hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Ingleton's inequality
In mathematics, Ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. In this sense it is a necessary condition for representability of a matroid over a finite field.  For a matroid M and its rank function ρ, Ingleton's inequality states that for any subsets X1, X2, X3 and X4 in the support of M, the inequality

ρ(X1) + ρ(X2) + ρ(X1∪X2∪X3) + ρ(X1∪X2∪X4) + ρ(X3∪X4) ≤ ρ(X1∪X2) + ρ(X1∪X3) + ρ(X1∪X4) + ρ(X2∪X3) + ρ(X2∪X4)

is satisfied.

Aubrey William Ingleton, an English mathematician, wrote an important paper in 1969 in which he surveyed the representability problem in matroids.  Although the article is mainly expository, in this paper Ingleton stated and proved Ingleton's inequality, which has found interesting applications in information theory, matroid theory, and network coding.

Matroid
In combinatorics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the language of partially ordered sets, a finite simple matroid is equivalent to a geometric lattice.

Matroid theory borrows extensively from the terms used in both linear algebra and graph theory, largely because it is the abstraction of various notions of central importance in these fields. Matroids have found applications in geometry, topology, combinatorial optimization, network theory, and coding theory.
Fuad Hussein
Fuad Mohammed Hussein (Arabic: فؤاد حسين; Kurdish: فوئاد حوسەین, Fuad Huseyn; born June 1, 1949) is an Iraqi politician from the Kurdistan Democratic Party who is the current Iraqi Minister of Foreign Affairs. He was previously the Minister of Finance in the Government of Adil Abdul-Mahdi.

Adil Abdul-Mahdi
Adil Abdul-Mahdi al-Muntafiki (Arabic: عادل عبد المهدي المنتفكي, born 1 January 1942) is an Iraqi politician  who served as Prime Minister of Iraq from October 2018 until May 2020. Abdul-Mahdi is an economist and was one of the vice presidents of Iraq from 2005 to 2011. He formerly served as Minister of Finance in the Interim government and Oil Minister from 2014 to 2016.

Abdul-Mahdi is a former member of the powerful Shi'a party the Supreme Islamic Iraqi Council, or SIIC. Long based in neighboring Iran, the group opposed a United States administration while holding close ties with the other, U.S.-backed, groups that opposed Saddam Hussein, including the Kurds and the Iraqi National Congress.

Abdul-Mahdi submitted his formal resignation as prime minister in November 2019, following widespread protests over political corruption and violent police responses.
Dalmacio Mera
Dalmacio Enrique Mera Figueroa (born 13 November 1970) is an Argentine lawyer and politician. Among other posts, he served as a National Senator for Catamarca Province from 2015 to 2021, as a National Deputy from 2009 to 2011, and as Vice Governor of Catamarca under Lucía Corpacci from 2011 to 2015. Mera belongs to the Justicialist Party.

Lucía Corpacci
Lucía Benigna Corpacci (born 4 December 1959) is an Argentine physician and politician. A member of the Justicialist Party, she was governor of Catamarca Province from 2011 to 2019, the first female governor in Catamarca and the fourth female governor of a province in Argentina.

From 2019 to 2021 she has been a member of the Argentine Chamber of Deputies, and since 2021 she is a National Senator representing Catamarca.
Rudkøbing
Rudkøbing is a town in Denmark, on the western coast of the island of Langeland. It is the seat of Langeland Municipality, in the Southern Denmark Region. The town is located 15 kilometres (9.3 mi) southeast of Svendborg and is connected to Siø through the Siøsund Bridge.

Svendborg
Svendborg (Danish: [ˈsvenˌpɒˀ] ⓘ) is a town on the island of Funen in south-central Denmark, and the seat of Svendborg Municipality. With a population of 27,616 (1 January 2025), Svendborg is Funen's second largest city. In 2000 Svendborg was declared "Town of the year" in Denmark, and in 2003 it celebrated its 750th anniversary as a market town. By road, Svendborg is located 195 kilometres (121 mi) southwest of Copenhagen, 183 kilometres (114 mi) south of Aarhus, 44.2 kilometres (27.5 mi) south of Odense, and 28.5 kilometres (17.7 mi) east of Faaborg.

Svendborg is home to "Danmarks Forsorgsmuseum" social history museum and "Naturama" natural history museum. The latter holds a wide variety of taxidermy from whales and bears to birds and Foxes.

