hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Dual curve
In projective geometry, a dual curve of a given plane curve C is a curve in the dual projective plane consisting of the set of lines tangent to C. There is a map from a curve to its dual, sending each point to the point dual to its tangent line. If C is algebraic then so is its dual and the degree of the dual is known as the class of the original curve. The equation of the dual of C, given in line coordinates, is known as the tangential equation of C. Duality is an involution: the dual of the dual of C is the original curve C.

The construction of the dual curve is the geometrical underpinning for the Legendre transformation in the context of Hamiltonian mechanics.

Hamiltonian mechanics
In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities  used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena.

Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics.
Assura plc
Assura is a British property business headquartered in Altrincham, Greater Manchester that has a focus on investing in buildings used for the healthcare sector. As of June 2025, it owned and operates more than 600 general practitioner and primary healthcare buildings in the UK.

The company was listed on the London Stock Exchange until it was acquired by Primary Health Properties in August 2025.

Primary care
Primary care is the day-to-day healthcare given by a health care provider. Typically, this provider acts as the first contact and principal point of continuing care for patients within a healthcare system, and coordinates any additional care the patient may require. Patients commonly receive primary care from professionals such as a primary care physician (general practitioner or family physician), a physician assistant, a physical therapist, or a nurse practitioner. In some localities, such a professional may be a registered nurse, a pharmacist, a clinical officer (as in parts of Africa), or an Ayurvedic or other traditional medicine professional (as in parts of Asia). Depending on the nature of the health condition, patients may then be referred for secondary or tertiary care.
Sebald Bopp
Sebald Bopp (died 1502) was a German painter active around Bamberg.  Little is known about him; his name is first recorded in Würzburg, where he was listed as a journeyman in 1474, but his earliest known work remains in his native town.  This is a depiction of the Sermon of John of Capistrano, painted around 1480 and now in the Neue Residenze in Bamberg.

The style of this painting, filled with representations of bourgeois figures, appears to have been derived from the work of the Master of the Bamberg Altar.  After 1480 his activity is recorded in Nuremberg, judging from a Crucifixion memorial plaque, dating to 1483, honoring Peter and Apollonia Volckamer.

Bopp returned to Bamberg at some point before his death; he died there in 1502.

John of Capistrano
John of Capistrano, OFM (Italian: San Giovanni da Capestrano, Hungarian: Kapisztrán János, Polish: Jan Kapistran, Croatian: Ivan Kapistran Serbian: Јован Капистран, Jovan Kapistran; 24 June 1386 – 23 October 1456) was an Italian Franciscan friar and Catholic priest from the town of Capestrano, Abruzzo. Famous as a preacher, theologian, and inquisitor, he earned himself the nickname "the Soldier Saint" when in 1456 at age 70 he led a Crusade against the invading Ottoman Empire at the siege of Belgrade with the Hungarian military commander John Hunyadi.

Elevated to sainthood, he is the patron saint of jurists and military chaplains, as well as the namesake of two Franciscan missions, one in Southern California and the other in San Antonio, Texas.
Johnny Byrne (footballer)
John Joseph Byrne (13 May 1939 – 27 October 1999) was an English professional footballer who played as a striker. He was nicknamed "Budgie" due to his constant chattering.

He played non-league football for Epsom Town and Guildford City Youth, before signing a professional contract with Crystal Palace in 1956. He joined West Ham United in 1962, and spent the next five years with the "Hammers". He returned to Crystal Palace in 1967, before joining Fulham the following year. He emigrated to South Africa in 1969 and spent four years with Durban City. He went on to coach in South Africa for many years, and turned out as a player for Hellenic in 1980.

He won seven caps for the England under-23 team, before scoring eight goals in eleven full England internationals between 1961 and 1965.

The Hawthorns
The Hawthorns is an all-seater football stadium in West Bromwich, in the Black Country borough of Sandwell, West Midlands, England, with a capacity of 27,087. It has been the home of Championship club West Bromwich Albion since 1900, when it became the sixth ground to be used by the club. The Hawthorns was the first Football League ground to be built in the 20th century, opening in September 1900 after construction work took only 4 months. The official record attendance at The Hawthorns stands at 64,815, set in March 1937.

