hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Logarithmically concave sequence
In mathematics, a sequence a =  (a0, a1, ..., an) of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if ai2 ≥ ai−1ai+1 holds for 0 < i < n .

Remark: some authors (explicitly or not) add two further conditions in the definition of log-concave sequences:

a  is non-negative

a  has no internal zeros; in other words, the support of a is an interval of Z.

These conditions mirror the ones required for log-concave functions.

Sequences that fulfill the three conditions are also called Pólya Frequency sequences of order 2 (PF2 sequences). Refer to chapter 2 of  for a discussion on the two notions. For instance, the sequence (1,1,0,0,1) satisfies the concavity inequalities but not the internal zeros condition.

Examples of log-concave sequences are given by the binomial coefficients along any row of Pascal's triangle and the elementary symmetric means of a finite sequence of real numbers.

Newton's inequalities
In mathematics, the Newton inequalities refer to a set of mathematical inequalities related to mathematical series. These inequalities are named after Isaac Newton who proved the theorem in 1707. Suppose a1, a2, ..., an are non-negative real numbers and let  denote the kth elementary symmetric polynomial in a1, a2, ..., an.  Then the elementary symmetric means, given by

satisfy the inequality

Equality holds if and only if all the numbers ai are equal.

It can be seen that S1 is the arithmetic mean, and Sn is the n-th power of the geometric mean.
America the Beautiful silver bullion coins
The America the Beautiful silver bullion coins comprise a series of silver bullion coins with a face value of a quarter dollar. The coins contain five troy ounces of silver, making them the largest silver bullion coins ever issued by the United States Mint. The design of the coins duplicates exactly—though enlarged—each of the America the Beautiful quarters. They were issued from 2010 to 2021. The coins were available for sale during the year in which their corresponding circulating coin is issued. The coins are distributed by the United States Mint's network of authorized bullion dealers, and may be resold at the discretion of the Director of the National Park Service.

Face value
The face value, sometimes called nominal value, is the value of a coin, bond, stamp or paper money as printed on the coin, stamp or bill itself by the issuing authority.

The face value of coins, stamps, or bill is usually its legal value. However, their market value need not bear any relationship to the face value. For example, some rare coins or stamps may be traded at prices considerably above their face value. Coins may also have a salvage value due to more or less valuable metals that they contain.
Glendower Golf Club
The Glendower Golf Club is an 18-hole golf complex located in Edenvale, Gauteng, South Africa. The course has been the home of the South African Open for eight competitions. Englishman Chris Paisley won his first European Tour title winning the 2018 SA Open. Englishman Graeme Storm won the 2017 SA Open beating Rory McIlroy in a play-off while South African golfer Brandon Stone won the 2016 SA Open.

Edenvale, South Africa
Edenvale is a small city on the East Rand in Gauteng, South Africa. It is part of the Ekurhuleni Metropolitan Municipality. It lies about halfway between the O.R. Tambo International Airport and the Johannesburg city centre and is located 12 km by road from Sandton and about 9 km from the closest Gautrain station.
Teenage Snuff Film
Teenage Snuff Film is the debut solo studio album by Rowland S. Howard, released in 1999. The album was produced by Lindsay Gravina and features Howard's former The Birthday Party bandmate Mick Harvey on drums, organ and guitar, with Brian Hooper of The Beasts of Bourbon on bass guitar. It contains eight original songs, and two cover versions: "White Wedding" by Billy Idol, and "She Cried" (previously performed by The Shangri-Las, Johnny Thunders, and others).

Teenage Snuff Film was produced, mixed and mastered at Birdland Studios in Prahran and Sing Sing Recording Studios in Cremorne. Although not a commercial success upon release, the album would go on to attract a cult following.

The album was reissued as a limited edition double LP in October 2011, with minor track listing changes. Remastered versions of both Howard's solo albums were released by Mute Records in Europe, Fat Possum in America and Bloodlines in Australia on 27 March 2020.

Lindsay Gravina
Lindsay Gravina is an Australian record producer and audio engineer known for his significant contributions to the Australian rock and post-punk music scenes. As the in-house producer at Melbourne's Birdland Studios, Gravina has collaborated with a diverse array of artists, including The Living End, Magic Dirt, Thirsty Merc, Eskimo Joe, Jet, Rowland S. Howard, Kate Miller-Heidke, Cosmic Psychos, Shihad, British India, and Society of Beggars.
WJDM (New Jersey)
WJDM (1530 AM, "Radio Cantico Nuevo") was a radio station licensed to Elizabeth, New Jersey (the seat of Union County, New Jersey), which last broadcast a Spanish language Christian radio format. The station's transmitter was located in nearby Union Township, Union County, New Jersey.

