hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Examples of Markov chains
This article contains examples of Markov chains and Markov processes in action.

All examples are in the countable state space. For an overview of Markov chains in general state space, see Markov chains on a measurable state space.

State space (computer science)
In computer science, a state space is a discrete space representing the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory.

For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space. The angular position of an undamped pendulum is a continuous (and therefore infinite) state space.
Heidelberg Catechism
The Heidelberg Catechism (1563), one of the Three Forms of Unity, is a Reformed catechism taking the form of a series of questions and answers for use in teaching Reformed Christian doctrine. It was published in 1563 in Heidelberg, Germany.: 230  Its original title translates to Catechism, or Christian Instruction, according to the Usages of the Churches and Schools of the Electoral Palatinate. Commissioned by the prince-elector of the Electoral Palatinate, it is sometimes referred to as the 'Palatinate Catechism.' It has been translated into many languages and is regarded as one of the most influential of the Reformed catechisms. Today, the Catechism is "probably the most frequently read Reformed confessional text worldwide".: 13

Peace of Augsburg
The Peace of Augsburg (German: Augsburger Frieden), also called the Augsburg Settlement, was a treaty between Charles V, Holy Roman Emperor, and the Schmalkaldic League, signed on 25 September 1555 in the German city of Augsburg. It officially ended the religious struggle between the two groups and made the legal division of Christianity permanent within the Holy Roman Empire, allowing rulers to choose either Lutheranism or Roman Catholicism as the official confession of their state. Calvinism was not allowed until the Peace of Westphalia.

The Peace of Augsburg has been described as "the first step on the road toward a European system of sovereign states." The system, created on the basis of the Augsburg Peace, collapsed at the beginning of the 17th century, which was one of the reasons for the Thirty Years' War.
Daily Planet (DC Comics house advertisement)
Daily Planet was a promotional page appearing in DC Comics publications from 1976 to 1981. The Daily Planet contained previews of upcoming stories, as well as recurring features like "The Answer Man", where DC writer/editor Bob Rozakis would answer questions sent in by readers, and a comic strip by cartoonist Fred Hembeck which poked fun at DC characters. Edited by Rozakis, the Daily Planet was set in the format of a page from the fictional Metropolis newspaper where Clark Kent worked.

Metropolis (comics)
Metropolis is a fictional city appearing in American comic books published by DC Comics, best known as the home of Superman, his closest allies and some of his foes. First appearing by name in Action Comics #16 (Sept. 1939), Metropolis is depicted as a prosperous and massive city somewhere in the Northeastern United States. In recent years, it has been stated to be located in New York or Delaware.
The co-creator and original artist of Superman, Joe Shuster, modeled the Metropolis skyline after Toronto, where he was born and lived until he was ten. Since then, however, the look and feel of Metropolis has been greatly influenced by New York City.

Within the DC Universe, Metropolis is depicted as being one of the largest and wealthiest cities in the world, having a population of 11 million citizens.

In addition to Superman, the city is also home to other superheroes, such as Booster Gold, Thorn, Gangbuster, Hawkgirl and others.
Sri Ragavendra Polytechnic College
Sri Ragavendra Polytechnic College was established in 1997 at Komarapalayam, Namakkal, Tamil Nadu, India. It is an ISO 9001:2015 Certified Institution.  It is affiliated to the All India Council for Technical Education (New Delhi) and the Directorate of Technical Education (Tamil Nadu).

Namakkal
Namakkal (Tamil: [nɑːməkkəl]) is a city and the headquarters of Namakkal district, Tamil Nadu. It is the first ISO 14001-2004 certified municipality in Asia for environmental management, specifically the provision and maintenance of water supply, solid waste and sewage management, town planning, lighting and other social services. Namakkal is known as the Egg City due to its large egg production and Transport city.
Canton of Toul-Sud
48°37′41″N 5°50′02″E﻿ / ﻿48.62802°N 5.83396°E﻿ / 48.62802; 5.83396

The canton of Toul-Sud (French: Canton de Toul-Sud) is a former French canton located in the department of Meurthe-et-Moselle in the Lorraine region (now part of Grand Est). It is now part of the canton of Toul and canton of Meine au Saintois.

The last general councillor from this canton was Alde Harmand (PS), elected in 2004.