Alongside being the home of West Bromwich Albion for over 125 years, The Hawthorns has also hosted a number of England internationals, as well as two FA Cup semi-finals.  At an altitude of 551 feet (168 m), it is the highest ground above sea level of all Premier League and Football League clubs.
Helder Giraldo
Helder Fernán Giraldo (born 31 December 1967) is a Colombian general who served as General Commander of the Military Forces from 2022 to 2024.

Born in Ibagué, Tolima. He studied at the José María Córdova Military School. He completed a specialization in human resources at the Sergio Arboleda University.

He is an expert in international humanitarian law. In August 2022, then President-elect Gustavo Petro appointed Giraldo as Commander General of the Military Forces, taking office on August 12.

General Commander of the Military Forces (Colombia)
The general commander of the Military Forces is the professional head of the Military Forces of Colombia. He is responsible for the administration and the operational control of the Colombian military. The current commander is General Helder Giraldo Bonilla.
Jordon Smith
Jordon Smith (born 5 February 1996) is an American professional Motocross and Supercross racer. Smith has competed professionally in the AMA Supercross Championship and AMA Motocross Championship since 2015.

During the 2025 AMA Supercross Championship, Smith took Triumph's first professional supercross win at the Glendale round.

In 2018, Smith was the runner-up in the AMA Supercross Championship in the 250SX East class. Despite having parts of his career impacted by injuries, Smith has five professional supercross wins.

AMA Motocross Championship
The AMA Motocross Championship (commercially known as Pro Motocross Championship) is an American motorcycle racing series. The motocross race series was founded and sanctioned by the American Motorcyclist Association (AMA) in 1972. The series is the major outdoor motocross series in the United States and is sanctioned by AMA Pro Racing and managed by MX Sports Pro Racing.

With respect to the MXGP holding the discipline's worldwide title, and the advent of the FIM Supercross World Championship resulting in the AMA Supercross Championship losing its world title status, the two series will form the SuperMotocross World Championship from 2023.
VPB-216
VPB-216 was a Patrol Bombing Squadron of the U.S. Navy. The squadron was established as Patrol Squadron Two Hundred Sixteen (VP-216) on 15 November 1943, redesignated Patrol Bombing Squadron Two Hundred Sixteen (VPB-216) on 1 October 1944 and disestablished on 7 April 1945.

Naval Air Station Alameda
Naval Air Station Alameda (NAS Alameda) was a United States Navy Naval Air Station mostly in Alameda, California, with a slight portion of it within San Francisco proper, on San Francisco Bay.

NAS Alameda had two runways: 13–31 measuring 8,000 ft × 200 ft (2,438 m × 61 m) and 07-25 measuring 7,200 ft × 200 ft (2,195 m × 61 m). Two helicopter pads and a control tower were also part of the facilities.
Malmö Symphony Orchestra
55°36′27″N 12°59′37″E﻿ / ﻿55.60750°N 12.99361°E﻿ / 55.60750; 12.99361

The Malmö Symphony Orchestra (Swedish: Malmö Symfoniorkester) is a Swedish orchestra, based in Malmö. Since 2015, it has been resident at the Malmö Live Concert Hall. The orchestra has a complement of 94 musicians.

Robert Treviño
Robert Treviño (born 1984) is an American conductor. He is the incoming principal conductor of the George Enescu Philharmonic Orchestra, and principal guest conductor of the Orchestra Sinfonica Nazionale della RAI.
Saint David's School (New York City)
Saint David's School is an independent primary and pre-primary school for boys on the Upper East Side of Manhattan, New York City.

The school educates boys from pre-kindergarten through to eighth grade. Saint David's was founded in 1951. The current headmaster is P. David O'Halloran.

