OpenLLM-France/wikimedia huggingface dataset:
# Saddlepoint approximation method

The saddlepoint approximation method, initially proposed by Daniels (1954) is a specific example of the mathematical saddlepoint technique applied to statistics, in particular to the distribution of the sum of $N$ independent random variables. It provides a highly accurate approximation formula for any PDF or probability mass function of a distribution, based on the moment generating function. There is also a formula for the CDF of the distribution, proposed by Lugannani and Rice (1980).

## Definition

If the moment generating function of a random variable $X=\sum _{i=1}^{N}X_{i}$ is written as $M(t)=E\left[e^{tX}\right]=E\left[e^{t\sum _{i=1}^{N}X_{i}}\right]$ and the cumulant generating function as $K(t)=\log(M(t))=\sum _{i=1}^{N}\log E\left[e^{tX_{i}}\right]$ then the saddlepoint approximation to the PDF of the distribution $X$ is defined as:
    ${\hat {f}}_{X}(x)={\frac {1}{\sqrt {2\pi K''({\hat {s}})}}}\exp(K({\hat {s}})-{\hat {s}}x)\,\left(1+{\mathcal {R}}\right)$
where ${\mathcal {R}}$ contains higher order terms to refine the approximation and the saddlepoint approximation to the CDF is defined as:
    ${\hat {F}}_{X}(x)={\begin{cases}\Phi ({\hat {w}})+\phi ({\hat {w}})\left({\frac {1}{\hat {w}}}-{\frac {1}{\hat {u}}}\right)&{\text{for }}x\neq \mu \\{\frac {1}{2}}+{\frac {K'''(0)}{6{\sqrt {2\pi }}K''(0)^{3/2}}}&{\text{for }}x=\mu \end{cases}}$
where ${\hat {s}}$ is the solution to $K'({\hat {s}})=x$, ${\hat {w}}=\operatorname {sgn} {\hat {s}}{\sqrt {2({\hat {s}}x-K({\hat {s}}))}}$ ,${\hat {u}}={\hat {s}}{\sqrt {K''({\hat {s}})}}$, and $\Phi (t)$ and $\phi (t)$ are the cumulative distribution function and the probability density function of a normal distribution, respectively, and $\mu$ is the mean of the random variable $X$:
$\mu \triangleq E\left[X\right]=\int _{-\infty }^{+\infty }xf_{X}(x)\,{\text{d}}x=\sum _{i=1}^{N}E\left[X_{i}\right]=\sum _{i=1}^{N}\int _{-\infty }^{+\infty }x_{i}f_{X_{i}}(x_{i})\,{\text{d}}x_{i}$.
When the distribution is that of a sample mean, Lugannani and Rice's saddlepoint expansion for the cumulative distribution function $F(x)$ may be differentiated to obtain Daniels' saddlepoint expansion for the probability density function $f(x)$ (Routledge and Tsao, 1997). This result establishes the derivative of a truncated Lugannani and Rice series as an alternative asymptotic approximation for the density function $f(x)$. Unlike the original saddlepoint approximation for $f(x)$, this alternative approximation in general does not need to be renormalized.
# Council, Georgia

Council is an unincorporated community in Clinch County, in the U.S. state of Georgia.

## History

A post office called Council was established in 1909, and remained in operation until 1958. The community was named after C. C. and John M. Council, proprietors of a local sawmill.
# Country Squire Lakes, Indiana

Country Squire Lakes is an unincorporated community and census-designated place (CDP) in Geneva Township, Jennings County, Indiana, United States. As of the 2010 census it had a population of 3,571.
It was founded in 1973 by a property developer as a planned community built around several artificial lakes.

## Geography

The community is in northwestern Jennings County, it is in the southeast corner of Geneva Township. It is built around Country Squire Lake, a reservoir on Six mile Creek, as well as several smaller lakes. The lakes in the western part of the community drain to Mutton Creek. Six mile and Mutton Creeks are southwest-flowing tributaries of the Vernon Fork of the Muscatatuck River and part of the White River watershed.
Indiana State Road 7 runs along the northeast edge of the community, leading southeast 3 miles (5 km) to North Vernon and northwest 18 miles (29 km) to Columbus. The older community of Queensville borders Country Squire Lakes to the northeast across Highway 7.
According to the U.S. Census Bureau, the Country Squire Lakes CDP has a total area of 2.7 square miles (7.0 km$^2$), of which 2.5 square miles (6.6 km$^2$) are land and 0.2 square miles (0.4 km$^2$), or 5.16%, are water.
# Crab Orchard, Illinois

