hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Stratonovich integral
In stochastic processes, the Stratonovich integral or Fisk–Stratonovich integral (developed simultaneously by Ruslan Stratonovich and Donald Fisk) is a stochastic integral, the most common alternative to the Itô integral. Although the Itô integral is the usual choice in applied mathematics, the Stratonovich integral is frequently used in physics.

In some circumstances, integrals in the Stratonovich definition are easier to manipulate. Unlike the Itô calculus, Stratonovich integrals are defined such that the chain rule of ordinary calculus holds.

Perhaps the most common situation in which these are encountered is as the solution to Stratonovich stochastic differential equations (SDEs). These are equivalent to Itô SDEs and it is possible to convert between the two whenever one definition is more convenient.

Chain rule
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions z and y in terms of the derivatives of z and y. More precisely, if  is the composition such that  for every x, then the chain rule is, in Lagrange's notation,

or, equivalently,

The chain rule may also be expressed in Leibniz's notation. If a variable z depends on the variable y, which itself depends on the variable x (that is, y and z are dependent variables), then z depends on x as well, via the intermediate variable y. In this case, the chain rule is expressed as
 
and

for indicating at which points the derivatives have to be evaluated.

In integration, the counterpart to the chain rule is the substitution rule.
Santos Lugares
Santos Lugares is a town in the southeast of the partido of Tres de Febrero. It is part of the urban agglomeration of Greater Buenos Aires in Buenos Aires Province, northwest of the Buenos Aires city proper. According to the 2001 census [INDEC], Santos Lugares had 17,023 inhabitants.

National Institute of Statistics and Census of Argentina
The National Institute of Statistics and Censuses (Spanish: Instituto Nacional de Estadística y Censos, mostly known for its acronym INDEC) is an Argentine decentralized public body that operates within the Ministry of Economy, which leads all official statistical activities carried out in the country.

In February 2013, the International Monetary Fund censured Argentina for failing to report accurate inflation data. Political intervention in the INDEC figures ended, and the IMF declared in November 2016 that Argentine statistics were again in accordance with international standards.
Sinkankasite
Sinkankasite, mineral formula: H2MnAl(PO4)2(OH)·6H2O, was named after John Sinkankas (1915–2002), noted author and mineral collector, Scripps Institute of Oceanography. It is triclinic; as colorless, bladed to prismatic crystals up to 4 mm in length, often as divergent, radial aggregates and as pseudomorphs after triphlyte crystals; occurs in the Barker pegmatite (formerly Ferguson pegmatite), east of Keystone, South Dakota, and in the Palermo pegmatite, North Groton, New Hampshire.

Scripps Institution of Oceanography
The Scripps Institution of Oceanography (SIO) is the center for oceanography and earth science at the University of California, San Diego. Its main campus is located in La Jolla, with additional facilities in Point Loma.

Founded in 1903 and incorporated into the University of California system in 1912, the institution has since broadened its research focus to encompass the physics, chemistry, geology, biology, and climate of the Earth. The institution awards the Nierenberg Prize annually to recognize researchers with exceptional contributions to science in public interest.
Overjoyed (Half Japanese album)
Overjoyed is an album by the American art punk band Half Japanese, released on September 2, 2014, on Joyful Noise Recordings. It is their first album since Hello, released in 2001. It was produced by John Dieterich of Deerhoof.

Deerhoof
Deerhoof is an American musical group formed in San Francisco in 1994. It consists of founding drummer Greg Saunier, bassist and singer Satomi Matsuzaki, and guitarists John Dieterich and Ed Rodriguez. Beginning as an improvised noise punk band, Deerhoof became widely renowned and influential in the 2000s through its self-produced albums.

Deerhoof has released 20 studio albums since 1997. Its most recent, Noble and Godlike in Ruin, was released on April 25, 2025.
Pedrão (nickname)
Pedrão is a hypocorism of the name Pedro, meaning "Big Pedro" in Portuguese.

Notable people named Pedrão include:

Pedrão (footballer, born 1978), full name Christiano Florêncio da Silva, Brazilian footballer

Pedrão (footballer, born 1986), full name Pedro Luiz Barone, Brazilian football defender

Pedrão (footballer, born 1992), full name Pedro Henrique Dias de Amorim, Brazilian football centre-back for Atlético Goianiense

Pedrão (footballer, born 1997), full name Pedro Henrique de Oliveira Correia, Brazilian footballer for Maccabi Haifa

Pedrão (footballer, born 2004), full name Pedro Henrique Franklim da Silva, Brazilian football centre-back for Pafos

Pedro
Pedro is a masculine given name. Pedro is the Spanish, Portuguese, and Galician name for Peter. Its French equivalent is Pierre while its English and Germanic form is Peter.

