hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Canonical bundle
In mathematics, the canonical bundle of a non-singular algebraic variety  of dimension  over a field is the line bundle  , which is the th exterior power of the cotangent bundle  on .

Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle . Equivalently, it is the line bundle of holomorphic -forms on .
This is the dualising object for Serre duality on . It may equally well be considered as an invertible sheaf.

The canonical class is the divisor class of a Cartier divisor  on  giving rise to the canonical bundle — it is an equivalence class for linear equivalence on , and any divisor in it may be called a canonical divisor. An anticanonical divisor is any divisor − with  canonical.

The anticanonical bundle is the corresponding inverse bundle . When the anticanonical bundle of  is ample,  is called a Fano variety.

Minimal model program
In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its origins in the classical birational geometry of surfaces studied by the Italian school, and is currently an active research area within algebraic geometry.
Johann Christian Poggendorff
Johann Christian Poggendorff (29 December 1796 – 24 January 1877) was a German physicist born in Hamburg. By far the greater and more important part of his work related to electricity and magnetism. Poggendorff is known for his electrostatic motor which is analogous to Wilhelm Holtz's electrostatic machine. In 1841 he described the use of the potentiometer for measurement of electrical potentials without current draw.

Annalen der Physik
Annalen der Physik (English: Annals of Physics) is one of the oldest scientific journals on physics; it has been published since 1799. The journal publishes original, peer-reviewed papers on experimental, theoretical, applied, and mathematical physics and related areas. The editor-in-chief is Stefan Hildebrandt. Prior to 2008, its ISO 4 abbreviation was Ann. Phys. (Leipzig), after 2008 it became Ann. Phys. (Berl.).

The journal is the successor to Journal der Physik, published from 1790 until 1794, and Neues Journal der Physik, published from 1795 until 1797. The journal has been published under a variety of names (Annalen der Physik, Annalen der Physik und der physikalischen Chemie, Annalen der Physik und Chemie, Wiedemann's Annalen der Physik und Chemie) during its history.
Seodaemun District
Seodaemun District (Korean: 서대문구; RR: Seodaemun-gu) is one of the 25 districts of Seoul, South Korea. It has a population of 313,814 (2010) and has a geographic area of 17.61 km2 (6.8 sq mi), and is divided into 14 dong (administrative neighborhoods). Seodaemun is located in northwestern Seoul, bordering the city districts of Eunpyeong to the northwest, Mapo to the southwest, Jung to the southeast, and Jongno to the east.

Seodaemun is part of the Seongjeosimni (Outer old Seoul) area and is named after Donuimun, one of the Eight Gates of Seoul which was formerly located within the district. Seodaemun is home to Seodaemun Independence Park, which contains several historic monuments and buildings such as the Seodaemun Prison museum and the Independence Gate.

Seongdong District
Seongdong District (Korean: 성동구; RR: Seongdong-gu) is one of the 25 districts which make up the city of Seoul, South Korea. It is situated on the north bank of the Han River. It is divided into 20 dong (neighbourhoods). The district is home to Hanyang University, one of the most prestigious universities in South Korea.
Park County, Montana
Park County is a county in the U.S. state of Montana. At the 2020 census, the population was 17,191. Its county seat is Livingston. A small part of Yellowstone National Park is in the southern part of the county.

Gallatin National Forest
The Gallatin National Forest (now known as the Custer-Gallatin National Forest) is a United States national forest located in South-West Montana. Most of the Custer-Gallatin goes along the state's southern border. Some of it is in North-West Wyoming.
1971 Algerian Cup final
The 1971 Algerian Cup final was the 8th final of the Algerian Cup. The final took place on June 13, 1971, at Stade 20 Août 1955 in Algiers with kick-off at 15:00. MC Alger beat USM Alger 2-0 to win their first Algerian Cup.

1973 Algerian Cup final
The 1973 Algerian Cup final was the 11th final of the Algerian Cup. The final took place on June 19, 1973, at Stade 5 Juillet 1962 in Algiers with kick-off at 21:00. MC Alger beat USM Alger 4–2 after extra time to win their second Algerian Cup.
Skonto FC
Skonto FC was a Latvian professional football club, active from 1991 until 2016. The club played at the Skonto Stadium in Riga. Skonto won the Virsliga in the first 14 seasons of the league's resumption (15 in total), and often provided the core of the Latvia national football team. With those 14 national championships in a row, they set a European record, across men and women's football combined, until the women of Faroese club KÍ Klaksvík won their 14th championship in a row in 2013.

