hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Law of total covariance
In probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if X, Y, and Z are random variables on the same probability space, and the covariance of X and Y is finite, then

The nomenclature in this article's title parallels the phrase law of total variance.  Some writers on probability call this the "conditional covariance formula" or use other names.

Note: The conditional expected values E( X | Z ) and E( Y | Z ) are random variables whose values depend on the value of Z.  Note that the conditional expected value of X given the event Z = z is a function of z.  If we write E( X | Z = z) = g(z) then the random variable E( X | Z ) is g(Z). Similar comments apply to the conditional covariance.

Law of total variance
The law of total variance is a fundamental result in probability theory that expresses the variance of a random variable Y in terms of its conditional variances and conditional means given another random variable X. Informally, it states that the overall variability of Y can be split into an “unexplained” component (the average of within-group variances) and an “explained” component (the variance of group means).

Formally, if X and Y are random variables on the same probability space, and Y has finite variance, then:

This identity is also known as the variance decomposition formula, the conditional variance formula, the law of iterated variances, or colloquially as Eve’s law, in parallel to the “Adam’s law” naming for the law of total expectation.

In actuarial science (particularly in credibility theory), the two terms  and  are called the expected value of the process variance (EVPV) and the variance of the hypothetical means (VHM) respectively.
Arkansas Highway 150
Highway 150 (AR 150, Ark. 150, and Hwy. 150) is a 14.19-mile-long (22.84 km) east–west state highway in Mississippi County, Arkansas. The route runs from Highway 181 north of Gosnell east across US Route 61 (US 61) and Interstate 55 (I-55) to Highway 137 at Huffman.

Arkansas Highway 181
Highway 181 (AR 181, Ark. 181, and Hwy. 181) is a designation for five segments of state highways in Mississippi County. A western route of 2.24 miles (3.60 km) runs from U.S. Route 61 (US 61) in Bassett to Interstate 55 (I-55). A second route, consisting of four segments connected by other state highways, of a total length of 31.19 miles (50.20 km) begins at Highway 14 in Marie and runs north to Missouri SSR-NN.
Florida Soccer Soldiers
Florida Soccer Soldiers is an American semi-professional soccer club based in North Miami Beach, Florida, that plays in the United Premier Soccer League. The club was established in 2018 and gained notoriety after they qualified for the third round of the 2019 U.S. Open Cup, defeating professional clubs Miami FC and Charlotte Independence.

Miami FC
Miami FC is an American professional soccer team based in Miami, Florida that competes in the USL Championship, the second tier of the American soccer pyramid.

The club began play in the North American Soccer League (NASL) in the 2016 season. Following the demise of the NASL, the club participated in the National Premier Soccer League (NPSL) and the National Independent Soccer Association (NISA) before moving to the USL Championship for the 2020 season. The team currently plays its home games at Pitbull Stadium on the campus of Florida International University.
Tezuka Productions
Tezuka Productions Co., Ltd. (株式会社手塚プロダクション, Kabushiki-gaisha Tezuka Purodakushon) is a Japanese mass media company founded by Osamu Tezuka in 1968, based in Shinjuku, Tokyo. The company is known for managing, supervising and licensing the intellectual property of Tezuka's works through various business areas such as publishing, animation, films, toys, video games among others. Aside from its licensing business, the company also handles an animation studio in Tezuka's former studio office in Niiza, Saitama and has produced notable works such as Marvelous Melmo, the 1980 and 2003 Astro Boy series, and Black Jack among others.

Astro Boy, the titular character of the media franchise of the same name serves as the company's mascot.

Black Jack (manga)
Black Jack (Japanese: ブラック・ジャック, Hepburn: Burakku Jakku), often abbreviated as B・J, is a Japanese manga series written and illustrated by Osamu Tezuka in the 1970s, dealing with the medical adventures of the title character, doctor Black Jack. Black Jack consists of hundreds of short, self-contained stories that are typically about 20 pages long. Black Jack has also been animated into an OVA, two television series (directed by Satoshi Kuwahara and Tezuka's son Makoto Tezuka) and two films.

