OpenLLM-France/wikimedia huggingface dataset:
# Road coloring theorem

In graph theory the road coloring theorem, known previously as the road coloring conjecture, deals with synchronized instructions. The issue involves whether by using such instructions, one can reach or locate an object or destination from any other point within a network (which might be a representation of city streets or a maze). In the real world, this phenomenon would be as if you called a friend to ask for directions to his house, and he gave you a set of directions that worked no matter where you started from. This theorem also has implications in symbolic dynamics.
The theorem was first conjectured by Roy Adler and Benjamin Weiss. It was proved by Avraham Trahtman.

## Example and intuition

The image to the right shows a directed graph on eight vertices in which each vertex has out-degree 2. (Each vertex in this case also has in-degree 2, but that is not necessary for a synchronizing coloring to exist.) The edges of this graph have been colored red and blue to create a synchronizing coloring.
For example, consider the vertex marked in yellow. No matter where in the graph you start, if you traverse all nine edges in the walk "blue-red-red—blue-red-red—blue-red-red", you will end up at the yellow vertex. Similarly, if you traverse all nine edges in the walk "blue-blue-red—blue-blue-red—blue-blue-red", you will always end up at the vertex marked in green, no matter where you started.
The road coloring theorem states that for a certain category of directed graphs, it is always possible to create such a coloring.

### Mathematical description

Let G be a finite, strongly connected, directed graph where all the vertices have the same out-degree k. Let A be the alphabet containing the letters 1, ..., k. A synchronizing coloring (also known as a collapsible coloring) in G is a labeling of the edges in G with letters from A such that (1) each vertex has exactly one outgoing edge with a given label and (2) for every vertex v in the graph, there exists a word w over A such that all paths in G corresponding to w terminate at v.
The terminology synchronizing coloring is due to the relation between this notion and that of a synchronizing word in finite automata theory.
For such a coloring to exist at all, it is necessary that G be aperiodic. The road coloring theorem states that aperiodicity is also sufficient for such a coloring to exist. Therefore, the road coloring problem can be stated briefly as:
    Every finite strongly connected aperiodic graph of uniform out-degree has a synchronizing coloring.

## Previous partial results

Previous partial or special-case results include the following:
* If G is a finite strongly connected aperiodic directed graph with no multiple edges, and G contains a simple cycle of prime length which is a proper subset of G, then G has a synchronizing coloring.
* If G is a finite strongly connected aperiodic directed graph (multiple edges allowed) and every vertex has the same in-degree and out-degree k, then G has a synchronizing coloring.
# Jonathan Jesus

Jonathan de Jesus Alves (born 27 May 2004), known as Jonathan Jesus or just Jonathan, is a Brazilian professional footballer who plays as a centre-back for Cruzeiro.

## Career
### Ceará

Born in São Vicente, São Paulo, Jonathan joined Ceará's youth sides in 2021 for a trial period, after being indicated by his uncle. After progressing through the youth setup, he made his first team debut on 8 June 2023, coming on as a late substitute for Zé Ricardo in a 3–0 Série B away win over Atlético Goianiense.
After being mainly a member of the under-20 squad, Jonathan was definitely promoted to the first team after the 2024 Copa São Paulo de Futebol Júnior, and became a regular starter in the first rounds of the 2024 Série B.

### Cruzeiro

On 14 June 2024, Ceará announced the transfer of Jonathan to Série A side Cruzeiro, after the club paid a R$ 8.25 million fee for 90% of his economic rights.

## Personal life

Jonathan's uncle Heleno was also a footballer. A defensive midfielder, he too represented Ceará.

