title: Coal tar

text: Long-term, consistent exposure to coal tar likely increases the risk of non-melanoma skin cancers. Evidence is inconclusive whether medical coal tar, which does not remain on the skin for the long periods seen in occupational exposure, causes cancer, because there is insufficient data to make a judgment. While coal tar consistently causes cancer in cohorts of workers with chronic occupational exposure, animal models, and mechanistic studies, the data on short-term use as medicine in humans has so far failed to show any consistently significant increase in rates of cancer.


title: Coal tar

text: Coal tar contains many polycyclic aromatic hydrocarbons, and it is believed that their metabolites bind to DNA, damaging it. The PAHs found in coal tar and air pollution induce immunosenescence and cytotoxicity in epidermal cells. It's possible that the skin can repair itself from this damage after short-term exposure to PAHs but not after long-term exposure. Long-term skin exposure to these compounds can produce "tar warts", which can progress to squamous cell carcinoma.


title: Coal tar

text: Coal tar was one of the first chemical substances proven to cause cancer from occupational exposure, during research in 1775 on the cause of chimney sweeps' carcinoma. Modern studies have shown that working with coal tar pitch, such as during the paving of roads or when working on roofs, increases the risk of cancer.


title: Coal tar

text: The International Agency for Research on Cancer lists coal tars as Group 1 carcinogens, meaning they directly cause cancer. The U.S. Department of Health and Human Services lists coal tars as known human carcinogens.


title: Coal tar

text: In response to public health concerns regarding the carcinogenicity of PAHs some municipalities, such as the city of Milwaukee, have banned the use of common coal tar-based road and driveway sealants citing concerns of elevated PAH content in groundwater.


title: Coal tar

text: Coal tar causes increased sensitivity to sunlight, so skin treated with topical coal tar preparations should be protected from sunlight.


title: Coal tar

text: The residue from the distillation of high-temperature coal tar, primarily a complex mixture of three or more membered condensed ring aromatic hydrocarbons, was listed on 13 January 2010 as a substance of very high concern by the European Chemicals Agency.


title: Coal tar

text: The exact mechanism of action is unknown. Coal tar is a complex mixture of phenols, polycyclic aromatic hydrocarbons (PAHs), and heterocyclic compounds.


title: Coal tar

text: It is a keratolytic agent, which reduces the growth rate of skin cells and softens the skin's keratin.


title: Coal tar

text: Coal tar is produced through thermal destruction (pyrolysis) of coal. Its composition varies with the process and type of coal used – lignite, bituminous or anthracite.


title: Coal tar

text: Coal tar is a mixture of approximately 10,000 chemicals, of which only about 50% have been identified. Most of the chemical compounds are polycyclic aromatic hydrocarbon:


title: Coal tar

text: Others: benzene, toluene, xylenes, cumenes, coumarone, indene, benzofuran, naphthalene and methyl-naphthalenes, acenaphthene, fluorene, phenol, cresols, pyridine, picolines, phenanthracene, carbazole, quinolines, fluoranthene. Many of these constituents are known carcinogens.


title: Coal tar

text: Various phenolic coal tar derivatives have analgesic (pain-killer) properties. These included acetanilide, phenacetin, and paracetamol aka acetaminophen. Paracetamol may be the only coal-tar derived analgesic still in use today. Industrial phenol is now usually synthesized from crude oil rather than coal tar.


title: Coal tar

text: Coal tar derivatives are contra-indicated for people with the inherited red cell blood disorder glucose-6-phosphate dehydrogenase deficiency (G6PD deficiency), as they can cause oxidative stress leading to red blood cell breakdown.


title: Coal tar

text: Coal tar is on the World Health Organization's List of Essential Medicines, the most effective and safe medicines needed in a health system. Coal tar is generally available as a generic medication and over the counter.


title: Coal tar

text: Exposure to coal tar pitch volatiles can occur in the workplace by breathing, skin contact, or eye contact. The Occupational Safety and Health Administration (OSHA) has set the permissible exposure limit) to 0.2 mg/m benzene-soluble fraction over an 8-hour workday. The National Institute for Occupational Safety and Health (NIOSH) has set a recommended exposure limit (REL) of 0.1 mg/m cyclohexane-extractable fraction over an 8-hour workday. At levels of 80 mg/m, coal tar pitch volatiles are immediately dangerous to life and health.


title: Coal tar

text: When used as a medication in the United States, coal tar preparations are considered over-the-counter drug pharmaceuticals and are subject to regulation by the Food and Drug Administration (FDA).


title: Katrina and the Waves

text: Katrina and the Waves were a British rock band widely known for the 1985 hit "Walking on Sunshine". They also won the 1997 Eurovision Song Contest with the song "Love Shine a Light".


title: Katrina and the Waves

text: The band's earliest incarnation was as the Waves, a group that played in and around Cambridge, from 1975 to 1977. The Waves featured guitarist Kimberley Rew and drummer Alex Cooper. This incarnation of the Waves never issued any recordings, and broke up when Rew left to join the Soft Boys.


title: Katrina and the Waves

text: A more direct ancestor of Katrina and the Waves was the band Mama's Cookin', a pop cover band from Feltwell. This band, founded in 1978, featured American Katrina Leskanich on vocals and keyboards, and fellow American, Vince de la Cruz on vocals and lead guitar. By late 1980, Alex Cooper had joined the band on drums, with Bob Jakins on bass. Mama's Cookin' proceeded to gig steadily in England over the next two years, specialising in covers of songs by American acts such as Heart, Foreigner, Linda Ronstadt and ZZ Top.


title: Katrina and the Waves

text: When The Soft Boys broke up in 1981, Rew contacted his old Wave-mate Cooper to see about renewing their musical partnership. Cooper convinced Rew to join Mama's Cookin', and the five-piece group (Leskanich/Rew/Cooper/de la Cruz/Jakins) was quickly renamed the Waves after the band Rew and Cooper had been in together in the mid-1970s.


title: Katrina and the Waves

text: The Waves were initially fronted by singer/songwriter/guitarist Rew, who brought a wealth of original material to the band. Leskanich, meanwhile, originally only sang lead vocals on the cover tunes in the band's repertoire. However, over the first year of the Waves' existence, Rew began to write material for Leskanich to sing, and she was soon the primary vocalist.


title: Katrina and the Waves

text: The Waves made their initial recorded appearances on a 1982 single ("The Nightmare"/"Hey, War Pig!"); both tracks were included on the 1982 Rew solo album called "The Bible of Bop". The Waves then issued their debut EP "Shock Horror!" later in 1982. Around this time, bassist Jakins left the band, and de la Cruz took over on bass. Now a quartet, the Waves issued the single "Brown Eyed Son" in the UK in August 1982 before permanently renaming themselves Katrina and the Waves.


title: Katrina and the Waves

text: In early 1983, the fledgling band recorded, at their own expense, an album of their original material designed to be sold at gigs. Rew wrote all the songs on this album, and Leskanich sang eight of the album's 10 tracks. (Rew sang lead on the other two.)


title: Katrina and the Waves

text: The album was shopped around to various labels, but only Attic Records in Canada responded with an offer. Consequently, although they were based in England, Katrina and the Waves' first album "Walking on Sunshine" was only released in Canada.


title: Katrina and the Waves

text: The album garnered enough critical attention and radio play (especially for the title track) to merit a Canadian tour. In 1984, the group released a follow-up album in Canada ("Katrina and the Waves 2"), with Leskanich now handling all the lead vocals. Rew was still the primary songwriter, but de la Cruz was also responsible for a few songs, including the Canadian airplay hit "Mexico".


title: Katrina and the Waves

text: Also in 1984, the band received their first ever airplay on BBC Radio 1 when DJ Richard Skinner played the track "Que te quiero", whilst their song "Going Down to Liverpool" was covered by the Bangles, which added to their profile. With the group building a fan base with their recordings and extensive touring, major label interest began to build, and Katrina and the Waves eventually signed an international deal with Capitol Records in 1985.


title: Katrina and the Waves

text: For the first Capitol album, the band re-recorded, remixed, or overdubbed 10 songs from their earlier Canadian releases to create their self-titled international debut album in 1985.


title: Katrina and the Waves

text: The "Katrina and the Waves" album was a substantial critical and commercial success, and the group had a worldwide hit with the song "Walking on Sunshine," (no. 9 US, no. 8 UK, a completely re-recorded, and substantially rearranged version of the song when compared to its initial 1983 Canada-only release). A Grammy award nomination for Best New Artist followed, as did constant touring, both of which helped to spur moderate sales of new releases.


title: Katrina and the Waves

text: A follow-up single to "Walking on Sunshine" called "Do You Want Crying" (written by de la Cruz) also became a top 40 US hit, reaching no. 37 in the late summer of 1985.


title: Katrina and the Waves

text: However, the band's follow-up album to "Katrina and the Waves" (simply entitled "Waves") did not meet with the same measure of success, either critically or commercially. Rew wrote only two of the 10 songs on the album; de la Cruz and Leskanich wrote the rest. Drummer Cooper, interviewed some years later, claimed "It was (a) mistake when we started taking over from Kimberley in the musical contribution side. The second Capitol album was awful".


title: Katrina and the Waves

text: The album did spin off a minor UK and US hit in the form of the Rew-penned "Is That It?" (no. 70 US, no. 82 UK), and "Sun Street" (a de la Cruz composition) was a UK top 30 hit in 1986. However, Capitol dropped the band after the "Waves" album.


title: Katrina and the Waves

text: The band subsequently recorded a 1989 album for Capitol-distributed SBK Records called "Break of Hearts", a harder, more rock-oriented effort than their previous releases. The album included "That's the Way" which reached no. 16 in the US (credited to Leskanich/Rew), but subsequent singles, including "Rock 'n' Roll Girl", failed to chart, and the band once again were dropped from their label.


title: Katrina and the Waves

text: Throughout the 1990s, Katrina and the Waves recorded fairly steadily, though most releases were available only in continental Europe and/or Canada, and they issued no charting singles. They also recorded the song "We Gotta Get Out of This Place" with Eric Burdon for the TV series "China Beach" in 1990.


title: Katrina and the Waves

text: On 3 May 1997, the band won the 1997 Eurovision Song Contest for the United Kingdom with the song "Love Shine a Light". The song won by a then-record margin of 70 points over the Irish runner-up. "Love Shine a Light" became Katrina and the Waves' biggest-ever UK hit, peaking at no. 3 in the UK Singles Chart.