In 1977, it won the first Kodansha Manga Award for the shōnen category. It has since then become one of Tezuka's best selling manga with over 47.66 million copies sold in Japan. Osamu Dezaki's anime film adaptation, Black Jack: The Movie, won Best Animation Film at the 1996 Mainichi Film Awards.
Bethlehem (House of Assembly of South Africa constituency)
Bethlehem was a constituency in the Orange Free State Province of South Africa, which existed from 1910 to 1994. Named after the town of Bethlehem, the seat covered a large rural area in the east of the province, bordering Natal as well as Lesotho. Throughout its existence it elected one member to the House of Assembly.

Orange Free State (province)
The Province of the Orange Free State (Afrikaans: Provinsie Oranje-Vrystaat), commonly referred to as the Orange Free State (Afrikaans: Oranje-Vrystaat), Free State (Afrikaans: Vrystaat) or by its abbreviation OFS, was one of the four provinces of South Africa from 1910 to 1994. After 27 April 1994 it was dissolved following the first non-racial election in South Africa. It is now called the Free State Province.

Its predecessor was the Orange River Colony which in 1902 had replaced the Orange Free State, a Boer republic.

Its outside borders were the same as those of the modern Free State Province; except for the bantustans ("homelands") of QwaQwa and one part of Bophuthatswana, which were contained on land inside of the provincial Orange Free State borders.
Kwasi Annoh Ankama
Kwasi Annoh Ankamah (1 June 1957 – 1 July 2010) was a Ghanaian lawyer and politician. He was a Member of Parliament of the Atiwa constituency and a member of the New Patriotic Party. He died while in office on an official delegation to London. He was succeeded as MP by Kwesi Amoako Atta.

Kwasi Amoako Atta
Kwasi Amoako-Attah (born 5 August 1951) is a Ghanaian lawyer, management consultant and politician. He is the Member of Parliament of the Atiwa West constituency in the Eastern Region of Ghana. He is a member of the New Patriotic Party and, as of 2017. He is a former Ghana's Minister for Roads and Highways.
Project Winter
Project Winter is a social deduction video game featuring survival game mechanics first released on May 23, 2019, for Windows. In Project Winter, players take on the roles of "survivors" and "traitors", having to repair two objectives to escape from an incoming blizzard, or stop an escape from happening.

Survival game
Survival games are a subgenre of action games which are often set in hostile, intense, open-world environments. Players generally start with minimal equipment and are required to survive as long as possible by finding the resources necessary to manage hunger, thirst, disease and/or mental state. Many survival games are based on randomly or procedurally generated persistent environments; more recently, survival games are often playable online, allowing players to interact in a single world. Survival games are generally open-ended with no set goals and often closely related to the survival horror genre, where the player must survive within a supernatural setting, such as a zombie apocalypse.
Piore River languages
The Piore River or Lagoon languages form a branch of Skou languages. Historically most have been lumped together as a single Warapu language, with Nouri variously classified. They are spoken in the Sissano Lagoon area of West Aitape Rural LLG, Sandaun Province, Papua New Guinea. The Piore River runs to the west of all the languages, and so speakers do not find it an acceptable name. However, it is not clear which name would be better, as the name of the lagoon, 'Sissano', is used for different neighboring languages.

Bauni language
Bauni is a language spoken in Barupu (Warapu) village (3°04′18″S 142°03′27″E﻿ / ﻿3.071595°S 142.057463°E﻿ / -3.071595; 142.057463﻿ (Barupu)) of West Aitape Rural LLG, Sandaun Province, Papua New Guinea.

The alternative name Barupu or Warapu, from the name of the Bauni village, has been applied to related languages as well, and 'Warapu' may be retained as a cover term.
Upney tube station
Upney (/ˈʌpni/) is a London Underground station on Upney Lane in Barking in the London Borough of Barking and Dagenham, east London. It is on the District line between Barking to the west and Becontree to the east. It is 11.0 kilometres (6.8 mi) along the line from the eastern terminus at Upminster and 13.7 kilometres (8.5 mi) to Tower Hill in central London. The station was opened on 12 September 1932 by the London, Midland and Scottish Railway with an additional pair of tracks that were constructed to serve the electric District Railway local service from Barking to Upminster. The single-storey brick building is of a common design also constructed at other stations on the eastern portion of the line. It is in London fare zone 4.

