OpenLLM-France/wikimedia huggingface dataset:
# Cantor distribution

The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function.
This distribution has neither a probability density function nor a probability mass function, since although its cumulative distribution function is a continuous function, the distribution is not absolutely continuous with respect to Lebesgue measure, nor does it have any point-masses. It is thus neither a discrete nor an absolutely continuous probability distribution, nor is it a mixture of these. Rather it is an example of a singular distribution.
Its cumulative distribution function is continuous everywhere but horizontal almost everywhere, so is sometimes referred to as the Devil's staircase, although that term has a more general meaning.

## Characterization

The support of the Cantor distribution is the Cantor set, itself the intersection of the (countably infinitely many) sets:
    ${\begin{aligned}C_{0}=&[0,1]\\[8pt]C_{1}=&[0,1/3]\cup [2/3,1]\\[8pt]C_{2}=&[0,1/9]\cup [2/9,1/3]\cup [2/3,7/9]\cup [8/9,1]\\[8pt]C_{3}=&[0,1/27]\cup [2/27,1/9]\cup [2/9,7/27]\cup [8/27,1/3]\cup \\[4pt]&[2/3,19/27]\cup [20/27,7/9]\cup [8/9,25/27]\cup [26/27,1]\\[8pt]C_{4}=&[0,1/81]\cup [2/81,1/27]\cup [2/27,7/81]\cup [8/81,1/9]\cup [2/9,19/81]\cup [20/81,7/27]\cup \\[4pt]&[8/27,25/81]\cup [26/81,1/3]\cup [2/3,55/81]\cup [56/81,19/27]\cup [20/27,61/81]\cup \\[4pt]&[62/81,21/27]\cup [8/9,73/81]\cup [74/81,25/27]\cup [26/27,79/81]\cup [80/81,1]\\[8pt]C_{5}=&\cdots \end{aligned}}$
The Cantor distribution is the unique probability distribution for which for any C$_t$ (t ∈ { 0, 1, 2, 3, ... }), the probability of a particular interval in C$_t$ containing the Cantor-distributed random variable is identically 2$^{−t}$ on each one of the 2$^t$ intervals.

## Moments

It is easy to see by symmetry and being bounded that for a random variable X having this distribution, its expected value E(X) = 1/2, and that all odd central moments of X are 0.
The law of total variance can be used to find the variance var(X), as follows. For the above set C$_1$, let Y = 0 if X ∈ [0,1/3], and 1 if X ∈ [2/3,1]. Then:
    ${\begin{aligned}\operatorname {var} (X)&=\operatorname {E} (\operatorname {var} (X\mid Y))+\operatorname {var} (\operatorname {E} (X\mid Y))\\&={\frac {1}{9}}\operatorname {var} (X)+\operatorname {var} \left\{{\begin{matrix}1/6&{\mbox{with probability}}\ 1/2\\5/6&{\mbox{with probability}}\ 1/2\end{matrix}}\right\}\\&={\frac {1}{9}}\operatorname {var} (X)+{\frac {1}{9}}\end{aligned}}$
From this we get:
    $\operatorname {var} (X)={\frac {1}{8}}.$
A closed-form expression for any even central moment can be found by first obtaining the even cumulants
    $\kappa _{2n}={\frac {2^{2n-1}(2^{2n}-1)B_{2n}}{n\,(3^{2n}-1)}},\,\!$
where B$_{2n}$ is the 2nth Bernoulli number, and then expressing the moments as functions of the cumulants.
# Flexi

Flexi may refer to:
* The flexi disc, a type of vinyl phonograph record
* The "Flexi truck", a type of Forklift truck
* Flexible-fuel vehicles
* Flexitarianism, a semi-vegetarian diet
* Flextime plans, a working arrangement with variable schedules
* Flexi was going to be the preliminary name of Tentro, a character from the Mixels franchise.
# Flexenbahn

The Flexenbahn is an aerial cableway (cable car) in Stuben am Arlberg in the Austrian province of Vorarlberg. The valley station is located in the area of Alpe Rauz.

## History

The Flexenbahn is part of the Ski Arlberg ski area and borders both of the Austrian provinces of Vorarlberg and Tyrol. The Flexenbahn is the key link with which the largest contiguous ski resort in Austria could be realized.
# Cape Broyle

The Town of Cape Broyle (population: 499) is an incorporated community located on the Avalon Peninsula in Newfoundland and Labrador, Canada. During King William's War, the village was destroyed in the Avalon Peninsula Campaign.