## Career statistics

    As of 16 June 2024
Appearances and goals by club, season and competition :
| Club | Season | League | League | League | State League | State League | National Cup | National Cup | Continental | Continental | Other | Other | Total | Total |
| Club | Season | Division | Apps | Goals | Apps | Goals | Apps | Goals | Apps | Goals | Apps | Goals | Apps | Goals |
| Ceará | 2023 | Série B | 2 | 0 | — | — | 0 | 0 | — | — | — | — | 2 | 0 |
| Ceará | 2024 | Série B | 6 | 0 | 1 | 0 | 1 | 0 | — | — | 5 | 0 | 13 | 0 |
| Ceará | Total | Total | 8 | 0 | 1 | 0 | 1 | 0 | — | — | 5 | 0 | 15 | 0 |
| Cruzeiro | 2024 | Série A | 0 | 0 | — | — | — | — | 0 | 0 | — | — | 0 | 0 |
| Career total | Career total | Career total | 8 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 5 | 0 | 15 | 0 |
* ↑ Appearance(s) in Copa do Nordeste
# Scotland Manufacturing

Scotland Manufacturing, Inc. is a full-service stamping company and manufacturer of deep drawn metal stampings, progressive stamping (die manufacturing) and value-added assembly solutions. Scotland has presses running from 110 to 1,000 tons and the company provides refrigerant, compressor housing, filter shells and other deep-drawn stampings from the industrial, automotive and heavy truck industries.
Scotland Manufacturing is ISO 9001 certified and produces stampings from a variety of metals including cold rolled steel, electro tin plate and stainless steel. Their facility has more than 50,000 square feet (4,600 m$^2$) of manufacturing space.

## History

Scotland Manufacturing, located in Laurinburg, North Carolina, was founded in 1979 as a supplier to the filter industry. Named for Scotland County located in Southeastern North Carolina, the company is situated between Charlotte, the state’s largest city and Wilmington, the state’s largest port. From an $8-million business in 2001, Scotland Manufacturing has grown to a $20-million business in 2009.
Scotland Manufacturing is part of The Reserve Group (TRG), a private equity group based in Akron, Ohio. The Reserve Group’s philosophy is to provide strategic business support and investment capital, allowing its portfolio of companies to remain competitive in the marketplace. Scotland Manufacturing is the oldest member company in the TRG portfolio.

## Products

For the automotive industry, Scotland Manufacturing creates door panels for the high-end automotive OEM, clutch plates, transmission plates, brackets and filter cans. Additionally, the company uses a variety of metals, from flat steel to stainless steel, to produce components for the construction industry such as chimney caps, and brackets and braces for pre-fabricated buildings. Scotland also creates railway brake intercasings, rail shoes, rail pads and rail friction products as well as fire extinguishers and other components for the aerospace industry.
Scotland Manufacturing offers shell supply in either low cost cold rolled steel or stronger, more corrosion-resistant tin plate steel. Deep drawn stampings are manufactured in diameters from 2 5/8 inches to 5 inches wide and up to 12 inches tall. The company’s production capacity offers low, medium and high volume capabilities on presses ranging from 110 to 1,000 tons. Stampings are manufactured in steel, stainless steel, pre-coated steel and aluminum.
Scotland Manufacturing products are used to create filters, Mack trucks, John Deere Tractors, Dodge pick-up trucks, chimney caps, fire extinguishers, railroad car brakes, end caps and retainer plates. The production facility offers welding, assembly, and pressure testing.

## Associations

Scotland Manufacturing is a member of the following associations: Filter Manufacturers Council and American Filtration & Separations Society.
In addition, Scotland Manufacturing has partnered with Richmond Community College of Hamlet, North Carolina for an Industrial Training Program.
# Hida-Hosoe Station

Hida-Hosoe Station (飛騨細江駅, Hida-Hosoe-eki) is a railway station on the Takayama Main Line in the city of Hida, Gifu Prefecture, Japan, operated by Central Japan Railway Company (JR Central).

## Lines

Hida-Hosoe Station is served by the JR Central Takayama Main Line, and is located 156.0 kilometers from the official starting point of the line at Gifu.

## Station layout

Hida-Hosoe Station has two opposed ground-level side platforms connected by a footbridge. The station is unattended.