The counterpart patronymic surname of the name Pedro, meaning "son of Peter" (compared with the English surname Peterson) is Pérez in Spanish, Peres in Galician and Portuguese, Pires also in Portuguese, and Peiris in coastal area of Sri Lanka (where it originated from the Portuguese version), with all ultimately meaning "son of Pero".

The name Pedro is derived via the Latin word "petra", from the Greek word "η πέτρα" meaning "stone, rock".

The name Peter itself is a translation of the Aramaic Kephas or Cephas meaning "stone".

An alternative archaic variant is Pero.

Notable people with the name Pedro include:
Phan Thai Norasing
Phan Thai Norasing (Thai: พันท้ายนรสิงห์) is a legendary figure mentioned in some later editions of the royal chronicles of Ayutthaya. He is described as a coxswain of King Sanphet VIII's royal barge in the Ayutthaya period. According to the legend, Phan Thai Norasing served his duty as the coxswain until around 1704 when an accident happened during the king's fishing trip, causing damage to the royal barge. From this, he willingly accepted the penalty according to ancient Thai law, which was execution, despite being given a pardon. Although his existence  cannot be fully confirmed, he remained as a famous symbol of honesty and integrity.  There are many monuments dedicated to him in places related to his story, such as those presumed to be his execution spot. The story of Phan Thai Norasing has been adapted into various forms of media including films, TV series, and musicals, with possibly altered or extended plots but preserving the core of the story regarding honesty.

Royal barge
A royal barge is a vessel that is used by a monarch for ceremonial processions, and (historically) for routine transport, usually on a river or inland waterway. It may also be known as a state barge, and may be used on occasion by other members of a royal family, heads of state, or particular VIPs.

Traditionally royal barges were used by European monarchies such as the United Kingdom, France, Belgium, and Sweden, and Southeast Asian monarchies such as Siam, Burma, Brunei, Riau and Cambodia.

In more recent years, royal barges have only been used in the United Kingdom, Sweden and Thailand.
Demos Commander
Demos Commander (deco) is an orthodox file manager for Unix-like systems and a clone of Norton Commander. The project started by Sergey Vakulenko in 1989 while working at the DEMOS ISP (thus the name Demos Commander: deco) and is considered one of the first orthodox file managers for the Unix-like systems.

Clone (computing)
In computing, a clone is hardware or software that is designed to function in exactly the same way as another system. A specific subset of clones are remakes (or remades), which are revivals of old, obsolete, or discontinued products.
Bengaluru Cantonment railway station
Bengaluru Cantonment railway station, also known as Bengaluru Cant (station code: BNC) is one of the four important railway stations serving the city of Bengaluru and it is located in the locality of Vasanth Nagar and adjoins Fraser Town, Benson Town and Shivajinagar. The Station started operations in 1864, with the launch of the Bengaluru Cantonment – Jolarpettai train services by the Madras Railway. The train line was broad-gauge and 149 km long, connecting the Bengaluru Cantonment with Vellore district.
A total of 119 passenger trains start/end/pass through Bengaluru Cantonment railway station.
Total 499 stations are directly connected to Bengaluru Cantonment railway station via these 269 passenger trains.

Jolarpettai
Jolarpettai is a Municipality in Tirupattur district, Tamil Nadu, India. It is a commuter rail hub in Southern Railway, which is one of the largest Railway Junction in Tamil nadu. It is 7 km from district headquarter Tirupattur and 18 km from Vaniyambadi.

As of 2011, the municipal town had a population of 29,662 and covered an area of 13.06 km2. The town is divided into 18 wards.
Waterford Hill (Michigan)
Waterford Hill is located in Independence Township, in Oakland County, Michigan, 0.4 miles north of Waterford Village.  The hill is classified as a summit.
It extends from east of Dixie Highway including Ottawa Park Cemetery to the east, to Maple Lane in Moon Valley to the north, to Parview Drive and Greens Lake to the west, to Van Norman Lake to the south.

Waterford Hill's elevation is 1,150 feet, making it the second highest point in Independence Township.  Three miles away is Pine Knob, the highest point in the township at 1,201 feet.