## Demographics

In the 2021 Census of Population conducted by Statistics Canada, Cape Broyle had a population of 499 living in 228 of its 314 total private dwellings, a change of 2% from its 2016 population of 489. With a land area of 10.09 km$^2$ (3.90 sq mi), it had a population density of 49.5/km$^2$ (128.1/sq mi) in 2021.
# Cape Bruny Lighthouse

The Cape Bruny Lighthouse is an inactive lighthouse located at the southern tip of Bruny Island, Tasmania, Australia.

## Features and location

It is the second oldest extant lighthouse tower in Australia, as well as having the longest (158 years) history of being continuously manned. It was first lit in March 1838 and was eventually decommissioned on 6 August 1996.
The project was commissioned by Governor George Arthur in 1835 after a series of shipwrecks south of Bruny Island and construction began in April 1836. The lighthouse was built by convict labour using locally quarried dolerite over two years. When first lit in March 1838 it was Tasmania's third lighthouse and Australia's fourth.
Cape Bruny was initially illuminated by a Wilkins lantern, consuming one pint of sperm whale oil per hour. In 1892, whale oil was replaced by better quality colza oil. In 1903 the original staircase was replaced with a cast-iron staircase and the Wilkins lantern replaced with a Chance Brothers lantern; both remain in the tower today. The lighthouse was converted to electricity only in 1959.
In December 2000 the light station area, including the lighthouse, became part of the South Bruny National Park. The lightstation was maintained by a permanent caretaker until 2011 when the Parks & Wildlife established a rotational volunteer caretaker program. Volunteers live on-site in the caretakers cottage for four-week periods, assisting with repairs and general maintenance.
In June 2012, the Tasmanian government sought expressions of interest from commercial operators wishing to take over the operation and management of the Cape Bruny Light Station. No tender was awarded and the site is managed by the Parks & Wildlife Service with assistance from volunteers. Following the tender process, only one company began tours of the South Bruny National Park and Cape Bruny Light Station that takes tourists to visit the Cape Bruny Lightstation, they also operate tours inside the lighthouse tower.
An active light tower is located nearby on a fiberglass construction of 4 metres (13 ft) height. Its light characteristic is "Fl. 10 s", i.e. a white flash every 10 seconds. The lightsource emits from a focal plane at 93 metres (305 ft) above sea level.
# Captains Mountain, Queensland

Captains Mountain is a locality in the Toowoomba Region, Queensland, Australia. In the 2021 census, Captains Mountain had a population of 74 people.

## Geography

The mountain Captains Mountain is in the north-east of the locality (27°55′09″S 151°09′18″E﻿ / ﻿27.9193°S 151.1549°E﻿ / -27.9193; 151.1549﻿ (Captains Mountain)) rising to 610 metres (2,000 ft)
The south-west of the locality is Western Creek State Forest. The remainder of the locality is used for farming, mostly grazing but with some cropping.
The Gore Highway passes through the locality from the north-east (Millmerran) and then exits to the south-west forming part of the south-western boundary (adjacent to Cypress Gardens and Millmerran Downs).

## History

The locality is presumably named after the mountain Captains Mountain.
In 1914, the Captain's Mountain Co-operative Dairy Company was formed with 275 shares at a cost of £1 each. The company built a cheese factory. In March 1916, the factory processed 3,449 imperial gallons (15,680 L; 4,142 US gal) to produce 3,961 pounds (1,797 kg) of cheese. The factory was still operating in 1931, but was contemplating closure in 1934, and had closed by 1939.
Captain's Mountain Provisional School opened on 30 January 1922, becoming Captain's Mountain State School in 1957. It closed in 1962.

## Demographics

In the 2016 census, Captains Mountain had a population of 77 people.
In the 2021 census, Captains Mountain had a population of 74 people.