### Platforms

| 1 | ■ Takayama Main Line | for Toyama |
| 2 | ■ Takayama Main Line | for Takayama and Gero |

## Adjacent stations

| « | Service | » |
| Takayama Main Line |||||
| Limited Express "Hida": Does not stop at this station |||||
| Sugisaki | Local | Tsunogawa |

## History

Hida-Hosoe Station opened on October 25, 1934. The station was absorbed into the JR Central network upon the privatization of Japanese National Railways (JNR) on April 1, 1987.

## Surrounding area

* National Route 41
* National Route 471
# Sakakami Station

Sakakami Station (坂上駅, Sakakami-eki) is a railway station on the Takayama Main Line in the city of Hida, Gifu Prefecture, Japan, operated by Central Japan Railway Company (JR Central).

## Lines

Sakakami Station is served by the JR Central Takayama Main Line, and is located 166.6 kilometers from the official starting point of the line at Gifu.

## Station layout

Sakakami Station has one ground-level side platform and one ground-level island platform connected by a footbridge. The station is unattended.

### Platforms

| 1 | ■ Takayama Main Line | for Toyama |
| 2, 3 | ■ Takayama Main Line | for Takayama and Gero |

## Adjacent stations

| « | Service | » |
| Takayama Main Line |||||
| Limited Express "Hida": Does not stop at this station |||||
| Tsunogawa | Local | Utsubo |

## History

Sakakami Station opened on November 12, 1933. The station was absorbed into the JR Central network upon the privatization of the Japanese National Railways (JNR) on April 1, 1987.

## Surrounding area

* Former Miyazawa Village Hall
# Nishi-Toyama Station

Nishi-Toyama Station (西富山駅, Nishi-Toyama-eki) is a railway station on the Takayama Main Line in city of Toyama, Japan, operated by West Japan Railway Company (JR West). It is also a freight terminal for the Japan Freight Railway Company.

## Lines

Nishi-Toyama Station is a station on the Takayama Main Line, and is located 222.2 kilometers from the end of the line at Gifu and 33.3 kilometers from the dividing point on the line between JR West and JR East at Inotani.

## Layout

The station has two ground-level opposed side platforms serving two tracks. The station is unattended.

### Platforms

| 1 | ■ Takayama Main Line | for Inotani and Takaoka |
| 2 | ■ Takayama Main Line | for Toyama |

## Adjacent stations

| « | Service | » |
| JR West |||||
| Takayama Main Line |||||
| Limited Express "Hida": Does not stop at this station |||||
| Fuchū-Usaka | Local | Toyama |

## History

The station opened on 1 September 1927. With the privatization of Japanese National Railways (JNR) on 1 April 1987, the station came under the control of JR West.

## Passenger statistics

In fiscal 2015, the station was used by an average of 364 passengers daily (boarding passengers only).

## Surrounding area

* Toyama University Gofuku campus
* Toyama Industrial High School
* Toyama Commercial High School
# Sōsa Station

Sōsa Station (宗佐駅, Sōsa-eki) was a railway station in Kakogawa, Hyōgo Prefecture, Japan.

## Lines

* Miki Railway
   * Miki Line - Abandoned on April 1, 2008

## Adjacent stations

| « | « | Service | » | » |
| Miki Railway (Abandoned) |||||
| Miki Line |||||
| Kunikane | Kunikane | - | Shimo-Ishino | Shimo-Ishino |
# Gakumon Station

Gakumon Station (学門駅, Gakumon-eki) is a passenger railway station located in the city of Gobō, Wakayama Prefecture, Japan. The station is operated by the private Kishū Railway. The station is named after the Wakayama Prefectural Hidaka High School, whose back gate is located adjacent to the station.

## Lines

Gakumon Station is served by the Kishū Railway Line and is 1.5 kilometers from the terminus of the line at Gobō.

