hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Linear independence
In linear algebra,  a set of vectors is said to be linearly independent if there exists no vector in the set that is equal to a linear combination of the other vectors in the set. If such a vector exists, then the vectors are said to be linearly dependent. Linear independence is part of the definition of linear basis.

A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors.  The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.

Set (mathematics)
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, geometric shapes, variables, or other sets.  A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton.

Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.  Instead, sets serve as foundational objects whose behavior is described by axioms modeled on intuition about collections, and then essentially all other mathematical objects are rigorously defined in terms of sets.

Set theory studies possible axiom systems and their consequences.
Since the first half of the 20th century, ZFC (Zermelo–Fraenkel set theory with the axiom of choice) has been the axiom system most commonly used.
Maggie Lloyd-Williams
Maggie Lloyd Williams (born 1975) is a Zimbabwean actress and author. She is best known for the roles in television serials, such as Silent Witness, Secret Diary of a Call Girl, Red Cap, and The Low Down.

Red Cap (TV series)
Red Cap is a British television drama series, produced by Stormy Pictures for the BBC and broadcast on BBC One. A total of thirteen episodes were broadcast over the course of two series, beginning with a feature-length pilot on 28 December 2001. The series follows the investigations and personal relationships of a British Army Special Investigation Branch unit of the Royal Military Police based in Germany.

The series initially focused on lead character, Sergeant Jo McDonagh (Tamzin Outhwaite), who was nicknamed McDoughnut, but later series played out as more of an ensemble piece, with several notable characters coming to prominence. A number of fictional regiments were featured in the series, including the Bedford Light Infantry, the Royal Cumbrian Fusiliers, the Wessex Regiment and the Derbyshire Light Infantry.
The Cutting Edge: Chasing the Dream
The Cutting Edge: Chasing the Dream is a 2008 sports-romantic drama television film, and the third installment in The Cutting Edge film series. The film was produced for the ABC Family cable channel, which aired on March 16, 2008. The film is rated PG-13.

Matt Lanter
Matthew MacKendree Lanter (born April 1, 1983) is an American actor and model. He began his career in modeling in 2004, the same year he appeared in the film Bobby Jones: Stroke of Genius and the television series Point Pleasant. He gained fame for his role of Liam Court in 90210 (2009–2013). Lanter is also known for his extensive voice work in the Star Wars franchise, voicing Anakin Skywalker / Darth Vader in projects such as the animated film Star Wars: The Clone Wars (2008) and its subsequent television series, Star Wars Rebels, and other Star Wars media. From 2016 to 2018, he played a lead role as Wyatt Logan in the sci-fi television series Timeless. His works also include Jupiter's Legacy, Disaster Movie, Sorority Row, Vampires Suck, The Roommate, and Pitch Perfect 3. Beyond film and television, his voice work also includes roles in video games and narration for audiobooks.
Dar Jellouli Museum
Dar Jellouli Museum (Arabic: متحف دار الجلولي), also known as the Regional Museum of Arts and Folk Traditions, is an art museum located in Tunisia. It was founded in 1939 by the French scholar on Maghrebi art Lucien Golvin, in a palace located in the heart of the ancient city of Sfax.

Lucien Golvin
Lucien Camille Golvin (18 July 1905 – 6 July 2002) was a French university professor and specialist in Maghreb art. Beginning his career in Tunisia in 1929, he went on to direct arts and crafts institutions and founded museums in Sfax, Oran, and Constantine. In Algeria, he collaborated with Georges Marçais on archaeological research at Kalâa of Béni Hammad and later became professor of Islamic art and archaeology at the Université d'Aix-Marseille (1962–1977). His career combined museum curation, field research, and academic teaching, shaping the study of Islamic and Maghreb art.
Erin McCarthy
Erin McCarthy (born July 7, 1990) is a right-handed American professional ten-pin bowler from Elkhorn, Nebraska, known for winning the 2022 U.S. Women's Open. She bowls professionally on the Professional Women's Bowling Association (PWBA) Tour, and has previously bowled internationally as a member of Team USA.

McCarthy is a member of the 900 Global pro staff, having previously been sponsored by MOTIV Bowling and Hammer. She is also sponsored by Turbo 2-n-1 grip inserts and Apparel EFX.

