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Tom Hardy

Edward Thomas "Tom" Hardy (born 15 September 1977) is an English actor. After studying acting at the Drama Centre London, he made his film debut in Ridley Scott's Black Hawk Down (2001). Hardy had supporting roles in Star Trek: Nemesis (2002) and RocknRolla (2008), and went on to star in Bronson (2008), Warrior (2011), Tinker Tailor Soldier Spy (2011), Lawless (2012), This Means War (2012), and Locke (2013). In 2015, he starred as "Mad" Max Rockatansky in Mad Max: Fury Road and both Kray twins in Legend, and was nominated for the Academy Award for Best Supporting Actor for his role in The Revenant. Hardy has appeared in three Christopher Nolan films: Inception (2010), The Dark Knight Rises (2012) as Bane, and Dunkirk (2017). He has since starred as the title character in the 2018 film Venom and its 2021 sequel Venom: Let There Be Carnage.

Hardy's television roles include the HBO war drama mini-series Band of Brothers (2001), the BBC historical drama mini-series The Virgin Queen (2005), Bill Sikes in the BBC's mini-series Oliver Twist (2007), Heathcliff in ITV's Wuthering Heights (2009), the Sky 1 drama series The Take (2009), and as Alfie Solomons in the BBC crime drama series Peaky Blinders (2014–2022). He created, co-produced, and took the lead in the eight-part historical fiction series Taboo (2017) on BBC One and FX.

Hardy has performed on both British and American stages. He was nominated for the Laurence Olivier Award for Most Promising Newcomer for his role as Skank in the production of In Arabia We'd All Be Kings (2003), and was awarded the 2003 Evening Standard Theatre Award for Outstanding Newcomer for his performances in both In Arabia We'd All Be Kings and Blood, in which he played Luca. He starred in the production of The Man of Mode (2007) and received positive reviews for his role in the play The Long Red Road (2010). Hardy is active in charity work and is an ambassador for the Prince's Trust. He was appointed a CBE in the 2018 Birthday Honours for services to drama.

Early life
Edward Thomas Hardy was born in the Hammersmith district of London on 15 September 1977, the only child of artist and painter Anne (née Barrett) and novelist and comedy writer Edward "Chips" Hardy. He is of Irish descent on his mother's side. He was raised in London's East Sheen suburb. Hardy attended Tower House School, Reed's School, and Duff Miller Sixth Form College. He later studied at Richmond Drama School and the Drama Centre London, now a part of Central Saint Martins. He has named Gary Oldman, with whom he would later work on Tinker Tailor Soldier Spy, as his "hero" and added that he mirrored scenes from Oldman while at drama school.

1998-2010: Early work
In 1998, Hardy won The Big Breakfast Find Me a Supermodel competition at the age of 21 (although the programme said he was 20), earning him a brief contract with Models 1. Hardy joined Drama Centre London in September 1998, and was taken out early after winning the part of US Army Private John Janovec in the HBO-BBC mini-series Band of Brothers. He made his feature film debut in Ridley Scott's war thriller Black Hawk Down (2001). During this time, Hardy also had a brief stint as a rapper and hip hop producer with his friend Edward Tracy (under the name "Tommy No 1 + Eddie Too Tall"), with whom he recorded a mixtape called Falling On Your Arse in 1999 that remained unreleased until 2018.

In 2002, Hardy appeared as the Reman Praetor Shinzon, a clone of USS Enterprise Captain Jean-Luc Picard in Star Trek: Nemesis. The following year, he appeared in the film Dot the i, and then travelled to North Africa for Simon: An English Legionnaire, a story of the French Foreign Legion. He then returned to the United Kingdom to feature in the horror film LD 50 Lethal Dose (2003).

Hardy was awarded the 2003 London Evening Standard Theatre Award for Outstanding Newcomer for his performances in Blood and In Arabia We'd All Be Kings performed at the Royal Court Theatre and Hampstead Theatre. He was also nominated for a 2004 Laurence Olivier Award for Most Promising Newcomer of 2003 in a Society of London Theatre Affiliate for his performance as Skank in the aforementioned production of In Arabia We'd All Be Kings. Hardy appeared with Emilia Fox in the BBC mini-series The Virgin Queen (2005) as Robert Dudley, a childhood friend of Elizabeth I. Dudley's character has been described as an ambiguous young man who is torn between the affection of his wife (played by Fox), his love for Elizabeth, and his own ambitions. Hardy featured in the BBC Four adaptation of the 1960s science fiction series A for Andromeda.

In 2007, he appeared in BBC Two's drama based on a true story, Stuart: A Life Backwards. He played the lead role of Stuart Shorter, a homeless man who had been subjected to years of abuse and whose death was possibly a suicide. The same year he played Bill Sikes in the BBC mini-series Oliver Twist, an adaptation of Charles Dickens's novel that aired on PBS Masterpiece Classic in the US. In February 2008, he played a drug-addicted rapist in the British horror-thriller WΔZ. In September 2008, he appeared in Guy Ritchie's London gangster film, RocknRolla; Hardy played the role of gay gangster Handsome Bob. In 2008, Hardy starred in the film Bronson, about the real-life English prisoner Charles Bronson, who has spent most of his adult life in solitary confinement. For the film, he put on three stone (42 lb or 19 kg).

In June 2009, Hardy starred in Martina Cole's four-part TV drama The Take on Sky One, as a drug and alcohol-fuelled gangster. The role gained him a Best Actor nomination at the 2009 Crime Thriller Awards. In August 2009, he appeared in ITV's Wuthering Heights, playing the role of Heathcliff. In early 2010, Hardy starred in The Long Red Road at the Goodman Theatre in Chicago. The play was written by Brett C. Leonard and directed by Philip Seymour Hoffman. Hardy won some good reviews for his portrayal of Sam, an alcoholic trying to drink away his past. In 2010, he starred as Eames in Christopher Nolan's science fiction thriller Inception for which he won a BAFTA Rising Star award. Hardy replaced Michael Fassbender in the 2011 film adaptation of Tinker Tailor Soldier Spy, released on 5 September 2011 at the 68th edition of the Mostra Internazionale d'Arte Cinematografica in Venice. In March 2010, Hardy signed a first-look deal at Warner Bros.

2011-2017: Rise to prominence
In 2011, Hardy appeared in the film Warrior, which was released on 9 September 2011 by Lionsgate Films. His performance as Tommy Riordan, who is trained by his father to fight in a mixed martial arts tournament against his brother, gained praise from critics. Hardy also starred in This Means War (2012), a romantic comedy directed by McG. He played the supervillain Bane in The Dark Knight Rises, the final film in Christopher Nolan's The Dark Knight Trilogy, released on 20 July 2012. He played a bootlegger in John Hillcoat's crime drama Lawless (2012). Hardy has signed up to play the lead role of Sam Fisher in Ubisoft's forthcoming film adaptation of their video game series Tom Clancy's Splinter Cell. He also appeared in Riz Mc's music video for the song "Sour Times".

In 2014, Hardy appeared in the crime film The Drop alongside James Gandolfini, in what would be the latter's final appearance in a feature film before his death. Hardy also joined the cast of the BBC crime drama Peaky Blinders in its second series. He portrays Alfie Solomons (who is based on a real-life East End Jewish gangster named Alfred Solomon), the head of a Jewish gang based in Camden Town, north London and runner of a distillery which disguises itself as a bakery. Writing for Medium, Shani Silver described Hardy's portrayal of Alfie Solomons as 'The Scene-Stealingest Character Of All Time', commenting that "I’ve never understood if Alfie was meant to be a villain or comedic foil or some pick-a-mix of both, but I’ve never loved every second of someone’s screen time more."

Hardy starred in five films in 2015. The first, Child 44, set in 1950s Soviet Union, saw him playing Leo Demidov, a Soviet secret police agent who investigates a series of child murders. Despite mild praise for his acting, Child 44 was reviewed negatively by critics and was a box office failure. Hardy then played the title character, Max Rockatansky, in the action film Mad Max: Fury Road (2015). His performance was praised by critics and overall the film received critical acclaim and became a box office success, grossing over $378 million against a $150 million budget, becoming the highest-grossing film in the Mad Max franchise. He played a dual role as London gangsters Reggie and Ronnie Kray in the crime thriller Legend (2015). On 7 December 2015, Hardy won Best Actor at the British Independent Film Awards for his portrayal of the Kray twins, and on the same night attended the premiere of the biographical western thriller The Revenant, in which he reunited with his Inception co-star Leonardo DiCaprio, at Leicester Square, London. On 14 January 2016, Hardy received his first Academy Award nomination for Best Supporting Actor for his performance in The Revenant.

Hardy played a Royal Air Force fighter pilot in Christopher Nolan's action-thriller Dunkirk (2017), based on the British military evacuation of the French port of Dunkirk in 1940 during the Second World War. He appeared alongside Mark Rylance, Kenneth Branagh, Cillian Murphy and Harry Styles. Hardy also co-produced and starred in the eight-part BBC One television drama series Taboo. It was created by Hardy, Steven Knight, and Hardy's father, Edward "Chips" Hardy. Taboo was aired in the United States by FX.

2018-present: Venom and beyond
In 2018, Hardy starred in the film Venom as the title comic book sometime hero, Eddie Brock, and the symbiote Venom. Based on the Marvel source material, the film was released on 5 October, and is the first instalment in Sony's Spider-Man Universe. In 2019, Hardy served as an executive producer in the 2019 BBC/FX three-part miniseries A Christmas Carol. In 2020, Hardy starred in Josh Trank's Al Capone biopic Capone.

Hardy is attached to star as British war photographer Don McCullin in a film based on McCullin's autobiography, Unreasonable Behaviour. Hardy reprised the role of Eddie Brock and Venom in the sequel Venom: Let There Be Carnage and co-wrote the story for the film. He is also slated to star as the Antarctic explorer Sir Ernest Shackleton in a biopic being created by the same makers of Taboo. The Shackleton film, which will cover one of the most harrowing stories of survival in exploration history, is also being produced by Hardy's production company Hardy Son & Baker. In May 2024, he and Mahershala Ali were announced to be working on the crime thriller 77 Blackout.

