title: Mitsubishi Triton

text: In Japan, the Triton was exclusively equipped with 3.5-litre petrol engine and 4-speed automatic transmission and was sold from 2006 to 2011 - the only pick-up truck in the market at that time (excluding kei trucks). Despite its success overseas, it was a critical failure in Japan as workmen and traders preferred vans and station wagons. As a result, in August 2011 the Triton was pulled out from Mitsubishi's Japanese lineup.


title: Mitsubishi Triton

text: In 2014, Mitsubishi unveiled the all new L200 which went on sale in early 2015 (Asia-Pacific) and late 2015 (Europe and the Caribbean). It is powered by a new 2.4-litre diesel engine. Since 2015, the current generation L200 shares the same underpinnings as the newly rebadged Fiat Fullback intended for the European and Middle East markets. Fiat Chrysler Automobiles currently has no plans to introduce the Fullback in the North American market due to the U.S. chicken tax as well as the introduction of the Jeep Gladiator, based on the fourth-generation Jeep Wrangler SUV. For the 2017 model year, Ram Trucks rebadged the Triton as the Ram 1200 for the Middle East market.


title: Mitsubishi Triton

text: In addition, due to being plagued by the previous-generation Triton's critical failure in Japanese market (in contrast to its overseas success), in addition to having heavy excise duties for pickup trucks there, Mitsubishi Motors currently has no plans to bring the current Triton to their home market.


title: Mitsubishi Triton

text: The L200 in its most basic Latin American configuration with no airbags and no ESC received 0 stars for adult occupants and 2 stars for toddlers from Latin NCAP in 2019.


title: Mitsubishi Triton

text: The fifth generation Triton was launched in Malaysia in May 2015 being fully imported from Thailand. It was available in five variants: Triton Quest (MT), Triton MT, Triton VGT MT, Triton VGT AT and Triton VGT Adventure (AT). The VGT models came with a 2.5L variable geometry turbo engine capable of producing and . The Triton MT had a 2.5L common rail turbo engine capable of producing and and the Triton Quest had a 2.5L DOHC common rail engine with and . Two limited editions were made available including the: Triton Phantom Edition in January 2016 and the Triton Knight Edition in May 2016. Both were limited to 200 units each.


title: Mitsubishi Triton

text: In September 2016, alongside of the change of engine for the VGT models to a 2.4L MIVEC VGT turbodiesel engine capable of and , the Triton VGT Adventure X was also launched as the new range topper.


title: Mitsubishi Triton

text: In April 2017, the Triton was updated. Changes included additional safety features for the VGT models, change in the steering wheel design and different colour choices.


title: Mitsubishi Triton

text: In September 2017, the Triton VGT AT GL was launched and was positioned in between the Triton MT and Triton VGT MT.


title: Mitsubishi Triton

text: In January 2019, the facelifted fifth generation Triton was launched in Malaysia with five variants: VGT (MT and AT), VGT Premium (MT and AT), Adventure X (AT only). The 4x2 Quest model remained unchanged.


title: Mitsubishi Triton

text: The fifth generation Triton, known locally as the Strada was launched on 20 March 2015 and was offered in 6 trim levels; GL 4x2, GL 4x4, GLX 4x2, GLX V, GLS V and GLS Sport V. All trims were initially offered with the 2.5-litre 4D56 engine. In August 2016, the 2.4-litre MIVEC VGT engine was added alongside the GT trim.


title: Mitsubishi Triton

text: The facelifted Strada was launched in January 2019. It is offered in 4 variants; GLX Plus, GLS 2WD, GLS 4WD and GT 4WD.


title: Mitsubishi Triton

text: The Triton was refreshed for the 2019 model year at the 2018 Thailand International Motor Expo in Bangkok, Thailand. This update consists of new front fascia, which is inspired from the Pajero/Montero Sport, Eclipse Cross and Xpander, new teardrop taillight design treatment as the Pajero/Montero Sport, and slight changes in the interior for some variants. This model also received a rear air circulator located at the interior roof.


title: Joseph of Arimathea

text: Joseph of Arimathea was, according to all four canonical gospels, the man who assumed responsibility for the burial of Jesus after his crucifixion. The historical location of Arimathea is uncertain, although it has been identified with several towns. A number of stories that developed during the Middle Ages connect him with Glastonbury, England and also with the Holy Grail legend.


title: Joseph of Arimathea

text: describes him simply as a rich man and disciple of Jesus, but according to Joseph of Arimathea was "a respected member of the council, who was also himself looking for the kingdom of God"; adds that he "had not consented to their decision and action".


title: Joseph of Arimathea

text: According to , upon hearing of Jesus' death, this secret disciple of Jesus "asked Pilate that he might take away the body of Jesus, and Pilate gave him permission." Joseph immediately purchased a linen shroud () and proceeded to Golgotha to take the body of Jesus down from the cross. There, according to , Joseph and Nicodemus took the body and bound it in linen cloths with the spices (myrrh and aloes) that Nicodemus had brought. Luke 23:55-56 states that the women "who had come with him from Galilee" prepared the spices and ointments.


title: Joseph of Arimathea

text: The disciples then conveyed the prepared corpse to a man-made cave hewn from rock in a garden nearby. The Gospel of Matthew alone suggests that this was Joseph's own tomb (). The burial was undertaken speedily, "for the Sabbath was drawing on".


title: Joseph of Arimathea

text: Joseph of Arimathea is venerated as a saint by the Roman Catholic, Eastern Orthodox, and some Protestant churches. The traditional Roman calendar marked his feast day on 17 March, but he is now listed, along with Saint Nicodemus, on 31 August in the Martyrologium Romanum. Eastern Orthodox churches commemorate him on the "Third Sunday of Pascha" (i.e., the second Sunday after Easter) and on 31 July, the date shared by Lutheran churches. He is included in the Myrrhbearers.


title: Joseph of Arimathea

text: Although a series of legends developed during the Middle Ages (perhaps elaborations of early New Testament apocrypha) tied this Joseph to Britain as well as the Holy Grail, he is not currently on the abbreviated liturgical calendar of the Church of England, although this Joseph is on the calendars of some churches of the Anglican Communion, such as the Episcopal Church, which commemorates him on 1 August.


title: Joseph of Arimathea

text: Many Christians interpret Joseph's role as fulfilling Isaiah's prediction that the grave of the "Suffering Servant" would be with a rich man (Isaiah 53:9), assuming that Isaiah was referring to the Messiah. The prophecy in Isaiah chapter 53 is known as the "Man of Sorrows" passage:


title: Joseph of Arimathea

text: Since the 2nd century, a mass of legendary detail has accumulated around the figure of Joseph of Arimathea in addition to the New Testament references. Joseph is referenced in apocryphal and non-canonical accounts such as the Acts of Pilate and the medieval Gospel of Nicodemus. Joseph is mentioned in the works of early church historians such as Irenaeus, Hippolytus, Tertullian, and Eusebius, who added details not found in the canonical accounts. Francis Gigot, writing in the "Catholic Encyclopedia", states that "the additional details which are found concerning him in the apocryphal "Acta Pilati" ("Acts of Pilate"), are unworthy of credence." The Narrative of Joseph of Arimathea, a medieval work, is even purportedly written by him directly, although it adds more details on the robbers at Jesus's crucifixion than Joseph himself. He also appears in the ancient non-canonical text the Gospel of Peter.


title: Joseph of Arimathea

text: Hilary of Poitiers (4th century) enriched the legend, and Saint John Chrysostom, the Patriarch of Constantinople from 397 to 403, was the first to write that Joseph was one of the Seventy Apostles appointed in Luke 10.


title: Joseph of Arimathea

text: During the late 12th century, Joseph became connected with the Arthurian cycle, appearing in them as the first keeper of the Holy Grail. This idea first appears in Robert de Boron's "Joseph d'Arimathie", in which Joseph receives the Grail from an apparition of Jesus and sends it with his followers to Britain. This theme is elaborated upon in Boron's sequels and in subsequent Arthurian works penned by others. Later retellings of the story contend that Joseph of Arimathea travelled to Britain and became the first Christian bishop in the Isles, a claim Gigot characterizes as a fable.