title: Katrina and the Waves

text: In a 2020 interview, Katrina Leskanich revealed that, as an American national winning the Eurovision Song Contest for the UK, she was the target of criticism, with some people arguing that UK should have instead sent an English singer to the contest; she also claimed she was asked if she could "try and talk like an English person".


title: Katrina and the Waves

text: Despite their return to the public eye in the UK, Katrina and the Waves were not able to follow up "Love Shine a Light" with another hit, and Leskanich left the group in 1998 after several disagreements within the band. Legal wrangling followed, preventing Leskanich from using the band name. Though attempts were made by the Waves to find a new "Katrina" to front the group, the three remaining group members eventually dissolved the band to pursue individual careers in 1999.


title: Katrina and the Waves

text: When Hurricane Katrina and its storm surge devastated much of the U.S. Gulf Coast on 29 August 2005, the MSNBC news program "Countdown with Keith Olbermann" dubbed its coverage of the storm "Katrina and the Waves"; the name also appeared in numerous headlines and blog postings. A "New York Times" reporter contacted Katrina Leskanich, who said: "The first time I opened the paper and saw 'Katrina kills 9,' it was a bit of a shock...I hope that the true spirit of 'Walking on Sunshine' will prevail. I would hate for the title to be tinged with sadness, and I will have to do my own part to help turn that around." She also stated that she hoped that "Walking on Sunshine" would become an anthem for the Gulf Coast's recovery.


title: Katrina and the Waves

text: 2010 marked the 25th anniversary of the release of "Walking on Sunshine" and a series of back-catalogue reissues and a re-recorded version of the track were released. A free download of one of the tracks from Kimberley Rew's solo album "The Bible of Bop" was given away in March 2010 from the band's website. Katrina Leskanich released "The Live Album" in July 2010 – a mix of Katrina and the Waves hits and new songs recorded in London and Germany.


title: Katrina and the Waves

text: In June 2011, the group threatened legal action against U.S. presidential candidate Michele Bachmann for playing their music on her campaign trail. A statement on the group's official website reads: "Katrina and the Waves would like it to be known that they do not endorse the use of "Walking on Sunshine" by Michele Bachmann and have instructed their lawyers accordingly." Leskanich stated that she wants to ban the Republican party from using the track because she does not agree with her politics.


title: Katrina and the Waves

text: In July 2013, Leskanich performed at the San Fermín festival in Spain for the penultimate gig of the season on Plaza del Castillo.


title: The Music Man (1962 film)

text: The Music Man is a 1962 American musical film directed and produced by Morton DaCosta, based on Meredith Willson's 1957 Broadway musical of the same name, which DaCosta also directed. Robert Preston reprises the title role from the stage version, starring alongside Shirley Jones, Buddy Hackett, Hermione Gingold, Ron Howard, and Paul Ford.


title: The Music Man (1962 film)

text: Released by Warner Bros. on June 19, 1962, the film was one of the biggest hits of the year and was widely acclaimed by critics. It was nominated for six Academy Awards, including Best Picture, with composer Ray Heindorf winning Best Music, Scoring of Music, Adaptation or Treatment. The film also won the Golden Globe Award for Best Motion Picture – Musical or Comedy, and Preston and Jones were both nominated in their respective acting categories. In 2005, the film was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant".


title: The Music Man (1962 film)

text: In 1912, notorious con man Professor Harold Hill arrives in River City, Iowa, anxious to swindle the famously stubborn citizens. Masquerading as a band instructor, Hill’s plan is to convince the townspeople into paying him to create a boys' marching band. Once he collects payment for instruments and uniforms he will take the next train out of town.


title: The Music Man (1962 film)

text: With his associate, Marcellus Washburn, Hill realizes he needs a red herring ploy, so he incites concern among River City's parents that their boys are being seduced into sin and vice by the town's new pool table. He convinces them that a marching band is the only way to keep boys out of trouble, and begins collecting money for the band. Anticipating that Marian Paroo, the town's conscientious librarian and piano instructor, will attempt to discredit him, Hill sets out to seduce her into silence. Also in opposition to Hill is the town's Mayor Shinn, owner of the billiard parlor, who orders the school board to obtain Hill's credentials. When they attempt to do so, Hill avoids their questions by teaching them to sing as a barbershop quartet via "sustained talking". Thereafter, Hill easily tricks them into breaking into four-part harmony whenever they ask for his credentials.


title: The Music Man (1962 film)

text: Hill's wooing of Marian, who distrusts him, has little effect, though he succeeds in winning the admiration of her mother Widow Paroo and attempts to befriend her unhappy younger brother, Winthrop. When Marian discovers that Hill's claim to being a graduate of "Gary Conservatory, Gold Medal, Class of '05" is a lie (the town of Gary was founded in 1906, so there could be no music conservatory with that name before that date), she attempts to expose him, but is interrupted by the arrival of the Wells Fargo wagon. When Winthrop, after years of moody withdrawal, joins in the townspeople's singing and speaks effusively about his new cornet, Marian sees Hill's work as beneficial and hides the evidence of his deceit from Mayor Shinn. Hill tells the boys to learn to play via the "Think System", in which they simply have to think of a tune over and over and will know how to play it without ever practicing on their instruments.


title: The Music Man (1962 film)

text: Hill's con is nearly complete: all he has to do is collect the rest of the money and disappear. Meeting Marian at the traditional footbridge – the first time she has ever been there with a man – he learns that she knew of his deception but did not tell because she is in love with him. He is about to leave town when Charlie Cowell, a disgruntled anvil salesman who was run out of Brighton, Illinois because Hill had conned the townspeople there, comes to River City and exposes Hill. Sought by an angry mob and pressed to leave town by Marcellus and Marian, Hill realizes he is in love with Marian and does not want to leave her.


title: The Music Man (1962 film)

text: Hill is captured by the mob and brought before a town meeting to be tarred and feathered. Marian defends Hill; the townspeople, reminded of how he has brought so many of them together, elect to relent. Mayor Shinn reminds the townspeople how much money Hill has taken, with no apparent result. When he demands to know "Where's the band?" Hill is saved by the town's boys, who play Beethoven's Minuet in G presumably via the "Think System." Although their technical expertise leaves much to be desired, the boys' parents are enthralled. As the boys march out of the town hall, they are suddenly transformed in the townspeople's imagination into a spectacular marching band in resplendent uniforms, playing and marching with perfection, led by Hill. Hill is reunited with Marian, and all the other main characters join in during the credits.


title: The Music Man (1962 film)

text: The members of the original Broadway cast who appear in the film are Robert Preston (Harold Hill), Pert Kelton (Mrs. Paroo), The Buffalo Bills (The School Board), Peggy Mondo (Ethel Toffelmier), and Adina Rice (Alma Hix). Paul Ford (Mayor Shinn) was a replacement during the original run. Susan Luckey (Zaneeta Shinn) and Harry Hickox (Charlie Cowell) both reprise their roles from the first national tour while Monique Vermont (Amaryllis) was a replacement.


title: The Music Man (1962 film)

text: Although Preston scored a great success in the original stage version of the show, he was not the first choice for the film version, mostly because he was not a major box office star. Jack L. Warner was notorious for wanting to film stage musicals with bigger stars than the ones who played the roles onstage. James Cagney and Bing Crosby were offered the role of Harold Hill, but both turned it down. Warner also offered the part to Cary Grant, but he declined, saying "Nobody could do that role as well as Bob Preston." Grant also told Warner that he wouldn't bother to see the film unless Preston was in it. Warner then intended Frank Sinatra for the Harold Hill role, but was finally foiled by Meredith Willson. Willson reminded Warner that the author-composer had cast approval written into his contract, and threatened to cancel the entire project unless Preston played the lead.


title: The Music Man (1962 film)

text: During the recording of the soundtrack musical numbers in late 1961 and early 1962 to which the cast would later lip-sync on the soundstage, some sessions included work on the song "Chicken Fat", a.k.a. President Kennedy's "Youth Fitness Song", performed by Preston.


title: The Music Man (1962 film)

text: Unusual for a musical film at the time, Morton DaCosta, who had directed the stage version of the musical, not only directed the film but produced it as well, ensuring that the film was faithful to the show. In addition to Preston, the actress Pert Kelton and the Buffalo Bills also reprised their stage roles.


title: The Music Man (1962 film)

text: All of the show's songs were retained in their full versions with three exceptions: "Rock Island" was slightly edited, the middle verse of "My White Knight" was retained but the remainder of the song was replaced with "Being In Love" with new music and lyrics by Willson, and "It's You" was initially heard as incidental music and later sung by the school board in abbreviated form in the fairground scene, prior to Cowell exposing Hill as a fraud to the River City townspeople.


title: The Music Man (1962 film)

text: Several phrases were altered for the film, as the writers felt they were too obscurely Midwestern to appeal to a broader audience; the minced oath "Jeely kly!" is Tommy Djilas's catchphrase in the play, while in the film he exclaims, "Great honk!" The word "shipoopi," which has no meaning and was concocted by Willson for the original Broadway show, was left unchanged.


title: The Music Man (1962 film)

text: When Amaryllis plays "Goodnight My Someone", she is playing the keys C, G, and E on the piano, but the notes actually heard are B, F#, and D#. Marian sings the song in B major.


title: The Music Man (1962 film)

text: It is revealed that "Harold Hill" is an alias used by the salesman while in River City. Early in the film, Hill runs into an old friend and crony Marcellus where the latter now works in the livery stable. Marcellus recognizes him and calls him by his (presumably) real name, "Gregory."


title: The Music Man (1962 film)

text: Shirley Jones was pregnant while the film was in production. When she and Preston embraced during the footbridge scene, the baby—who would be born on January 4 and would be named Patrick Cassidy—kicked Preston. The costume designers had to adjust her dresses several times to conceal her pregnancy.


title: The Music Man (1962 film)

text: For the final parade scene, Jack L. Warner selected the University of Southern California's marching band, the Spirit of Troy. Many junior high school students from Southern California were also included, forming the majority of the band. It took approximately eight hours of shooting over two days to film the scene. All the musical instruments for the production were specially made for the film by the Olds Instrument Company in Fullerton, California. The instruments were then refurbished and sold by Olds with no indication they were ever used in the film.


