hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Layer cake representation
In mathematics, the layer cake representation of a non-negative, real-valued measurable function  defined on a measure space  is the formula

for all , where  denotes the indicator function of a subset  and  denotes the (strict) super-level set:

The layer cake representation follows easily from observing that

where either integrand gives the same integral:

The layer cake representation takes its name from the representation of the value  as the sum of contributions from the "layers" : "layers"/values  below  contribute to the integral, while values  above  do not.
It is a generalization of Cavalieri's principle and is also known under this name.: cor. 2.2.34

Measure space
A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes. It contains an underlying set, the subsets of this set that are feasible for measuring (the σ-algebra), and the method that is used for measuring (the measure). One important  example of a measure space is a probability space.

A measurable space consists of the first two components without a specific measure.
Michael Sipser
Michael Fredric Sipser (born September 17, 1954) is an American theoretical computer scientist who has made early contributions to computational complexity theory. He is a professor of applied mathematics and was the dean of science at the Massachusetts Institute of Technology.

Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, social science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.

In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics.
Jon the Dentist
John David Vaughan (born 2 October 1965), known professionally as Jon the Dentist, is a British hardhouse and trance music record producer. He released many popular singles including "Feel So Good" and "Imagination" with Ollie Jaye, both of which reached the UK Singles Chart.

Vaughan was born to parents Shirley and David in Eltham, London, and grew up in nearby Shooter's Hill with his sister Kate. A short period of time training to be a dentist resulted in his professional DJ name.

Eltham
Eltham (/ˈɛltəm/ EL-təm) is a district of southeast London, England, within the Royal Borough of Greenwich. It is 8.7 miles (14.0 km) east-southeast of Charing Cross, and is identified in the London Plan as one of 35 major centres in Greater London. The three wards of Eltham North, South and West have a total population of 35,459. 88,000 people live in Eltham.
Daniel MacParland
Daniel Henry MacParland was an Irish politician. He was a Fianna Fáil member of the Free State Seanad Éireann from 1931 to 1936. He was elected to the Seanad in 1931 for 9 years and served until the Free State Seanad was abolished in 1936.

Seanad Éireann (Irish Free State)
Seanad Éireann (Irish pronunciation: [ˈʃan̪ˠəd̪ˠ ˈeːɾʲən̪ˠ]; Senate of Ireland) was the upper house of the Oireachtas (parliament) of the Irish Free State from 1922 to 1936. It has also been known simply as the Senate, First Seanad, Free State Senate or Free State Seanad. The Seanad was established under the 1922 Constitution of the Irish Free State. A number of constitutional amendments were made to change the manner of its election and its powers. It was eventually abolished in 1936 when it attempted to obstruct constitutional reforms favoured by the government. It sat, like its modern successor, in Leinster House.
Tutaleni Housing Project
Tutaleni (meaning let’s watch in Oshiwambo) is an informal settlement on the northern outskirts of Walvis Bay, in the Erongo region of Namibia. Popularly known by locals as the Tutaleni village or simply Tuta, it is home to about 1000 families living on 1200 plots measuring 300 sq.m each. The project is an initiative of the Walvis Bay municipality in its efforts to reduce the negative effects of a high number of shacks in the coastal town.  A cement floor, toilet and kitchen sink are readily found on the plot, occupants are then free to complete their house structures with certain permitted building material. Residents of the settlement have access to clean water, power, waste removal and other basic municipal services.

Ovambo language
The Ovambo (English:  /ɒˈvæmboʊ/) language, also known as the Namibian language, is a dialect cluster spoken by the Ovambo people in southern Angola and northern Namibia, of which the written standards are Kwanyama and Ndonga.

The native name for the language is Oshiwambo (also written Oshivambo), which is also used specifically for the Kwanyama and Ndonga dialects. It is the largest spoken local language in Namibia, particularly by the Ovambo people.