Philanthropy
In 2010, Hardy became an ambassador for the Prince's Trust, a UK youth charity which provides training, personal development, business start-up support, mentoring, and advice. In 2012, he and his then-girlfriend (now-wife) Charlotte Riley became patrons of Bowel Cancer UK. Prior to the inaugural Invictus Games held in London in September 2014, he, along with other entertainers and athletes, read the poem "Invictus" in a promotional video.

Personal life
Hardy married producer Sarah Ward in 1999, and they divorced in 2004. He met and began dating assistant director Rachael Speed on the set of The Virgin Queen in 2005, and they later had a son before separating in 2009. That year, he began a relationship with actress Charlotte Riley after they met on the set of Wuthering Heights, and they were married in July 2014. Together, they have two sons born in October 2015 and December 2018. They had one rescue dog, Woodstock, and Hardy appeared with Woodstock in a PETA advert to promote pet adoption. Woodstock died on 5 June 2017 due to an aggressive case of polymyositis.

Hardy spent much time in his youth drinking alcohol and using crack cocaine to cope with stresses and has suffered significant bouts of dysthymia. He has previously said that he was "out of control" with his alcohol and drug use before going to rehab in 2003.

While portraying prisoner Charles Bronson during the production of Bronson, Hardy met Bronson several times and the two became friends. Bronson was impressed with how Hardy managed to match his muscularity and how well he could mimic Bronson's personality and voice; stating that he believed Hardy was the only person who could play him, he also shaved off his trademark moustache and sent it to Hardy in the hopes that Hardy would wear it in the film. According to Bronson's son, George Bamby, Hardy was banned from visiting Charles Bronson in prison by the prison service.

Hardy appeared on a 2016 Debrett's list of the most influential people in the United Kingdom. He was appointed a Commander of the Order of the British Empire (CBE) in the 2018 Birthday Honours for services to drama.

An avid practitioner of Brazilian jiu-jitsu, Hardy has been seen training at Roger Gracie's affiliate schools and with John Danaher. He has won a number of jiu-jitsu competitions,  with one such occurrence being at the UMAC Brazilian Jiu-Jitsu Open Championships in September 2022. He is the lead ambassador for the REORG Brazilian Jiu-Jitsu Foundation, a Royal Marines-backed charity allowing current and former military personnel to learn the martial art as part of their recovery and to combat physical and mental challenges. Hardy was promoted to purple belt in Brazilian jiu-jitsu on 19 June 2023. Hardy is also a rapper, performing as Face Puller or Frankie Pulitzer, and was featured on the 2022 Czarface album Czarmageddon.

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Henry McNamara

Henry P. McNamara (December 9, 1934 – August 27, 2018) was an American Republican Party politician, who served in the New Jersey State Senate from 1985 to 2008, where he represented the 40th Legislative District. In the Senate, he was Minority Whip from 1990 to 1991. He was also a member of the Senate Environment Committee and the Transportation Committee.

Biography
He was born in Passaic, New Jersey on December 9, 1934, and attended Pope Pius XII High School. He received a B.A. in 1956 from Seton Hall University in classical languages. Before entering the Senate, McNamara spent six years in the New Jersey National Guard. Senator McNamara also spent a year as Mayor of Wyckoff in 1979, and served as Deputy Mayor in 1980, and was a member of the Bergen County Board of Chosen Freeholders from 1984 to 1986. In 2002, McNamara ran for County Executive of Bergen County, losing to Dennis McNerney in the general election.

McNamara decided against running for re-election in 2007 and announced he would step down at the end of his term in 2008.

McNamara sponsored New Jersey's open space trust fund, wrote the law to clean up underground storage tanks, re-wrote the laws governing toxic waste cleanup and led the way for a Brownfields law – a plan to get private investors to clean up polluted industrial sites and make those sites clean and useful again.

He died on August 27, 2018, in Wyckoff, New Jersey at age 83.

District 40
Each of the forty districts in the New Jersey Legislature has one representative in the New Jersey Senate and two members in the New Jersey General Assembly. At the end of McNamara's term, the other representatives from the 40th Legislative District were:
 * Assemblyman David C. Russo, and
 * Assemblyman Kevin J. O'Toole

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Henry McNamara


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User talk:Snowknight26

Sorry, nobody has ever given you the formal greeting. So if you don't mind, here it is...

Welcome!

Hello, and welcome to Wikipedia. Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! By the way, you can sign your name on Talk and vote pages using three tildes, like this: ~~~. Four tildes (~~~~) produces your name and the current date. If you have any questions, see the help pages, add a question to the village pump or ask me on my Talk page. Again, welcome!
 * How to edit a page
 * Editing, policy, conduct, and structure tutorial
 * Picture tutorial
 * How to write a great article
 * Naming conventions
 * Manual of Style
 * If you're ready for the complete list of Wikipedia documentation, there's also Topical index.

Zzyzx11 | Talk 02:00, 25 Apr 2005 (UTC)

title: User talk:Snowknight26


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Reagan coalition

The Reagan coalition was the combination of voters that Republican Ronald Reagan assembled to produce a major political realignment with his electoral landslide in the 1980 United States presidential election. The coalition was possible because of Democrat Jimmy Carter's losses in most social-economic groups. In 1984, Reagan confirmed his support by winning nearly 60% of the popular vote and carried 49 of the 50 states.

The Reagan Democrats were members of the Democratic Party before and after the Reagan presidency, but voted for Reagan in 1980 and 1984 and for his vice president, George H. W. Bush, in 1988, producing their landslide victories. They were mostly white socially conservative blue-collar workers who lived in the Northeast and were attracted to Reagan's social conservatism on issues such as abortion and to his hawkish foreign policy. They did not continue to vote Republican in 1992 or 1996, causing the term to fall into disuse except as a reference to the 1980s. The term is not generally used to describe the white Southerners who permanently changed party affiliation from Democrat to Republican during Reagan's presidency. They have largely remained Republican to this day.

Democratic pollster Stan Greenberg analyzed white, largely unionized auto workers in suburban Macomb County, Michigan, just north of Detroit. The county voted 63% for John F. Kennedy in the 1960 presidential election and 66% for Reagan in 1984. He concluded that Reagan Democrats no longer saw Democrats as champions of their middle class aspirations. They instead viewed the Democratic Party as working primarily for the benefit of others, especially African Americans and the very poor.

The Reagan coalition began to fall apart after 1988 when Reagan was ineligible for reelection and Bush won over Democrat Michael Dukakis. Bush lost over 5 million votes and 100 electoral votes in comparison to what Reagan won four years prior. In 1992, Bush faced a competitive primary competition with Pat Buchanan, still winning the Republican nomination with 72% of the vote. Bush went on to lose the general election against Democrat Bill Clinton, with exit polling showing Bush retaining 66% of the Republican vote, Clinton winning 12%, and independent candidate Ross Perot winning 21%. In 1996, Republican Bob Dole lost to Clinton, taking 68% of the Republican vote, improving on Bush's margin, while Clinton took 23% and Perot 7%.

title: Reagan coalition


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Talk:Vittorio Emanuele, Prince of Naples

Titular
I'm not sure I understand the problem with "titular"; it certainly seems it applies to anyone calling himself "Prince of Naples". "Titular" means "existing in title only;" or "having the title and usually the honors belonging to an office or dignity without the duties, functions, or responsibilities". Clearly "Prince of Naples" is a title only, with no duties, functions, or responsibilities. "Prince of Naples" falsely suggests that Naples is a principality, while "titular Prince of Naples" does not mislead. - Nunh-huh 00:34, 25 October 2006 (UTC)

 * You are very much mistaken. He is the Prince of Naples as this is his highest Royal title.  His father was a ruling King of Italy.  What you are suggesting implied that we should refer to Lords of Great Britain who lost their seats in the House as titulae.  It is nonsensical.--Couter-revolutionary 01:17, 25 October 2006 (UTC)
 * His father was king for about a month. He himself never was. Your analogy is rather imprecise. He has never ruled anywhere. - Nunh-huh 02:13, 25 October 2006 (UTC)

 * Technically yes, he has, as Prince of Naples. It does not matter one bit how long his father was King for, the undeniable fact is that he was. He is the titular King of Italy, not the titular Prince of Naples.  This is what the article says at the moment and what it should say, please do not attempt to edit it to purport your own agenda.--Couter-revolutionary 06:10, 25 October 2006 (UTC)

 * I don't have any agenda, so stop being obnoxious by claiming I do. The "Prince of Naples" doesn't rule anything, and never has. - Nunh-huh 06:37, 25 October 2006 (UTC)
 * I agree that Vittorio Emanuele has never reigned under any title or over any territory, including as "Prince of Naples". But I also agree that it would be unconventional to refer to that style as "titular". The problem is that there are at least two conflicting "conventions" applicable here. One is that of the Italian Republic, whose current law does not normally recognize historical titles. The other convention dates back to the Almanach de Gotha during the Napoleonic era when many dynasties were exiled. The Gotha, Europe's primary gazette of international dynastic news, often continued to accord deposed monarchs and their dynasties the titles they held while reigning, but added to them the Bonaparte rulers. Since many of the exiled dynasties were restored to sovereignty after Napoleon's downfall in 1815, the Gotha's tradition of according former regnal dignities became the norm at European courts and remains so. It is also regularly used in heraldry, genealogy and historical biography. By that convention, "titular" is used as a prefix for a sovereign title, not a subordinate one. Thus, if dethroned, Elizabeth II would, by custom, continue to be referred to as "Queen Elizabeth II", but her territorial designation "of the United Kingdom" would be omitted at monarchical courts, while journalists would, on first reference, qualify her queenly title with a prefix such as "former" or "ex-" (although "titular" would not be incorrect or ahistorical). In Gotha convention, her eldest son remains "Prince of Wales", not "titular Prince of Wales" (although future heirs-in-pretence, who never held the title under the monarchy, are not automatically so entitled). That's partially very old custom adhered to, for example, by the respected Encyclopædia Britannica Eleventh Edition (ex-dynasts retain for life use of their highest title -- e.g. Empress Matilda, Charles V, Holy Roman Emperor, Queen Christina of Sweden, Grand Duke Jean of Luxembourg, etc.), and partially historic reality (Wales has been a "titular" principality for hundreds of years, as have the territories from which derive the titles of most modern royal heirs, i.e. Prince of Orange, Duke of Brabant, Prince of Asturias, and Prince of Naples). With respect to dethroned dynasties, Don Juan was not referred to as the "titular" Count of Barcelona, but simply as "HRH the Count of Barcelona", and sometimes as the "titular King of Spain". "Titular Prince of Naples" isn't used by anybody, not the Italian Republic nor by Italian monarchists nor by protocol at foreign courts. Lethiere 11:29, 25 October 2006 (UTC)