title: Joseph of Arimathea

text: The Gospel of Nicodemus, a text appended to the Acts of Pilate, provides additional details about Joseph. For instance, after Joseph asked Pilate for the body of the Christ and prepared the body with Nicodemus' help, Christ's body was delivered to a new tomb that Joseph had built for himself. In the Gospel of Nicodemus, the Jewish elders express anger at Joseph for burying the body of Christ, saying:


title: Joseph of Arimathea

text: The Jewish elders then captured Joseph, imprisoned him, and placed a seal on the door to his cell after first posting a guard. Joseph warned the elders, "The Son of God whom you hanged upon the cross, is able to deliver me out of your hands. All your wickedness will return upon you."


title: Joseph of Arimathea

text: Once the elders returned to the cell, the seal was still in place, but Joseph was gone. The elders later discover that Joseph had returned to Arimathea. Having a change in heart, the elders desired to have a more civil conversation with Joseph about his actions and sent a letter of apology to him by means of seven of his friends. Joseph travelled back from Arimathea to Jerusalem to meet with the elders, where they questioned him about his escape. He told them this story:


title: Joseph of Arimathea

text: According to the Gospel of Nicodemus, Joseph testified to the Jewish elders, and specifically to chief priests Caiaphas and Annas that Jesus had risen from the dead and ascended to heaven, and he indicated that others were raised from the dead at the resurrection of Christ (repeating –). He specifically identified the two sons of the high-priest Simeon (again in Luke 2:25–35). The elders Annas, Caiaphas, Nicodemus, and Joseph himself, along with Gamaliel under whom Paul of Tarsus studied, travelled to Arimathea to interview Simeon's sons Charinus and Lenthius.


title: Joseph of Arimathea

text: Medieval interest in Joseph centered on two themes, that of Joseph as the founder of British Christianity (even before it had taken hold in Rome), and that of Joseph as the original guardian of the Holy Grail.


title: Joseph of Arimathea

text: Many legends about the arrival of Christianity in Britain abounded during the Middle Ages. Early writers do not connect Joseph to this activity, however. Tertullian wrote in "Adversus Judaeos" that Britain had already received and accepted the Gospel in his lifetime, writing, "all the limits of the Spains, and the diverse nations of the Gauls, and the haunts of the Britons—inaccessible to the Romans, but subjugated to Christ."


title: Joseph of Arimathea

text: Tertullian does not say how the Gospel came to Britain before AD 222. However, Eusebius of Caesaria, one of the earliest and most comprehensive of church historians, wrote of Christ's disciples in "Demonstratio Evangelica," saying that "some have crossed the Ocean and reached the Isles of Britain." Saint Hilary of Poitiers also wrote that the Apostles had built churches and that the Gospel had passed into Britain. The writings of Pseudo-Hippolytus include a list of the seventy disciples whom Jesus sent forth in Luke 10, one of which is Aristobulus of Romans 16:10, called "bishop of Britain".


title: Joseph of Arimathea

text: In none of these earliest references to Christianity's arrival in Britain is Joseph of Arimathea mentioned. William of Malmesbury's "De Antiquitate Glastoniensis Ecclesiae" ("On the Antiquity of the Church of Glastonbury", circa 1125) has not survived in its original edition, and the stories involving Joseph of Arimathea are contained in subsequent editions that abound in interpolations placed by the Glastonbury monks "in order to increase the Abbey's prestige – and thus its pilgrim trade and prosperity" In his "Gesta Regum Anglorum" ("History of The Kings of England", finished in 1125), William of Malmesbury wrote that Glastonbury Abbey was built by preachers sent by Pope Eleuterus to Britain, however also adding: "Moreover there are documents of no small credit, which have been discovered in certain places to the following effect: 'No other hands than those of the disciples of Christ erected the church of Glastonbury'", but here William did not explicitly link Glastonbury with Joseph of Arimathea, but instead emphasizes the possible role of Philip the Apostle: "if Philip, the Apostle, preached to the Gauls, as Freculphus relates in the fourth chapter of his second book, it may be believed that he also planted the word on this side of the channel also."


title: Joseph of Arimathea

text: In 1989 A. W. Smith critically examined the accretion of legends around Joseph of Arimathea, by which the poem hymn of William Blake "And did those feet in ancient time" is commonly held as "an almost secret yet passionately held article of faith among certain otherwise quite orthodox Christians" and Smith concluded "that there was little reason to believe that an oral tradition concerning a visit made by Jesus to Britain existed before the early part of the twentieth century". Sabine Baring-Gould recounted a Cornish story how "Joseph of Arimathea came in a boat to Cornwall, and brought the child Jesus with him, and the latter taught him how to extract the tin and purge it of its wolfram. This story possibly grew out of the fact that the Jews under the Angevin kings farmed the tin of Cornwall." In its most developed version, Joseph, a tin merchant, visited Cornwall, accompanied by his nephew, the boy Jesus. Reverend C.C. Dobson (1879–1960) made a case for the authenticity of the Glastonbury "legenda". The case was argued more recently by the Church of Scotland minister Dr Gordon Strachan (1934–2010) and by the former archaeologist Dennis Price.


title: Joseph of Arimathea

text: The legend that Joseph was given the responsibility of keeping the Holy Grail was the product of Robert de Boron, who essentially expanded upon stories from "Acts of Pilate". In Boron's "Joseph d'Arimathe", Joseph is imprisoned much as in the "Acts of Pilate", but it is the Grail that sustains him during his captivity. Upon his release he founds his company of followers, who take the Grail to Britain, though Joseph does not go. The origin of the association between Joseph and Britain is not entirely clear, though in subsequent romances such as "Perlesvaus", Joseph travels to Britain, bringing relics with him. In the Lancelot-Grail cycle, a vast Arthurian composition that took much from Robert, it is not Joseph but his son Josephus who is considered the primary holy man of Britain.


title: Joseph of Arimathea

text: Later authors sometimes mistakenly or deliberately treated the Grail story as truth. Such stories were inspired by the account of John of Glastonbury, who assembled a chronicle of the history of Glastonbury Abbey around 1350 and who wrote that Joseph, when he came to Britain, brought with him vessels containing the blood and sweat of Christ (without using the word Grail). This account inspired the future claims of the Grail, including the claim involving the Nanteos Cup on display in the museum in Aberystwyth. There is no reference to this tradition in ancient or medieval text. John of Glastonbury further claims that King Arthur was descended from Joseph, listing the following imaginative pedigree through King Arthur's mother:


title: Joseph of Arimathea

text: Elizabeth I cited Joseph's missionary work in England when she told Roman Catholic bishops that the Church of England pre-dated the Roman Church in England.


title: Joseph of Arimathea

text: When Joseph set his walking staff on the ground to sleep, it miraculously took root, leafed out, and blossomed as the "Glastonbury Thorn". The retelling of such miracles encouraged the pilgrim trade at Glastonbury until the abbey was dissolved in 1539, during the English Reformation. The mytheme of the staff that Joseph of Arimathea set in the ground at Glastonbury, which broke into leaf and flower as the Glastonbury Thorn is a common miracle in hagiography. Such a miracle is told of the Anglo-Saxon saint Etheldreda:


title: Joseph of Arimathea

text: Medieval interest in genealogy raised claims that Joseph was a relative of Jesus; specifically, Mary's uncle, or according to some genealogies, Joseph's uncle. A genealogy for the family of Joseph of Arimathea and the history of his further adventures in the east provide material for Holy Grail romances "Estoire del Saint Graal", "Perlesvaus", and the "Queste del Saint Graal".


title: Joseph of Arimathea

text: Another legend, as recorded in "Flores Historiarum" is that Joseph is in fact the Wandering Jew, a man cursed by Jesus to walk the Earth until the Second Coming.


title: Joseph of Arimathea

text: Arimathea is not otherwise documented, though it was "a town of Judea" according to Luke 23:51. Arimathea is usually identified with either Ramleh or Ramathaim-Zophim, where David came to Samuel ("1 Samuel" chapter 19).


