hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Logarithmically concave function
In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality

for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ∘ f, is concave; that is,

for all x,y ∈ dom f and 0 < θ < 1.

Examples of log-concave functions are the 0-1 indicator functions of convex sets (which requires the more flexible definition), and the Gaussian function.

Similarly, a function is log-convex if it satisfies the reverse inequality

for all x,y ∈ dom f and 0 < θ < 1.

For non-negative discrete functions f : Z → R+, it is log-concave  if

Indicator function
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if A is a subset of some set X, then the indicator function of A is the function  defined by  if  and  otherwise. Other common notations are 𝟙A and

The indicator function of A is the Iverson bracket of the property of belonging to A; that is,

For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers.
Ferdynand Obtułowicz
Ferdynand Jakub Obtułowicz (born 1 January 1851 in Żywiec, died 6 August 1912 in Lwów) was a Polish hygienist doctor, a social worker, the president of Towarzystwo Higieniczne (Hygienic's Society) in Lwów, a member of council of Lwów.

He was son of Jakub and Józefa née Staszkiewicz. Obtułowicz studied medicine at the Jagiellonian University. He gained his Ph.D. in 1874. Later he was working in Kraków, Buczacz and Lwów.

Obtułowicz was an author of over 45 publications about hygienic, forensic pathology and epidemiology.

He was married to Stanisława Westfalewicz.

Buchach
Buchach (Ukrainian: Бучач, IPA: [ˈbutʃɐtʃ] ⓘ; Polish: Buczacz; Yiddish: בעטשאָטש, romanized: Betshotsh or ביטשאָטש Bitshotsh; Hebrew: בוצ'אץ' Buchach; German: Butschatsch; Turkish: Bucaş) is a city located on the Strypa River (a tributary of the Dniester) in Chortkiv Raion of Ternopil Oblast (province) of Western Ukraine. It hosts the administration of Buchach urban hromada, one of the hromadas of Ukraine. Buchach rests 135 kilometres (84 miles) south-east of Lviv, in the historic region of Halychyna (Galicia).

The city was located in the Polish–Lithuanian Commonwealth until the partitions, followed by the Habsburg monarchy (1772–1804), Austrian Empire (1804–1867), Austria-Hungary (1867–1918), West Ukrainian People's Republic (1918–1919), the Second Polish Republic (1919–1939), and the Ukrainian SSR of the Soviet Union (1939–1991). In 2022 the population was estimated to be 12,171 (2022 estimate)..
George Moellring
George Moellring (November 14, 1878 – May 31, 1935) was a justice of the North Dakota Supreme Court from December 1, 1933, to the end of 1934.

Born in Quincy, Illinois, Moellring studied law at Chaddock College of Law and Highland Park College, gaining admission to the bar in 1901. He moved to North Dakota the following year and in 1920 was elected to a seat on the District Court for the Fifth Judicial District, and was thereafter reelected to the seat. On December 1, 1933, he was appointed by Governor William Langer to a seat on the state supreme court vacated by the resignation of Justice Luther E. Birdzell. Moellring failed to win re-election to a full term in the 1934 election, and died the following year at the age of 56.

Admission to practice law
An admission to practice law is occupational licensing required to practice law. In jurisdictions with two types of lawyer, as with barristers and solicitors, barristers must gain admission to the bar whereas for solicitors there are distinct practising certificates.

Becoming a lawyer is a widely varied process around the world. Common to all jurisdictions are requirements of age and competence; some jurisdictions also require documentation of citizenship or immigration status. However, the most varied requirements are those surrounding the preparation for the license, whether it includes obtaining a law degree, passing an exam, or serving in an apprenticeship. In English, admission is also called a law license. Basic requirements vary from country to country, as described below.

In some jurisdictions, after admission the lawyer needs to maintain a current practising certificate to be permitted to offer services to the public.
Data-oriented parsing
Data-oriented parsing (DOP, also data-oriented processing) is a probabilistic model in computational linguistics. DOP was conceived by Remko Scha in 1990 with the aim of developing a performance-oriented grammar framework. Unlike other probabilistic models, DOP takes into account all subtrees contained in a treebank rather than being restricted to, for example, 2-level subtrees (like PCFGs), thus allowing for more context-sensitive information.