 * Lethiere, you say that "the problem is that there are at least two conflicting "conventions" applicable here". OK. Assuming that is correct, why in the face of such a conflict is one of the conventions, and the minority one at that, represented in this article (and apparently in others) as settled fact? Surely we should go with the view which is not only adopted by the majority, but also under the relevant legal systems, and state the name of the person without the abolished titles, and then state that some people still attribute such titles to them? --SandyDancer 11:44, 25 October 2006 (UTC)
 * I was not advocating either convention, merely providing their histories and applications. But to play Devil's Advocate and answer your question, it is not clear that we should use the Italian convention because it is "local" to Italy, whereas English Wiki isn't, and seeks some consistency in how it deals with similar situations across nations. Germany, for instance, incorporates former royal titles into the surname, and allows their use socially as titles. Its next door neigbor Austria forbids both legal (e.g. documents) and official (e.g. phone listings) usage. Austria's neighbor, Liechtenstein, not only allows use of foreign monarchical titles, but uses them itself (the reigning Prince's grandmother was an Austrian archduchess). Italy's legal stance applies to government, not to society. In fact, when the Italian president greeted Vittorio Emanuele upon his return to Italy, he referred to him as "Prince", which was objected to by the socialist party leadership -- but not by the other parliamentary parties. The Italian media, like most media the world over, varies depending upon its political slant, and is notoriously inconsistent -- how an ex-royal is titled often depends upon which editor happens to be in charge the day that a story about royalty is filed for publication. We should certainly acknowledge and report the Italian state's position, but we are not an arm of that state. Conversely, the advantage of the Gotha convention is that it has been much more carefully elaborated than republican conventions on titles, is widely adhered to by those who have most occasiont to mention royalty in print, and ignoring an already widely used convention puts WP in the position of inventing its own standard, since no other exists supranationally. For instance, legally there is no difference between Vittorio Emanuele's former title and those of any Joe Blow in Italy suffering from delusions of grandeur who declares himself "Prince of Naples". But the Gotha's convention would unhesitatingly distinguish between someone whose dynasty reigned over part or all of Italy for the last millenium and someone who merely needs to be reminded to take his morning meds. That convention is quite clear: deposed royalty get to keep a modified version of their titles; their descendants also get to use titles, but not (for the pretender, his wife and his heir) the same ones as were used under the monarchy -- thus the Gotha convention does defer to the reality of royal depositions and exiles. That convention has indeed been influenced by monarchists -- because they are the folks who care enough about how ex-royalty is styled to develop coherent rules and adhere to them. Nonetheless, encyclopedic practice has been to make use of the Gotha tradition: The legitimist French pretender's legal name may have been "Henri d'Artois", but he will be found in Encyclopædia Britannica Eleventh Edition under Henri, comte de Chambord -- and in every other encyclopedia and journal of public record except, perhaps, those of the French republic during his lifetime. Encyclopedic precedent is not to substitute legal name for royal titulature once a monarchy has been abolished -- or ex-King Constantine II of Greece would be known everywhere (instead of just among anti-monarchists) as "Constantine Glucksburg". Lethiere 21:52, 27 October 2006 (UTC)

 * Fair enough. That was very interesting and to be honest you've convinced me. --SandyDancer 22:15, 27 October 2006 (UTC)

 * Why is it that people that do have agendas (normally right wing ones) on Wikipedia always accuse others of having them? It is so tiresome. The title of Prince of Naples is clearly "titular", i.e. existing as a title only, because the title was abolished under Italian law in 1946, and certainly isn't recognised under any other legal system. The difference to the Lords of GB who lost their seats in the House of Lords is that they are still Lords under law - their titles were not abolished, just their right to sit and vote in the House (though they can still sit on the steps of the throne, and some do). --SandyDancer 09:10, 25 October 2006 (UTC)

 * Thank you, I am all too aware of the Lords issue, believe me. What I am trying to say is that he was the Prince of (the pincipality of) Naples and, as result should be known by his highest royal title, out of courtesey if nothing else.  This is practice across Wikipedia and I have seen no Royal described as Titular outside of sucsession boxes, where it is appropriate for clarity.  My final point is that he is the Titular King of Italy, he cannot be a titular Prince too.  The article is fine the way it is.--Couter-revolutionary 09:16, 25 October 2006 (UTC)

 * If it truly is the position in other Wikipedia articles that people are given titles they no longer hold as if they still do, I disagree with it in those articles too. It runs counter to common sense and needs to be challenged.
 * Turning back to this article, the one we are discussing, you admit he was called Prince of Naples - and the article should state this. But I see no reason why it follows from this that we have to pretend he still holds this title "out of courtesy". It is, however, worth stating that some people (principally Italian monarchists) nevertheless continue to refer to him in this way out of courtesy - but Wikipedia shouldn't do so as it just isn't factual.
 * It is simply a statement of POV to say that deposed royals/nobles still hold defunct titles. In effect you are asking Wikipedia to support your personal, minority view that these royal titles exist forever in perpetuity, even when legislatures / constitutional conventions / referenda have purported to abolish them, and this has been accepted in practice. This is precisely the kind of thing that the Wikipedia NPOV policy is aimed at.
 * To conclude, the article should not state that he still holds abolished titles as a matter of fact - and the title needs to be amended to reflect this too. --SandyDancer 10:36, 25 October 2006 (UTC)
 * While I understand your rationale, it flies in the face of the convention that has been developed and applied over the last several years to guide articles on reigning and deposed dynasties. Specifically, Rule # 7. Lethiere 11:29, 25 October 2006 (UTC)

 * Hilariously, Rule # 7 doesn't support what you are saying at all, and in fact says the contrary - read it:
 * Former or deposed monarchs should be referred to by their previous monarchical title with the exception of those who are still alive and are most commonly referred to by a non-monarchial title; all former or deposed monarchs should revert to their previous monarchical title upon death; for example, Constantine II of Greece not ex-King Constantine II or Constantine Gluckberg, Edward VIII of the United Kingdom not the Prince Edward, Duke of Windsor, but Simeon Saxe-Coburg-Gotha not Simeon II of Bulgaria.
 * Just as the living Simeon Saxe-Coburh-Gotha isn't called Simeon II of Bulgaria (his highest royal title before it was abolished) now, but rather by his actual name, Vittorio Emanuele should be "Vittorio Emanuele" here, and when he dies he will revert to being called by the highest title he held in his lifetime - Prince of Naples. Can I rest my case??? --SandyDancer 13:42, 25 October 2006 (UTC)

 * I quite agree, although I don't understand the rationale myself. He is the Prince of Naples, however Italian Monarchists (many of them anyway) will refer to him as King of Italy, since his father's death.  This is his titular position, that of King.  The Prince of Naples is his title as a right, it is not a titular one.--Couter-revolutionary 11:33, 25 October 2006 (UTC)

 * No. He isn't the Prince of Naples. There is no such thing as the Principality of Naples, there is no such title as the Prince of Naples. The title was abolished in 1946 and consequently Vittorio Emanuele of Savoy, who is a private citizen just like you or I, holds no titles whatsoever. Lots of people like to think that he still holds titles due to their personal belief that such titles exist irrespective of Italian law, but this is a minority view and should not be presented as fact, which it currently is. How much clearer do I have to be before you understand the rationale? Your arguments run counter to common sense. --SandyDancer 11:38, 25 October 2006 (UTC)

 * Righto, what you are saying is that the accepted Wikipedia guidelines and I are running counter to common sense. Please, by all means attempt to change them all, change the guidelines to what you would like them to say if you will.  Call Edward VIII the Duke of Windsor because he abdicated the Throne, as this is what you are supporting, against the tide of accepted practice.  If you want to change the guidelines do, however, I am sure that then you will see it is you who is acting without reason.--Couter-revolutionary 12:06, 25 October 2006 (UTC)

 * Do you deliberately use false analogies in order to avoid sensible argument? The Edward VIII thing is completely different in so many ways its hardly worth bothering to explain why.
 * It cannot be considered accepted practice to use Wikipedia to assert as undisputed fact that claimants to abolished titles still actually hold such titles. This is an encylopedia. It is supposed to deal in facts, not points of view. Stop trying to obscure the argument by falsely characterising what I am saying. It just makes you look bad, as does deleting sections of a discussion we previously had where you laid out your own highly unusual POV on this topic in detail (see - it speaks volumes - he took that action after I cross-referred to it here . --SandyDancer 12:25, 25 October 2006 (UTC)

 * I think the Wikipedia naming conventions, which another kind user has posted a link to above, clearly show that to call him the Prince of Naples is accepted practice. But, as I say, please do change them, it shall clear up any confusion.--Couter-revolutionary 12:34, 25 October 2006 (UTC)

 * Why did you just try and edit my comments above? See here for the edit, which I have naturally reverted . You shouldn't do that. --SandyDancer 12:49, 25 October 2006 (UTC)

 * "Titular" has caused so much debate. Another user removed it. I have now removed the "Prince of Naples" after VE's name, as the intro paragraph already states he is sometimes styled as such out of courtesy, despite the fact that the title was abolished in 1946. I have done so because that is the truth. --SandyDancer 13:16, 25 October 2006 (UTC)