title: Jeon Mi-do

text: Jeon Mi-do (; born August 4, 1982) is a South Korean actress and singer. She is known for her role as Dr. Chae Song-hwa in "Hospital Playlist". In 2022, Jeon appeared in lead role alongside Son Ye-jin and Kim Ji-hyun in JTBC's TV series "Thirty, Nine", a romantic drama about three friends.


title: Jeon Mi-do

text: Jeon made her acting debut in the musical "Mr. Mouse" in 2006 and has had a long career since then acting in plays and musicals.


title: Jeon Mi-do

text: Jeon made her television debut in the 2018 series "Mother" in which she played a minor role. The following year, she made her big screen debut in the fantasy film "Metamorphosis".


title: Jeon Mi-do

text: Jeon landed her first lead role in a television series with the medical drama "Hospital Playlist". When she first auditioned, she thought it was to play one of the patients but director Shin Won-ho told her he was considering her for the lead role. During an interview, director Shin said that "Although we make the character, [we] felt she was destined to play Song-hwa." Her performance earned her a nomination for Best New Actress in the television category at the 56th Baeksang Arts Awards. For the drama's soundtrack, she sang a cover of Shin Hyo-beom's song "I Knew I Love" (사랑하게 될 줄 알았어) which was originally released in 2006. It peaked at number 1 on the Gaon Digital Chart.


title: Jeon Mi-do

text: In 2022, Jeon appeared alongside Son Ye-jin and Kim Ji-hyun in JTBC's TV series "Thirty, Nine", a drama that revolves around three friends.


title: Chris Hughes

text: Chris Hughes (born November 26, 1983) is an American entrepreneur and author who co-founded and served as spokesman for the online social directory and networking site Facebook until 2007. He was the publisher and editor-in-chief of "The New Republic" from 2012 to 2016.


title: Chris Hughes

text: Hughes co-founded the Economic Security Project in 2016. In 2018, he published "Fair Shot: Rethinking Inequality and How We Earn".


title: Chris Hughes

text: Hughes grew up in Hickory, North Carolina, as the only child of Arlen "Ray" Hughes, an industrial paper salesman, and Brenda Hughes, a mathematics teacher. He was raised as an evangelical Lutheran.<ref name="NYT Hughes/Eldrigde bio"></ref> He graduated from Phillips Academy in Andover, Massachusetts, before earning a Bachelor of Arts in History and English Literature, "magna cum laude", from Harvard College.


title: Chris Hughes

text: In February 2020, it was reported that Hughes was in the process of earning his Master of Arts in Economics from The New School for Social Research in New York City.


title: Chris Hughes

text: Hughes is a co-founder of Facebook. At Harvard, Hughes met and was recruited by Mark Zuckerberg, who at the time was still working in the early stages of the website. During their summer break in 2004, Hughes and Zuckerberg traveled to Palo Alto, California. While Zuckerberg decided to remain in Palo Alto after the break, Hughes decided to return to Harvard to continue his studies. In 2006, after graduating from Harvard, Hughes relocated to Palo Alto to rejoin Zuckerberg and became involved in Facebook again.


title: Chris Hughes

text: Hughes was unofficially responsible for beta testing and product suggestions. When the group had the idea to open Facebook to other schools, Hughes argued that schools should have their own networks to maintain the intimacy feel. He was also a key driver in developing many of Facebook's popular features, which led to the opening of Facebook to the outside world. As a result, Hughes became the de facto Facebook spokesman.


title: Chris Hughes

text: In March 2009, Hughes was named Entrepreneur in Residence at General Catalyst, a Cambridge, Massachusetts, venture-capital firm.


title: Chris Hughes

text: Hughes was the executive director of Jumo, a non-profit social network organization which he founded in 2010, which "aims to help people find ways to help the world". In July 2010, UNAIDS (Joint United Nations Programme on HIV/AIDS) appointed him to a 17-member "High Level Commission" of renowned politicians, business leaders, human rights activists, and scientists tasked with spearheading a "social and political action campaign over the coming year aimed at galvanizing support for effective HIV prevention programmes."


title: Chris Hughes

text: In March 2012, Hughes purchased a majority stake in "The New Republic" magazine. He became the publisher and executive chairman, and also served as editor-in-chief of the magazine. In December 2014, shortly after the magazine's centennial celebration, editor Franklin Foer and literary editor Leon Wieseltier were "driven out" and dozens of other staff and contributing editors resigned after a new chief executive, Guy Vidra, a former Yahoo! employee, described the new direction of the magazine as a "vertically integrated digital media company." The magazine was forced to cancel its upcoming issue due to the staff departures.


title: Chris Hughes

text: The magazine was not profitable during Hughes' tenure. On January 11, 2016, Hughes put "The New Republic" up for sale, saying he had "underestimated the difficulty of transitioning an old and traditional institution into a digital media company in today's quickly evolving climate." Hughes' ownership of "The New Republic" was described by "The New York Times" as a "vanity project." He sold the magazine on February 26, 2016 to Oregon publisher Win McCormack.


title: Chris Hughes

text: In May 2019, he published an op-ed in the "New York Times", calling for the break-up of Facebook and for government regulation of content on it; in June of the same year, he criticized the Facebook decision to launch Libra, saying that the cryptocurrency "would shift power into the wrong hands if, at least, the coin be modestly successful".


title: Chris Hughes

text: Hughes and Sean Eldridge bought a $2 million residence in New York's 19th congressional district with the reported purpose of permitting Eldridge to run for the congressional seat there. In 2014, Eldridge lost his congressional bid by 29 points.


title: Chris Hughes

text: Hughes endorsed Democratic candidate Hillary Clinton in the run-up for the 2016 U.S. presidential election.


title: Chris Hughes

text: Hughes is openly gay and is married to Sean Eldridge. Hughes and Eldridge announced their engagement in January 2011 at a reception in support of Freedom to Marry. They married on June 30, 2012.


title: Diablo Cody

text: Brook Maurio ("née" Busey; born June 14, 1978), known professionally by the pen name Diablo Cody, is an American writer and producer. She gained recognition for her candid blog and subsequent memoir, "" (2005). Cody received critical acclaim for her screenwriting debut film, "Juno" (2007), winning the Academy Award for Best Original Screenplay, the BAFTA Award for Best Original Screenplay, the Independent Spirit Award for Best First Screenplay, and the Writers Guild of America Award for Best Original Screenplay.


title: Diablo Cody

text: Cody created, wrote, and produced the Showtime comedy drama series "United States of Tara" (2009–2011). She wrote, produced, and made her directorial debut with the comedy drama film "Paradise" (2013). Cody also wrote and produced the horror comedy film "Jennifer's Body" (2009), the comedy drama film "Young Adult" (2011), which earned her a second nomination for the Writers Guild of America Award for Best Original Screenplay, the musical comedy film "Ricki and the Flash" (2015), and the comedy drama film "Tully" (2018).


title: Diablo Cody

text: Cody won a Tony Award for Best Book of a Musical for "Jagged Little Pill", her first musical-theater undertaking. She has been a member of the Academy of Motion Picture Arts and Sciences in the Writer's Branch since 2008.


title: Diablo Cody

text: Diablo Cody was born Brook Busey on June 14, 1978 in Lemont, Illinois, a suburb of Chicago, where she and her older brother Marc were raised. She is the daughter of Pam and Greg Busey. Her mother is of Italian descent and her father is of German ancestry. Cody was raised Apostolic Christian and attended Benet Academy, a Roman Catholic school in Lisle, Illinois. At this time, she went by her birth name Brook.


title: Diablo Cody

text: In 2000, she graduated from the University of Iowa with a Bachelor of Arts in Media. While at the University of Iowa, she worked in the acquisitions department in the main university library. Her first jobs were doing secretarial work at a Chicago law firm and later proofreading copy for advertisements that played on Twin Cities radio stations.


title: Diablo Cody

text: Cody began a parody blog called "Red Secretary", detailing the (fictional) exploits of a secretary living in Belarus. The events were thinly-veiled allegories for events that happened in Cody's real life, but told from the perspective of a disgruntled, English-idiom-challenged Eastern Bloc girl.


title: Diablo Cody

text: Cody's first "bona fide" blog appeared under the nickname "Darling Girl" after she had moved from Chicago to Minneapolis, Minnesota.


