hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Haynsworth inertia additivity formula
In mathematics, the Haynsworth inertia additivity formula, discovered by Emilie Virginia Haynsworth (1916–1985), concerns the number of positive, negative, and zero eigenvalues of a Hermitian matrix and of block matrices into which it is partitioned.

The inertia of a Hermitian matrix H is defined as the ordered triple

whose components are respectively the numbers of positive, negative, and zero eigenvalues of H.  Haynsworth considered a partitioned Hermitian matrix

where H11 is nonsingular and H12* is the conjugate transpose of H12.  The formula states:

where H/H11 is the Schur complement of H11 in H:

Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a  square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j. In index form, or in matrix form:

Hermitian matrices can be understood as the complex extension of real symmetric matrices.

If the conjugate transpose of a matrix  is denoted by  then the Hermitian property can be written concisely as

Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are  although in quantum mechanics,  typically means the complex conjugate only, and not the conjugate transpose.
North Shore Country Club
North Shore Country Club is a private country club in Glenview, Illinois, a suburb of Chicago.

Founded in 1900, it features a 7,031 yard 18-hole golf course.  In 1933, it hosted the U.S. Open that was won by Johnny Goodman. It has also hosted the Western Open once and the U.S. Amateur twice. It was host site of the Encompass Championship on the Champions Tour from 2013 to 2015.

The course was designed by English architect Charles Allison of Colt MacKenzie and Alison.

Encompass Championship
The Encompass Championship was a golf tournament on the Champions Tour. It was played for the first time in 2013 at the North Shore Country Club in Glenview, Illinois.

The purse for the 2013 tournament was $1,800,000, with $270,000 going to the winner.
Afimkibart
Afimkibart (also known as PF-06480605, RVT-3101, or RG6631) is an investigational human IgG1 monoclonal antibody developed by Roche, formerly by Pfizer and Roivant Sciences, for the treatment of inflammatory diseases, including inflammatory bowel disease (ulcerative colitis, Crohn’s disease) and atopic dermatitis. It targets Tumor Necrosis Factor-like Ligand 1A (TL1A, also known as TNFSF15 or VEGI), a pro-inflammatory cytokine implicated in immune dysregulation and chronic inflammation. As of June 2025, afimkibart is in Phase III trials for ulcerative colitis and Phase II trials for Crohn’s disease and atopic dermatitis.

Vascular endothelial growth inhibitor
Vascular endothelial growth inhibitor (VEGI), also known as TNF-like ligand 1A (TL1A) and TNF superfamily member 15 (TNFSF15), is protein that in humans is encoded by the TNFSF15 gene. VEGI is an anti-angiogenic protein. It belongs to tumor necrosis factor (ligand) superfamily, where it is member 15. It is the sole known ligand for death receptor 3, and it can also be recognized by decoy receptor 3.
2021 Israeli Labor Party leadership election
The 2021 Israeli Labor Party leadership election was held on 24 January 2021 in the lead-up to the  2021 Israeli legislative election.

The candidates were Merav Michaeli, Avi Shaked, Yitzhak Taym, Gil Beilin, Navah Katz, David Landsman, and Ofer Segman. Michaeli won the leadership election with 77.5% of the vote.

Merav Michaeli
Merav Michaeli (Hebrew: מרב מיכאלי; born 24 November 1966) is an Israeli politician, journalist, TV anchor, radio broadcaster, feminist and activist currently serving as a member of the Knesset for the Democrats, which was formed in 2024 by a merger of Labor and Meretz. She served as leader of the Labor Party from 2021 until 2024, and as Minister of Transport in the thirty-sixth government of Israel.
Avenida Juan Ponce de León
Avenida Juan Ponce de León (Juan Ponce de León Avenue), also known as Avenida de la Constitución (Constitution Avenue), and coextensive as Puerto Rico Highway 25 (PR-25) along its entire length, is one of the main thoroughfares in San Juan, the capital municipality of Puerto Rico. Named after Juan Ponce de León, the Spanish conquistador who led the European colonization of the archipelago in 1508 after its discovery by Christopher Columbus during his second voyage in 1493, it connects the historic quarter of Old San Juan in San Juan Islet with the residential and resort barrio of Santurce, the business center of Hato Rey, and the commercial and residential district of Río Piedras in the main island. It is one of the oldest roadways in Puerto Rico, as some sections are dated to at least 1519.