Storm Products
Storm Products Inc. is an American company involved in the manufacture and sale of bowling balls and bowling-related accessories. The company headquarters and main manufacturing facility are in Brigham City, Utah. Storm has produced many bowling balls used in the sport by competitive players, and has numerous sponsorship agreements on both the PBA and PWBA Tours. Storm currently employs about 165 people (about 120 in Utah). The company manufactures about 500,000 balls a year, and ships to 70 countries.

Storm Products also owns the Roto Grip and 900 Global bowling ball brands, and 3G Shoes.
You Never Forget Your First
You Never Forget Your First: A Biography of George Washington is a biography about George Washington, the first president of the United States. The book was written by Alexis Coe, a historian and former research curator at the New York Public Library, and is the third complete biography of Washington written by a female author. It was published on February 4, 2020, and appeared on The New York Times Best Sellers list.

Alexis Coe
Alexis Coe is an American presidential historian, columnist, podcast host, exhibition curator and tv commenter. She is a senior fellow at New America, the American history columnist at the New York Times Book Review, and the author of award-winning Alice and Freda Forever: A Murder in Memphis (2014) and the New York Times best-selling You Never Forget Your First: A Biography of George Washington (2020).
Listed buildings in Carburton
Carburton is a civil parish in the Bassetlaw District of Nottinghamshire, England.  The parish contains seven listed buildings that are recorded in the National Heritage List for England.  Of these, one is listed at Grade II*, the middle of the three grades, and the others are at Grade II, the lowest grade.  The parish contains the village of Carburton and the surrounding area.  To the east of the area is the west part of Clumber Park, and the listed buildings here are lodges, gate piers and a bridge.  The other listed buildings consist of a church, houses and farm buildings.

Carburton
Carburton or Carberton is a small village on the west side of Clumber within the Bassetlaw district of Nottinghamshire, England. It is primarily rural and residential. The church of Saint Giles is an unusual shape and dates back to the early 12th century, parish records date back to the 1530s

Carburton stands on the River Poulter, on the Ollerton Road and is very close to Clumber Park. It is surrounded by four major cities, those being Doncaster, Lincoln, Sheffield and Nottingham, which is around 24 miles (39 km) away. Whilst London is 154 miles (248 km) away via the M1.
Nadin, Croatia
Nadin is a Croatian village in the Zadar County, located between Benkovac and Škabrnja. The population is 406 (census 2011).

The village was inhabited since the time of the Liburnians when it was named Nedainium. It was conquered by Ottoman Empire in 1527 and was part of Sanjak of Krka till 1683 except brief occupation of Republic of Venice in 1647. It was also ruled by Venice between 1683 and 1797. Nadin was included in Republic of Serbian Krajina between 1991 and 1995. The Nadin massacre was a Serbian war crime carried out by the JNA on November 19, 1991. Five Croatian soldiers and 14 civilians were killed, while three civilians are still missing.

Liburnians
The Liburnians or Liburni (Ancient Greek: Λιβυρνοί) were an ancient tribe inhabiting the district called Liburnia, a coastal region of the northeastern Adriatic between the rivers Arsia (Raša) and Titius (Krka) in what is now Croatia. According to Strabo's Geographica, they populated Kerkyra until shortly after the Corinthians settled the island, c. 730 BC. Their ethnic and linguistic origins are unknown.
Chavagnac, Dordogne
Chavagnac (French pronunciation: [ʃavaɲak]; Occitan: Chavanhac) is a former commune in the Dordogne department in Nouvelle-Aquitaine in southwestern France. On 1 January 2017, it was merged into the new commune Les Coteaux Périgourdins.

Les Coteaux Périgourdins
Les Coteaux Périgourdins (French pronunciation: [le kɔto peʁiɡuʁdɛ̃]; Occitan: Los Termes Perigòrds) is a commune in the department of Dordogne, southwestern France. The municipality was established on 1 January 2017 by merger of the former communes of Chavagnac (the seat) and Grèzes.
Śluza, Chojnice County
Śluza [ˈɕluza] is a settlement in the administrative district of Gmina Chojnice, within Chojnice County, Pomeranian Voivodeship, in northern Poland.

For details of the history of the region, see History of Pomerania.

Gmina Chojnice
Gmina Chojnice (Kashubian: Chojnice) is a rural gmina (administrative district) in Chojnice County, Pomeranian Voivodeship, in northern Poland. Its seat is the town of Chojnice, although the town is not part of the territory of the gmina.

The gmina covers an area of 458.34 square kilometres (177.0 sq mi), and as of 2006 its total population is 16,014.