Several variants of DOP have been developed. The initial version developed by Rens Bod in 1992 was based on tree-substitution grammar, while more recently, DOP has been combined with lexical-functional grammar (LFG). The resulting DOP-LFG finds an application in machine translation. Other work on learning and parameter estimation for DOP has also found its way into machine translation.

Computational linguistics
Computational linguistics is an interdisciplinary field concerned with the computational modelling of natural language, as well as the study of appropriate computational approaches to linguistic questions. In general, computational linguistics draws upon linguistics, computer science, artificial intelligence, mathematics, logic, philosophy, cognitive science, cognitive psychology, psycholinguistics, anthropology and neuroscience, among others. Computational linguistics is closely related to mathematical linguistics.
Miami Fort Power Station
The Miami Fort Generating Station is a dual-fuel power generating facility. It is a major coal-fired electrical power station, supplemented with a small oil-fired facility. Miami Fort is located in Miami Township, Hamilton County, immediately east of the tripoint of Indiana, Kentucky, and Ohio. Miami Fort Station is named for the nearby Miami Fort (not to be confused with Fort Miami in the same state).

Fort Miami (Ohio)
Fort Miami (Miamis) was a British fort built in spring 1794 on the Maumee River in what was at the time territory claimed by the United States, and designated by the federal government as the Northwest Territory. The fort was located at the eastern edge of present-day Maumee, Ohio, southwest of Toledo.
The British built the fort to forestall a putative assault on Fort Detroit by Gen. "Mad" Anthony Wayne's army, then advancing northward in southwestern Ohio.
Orsa, Sweden
Orsa (Swedish pronunciation: [ˈʊ̂ʂːa]) is a locality and the seat of Orsa Municipality, Dalarna County, Sweden, with 5,308 inhabitants (2010). It is located in the northern part of lake Siljan, about 15 kilometres (9 miles) north of the town Mora. Inlandsbanan and European route E45 run through the town and the railroad Bollnäs-Orsa connects.

Urban areas in Sweden
An urban area or tätort (lit. 'dense locality') in Sweden has a minimum of 200 inhabitants and may be a city, town or larger village. It is a purely statistical concept, not defined by any municipal or county boundaries. Larger urban areas synonymous with cities or towns (Swedish: stad for both terms) for statistical purposes have a minimum of 10,000 inhabitants. The same statistical definition is also used for urban areas in the other Nordic countries.

In 2018, there were nearly two thousand urban areas in Sweden, which were inhabited by 87% of the Swedish population.

Urban area is a common English translation of the Swedish term tätort. The official term in English used by Statistics Sweden is, however, "locality" (Swedish: ort). It could be compared with "census-designated places" in the United States.
1968 Waterford Senior Hurling Championship
The 1968 Waterford Senior Hurling Championship was the 68th staging of the Waterford Senior Hurling Championship since its establishment by the Waterford County Board in 1897.

Ballygunner were the defending champions.

On 15 September 1968, Ballygunner won the championship after a 2–10 to 3–02 defeat of Mount Sion in the final. This was their third championship title overall and their third title in succession.

Waterford GAA
The Waterford County Board of the Gaelic Athletic Association (GAA) (Irish: Cumann Lúthchleas Gael Coiste Phort Láirge) or Waterford GAA is one of the 32 county boards of the GAA in Ireland, and is responsible for all levels of Gaelic games in County Waterford. The County Board is also responsible for the Waterford county teams. The county board's offices are based at Walsh Park in the city of Waterford. The Waterford County Board was founded in 1886.

Hurling is the dominant sport, with the county having won the All-Ireland Senior Hurling Championship (SHC) on two occasions: in 1948 and 1959. While football is the secondary sport in the county, it is widely played nonetheless. Waterford's greatest footballing achievement was reaching the 1898 All-Ireland Senior Football Championship Final, which the team lost to Dublin.
Armanaz massacre
On 29 September 2017, aircraft attacked Armanaz and killed at least 35 people, including at least 3 children, according to 5 witnesses and photos and video footage analyzed by Human Rights Watch. The Syrian Observatory for Human Rights reported that the death toll included 8 children and 8 women.

