hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Weak trace-class operator
In mathematics, a weak trace class operator  is a compact operator on a separable Hilbert space H with singular values the same order as the harmonic sequence.
When the dimension of H is infinite, the ideal of weak trace-class operators is strictly larger than the ideal of trace class operators, and has fundamentally different properties. The usual operator trace on the trace-class operators does not extend to the weak trace class. Instead the ideal of weak trace-class operators admits an infinite number of linearly independent quasi-continuous traces, and it is the smallest two-sided ideal for which all traces on it are singular traces.

Weak trace-class operators feature in the noncommutative geometry of French mathematician Alain Connes.

Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910).

Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces are used also in the theoretical discussion of problems in physics, statistics, economics, finance, engineering, and other disciplines.
Catalog of Components of Double and Multiple Stars
The Catalog of Components of Double and Multiple Stars, or CCDM, is an astrometric star catalogue of double and multiple stars.  It was made by Jean Dommanget and Omer Nys at the Royal Observatory of Belgium in order to provide an input catalogue of stars for the Hipparcos mission.  The published first edition of the catalog, released in 1994, has entries for 74,861 components of 34,031 double and multiple stars; the second edition, in 2002, has been expanded to provide entries for 105,838 components of 49,325 double and multiple stars.  The catalog lists positions, magnitudes, spectral types, and proper motions for each component.

Star catalogue
A star catalogue is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers. There are a great many different star catalogues which have been produced for different purposes over the years, and this article covers only some of the more frequently quoted ones. Star catalogues were compiled by many different ancient people, including the Babylonians, Greeks, Chinese, Persians, and Arabs. They were sometimes accompanied by a star chart for illustration. Most modern catalogues are available in electronic format and can be freely downloaded from space agencies' data centres. The largest is being compiled from the spacecraft Gaia and thus far has over a billion stars.

Completeness and accuracy are described by the faintest limiting magnitude V (largest number) and the accuracy of the positions.
Congressional canvass for the 2010 Philippine presidential election
The following is the official canvassing of votes by the Congress of the Philippines for the 2010 Philippine presidential and vice presidential election. The canvassing, originally scheduled to start on May 31, started on May 25, 2010, and ended on June 9, 2010. The Congress is mandated to declare a winner 30 days after the elections (June 9).

Arthur Defensor Sr.
Arthur "Art" Doligosa Defensor Sr.  (born December 25, 1941) is a Filipino politician and a statesman who served as the governor of Iloilo from 1992 until 2001, and again from 2010 until 2019. He also served as Representative of the 3rd District of Iloilo from 2001 to 2010. He was the Majority Leader of the 14th Congress of the Philippines. He is currently a member of the PDP–Laban. He is married to Cosette Rivera Defensor.
Gomadingen
Gomadingen is a town in the district of Reutlingen in Baden-Württemberg in Germany. About 85% of its territory is located on the Swabian Alps. It's the district where the Grafeneck Castle  is situated. During the II World War, the castle was home of the Grafeneck Euthanasia Centre  (German: NS-Tötungsanstalt Grafeneck), one of the main Nazi Germany's killing centres part of their Action T4 programme.

Reutlingen (district)
Reutlingen, nicknamed "The Gate to the Swabian Alb" (German: "Das Tor zur Schwäbischen Alb"), is a Landkreis (district) in the middle of Baden-Württemberg, Germany.
The former free imperial city (until 1802) reached the limit of 100,000 residents in 1989. It is the ninth-largest city in Baden-Württemberg. Reutlingen district's neighbouring districts are (from north clockwise) Esslingen, Göppingen, Alb-Donau, Biberach, Sigmaringen, Zollernalbkreis, Tübingen and Böblingen.
V1429 Aquilae
V1429 Aquilae is a candidate luminous blue variable multiple star system located in the constellation of Aquila.  It is often referred to by its Mount Wilson Observatory catalog number as MWC 314.  It is a hot luminous star with strong emission lines in its spectrum.

Aquila (constellation)
Aquila is a constellation on the celestial equator. Its name is Latin for 'eagle' and it represents the bird that carried Zeus/Jupiter's thunderbolts in Greek-Roman mythology.

Its brightest star, Altair, is one vertex of the Summer Triangle asterism. The constellation is best seen in the northern summer, as it is located along the Milky Way. Because of this location, many clusters and nebulae are found within its borders, but they are dim and galaxies are few.
Pseudo-Boolean function
In mathematics and optimization, a pseudo-Boolean function is a function of the form

where B = {0, 1} is a Boolean domain and n is a nonnegative integer called the arity of the function. A Boolean function is then a special case, where the values are also restricted to 0 or 1.

