title: Osamu Dazai

text: Dazai's literary work "No Longer Human" has received quite a few adaptations: a graphic novel written by the horror manga artist Junji Ito, a film directed by Genjiro Arato, the first four episodes of the anime series "Aoi Bungaku", and a variety of mangas one of which was serialized in Shinchosha's "Comic Bunch" magazine. It is also the name of an ability in the anime "Bungo Stray Dogs" and "Bungo and Alchemist", used by a character named after Dazai himself.


title: Osamu Dazai

text: The book is also the central work in one of the volumes of the Japanese light novel series "Book Girl", "Book Girl and the Suicidal Mime", although other works of his are also mentioned. Dazai's works are also discussed in the "Book Girl" manga and anime series. Dazai is often quoted by the male protagonist, Kotaro Azumi, in the anime series "Tsuki ga Kirei", as well as by Ken Kaneki in "Tokyo Ghoul".


title: Big Fish

text: Big Fish is a 2003 American fantasy comedy-drama film directed by Tim Burton, and based on the by Daniel Wallace. The film stars Ewan McGregor, Albert Finney, Billy Crudup, Jessica Lange, Helena Bonham Carter, Alison Lohman, Robert Guillaume, Marion Cotillard, Steve Buscemi, and Danny DeVito. The film tells the story of a frustrated son who tries to distinguish fact from fiction in his dying father's life.


title: Big Fish

text: Screenwriter John August read a manuscript of the novel six months before it was published and convinced Columbia Pictures to acquire the rights. August began adapting the novel while producers negotiated with Steven Spielberg who planned to direct after finishing "Minority Report" (2002). Spielberg considered Jack Nicholson for the role of Edward Bloom, but eventually dropped the project to focus on "Catch Me If You Can" (2002). Tim Burton and Richard D. Zanuck took over after completing "Planet of the Apes" (2001) and brought Ewan McGregor and Albert Finney on board.


title: Big Fish

text: The film's theme of reconciliation between a dying father and his son had special significance for Burton, as his father had died in 2000 and his mother in 2002, a month before he signed on to direct. "Big Fish" was shot on location in Alabama in a series of fairy tale vignettes evoking the tone of a Southern Gothic fantasy. "Big Fish" premiered on December 4, 2003, at the Hammerstein Ballroom and was released in limited capacity on December 10, 2003, by Columbia Pictures followed by a wide release on January 9, 2004. It garnered mostly positive reviews from critics, and grossed $122.9 million against a $70 million budget. The film received award nominations in multiple film categories, including four Golden Globe Award nominations, seven nominations from the British Academy of Film and Television Arts, two Saturn Award nominations, and an Oscar and a Grammy Award nomination for Danny Elfman's original score. The set for the town of Spectre still remains and can be found in Wetumpka, Alabama at Jackson Lake Island.


title: Big Fish

text: At Will Bloom's wedding party in 2000, his father Edward recalls the day Will was born, claiming he caught an enormous catfish using his wedding ring as bait. Will, having heard these stories all his life, has gradually grown exasperated with Edward's histronics, coming to believe all these tales to be just a ruse to captivate attention, and eventually falling out with his father.


title: Big Fish

text: Three years later in 2003, Edward gets a cancer diagnosis. When the illness approaches its terminal stage, Will and his pregnant French wife Joséphine return to his home town of Ashton, Alabama, to spend time with him in the last days. During the plane ride, Will begins to recall some of his father's usual stories, such as the tale of Edward's childhood encounter with a witch in 1932, who shows him his death in her glass eye. Edward, in spite of his illness, continues to tell the story of his life to Will and Joséphine through this and other bits of personal lore and unlikely feats. As another example, he claims to have once been bedridden for three years due to his rapid growth spurts, and to have then became a locally famous sportsman, a mogul in grass-mowing in his neighborhood and other things, before being driven by his ambition to leave his hometown and pursue even bigger achievements.


title: Big Fish

text: In 1944, he sets out into the world with a misunderstood giant, Karl, who was terrorizing the town by eating livestock from the surrounding farms and had been risking lynching by the scared and angry town folk. Edward and Karl leave Ashton with the major's blessing and celebrated by all local characters. Soon they encounter a fork in the road, and decide travel down separate paths and re-meet where they merge again. Edward chooses a dangerous-looking path through a swamp, confident that nothing can really harm him, since the witch had forecast a different death at an older age. Soon he discovers along this way the secret and otherworldy town of Spectre, where the cheery but strange locals claim that he was early but expected. Among them, he befriends Ashton poet laureate Norther Winslow, who had similarly left their town years ago and suddenly stopped to send any news. Edward makes also a big impression on the Spectre mayor's child daughter Jenny, who claims their big age different not to be a big obstacle to love, as it will get less significant once they are both adult. However, Edward leaves Spectre, unwilling to settle down so soon, but promising Jenny and the others that he will return.


title: Big Fish

text: Edward and Karl reunite. Continuing their wandering, they visit the Calloway Circus in 1948, where Karl turns out to be a more spectacular attraction than the local giant 'El Penumbra' (just a tall man) and Edward spots among the public a beautiful young woman, getting immediately infatuated. Karl is offered a job in the circus and Edward too convinces the ringmaster Amos Calloway to hire him, in exchange for one detail about the woman at the end of every month, instead of a normal salary. After three years of this arrangement and many small bits of information, in 1951 Edward discovers that Amos is secretly a werewolf. He is attacked by him during one of his periodic transformations, and similarly to the initial situation with Karl in Ashton, the circus people are about to shoot the dangerous-looking "freak" with a silver bullet out of fear, but Edward manages to de-escalate the situation and shows the werewolf's playful and dog-like attitude instead, playing fetch until he turns back into a human in the morning. Amos, impressed by Edward's courage, finally reveals the woman's name to be Sandra Templeton, and where to find her: she attends Auburn University, but her graduation date is near and she will depart soon.


title: Big Fish

text: Edward rushes to Auburn, and begins to closely court the friendly but already engaged Sandra over many days. He tries to win her over with more and more garish love declarations, going so far as to plant thousands of daffodils (her favorite flower, according to one of the personal details gathered from Amos) outside of her sorority house bedroom. This annoys her fiance, Edward's childhood peer Don Price, also from Ashton. Don was already envious of Edward's always gaining the spotlight in every endeavor, and brutally beats up him up eventually. This however prompts Sandra to break off their engagement and actually decide to marry Edward. Not long after, Don dies an obscure death due to a heart attack in the toilet, as the witch had prophesied.


title: Big Fish

text: Shortly after the happy marriage with Sandra, Edward is drafted into the army in 1952. He is sent to fight in the Korean War, but tries to shorten his tour of duty by volunteering for all the riskiest missions, in attempt to gain an honorable early discharge and return to his wife. In one of such missions, he parachutes alone into the middle of a North Korean military show, steals important documents, and convinces local troop entertainers conjoined twins Ping and Jing to help him go home and flee the country all together, in exchange for making them celebrities on the larger stage of American show business.


title: Big Fish

text: Upon returning home, Edward decides to turn his skills into making money to buy his dream family home. He becomes again without effort a successful but fairly ordinary travelling salesman, until he crosses paths by chance with Winslow in a bank in 1963. It turns out that Winslow is there as a robber, claiming to have been inspired to also leave Spectre by Edward's example. Edward is unwittingly brought to help with the robbery, but the bank staff reveals not to have any money and to have kept pretension of solvency only to avoid a bank run. During their escape, Edward lectures the poet about where real money can be made in quicker but riskier ways than armed robberies, i.e. on the stock market. Winslow decides to follow such advice and parts ways, to start a career in Wall Street where he will become a wealthy broker. In gratitude, he repays Edward with ten thousand dollars, which allows Edward and his wife to finally move into their dream house.


title: Big Fish

text: In the present, Will is beginning to set his father's affairs into order and this gradually brings him to investigate the truth behind the above many tales. Upon finding some documents actually citing the town of Spectre, he travels there and meets an older Jenny, living alone in a dilapidated house. The aged woman explains that in 1968, Edward had indeed returned to the town of his first side-stop out of Ashton, and that he was instrumental in rescuing all the citizenship from bankruptcy, by buying all properties in an auction and letting all the people stay for free, thanks to the financial backing of his rich friends like Winslow or Ping and Jing. In particular, he had saved and rebuilt Jenny's old house with help of the giant Karl. Will figures out that Jenny and his father had actually had an affair during his travel salesman's days, although dates and chronology of the embellished tales don't entirely add up. The woman acknowledges that there was indeed some truth in that, but that Edward had never stopped really loving his wife Sandra.


title: Big Fish

text: Will returns home, but finds out that during this absence Edward's condition has suddenly deteriorated further. He has had a stroke, requiring urgent care back at the hospital. Will rushes to his death bed, where Edward briefly regains consciousness but is unable to speak much. They seem to have reached however a better degree of understanding and reconciliation than in years. Will calms down his dying father by taking over his usual role of narrating magic tales barely linked to the more prosaic reality, imagining in particular how the witch's glass eye prophecy could be reconciled with the present hospitalization, and lead to a spectacular happy ending among all other characters of a lifetime. His father dies peacefully in his arms during the tale.


title: Big Fish

text: At the funeral, Will and Joséphine are surprised when they start noticing all the people from Edward's stories. Everybody is slightly less fantastical than described, but still clearly recognizable from his father's over-the-top tales. They also share their own memories of Edward's life and of the experiences together, which may have not been so incredible but clearly left all of them inspired and enriched. Some time later, Will is shown to be also a father, now having fully endorsed Edward's tales which he passes on to his own young son.


title: Big Fish

text: The reconciliation of the father-son relationship between Edward and William is the key theme in "Big Fish". Novelist Daniel Wallace's interest in the theme of the father-son relationship began with his own family. Wallace found the "charming" character of Edward Bloom similar to his father, who used charm to keep his distance from other people. In the film, Will believes Edward has never been honest with him because Edward creates extravagant myths about his past to hide himself, using storytelling as an avoidance mechanism. Edward's stories are filled with fairy tale characters (a witch, mermaid, giant, and werewolf) and places (the circus, small towns, the mythological town of Spectre), all of which are classic images and archetypes. The quest motif propels both Edward's story and Will's attempt to get to the bottom of it. Wallace explains: "The father's quest is to be a big fish in a big pond, and the son's quest is to see through his tall tales."