Union Township, Union County, New Jersey
Union Township is a township in Union County, in the U.S. state of New Jersey. In the 18th century, the area that is now Union was then called Connecticut Farms. As of the 2020 United States census, the township's population was 59,728, its highest decennial census count ever and an increase of 3,086 (+5.4%) from the 2010 census count of 56,642, which in turn had reflected an increase of 2,237 (+4.1%) from the 54,405 counted at the 2000 census.
2018 National
The 2018 BOOST National was held from December 11 to 16 at the Conception Bay South Arena in Conception Bay South, Newfoundland and Labrador. This will be the fourth Grand Slam and second major of the 2018–19 curling season.

The first all-Scottish Grand Slam final  saw Ross Paterson of Glasgow beat defending champions Bruce Mouat of Edinburgh 4–3 in an extra end to win his team's first Grand Slam. Rachel Homan beat Kerri Einarson 4–1 in the women's final, to win her ninth slam.

The event was sold out all week, owing to the popularity of the hometown Brad Gushue rink. The total attendance was 23,500 which was a Grand Slam record at the time.

Newfoundland Time Zone
The Newfoundland Time Zone (NT) is a geographic region that keeps time by subtracting 3.5 hours from Coordinated Universal Time (UTC) during standard time, resulting in UTC−03:30; or subtracting 2.5 hours during daylight saving time. The clock time in this zone is based on the mean solar time of the meridian 52 degrees and 30 arcminutes west of the Greenwich Observatory. It is observed solely in the Canadian province of Newfoundland and Labrador. The Newfoundland Time Zone is the only active time zone with a half-hour offset from UTC in the Americas.
Dossa Júnior
Dossa Momad Omar Hassamo Júnior (Greek: Ντόσσα Τζούνιορ; born 28 July 1986), known as Dossa Júnior, is a former professional footballer who played as a central defender.

He spent the better part of his 15-year senior career in the Cypriot First Division, mainly with AEL Limassol. He also competed in Portugal (where he was born), Poland and Turkey.

Born in Portugal, Júnior won 24 caps for Cyprus, making his debut in 2012.

Cypriot Cup
The Cypriot Cup, formally known as the Cypriot Coca-Cola Cup of First and Second Division (Greek: Κύπελλο Κύπρου Coca-Cola A' B' Κατηγορίας) for sponsorship purposes, is a Cypriot knockout football club competition, hosted annually by the Cyprus Football Association.

First held in 1934, it is the second most important competition in Cypriot football, after the Cypriot First Division. Since 2008, it is contested by teams from the first and second division, while teams from the third and fourth division compete in the Cypriot Cup for lower divisions.

The winners of the Cypriot Cup qualify for one of UEFA's European competitions, and a place in the Cypriot Super Cup. APOEL are the most successful team in the competition with 21 titles. AEK Larnaca FC are the current champions, having defeated the previous champions Pafos FC in the 2024–25 Final.
The Pattern of Painful Adventures (radio play)
The Pattern of Painful Adventures is a 90-minute 2008 radio play by Stephen Wakelam on the circumstances surrounding the writing of the play Pericles, Prince of Tyre by William Shakespeare and the sickness of his brother Edmund's child, introduced by a flashback by his daughter Susannah, playwright John Marston and William's secretary Robinson. It links the play to the marriage of Susannah and the birth of her daughter and to the similar themes of daughters, forests, storms, shipwrecks and lost infants from As You Like It, The Winter's Tale, and The Tempest. It is named after The Pattern of Painful Adventures, a main source for Pericles. It was first broadcast on BBC Radio 3 at 8pm on 23 November 2008, directed and produced by Jeremy Mortimer, and was followed in the same slot on 30 November by a repeat of a 2005 radio production of Pericles, with Tom Mannion as Pericles and Benjamin Zephaniah as Gower.

As You Like It
As You Like It is a pastoral comedy by William Shakespeare believed to have been written in 1599 and first published in the First Folio in 1623.