Syrian Observatory for Human Rights
The Syrian Observatory for Human Rights (also known as SOHR; Arabic: المرصد السوري لحقوق الإنسان), founded in May 2006, is a United Kingdom-based information office whose stated aim is to document human rights abuses in Syria; since 2011 it has focused on the Syrian civil war. It has been frequently quoted by major news outlets since the beginning of the war about daily numbers of deaths from all sides in the conflict and particularly civilians killed in airstrikes in Syria. The SOHR has been described as being anti-Assad and supporting the Syrian opposition, but has reported on war crimes committed by all sides of the conflict.
1988 NHL entry draft
The 1988 NHL entry draft was the 26th NHL entry draft. It was held at the Forum in Montreal, Quebec.

The last active player in the NHL from this draft class was Teemu Selanne, who retired after the 2013–14 season.

Tony McKegney
Anthony Syiid McKegney  (born February 15, 1958) is a Canadian former professional ice hockey player who played 13 seasons in the National Hockey League from 1978–79 until 1990–91. He is the first Black player in NHL history to score 40 goals in a season.
Mun'ak station
Mun'ak station is a railway station in Mun'ak-tong, Manp'o municipal city, Chagang Province, North Korea, on the Pukbunaeryuk Line of the Korean State Railway; it is also the starting point of the An'gol Line.

Chagang Province
Chagang Province (Korean: 자강도; MR: Chagang-do; Korean pronunciation: [tɕa.ɡaŋ.do]) is a province of North Korea; it is bordered by China's Jilin and Liaoning provinces to the north, Ryanggang and South Hamgyong to the east, South Pyongan to the south, and North Pyongan to the west.  Chagang was formed in 1949, after being demarcated from North Pyongan.  The provincial capital is Kanggye. Before 2019, Chagang was the only province of North Korea  completely inaccessible to tourists, possibly due to weapons factories and nuclear weapon facilities located there. In 2019 the city of Manpo became accessible to tourists. In May 2018, the province became a "Special Songun (military first) Revolutionary Zone" in relations to concealing the nuclear weapon and weapon's factories within the province.
1966 Brazilian presidential election
Indirect presidential elections were held in Brazil on 3 October 1966 through an electoral college system. It was the second election during the Brazilian military government, with Artur da Costa e Silva as the sole candidate. Costa e Silva was elected with 294 votes from the ruling National Renewal Alliance Party (ARENA).

Electoral college
An electoral college is a body of representatives empowered to formally select a candidate for a specific office, most often the head of state. Electoral colleges exist in several countries and may serve to balance regional representation or ensure indirect election mechanisms. It is mostly used in the political context for a constitutional body that appoints the head of state or government, and sometimes the upper parliamentary chamber, in a democracy. Its members, called electors, are elected either by the people for this purpose (making the whole process an indirect election) or by certain subregional entities or social organizations.

If a constituent body that is not only summoned for this particular task, like a parliament, elects or appoints certain officials, it is not referred to as "electoral college" (see e.g. parliamentary system). Also, other appointing bodies (like committees appointing judges, as in Canada or Germany) normally do not fall into this definition.
Parapropalaehoplophorus
Parapropalaehoplophorus is an extinct genus of comparatively small (compared to Glyptodon) species of glyptodont, extinct relatives of the modern armadillo. The sole species, P. septentrionalis, identified in 2007 from the fossilized remains of a specimen found in 2004, weighed approximately 200 pounds and had a shell covered by tiny circular bumps. It lumbered around northern Chile in the Chucal Formation, an area now dominated by the Andes mountain range, some 18 million years ago. Fossils of the glyptodont also have been found in Peru (Ipururo and Pebas Formations).

Chucal Formation
Chucal Formation (Spanish: Formación Chucal) is a volcano-sedimentary geological formation in the Andes of Arica y Parinacota Region in northernmost Chile. Sediments of the formation deposited sometime during the Miocene epoch (23 to 5 million years ago) and represent fluvial and lacustrine environments. It overlies Lupica Formation.
18th Independent Battery New York Light Artillery
The 18th Independent Battery New York Light Artillery was an artillery battery that served in the Union Army during the American Civil War. The unit was organized in September 1862 and shipped to New Orleans. The battery fought at Fort Bisland, Vermilion Bayou, Plains Store, and Port Hudson in 1863. The battery served in garrison until 1865 when it fought at Spanish Fort and Fort Blakeley. It was mustered out of federal service in July 1865.