Following financial problems, the club was demoted to the Latvian First League in 2016 and went bankrupt in December of that year.

FK Auda
Futbola klubs Auda is a Latvian professional football club, playing in the Latvian Higher League, the highest division of domestic football. They are based in Ķekava, near the capital Riga. Auda won their first ever major trophy in the final of the Latvian Cup.
Lancaster, Ohio
Lancaster (locally /ˈlæŋk(ə)stər/ LANK-(ə-)stər) is a city in Fairfield County, Ohio, and its county seat. The population was 40,552 at the 2020 United States census, making it Ohio's 30th largest city, having surpassed Warren and Findlay due to its own growth while the latter two cities declined. The city is near the Hocking River in the south-central part of the state, about 33 miles (53 km) southeast of Columbus and 38 miles (61 km) southwest of Zanesville. It is part of the Columbus metropolitan area.

Chillicothe, Ohio
Chillicothe (/ˌtʃɪlɪˈkɒθi/ CHIL-ih-KOTH-ee) is a city in Ross County, Ohio, United States, and its county seat. The population was 22,059 at the 2020 census. Located along the Scioto River 45 miles (72 km) south of Columbus, Chillicothe was the first and third capital of Ohio. It is the only city in Ross County and the center of the Chillicothe micropolitan area, which is a part of the Columbus, Ohio Combined Statistical Area. Chillicothe is a designated Tree City USA by the National Arbor Day Foundation.
First Battle of the Aisne
The First Battle of the Aisne (French: 1ère Bataille de l'Aisne) was the Allied follow-up offensive against the right wing of the German First Army (led by Alexander von Kluck) and the Second Army (led by Karl von Bülow) as they retreated after the First Battle of the Marne earlier in September 1914. The Advance to the Aisne (6 September – 1 October) consisted of the Battle of the Marne (7–10 September) and the Battle of the Aisne (12–15 September).

Battle of the Avre
The Battle of the Avre (4–5 April 1918), part of the First Battle of Villers-Bretonneux, constituted the final German attack towards Amiens in World War I. It was the point at which the Germans got the closest to Amiens. It was fought between attacking German troops and defending Australian and British troops. The attack was an attempt to take Amiens, where other aspects of Operation Michael had failed. The Avre marked the beginning of the end for Ludendorf's German spring offensive.
Silver Line (DART)
The Silver Line, also known as the Cotton Belt Rail Line, is a 26-mile (42 km) hybrid rail service in Tarrant, Dallas, and Collin counties and in the U.S. state of Texas operated by Dallas Area Rapid Transit (DART). The line provides service from Dallas's northern suburbs of Plano, Richardson, Addison, and Carrollton to Dallas/Fort Worth International Airport Terminal B.

According to DART, the Silver Line is "designed to provide a high-speed, reliable transit option for residents and commuters with connections to the existing and planned transit systems" and aims to improve transit travel times by providing an alternative to congested roadway networks.

The working name for the project, the Cotton Belt Rail Line, comes from a former subsidiary of the Southern Pacific Railroad, the St. Louis Southwestern Railway, commonly known as the Cotton Belt, which previously owned the line. DART purchased the right-of-way in 1990 for future transit use.

DART rail
Dallas Area Rapid Transit operates light rail and hybrid rail in the Dallas metropolitan area. The agency's rail system consists of four light rail lines (Red, Blue, Green, and Orange) and one hybrid rail line (Silver), which together span 73 stations across 119 miles (191.5 km) of track.

In 2025, the four light rail lines had a ridership of 22,237,700, or about 64,000 per weekday as of the fourth quarter of 2025. DART's light rail lines have the 7th highest ridership of light rail systems in the United States.  However, the system was also one of the country's worst financial performers.
Wutach (river)
The Wutach (German pronunciation: [ˈvuːtax]) is a river, 91 kilometres long, in the southeastern part of the Black Forest in the German state of Baden-Württemberg. It is a right-hand tributary of the Rhine. In its lower reaches it flows for about 6 kilometres along the border with the canton of Schaffhausen, Switzerland.