Barking station
Barking is an interchange station serving the town of Barking, east London. It is served by London Underground, London Overground and National Rail main line services. It is located on Station Parade, in the town centre.

On the London Underground, Barking is a stop on the District line and is also the eastern terminus of the Hammersmith & City line. On the London Overground, it is on the Suffragette line. On the National Rail network, it is served by c2c services operating to and from Fenchurch Street. There is also interchange with London Buses and East London Transit routes on the station frontage.

The station was opened in 1854 by the London, Tilbury and Southend Railway as one of the first stations on the route. It was rebuilt in 1908 and again in 1959.
Punjabi Mexican Americans
Punjabi Mexican Americans or Punjabi Chicanos, originally Punjabi Mexicans, are a distinctive ethnicity holding its roots in a migration pattern that occurred since the British Raj. The first conglomeration of these cultures occurred in the Imperial and Central Valleys in 1907, near the largest irrigation system in the Western Hemisphere. The majority of them localized to Yuba City, California.

Yuba City, California
Yuba City (Maidu: Yubu) is a city in and the county seat of Sutter County, California, United States. The population was 70,117 at the 2020 census. Yuba City is the principal city of the Yuba City Metropolitan Statistical Area which encompasses all of Sutter County and Yuba County. The metro area's population is 164,138. It is the 21st largest metropolitan area in California, ranked behind Redding and Chico. Its metropolitan statistical area is part of the Greater Sacramento CSA.
Phenylethanolamine
Phenylethanolamine (sometimes abbreviated PEOH), or β-hydroxyphenethylamine, is a trace amine with a structure similar to those of other trace phenethylamines as well as the catecholamine neurotransmitters dopamine, norepinephrine, and epinephrine. As an organic compound, phenylethanolamine is a β-hydroxylated phenethylamine that is also structurally related to a number of synthetic drugs in the substituted phenethylamine class. In common with these compounds, phenylethanolamine has strong cardiovascular activity and, under the name Apophedrin, has been used as a drug to produce topical vasoconstriction.

In appearance, phenylethanolamine is a white solid.

Phenylethanolamine is perhaps best known in the field of bioscience as part of the enzyme name "phenylethanolamine N-methyl transferase", referring to an enzyme which is responsible for the conversion of norepinephrine into epinephrine, as well as other related transformations.

Adrenaline
Adrenaline, also known as epinephrine and alternatively spelled adrenalin, is a hormone and medication which is involved in regulating visceral functions (e.g., respiration). It appears as a white microcrystalline granule. Adrenaline is normally produced by the adrenal glands and by a small number of neurons in the medulla oblongata. It plays an essential role in the fight-or-flight response by increasing blood flow to muscles, heart output by acting on the SA node, pupil dilation response, and blood sugar level. It does this by binding to alpha and beta receptors. It is found in many animals, including humans, and some single-celled organisms. It has also been isolated from the plant Scoparia dulcis found in Northern Vietnam.
Motherwell (district)
55°48′N 3°56′W﻿ / ﻿55.80°N 3.93°W﻿ / 55.80; -3.93

Motherwell (Scottish Gaelic: Tobar na Màthar, Scots: Mitherwall or Murwall) was a local government district in the Strathclyde region of Scotland from 1975 to 1996, lying to the south-east of the regional capital Glasgow.

Strathclyde
Strathclyde (Ystrad Clud in Welsh; Srath Chluaidh [s̪t̪ɾa ˈxl̪ˠɯi] in Gaelic, meaning 'strath [valley] of the River Clyde') was one of nine former local government regions of Scotland created in 1975 by the Local Government (Scotland) Act 1973 and abolished in 1996 by the Local Government etc. (Scotland) Act 1994. The Strathclyde region had 19 districts. The region was named after the early medieval Kingdom of Strathclyde centred on Govan, but covered a broader geographic area than its namesake by including Argyll and various Western islands in addition to its Southwestern core.
Bramlage Coliseum
Fred Bramlage Coliseum is a multi-purpose indoor arena in Manhattan, Kansas, with an official capacity of 11,000. It is the home to the Kansas State University men's and women's basketball teams, and used to serve as the venue for Kansas State's women's volleyball team. The facility currently holds offices for various administrative and business units for K-State Athletics, and the track & field team. Bramlage was previously the home for other K-State team offices, including women's soccer and baseball.