Crab Orchard is an unincorporated census-designated place east of Marion in Williamson County, Illinois, located along an old route of Illinois Route 13 now designated Crab Orchard Road. The upper branches of Crab Orchard Creek which eventually feed into Crab Orchard Lake flow nearby and gave the community its name. For a brief time during the Civil War, it was known as Erwinsville, which is the name in the original plat of the village. In its early days, it had the nickname "Steal-Easy." The Crab Orchard post office was established 18 August 1853 and discontinued operations 15 May 1924. It's now served by the Marion post office. As of the 2010 census, Crab Orchard has a population of 333. Crab Orchard has an area of 1.430 square miles (3.70 km$^2$); 1.395 square miles (3.61 km$^2$) of this is land, and 0.035 square miles (0.091 km$^2$) is water.

## Community services

Crab Orchard Community Unit School District 3 serves the community and surrounding area.
The Crab Orchard Public Library District serves the area with its main library in Crab Orchard and satellite services at Pittsburg and Creal Springs.
Fire protection is provided by Williamson County Fire Protection District. Station #3 is located on the north edge of the community. Treated water is provided by the private Coal Valley Water District.

## Notable people

* Cory Bailey, professional baseball player, attended school in Crab Orchard.
* Gerry Glasco, college softball coach at Louisiana and former head coach at the USSSA Pride and the Scrap Yard Dawgs of the National Pro Fastpitch
# Crumb Corner, Indiana

Crumb Corner is an unincorporated community in Wabash Township, Tippecanoe County, in the U.S. state of Indiana.
Located within the city limits of West Lafayette, the community is part of the Lafayette, Indiana Metropolitan Statistical Area.

## Geography

Crumb Corner is located a little west of the intersection of Yeager and Sagamore streets.
# Samuel Randlett

Samuel L Randlett (January 11, 1930 – July 2023) was an American origami artist who helped develop the modern system for diagramming origami folds. Together with Robert Harbin he developed the notation introduced by Akira Yoshizawa to form what is now called the Yoshizawa-Randlett system (sometimes known as Yoshizawa-Randlett-Harbin system). This was first described in Samuel Randlett's Art of Origami in 1961.

## Career and Origami

He was born in New Jersey on January 11, 1930. He graduated from Northwestern University and became a music professor.
He became interested in paper-folding in 1958 and within a year had his own figures on display at the Cooper Union Museum for the Arts of Decoration in New York. At the age of 30 started work on The Art of Origami. His first wife Jean illustrated this and most of his subsequent books. He came to know most of the then fairly small origami community around the world and edited an origami newsletter called The Flapping Bird from 1969 to 1976.
He died in Wisconsin in July 2023.
# Dennard, Arkansas

Dennard is a census-designated place in Van Buren County, Arkansas, United States. Its population was 496 as of the 2020 census.

## History

Dennard's post office was established in 1886. It first appeared as a census-designated place in the 2010 census.

## Demographics
### 2020 census

Dennard racial composition :
| Race | Num. | Perc. |
| White | 471 | 94.96% |
| Black or African American | 0 | 0.0% |
| Native American | 1 | 0.2% |
| Asian | 0 | 0.0% |
| Pacific Islander | 0 | 0.0% |
| Other/Mixed | 24 | 4.83% |
| Hispanic or Latino | 15 | 3.02% |
At the 2020 United States Census, there were 496 people and 216 households residing in Dennard.
The population density was 22.65 people per square mile (8.75 people/km$^2$), with 301 housing units at an average density of 13.74 per square mile (5.31/km$^2$).

### 2010 census

At the 2010 United States census, there were 530 people, 220 households, and 148 families residing in Dennard. The population density was 24.4 people per square mile (9.4 people/km$^2$), with 288 housing units at an average density of 13.3 per square mile (5.1/km$^2$). The racial makeup was 505 (95.3%) White, 0 (0.0%) Black, 0 (0.0%) Native American, 0 (0.0%) Asian, 0 (0.0%) Pacific Islander, 1 (0.2%) from other races, and 24 (4.5%) from two or more races. 7 people (1.3%) of any race were Hispanic or Latino.
There were 220 households, of which 51 (34.5%) had children under the age of 18 living with them, 112 (50.9%) were married couples living together, 23 (4.3%) were unmarried opposite-sex partnerships, 1 (0.2%) were unmarried same-sex partnerships, 27 (12.2%) had a female householder with no husband present, and 72 (32.7%) were non-families. 54 (24.5%) households were made up of individuals, and 20 (9.0%) had someone living alone who was 65 years of age or older. The average household size was 2.41, and the average family size was 2.86.
The population was spread out, with 123 people (23.2%) under the age of 18, 26 people (4.9%) aged 18 to 24, 116 people (21.8%) aged 25 to 44, 178 people (33.5%) aged 45 to 64, and 87 people (16.6%) who were 65 years of age or older. The median age was 45 years. For every 100 females, there were 100.8 males.

