hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Orthogonal complement
In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace  of a vector space  equipped with a bilinear form  is the set  of all vectors in  that are orthogonal to every vector in .  Informally, it is called the perp, short for perpendicular complement. It is a subspace of .

Bilinear form
In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately:

B(u + v, w) = B(u, w) + B(v, w)     and     B(λu, v) = λB(u, v)

B(u, v + w) = B(u, v) + B(u, w)     and     B(u, λv) = λB(u, v)

The dot product on  is an example of a bilinear form which is also an inner product. An example of a bilinear form that is not an inner product would be the four-vector product.

The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms.

When K is the field of complex numbers C, one is often more interested in sesquilinear forms, which are similar to bilinear forms but are conjugate linear in one argument.
Adolph Ochs
Adolph Simon Ochs (March 12, 1858 – April 8, 1935) was an American newspaper publisher and former owner of The New York Times and The Chattanooga Times, which is now the Chattanooga Times Free Press. Through his only child, Iphigene Ochs Sulzberger, and her husband Arthur Hays Sulzberger, Ochs's descendants continue to publish The New York Times through the present day.

Arthur Hays Sulzberger
Arthur Hays Sulzberger (September 12, 1891 – December 11, 1968) was publisher of The New York Times from 1935 to 1961. During that time, daily circulation rose from 465,000 to 713,000 and Sunday circulation from 745,000 to 1.4 million; the staff more than doubled, reaching 5,200; advertising linage grew from 19 million to 62 million column inches per year; and gross income increased almost sevenfold, reaching $117 million.
Jean Graetz
Jean Graetz (December 24, 1929 – December 16, 2020), born Jean Ellis, was an American civil rights activist. She and her clergyman husband Robert Graetz were active white supporters of the Montgomery bus boycott in 1955.

Robert Graetz
Robert Sylvester Graetz Jr. (May 16, 1928 – September 20, 2020) was a Lutheran clergyman who, as the white pastor of a black congregation in Montgomery, Alabama, openly supported the Montgomery bus boycott, a landmark event of the civil rights movement.
Coat of arms of British Columbia
The coat of arms of British Columbia is the heraldic symbol representing the Canadian province of British Columbia. The arms contain symbols reflecting British Columbia's British heritage along with local symbols. At the upper part of the shield is the Union Jack, representing the United Kingdom. The lower portion of the shield features a golden sun setting into the ocean, representing the province's location on the Pacific.

The original arms, consisting of only the shield, were granted by royal warrant of King Edward VII on 31 March 1906. The arms were further augmented with supporters, a crest, and a compartment, by royal warrant of Queen Elizabeth II on 15 October 1987.

A banner of arms comprises the provincial flag, which was adopted in 1960.

Flag of British Columbia
The flag of British Columbia is based upon the shield of the provincial arms of British Columbia. At the top of the flag is a rendition of the Royal Union Flag, defaced in the centre by a crown, while the bottom of the flag features a setting sun over stylized waves, representing British Columbia's connection to the Pacific Ocean and its westernmost location in Canada.
Roger de Moulins
Roger de Moulins was the master of the Knights Hospitaller from 1177 until his death in 1187. He succeeded Jobert of Syria. His successors were two interim masters, William Borrel and then Armengol de Aspa, before Garnier of Nablus was selected in 1190.

William Borrel
William Borrel (died 4 July 1187) was acting Grand Master of the Knights Hospitaller, ad interim, from 1 May 1187 until his death at the Battle of Hattin in 1187. He became custodian of the Hospitallers after the Grand Master Roger de Moulins was killed in the Battle of Cresson on 1 May 1187.
Lying in repose
Lying in repose is the tradition in which the body of a deceased person, often of high social stature, is made available for public viewing. Lying in repose differs from the more formal honor of lying in state, which is generally held at the principal government building of the deceased person's country and often accompanied by a guard of honour.