Alb (High Rhine)
The Alb (also: Hauensteiner Alb) is a river in the southern Black Forest.  It arises from two headwaters, the Menzenschwander Alb and Bernauer Alb, and flows in a southerly direction. It ends after 43.6 kilometres (27.1 mi) (including Menzenschwander Alb) at a confluence with the High Rhine at Albbruck.
307th Fighter Squadron
The 307th Fighter Squadron is a McDonnell Douglas F-15E Strike Eagle unit and is part of Air Force Reserve Command's 414th Fighter Group stationed at Seymour Johnson Air Force Base, North Carolina.

The mission of the 307 FS is to assist the 4th Fighter Wing at Seymour Johnson to produce qualified F-15E aircrew. The squadron became operational in September 2011.

309th Fighter Squadron
The 309th Fighter Squadron (309 FS) is part of the 56th Operations Group at Luke Air Force Base, Arizona.  It operates the General Dynamics F-16 Fighting Falcon (F-16C and F-16D variants) aircraft conducting advanced fighter training.
Belgium national under-21 football team
The Belgium national under-21 football team is the national under-21 football team of Belgium and is controlled by the Belgian Football Association. The team competes in the UEFA European Under-21 Championship, held every two years. Their biggest successes were winning the 2007–09 International Challenge Trophy and reaching the European Championship semi-finals in 2007 in the Netherlands. Thanks to the latter achievement, Belgium qualified for the football tournament at the 2008 Summer Olympics. Their current home stadium is Den Dreef in Leuven.

Slovakia national under-21 football team
The Slovakia national under-21 football team, controlled by the Slovak Football Association, is Slovakia's national under-21 football team and is considered to be a feeder team for the Slovakia national football team.
Alexander Naumov
Alexander Alexandrovich Naumov (Russian: Алекса́ндр Алекса́ндрович Нау́мов; 28 December 1935 – 31 December 2010) was a Soviet, Russian painter, lived and worked in Saint Petersburg, member of the Saint Petersburg Union of Artists (before 1992 - the Leningrad branch of Union of Artists of Russian Federation), regarded as a representative of the Leningrad school of painting, the most known for his works depicting Central Asia.

Vecheslav Zagonek
Vecheslav Frantsevich Zagonek (Russian: Вячесла́в Фра́нцевич Заго́нек; December 19, 1919 – June 24, 1994) was a Soviet painter, People's Artist of the USSR, Member of the Academy of Arts of the USSR, who lived and worked in Leningrad. He was a member of the Leningrad Union of Artists and regarded as one of the brightest representatives of the Leningrad school of painting, most famous for his lyrical landscapes and genre paintings.
Colin Charvis
Colin Charvis (born 27 December 1972) is a former professional rugby union player. A back row forward, Charvis was equally adept as a flanker or at number 8. Born in Sutton Coldfield, England, he captained the Wales national team from 2002 to 2004, and also played for the British & Irish Lions on their tour of Australia in 2001.

Charvis became the world record try scorer for a forward in test match rugby with his 22nd international try on 24 November 2007 in a match against South Africa at the Millennium Stadium, Cardiff. In 2011, he was overtaken by Takashi Kikutani of Japan on the list of leading rugby union test try scorers.

Mike Phillips (rugby union)
William Michael Phillips (born 29 August 1982) is a retired Welsh rugby union player who played at scrum-half. On 16 March 2013, Phillips surpassed the record of 76 caps set by Dwayne Peel as the most capped scrum-half for Wales.

Tall and powerful, unusual properties in a scrum half, he has been compared to ex-Wales international Terry Holmes.
Guerrero Maya Jr.
Guerrero Maya Jr. (Spanish for "Maya Warrior Junior", born August 8, 1985) is a Mexican luchador enmascarado (or masked professional wrestler), currently working for the Mexican professional wrestling promotion Consejo Mundial de Lucha Libre (CMLL). He portrays a tecnico ("Good guy") wrestling character. Guerrero Maya Jr.'s real name is not a matter of public record, as is often the case with masked wrestlers in Mexico where their private lives are kept a secret from the wrestling fans. He is the son of Esteban Mares Castañeda, better known under the ring names Black Terry and Guerrero Maya. He has previously competed as the enmascarado characters Samba and Multifacético (the third person to use that name).