title: Big Fish

text: Screenwriter John August identified with Will's character and adapted it after himself. In college, August's father died, and like Will, August had attempted to get to know him before his death, but found it difficult. Like Will, August had studied journalism and was 28 years old. In the film, Will says of Edward, "I didn't see anything of myself in my father, and I don't think he saw anything of himself in me. We were like strangers who knew each other very well." Will's description of his relationship with Edward closely resembled August's own relationship with his father. Burton also used the film to confront his thoughts and emotions concerning the death of his father in 2000: "My father had been ill for a while ... I tried to get in touch with him, to have, like in this film, some sort of resolution, but it was impossible."


title: Big Fish

text: Religion and film scholar Kent L. Brintnall observes how the father-son relationship resolves itself at the end of the film. As Edward dies, Will finally lets go of his anger and begins to understand his father for the first time:


title: Big Fish

text: In a final gesture of love and comprehension, after a lifetime of despising his father's stories and his father as story-teller, Will finishes the story his father has begun, pulling together the themes, images and characters of his father's storied life to blend reality and fantasy in act of communion and care. By unselfishly releasing the anger he has held about his father's stories, Will gains the understanding that all we are is our stories and that his father's stories gave him a reality and substance and a dimension that was as real, genuine, and deep as the day-to-day experiences that Will sought out. Will comes to understand, then, that his father—and the rest of us—are our stories and that the deeper reality of our lives may, in fact, not be our truest self.


title: Big Fish

text: About six months before it was published, screenwriter John August read a manuscript of "" (1998) by author Daniel Wallace. August read the unpublished novel following the death of his father. In September 1998, August convinced Columbia Pictures to acquire the film rights on his behalf. August worked hard to make the episodic book into a cohesive screenplay, deciding on several narrators for the script. In August 2000, producers Bruce Cohen and Dan Jinks began discussions for Steven Spielberg to direct. Spielberg planned to have DreamWorks co-finance and distribute "Big Fish" with Columbia, and planned to have filming start in late 2001, after completing "Minority Report" (2002).


title: Big Fish

text: Spielberg courted Jack Nicholson for the role of Edward Bloom Sr. and towards this end, had August compose two additional drafts for Nicholson's part. August recalls: "There was this thought that there wasn't enough for Jack Nicholson to do in the movie so we built new sequences. Pieces got moved around, but it wasn't a lot of new stuff being created. It ended up being a really good intellectual exercise in my explaining and defending and reanalyzing pieces of the story." Spielberg eventually left "Big Fish" when he became involved with "Catch Me If You Can" (2002), and DreamWorks also backed out of the film.


title: Big Fish

text: With Spielberg no closer to committing, August, working with Jinks and Cohen, considered Stephen Daldry as a potential director. "Once Steven decided he wasn't going to do it, we put the script back to the way it was," recalls Jinks. "Steven even said, 'I think I made a mistake with a couple of things I asked you guys to try.'" August took his favorite elements from the previous drafts, coming up with what he called "a best-of "Big Fish" script". "By the time we approached Tim Burton, the script was in the best shape it had ever been."


title: Big Fish

text: Burton had never been particularly close to his parents, but his father's death in October 2000 and his mother's in March 2002 affected him deeply. Following the production of "Planet of the Apes" (2001), the director wanted to get back to making a smaller film. Burton enjoyed the script, feeling that it was the first unique story he was offered since "Beetlejuice" (1988). Burton also found appeal in the story's combination of an emotional drama with exaggerated tall tales, which allowed him to tell various stories of different genres. He signed to direct in April 2002, which prompted Richard D. Zanuck, who worked with Burton on "Planet of the Apes", to join "Big Fish" as a producer. Zanuck also had a difficult relationship with his own father, Darryl F. Zanuck, who once fired him as head of production at 20th Century Fox.


title: Big Fish

text: For the role of Edward Bloom, Burton spoke with Jack Nicholson, Spielberg's initial choice for the role. Burton had previously worked with Nicholson on "Batman" (1989) and "Mars Attacks!" (1996). In order to depict Nicholson as the young Bloom, Burton intended to use a combination of computer-generated imagery and prosthetic makeup. The director then decided to cast around for the two actors in question. Jinks and Cohen, who were then working with Ewan McGregor on "Down with Love" (2003), suggested that Burton cast both McGregor and Albert Finney for Edward. Burton later compared McGregor's acting style to regular colleague Johnny Depp. Viewing Finney's performance in "Tom Jones" (1963), Burton found him similar to McGregor, and coincidentally found a "People" magazine article comparing the two. McGregor, being Scottish, found it easier performing with a Southern American English accent. "It's a much easier accent to do than a standard American accent because you can really hear it. You can get your teeth into it. Standard American is much harder because it's more lyrical." The same dual casting applied to the role of Bloom's wife, Sandra, who would be played by Jessica Lange and Alison Lohman. Burton commented that he was impressed with Lohman's performance in "White Oleander" (2002). Burton's girlfriend, Helena Bonham Carter, was also cast in two roles. Her prosthetic makeup for The Witch took five hours to apply. "I was pregnant throughout filming, so it was weird being a pregnant witch," the actress reflected. "I had morning sickness, so all those fumes and the make-up and the rubber ... it was hideous."


title: Big Fish

text: Burton personalized the film with several cameos. While filming in Alabama, the crew tracked down Billy Redden, one of the original banjo players from "Deliverance" (1972). Redden was working as a part-owner of a restaurant in Clayton, Georgia, and he agreed to reprise his role in the Spectre vignette. As Edward Bloom first enters the town, Redden can be seen on a porch plucking a few notes from "Dueling Banjos". Burton was pleased with the result: "If you're watching the film and don't recognise the solitary, enigmatic figure on the porch, that's fine. But if you do – well, it just makes me so happy to see him and I think other people will feel the same way." Original "Big Fish" author Daniel Wallace makes a brief appearance as Sandra's economics teacher in the "Courtship of Sandra Templeton" sequence.


title: Big Fish

text: Burton planned to start filming in October 2002, but principal photography in Alabama did not begin until January 13, 2003. Apart from filming in Paris for one week in May, "Big Fish" was entirely shot in Alabama, mostly in Wetumpka and Montgomery (such as the Cloverdale neighborhood). Brief filming also took place in Tallassee and on the campus of Huntingdon College. Scenes for the town of Spectre were filmed on a custom set located on Jackson Lake Island between Montgomery and Millbrook, Alabama, adjacent to the Alabama River. Principal photography for "Big Fish" in Alabama continued until the first week of April. and is estimated to have generated as much as $25 million for the local economy.


title: Big Fish

text: Burton filmed all the dramatic hospital scenes and most of those involving Finney first, before moving on to the McGregor section of Bloom's life. Although McGregor was on set from the beginning of filming, Burton chose to shoot all Finney's scenes first. Location filming in Alabama was delayed by inclement weather; during the Calloway circus scenes filming, a tornado watch was issued and flooding on the set interrupted filming for several weeks. Despite the delays, Burton delivered the film on budget and on schedule.


title: Big Fish

text: The director attempted to limit the use of digital effects. However, because he wanted to evoke a Southern Gothic fantasy tone for "Big Fish", color grading techniques were applied by Sony Pictures Imageworks. Stan Winston Studios, with whom Burton worked with on "Edward Scissorhands" (1990) and "Batman Returns" (1992), designed Helena Bonham Carter's prosthetic makeup and created the animatronics. Scenes with Karl the Giant were commissioned using forced perspective filmmaking.


title: Big Fish

text: The soundtrack was composed by regular Burton collaborator Danny Elfman. Burton approached Pearl Jam during post-production to request an original song for the soundtrack and closing credits. After screening an early print of the film, Pearl Jam vocalist Eddie Vedder wrote "Man of the Hour", completing the demo by the next day. It was recorded by the band four days later. Guitarist Mike McCready stated, "We were so blown away by the movie ... Eddie and I were standing around talking about it afterwards and were teary-eyed. We were so emotionally charged and moved by the imagination and humanity that we felt because of the movie."


title: Big Fish

text: Columbia Pictures planned to wide release "Big Fish" in the United States on November 26, 2003 before pushing it back to December 10 for a limited release. The film premiered on December 4, 2003 at the Hammerstein Ballroom in Manhattan. The domestic wide release in the US came on January 9, 2004, with the film appearing in 2,406 theaters and earning $13.81 million in its opening weekend. The film eventually grossed $66.81 million in U.S. totals and $56.11 million in foreign countries, with a total of $122.92 million worldwide.


title: Big Fish

text: "Big Fish" received positive reviews from film critics. Based on 219 reviews collected by Rotten Tomatoes, 75% of critics positively reviewed "Big Fish", with an average score of 7.13/10. The site's consensus states: "A charming father-and-son tale filled with typical Tim Burton flourishes." Metacritic calculated an average score of 58/100, based on 43 reviews, indicating "mixed or average reviews". Audiences polled by CinemaScore gave the film an average grade of "B+" on an A+ to F scale.


title: Big Fish

text: Critics compared the film to "Forrest Gump" (1994). ""Big Fish" turns into a wide-eyed Southern Gothic picaresque in which each lunatic twist of a development is more enchanting than the last," Owen Gleiberman of "Entertainment Weekly" wrote. "It's like "Forrest Gump" without the bogus theme-park politics." Peter Travers from "Rolling Stone" magazine praised Burton's direction, feeling it was a celebration of the art of storytelling and a touching father–son drama.


title: Big Fish

text: Mike Clark of "USA Today" commented that he was most fascinated by the casting choices. "Equally delightful is the Alison Lohman character's evolution into an older woman (Jessica Lange). It's a metamorphosis to equal any in screen history." Internet reviewer James Berardinelli found the fairy tale approach reminiscent of "The Princess Bride" (1987) and the films of Terry Gilliam. ""Big Fish" is a clever, smart fantasy that targets the child inside every adult," Berardinelli said, "without insulting the intelligence of either." Roger Ebert, in a mixed review, wrote "there is no denying that Will has a point: The old man is a blowhard. There is a point at which his stories stop working as entertainment and segue into sadism." Richard Corliss of "Time" magazine was disappointed, finding the father-son reconciliation storyline to be over-dramatically cliché. "You recall "The Boy Who Cried Wolf"? Edward Bloom is the man who cried fish." "Big Fish" was No. 85 on Slant Magazine's best films of the 2000s.