Meurthe-et-Moselle
Meurthe-et-Moselle (French pronunciation: [mœʁt e mɔzɛl] ⓘ, lit. 'Meurthe and Moselle') is a department in the Grand Est region of France, named after the rivers Meurthe and Moselle. Its prefecture and largest city is Nancy and it borders the departments of Meuse to the west, Vosges to the south, Moselle and Bas-Rhin and it borders the Belgian province of Luxembourg and the country of Luxembourg by the canton of Esch-sur-Alzette to the north. It had a population of 733,760 in 2019.
Dear Friend (2022 film)
Dear Friend is a 2022 Indian Malayalam-language thriller film directed by Vineeth Kumar. The film stars Tovino Thomas, Darshana Rajendran, Basil Joseph, Arjun Radhakrishnan and Arjun Lal. The film was released on 10 June 2022, and was a box office failure.

Basil Joseph
Basil Joseph (born 28 April 1989) is an Indian film actor and director who works in the Malayalam film industry. He started his film career as an assistant director of Vineeth Sreenivasan in the 2013 film Thira. He has directed three films till date, Kunjiramayanam (2015), Godha (2017) and Minnal Murali (2021).

Basil made his acting debut in the 2013 film Up & Down: Mukalil Oralundu. Basil has played supporting roles in numerous Malayalam films and is well appreciated for his role in Joji (2021). He has since received praise for his lead roles in films such as Jan. E. Man (2021), Jaya Jaya Jaya Jaya Hey (2022), Palthu Janwar (2022), Falimy (2023), Nunakkuzhi (2024), Sookshmadarshini (2024), and Ponman (2025).
Pandurang Fundkar
Pandurang Pundalik Fundkar (21 August 1950 – 31 May 2018), alias Bhausaheb Fundkar, was leader of opposition in Maharashtra Legislative Council in India. He was a leader of Bharatiya Janata Party.

He was a member of 9th Lok Sabha (1989-1991), 10th Lok Sabha (1991-1996) and 11th Lok Sabha from Akola from Maharashtra. He was also former president of State BJP. He was born in 1950 in Buldhana.

He was elected as member of Maharashtra Vidhan Sabha from Khamgaon (Vidhan Sabha constituency) in 1978 and 1980. On July 8, 2016, he was sworn in as a Cabinet Minister in Devendra Fadnavis government.

He died on 31 May 2018 in Breach Candy hospital, Mumbai due to a massive heart attack.

Maharashtra Legislative Assembly
The Maharashtra Legislative Assembly (ISO: Mahārāṣṭra Vidhānasabhā) is the lower house of the bicameral legislature of Maharashtra state in western India. It consists of 288 members directly elected from single-seat constituencies. The Assembly meets at Vidhan Bhavan in Mumbai, though the winter session is held in Nagpur. Along with the Maharashtra Legislative Council, it constitutes the legislature of Maharashtra. The presiding officer of the Assembly is the Speaker. Members of the Assembly are directly elected by the people of Maharashtra through elections held every five years, unless the Assembly is dissolved earlier. The current Assembly was elected in November 2024.
Niedersachsen Rundfahrt
The Internationale Niedersachsen–Rundfahrt is a multi-stage road bicycle race held in Lower Saxony, Germany. It was first held in 1977 and since 2005 it has been organised as a 2.1 event on the UCI Europe Tour.

UCI race classifications
The Union Cycliste Internationale (UCI), the world's governing body in the sport of bicycle racing, classifies races according to a rating scale.

The rating is represented by a code made of two or three parts and indicates both the type or style of race (the first part), and its importance or difficulty (the second and third parts, lower being harder). The first part can be an integer or an abbreviation, and the second part, when present, are usually integers. Both parts are separated by a period or decimal point (.).

A higher rated race will result in the successful riders receiving more world ranking points.
Reformed Presbyterian Church in Taiwan
The Reformed Presbyterian Church in Taiwan (RPCT; Chinese: 基督教改革宗長老會; Pe̍h-ōe-jī: Ki-tok-kàu Kái-kek-chong Tiúⁿ-ló-hōe) was officially established in 1971 when the First Presbytery was formed as a result of the union of various conservative Presbyterian and Continental Reformed congregations planted by various missionary groups. Its origin could be traced back to the 1950s when the very first missionaries of those Presbyterian and Continental Reformed missionaries arrived in Taiwan.

