician, businesswoman, and realtor. She is a former Republican member of the Minnesota House of Representatives, representing District 56B in the southern Twin Cities metropolitan area.

## Early life

Peterson attended Gustavus Adolphus College, graduating with a bachelor's degree in 1987. She served on the Lakeville school board prior to being elected to the Minnesota House of Representatives.

## Minnesota House of Representatives

Peterson was first elected to the Minnesota House of Representatives in 2014. She had previously sought election in 2012. Peterson served two terms in the Minnesota House, and was defeated by Alice Mann in the 2018 elections. In the 2020 elections, Peterson ran for her previously held District 56B seat, losing to Kaela Berg.

## Personal life

Peterson married her husband, Tim, in 1987. They have two children and reside in Lakeville, Minnesota.
# Barn Burning (film)

Barn Burning is a 1980 American short film directed by Peter Werner and starring Tommy Lee Jones. It is based on the 1939 short story of the same name by William Faulkner.

## Cast

* Tommy Lee Jones as Abner Snopes
* Diane Kagan as Mother Snopes
* Carolyn Coates as Lula De Spain
* Michael Riney as Brother
* Shawn Whittington as Sarty Snopes
* Jimmy Faulkner as Major De Spain
* Jennie Hughes
* Julie Kaye Townery
* Al Scott
* Jean Pettigrew
* Henry Fonda as narrator
# Derek Grier (politician)

Derek Grier is an American politician who served as a Republican member of the Missouri House of Representatives from the state's 100th House district.

## Career

Grier graduated from Principia College with a B.A. in business administration, and works in the real estate industry.
Grier is known for promoting professional licensing reform. He also advocated for improvement of rural healthcare in the wake of the COVID-19 pandemic.
# Lucius Quintus Cincinnatus Lamar I

Lucius Quintus Cincinnatus Lamar (July 15, 1797 – July 4, 1834) was an American attorney and jurist in his native Georgia. His son Lucius Quintus Cincinnatus Lamar II followed him into law and was appointed from Mississippi as a U.S. Supreme Court Justice.

## Early life and education

Lucius was the first son in his family, and born on his father's plantation in Milledgeville, Georgia, where he grew up. His parents, John and Rebecca (Lamar) Lamar had allowed his mother's brother to name their sons; he named them after his favorite historical heroes. Lamar was named for the Roman statesman Lucius Quinctius Cincinnatus. His younger brother was Mirabeau Buonaparte Lamar, who became known for fighting for the independence of the Republic of Texas and was elected as its second president. His parents were first cousins. Their family was well-connected in Georgia and the South; first cousins Gazaway Bugg Lamar and his brother G. W. became bankers in Augusta, Savannah, and New York City.
Lucius Lamar studied law at Milledgeville, Georgia, and at Litchfield Law School in Litchfield, Connecticut. He was admitted to the Georgia bar in 1819. He set up his practice in his hometown of Milledgeville. After getting established, he married and started a family.

## Law career

Lamar revised Augustin Smith Clayton's Georgia Justice about 1819. He was commissioned by the legislature to compile The Laws of Georgia from 1810 to 1819 (Augusta, 1821).
He gained respect as an attorney. In 1830, Lamar was elected as judge of the Superior Court, succeeding Thomas W. Cobb.
In 1834, he committed suicide by gunshot. He was said to have been despondent after learning that a man he had convicted of murder and sentenced to death was in fact innocent of the crime. But this account has been questioned. He was buried at Memory Hill Cemetery in Milledgeville.
# 3'-phosphoadenylyl-sulfate:(heparan sulfate)-glucosamine 3-sulfotransferase

3'-phosphoadenylyl-sulfate:(heparan sulfate)-glucosamine 3-sulfotransferase may refer to the following:
* (heparan sulfate)-glucosamine 3-sulfotransferase 1, an enzyme
* (heparan sulfate)-glucosamine 3-sulfotransferase 2, an enzyme
* (heparan sulfate)-glucosamine 3-sulfotransferase 3, an enzyme
# Gyan Jyoti College

Gyan Jyoti College, is the self-financed degree college in Dagapur, on the outskirts of Siliguri, Darjeeling district. It offers undergraduate courses in arts, science and commerce. It is affiliated to the University of North Bengal.