Kansas State Wildcats men's basketball
The Kansas State Wildcats men's basketball team represents Kansas State University in college basketball competition. The program is classified in the NCAA Division I, and is a member of the Big 12 Conference. The Interim Head Coach is  Matthew Driscoll.

The program began competition in 1902. The first two major-conference regular season titles won by the school were won by the men's basketball team, in 1917 and 1919 (in the Missouri Valley Intercollegiate Athletic Association). Kansas State has gone on to win 19 regular season conference crowns. The Wildcats have appeared in the NCAA tournament 32 times, most recently in 2023. Kansas State's best season finish came in 1951, losing the national final to Kentucky. Jeff Sagarin listed the program 27th in his all-time rankings in the ESPN College Basketball Encyclopedia. Following the 2024-25 season, the Wildcats have a record of 1,752-1,254.
2014–15 Bremen-Liga
The 2014–15 season of the Bremen-Liga, the highest association football league in the German state of Bremen, was the seventh season of the league at tier five (V) of the German football league system.

Bremen-Liga
The Bremen-Liga, sometimes also referred to as Oberliga Bremen, is a fifth tier of the German football league system and the highest league in the German state Free Hanseatic City of Bremen. It is one of fourteen Oberligas in German football, the fifth tier of the German football league system.
John 9
John 9 is the ninth chapter of the Gospel of John in the New Testament of the Christian Bible. It maintains the previous chapter's theme "Jesus is light", recording the healing of an unnamed man who had been blind from birth, a miracle performed by Jesus, and their subsequent dealings with the Pharisees.  The man born blind comes to complete faith in Jesus, while some of the Pharisees remain in their sin. The author of the book containing this chapter is anonymous, but early Christian tradition uniformly affirmed that John composed this Gospel.

John 8
John 8 is the eighth chapter in the Gospel of John in the New Testament of the Christian Bible. It continues the account of Jesus' debate with the Pharisees after the Feast of Tabernacles, which began in the previous chapter.

Verses 1-11, along with John 7:53, form a pericope which is missing from some ancient Greek manuscripts. In verse 12, Jesus describes himself as "the light of the world" and verse 32 contains the well-known teaching "ye shall know the truth, and the truth shall make you free". In verses 56–58, Jesus claims to have existed before Abraham: "Verily, verily, I say unto you, Before Abraham was, I am."
St. Gallen Cathedral
The Stiftskirche St. Gallus und Otmar (Collegiate Church of St. Gall and Otmar) is a Roman Catholic church in the city of St. Gallen, Switzerland. Once part of the Abbey of St. Gall, it has been the cathedral of the Diocese of St. Gallen since 1847. It is considered one of the last great sacred structures of the Baroque era, and is a UNESCO World Heritage site.

Saint Gall
Gall (Latin: Gallus; c. 550 – c. 645) according to hagiographic tradition was a disciple and one of the traditional twelve companions of Columbanus on his mission from Ireland to the continent. However, he may have originally come from the border region between Lorraine and Alemannia and only met Columbanus at the monastery of Luxeuil in the Vosges. Gall is known as a representative of the Irish monastic tradition. The Abbey of Saint Gall in the city of Saint Gallen, Switzerland was built upon his original hermitage. Deicolus was the elder brother of Gall.
Poor Mountain Natural Area Preserve
Poor Mountain Natural Area Preserve is a 1,404-acre (568 ha) Natural Area Preserve located on Poor Mountain in Roanoke County, Virginia.  The preserve protects the world's largest population of piratebush (Buckleya distichophylla), a globally rare parasitic shrub.  The mountain derives its name from the fact that the soils on its slopes are poor, due to their base of metamorphosed sandstone bedrock. The preserve's pine-oak/heath woodlands include Table Mountain pine, eastern hemlock, several species of oak, and shrubs including huckleberry, mountain laurel, and fetterbush.

Poor Mountain Natural Area Preserve is owned and maintained by the Virginia Department of Conservation and Recreation. The preserve is open to the public, with improvements including a small parking area and four miles (6.4 km) of trails.

Virginia Natural Area Preserve System
The Virginia Natural Area Preserve System is a system of protected areas in the state of Virginia. It is managed by the Virginia Department of Conservation and Recreation.