title: Diablo Cody

text: In March 2003, Cody started an adult blog called "The Pussy Ranch", using a pen name invented while speeding through Cody, Wyoming listening to the song "El Diablo" by Arcadia. On a whim, Cody signed up for amateur night at a Minneapolis strip club called the Skyway Lounge. Having enjoyed the experience, and seeing reader interest, she eventually quit her day job to become a full-time stripper. Cody also spent time working peep shows at Sex World, a Minneapolis adult novelty and DVD store.


title: Diablo Cody

text: While still stripping, Cody began writing for "City Pages", an alternative Twin Cities weekly newspaper. She left "City Pages" just before it changed editorial hands, and has since written for the now-defunct "Jane" magazine. In December 2007, Cody began writing a column for the magazine "Entertainment Weekly".


title: Diablo Cody

text: At the age of 27, Cody wrote her memoir "". The memoir began after Mason Novick, who would soon become Cody's manager, showed interest in her sharp and sarcastic voice. Based on the popularity of her blog, Novick was able to secure her a publishing contract with Gotham Books.


title: Diablo Cody

text: After the completion of her book, Cody was encouraged by Mason Novick to try writing a screenplay. Within months she wrote "Juno," a coming-of-age story about a teenager's unplanned pregnancy. The script was completed in February 2005, and was optioned by a producer by that summer. The Jason Reitman-directed comedy stars Elliot Page and Michael Cera.


title: Diablo Cody

text: "Juno" was runner-up for the Toronto International Film Festival People's Choice Award, won second prize at the Rome Film Festival, and earned four Academy Award nominations, including for Best Picture. Cody herself won an Academy Award for Best Original Screenplay for her debut script, which also picked up a Golden Globe nomination and an Independent Spirit Award for Best First Screenplay. She also won screenplay honors from BAFTA, the Writers Guild of America, the Broadcast Film Critics Association, the National Board of Review, the Satellite Awards, and the 2008 Cinema for Peace Award for Most Valuable Work of Director, Producer & Screenwriter (shared with Jason Reitman, John Malkovich, Mason Novick, Russel Smith and Lianne Halfon).


title: Diablo Cody

text: The Juno script was read by many in Hollywood before the film was released, bringing Cody more opportunities. In July 2007, Showtime announced that it would be producing a pilot of Cody's DreamWorks television series, "United States of Tara". Based on an idea by Steven Spielberg, "Tara" is a comedy about a mother with dissociative identity disorder, starring Toni Collette. The series began filming in Spring 2008, and premiered on January 18, 2009.


title: Diablo Cody

text: In October 2007, Cody sold a script titled "Girly Style" to Universal Studios, and a horror script called "Jennifer's Body" to Fox Atomic. Released on September 18, 2009, "Jennifer's Body" starred Megan Fox as the title character and Amanda Seyfried as the supporting character. She revised writer-director Steven Antin's script for his musical film "Burlesque".


title: Diablo Cody

text: Cody made a small cameo appearance as herself in a 2008 episode of the television series "90210". She appeared in the same episode that marked the return of Tori Spelling as Donna Martin, in which Cody needed Spelling's character to make a dress for a red carpet event. In 2009, Cody signed on to script and produce a film adaptation of the "Sweet Valley High" young adult book series. Diablo Cody is co-writing that the untold true story .


title: Diablo Cody

text: In 2011, she was brought in to revise first-time feature director Fede Alvarez's script for the remake of Sam Raimi's 1980s horror film "The Evil Dead". In October 2011, Cody began hosting an online celebrity interview program called "Red Band Trailer," on the broadband channel, L-studio. She originally launched the series privately on YouTube in summer 2010, and the Lexus channel picked it up the following year.


title: Diablo Cody

text: In 2011, Cody wrote and produced the comedy-drama film "Young Adult". Cody was nominated by awards associations such as the Broadcast Film Critics Association and the Writers Guild of America. With Jason Reitman, Charlize Theron and Patton Oswalt, she shared the Chairman's Vanguard Award at the Palm Springs International Film Festival. In 2012, the Fempire, the collaboration of writers Cody, Dana Fox, Liz Meriwether, and Lorene Scafaria received the Creativity and Sisterhood Award from the Athena Film Festival for their support for one another in the competitive film industry.


title: Diablo Cody

text: On the "WTF with Marc Maron" podcast, on February 24, 2012, she said her next project would be directing her first film, which is about a young woman who abandons religion after surviving a plane crash. In February 2013, she announced that the film was called "Paradise" (firstly known as "Lamb of God"). Julianne Hough, Holly Hunter, Octavia Spencer, and Russell Brand starred in the cast. Mandate Pictures produced the film, which was released in October 2013.


title: Diablo Cody

text: In May 2013, it was announced that Cody would host her own talk show, "Me Time with Diablo Cody", on TBS. The program would tailor "around Diablo’s unique perspective on all things pop culture and told in her very own tongue-in-cheek way," and "reveal a side of Hollywood and celebs that the public very rarely gets to see." Steve Agee was to be presenting and writing with her. Cody was a producer, alongside Mark Cronin and Courtland Cox. The series never materialized or made it to air.


title: Diablo Cody

text: Cody had numerous projects that were cancelled or stuck in development hell, including "Time and a Half", which was to star Julianne Hough with Ol Parker directing. She also developed a teen drama series with Josh Schwartz for Fox called "Prodigy". According to "The Hollywood Reporter", it focused on "a 16-year-old genius who through home schooling has been isolated from her peers. Hoping to experience a "normal" teen social life before she enters the adult world of academia, she enrolls in her local high school. Her experiment goes off the rails when she finds herself adopted by a wild crowd, getting caught up in a whirlwind of romance and crime." Cody also created and wrote Warner Bros. Television's romantic comedy series pilot "Alex+Amy".


title: Diablo Cody

text: Cody wrote and produced the musical comedy film "Ricki and the Flash" (2015), starring Meryl Streep and directed by Jonathan Demme in his last feature film. She also wrote and produced the comedy drama film "Tully" (2018), reuniting her with "Young Adult" star Charlize Theron. The film was directed by Jason Reitman, who previously directed Cody's scripts for "Juno" and "Young Adult".


title: Diablo Cody

text: She wrote the script for the Broadway musical "Jagged Little Pill", based on the Alanis Morissette album of the same name. The musical premiered in November 2019.


title: Diablo Cody

text: In her memoir, Cody wrote fondly of her boyfriend "Jonny" (Jon Hunt). They were married from 2004 until 2007, during which time she was known in personal life as Brook Busey-Hunt.


title: Diablo Cody

text: On April 6, 2010, Cody announced that she was expecting her first child with her husband Dan Maurio, who worked on "Chelsea Lately", on which Cody also appeared frequently as a "roundtable" guest. The couple married in the summer of 2009. Their son was born in 2010. Cody had her second child in 2012. , Cody and Maurio have three children.


title: Diablo Cody

text: Cody is a friend of screenwriters Dana Fox ("What Happens in Vegas", "Couples Retreat") and Lorene Scafaria ("Hustlers") and they often write their screenplays together in order to get advice from one another.


title: Diablo Cody

text: In light of Georgia’s 2019 anti-abortion law, Cody stated that she has regretted writing "Juno", as critics have perceived it as an anti-abortion film.


title: Diablo Cody

text: Cody is a lifelong roller coaster enthusiast and has a tattoo of the Giant Dipper at San Diego’s Belmont Park on her right arm.


title: Tesla Semi

text: The Tesla Semi is a battery electric Class 8 semi-truck by Tesla, Inc. The truck is powered by three motors, and is claimed by Tesla to have approximately three times the power of a typical diesel semi truck, a range of , and operate at an energy use of less than .


title: Tesla Semi

text: Two concept vehicles were unveiled in November 2017. Production was originally planned to begin as early as 2019, with Tesla projecting manufacture of as many as 100,000 trucks per year by 2022. Production began in October 2022, and initial deliveries were made to PepsiCo on December 1, 2022.


title: Tesla Semi

text: The Semi was first mentioned in the Tesla 2016 Master Plan. Tesla said at the time that they had a working prototype that used "a bunch" of Tesla Model 3 electric motors.