The largest container ship company in the world, A.P. Møller-Mærsk has its origins in Svendborg, in the "Villa Anna".
Nebih Meha
Nebih Meha (December 15, 1910 – May 13, 1981 (1910-12-15 – 1981-05-13)) was a Kosovar Albanian soldier. He died on 13 May 1981 along with his son Tahir Meha, following an armed confrontation with Yugoslav authorities at their residence.

Tahir Meha
Tahir Meha (10 October 1943 – 13 May 1981) was an Albanian political activist and major figure in the Kosovar Albanian resistance during Yugoslav rule. His refusal to surrender his weapons to Yugoslav authorities escalated into armed confrontation, ending with his death alongside his father, Nebih Meha on 13 May 1981. He remains a significant figure in Albanian folklore where he is remembered as a hero.
Michael Jeffery
Major General Philip Michael Jeffery (12 December 1937 – 18 December 2020) was a senior Australian Army officer and vice-regal representative. He was the 28th governor of Western Australia from 1993 to 2000, and the 24th governor-general of Australia, serving from 2003 to 2008.

From Perth, Western Australia, Jeffery graduated from the Royal Military College, Duntroon, and served in the Malayan Emergency and the Vietnam War, being awarded the Military Cross during the latter conflict.

Jeffery was at various stages commander of the Special Air Service Regiment and the 1st Division, and subsequently Deputy Chief of General Staff, before retiring from active service in 1993. After serving for seven years as Governor of Western Australia, Jeffery was appointed Governor-General of Australia in 2003, following the resignation of Peter Hollingworth. He was the first career Australian Army officer to hold the position, and was succeeded by Quentin Bryce.

Deputy Chief of Army
The Deputy Chief of Army (DCA) is the second most senior appointment in the Australian Army, responsible to the Chief of Army (CA). The rank associated with the position is major general (2-star).

The current appointee is Major General Chris Smith, who took up the posting on 31 January 2024.
Huntingdonshire Rifles
The Huntingdonshire Militia, later the Huntingdonshire Rifles, was an auxiliary military force in the county of Huntingdonshire in the East Midlands of England. From their formal organisation as Trained Bands in 1558 the Militia of Huntingdonshire served during times of international tension and Britain's major wars. They provided internal security and home defence, relieving regular troops from routine garrison duties, and acting as a source of trained officers and men for the Regular Army. The regiment later became a battalion of the King's Royal Rifle Corps, and trained thousands of reservists and recruits during World War I. It maintained a shadowy existence until final disbandment in 1953.

Militia (United Kingdom)
The British Militia was the principal military reserve force of the United Kingdom of Great Britain and Ireland. Militia units were repeatedly raised in Great Britain during the Victorian and Edwardian eras for internal security duties and to defend against external invasions. The British Militia was transformed into the Special Reserve under the Territorial and Reserve Forces Act 1907 (7 Edw. 7. c. 9), which integrated all militia formations into the British Army.
2008 United States presidential election in Idaho
The 2008 United States presidential election in Idaho took place on November 4, 2008, and was part of the 2008 United States presidential election. Voters chose four representatives, or electors to the Electoral College, who voted for president and vice president.

Idaho was won by Republican nominee John McCain by a 25.3% margin of victory. Prior to the election, all 17 major news organizations considered this a state McCain would win, or a red state. Polling in the state gave a sizable lead to McCain over Democrat Barack Obama, with most polling predicting a McCain win of at least 30 percentage points. Despite his landslide defeat in the state, Obama over-performed his polls and greatly improved on Kerry's performance four years earlier. Idaho has not gone Democratic for President since Lyndon B. Johnson narrowly won it in 1964.

2004 United States presidential election in Idaho
The 2004 United States presidential election in Idaho was held on November 2, 2004, as part of the 2004 presidential election. Voters chose four representatives, or electors to the Electoral College, who voted for president and vice president.

Idaho was won by incumbent President George W. Bush by a 38.1 point margin of victory. Prior to the election, all twelve news organizations considered this a state Bush would win, or otherwise considered as a safe red state. No Democratic presidential nominee had won the state since Lyndon B. Johnson in 1964, and even then, the race was closely contested. In 2004, President George W. Bush easily won the state and every congressional district and county, except the Democratic stronghold of Blaine County.