The gmina contains parts of the protected areas of Tuchola Landscape Park and Zaborski Landscape Park.
U.S. Route 29 in North Carolina
U.S. Highway 29 (US 29) is a United States Numbered Highway that runs for 168.7 miles (271.5 km) from the South Carolina state line, near Blacksburg, to the commonwealth of Virginia, near Danville. It is signed with north–south cardinal directions but is actually a northeast and southwest diagonal highway throughout the state. The route serves the North Carolina Piedmont, including the cities of Charlotte, Salisbury, High Point, and Greensboro. From Salisbury to Greensboro, US 29 spends roughly a third of its length in the state being concurrent with US 70.

Kannapolis, North Carolina
Kannapolis (/kəˈnæpəlɪs/) is a city in Cabarrus and Rowan counties in North Carolina, northwest of Concord and northeast of Charlotte, and is a suburb in the Charlotte metropolitan area. The city of Kannapolis was incorporated in 1984. The population was 53,114 at the 2020 census, which makes Kannapolis the 19th-most populous city in North Carolina. It is the home of the Kannapolis Cannon Ballers, the Low-A baseball affiliate of the Chicago White Sox, and it is the hometown of the Earnhardt racing family. It is also the headquarters for the Haas F1 racing team. The center of the city is home to the North Carolina Research Campus, a public-private venture that focuses on food, nutrition, and biotech research.
Vasil Levski National Military University
43°5′5″N 25°36′10″E﻿ / ﻿43.08472°N 25.60278°E﻿ / 43.08472; 25.60278

The Vasil Levski National Military University (Bulgarian: Национален военен университет "Васил Левски", romanized: Natsionalen voenen universitet "Vasil Levski") is Bulgaria's national military academy.

Military academy
A military academy or service academy is an educational institution which prepares candidates for service in the officer corps. It normally provides education in a military environment, the exact definition depending on the country concerned.

Three types of academy exist: pre-collegiate-level institutions awarding academic qualifications, university-level institutions awarding bachelor's-degree-level qualifications, and those preparing officer cadets for commissioning into the armed services of the state.

A naval academy is either a type of military academy (in the broad sense of that term) or is distinguished from one (in the narrow sense). In U.S. usage, the Military, Merchant Marine, Naval, Coast Guard, and the Air Force Academy serve as military academies under the categorization of service academies in that country.
Brant County Board of Education
The Brant County Board of Education is a former school district in the Canadian province of Ontario. In the late 1990s, it was amalgamated with the Norfolk County Board of Education and the Haldimand County Board of Education to create the Grand Erie District School Board.

Grand Erie District School Board
The Grand Erie District School Board (GEDSB, Originally known as Haldimand Norfolk Brant (English-language Public) District School Board No. 23 prior to May 1998)  is a school board that has legal jurisdiction over Norfolk County, Haldimand County, and Brant County in the province of Ontario, Canada. The main headquarters are in Brantford.
1930 International Lawn Tennis Challenge
The 1930 International Lawn Tennis Challenge was the 25th edition of what is now known as the Davis Cup. For the silver anniversary, 24 teams would enter the Europe Zone, while 4 would enter the America Zone.

The United States defeated Italy in the Inter-Zonal play-off, but would lose to France in the Challenge Round, giving France their fourth straight title, in the sixth straight Challenge Round matchup between these teams. The final was played 25–27 July at Stade Roland Garros in Paris.

Italy Davis Cup team
The Italy men's national tennis team represents Italy in Davis Cup tennis competition and is governed by the Italian Tennis Federation.

Italy is the reigning champion, claiming the Davis Cup in 2025. It is a four-time champion overall, also winning in 1976, 2023, and 2024. It finished runner-up six times (1960, 1961, 1977, 1979, 1980, 1998).

The most awarded player (by titles won when part of the team) is Simone Bolelli, with three victories. Matteo Berrettini, Lorenzo Musetti, Jannik Sinner, Lorenzo Sonego and Andrea Vavassori won the Davis Cup twice. The most awarded captain is Filippo Volandri, with three victories.

For the past three years, Italy has won the title, becoming the first country to win the event three consecutive times since the United States in 1972. In 2024 and 2025, Italy was also champion in the Billie Jean King Cup, making it the only country to win both events in consecutive years.
Willem de Zwart
Wilhelmus "Willem" Hendrikus Petrus Johannes de Zwart (16 May 1862 – 11 December 1931) was a Dutch painter, engraver, and watercolorist with many connections to the Hague School and later associated with the Amsterdam Impressionism movement.

