hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Poussin proof
In number theory, a branch of mathematics, the Poussin proof is the proof of an identity related to the fractional part of a ratio.

In 1838, Peter Gustav Lejeune Dirichlet proved an approximate formula for the average number of divisors of all the numbers from 1 to n:

where d represents the divisor function, and γ represents the Euler-Mascheroni constant.

In 1898, Charles Jean de la Vallée-Poussin proved that if a large number n is divided by all the primes up to n, then the average fraction by which the quotient falls short of the next whole number is γ:

where {x} represents the fractional part of x, and π represents the prime-counting function.
For example, if we divide 29 by 2, we get 14.5, which falls short of 15 by 0.5.

Charles Jean de la Vallée Poussin
Charles-Jean Étienne Gustave Nicolas, baron de la Vallée Poussin (French pronunciation: [ʃaʁl ʒɑ̃ etjɛn ɡystav nikɔla baʁɔ̃ də la vale pusɛ̃]; 14 August 1866 – 2 March 1962) was a Belgian mathematician. He is best known for proving the prime number theorem.

The King of Belgium ennobled him with the title of baron.
North Fork Creek
North Fork Creek is a tributary of Redbank Creek in northwest Pennsylvania in the United States. It is formed by the confluence of Muddy Run and Williams Run in Polk Township, Jefferson County.

North Fork Creek and Sandy Lick Creek join to form Redbank Creek in the borough of Brookville, Jefferson County.

Jefferson County, Pennsylvania
Jefferson County is a county in the Commonwealth of Pennsylvania. As of the 2020 census, the population was 44,492. Its county seat is Brookville. The county was established on March 26, 1804, from part of Lycoming County and later organized in 1830. It is named after President Thomas Jefferson. It is home to Punxsutawney Phil, the most famous groundhog that predicts when spring will come every February 2 on Groundhog Day. The county is part of the North Central region of the commonwealth.
The Last Rose of Summer (1920 film)
The Last Rose of Summer is a British silent motion picture of 1920 directed by Albert Ward, produced by G. B. Samuelson, and starring Owen Nares and Daisy Burrell. A drama, it was written by Roland Pertwee, based on a novel by Hugh Conway.

Roland Pertwee
Roland Pertwee (15 May 1885 – 26 April 1963) was an English playwright, film and television screenwriter, director and actor. He was the father of Doctor Who actor Jon Pertwee and playwright and screenwriter Michael Pertwee. He was also the second cousin of actor Bill Pertwee and grandfather of actors Sean Pertwee and Dariel Pertwee.

From the 1910s to 1950s, he worked as a writer on many British films, providing either the basic story or full screenplay. He was one of many writers who worked on the script of A Yank at Oxford starring Robert Taylor and Vivien Leigh, the film in which his son Jon made his screen debut, and on Caravan.

While he seemingly preferred writing, he acted in ten films (1915–45) and directed Breach of Promise (1942), which he also wrote.
The Garden of Evening Mists (film)
The Garden of Evening Mists (Chinese: 夕霧花園) is a 2019 Malaysian English-language historical drama film directed by Tom Lin Shu-yu from the screenplay of Richard Smith and adapted from Tan Twan Eng's 2012 novel of same name. A woman, still haunted by her experiences in a Japanese internment camp as a child, travels to Cameron Highlands during the Malayan Emergency and becomes the apprentice of a mysterious Japanese gardener. It stars Lee Sin-je, Sylvia Chang and Hiroshi Abe.

A co-production between Malaysia's Astro Shaw and HBO Asia, the film was filmed on location in Malaysia. It premiered in 2019 in South Korea, Taiwan and Hong Kong, 16 January 2020 in Malaysia, Brunei and Singapore, and 24 July 2021 in Japan.

The film received generally positive reviews. It received nine nominations at the 56th Golden Horse Awards, winning for Best Makeup and Costume Design, won Best Film at the 2020 Asian Academy Creative Awards and won three awards at the 2021 Malaysia Film Festival.

Tom Lin Shu-yu
Thomas Lin Shu-yu (Chinese: 林書宇; born 1976) is a Taiwanese director and screenwriter. After the critical success of his first two features, Winds of September (2008), for which he won  Best Original Screenplay at the 45th Golden Horse Awards, and Starry Starry Night (2011), he has been considered a leading filmmaker of his generation. His films often deal with autobiographical elements.
Massif des Cerces
Massif des Cerces (French pronunciation: [masif de sɛʁs]) is a region of the French Alps on the Franco-Italian border. On the French side it lies in the departments of Hautes-Alpes and Savoie.