Pre-kindergarten
Pre-kindergarten (also called pre-K or PK) is a voluntary classroom-based preschool program for children below the age of five in the United States, Canada, Turkey and Greece (when kindergarten starts). It may be delivered through a preschool or within a reception year in elementary school. Pre-kindergartens play an important role in early childhood education. They have existed in the US since 1922, normally run by private organizations. The U.S. Head Start program, the country's first federally funded pre-kindergarten program, was founded in 1967. This attempts to prepare children (especially disadvantaged children) to succeed in school.
Innovative Vector Control Consortium
The Innovative Vector Control Consortium (IVCC) is a not-for-profit, product development partnership (PDP) designed to facilitate the development and delivery of new and improved vector control tools to prevent malaria and other neglected tropical diseases. Their mission is to save lives, protect health, and increase prosperity in areas where disease transmitted by insects is endemic.

Sumitomo Chemical
Sumitomo Chemical Co., Ltd. (住友化学株式会社, Sumitomo Kagaku Kabushiki-gaisha) is a major Japanese chemical company. The company is listed on the first section of the Tokyo Stock Exchange and is a constituent of the Nikkei 225 stock index. It is a member of the Sumitomo group and was founded in 1913 as a fertilizer manufacturing plant.
Bearden (surname)
Bearden is a surname. Notable people with the surname include:

Gene Bearden (1920–2004), American baseball player

Milton Bearden (born 1940s), American intelligence officer, author, and film consultant

Romare Bearden (1911–1988), African-American artist

Milton Bearden
Milton Bearden is an American author, film consultant, and former CIA officer. Bearden served as the president and CEO of the Asia-Africa Projects Group, a Washington, D.C.–based firm that provides resource development and advisory services, from 2010 to 2015. He has been engaged in authorship and film consultancy since 1998.

As of 2016, Bearden resides in Austin, Texas, with his wife, Marie-Catherine, a retired university professor, at Georgetown University and the University of Texas at Austin, and currently a professional consultant on inter-cultural protocols and etiquette.
Richard Davies (American actor)
Richard Davies (1915–1994) was an American actor.

Davies was born in Provo, Utah. His first films date from 1941, and he was active through the early 1960s, ranging from lead roles to small bit and character parts.

Provo, Utah
Provo (/ˈproʊ.voʊ/ PROH-voh) is a city in and the county seat of Utah County, Utah, United States. It is 43 miles (69 km) south of Salt Lake City along the Wasatch Front, and lies between the cities of Orem to the north and Springville to the south. With a population at the 2020 census of 115,162, Provo is the fourth-largest city in Utah and the principal city in the Provo-Orem metropolitan area, which had a population of 526,810 at the 2010 census. It is Utah's second-largest metropolitan area after Salt Lake City.

Provo is the home to Brigham Young University (BYU), a private higher education institution operated by the Church of Jesus Christ of Latter-day Saints (LDS Church). Provo also has the LDS Church's largest Missionary Training Center (MTC). The city is a focus area for technology development in Utah, with several billion-dollar startups. The city's Peaks Ice Arena was a venue for the Salt Lake City Winter Olympics in 2002.
Gara (given name)
Gara is a given name.

Gara Garayev (1918–1982), Azerbaijani composer

Gara Garayev (footballer) (born 1992), Azerbaijani football defender

Gara LaMarche (born 1954), an American politician

Gara Takashima, Japanese voice actress

Gara Takashima
Yumiko Takashima (高島 由美子, Takashima Yumiko; born March 2, 1954), known by her stage name Gara Takashima (高島 雅羅, Takashima Gara) is a Japanese actress and voice actress who works for Aoni Production. She is married to voice actor Banjō Ginga.
Tommy Runar
Tommy Runar (born 25 April 1982) is a retired Norwegian football goalkeeper. Runar played for Jerv, joining Start in 2004. He spent the majority of the 2008 season on loan at Fredrikstad, serving as cover for Lasse Staw.

He retired after the 2012 season, and has since worked as goalkeeping coach for FK Jerv and Amazon Grimstad.

Amazon Grimstad
Amazon Grimstad FK is a Professional Norwegian women's football club from Grimstad. It is named after the Amazons of Greek mythology.