Miramar (Santurce)
Miramar is one of the forty subbarrios of Santurce, San Juan, Puerto Rico. The neighborhood has many historic Spanish Revival-style homes with patios and gardens, and it was listed on the Puerto Rico Register of Historic Sites and Zones in 2007 for its historical and architectural value.
2022 Manitoba Scotties Tournament of Hearts
The 2022 Manitoba Scotties Tournament of Hearts presented by Bayer, the provincial women's curling championship for Manitoba, was held from December 15 to 19, 2021 at the Carberry Plains Community Centre in Carberry, Manitoba. The winning Mackenzie Zacharias team represented Manitoba at the 2022 Scotties Tournament of Hearts in Thunder Bay, Ontario.

The event included the World #1 ranked Tracy Fleury rink, who failed to make it to the playoffs in a shocking result.

Mackenzie Zacharias
Mackenzie Marie Zacharias (born June 8, 1999) is a retired Canadian curler from Altona, Manitoba. She skipped her Manitoba rink to a gold medal at both the 2020 Canadian Junior Curling Championships and the 2020 World Junior Curling Championships. Prior to focusing solely on curling, she was also a competitive softball player
1972 Larrakia Petition
The 1972 Larrakia Petition was a petition sent by the Larrakia people, the traditional owners of the Darwin region in the Northern Territory, to Queen Elizabeth II in October 1972. Seeking the establishment of formal land rights for First Nations people, the petition was 11 feet (3.4 m) long and contained around 1000 signatures. It is now considered a landmark document in the land rights movement in Australia.

Larrakia people
The Larrakia people are a group of Aboriginal Australian people in and around Darwin in the Northern Territory.  The Larrakia, who refer to themselves as "Saltwater People", have a vibrant traditional society based on a close relationship with the sea and trade with neighbouring groups such as the Tiwi, Wadjiginy and Djerimanga. These groups share ceremonies and songlines, and intermarry.
Wyoming Highway 24
Wyoming Highway 24 (WYO 24), also known as the Bear Lodge Highway, is a 46.72-mile (75.19 km) state highway in Crook County, Wyoming, United States. that connects U.S. Route 14 (US 14) in Carlile Junction with South Dakota Highway 34 (SD 34) at the South Dakota state line. The route passes through the northern portion of the Bear Lodge Mountains, part of the Black Hills National Forest. The highway also passes by Devils Tower National Monument.

South Dakota Highway 34
South Dakota Highway 34 (SD 34) is a state route that runs parallel to Interstate 90 across the entire state of South Dakota.  It begins at the Wyoming border west of Belle Fourche, as a continuation of Wyoming Highway 24 (WYO 24).  The eastern terminus is at the Minnesota border east of Egan, or southwest of Airlie, Minnesota, where it continues as Minnesota State Highway 30 (MN 30). It is just over 419 miles (674 km) in length, making it the longest state highway in South Dakota.
Protein O-GlcNAcase
Protein O-GlcNAcase (EC 3.2.1.169, OGA, glycoside hydrolase O-GlcNAcase, O-GlcNAcase, BtGH84, O-GlcNAc hydrolase) is an enzyme with systematic name (protein)-3-O-(N-acetyl-D-glucosaminyl)-L-serine/threonine N-acetylglucosaminyl hydrolase. OGA is encoded by the OGA gene. This enzyme catalyses the removal of the O-GlcNAc post-translational modification in the following chemical reaction:

[protein]-3-O-(N-acetyl-β-D-glucosaminyl)-L-serine + H2O ⇌ [protein]-L-serine + N-acetyl-D-glucosamine

[protein]-3-O-(N-acetyl-β-D-glucosaminyl)-L-threonine + H2O ⇌ [protein]-L-threonine + N-acetyl-D-glucosamine

Protein O-GlcNAc transferase
Protein O-GlcNAc transferase also known as OGT or O-linked N-acetylglucosaminyltransferase is an enzyme (EC 2.4.1.255) that in humans is encoded by the OGT gene. OGT catalyzes the addition of the O-GlcNAc post-translational modification to proteins.
Party Mix (video game)
Party Mix is a 1983 party video game developed and published by Starpath for the Atari 2600. It was designed to be used with the Supercharger add-on, which gave the Atari 2600 the ability to multi-load games and is required for the game to function.

Starpath Supercharger
The Starpath Supercharger (originally called the Arcadia Supercharger) is an expansion peripheral cartridge created by Starpath, for playing cassette-based proprietary games on the Atari 2600 video game console.