title: Big Fish

text: The Region 1 DVD was released on April 27, 2004, and Region 2 was released on June 7. The DVD features a Burton audio commentary track, seven featurettes and a trivia quiz. A special edition was released on November 1, 2005, with a 24-page hardback book entitled "Fairy Tale for a Grown Up". The film was released on Blu-ray Disc on March 20, 2007.


title: Nancy Cartwright

text: Nancy Cartwright (born October 25, 1957) is an American actress. She is the long-time voice of Bart Simpson on the animated television series "The Simpsons", for which she has received a Primetime Emmy Award for Outstanding Voice-Over Performance and an Annie Award for Best Voice Acting in the Field of Animation. Cartwright also voices other characters for the show, including Nelson Muntz, Ralph Wiggum, Todd Flanders, Kearney, Database, and Maggie.


title: Nancy Cartwright

text: Cartwright was born in Dayton, Ohio. She moved to Hollywood in 1978 and trained alongside voice actor Daws Butler. Her first professional role was voicing Gloria in the animated series "Richie Rich", which she followed with a starring role in the television movie "Marian Rose White" (1982) and her first feature film, "" (1983). In 1987, Cartwright auditioned for a role in a series of animated shorts about a dysfunctional family that was to appear on "The Tracey Ullman Show". Cartwright intended to audition for the role of Lisa Simpson, the middle child; when she arrived at the audition, she found the role of Bart—Lisa's brother—to be more interesting. Matt Groening, the series' creator, allowed her to audition for Bart and offered her the role on the spot. She voiced Bart for three seasons on "The Tracey Ullman Show", and in 1989, the shorts were spun off into a half-hour show called "The Simpsons".


title: Nancy Cartwright

text: Besides "The Simpsons", Cartwright has also voiced numerous other animated characters, including Daffney Gillfin in "Snorks", Rufus in "Kim Possible", Mindy in "Animaniacs", Pistol in "Goof Troop", the Robots in "Crashbox", Margo Sherman in "The Critic", Todd Daring in "The Replacements", and Charles "Chuckie" Finster in "Rugrats" and "All Grown Up!" (a role she assumed in 2002, following the retirement of Christine Cavanaugh). In 2000, she published her autobiography, "My Life as a 10-Year-Old Boy", and four years later, adapted it into a one-woman play. In 2017, she wrote and produced the film "In Search of Fellini".


title: Nancy Cartwright

text: Cartwright was born in Dayton, Ohio, Frank and Miriam Cartwright's fourth of six children. She grew up in Kettering, Ohio, and discovered her talent for voices at an early age. While in the fourth grade at the school of St. Charles Borromeo, she won a school-wide speech competition with her performance of Rudyard Kipling's "How the Camel Got His Hump". Cartwright attended Fairmont West High School, and participated in the school's theater and marching band. She regularly entered public speaking competitions, placing first in the "Humorous Interpretation" category at the National District Tournament two years running. The judges often suggested to her that she should perform cartoon voices. Cartwright graduated from high school in 1976 and accepted a scholarship from Ohio University. She continued to compete in public speaking competitions; during her sophomore year, she placed fifth in the National Speech Tournament's exposition category with her speech "The Art of Animation".


title: Nancy Cartwright

text: In 1976, Cartwright landed a part-time job doing voice-overs for commercials on WING radio in Dayton. A representative from Warner Bros. Records visited WING and later sent Cartwright a list of contacts in the animation industry. One of these was Daws Butler, known for voicing characters such as Huckleberry Hound, Snagglepuss, Elroy Jetson, Spike the Bulldog, and Yogi Bear. Cartwright called him and left a message in a Cockney accent on his answering machine. Butler immediately called her back and agreed to be her mentor. He mailed her a script and instructed her to send him a tape recording of herself reading it. Once he received the tape, Butler critiqued it and sent her notes. For the next year, they continued in this way, completing a new script every few weeks. Cartwright described Butler as "absolutely amazing, always encouraging, always polite".


title: Nancy Cartwright

text: Cartwright returned to Ohio University for her sophomore year, but transferred to the University of California, Los Angeles (UCLA) so she could be closer to Hollywood and Butler. Her mother, Miriam, died late in the summer of 1978. Cartwright nearly changed her relocation plans but, on September 17, 1978, "joylessly" left for Westwood, Los Angeles.


title: Nancy Cartwright

text: While attending UCLA, which did not have a public speaking team, Cartwright continued training as a voice actress with Butler. She recalled, "every Sunday I'd take a 20-minute bus ride to his house in Beverly Hills for a one-hour lesson and be there for four hours ... They had four sons, they didn't have a daughter and I kind of fitted in as the baby of the family." Butler introduced her to many of the voice actors and directors at Hanna-Barbera. After she met the director Gordon Hunt, he asked her to audition for a recurring role as Gloria in "Richie Rich". She received the part, and later worked with Hunt on several other projects. At the end of 1980, Cartwright signed with a talent agency and landed a lead role in a pilot for a sitcom called "In Trouble". Cartwright described the show as "forgettable, but it jump-started my on-camera career". She graduated from UCLA in 1981 with a degree in theater. During the summer, Cartwright worked with Jonathan Winters as part of an improvisation troupe at Kenyon College in Gambier, Ohio.


title: Nancy Cartwright

text: Returning to Los Angeles, Cartwright won the lead role in the television movie "Marian Rose White". Janet Maslin, a critic for "The New York Times", described Cartwright as "a chubby, lumbering, slightly cross-eyed actress whose naturalness adds greatly to the film's impact". Cartwright replied by sending Maslin a letter insisting she was not cross-eyed, and included a photograph. Later, Cartwright auditioned for the role of Ethel, a girl who becomes trapped in a cartoon world in the third segment of "". She met with director Joe Dante and later described him as "a total cartoon buff, and once he took a look at my resume and noticed Daws Butler's name on it, we were off and running, sharing anecdotes about Daws and animation. After about twenty minutes, he said, 'considering your background, I don't see how I could cast anyone "but" you in this part! It was her first role in a feature film. The segment was based on "The Twilight Zone" television series episode "It's a Good Life", which was later parodied in "The Simpsons" episode "Treehouse of Horror II" (1991).


title: Nancy Cartwright

text: Cartwright continued to do voice work for projects including "Pound Puppies", "Popeye and Son", "Snorks", "My Little Pony" and "Saturday Supercade". She joined a "loop group", and recorded vocals for characters in the background of films, although in most cases the sound was turned down so that very little of her voice was heard. She did minor voice-over work for several films, including "The Clan of the Cave Bear" (1986), "Silverado" (1985), "Sixteen Candles" (1984), "Back to the Future Part II" , and "The Color Purple" (1985). Cartwright also voiced a shoe that was "dipped" in acid in "Who Framed Roger Rabbit" (1988), describing it as her first "off-screen death scene", and worked to correctly convey the emotion involved.


title: Nancy Cartwright

text: In 1985, she auditioned for a guest spot as Cynthia in "Cheers". The audition called for her to say her line and walk off the set. Cartwright decided to take a chance on being different and continued walking, leaving the building and returning home. The production crew was confused, but she received the part. In search of more training as an actress, Cartwright joined a class taught by Hollywood coach Milton Katselas. He recommended that Cartwright study "La Strada", a 1956 Italian film starring Giulietta Masina and directed by Federico Fellini. She began performing "every imaginable scene" from "La Strada" in her class and spent several months trying to secure the rights to produce a stage adaptation. She visited Italy with the intention of meeting Fellini and requesting his permission in person. Although they never met, Cartwright kept a journal of the trip and later wrote a one-woman play called "In Search of Fellini", partially based on her voyage. The play was co-written by Peter Kjenaas, and Cartwright won a Drama-Logue Award after performing it in Los Angeles in 1995. In a 1998 interview, she stated her intention to make it into a feature film, which she succeeded in doing in 2017.


title: Nancy Cartwright

text: Cartwright voices the character Bart Simpson on the long-running animated television show "The Simpsons". On March 13, 1987, she auditioned for a series of animated shorts about a dysfunctional family that was to appear on "The Tracey Ullman Show", a sketch comedy program. Cartwright had intended to audition for the role of Lisa Simpson, the elder daughter. After arriving at the audition, she found that Lisa was simply described as the middle child and at the time did not have much personality. Cartwright became more interested in the role of Bart, described as "devious, underachieving, school-hating, irreverent, [and] clever". Creator Matt Groening let her try out for Bart and gave her the job on the spot. Bart's voice came naturally to Cartwright, as she had previously used elements of it in "My Little Pony", "Snorks", and "Pound Puppies". Cartwright describes Bart's voice as easy to perform compared with other characters. The recording of the shorts was often primitive; the dialog was recorded on a portable tape deck in a makeshift studio above the bleachers on the set of "The Tracey Ullman Show". Cartwright, the only cast member to have been professionally trained in voice acting, described the sessions as "great fun". However, she wanted to appear in the live-action sketches and occasionally showed up for recording sessions early, hoping to be noticed by a producer.


title: Nancy Cartwright

text: In 1989, the shorts were spun off into a half-hour show on the Fox network called "The Simpsons". Bart quickly became the show's breakout personality and one of the most celebrated characters on television—his popularity in 1990 and 1991 was known as "Bartmania". Bart was described as "television's brightest new star" by Mike Boone of "The Gazette" and was named 1990's "entertainer of the year" by "Entertainment Weekly". Despite Bart's fame, however, Cartwright remained relatively unknown. During the first season of "The Simpsons", Fox ordered Cartwright not to give interviews, because they did not want to publicize the fact that Bart was voiced by a woman. Cartwright's normal speaking voice is said to have "no obvious traces of Bart", and she believes her role is "the best acting job in the world" since she is rarely recognized in public. When she is recognized and asked to perform Bart's voice in front of children, Cartwright refuses because it "freaks [them] out". Bart's catchphrase "Eat My Shorts" was an ad-lib by Cartwright in one of the original table readings, referring to an incident from her high school days. Once while performing, members of the Fairmont West High School marching band switched their chant from the usual "Fairmont West! Fairmont West!" to the irreverent "Eat my shorts!" Cartwright felt it appropriate for Bart, and improvised the line; it became a popular catchphrase on the show.