It was founded in 1999 when the women's football section split from FK Jerv. The senior team currently plays in the Norwegian First Division following relegation from the Toppserien at the conclusion of the 2015 Toppserien.
Berrien (surname)
Berrien is a French surname. Notable people with the surname include:

Frank Berrien (1877–1951), American football coach

Jacqueline A. Berrien (1961–2015), American lawyer

John Berrien (1711–1772), American judge

John Berrien (major) (1759–1815), American military officer

John M. Berrien (1781–1856), American senator

Lucille Berrien (born 1928) American political activist

John Berrien
John Berrien (November 19, 1711 – April 22, 1772) was a farmer and merchant from Rocky Hill, New Jersey. He was appointed a justice of the New Jersey Supreme Court in 1764 and was a trustee of the College of New Jersey, now Princeton University, for eleven years.
Kilometre zero
Kilometre zero (or km 0), also known as zero mile marker or zero milepost, is a particular location (usually in the nation's capital city) from which traveled distances are traditionally measured, as in distance markers. Historically, they were markers where drivers could set their odometers to follow the directions in early roaming guidebooks.

One such marker is the Milliarium Aureum ("Golden Milestone") of the Roman Empire, believed to be the origin for the maxim "All roads lead to Rome".

Odometer
An odometer or odograph is an instrument used for measuring the distance traveled by a vehicle, such as a bicycle or car. The device may be electronic, mechanical, or a combination of the two (electromechanical). The noun derives from ancient Greek ὁδόμετρον, hodómetron, from ὁδός, hodós ('path' or 'gateway') and μέτρον, métron ('measure'). Early forms of the odometer existed in the ancient Greco-Roman world as well as in ancient China. In countries using Imperial units or US customary units it is sometimes called a mileometer or milometer, the former name especially being prevalent in the United Kingdom and among members of the Commonwealth.
Gymnastics at the 2011 Pan American Games – Women's trampoline
The women's trampoline competition of the trampoline events at the 2011 Pan American Games was held between October 17–18 at the Nissan Gymnastics Stadium. The draw for the competition took place on August 1, 2011, in Guadalajara. The defending Pan American Games champion was Karen Cockburn of Canada.

Complejo Nissan de Gimnasia
The Nissan Gymnastics Stadium is a stadium located in Guadalajara, Mexico.  It opened in February 2008 and hosted the gymnastics competition at the 2011 Pan American Games.   It has a capacity of 3,434.
Oxford Science Enterprises
Oxford Science Enterprises (OSE) (Previously known as Oxford Sciences Innovation) is a British early-stage venture capital firm with over $800M in AUM based in Oxford, UK. It operates in partnership with the University of Oxford, as the university's preferred investor, several prominent financiers back the firm, including Google Ventures, Sequoia Capital, Tencent, Huawei and Invesco.

The firm uses academic research from the university's science departments to form commercial businesses, also known as spin-outs.

Sequoia Capital
Sequoia Capital Operations, LLC, doing business as Sequoia Capital or simply Sequoia, is an American venture capital firm headquartered in Menlo Park, California. It specializes in seed stage, early stage, and growth stage investments in private companies across technology sectors. As of January 2025, the firm had approximately US$56 billion in assets under management (AUM).

The firm operates three regionally-focused venture entities, as Sequoia in Europe, Peak XV Partners in Southeast Asia, and formerly HongShan in China. Sequoia has made a wide variety of venture investments since inception, including in Apple, ByteDance, and Cisco, among many others.
Mr. Walkie Talkie
Mr. Walkie Talkie is a 1952 American comedy film directed by Fred Guiol and starring William Tracy, Joe Sawyer and Margia Dean. Released by Lippert Pictures, it is the final film of the Doubleday and Ames army comedy films originally produced by Hal Roach with the pair returning for service in the Korean War.

Hal Roach
Harold Eugene "Hal" Roach Sr. (January 14, 1892 – November 2, 1992) was an American film and television producer, director and screenwriter, who was the founder of the namesake Hal Roach Studios.

Roach was active in the industry from the 1910s to the 1990s. He is known for producing a number of early media franchise successes, including the Laurel and Hardy franchise, Harold Lloyd's early films, the films of entertainer Charley Chase, and the Our Gang short film comedy series.
George Walker (cricketer, born 1919)
George Arthur Walker (25 January 1919 – 31 August 1995) was an English cricketer. Walker was a right-handed batsman who bowled right-arm fast. He was born at West Bridgford, Nottinghamshire.

