hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Topological degree theory
In mathematics, topological degree theory is a generalization of the winding number of a curve in the complex plane. It can be used to estimate the number of solutions of an equation, and is closely connected to fixed-point theory. When one solution of an equation is easily found, degree theory can often be used to prove existence of a second, nontrivial, solution. There are different types of degree for different types of maps: e.g.  for maps between Banach spaces there is the Brouwer degree in Rn, the Leray-Schauder degree for compact mappings in normed spaces, the coincidence degree and various other types. There is also a degree for continuous maps between manifolds.

Topological degree theory has applications in complementarity problems, differential equations, differential inclusions and dynamical systems.

Leray–Schauder degree
In mathematics, the Leray–Schauder degree is an extension of the degree of a base point preserving continuous map between spheres  or equivalently to boundary-sphere-preserving continuous maps between balls  to boundary-sphere-preserving maps between balls in a Banach space , assuming that the map is of the form  where  is the identity map and  is some compact map (i.e. mapping bounded sets to sets whose closure is compact).

The degree was invented by Jean Leray and Juliusz Schauder to prove existence results for partial differential equations.
2024 New Jersey's 10th congressional district special election
The 2024 New Jersey's 10th congressional district special election was held on September 18, 2024, to fill the vacant seat in New Jersey's 10th congressional district. The winner will serve in the United States House of Representatives for the remainder of the 118th United States Congress. The seat became vacant on April 24, 2024, when Donald Payne Jr. died following a heart attack related to complications from diabetes. The urban district is considered a safely Democratic seat; Payne Jr. had won all 7 bids for this seat with at least 77.6% of the vote.

On May 3, Governor Phil Murphy scheduled the special election for September 18, with primaries being held on July 16. This was the first non-November special election for a vacant House seat in New Jersey since 1950 which Republican William Widnall won after incumbent Representative J. Parnell Thomas was convicted on corruption charges. This was the first time since 1989 where no one from the Payne family represented this district.

2020 United States House of Representatives elections in New Jersey
The 2020 United States House of Representatives elections in New Jersey were held on November 3, 2020, to elect the 12 U.S. representatives from the state of New Jersey, one from each of the state's 12 congressional districts. The primary election in which candidates were chosen took place on July 7, 2020. The general election coincided with the 2020 U.S. presidential election, as well as other elections to the House of Representatives, elections to the United States Senate and various state and local elections.

No seats changed parties, although Rep. Jeff Van Drew was re-elected as a Republican after switching parties earlier in the year.
Paracas Candelabra
The Paracas Candelabra, also called the Candelabra of the Andes, or El Candelabro (the Trident), is a well-known prehistoric geoglyph found on the northern face of the Paracas Peninsula at Pisco Bay in Peru.  Pottery found nearby has been radio carbon dated to 200 BCE, the time of the Paracas culture. The design is cut 60 cm (2 ft) into the soil, with stones possibly from a later date placed around it. The figure is 170 m (560 ft) tall and 60 m (200 ft) wide, large enough to be seen 19 km (12 mi) at sea.

In 2016, it was designated as a national heritage site by Peru, with Peruvian law dictating a jail term of between three and six years for anyone damaging any archaeological monument.

Peruvian archaeologist Maria Reiche measured the geoglyph and found Paracas style pottery which she dated to around 200 BCE. The geoglyph is related to the Nazca lines.

Geoglyph
A geoglyph is a large design or motif – generally longer than 4 metres (13 ft) – produced on the ground by durable elements of the landscape, such as stones, stone fragments, gravel, or earth.  A positive geoglyph is formed by the arrangement and alignment of materials on the ground in a manner akin to petroforms, while a negative geoglyph is formed by removing part of the natural ground surface to create differently coloured or textured ground in a manner akin to petroglyphs.

Geoglyphs are generally a type of land art, and sometimes rock art.  A hill figure is created on a slope, so that it can be seen from a distance.
BMW R1100R
The BMW R 1100 R is a standard motorcycle with a 1,085 cc (66.2 cu in) air/oil-cooled flat twin engine, made by BMW Motorrad from 1994 through to 1999. Like all of the brand's motorcycles of this period, all 53,685 units were made at BMW's Spandau, Berlin factory. The R 1100 R was succeeded by the model year 2001 R 1150 R.