As You Like It follows its heroine Rosalind as she flees persecution in her uncle's court, accompanied by her cousin Celia to find safety and, eventually, love, in the Forest of Arden. In the forest, they encounter a variety of memorable characters, notably the melancholy traveller Jaques, who speaks one of Shakespeare's most famous speeches ("All the world's a stage") and provides a sharp contrast to the other characters in the play, always observing and disputing the hardships of life in the country.

Historically, critical response has varied, with some critics finding the play a work of great merit and some finding it to be of lesser quality than other Shakespearean works.

The play has been adapted for radio, film, and musical theatre.
1886 Maine gubernatorial election
The 1886 Maine gubernatorial election was held on September 13, 1886, in order to elect the Governor of Maine. Republican nominee and former Mayor of Hallowell Joseph R. Bodwell defeated Democratic nominee Clark S. Edwards and Prohibition nominee Aaron Clark.

Hallowell, Maine
Hallowell (/ˈhɔːləwɛl/ HAW-lə-wel) is a city in Kennebec County, Maine, United States. The population was 2,570 at the 2020 census. Popular with tourists, Hallowell is noted for its culture and old architecture. Hallowell is included in the Augusta, Maine, micropolitan New England City and Town Area.
Deneve
Deneve is a surname of French origin, being a variant of the surname Denefe, which originated as a habitational surname for someone from places called Neffe in Belgium. Notable people with the surname include:

Paul Deneve (born 1961), Belgian businessman

Rita Deneve (1944–2018), Belgian singer

Stéphane Denève (born 1971), French conductor

Rita Deneve
Rita Deneve (December 6, 1944, Liedekerke - January 21, 2018, Mechelen) was a Belgian singer. She had a #1 hit in Flanders in 1971 with the song "De allereerste keer" ("The Very First Time"), and competed several times to be the Belgian entrant in the Eurovision Song Contest.
Jacinto (surname)
Jacinto is the surname of:

Andreia Jacinto (born 2002), Portuguese footballer

António Jacinto (1924–1991), Angolan poet and politician

Bayani Jacinto (born 1969), Filipino lawyer and jurist

Emilio Jacinto (1875–1899), Filipino general during the Philippine Revolution

Juan Jacinto (born 1978), Dominican judoka

Manny Jacinto, Filipino-Canadian actor

Ramon Jacinto (born 1945), Filipino businessman, musician, radio TV personality and former government official

RJ Jacinto
Ramón Pereyra Jacinto (born June 3, 1945), best known as RJ Jacinto or the mononym RJ, is a Filipino businessman, musician and radio TV personality. He previously served as Undersecretary for Government Digital Broadcast Television and the Digitization of the Entertainment Industry Sector in Department of Information and Communications Technology. He is also the founder and chairman of Philippine rock-and-roll radio station DZRJ and the Rajah Broadcasting Network.
The Michael Essany Show
The Michael Essany Show is an American television talk show hosted by Michael Essany that aired on local, national, and international television from 1997 to 2004.  Hosted by Valparaiso, Indiana resident Michael Essany, the program was originally broadcast on public access television through TCI Cable before developing a deal with Leeza Gibbons and broadcast for two seasons on E! Entertainment Television. Gibbons, who was the second guest on the cable access show, would later sign Essany to a development deal two years after her appearance on the show. Essany, a teenager when the show began, based the show on The Tonight Show Starring Johnny Carson.

The show, which broadcast out of the Essany family home in Valparaiso, included Essany's mother as the director and makeup artist, as well as his father as the camera operator. Essany's friend Mike Randazzo served as his sidekick on the show.

Tele-Communications Inc.
Tele-Communications, Inc. (TCI) was a cable television provider in the United States, and for most of its history was controlled by Bob Magness and John Malone.

The company was started in 1958 in Bozeman, Montana, as Western Microwave, Inc. and Community Television, Inc., two firms with common ownership. The companies merged in 1968 and operations moved to Denver, taking the name Tele-Communications Inc. It was the largest cable operator in the United States at one time.

After going public in 1970, the company grew rapidly, and became the top cable provider in the United States. After a failed merger attempt with Bell Atlantic in 1994, it was purchased in 1999 by AT&T, whose cable television assets in select markets were later acquired by Charter Communications, Cox Communications, and then Cablevision and Comcast Corporation.
Oregon Tourism Commission
The Oregon Tourism Commission, which does business as Travel Oregon, is a semi-independent agency of the government of Oregon based in the state capital of Salem. The agency is run by a nine-member board appointed by the state's governor, and governs several programs that work to grow the state economy by promoting tourism.