The massif consists of smaller mountain chains including Mont Thabor as well as those of the Grand Galibier, Mont Chaberton and the Rois Mages. It is bordered by the massif de la Vanoise to the north, the massif du Mont-Cenis to the north-east, the  Alpes Cottiennes to the east, the massif du Queyras and Écrins to the south and the massif d'Arvan-Villards to the west.

The northernmost end of the range is bordered by the Arc river to the north in the Maurienne valley, and the Guisane river to the south.

Ibexes populate the slopes of the massif. Wolves have also been spotted on the massif.

Savoie
Savoie (French pronunciation: [savwa]; Arpitan: Savouè or Savouè-d'Avâl, lit. 'Lower Savoy'; Italian: Savoia; Occitan: Savòia; English: Savoy, /səˈvɔɪ/) is a department in the region of Auvergne-Rhône-Alpes, Southeastern France. Located in the French Alps, its prefecture is Chambéry. In 2019, Savoie had a population of 436,434.

Together with Haute-Savoie, it is one of the two departments of the historical region of Savoy; the Duchy of Savoy was annexed by France in 1860, following the signing of the Treaty of Turin. The area is known for its numerous ski resorts and contribution to French cuisine, with culinary specialities such as fondue savoyarde, tartiflette, génépi, as well as various sorts of saucisson.
The Refreshments (American band)
The Refreshments were an alternative rock band from Tempe, Arizona. The band is best known for the single "Banditos" from their 1996 breakthrough album Fizzy Fuzzy Big & Buzzy, and also for "Yahoos and Triangles", the theme song to the long-running animated series King of the Hill. The Refreshments changed their name in 1998 to Roger Clyne and the Peacemakers with Roger Clyne and P.H. Naffah continuing to tour and play Refreshments songs.

Banditos (song)
"Banditos" is a song by American band The Refreshments from their album Fizzy Fuzzy Big & Buzzy. The song is the band's best-known hit.

A music video was produced to accompany the single, in which the members of the band robbed a bank in Mexico and fled in lead singer Roger Clyne's Toyota Land Cruiser. They eventually give the police the slip through the use of a ridiculous disguise. The video was directed by David Dobkin.
Świękity
Świękity (Polish: [ɕfjɛŋˈkʲitɨ]) is a village in the administrative district of Gmina Lubomino, within Lidzbark County, Warmian-Masurian Voivodeship, in northern Poland. It is located 2 kilometers north of Ełdyty Wielkie.

Gmina Lubomino
Gmina Lubomino is a rural gmina (administrative district) in Lidzbark County, Warmian-Masurian Voivodeship, in northern Poland. Its seat is the village of Lubomino, which lies approximately 24 kilometres (15 mi) west of Lidzbark Warmiński and 36 km (22 mi) north-west of the regional capital Olsztyn.

The gmina covers an area of 149.56 square kilometres (57.7 sq mi), and as of 2006 its total population is 3,717.
AFC Telford United
AFC Telford United is a football club based in Telford, Shropshire, England. The club was formed in 2004 after the original Telford United, founded in 1872, folded due to financial problems. They are currently members of the National League North and play at the New Bucks Head in Wellington, part of the new town of Telford. The club's colours are white and black.

Wellington, Shropshire
Wellington is a market town and a civil parish in the borough of Telford and Wrekin, Shropshire, England. It is situated 3 miles (4.8 km) north-west of Telford and 12 miles (19 km) east of Shrewsbury, near the western terminus of the M54 motorway. The summit of The Wrekin lies 3 miles to the south-west. Wellington’s population was 25,554 in the 2011 census.
T-vertices
T-vertices is a term used in computer graphics to describe a problem that can occur during mesh refinement or mesh simplification.  The most common case occurs in naive implementations of continuous level of detail, where a finer-level mesh is "sewn" together with a coarser-level mesh by simply aligning the finer vertices on the edges of the coarse polygons.  The result is a continuous mesh, however due to the nature of the z-buffer and certain lighting algorithms such as Gouraud shading, visual artifacts can often be detected.

Some modeling algorithms such as subdivision surfaces will fail when a model contains T-vertices.