The R 1100 R was reviewed favorably by Ulf Böhringer of the Süddeutsche Zeitung. Cycle World was impressed with the 1995 R 1100 R's comfort, versatility, overall quality, and successful combination of a venerable engine and frame layout with the latest technology, while noting the "fussiness" of the idiosyncratic control and accessory operations.

BMW Motorrad
BMW Motorrad is the motorcycle brand and division of German automotive manufacturer, BMW. It has produced motorcycles since 1923, and achieved record sales for the fifth year in succession in 2015. With a total of 136,963 vehicles sold in 2015, BMW registered a growth of 10.9%  in sales in comparison with 2014.
In May 2011, the 2,000,000th motorcycle produced by BMW Motorrad was an R1200GS.
2013 Orange Open Guadeloupe
The 2013 Orange Open Guadeloupe was a professional tennis tournament played on hard courts. It was the third edition of the tournament which was part of the 2013 ATP Challenger Tour. It took place in Le Gosier, Guadeloupe between 25 and 31 March 2013.

Open de Guadeloupe
The Open de Guadeloupe (formerly known as Orange Open Guadeloupe) is a tennis tournament held in Le Gosier, Guadeloupe since 2011. The event is part of the ATP Challenger Tour and is played on hard courts.
Doman Singh Nagpure
Doman Singh Nagpure (born March 1, 1944, in Khairlanji, Madhya Pradesh) is an Indian politician and member of the Republican Party of India (Khobragade). He is a follower of B. R. Ambedkar. Nagpure was a member of the Madhya Pradesh Legislative Assembly from the Khairlanji constituency in Balaghat district. He was inducted into Digvijay Singh's Cabinet in 1993.

Digvijaya Singh
Digvijaya Singh (born 28 February 1947) is an Indian politician and a  Member of Parliament in the Rajya Sabha since 2014. He is a senior leader of the Indian National Congress and ex-general secretary of the Indian National Congress's All India Congress Committee. Previously, he had served as the 14th and 15th Chief Minister of Madhya Pradesh, a central Indian state, in two terms from 1993 to 1998 and from 1998 to 2003. Prior to that he was a minister in Chief Minister Arjun Singh's cabinet between 1980 and 1984. In the 2019 Indian general election he was defeated by Pragya Singh Thakur for the Bhopal Lok Sabha seat.

Singh was appointed as a member of Empowered Action Group of Leaders and Experts (EAGLE) which was constituted by Indian National Congress on 2 February 2025 to monitor the conduct of free and fair elections by the Election Commission of India.
Pterobilin
Pterobilin also called biliverdin IXγ in the Fischer nomenclature, is a blue bile pigment found in Nessaea spp., Graphium agamemnon, G. antiphates, G. doson, and G. sarpedon.  It is one of only a few blue pigments found in any animal species, as most animals use structural coloration to create blue coloration.  Other blue pigments of animal origin include phorcabilin, used by other butterflies in Graphium and Papilio (specifically P. phorcas and P. weiskei), and sarpedobilin, which is used by Graphium sarpedon.

Graphium agamemnon
Graphium agamemnon, the tailed jay, is a predominantly green and black tropical butterfly that belongs to the swallowtail family. The butterfly is also called the green-spotted triangle, tailed green jay, or green triangle. It is a common, non-threatened species native to Nepal, India and Sri Lanka, through Southeast Asia to Australia. Several geographic races are recognized. The species was first described by Carl Linnaeus in his 1758 10th edition of Systema Naturae.
Table tennis at the 2015 Pan American Games – Men's singles
The men's singles table tennis event at the 2015 Pan American Games will be held between July 22 and July 25, 2015 at the Atos Markham Pan Am Centre in Toronto, Canada. The winners of each the individual events will qualify to compete at the 2016 Summer Olympics in Rio de Janeiro, Brazil.

Table tennis at the 2015 Pan American Games
Table tennis competitions at the 2015 Pan American Games in Toronto were held from July 19 to 25 at the Markham Pan Am Centre (Atos Markham Pan Am Centre) in Markham. Due to naming rights, the arena was known as the latter for the duration of the games. A total of four table tennis events were held: two each for men and women.