The agency was established in 1995 and became a semi-independent agency in 2003. It is funded by a 1.5% statewide transient lodging tax. Travel Oregon's former executive director's base salary of $365,000 faced scrutiny.

Government of Oregon
The government of the U.S. state of Oregon, as prescribed by the Oregon Constitution, is composed of three government branches: the executive, the legislative, and the judicial. These branches operate in a manner similar to that of the federal government of the United States.

Oregon also has a system of commissions, wherein private citizens are appointed by the governor and confirmed by the Senate; these commissions have the authority to hire and fire the heads of the agencies they govern, and must confirm changes to the permanent rules governing those agencies.
Siege of Luxembourg (1684)
The siege of Luxembourg, in which Louis XIV of France (husband of Maria Theresa of Spain) laid siege to the Spanish-controlled Fortress of Luxembourg from 27 April to 7 June 1684, was the most significant confrontation of the War of the Reunions between France and Spain. The action caused alarm among France's neighbours and resulted in the formation of the League of Augsburg in 1686. In the ensuing war France was forced to give up the duchy, which was returned to the Habsburgs by the Treaty of Ryswick in 1697.

Grand Alliance (League of Augsburg)
The Grand Alliance  was signed on 20 December 1689 by William III, King of England and Scotland, and  Leopold I, Holy Roman Emperor. A coalition between the Dutch Republic, England, and the Habsburg Monarchy, its primary purpose was to oppose the expansionist policies of Louis XIV of France.

With the subsequent additions of Spain and Savoy, the Grand Alliance fought the 1688 to 1697 Nine Years' War against France that ended with the Peace of Ryswick. It was reformed by the 1701 Treaty of The Hague prior to the War of the Spanish Succession, and dissolved in 1713 following the Peace of Utrecht.
Vélodrome Caisse Populaire de Dieppe
The Vélodrome Caisse Populaire de Dieppe was a 250-meter bicycle racing track located in Dieppe, New Brunswick, Canada, which opened in July 2001. It was the National Cycling Centre for Atlantic Canada. The track was found to be beyond repair when inspected in spring 2018 and it was subsequently demolished.

In 2006 and 2007, it was the host for the Tim Hortons National Track Championships.

Atlantic Canada
Atlantic Canada, also called the Atlantic provinces (French: provinces de l'Atlantique), is the region of Eastern Canada comprising four provinces: New Brunswick, Newfoundland and Labrador, Nova Scotia, and Prince Edward Island. As of 2021, the landmass of the four Atlantic provinces was approximately 488,000 km2 (188,000 sq mi), and had a population of over 2.4 million people. The term Atlantic Canada was popularized following the admission of Newfoundland as a Canadian province in 1949. The province of Newfoundland and Labrador is not included in the Maritimes, another significant regional term, but is included in Atlantic Canada.
Dixon Arroyo (weightlifter)
Dixon Bladimir Arroyo Valdez (born 12 August 1997) is an Ecuadorian weightlifter. He won the gold medal in men's +109 kg event at the 2022 South American Games held in Asunción, Paraguay. He is also a two-time gold medalist at the 2022 Bolivarian Games held in Valledupar, Colombia.

In 2019, Arroyo competed in the men's 109 kg event at the Pan American Games held in Lima, Peru. In 2021, he competed in the men's +109 kg event at the World Weightlifting Championships held in Tashkent, Uzbekistan. Arroyo won the bronze medal in the men's +102 kg event at the 2023 Pan American Games held in Santiago, Chile.

He won the bronze medal in his event at the 2024 Bolivarian Games held in Ayacucho, Peru.

Weightlifting at the 2023 Pan American Games – Men's +102 kg
The men's +102 kg competition of the weightlifting events at the 2023 Pan American Games in Santiago, Chile, was held on 24 October at the Gimnasio Chimkowe.

Each lifter performed in both the snatch and clean and jerk lifts, with the final score being the sum of the lifter's best result in each. The athlete received three attempts in each of the two lifts; the score for the lift was the heaviest weight successfully lifted. This weightlifting event was limited to competitors with a minimum of 102 kilograms of body mass.
Madrid Ladies Masters
The Madrid Ladies Masters was a professional golf tournament in Spain on the Ladies European Tour.  The 54-hole event was held at the par-73 Casino Club de Golf Retamares in early October and played for three years, from 2007 to 2009.