## Departments

* English
* Political Science
* Journalism
* Economics
* Mass Communication
* Commerce
* Finance Management
# Gyaneshwar, Kathmandu

Gyaneshwor is one of the central neighborhoods in the city of Kathmandu, Nepal. It is named after the ancient temple of Gyaneshwor Mahadev & Bhairavsthan located there. It is a multi-cultural residential area with good facilities. Some major establishments located there are the German embassy to Nepal, USEF, Mega Bank, Kaveri Inn, Valley Petrol Station, AT Burger House, Galaxy Public School, Mahendra Bhawan School etc.
The well-known International Primary School, closed in 2011, was also located in Gyaneshwor, where multiple generations of Nepalis from all over Kathmandu started their early education.
The football field of Sano Gaucharan is located on the northern side of Gyaneshwor. It is one of the best areas to live in Kathmandu.
# Wachenburg

The Wachenburg (German: ) is a castle on a hill overlooking Weinheim an der Bergstrasse, in Baden-Württemberg, Germany. It was built between 1907 and 1928 by the Weinheimer Senioren-Convent, a Corps of former students. The castle contains a restaurant with a nice view of the country.
# J. Raymond McGovern

J. Raymond McGovern (December 22, 1898 – March 14, 1974) was an American lawyer and politician. he served in the New York State Senate for three two-year terms (1946 to 1950), and as New York State Comptroller from 1951 to 1954.

## Early life and education

He was born on December 22, 1898, in New Rochelle, New York. McGovern graduated from Fordham University and the Fordham University School of Law.

## Career

He was a partner in the law firm of McGovern, Connelly & Davidson in New Rochelle.
He was a member of the New York State Senate from 1945 to 1950. He served as New York State Comptroller from 1951 to 1954, elected on the Republican ticket at the New York state election, 1950. In 1954, he ran for Lieutenant Governor of New York as the running mate of Irving Ives, but they were narrowly defeated by the Democratic–Liberal Party nominees.

## Death

He died on March 14, 1974, in New Rochelle, New York.
# Palazzo Massimo alle Colonne

The Palazzo Massimo alle Colonne is a Renaissance palace in Rome, Italy.

## History

The palace was designed by Baldassarre Peruzzi in 1532–1536 on a site of three contiguous palaces owned by the old Roman Massimo family and built after arson destroyed the earlier structures during the Sack of Rome (1527). In addition the curved facade was dictated by foundations built upon the stands for the stadium (odeon) of the emperor Domitian. It fronts the now-busy Corso Vittorio Emanuele II, a few hundred yards from the front of the church of Sant'Andrea della Valle.

## Entrance

The entrance is characterized by a central portico with six Doric columns, paired and single. Inside there are two courtyards, of which the first one has a portico with Doric columns as a basement for a rich loggia, which is also made of Doric columns. The column decorations gave the name to the palace, alle Colonne. The facade is renowned as one of the most masterful of its time, combining both elegance with stern rustication. The recessed entrance portico differs from typical palazzo models such as exemplified by the Florentine Palazzo Medici. In addition, there is a variation of size of windows for different levels, and the decorative frames of the windows of the third floor. Unlike the Palazzo Medici, there is no academic adherence to superimposition of orders, depending on the floor. On the opposite facade of this palace, opening onto the Piazzetta de' Massimi, the palace connects with the frescoed facade of the conjoined annex, the Palazzetto Massimo (or Palazzetto Istoriato). For many centuries, this used to be the central post office of Rome, a Massimo family perquisite. To the left of the palace is the Palazzo di Pirro, built by a pupil of Antonio da Sangallo.

## Interior

The interior ceilings and vestibules are elaborately ornamented with rosettes and coffered roofs. The entrance ceiling is decorated with a fresco by Daniele da Volterra, who represented scenes from the Life of Fabio Massimo, the supposed Roman founder of the Massimo family.

## Chapel

The chapel on the second floor was a room where the 14-year-old Paolo Massimo, son of Fabrizio Massimo, was recalled briefly to life by Saint Philip Neri on March 16, 1583. The interior of the palace is open to the public annually only on that day. Other notable events in the palace of the 16th century including various intrafamilial murders.
# Berry v. Superior Court

Berry v. Superior Court, 256 Cal. Rptr. 344 (1989), is an unofficially reported California Court of Appeal case. The case is relevant to the legal topic of criminal homicide and liability for unintentional killings.