I agree with Lethiere here, and don't think I have anything to add to what he says. Nunh Huh's definition would have to lead to us calling Prince Charles the "titular Prince of Wales," since he does not rule over a Principality of Wales. Even when the Italian monarchy existed, the titles "Prince of Piedmont" and "Prince of Naples" were titular in that sense. Beyond that, as Lethiere says, for royal pretenders, the word "titular" is used in a different sense from how it is used more broadly. Vittorio Emanuele is the titular King of Italy. But former monarchs are generally considered to retain the titles they held under the monarchy. Thus, Vittorio Emanuele's father was still called "King Umberto II" after he was kicked out of the country, and Vittorio Emanuele himself is still called "Prince of Naples." The government of the Italian Republic has banned noble and royal titles, but they don't get to dictate usage, which remains in the traditional place, I think. john k 13:19, 25 October 2006 (UTC)

 * I quite agree with what you are saying, finally some sense.--Couter-revolutionary 13:24, 25 October 2006 (UTC)

 * Are you admitting you haven't been adding any sense to the discussion, then? ;-)
 * Just to be clear I am not a proponent of the view that use of the word "titular" is necessarily the right way to represent the facts here - the facts being that you want a Wikipedia article to state that someone who was Prince of Naples is Prince of Naples, when no such title is recognised under any legal system and is only used by monarchists as a form of expression of their own point of view. Although I think John Kenney does make sense, and perhaps points out why use of the word "titular" is perhaps not the right approach, that doesn't mean that Wikipedia should mislead readers by saying someone is "Prince of Naples" when they aren't. --SandyDancer 13:38, 25 October 2006 (UTC)

 * Although I reverted you when you removed "Prince of Naples" from the first line, I'm beginning to think that that may have been the right approach. As far as I have seen, he is normally called "Vittorio Emanuele of Savoy," and not "the Prince of Naples."  I would add that I have no idea whether Vittorio Emanuele is the Prince of Naples, as I'm not sure what that means.  For instance, the head of the Bavarian Royal House is universally called "the Duke of Bavaria" (der Herzog von Bayern), but his legal name is actually Franz Herzog von Bayern, and he is not a duke - Herzog von Bayern is merely his surname.  I don't think it's our place to say that a title of pretense used by custom is not "real" simply because it is not recognized by the Republican government of the place that it used to be a title for.  The German pretenders are certainly universally known by their titles of pretense - the Duke of Bavaria, the Prince of Prussia, the Prince of Hanover, the Duke of Württemberg, the Margrave of Meissen, the Margrave of Baden, the Landgrave of Hesse, and so forth.  It would be pedantic to assert the German legal fiction that they are merely surnames in order to change the way we refer to these people.  I'm less certain with Vittorio Emanuele of how universally he is called "Prince of Naples."  I think the article should stay here because it's his highest title, and he certainly was Prince of Naples before June 1946.  Beyond that I'm not really sure.  Might be best to remove it from the first line. I won't re-revert if you do so again. john k 14:16, 25 October 2006 (UTC)

 * If you're going to play that game...I propose we don't even use "of Savoy", why should we apparently he's not Royalty. Let's just call him "Emanuele Savoia", and, of course we'll have to change the article name.  Oh, and don't forget to do the same for his father King Umberto as he had to abdicate.  PS, I'm so pleased you are changing the name on Tsar Simeon II of Bulgaria's article.  PPS, I'm being sarcastic.--Couter-revolutionary 14:37, 25 October 2006 (UTC)

 * So lets get this straight, you only like Wikipedia guidelines when they support your view, but get very upset when you read them and find they don't? I ask because you seemed very keen to wave them at me earlier, but now seem to take a rather different approach.
 * If you don't want to engage, then don't. Let the rest of us get on with the enjoyable and challenging task of contributing to an encyclopedia which represents a neutral point of view, and isn't just a scrapbook of article representing minority opinions on various topics. --SandyDancer 14:47, 25 October 2006 (UTC)

Reverted per what discussion?
As far as I can, there was no real consensus to remove the title. At any rate, I wholly disagree. The treatment that SandyDancer is trying to apply to VE is not symmetrical with all other pretenders. I am going to revert it. Charles 18:02, 25 October 2006 (UTC)

Not true. And it isn't just me that believes that it wrong to refer to VE as Prince of Naples when he isn't. I believe the distinction is that he is a living ex-Royal - when he passes away, he will be referred to on this page as Prince of Naples, which was the highest title that he held during his life. See the Wikipedia guidelines on this, which you no doubt have a view on. Telling readers the subject of this article is Prince of Naples is wrong because he isn't. --SandyDancer 18:28, 25 October 2006 (UTC)

 * VE is in the same situation as Crown Prince Paul of Greece and Crown Prince Alexander of Yugoslavia. They gained those titles while the monarchy still existed and they continue to bear them. It is almost international as a practice to freeze the titles as they are at the end of a monarchy and to let non-sovereign titles pass as they normally do. Charles 01:00, 26 October 2006 (UTC)

 * I don't agree. Just because the families and themselves try and perpetuate abolished titles, that doesn't mean Wikipedia should join them. Wikipedia is supposed to represent a neutral point of view - pretending that legally abolished titles are still valid is adopting a monarchist viewpoint. You revealed your personal view with your statement "They gained those titles while the monarchy still existed and they continue to bear them" - can't you just accept that's your view but isn't neutral? If VE himself can accept titles have been legally abolished in Italy, can't you? --SandyDancer 08:00, 26 October 2006 (UTC)

 * It's not just the Savoys and monarchists who call VE "Prince of Naples". ANSA, the largest of the Italian news agencies (comparable to Reuters or Associated Press) often (but not always) gives him this designation; check Factiva.  The Italian constitution says nothing about titles being abolished, merely not recognised. While the Italian government doesn't recognise VE officially as "Prince of Naples", it does recognise him as having the name "Principe di Savoia" since this predicate existed before 1922 and is therefore recognised as part of his name. Noel S McFerran 11:23, 26 October 2006 (UTC)
 * I agree that he has been referred to by his princely title by the Italilan government. But I understood that this was defended based upon a similar reference in a post-monarchical law. I don't think that Italy's recognition of pre-1922 predicates in the surname includes legal recognition of the noble title to which it was attached, e.g. "Luigi di Roma" not "Luigi, principe di Roma". OTOH, surely Vatican titles may be legally borne in Italy today? Lethiere 18:55, 28 October 2006 (UTC)

 * If what you say is true (and I have no reason to doubt it is), I would concede the point that he should be described as "Prince of Naples". Maybe also on that basis we need to revise the article to make it clear the consitution states titles aren't recognised in Italy due to the constitution, but that the constitution doesn't purport to abolish the titles. However I am not comfortable doing so unless we can get a source for this. Thanks. --SandyDancer 12:26, 27 October 2006 (UTC)

Opening paragraph
The Manual of Style (biographies) guideline gives clear directions on what should be included in an opening paragraph (i.e. before the table of contents). There is no justification for four paragraphs of material here which merely repeats information which is given below at its proper place. Noel S McFerran 13:40, 13 November 2006 (UTC)

 * Are you saying the murder trial and the other scandals don't fall into the category of:
 * What they did
 * Why they are significant
 * Like it or not, VE has been known primarily for these occurrences - he was only a royal as a child - he has been an exile from Italy all his life and has come to public attention only for the things mentioned in the opening para. As I said on McFerran's talk page, this opening para and the whole article have been discussed at length and agreed between people with very different views on the subject. --SandyDancer 14:14, 13 November 2006 (UTC)
 * Some examples of biographies of very prominent figures which have similar content in the opening paragraph are below. I have chosen these because the figures in question are so prominent, one would assume that if this kind opening paragraph content was indeed contrary to guidelines, it would have been removed:
 * Michael Jackson - scandals about child sex abuse allegations are mentioned in intro.
 * Jeremy Thorpe - British Liberal party leader, criminal charges mentioned in intro.
 * George Galloway - controversial comments and controversial TV appearance mentioned in intro.
 * Yasser Arafat - general and wide-ranging criticisms in the intro.
 * I could go on. The kind of trimmed down intro you suggest is in fact - and quite correctly - not the norm on wikipedia. The intro should tell people why the person is notable and what they have been famous for. --SandyDancer 14:35, 13 November 2006 (UTC)

Image
The man in the picture doesn't look like Vittorio Emanuele. Compare --87.1.70.118 (talk) 20:44, 10 February 2008 (UTC)

 * You are right, it really doesn't look much like him, although they do look similar. The Prince has a cleft in his nose and much lighter eyes in the picture you linked to, as well as a narrower appearing face. Charles 20:50, 10 February 2008 (UTC)

 * I agree with Charles, I don't think that's VE. The man in the photograph has a much fuller face. Here's a picture of VE smiling (no teeth, though) Definitely not the same man, I think. Morhange (talk) 23:39, 10 February 2008 (UTC)

No longer a pretender?
Should we have Vittorio Emanuele presented still as a claimant to the defunct throne of Italy? Are his official declarations not considered a relinquishing of these claims? And, if this is the case, it would be strange to consider the Belgian acknowledgment of his past pretension to be presently valid. __meco (talk) 09:01, 24 April 2008 (UTC) He broke the house of rule of asking the king for the right to marry well the king was still alive the king delcare Prince ameado(Who should have became King Ameado I of Itlay) heir so no he not a pretender but he still cliams but he is NOT pretender. (KingOscarXIX (talk) 17:54, 31 July 2015 (UTC))

He is not a prince
''Vittorio Emanuele di Savoia è conosciuto all'interno di ambienti monarchici come principe di Napoli. La Repubblica Italiana non riconosce i titoli nobiliari italiani.'' Naples is not a principality, of course is impossible to be prince of Naples. Is like to be Prince of New York, Duchess of Buenos Aires or Queen of California. --84.120.9.13 (talk) 04:12, 5 October 2008 (UTC)

Move?