## Education

Public education for elementary and secondary school students in the majority of the CDP is provided by the Clinton School District, which leads students to graduate from Clinton High School.
A very small portion is in the Searcy County School District.
# Dexter, Texas

Dexter is an unincorporated community in Cooke County, Texas, United States. According to the Handbook of Texas, the community had a population of 18 in 2000. It is located within the Dallas-Fort Worth Metroplex.

## History

On September 8, 1986, an Amoco gas condensate pipeline leaked.14 people were injured.
The Washington House on Sycamore Creek Ranch in the community was listed on the National Register of Historic Places.

## Geography

Dexter is located on Farm to Market Road 678 near the Red River, 25 mi (40 km) northeast of Gainesville, 8.7 mi (14.0 km) east-northeast of Callisburg, and 11.5 mi (18.5 km) west-northwest of Whitesboro in extreme northeastern Cooke County.

## Education

Dexter had its own school in the early 1880s. Today, Dexter is served by the Whitesboro Independent School District.

## Notable people

* William H. Bourland, Speaker of the Texas House of Representatives during the First Texas Legislature.
* Charlie Robertson, former MLB pitcher.
# Dover Bluff, Georgia

Dover Bluff is an unincorporated community in Camden County, in the U.S. state of Georgia.

## History

The community most likely was named after the White Cliffs of Dover, in England.
# Drakes Branch, Virginia

Drakes Branch is a town in Charlotte County, Virginia, United States. The population was 530 at the 2010 census.

## Geography

Drakes Branch is located southeast of the center of Charlotte County at 36°59′35″N 78°36′6″W﻿ / ﻿36.99306°N 78.60167°W﻿ / 36.99306; -78.60167 (36.992958, −78.601714). Virginia State Route 47 passes through the town, leading north 5 miles (8 km) to Charlotte Court House, the county seat, and southeast 7 miles (11 km) to U.S. Route 15. Virginia State Route 59 intersects Route 47 in the north part of town and leads northeast 8 miles (13 km) to Keysville.
According to the United States Census Bureau, Drakes Branch has a total area of 4.1 square miles (10.7 km$^2$), all of it land.

## Demographics

At the 2000 census there were 504 people, 231 households, and 134 families living in the town. The population density was 121.8 people per square mile (47.0/km²). There were 262 housing units at an average density of 63.3 per square mile (24.4/km²). The racial makeup of the town was 59.33% White, 40.08% African American, 0.20% from other races, and 0.40% from two or more races. Hispanic or Latino of any race were 1.98%.
Of the 231 households 21.6% had children under the age of 18 living with them, 39.0% were married couples living together, 14.3% had a female householder with no husband present, and 41.6% were non-families. 35.5% of households were one person and 14.7% were one person aged 65 or older. The average household size was 2.18 and the average family size was 2.81.
The age distribution was 20.4% under the age of 18, 6.5% from 18 to 24, 24.4% from 25 to 44, 28.4% from 45 to 64, and 20.2% 65 or older. The median age was 44 years. For every 100 females, there were 88.8 males. For every 100 females age 18 and over, there were 91.0 males.
The median income for a household in the town was $25,583, and the median family income was $35,000. Males had a median income of $25,469 versus $17,500 for females. The per capita income for the town was $15,701. About 8.2% of families and 16.8% of the population were below the poverty line, including 20.5% of those under age 18 and 14.3% of those age 65 or over.
# Schefflera digitata

Schefflera digitata, the patē, seven-finger, or umbrella tree, is a tree endemic to New Zealand belonging to the family Araliaceae. Māori names include: patē, patatē, patete, and kōtētē. It occurs in lowland to lower montane forests from sea level to 1,200 m (3,900 ft) in the North Island, South Island, and Stewart Island, covering a latitudinal range from 34°S to 47°S. It prefers damp, shady parts of the forest and is common along stream banks and on shady forest roadsides. It is the only New Zealand representative of the genus Schefflera, which has 12 other species on the Pacific islands.