Amsterdam Impressionism
Amsterdam Impressionism was an art movement in late 19th-century Holland. It is associated especially with George Hendrik Breitner and is also known as the School of Allebé.

The innovative ideas about painting of the French Impressionists were introduced into the Netherlands by the artists of the Hague School. This new style of painting was also adopted in Amsterdam by the young generation of artists of the late 19th century. Like their French colleagues, these Amsterdam painters put their impressions onto canvas with rapid, visible strokes of the brush. They focused on depicting the everyday life of the city.
2025 United States Olympic mixed doubles curling trials
The 2025 United States Mixed Doubles Curling Olympic Trials were held from February 17 to 23, 2025, at Rock Creek Curling in Lafayette, Colorado. The trials featured ten teams that played in a round robin tournament with the top four teams qualifying for the page playoff. The final was then a best of three to determine the winner.

The winning team of Cory Thiesse and Korey Dropkin represented the United States at the 2025 World Mixed Doubles Curling Championship in Fredericton, New Brunswick, where they qualified for the 2026 Winter Olympics in Cortina d'Ampezzo, Italy.

Korey Dropkin
Korey Dropkin (born June 11, 1995) is an American curler originally from Southborough, Massachusetts. At the 2026 Olympics, he and Cory Thiesse became the first American team to win a medal in Olympic mixed doubles curling, winning the silver medal.
Suhail Yusuf Khan
Suhail Yusuf Khan (Hindi: सुहेल युसूफ खान; born 1988) is an Indian sarangi player and vocalist. He is the grandson of Sarangi maestro Ustad Sabri Khan (1927-2015).

In 2016, Khan released Everything Sacred, a collaborative folk album with James Yorkston and Jon Thorne under the name Yorkston/Thorne/Khan. The trio went on to release two further albums, Neuk Wight Delhi All-Stars (2017) and Navarasa: Nine Emotions (2020).

Khan is also a member of Welsh-Indian folk fusion group Khamira, who released their debut self-titled album in May 2017. The group includes Indian musicians and members of Welsh folk-jazz group Burum; both Khamira (Hindi) and Burum (Welsh) mean "yeast" in English.

James Yorkston
James Yorkston (born James Patrick Yorkston Wright; 21 December 1971) is a Scottish folk musician, singer-songwriter and author from the village of Kingsbarns, Fife. He has been releasing music since 2001. As well as recording as a solo artist, he has released music with his backing band the Athletes, as part of the Fence Collective, and as a member of the trio Yorkston/Thorne/Khan. He has also written fiction and non-fiction books.
Chekiang First Bank
Chekiang First Bank was a bank in Hong Kong incorporated in 1950 by Li Ming. It is now merged to Wing Hang Bank. At the time of the merger with Wing Hang, Chekiang First Bank had 17 branches in Hong Kong, a wholly owned subsidiary in Luxembourg, an agency in San Francisco, and a representative office in Shanghai. As of 31 December 2002, Chekiang First had total assets of HK$27.8 billion. Wing Hang subsequent re-branded all services under the Wing Hang brand.

OCBC Bank (Hong Kong)
OCBC Bank (Hong Kong) Limited, formerly Wing Hang Bank Limited and OCBC Wing Hang Bank Limited, is a licensed bank with its head office in Hong Kong. Since 15 October 2014, Wing Hang Bank has been a wholly owned subsidiary of the Oversea-Chinese Banking Corporation (OCBC) headquartered in Singapore. The acquisition of Wing Hang has given OCBC a network of about seventy branches spanning Hong Kong, Macau and mainland China to add to OCBC's existing operations in Hong Kong and China.
Deb Adair
Deb Adair (born April 22, 1966, in Manchester, Connecticut) is an American re-recording mixer. 
She won 3 Emmy Awards for Outstanding Film Sound Mixing and Outstanding Sound Mixing - Special Class for her work on Aladdin in 1995-1996 and Timon & Pumbaa in 1997. On January 24, 2012, she was nominated for an Academy Award for the movie Moneyball.

Adair attended Syracuse University in the TV, Radio, and Film Production program.

24th Daytime Emmy Awards
The 24th Daytime Emmy Awards were held on May 21, 1997, at Radio City Music Hall, New York City to commemorate excellence in daytime programming from the previous year (1996). The Lifetime Achievement award was presented to Fred Rogers (Mr. Rogers).