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the move request was: Move. Jafeluv (talk) 11:23, 15 May 2010 (UTC)

Vittorio Emanuele di Savoia → —
 * Victor Emanuel's article was moved without discussion. Former royals are overwhelming known by historic titles or by their courtesy titles. 142.68.215.91 (talk) 19:42, 3 May 2010 (UTC)
 * See also Special:Contributions/F_l_a_n_k_e_r, all moves from the 27th of April, all undiscussed and falling along the same lines as above. Do they have to be put up individually? 142.68.215.91 (talk) 19:49, 3 May 2010 (UTC)
 * Support This was his title from birth and pretenders are known by their last title. The pages were also moved without discussion, and so they should be reverted back. Morhange (talk) 02:45, 5 May 2010 (UTC)
 * Support The current title ignores his tis titles. Dimadick (talk) 12:59, 7 May 2010 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Remove pretender boxs thiing
He is not a pretender he rights were remove from the his majesty the king (KingOscarXIX (talk) 00:27, 21 August 2015 (UTC))

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Article name
It should be Victor Emmanuel, Prince of Piedmont, as that was the highest position he held, even if only for about a month. See Alexander, Crown Prince of Yugoslavia for example. GoodDay (talk) 20:46, 8 August 2021 (UTC)

Requested move 7 September 2023

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Withdrawn. Looking at similar articles, this is consistent with those. estar8806 (talk) ★ 00:25, 9 September 2023 (UTC)

Vittorio Emanuele, Prince of Naples → ? – Almost none of the cited sources refer to him this way. A quick look through this article's references shows us he is called simply "Vittorio Emmanuele", "Vittorio Emmanuele di Savoia", and "Prince Victor Emmanuel". However, I'm unsure of which of these this should be moved to (if any). estar8806 (talk) ★ 11:44, 7 September 2023 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.


text:
Talk:Twix

Are ingredients notable?
On various pages such as Twix and Whoppers, there is an extra-long, extremely pointless ingredient listing on the pages. These really hamper the quality of wikipedia and come across as filler to the masses. I propose that for various food items (name brand), that it is strongly discouraged to have a full ingredient list on the page. I feel that eliminating the ingredient listings will make the pages more concise and of a premium quality. Mcfly85 23:19, 26 Apr 2005 (UTC)
 * The person who originally put them there probably thought they would be useful to people with dietary requirements. However, I think putting the whole ingredient lists is overdoing it; maybe a note like "Twix can contain peanuts" for people who die if they eat peanuts.  I can't see any good reason for having an ingredient list, though.  —Sean κ. ⇔ 00:10, 27 Apr 2005 (UTC)

 * I don't think the lists are pointless at all. In fact, it's probably the only reason I would view such articles.  It might be nice to format them in small text, but it doesn't work in lists.  It's also very helpful to be able to click on ingredients like thiamine mononitrate and find out what exactly they are.  — Teknic Talk / Mail 00:21, 27 Apr 2005 (UTC)

 * As the person who originally listed the ingredients, I do think they are useful. For example, someone researching candy bars would be able to find out what they are made from.  I realize, however, the format of the ingredients list I used is very large.  I am not concerned with keeping that particular format but rather I am concerned that the information be available in some format.  For comparison, I have changed the list in Twix to comma separated.  This can be compared to the list in the Whoppers article.  Some compromise will need to be made for size vs. readability. -SCEhardt 00:32, 27 Apr 2005 (UTC)

 * I don't see how it could ever pose a problem. It would be useful too. Howabout1 00:37, 27 Apr 2005 (UTC)
 * I still don't see how the ingredients of a candy are any more notable than, say, the hair color, eye color, and height of George W Bush. Are the ingredients useful?  Perhaps, but Wikipedia isn't a knowledge base.  I think this falls under the category of information overload.  —Sean κ. ⇔ 02:14, 27 Apr 2005 (UTC)

 * It's just kinda silly to have an entire ingredients listing when the very few that need it would just search the website or buy one item and look at the wrapper. Of course, the general/main ingredients are important (ex. A Milky Way is a candy bar made of chocolate, caramel and nougut), but to have a retelling of the label is just not usful. And even if you really cared to know more about the ingredients, the compounds are just linked to the separate words. This is not a widespread problem, but I feel that it could be. I like that Wikipedia can contain info about candy bars and other things you wouldn't see in print. The quality of the article is based on solid, concise research and writing, not just doing a verbatim listing of ingredients. A majority of the candy pages follow the format very well, without resorting to a full-blown ingredient listing. Mcfly85 03:30, 27 Apr 2005 (UTC)
 * Not everyone lives in an area that sells Mars or Whoppers, so they can't easily buy them. I think the lists are useful, particularly for Teknic's reasons. (Mcfly85, if you really want to fight against unnecessary and useless information on Wikipedia, you may be interested in a little category called Fancruft.) Besides, this issue really should be decided on each article's talk page -- it's not really a proposal. jdb ❋ (talk) 04:01, 27 Apr 2005 (UTC)

Deletionists - Just because you can not see the value of content (including lists) does not mean that it has no value. In this case the mentioning of an obscure ingredient may reveal that it does not have a page describing what it is. That may lead someone to research and add the article. I for one think a list of ingredients is a great thing to have on food pages. If you don't think it works in the article perhaps it would be better served elsewhere with a link. Perhaps http://en.wikibooks.org/wiki/Cookbook. Never delete valid and true content, just find a better place for it. Rottweiler 04:08, 27 Apr 2005 (UTC)

At first I was skeptical, but after looking at those articles I think having ingredient lists with links is a good idea. I prefer the more compact format used on the Twix page, though. --Coolcaesar 05:15, 27 Apr 2005 (UTC)

For generic food items, like pizza, a list of ingredients is silly. In the case of specific, commercially-produced food items, however, I have to agree that the list of ingredients is helpful, beneficial, and interesting. Roodog2k 12:22, 27 Apr 2005 (UTC)

I fixed the whoopers page - keep.

Again, wouldn't a link that has the official snack website (which usually has info for the few that need the listing) suffice? I doubt a vast majority would find an ingredient listing useful or interesting. Even with the smaller format for the ingredients, it still looks like needless filler on the page. If this doesn't stop, time will be wasted and the quality of the pages will suffer. I do find Rottweiler's suggestion of putting a link or using the cookbook to be a perfect solution. Mcfly85 02:10, 28 Apr 2005 (UTC)

 * The ingrediants ARE the food. How can you sensibly justify NOT listing them in an encyclopedic context? That would be like not mentioning that Lassie is a dog. An enyclopedia of food would certainly have the ingrediants listed. Why should we do any less? The Twix list, for example, is compact and well linked. Ingrediants are useful to nutritionists, vegetarians, Jews, Muslems, and anyone who cares about what's in their food. You may not care if you're eating soybeans or soylent green, but many people do. Also, having a well linked list like this lets people easily find out more about specific ingrediants. (I mean, just what IS high fructose corn syrup, anyway?)

 * - Pioneer-12 03:17, 28 Apr 2005 (UTC)
 * What say ye then to my analogy with hair color and George Bush? Does that mean I can start putting the hair color, eye color, height, weight, and favorite foods of my favority celebrities on their pages? —Sean κ. ⇔ 03:34, 28 Apr 2005 (UTC)

 * Alright, while the ingredients are the food, it is certainly not notable to make a listing of each ingredient. A general consise description of the bar is all that is needed. If anyone really cares enough to know the ingredients, they will search on the link provided on the page or pay 50 cents to buy the bar. An encylclopedia is made to give a general overview of a topic, not list every detail. I am still stunned that the majority of you don't see my side of this issue. Most of the other food pages do not have mass ingredients listings, and they are very well-constructed pages. I do not want to see these unnotable listings that can easily be read off a container. I do not want writers to waste time writing listings when there are tons of stubs that need to be expanded. Here is what I feel should be done:

1. Please save your time and do not add similar ingredients listings for the time being. And please keep the few that remain for now.

2. Consider making the ingredient listings part of the cookbook project, or leave a link to the company website which likely has the listing.

3. Consider the pandora's box effect that may result, and consider what adding an ingredients listing would be to the masses. Also keep in mind that Wikipedia isn't a knowledge base. Mcfly85 04:30, 28 Apr 2005 (UTC)

 * I don't see anything in Wikipedia is not a general knowledge base that even infers that the ingredients of a foodstuff should not be part of that foodstuff's article. Personally, I wouldn't bother including them in an article I was writing (as I'm lazy), but I don't see a problem if anyone does choose to, and it could be useful information Proto 12:38, 28 Apr 2005 (UTC)
 * This is just absurd. The argument for keeping them always seems to end in "it could be useful information."  But I just don't see why that's a valid argument.  Why not include the nutritional facts as well?  That could be useful.  Again, I am going to say that the ingredient list doesn't help anyone get an understanding of what Twix are, and could not possibly be notable. (except in the case of allergies, as discussed).
 * Also, Wikipedia is not a general knowledge base is comletely relevant to the discussion, since it begins,
 * Wikipedia is not a general knowledge base, that is, it is not an indiscriminate collection of items of information. That something is 100% true does not mean it is suitable for inclusion in an encyclopedia.
 * —Sean κ. ⇔ 14:33, 28 Apr 2005 (UTC)
 * You know, nutritional information would be even better than a list of ingredients, particularly given how health-obsessed a lot of people are. Proto 15:17, 28 Apr 2005 (UTC)
 * Clearly information is not useful until it is used. I assert that all of the information added to Wikipedia is put here under the assumption that "it could be useful information."  There is no way to prove it will ever be useful to anyone in the future.  The point being that most people (all but two who have commented here) seem to think that the ingredient list will be useful information. -SCEhardt 19:11, 28 Apr 2005 (UTC)

 * Having nutrition facts would be great. Sure, Wikipedia isn't for everything, but I beleive, Wikipedia is not a general knowledge base, that is, it is not an indiscriminate collection of items of information. That something is 100% true does not mean it is suitable for inclusion in an encyclopedia. applies mainly to articles, not facts in them. There may be no need for very small facts, but ingrediants are important. What if someone, let's call him Jeff, loves twix, but is also health concious. Then a news report comes out saying thiamine is harmful for your health. Jeff wants to know if there is thiamine in twix, but lost his glasses and can't read the label. He goes to wikipedia and looks for twix. Hey! There's an ingrediant listing! Jeff is saved and never again eats twix. Howabout1 22:48, 28 Apr 2005 (UTC)

 * Oh man, this is just so pointless. I will say it once, and I will say it one more time. An encyclopedia just gives a concise overview on a topic, it does not need detailed information. I think it is a horrible idea to have an ingredients listing and it will just lower the quality of the pages. The above example is just a stretch to make things relevant, and it made me laugh in disbelief when I read it. I don't have anything nice to say about this issue anymore. Have some common sense, remove the ingredients listings, do not add anymore, and focus on the quality of the page rather than cut-and-pasting unnotable info. Mcfly85 03:41, 29 Apr 2005 (UTC)

 * I think the only problem with the ingredients listing is there's not enough of them. All chocolate snacks, delicious and biscuity or otherwise, should have the ingredients on there, because it is a pertinent and useful addendum to the article. I still want to know what PGPR is, though.  But on another point, without wanting to start any kind of argument, an encyclopedia does not have to be a concise overview - wikipedia is not limited by printing constraints or page limits, and users are free to have as much or as little relevant (ingredients are relevant) detailed information as they desire to add.