Waterford Village, Michigan
Waterford Village is an historic community in Waterford Township, Michigan. First settled in 1819, the village is located in the northernmost part of the township along Dixie Highway, on the southeast shore of Van Norman Lake.
2016 Women's Bandy World Championship
2016 Women's Bandy World Championship was held in Roseville, Minnesota, USA, on February 18–21, 2016. The Guidant John Rose Minnesota Oval hosted the games.

This was the eighth Women's Bandy World Championship and the second Women's Bandy World Championship hosted by the United States. China made its championship debut.

Sweden had won all the previous Women's World Championships of bandy except the last one in 2014, which was won by Russia. The Swedes responded this year by defeating the Russians in the final by 1 goal to 0.

Guidant John Rose Minnesota Oval
The Guidant John Rose Minnesota Oval (officially stylized as OVAL), formerly the John Rose Minnesota Oval, is an outdoor ice rink in Roseville, Minnesota, United States. It is claimed to be the largest artificial outdoor skating surface in North America. The facility was constructed from June to December 1993. It was the subject of a $3.9 million renovation project which was set to be completed before the opening of the rink's 29th season on November 18, 2022. It is the home of bandy in the United States and is used by the United States men's national bandy team and the United States women's national bandy team.
Cobscook Bay
Cobscook Bay is located in Washington County in the state of Maine.  It opens into Passamaquoddy Bay, within the Bay of Fundy. Cobscook Bay is immediately south of the island city of Eastport, the main island of which (Moose Island) straddles the two bays.  In the 1930s, Cobscook Bay was part of the aborted Passamaquoddy Bay Tidal Power Project (a.k.a., Quoddy Dam Project) to generate electricity from its large tidal range.

Washington County, Maine
Washington County is a county located in the U.S. state of Maine. As of the 2020 census, its population was 31,095, making it the third-least populous county in Maine. Its county seat is Machias. The county was established on June 25, 1789. It borders the Canadian province of New Brunswick. It is sometimes referred to as "Sunrise County" because it includes the easternmost point in the 48 contiguous United States. Claims have been made that Washington County is where the sun first rises on the 48 contiguous states.  Many small seaside communities have small-scale fishing-based economies. Tourism is also important along the county's shoreline, but it is not as important as elsewhere in the state. The blueberry crop plays a major role in the county's economy.
Mary of Burgundy, Duchess of Cleves
Mary of Burgundy, Duchess of Cleves (1393 – 30 October 1466) was the second child of John the Fearless and Margaret of Bavaria, and an elder sister of Philip the Good.

Born in Dijon, she became the second wife of Adolph, Count of Mark in May 1406. He was made the 1st Duke of Cleves in 1417. They were the grandparents of King Louis XII of France and the great-grandparents of John III, Duke of Cleves, father of Anne of Cleves, who was fourth Queen consort of Henry VIII of England. By their daughter, Catherine, they were ancestors of Mary, Queen of Scots.

The Duke and Duchess of Cleves lived at Wijnendale Castle in West Flanders. She died in Cleves in present-day Monterberg, Kalkar.

John III, Duke of Cleves
John III, Duke of Cleves and Count of Mark (German: Johann III der Friedfertige; 10 November 1490 – 6 February 1539), known as John the Peaceful, was the Lord of Ravensberg, Count of Mark, and founder of the United Duchies of Jülich-Cleves-Berg.
Murphy Grist Mill
Murphy Grist Mill, also known as the Old Mill, is a historic grist mill located at Poughquag, Dutchess County, New York.  It was built in 1889, and is a two-story, front-gabled, vernacular frame building with a stone and concrete foundation.  It has a one-story, hipped roof porch supported by simple contemporary posts.  Also on the property are the contributing ruins of a stone mill dam. During his 1909 campaign for New York State Senate, Franklin Delano Roosevelt gave a political speech from the porch of the mill building. The mill remained in use until about 1940.  Franklin Delano Roosevelt Jr. purchased the property in 1949 and the mill was used primarily for storage. During the mid-1980s, it was given to the Town of Beekman and restoration began in 2014.

It was added to the National Register of Historic Places in 2015 by local non-profit Youth for Restoration.