The winners of each the individual events, provided they are not already qualified, qualified to compete at the 2016 Summer Olympics in Rio de Janeiro, Brazil.
2012 Mountain West Conference men's basketball tournament
The 2012 Mountain West Conference men's basketball tournament was  played at the Thomas & Mack Center in Las Vegas, Nevada in March 2012. Sponsored by Conoco; it was the first tournament without BYU or Utah, but included newcomer Boise State.

Mountain West Conference men's basketball tournament
The Mountain West Conference men's basketball tournament is held annually to determine the men's basketball champion from the Mountain West Conference. The winner receives an automatic bid to the NCAA Division I Basketball tournament, although they did not in the 1998-1999 season, the conference's first year in existence. The Thomas & Mack Center in Paradise, Nevada has hosted the most tournaments (15), including the last 11 consecutive tournaments.

San Diego State have won the tournament seven times, the most of any team. The No. 2 seed has won the tournament eight times, the most of any seed. The lowest seed to win the tournament was Colorado State as a No. 6 seed in 2003. New Mexico also won as a No. 6 seed, becoming the first team to play all four rounds and win in 2024.
Colin Upton
Colin Upton (born April 2, 1960) is a Canadian cartoonist and artist who was born in Winnipeg, Manitoba and grew up in Vancouver, British Columbia. Many of his comics are self-published in the minicomic format, although he has also had his work issued by commercial publishers such as Fantagraphics Books and included in anthology collections such as Drippytown Comics & Stories.  He is a co-host of the Inkstuds radio program, broadcast on CITR-FM at the University of British Columbia in Vancouver.

Since the mid-1980s, Upton has performed numerous times as a member of GX Jupitter-Larsen's noise band/performance art troupe The Haters. Upton's Happy Hater minicomics are based on the group's concepts and ideas.

Minicomic
A minicomic is a creator-published comic book, often photocopied and stapled or with a handmade binding such as a saddle-stitched or hand-sewn binding. In the United Kingdom and Europe the term small press comic is equivalent with minicomic, reserved for those publications measuring A6 (105 mm × 148 mm) or less.

Minicomics, sometimes called ashcan copies, and sometimes zine comics, are a common inexpensive way for those who want to make their own comics on a very small budget, with mostly informal means of distribution. A number of cartoonists — such as Jessica Abel, Julie Doucet, Art Spiegelman, and Adrian Tomine — started their careers this way and later went on to more traditional types of publishing, while other established artists — such as Matt Feazell and John Porcellino — continue to publish minicomics as their main means of production.
Theodore (prefect of Egypt)
Theodore (Latin: Theodorus, Greek: Θεόδωρος; fl. 7th century) was a Byzantine military commander who led the Byzantine army in the defence of Egypt during the Arab conquest, and served as the last Roman governor of Egypt from 21 March to 17 September 642.

Non-Chalcedonian Christianity
Non-Chalcedonian Christianity comprises the branches of Christianity that do not accept and uphold theological resolutions of the Council of Chalcedon, the council following Ephesus, held in 451. Non-Chalcedonian denominations reject the Christological Definition of Chalcedon (which asserted a carefully balanced compromise between Miaphysitism and Dyophysitism), for varying reasons. Non-Chalcedonian Christianity thus stands in contrast to Chalcedonian Christianity.

Today, the Oriental Orthodox Churches predominantly comprise most of non-Chalcedonian Christianity.
Chip Bok
Arthur Bernard "Chip" Bok III (born July 25, 1952) is an American editorial cartoonist for the Akron (Ohio) Beacon Journal and the Tampa Bay Times. He has illustrated some of Dave Barry's books, and was a finalist for the Pulitzer Prize in 1997.

Tampa Bay Times
The Tampa Bay Times, called the St. Petersburg Times until 2011, is an American newspaper published in St. Petersburg, Florida, United States. It is published by the Times Publishing Company, which is owned by The Poynter Institute for Media Studies, a nonprofit journalism school directly adjacent to the University of South Florida St. Petersburg campus.