title: Nancy Cartwright

text: Cartwright voices several other characters on the show, including Nelson Muntz, Ralph Wiggum, Todd Flanders, Kearney, and Database. She first voiced Nelson in the episode "Bart the General" (season one, 1990). The character was to be voiced by Dana Hill, but Hill missed the recording session and Cartwright was given the role. She developed Nelson's voice on the spot and describes him as "a throat-ripper". Ralph Wiggum had originally been voiced by Jo Ann Harris, but Cartwright was assigned to voice the character in "Bart the Murderer" (season three, 1991). Todd Flanders, the only voice for which Cartwright used another source, is based on Sherman (voiced by Walter Tetley), the boy from "Peabody's Improbable History", a series of shorts aired on "The Rocky and Bullwinkle Show".


title: Nancy Cartwright

text: Cartwright received a Primetime Emmy Award for Outstanding Voice-Over Performance in 1992 for her performance as Bart in the episode "Separate Vocations" and an Annie Award in 1995 for Best Voice Acting in the Field of Animation. Bart was named one of the by "Time", and in 2000, Bart and the rest of the Simpson family were awarded a star on the Hollywood Walk of Fame, located at 7021 Hollywood Boulevard.


title: Nancy Cartwright

text: Until 1998, Cartwright was paid $30,000 per episode. During a pay dispute in 1998, Fox threatened to replace the six main voice actors and made preparations for casting new actors. The dispute was resolved, however, and Cartwright received $125,000 per episode until 2004, when the voice actors demanded $360,000 an episode. A compromise was reached after a month, and Cartwright's pay rose to $250,000 per episode. Salaries were re-negotiated in 2008 with the voice actors receiving approximately $400,000 per episode. Three years later, with Fox threatening to cancel the series unless production costs were cut, Cartwright and the other cast members accepted a 25 percent pay cut, down to just over $300,000 per episode.


title: Nancy Cartwright

text: In addition to her work on "The Simpsons", Cartwright has voiced many other characters on several animated series, including Chuckie Finster in "Rugrats" and "All Grown Up!", Margo Sherman in "The Critic", Mindy in "Animaniacs," and Rufus the naked mole-rat in "Kim Possible". For the role of Rufus, Cartwright researched mole-rats extensively, and became "a font of useless trivia". She was nominated for a Daytime Emmy Award for Outstanding Performer in an Animated Program in 2004 for her work on the show. In 2001, Cartwright took over the "Rugrats" role of Chuckie Finster when Christine Cavanaugh retired. Cartwright describes Rufus and Chuckie as her two most difficult voices: "Rufus because my diaphragm gets a workout while trying to utilize the 18 vocal sounds a mole makes. Chuckie because ... he's an asthmatic with five personalities rolled into one—plus I have to do the voice the way [Cavanaugh] did it for 10 years." Other television shows that have used her voice work include "Galaxy High," "God, the Devil and Bob," "Goof Troop," "Mike, Lu & Og," "The Replacements," "Pinky and the Brain" and "Timberwolf". Cartwright has appeared on camera in numerous television shows and films, including "Fame", "Empty Nest", "The Fresh Prince of Bel-Air", "Flesh and Blood", "Godzilla," and "24".


title: Nancy Cartwright

text: In 2000, Cartwright published her autobiography, "My Life as a 10-Year-Old Boy". The book details her career (particularly her experiences as the voice of Bart) and contains stories about life behind the scenes of "The Simpsons." Laura A. Bischoff of the "Dayton Daily News" commented that the book was the "ultimate insider's guide to "The Simpsons"". Critics complained that the book lacked interesting stories and was aimed mostly at fans of "The Simpsons" rather than a general audience.


title: Nancy Cartwright

text: Cartwright adapted "My Life as a 10-Year-Old Boy" into a one-woman play in 2004. Cartwright has performed it at a variety of venues, including the August 2004 Edinburgh Festival Fringe in Scotland. The play received modest reviews, including criticism for a lack of inside stories about "The Simpsons", and its "overweeningly upbeat" tone. David Chatterton of "The British Theatre Guide" described the show as "interesting and entertaining, but not really a 'must see' even for Simpsons fans".


title: Nancy Cartwright

text: Cartwright has shown an interest in stock car racing and as of 2007 was seeking a NASCAR license. In 2001, she founded a production company called SportsBlast and created an online animated series called "The Kellys". The series is focused on racing; Cartwright voices a seven-year-old named Chip Kelly.


title: Nancy Cartwright

text: In 2016, Cartwright launched Spotted Cow Entertainment, her own film and television production company, with Peter Kjenaas, Monica Gil and Kevin Burke. With a focus on international audiences, Spotted Cow is seeking "to finance, produce and acquire live action and animated films, television series, as well as entertainment for digital platforms with budgets up to $15M." With Spotted Cow, Cartwright made her first film as a screenwriter and producer, "In Search of Fellini", which was released on September 15, 2017. Based on her own journey to Italy in 1985 in a bid to meet the famed director Federico Fellini, the film fulfilled Cartwright's longtime vision of turning her 1995 one-woman play "In Search of Fellini" into a movie.


title: Nancy Cartwright

text: Cartwright met Warren Murphy, 24 years her senior, on her birthday in 1988 and married him two months later. In her book, she describes Murphy as her "personal laugh track". The couple had two children, Lucy and Jack, before divorcing in 2002.


title: Nancy Cartwright

text: Cartwright was raised a Roman Catholic but joined the Church of Scientology in 1991. She was awarded Scientology's Patron Laureate Award after donating $10,000,000, almost twice her annual salary, to the Church in 2007.


title: Nancy Cartwright

text: Cartwright is a contributor to ASIFA-Hollywood's Animation Archive Project. In September 2007, Cartwright received the Make-a-Wish Foundation's Wish Icon Award "for her tremendous dedication to the Foundation's fundraising and wish-fulfillment efforts." In 2005, Cartwright created a scholarship at Fairmont High School "designed to aid Fairmont [graduates] who dream of following in her footsteps and studying speech, debate, drama or music" at Ohio University. In 2005, Cartwright was given the title of Honorary Mayor of Northridge, California (a neighborhood of Los Angeles) by the Northridge Chamber of Commerce.


title: Nancy Cartwright

text: In 2007, Cartwright was in a romantic relationship with contractor Stephen Brackett, a fellow member of Scientology. In early 2008, the couple had made plans to marry, but Brackett died in May 2009, after he "apparently leaped" off the Bixby Creek Bridge in Big Sur, California.


title: Nancy Cartwright

text: In 2012, Cartwright received an honorary doctorate degree in communication from Ohio University, where she was a student from 1976 to 1977 before transferring to UCLA.


title: Nancy Cartwright

text: Cartwright is also a painter, sculptor and philanthropist. She co-founded the Know More About Drugs alliance.


title: Laplace transform

text: In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually formula_1, in the "time domain") to a function of a complex variable formula_2 (in the complex frequency domain, also known as "s"-domain, or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms ordinary differential equations into algebraic equations and convolution into multiplication.


title: Laplace transform

text: The Laplace transform is named after mathematician and astronomer Pierre-Simon, marquis de Laplace, who used a similar transform in his work on probability theory. Laplace wrote extensively about the use of generating functions in "Essai philosophique sur les probabilités" (1814), and the integral form of the Laplace transform evolved naturally as a result.


title: Laplace transform

text: Laplace's use of generating functions was similar to what is now known as the z-transform, and he gave little attention to the continuous variable case which was discussed by Niels Henrik Abel. The theory was further developed in the 19th and early 20th centuries by Mathias Lerch, Oliver Heaviside, and Thomas Bromwich.


title: Laplace transform

text: The current widespread use of the transform (mainly in engineering) came about during and soon after World War II, replacing the earlier Heaviside operational calculus. The advantages of the Laplace transform had been emphasized by Gustav Doetsch, to whom the name Laplace transform is apparently due.


title: Laplace transform

text: as solutions of differential equations, but did not pursue the matter very far. Joseph Louis Lagrange was an admirer of Euler and, in his work on integrating probability density functions, investigated expressions of the form


title: Laplace transform

text: These types of integrals seem first to have attracted Laplace's attention in 1782, where he was following in the spirit of Euler in using the integrals themselves as solutions of equations. However, in 1785, Laplace took the critical step forward when, rather than simply looking for a solution in the form of an integral, he started to apply the transforms in the sense that was later to become popular. He used an integral of the form


title: Laplace transform

text: akin to a Mellin transform, to transform the whole of a difference equation, in order to look for solutions of the transformed equation. He then went on to apply the Laplace transform in the same way and started to derive some of its properties, beginning to appreciate its potential power.


title: Laplace transform

text: Laplace also recognised that Joseph Fourier's method of Fourier series for solving the diffusion equation could only apply to a limited region of space, because those solutions were periodic. In 1809, Laplace applied his transform to find solutions that diffused indefinitely in space.


title: Laplace transform

text: The Laplace transform of a function , defined for all real numbers , is the function , which is a unilateral transform defined by


title: Laplace transform

text: The meaning of the integral depends on types of functions of interest. A necessary condition for existence of the integral is that must be locally integrable on . For locally integrable functions that decay at infinity or are of exponential type (formula_9), the integral can be understood to be a (proper) Lebesgue integral. However, for many applications it is necessary to regard it as a conditionally convergent improper integral at . Still more generally, the integral can be understood in a weak sense, and this is dealt with below.


title: Laplace transform

text: An important special case is where is a probability measure, for example, the Dirac delta function. In operational calculus, the Laplace transform of a measure is often treated as though the measure came from a probability density function . In that case, to avoid potential confusion, one often writes


title: Laplace transform

text: This limit emphasizes that any point mass located at is entirely captured by the Laplace transform. Although with the Lebesgue integral, it is not necessary to take such a limit, it does appear more naturally in connection with the Laplace–Stieltjes transform.