Siege of Port Hudson
The siege of Port Hudson (May 22 – July 9, 1863) was the final engagement in the Union campaign to recapture the Mississippi River in the American Civil War. While Union General Ulysses Grant was besieging Vicksburg upriver, General Nathaniel Banks was ordered to capture the lower Mississippi Confederate stronghold of Port Hudson, Louisiana, then to go to Grant's aid. When his assault failed, Banks settled into a 48-day siege, the longest in US military history up to that point. A second attack also failed, and it was only after the fall of Vicksburg that the Confederate commander, General Franklin Gardner, surrendered the port. The Union gained control of the river and navigation from the Gulf of Mexico through the Deep South and to the river's upper reaches.
Florida (30 Rock)
"Florida" is the tenth episode of the seventh season of the American television comedy series 30 Rock, and the 135th overall episode of the series. It was directed by Claire Cowperthwaite and written by Tom Ceraulo and Matt Hubbard. The episode originally aired on NBC in the United States on January 17, 2013.

The episode received generally positive critical reviews and was watched by 3.44 million viewers.

Matt Hubbard
Matt Hubbard (born July 12, 1978) is an American screenwriter who has worked on many television shows.  He graduated from Beverly High School, in Beverly, Massachusetts in 1996. He later went on to attend Harvard University where he was an editor for the Harvard Lampoon. He has worked as a writer on the NBC comedy series 30 Rock. He won Emmy awards in 2009 for both Outstanding Writing for a Comedy Series for writing the episode "Reunion" and for Outstanding Comedy Series as a producer on the series. He worked as a Consulting Producer and writer on the last two seasons of Parks and Recreation.
James B. Jameson House
The James B. Jameson House, also known as the Jameson-Harsh House, is a historic house in Sumner County, Tennessee near Gallatin.

The house was built circa 1844 by John Fontville, who also built Oakland in Gallatin and Greenfield in Castalian Springs. The original owner, James B. Jameson, was a plantation owner who owned 19 slaves in 1860. It was later owned by his granddaughter Eliza, who lived here with her husband, physician Edward Carr. The house remained in the Jameson family until 1920.

The house was designed in the Federal architectural style, with a Greek Revival portico. It has been listed on the National Register of Historic Places since November 25, 1985.

Sumner County, Tennessee
Sumner County is a county located on the central northern border of Tennessee in the United States. As of the 2020 United States census, the population was 196,281. Its county seat is Gallatin, and its most populous city is Hendersonville. The county is named after an American Revolutionary War hero, General Jethro Sumner.

Sumner County is part of the Nashville-Davidson–Murfreesboro–Franklin, TN Metropolitan Statistical Area. The county is made up of eight cities, including Gallatin, Goodlettsville, Hendersonville, Millersville, Mitchellville, Portland, Westmoreland, and White House. Sumner County is 25 miles (40 km) northeast of Nashville, Tennessee.
Mohini Bhasmasura
Mohini Bhasmasura (pronunciationⓘ) is a 1966  Kannada-language  Indian Hindu mythological film directed by S. S. Verma and produced by T. Madaar and V.M.Kuppayya Chettiyar. The film stars Rajkumar, Leelavathi, Udaykumar and TN Balakrishna in the lead roles. The musical score was composed by T. Chalapathi Rao. Vijaya Narasimha wrote both dialogues and songs for the film.

T. Chalapathi Rao
Tatineni Chalapathi Rao (22 December 1920 – 22 February 1994) was an Indian music composer who worked in Telugu cinema. His career spanned more than three decades from early 1950s, till 1980s. He was the cousin of T. Prakash Rao.
Saint-Stanislas, Saguenay–Lac-Saint-Jean
Saint-Stanislas (French pronunciation: [sɛ̃ stanislas]) is a municipality in Maria-Chapdelaine Regional County Municipality in the Saguenay–Lac-Saint-Jean region of Quebec, Canada. Its population was 376 in the Canada 2021 Census.