title: Tesla Semi

text: A concept prototype of the Semi was unveiled at a press conference on November 16, 2017, where Musk provided additional specifics. He claimed that the electric Semi would cost less to operate than a diesel truck if charged at a Megacharger, which Tesla said in 2017 they could guarantee a price of 7 ¢/kWh (in the United States).


title: Tesla Semi

text: Tesla indicated that the Semi would be equipped with Enhanced Autopilot as standard equipment, offering semi-autonomous capability, and that new technology with active safety controls on the independent motors and wheels would detect and prevent jackknifing. Musk said that the system could eventually allow several units to operate in an autopilot-based convoy, led by a truck with a driver, that would be a cheaper alternative to rail transport. At the time, platooning was legal in only eight U.S. states and all required a human driver in each truck, so changes in legislation would be necessary to achieve that technology capability. The battery packs would be located under the floor of the cab, between the front and driving wheels. Running empty, the long-range Tesla Semi was expected to have a range of .


title: Tesla Semi

text: Tesla projected that the price of production versions for the and range versions would be and respectively. The company stated they would offer a Founder's Series Semi at .


title: Tesla Semi

text: At the Semi and Roadster unveiling event, Musk stated "Production [of the semi] begins in 2019, so if you order now, you get the truck in 2 years." Tesla intends to warrant the drivetrain for 1 million miles.


title: Tesla Semi

text: In 2018, Tesla announced that Semi prototypes were being tested with real cargo, hauling battery packs from Nevada to California.


title: Tesla Semi

text: Company plans to put the semi into production were substantially delayed. At the 2017 unveiling, production was slated to begin in 2019. In June 2019, Tesla projected that production would start by the end of 2020. In January 2020, Musk stated that a lack of battery production capability was one limiting factor for the conservative Semi production timeline, with the company choosing to use battery supply for passenger cars instead.


title: Tesla Semi

text: In January 2021, the company announced that Semi production would be delayed until the end of 2021, as the company hoped to ramp up high-volume production of its tabless 4680 battery cells (previewed in September 2020) to meet the demand for the Semi and other vehicles. In October 2021, Musk announced that the production of the Semi would not start in 2021 and that it could slip into 2023.


title: Tesla Semi

text: In October 2022, Musk announced on Twitter the start of production of the range model that would be delivered in December.


title: Tesla Semi

text: On December 1, 2022, Tesla began customer deliveries at an evening event hosted at the manufacturing facility in Nevada. PepsiCo received the first Semis of their large order for use with Pepsi beverage and Frito-Lay snack food transportation fleets.


title: Tesla Semi

text: The first pre-orders came in the day of the press conference and by mid-January 2018 approximately 450 Semis had been pre-ordered. The original deposit required with an order was $5,000, which was increased to $20,000 after the event in November 2017. In the Q1 2018 Tesla earnings call, Musk said that there were about 2,000 total pre-orders of the Semi.


title: Tesla Semi

text: Tesla Semi is powered by three carbon-fiber wrapped motors, offering three times the power of typical diesel semi trucks, although it consumes only . One motor operates continuously at optimal efficiency, while the other two motors provide additional power for acceleration and hills.


title: Tesla Semi

text: The driver's seat is centered in the cab. The ceiling allows an adult to stand up. Touchscreen displays are set on both sides of the steering wheel, with no other instrument panels.


title: Tesla Semi

text: It includes the same camera set as Tesla's passenger vehicles. Tesla claims that its safety system can prevent jackknifing.


title: Tesla Semi

text: Tesla Semi has a 1,000 volt power train and charging system, an increase from Tesla's standard 400 volt system, but a capability Tesla also intends to extend to the Cybertruck. Charging will be supported at a new generation of Tesla vehicle charging infrastructure called the Tesla Megacharger.


title: Tesla Semi

text: , some industry experts viewed heavy-duty freight as impractical for battery trucks due to cost and weight. A senior VP at Daseke, a large trucking company, said that the limited range affected their likelihood of operating the Semi until the necessary infrastructure was in place. Bill Gates also held similar concerns.


title: Tesla Semi

text: A Bloomberg L.P. report stated that given the battery technology available in November 2017 with the assumption that the technology would be the same when Tesla brought the Semi to market, the company's estimates for charging times, range per charge, and costs could not be achieved with 2017 technology, with other analysts explicitly suggesting that Tesla could be planning on increased battery energy density advances in the next few years to meet its stated goals.


title: Tesla Semi

text: A June 2017 theoretical analysis of arbitrary electric semi trucks, was made by researchers from the Carnegie Mellon College of Engineering, ostensibly in response to Musk's description of Tesla's work on a "a heavy duty, long-range semi truck" at a talk in April 2017. The analysis estimated power needs, loads and ranges for an electric truck, given battery technologies known at that time. The analysis indicated that an electric semi might be feasible for short- or medium-range hauling, but would not be for long-range hauling, as the weight of the batteries required would take up too much of the weight allowed by US law. One estimate for the battery weight, at , was estimated to account for one third of the payload, and would increase the capital cost of the truck to about double that of an equivalent diesel.


title: Tesla Semi

text: Other electric semi trucks in production in the US and Canada as of 2022 include the Volvo VNR Electric, Peterbilt 579 EV, Kenworth T680E, Freightliner eCascadia, and Nikola Tre.


title: Tesla Semi

text: Other companies developing electric trucks, which are not class 8, include Cummins, DAF Trucks, Einride, and Volkswagen..


title: Tesla Semi

text: On November 24, 2022 Renault Trucks (subsidiary of Volvo AB) delivered the first electric trucks to Coca-Cola Europacific Partners in Belgium.


title: Denise Bidot

text: Bidot was born in Miami, Florida. Her mother is of Puerto Rican descent while her father is of Kuwaiti descent. Bidot’s mother was a beauty pageant winner who was aspiring to become a professional model, but had struggled to make it in the business due to her plus-size figure and was failing to lose weight. Bidot had started acting at the age of 12, then started traveling to California at the age of 18 to pursue an acting career. She had faced the same challenges as her mother did with being told to lose weight in order to make it in acting. After giving up on acting, Bidot decided to work behind the scenes as a makeup artist.


title: Denise Bidot

text: While working as a makeup artist, Bidot was discovered by a photographer who had approached her about getting into modelling, to which she agreed. In 2014, Bidot became the first plus-size model to walk the runway for two straight-size brands during New York Fashion Week. Bidot has worked for clients such as Nordstrom, Forever21, Target, Old Navy, Lane Bryant, Levi's, Macy's. Bidot has been featured on several television shows including nuvoTV's "Curvy Girls", HBO's "Habla Women", and Yahoo! En Español web series "Mama vs. Mama". She has also been included on segments on "The Tyra Banks Show" and "The Real". In 2016, Bidot launched a lifestyle movement called "There Is No Wrong Way to Be a Woman". Bidot is one of the featured models in the 2016 documentary film "Straight/Curve". In December 2016, Bidot's picture of her wearing a two piece bathing suit in Lane Bryant's new resort collection ad campaign with the photo unretouched showing her stretch marks went viral within hours. In 2018, Bidot joined Univision’s reality television beauty pageant Nuestra Belleza Latina as a main judge.


title: Denise Bidot

text: Bidot began dating rapper Lil Wayne in June 2020. Bidot also has a daughter named Joselyn Adams (b. 2008) from a previous relationship.


title: Joe Locke (actor)

text: Joseph William Locke (born 24 September 2003) is a Manx actor. He is known for his lead role as Charlie Spring in the Netflix teen series "Heartstopper" (2022), for which he received a nomination for the Children's and Family Emmy Award for Outstanding Lead Performance.


title: Joe Locke (actor)

text: Joseph William Locke was born on 24 September 2003. He grew up in Douglas, Isle of Man. He attended Ballakermeen High School. He told ITV's "This Morning" in April 2022 that he was studying for A-Level exams in politics, history and English.


title: Joe Locke (actor)

text: While in high school, Locke and three fellow students submitted a petition to government officials to investigate the feasibility of welcoming Syrian refugees to the Isle of Man.


title: Joe Locke (actor)

text: He participated in the 2020 National Theatre Connections as well as productions at the Gaiety Theatre and with the Kensington Art Centre's youth group.