Mathematical optimization
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics.
Zulfiqar Ali Khan
Zulfiqar Ali Khan (Urdu: ذوالفقار علی خان; 10 December 1930 – 8 March 2005) NI(M), was the first four-star air officer in the Pakistan Air Force and later a diplomat.: contents  He was the Air Force's Chief of Air Staff from 15 April 1974 to 22 July 1978. Upon retirement, he served on a diplomatic assignment, and headed the diplomatic mission to the United States as Pakistan's ambassador from 1989 to 1990.

Group captain
Group captain (Gp Capt or G/C) is a senior officer rank used by some air forces, with origins from the Royal Air Force. The rank is used by air forces of many countries that have historical British influence.

Group captain is immediately senior to wing commander and immediately below air commodore. It is equivalent to the rank of captain in the navy and of colonel in other services.

The equivalent rank in the Women's Auxiliary Air Force, Women's Auxiliary Australian Air Force, Women's Royal Air Force (until 1968) and Princess Mary's Royal Air Force Nursing Service (until 1980) was "group officer".
The Merman's Children
The Merman's Children is a 1979 fantasy novel by American writer Poul Anderson, inspired by legends of Mermen and Mermaids from Danish folklore, in particular the ballad Agnete og Havmanden. Set at the end of the medieval era, The Merman's Children details the Faery peoples being displaced by the advancing tide of Christianity.

Danish folklore
Danish folklore consists of folk tales, legends, songs, music, dancing, popular beliefs, myths and traditions communicated by the inhabitants of towns and villages across the country of Denmark, often passed on from generation to generation by word of mouth. As in neighbouring countries, interest in folklore grew with an emerging feeling of national consciousness in 19th century Denmark. Researchers travelled across the country collecting innumerable folktales, songs and sayings while observing traditional dress in the various regions. Folklore today is part of the national heritage, represented in particular by national and local traditions, songs, folk dances and literature.
2015 Corrientes Challenger
The 2015 Corrientes Challenger was a professional tennis tournament played on clay courts. It was the inaugural edition of the tournament which was part of the 2015 ATP Challenger Tour. It took place in Corrientes, Argentina between 12 and 18 October 2015.

2015 ATP Challenger Tour
The ATP Challenger Tour, in 2015 was the secondary professional tennis circuit organized by the ATP. The 2015 ATP Challenger Tour calendar comprised 166 tournaments, with prize money ranging from $40,000 up to $220,000. It was the 38th edition of challenger tournaments cycle, and 7th under the name of Challenger Tour.
Geraci Siculo
Geraci Siculo (Sicilian: Jiraci) is a comune (municipality) in the Metropolitan City of Palermo in the Italian region Sicily, located about 70 kilometres (43 mi) southeast of Palermo. It is one of I Borghi più belli d'Italia ("The most beautiful villages of Italy").

Geraci Siculo borders the following municipalities: Castel di Lucio, Castelbuono, Gangi, Nicosia, Petralia Soprana, Petralia Sottana, San Mauro Castelverde.

Castelbuono
Castelbuono (Sicilian: Casteḍḍu-bonu or, locally, Castiḍḍubbuonu) is a town and comune in the Metropolitan City of Palermo, Sicily (southern Italy).

It is known for the castle from which its name derives, around which the city developed in the 14th century.
Food Network Star season 13
The thirteenth season of the American reality television series Food Network Star premiered June 4, 2017 on Food Network. Food Network chefs Bobby Flay and Giada de Laurentiis returned to the series as judges.

Food Network Star
Food Network Star is a reality television series that aired from June 5, 2005, to August 5, 2018. It was produced by CBS EYEtoo Productions for seasons 1–8 and by Triage Entertainment for seasons 9–14. It aired on the Food Network in the United States. Prior to season seven, the series was known as The Next Food Network Star.
Garrett Swasey
Garrett Preston Russell Swasey (November 16, 1971 – November 27, 2015) was an American competitive ice skater, figure skating coach, and police officer. As an ice dancer, he won the 1992 U.S. junior ice dance title at the U.S. Figure Skating Championships and went on to participate twice more at the senior level. He coached along with Doreen Denny. Swasey was shot and killed in the line of duty during the Colorado Springs Planned Parenthood shooting in 2015.

Melrose, Massachusetts
Melrose is a city located in the Greater Boston metropolitan area in Middlesex County, Massachusetts, United States. Its population as of the 2020 census was 29,817. It is a suburb located approximately seven miles north of Boston. It is situated in the center of the triangle created by Interstates 93, 95 and U.S. Route 1.

The land that comprises Melrose was first settled in 1628 and was once part of Charlestown and then Malden. It became the Town of Melrose in 1850 and then the City of Melrose in 1900.
Gillette Children's
Gillette Children's, officially known as Gillette Children's Specialty Healthcare, is a non-profit pediatric hospital located in St. Paul, Minnesota. Founded in 1897, it was the first hospital in the United States dedicated exclusively to the care of children with physical disabilities. The hospital operates independently of larger health systems and focuses on the treatment of complex orthopedic, neurologic, and rehabilitative conditions, serving patients from Minnesota, the wider United States, and internationally.