Winners in each category are in bold.
The Suburbanite
The Suburbanite is a 1904 American short comedy silent film directed by Wallace McCutcheion and starring John Troiano. The film was produced and distributed by the American Mutoscope & Biograph Company. Prints exist in the Library of Congress film archive and in the Museum of Modern Art film archive.

Wallace McCutcheon Sr.
Wallace McCutcheon Sr. (New York City, 1858 or 1862 – Brooklyn, New York, October 3, 1918) was a pioneer cinematographer and director in the early American motion picture industry, working with the American Mutoscope & Biograph, Edison and American Star Film companies. McCutcheon's wealth of credits are often mixed up with the small handful of films directed by his son, Wallace McCutcheon Jr. (1884–1928).
Randy Hippeard
Randy Hippeard (born December 6, 1985) is an American former professional football quarterback who played in the Arena Football League (AFL). He is currently the offensive coordinator for the Billings Outlaws of Arena Football One (AF1). He was signed by the Winterthur Warriors of Nationalliga A in Switzerland as an undrafted free agent in 2009. He played college football at University of Virginia's College at Wise.

Billings Outlaws (AF1)
The Outlaws Arena Football Team, historically known as the Billings Outlaws, were a professional indoor football team based in Billings, Montana, that compete in Arena Football One (AF1). The Outlaws played their home games at MetraPark First Interstate Arena until 2025. They were founded in 2022 as members of Champions Indoor Football. In 2024, they joined the revived Arena Football League and won ArenaBowl XXXIII. In 2025, they became inaugural members of the newly-formed AF1.
Black Widows (2016 TV series)
Black Widows is a Nordic television series created by Mikko Pöllä, directed by Venita Ozols-Graham and starring Cecilia Forss as Rebeka Axelsson, Beate Bille as Kira Just Bergman and Synnøve Macody Lund as Johanne Rønningen. It is a remake of the Finnish 2014 TV series Mustat lesket.

The series follows three best friends who are all in abusive marriages and whose husbands work at the same company. The women go through a life-changing event after their husbands die in an explosion during a boating trip.

Produced by the Finnish company Moskito Television, Black Widows is a Nordic collaboration: the production team is mainly Finnish, but the cast and the directors are Scandinavian. Although shot almost entirely in Finland, the series is set in Scandinavia.

Mustat lesket
Mustat lesket is a 2014 Finnish drama television series created by Mikko Pöllä, directed by Veikko Aaltonen and starring Pihla Viitala as Veera Joentie, Wanda Dubiel as Johanna Koskinen and Malla Malmivaara as Kirsi Lundberg.
Hugolino Cerasuolo Stacey
Hugolino Cerasuolo Stacey (4 April 1932 – 24 May 2019) was an Ecuadorian Roman Catholic bishop.

Cerasuolo Stacey was born in Ecuador and was ordained to the priesthood in 1954.

He served as prefect apostolic of Galápagos, Ecuador, from 1967 to 1975.

In 1975, he was ordained a bishop and served as titular bishop of Valeria and as auxiliary bishop of the Roman Catholic Archdiocese of Guayaquil, Ecuador from 1975 to 1985.

He then served as bishop of the Roman Catholic Diocese of Loja, Ecuador, from 1985 to 2007.

Roman Catholic Diocese of Loja
The Roman Catholic Diocese of Loja (Latin: Dioecesis Loianus) is a diocese located in the city of Loja in the ecclesiastical province of Cuenca in Ecuador. It was erected on 29 December 1862 from territory of the Diocese of Cuenca.
Baira Kovanova
Baira Kovanova (born 12 May 1987) is a Russian chess player, and a woman grandmaster.

She made it to the second round of the Women's World Chess Championship 2010.

She also came 17th in the FIDE Women's Grand Prix 2009–11.

FIDE Women's Grand Prix 2009–2011
The FIDE Women's Grand Prix 2009–2011 was a series of six chess tournaments exclusively for women, which formed part of the qualification cycle for the Women's World Chess Championship 2011. The winner of the Grand Prix (the one with most Grand Prix points) was to challenge Hou Yifan—the 2010 world champion— in the third quarter of 2011. As Hou Yifan also won the Grand Prix, Koneru Humpy as the runner-up qualified for the championship match.

The final tournament was originally scheduled to take place in Santiago de Chile starting on October 23, 2010. However, due to problems with financing, the host was replaced and the final tournament was then played in Doha, Qatar.