title: Joe Locke (actor)

text: In April 2021, it was announced Locke would star as lead character Charlie Spring in his debut television role in the 2022 Netflix coming-of-age series "Heartstopper", an adaptation of the webcomic and graphic novel of the same name by Alice Oseman. He was chosen out of 10,000 other potential actors who were up for the role through an open casting call. While Locke was 17 at the time of the filming, his role has him playing a 14-15 year old student in an English boys' grammar school.


title: Joe Locke (actor)

text: In November 2022, it was announced that Locke had been cast in Marvel Studios' "WandaVision" spin-off television series "" for Disney+.


title: Joe Locke (actor)

text: Locke has spoken about his experiences of being a young gay man from the Isle of Man and their parallels with Charlie's story in the "Heartstopper" series. In August 2022, the Isle of Man's health minister, Lawrie Hooper, announced that the government would change its blanket ban on gay men donating blood after Locke called for the "archaic" rule to be changed in a video message played at the island's annual pride celebration.


title: False Positive (film)

text: False Positive is a 2021 American horror film, directed by John Lee, from a screenplay by Lee and Ilana Glazer. It stars Glazer, Justin Theroux, Pierce Brosnan, and Sophia Bush.


title: False Positive (film)

text: It had its world premiere at the Tribeca Film Festival on June 18, 2021. It was released on June 25, 2021 by Hulu.


title: False Positive (film)

text: Copywriter Lucy Martin lives with her husband Adrian in Manhattan. The couple have been trying to conceive for two years and decide to seek out Dr. John Hindle, Adrian's former teacher and a leading fertility doctor. Lucy becomes pregnant after Dr. Hindle inseminates her, using a technique he invented. During an ultrasound she discovers she is pregnant with triplets: male twins and a female. Hindle suggests a selective reduction; either the twins or the daughter should be terminated to ensure a healthy pregnancy and birth. Adrian and Lucy decide to keep the girl. Lucy joins a group of expecting mothers, where she befriends Corgan, who got pregnant using IVF. Online, Lucy discovers Grace Singleton, a spiritual midwife with a natural approach and develops a fascination with her.


title: False Positive (film)

text: During the reduction, Lucy passes out and hears Adrian and Hindle talk. Later, she bleeds excessively from her uterus, which Hindle dismisses as a common instance. Adrian presents Hindle with an award and Lucy grows wary of him. Lucy finds a safe in Adrian's office and shares with Corgan her growing suspicions that Hindle did something to her unborn daughter and Adrian is aware. After Lucy has further complications, Hindle blames this on antenatal depression and prescribes her medication, which she takes. After having a dream where she sees Hindle and Adrian having sex, Lucy opens Adrian's safe and finds a file on her, including evidence that she is being monitored. Corgan takes the file to show her lawyer husband and suggests that Lucy behave normally until she knows more. Lucy confronts Adrian, admitting she doesn't feel safe with Hindle. Lucy experiences further strange dreams and visions including nearly drowning in a bathful of bloody water.


title: False Positive (film)

text: During her baby shower, Lucy realizes that Corgan knows her real name, despite never having shared it. Corgan gifts her a copy of a first edition of J. M. Barrie's book "Peter Pan and Wendy" and Lucy seems to see Peter Pan's shadow morph into a weird expanding bloodstain on the book cover. Lucy confronts her and Corgan admits that she now consults Hindle too and that she gave the file to Adrian due to her worry about Lucy's mental state. She tells Lucy that Adrian denies he has a safe in his office. Lucy experiences contractions and goes to Grace to give birth, discovering she is giving birth to the male twins instead of the female baby. Before she can birth the second twin, Grace urges them to a hospital after strong bleeding but Adrian takes her to Hindle, who delivers the second baby. Disillusioned and depressed, Lucy talks to Grace but realizes that the image of her as an African-American midwife 'goddess' was unrealistic and elaborated. Grace tells Lucy that she must solve her own problem.


title: False Positive (film)

text: Lucy goes to Hindle's clinic to confront him, where she is shocked to learn Adrian will join Hindle's gynecological practice. Lucy sneaks into a secret room labelled "The Lab" in the clinic, where she finds her removed placenta and reduced female fetus. Hindle reveals it was his sperm used for inseminating Lucy, as he does with all his patients, believing his genes to be superior. He has a refrigerator full of vials of his own sperm which are used to inseminate his female patients and spread his own bloodline further through the world through male births. He attempts to drug Lucy but she kicks him and smashes his head with a mirror, then restrains him to a medical chair, after which she is attacked by a nurse, Dawn. She drugs Dawn and beats Hindle bloody, destroying his refrigerator full of sperm vials and leaving the office with the fetus.


title: False Positive (film)

text: Arriving home, she imagines herself releasing the twins to float out the window (a reference to the "Peter Pan and Wendy" submotif of the narrative). When Adrian comes home, he claims that the deal with Hindle would have been good for them both. Lucy gives him the twins and orders him to leave. She then picks up the female fetus and attempts to breastfeed it, hallucinating that it begins to suckle.


title: False Positive (film)

text: In February 2019, it was announced Ilana Glazer would star in the film, with John Lee producing from a screenplay by himself and Glazer. A24 would produce. In March 2019, Pierce Brosnan, Zainab Jah, Gretchen Mol, Sophia Bush and Josh Hamilton joined the cast of the film.


title: False Positive (film)

text: In December 2020, Hulu acquired U.S. distribution rights to the film. It had its world premiere at the Tribeca Film Festival on June 18, 2021. The film was released on Hulu on June 25, 2021.


title: False Positive (film)

text: "False Positive" holds a 47% approval rating on review aggregator website Rotten Tomatoes based on 73 reviews with a weighted average of 5.50/10. The website's critics consensus reads: "Its classic horror aims exceed its blood-slicked grasp, but "False Positive" works its way sneakily under the skin." On Metacritic, the film holds a rating of 54 out of 100, based on 19 critics, indicating "mixed or average reviews".


title: False Positive (film)

text: "The Hollywood Reporter" gave the film a positive review calling it "a juicy genre entry" while conceding it "might not quite stick the landing." "The A.V. Club" gave the film a B− rating but said "for a movie with this much blood, it doesn't leave much of a stain." "IndieWire" gave the film a D+ and criticized its obvious debts to other films such as "Rosemary's Baby."


title: Random walk

text: In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space.


title: Random walk

text: An elementary example of a random walk is the random walk on the integer number line formula_1 which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term "random walk" was first introduced by Karl Pearson in 1905.


title: Random walk

text: A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In a "simple random walk", the location can only jump to neighboring sites of the lattice, forming a lattice path. In a "simple symmetric random walk" on a locally finite lattice, the probabilities of the location jumping to each one of its immediate neighbors are the same. The best-studied example is the random walk on the "d"-dimensional integer lattice (sometimes called the hypercubic lattice) formula_2.


title: Random walk

text: If the state space is limited to finite dimensions, the random walk model is called a "simple bordered symmetric random walk", and the transition probabilities depend on the location of the state because on margin and corner states the movement is limited.


title: Random walk

text: An elementary example of a random walk is the random walk on the integer number line, formula_3, which starts at 0 and at each step moves +1 or −1 with equal probability.


title: Random walk

text: This walk can be illustrated as follows. A marker is placed at zero on the number line, and a fair coin is flipped. If it lands on heads, the marker is moved one unit to the right. If it lands on tails, the marker is moved one unit to the left. After five flips, the marker could now be on -5, -3, -1, 1, 3, 5. With five flips, three heads and two tails, in any order, it will land on 1. There are 10 ways of landing on 1 (by flipping three heads and two tails), 10 ways of landing on −1 (by flipping three tails and two heads), 5 ways of landing on 3 (by flipping four heads and one tail), 5 ways of landing on −3 (by flipping four tails and one head), 1 way of landing on 5 (by flipping five heads), and 1 way of landing on −5 (by flipping five tails). See the figure below for an illustration of the possible outcomes of 5 flips.


title: Random walk

text: To define this walk formally, take independent random variables formula_4, where each variable is either 1 or −1, with a 50% probability for either value, and set formula_5 and formula_6 The series formula_7 is called the "simple random walk on formula_3". This series (the sum of the sequence of −1s and 1s) gives the net distance walked, if each part of the walk is of length one.