## Background

In Berry v. Superior Court the defendant, Berry, was charged with the murder and negligent keeping of a mischievous animal which kills a human being (Pen. Code,§ 399); marijuana cultivation; and misdemeanor keeping of a fighting dog. This is a petition for a writ of prohibition seeking dismissal for the charges of murder and Penal Code section 399. Berry contended that the evidence presented at the preliminary hearing failed to establish implied malice; and there was no evidence that the animal was mischievous or was kept without ordinary care.
On June 13, 1987, Berry's pit bull dog killed 21⁄2 year old James Soto after the child had wandered into the area where "Willy" was tethered. The victim's parents had four other children and were warned by Berry about the dangerousness of Willy. The victim and his family lived on the same lot as Berry, and there was no enclosure around the dog. The dog was behind a six-foot fence, but the area was readily accessible to anyone.
There were 243 marijuana plants by Berry's house that could not be approached without crossing Willy's area. Berry bought the dog from a breeder of fighting dogs, and possessed considerable literature and equipment for dog fighting. "Willy" was known for his fighting abilities, his gameness, wind, and exceptionally hard bite. An animal control officer, who qualified as a fighting dog expert, testified that pit bull dogs are selectively bred to be aggressive towards other animals and that they are considered by animal control to be dangerous unless proven otherwise.

## Findings

The court used the test for implied malice in an unintentional killing to assess the merits of the defendants argument. Implied malice in an unintentional killing is an actual appreciation of a high risk that is objectively present. The act must be done with wanton disregard to life and with a base antisocial motive and a high probability that death will result.
The court found that Berry was aware of the dangerousness to human beings by his tethering of the dog, giving a warning to the parents that the dog was dangerous, his knowledge of the breed. The arguably antisocial purpose involved Berry owning a fighting dog and the apparent evidence that the dog was kept to guard illegal marijuana plants. The probability that death could result from Berry keeping the dog was found to be a question of fact for the jury to find. The writ of prohibition was denied.
Berry was convicted of involuntary manslaughter at trial, and sentenced to imprisonment for 3 years and 8 months.
# Paul Byrne (hurler)

Paul Byrne is an Irish retired sportsperson. He played hurling with his local club Thurles Sarsfield's and was a member of the Tipperary senior inter-county team in the 1960s and 1970s. Byrne won his sole set of All-Ireland and Munster winners' medals with Tipp in 1971.
Paul is an accomplished button accordion player and former primary school principal.
# Ian Crookenden

Ian Sinclair Crookenden (born 10 December 1943) is a former professional tennis player from New Zealand. Crookenden currently serves as the Head Men's and Women's Coach at Saint Joseph's University. He is a member of the Intercollegiate Tennis Hall of Fame.

## Biography

Crookenden first represented the New Zealand Davis Cup team in 1962, for a tie against Denmark in Copenhagen. It came soon after he had finished runner-up to Rod Laver at the 1962 British Hard Court Championships in Bournemouth. He also competed at the French Championships and Wimbledon that year, making the third round of the latter.
In 1963 he won the Newport Casino Invitational and also finished runner-up in the All England Plate.
He played collegiate tennis in the United States for UCLA from 1963 to 1967 and won two NCAA Division I doubles titles. In 1965, his third year, he was a member of the championship winning team. He also partnered Arthur Ashe to win the NCAA doubles title, then in 1966 claimed the doubles again, to become the second UCLA player to achieve this feat. On this occasion he teamed up with Charlie Pasarell. His final year in 1967 was served as captain and he steered UCLA to second place in the championships. He earned All-American selection in each of his last three seasons.
During his time at UCLA he continued to represent the New Zealand Davis Cup team in international competition. He made his last Davis Cup appearance in the 1965 competition and finished with a 4/9 record from five ties.
Crookenden reached the fourth round of the 1966 U.S. National Championships, which was the furthest he went in singles at a Grand Slam tournament. He did however make the semi-finals in men's doubles with countryman Lew Gerrard at the 1964 Wimbledon Championships.
He continued competing professionally in the 1970s in both singles and doubles events. His best singles performances were semi-final appearances at Grand Prix tournaments in the Omaha Open and Calgary Indoor in 1974. He also won a set against world number one Jimmy Connors when they met in a Washington quarter-final that year. In doubles he won one Grand Prix title, at Hampton in 1975, with Ian Fletcher.
A coaching pro for many years, Crookenden joined Wake Forest University in 1984 as the head men's tennis coach and indoor tennis club director, a role he held for 12 years. From 1997 to 2008 he served as director of tennis at the Philadelphia Cricket Club. He returned to collegiate tennis in 2008 when he was appointed head coach of the tennis programs at Saint Joseph's University.

## Grand Prix career finals
### Doubles: 3 (1–2)

| Result | W–L | Date | Tournament | Surface | Partner | Opponents | Score |
| Loss | 0–1 | Jan 1972 | Roanoke, U. S. | Carpet | Vladimír Zedník | Jimmy Connors Haroon Rahim | 4–6, 6–3, 3–6 |
| Loss | 0–2 | Jan 1974 | Roanoke, U. S. | Carpet | Jeff Simpson | Vitas Gerulaitis Sandy Mayer | 6–7, 1–6 |
| Win | 1–2 | Mar 1975 | Hampton, U. S. | Carpet | Ian Fletcher | Karl Meiler Jan Písecký | 6–2, 6–7, 6–4 |
# Youssef Fennich

Youssef Fennich (born 12 February 1993 in the Netherlands) is a Dutch retired footballer.

