hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Azuma's inequality
In probability theory, Azuma's inequality or the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.

Suppose  is a martingale (or super-martingale) and

almost surely. Then for all positive integers N and all positive reals ,

And symmetrically (when Xk is a sub-martingale):

If X is a martingale, using both inequalities above and applying the union bound allows one to obtain a two-sided bound:

Boole's inequality
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of occurrence of at least one of a countable number of events in terms of the individual probabilities of the events. Boole's inequality is named for its discoverer, George Boole.

Formally, for a countable set of events A1, A2, A3, ..., we have

In measure-theoretic terms, Boole's inequality follows from the fact that a measure (and certainly any probability measure) is σ-sub-additive. Thus Boole's inequality holds not only for probability measures , but more generally when  is replaced by any measure.
Uchkoʻprik District
Uchkoʻprik District (Uzbek: Uchkoʻprik tumani) is a district of Fergana Region in Uzbekistan. The capital lies at the town Uchkoʻprik. It has an area of 280 km2 (110 sq mi) and it had 237,300 inhabitants in 2022. The district consists of 11 urban-type settlements (Uchkoʻprik, Begobod, Gʻijdan, (Katta Qashqar), Qumariqobod, Bogʻiboʻston, Mirzaxoʻja, Palaxon, Sobirjon, Turgʻoq, Yangiqishloq) and 9 rural communities.

Fergana Region
Fergana Region is one of the regions of Uzbekistan, located in the southern part of the Fergana Valley in the far east of the country. It borders the Namangan and Andijan Regions of Uzbekistan, as well as Kyrgyzstan (Batken and Osh Regions) and Tajikistan (Sughd Region). Its capital is the city of Fergana. It covers an area of 6,760 km2. The population is approximately 4,014,895 as of 2023, with 45% of the population living in rural areas.
2005–06 USHL season
The 2005–06 season was the 27th season of the United States Hockey League as an all-junior league. The regular season began on September 23, 2005, and concluded on March 1, 2006, with the regular season champion winning the Anderson Cup.

The Clark Cup playoffs featured the top four teams from each division competing for the league title.

United States Hockey League
The United States Hockey League (USHL) is the top junior ice hockey league sanctioned by USA Hockey. The league consists of 16 active teams located in the Midwestern United States and Great Plains, for players between the ages of 16 and 21. The USHL is strictly amateur, allowing former players to compete in National Collegiate Athletic Association (NCAA) college hockey.

The Lincoln Stars won the Anderson Cup as the 2024–25 regular season champions. The Muskegon Lumberjacks won the 2025 Clark Cup playoff championship, their first in franchise history.
Miss Ecuador 1999
The Miss Ecuador 1999 was held on April 16, 1999. There were 19 candidates for the national title; at the end of the night Soraya Hogonaga from Pichincha crowned Carolina Alfonso from Pichincha as Miss Ecuador 1999. The Miss Ecuador competed at Miss Universe 1999.

Pichincha Province
Pichincha (Spanish pronunciation: [piˈtʃintʃa]) is a province of Ecuador located in the northern Sierra region; its capital and largest city is Quito. It is bordered by Imbabura and Esmeraldas to the north, Cotopaxi and Santo Domingo de los Tsáchilas to the south, Napo and Sucumbíos to the east, and Esmeraldas and Santo Domingo de los Tsáchilas to the west.

Prior to 2008, the canton Santo Domingo de los Colorados was part of the Pichincha Province. It has since become its own province, Santo Domingo de los Tsáchilas.

The province is home to many rose plantations, which make up the bulk of Ecuador's floriculture industry.
Katarina Vuković
Katarina Vuković, from the medieval Bosnian noble lineage of Hrvatinić, was the second wife of Grand Duke of Bosnia, Sandalj Hranić.

Katarina was the daughter of the Hungarian-Croatian ban Vuk Vukčić from the Bosnian noble family of Hrvatinić. Her uncle was the famous Bosnian Grand Duke Hrvoje Vukčić Hrvatinić. Her mother was Banness Anka, and her sister was Jelena, married to Sandalj's brother, Knyaz Vuk Hranić.

Katarina married Sandalj Hranić in the spring of 1405, when her sister Jelena married Sandalj's brother Knyaz Vuk Hranić. Katarina's marriage to Sandalj existed as a result of political ties between Hrvatinić and Kosača noble families. Katarina, her mother Anka, and Duke Sandalj Hranić kept their property in a deposit in Dubrovnik. The marriage between Katarina and Sandalj broke up during 1410–1411, when good relations between Hrvatinićs and Kosačas soured.