title: The Music Man (1962 film)

text: The film had its premiere in Mason City, Iowa, the home town of Meredith Willson, during the North Iowa Band Festival on June 19, 1962.


title: The Music Man (1962 film)

text: The film received positive reviews and grossed $14,953,846 at the box office, earning $8.1 million in US theatrical rentals. It was the 3rd highest-grossing film of 1962.


title: The Music Man (1962 film)

text: Bosley Crowther in "The New York Times" wrote "It's here, and the rich, ripe roundness of it, the lush amalgam of the many elements of successful American show business that Mr. Willson brought together on the stage, has been preserved and appropriately made rounder and richer through the magnitude of film."


title: The Music Man (1962 film)

text: Robert Landry of "Variety" wrote: "Call this a triumph, perhaps a classic, of corn, smalltown nostalgia and American love of a parade...DaCosta’s use of several of the original Broadway cast players is thoroughly vindicated...But the only choice for the title role, Robert Preston, is the big proof of showmanship in the casting. Warners might have secured bigger screen names but it is impossible to imagine any of them matching Preston’s authority, backed by 883 stage performances."


title: The Music Man (1962 film)

text: Stanley Kauffmann of "The New Republic" wrote 'Robert Preston is a likable man whose likableness let him give one of the best phony performances of the postwar era, in that phony musical The Music Man'.


title: The Music Man (1962 film)

text: Leo Charney reviewing for "AllMovie" wrote that the film "is among the best movie musicals, transforming Meredith Willson's Broadway hit into an energetic slice of Americana. Robert Preston's virtuoso portrayal of con man Harold Hill transfers from the stage (despite the studio's nervousness about casting no-name Preston), and the result is one of the most explosively vital performances in any movie musical."


title: The Music Man (1962 film)

text: In 2005, "The Music Man" was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant".


title: AJ Tracey

text: Ché Wolton Grant (born 4 March 1994), known professionally as AJ Tracey, is a British rapper, singer, songwriter and record producer. He is from Ladbroke Grove, West London. Tracey rose to popularity in 2016 and was listed by "The Guardian" in a list of "best new acts to catch at festivals in 2016".


title: AJ Tracey

text: Tracey's first mainstream EP, "Secure the Bag!" (2017) entered the UK Albums Chart at number thirteen. In 2018, Tracey released the single "Butterflies" featuring British rapper Not3s which served as his commercial breakthrough, peaking in the top 20 on the UK Singles Chart. His self-titled debut album, which was released in 2019 by Warner Records, received critical acclaim and peaked at number three on the UK Albums Chart. It featured his highest-charting single as a solo artist, "Ladbroke Grove", which peaked at number three on the UK Singles Chart and was certified platinum by the BPI.


title: AJ Tracey

text: Grant was born in Brixton and raised in Ladbroke Grove, West London. Grant's father, of Afro-Trinidadian origin, is a former rapper, and his Welsh mother is a former jungle DJ. He was named by his mother after the revolutionary Che Guevara.


title: AJ Tracey

text: He has been rapping since the age of six. He was educated locally at Middle Row Primary school and went on to attend Holland Park School. He dropped out of a criminology course at London Metropolitan University to pursue his music career. He is an avid supporter of Tottenham Hotspur.


title: AJ Tracey

text: Under the stage names Looney and Loonz, Tracey's music can be found online dating back to June 2011. An early SoundCloud account, Looney Tell 'Em, contains eleven tracks, each with free downloads enabled. These include four songs from the scrapped grime EP "The Dungeon" (featuring non-exclusive beats from Spooky and Rude Kid) and two songs from "Didn't Make the Cut", originally slated for release on the scrapped hip hop mixtape "Fuck a Fairytale". His debut mixtape, "Didn't Make the Cut", was released 13 September 2012, and comprises 21 UK rap and grime songs and freestyles which, in his own words, are "the tracks that didn't make it onto my actual mixtape". The project was initially to be titled "Scirocco Musik" and its artwork still reflects this title. In August 2013, his collective, My Team Paid, announced that they were to release a joint mixtape entitled "My Team Paid". One single, "Clouded Skies", emerged, but the project was ultimately scrapped. Tracey's second mixtape, "No More Looney", was released through DatPiff on 30 August 2014. The project includes thirty-three tracks, many of which feature fellow My Team Paid members Big Zuu, Jay Amo, Wax and Sketch.


title: AJ Tracey

text: Tracey first gained attention through appearances on pirate radio stations and the release of his debut EP "The Front" in mid-2015. In December 2015, Tracey released his second EP "Alex Moran", which featured acclaimed tracks including "Spirit Bomb" and "Naila". BBC Radio 1Xtra DJ Sian Anderson also played "Swerve and Skid" heavily on her show during 2015, which was the first song of his that was on commercial radio. During this period, Tracey also recorded (but did not release) a trap EP entitled "Rain". In 2016, Tracey – a Tottenham Hotspur fan – appeared in promotional material for BT Sport's coverage of the Premier League. He also collaborated with Dave over a remix of Ruff Sqwad's Pied Piper to create a well received track entitled "Thiago Silva".


title: AJ Tracey

text: In October 2017, Tracey released his fifth EP, "Secure the Bag!". He also began producing records that year. He made his production debut on "LA4AWEEK", co-produced by Nyge and released in April 2017, and later produced label-mate Big Zuu's "Tell Man Twice", released in August 2017.


title: AJ Tracey

text: In early 2018, AJ Tracey modelled for the OVO clothing line in 2018. In May 2018, Tracey released the single "Butterflies" featuring Not3s. The song served as AJ Tracey's commercial breakthrough, peaking at number 19 on the UK Singles Chart. The single was followed up with "Lo(v/s)er", which peaked at number 38. Tracey also featured on Craig David's album "The Time is now" collaborating on the track "Somebody like me". In early July 2019 the Swedish rapper released his second album, "Mer än rap" ("more than rap"). Tracey was featured on the title track "More Than Rap".


title: AJ Tracey

text: On 21 November 2018, Tracey announced the pre-order of his self-titled debut album, released on 8 February 2019. The lead single, "Doing It", was released for streaming and digital on the same day. Four more singles were released to promote "AJ Tracey": "Butterflies" featuring Not3s, "Psych Out!", "Necklace" featuring Jay Critch and "Ladbroke Grove". "AJ Tracey" debuted at number three on the UK Albums Chart and is certified Silver by the British Phonographic Industry (BPI). "Ladbroke Grove" became Tracey's highest-charting single peaking at number three on the UK Singles Chart. On 10 October 2019, Tracey announced the upcoming release of a deluxe edition of "AJ Tracey", to feature five new songs and a couple of surprises. The album was released on 25 October. On 14 February 2020, AJ Tracey announced his Australian tour starting in Adelaide on 24 April, but was later postponed due to the COVID-19 pandemic.


title: AJ Tracey

text: On 6 October 2020, AJ Tracey released the tracklist for his sixth EP, "Secure the Bag! 2" on Twitter and was later released on 27 November 2020. The EP debuted at number 75 on the UK Albums Charts.


title: AJ Tracey

text: On 4 February 2021, Tracey featured on the track "Bringing It Back" by Digga D. The song topped the UK Chart's Official Trending Chart and debuted at number 5 on the UK Singles Chart.


title: AJ Tracey

text: On 22 March 2021, Tracey announced via a fake press conference on YouTube his second studio album titled "Flu Game" as well as the album's tracklist, which was released on 16 April 2021. The album includes singles such as "Dinner Guest", "West Ten", "Anxious" and "Bringing It Back". Five hours prior to the release of the album, AJ released the single "Little More Love" as well as releasing a music video on YouTube.


title: AJ Tracey

text: On 26 August 2021, Tracey was featured on the Gorillaz track "Jimmy Jimmy" from their "Meanwhile EP".


title: AJ Tracey

text: In June 2017, Tracey endorsed Labour Party leader Jeremy Corbyn in the 2017 UK general election. In a Labour Party campaign video he said: "The Labour Party strongly support the youth in following their dreams and giving people a chance." He added: "In my opinion we need a Labour government to give young people a hope, a chance for their future and I genuinely believe that Corbyn is the man to do it."


title: AJ Tracey

text: In an October 2019 interview with "The Observer", Tracey voiced concerns about climate change and said: "If I'm voting for anyone now it's the Green Party."


title: David Pelletier

text: David Jacques Pelletier (born November 22, 1974) is a Canadian pairs figure skater. With his former wife Jamie Salé, he was the co-gold medal winner at the 2002 Olympic Winter Games. They shared the gold medal with the Russian pair Elena Berezhnaya and Anton Sikharulidze after the 2002 Olympic Winter Games figure skating scandal.


title: David Pelletier

text: Pelletier was born in Sayabec, Quebec, and grew up near the hockey rink. His mother said if he wanted to play hockey, he also had to take figure-skating lessons. He achieved early success as a pair skater with Julie Laporte. They won both the novice and junior titles at the Canadian Figure Skating Championships and placed 7th at the World Junior Figure Skating Championships in 1992. Despite these accomplishments, Pelletier felt his career needed a "shake up" and paired up with Allison Gaylor. They trained in part with Isabelle Brasseur and Lloyd Eisler, and had their biggest success in 1995 when they captured the 1995 Canadian silver medal and represented Canada at the World Figure Skating Championships in Birmingham, England where they placed 15th. That same year, as a single skater, Pelletier placed second in the short program of the men's event at the Canadian championships. He struggled in the long program, falling to fourth overall.


title: David Pelletier

text: After failing to reach the podium the next two years, Pelletier and Gaylor split and Pelletier paired up with young singles skater Caroline Roy. Just before the 1998 Canadian championships, Pelletier's former partner Julie Laporte was killed in a car accident. Pelletier and Roy had a strong skate, but placed 6th and split soon after the event.


title: David Pelletier

text: Pelletier asked coach Richard Gauthier to help him find another partner, and he suggested Salé. They traveled to Edmonton in February 1998 to try out with Salé again. "The first time we grabbed hands, it was just great," said Pelletier, and by the next month Salé had moved to Montreal to skate with him.


title: David Pelletier

text: The Canadian Figure Skating Association invited the pair to compete at Skate Canada, where they immediately made a statement by placing second in the short program, ahead of reigning Canadian Champions Kristy Sargeant and Kris Wirtz, and third in the long program to win the bronze medal. Because of their success, they were invited to the NHK Trophy in Japan and brought home another bronze medal.