The device consists of a long cartridge with a handle on the end, and an audio cassette cable. It multiplies the Atari 2600's 128 bytes of RAM by 49 for a total of 6,272 bytes of RAM, allowing for the creation of specially compatible games which are larger and have higher resolution graphics than normal cartridges. A cable coming out of the side of the cartridge plugs into the earphone jack of any standard cassette player, for loading all Supercharger games from standard audio cassettes.
Per due come noi
"Per due come noi" (transl. For two like us) is a song by Italian singer-songwriters Olly and Angelina Mango and record producer Juli. It was released on 6 September 2024. The song was included in Olly and Juli's second studio album Tutta vita.

The song topped the Italian Singles Chart.

Tutta vita
Tutta vita is the second studio album by the Italian singer-songwriter Olly and record producer Juli, released on 25 October 2024 by Epic.

The release of the album was preceded by the singles "A squarciagola", "Devastante", and "Per due come noi", the latter a duet with Angelina Mango. In 2025, the album was reissued including the song "Balorda nostalgia", which won the 75th Sanremo Music Festival. Tutta vita topped the Italian Albums Chart and was certified seven times platinum by the Federazione Industria Musicale Italiana.

An expanded reissue, Tutta vita (sempre), was released on 26 September 2025.
Bracket (mathematics)
In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets ⟨ ⟩, are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take precedence over those surrounding it. Sometimes, for the clarity of reading, different kinds of brackets are used to express the same meaning of precedence in a single expression with deep nesting of sub-expressions.

Historically, other notations, such as the vinculum, were similarly used for grouping. In present-day use, these notations all have specific meanings. The earliest use of brackets to indicate aggregation (i.e. grouping) was suggested in 1608 by Christopher Clavius, and in 1629 by Albert Girard.

Christopher Clavius
Christopher Clavius, SJ (25 March 1538 – 6 February 1612) was a Jesuit German mathematician and physicist, head of mathematicians at the Collegio Romano, and astronomer who was a member of the Vatican commission that accepted the proposed calendar invented by Aloysius Lilius, that is known as the Gregorian calendar. Clavius would later write defences and an explanation of the reformed calendar, including an emphatic acknowledgement of Lilius' work. In his last years, he was probably the most respected astronomer in Europe and his textbooks were used for astronomical education for over fifty years in and even out of Europe.
Home on Monday
"Home on Monday" is a song by Australian band Little River Band, released in September 1977 as the third single from the group's third studio album, Diamantina Cocktail. The song peaked at number 73 on the Australian Kent Music Report singles chart and at number 12 on the Dutch Single Top 100.

The "Las Vegas Hilton" in the song is now called the Westgate Las Vegas.

Diamantina Cocktail
Diamantina Cocktail is the third studio album by the Australian rock group Little River Band, released in April 1977. It peaked at No. 2 on the Australian Kent Music Report Albums Chart and reaching No. 49 on the Billboard 200. A different version was released in the US by Harvest in May 1977. The album was certified Gold in the US by the RIAA in January 1978 for over 500,000 copies sold.

The titled refers to a drink invented in the area of the Diamantina River in Queensland, Australia. It consists of Bundaberg Rum, condensed milk and an emu egg.
1948–49 NHL transactions
The following is a list of all team-to-team transactions that have occurred in the National Hockey League (NHL) during the 1948–49 NHL season. It lists which team each player has been traded to and for which player(s) or other consideration(s), if applicable.

1948–49 NHL season
The 1948–49 NHL season was the 32nd season of the National Hockey League. Six teams played 60 games each. In a rematch of the previous season, Toronto defeated Detroit in the Stanley Cup Finals to win the championship.
Elie Rosenblatt
Elie Rosenblatt (Hebrew: אלי רוזנבלט) is a klezmer violinist known for his interpretation and recreation of early nineteenth century klezmer violin style. Hailing from Canada, he immigrated to Israel where he is involved in klezmer performances with the Jerusalem Klezmer Association. He has performed and taught internationally, and had participated at the annual Klezkanada program from its inception. In 2001, Rosenblatt released his first CD with tsimbl player Pete Rushefsky entitled Tsimbl un Fidl: Klezmer Music for Hammered Dulcimer & Violin. The album was hailed as a work of "impeccable scholarship with virtuoso performances" and considered "essential in any klezmer collection".