Sandalj Hranić
Sandalj Hranić Kosača (Cyrillic: Сандаљ Хранић Косача; 1370 – 15 March 1435) was a powerful Bosnian nobleman whose primary possessions consisted of Hum, land areas between Adriatic coast, the Neretva and the Drina rivers in Bosnia, and served the court as the Grand Duke of Bosnia sometime between 1392 and his death in 1435, although the first mention as a Grand Duke in sources comes from 16 June 1404. He was married three times, but had no children. After his death, he was succeeded by his nephew Stjepan Vukčić Kosača.

His father was Hrana Vuković.
2019 Men's Oceania Cup
The 2019 Men's Oceania Cup was the eleventh edition of the men's field hockey tournament. It was held from 5 to 8 September in Rockhampton.

The tournament served as a qualifier for the 2020 Summer Olympics.

Australia won the tournament for the eleventh time, finishing ahead of New Zealand at the conclusion of the pool stage.

Men's Oceania Cup
The Oceania Cup is an international men's field hockey competition organised by Oceania Hockey Federation (OHF). It is held every two years to determine which teams will receive an automatic berth to the Men's FIH Hockey World Cup and Summer Olympics.

Only Australia and New Zealand have reached the finals as of 2023. Australia has won all titles.
Nioclás Tóibín
Nioclás Tóibín (5 February 1928 – 19 September 1994) was a sean-nós singer from the Déise tradition of County Waterford in Ireland. Nioclás was the winner of the main competition at Oireachtas na Gaeilge (this award is now called Corn Uí Riada) consecutively from 1961 to 1963. This was the principal national singing prize in Ireland at the time.

Born in the Gaeltacht parish of An Rinn (Ring) in County Waterford. His father and mother, Séamas Tóibín and Maighréad Ní Sheanacháin, were well known singers in the sean-nós style who had inherited the tradition from their own parents. Nioclás was known to sing songs such as 'Ar Éirinn Ní Neosfainn Cé Hí', 'Na Connerys' and 'Róisín Dubh'.

Corn Uí Riada
Corn Uí Riada is the premier sean-nós singing competition at Oireachtas na Gaeilge, an annually held arts festival of Irish culture. It is named in honour of the composer and founder of the male choir Cór Chúil Aodha, Seán Ó Riada. A 'Cóisir Uí Riada' is held while tuning into the broadcast of Corn Uí Riada, on the internet.
Gobius
Gobius is a genus of fish in the family Gobiidae native to fresh, brackish and marine waters of and around Europe, Africa and Asia. It contains the typical gobies, being the type genus of the formerly recognised subfamily Gobiinae and family and the namesake genus of its order Gobiiformes.

Gobiinae
True gobies were a subfamily, the  Gobiinae, of the goby family Gobiidae, although the 5th edition of the Fishes of the World does not subdivide the Gobiidae into subfamilies. They are found in all oceans and a few rivers and lakes, but most live in warm waters. Altogether, the Gobiinae unite about 1149 described species in 160 genera, and new ones are still being discovered in numbers.
Louisa Petty, Marchioness of Lansdowne
Louisa Petty, Marchioness of Lansdowne (née Lady Louisa FitzPatrick; later Petty Fitzmaurice; 1755 – 7 August 1789), known as the Countess of Shelburne from 1779–84, was an Anglo-Irish aristocrat from the Mac Giolla Phádraig dynasty. She was the wife of Prime Minister William Petty, 2nd Earl of Shelburne.

Mac Giolla Phádraig dynasty
Mac Giolla Phádraig (Irish: [mˠək ɟɪl̪ˠə fˠaːd̪ˠɾˠəɟ]; Old Irish: Mac Gilla Pátraic) is a native Irish dynastic surname which translates into English as "Son of the Devotee of (St.) Patrick".  In the medieval period, the Mac Giolla Phádraigs were hereditary kings of Osraige; today, the anglicised version of the name is commonly "Fitzpatrick".
225th Engineer Brigade (United States)
The 225th Engineer Brigade is a combat heavy engineer brigade of the Louisiana Army National Guard. It is one of the largest engineer formations in the United States Army National Guard. The 225th Engineer Brigade is headquartered at Camp Beauregard near Pineville, Louisiana in Rapides Parish. The brigade conducts missions of mobility, counter-mobility, survivability, and civil engineering support. The brigade possesses a mixture of civil and combat engineer units to accomplish these missions.