Bárbaro Cavernario
Leonardo Moreno Ayala (born November 6, 1993), better known by his ring name Bárbaro Cavernario, is a Mexican luchador (or professional wrestler), working for Mexican wrestling promotion Consejo Mundial de Lucha Libre (CMLL). He portrays a rudo ("bad guy") wrestling character.

In professional wrestling, Moreno is a two-time Occidente Middleweight Champion, a one-time Welterweight Champion, a one time Light Heavyweight Champion, and a six-time tournament winner (En Busca de un Ídolo 2014, Gran Alternativa 2014, CMLL Reyes del Aire 2016, Torneo de Parejas Increíbles 2017, Leyenda de Plata 2018 and Torneo de Parejas Increíbles 2019). He was formerly a member of the wrestling group known as La Peste Negra ("The Black Plague").
Dennis Cooper
Dennis Cooper (born January 10, 1953) is an American novelist, poet, critic, film director, editor and performance artist. He is best known for the George Miles Cycle, a series of five semi-autobiographical novels published between 1989 and 2000 and described by Tony O'Neill "as intense a dissection of human relationships and obsession that modern literature has ever attempted." Cooper is the founder and editor of Little Caesar Magazine, a punk zine, that ran between 1976 and 1982.

Gary Indiana
Gary Hoisington (July 16, 1950 – October 23, 2024), known as Gary Indiana, was an American writer, actor, artist, and cultural critic. He served as the art critic for the Village Voice weekly newspaper from 1985 to 1988. Indiana is best known for his classic American true-crime trilogy, Resentment, Three Month Fever: The Andrew Cunanan Story, and Depraved Indifference, chronicling the less permanent state of "depraved indifference" that characterized American life at the millennium's end. In the introduction to the recently re-published edition of Three Month Fever, critic Christopher Glazek has coined the phrase 'deflationary realism' to describe Indiana's writing, in contrast to the magical realism or hysterical realism of other contemporary writing.
Long Island Ducks
The Long Island Ducks are an American professional minor league baseball team based on Long Island in Central Islip, New York. The Ducks compete in the North Division of the Atlantic League of Professional Baseball (ALPB), an independent "partner league" of Major League Baseball. The Ducks played their first season in 2000, two years after the ALPB inaugural season. Since their inception, the Ducks' home ballpark has been Fairfield Properties Ballpark, formerly known as Bethpage Ballpark (2010-2020), Suffolk County Sports Park (1999 and 2010), EAB Park (2000–2001), and Citibank Park (2002–2009). The "Ducks" name refers to Long Island's duck-farming heritage (itself represented by the Big Duck ferrocement) and recalls the former Long Island Ducks professional ice hockey team. The team's first manager was Bud Harrelson, a part-owner of the team and a former major league player.

Lancaster Stormers
The Lancaster Stormers (formerly known as the Lancaster Barnstormers) are an American professional baseball team based in Lancaster, Pennsylvania. They are members of the North Division of the Atlantic League of Professional Baseball, a "partner league" of Major League Baseball. Since 2005, the team has played its home games at Penn Medicine Park in the city's Northwest Corridor, following the stadium's completion.
Charlie Musselwhite
Charles Douglas Musselwhite (born January 31, 1944) is an American blues harmonica player and bandleader who came to prominence, along with Mike Bloomfield, Paul Butterfield, and Elvin Bishop, as a pivotal figure in helping to revive the Chicago Blues movement of the 1960s. He has often been identified as a "white bluesman".

Musselwhite was reportedly the inspiration for Elwood Blues, the character played by Dan Aykroyd in the 1980 film, The Blues Brothers.

Nick Gravenites
Nicholas George Gravenites (/ɡrævɪˈnaɪtɪs/ grav-ih-NY-tis; October 2, 1938 – September 18, 2024) was an American blues, rock and folk singer, songwriter, and guitarist, best known for his work with Electric Flag (as their lead singer), Janis Joplin, Mike Bloomfield, and several influential bands and individuals of the generation springing from the 1960s and 1970s. He sometimes performed under the stage names Nick "The Greek" Gravenites and Gravy.
Achillea millefolium
Achillea millefolium, commonly known as yarrow (/ˈjæroʊ/) or common yarrow, is a flowering plant in the family Asteraceae. Growing to 1 metre (3+1⁄3 feet) tall, it is characterized by small whitish flowers, a tall stem of fernlike leaves, and a pungent odor.