Orthodox Presbyterian Church
The Orthodox Presbyterian Church (OPC) is a confessional Presbyterian denomination located primarily in the United States, with additional congregations in Canada, Bermuda, and Puerto Rico. It was founded by conservative members of the Presbyterian Church in the United States of America (PCUSA), who objected to the rise of Liberal and Modernist theology in the 1930s. The OPC is considered to have had an influence on evangelicalism far beyond its size.
Sudhir Mahato
Sudhir Mahato was an Indian politician. He was elected to the Bihar Legislative Assembly and then Jharkhand Legislative Assembly from Ichagarh from 1990 Bihar Legislative Assembly election and 2005 Jharkhand Legislative Assembly election as a member of the Jharkhand Mukti Morcha. He was Deputy Chief Minister of Jharkhand under Madhu Koda from 14 September 2006 to 23 August 2008.

He died on 22 January 2014 due to a massive heart attack at Ghatsila in East Singhbhum district at the age of 53 years.

Jharkhand Legislative Assembly
The Jharkhand Legislative Assembly, commonly known as the Jharkhand Vidhan Sabha, is the unicameral state legislature of Jharkhand state in India. The seat of the Legislative Assembly is at Ranchi, the capital of the state.
Mount Bagineti
Mount Bagineti (Georgian: ბაგინეთი), is a mountain (662 m a.s.l.) on the eastern slope of Trialeti Range, a part of Lesser Caucasus Mountains, in the Republic of Georgia, situated at the confluence of rivers Kura and Aragvi, near the ancient city of Mtskheta.

Lesser Caucasus
The Lesser Caucasus or Lesser Caucasus Mountains, also called Caucasus Minor, is the second of the two main ranges of the Caucasus Mountains, of length about 600 km (370 mi). The western portion of the Lesser Caucasus overlaps and converges with east Turkey and northwest Iran. It runs parallel to the Greater Caucasus, at a distance averaging about 100 km (62 mi) south from the Likhi Range (Georgia), and limits east Turkey from the north and north-east. It is connected with the Pontic range and separated from it by the Kolkhida Lowland (Georgia) in the west and Kura-Aras Lowland (Azerbaijan) (by the Kura River) in the east.
Carlo Maria Badini
Carlo Maria Badini (2 June 1925, in Bologna – 19 April 2007, in Bologna) was a renowned Italian arts administrator. From 1964 to 1977 he was the Sovrintendente or General Manager of the Teatro Comunale di Bologna and from 1977 through 1990 he was the Sovrintendente of La Scala. Badini created controversy as a result of the unorthodox methods he used to revitalize La Scala's finances, which had reportedly reached a 2.8 million dollar (US) deficit, such as the introduction of television cameras to record performances and allowing advertisements on the programmes. These innovations allowed the opera house to emerge from the deficit within two years of their implementation. Upon his 1990 departure from La Scala, Badini continued work in the Italian artistic community, becoming chairman of the National Theatre Organization in Italy and co-founding the Mozart Orchestra in Bologna, which he formed alongside former La Scala music director Claudio Abbado.

Programme (booklet)
A programme or program (see spelling differences) is a booklet available for patrons attending a live event such as theatre performances, concerts, fêtes, sports events, etc. It is a printed leaflet outlining the parts of the event scheduled to take place, principal performers and background information. In the case of theatrical performances, the term playbill is also used. It may be provided free of charge by the event organisers or a charge may be levied.
1990 FIFA World Cup qualification (AFC)
The Asian Football Confederation was allocated two assured qualifying berths for the 1990 FIFA World Cup. 26 teams were in the running for these spots; Bahrain, India, Maldives and South Yemen withdrew without playing a qualifying match.

Asia's two automatic qualifying berths were taken by Korea Republic and the United Arab Emirates.

South Yemen national football team
The South Yemen national football team (Arabic: منتخب اليمن الجنوبي الوطني لكرة القدم), recognised as Yemen DPR by FIFA, represented South Yemen in men's international football, playing as one of two Yemeni teams, along with North Yemen.

After Yemeni unification in 1990, the PDR Yemen Football Federation, and with it the South Yemeni team, joined the Yemen Football Association (YFA) and the North Yemen national football team.
Mount Earnslaw
Mount Earnslaw / Pikirakatahi is a 2,819-metre (9,249 ft) mountain in the South Island of New Zealand. It is named after Earnslaw (formerly Herneslawe) village in the parish of
Eccles, Berwickshire, hometown of the surveyor John Turnbull Thomson's father.