Digital artifact
Digital artifact in information science, is any undesired or unintended alteration in data introduced in a digital process by an involved technique and/or technology.

Digital artifact can be of any content types including text, audio, video, image, animation or a combination.
Shavertown, New York
Shavertown was a hamlet in Delaware County, New York. It was submerged by the construction of the Pepacton Reservoir in 1954. Shavertown had a few hundred inhabitants, mostly reliant on the town's timber industry. Acid factories in Shavertown produced wood alcohol and other chemicals. The Delaware and Eastern Railroad ran through the town.

Pepacton Reservoir
The Pepacton Reservoir is a reservoir in the New York City water supply system located in Delaware County, New York.  Lying in the Catskill Mountains on the East Branch of the Delaware River, it was formed by the construction of Downsville Dam, and impounds over one-quarter of the tributary's flow.
National Register of Historic Places listings in Stanislaus County, California
This is a list of the National Register of Historic Places listings in Stanislaus County, California.

This is intended to be a complete list of the properties and districts on the National Register of Historic Places in Stanislaus County, California, United States. Latitude and longitude coordinates are provided for many National Register properties and districts; these locations may be seen together in a Google map.

There are 24 properties and districts listed on the National Register in the county, including 1 National Historic Landmark.

This National Park Service list is complete through NPS recent listings posted March 21, 2025.

Stanislaus County, California
Stanislaus County (/ˈstænɪslɔː(s)/ ⓘ STAN-iss-law(ss); Spanish: Condado de Estanislao) is a county located in the San Joaquin Valley of the U.S. state of California. As of 2023, its estimated population  is 564,404. The county seat is Modesto.

Stanislaus County makes up the Modesto metropolitan statistical area. The county is located just east of the San Francisco Bay Area and serves as a bedroom community for those who work in the eastern part of the Bay Area.
Philip Taft Labor History Book Award
The Philip Taft Labor History Book Award is sponsored by the Cornell University School of Industrial and Labor Relations in cooperation with the Labor and Working-Class History Association for books relating to labor history of the United States. Labor history is considered "in a broad sense to include the history of workers (free and unfree, organized and unorganized), their institutions, and their workplaces, as well as the broader historical trends that have shaped working-class life, including but not limited to: immigration, slavery, community, the state, race, gender, and ethnicity." The award is named after the noted labor historian Philip Taft (1902–1976).

Alice Kessler-Harris
Alice Kessler-Harris (June 2, 1941, Leicester) is R. Gordon Hoxie Professor Emerita of American History at Columbia University, and former president of the Organization of American Historians, and specialist in the American labor and comparative and interdisciplinary exploration of women and gender.
Mathematicians of the African Diaspora
Mathematicians of the African Diaspora (MAD) is a website created in 1997 by Scott W. Williams of the University at Buffalo, SUNY dedicated to promoting and highlighting the contributions of members of the African diaspora to mathematics, especially contributions to current mathematical research.

Scott W. Williams
Scott Williams (born April 22, 1943, in Staten Island, New York) is a professor of mathematics at the University at Buffalo, SUNY. He was recognized by Mathematically Gifted & Black as a Black History Month 2017 Honoree.
Borgofranco d'Ivrea
Borgofranco d'Ivrea is a comune (municipality) in the Metropolitan City of Turin in the Italian region Piedmont, about 50 kilometres (31 mi) north of Turin.

Borgofranco d'Ivrea borders the following municipalities: Settimo Vittone, Andrate, Nomaglio, Brosso, Quassolo, Chiaverano, Montalto Dora, and Lessolo.

The "Balmetti"

Characteristic of this area of Canavese, these are natural cavities in the mountain, adapted over the centuries by the inhabitants to cellars and food storage, where the temperature is constant thanks to the circulation of air caused by complex natural geothermal phenomena. The term balmetti (balmit in the Canavese variant of the Piedmontese language) derives from balma, meaning shelter under rock, cave.

Metropolitan City of Turin
The Metropolitan City of Turin (Italian: città metropolitana di Torino; Piedmontese: sità metropolitan-a 'd Turin) is a metropolitan city in the Piedmont region of Italy. Its capital is the city of Turin. It replaced the province of Turin and comprises 312 comuni (sg.: comune). It was created by the reform of local authorities (Law 142/1990) and established by the Law 56/2014. It has been officially operating since 1 January 2015. With a population of 2,204,276, it is the 4th most populous metropolitan city in Italy.