Franklin D. Roosevelt Jr.
Franklin Delano Roosevelt Jr. (August 17, 1914 – August 17, 1988) was an American lawyer, politician, and businessman. He served as a United States congressman from New York from 1949 to 1955 and in 1963 was appointed United States Under Secretary of Commerce by President John F. Kennedy. Roosevelt was appointed as the first chairman of the Equal Employment Opportunity Commission from 1965 to 1966 by President Lyndon B. Johnson. Roosevelt also ran for governor of New York twice. Just after World War II, he served on Harry S. Truman's President's Committee on Civil Rights. Roosevelt was a son of President Franklin D. Roosevelt and First Lady Eleanor Roosevelt, and served as an officer in the United States Navy during World War II.
Tlāhuizcalpantecuhtli
Tlāhuizcalpantēcuhtli [t͡ɬaːwisˈkaɬpanteːˈkʷt͡ɬi] is a principal member of the pantheon of gods within the Aztec religion, representing the Morning Star Venus. The name comes from the Nahuatl words tlāhuizcalpan [t͡ɬaːwisˈkaɬpan] "dawn" and tēcuhtli [ˈteːkʷt͡ɬi] "lord". Tlahuizcalpantecuhtli is one of the thirteen Lords of the Day, representing the 12th day of the Aztec trecena.

Codex Chimalpopoca
Codex Chimalpopoca or Códice Chimalpopoca is a postconquest cartographic Aztec codex which is officially listed as being in the collection of the Instituto Nacional de Antropología e Historia located in Mexico City under "Collección Antiguo no. 159".  It is best known for its stories of the hero-god Quetzalcoatl. The current whereabouts of the codex are unknown. It appears to have disappeared in the mid-twentieth century,  so that study of the codex can be done only through copies and photographs. The codex consists of three parts, two of which are more important, one that regards the pre-Hispanic history of Central Mexico, the Anales de Cuauhtitlan and the other that regards the study of Aztec cosmology, the Leyenda de los Soles.
1996 UAW-GM Quality 500
The 1996 UAW-GM Quality 500 was the 28th stock car race of the 1996 NASCAR Winston Cup Series and the 37th iteration of the event. The race was held on Sunday, October 6, 1996, in Concord, North Carolina, at Charlotte Motor Speedway, a 1.5 miles (2.4 km) permanent quad-oval. The race took the scheduled 334 laps to complete. In the late stages of the race, Hendrick Motorsports driver Terry Labonte would manage to make a late-race charge to the front, managing to close and come within one point of teammate Jeff Gordon in the point standings after a late season slump by Gordon. The win was Labonte's 18th career NASCAR Winston Cup Series victory and his second and final victory of the season. To fill out the top three, Roush Racing driver Mark Martin and Robert Yates Racing driver Dale Jarrett would finish second and third, respectively.

Terry Labonte
Terrance Lee Labonte (born November 16, 1956), nicknamed "Texas Terry" or "the Iceman", is an American former stock car driver. He raced from 1978 to 2014 in the former NASCAR Winston Cup and Sprint Cup Series (now called the NASCAR Cup Series). A two-time Cup Series champion in 1984 and 1996 and the 1989 IROC champion, he is the older brother of 2000 Cup Series champion Bobby Labonte, and the father of former Nationwide Series driver Justin Labonte. He also co-owns a Chevrolet dealership in Greensboro, North Carolina with Rick Hendrick. He appeared on the CBS series The Dukes of Hazzard in 1984, where he played an unnamed pit crew member.
Nogata
There are a few different places in Japan named either Nogata　(野方) or Nōgata　(直方). They include the following:

Nōgata, Fukuoka, a city in Fukuoka Prefecture

Nogata, Tokyo, a district in Nakano, Tokyo

Nogata, Kita-ku, Nagoya, a district in Kita-ku, Nagoya

Nogata, Nakamura-ku, Nagoya, a district in Nakamura-ku, Nagoya

Nogata, Ichinomiya, an area in Oku-chō, Ichinomiya, Aichi

Nogata, Aisai, an area in Yamaji-chō, Aisai, Aichi

Nogata, Yatomi, an area in Maegasu-chō, Yatomi, Aichi

Nogata, Tōhaku, an area in Yurihama-chō, Tōhaku District

Nogata, Soo, an area in Ōsaki-chō, Soo District

Aisai
Aisai (愛西市, Aisai-shi) is a city located in Aichi Prefecture, Japan. As of 1 October 2019, the city had an estimated population of 61,320 in 23,451 households, and a population density of 919 persons per km2. The total area of the city is 66.70 square kilometres (25.75 sq mi). Aisai is a member of the World Health Organization’s Alliance for Healthy Cities (AFHC).
Mendocino County Line
"Mendocino County Line" is a song written by Matt Serletic and Bernie Taupin, and recorded as a duet by American country music artists Willie Nelson and Lee Ann Womack. It was released in January 2002 as the lead-off single from  Nelson's album The Great Divide. It was a Top 40 hit on the U.S. country chart, peaking at number 22. It was Nelson's first Top 40 hit on that chart since "Ain't Necessarily So" in 1990. It won the Grammy Award for Best Country Collaboration.