Lying in state
Lying in state is the tradition in which the body of a deceased official, such as a head of state, is placed in a state building, either outside or inside a coffin, to allow the public to pay their respects. It traditionally takes place in a major government building of a country, state, or city. While the practice differs among countries, in the United States, a viewing in a location other than a  government building, such as a church, may be referred to as lying in repose. These rituals are in effect a more formal and public wake or funeral viewing. Lying in state may precede a state funeral, or it may be the public honor preceding a private funeral.
Low Westwood
Low Westwood is a village in County Durham, England. It is situated immediately to the west of Hamsterley. Low Westwood is probably best known for Hamsterley Christ Church and Derwent care home.

Low Westwood grew as a result of coal mining. Westwood Colliery, located on the Shotley Bridge to Newcastle road, was operational from the 1840s (appearing on the 1856 Ordnance Survey map Durham sheet V). By the 1870s the original colliery had been replaced by the High Westwood colliery.

By the 1890s there was housing for the miners as well as a Church Of England church, Christ Church. A Roman Catholic church, dedicated to the Sacred Heart, was established in 1898 and closed in 1998. A school (1898) and cemetery, associated with the church, were also established.

The Derwent Valley Railway served the village from 1868 until the closure of High Westwood station in 1942.

Hamsterley, Consett
Hamsterley is a village in County Durham, England. It is situated to the north of Consett and borders the hamlet of Low Westwood.

The name Hamsterley possibly derives from the Old English ‘hamstra’, meaning a corn weevil and ‘ley’ meaning clearing, hence a clearing frequented by corn weevils, perhaps indicating the poor quality of farming in the area.

Hamsterley is mentioned in Bishop Hatfield’s survey of 1382, the land being held by John de Felton and the heirs of Hugh del Redhugh. By 1500 the lands were held by the Swinburne family whose descendants continued to hold the land until the early century 19th century. Hamsterley Hall was built by the Swinburnes in the early 17th century and later enlarged in the following centuries. The Surtees family took over the estate and hall in 1806, passing to the Viscounts Gort in 1885. Hamsterley Hall was the birthplace of the hunting novelist Robert Smith Surtees, author of Jorrocks' Jaunts and Jollities.
Tridiminished rhombicosidodecahedron
In geometry, the tridiminished rhombicosidodecahedron is one of the Johnson solids (J83). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed.

A Johnson solid is one of 92 strictly convex polyhedra that are composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.

Related Johnson solids are:

J76: diminished rhombicosidodecahedron with one cupola removed,

J80: parabidiminished rhombicosidodecahedron with two opposing cupolae removed,

J81: metabidiminished rhombicosidodecahedron with two non-opposing cupolae removed, and

J82: gyrate bidiminished rhombicosidodecahedron with two non-opposing cupolae removed and one cupola rotated 36 degrees.

Johnson solid
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedra. There are 92  solids with such a property: the first solids are the pyramids, cupolas, and a rotunda; some of the solids may be constructed by attaching with those previous solids, whereas others may not.
London Scottish F.C.
London Scottish Football Club is a rugby union club in England. The club is a member of both the Rugby Football Union and the Scottish Rugby Union. The club is currently playing in the 2nd tier of the English rugby union system, Champ Rugby, and share the Athletic Ground with Richmond.

Richmond F.C.
Richmond Rugby Club is a rugby union club in Richmond, London, England. It is a founding member of the Rugby Football Union, and is one of the oldest football clubs (of any code). It fields teams in both men's and women's rugby; the men's first team currently play in Champ Rugby in the 2nd tier of the English rugby union system, following their promotion from the 2024–25 National League 1, while the women's first team play in the Women's Championship.
Pan-European nationalism
European nationalism (sometimes called pan-European nationalism or Euro-nationalism) is a form of pan-nationalism based on a pan-European identity. It has been only a minor far-right tendency since the National Party of Europe disintegrated in the 1970s.

It is distinct from Pro-Europeanism and European Federalism in being a chiefly neo-fascist ideology, as opposed to support of the European Union and European integration.

Neo-fascism
Neo-fascism is a post-World War II far-right ideology which includes significant elements of fascism. Neo-fascism usually includes ultranationalism, ultraconservatism, racial supremacy, right-wing populism, authoritarianism, nativism, xenophobia, and anti-immigration sentiment, as well as opposition to social democracy, parliamentarianism, Marxism, communism, socialism, liberalism, neoliberalism, and liberal democracy.
Pterygopalatine ganglion
The pterygopalatine ganglion (aka Meckel's ganglion, nasal ganglion, or sphenopalatine ganglion) is a parasympathetic ganglion in the pterygopalatine fossa. It is one of four parasympathetic ganglia of the head and neck, (the others being the submandibular, otic, and ciliary ganglion).