title: Laplace transform

text: When one says "the Laplace transform" without qualification, the unilateral or one-sided transform is usually intended. The Laplace transform can be alternatively defined as the "bilateral Laplace transform", or two-sided Laplace transform, by extending the limits of integration to be the entire real axis. If that is done, the common unilateral transform simply becomes a special case of the bilateral transform, where the definition of the function being transformed is multiplied by the Heaviside step function.


title: Laplace transform

text: Two integrable functions have the same Laplace transform only if they differ on a set of Lebesgue measure zero. This means that, on the range of the transform, there is an inverse transform. In fact, besides integrable functions, the Laplace transform is a one-to-one mapping from one function space into another in many other function spaces as well, although there is usually no easy characterization of the range.


title: Laplace transform

text: Typical function spaces in which this is true include the spaces of bounded continuous functions, the space , or more generally tempered distributions on . The Laplace transform is also defined and injective for suitable spaces of tempered distributions.


title: Laplace transform

text: In these cases, the image of the Laplace transform lives in a space of analytic functions in the region of convergence. The inverse Laplace transform is given by the following complex integral, which is known by various names (the Bromwich integral, the Fourier–Mellin integral, and Mellin's inverse formula):


title: Laplace transform

text: where is a real number so that the contour path of integration is in the region of convergence of . In most applications, the contour can be closed, allowing the use of the residue theorem. An alternative formula for the inverse Laplace transform is given by Post's inversion formula. The limit here is interpreted in the weak-* topology.


title: Laplace transform

text: In practice, it is typically more convenient to decompose a Laplace transform into known transforms of functions obtained from a table, and construct the inverse by inspection.


title: Laplace transform

text: In pure and applied probability, the Laplace transform is defined as an expected value. If is a random variable with probability density function , then the Laplace transform of is given by the expectation


title: Laplace transform

text: By convention, this is referred to as the Laplace transform of the random variable itself. Here, replacing by gives the moment generating function of . The Laplace transform has applications throughout probability theory, including first passage times of stochastic processes such as Markov chains, and renewal theory.


title: Laplace transform

text: Of particular use is the ability to recover the cumulative distribution function of a continuous random variable , by means of the Laplace transform as follows:


title: Laplace transform

text: If is a locally integrable function (or more generally a Borel measure locally of bounded variation), then the Laplace transform of converges provided that the limit


title: Laplace transform

text: exists as a proper Lebesgue integral. The Laplace transform is usually understood as conditionally convergent, meaning that it converges in the former but not in the latter sense.


title: Laplace transform

text: The set of values for which converges absolutely is either of the form or , where is an extended real constant with (a consequence of the dominated convergence theorem). The constant is known as the abscissa of absolute convergence, and depends on the growth behavior of . Analogously, the two-sided transform converges absolutely in a strip of the form , and possibly including the lines or . The subset of values of for which the Laplace transform converges absolutely is called the region of absolute convergence, or the domain of absolute convergence. In the two-sided case, it is sometimes called the strip of absolute convergence. The Laplace transform is analytic in the region of absolute convergence: this is a consequence of Fubini's theorem and Morera's theorem.


title: Laplace transform

text: Similarly, the set of values for which converges (conditionally or absolutely) is known as the region of conditional convergence, or simply the region of convergence (ROC). If the Laplace transform converges (conditionally) at , then it automatically converges for all with . Therefore, the region of convergence is a half-plane of the form , possibly including some points of the boundary line .


title: Laplace transform

text: In the region of convergence , the Laplace transform of can be expressed by integrating by parts as the integral


title: Laplace transform

text: That is, can effectively be expressed, in the region of convergence, as the absolutely convergent Laplace transform of some other function. In particular, it is analytic.


title: Laplace transform

text: There are several Paley–Wiener theorems concerning the relationship between the decay properties of , and the properties of the Laplace transform within the region of convergence.


title: Laplace transform

text: In engineering applications, a function corresponding to a linear time-invariant (LTI) system is "stable" if every bounded input produces a bounded output. This is equivalent to the absolute convergence of the Laplace transform of the impulse response function in the region . As a result, LTI systems are stable, provided that the poles of the Laplace transform of the impulse response function have negative real part.


title: Laplace transform

text: The Laplace transform has a number of properties that make it useful for analyzing linear dynamical systems. The most significant advantage is that differentiation becomes multiplication, and integration becomes division, by (reminiscent of the way logarithms change multiplication to addition of logarithms).


title: Laplace transform

text: Because of this property, the Laplace variable is also known as "operator variable" in the domain: either "derivative operator" or (for "integration operator". The transform turns integral equations and differential equations to polynomial equations, which are much easier to solve. Once solved, use of the inverse Laplace transform reverts to the original domain.


title: Laplace transform

text: The Laplace transform can be viewed as a continuous analogue of a power series. If is a discrete function of a positive integer , then the power series associated to is the series


title: Laplace transform

text: where is a real variable (see Z transform). Replacing summation over with integration over , a continuous version of the power series becomes


title: Laplace transform

text: For this to converge for, say, all bounded functions , it is necessary to require that . Making the substitution gives just the Laplace transform:


title: Laplace transform

text: In other words, the Laplace transform is a continuous analog of a power series, in which the discrete parameter is replaced by the continuous parameter , and is replaced by .


title: Laplace transform

text: are the "moments" of the function . If the first moments of converge absolutely, then by repeated differentiation under the integral,


title: Laplace transform

text: This is of special significance in probability theory, where the moments of a random variable are given by the expectation values formula_32. Then, the relation holds


title: Laplace transform

text: It is often convenient to use the differentiation property of the Laplace transform to find the transform of a function's derivative. This can be derived from the basic expression for a Laplace transform as follows:


title: Laplace transform

text: under suitable assumptions on the behaviour of formula_40 in a right neighbourhood of formula_41 and on the decay rate of formula_40 in a left neighbourhood of formula_43. The above formula is a variation of integration by parts, with the operators


title: Laplace transform

text: formula_44 and formula_45 being replaced by formula_46 and formula_47. Let us prove the equivalent formulation:


title: Laplace transform

text: but assuming Fubini's theorem holds, by reversing the order of integration we get the wanted right-hand side.


title: Laplace transform

text: This method can be used to compute integrals that would otherwise be difficult to compute using elementary methods of real calculus. For example,


title: Laplace transform

text: The (unilateral) Laplace–Stieltjes transform of a function is defined by the Lebesgue–Stieltjes integral


title: Laplace transform

text: then the Laplace–Stieltjes transform of and the Laplace transform of coincide. In general, the Laplace–Stieltjes transform is the Laplace transform of the Stieltjes measure associated to . So in practice, the only distinction between the two transforms is that the Laplace transform is thought of as operating on the density function of the measure, whereas the Laplace–Stieltjes transform is thought of as operating on its cumulative distribution function.


title: Laplace transform

text: The Fourier transform is a special case (under certain conditions) of the bilateral Laplace transform. While the Fourier transform of a function is a complex function of a "real" variable (frequency), the Laplace transform of a function is a complex function of a "complex" variable. The Laplace transform is usually restricted to transformation of functions of with . A consequence of this restriction is that the Laplace transform of a function is a holomorphic function of the variable . Unlike the Fourier transform, the Laplace transform of a distribution is generally a well-behaved function. Techniques of complex variables can also be used to directly study Laplace transforms. As a holomorphic function, the Laplace transform has a power series representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in probability theory.


title: Laplace transform

text: The Fourier transform is equivalent to evaluating the bilateral Laplace transform with imaginary argument or when the condition explained below is fulfilled,


title: Laplace transform

text: This convention of the Fourier transform (formula_55 in ) requires a factor of on the inverse Fourier transform. This relationship between the Laplace and Fourier transforms is often used to determine the frequency spectrum of a signal or dynamical system.


title: Laplace transform

text: The above relation is valid as stated if and only if the region of convergence (ROC) of contains the imaginary axis, .


title: Laplace transform

text: For example, the function has a Laplace transform whose ROC is . As is a pole of , substituting in does not yield the Fourier transform of , which is proportional to the Dirac delta-function .


title: Laplace transform

text: holds under much weaker conditions. For instance, this holds for the above example provided that the limit is understood as a weak limit of measures (see vague topology). General conditions relating the limit of the Laplace transform of a function on the boundary to the Fourier transform take the form of Paley–Wiener theorems.


title: Laplace transform

text: The Mellin transform and its inverse are related to the two-sided Laplace transform by a simple change of variables.


title: Laplace transform

text: The unilateral or one-sided Z-transform is simply the Laplace transform of an ideally sampled signal with the substitution of


title: Laplace transform

text: where is the sampling interval (in units of time e.g., seconds) and is the sampling rate (in samples per second or hertz).


title: Laplace transform

text: Comparing the last two equations, we find the relationship between the unilateral Z-transform and the Laplace transform of the sampled signal,


title: Laplace transform

text: The similarity between the and Laplace transforms is expanded upon in the theory of time scale calculus.


title: Laplace transform

text: for some constants and . The generalized Borel transform allows a different weighting function to be used, rather than the exponential function, to transform functions not of exponential type. Nachbin's theorem gives necessary and sufficient conditions for the Borel transform to be well defined.


title: Laplace transform

text: Since an ordinary Laplace transform can be written as a special case of a two-sided transform, and since the two-sided transform can be written as the sum of two one-sided transforms, the theory of the Laplace-, Fourier-, Mellin-, and Z-transforms are at bottom the same subject. However, a different point of view and different characteristic problems are associated with each of these four major integral transforms.


title: Laplace transform

text: The following table provides Laplace transforms for many common functions of a single variable. For definitions and explanations, see the "Explanatory Notes" at the end of the table.


title: Laplace transform

text: Using this linearity, and various trigonometric, hyperbolic, and complex number (etc.) properties and/or identities, some Laplace transforms can be obtained from others more quickly than by using the definition directly.


title: Laplace transform

text: The unilateral Laplace transform takes as input a function whose time domain is the non-negative reals, which is why all of the time domain functions in the table below are multiples of the Heaviside step function, .


title: Laplace transform

text: The entries of the table that involve a time delay are required to be causal (meaning that ). A causal system is a system where the impulse response is zero for all time prior to . In general, the region of convergence for causal systems is not the same as that of anticausal systems.