Walker made two first-class appearances for Nottinghamshire in the 1937 County Championship against Yorkshire at Headingley, and Lancashire at Trent Bridge. Despite bowling a total of 48 overs in his two matches, Walker took just a solitary wicket, that of Lancashire's Eddie Phillipson. With the bat he scored a total of 24 runs with a high score of 10 not out.

At the end of the 1937 season Walker retired from professional cricket and joined the Nottingham City Police.

He died at Bridlington, Yorkshire, on 31 August 1995.

Over (cricket)
In cricket, an over consists of six legal deliveries bowled from one end of a cricket pitch to the player batting at the other end, almost always by a single bowler.

A maiden over is an over in which no runs are scored that count against the bowler (so leg byes and byes may be scored as they are not counted against the bowler). A wicket maiden is a maiden over in which a wicket is also taken. Similarly, double and triple wicket maidens are when two and three wickets are taken in a maiden over.

After six deliveries the umpire calls 'over'; the fielding team switches ends, and a different bowler is selected to bowl from the opposite end. The captain of the fielding team decides which bowler will bowl any given over, and no bowler may bowl two overs in succession.
Fig Tree Bridge
The Fig Tree Bridge is a road bridge which carries Burns Bay Road across the Lane Cove River, and connects the suburbs of Hunters Hill in the south and Linley Point in the north, located approximately seven kilometres (four miles) northwest of the central business district of Sydney in New South Wales, Australia. The concrete girder bridge carries motor vehicles, and a grade-separated footpath and cycleway.

Cycling infrastructure
Cycling infrastructure is all infrastructure cyclists are allowed to use. Bikeways include bike paths, bike lanes, cycle tracks, rail trails and, where permitted, sidewalks. Roads used by motorists are also cycling infrastructure, except where cyclists are barred such as many freeways/motorways. It includes amenities such as bike racks for parking, shelters, service centers and specialized traffic signs and signals. The more cycling infrastructure there is, the more people travel by bicycle.

Good road design, road maintenance and traffic management can make cycling safer and more useful. Settlements with a dense network of interconnected streets tend to be places for getting around by bike. Their cycling networks can give people direct, fast, easy and convenient routes.
Dewey, Montana
Dewey is an unincorporated community and census-designated place (CDP) in Beaverhead County, Montana, United States. It is in the northeast part of the county, on the south side of the Big Hole River, and bordered to the north, across the river, by Silver Bow County. Montana Highway 43 passes through Dewey, leading east 7 miles (11 km) to Interstate 15 at Divide, and west up the Big Hole River valley 5.5 miles (8.9 km) to Wise River and 44 miles (71 km) to Wisdom.

Dewey was first listed as a CDP prior to the 2020 census.

Wise River, Montana
Wise River is an unincorporated community in northern Beaverhead County, Montana, United States.

This community takes its name from the Wise River, which flows into the Big Hole River nearby. A post office was established in 1913.

The Elkhorn-Coolidge Historic District on the National Register of Historic Places is nearby. The district includes the Elkhorn mine site and the ghost town of Coolidge. The mine was for silver and began operation in 1872.
Pauline Rita
Pauline Rita (1 June 1842 – 28 June 1920), born Margaret Glenister, was an English soprano and actress. During her early career, she was best known for her performances in operettas and comic operas at the Opera Comique and was associated with impresario Richard D'Oyly Carte. Later she married flautist John Radcliff, and the two performed together for many years.

Comic opera
Comic opera, sometimes known as light opera, is a sung dramatic work of a light or comic nature, usually with a happy ending and often including spoken dialogue.

Forms of comic opera first developed in late 17th-century Italy. By the 1730s, a new operatic genre, opera buffa, emerged as an alternative to opera seria. It quickly made its way to France, where it became opéra comique, and eventually, in the following century, French operetta, with Jacques Offenbach as its most accomplished practitioner.

The influence of Italian and French forms spread to other parts of Europe. Many countries developed their own genres of comic opera, incorporating the Italian and French models along with their own musical traditions. Examples include German singspiel, Viennese operetta, Spanish zarzuela, Russian comic opera, English ballad and Savoy opera, North American operetta and musical comedy.