It has won fourteen Pulitzer Prizes since 1964, and in 2009, won two in a single year for the first time in its history, one of which was for its PolitiFact project.
Maruyama Kofun (Kaizuka)
Maruyama Kofun (丸山古墳)  is a Kofun period keyhole-shaped burial mound, located in the Jizodō neighborhood of the city of Kaizuka, Osaka in the Kansai region of Japan. The tumulus was designated a National Historic Site of Japan in 1956. It is also called the Jizo-dō Maruyama Kofun (地蔵堂丸山古墳)

Kaizuka, Osaka
Kaizuka (貝塚市, Kaizuka-shi) is a city located in Osaka Prefecture, Japan. As of 1 January 2022, the city had an estimated population of 83,995 in 37,778 households and a population density of 1900 persons per km2. The total area of the city is 43.93 square kilometres (16.96 sq mi).
National service in the United States
National service in the United States has a long tradition, extending to the founding of the country. National service takes multiple forms in the U.S., including community service, military service, and other forms.

ServiceNation
ServiceNation was a campaign of Be The Change, Inc., a 501(c)(3) organization based in Boston, Massachusetts. Its mission was to rekindle an ethic of civic responsibility in America through universal national service. ServiceNation's goal was to expand opportunities for Americans to spend a year in non-military national service such as AmeriCorps.  National service programs like Americorps pay a living stipend and reward volunteers who have completed service with a monetary education award.

In January 2016, ServiceNation merged with the Franklin Project at the Aspen Institute and the Service Year Exchange (which was incubated at the National Conference on Citizenship) to form the Service Year Alliance.
1864 United States presidential election in Massachusetts
The 1864 United States presidential election in Massachusetts took place on November 8, 1864, as part of the 1864 United States presidential election. Voters chose 12 representatives, or electors to the Electoral College, who voted for president and vice president.

Massachusetts voted for the National Union candidate, incumbent Republican president Abraham Lincoln and his running mate Andrew Johnson. They defeated the Democratic candidate, George B. McClellan and his running mate George H. Pendleton. Lincoln won the state by a margin of 44.44%.

Although Lincoln ran under the National Union banner, this is the best Republican performance in Massachusetts as of the 2024 election. With 72.22% of the popular vote, Lincoln's performance in Massachusetts made it his third best performance in the 1864 election after Kansas and neighboring Vermont.

This is the last election in which the city of Roxbury voted in a presidential election, as it was annexed by the city of Boston in 1868.

1864 United States presidential election in Vermont
The 1864 United States presidential election in Vermont took place on November 8, 1864, as part of the 1864 United States presidential election. Voters chose five representatives, or electors to the Electoral College, who voted for president and vice president.

Vermont voted for the National Union candidate, incumbent Republican President Abraham Lincoln and his running mate Andrew Johnson. They defeated the Democratic candidate, George B. McClellan and his running mate George H. Pendleton. Lincoln won the state by a wide margin of 52.20%.

With 76.10% of the popular vote, Lincoln's victory with in the state would be his second strongest victory in the country in terms of percentage in the popular vote after Kansas.
John Bull Chase
The John Bull Chase was a National Hunt Conditions chase in England which was open to horses aged five years or older. 
It was run at Wincanton over a distance of 2 miles and 5 furlongs (4,224 metres), and was scheduled to take place each year in January.

The race was last run in 2003.

Wincanton Racecourse
Wincanton Racecourse is a thoroughbred horse racing venue located in Wincanton, Somerset, England.

The steeplechase fences are large, making it a good test of a chaser. Three fences in quick succession in the second half of the home-straight make for exciting racing and often change the complexion of a finish dramatically; resulting in a great many close finishes.

The track stages several big races, including the Kingwell Hurdle in February. The CGA Chase (previously the Jim Ford Challenge Cup, last run in 2012) was run on the same day; these races were significant trials for the Champion Hurdle and Cheltenham Gold Cup respectively. Several of the races at the course were shown on Channel 4 and are now occasionally shown on ITV.

The track is located near to the yard of the trainer, Paul Nicholls and as such many of his young horses run here.
Binghamton Triplets
The Binghamton Triplets were a minor league baseball team based in Binghamton, New York between 1923 and 1963. The franchise played as members of the New York–Penn League (1923–1937), Eastern League (1938–1963), New York–Penn League (1964–1966) and Eastern League (1967–1968). Binghamton was a minor league affiliate of the New York Yankees, Milwaukee Braves and Kansas City Athletics, winning ten league championships.

Cloyd Boyer
Cloyd Victor Boyer Jr. (September 1, 1927 – September 20, 2021) was an American professional baseball right-handed pitcher and coach in Major League Baseball (MLB) who played from 1949 and 1955 for the St. Louis Cardinals (1949–52) and the Kansas City Athletics (1955). Boyer was born in Alba, Missouri, the eldest son in a family that included Gold Glove Award-winning third basemen Ken and Clete Boyer.