title: Laplace transform

text: The Laplace transform is often used in circuit analysis, and simple conversions to the -domain of circuit elements can be made. Circuit elements can be transformed into impedances, very similar to phasor impedances.


title: Laplace transform

text: Note that the resistor is exactly the same in the time domain and the -domain. The sources are put in if there are initial conditions on the circuit elements. For example, if a capacitor has an initial voltage across it, or if the inductor has an initial current through it, the sources inserted in the -domain account for that.


title: Laplace transform

text: The equivalents for current and voltage sources are simply derived from the transformations in the table above.


title: Laplace transform

text: The Laplace transform is used frequently in engineering and physics; the output of a linear time-invariant system can be calculated by convolving its unit impulse response with the input signal. Performing this calculation in Laplace space turns the convolution into a multiplication; the latter being easier to solve because of its algebraic form. For more information, see control theory. The Laplace transform is invertible on a large class of functions. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.


title: Laplace transform

text: The Laplace transform can also be used to solve differential equations and is used extensively in mechanical engineering and electrical engineering. The Laplace transform reduces a linear differential equation to an algebraic equation, which can then be solved by the formal rules of algebra. The original differential equation can then be solved by applying the inverse Laplace transform. English electrical engineer Oliver Heaviside first proposed a similar scheme, although without using the Laplace transform; and the resulting operational calculus is credited as the Heaviside calculus.


title: Laplace transform

text: provided that the interchange of limits can be justified. This is often possible as a consequence of the final value theorem. Even when the interchange cannot be justified the calculation can be suggestive. For example, with , proceeding formally one has


title: Laplace transform

text: In the theory of electrical circuits, the current flow in a capacitor is proportional to the capacitance and rate of change in the electrical potential (in SI units). Symbolically, this is expressed by the differential equation


title: Laplace transform

text: where is the capacitance (in farads) of the capacitor, is the electric current (in amperes) through the capacitor as a function of time, and is the voltage (in volts) across the terminals of the capacitor, also as a function of time.


title: Laplace transform

text: The definition of the complex impedance (in ohms) is the ratio of the complex voltage divided by the complex current while holding the initial state at zero:


title: Laplace transform

text: which is the correct expression for the complex impedance of a capacitor. In addition, the Laplace transform has large applications in control theory.


title: Laplace transform

text: To evaluate this inverse transform, we begin by expanding using the method of partial fraction expansion,


title: Laplace transform

text: The unknown constants and are the residues located at the corresponding poles of the transfer function. Each residue represents the relative contribution of that singularity to the transfer function's overall shape.


title: Laplace transform

text: By the residue theorem, the inverse Laplace transform depends only upon the poles and their residues. To find the residue , we multiply both sides of the equation by to get


title: Laplace transform

text: Finally, using the linearity property and the known transform for exponential decay (see "Item" #"3" in the "Table of Laplace Transforms", above), we can take the inverse Laplace transform of to obtain


title: Laplace transform

text: The same result can be achieved using the convolution property as if the system is a series of filters with transfer functions of and . That is, the inverse of


title: Laplace transform

text: In statistical mechanics, the Laplace transform of the density of states formula_129 defines the partition function. That is, the canonical partition function formula_130 is given by


title: Laplace transform

text: The wide and general applicability of the Laplace transform and its inverse is illustrated by an application in astronomy which provides some information on the "spatial distribution" of matter of an astronomical source of radiofrequency thermal radiation too distant to resolve as more than a point, given its flux density spectrum, rather than relating the "time" domain with the spectrum (frequency domain).


title: Laplace transform

text: Assuming certain properties of the object, e.g. spherical shape and constant temperature, calculations based on carrying out an inverse Laplace transformation on the spectrum of the object can produce the only possible model of the distribution of matter in it (density as a function of distance from the center) consistent with the spectrum. When independent information on the structure of an object is available, the inverse Laplace transform method has been found to be in good agreement.


title: Spencer Haywood

text: Spencer Haywood (born April 22, 1949) is an American former professional basketball player and Olympic gold medalist. Haywood is a member of the Naismith Memorial Basketball Hall of Fame, being inducted in 2015.


title: Spencer Haywood

text: In 1964, Haywood moved to Detroit, Michigan residing in the Krainz Woods neighborhood. In 1967, while attending Pershing High School, Haywood led the school's basketball team to the state championship.


title: Spencer Haywood

text: Haywood attended Trinidad State Junior College in Trinidad, Colorado, during the 1967–68 college season, where he averaged 28.2 points and 22.1 rebounds per game. Due to his exceptional performance and talent, Haywood made the 1968 U.S. Olympic team at age 19, becoming the youngest American basketball player in Olympic history. Haywood was the leading scorer on the gold medal winning team at 16.1 points per game, and he set a Team USA field goal percentage record of .719. Haywood transferred to the University of Detroit in the fall of that year, and led the NCAA in rebounding with a 21.5 average per game while scoring 32.1 points per game during the 1968–69 season.


title: Spencer Haywood

text: Haywood decided to turn pro after his sophomore year, but National Basketball Association (NBA) rules, which then required a player to wait until four years after his high school class graduated, prohibited him from entering the league. The American Basketball Association (ABA) had a similar rule, but league executive Mike Storen came up with the idea for a hardship exemption. With his mother raising 10 children while picking cotton at $2 per day in Mississippi, Haywood met the criteria. He joined the Denver Rockets after they selected him in the ABA draft.


title: Spencer Haywood

text: In his 1969–70 rookie season, Haywood led the ABA in both scoring at 30.0 points per game and rebounding at 19.5 rebounds per game, while leading the Rockets to the ABA's Western Division Title. In the playoffs, Denver defeated the Washington Caps in 7 games in the Western Division Semifinals before falling to the Los Angeles Stars in the division finals, 4 games to 1. He was named both the ABA Rookie of the Year and ABA MVP during the season, and became the youngest ever recipient of the MVP at the age of 21. His 986 field goals made, 1,637 rebounds, and 19.5 rebound per game average are the all-time ABA records for a season. Haywood also won the ABA's 1970 All-Star Game MVP that year after recording 23 points, 19 rebounds, and 7 blocked shots for the West team.


title: Spencer Haywood

text: In 1970, despite the NBA's eligibility rules, Haywood joined the Seattle SuperSonics, and with SuperSonics owner Sam Schulman launched an antitrust suit against the league ("Haywood v. National Basketball Association"). The case went all the way to the U.S. Supreme Court before the NBA agreed to a settlement. The suit and its impact on college basketball and the NBA was the focus of a 2020 book "The Spencer Haywood Rule: Battles, Basketball, and the Making of an American Iconoclast" by Marc J. Spears and Gary Washburn.


title: Spencer Haywood

text: Haywood was named to the All-NBA First Team in 1972 and 1973 and the All-NBA Second Team in 1974 and 1975. Haywood's 29.2 points per game in the 1972–73 season and 13.4 rebounds per game in 1973–74 are the single-season record averages for the SuperSonics for these categories. Haywood played in four NBA All-Star Games while with Seattle, including a strong 23-point, 11-rebound performance in 1974. In the 1974–75 season, he helped lead the SuperSonics to their first playoff berth. Overall, during his five seasons with Seattle, Haywood averaged 24.9 points per game and 12.1 rebounds per game.


title: Spencer Haywood

text: In 1975, the SuperSonics traded him to the New York Knicks where he later teamed with Bob McAdoo. Haywood later played for the New Orleans Jazz, Los Angeles Lakers, and Washington Bullets.


title: Spencer Haywood

text: During the late 1970s, Haywood became addicted to cocaine. He was dismissed from the Lakers by then-coach Paul Westhead during the 1980 NBA Finals for falling asleep during practice due to his addiction.


title: Spencer Haywood

text: The next season Haywood played in Italy for Reyer Venezia Mestre (then under the sponsor name "Carrera Reyer Venezia") along with Dražen Dalipagić before returning to the NBA to play two seasons with the Washington Bullets.


title: Spencer Haywood

text: Haywood's no. 24 jersey was retired by the SuperSonics during a halftime ceremony on February 26, 2007.


title: Spencer Haywood

text: Haywood currently resides in Las Vegas. He was married to fashion model Iman from 1977 until 1987, and they had a daughter, Zulekha Haywood (born 1978). He remarried in 1990, and he and his wife, Linda, have three daughters.


title: Spencer Haywood

text: Haywood is a huge fan of jazz and has hosted weekly two-hour weekend jazz shows in Seattle (1971–1975, KYAC) and New York (1976–1978, WRVR).


title: Graphics processing unit

text: A graphics processing unit (GPU) is a specialized electronic circuit designed to manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display device. GPUs are used in embedded systems, mobile phones, personal computers, workstations, and game consoles.


title: Graphics processing unit

text: Modern GPUs are efficient at manipulating computer graphics and image processing. Their parallel structure makes them more efficient than general-purpose central processing units (CPUs) for algorithms that process large blocks of data in parallel. In a personal computer, a GPU can be present on a video card or embedded on the motherboard. In some CPUs, they are embedded on the CPU die.


title: Graphics processing unit

text: In the 1970s, the term "GPU" originally stood for "graphics processor unit" and described a programmable processing unit independently working from the CPU and responsible for graphics manipulation and output. Later, in 1994, Sony used the term (now standing for "graphics processing unit") in reference to the PlayStation console's Toshiba-designed Sony GPU in 1994. The term was popularized by Nvidia in 1999, who marketed the GeForce 256 as "the world's first GPU". It was presented as a "single-chip processor with integrated transform, lighting, triangle setup/clipping, and rendering engines". Rival ATI Technologies coined the term "visual processing unit" or VPU with the release of the Radeon 9700 in 2002.


title: Graphics processing unit

text: Arcade system boards have been using specialized graphics circuits since the 1970s. In early video game hardware, the RAM for frame buffers was expensive, so video chips composited data together as the display was being scanned out on the monitor.


title: Graphics processing unit

text: A specialized barrel shifter circuit was used to help the CPU animate the framebuffer graphics for various 1970s arcade games from Midway and Taito, such as "Gun Fight" (1975), "Sea Wolf" (1976) and "Space Invaders" (1978). The Namco Galaxian arcade system in 1979 used specialized graphics hardware supporting RGB color, multi-colored sprites and tilemap backgrounds. The Galaxian hardware was widely used during the golden age of arcade video games, by game companies such as Namco, Centuri, Gremlin, Irem, Konami, Midway, Nichibutsu, Sega and Taito.