## Station layout

The station consists solely of a side platform located next to the single track. The only entrance to the station is located on the Gobo-bound end of the platform. No ticket gates are present within the station premises as the station is unmanned. There is a waiting shelter located on the platform, but there is no station building or toilet.

## Adjacent stations

| « | « | Service | » | » |
| Kishū Railway Line |||||
| Gobō | | Local | | Kii-Gobō |

## History

Chugakumae Station (中学前駅, Chugakumae-eki) was a former railway station which opened on 15 June 1931. The station was closed on 8 December 1941 and was subsequently demolished. Gakumon Station was built near the site of where Chugakumae Station had been located, and was opened on 10 August 1979 as an infill station.

## Passenger statistics

In fiscal 2019, the station was used by an average of 9 passengers daily (boarding passengers only).

## Surrounding Area

* Wakayama Prefectural Hidaka High School
* Hidaka River
* Gobo City Fujita Elementary School
* Taisei Junior High School
# Hira Station (Aichi)

Hira Station (比良駅, Hira-eki) is a railway station in Nishi-ku, Nagoya, Aichi Prefecture, Japan, operated by JR-Central Transport Service Company (TKJ).

## Lines

Hira Station is served by the TKJ Jōhoku Line, and is located 4.5 kilometers from the starting point of the line at Kachigawa.

## Station layout

The station has two opposed elevated island platforms with the station building underneath. The station building has automated ticket machines, TOICA automated turnstiles and is unattended.

### Platforms

| 1 | ■ Tōkai Transport Service Jōhoku Line | For Kachigawa |
| 2 | ■ Tōkai Transport Service Jōhoku Line | For Biwajima |

## Adjacent stations

| « | Service | » |
| Tōkai Transport Service Company |||||
| Jōhoku Line |||||
| Ajiyoshi | Local | Otai |

## Station history

Hira Station was opened on 1 December 1991.

## Passenger statistics

In fiscal 2017, the station was used by an average of 115 passengers daily.

## Surrounding area

* Site of Hira Castle
* Hira Elementary School
# Gakunan-Harada Station

Gakunan-Harada Station (岳南原田駅, Gakunan-Harada-eki) is a railway station in the city of Fuji, Shizuoka Prefecture, Japan, operated by the private railway operator Gakunan Railway.

## Lines

Gakunan-Harada Station is served by the Gakunan Railway Line, and is located 4.4 kilometers from the terminal of the line at Yoshiwara.

## Station layout

Gakunan-Harada Station has one island platform connected to the station building by a level crossing. It is staffed only during the morning commuting hours. In addition, adjacent multiple tracks used for container freight services as well as private freight services to the nearby Nippon Daishowa Paperboard Company factories parallel the passenger tracks.

## Adjacent stations

| « | « | Service | » | » |
| Gakunan Railway Line |||||
| Hon-Yoshiwara | Hon-Yoshiwara | - | Hina | Hina |

## Station history

Gakunan-Harada Station was opened on December 20, 1951.

## Passenger statistics

In fiscal 2017, the station was used by an average of 263 passengers daily (boarding passengers only).

## Surrounding area

* Harada Elementary School
# Paden

Paden may refer to:

## Places in the United States

* Paden, Mississippi, a village
* Paden, Oklahoma, a town
* Paden City, West Virginia, a city
** Paden City Elementary School
** Paden City High School
* Paden Island, West Virginia

## Other uses

* Paden (surname)
* Paden Tolbert (c. 1863 or 1870–1904), American Old West marshal
* Paden's Drug Store, Carrizozo, New Mexico
* Paden, a character in the 1985 movie Silverado
* Paden, a clothing line created by Davey Havok
# Come On In (film)

Come on In is a 1918 American comedy silent film directed by John Emerson and written by John Emerson and Anita Loos. The film stars Shirley Mason, Ernest Truex, Carl De Planta, Joseph Burke, Renault Tourneur, and Bernard Randall. The film was released on September 22, 1918, by Paramount Pictures. It is not known whether the film currently survives.