The Metropolitan City of Turin is headed by the Metropolitan Mayor (sindaco metropolitano) and by the Metropolitan Council (consiglio metropolitano). Since 27 October 2021, Stefano Lo Russo has served as the mayor of the capital city, succeeding Chiara Appendino. The largest metropolitan city of Italy, it is the only one to border a foreign state, France.
Abby Dernburg
Abby F. Dernburg is a professor of Cell and Developmental Biology at the University of California, Berkeley, an Investigator of the Howard Hughes Medical Institute, a Faculty Senior Scientist at Lawrence Berkeley National Laboratory and one of two professors at UC Berkeley who was recognized into The National Academy of Sciences..

Abby F. Dernburg was elected to the National Academy of Sciences, alongside Professor Ramamoorthy Ramesh, bringing the total number of active members to 2,617.

Larry Sandler Memorial Award
The Larry Sandler Memorial Award is a prestigious international award given for research in the Drosophila community.  The award is given for the best dissertation of the preceding year, and is given at the annual Drosophila Research Conference.  Awardees may be nominated only by their graduate advisors.

The awardees give the Larry Sandler Memorial Lecture at the annual Drosophila Research Conference.  The award honors Dr. Larry Sandler.
Usman Nurmagomedov
Usman Magomednabiyevich Nurmagomedov (born 17 April 1998) is a Russian professional mixed martial artist. He currently competes in the Lightweight division of the Professional Fighters League (PFL), where he is the current and inaugural PFL Lightweight World Champion. He formerly competed in Bellator MMA, where he was the last Lightweight World Champion. He has also previously competed in the UAE Warriors and Eagle Fighting Championship (then Gorilla Fighting Championship). As of January 27, 2026, he is #1 in the PFL men's pound-for-pound rankings.

He is the younger brother of UFC fighter Umar Nurmagomedov and a cousin of former UFC Lightweight Champion Khabib Nurmagomedov.

Eagle Fighting Championship
Eagle Fighting Championship (EFC), commonly referred to as Eagle FC, is a Russian mixed martial arts promotion company established in 2020 by former UFC Lightweight Champion Khabib Nurmagomedov. It was renamed to Eagle Fighting Championship (EFC) after Nurmagomedov bought Gorilla Fighting Championship (GFC) for $1 million.
Inka Raqay, Bolivia
Inka Raqay (Quechua Inka Inca, raqay ruin, a demolished building; shed, storehouse or dormitory for the laborers of a farm; a generally old building without roof, only with walls) is an  archaeological site in Bolivia. It is located in the Cochabamba Department, Quillacollo Province, Sipe Sipe Municipality, near the community of Linku.

Inka Raqay was declared a National Archaeological Monument by Law No. 3479 of September 22, 2006. By Law No. 295 of September 28, 2012, it was declared a Historical and Cultural Heritage of the Bolivian state. It is one of the historical places where Willkakuti, the Andean-Amazonic New Year, is celebrated.

Sipe Sipe Municipality
Sipe Sipe Municipality is the second municipal section of the Quillacollo Province in the Cochabamba Department, Bolivia. Its seat is Sipe Sipe. At the time of census 2001 the municipality had 31,337 inhabitants.
Epididymis
The epididymis (/ɛpɪˈdɪdɪmɪs/; pl.: epididymides /ɛpɪdɪˈdɪmədiːz/ or /ɛpɪˈdɪdəmɪdiːz/) is an elongated tubular genital organ attached to the posterior side of each one of the two male reproductive glands, the testicles. It is a single, narrow, tightly coiled tube in adult humans, 6 to 7 centimetres (2.4 to 2.8 in) in length; uncoiled the tube would be approximately 6 m (20 feet) long. It connects the testicle to the vas deferens in the male reproductive system. The epididymis serves as an interconnection between the multiple efferent ducts at the rear of a testicle (proximally), and the vas deferens (distally). Its primary function is the storage, maturation and transport of sperm cells.