## Career

In 2011/12, Fennich won the youth league and reached the finals of the youth cup as well as that year's NextGen Series with A.F.C. Ajax, the most successful team in the Netherlands.
In 2012, he joined fellow Dutch side SC Heerenveen, where he failed to make an appearance.
After making one appearance with PEC Zwolle in the Dutch top flight, Fennich signed for Azerbaijani outfit Keşla FK, where he again failed to make an appearance.
In 2017, he signed for Moroccan club Chabab Rif Al Hoceima before sealing a move to Mouloudia Oujda in the same country the following season.
# Ziadie family

The Ziadie family is a Maronite family residing in Jamaica, where they were prominent merchants. A branch of the family now resides in the United States and its members have become successful horse trainers. They are the descendants of half a dozen Greek Orthodox brothers who emigrated from Lebanon.
Lady Colin Campbell, previously Georgia Ziadie, is descended from this family through her father, department store owner Michael George Ziadie. She claims that the Ziadies are a wealthy and well-known family in Jamaica. The opera director Sir Peter Jonas was her cousin.
By 1969, the family's alleged eminence had waned, with only one person of the name- dry goods merchant Edward George Ziadie- appearing in that year's Who's Who in Jamaica, detailing the "Careers of Principal Public Men and Women of Jamaica", alongside an advertisement for a real estate company, "Victor Ziadie Realty".
# Matt Entenza

Matthew "Matt" Keating Entenza (born October 4, 1961) is a Minnesota lawyer and former politician who served six terms in the Minnesota House of Representatives. He served as House Minority Leader from 2003 to 2006. After leaving the legislature, he was an unsuccessful candidate for various statewide offices, including governor, attorney general, and most recently state auditor.

## Background

Entenza was born in Santa Monica, California. He studied at Augustana College in South Dakota before transferring to Macalester College. After graduating, Entenza studied law at Oxford University and taught high school. After returning to Minnesota, he received his J.D. with honors from the University of Minnesota Law School.

## Service in the Minnesota House of Representatives

A Democrat, Entenza was elected to the Minnesota House of Representatives from District 64A in 1994. The district includes portions of the city of Saint Paul in Ramsey County. He served on the K-12 Finance, Education Policy, and Commerce committees.

## 2006 Minnesota Attorney General race

In 2006, Entenza resigned as House Minority Leader to focus on a campaign for Minnesota Attorney General. He withdrew from that race on July 18, 2006. Critics had raised concerns of a conflict of interest due to Entenza's wife's high ranking executive position at UnitedHealth Group. Entenza's political campaign committee was also fined $28,000 by the Minnesota Campaign Finance and Disclosure Board on August 15, 2006, for exceeding the legal amount for contributions.

## 2010 gubernatorial campaign

Entenza sought the office of governor in 2010. He first announced that he would seek the Minnesota DFL's endorsement for the 2010 Minnesota gubernatorial race, later dropping out of the endorsement process and running a primary campaign without the DFL endorsement. Before removing himself from the official endorsement process, he was endorsed by Minnesota Congressman Keith Ellison in May 2009 and Minnesota Stonewall DFL in December 2009. On May 27, 2010, he announced television broadcaster Robyne Robinson as his lieutenant governor running mate.
Entenza was not endorsed by the state party, and elected to participate in the primary election, in which he finished third, after Mark Dayton and Margaret Anderson Kelliher.

## 2014 Minnesota State Auditor race

In the 2014 election, Entenza ran for Minnesota State Auditor against the DFL-endorsed incumbent, Rebecca Otto. He bypassed public financing, which allowed him to exceed state spending limits. Despite spending more than $675,000 of his personal money on the race, Entenza received only 19% of the votes cast in the primary contest on August 12.

## Personal life

Entenza has three adult sons and is divorced from their mother, Lois Quam. He has since remarried, to Minnesota-native Jean Fox Entenza. Entenza is a Lutheran.
# Jack Tynan

John Christopher Tynan (5 December 1925 – 23 August 2020) was a New Zealand field hockey player and cricketer. He represented New Zealand in field hockey between 1948 and 1956, including at the 1956 Olympic Games in Melbourne. He played four first-class cricket matches for Wellington between 1952 and 1954.
Tynan died on 23 August 2020.