## Plot

As described in a film magazine, after war is declared on Germany Ernest Short (Truex) enlists, and his best girl Emmy Little (Mason) determines to do her bit by running down a German spy. She falls in love with a German-American and, when he gets orders to kill an American officer, he proposes and they are married. Emmy's uncle, an army officer, is invited to the wedding. The plotters overcome the officer after the wedding and attempt to kill him. Ernest rescues the officer, trails the wedding party, and has the German placed under arrest. He and Emmy later marry.

## Cast

* Shirley Mason as Emmy Little
* Ernest Truex as Ernest Short
* Carl De Planta as Count von Bumstuff
* Joseph Burke as Professor G. Wottan Orphul-Schmell
* Renault Tourneur as A. Schlobb
* Bernard Randall as Otto B. Schott
* Blanche Craig as Mrs. schroeder
* Meyer Berenson as Office Boy
* Richie Ling as The Colonel
* Louis Hendricks as German Spy
# Paden (surname)

Paden is a surname. Notable people with the surname include:
* Clifton Paden ("John Emerson"), American silent filmmaker, 1874–1956
* Khalil Paden, American football player
* Cline Paden, American evangelist and missionary, (1919–2007)
* Jurica Pađen, Croatian musician
* Frank Paden and Johnny Paden (of The Marvelows)
# Lee Chun-yee

Lee Chun-yee (Chinese: 李俊毅; born 20 March 1959) is a Taiwanese politician. A member of the Democratic Progressive Party, he served in the Legislative Yuan from 1996 to 2012 as a representative of Tainan.

## Early life and education

Lee was born in Tainan County in 1959. He earned a bachelor's degree in public administration from National Chengchi University and then earned a master's degree in public administration from the university.

## Political career

Lee represented Tainan County as a member of the Legislative Yuan from 1996 to 2012. Affiliated with the Democratic Progressive Party's Welfare State Alliance, he has also served as the DPP caucus whip. In 2009, Lee was named the Democratic Progressive Party candidate for the Tainan County magistracy. The election was cancelled, as both Tainan City and Tainan County were consolidated into the special municipality of Tainan the next year. Subsequently, Lee declared his candidacy for the mayoralty of Tainan, and he was challenged by Yeh Yi-jin, Su Huan-chih, and Hsu Tain-tsair. A fifth Democratic Progressive Party candidate, William Lai, later received official party support and won the office. Lee lost to Wang Ting-yu in a contentious 2011 party primary and eventually yielded his legislative seat to Wang's replacement candidate Mark Chen. Su Tseng-chang named Lee one of three deputy secretaries-general of the Democratic Progressive Party in 2012. Lee resigned from the position in 2017 to prepare his second campaign for the Tainan mayoralty. He was one of six candidates vying for the DPP mayoral nomination won by Huang Wei-cher.

## Controversy

Lee was accused of accepting bribes in 2007, charges that originally stemmed from 1998. In 2010, the Taiwan High Court sentenced Lee to seven years and six months imprisonment. Two years later, he was cleared of corruption.
# Upavon Fillies' Stakes

The Upavon Fillies' Stakes is a Listed flat horse race in Great Britain open to mares and fillies aged three years or older. It is run at Salisbury over a distance of 1 mile 1 furlong and 201 yards (1,994 metres), and it is scheduled to take place each year in August.

## Records

Most successful horse since 1988 (2 wins):
* Chain Of Daisies – 2016, 2018
Leading jockey since 1988 (5 wins):
* Frankie Dettori – Mill Run (1990), Dana Springs (1993), Altamura (1996), Ajhiba (1999), Pictavia (2006)
Leading trainer since 1988 (4 wins):
* Sir Michael Stoute – Rumoosh (1988), Promising Lead (2007), Ave (2009), Mango Diva (2013)
# Jina Station

Jina Station (地名駅, Jina-eki) is a railway station in the town of Kawanehon, Haibara District, Shizuoka Prefecture, Japan operated by the Ōigawa Railway.