title: Random walk

text: The expectation formula_9 of formula_10 is zero. That is, the mean of all coin flips approaches zero as the number of flips increases. This follows by the finite additivity property of expectation:


title: Random walk

text: A similar calculation, using the independence of the random variables and the fact that formula_12, shows that:


title: Random walk

text: This hints that formula_14, the expected translation distance after "n" steps, should be of the order of formula_15. In fact,


title: Random walk

text: This result shows that diffusion is ineffective for mixing because of the way the square root behaves for large formula_17.


title: Random walk

text: To answer the question of how many times will a random walk cross a boundary line if permitted to continue walking forever, a simple random walk on formula_1 will cross every point an infinite number of times. This result has many names: the "level-crossing phenomenon", "recurrence" or the "gambler's ruin". The reason for the last name is as follows: a gambler with a finite amount of money will eventually lose when playing "a fair game" against a bank with an infinite amount of money. The gambler's money will perform a random walk, and it will reach zero at some point, and the game will be over.


title: Random walk

text: If "a" and "b" are positive integers, then the expected number of steps until a one-dimensional simple random walk starting at 0 first hits "b" or −"a" is "ab". The probability that this walk will hit "b" before −"a" is formula_19, which can be derived from the fact that simple random walk is a martingale. And these expectations and hitting probabilities can be computed in formula_20 in the general one-dimensional random walk Markov chain.


title: Random walk

text: Some of the results mentioned above can be derived from properties of Pascal's triangle. The number of different walks of "n" steps where each step is +1 or −1 is 2. For the simple random walk, each of these walks is equally likely.


title: Random walk

text: In order for "S" to be equal to a number "k" it is necessary and sufficient that the number of +1 in the walk exceeds those of −1 by "k". It follows +1 must appear ("n" + "k")/2 times among "n" steps of a walk, hence the number of walks which satisfy formula_21 equals the number of ways of choosing ("n" + "k")/2 elements from an "n" element set, denoted formula_22. For this to have meaning, it is necessary that "n" + "k" be an even number, which implies "n" and "k" are either both even or both odd. Therefore, the probability that formula_21 is equal to formula_24. By representing entries of Pascal's triangle in terms of factorials and using Stirling's formula, one can obtain good estimates for these probabilities for large values of formula_25.


title: Random walk

text: If space is confined to formula_1+ for brevity, the number of ways in which a random walk will land on any given number having five flips can be shown as {0,5,0,4,0,1}.


title: Random walk

text: This relation with Pascal's triangle is demonstrated for small values of "n". At zero turns, the only possibility will be to remain at zero. However, at one turn, there is one chance of landing on −1 or one chance of landing on 1. At two turns, a marker at 1 could move to 2 or back to zero. A marker at −1, could move to −2 or back to zero. Therefore, there is one chance of landing on −2, two chances of landing on zero, and one chance of landing on 2.


title: Random walk

text: The central limit theorem and the law of the iterated logarithm describe important aspects of the behavior of simple random walks on formula_1. In particular, the former entails that as "n" increases, the probabilities (proportional to the numbers in each row) approach a normal distribution.


title: Random walk

text: As a direct generalization, one can consider random walks on crystal lattices (infinite-fold abelian covering graphs over finite graphs). Actually it is possible to establish the central limit theorem and large deviation theorem in this setting.


title: Random walk

text: A one-dimensional "random walk" can also be looked at as a Markov chain whose state space is given by the integers formula_28 For some number "p" satisfying formula_29, the transition probabilities (the probability "P" of moving from state "i" to state "j") are given by


title: Random walk

text: In higher dimensions, the set of randomly walked points has interesting geometric properties. In fact, one gets a discrete fractal, that is, a set which exhibits stochastic self-similarity on large scales. On small scales, one can observe "jaggedness" resulting from the grid on which the walk is performed. The trajectory of a random walk is the collection of points visited, considered as a set with disregard to "when" the walk arrived at the point. In one dimension, the trajectory is simply all points between the minimum height and the maximum height the walk achieved (both are, on average, on the order of formula_31).


title: Random walk

text: To visualize the two-dimensional case, one can imagine a person walking randomly around a city. The city is effectively infinite and arranged in a square grid of sidewalks. At every intersection, the person randomly chooses one of the four possible routes (including the one originally travelled from). Formally, this is a random walk on the set of all points in the plane with integer coordinates.


title: Random walk

text: To answer the question of the person ever getting back to the original starting point of the walk, this is the 2-dimensional equivalent of the level-crossing problem discussed above. In 1921 George Pólya proved that the person almost surely would in a 2-dimensional random walk, but for 3 dimensions or higher, the probability of returning to the origin decreases as the number of dimensions increases. In 3 dimensions, the probability decreases to roughly 34%. The mathematician Shizuo Kakutani was known to refer to this result with the following quote: "A drunk man will find his way home, but a drunk bird may get lost forever".


title: Random walk

text: Another variation of this question which was also asked by Pólya is: "if two people leave the same starting point, then will they ever meet again?" It can be shown that the difference between their locations (two independent random walks) is also a simple random walk, so they almost surely meet again in a 2-dimensional walk, but for 3 dimensions and higher the probability decreases with the number of the dimensions. Paul Erdős and Samuel James Taylor also showed in 1960 that for dimensions less or equal than 4, two independent random walks starting from any two given points have infinitely many intersections almost surely, but for dimensions higher than 5, they almost surely intersect only finitely often.


title: Random walk

text: The asymptotic function for a two-dimensional random walk as the number of steps increases is given by a Rayleigh distribution. The probability distribution is a function of the radius from the origin and the step length is constant for each step.


title: Random walk

text: A Wiener process is a stochastic process with similar behavior to Brownian motion, the physical phenomenon of a minute particle diffusing in a fluid. (Sometimes the Wiener process is called "Brownian motion", although this is strictly speaking a confusion of a model with the phenomenon being modeled.)


title: Random walk

text: A Wiener process is the scaling limit of random walk in dimension 1. This means that if there is a random walk with very small steps, there is an approximation to a Wiener process (and, less accurately, to Brownian motion). To be more precise, if the step size is ε, one needs to take a walk of length "L"/ε to approximate a Wiener length of "L". As the step size tends to 0 (and the number of steps increases proportionally), random walk converges to a Wiener process in an appropriate sense. Formally, if "B" is the space of all paths of length "L" with the maximum topology, and if "M" is the space of measure over "B" with the norm topology, then the convergence is in the space "M". Similarly, a Wiener process in several dimensions is the scaling limit of random walk in the same number of dimensions.


title: Random walk

text: A random walk is a discrete fractal (a function with integer dimensions; 1, 2, ...), but a Wiener process trajectory is a true fractal, and there is a connection between the two. For example, take a random walk until it hits a circle of radius "r" times the step length. The average number of steps it performs is "r". This fact is the "discrete version" of the fact that a Wiener process walk is a fractal of Hausdorff dimension 2.


title: Random walk

text: In two dimensions, the average number of points the same random walk has on the "boundary" of its trajectory is "r". This corresponds to the fact that the boundary of the trajectory of a Wiener process is a fractal of dimension 4/3, a fact predicted by Mandelbrot using simulations but proved only in 2000


title: Random walk

text: A Wiener process enjoys many symmetries a random walk does not. For example, a Wiener process walk is invariant to rotations, but the random walk is not, since the underlying grid is not (random walk is invariant to rotations by 90 degrees, but Wiener processes are invariant to rotations by, for example, 17 degrees too). This means that in many cases, problems on a random walk are easier to solve by translating them to a Wiener process, solving the problem there, and then translating back. On the other hand, some problems are easier to solve with random walks due to its discrete nature.


title: Random walk

text: Random walk and Wiener process can be "coupled", namely manifested on the same probability space in a dependent way that forces them to be quite close. The simplest such coupling is the Skorokhod embedding, but there exist more precise couplings, such as Komlós–Major–Tusnády approximation theorem.