With 68.38 percent of the popular vote, Idaho would prove to be Bush's third strongest state in the 2004 election after neighboring Utah and Wyoming.
Isabel Bassett
Isabel Bassett CM OOnt (born August 23, 1939) is a Canadian broadcaster and former politician.  From 1999 until 2005 she was the chair and CEO of TVOntario/TFO, Ontario's provincial public television network. She has been a controversial figure at times, but is also a highly regarded pioneer in Canadian broadcasting.

Order of Ontario
The Order of Ontario (French: Ordre de l'Ontario) is a civilian honour for merit in the Canadian province of Ontario. Instituted in 1986 by Lieutenant Governor Lincoln Alexander, on the advice of the Cabinet under Premier David Peterson, the civilian order is administered by the Lieutenant Governor-in-Council and is intended to honour current or former Ontario residents for conspicuous achievements in any field.
Iron Maiden: Flight 666
Iron Maiden: Flight 666 is a concert documentary film featuring the English heavy metal band Iron Maiden. The film follows the band on the first leg of their Somewhere Back in Time World Tour in February and March 2008, during which they travelled on their own customised Boeing 757, Ed Force One, which used the call-sign "666".

Flight 666 is co-produced by Toronto-based Banger Films, known for their documentaries Metal: A Headbanger's Journey, Global Metal and Rush: Beyond the Lighted Stage. The film was shot in high-definition video with accompanying 5.1 surround sound produced by Kevin Shirley (who has worked with the band since their 2000 album Brave New World). It was distributed by Arts Alliance Media and EMI (except in the US, where it was sub-distributed by D&E Entertainment) in select digital theatres on 21 April 2009.

Metal: A Headbanger's Journey
Metal: A Headbanger's Journey is a 2005 documentary film directed by Sam Dunn with Scot McFadyen and Jessica Wise. The film follows 31-year-old Dunn, a Canadian anthropologist, who has been a heavy metal fan since the age of 12. Dunn sets out across the world to uncover the various opinions on heavy metal music, including its origins, culture, controversy, and the reasons it is loved by so many people. The film made its debut at the 2005 Toronto International Film Festival, and was released as a two-disc special edition DVD in the US on 19 September 2006.

A follow-up to the film titled Global Metal premiered at the Bergen International Film Festival on 17 October 2007, and saw limited release in theatres in June 2008. Dunn has also elaborated upon his "Heavy Metal Family Tree" in the VH1 series Metal Evolution, which focuses on one subgenre per episode.
2/14th Field Regiment (Australia)
The 2/14th Field Regiment was an Australian Army artillery unit that served during the Second World War. Raised in late 1940 as part of the 8th Division, the regiment remained in Australia as a garrison force in Darwin when the division's infantry brigades were sent to various places around Southeast Asia to meet the threat posed by Japan. As a result, it did not deploy overseas until late 1943. In New Guinea, the regiment supported the 5th Division's operations on the Huon Peninsula throughout 1944 before deploying with them to New Britain in early 1945. From then, until the end of the war, the regiment engaged in operations against the large Japanese garrison on the island. At the end of the war, the 2/14th briefly undertook garrison duties on Rabaul as part of the 11th Division before returning to Australia and disbanding in January 1946.

11th Division (Australia)
The 11th Division was an Australian Army unit formed during World War II by the renaming of Milne Force in December 1942. Predominately a Militia formation, the division's main role during the war was as a base command headquarters, although elements saw action in New Guinea against Japanese forces during the Finisterre Range campaign and in New Britain. It was disbanded in July 1946.
The Witches' Kitchen
The Witches' Kitchen (Spanish: La cocina de las brujas or Berganza y Cañizares) is a painting by the Spanish artist Francisco Goya, located in a private collection in Mexico. It is part of a series of six cabinet paintings, each measuring approximately 43 × 30 cm, with the theme of witchcraft. The paintings do not together form a single narrative and do not share a common meaning, so it is appropriate to interpret each one individually. The entire series was owned by the Dukes of Osuna and adorned their summer residence, Alameda de Osuna. In addition to The Witches' Kitchen, the series includes: Witches' Sabbath, Witches' Flight, The Incantation, The Bewitched Man, and Don Juan and the Commendatore. Four of the paintings are in various public collections, one in a private collection, and the last is considered lost.

Witches' Sabbath (Goya, 1798)
Witches' Sabbath (Spanish: El Aquelarre) is a 1798 oil painting on canvas by the Spanish artist Francisco Goya.  Today it is held in the Museo Lázaro Galdiano, Madrid. It depicts a Witches' Sabbath.