It is innervated by the Vidian nerve (formed by the greater superficial petrosal nerve branch of the facial nerve and deep petrosal nerve) and maxillary division of the trigeminal nerve. Its postsynaptic axons project to the lacrimal glands and nasal mucosa.

The flow of blood to the nasal mucosa, in particular the venous plexus of the conchae, is regulated by the pterygopalatine ganglion and heats or cools the air in the nose.

Facial nerve
The facial nerve, also known as the seventh cranial nerve, cranial nerve VII, or simply CN VII, is a cranial nerve that emerges from the pons of the brainstem, controls the muscles of facial expression, and functions in the conveyance of taste sensations from the anterior two-thirds of the tongue. The nerve typically travels from the pons through the facial canal in the temporal bone and exits the skull at the stylomastoid foramen. It arises from the brainstem from an area posterior to the cranial nerve VI (abducens nerve) and anterior to cranial nerve VIII (vestibulocochlear nerve).

The facial nerve also supplies preganglionic parasympathetic fibers to several head and neck ganglia.

The facial and intermediate nerves can be collectively referred to as the nervus intermediofacialis.
Mary Sidney
Mary Herbert, Countess of Pembroke (née Sidney, 27 October 1561 – 25 September 1621) was among the first Englishwomen to gain notice for her poetry and her literary patronage. By the age of 39, she was listed with her brother Philip Sidney and with Edmund Spenser and William Shakespeare among the notable authors of the day in John Bodenham's verse miscellany Belvidere. Her play Antonius (a translation of Robert Garnier's Marc Antoine) is widely seen as reviving interest in soliloquy based on classical models and as a likely source of Samuel Daniel's closet drama Cleopatra (1594) and of Shakespeare's Antony and Cleopatra (1607). She was also known for translating Petrarch's "Triumph of Death", for the poetry anthology Triumphs, and above all for a lyrical, metrical translation of the Psalms.

Philip Sidney
Sir Philip Sidney (30 November 1554 – 17 October 1586) was an English poet, courtier, scholar and soldier who is remembered as one of the most prominent figures of the Elizabethan age.

His works include a sonnet sequence, Astrophil and Stella, a treatise, The Defence of Poesy (also known as The Defence of Poesie or An Apology for Poetrie) and a pastoral romance, The Countess of Pembroke's Arcadia. He died fighting the Spanish in the Netherlands, age 31, and his funeral procession in London was one of the most lavish ever seen.
Tōgō, Kagoshima
Tōgō (東郷町, Tōgō-chō) was a town located in Satsuma District, Kagoshima Prefecture, Japan.

As of 2003, the town had an estimated population of 5,987 and a density of 74.70 persons per km2. The total area was 80.15 km2.

On October 12, 2004, Tōgō, along with the city of Sendai, the towns of Hiwaki, Iriki and Kedōin, and the villages of Kamikoshiki, Kashima, Sato and Shimokoshiki (all from Satsuma District), was merged to create the city of Satsumasendai.

Kamikoshiki, Kagoshima
Kamikoshiki (上甑村, Kamikoshiki-mura) was a village located in Satsuma District, Kagoshima Prefecture, Japan.

As of 2003, the village had an estimated population of 1,900 and the density of 54.10 persons per km2. The total area was 35.12 km2.

On October 12, 2004, Kamikoshiki, along with the city of Sendai, the towns of Hiwaki, Iriki, Kedōin and Tōgō, and the villages of Kashima, Sato and Shimokoshiki (all from Satsuma District), was merged to create the city of Satsumasendai.
L-1 Visa Reform Act of 2004
The L-1 Visa Reform Act of 2004, referred to more briefly as the L-1 Reform Act, was a part of Title IV of the Consolidated Appropriations Act, 2005 (sometimes also called the Omnibus Appropriations Act of 2005) in the United States that focused on changes to regulations governing L-1 visas. The Consolidated Appropriations Act was signed by George W. Bush, then President of the United States, in early December 2004. Title IV of the Consolidated Appropriations Act also included the H-1B Visa Reform Act of 2004, that focused on H-1B visas.