Rosenblatt is a brother of renowned multi-instrumentalist and vocalist, Jason Rosenblatt.

Pete Rushefsky
Pete Rushefsky is an American klezmer musician and executive director of New York City's Center for Traditional Music and Dance.  He plays the cimbalom or "tsimbl" as well as the 5-string banjo.

He has a book published called Essentials of Klezmer 5-String Banjo, Volume I.

In 2022, Rushefsky won a Bubbe Award for “Best Original Klezmer Composition”
Grand Illusion Cinema
The Grand Illusion Cinema is the longest running independent cinema in the city of Seattle, Washington, and has become a landmark of the film community. Opened as The Movie House in 1970, the cinema became the city's first intimate arthouse and showcased foreign and revival films. The Grand Illusion is located in Seattle's University District.

The Grand Illusion shows a wide variety of DCP, VHS, 16mm, and 35mm films ranging from new, independent, foreign, repertory classics, documentaries, and a consistent supply of "late nights" on the weekend which feature horror, sci-fi, and exploitation films. Over the years the cinema has been host to such people as Quentin Tarantino, Takashi Miike, Alex Cox, Eddie Izzard, Stuart Gordon, Don Hertzfeldt, Dennis Nyback, and the cast of Troll 2.

University District, Seattle
The University District (commonly the U District) is a neighborhood and a major district in central northeastern Seattle, Washington, comprising several distinct neighborhoods. The main campus of the University of Washington (UW) is located in the district, lending its name to both the district as well as University Way NE (commonly The Ave). The neighborhood lies north of Portage Bay and the Lake Washington Ship Canal and generally east of Interstate 5.

The area, originally a Duwamish settlement, was surveyed by the territorial government in 1855 and opened to settlement in 1867. Real estate developers created the Brooklyn neighborhood on the west side of the district in the 1890s, which was followed by the relocation of the UW campus to the east side of the district in 1895. The name Brooklyn faded from use in favor of "University District", which was adopted after a public contest in 1919.
Kill My Doubt
Kill My Doubt (stylized in all caps) is the seventh extended play (EP) by South Korean girl group Itzy, released on July 31, 2023, through JYP Entertainment, and Republic Records, eight months following the release of Cheshire (2022).

Inspired by the conversations shared by the members and their company following the release of Cheshire, Kill My Doubt lyrically revolves around the message of overcoming adversity and self-doubt. The EP comprises six tracks and is supported by the lead single "Cake". The release of the EP was preceded by music videos for album tracks "Bet on Me" and "None of My Business". Commercially, Kill My Doubt debuted at number one on South Korea's Circle Album Chart with 1,299,329 copies sold in the first week of release, becoming Itzy's sixth number-one album on the chart. In October 2023, the EP was certified Million by the Korea Music Content Association (KMCA) for surpassing 1,000,000 copies sold, the group's third million-seller album.

Cake (Itzy song)
"Cake" is a song recorded by South Korean girl group Itzy for their seventh extended play Kill My Doubt. It was released as the EP's lead single by JYP Entertainment and Republic Records on July 31, 2023.
Extreme Ghostbusters
Extreme Ghostbusters is an American animated television series, based on the Ghostbusters franchise, which initially aired from September 1 to December 8, 1997. A sequel to The Real Ghostbusters, which aired from 1986 to 1991 on ABC, Extreme Ghostbusters is set after that series' finale. The 40-episode series initially aired on the syndicated Bohbot Kids Network's "Extreme Block" in 1997, and featured a team of college-aged Ghostbusters led by veteran Ghostbuster Egon Spengler. In some TV listings, the series was called Ghostbusters Dark.

Maurice LaMarche
Maurice LaMarche (born March 30, 1958) is a Canadian voice actor. Across a career spanning more than four decades he has voiced Chief Quimby on Inspector Gadget, Egon Spengler on The Real Ghostbusters, The Brain on Animaniacs and its spin-off Pinky and the Brain, Big Bob on Hey Arnold!,  Alec Baldwin in Team America: World Police, Kif Kroker and Calculon on Futurama and dozens of other highly recognizable characters in central and minor roles across film, television, and video games.
Louis Johnson (bassist)
Louis Johnson (April 13, 1955 – May 21, 2015) was an American bass guitarist. Johnson was best known for his work with the group the Brothers Johnson and his session playing on several hit albums of the 1970s and 1980s, including the best-selling album of all time, Michael Jackson's Thriller.