Also, ingredients would be a useful resource for Muslim/Jewish/any other dietary-restricted group of readers wishing to find out if a food is permissible - for example, Twixes are halaal, but Skittles are haraam due to the ingredients including carmine. Islam considers confectionaries containing calf rennet permissible but feel it is praiseworthy to refrain from them. More useful arguments for the inclusion of ingredients!Proto 09:58, 29 Apr 2005 (UTC)

King Size Twix / Twix 'Xtra
King Size Twixes no longer exist in the UK. They became Twix 'Xtra a number of years ago. Does anybody know when the change occurred and is it worth noting in the article?

Right and Left Twix
Some Twix packages are labeled Right Twix ("100% Left Twix free") and Left Twix ("contains absolutely no Right Twix"). So far as my eyes and tongue can tell, there is no difference between Right and Left. What's up with this?   Solo Owl   21:03, 24 June 2017 (UTC)
 * It's called advertising and should rightfully be ignored. Why they confuse people with this 'Right & Left Twix' nonsense is inexplicable.  Nate  • ( chatter ) 02:39, 24 July 2017 (UTC)

There's definitely a difference. The Left Twix tastes more 'lefty' while the Right Twix has a more 'right-like' taste. Bigsam0914 (talk) 20:19, 10 August 2022 (UTC)

Left Twix vs Right Twix
While both bars are made of a cookie, a thin layer of chocolate, a layer of caramel, and an outer layer of chocolate, there is a distinct difference in taste between the Left & Right Twix bars. The Left bar tastes more 'left-ee' while the right bar tastes more 'right-like'. People who prefer the Left bar say that the Right bars has a slight, rightish after taste. People who prefer the Right bar have been known to criticize the Left bar for it's overly left-like flavor. Bigsam0914 (talk) 20:17, 10 August 2022 (UTC)

 * Another sucker for a marketing campaign ThunderHenry (talk) 02:40, 27 September 2022 (UTC)

Chart Show sponsorship
Should we mention the snack's sponsorship of the Chart Show? Visokor (talk) 20:42, 30 August 2023 (UTC)

Naming the brand twix honey twix
You guys should call it takis honey twix. 72.24.118.7 (talk) 18:39, 6 April 2024 (UTC)

title: Talk:Twix


text:
Copula (probability theory)

In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]. Copulas are used to describe/model the dependence (inter-correlation) between random variables. Their name, introduced by applied mathematician Abe Sklar in 1959, comes from the Latin for "link" or "tie", similar but unrelated to grammatical copulas in linguistics. Copulas have been used widely in quantitative finance to model and minimize tail risk and portfolio-optimization applications.

Sklar's theorem states that any multivariate joint distribution can be written in terms of univariate marginal distribution functions and a copula which describes the dependence structure between the variables.

Copulas are popular in high-dimensional statistical applications as they allow one to easily model and estimate the distribution of random vectors by estimating marginals and copulae separately. There are many parametric copula families available, which usually have parameters that control the strength of dependence. Some popular parametric copula models are outlined below.

Two-dimensional copulas are known in some other areas of mathematics under the name permutons and doubly-stochastic measures.

Mathematical definition
Consider a random vector $$(X_1,X_2,\dots,X_d)$$. Suppose its marginals are continuous, i.e. the marginal CDFs $$F_i(x) = \Pr[X_i\leq x] $$ are continuous functions. By applying the probability integral transform to each component, the random vector
 * $$(U_1,U_2,\dots,U_d)=\left(F_1(X_1),F_2(X_2),\dots,F_d(X_d)\right)$$

has marginals that are uniformly distributed on the interval [0, 1].

The copula of $$(X_1,X_2,\dots,X_d)$$ is defined as the joint cumulative distribution function of $$(U_1,U_2,\dots,U_d)$$:
 * $$C(u_1,u_2,\dots,u_d)=\Pr[U_1\leq u_1,U_2\leq u_2,\dots,U_d\leq u_d].$$

The copula C contains all information on the dependence structure between the components of $$(X_1,X_2,\dots,X_d)$$ whereas the marginal cumulative distribution functions $$F_i$$ contain all information on the marginal distributions of $$X_i$$.

The reverse of these steps can be used to generate pseudo-random samples from general classes of multivariate probability distributions. That is, given a procedure to generate a sample $$(U_1,U_2,\dots,U_d)$$ from the copula function, the required sample can be constructed as
 * $$(X_1,X_2,\dots,X_d) = \left(F_1^{-1}(U_1),F_2^{-1}(U_2),\dots,F_d^{-1}(U_d)\right).$$

The generalized inverses $$F_i^{-1}$$ are unproblematic almost surely, since the $$F_i$$ were assumed to be continuous. Furthermore, the above formula for the copula function can be rewritten as:
 * $$C(u_1,u_2,\dots,u_d)=\Pr[X_1\leq F_1^{-1}(u_1),X_2\leq F_2^{-1}(u_2),\dots,X_d\leq F_d^{-1}(u_d)] .$$

Definition
In probabilistic terms, $$C:[0,1]^d\rightarrow [0,1]$$ is a d-dimensional copula if C is a joint cumulative distribution function of a d-dimensional random vector on the unit cube $$[0,1]^d$$ with uniform marginals.

In analytic terms, $$C:[0,1]^d\rightarrow [0,1]$$ is a d-dimensional copula if
 * $$C(u_1,\dots,u_{i-1},0,u_{i+1},\dots,u_d)=0 $$, the copula is zero if any one of the arguments is zero,
 * $$C(1,\dots,1,u,1,\dots,1)=u $$, the copula is equal to u if one argument is u and all others 1,
 * C is d-non-decreasing, i.e., for each hyperrectangle $$B=\prod_{i=1}^{d}[x_i,y_i]\subseteq [0,1]^d $$ the C-volume of B is non-negative:
 * $$ \int_B \mathrm{d} C(u) =\sum_{\mathbf z\in \prod_{i=1}^{d}\{x_i,y_i\}} (-1)^{N(\mathbf z)} C(\mathbf z)\ge 0,$$
 * where the $$N(\mathbf z)=\#\{k : z_k=x_k\}$$.

For instance, in the bivariate case, $$C:[0,1] \times[0,1]\rightarrow [0,1]$$ is a bivariate copula if $$C(0,u) = C(u,0) = 0 $$, $$C(1,u) = C(u,1) = u $$ and $$C(u_2,v_2)-C(u_2,v_1)-C(u_1,v_2)+C(u_1,v_1) \geq 0 $$ for all $$0 \leq u_1 \leq u_2 \leq 1$$ and $$0 \leq v_1 \leq v_2 \leq 1$$.

Sklar's theorem

Sklar's theorem, named after Abe Sklar, provides the theoretical foundation for the application of copulas. Sklar's theorem states that every multivariate cumulative distribution function
 * $$H(x_1,\dots,x_d)=\Pr[X_1\leq x_1,\dots,X_d\leq x_d]$$

of a random vector $$(X_1,X_2,\dots,X_d)$$ can be expressed in terms of its marginals $$F_i(x_i) = \Pr[X_i\leq x_i] $$ and a copula $$C$$. Indeed:
 * $$H(x_1,\dots,x_d) = C\left(F_1(x_1),\dots,F_d(x_d) \right). $$

If the multivariate distribution has a density $$h$$, and if this density is available, it also holds that
 * $$h(x_1,\dots,x_d)= c(F_1(x_1),\dots,F_d(x_d))\cdot f_1(x_1)\cdot\dots\cdot f_d(x_d),$$

where $$c$$ is the density of the copula.

The theorem also states that, given $$H$$, the copula is unique on $$ \operatorname{Ran}(F_1)\times\cdots\times \operatorname{Ran}(F_d) $$ which is the cartesian product of the ranges of the marginal cdf's. This implies that the copula is unique if the marginals $$F_i$$ are continuous.

The converse is also true: given a copula $$C:[0,1]^d\rightarrow [0,1] $$ and marginals $$F_i(x)$$ then $$C\left(F_1(x_1),\dots,F_d(x_d) \right)$$ defines a d-dimensional cumulative distribution function with marginal distributions $$F_i(x)$$.

Stationarity condition
Copulas mainly work when time series are stationary and continuous. Thus, a very important pre-processing step is to check for the auto-correlation, trend and seasonality within time series.

When time series are auto-correlated, they may generate a non existing dependence between sets of variables and result in incorrect copula dependence structure.

Fréchet–Hoeffding copula bounds

The Fréchet–Hoeffding theorem (after Maurice René Fréchet and Wassily Hoeffding ) states that for any copula $$C:[0,1]^d\rightarrow [0,1]$$ and any $$(u_1,\dots,u_d)\in[0,1]^d$$ the following bounds hold:
 * $$W(u_1,\dots,u_d) \leq C(u_1,\dots,u_d) \leq M(u_1,\dots,u_d).$$

The function $W$ is called lower Fréchet–Hoeffding bound and is defined as
 * $$ W(u_1,\ldots,u_d) = \max\left\{1-d+\sum\limits_{i=1}^d {u_i} ,\, 0 \right\}.$$

The function $M$ is called upper Fréchet–Hoeffding bound and is defined as
 * $$ M(u_1,\ldots,u_d) = \min \{u_1,\dots,u_d\}.$$

The upper bound is sharp: $M$ is always a copula, it corresponds to comonotone random variables.