It was purchased in 1798 along with five other paintings related to witchcraft by the Duke and Duchess of Osuna. The acquisition of the witchcraft paintings is attributed to the duchess rather than her husband, but it is not known whether they were commissioned or bought after completion.
In the twentieth century the painting was purchased by the financier José Lázaro Galdiano and donated to the Spanish state upon his death.
Korv stroganoff
Korv stroganoff or korvstroganoff, Swedish for sausage stroganoff, is a Swedish dish, originally based on the Russian dish beef Stroganoff, where the beef is replaced with pieces of sausage (traditionally falukorv) and the sauce features a partial tomato base.

Swedish cuisine
Swedish cuisine (Swedish: svenska köket) is the traditional food of Sweden. Due to Sweden's large north-to-south expanse, there are regional differences between the cuisine of North and South Sweden.

Historically, in the far north, meats such as reindeer, and other game dishes were eaten, some of which have their roots in the Sami culture, while fresh vegetables have played a larger role in the South. Many traditional dishes employ simple, contrasting flavours, such as the traditional dish of meatballs and brown cream sauce with tart, pungent lingonberry jam.
Music of Austria
Vienna has been an important center of musical innovation. 18th- and 19th-century composers were drawn to the city due to the patronage of the Habsburgs, and made Vienna the European capital of classical music. Joseph Haydn, Wolfgang Amadeus Mozart, Ludwig van Beethoven, Franz Schubert and Johann Strauss II, among others, were associated with the city, with Schubert being born in Vienna. During the Baroque period, Slavic and Hungarian folk forms influenced Austrian music. Vienna's status began its rise as a cultural center in the early 16th century, and was focused on instruments including the lute.

Music of Vienna
Vienna is the capital and largest city of Austria, and has long been one of the major centers for cultural development in central Europe.

Music organizations in Vienna include the Gesellschaft der Musikfreunde, which has been promoting musical development in the city since 1812.  The Vienna Boys Choir has an even longer history, dating back to 1498, while the Vienna Philharmonic Orchestra is also renowned .

Major music venues in Vienna include the State Opera House, the People's Opera House, the Burgtheater, and the Theater an der Wien, the former three of which are owned by the federal government .
SLAM! (radio station)
SLAM! (Sound Lifestyle And More, stylized as ►SLAM! and previously SLAM!FM) is a Dutch commercial national radio station that plays current-based rhythmic and dance hits. SLAM! has a strong commitment in breaking new dance music. The playlist and presentation serves as a combination of 538 and 3FM. The station is broadcasting in the Netherlands and can be received via FM in the Randstad, Internet (worldwide) and cable. The broadcasting building and studios of SLAM! are located in Naarden, North Holland. In 2012, it was announced that SLAM! has the largest market share among the country's young people (16.8%). It is a sister station of 100% NL, Radio Veronica and Sublime.

In 2016, SLAM! was reported to have a 0% market share for the 65-or-more age group. Carlo de Boer, SLAM!’s General Manager, then argued that SLAM! listeners were 30 years old in average, and that this market share "distinguished" SLAM! from other radio stations.

100% NL
52°17′10″N 5°11′42″E﻿ / ﻿52.28611°N 5.19500°E﻿ / 52.28611; 5.19500

100% NL (Dutch: 100 procent NL) is a Dutch commercial radio station which broadcasts nationwide on FM since 8 July 2006. 100% NL runs primarily Dutch products.
First United Methodist Church (Prestonburg, Kentucky)
The First United Methodist Church in Prestonburg, Kentucky is a historic church.

It was listed on the National Register of Historic Places as Methodist Episcopal Church, South in 1989.  It is a historic Methodist church building on S. Arnold Avenue between Ford Street and W. Graham Street in Prestonsburg, Kentucky.

It was built in 1917 in a Late Gothic Revival style.  It is a brick building with yellow sandstone trim on a raised concrete block foundation.  The brick is glazed with a yellow-orange mottled finish and is laid in running bond.

Prestonsburg, Kentucky
Prestonsburg is a home rule-class city in and the county seat of Floyd County, Kentucky, United States. It is in the eastern part of the state in the valley of the Big Sandy River. As of the 2020 census, Prestonsburg had a population of 3,681.
Ahora (Christian Nodal album)
Ahora (transl. Now) is the second studio album released by Mexican singer-songwriter Christian Nodal. It was released on May 10, 2019 via Fonovisa Records and Universal Music Latin. Produced by Jaime González, it follows Nodal's success with regional Mexican music in his debut studio album, Me Dejé Llevar (2017). Nodal served as the primary co-writer for the album, having co-written eight of the 14 songs. The album spawned three singles, "No Te Contaron Mal", "Nada Nuevo" and "De Los Besos Que Te Di", all of which charted in the top ten on Mexican charts.