Classification of municipalities in Quebec
The following is a list of the types of local and supralocal territorial units in Quebec, Canada, including those used solely for statistical purposes, as defined by the Ministry of Municipal Affairs, Regions and Land Occupancy and compiled by the Institut de la statistique du Québec

Not included are the urban agglomerations in Quebec, which, although they group together multiple municipalities, exercise only what are ordinarily local municipal powers.

A list of local municipal units in Quebec by regional county municipality can be found at List of municipalities in Quebec.
Old King Cole
"Old King Cole" is a British nursery rhyme first attested in 1709. Though there is much speculation about the identity of King Cole, it is unlikely that he can be identified reliably as any historical figure. It has a Roud Folk Song Index number of 1164. The poem describes a merry king who called for his pipe, bowl, and musicians, with the details varying among versions.

The "bowl" is a drinking vessel, while it is unclear whether the "pipe" is a musical instrument or a tobacco pipe.

Geoffrey of Monmouth
Geoffrey of Monmouth (Latin: Galfridus Monemutensis, Galfridus Arturus; Welsh: Gruffudd ap Arthur, Sieffre o Fynwy; c. 1095 – c. 1155) was a  Christian cleric from Monmouth, Wales, and one of the major figures in the popularity of tales of King Arthur.

He is best known for his chronicle The History of the Kings of Britain (Latin: De gestis Britonum or Historia Regum Britanniae) which was widely popular in its day, being translated into other languages from its original Latin. It was given historical credence well into the 16th century, but is now considered historically unreliable.
Amit Verma
Amit Verma (born 30 August 1987) is an Indian cricketer. He is a left-hander batsman and leg-break bowler. Verma made his first-class debut for Karnataka against Delhi in 2007–08 Ranji Trophy.

Ahead of the 2018–19 Ranji Trophy, he transferred from Assam to Goa. He was the leading run-scorer for Goa in the tournament, with 549 runs in nine matches.

2018–19 Ranji Trophy
The 2018–19 Ranji Trophy was the 85th season of the Ranji Trophy, the premier first-class cricket tournament that took place in India between November 2018 and February 2019. Vidarbha were the defending champions. The final took place between Vidarbha and Saurashtra, starting on 3 February 2019. Vidarbha defeated Saurashtra by 78 runs in the final, to become the sixth team in the tournament's history to retain their title.
The Glorification of the Virgin
The Glorification of the Virgin (Dutch: De verheerlijking van Maria) is a 15th-century painting attributed to Geertgen tot Sint Jans. It was painted c, 1490–1495 and was originally part of a diptych. It shows the Virgin Mary holding Jesus and surrounded by three rings of angels.

Mary wears a crown lined by five white and one red roses. She is surrounded by a two golden radiant and glowing circle. The inner ring contains six angles holding the Arma Christi (instruments of the Passion of Jesus): the cross, spear, crown of thorns, tammer and nails, the whip and the a sponge soaked in vinegar. In the outer ring, musical angels play various instruments and wave bells.

The panel is held in the collection of Museum Boijmans Van Beuningen, Rotterdam, Netherlands.

Arma Christi
Arma Christi ("weapons of Christ"), or the Instruments of the Passion, are the objects associated with the Passion of Jesus Christ in Christian symbolism and art. They are seen as arms in the sense of heraldry, and also as the weapons Christ used to achieve his conquest over Satan. There is a group, at a maximum of about 20 items, which are frequently used in Christian art, especially in the Late Middle Ages. Typically, they surround either a cross or a figure of Christ of the Man of Sorrows type, either placed around the composition, or held by angels.
Fanderson
Fanderson is the official appreciation society for the works of British film and television producers Gerry and Sylvia Anderson. Based in the United Kingdom, but with an international membership, it is a not-for-profit organisation run by a small committee of volunteers.

The club is endorsed by ITV Studios Global Entertainment, ITC Entertainment Group, The Indestructible Production Company, Anderson Entertainment and the family of Sylvia Anderson.

ITV Studios
ITV Studios Limited is a British multinational television media company owned by British television broadcaster ITV plc. It handles production and distribution of programmes broadcast on the ITV network and third-party broadcasters, and is based in 12 countries across 60 production labels, with local production offices in the UK, the US, Belgium, Australia, Germany, the Netherlands, Italy, Israel, France, Spain, and Scandinavia.