title: David Pelletier

text: Their fall successes made them favorites for the Canadian title, but they struggled technically and finished second. The silver medal earned them a spot on the Four Continents and World teams, but Pelletier's back pain forced the pair to withdraw from both competitions. They would ultimately spend two months off the ice recuperating.


title: David Pelletier

text: In the summer of 1999, Gaulthier enlisted the help of Lori Nichol, a Canadian choreographer, to choreograph Salé & Pelletier's programs for the upcoming season. Nichol created a tango piece for their short program, and, after a suggestion from coach Marijane Stong, set their long program to music from the movie "Love Story". The programs got off to a good start. At the 1999 Skate America, Salé & Pelletier won both the short and the long programs, defeating the two-time and reigning world champions, Yelena Berezhnaya and Anton Sikharulidze. At the Nations Cup, their second Grand Prix event, they finished second. However, at the Grand Prix Final, they made several errors in both programs and finished fifth.


title: David Pelletier

text: They competed at the 2000 Canadian Figure Skating Championships in Calgary, Salé's hometown. The two skated a strong short program and a nearly flawless long program, earning five 6.0 marks in presentation—the first for a pair at the championships. Sale & Pelletier captured another 6.0 and the gold medal at the Four Continents Championships in Osaka, Japan. In the 2000 World Figure Skating Championships in Nice, France, they were third after the short program due to an error in a spin. They dropped in the long program, finishing fourth overall.


title: David Pelletier

text: Salé and Pelletier returned to Lori Nichol for their 2000–01 programs. She choreographed a jazzy short to "Come Rain or Come Shine" and a dramatic, mature long to Wagner's opera "Tristan und Isolde." They returned to Skate America and Skate Canada that fall, winning both over Shen/Zhao and Berezhnaya/Sikharulidze, respectively. Berezhnaia/Sikharulidze then narrowly defeated them at Trophée Lalique.


title: David Pelletier

text: The pair was again a great hit at the 2001 Canadian Championships in Winnipeg, but did not earn the string of 6.0s that "Love Story" had brought them the previous year. They went on to win again at Four Continents in Salt Lake City, the site for the 2002 Olympics, and dusted off "Love Story" to win the Grand Prix Final – despite Sale missing the side-by-side triple toe loop in all three phases of the competition.


title: David Pelletier

text: The 2001 World Championships were held in Vancouver, and Salé and Pelletier entered as heavy favorites. Trouble on the side-by-side jumps landed them in third place in the short program, but the team was placed first in the long program despite Salé singling a side-by-side double axel. They were the first Canadian pair to win Worlds since Isabelle Brasseur and Lloyd Eisler in 1993, and the first pair to win at a Worlds held in Canada since Barbara Underhill and Paul Martini in 1984. They would later win the Lou Marsh Trophy as outstanding Canadian athlete in 2001.


title: David Pelletier

text: Salé and Pelletier again demonstrated early success in the 2001–02 season, winning both Skate America and Skate Canada with their new long program to "Adagio Sostenuto" by Rachmaninoff, nicknamed "Orchid" for its flower theme. Perhaps more importantly, they demonstrated technical consistency in both competitions.


title: David Pelletier

text: The Grand Prix Final, held in Kitchener, Ontario, was important because it was the only chance to test their programs against the top contenders before the Olympics. Despite a rough performance of "Orchid" in the first long program, Salé and Pelletier once again won skating a flawless performance of "Love Story" for their second long program. They headed into the 2002 Canadian Championships in Hamilton, Ontario with confidence, having defeated Berezhnaya and Sikharulidze, their biggest rivals. They were able to win the title despite a badly flawed long program.


title: David Pelletier

text: The pressure for the Olympics was intense. Despite several silvers and bronzes, Canada had only won two gold medals in figure skating, in 1948 and 1960. All eyes were on Salé and Pelletier to break the streak and win, overcoming the Russian pairs dominance that had lasted for 40 years. They skated their short program well, only to trip and fall on their closing pose. Because the fall was not on an element, it did not receive a deduction. They placed second behind Berezhnaya and Sikharulidze. In the long program, Salé and Pelletier had no obvious mistakes. Berezhnaya and Sikharludize, meanwhile, skated a more difficult program in which Sikharulidze had a minor step out on a jump element before quickly regaining unison with his partner. The minor error from the Russians had many convinced that the Canadians had won the gold but when the judges' scores came up, Salé and Pelletier were placed second in the long program. Four judges placed Salé and Pelletier first, while five had Berezhnaya and Sikharulidze as the winners, with the Canadians receiving higher technical scores and the Russians higher presentation scores. This result spurred an outcry from the North American media who emphasized Sikharulidze's stepout, although there was no media criticism a year earlier when Salé and Pelletier were awarded gold at the 2001 World Championships, while ignoring that Salé and Pelletier had fallen in the short program and not received a deduction. The commentators received criticism for failing to mention Berezhnaya and Sikharulidze's strengths, with some observers stating that the Russians had performed a more challenging program with greater speed, more interweaving moves and transitions, and less distance between the partners. After the competition, the French judge Marie-Reine Le Gougne admitted she had been pressured by the head of her federation, Didier Gailhaguet, into awarding the long program to the Russians and a judging controversy quickly blew up. The scandal ultimately resulted in the suspension of several judges and officials, and Le Gougne's vote was discarded. Salé and Pelletier were awarded gold medals in a special ceremony later in the week.


title: David Pelletier

text: The controversy resulted in several changes to the judging system after Salt Lake City. First anonymous judging was incorporated to "relieve outside pressure" from judges by separating their names from their marks so pressurers could not assert whether the judge had acted as they wished or not. The ISU Judging System, based on a Code of Points rather than a 6.0 scale, was adopted for use in the Grand Prix season of 2003–04, and for all 2004–05 competitions and thereafter.


title: David Pelletier

text: After the Olympics, having settled in Edmonton, Alberta, the pair turned professional and toured North America with Stars on Ice, a popular figure skating show.


title: David Pelletier

text: Salé and Pelletier were inducted into the Skate Canada Hall of Fame in 2008. They were inducted into the Canadian Olympic Hall of Fame on March 26, 2009.


title: David Pelletier

text: On August 22, 2011, CBC television announced that Pelletier would compete in Season 3 of their figure skating competition TV program "Battle of the Blades". He was paired with hockey player Tessa Bonhomme, and on November 14, 2011, the pair won the $100,000 first prize for the charities of their choice, Ronald McDonald House Southern Alberta (Pelletier) and Canadian Breast Cancer Foundation ‘CIBC Run for the Cure’ – Sudbury Run Site (Bonhomme).


title: David Pelletier

text: After retiring from competition, Pelletier became an ice hockey power skating coach, working with professional and high level amateur players, including players from the Canadian women's hockey team.


title: David Pelletier

text: In September 2014, Pelletier was hired as a skating coach for the Edmonton Oilers of the National Hockey League, a role he still holds as of the 2021–22 season.


title: David Pelletier

text: Pelletier was married to ice dancer Marie-Josee Fortin for a year before he began skating with Salé and ended his marriage. Pelletier proposed to Salé on Christmas Day of 2004 in front of his parents and Salé's mother. The couple was married on December 30, 2005, at the Fairmont Banff Springs hotel in Alberta. In 2006, they served as commentators on the television program "Olympic Ice" which aired on USA Network during the Winter Olympics in Torino Italy. Pelletier and Salé welcomed a son, Jesse Joe Pelletier, on September 30, 2007, at the Sturgeon Community Hospital and Health Centre in St. Albert, Alberta.


title: David Pelletier

text: In June 2010, Salé and Pelletier announced plans to divorce following an 18-month separation, sharing custody of their son. They continued to skate together until retiring in 2012. Pelletier married Russian figure skater Ekaterina Gordeeva on July 25, 2020. They live in Edmonton, Alberta, Canada.


title: What a Girl Wants (film)

text: What a Girl Wants is a 2003 American teen comedy film directed by Dennie Gordon and written by Jenny Bicks and Elizabeth Chandler. Based on the 1955 play "The Reluctant Debutante" by William Douglas-Home, it is the second adaptation for the screen of this work. It stars Amanda Bynes, Colin Firth, and Kelly Preston. The film was released on April 4, 2003, received mixed reviews and grossed $50 million worldwide.


title: What a Girl Wants (film)

text: Daphne Reynolds is a 17-year-old American girl, living with her wedding singer mother, Libby, above a restaurant in Chinatown, New York City. Libby had met Briton Henry Dashwood in Morocco, and they married in a Bedouin wedding ceremony of uncertain legality. They returned to his family estate in England. His father soon died, making Henry the Lord Dashwood. Alistair Payne, the family's aristocratic advisor, tricks Libby into leaving, telling her it is best for Henry's duties not to know she is pregnant, then he lies to Henry, hiding the pregnancy from him and saying that Libby claimed to be leaving because she was in love with someone else.


title: What a Girl Wants (film)

text: Libby has always been honest with Daphne about who her father is, though Daphne feels a sense of emptiness without him. When Daphne graduates from high school, she runs off to London to try and meet her father. Henry has disclaimed his seat in the House of Lords to run for election to the House of Commons, hoping to eventually become Prime Minister of the United Kingdom. Henry is being pushed by Alistair, acting as his political advisor. Henry is engaged to Alistair's daughter, the snobby Glynnis, who has an equally snobby teenage daughter, Clarissa.


title: What a Girl Wants (film)

text: Checking into a London hostel, Daphne meets Ian Wallace, a local boy who works there to support his dream of making it as a musician. After forming a friendship when Ian shows Daphne around London, they start dating. When Henry catches Daphne at his estate, he is stunned to learn he has a child, but his mother, Jocelyne, immediately welcomes her in, giving her a room at the estate. After confirming things in a phone call with Libby, Henry embraces the opportunity to connect with Daphne. Daphne tries to win the acceptance of her father's social circle, but is repeatedly thwarted by Glynnis and Clarissa. In addition, Daphne has to ward off the advances of Armistead Stewart, a sleazy and arrogant upper-class boy whom Clarissa fancies and with whom Ian has long-standing rivalry. Daphne eventually pushes him into the Thames.


title: What a Girl Wants (film)

text: Daphne inadvertently wins over the aristocracy, including the elderly Princess Charlotte, whenever she interacts with them. However, Henry's political campaign suffers due to Daphne's flamboyant behavior, and his subsequent misbehavior with her. He asks her to assume the more dignified manner of the Dashwood lineage, after which Henry's polling numbers quickly improve. Ian is disappointed in her new behavior, made worse when she stands him up in favor of attending an upper-class social function.