## Lines

Jina Station is served by the Ōigawa Main Line, and is located 22.9 kilometers from the official starting point of the line at Kanaya.

## Station layout

The station has a single island platform connected to a small wooden station building by a level crossing. The station is staffed.

## Adjacent stations

| « | Service | » |
| Ōigawa Railway |||||
| Ōigawa Main Line |||||
| SL Express: Does not stop at this station |||||
| Kawaneonsen-Sasamado | Local | Shiogō |

## Station history

Jina Station was one of the original stations of the Ōigawa Main Line, and was opened on July 16, 1930.

## Passenger statistics

In fiscal 2017, the station was used by an average of 8 passengers daily (boarding passengers only).

## Surrounding area

* Japan National Route 473
# Rajasthan Patrika

Rajasthan Patrika (lit. 'The Rajasthan Newsletter') is an Indian Hindi-Rajasthani language daily newspaper. It was founded by Karpoor Chandra Kulish in 1956 and published as Rajasthan Patrika in Delhi and Rajasthan, and as Patrika in 9 other states.
As per Indian Readership Survey 2013, Rajasthan Patrika emerged as the fourth most-read Hindi language newspaper in India, and Patrika emerged sixth.

## History

Rajasthan Patrika was founded by Karpoor Chandra Kulish on 7 March 1956. Mr. Karpoor Chand Kulish is follower of Jain religion. Over the years, it became a leading national daily.

## Editions

Rajasthan Patrika prints editions in New Delhi and the seven cities of Chhattisgarh (in Bilaspur, Jagdalpur and Raipur), Gujarat (in Ahmedabad and Surat), Karnataka (in Bangalore and Hubli), Madhya Pradesh (under the shorter name of Patrika in Bhopal, Gwalior, Indore, Jabalpur, Ujjain and eight other cities), Rajasthan in (Jaipur, Jodhpur, Kota, Gangapur City and 13 other cities) and in Tamil Nadu (at Chennai and Coimbatore).
Early in 2015, Rajasthan Patrika announced a Delhi-based English news website, called Catch News under the aegis of senior journalist and editor Shoma Chaudhry. Rajasthan Patrika also publish two bimonthly Hindi language child magazines — "Balhans" and "Chotu-Motu".

## Television

The newspaper also has a television division, Patrika TV, which covers news events and airs via satellite domestically and through its YouTube channel worldwide. The network launched on 9 June 2015.

## Criticism

Patrika has been criticised for non-implementation of Majithia Wage Board's recommendations for hiking wages of employees of newspapers, several cases have been lodged in various high courts of states in India and even in Supreme Court of India.

## Social awareness activities

* Amritam Jalam: The campaign focuses on saving water through restoration and renovation of neglected and derelict water bodies.

## Awards given by Patrika
### Karpoor Chandra Kulish International Journalism Award

In 2007, Rajasthan Patrika instituted the Karpoor Chandra Kulish International Journalism Award in the memory of Karpoor Chand Kulish, the founder editor. This annual international award carries prize money of US$11,000 and a trophy. The award is aimed at recognizing efforts of thought leaders in media, journalist's outstanding contributions to upholding professional values as well as protecting and promoting ethics and morality, right and freedom of the people for better quality of life. Dawn Pakistan and Hindustan Times Delhi were jointly given the inaugural award in New Delhi on 12 March 2008.

### Concerned Communicator Award

As a part of its CSR initiatives and social partnering for a better world, Rajasthan Patrika instituted the Concerned Communicator Award in 1997. The winner is awarded a cash prize of US$11,000 and a certificate.

## Achievements

* India's First News site on IDN domain (पत्रिका.भारत)

## Notable columnist

* S. Gurumurthy
* Feroze Varun Gandhi