Ladies European Tour
The Ladies European Tour is a professional golf tour for women which was founded in 1978. Most of the players on the tour are European, with members from more than 40 countries internationally. Despite its name, the tour also has tournaments in Africa, Asia, North America and Oceania.

The organization is based at Buckinghamshire Golf Club near London in England. Like many British-based sports organisations it is a company limited by guarantee, a legal structure which enables it to focus on maximising returns to its members through prize money, rather than on making profits for investors. The tour is run by a board of directors and a Players' Council.
Gherla Synagogue
The Gherla Synagogue is a synagogue, located at 46 Crisan Street, in Gherla (Hungarian: Szamosújvár) in the Cluj County of northern Romania. Designed in Moorish Revival and Romanesque Revival styles, the synagogue was completed in 1903 and operated as a synagogue until c. 1970s. The building was in danger of collapse in 2012 when fundraising was commenced to complete structural repairs and the building has since been handed to municipal authorities for restoration and renovation as a cultural center.

Cultural center
A cultural center or cultural centre is an organization, building or complex that promotes culture and arts. Cultural centers can be neighborhood community arts organizations, private facilities, government-sponsored, or activist-run.
Adventures with Purpose
Adventures with Purpose is an American group of professional scuba divers who use underwater sonar imaging equipment and bathymetry mapping technology to locate missing persons and their vehicles in waterbodies. Originally focused on clean-up, their channel's focus was turned to missing persons cold cases after their accidental discovery of a missing person. The group documents their efforts on their YouTube channel.

Clean-up (environment)
A cleanup or clean-up is a form of environmental volunteering where a group of people get together to pick-up and dispose of litter in a designated location. Cleanups can take place on a street, in a neighborhood, at a park, on a water stream, or other public spaces. Cleanup events are often volunteer run. The cleanup volunteers make sure the waste picked-up is disposed of in its appropriate place. Cleanup events are often community-centered and led.

During the COVID-19 pandemic litter picking participation has greatly increased in the UK.   There are a vast range of reasons that people take part in litter picking activities. These include: clearing up unsightly areas; protecting wildlife; keeping people safe, connecting with nature, finding valuables, being part of a community, mental and physical health benefits and acting to protect the environment.
Material Thangz
Material Thangz is the second album by The Deele. Released on June 4, 1985 on the SOLAR Records label, which was distributed by Elektra/Asylum Records, a division of Warner Bros. Records. It was produced by L.A. Reid. It's notable for the composition "Sweet November", composed by then-member Kenneth "Babyface" Edmonds, who also sung lead vocals on the composition. The song was later covered by R&B group Troop, who turned the song into a #1 R&B hit in 1992.

SOLAR Records
SOLAR (acronym for Sound of Los Angeles Records)  was an American record label founded in 1978 by Dick Griffey, reconstituted out of Soul Train Records only three years after it was founded with Soul Train television show host and creator Don Cornelius.
1972 Washington Star International – Singles
The 1972 Washington Star International – Singles was an event of the 1972 Washington Star International tennis tournament and was played in Washington, D.C., United States from July 17 through July 23, 1972. The draw comprised 64 players. Ken Rosewall was the defending champion but did not compete in this edition. Tony Roche won the singles title, defeating Marty Riessen in the final, 3–6, 7–6, 6–4.

Tony Roche
Anthony Dalton Roche AO MBE (born 17 May 1945), professionally known as Tony Roche is an Australian former professional tennis player.

A native of Tarcutta, Roche played junior tennis in the New South Wales regional city of Wagga Wagga. He won one Grand Slam singles title, the 1966 French Open at Roland Garros, and 15 Grand Slam doubles titles (12 of these with John Newcombe).

In 1968, Roche won the WCT/NTL combined professional championship in men's singles in the final event of the season at Madison Square Garden. He was ranked World No. 2 by Lance Tingay of The Daily Telegraph in 1969.

He won the U.S. Pro Championships in 1970 at Longwood in Boston. Roche won the New South Wales Open twice, in 1969 and 1976. He won a key Davis Cup singles match in 1977.

He also coached multi-Grand Slam winning world No. 1s Ivan Lendl, Patrick Rafter, Roger Federer and Lleyton Hewitt.