H-1B Visa Reform Act of 2004
The H-1B Visa Reform Act of 2004 was a part of Title IV of the Consolidated Appropriations Act, 2005 (sometimes also called the Omnibus Appropriations Act of 2005) in the United States that focused on changes to regulations governing H-1B visas. It was a successor to previous legislative changes affecting the H-1B, namely: the Immigration Act of 1990, American Competitiveness and Workforce Improvement Act (ACWIA) of 1998, and the American Competitiveness in the 21st Century Act (AC21) of 2000. The Consolidated Appropriations Act was signed by George W. Bush, then President of the United States, in early December 2004.

Title IV of the Consolidated Appropriations Act had another component pertaining to immigration regulations, namely the L-1 Visa Reform Act of 2004, that pertained to L-1 visas.
2 21 polytope
In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 6-ic semi-regular figure. It is also called the Schläfli polytope.

Its Coxeter symbol is 221, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 2-node sequences.  He also studied its connection with the 27 lines on the cubic surface, which are naturally in correspondence with the vertices of 221.

The rectified 221 is constructed by points at the mid-edges of the 221. The birectified 221 is constructed by points at the triangle face centers of the 221, and is the same as the rectified 122.

These polytopes are a part of family of 39 convex uniform polytopes in 6-dimensions, made of uniform 5-polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: .

Uniform 6-polytope
In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes.

The complete set of convex uniform 6-polytopes has not been determined, but most can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations of rings of the Coxeter-Dynkin diagrams. Each combination of at least one ring on every connected group of nodes in the diagram produces a uniform 6-polytope.

The simplest uniform polypeta are regular polytopes: the 6-simplex {3,3,3,3,3}, the 6-cube (hexeract) {4,3,3,3,3}, and the 6-orthoplex (hexacross) {3,3,3,3,4}.
Faridabad district
Faridabad district is one of the 22 districts of the Indian state of Haryana with Faridabad city being the district headquarters. The District is a Part of Central National Capital Region of Delhi. The Delhi-Mathura-Agra National Highway 44 (Grand Trunk Road) passes through the centre of the district, which occupies an area of 741 square kilometres (286 sq mi) and as of the 2011 census of India had a population of 1,809,733. Haryana government has created a new Faridabad division which would cover the districts – Faridabad, Nuh and Palwal.

As of 2011 it was the second most populous district of Haryana after Gurugram district.

Gurgaon district
Gurgaon district, officially known as Gurugram district, is one of the 22 districts of Haryana in northern India. The city of Gurgaon is the administrative headquarters of the district. The population is 1,514,432. It is one of the southern districts of Haryana. On its north, it is bounded by the district of Jhajjar and the Union Territory of Delhi. Faridabad district lies to its east. To its south lie the districts of Palwal and Nuh. To the west lies Rewari district.
Miranda Cooper
Miranda Cooper (born 1975) is an English singer, songwriter, record producer, dancer and television presenter. Miranda Cooper has worked in the music industry since 1996 when she gained her first recording contract. She worked as a professional dancer for artists such as Dannii Minogue before going into television presenting.

In 1997, Cooper met Brian Higgins, the founder of Kent-based songwriting and production team Xenomania. Miranda Cooper signed a deal with London Records under the alias Moonbaby, releasing the single "Here We Go" to little success, although it was used as the theme tune to the cartoon series Totally Spies! with some lyrics adjusted. Cooper started songwriting with Higgins, eventually finding commercial success and critical acclaim with their productions for Girls Aloud and Sugababes. Cooper has co-written for successful artists such as Alesha Dixon, Gabriella Cilmi and Kylie Minogue.

Brian Higgins (producer)
Brian Thomas Higgins (born November 4, 1966) is a British record producer and songwriter who has written and produced albums and tracks for several successful pop music singers and groups, including Girls Aloud, S Club 7, Sugababes, and the Saturdays, through his Xenomania production team. Miranda Cooper is a key collaborator who has co-writing credits in nearly all Xenomania-created tracks.