## Education

There are no schools in Captains Mountain. The nearest government primary and secondary school to Year 10 is Millmerann State School in neighbouring Millmerran to the north-east and the nearest government secondary school to Year 12 in Pittsworth State High School in Pittsworth to the north-east.
# Flaveria cronquistii

Flaveria cronquistii is a rare Mexican plant species of Flaveria within the family Asteraceae. It has been found only in the States of Puebla and Oaxaca in central Mexico.
Flaveria cronquistii is a shrub up to 170 cm (68 inches or 5 2/3 feet) tall. One plant can produce numerous small flower heads in loose, branching arrays. Each head contains about 7 disc flowers but no ray flowers.
# Flaveria kochiana

Flaveria kochiana is a rare Mexican plant species of Flaveria within the family Asteraceae. It has been found only in the State of Oaxaca in southwestern Mexico.
Flaveria kochiana is a subshrub up to 30 cm (12 in) tall. Leaves are long and narrow, generally about 9 cm (3.5 in) long. One plant can produce numerous small yellow flower heads densely packed in a tight clump. Each head contains 2-4 disc flowers plus usually a few ray flowers, though some heads lack rays.
# Flight 650

Flight 650 may refer to:
* Ozark Air Lines Flight 650, crashed on 20 December 1983
* Northwest Flight 650, pilots drunk on 8 March 1990
# Flavoparmelia baltimorensis

Flavoparmelia baltimorensis, the rock greenshield lichen (from Lichens of North America), is a medium to large foliose lichen with a yellow green upper thallus surface when dry; its lobes are rounded without pseudocyphellae; and the upper surface is covered with globose, pustule-like growths resembling isidia. The lower surface is black with a narrow brown zone at the margins.

## Chemistry

Cortex, PD−, K−, KC+ yellowish, C− (usnic acid).
Medulla, PD+ red-orange, K−, KC+ pink, C− (protocetraric acid, with or without gyrophoric acid).

## Habitat

On rock in shaded or exposed areas.

## Similar species

The very similar Flavoparmelia caperata usually grows on the bark of trees, but may be found on rock. The granular soredia produced in irregular soralia distinguishes it from F. baltimorensis, which lacks true soredia.
Flavopunctelia flaventior and Flavopunctelia soredica have pseudocyphellae in the upper surface of the thallus, and the medulla is C+ red.

## Lichen checklists containing Flavoparmelia baltimorensis

* A cumulative checklist for the lichen-forming, lichenicolous and allied fungi of the continental United States and Canada. North Dakota State University.

## Gallery

* Flavoparmelia baltimorensis
# Flicksville, Pennsylvania

Flicksville is a village located in Northampton County, Pennsylvania. It is located 75 miles (121 km) west of New York City and is part of the Lehigh Valley metropolitan area, which had a population of 861,899 and was the 68th-most populous metropolitan area in the U.S. as of the 2020 census.
It is part of Washington Township. Flicksville previously had a post office with a ZIP Code of 18050; however, this ZIP Code was retired in 2016 and the community is now served by the Bangor ZIP Code of 18013.

## Geography

Flicksville is located at 40°50′39″N 75°12′06″W﻿ / ﻿40.84417°N 75.20167°W﻿ / 40.84417; -75.20167 (40.8442630,-75.2015672). It lies few km in south of the borough of Bangor and is crossed by the river Martins Creek.

## Education

The village is served by the Bangor Area School District. Students in grades nine through 12 attend Bangor Area High School in Bangor.
# Capel railway station

Capel railway station was a station in Capel St Mary, Suffolk, on a short branch line from Bentley Junction to Hadleigh. The station buildings were remarkably ornate for a village with a population of 649 in 1851 and 504 in 1931. There were goods sidings on the northern side of the station, which were used extensively in World War II handling supplies to a nearby United States Army Air Forces base, later known as RAF Raydon.
| Preceding station | Disused railways | Following station |
| Raydon Wood Line and station closed | Great Eastern Railway Eastern Union and Hadleigh Junction Railway | Bentley (Suffolk) Line and station closed |
The line opened in 1847 and closed to passenger traffic in 1932 and for freight services in 1964 a year before closure of the line. As the railway line through the station crossed the A12 road at a level-crossing, when the road was widened in the early 1970s the station was demolished. Capel Station Garage and car repairs workshop now occupies part of the site.
# Floor loan

A floor loan refers to the minimum amount of money that a lender is willing to lend in order to enable the builder to begin the construction of a building that is to be occupied by tenants. The term is thus closely associated with mortgage and property loans. The rest of the loan's balance (called "holdback") is given to the builder upon the achievement of certain milestones related to the sale or lease of its residential space. For example, a bank may advance 80% of the balance of a property loan to the builder, and release the remaining 20% upon the successful construction lease or sale of the building's residential units. This partition of funding means the lower risk for lender.
A word floor is used for more financial terms in financial area and means minimum, e.g. the interest rate floor is the lowest interest rate the lender can offer you to an adjustable (sometimes called variable) rate mortgage.