title: What a Girl Wants (film)

text: During her coming-out party, hosted by her father (who flies Libby over to attend), Daphne overhears Alistair telling Glynnis how he "got rid of" Libby 17 years earlier. When Daphne confronts him, Glynnis locks her in another room. Glynnis then asks Ian, the band's lead singer, to announce the father–daughter dance, knowing Henry will have to dance with Clarissa. Libby frees Daphne, but when they see Henry dancing with Clarissa, Daphne rejects her new self, telling Henry she is returning to the United States. Sometime later, Henry surprises everyone by announcing that he is withdrawing from the election. As he leaves the press conference, Henry discovers that Alistair knew about Libby's pregnancy and manipulated their separation. Henry punches Alistair in the face, then breaks off his engagement to Glynnis.


title: What a Girl Wants (film)

text: Daphne is serving as a caterer at a wedding, where Libby is the singer. When the father–daughter dance begins, Henry shows up, telling Daphne that he loves her for who she is. Daphne embraces him, calling him "Dad" for the first time. Daphne finally gets the father–daughter dance she has been longing for her whole life. Henry informs Daphne that he has brought a large apology present for her—at which point Ian appears and asks her to dance. As Ian and Daphne dance, Henry apologizes to Libby, and the two also start dancing.


title: What a Girl Wants (film)

text: In the epilogue, Glynnis marries a wealthy nobleman (who bores her to death), Clarissa marries Armistead (who still womanizes), and Alistair works on a London tour bus. Henry and Libby are legally married in a Bedouin ceremony. Daphne is accepted into Oxford and is dating Ian.


title: What a Girl Wants (film)

text: On Rotten Tomatoes the film holds an approval rating of 36% based on 109 reviews, with an average rating of 4.80/10. The website's critical consensus reads, "Little girls will definitely enjoy it, but it's too syrupy and predictable for adults." On Metacritic, the film has a weighted average score of 41 out of 100, based on 27 critics, indicating "mixed or average reviews". Audiences surveyed by CinemaScore gave the film a grade "A" on scale of A to F.


title: What a Girl Wants (film)

text: Edward Guthmann of The "San Francisco Chronicle" called it a "dreadful teen comedy." Anya Kamenetz of "The Village Voice" described the film as "a sanitized adventure for the Mary Kate-and-Ashley set."


title: What a Girl Wants (film)

text: In its opening weekend, the film grossed $11.4 million in 2,964 theaters in the United States and Canada, ranking #2 at the box office behind fellow newcomer "Phone Booth" ($15 million). By the end of its run, the film had grossed $36.1 million domestically and $14.6 million internationally, totaling $50.7 million worldwide.


title: What a Girl Wants (film)

text: Before the US release of the film, print advertisements were altered to remove the peace sign that Bynes was giving in the poster as the 2003 invasion of Iraq by the United States, the United Kingdom and their allied forces had begun. A rep for Warner Bros. explained "'In a time of war, we made a slight alteration so that we could avoid any potential political statement in a completely nonpolitical film."


title: Convex hull

text: In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset.


title: Convex hull

text: Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points.


title: Convex hull

text: The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its dual problem of intersecting half-spaces, are fundamental problems of computational geometry. They can be solved in time formula_1 for two or three dimensional point sets, and in time matching the worst-case output complexity given by the upper bound theorem in higher dimensions.


title: Convex hull

text: As well as for finite point sets, convex hulls have also been studied for simple polygons, Brownian motion, space curves, and epigraphs of functions. Convex hulls have wide applications in mathematics, statistics, combinatorial optimization, economics, geometric modeling, and ethology. Related structures include the orthogonal convex hull, convex layers, Delaunay triangulation and Voronoi diagram, and convex skull.


title: Convex hull

text: A set of points in a Euclidean space is defined to be convex if it contains the line segments connecting each pair of its points. The convex hull of a given set formula_2 may be defined as


title: Convex hull

text: For bounded sets in the Euclidean plane, not all on one line, the boundary of the convex hull is the simple closed curve with minimum perimeter containing formula_2. One may imagine stretching a rubber band so that it surrounds the entire set formula_8 and then releasing it, allowing it to contract; when it becomes taut, it encloses the convex hull of formula_8. This formulation does not immediately generalize to higher dimensions: for a finite set of points in three-dimensional space, a neighborhood of a spanning tree of the points encloses them with arbitrarily small surface area, smaller than the surface area of the convex hull. However, in higher dimensions, variants of the obstacle problem of finding a minimum-energy surface above a given shape can have the convex hull as their solution.


title: Convex hull

text: For objects in three dimensions, the first definition states that the convex hull is the smallest possible convex bounding volume of the objects.


title: Convex hull

text: The definition using intersections of convex sets may be extended to non-Euclidean geometry, and the definition using convex combinations may be extended from Euclidean spaces to arbitrary real vector spaces or affine spaces; convex hulls may also be generalized in a more abstract way, to oriented matroids.


title: Convex hull

text: It is not obvious that the first definition makes sense: why should there exist a unique minimal convex set containing formula_2, for every formula_2? However, the second definition, the intersection of all convex sets containing formula_2, is well-defined. It is a subset of every other convex set formula_13 that contains formula_2, because formula_13 is included among the sets being intersected. Thus, it is exactly the unique minimal convex set containing formula_2. Therefore, the first two definitions are equivalent.


title: Convex hull

text: Each convex set containing formula_2 must (by the assumption that it is convex) contain all convex combinations of points in formula_2, so the set of all convex combinations is contained in the intersection of all convex sets containing formula_2. Conversely, the set of all convex combinations is itself a convex set containing formula_2, so it also contains the intersection of all convex sets containing formula_2, and therefore the second and third definitions are equivalent.


title: Convex hull

text: In fact, according to Carathéodory's theorem, if formula_2 is a subset of a formula_23-dimensional Euclidean space, every convex combination of finitely many points from formula_2 is also a convex combination of at most formula_25 points in formula_2. The set of convex combinations of a formula_27-tuple of points is a simplex; in the plane it is a triangle and in three-dimensional space it is a tetrahedron. Therefore, every convex combination of points of formula_2 belongs to a simplex whose vertices belong to formula_2, and the third and fourth definitions are equivalent.


title: Convex hull

text: In two dimensions, the convex hull is sometimes partitioned into two parts, the upper hull and the lower hull, stretching between the leftmost and rightmost points of the hull. More generally, for convex hulls in any dimension, one can partition the boundary of the hull into upward-facing points (points for which an upward ray is disjoint from the hull), downward-facing points, and extreme points. For three-dimensional hulls, the upward-facing and downward-facing parts of the boundary form topological disks.


title: Convex hull

text: The "closed convex hull" of a set is the closure of the convex hull, and the "open convex hull" is the interior (or in some sources the relative interior) of the convex hull.


title: Convex hull

text: The closed convex hull of formula_2 is the intersection of all closed half-spaces containing formula_2.


title: Convex hull

text: If the convex hull of formula_2 is already a closed set itself (as happens, for instance, if formula_2 is a finite set or more generally a compact set), then it equals the closed convex hull. However, an intersection of closed half-spaces is itself closed, so when a convex hull is not closed it cannot be represented in this way.


title: Convex hull

text: If the open convex hull of a set formula_2 is formula_23-dimensional, then every point of the hull belongs to an open convex hull of at most formula_36 points of formula_2. The sets of vertices of a square, regular octahedron, or higher-dimensional cross-polytope provide examples where exactly formula_36 points are needed.


title: Convex hull

text: Topologically, the convex hull of an open set is always itself open, and the convex hull of a compact set is always itself compact. However, there exist closed sets for which the convex hull is not closed. For instance, the closed set


title: Convex hull

text: (the set of points that lie on or above the witch of Agnesi) has the open upper half-plane as its convex hull.


title: Convex hull

text: The compactness of convex hulls of compact sets, in finite-dimensional Euclidean spaces, is generalized by the Krein–Smulian theorem, according to which the closed convex hull of a weakly compact subset of a Banach space (a subset that is compact under the weak topology) is weakly compact.


title: Convex hull

text: An extreme point of a convex set is a point in the set that does not lie on any open line segment between any other two points of the same set.


title: Convex hull

text: For a convex hull, every extreme point must be part of the given set, because otherwise it cannot be formed as a convex combination of given points.


title: Convex hull

text: According to the Krein–Milman theorem, every compact convex set in a Euclidean space (or more generally in a locally convex topological vector space) is the convex hull of its extreme points. However, this may not be true for convex sets that are not compact; for instance, the whole Euclidean plane and the open unit ball are both convex, but neither one has any extreme points. Choquet theory extends this theory from finite convex combinations of extreme points to infinite combinations (integrals) in more general spaces.


title: Convex hull

text: When applied to a finite set of points, this is the closure operator of an antimatroid, the shelling antimatroid of the point set.


title: Convex hull

text: Every antimatroid can be represented in this way by convex hulls of points in a Euclidean space of high-enough dimension.


title: Convex hull

text: The operations of constructing the convex hull and taking the Minkowski sum commute with each other, in the sense that the Minkowski sum of convex hulls of sets gives the same result as the convex hull of the Minkowski sum of the same sets. This provides a step towards the Shapley–Folkman theorem bounding the distance of a Minkowski sum from its convex hull.


title: Convex hull

text: The projective dual operation to constructing the convex hull of a set of points is constructing the intersection of a family of closed halfspaces that all contain the origin (or any other designated point).


title: Convex hull

text: The convex hull of a finite point set formula_50 forms a convex polygon when formula_51, or more generally a convex polytope in formula_52. Each extreme point of the hull is called a vertex, and (by the Krein–Milman theorem) every convex polytope is the convex hull of its vertices. It is the unique convex polytope whose vertices belong to formula_8 and that encloses all of formula_8.


title: Convex hull

text: According to the upper bound theorem, the number of faces of the convex hull of formula_55 points in formula_23-dimensional Euclidean space is formula_57. In particular, in two and three dimensions the number of faces is at most linear in formula_55.