Mount Earnslaw is within Mount Aspiring National Park at the southern end of the Forbes Range of the Southern Alps. It is located 25 kilometres north of the settlement of Glenorchy, which lies at the northern end of Lake Wakatipu.

Mount Earnslaw and various other sites in its vicinity feature in the live-action film version of The Lord of the Rings.

John Turnbull Thomson
John Turnbull Thomson (10 August 1821 – 16 October 1884) was a British civil engineer and artist who played an instrumental role in the development of the early infrastructure of nineteenth-century Singapore and New Zealand. He lived the last 28 years of his life in New Zealand, and prior to that 15 years in the Malay Straits and Singapore.
National Maritime College of Ireland
51°49′58″N 8°18′18″W﻿ / ﻿51.8329°N 8.3051°W﻿ / 51.8329; -8.3051

The National Maritime College of Ireland (Irish: Coláiste Náisiúnta Mara na hÉireann, NMCI) is a public maritime college located in Ringaskiddy, County Cork, Ireland. It is a constituent college of the Munster Technological University. Founded in 2004, it is situated on former Department of Defence land aside the Haulbowline naval base, the headquarters of the Irish Naval Service. It is the first dedicated maritime college of its kind in the State, and was built under the Irish Government's Public-Private Partnership scheme, involving the Munster Technological University (formerly, Cork Institute of Technology), the Naval Service and a number of other partners.

The Irish Naval Service and other Defence Forces personnel carry out non-combat training at the National Maritime College of Ireland, with a permanent Naval Service cadre present on site to assist in the carrying out of this training.

Haulbowline
Haulbowline (Irish: Inis Sionnach; Old Norse: Ál-boling) is an island in Cork Harbour off the coast of Ireland. The world's first yacht club was founded on Haulbowline in 1720. The western side of the island is the main naval base and headquarters for the Irish Naval Service, with the eastern side previously used for heavy industry and later redeveloped as a park.

Since 1966, the island has been connected to the mainland by a roadbridge.
Jeff Essmann
Jeff Essmann (born June 29, 1952) is an American politician and a Republican former member of the Montana Senate. Essmann was appointed to the Montana Senate in 2005 to represent Senate District 28. He was subsequently elected in 2006, and reelected in 2010. Essmann served as the president of the Montana Senate from 2013 to 2015.

He is most notable for proposing Senate Bill 423 to legalize use of medical marijuana in Montana.

Essmann ran for Governor of Montana in 2012 election. He withdrew after it was determined that he lacked the necessary funds and support. He also ran in the 2017 Billings mayoral election, but was defeated by Bill Cole in the second round by a 28% margin.

Essmann served as the chairman of the Montana Republican Party from 2015 to 2017.

Montana Republican Party
The Montana Republican Party (MTGOP) is the affiliate of the Republican Party in Montana. It is headquartered in Helena. It is the dominant ruling party of the state.

The party is chaired by Art Wittich. Republican officials control both of Montana's U.S. House seats, both of its U.S. Senate seats, both chambers of the state legislature, and all of the statewide executive offices, including the governorship.
Sakura Genesis (2024)
Sakura Genesis was professional wrestling event promoted by New Japan Pro-Wrestling (NJPW). The event took place on April 6, 2024, in Tokyo at Ryōgoku Kokugikan. Previously held under the Invasion Attack name, this was the fifth event to be held under the Sakura Genesis name.

Ryōgoku Kokugikan
Ryōgoku Kokugikan (Japanese: 両国国技館; lit. "Ryōgoku National Sports Hall"), also known as Ryōgoku Sumo Hall or Kokugikan Arena, refers to two different indoor sporting arenas located in Tokyo. The first Ryōgoku Kokugikan opened its doors in 1909 and was located on the premises of the Ekōin temple in Ryōgoku, Tokyo. Although no sumo bouts were held after 1945, following the capitulation of Japan and the requisition of the building by the occupying forces, the building itself remained active until 1983, being notably used by the Nihon University. The second Ryōgoku Kokugikan is currently located in the Yokoami neighborhood of Sumida next to the Edo-Tokyo Museum. It opened in 1985, following the closure of the Kuramae Kokugikan, and is still in use today.
Sudan Defence Force
The Sudan Defence Force (SDF) was a formation of the British Colonial Auxiliary Forces raised in the Anglo-Egyptian Sudan in 1925 to assist local police in internal security duties and maintain the condominium's territorial integrity. During World War II, it also served in East Africa as part of the East African campaign and in North Africa during the Western Desert campaign.