Operation New Horizons
Operation New Horizons is a series of recurring U.S.-led operations in Central and South America and the Caribbean Islands. It has had several names over the years, including New Horizons and Beyond the Horizons (as of 2008).  U.S. Southern Command sponsors these operations and uses active duty, reserve and National Guard forces from throughout the United States to conduct the missions.  The units involved focus on engineering type endeavors to enhance the infrastructure of a region by building schools, medical clinics and roads and similar projects.  The units also conduct medical assistance by providing such support to an area. Joint Task Force Bravo coordinates a number of these activities.  In addition, these operations often include non-military assistance, such as from the United States Agency for International Development and the United States Department of Agriculture.
Andre Eason
Andre Eason (born December 19, 1975, in Brooklyn, New York) is a professional boxer.  He appeared on the reality show, Contender Season 2, where he lost to Walter Wright.

Prior to appearing on The Contender, Eason, known as "Daredevil", had come up short in each of his high-profile opportunities; losses to Juan Urango, Francisco Bojado, and Demetrius Hopkins.

Juan Urango
Juan Fernando Urango Rivas (born October 4, 1980), best known as Juan Urango, is a Colombian former professional boxer who competed from 2002 to 2012. He held the IBF junior welterweight title twice between 2006 and 2010, and challenged once for the WBC welterweight title in 2009. His nickname of "Iron Twin" is a reference to his twin brother, Pedro Urango, who is also a former boxer.
Napęków
Napęków [naˈpɛŋkuf] is a village in the administrative district of Gmina Bieliny, within Kielce County, Świętokrzyskie Voivodeship, in south-central Poland. It lies approximately 4 km (2 mi) south of Bieliny and 22 km (14 mi) east of the regional capital Kielce.

Bieliny, Świętokrzyskie Voivodeship
Bieliny [bjɛˈlinɨ] is a village in Kielce County, Świętokrzyskie Voivodeship, in south-central Poland. It is the seat of the gmina (administrative district) called Gmina Bieliny. It lies approximately 21 km (13 mi) east of the regional capital Kielce.
Bieliny is near the highest peaks of the Świętokrzyskie Mountains - Łysica, Agata and Łysa Góra.
Canidrome (Shanghai)
The Shanghai Culture Plaza precinct (simplified Chinese: 文化广场; traditional Chinese: 文化廣場; pinyin: Wénhuà Guǎngchǎng) is a park and cultural precinct in Shanghai's Luwan District, in the former French Concession of Shanghai, China. The area began as the Canidrome (simplified Chinese: 逸园跑狗场; traditional Chinese: 逸園跑狗場; pinyin: Yíyuán Pǎogǒuchǎng), a stadium structure originally built for greyhound racing in 1928.

The clubhouse and racetrack became a multi-purpose entertainment venue, but became a place for political rallies after the founding of the People's Republic of China and a mass execution facility.  Later it became a theatre and exhibition space before it was demolished in 2006.  The original Canidrome grandstand was demolished as part of the reconstruction of the precinct to become a park incorporating various cultural venues.

Shanghai French Concession
The Shanghai French Concession was a foreign concession in Shanghai, China from 1849 until 1943. For much of the 20th century, the area covered by the former French Concession remained the premier residential and retail district of Shanghai. It was also one of the centers of Catholicism in China. Despite re-development over the last few decades, the area retains a distinct character and is a popular tourist destination.
Ferrari 315 S
The Ferrari 315 S is a sports racing car produced by Ferrari in 1957. The model served as the replacement of the Ferrari 290 MM, which had won the 1956 Mille Miglia and was an effort to dethrone the ever powerful Maserati 450S.

Mille Miglia
The Mille Miglia (Italian pronunciation: [ˈmille ˈmiʎʎa], Thousand Miles) was an open-road, motorsport endurance race established in 1927 by the young Counts Francesco Mazzotti and Aymo Maggi. It took place in Italy 24 times from 1927 to 1957 (13 times before World War II, and 11 times from 1947).

Like the older Targa Florio and later the Carrera Panamericana in Mexico, the MM made grand tourers like Alfa Romeo, BMW, Ferrari, Maserati, Mercedes-Benz, and Porsche famous. The race brought out an estimated 5 million spectators.

From 1953 until 1957, the Mille Miglia was also a round of the World Sports Car Championship.