## Description

Patē is a small, spreading tree up to 8 m (26 ft) high with stout branches. The leaves may have from three to nine leaflets. The leaflets are thin and soft to the touch with sharply serrated margins. In the north of the North Island, S. digitata has a juvenile stage in which the leaflets are divided into irregular toothed lobes. The inflorescence is a large, multi-branched panicle up to 35 cm across, with umbels of small greenish flowers arising at irregular intervals along its length. Each umbel contains up to ten flowers each about 1,200 mm (47 in) in diameter. The dark violet fruits are fleshy, round, and grooved when dry. They are about 3.5 mm in diameter and take two or three months to ripen.

## Ecology and uses

The sap of the tree has medicinal uses, and has been used to treat ringworm and sores on the skin. The wood was used by Māori to make fire by friction. Patē is the most common host of the parasitic plant Dactylanthus taylori. This is a root parasite that was known to the Māori as pua-o-te-reinga, 'the flower of the underworld'. Wood rose is threatened with extinction, which is thought to be due to several factors including the poaching of plants for sale as curios. Although patē is easy to grow in New Zealand, it is not popular in cultivation, as its thin, soft foliage cannot match the glossy attractiveness of the similar Pseudopanax species, nor that of the Australian species Heptapleurum actinophyllum, which is also easy to grow in the North Island. S. digitata is sometimes grown by Northern Hemisphere gardeners thinking it may be relatively hardy, but like many New Zealand trees, patē is not tolerant of prolonged cold conditions.
# Egypt, Georgia, U.S.

Egypt is an unincorporated community in Effingham County, in the U.S. state of Georgia.

## History

A post office called Egypt was established in 1850, and remained in operation until 1956. The community was named after Egypt, alluding to that country's fertile soil.
# Eldridge, Texas

Eldridge is an unincorporated community in Colorado County, Texas, United States. According to the Handbook of Texas, the community had a population of 20 in 2000.

## Geography

Eldridge is located at the intersection of Farm to Market Roads 950 and 2614, between Garwood and Eagle Lake in southeastern Colorado County.

## Education

Today, Eldridge is served by the Rice Consolidated Independent School District.
# National Museum of the Faroe Islands

The Faroe Islands National Museum (Faroese: Tjóðsavnið, Danish: Færøernes Nationalmuseum) is the national museum of the Faroe Islands, located in Tórshavn.

## The exhibition at Brekkutún 6

The Faroe Islands National Museum has exhibitions in the museum building at Brekkutún 6 in Tórshavn. The galleries tell the natural and cultural history of the Faroe Islands. This stretches from the origin of the landmass dating back 65 million years, through the pre-settlement era and the culture of the Viking Ages and the Middle Ages. Displays include rocks and minerals, birds, plants and fish, as well as items from the farming life and the maritime life in the Faroe Islands. The famous Kirkjubøstólarnir, which are parts of the original benches from Ólavskirkjan (St. Olav's Church) at Kirkjubøur are amongst the most valued cultural items of the National Museum. These were in Denmark for many years but have now returned to the Faroe Islands.

## Heima á Garði in Hoyvík

Heima á Garði is a farmhouse in Hoyvík, near Tórshavn. The farmhouse is now a part of the National Museum of the Faroe Islands. The main building was built around 1812, but it is furnished like Faroese houses were in 1920s. The museum is an outdoors museum with all the buildings, tools, and other items which belonged to the farmhouse.

## Pew ends

The medieval pew ends from Saint Olav's church at Kirkjubøur (mentioned above) featured in three series of Faroese stamps, engraved by Czeslaw Slania.
Faroese stamps 1980:
* FR 49: Maria and Baby Jesus
* FR 50: St. John the Baptist
* FR 51: St. Peter
* FR 52: St. Paul
Faroese stamps 1984:
* FR 087: Saint John, the Evangelist.
* FR 088: Saint James.
* FR 089: Saint Thomas.
* FR 090: Saint Judas Thaddeus.
Faroese stamps 2001:
* FR 379: Saint Andrew.
* FR 380: Saint Bartholomew.
* FR 381: Unidentified apostle.
* FR 382: Unidentified apostle.
# Elm Ridge, Texas

Elm Ridge is an unincorporated community located in Milam County, Texas, United States. According to the Handbook of Texas, the community had a population of 25 in 2000.