His musical style has been described as part electro, part power pop, part basic pop, with elements of new wave, rave and dance found in many of his collaborations.
Kuna Crest Granodiorite
Kuna Crest Granodiorite (also called Granodiorite of Glen Aulin), is found, in Yosemite National Park, United States. The granodiorite forms part of the Tuolumne Intrusive Suite (aka Tuolumne Batholith), one of the four major intrusive suites within the Sierra Nevada. Of the Tuolumne Intrusive Suite, it is the oldest and darkest rock.

Kuna Crest granodiorite forms most of the outer part of the Tuolumne Intrusive Suite, on the edges.

Tuolumne Intrusive Suite
The Tuolumne Intrusive Suite is the youngest and most extensive of the intrusive suites of Yosemite National Park, and also comprises about 1/3 of the park's area. The Suite includes Half Dome Granodiorite, Cathedral Peak Granite, and Kuna Crest Granodiorite.

The largest pluton of the Tuolumne Intrusive Suite is Cathedral Peak Granodiorite, which extends long distances both the north and south of Tuolumne Meadows. The southwestern part of the Tuolumne Intrusive Suite is made up of Half Dome Granodiorite. The youngest, smallest, and most central rock body is of the Johnson Granite Porphyry
2026 Michigan Secretary of State election
The 2026 Michigan Secretary of State election is scheduled to take place on November 3, 2026, to elect the Secretary of State of Michigan. Incumbent Democratic Secretary of State Jocelyn Benson is term-limited and ineligible to seek a third term. Instead, Benson is running for Governor. The major-party nominees will be decided by state party conventions.

2026 Michigan gubernatorial election
The 2026 Michigan gubernatorial election is scheduled to take place on November 3, 2026, to elect the governor of Michigan. The primary elections will take place on August 4, 2026. Incumbent Democratic Governor Gretchen Whitmer is term-limited and cannot seek election to a third term. This will be one of five Democratic-held governorships up for election in 2026 in a state won by Donald Trump in the 2024 presidential election.

Incumbent Democratic Secretary of State Jocelyn Benson and Republican U.S. Representative John James are the frontrunners for their respective nominations. Independent Mike Duggan's bid for governor is expected to make the race more competitive after Democrats' wide margins in the 2018 and 2022 Michigan elections.
Balbino Clemente
Balbino Clemente Núñez (6 September 1896 – 28 March 1941), better known as Balbino, was a Spanish footballer who played as a midfielder. He was part of the first-ever team fielded by Celta de Vigo in 1923. His brother Juanito was also a footballer.

Juanito Clemente
Juan Clemente Núñez, better known as Juanito, was a Spanish footballer who played as a defender. His brother Balbino was also a defender. He was a member of the first-ever team fielded by Celta de Vigo in 1923.
Lodovico of Bulgaria
Lodovico (as attested in Italian sources; Latin Ludovicus; Bulgarian: Людовик, Ljudovik) was a son of Emperor (tsar) Michael Asen III "Šišman" of Bulgaria (1323–1330) and his first wife, Ana, daughter of King Stefan Uroš II Milutin of Serbia by Elizabeth of Hungary. He may have borne a different name before becoming a catechumen and converting to Catholic Christianity. Although he has been variously identified with any of his three known brothers, Ivan Stephen, Šišman, and Michael, but was probably a distinct person. Recent research has established he is definitely distinct from Ivan Stephen.

Michael, Bulgarian despot
Michael (Bulgarian: Михаил, Mihail) was a son of Emperor (tsar) Michael Asen III "Shishman" of Bulgaria (1323–1330), and probably his first wife, Ana, daughter of King Stefan Uroš II Milutin of Serbia by Elizabeth of Hungary. He is attested solely in a fresco in the Church of the Holy Mother of God at Donja Kamenica, now in Serbia, which attests that he held the title of despot at some point after his father's accession in 1323. The various possibilities for the precise identification and chronological placement of the despot Michael carry significant implications for both the political history and social practice of medieval Bulgaria.