title: Convex hull

text: The convex hull of a simple polygon encloses the given polygon and is partitioned by it into regions, one of which is the polygon itself. The other regions, bounded by a polygonal chain of the polygon and a single convex hull edge, are called "pockets". Computing the same decomposition recursively for each pocket forms a hierarchical description of a given polygon called its "convex differences tree". Reflecting a pocket across its convex hull edge expands the given simple polygon into a polygon with the same perimeter and larger area, and the Erdős–Nagy theorem states that this expansion process eventually terminates.


title: Convex hull

text: The curve generated by Brownian motion in the plane, at any fixed time, has probability 1 of having a convex hull whose boundary forms a continuously differentiable curve. However, for any angle formula_59 in the range formula_60, there will be times during the Brownian motion where the moving particle touches the boundary of the convex hull at a point of angle formula_59. The Hausdorff dimension of this set of exceptional times is (with high probability) formula_62.


title: Convex hull

text: For the convex hull of a space curve or finite set of space curves in general position in three-dimensional space, the parts of the boundary away from the curves are developable and ruled surfaces. Examples include the oloid, the convex hull of two circles in perpendicular planes, each passing through the other's center, the sphericon, the convex hull of two semicircles in perpendicular planes with a common center, and D-forms, the convex shapes obtained from Alexandrov's uniqueness theorem for a surface formed by gluing together two planar convex sets of equal perimeter.


title: Convex hull

text: The convex hull or lower convex envelope of a function formula_63 on a real vector space is the function whose epigraph is the lower convex hull of the epigraph of formula_63.


title: Convex hull

text: It is the unique maximal convex function majorized by formula_63. The definition can be extended to the convex hull of a set of functions (obtained from the convex hull of the union of their epigraphs, or equivalently from their pointwise minimum) and, in this form, is dual to the convex conjugate operation.


title: Convex hull

text: In computational geometry, a number of algorithms are known for computing the convex hull for a finite set of points and for other geometric objects.


title: Convex hull

text: Computing the convex hull means constructing an unambiguous, efficient representation of the required convex shape. Output representations that have been considered for convex hulls of point sets include a list of linear inequalities describing the facets of the hull, an undirected graph of facets and their adjacencies, or the full face lattice of the hull. In two dimensions, it may suffice more simply to list the points that are vertices, in their cyclic order around the hull.


title: Convex hull

text: For convex hulls in two or three dimensions, the complexity of the corresponding algorithms is usually estimated in terms of formula_55, the number of input points, and formula_67, the number of points on the convex hull, which may be significantly smaller than formula_55. For higher-dimensional hulls, the number of faces of other dimensions may also come into the analysis. Graham scan can compute the convex hull of formula_55 points in the plane in time formula_1. For points in two and three dimensions, more complicated output-sensitive algorithms are known that compute the convex hull in time formula_71. These include Chan's algorithm and the Kirkpatrick–Seidel algorithm. For dimensions formula_72, the time for computing the convex hull is formula_57, matching the worst-case output complexity of the problem. The convex hull of a simple polygon in the plane can be constructed in linear time.


title: Convex hull

text: Dynamic convex hull data structures can be used to keep track of the convex hull of a set of points undergoing insertions and deletions of points, and kinetic convex hull structures can keep track of the convex hull for points moving continuously.


title: Convex hull

text: The construction of convex hulls also serves as a tool, a building block for a number of other computational-geometric algorithms such as the rotating calipers method for computing the width and diameter of a point set.


title: Convex hull

text: Several other shapes can be defined from a set of points in a similar way to the convex hull, as the minimal superset with some property, the intersection of all shapes containing the points from a given family of shapes, or the union of all combinations of points for a certain type of combination. For instance:


title: Convex hull

text: The Delaunay triangulation of a point set and its dual, the Voronoi diagram, are mathematically related to convex hulls: the Delaunay triangulation of a point set in formula_77 can be viewed as the projection of a convex hull in formula_78


title: Convex hull

text: The alpha shapes of a finite point set give a nested family of (non-convex) geometric objects describing the shape of a point set at different levels of detail.


title: Convex hull

text: Each of alpha shape is the union of some of the features of the Delaunay triangulation, selected by comparing their circumradius to the parameter alpha. The point set itself forms one endpoint of this family of shapes, and its convex hull forms the other endpoint.


title: Convex hull

text: The convex layers of a point set are a nested family of convex polygons, the outermost of which is the convex hull, with the inner layers constructed recursively from the points that are not vertices of the convex hull.


title: Convex hull

text: The convex skull of a polygon is the largest convex polygon contained inside it. It can be found in polynomial time, but the exponent of the algorithm is high.


title: Convex hull

text: Convex hulls have wide applications in many fields. Within mathematics, convex hulls are used to study polynomials, matrix eigenvalues, and unitary elements, and several theorems in discrete geometry involve convex hulls. They are used in robust statistics as the outermost contour of Tukey depth, are part of the bagplot visualization of two-dimensional data, and define risk sets of randomized decision rules. Convex hulls of indicator vectors of solutions to combinatorial problems are central to combinatorial optimization and polyhedral combinatorics. In economics, convex hulls can be used to apply methods of convexity in economics to non-convex markets. In geometric modeling, the convex hull property Bézier curves helps find their crossings, and convex hulls are part of the measurement of boat hulls. And in the study of animal behavior, convex hulls are used in a standard definition of the home range.


title: Convex hull

text: Newton polygons of univariate polynomials and Newton polytopes of multivariate polynomials are convex hulls of points derived from the exponents of the terms in the polynomial, and can be used to analyze the asymptotic behavior of the polynomial and the valuations of its roots. Convex hulls and polynomials also come together in the Gauss–Lucas theorem, according to which the roots of the derivative of a polynomial all lie within the convex hull of the roots of the polynomial.


title: Convex hull

text: In discrete geometry, both Radon's theorem and Tverberg's theorem concern the existence of partitions of point sets into subsets with intersecting convex hulls.


title: Convex hull

text: The definitions of a convex set as containing line segments between its points, and of a convex hull as the intersection of all convex supersets, apply to hyperbolic spaces as well as to Euclidean spaces. However, in hyperbolic space, it is also possible to consider the convex hulls of sets of ideal points, points that do not belong to the hyperbolic space itself but lie on the boundary of a model of that space. The boundaries of convex hulls of ideal points of three-dimensional hyperbolic space are analogous to ruled surfaces in Euclidean space, and their metric properties play an important role in the geometrization conjecture in low-dimensional topology. Hyperbolic convex hulls have also been used as part of the calculation of canonical triangulations of hyperbolic manifolds, and applied to determine the equivalence of knots.


title: Convex hull

text: See also the section on Brownian motion for the application of convex hulls to this subject, and the section on space curves for their application to the theory of developable surfaces.


title: Convex hull

text: In robust statistics, the convex hull provides one of the key components of a bagplot, a method for visualizing the spread of two-dimensional sample points. The contours of Tukey depth form a nested family of convex sets, with the convex hull outermost, and the bagplot also displays another polygon from this nested family, the contour of 50% depth.


title: Convex hull

text: In statistical decision theory, the risk set of a randomized decision rule is the convex hull of the risk points of its underlying deterministic decision rules.


title: Convex hull

text: In combinatorial optimization and polyhedral combinatorics, central objects of study are the convex hulls of indicator vectors of solutions to a combinatorial problem. If the facets of these polytopes can be found, describing the polytopes as intersections of halfspaces, then algorithms based on linear programming can be used to find optimal solutions. In multi-objective optimization, a different type of convex hull is also used, the convex hull of the weight vectors of solutions. One can maximize any quasiconvex combination of weights by finding and checking each convex hull vertex, often more efficiently than checking all possible solutions.


title: Convex hull

text: In the Arrow–Debreu model of general economic equilibrium, agents are assumed to have convex budget sets and convex preferences. These assumptions of convexity in economics can be used to prove the existence of an equilibrium.


title: Convex hull

text: When actual economic data is non-convex, it can be made convex by taking convex hulls. The Shapley–Folkman theorem can be used to show that, for large markets, this approximation is accurate, and leads to a "quasi-equilibrium" for the original non-convex market.


title: Convex hull

text: In geometric modeling, one of the key properties of a Bézier curve is that it lies within the convex hull of its control points. This so-called "convex hull property" can be used, for instance, in quickly detecting intersections of these curves.


title: Convex hull

text: In the geometry of boat and ship design, chain girth is a measurement of the size of a sailing vessel, defined using the convex hull of a cross-section of the hull of the vessel. It differs from the skin girth, the perimeter of the cross-section itself, except for boats and ships that have a convex hull.


title: Convex hull

text: The convex hull is commonly known as the minimum convex polygon in ethology, the study of animal behavior, where it is a classic, though perhaps simplistic, approach in estimating an animal's home range based on points where the animal has been observed. Outliers can make the minimum convex polygon excessively large, which has motivated relaxed approaches that contain only a subset of the observations, for instance by choosing one of the convex layers that is close to a target percentage of the samples, or in the local convex hull method by combining convex hulls of neighborhoods of points.


title: Convex hull

text: In quantum physics, the state space of any quantum system — the set of all ways the system can be prepared — is a convex hull whose extreme points are positive-semidefinite operators known as pure states and whose interior points are called mixed states. The Schrödinger–HJW theorem proves that any mixed state can in fact be written as a convex combination of pure states in multiple ways.


title: Convex hull

text: A convex hull in thermodynamics was identified by Josiah Willard Gibbs (1873), although the paper was published before the convex hull was so named.


title: Convex hull

text: In a set of energies of several stoichiometries of a material, only those measurements on the lower convex hull will be stable. When removing a point from the hull and then calculating its distance to the hull, its distance to the new hull represents the degree of stability of the phase.


title: Convex hull

text: The lower convex hull of points in the plane appears, in the form of a Newton polygon, in a letter from Isaac Newton to Henry Oldenburg in 1676. The term "convex hull" itself appears as early as the work of , and the corresponding term in German appears earlier, for instance in Hans Rademacher's review of . Other terms, such as "convex envelope", were also used in this time frame. By 1938, according to Lloyd Dines, the term "convex hull" had become standard; Dines adds that he finds the term unfortunate, because the colloquial meaning of the word "hull" would suggest that it refers to the surface of a shape, whereas the convex hull includes the interior and not just the surface.