The language is closely related to that of the Herero and Himba, the Herero language (Otjiherero). An obvious sign of proximity is the prefix used for language and dialect names, Proto-Bantu *ki- (class 7, as in the name of the Swahili language, Kiswahili), which in Herero has evolved to Otji- and in Ovambo further to Oshi-.
Jagdish Kashibhai Patel
Khda Reh Ke Dalvaunga, popularly known as Jagdishbhai, is an Indian visually impaired social worker and one of the 3 founders of the Blind People's Association of India, along with his wife and Kanubhai Ambalal Thaker (Educationist, Activist, Principal of the Blind School- Andhajan Mandal, Ahmedabad) an Ahmedabad based  non governmental organization promoting the interests of the people with physical disabilities. He is a recipient of the Indian civilian honour of the Padma Shri.

Help the Aged
Help the Aged was a United Kingdom based international charity founded in 1961 by Cecil Jackson-Cole and Hugh Faulkner to help disadvantaged older people who were affected by poverty, isolation and neglect. It merged with Age Concern in 2009 to form Age UK.
Balasore Roads
Balasore Roads is a roadstead (a sheltered anchorage), on the Indian coast near Balasore. It was the location of the Bengal Pilot Service pilot boarding station (see chart). It was considered to be a generally safe anchorage, with depths varying from 5 to 15 fathoms, and with the sea bottom consisting of mud and sand.

The entrance to the Hooghly River was considered to be the most difficult of any river in India, and the river pilot station was located in close proximity to the mouth of the river.

During the French Revolutionary and Napoleonic Wars French privateer captains such as Jean-François Hodoul and Robert Surcouf would cruise the mouth of the Hooghly River hoping to capture vessels anchored in the Roads, or proceeding to or from Calcutta. The French captured both pilot vessels such as Cartier, and large East Indiamen such as Triton.

Hooghly River
The Hooghly River (/ˈhuːɡli/; Bengali: Hugli [ˈɦuɡli]) is the westernmost distributary of the Ganges, situated in West Bengal, India. It is known in its upper reaches as the Bhagirathi. The Bhagirathi splits off from the main branch of the Ganges at Giria. A short distance west, it meets the man-made Farakka Feeder Canal, which massively increases its flow. The river then flows south to join the Jalangi at Nabadwip, where it becomes the Hooghly proper. The Hooghly continues southwards, passing through the metropolis of Kolkata. Thereafter, it empties into the Bay of Bengal. Its tributaries include the Ajay, Damodar, Rupnarayan, and Haldi.

The Hooghly has religious significance as Hindus consider the river sacred. It also plays a major role in the agriculture, industry, and climate of the state.
Compression belt
A compression belt is a type of spinal brace worn around the waist and lower back that compresses the abdomen.

It centers the body's mass, and effectively decompresses the spine. As a result, the user experiences improved posture, core stability, lower back pain relief, and reduced spinal cord compression stress.

Spinal cord compression
Spinal cord compression is a form of myelopathy in which the spinal cord is compressed. Causes can be bone fragments from a vertebral fracture, a tumor, abscess, ruptured intervertebral disc or other lesion.

When acute it can cause a medical emergency independent of its cause, and require swift diagnosis and treatment to prevent long-term disability due to irreversible spinal cord injury.
Rampton Castle
Rampton Castle, known locally as Giant's Hill, is the earthwork remains of a motte and bailey castle in Rampton, Cambridgeshire. It is believed that the castle was constructed during The Anarchy by the forces of King Stephen to contain the revolt of Geoffrey de Mandeville. The castle was not completed; construction was probably halted by de Mandeville's death at nearby Burwell Castle in 1144. Sited near to the churchyard of All Saints' Church, the castle is thought to have been built over the eastern end of the medieval village.

Motte-and-bailey castle
A motte-and-bailey castle is a European fortification with a wooden or stone keep situated on a raised area of ground called a motte, accompanied by a walled courtyard, or bailey, surrounded by a protective ditch and palisade. Relatively easy to build with unskilled labour, but still militarily formidable, these castles were built across northern Europe from the 10th century onwards, spreading from Normandy and Anjou in France, into the Holy Roman Empire, as well as the Low Countries it controlled, in the 11th century, when these castles were popularized in the area that became the Netherlands. The Normans introduced the design into England and Wales. Motte-and-bailey castles were adopted in Scotland, Ireland, and Denmark in the 12th and 13th centuries. By the end of the 13th century, the design was largely superseded by alternative forms of fortification, but the earthworks remain a prominent feature in many countries.
Stembridge
Stembridge is a surname. Notable people with the surname include:

Gerard Stembridge (born 1958), Irish writer, director, and actor

James Stembridge, American prop weapons supplier

John Stembridge, American mathematician

Terry Stembridge, American basketball broadcaster

John Stembridge
John Stembridge is a Professor of Mathematics at the University of Michigan. He received his Ph.D. from the Massachusetts Institute of Technology in 1985 under the direction of Richard P. Stanley. His dissertation was entitled Combinatorial Decompositions of Characters of SL(n,C). He has had 8 Ph.D. students.

He is one of the participants in the Atlas of Lie Groups and Representations.
Langhorne Manor School
The Langhorne Manor School, now known as Langhorne Manor Borough Hall, is an historic, American one-room school building that is located in Langhorne Manor, Bucks County, Pennsylvania.

It was added to the National Register of Historic Places in 2008.

Bucks County, Pennsylvania
Bucks County is in the Commonwealth of Pennsylvania. As of the 2020 census, the population was 646,538, making it the fourth-most populous county in Pennsylvania. Its county seat is Doylestown. The county is named after the English county of Buckinghamshire. The county is part of the Southeast region of the commonwealth.

The county represents the northern boundary of the Philadelphia–Camden–Wilmington, PA–NJ–DE–MD metropolitan statistical area.

To its southwest, Bucks County borders Montgomery County and Philadelphia, the nation's sixth-largest city. To its east, the county borders the Delaware River and U.S. state of New Jersey. To its north, the county borders Lehigh and Northampton counties in the state's Lehigh Valley region. The county is approximately 30 miles (48 km) southeast of Allentown, the state's third-largest city, and 40 miles (64 km) north of Philadelphia, the state's largest city.
Thomas Rudolph
Thomas Rudolph (born 15 June 1970 in Erfurt, Thuringia) is a German luger who competed in the early 1990s. Together with Yves Mankel he won the silver medal in the men's doubles event at the 1992 Winter Olympics in Albertville.

Rudolph also won a silver in the men's doubles event at the 1991 FIL World Luge Championships in Winterberg, Germany. He also won a complete set of medals at the FIL European Luge Championships with a gold in the mixed team event (1992), a silver in the mixed team event (1994), and a bronze in the men's doubles event (1994).

Rudolph's best overall finish in the Luge World Cup was second in men's doubles twice (1991-2, 1995–6).

Winterberg
Winterberg (German pronunciation: [ˈvɪntɐˌbɛʁk] ⓘ; Westphalian: Winnenmerg) is a town in the Hochsauerland district of North Rhine-Westphalia, central Germany and a major winter sport resort of the Wintersport Arena Sauerland.
Shpaky
Shpaky (Ukrainian: Шпаки) is a village (selo) in Zolochiv Raion, Lviv Oblast, in western Ukraine. It belongs to Pidkamin settlement hromada, one of the hromadas of Ukraine.

From 1918 to 1939 the village was in Tarnopol Voivodeship in Poland.

Until 18 July 2020, Shpaky belonged to Brody Raion. The raion was abolished in July 2020 as part of the administrative reform of Ukraine, which reduced the number of raions of Lviv Oblast to seven. The area of Brody Raion was merged into Zolochiv Raion.

Tarnopol Voivodeship
Tarnopol Voivodeship (Polish: Województwo tarnopolskie; Ukrainian: Тернопільське воєводство, romanized: Ternopilske voievodstvo) was an administrative region of interwar Poland (1918–1939), created on 23 December 1920, with an area of 16,500 km2 and provincial capital in Tarnopol (now Ternopil, Ukraine). The voivodeship was divided into 17 districts (powiaty). At the end of World War II, at the insistence of Joseph Stalin during the Tehran Conference of 1943 without official Polish representation whatsoever, the borders of Poland were redrawn by the Allies. The Polish population was forcibly resettled after the defeat of Nazi Germany and the Tarnopol Voivodeship was incorporated into the Ukrainian SSR of the Soviet Union. Since 1991, the territory of the voivodeship has been split between the eastern part of the Lviv region and the central and southern parts of the Ternopil region in sovereign Ukraine.
East Georgia (region)
East Georgia is a thirteen-county region in the U.S. state of Georgia, bordering South Carolina. North of Coastal and South Georgia as well as the Lower Coastal Plain, part of the region lies in the Fall Line section of the state. The largest county by population in East Georgia is Richmond County, and its most populous city is Augusta, anchoring the Augusta metropolitan statistical area. Tabulating the region's counties, its population as of the 2020 U.S. census was 479,864.