## Floor to ceiling loan

The related term is a floor to ceiling loan. In this type of loan there are two separate funding amounts: first upon satisfactory completion of construction and the second when a building is fully occupied by tenants or cash flows claimed by lender are fulfilled. The additional funds between floor and ceiling needed for construction costs are called "gap".
# Caradrinini

The Caradrinini are a mid-sized tribe of moths in the family Noctuidae .

## Genera

* Andropolia Grote, 1895
* Athetis Hübner, 1821
* Bellura Walker, 1865
* Callopistria Hübner, 1821
* Caradrina
* Conservula Grote, 1874
* Elaphria Hübner, 1818
* Enargia Hübner, 1821
* Euherrichia Grote, 1882
* Euplexia Stephens, 1829
* Hoplodrina
* Hyppa Duponchel, 1845
* Ipimorpha Hübner, 1821
* Nedra Clarke, 1940
* Paradrina
* Phlogophora Treitschke, 1825
* Platyperigea Smith, 1894
* Proxenus
* Spodoptera Guenée, 1852
# Caradrinopsis

Caradrinopsis is a genus of moths in the family Geometridae.
# Flor Silvestre con el Mariachi México

Flor Silvestre con el Mariachi México is a studio album by Mexican singer Flor Silvestre, released by Musart Records. It is Flor Silvestre's second Musart album and contains her 1961 version of "Cielo rojo", one of her signature songs.
It was a great success, and all twelve of its tracks were included in the greatest hits album Los éxitos de Flor Silvestre.

## Background

This is Flor Silvestre's second studio album for Musart. It features her hit singles from the early 1960s as well as "Échame a mí la culpa" and "Amémonos", two tracks from her previous Musart album, Flor Silvestre. She is accompanied by Pepe Villa's Mariachi México on all tracks except "Amémonos", which she recorded with the Mariachi Zapopan.

## Track listing

Side one
Side two

## Personnel

* Mariachi México de Pepe Villa – accompaniment
* Mariachi Zapopan – accompaniment
# Car Fulla White Boys

Professional ratings :
| Review scores ||
| Source | Rating |
| AllMusic | |
| HipHopDX | |
Car Fulla White Boys is the second solo studio album by American rapper Haystak. It was released on July 20, 2000, via Street Flava Records and Koch Records. Recording sessions took place at Street Flavor Recording Studios in Nashville, Tennessee. Production was handled by Kevin "DJ Dev" Grisham, Sonny Paradise and Shannon Sanders.

## Track listing

All music is composed by Sonny Paradise, Kevin Grisham and Shannon "Mr. Wang" Sanders

## Personnel

* Jason Winfree – main artist
* Ayesha Porter – background vocals
* Ivy Brown – background vocals
* Jeff Priebe – background vocals
* Shannon Sanders – background vocals, horns, producer
* Terry Hudson – background vocals
* Andrew Ramsey – guitar & bass
* Charlie Barrett – guitar (track 10)
* Kevin "DJ Dev" Grisham – scratches, producer
* David Davidson – strings
* Sonny Paradise – producer, executive producer
* Brian Hardin – mixing
* Bernard Grundman – mastering
* Larry Paradise – executive producer
* Manor Graphix – graphics, layout, design
# Florida Northern Railroad

The following railroads have been called Florida Northern Railroad:
* Florida Northern Railroad (defunct), a former railroad north of Jacksonville, Florida
* Florida Northern Railroad (current), a short line railroad near Ocala, Florida
# Florence Newman Trefethen

Florence Marion Newman Trefethen (1921–2012) was an American codebreaker, historian of operations research, poet, and English professor.

## Early life and education

Florence Marion Newman was born in 1921, in Philadelphia. She graduated magna cum laude from Bryn Mawr College in 1943.
She enlisted as a Naval officer during World War II, and served in the WAVES as a codebreaker. She was part of the Magic project, whose decryptions of Japanese communications led to the ambush and death of Japanese Admiral Isoroku Yamamoto. During this service she met Merchant Marine and later mechanical engineer Lloyd M. Trefethen; they married in 1944.
After the war, she came to Girton College, Cambridge on an Ottilie Hancock Bye Fellowship. She earned a Master of Letters there in 1946.