Omdurman
Omdurman (Arabic: أُمّ دُرمان, romanized: Umm Durmān) is a major city in Sudan. It is the second most populous city in the country, located in the State of Khartoum. Omdurman lies on the west bank of the River Nile, opposite and northwest of the capital city of Khartoum. The city acts as an important road hub, with the Nile boosting transportation even further.
India Pride Project
India Pride Project (IPP) is a grassroots group of art enthusiasts who use open source intelligence to identify stolen religious artefacts from temples in India in order to facilitate their return. Co-founded in 2014 by two Singapore-based art enthusiasts, S. Vijay Kumar and Anuraag Saxena, it now has activist volunteers from all over the world.

Open-source intelligence
Open-source intelligence (OSINT) is the collection and analysis of data gathered from open sources (overt sources and publicly available information) to produce actionable intelligence. OSINT is primarily used in national security, law enforcement, and business intelligence functions and is of value to analysts who use non-sensitive intelligence in answering classified, unclassified, or proprietary intelligence requirements across the previous intelligence disciplines.
Squires Gate F.C.
Squires Gate Football Club is a football club based in Squires Gate, Blackpool, Lancashire, England, formed in 1948. After spending thirty years in the West Lancashire League, in 1991 it was elected to the North West Counties Football League Division Two, and is currently in the Division One.

FA Vase
The Football Association Challenge Vase, also known as the Isuzu FA Vase for sponsorship reasons, is an annual football competition run by and named after The Football Association (The FA), for teams playing in Steps 5 and 6 of the English National League System. Nearly 600 teams participate in this knockout competition with semi-finals played over two legs. The final is played at Wembley Stadium.

The 2025 winners were Whitstable Town, who beat AFC Whyteleafe 2–1 at Wembley Stadium.
Ezhamkadalinakkare
Ezhamkadalinakkare (transl. Across The Seventh Sea) is a 1979 Indian Malayalam-language film, directed by I. V. Sasi and produced by N. G. John. The film stars K. R. Vijaya in the lead role, whereas supporting roles were played by Soman, Seema, Ravikumar, Vidhubala, P. Bhaskaran, Henry Marsal, Janardanan and Joe Waddington. It is the first Malayalam film to be shot in North America, with Manhattan being one of its locations. The song "Suralokajaladhaara" was filmed near in Niagara Falls, Ontario, Canada. This film was a remake of the Tamil film Ore Vaanam Ore Bhoomi by the same director.

K. R. Vijaya
Deivanayaki, better known by her stage name K. R. Vijaya, is an Indian actress who has featured in Tamil, Malayalam, Telugu and Kannada films. She started her career in 1963 and has been acting for more than six decades in South Indian cinema. The actress has worked with almost all the stalwarts of South Indian cinema and has played many key roles.
1976 ABN World Tennis Tournament
The 1976 ABN World Tennis Tournament was a men's tennis tournament played on indoor carpet courts at Rotterdam Ahoy in the Netherlands. It was part of the 1976 World Championship Tennis circuit. It was the fourth edition of the tournament was held from 23 February through 29 February 1976. Arthur Ashe won the singles title.

Rotterdam Ahoy
Rotterdam Ahoy (formerly known as Ahoy Rotterdam or simply as Ahoy) is a multi-purpose complex with a convention centre and an indoor arena located in Rotterdam, Netherlands. Opened originally in 1950, the current complex consists of three main venues: a fairs and events hall, a congress and conference centre, and the main venue the Ahoy Arena. The latter (informally known as the Sportpaleis, lit. 'Sport Palace') opened on 15 January 1971 and is the largest multi-purpose venue in the Netherlands, with a capacity of 16,426 as of May 2019.
2008 Austrian Open – Doubles
Luis Horna and Potito Starace were the defending champions, but lost in the first round to James Cerretani and Victor Hănescu.

James Cerretani and Victor Hănescu won in the final 6–3, 7–5, against Lucas Arnold Ker and Olivier Rochus.

Olivier Rochus
Olivier Rochus (French pronunciation: [ɔlivje ʁɔkys]; born 18 January 1981) is a former Belgian tennis player.
Rochus won two singles titles in his career and in 2004 won the French Open doubles title, partnering fellow Belgian Xavier Malisse. His career-high singles ranking is world No. 24.