title: Nintendo eShop

text: The Nintendo eShop is a digital distribution service powered by the Nintendo Network for the Wii U and Nintendo 3DS, and by a dedicated online infrastructure for the Nintendo Switch. Launched in June 2011 on the Nintendo 3DS, the eShop was enabled by the release of a system update that added the functionality to the Nintendo 3DS's HOME Menu. It is the successor to both the Wii Shop Channel and DSi Shop. Unlike on the Nintendo 3DS, the eShop was made available on the launch date of the Wii U, although a system update is required in order to access it. It is also a multitasking application, which means it is easily accessible even when a game is already running in the background through the system software, though this feature is exclusive to the Wii U and the Nintendo Switch. The Nintendo eShop features downloadable games, demos, applications, streaming videos, consumer rating feedback, and other information on upcoming game releases.


title: Nintendo eShop

text: A limited variant of the Nintendo eShop for the Nintendo 3DS family was discontinued on July 31, 2020, for various Latin American and Caribbean markets, as well as for the Southeast Asian and Middle Eastern markets. A limited variant of the Nintendo eShop for the Wii U was also discontinued at the same day for said Latin American and Caribbean markets. As of that date, the ability to download, redownload, and update any software became unavailable, and games using the eShop were also affected. It was later announced on July 19, 2022, that the ability to purchase, download, and play new content --Virtual Console games-- on the Nintendo eShop for the Wii U and the Nintendo 3DS would be discontinued for the rest of the world on March 27, 2023, with the ability to add credit cards ceasing by May 23, 2022, followed by the inability to add funds by August 29, 2022 (except for users who linked their Nintendo Network ID with their Nintendo Account, who can add funds until March 27, 2023). Redownloading previously purchased content and/or updating will remain available.<ref name="NOA closes eShop on 3DS/Wii U"></ref>


title: Nintendo eShop

text: Initially, the two versions of the Nintendo eShop between the Nintendo 3DS and Wii U were independent of each other. Whilst this remains largely true, after the implementation of Nintendo Network ID for the Nintendo 3DS, users that register the same ID account between both systems (currently at one time per console) can share a combined funds balance, home address, saved credit and debit card information, wish list entries, and (formerly) linked Club Nintendo accounts. With the release of the Nintendo Switch version of the Nintendo eShop, the balance stored on a Nintendo Network ID can be shared or transferred to a Nintendo Account to be spent on the Nintendo Switch.


title: Nintendo eShop

text: The eShop stores a record of all downloads and purchases, allowing users to re-download previously purchased software at no additional charge, provided the software is still available on the eShop. Downloads can be started immediately, or they can be queued up and be pushed to the console while it is not in use or when the eShop application is not running. Users upgrading from a Nintendo DSi system can transfer their previous DSiWare purchases to the Nintendo 3DS, with limited exceptions, such as "Flipnote Studio". A December 2011 update enabled a similar feature allowing users to transfer their purchases between 3DS systems. Before the implementation of Nintendo Network ID for the Nintendo 3DS in December 2013, only five transfers between Nintendo 3DS systems were permitted. The limit on system transfers has since been permanently waived.


title: Nintendo eShop

text: Unlike the Wii Shop Channel and the DSi Shop services, which use Nintendo Points for purchases, the Nintendo eShop lists prices in the appropriate regional currencies (e.g. United States dollars and euros). Accounts can be funded using either credit cards or prepaid cards purchased in stores.


title: Nintendo eShop

text: In China, the Nintendo eShop was opened on December 10, 2019. Users can only log in with a WeChat account, and the account can only be funded via WeChat Pay. In addition, purchasing downloadable content from other regions is disabled due to the lack of the ability to sign in with a Nintendo Account and the general region locking of the Nintendo Switch for the Chinese market.


title: Nintendo eShop

text: The Nintendo eShop can be accessed any time via the HOME menu screen, even when a game is already running, on Wii U and Nintendo Switch. Background downloading is also possible via SpotPass while using any other application on the Wii U or Nintendo 3DS, and while in Sleep Mode on Nintendo Switch. Currently, 10 downloads can be queued at a time. The status of the downloads can be checked on the HOME menu under the "Download Manager". If notifications are activated, a pop-up message will appear in the top right corner of the screen to notify the user that a download is finished.


title: Nintendo eShop

text: The Nintendo eShop supports user reviews of games, applications, and other media. After an eShop title has been acquired and used for at least one hour, users can then submit a review consisting of a crescent range of one to five "stars", representing the title's quality. Users can also categorize games by age and gender, and as being suitable for either hardcore or casual gamers. The Wii U had Miiverse integration for user reviews on the Nintendo eShop.


title: Nintendo eShop

text: On September 13, 2012, during a Japanese Nintendo Direct presentation, Satoru Iwata introduced a new service called Deluxe Digital Promotion (North America)/Nintendo Network Premium (Europe, Australia, and Japan). It was a loyalty program similar to PlayStation Plus offered on PlayStation Network and Xbox Live Gold on Xbox Live.


title: Nintendo eShop

text: Consumers who purchased the Wii U Deluxe Pack in North America, or the Wii U Premium Pack in Europe and Japan, would receive a free two-year subscription to this service which lets Wii U owners receive points for each digital purchase.


title: Nintendo eShop

text: Members who bought games and apps through the Wii U Nintendo eShop would receive ten percent of the price back in the form of Nintendo Points, which could subsequently be put towards future online purchases on both the Wii U and Nintendo 3DS eShop. The promotion was available through March 31, 2015.


title: Nintendo eShop

text: The program was discontinued on April 1, 2015, and the URL just leads to a discontinuation message and the reader gets a link to Nintendo's official website. The service was never fully implemented beyond its promotional period. The My Nintendo program features a similar concept for anyone who links their Nintendo Network ID to their Nintendo Account profile, where users can earn Gold Points via any Nintendo eShop purchase and redeem them for full downloads or discount coupons available.


title: Nintendo eShop

text: The following types of games, applications and media are available to download from the Nintendo eShop (or Wii Shop Channel in the Wii U's Wii Mode):


title: Nintendo eShop

text: The majority of Wii U, Nintendo 3DS, Nintendo Switch, and select Wii retail releases are on the Nintendo eShop. The first is "New Super Mario Bros. 2", launched on the Nintendo 3DS eShop alongside its retail release in August 2012. A system update in March 2013 allowed players to transfer save data from a physical version of a game to a download version.


title: Nintendo eShop

text: Any video game company, particularly independent video game developers, may publish via the Nintendo eShop as download-only software for the Nintendo 3DS, Wii U, and Nintendo Switch. Various games, which may be sold as retail games in some regions, might be released as download-only software in others for various reasons, such as cost-effective localization.


title: Nintendo eShop

text: "3D Classics" is a series of NES/Famicom, Arcade, Sega Mega Drive/Genesis, and Sega Master System/SG-1000 games remade with added 3D visuals and updated features, although the overall graphics retain their original art style and appearance. These are exclusive to the Nintendo 3DS family.


title: Nintendo eShop

text: Add-on content includes downloadable content (DLC) or microtransactions to augment existing games with new features, and patches. This content can both be free to download or purchasable. Add-on software can be added to both downloadable and physical games, and be purchased either individually or via in-game stores.


title: Nintendo eShop

text: As of December 6, 2011, a system update upgraded the service to feature downloadable demos of retail games and eShop games. Developers have the option to limit access to demos, such as limiting the number of plays available to the user. When the number of plays reaches zero, the demo cannot be opened. The first paid demo was released in Japan on August 4, 2011, and free demos were further released in Japan on December 27, 2011 and in North America on January 19, 2012. As of December 9, 2013, Nintendo Network IDs were implemented onto the Nintendo 3DS, becoming required for downloading free demos from the eShop.


title: Nintendo eShop

text: Software updates, more commonly known as patches, have been available on both Nintendo 3DS, since April 25, 2012, and Wii U, since November 18, 2012, via a system update. These system updates gave the ability to patch downloadable and retail releases, through both the Nintendo eShop and HOME Menu. These patches have the main purpose of fixing security vulnerabilities and other bugs and improving usability or performance. Patches can also be downloaded while using other applications via the systems' Download Manager.


title: Nintendo eShop

text: , sometimes abbreviated as VC, is a specialized section of the Nintendo eShop that allows players to purchase and download games and other software for Nintendo's Wii U and Nintendo 3DS consoles.


title: Nintendo eShop

text: The Wii U uses the Wii U Menu and Nintendo eShop to access and purchase Virtual Console games, respectively. Virtual Console games on the Wii U can be suspended and users can also create save states anytime. The GamePad is only compatible with these games through Off-TV Play.


title: Nintendo eShop

text: Select games from the NES, SNES, Nintendo 64, Game Boy Advance, and Nintendo DS libraries are available for purchase on the eShop. Most of the Virtual Console library available on the original Wii is also available on Wii U through the implementation of the console's Wii Mode and Wii Shop Channel, to access and purchase Virtual Console games. Wii Virtual Console games cannot be controlled using the Wii U GamePad, though the current versions of the system software support displaying Wii Virtual Console games on the GamePad screen as if playing any other Wii game.


title: Nintendo eShop

text: The Nintendo 3DS uses the Home Menu and Nintendo eShop to access and purchase Virtual Console games, respectively. Virtual Console games on the Nintendo 3DS can be suspended and users can also create save states anytime. Functionality is available to display the games at native resolution.


title: Nintendo eShop

text: Currently, games for the Game Boy, Game Boy Color, Game Boy Advance (for Nintendo 3DS Ambassadors only) NES, SNES (New Nintendo 3DS exclusive), Sega Game Gear, and Turbografx16 (Japan only) are available on the eShop.


title: Nintendo eShop

text: Twenty free NES and GBA games are available to 3DS owners who became eligible in the Ambassador Program (users who logged onto the Nintendo eShop before August 12, 2011, and did not erase their eShop details). Special features in this interpretation of the Virtual Console allow players to create Restore Points, temporarily saving the game state for use later, and the optional ability to view games in their original resolution accompanied with special borders or templates.


title: Nintendo eShop

text: Game Boy Advance games can be displayed at their original screen resolution like other Virtual Console games but they do not support Sleep Mode, Restore Points, and Home Menu functionality while the game is running.