## Career and later life

Trefethen was for many years a professor of English at Tufts University, and served for 18 years as executive editor for the Council of East Asian Studies at Harvard University.
She and her husband had had two children, quilter Gwyned Trefethen in 1953 and mathematician Lloyd N. Trefethen in 1955. She died on March 1, 2012.

## Books

With Joseph F. McCloskey, Trefethen edited the book Operations Research for Management (Johns Hopkins University Press, 1954). She wrote the first chapter of the book, an early history of the field of operations research.
She is also the author of Writing a Poem (The Writer, 1970), on the process of writing poetry.
# Cappy Mountain

Cappy Mountain, located in Klamath County in the U.S. state of Oregon, is a stratovolcano in the Cascade Range. It last erupted in the Pleistocene.

## Geography

Cappy Mountain lies on the northern border of the Mount Thielsen Wilderness. It is surrounded by other Cascade volcanoes, such as the Cinnamon Butte volcanic field to the southwest, Howlock Mountain and Mount Thielsen to the south, and Cowhorn Mountain and Sawtooth Mountain to the north and northwest respectively.
# Flow sampling

In statistics, in flow sampling, as opposed to stock sampling, observations are collected as they enter the particular state of interest during a particular interval. When dealing with duration data (such as employment spells or mortality outcomes), the data sampling method has a direct impact on subsequent analyses and inference. An example in demography would be sampling the number of people who die within a given time frame (e.g. a specific calendar year); a popular example in economics would be the number of people leaving unemployment within a given time frame (e.g. a specific quarter). Researchers imposing similar assumptions but using different sampling methods, can reach fundamentally different conclusions if the joint distribution across the flow and stock samples differ.
Typically, flow samples suffer from right censoring. After a certain amount of time, as the sampling interval ends, the individuals in the sample are not followed any longer, outcomes are recorded and the data is analyzed. In the unemployment example outlined above, we observe the exact duration for individuals leaving unemployment within the time frame. For people that haven't left unemployment yet, we only observe the lower bound of the unemployment spell. The difference between stock and flow sampling can also help explain why certain statistics that measure similar duration measures can differ in important ways. Consider, for instance, the Average Interrupted Duration (AID), the average period for which people that are currently unemployed have been unemployed, and ACD, the average duration of the complete unemployment spell for employed people. Salant shows that heterogeneity in hazard rates between the stock and the flow distribution provides a key to understanding why these two statistics differ. For instance, if the probability of getting a job offer goes down with time unemployed, E[T] < E[S], where S and T stand for observed and actual duration respectively.
Renewal theory is the appropriate tool for handling these issues, and a wide range of estimators have been proposed. These estimators range from fully parametric models such as the Mixed Proportional Hazard model, to nonparametric and semiparametric methods.
# Flow to HDL

Flow to HDL tools and methods convert flow-based system design into a hardware description language (HDL) such as VHDL or Verilog. Typically this is a method of creating designs for field-programmable gate array, application-specific integrated circuit prototyping and digital signal processing (DSP) design. Flow-based system design is well-suited to field-programmable gate array design as it is easier to specify the innate parallelism of the architecture.

## History

The use of flow-based design tools in engineering is a reasonably new trend. Unified Modeling Language is the most widely used example for software design. The use of flow-based design tools allows for more holistic system design and faster development. C to HDL tools and flow have a similar aim, but with C or C-like programming languages.

## Applications

Most applications are ones which take too long with existing supercomputer architectures. These include bioinformatics, CFD, financial processing and oil and gas survey data analysis. Embedded applications that require high performance or real-time data processing are also an area of use. System-on-a-chip design can also be done using this flow.

## Examples

* Xilinx System Generator from Xilinx
* StarBridge VIVA from defunct
* Nimbus from defunct Exsedia
# Arcesis threnodes

Arcesis threnodes is a moth of the family Tortricidae first described by Edward Meyrick in 1905. It is found in India, Sri Lanka and Taiwan.
Larval host plants are Amherstia nobilis and Michelia champaca.