The plant is native to temperate regions of Eurasia and North America. It has been introduced as feed for livestock in New Zealand and Australia. It has some potential uses, including in traditional medicine.

Holcus lanatus
Holcus lanatus is a perennial flowering plant in the grass family Poaceae. The specific epithet lanatus is Latin for 'woolly' which describes the plant's hairy texture. Common names include Yorkshire fog, tufted grass, and meadow soft grass. In North America, where it is an invasive species, names include velvet grass and common velvet grass.

In parts of northern Europe the grass is a common native species and a hardy pasture grass.
Row and column vectors
In linear algebra, a column vector with ⁠⁠ elements is an  matrix consisting of a single column of ⁠⁠ entries. Similarly, a row vector is a  matrix, consisting of a single row of ⁠⁠ entries. For example, ⁠⁠ is a column vector and ⁠⁠ is a row matrix:

(Throughout this article, boldface is used for both row and column vectors.)

The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector:

Taking the transpose twice returns the original (row or column) vector: ⁠⁠.

The set of all row vectors with n entries in a given field (such as the real numbers) forms an n-dimensional vector space; similarly, the set of all column vectors with m entries forms an m-dimensional vector space.

The space of row vectors with n entries can be regarded as the dual space of the space of column vectors with n entries, since any linear functional on the space of column vectors can be represented as the left-multiplication of a unique row vector.

Conjugate transpose
In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an  complex matrix  is an  matrix obtained by transposing  and applying complex conjugation to each entry (the complex conjugate of  being , for real numbers  and ). There are several notations, such as  or , , or (often in physics) .

For real matrices, the conjugate transpose is just the transpose, .
Biohazard (band)
Biohazard is an American hardcore band formed in Brooklyn, New York City, in 1987. They are one of the earliest bands to fuse hardcore punk and heavy metal with elements of hip hop. The original lineup consisted of bassist/vocalist Evan Seinfeld, guitarist Bobby Hambel, and drummer Anthony Meo. Guitarist/vocalist Billy Graziadei joined soon after, and drummer Danny Schuler replaced Meo before the recording of their first album, thus solidifying the band's lineup from 1988 to 1995.

After several lineup changes, a breakup, a 2008 reunion, and a seven-year period of inactivity, the classic lineup of Seinfeld, Graziadei, Hambel, and Schuler reunited in 2022 and began performing again in 2023.

Dog Eat Dog (band)
Dog Eat Dog is an American band that fuses a variety of genres, such as hardcore punk, rock, metal, hip-hop, and funk. Formed in Bergen County, New Jersey in 1990, the band was one of the earliest to combine metal and rap together. The group has released five full-length albums and two EPs. As of 2009, the lineup consists of Dave Neabore (bass), John Connor (vocals), Brandon Finley (drums), and Roger Haemmerli (guitar).
Blue Man Group
Blue Man Group is an American performance art company based in New York City in 1987. It is known for its stage productions that incorporate many kinds of music and art, both popular and obscure. Its performers, known as Blue Men, have their skin painted blue. They are mute during shows and always appear in groups of three.

As of 2025, the company's only United States show is in Las Vegas.

A typical production employs seven to nine full-time Blue Men who are selected by audition. In addition to their stage shows, Blue Man Group has toured nationally and internationally, appeared on television programs as characters and performers, released multiple studio albums, contributed to a number of film scores, and performed with orchestras around the United States.

List of Arrested Development characters
Arrested Development is an American television sitcom that originally aired on Fox from November 2, 2003, to February 10, 2006. A fourth season of 15 episodes was released on Netflix on May 26, 2013, and a fifth season was released in two parts on May 29, 2018, and March 15, 2019. Created by Mitchell Hurwitz, the show centers the Bluth family. The Bluths are formerly wealthy and a habitually dysfunctional family. It is presented in a continuous format, and incorporates hand-held camera work, narration, archival photos, and historical footage. The series stars Jason Bateman, Portia de Rossi, Will Arnett, Michael Cera, Alia Shawkat, Tony Hale, David Cross, Jeffrey Tambor, and Jessica Walter. In addition, Ron Howard serves as the series narrator and an executive producer on the show.

The main characters of Arrested Development can be divided into the Bluth (/bluːθ/ BL
OOTH) and Fünke (/ˈfjuːŋkeɪ/ FYOON-kay) families.