Augusta metropolitan area
The Augusta metropolitan area, officially the Augusta-Richmond County metropolitan statistical area according to the U.S. Office of Management and Budget, Census Bureau and other agencies, is a metropolitan statistical area centered on the city of Augusta, Georgia. It straddles two U.S. states, Georgia and South Carolina, and includes the Georgia counties of Richmond, Burke, Columbia, Lincoln, and McDuffie as well as the South Carolina counties of Aiken and Edgefield. The official 2023 U.S. census estimate for the area was 629,429 residents, up from 611,000 at the 2020 U.S. census.
Thrissur Pooram
The Thrissur Pooram is an annual Hindu temple festival held in Thrissur, Kerala, India. It is held at the Vadakkunnathan Temple in Thrissur every year on the Pooram day—the day when the moon rises with the Pooram star in the Malayalam Calendar month of Medam. It is the largest and most famous of all poorams in India. Thrissur pooram is also one of the largest festivals in Asia with more than 1 million visitors. The Thrissur Pooram Exhibition is conducted over a period of 40 to 50 days during the Thrissur Pooram.

Thrissur City Police
Thrissur City Police (TCPD) (Malayalam: തൃശൂര്‍ സിറ്റി പോലീസ്‌ ), a division of the Kerala Police, is the law enforcement agency for the City of Thrissur, Kunnamkulam and the temple town of Guruvayoor. The city police force is headed by a Commissioner of Police, an IPS officer, and the administrative control vests with the Home Ministry of Kerala. Thrissur City Police is the largest Police District in Kerala state covering an area of 570.79 Square kilometre.

The city police came into existence on March 3, 2011, after dividing the Thrissur District Police. The police commissionerate is situated in Thrissur City. The commissionerate cover 24 police stations and has four sub-divisions, Thrissur, Ollur, Guruvayur and Kunnamkulam. Nakul Rajendra Deshmukh IPS, is the current Police Commissioner of Thrissur.
West Brompton station
West Brompton is a Grade II-listed interchange station located on Old Brompton Road (A3218) in West Brompton, West London. The station is served by the District line of the London Underground; the Mildmay line of the London Overground; and National Rail services operated by Southern along the West London line.

The station is situated immediately south of the demolished Earls Court Exhibition Centre and west of Brompton Cemetery in the Royal Borough of Kensington and Chelsea. The station's location on the West London line forms a borough boundary and its tracks are shared between Kensington & Chelsea and the London Borough of Hammersmith and Fulham.

Interchange station
An interchange station or a transfer station is a train station for more than one railway route in a public transport system that allows passengers to change from one route to another, often without having to leave a station or pay an additional fare.

Transfer may occur within the same mode, or between rail modes, or to buses (for stations with bus termini attached). Such stations usually have more platforms than single route stations. These stations can exist in either commercial centers or on the city outskirts in residential areas. Cities typically plan for land use around interchange stations for development. Passengers may be required to pay extra fare for the interchange if they leave a paid area.
Kaset (album)
Kaset (Cassette) is the fourteenth studio album by Malaysian boy band, KRU, released on 25 April 2025 by KRU Music and Sony Music Malaysia. It is their first studio album in 12 years since KRUnomena (2013), following their reunion in October 2024 and their first album with Sony Music Malaysia. It is also their first album to included English tracks since 10 di Skala Richter (2006).

The overall sound of the album marks a return to the pop, rap and R&B style the group became famous for in the 1990s. Norman described it as "a collaborative effort, created as a family". The album yielded two lead singles, "Voodoo", released on 22 November 2024 and "One More Time", on 17 January 2025.