As of 2025, there are sixty-seven (67) dedicated preserves totaling 65,107 acres (263.48 km2). These preserves contain examples of some of the rarest natural communities in the state; in addition, many serve as a home for locally, nationally, and globally rare species.
Clancy Street Boys
Clancy Street Boys is a 1943 comedy film directed by William Beaudine and starring the East Side Kids. It is Beaudine's first film with the team; he would direct several more in the series and many in the Bowery Boys canon. Leo Gorcey married the female lead Amelita Ward. There is no mention of "Clancy Street" in the film, but a rival gang at Cherry Street appears at the beginning and climax of the film.

East Side Kids
The East Side Kids were characters in a series of 22 films released by Monogram Pictures from 1940 through 1945. The series was a low-budget imitation of the Dead End Kids, a successful film franchise of the late 1930s.
Espantito
Martín Rodríguez (April 24, 1968 – October 12, 2020), better known by the ring name Espantito (Spanish for "Little Terror" or "Little Scare"), was a Mexican luchador enmascarado (or masked professional wrestler) working in the Mini-Estrella ("Mini-Star") division. Working in the Mini-Estrella division does not automatically mean that Espantito had dwarfism as several wrestlers who are just shorter in stature work in the "Mini" division. As a luchador enmascarado, Espantito's real name was not a matter of public record, but it was revealed upon his death in 2020.

Espantito made his professional wrestling debut in 1993 and was allowed to use a version of the Espanto mask and name with permission of the only surviving Espanto, Espanto III. He worked primarily on the Mexican independent circuit, but also worked for AAA, one of Mexico's largest professional wrestling promotions.

Wrestling mask
A wrestling mask is a fabric-based mask that some professional wrestlers wear as part of their in-ring persona or gimmick. Professional wrestlers have been using masks as far back as 1915 and they are still widely used today, especially in Mexican lucha libre.
The Slide (Atlanta Braves)
The Slide was a baseball play that occurred in Game 7 of the 1992 National League Championship Series (NLCS) on October 14, 1992, at Atlanta–Fulton County Stadium in Atlanta, Georgia. In 1992, the Atlanta Braves returned to the NLCS and once again defeated the Pittsburgh Pirates in seven games, culminating in a dramatic game seven win. Francisco Cabrera's two-out single that scored David Justice and Sid Bream capped a three-run rally in the bottom of the ninth inning that gave the Braves a 3–2 victory. It was the third time in post-season history that the tying and winning runs had scored on a single play in the ninth inning.

This marked the end of the three-year divisional championship run of the Pirates, who after the 1992 season lost Barry Bonds, Doug Drabek, and other key players from those championship teams. The Pirates did not have another winning season until 2013.

1992 Atlanta Braves season
The 1992 Atlanta Braves season was the 27th in Atlanta and the 122nd overall. It involved the Braves finishing first in the National League West with a record of 98 wins and 64 losses, clinching their second straight division title.

In the NLCS, the Braves defeated the Pittsburgh Pirates in seven games. In the World Series, Atlanta faced the Toronto Blue Jays, who were making their first appearance in the World Series. However, the Blue Jays won in six games, becoming the first non-U.S.-based team to win a World Series.
Pan Tianshou
Pan Tianshou (simplified Chinese: 潘天寿; traditional Chinese: 潘天壽; pinyin: Pān Tiānshòu; March 14, 1897– September 5, 1971) was a Chinese painter and art educator.

Pan was born in Guanzhuang, Ninghai County, Zhejiang Province, and graduated from Zhejiang First Normal School (now Hangzhou High School). He studied Chinese traditional painting with Wu Changshuo, and built the foundation of Chinese traditional painting education.  He was persecuted during the Cultural Revolution until his death in 1971.

Wu Changshuo
Wu Changshuo (Chinese: 吳昌碩; pinyin: Wú Chāngshuò, September 12, 1844 – November 29, 1927, also romanised as Wu Changshi, Chinese: 吳昌石; pinyin: Wú Chāngshí), born Wu Junqing (Chinese: 吳俊卿; pinyin: Wú Jùnqīng), was a Chinese calligrapher, painter, and seal artist of the late Qing Period.