Since 1977, the "Mille Miglia" has been reborn as a regularity race for classic and vintage cars. Participation is limited to cars, produced no later than 1957, which had attended (or were registered to) the original race. The route (Brescia–Rome round trip) is similar to that of the original race, maintaining the point of departure/arrival in Viale Venezia in Brescia.
Customer data
Customer data or consumer data refers to all personal, behavioural, and demographic data that is collected by marketing companies and departments from their customer base. To some extent, data collection from customers intrudes into customer privacy, the exact limits to the type and amount of data collected need to be regulated. The data collected is processed in customer analytics. The data collection is thus aimed at insights into customer behaviour (buying decisions, etc.) and, eventually, profit maximization by consolidation and expansion of the customer base.

Customer data may be collected from Internet users through online surveys, but also through the recording of user activity through measures such as click-through and abandonment rates.

Customer analytics
Customer analytics is the process of using data from customer behavior to support key business decisions through market segmentation and predictive analytics. This information is used by businesses for direct marketing, site selection, and customer relationship management. Customer analytics plays an important role in predicting customer behavior.
1998–99 Estonian Cup
The 1998–99 Estonian Cup (Estonian: Eesti Karikas) was the ninth season of the Estonian football knockout tournament. Originally, winners of the cup qualified for the 1999–2000 UEFA Cup qualifying round. The defending champion, Flora, was knocked out in the semi-final against later cup winners Levadia Maardu.

The competition culminated with the final held at Valga linnastaadion, Valga on 25 May 1999 with Levadia Maardu taking the title 3–2. Since the Tallinna Sadam were placed second in the 1998 Meistriliiga and then were merged with Levadia Maardu the UEFA Cup place was also given to the third positioned team in the league.

All in all, 40 teams took part of the competition.

1998 Meistriliiga
The 1998 Meistriliiga was the eighth season of the Meistriliiga, Estonia's premier football league. The season was unusually short, played in the second half of 1998 to switch back to Nordic spring-to-autumn season format in the next year. Flora won their fourth title.
Mexico national badminton team
The Mexico national badminton team (Spanish: Selección de bádminton de México) represents Mexico in international badminton team competitions and is controlled by the Mexican Badminton Federation. Mexico competed in the Sudirman Cup four times from 1991 until 2001.

The Mexico men's team qualified for their first Thomas Cup in 2016 after winning the 2016 Pan Am Team Badminton Championships after beating Canada in the gold medal tie with a score of 3–0. The team later debuted in the 2016 Thomas Cup. The team were eliminated in the group stages and finished in 16th place.

The Mexico women's team also achieved a podium position, finishing third place at the 2016 Pan Am Team Badminton Championships. The mixed team finished third twice in 1993 and 2009. The Mexico team also participates in the Pan American Games and has won four bronze medals in badminton at the Games.

Canada national badminton team
The Canada national badminton team (French: Équipe nationale de badminton du Canada) represents Canada in international badminton team competitions. It is controlled by the nation's governing body of badminton, Badminton Canada. The team's best result was achieving two semifinal finishes in both Thomas Cup and the Uber Cup.

Canada is one of the most prestigious badminton countries in the Americas, winning almost every mixed team event in the Pan American Badminton Championships and also winning gold in both men and women's teams. Next to the United States, Canada has won 21 gold medals, 22 silvers and 12 bronzes in badminton at the Pan American Games.

The national team has won almost every edition of the Pan American Badminton Championships mixed team events except for one in 2001. The men's team have also became recent champions while the women's team lost to the United States in 2022.
Pirot rebellion
The Pirot rebellion (Serbian: Пиротска буна/Pirotska buna) (Bulgarian: Пиротскo въстание) broke out in the town Pirot in Ottoman Bulgaria after the Orthodox Christian population[a] in the area suffered oppression by the local Ottoman leader and Orthodox bishop. Refugees across the border in Serbia planned the rebellion and rose up together with villagers from the area during a scheduled meeting of the two sides agreed upon by the Serbian Prince Miloš Obrenović, the community protector, and the Vali of Rumelia. He had promised to help the rebels, but broke out his promise and remained loyal to the Ottoman Sultan. The Serbian prince suppressed the rebels and punished the fugitives.