KRU Music
KRU Music Sdn Bhd is a Malaysian record label formed in 1996 by the singers-songwriters-producers jointly known as "KRU". Initially formed as KRU Records as a joint venture company with EMI, KRU Music changed its name and went fully independent in 1999 and have worked with Taiwan-based label Rock Records (1999 to 2001), Warner Music (2002 to 2004), EMI (2004 to 2006), United Studios (2007 to 2013) and currently Sony Music as distributors for their physical album releases. One Stop Music has released KRU Music's catalogue on digital formats since 2006.

KRU Music is one of the biggest independent labels in South East Asia with offices in Kuala Lumpur and Singapore.
Red Socks Pugie
"Red Socks Pugie" is the third single from the album Antidotes by Foals. It is their sixth single in total to date. It was released as a digital download, CD and vinyl on 9 June 2008.

Lead singer Yannis Philippakis stated that the track was about "the amazing energy, the flows you feel when you're in love, or you think you are".

The video was directed by Dave Ma and features footage of the band near a lake, nuclear weapon test explosions and medical animations.

"Red Socks Pugie" peaked at number 89 on the UK Singles Chart. The song was used by ITV during their coverage of the FA Cup during the 2009-10 football season.

2009–10 in English football
The 2009–2010 season was the 130th season of competitive football in England.

The 2009 season officially began on 8 August 2009 for the Championship, League One, League Two and the Premier League. The Championship season finished on 2 May 2010, with the Premier League, League One and League Two concluding on the weekend of 8–9 May.
McEvers Island
McEvers Island is an uninhabited fluvial island in the Illinois River.  Approximately 1 mile (1.6 km) long, it is legally part of Montezuma Township within Pike County in the U.S. state of Illinois.  The island, at Mile 48.5, is often used as a landmark by commercial and pleasure boaters traversing the river.  Boaters often anchor or tie up in the narrow, sheltered channel east of the island, bordering the Scott County Illinois mainland.

River island
A river island is any exposed landmass surrounded by river water. Properly defined, it excludes shoals between seasonally varying flows and may exclude semi-coastal islands in river deltas such as Marajó.

These islands result from changes in the course of a river. Such changes may be caused by interactions with a tributary, or by the opposing fluvial actions of deposition and/or erosion that form a natural cut and meander. Nascent vegetation-free shoals and mudflats may dissipate and shift or build up into such islands through deposition; the process may be assisted through artificial reinforcement or natural factors, such as reeds, palms, evergreen trees or willows, that act as obstacles or erosion barriers, so that water flows around them. Islands may be small or large, covering many square kilometers, examples of which are given below.
Haruka Suenaga
Haruka Suenaga (末永 遥, Suenaga Haruka; born July 22, 1986) is a Japanese actress. At a young age, she began making TV appearances on Oha Suta and was part of the Oha-Girls. She has done some commercials for Glico. One of her most notable roles was Sakura Nishihori/Bouken Pink in the Super Sentai series GoGo Sentai Boukenger.

Glico
Ezaki Glico Co., Ltd. (江崎グリコ株式会社, Ezaki Guriko Kabushiki-gaisha), commonly known as Glico, is a Japanese multinational food processing company headquartered in Nishiyodogawa-ku, Osaka. It does business across 30 countries, in North America, Asia-Pacific and Europe.
FAS Finance and Investment Limited
FAS Finance and Investment Limited is a major non-bank financial institution in Bangladesh providing lease financing and investment services.

In 2020, it was one of the financial institutions targeted by Prashanta Kumar Halder, nicknamed the Sultan of Swindle by The Daily Star, who had stolen 102 billion taka from FAS Finance and Investment Limited, People's Leasing and Financial Services Limited, International Leasing and Financial Services Limited, Reliance Finance Limited, and NRB Global Bank Limited.

It is listed on the Dhaka Stock Exchange.

Dhaka Stock Exchange
The Dhaka Stock Exchange (DSE; Bengali: ঢাকা স্টক এক্সচেঞ্জ Dhaka stôk ekschenj), located in Nikunja, Dhaka, is one of the two stock exchanges of Bangladesh, the other being the Chittagong Stock Exchange.