Prosthesis
In medicine, a prosthesis (pl.: prostheses; from Ancient Greek: πρόσθεσις, romanized: prósthesis, lit. 'addition, application, attachment'), or a prosthetic implant, is an artificial device that replaces a missing body part, which may be lost through physical trauma, disease, or a condition present at birth (congenital disorder). Prostheses may restore the normal functions of the missing body part, or may perform a cosmetic function.

A person who has undergone an amputation is sometimes referred to as an amputee, Rehabilitation for someone with an amputation is primarily coordinated by a physiatrist as part of an inter-disciplinary team consisting of physiatrists, prosthetists, nurses, physical therapists, and occupational therapists. Prostheses can be created by hand or with computer-aided design (CAD), a software interface that helps creators design and analyze the creation with computer-generated 2-D and 3-D graphics as well as analysis and optimization tools.
2017 General Aung San Shield final
The 2017 General Aung San Shield final is the 7th final of the MFF Cup.
The General Aung San Shield winner will qualify to AFC Cup competition. 
The match was contested by Shan United and Yangon United  at Bogyoke Aung San Stadium in Yangon. The match will play  on 25 October 2017 and was the final match of the Bogyoke Aung San Cup.

Myanmar National League
Myanmar National League (Burmese: မြန်မာနေရှင်နယ်လိဂ်) often referred to as MNL, is the highest level of the Myanmar football league system. Contested by 12 clubs, it operates on a system of promotion and relegation with the MNL-2. Seasons typically run from August to May, with each team playing 22 games.
Outline of natural science
The following outline is provided as an overview of and topical guide to natural science:

Natural science – a major branch of science that tries to explain, and predict, nature's phenomena based on empirical evidence. In natural science, hypothesis must be verified scientifically to be regarded as scientific theory.  Validity, accuracy, and social mechanisms ensuring quality control, such as peer review and repeatability of findings, are amongst the criteria and methods used for this purpose. Natural science can be broken into 2 main branches: life science, and physical science. Each of these branches, and all of their sub-branches, are referred to as natural sciences.

Biomechanics
Biomechanics is the study of the structure, function and motion of the mechanical aspects of biological systems, at any level from whole organisms to organs, cells and cell organelles, and even proteins using the methods of mechanics. Biomechanics is a branch of biophysics.
Álvaro Negredo
Álvaro Negredo Sánchez (Spanish pronunciation: [ˈalβaɾo neˈɣɾeðo ˈsantʃeθ]; born 20 August 1985) is a Spanish former professional footballer who played as a striker.

Nicknamed La fiera de Vallecas (The beast of Vallecas), he amassed totals of 361 matches and 128 goals over 12 La Liga seasons, for Almería, Sevilla, Valencia and Cádiz, while winning the Copa del Rey with the second of those teams in 2010. Abroad, he played in the Premier League for Manchester City – lifting the league and League Cup in 2014 – and Middlesbrough, as well as representing Beşiktaş in Turkey and Al-Nasr in the United Arab Emirates.

Negredo earned 21 caps for Spain, scoring ten goals and being part of the team that won Euro 2012.

2015–16 Copa del Rey
The 2015–16 Copa del Rey was the 114th staging of the Copa del Rey (including two seasons where two rival editions were played). Going into the tournament, the winners were assured a place for the 2016–17 UEFA Europa League Group stage. However, since the two finalists, Barcelona and Sevilla, both qualified for the 2016–17 UEFA Champions League, respectively by winning the 2015–16 La Liga title and the 2015–16 Europa League, the cup winner's place in the 2016–17 Europa League group stage instead passed to the fifth-place team in La Liga, Athletic Bilbao.

Barcelona entered as the defending champions after winning the 2014–15 edition. They defeated Sevilla 2–0 in the final, winning their 28th title.
Abound Solar
Abound Solar was a manufacturer of cadmium telluride modules–a thin-film photovoltaic technology–based in the United States.  It operated a production facility in Longmont, Colorado.  The company was incorporated as AVA Solar in 2007 and was rebranded as Abound Solar in March 2009. In 2012 the company laid off almost half its employees before suspending operations and filing for bankruptcy.

Longmont, Colorado
Longmont is a home rule city located in Boulder and Weld counties, Colorado, United States. Its population was 98,885 as of the 2020 U.S. census.  Longmont is located northeast of the county seat of Boulder. It is named after Longs Peak, a prominent mountain that is clearly visible from the city (mont means "mountain" in French).
Víctor González Torres
Víctor González Torres (born July 1, 1937, in Mexico City) is a Mexican pharmaceutical businessman and politician, popularly known as Doctor Simi, the name of the character that represents his chain of companies, collectively called Farmacias Similares. In 2022 it became a trend to throw Doctor Simi plushies to singers in Mexico, and this was widely covered in social media.