His signature sound came from the Music Man StingRay bass guitar, which Leo Fender made for him, and from his slapping technique. He is ranked number 38 on Bass Player magazine's list of "the 100 Greatest Bass Players of All Time".

Music Man StingRay
The Music Man StingRay is an electric bass originally made by Music Man.  Introduced in 1976, the StingRay was co-designed by Leo Fender and followed a similar format to his namesake company's influential Precision Bass.  The more notable design changes to the "P-Bass" were the use of an oversized humbucker pickup in the bridge position and the introduction of active electronics, which allowed for expanded EQ controls.  Following Music Man's sale to Ernie Ball Inc. in 1984, the StingRay continued to be produced as the Ernie Ball Music Man StingRay.  The StingRay was considered revolutionary upon its release and it has since become one of the industry's "go-to" electric bass models.
Riñihue, Chile
Riñihue (Spanish pronunciation: [riˈɲiwe]) is a hamlet (Spanish: caserío) on the shores of Riñihue Lake, Los Ríos Region, Chile. It is located south of the mountain Tralcán in the western end of Riñihue Lake. In early 20th century Riñihue grew out as a settlement due to the exploitation of wood in Riñihue Lake. Riñihue was the first Chilean lakeshore settlement to be reached by the railroad. The hamlet was flooded in 1960 during the Riñihuazo.

It had a population of 92 as 2017 down from 243 in 2002. Riñihue is served by El Vergel Airport.

El Vergel Airport
El Vergel Airport (Spanish: Aeropuerto El Vergel, (ICAO: SCVG)) is an airport 3.5 kilometres (2.2 mi) west of Riñihue, a lakeside village in the Los Ríos Region of Chile.

The Tralcán mountain is 1 kilometre (0.62 mi) north of the runway.
It Happened in Aden
It Happened in Aden (French: C'est arrivé à Aden...) is a 1956 French historical comedy film directed by Michel Boisrond and starring André Luguet, Jacques Dacqmine and Dany Robin. It is based on the 1940 novel The Environs of Aden by Pierre Benoît.

The film's sets were designed by the art director René Moulaert.

Pierre Benoit (novelist)
Pierre Benoit (French pronunciation: [pjɛʁ bənwa]; 16 July 1886 – 3 March 1962) was a French novelist, screenwriter and member of the Académie française. He is perhaps best known for his second novel L'Atlantide (1919) that has been filmed several times.
Woodland Beach, Delaware
Woodland Beach is an unincorporated community in Kent County, Delaware, United States. Woodland Beach is along the Delaware Bay, east of Smyrna at the eastern terminus of Delaware Route 6. The Woodland Beach Wildlife Area is located in Woodland Beach.

Smyrna, Delaware
Smyrna is a town in Kent and New Castle counties in the U.S. state of Delaware. It is part of the Dover metropolitan statistical area. According to the U.S. Census Bureau, as of 2020, the population of the town is 12,883.

The international jurist John Bassett Moore was born in Smyrna, as were politicians Louis McLane and James Williams.
Alan Cardy
Alan Cardy (19 September 1945 – 19 December 2021) was a representative of Australia in rugby union. As a young man he concentrated on track and field, winning the Australian Junior Championships discus throw in 1963, aged just seventeen. In 1965, he ran 22.0 seconds in the 220 yards to finish third at the Australian National Championships – one-tenth of a second ahead of Peter Norman, the future silver medallist in the 200 metres at the 1968 Summer Olympics.

Cardy did not play any rugby until 1963 in his final year at Katoomba High School, where he was school captain. He played a few games for the Blue Mountains Rugby Club during 1962 and 1963, and later joined Drummoyne in 1965.

Cardy switched to the other rugby code – rugby league in 1969. However, his wing-threequarters career never reached any great heights in rugby league after suffering a broken leg in the pre-season.

He died on 19 December 2021 at the age of 76, and was survived by his three children.

Blue Mountains Rugby Club
Blue Mountains Rugby Club is based in the township of Lapstone within Greater Sydney, Australia. The club plays rugby union in the first division of the New South Wales Subbies competition  and currently fields teams in five men's grades, plus women's  and colts teams.

The Blue Mountains Rugby Club also has an associated junior club known as the Blue Tongues for young players ranging from under-6 to under-18 age groups, including both boys and girls.