The album received mainly positive reception from critics. Ahora peaked at number 19 on the Top 100 Mexico chart, and debuted at number seven on the Billboard Top Latin Albums chart in the United States. The album won Favorite Regional Mexican Album at the 2022 Latin American Music Awards and Best Ranchero/Mariachi Album at the 20th Annual Latin Grammy Awards. The album was certified platinum by the RIAA.

Me Dejé Llevar
Me Dejé Llevar (transl. I Got Carried Away) is the debut studio album by Mexican musician and singer-songwriter Christian Nodal, released on August 25, 2017. Produced by Jaime González, it sees Nodal experiment with "mariacheño", a fusion of mariachi and norteño.

Me Dejé Llevar reached number two on the Billboard Top Latin Albums chart in the United States and number seven on the Mexican Albums Chart. Four singles were released from the album: "Adiós Amor", "Probablemente", "Me Dejé Llevar", and "Te Fallé". Thom Jurek of AllMusic gave the album a positive review and called it, "lush and elegant". The album garnered a Latin Grammy nomination for Best Ranchero Album at the 19th Annual Latin Grammy Awards in 2018, while "Probablemente", was awarded a Latin Grammy Award for Best Regional Mexican Song.
Adamello-Presanella Alps
The Adamello-Presanella Alps Alpine group is a mountain range in the Southern Limestone Alps mountain group of the Eastern Alps. It is located in northern Italy, in the provinces of Trentino and Brescia. The name stems from its highest peaks: Adamello and Presanella.

The Adamello-Presanella Group is separated from the Ortler Alps in the north by the Tonale Pass; from the Bergamo Alps in the west by the Oglio valley (Val Camonica); from the Brenta Group in the east by the Campo Carlo Magno Pass and the river Sarca; to the south it continues towards Lake Iseo.

Southern Limestone Alps
The Southern Limestone Alps (Italian: Alpi Sud-orientali, German: Südliche Kalkalpen), also called the Southern Calcareous Alps, are the ranges of the Eastern Alps south of the Central Eastern Alps mainly located in northern Italy and the adjacent lands of Austria and Slovenia. The distinction from the Central Alps, where the higher peaks are located, is based on differences in geological composition. The Southern Limestone Alps extend from the Sobretta-Gavia range in Lombardy in the west to the Pohorje in Slovenia in the east.
Shoot A Line
Shoot A Line (foaled 2 April 1977) was a British Thoroughbred racehorse and broodmare. After winning her only race as a two-year-old she developed into one of the best fillies in Europe in 1980, winning the Cheshire Oaks, Ribblesdale Stakes, Irish Oaks, Yorkshire Oaks and Park Hill Stakes. In the following year she failed to win but ran creditably when finishing second to Ardross in the Ascot Gold Cup. As a five-year-old she was campaigned in the United States with little success before being retired to stud. She is the grand-dam of the Kentucky Derby winner Thunder Gulch.

Thunder Gulch
Thunder Gulch (May 23, 1992 – March 19, 2018)  was a Champion American Thoroughbred racehorse best known for his wins in the Kentucky Derby and the Belmont Stakes in 1995, which earned him the title of U.S. Champion 3-Yr-Old Colt.
Rollback (roller coaster)
A rollback occurs on a launched roller coaster when the train is not launched fast enough to reach the top of the tower or hill. It will roll backwards down the tower, and will be stopped by brakes on the launch track. Any roller coaster on which it is possible for a rollback to occur will have these brakes. Intamin, a manufacturer of roller-coasters, refers to the "rollback" as a "short shot".

Most coasters contain at least one anti-rollback device to prevent a train from rolling backwards while ascending the main lift. This is typically with chain-driven lifts, not hydraulic launchers such as Kingda Ka.

Launched roller coaster
The launched roller coaster is a type of roller coaster that initiates a ride with high amounts of acceleration via one or a series of linear induction motors (LIM), linear synchronous motors (LSM), catapults, tires, chains, or other mechanisms employing hydraulic or pneumatic power, along a launch track. This mode of acceleration powers many of the fastest roller coasters in the world.