The lower bound is point-wise sharp, in the sense that for fixed u, there is a copula $$\tilde{C}$$ such that $$\tilde{C}(u) = W(u)$$. However, $W$ is a copula only in two dimensions, in which case it corresponds to countermonotonic random variables.

In two dimensions, i.e. the bivariate case, the Fréchet–Hoeffding theorem states
 * $$\max\{u+v-1, \,0\} \leq C(u,v) \leq \min\{u,v\}.$$

Families of copulas
Several families of copulas have been described.

Gaussian copula

The Gaussian copula is a distribution over the unit hypercube $$[0,1]^d$$. It is constructed from a multivariate normal distribution over $$\mathbb{R}^d$$ by using the probability integral transform.

For a given correlation matrix $$R\in[-1, 1]^{d\times d}$$, the Gaussian copula with parameter matrix $$R$$ can be written as
 * $$ C_R^{\text{Gauss}}(u) = \Phi_R\left(\Phi^{-1}(u_1),\dots, \Phi^{-1}(u_d) \right), $$

where $$\Phi^{-1}$$ is the inverse cumulative distribution function of a standard normal and $$\Phi_R$$ is the joint cumulative distribution function of a multivariate normal distribution with mean vector zero and covariance matrix equal to the correlation matrix $$R$$. While there is no simple analytical formula for the copula function, $$C_R^{\text{Gauss}}(u)$$, it can be upper or lower bounded, and approximated using numerical integration. The density can be written as
 * $$ c_R^{\text{Gauss}}(u)

= \frac{1}{\sqrt{\det{R}}}\exp\left(-\frac{1}{2} \begin{pmatrix}\Phi^{-1}(u_1)\\ \vdots \\ \Phi^{-1}(u_d)\end{pmatrix}^T \cdot \left(R^{-1}-I\right) \cdot \begin{pmatrix}\Phi^{-1}(u_1)\\ \vdots \\ \Phi^{-1}(u_d)\end{pmatrix} \right), $$ where $$\mathbf{I}$$ is the identity matrix.

Archimedean copulas
Archimedean copulas are an associative class of copulas. Most common Archimedean copulas admit an explicit formula, something not possible for instance for the Gaussian copula. In practice, Archimedean copulas are popular because they allow modeling dependence in arbitrarily high dimensions with only one parameter, governing the strength of dependence.

A copula C is called Archimedean if it admits the representation

 * $$ C(u_1,\dots,u_d;\theta) = \psi^{-1}\left(\psi(u_1;\theta)+\cdots+\psi(u_d;\theta);\theta\right) $$

where $$\psi\!:[0,1]\times\Theta \rightarrow [0,\infty)$$ is a continuous, strictly decreasing and convex function such that $$\psi(1;\theta)=0$$, $$\theta$$ is a parameter within some parameter space $$\Theta$$, and $$\psi$$ is the so-called generator function and $$\psi^{-1}$$ is its pseudo-inverse defined by

 * $$ \psi^{-1}(t;\theta) = \left\{\begin{array}{ll} \psi^{-1}(t;\theta) & \mbox{if }0 \leq t \leq \psi(0;\theta) \\ 0 & \mbox{if }\psi(0;\theta) \leq t \leq\infty. \end{array}\right. $$

Moreover, the above formula for C yields a copula for $$\psi^{-1}$$ if and only if $$\psi^{-1}$$ is d-monotone on $$[0,\infty)$$. That is, if it is $$d-2$$ times differentiable and the derivatives satisfy

 * $$ (-1)^k\psi^{-1,(k)}(t;\theta) \geq 0 $$

for all $$t\geq 0$$ and $$k=0,1,\dots,d-2$$ and $$(-1)^{d-2}\psi^{-1,(d-2)}(t;\theta)$$ is nonincreasing and convex.

Most important Archimedean copulas
The following tables highlight the most prominent bivariate Archimedean copulas, with their corresponding generator. Not all of them are completely monotone, i.e. d-monotone for all $$d\in\mathbb{N}$$ or d-monotone for certain $$\theta \in \Theta$$ only.

Expectation for copula models and Monte Carlo integration
In statistical applications, many problems can be formulated in the following way. One is interested in the expectation of a response function $$g:\mathbb{R}^d\rightarrow\mathbb{R}$$ applied to some random vector $$(X_1,\dots,X_d)$$. If we denote the CDF of this random vector with $$H$$, the quantity of interest can thus be written as

 * $$ \operatorname{E}\left[ g(X_1,\dots,X_d) \right] = \int_{\mathbb{R}^d} g(x_1,\dots,x_d) \, \mathrm{d}H(x_1,\dots,x_d).$$

If $$H$$ is given by a copula model, i.e.,

 * $$H(x_1,\dots,x_d)=C(F_1(x_1),\dots,F_d(x_d))$$

this expectation can be rewritten as

 * $$\operatorname{E}\left[g(X_1,\dots,X_d)\right]=\int_{[0,1]^d}g(F_1^{-1}(u_1),\dots,F_d^{-1}(u_d)) \, \mathrm{d}C(u_1,\dots,u_d).$$

In case the copula C is absolutely continuous, i.e. C has a density c, this equation can be written as

 * $$\operatorname{E}\left[g(X_1,\dots,X_d)\right]=\int_{[0,1]^d}g(F_1^{-1}(u_1),\dots,F_d^{-1}(u_d))\cdot c(u_1,\dots,u_d) \, du_1\cdots \mathrm{d}u_d,$$

and if each marginal distribution has the density $$f_i$$ it holds further that
 * $$\operatorname{E}\left[g(X_1,\dots,X_d)\right]=\int_{\mathbb{R}^d}g(x_1,\dots x_d)\cdot c(F_1(x_1),\dots,F_d(x_d))\cdot f_1(x_1)\cdots f_d(x_d) \, \mathrm{d}x_1\cdots \mathrm{d}x_d.$$

If copula and marginals are known (or if they have been estimated), this expectation can be approximated through the following Monte Carlo algorithm:
 * 1) Draw a sample $$(U_1^k,\dots,U_d^k)\sim C\;\;(k=1,\dots,n)$$ of size n from the copula C
 * 2) By applying the inverse marginal cdf's, produce a sample of $$(X_1,\dots,X_d)$$ by setting $$(X_1^k,\dots,X_d^k)=(F_1^{-1}(U_1^k),\dots,F_d^{-1}(U_d^k))\sim H\;\;(k=1,\dots,n)$$
 * 3) Approximate $$\operatorname{E}\left[g(X_1,\dots,X_d)\right]$$ by its empirical value:
 * $$\operatorname{E}\left[g(X_1,\dots,X_d)\right]\approx \frac{1}{n}\sum_{k=1}^n g(X_1^k,\dots,X_d^k)$$

Empirical copulas
When studying multivariate data, one might want to investigate the underlying copula. Suppose we have observations
 * $$(X_1^i,X_2^i,\dots,X_d^i), \, i=1,\dots,n$$

from a random vector $$(X_1,X_2,\dots,X_d)$$ with continuous marginals. The corresponding “true” copula observations would be
 * $$(U_1^i,U_2^i,\dots,U_d^i)=\left(F_1(X_1^i),F_2(X_2^i),\dots,F_d(X_d^i)\right), \, i=1,\dots,n.$$

However, the marginal distribution functions $$F_i$$ are usually not known. Therefore, one can construct pseudo copula observations by using the empirical distribution functions
 * $$F_k^n(x)=\frac{1}{n} \sum_{i=1}^n \mathbf{1}(X_k^i\leq x)$$

instead. Then, the pseudo copula observations are defined as
 * $$(\tilde{U}_1^i,\tilde{U}_2^i,\dots,\tilde{U}_d^i)=\left(F_1^n(X_1^i),F_2^n(X_2^i),\dots,F_d^n(X_d^i)\right), \, i=1,\dots,n.$$

The corresponding empirical copula is then defined as
 * $$C^n(u_1,\dots,u_d) = \frac{1}{n} \sum_{i=1}^n \mathbf{1}\left(\tilde{U}_1^i\leq u_1,\dots,\tilde{U}_d^i\leq u_d\right).$$

The components of the pseudo copula samples can also be written as $$\tilde{U}_k^i=R_k^i/n$$, where $$R_k^i$$ is the rank of the observation $$X_k^i$$:
 * $$R_k^i=\sum_{j=1}^n \mathbf{1}(X_k^j\leq X_k^i)$$

Therefore, the empirical copula can be seen as the empirical distribution of the rank transformed data.

The sample version of Spearman's rho:
 * $$r=\frac{12}{n^2-1}\sum_{i=1}^n\sum_{j=1}^n \left[C^n \left(\frac{i}{n},\frac{j}{n}\right)-\frac{i}{n}\cdot\frac{j}{n}\right]$$

Quantitative finance
In quantitative finance copulas are applied to risk management, to portfolio management and optimization, and to derivatives pricing.

For the former, copulas are used to perform stress-tests and robustness checks that are especially important during "downside/crisis/panic regimes" where extreme downside events may occur (e.g., the global financial crisis of 2007–2008). The formula was also adapted for financial markets and was used to estimate the probability distribution of losses on pools of loans or bonds.

During a downside regime, a large number of investors who have held positions in riskier assets such as equities or real estate may seek refuge in 'safer' investments such as cash or bonds. This is also known as a flight-to-quality effect and investors tend to exit their positions in riskier assets in large numbers in a short period of time. As a result, during downside regimes, correlations across equities are greater on the downside as opposed to the upside and this may have disastrous effects on the economy. For example, anecdotally, we often read financial news headlines reporting the loss of hundreds of millions of dollars on the stock exchange in a single day; however, we rarely read reports of positive stock market gains of the same magnitude and in the same short time frame.