Ken, 1964 National League Most Valuable Player, an 11-time Major League Baseball All-Star and five-time Gold Glove recipient, had a 15-year big-league career with the Cardinals, New York Mets, Chicago White Sox and Los Angeles Dodgers; Clete won only one Gold Glove because of the presence of Brooks Robinson, but played all or parts of 16 MLB seasons for the Athletics, New York Yankees and Atlanta Braves.
MuchMusic Video Award for Peoples Choice: Favourite International Group
The following is a list of the MuchMusic Video Awards, a Canadian music awards show, winners and nominees for "Favourite International Group". While the awards show itself ran until 2018, the "Favourite International Group" category existed only from 1997 until 2007.

IHeartRadio MMVAs
The iHeartRadio Much Music Video Awards were an awards show broadcast annually on Much from 1990 to 2018, and Fuse from 2010 to 2013 that honoured the year's best music videos.

Originally debuting in 1990 as the Canadian Music Video Awards, the awards were renamed in 1995 to the MuchMusic Video Awards. In 2016, the show was rebranded under the iHeartRadio banner after Much's parent company, Bell Media, reached a licensing agreement with iHeartMedia. The show's full name was officially dropped in 2018. The 2018 edition would ultimately be the last, amidst the scaling back and eventual discontinuation of all music programming on the channel due to declining ratings.
Ottawa Sooners
The Ottawa Sooners are a Canadian football team based in Ottawa. The team plays in the Ontario Football Conference of the Canadian Junior Football League.  The team has achieved success during its play in the CJFL, winning a total of four National Championships (1974, 1979, 1984 and 1992).  After 35 years of competition (1960–1995) in the CJFL, the Sooners moved to the Quebec Junior Football League for the beginning of the 1996 season.  There, the Sooners would win three Manson Cup Championships (1997, 2001 and 2002).  The Sooners rejoined the CJFL for the start of the 2009 season. The Sooners have a long history in the city of Ottawa, and while playing in the QJFL they had developed a good rivalry with the Ottawa Junior Riders.

The Sooners play home games at Keith Harris Stadium located on the campus of Carleton University, but previously played at the Nepean Sportsplex and Landsdowne Park Stadium.

Ottawa Rough Riders
The Ottawa Rough Riders were a Canadian Football League team based in Ottawa, Ontario, founded on September 19, 1876. Formerly one of the oldest and longest-lived professional sports teams in North America, the Rough Riders won the Grey Cup championship nine times. Their most dominant era was the 1960s and 1970s,  in which they won five Grey Cups. The team's fortunes waned in the 1980s and 1990s, and they ultimately ceased operations following the 1996 season. Five years later, a new CFL team known as the Ottawa Renegades was founded, though they suspended operations in 2006. The Ottawa Redblacks, which own the Rough Riders and Renegades intellectual properties, joined the league in 2014.
Outline of Liechtenstein
The following outline is provided as an overview of and topical guide to Liechtenstein:

Liechtenstein is a tiny, doubly landlocked alpine country located in Western Europe, bordered by Switzerland to its west and by Austria to its east. Mountainous, it is a winter-sport destination. It is also a tax haven. Despite this, it is not heavily urbanised. Many cultivated fields and small farms characterise its landscape both in the north (Unterland) and in the south (Oberland). It is the smallest German-speaking country in the world.

Military history of Liechtenstein
The military history of Liechtenstein dates back to its predecessors in the County of Vaduz and Lordship of Schellenberg. Liechtenstein disbanded its army in 1868, and has had no standing army since. However, under the constitution of Liechtenstein citizens are still obligated to defend the country in the event of an external threat, and the army may be reformed if deemed necessary.
Jataí Ecological Station
The Jataí Ecological Station (Portuguese: Estação Ecológica de Jataí) is an ecological station (ESEC) in the state of São Paulo, Brazil.
It protects an area of cerrado and a lagoon system that is important for fish breeding.

Ecological station (Brazil)
An ecological station (Portuguese: Estação Ecológica) in Brazil is a type of protected area of Brazil as defined by the National System of Conservation Units (SNUC).
The purpose is to preserve untouched representative samples of the different biomes in Brazil.