title: Graphics processing unit

text: In the home market, the Atari 2600 in 1977 used a video shifter called the Television Interface Adaptor. The Atari 8-bit computers (1979) had ANTIC, a video processor which interpreted instructions describing a "display list"—the way the scan lines map to specific bitmapped or character modes and where the memory is stored (so there did not need to be a contiguous frame buffer). 6502 machine code subroutines could be triggered on scan lines by setting a bit on a display list instruction. ANTIC also supported smooth vertical and horizontal scrolling independent of the CPU.


title: Graphics processing unit

text: The NEC µPD7220 was the first implementation of a PC graphics display processor as a single Large Scale Integration (LSI) integrated circuit chip, enabling the design of low-cost, high-performance video graphics cards such as those from Number Nine Visual Technology. It became the best-known GPU up until the mid-1980s. It was the first fully integrated VLSI (very large-scale integration) metal-oxide-semiconductor (NMOS) graphics display processor for PCs, supported up to 1024x1024 resolution, and laid the foundations for the emerging PC graphics market. It was used in a number of graphics cards and was licensed for clones such as the Intel 82720, the first of Intel's graphics processing units. The Williams Electronics arcade games "Robotron 2084", "Joust", "Sinistar", and "Bubbles", all released in 1982, contain custom blitter chips for operating on 16-color bitmaps.


title: Graphics processing unit

text: In 1984, Hitachi released ARTC HD63484, the first major CMOS graphics processor for PC. The ARTC was capable of displaying up to 4K resolution when in monochrome mode, and it was used in a number of PC graphics cards and terminals during the late 1980s. In 1985, the Commodore Amiga featured a custom graphics chip, with a blitter unit accelerating bitmap manipulation, line draw, and area fill functions. Also included is a coprocessor with its own simple instruction set, capable of manipulating graphics hardware registers in sync with the video beam (e.g. for per-scanline palette switches, sprite multiplexing, and hardware windowing), or driving the blitter. In 1986, Texas Instruments released the TMS34010, the first fully programmable graphics processor. It could run general-purpose code, but it had a graphics-oriented instruction set. During 1990–1992, this chip became the basis of the Texas Instruments Graphics Architecture ("TIGA") Windows accelerator cards.


title: Graphics processing unit

text: In 1987, the IBM 8514 graphics system was released as one of the first video cards for IBM PC compatibles to implement fixed-function 2D primitives in electronic hardware. Sharp's X68000, released in 1987, used a custom graphics chipset with a 65,536 color palette and hardware support for sprites, scrolling, and multiple playfields, eventually serving as a development machine for Capcom's CP System arcade board. Fujitsu later competed with the FM Towns computer, released in 1989 with support for a full 16,777,216 color palette. In 1988, the first dedicated polygonal 3D graphics boards were introduced in arcades with the Namco System 21 and Taito Air System.


title: Graphics processing unit

text: IBM's proprietary Video Graphics Array (VGA) display standard was introduced in 1987, with a maximum resolution of 640×480 pixels. In November 1988, NEC Home Electronics announced its creation of the Video Electronics Standards Association (VESA) to develop and promote a Super VGA (SVGA) computer display standard as a successor to IBM's proprietary VGA display standard. Super VGA enabled graphics display resolutions up to 800×600 pixels, a 36% increase.


title: Graphics processing unit

text: In 1991, S3 Graphics introduced the "S3 86C911", which its designers named after the Porsche 911 as an indication of the performance increase it promised. The 86C911 spawned a host of imitators: by 1995, all major PC graphics chip makers had added 2D acceleration support to their chips. By this time, fixed-function "Windows accelerators" had surpassed expensive general-purpose graphics coprocessors in Windows performance, and these coprocessors faded away from the PC market.


title: Graphics processing unit

text: Throughout the 1990s, 2D GUI acceleration continued to evolve. As manufacturing capabilities improved, so did the level of integration of graphics chips. Additional application programming interfaces (APIs) arrived for a variety of tasks, such as Microsoft's WinG graphics library for Windows 3.x, and their later DirectDraw interface for hardware acceleration of 2D games within Windows 95 and later.


title: Graphics processing unit

text: In the early- and mid-1990s, real-time 3D graphics were becoming increasingly common in arcade, computer, and console games, which led to increasing public demand for hardware-accelerated 3D graphics. Early examples of mass-market 3D graphics hardware can be found in arcade system boards such as the Sega Model 1, Namco System 22, and Sega Model 2, and the fifth-generation video game consoles such as the Saturn, PlayStation and Nintendo 64. Arcade systems such as the Sega Model 2 and SGI Onyx-based Namco Magic Edge Hornet Simulator in 1993 were capable of hardware T&L (transform, clipping, and lighting) years before appearing in consumer graphics cards. Some systems used DSPs to accelerate transformations. Fujitsu, which worked on the Sega Model 2 arcade system, began working on integrating T&L into a single LSI solution for use in home computers in 1995; the Fujitsu Pinolite, the first 3D geometry processor for personal computers, released in 1997. The first hardware T&L GPU on home video game consoles was the Nintendo 64's Reality Coprocessor, released in 1996. In 1997, Mitsubishi released the 3Dpro/2MP, a fully featured GPU capable of transformation and lighting, for workstations and Windows NT desktops; ATi utilized it for their FireGL 4000 graphics card, released in 1997.


title: Graphics processing unit

text: The term "GPU" was coined by Sony in reference to the 32-bit Sony GPU (designed by Toshiba) in the PlayStation video game console, released in 1994.


title: Graphics processing unit

text: In the PC world, notable failed first tries for low-cost 3D graphics chips were the S3 "ViRGE", ATI Rage, and Matrox "Mystique". These chips were essentially previous-generation 2D accelerators with 3D features bolted on. Many were even pin-compatible with the earlier-generation chips for ease of implementation and minimal cost. Initially, performance 3D graphics were possible only with discrete boards dedicated to accelerating 3D functions (and lacking 2D GUI acceleration entirely) such as the PowerVR and the 3dfx "Voodoo". However, as manufacturing technology continued to progress, video, 2D GUI acceleration and 3D functionality were all integrated into one chip. Rendition's "Verite" chipsets were among the first to do this well enough to be worthy of note. In 1997, Rendition went a step further by collaborating with Hercules and Fujitsu on a "Thriller Conspiracy" project which combined a Fujitsu FXG-1 Pinolite geometry processor with a Vérité V2200 core to create a graphics card with a full T&L engine years before Nvidia's GeForce 256. This card, designed to reduce the load placed upon the system's CPU, never made it to market.


title: Graphics processing unit

text: OpenGL appeared in the early '90s as a professional graphics API, but originally suffered from performance issues which allowed the Glide API to step in and become a dominant force on the PC in the late '90s. However, these issues were quickly overcome and the Glide API fell by the wayside. Software implementations of OpenGL were common during this time, although the influence of OpenGL eventually led to widespread hardware support. Over time, a parity emerged between features offered in hardware and those offered in OpenGL. DirectX became popular among Windows game developers during the late 90s. Unlike OpenGL, Microsoft insisted on providing strict one-to-one support of hardware. The approach made DirectX less popular as a standalone graphics API initially, since many GPUs provided their own specific features, which existing OpenGL applications were already able to benefit from, leaving DirectX often one generation behind. (See: Comparison of OpenGL and Direct3D.)


title: Graphics processing unit

text: Over time, Microsoft began to work more closely with hardware developers and started to target the releases of DirectX to coincide with those of the supporting graphics hardware. Direct3D 5.0 was the first version of the burgeoning API to gain widespread adoption in the gaming market, and it competed directly with many more-hardware-specific, often proprietary graphics libraries, while OpenGL maintained a strong following. Direct3D 7.0 introduced support for hardware-accelerated transform and lighting (T&L) for Direct3D, while OpenGL had this capability already exposed from its inception. 3D accelerator cards moved beyond being just simple rasterizers to add another significant hardware stage to the 3D rendering pipeline. The Nvidia "GeForce 256" (also known as NV10) was the first consumer-level card released on the market with hardware-accelerated T&L, while professional 3D cards already had this capability. Hardware transform and lighting, both already existing features of OpenGL, came to consumer-level hardware in the '90s and set the precedent for later pixel shader and vertex shader units which were far more flexible and programmable.


title: Graphics processing unit

text: Nvidia was first to produce a chip capable of programmable shading; the "GeForce 3" (code named NV20). Each pixel could now be processed by a short "program" that could include additional image textures as inputs, and each geometric vertex could likewise be processed by a short program before it was projected onto the screen. Used in the Xbox console, it competed with the PlayStation 2, which used a custom vector unit for hardware accelerated vertex processing (commonly referred to as VU0/VU1). The earliest incarnations of shader execution engines used in Xbox were not general purpose and could not execute arbitrary pixel code. Vertices and pixels were processed by different units which had their own resources with pixel shaders having much tighter constraints (being as they are executed at much higher frequencies than with vertices). Pixel shading engines were actually more akin to a highly customizable function block and didn't really "run" a program. Many of these disparities between vertex and pixel shading were not addressed until much later with the Unified Shader Model.


title: Graphics processing unit

text: By October 2002, with the introduction of the ATI "Radeon 9700" (also known as R300), the world's first Direct3D 9.0 accelerator, pixel and vertex shaders could implement looping and lengthy floating point math, and were quickly becoming as flexible as CPUs, yet orders of magnitude faster for image-array operations. Pixel shading is often used for bump mapping, which adds texture, to make an object look shiny, dull, rough, or even round or extruded.