Rumelia Eyalet
The Eyalet of Rumeli, or Eyalet of Rumelia (Ottoman Turkish: ایالت روم ایلی, romanized: Eyālet-i Rūm-ėli), known as the Beylerbeylik of Rumeli until 1591, was a first-level province (beylerbeylik or eyalet) of the Ottoman Empire encompassing most of the Balkans ("Rumelia"). For most of its history, it was the largest and most important province of the Empire, containing key cities such as Edirne, Yanina (Ioannina), Sofia, Filibe (Plovdiv), Manastır/Monastir (Bitola), Üsküp (Skopje), and the major seaport of Selânik/Salonica (Thessaloniki). It was also among the oldest Ottoman eyalets, lasting more than 500 years with several territorial restructurings over the long course of its existence.

The capital was in Adrianople (Edirne), Sofia, and finally Monastir (Bitola). Its reported area in an 1862 almanac was 48,119 square miles (124,630 km2).
Dinky Toys
Dinky Toys was a brand of die-cast zamak zinc alloy scale model vehicles, traffic lights, and road signs produced by British toy company Meccano Ltd. They were made in England from 1934 to 1979, at a factory in Binns Road in Liverpool.

Toy vehicles commercialised under the "Dinky" name include cars, trucks, aircraft, military vehicles, and ships.

Short Mayo Composite
The Short Mayo Composite was a piggy-back long-range seaplane and flying boat combination produced by Short Brothers to provide a reliable long-range air transport service to North America and, potentially, to other distant places in the British Empire and the Commonwealth.
Miss World 2019
Miss World 2019 was the 69th edition of the Miss World pageant, held at the Exhibition Centre London in London, England, on 14 December 2019.

At the end of the event, Vanessa Ponce of Mexico crowned Toni-Ann Singh of Jamaica as Miss World 2019. It is the fourth victory of Jamaica in the history of the pageant.

Contestants from 111 countries and territories competed in the pageant. The pageant was hosted by Peter Andre, Miss World 2013 Megan Young, Miss World 2016 Stephanie Del Valle, and Fernando Allende. Peter Andre, Lulu, Misunderstood, and Kerry Ellis performed in this edition.

Julia Morley
Julia Evelyn Morley CBE (née Pritchard; born 25 October 1939) is an English businesswoman, charity worker and former model. She is the chairwoman and CEO of the Miss World Organization, which organizes the Miss World  and Mister World pageants. She is the widow of Miss World creator, the late Eric Morley who organized the pageant from its inception in July 1951, until his death in 2000.
Murchison, New Zealand
Murchison is a town in the Tasman Region of the South Island of New Zealand. It is near the western end of the "Four Rivers Plain", at the confluence of the Buller River and the Mātakitaki River. The other two rivers are the Mangles River, and the Matiri River.
It is a rural service town for the surrounding mixed farming district, approximately halfway between Westport and Nelson. Murchison was named after the Scottish geologist Roderick Murchison, one of the founders of the Royal Geographical Society.

Richmond, Tasman
Richmond (Māori: Waimea) is a town and the seat of the Tasman District Council in New Zealand. It lies 13 kilometres (8 mi) south of Nelson in the South Island, close to the southern extremity of Tasman Bay. The town, first settled by Europeans in 1842, was named in 1854 after the town of Richmond on Thames near London. The town has an estimated population of 19,950 as of June 2025.

Although most of Richmond lies outside the boundaries of Nelson City and the town is considered a separate urban area, Richmond is part of the wider Nelson metropolitan area along with nearby Brightwater, Hope, Māpua and Wakefield. The two unitary authorities (Nelson and Tasman) co-operate for tourism-marketing purposes via "Latitude Nelson". As of 2020 Richmond forms part of the Nelson parliamentary electorate.
1992 Senior British Open
The 1992 Senior British Open was a professional golf tournament for players aged 50 and above and the sixth Senior British Open, held from 23 to 26 July at Royal Lytham & St Annes Golf Club in Lytham St Annes, Lancashire, England, United Kingdom.

52-year-old John Fourie won by three strokes over Bob Charles and Neil Coles, to claim his first Senior British Open title and first senior major championship victory.

Senior Open Championship
The Senior Open Championship, or simply The Senior Open (and originally known as the Senior British Open), is a professional golf tournament for players aged 50 and over. It is jointly owned and run by The R&A, the same body that organises The Open Championship, and the PGA European Tour. Prize money won in the event is official money on both PGA Tour Champions (formerly the Senior PGA Tour and Champions Tour) and the European Senior Tour. The purse, which is fixed in United States dollars, had increased to $2.75 million for 2023.