Reproductive system
The reproductive system of an organism, also known as the genital system, is the biological system made up of all the anatomical organs involved in sexual reproduction.  Many non-living substances such as fluids, hormones, and pheromones are also important accessories to the reproductive system. Unlike most organ systems, the sexes of differentiated species often have significant differences. These differences allow for a combination of genetic material between two individuals, which allows for the possibility of greater genetic fitness of the offspring.
West Virginia Route 480
West Virginia Route 480 (WV 480) is a 5.64-mile-long (9.08 km) state highway in the U.S. state of West Virginia.  Known for most of its length as Kearneysville Pike, the highway extends from WV 115 in Kearneysville north to the Maryland state line at the Potomac River in Shepherdstown, from where the highway continues as Maryland Route 34 (MD 34). The route is one of the main north–south highways of northern Jefferson County and passes through the campus of Shepherd University. WV 480 was originally established in the early 1920s as West Virginia Route 48. The highway was paved in the mid-1920s, which included a different routing through Shepherdstown. WV 48's present routing through the town was established in the late 1930s when the first James Rumsey Bridge was completed; that bridge was replaced with the current bridge in the mid-2000s. WV 48 was renumbered to WV 480 in the mid-1970s after U.S. Route 48 (US 48) was established in West Virginia and Maryland.

Maryland Route 34
Maryland Route 34 (MD 34) is a state highway in the U.S. state of Maryland.  Known for most of its length as Shepherdstown Pike, the state highway begins at the West Virginia state line at the Potomac River, where the highway continues south as West Virginia Route 480 (WV 480) through Shepherdstown.  The state highway runs 9.95 miles (16.01 km) east to U.S. Route 40 Alternate (US 40 Alternate) in Boonsboro.  MD 34 is the main east–west highway of southern Washington County, connecting Shepherdstown and Boonsboro with Sharpsburg and Keedysville.  The state highway, which was preceded by the Boonsboro and Sharpstown Turnpike, was constructed as a modern highway in the late 1910s and early 1920s.  MD 34's bypass of Keedysville opened around 1960.  The western end of the state highway has had three bridges.  A 19th-century bridge was destroyed in a 1936 flood and replaced by the James Rumsey Bridge in 1939.  The present bridge, also named for James Rumsey, opened in 2005.
Argegno
Argegno (Comasco: Argegn) is a comune (municipality) in the Province of Como in the Italian region Lombardy, located about 50 kilometres (31 mi) north of Milan and about 15 kilometres (9 mi) north of Como. As of March 2024, it had a population of 679 and an area of 4.3 square kilometres (1.7 mi2).

The local economy is heavily dependent upon tourism and the service industry.  the official tourist website for Argegno is www.visitargegno.com.

A cable car can transport people up to the nearby village of Pigra.

Argegno is situated on an inlet in the lake, and is built alongside the River Telo which flows into the lake, the discharge of which is heavily dependent upon the season.

Argegno borders the following municipalities: Brienno, Colonno, Dizzasco, Lezzeno, Nesso, Pigra, Schignano. It is situated between the villages of Menaggio and Cernobbio.

Province of Como
The province of Como (Italian: provincia di Como; Comasco: pruincia de Comm) is a province in the Lombardy region of Italy. It borders the Swiss cantons of Ticino and Grigioni to the north, the Italian provinces of Sondrio and Lecco to the East, the province of Monza and Brianza to the south and the province of Varese to the West. The city of Como is its capital—other large towns, with more than 10,000 inhabitants, include Cantù, Erba, Mariano Comense and Olgiate Comasco. Campione d'Italia also belongs to the province and is enclaved in the Swiss canton of Ticino. The Lugano Prealps cover the territory of the province, and the most important body of water is the glacial Lake Como.
Salah Farah
Salah Abdow Farah was a Kenyan teacher who lost his life after defending his fellow passengers on a bus. He survived the December 2015 attack but died on January 18, 2016, from complications after a surgery to remove a bullet lodged in his hip. His story of courage inspired the short film Watu Wote by Katja Benrath. At the time of his death, Farah was the Deputy Headteacher of Mandera Township Primary School.

Watu Wote
Watu Wote: All of Us, or simply Watu Wote is a 2017 Kenyan-German, live-action short film directed by Katja Benrath, as her graduation project at Hamburg Media School. The film is based on a December 2015 bus attack by Al-Shabaab in Mandera, Kenya. The film received critical acclaim, winning a Student Academy Award for Narrative, and received an Academy Award nomination for Academy Award for Best Live Action Short Film at the 90th Academy Awards. Production faced difficulties when the crew's camera was stolen before filming had begun.