title: Nintendo eShop

text: WiiWare, for the Wii video game console, has been available for the Wii U since launch day when an update added support for the Wii Shop Channel's library of WiiWare games. Unlike DSiWare on the Nintendo 3DS, WiiWare software is only available for download on the Wii U through Wii Mode, not the Nintendo eShop. Similarly to using Wii software on the Wii U, WiiWare can only be played in its original resolution, via Wii Mode, and Wii U Home Menu functionality is disabled while WiiWare software is being played. Prior to the Wii Shop Channel's closure, there were over 450 downloadable games available in North America . Initially all games except "LostWinds" were published on the Wii U. "LostWinds" had since been patched and made available for transfer and purchase on the Wii U. It was discontinued in January 2019.


title: Nintendo eShop

text: DSiWare, for the Nintendo DSi handheld game console, has been available for the Nintendo 3DS since June 2011, when the Nintendo eShop was first introduced. With a few exceptions for certain games or applications such as "Flipnote Studio", the majority of existing DSiWare software is available for download on the Nintendo 3DS through the Nintendo eShop. Similar to using Nintendo DS software, DSiWare can be optionally viewed in its original resolution and Home Menu functionality, SpotPass, StreetPass, Auto Brightness (New Nintendo 3DS only) and 3D Functionality is disabled whilst DSiWare software is being played. There are over 550 downloadable DSiWare games available in North America as of January 2016. DSiWare games and software on the Nintendo eShop are largely priced near-identically as on the original DSi Shop. Online functionality has been defunct in DSiWare games due to the Nintendo Wi-Fi Connection service ceasing operations as of May 20, 2014.


title: Nintendo eShop

text: The Nintendo eShop offers a wide range of video streaming applications, which correspond to third party streaming services. Some of these services' applications are available for download on Nintendo 3DS and are preinstalled on North American Wii U consoles, such as Netflix, Hulu, and Amazon Prime Video applications. These streaming services are available independently from Nintendo Network services.


title: Nintendo eShop

text: Additionally, some videos can either be downloaded to the system's memory through SpotPass. On the Nintendo 3DS, many of these videos are offered in autostereoscopic 3D; on the Wii U, only 2D high definition videos are available. The exact content available varies by region.


title: Nintendo eShop

text: "Nintendo Unleashed" was a video gaming online magazine published by Future Publishing for Nintendo Network. It is produced by the team behind the Official Nintendo Magazine and features video reviews and previews and footage of upcoming and recently released Nintendo games. Episodes are released monthly on the Nintendo eShop, Nintendo Channel and YouTube where users can watch all the latest news, reviews and previews of Wii, Wii U, Nintendo DS, Nintendo 3DS and Virtual Console games. The show's original name and format was called "Nintendo TV". The show ended sometime in 2014 before the Official Nintendo Magazine ceased publication.


title: Nintendo eShop

text: Nintendo Show 3D was a video gaming online show produced by Nintendo and hosted by Jessie Cantrell. It featured video previews and footage of upcoming and recently released Nintendo 3DS retail and downloadable games. Episodes were released every two weeks on the Nintendo eShop free of charge. This series was exclusive to North American Nintendo 3DS consoles. Nintendo Show 3D released its last episode on March 28, 2013, two years after the North American release of the original Nintendo 3DS.


title: Nintendo eShop

text: The Nintendo eShop offers a wide range of downloadable video content for the Nintendo 3DS. These videos are mostly offered in 3D and are downloaded to the system's storage. To produce and distribute these short films, Nintendo partnered with companies such as Breakthru Films, Black Box Productions, Atlantic Productions, Ka-Ching Cartoons and DreamWorks Animation.


title: Nintendo eShop

text: The Norwegian Consumer Council (NCC) filed suit against Nintendo in February 2018, asserting that the eShop's policy on pre-order refunds violated European consumer law. As the NCC outlined, while European law requires digital storefronts to provide refunds on pre-orders, Nintendo bypassed this for the Switch eShop by having the user click an acknowledgement checkbox that waived their rights to refunds. NCC argued this violated the EU's Consumer Rights Directive 2011 as all pre-orders must be able to be refunded. Nintendo cited that under the directive that offering the checkbox to waive this right was valid. The ("Verbraucherzentrale Bundesverband e. V.", or VBEV) took the lead on the lawsuit by December 2018 as Nintendo's European headquarters were located in Großostheim.


title: Nintendo eShop

text: The Regional Court of Frankfurt ruled in December 2019 for Nintendo, but both the NCC and VBEV appealed the decision. During the appeal, in September 2020 Nintendo changed its pre-order policy to allow refunds for games but only before a week before the game is scheduled for release. Despite this change, the Higher Regional Court of Frankfurt reversed the lower court's decision and ruled against Nintendo in December 2021, stating that its policy still violated the EU consumer's directive, as "the prerequisites for the right of revocation were not met, as the download made available after the pre-order did not yet contain any usable game."


title: Hoʻoponopono

text: Hooponopono () is a traditional Hawaiian practice of reconciliation and forgiveness. The Hawaiian word translates into English simply as "correction", with the synonyms "manage" or "supervise". Similar forgiveness practices are performed on islands throughout the South Pacific, including Hawaii, Samoa, Tahiti and New Zealand. Traditional "Hooponopono" is practiced by Indigenous Hawaiian healers, often within the extended family by a family member.


title: Hoʻoponopono

text: In many Polynesian cultures, it is believed that a person's errors (called "hara" or "hala") caused illness. Some believe error angers the gods, others that it attracts malevolent gods, and still others believe the guilt caused by error made one sick. "In most cases, however, specific 'untie-error' rites could be performed to atone for such errors and thereby diminish one's accumulation of them."


title: Hoʻoponopono

text: Among the islands of Vanuatu in the South Pacific, people believe that illness usually is caused by sexual misconduct or anger. "If you are angry for two or three days, sickness will come," said one local man. The therapy that counters this sickness is confession. The patient, or a family member, may confess. If no one confesses an error, the patient may die. The Vanuatu people believe that secrecy is what gives power to the illness. When the error is confessed, it no longer has power over the person.


title: Hoʻoponopono

text: Like many other islanders, including Hawaiians, people of Tikopia in the Solomon Islands, and on Rarotonga in the Cook Islands, believe that the sins of the father will fall upon the children. If a child is sick, the parents are suspected of quarreling or misconduct. In addition to sickness, social disorder could cause sterility of land or other disasters. Harmony could be restored only by confession and apology.


title: Hoʻoponopono

text: In Pukapuka, it was customary to hold sort of a confessional over patients to determine an appropriate course of action in order to heal them.


title: Hoʻoponopono

text: (a) "To put to rights; to put in order or shape, correct, revise, adjust, amend, regulate, arrange, rectify, tidy up make orderly or neat, administer, superintend, supervise, manage, edit, work carefully or neatly; to make ready, as canoemen preparing to catch a wave."


title: Hoʻoponopono

text: (b) "Mental cleansing: family conferences in which relationships were set right ("hooponopono") through prayer, discussion, confession, repentance, and mutual restitution and forgiveness."


title: Hoʻoponopono

text: Literally, "hoo" is a particle used to make an actualizing verb from the following noun. Here, it creates a verb from the noun "pono", which is defined as: "...goodness, uprightness, morality, moral qualities, correct or proper procedure, excellence, well-being, prosperity, welfare, benefit, true condition or nature, duty; moral, fitting, proper, righteous, right, upright, just, virtuous, fair, beneficial, successful, in perfect order, accurate, correct, eased, relieved; should, ought, must, necessary."


title: Hoʻoponopono

text: "Ponopono" is defined as "to put to rights; to put in order or shape, correct, revise, adjust, amend, regulate, arrange, rectify, tidy up, make orderly or neat."


title: Hoʻoponopono

text: Hawaiian scholar Nana Veary in her book, "Change We Must: My Spiritual Journey" wrote that ho'oponopono was a practice in Ancient Hawaii and this is supported by oral histories from contemporary Hawaiian elders. Pukui first recorded her experiences and observations from her childhood (born 1895) in her 1958 book.


title: Hoʻoponopono

text: Although the word "hooponopono" was not used, early Hawaiian historians documented a belief that illness was caused by breaking kapu, or spiritual laws, and that the illness could not be cured until the sufferer atoned for this transgression, often with the assistance of a praying priest ("kahuna pule") or healing priest ("kahuna lapaau"). Forgiveness was sought from the gods or from the person with whom there was a dispute.


title: Hoʻoponopono

text: Pukui described it as a practice of extended family members meeting to "make right" broken family relations. Some families met daily or weekly, to prevent problems from erupting. Others met when a person became ill, believing that illness was caused by the stress of anger, guilt, recriminations and lack of forgiveness. Kupuna Nana Veary wrote that when any of the children in her family fell ill, her grandmother would ask the parents, "What have you done?" They believed that healing could come only with complete forgiveness of the whole family.


title: Hoʻoponopono

text: Hooponopono corrects, restores and maintains good relationships among family members and with their gods or God by getting to the causes and sources of trouble. Usually the most senior member of the family conducts it. He or she gathers the family together. If the family is unable to work through a problem, they turn to a respected outsider.


title: Hoʻoponopono

text: The process begins with prayer. A statement of the problem is made, and the transgression discussed. Family members are expected to work problems through and cooperate, not "hold fast to the fault". One or more periods of silence may be taken for reflection on the entanglement of emotions and injuries. Everyone's feelings are acknowledged. Then confession, repentance and forgiveness take place. Everyone releases ("kala") each other, letting go. They cut off the past ("oki"), and together they close the event with a ceremonial feast, called "pani", which often included eating "limu kala" or kala seaweed, symbolic of the release.


title: Hoʻoponopono

text: In a form used by the family of "kahuna" Makaweliweli of the island of Molokai, the completion of hooponopono is represented by giving the person forgiven a lei made from the fruit of the hala tree.


title: Hoʻoponopono

text: "Aunty" Malia Craver, who worked with the Queen Liliuokalani Children's Centers (QLCC) for more than 30 years, taught courses in traditional hooponopono. On August 30, 2000, she spoke about it to the United Nations.


title: Hoʻoponopono

text: In the late 20th century, courts in Hawaii began to order juvenile and adult offenders to work with an elder who would conduct hooponopono for their families, as a form of alternative dispute resolution. The hooponopono is conducted in the traditional way, without court interference, with a practitioner picked by the family from a list of court-approved providers.


title: Hoʻoponopono

text: In 1976 Morrnah Simeona, regarded as a healing priest or "kahuna lapaau", adapted the traditional hooponopono of family mutual forgiveness to the social realities of the modern day. For this she extended it both to a general problem solving process outside the family and to a psycho-spiritual self-help rather than group process.