title: Graphics processing unit

text: With the introduction of the Nvidia GeForce 8 series, and then new generic stream processing unit GPUs became a more generalized computing devices. Today, parallel GPUs have begun making computational inroads against the CPU, and a subfield of research, dubbed GPU Computing or GPGPU for "General Purpose Computing on GPU", has found its way into fields as diverse as machine learning, oil exploration, scientific image processing, linear algebra, statistics, 3D reconstruction and even stock options pricing determination. GPGPU at the time was the precursor to what is now called a compute shader (e.g. CUDA, OpenCL, DirectCompute) and actually abused the hardware to a degree by treating the data passed to algorithms as texture maps and executing algorithms by drawing a triangle or quad with an appropriate pixel shader. This obviously entails some overheads since units like the Scan Converter are involved where they aren't really needed (nor are triangle manipulations even a concern—except to invoke the pixel shader).


title: Graphics processing unit

text: Nvidia's CUDA platform, first introduced in 2007, was the earliest widely adopted programming model for GPU computing. More recently OpenCL has become broadly supported. OpenCL is an open standard defined by the Khronos Group which allows for the development of code for both GPUs and CPUs with an emphasis on portability. OpenCL solutions are supported by Intel, AMD, Nvidia, and ARM, and according to a recent report by Evan's Data, OpenCL is the GPGPU development platform most widely used by developers in both the US and Asia Pacific.


title: Graphics processing unit

text: In 2010, Nvidia began a partnership with Audi to power their cars' dashboards, using the Tegra GPUs to provide increased functionality to cars' navigation and entertainment systems. Advances in GPU technology in cars has helped push self-driving technology. AMD's Radeon HD 6000 Series cards were released in 2010 and in 2011, AMD released their 6000M Series discrete GPUs to be used in mobile devices. The Kepler line of graphics cards by Nvidia came out in 2012 and were used in the Nvidia's 600 and 700 series cards. A feature in this new GPU microarchitecture included GPU boost, a technology that adjusts the clock-speed of a video card to increase or decrease it according to its power draw. The Kepler microarchitecture was manufactured on the 28 nm process.


title: Graphics processing unit

text: The PS4 and Xbox One were released in 2013, they both use GPUs based on AMD's Radeon HD 7850 and 7790. Nvidia's Kepler line of GPUs was followed by the Maxwell line, manufactured on the same process. 28 nm chips by Nvidia were manufactured by TSMC, the Taiwan Semiconductor Manufacturing Company, that was manufacturing using the 28 nm process at the time. Compared to the 40 nm technology from the past, this new manufacturing process allowed a 20 percent boost in performance while drawing less power. Virtual reality headsets have very high system requirements. VR headset manufacturers recommended the GTX 970 and the R9 290X or better at the time of their release. Pascal is the next generation of consumer graphics cards by Nvidia released in 2016. The GeForce 10 series of cards are under this generation of graphics cards. They are made using the 16 nm manufacturing process which improves upon previous microarchitectures. Nvidia has released one non-consumer card under the new Volta architecture, the Titan V. Changes from the Titan XP, Pascal's high-end card, include an increase in the number of CUDA cores, the addition of tensor cores, and HBM2. Tensor cores are cores specially designed for deep learning, while high-bandwidth memory is on-die, stacked, lower-clocked memory that offers an extremely wide memory bus that is useful for the Titan V's intended purpose. To emphasize that the Titan V is not a gaming card, Nvidia removed the "GeForce GTX" suffix it adds to consumer gaming cards.


title: Graphics processing unit

text: On August 20, 2018, Nvidia launched the RTX 20 series GPUs that add ray-tracing cores to GPUs, improving their performance on lighting effects. Polaris 11 and Polaris 10 GPUs from AMD are fabricated by a 14-nanometer process. Their release results in a substantial increase in the performance per watt of AMD video cards. AMD has also released the Vega GPUs series for the high end market as a competitor to Nvidia's high end Pascal cards, also featuring HBM2 like the Titan V.


title: Graphics processing unit

text: In 2019, AMD released the successor to their Graphics Core Next (GCN) microarchitecture/instruction set. Dubbed as RDNA, the first product lineup featuring the first generation of RDNA was the Radeon RX 5000 series of video cards, which later launched on July 7, 2019. Later, the company announced that the successor to the RDNA microarchitecture would be a refresh. Dubbed as RDNA 2, the new microarchitecture was reportedly scheduled for release in Q4 2020.


title: Graphics processing unit

text: AMD unveiled the Radeon RX 6000 series, its next-gen RDNA 2 graphics cards with support for hardware-accelerated ray tracing at an online event on October 28, 2020. The lineup initially consists of the RX 6800, RX 6800 XT and RX 6900 XT. The RX 6800 and 6800 XT launched on November 18, 2020, with the RX 6900 XT being released on December 8, 2020. The RX 6700 XT, which is based on Navi 22, was launched on March 18, 2021.


title: Graphics processing unit

text: The PlayStation 5 and Xbox Series X and Series S were released in 2020, they both use GPUs based on the RDNA 2 microarchitecture with proprietary tweaks and different GPU configurations in each system's implementation.


title: Graphics processing unit

text: Many companies have produced GPUs under a number of brand names. In 2009, Intel, Nvidia and AMD/ATI were the market share leaders, with 49.4%, 27.8% and 20.6% market share respectively. However, those numbers include Intel's integrated graphics solutions as GPUs. Not counting those, Nvidia and AMD control nearly 100% of the market as of 2018. Their respective market shares are 66% and 33%. In addition, Matrox produces GPUs.


title: Graphics processing unit

text: Modern smartphones also use mostly Adreno GPUs from Qualcomm, PowerVR GPUs from Imagination Technologies and Mali GPUs from ARM.


title: Graphics processing unit

text: Modern GPUs use most of their transistors to do calculations related to 3D computer graphics. In addition to the 3D hardware, today's GPUs include basic 2D acceleration and framebuffer capabilities (usually with a VGA compatibility mode). Newer cards such as AMD/ATI HD5000-HD7000 even lack dedicated 2D acceleration; it has to be emulated by 3D hardware. GPUs were initially used to accelerate the memory-intensive work of texture mapping and rendering polygons, later adding units to accelerate geometric calculations such as the rotation and translation of vertices into different coordinate systems. Recent developments in GPUs include support for programmable shaders which can manipulate vertices and textures with many of the same operations supported by CPUs, oversampling and interpolation techniques to reduce aliasing, and very high-precision color spaces. Given that most of these computations involve matrix and vector operations, engineers and scientists have increasingly studied the use of GPUs for non-graphical calculations; they are especially suited to other embarrassingly parallel problems.


title: Graphics processing unit

text: Several factors of the GPU's construction enter into the performance of the card for real-time rendering. Common factors can include the size of the connector pathways in the semiconductor device fabrication, the clock signal frequency, and the number and size of various on-chip memory caches. Additionally, the number of Streaming Multiprocessors (SM) for NVidia GPUs, or Compute Units (CU) for AMD GPUs, which describe the number of core on-silicon processor units within the GPU chip that perform the core calculations, typically working in parallel with other SM/CUs on the GPU. Performance of GPUs are typically measured in floating point operations per second or FLOPS, with GPUs in the 2010s and 2020s typically delivering performance measured in teraflops (TFLOPS). This is an estimated performance measure as other factors can impact the actual display rate.


title: Graphics processing unit

text: With the emergence of deep learning, the importance of GPUs has increased. In research done by Indigo, it was found that while training deep learning neural networks, GPUs can be 250 times faster than CPUs. There has been some level of competition in this area with ASICs, most prominently the Tensor Processing Unit (TPU) made by Google. However, ASICs require changes to existing code and GPUs are still very popular.


title: Graphics processing unit

text: Most GPUs made since 1995 support the YUV color space and hardware overlays, important for digital video playback, and many GPUs made since 2000 also support MPEG primitives such as motion compensation and iDCT. This process of hardware accelerated video decoding, where portions of the video decoding process and video post-processing are offloaded to the GPU hardware, is commonly referred to as "GPU accelerated video decoding", "GPU assisted video decoding", "GPU hardware accelerated video decoding" or "GPU hardware assisted video decoding".


title: Graphics processing unit

text: More recent graphics cards even decode high-definition video on the card, offloading the central processing unit. The most common APIs for GPU accelerated video decoding are DxVA for Microsoft Windows operating system and VDPAU, VAAPI, XvMC, and XvBA for Linux-based and UNIX-like operating systems. All except XvMC are capable of decoding videos encoded with MPEG-1, MPEG-2, MPEG-4 ASP (MPEG-4 Part 2), MPEG-4 AVC (H.264 / DivX 6), VC-1, WMV3/WMV9, Xvid / OpenDivX (DivX 4), and DivX 5 codecs, while XvMC is only capable of decoding MPEG-1 and MPEG-2.


title: Graphics processing unit

text: The GPUs of the most powerful class typically interface with the motherboard by means of an expansion slot such as PCI Express (PCIe) or Accelerated Graphics Port (AGP) and can usually be replaced or upgraded with relative ease, assuming the motherboard is capable of supporting the upgrade. A few graphics cards still use Peripheral Component Interconnect (PCI) slots, but their bandwidth is so limited that they are generally used only when a PCIe or AGP slot is not available.


title: Graphics processing unit

text: A dedicated GPU is not necessarily removable, nor does it necessarily interface with the motherboard in a standard fashion. The term "dedicated" refers to the fact that dedicated graphics cards have RAM that is dedicated to the card's use, not to the fact that "most" dedicated GPUs are removable. Further, this RAM is usually specially selected for the expected serial workload of the graphics card (see GDDR). Sometimes, systems with dedicated, "discrete" GPUs were called "DIS" systems, as opposed to "UMA" systems (see next section). Dedicated GPUs for portable computers are most commonly interfaced through a non-standard and often proprietary slot due to size and weight constraints. Such ports may still be considered PCIe or AGP in terms of their logical host interface, even if they are not physically interchangeable with their counterparts.


title: Graphics processing unit

text: Technologies such as SLI and NVLink by Nvidia and CrossFire by AMD allow multiple GPUs to draw images simultaneously for a single screen, increasing the processing power available for graphics. These technologies, however, are increasingly uncommon, as most games do not fully utilize multiple GPUs, as most users cannot afford them. Multiple GPUs are still used on supercomputers (like in Summit), on workstations to accelerate video (processing multiple videos at once) and 3D rendering, for VFX and for simulations, and in AI to expedite training, as is the case with Nvidia's lineup of DGX workstations and servers and Tesla GPUs and Intel's upcoming Ponte Vecchio GPUs.