Matt Serletic
Matthew Michael Serletic II (born 1971) is an American record producer, songwriter, record executive and technologist serving since 2024 as Director of AI Innovation and Interactive Experiences at Amazon Music. Previously, he served as Director of Product at Google from 2019 to 2024, and founded the record label Emblem Music Group in 2007.
Kovy
Karel Kovář (born 11 September 1996), commonly known as Kovy (Czech pronunciation: ['kovɪ]), is a Czech YouTube personality, vlogger, and former let's player. He started his YouTube career in 2012 at the age of 16 with his first channel Gameballcz, focused mainly on let's plays and parodies. In 2014, Kovář founded a new channel called Kovy (his own nickname), focused on vlogging and infotainment videos. He became known for his originality and difference from other Czech YouTubers.

Infotainment
Infotainment, a portmanteau of information and entertainment, is a type of media, usually television or online, that provides a combination of information and entertainment. The term may be used disparagingly to devalue infotainment or soft news subjects in favor of more serious hard news subjects. Infotainment-based websites and social media apps gained traction due to their focused publishing of infotainment content, e.g. BuzzFeed. It is also called soft news as a way to distinguish it from serious journalism or hard news.
Global Cycling Network
Global Cycling Network (GCN) is a cycling-related YouTube channel which was launched in the United Kingdom in 2013. The channel's parent company, Play Sports Network, became a subsidiary of Warner Bros. Discovery through its TNT Sports unit in 2019 and returned to private ownership in 2024.

Content on the channel is presented by former professional cyclists and cycling journalists including 2008 Vuelta a Extremadura winner Daniel Lloyd, under-23 British National Mountain Biking champion Simon Richardson and 2018 Irish national road race champion Conor Dunne.

Vuelta a Extremadura
The Tour of Extremadura (Spanish: Vuelta Ciclista Internacional a Extremadura  or Vuelta a Extremadura) was an annual multiple stage bicycle race in Spain, visiting the main towns of the Extremadura region. Beginning as an amateur event in 1987, it became part of the professional UCI Europe Tour in 2005, and was last run in 2011.
2014 Tsunami March
The 2014 Tsunami March (Urdu: سونامی مارچ, romanized: Sunāmī Mārch), also called the Azadi movement, was a protest march in Pakistan from 14 August to 17 December 2014. The march was organized by the Pakistan Tehreek-e-Insaf (PTI) and Pakistan Awami Tehreek (PAT) against the Pakistani government of Nawaz Sharif. PTI claimed systematic election-rigging in the 2013 general election, and PAT demanded justice for the culprits in the 2014 Lahore clash. Then PTI chairman Imran Khan had announced plans for an August march from Lahore to Islamabad with a group of protesters in a PTI jalsa (demonstration) in Bahawalpur on 27 June 2014. On 17 December, a day after the 2014 Peshawar school massacre, Khan called off the protest.

Altaf Hussain (Pakistani politician)
Altaf Hussain (Urdu: الطاف حسین; pronounced [əltaːf ɦʊseːn]; born 17 September 1953 in Karachi) is a British Pakistani politician who is known as the founder of the Muttahida Qaumi Movement. He holds United Kingdom citizenship and has been living in exile in the UK since the start of Operation Clean-up. Since 2015, he has been a fugitive from the Anti Terrorism Court of Pakistan on the charges of 'murder, targeted killing, treason, inciting violence and hate speech'. He went on trial in the UK in January 2022 for 'promoting terrorism and unrest through hate speech in Pakistan', and was acquitted the next month. He had fled the country in 1992 after a crackdown against his party was launched.

His supporters refer to him as Pir Sahib (Sufi spiritual guide), Quaid-e-Tehrik (leader of the movement), Rahbar (guide) or Altaf Bhai (brother Altaf).