Copulas aid in analyzing the effects of downside regimes by allowing the modelling of the marginals and dependence structure of a multivariate probability model separately. For example, consider the stock exchange as a market consisting of a large number of traders each operating with his/her own strategies to maximize profits. The individualistic behaviour of each trader can be described by modelling the marginals. However, as all traders operate on the same exchange, each trader's actions have an interaction effect with other traders'. This interaction effect can be described by modelling the dependence structure. Therefore, copulas allow us to analyse the interaction effects which are of particular interest during downside regimes as investors tend to herd their trading behaviour and decisions. (See also agent-based computational economics, where price is treated as an emergent phenomenon, resulting from the interaction of the various market participants, or agents.)

The users of the formula have been criticized for creating "evaluation cultures" that continued to use simple copulæ despite the simple versions being acknowledged as inadequate for that purpose. Thus, previously, scalable copula models for large dimensions only allowed the modelling of elliptical dependence structures (i.e., Gaussian and Student-t copulas) that do not allow for correlation asymmetries where correlations differ on the upside or downside regimes. However, the development of vine copulas (also known as pair copulas) enables the flexible modelling of the dependence structure for portfolios of large dimensions. The Clayton canonical vine copula allows for the occurrence of extreme downside events and has been successfully applied in portfolio optimization and risk management applications. The model is able to reduce the effects of extreme downside correlations and produces improved statistical and economic performance compared to scalable elliptical dependence copulas such as the Gaussian and Student-t copula.

Other models developed for risk management applications are panic copulas that are glued with market estimates of the marginal distributions to analyze the effects of panic regimes on the portfolio profit and loss distribution. Panic copulas are created by Monte Carlo simulation, mixed with a re-weighting of the probability of each scenario.

As regards derivatives pricing, dependence modelling with copula functions is widely used in applications of financial risk assessment and actuarial analysis – for example in the pricing of collateralized debt obligations (CDOs). Some believe the methodology of applying the Gaussian copula to credit derivatives to be one of the reasons behind the global financial crisis of 2008–2009; see.

Despite this perception, there are documented attempts within the financial industry, occurring before the crisis, to address the limitations of the Gaussian copula and of copula functions more generally, specifically the lack of dependence dynamics. The Gaussian copula is lacking as it only allows for an elliptical dependence structure, as dependence is only modeled using the variance-covariance matrix. This methodology is limited such that it does not allow for dependence to evolve as the financial markets exhibit asymmetric dependence, whereby correlations across assets significantly increase during downturns compared to upturns. Therefore, modeling approaches using the Gaussian copula exhibit a poor representation of extreme events. There have been attempts to propose models rectifying some of the copula limitations.

Additional to CDOs, copulas have been applied to other asset classes as a flexible tool in analyzing multi-asset derivative products. The first such application outside credit was to use a copula to construct a basket implied volatility surface, taking into account the volatility smile of basket components. Copulas have since gained popularity in pricing and risk management of options on multi-assets in the presence of a volatility smile, in equity-, foreign exchange- and fixed income derivatives.

Civil engineering
Recently, copula functions have been successfully applied to the database formulation for the reliability analysis of highway bridges, and to various multivariate simulation studies in civil engineering, reliability of wind and earthquake engineering, and mechanical & offshore engineering. Researchers are also trying these functions in the field of transportation to understand the interaction between behaviors of individual drivers which, in totality, shapes traffic flow.

Reliability engineering
Copulas are being used for reliability analysis of complex systems of machine components with competing failure modes.

Warranty data analysis
Copulas are being used for warranty data analysis in which the tail dependence is analysed.

Turbulent combustion
Copulas are used in modelling turbulent partially premixed combustion, which is common in practical combustors.

Medicine
Copulæ have many applications in the area of medicine, for example,

 * 1) Copulæ have been used in the field of magnetic resonance imaging (MRI), for example, to segment images, to fill a vacancy of graphical models in imaging genetics in a study on schizophrenia, and to distinguish between normal and  Alzheimer patients.
 * 2) Copulæ have been in the area of brain research based on EEG signals, for example, to detect drowsiness during daytime nap, to track changes in instantaneous equivalent bandwidths (IEBWs), to derive synchrony for early diagnosis of Alzheimer's disease, to characterize dependence in oscillatory activity between EEG channels, and to assess the reliability of using methods to capture dependence between pairs of EEG channels using their time-varying envelopes. Copula functions have been successfully applied to the analysis of neuronal dependencies and spike counts in neuroscience.
 * 3) A copula model has been developed in the field of oncology, for example, to jointly model genotypes, phenotypes, and pathways to reconstruct a cellular network to identify interactions between specific phenotype and multiple molecular features (e.g. mutations and gene expression change). Bao et al. used NCI60 cancer cell line data to identify several subsets of molecular features that jointly perform as the predictors of clinical phenotypes. The proposed copula may have an impact on biomedical research, ranging from cancer treatment to disease prevention. Copula has also been used to predict the histological diagnosis of colorectal lesions from colonoscopy images, and to classify cancer subtypes.
 * 4) A copula-based analysis model has been developed in the field of heart and cardiovascular disease, for example, to predict heart rate (HR) variation. Heart rate (HR) is one of the most critical health indicators for monitoring exercise intensity and load degree because it is closely related to heart rate. Therefore, an accurate short-term HR prediction technique can deliver efficient early warning for human health and decrease harmful events. Namazi (2022) used a novel hybrid algorithm to predict HR.

Geodesy
The combination of SSA and copula-based methods have been applied for the first time as a novel stochastic tool for Earth Orientation Parameters prediction.

Hydrology research
Copulas have been used in both theoretical and applied analyses of hydroclimatic data. Theoretical studies adopted the copula-based methodology for instance to gain a better understanding of the dependence structures of temperature and precipitation, in different parts of the world. Applied studies adopted the copula-based methodology to examine e.g., agricultural droughts or joint effects of temperature and precipitation extremes on vegetation growth.

Climate and weather research
Copulas have been extensively used in climate- and weather-related research.

Solar irradiance variability
Copulas have been used to estimate the solar irradiance variability in spatial networks and temporally for single locations.

Random vector generation
Large synthetic traces of vectors and stationary time series can be generated using empirical copula while preserving the entire dependence structure of small datasets. Such empirical traces are useful in various simulation-based performance studies.

Ranking of electrical motors
Copulas have been used for quality ranking in the manufacturing of electronically commutated motors.

Signal processing
Copulas are important because they represent a dependence structure without using marginal distributions. Copulas have been widely used in the field of finance, but their use in signal processing is relatively new. Copulas have been employed in the field of wireless communication for classifying radar signals, change detection in remote sensing applications, and EEG signal processing in medicine. In this section, a short mathematical derivation to obtain copula density function followed by a table providing a list of copula density functions with the relevant signal processing applications are presented.

Astronomy
Copulas have been used for determining the core radio luminosity function of Active galactic Nuclei (AGNs), while this cannot be realized using traditional methods due to the difficulties in sample completeness.

Mathematical derivation of copula density function
For any two random variables X and Y, the continuous joint probability distribution function can be written as

 * $$F_{XY}(x,y) = \Pr \begin{Bmatrix} X \leq{x},Y\leq{y} \end{Bmatrix}, $$

where $F_X(x) = \Pr \begin{Bmatrix} X \leq{x} \end{Bmatrix} $ and $ F_Y(y) = \Pr \begin{Bmatrix} Y \leq{y} \end{Bmatrix} $ are the marginal cumulative distribution functions of the random variables X and Y, respectively.

then the copula distribution function $$C(u, v)$$ can be defined using Sklar's theorem as:

 * $$F_{XY}(x,y) = C( F_X (x), F_Y (y) ) \triangleq C( u, v ), $$

where $$u = F_X(x) $$ and $$v = F_Y(y) $$ are marginal distribution functions, $$ F_{XY}(x,y) $$ joint and $$ u, v \in (0,1) $$.

Assuming $$F_{XY}(\cdot,\cdot) $$ is a.e. twice differentiable, we start by using the relationship between joint probability density function (PDF) and joint cumulative distribution function (CDF) and its partial derivatives.

 * $$\begin{alignat}{6}

f_{XY}(x,y) = {} & {\partial^2 F_{XY}(x,y) \over\partial x\,\partial y } \\ \vdots \\ f_{XY}(x,y) = {} & {\partial^2 C(F_X(x),F_Y(y)) \over\partial x\,\partial y} \\ \vdots \\ f_{XY}(x,y) = {} & {\partial^2 C(u,v) \over\partial u\,\partial v} \cdot {\partial F_X(x) \over\partial x} \cdot {\partial F_Y(y) \over\partial y} \\ \vdots \\ f_{XY}(x,y) = {} & c(u,v) f_X(x) f_Y(y) \\ \vdots \\ \frac{f_{XY}(x,y)}{f_X(x) f_Y(y) } = {} & c(u,v) \end{alignat}

$$

where $$c(u,v)$$ is the copula density function, $$f_X(x) $$ and $$f_Y(y) $$ are the marginal probability density functions of X and Y, respectively. There are four elements in this equation, and if any three elements are known, the fourth element can be calculated. For example, it may be used,

 * when joint probability density function between two random variables is known, the copula density function is known, and one of the two marginal functions are known, then, the other marginal function can be calculated, or
 * when the two marginal functions and the copula density function are known, then the joint probability density function between the two random variables can be calculated, or
 * when the two marginal functions and the joint probability density function between the two random variables are known, then the copula density function can be calculated.

List of copula density functions and applications
Various bivariate copula density functions are important in the area of signal processing. $$u=F_X(x) $$ and $$v=F_Y(y) $$ are marginal distributions functions and $$f_X(x) $$ and $$f_Y(y) $$ are marginal density functions. Extension and generalization of copulas for statistical signal processing have been shown to construct new bivariate copulas for exponential, Weibull, and Rician distributions. Zeng et al. presented algorithms, simulation, optimal selection, and practical applications of these copulas in signal processing.

title: Copula (probability theory)