## History

The Gulf, Colorado and Santa Fe Railway built a track through Elm Ridge in 1881 and the community may have been established here. It was named for a nearby creek. The 1941 county highway map showed some scattered houses in the vicinity. Its population was 25 from 1990 through 2000.

## Geography

Elm Ridge is located on U.S. Highway 190, 4 mi (6.4 km) west of Cameron in central Milam County.

## Education

In 1903, Elm Ridge had a school with two teachers and 80 students. It continued to operate in 1941. Today, the community is served by the Cameron Independent School District.
# Princess Pat Ajudua

Princess Patience Adankele Ajudua (born 7 April 1962), known as Pat Ajudua is a Nigerian lawyer and parliamentarian. She was the Chief whip of the Delta State House of Assembly.

## Early life and education

Ajudua is from Eleme, Rivers State. She is of the Ngegwe royal family. She attended Federal Government Girls' College, Abuloma, from 1974 to 1979. And then School of Basic Studies from 1979 to 1981. Both schools are in Port Harcourt.
She attended University of Lagos from 1981 to 1984; Rivers State University of Science and Technology from 1989 to 1990; and then Lagos State University from 1990 to 1992; obtaining her law degree. She was called to bar in 2015, having enrolled in the Nigerian Law School in the previous year. She attended University of Lagos again from 1996 to 1997 for a postgraduate degree. She is a member of the Chartered Institute of Arbitrators (MCIARB).

## Political career

Ajudua was first elected into the Delta state assembly to represent Oshimili North in 2007. She has occupied the seat since then, culminating four terms. She was a member of Accord party when she contested and won in 2007 and 2011. In 2011, a different candidate was declared winner after the 2011 Nigerian general election, she took the matter to court and after a legal battle, it was determined that her opponent was wrongfully declared as victorious and she was announced as the substantive winner.
She won a re-election in the 2019 Delta State House of Assembly election under the People's Democratic Party (PDP).
She contested in the primary election to represent the PDP for the in forthcoming general elections for Aniocha/Oshimili Federal Constituency in the Nigerian House of Representatives. She lost to the incumbent, Ndudi Elumelu, coming in second place by 80 votes to 35 votes.
She was appointed the chairperson of the PDP campaign council of Oshimili North for the forthcoming 2023 Nigerian general election. She was part of Governor Ifeanyi Okowa's entourage that paid a condolence visit to the Keshi family after the death of former Nigerian football team captain and coach Stephen Keshi.
She was the chairperson of the joint committee on Special Bills, Agriculture and Natural Resources, she was also the chairperson of the committee for Judiciary. She was a member of the Central organizing committee of the Delta state 30th anniversary celebration, and she was also a member of the joint committee on Housing, Women Affairs and Social Development. She was a member of the ad-hoc committee for the review of the Delta state 2019 customary court law. Ajudua is currently the commissioner of women affairs and social development

## Personal life

She is married to Fred Ajudua. They have a son together, Bobo Ajudua.
# Peter Wall (footballer)

Peter Thomas Wall (13 September 1944 – 30 October 2024) was an English professional footballer who played in England and the United States as a full-back. He subsequently became a coach in the United States.

## Playing career

Wall was born on 13 September 1944 in Shrewsbury, although the nearby village of Westbury has also been stated as his birthplace. After leaving education at Pontesbury Secondary Modern School, he signed a professional contract with Shrewsbury Town in 1963, making 18 league appearances during the next two seasons. He signed for Wrexham in 1965, and made 22 league appearances over the next two seasons. Wall moved to Liverpool in 1967, and over the next three seasons made 31 league appearances. Wall then signed for Crystal Palace, where he made 177 league appearances over seven seasons. While at Crystal Palace, Wall spent the 1972–73 season on loan with Leyton Orient. Wall later played in the NASL for the St. Louis Stars and the California Surf.

## Coaching career

Following his retirement as a player following the end of the 1980 season, Wall became manager of the California Surf for the 1981 season, and the Los Angeles Lazers between 1982 and 1987.

## Personal life and death

After his coaching career in America, Wall returned to Shropshire, where he was living in Oswestry and employed at motor dealers Furrow's in 2008.
Wall died on 30 October 2024, aged 80. A grandfather, he was survived by his wife, Kathleen. His funeral took place at All Saints' Church, Worthen, Shropshire, where he was buried, on 2 December 2024.
# Wickwire Hill

Wickwire Hill is a summit located in Central New York Region of New York located in the Town of Florence in Oneida County, north of Camden.