National Electoral Institute
The National Electoral Institute (Spanish: Instituto Nacional Electoral; INE), formerly the Federal Electoral Institute (Spanish: Instituto Federal Electoral; IFE), is an autonomous, public agency responsible for organizing federal elections in Mexico: that is, those related to the election of the President of the United Mexican States, the members of the Congress of the Union as well as elections of authorities and representatives at local and state levels. The agency's president is Guadalupe Taddei Zavala, appointed in 2023 for a nine-year term.
Fees in proceedings before the European Patent Office
The fees due at the European Patent Office (EPO) in relation to a European patent application are laid out in the Rules relating to Fees of 20 October 1977, as adopted by decision of the Administrative Council of the European Patent Organisation of 7 December 2006 and as last amended by decision of the Administrative Council of 12 December 2018.

European Patent Office
The European Patent Office (EPO) is one of the two organs of the European Patent Organisation (EPOrg), the other being the Administrative Council. The EPO acts as executive body for the organisation while the Administrative Council acts as its supervisory body as well as, to a limited extent, its legislative body. The actual legislative power to revise the European Patent Convention lies with the Contracting States themselves when meeting at a Conference of the Contracting States.

Within the European Patent Office, examiners are notably in charge of studying European patent applications, filed by applicants, to decide whether to grant a patent for an invention. The patents granted by the European Patent Office are called European patents.
Miss Bahamas 2011
The Miss Bahamas 2011 pageant was held on May 6, 2011. Twenty-six candidates competed for the national crown. The chosen winner represented The Bahamas at the Miss Universe 2011 pageant. The costume of the winner of the best national costume award will be used at Miss Universe 2011. Miss World Bahamas entered Miss World 2011. The First Runner Up entered Miss Intercontinental, the Second Runner Up entered Miss Supranational, and the Third Runner Up entered Top Model of the World.

Top Model of the World
Top Model of the World is an international beauty pageant that focuses on finding the ultimate model. It was founded in 1993 in Miami, organized by the Globana Group, and is now owned and managed by the World Beauty Organization.
Riccarton, Edinburgh
Riccarton is an area in Edinburgh's Green Belt, in Scotland. It is mainly undeveloped, with much farmland and few houses.

Riccarton is to the west of the Edinburgh City Bypass (the A720), and is known for being the location of Heriot-Watt University's main campus, including Oriam, Scotland's National Performance Centre for Sport which opened to the public in August 2016.

In recent years, there have been numerous controversies surrounding potential development in the area.

The area is bordered by Currie, Juniper Green and Curriehill to the south, The Calders (Wester Hailes) to the east, and Hermiston to the north.

Juniper Green
Juniper Green is a village on the outskirts of Edinburgh, Scotland, situated about 5.5 miles (8.9 km) south-west of the city centre. It bridges the city bypass, and extends along the foothills of the Pentlands. It is bordered by Colinton to the east, Baberton immediately to the north, and Currie to the south-west. It centres on Lanark Road, the main route leading out south-west of Edinburgh into the Central Borders. The village stands on an elevated ridge above the Water of Leith to its south.

Administratively, Juniper Green falls within the jurisdiction of the City of Edinburgh Council having been officially absorbed into the city in 1920.
Nurhajizah Marpaung
Nurhajizah Marpaung (born 7 August 1956) is an Indonesian retired military officer and politician who became the Vice Governor of North Sumatra from 2017 until 2018. Her last position in the military was as the General Counsel of the Ministry of Defense. She unsuccessfully ran for Regent of Asahan in 2015 and 2020.

People's Conscience Party
The People's Conscience Party (Indonesian: Partai Hati Nurani Rakyat), better known by its abbreviation, Hanura, is a political party in Indonesia. It was established following a meeting in Jakarta on 13–14 December 2006 and first headed by former Indonesian National Armed Forces commander Wiranto.

The party lost its seats in the House of Representatives (DPR) after a poor performance in the 2019 general election.
1978–79 FC Basel season
The Fussball Club Basel 1893 1978–79 season was their 85th season since the club was founded. It was their 33rd consecutive season in the top flight of Swiss football after they won promotion during the season 1945–46. They played their home games in the St. Jakob Stadium. This was René Theler's third period as chairman.

St. Jakob Stadium
The St. Jakob Stadium was a football stadium in Basel, Switzerland and the former home of Swiss club FC Basel. It was built in view of the 1954 FIFA World Cup, and as well as serving as a club stadium, it hosted several important matches, including some FIFA World Cup matches in 1954 and four European Cup Winners' Cup finals.

After closing in 1998, St. Jakob-Park was built in its place. It was nicknamed "Joggeli" (a diminutive of "Jakob" in the local dialect) by Basel supporters.