title: Random walk

text: The convergence of a random walk toward the Wiener process is controlled by the central limit theorem, and by Donsker's theorem. For a particle in a known fixed position at "t" = 0, the central limit theorem tells us that after a large number of independent steps in the random walk, the walker's position is distributed according to a normal distribution of total variance:


title: Random walk

text: where "t" is the time elapsed since the start of the random walk, formula_34 is the size of a step of the random walk, and formula_35 is the time elapsed between two successive steps.


title: Random walk

text: This corresponds to the Green's function of the diffusion equation that controls the Wiener process, which suggests that, after a large number of steps, the random walk converges toward a Wiener process.


title: Random walk

text: By equalizing this quantity with the variance associated to the position of the random walker, one obtains the equivalent diffusion coefficient to be considered for the asymptotic Wiener process toward which the random walk converges after a large number of steps:


title: Random walk

text: The two expressions of the variance above correspond to the distribution associated to the vector formula_38 that links the two ends of the random walk, in 3D. The variance associated to each component formula_39, formula_40 or formula_41 is only one third of this value (still in 3D).


title: Random walk

text: A random walk having a step size that varies according to a normal distribution is used as a model for real-world time series data such as financial markets. The Black–Scholes formula for modeling option prices, for example, uses a Gaussian random walk as an underlying assumption.


title: Random walk

text: Here, the step size is the inverse cumulative normal distribution formula_44 where 0 ≤ "z" ≤ 1 is a uniformly distributed random number, and μ and σ are the mean and standard deviations of the normal distribution, respectively.


title: Random walk

text: If μ is nonzero, the random walk will vary about a linear trend. If v is the starting value of the random walk, the expected value after "n" steps will be v + "n"μ.


title: Random walk

text: For the special case where μ is equal to zero, after "n" steps, the translation distance's probability distribution is given by "N"(0, "n"σ), where "N"() is the notation for the normal distribution, "n" is the number of steps, and σ is from the inverse cumulative normal distribution as given above.


title: Random walk

text: Proof: The Gaussian random walk can be thought of as the sum of a sequence of independent and identically distributed random variables, X from the inverse cumulative normal distribution with mean equal zero and σ of the original inverse cumulative normal distribution:


title: Random walk

text: but we have the distribution for the sum of two independent normally distributed random variables, , is given by


title: Random walk

text: For steps distributed according to any distribution with zero mean and a finite variance (not necessarily just a normal distribution), the root mean square translation distance after "n" steps is (see Bienaymé's identity)


title: Random walk

text: But for the Gaussian random walk, this is just the standard deviation of the translation distance's distribution after "n" steps. Hence, if μ is equal to zero, and since the root mean square(RMS) translation distance is one standard deviation, there is 68.27% probability that the RMS translation distance after "n" steps will fall between formula_50. Likewise, there is 50% probability that the translation distance after "n" steps will fall between formula_51.


title: Random walk

text: The number of distinct sites visited by a single random walker formula_52 has been studied extensively for square and cubic lattices and for fractals. This quantity is useful for the analysis of problems of trapping and kinetic reactions. It is also related to the vibrational density of states, diffusion reactions processes


title: Random walk

text: The information rate of a Gaussian random walk with respect to the squared error distance, i.e. its quadratic rate distortion function, is given parametrically by


title: Random walk

text: where formula_55. Therefore, it is impossible to encode formula_56 using a binary code of less than formula_57 bits and recover it with expected mean squared error less than formula_58. On the other hand, for any formula_59, there exists an formula_60 large enough and a binary code of no more than formula_61 distinct elements such that the expected mean squared error in recovering formula_56 from this code is at most formula_63.


title: Random walk

text: As mentioned the range of natural phenomena which have been subject to attempts at description by some flavour of random walks is considerable, particularly in physics and chemistry, materials science, and biology. The following are some specific applications of random walks:


title: Random walk

text: A number of types of stochastic processes have been considered that are similar to the pure random walks but where the simple structure is allowed to be more generalized. The "pure" structure can be characterized by the steps being defined by independent and identically distributed random variables. Random walks can take place on a variety of spaces, such as graphs, the integers, the real line, the plane or higher-dimensional vector spaces, on curved surfaces or higher-dimensional Riemannian manifolds, and on groups. It is also possible to define random walks which take their steps at random times, and in that case, the position has to be defined for all times . Specific cases or limits of random walks include the Lévy flight and diffusion models such as Brownian motion.


title: Random walk

text: A random walk of length "k" on a possibly infinite graph "G" with a root "0" is a stochastic process with random variables formula_64 such that formula_65 and


title: Random walk

text: Then the number formula_68 is the probability that a random walk of length "k" starting at "v" ends at "w".


title: Random walk

text: In particular, if "G" is a graph with root "0", formula_69 is the probability that a formula_70-step random walk returns to "0".


title: Random walk

text: Building on the analogy from the earlier section on higher dimensions, assume now that our city is no longer a perfect square grid. When our person reaches a certain junction, he picks between the variously available roads with equal probability. Thus, if the junction has seven exits the person will go to each one with probability one-seventh. This is a random walk on a graph. Will our person reach his home? It turns out that under rather mild conditions, the answer is still yes, but depending on the graph, the answer to the variant question 'Will two persons meet again?' may not be that they meet infinitely often almost surely.


title: Random walk

text: An example of a case where the person will reach his home almost surely is when the lengths of all the blocks are between "a" and "b" (where "a" and "b" are any two finite positive numbers). Notice that we do not assume that the graph is planar, i.e. the city may contain tunnels and bridges. One way to prove this result is using the connection to electrical networks. Take a map of the city and place a one ohm resistor on every block. Now measure the "resistance between a point and infinity". In other words, choose some number "R" and take all the points in the electrical network with distance bigger than "R" from our point and wire them together. This is now a finite electrical network, and we may measure the resistance from our point to the wired points. Take "R" to infinity. The limit is called the "resistance between a point and infinity". It turns out that the following is true (an elementary proof can be found in the book by Doyle and Snell):


title: Random walk

text: Theorem: "a graph is transient if and only if the resistance between a point and infinity is finite. It is not important which point is chosen if the graph is connected."


title: Random walk

text: In other words, in a transient system, one only needs to overcome a finite resistance to get to infinity from any point. In a recurrent system, the resistance from any point to infinity is infinite.


title: Random walk

text: This characterization of transience and recurrence is very useful, and specifically it allows us to analyze the case of a city drawn in the plane with the distances bounded.


title: Random walk

text: A random walk on a graph is a very special case of a Markov chain. Unlike a general Markov chain, random walk on a graph enjoys a property called "time symmetry" or "reversibility". Roughly speaking, this property, also called the principle of detailed balance, means that the probabilities to traverse a given path in one direction or the other have a very simple connection between them (if the graph is regular, they are just equal). This property has important consequences.


title: Random walk

text: Starting in the 1980s, much research has gone into connecting properties of the graph to random walks. In addition to the electrical network connection described above, there are important connections to isoperimetric inequalities, see more here, functional inequalities such as Sobolev and Poincaré inequalities and properties of solutions of Laplace's equation. A significant portion of this research was focused on Cayley graphs of finitely generated groups. In many cases these discrete results carry over to, or are derived from manifolds and Lie groups.


title: Random walk

text: In the context of random graphs, particularly that of the Erdős–Rényi model, analytical results to some properties of random walkers have been obtained. These include the distribution of first and last hitting times of the walker, where the first hitting time is given by the first time the walker steps into a previously visited site of the graph, and the last hitting time corresponds the first time the walker cannot perform an additional move without revisiting a previously visited site.


title: Random walk

text: A good reference for random walk on graphs is the online book by Aldous and Fill. For groups see the book of Woess.


title: Random walk

text: If the transition kernel formula_71 is itself random (based on an environment formula_72) then the random walk is called a "random walk in random environment". When the law of the random walk includes the randomness of formula_72, the law is called the annealed law; on the other hand, if formula_72 is seen as fixed, the law is called a quenched law. See the book of Hughes, the book of Revesz, or the lecture notes of Zeitouni.


title: Random walk

text: We can think about choosing every possible edge with the same probability as maximizing uncertainty (entropy) locally. We could also do it globally – in maximal entropy random walk (MERW) we want all paths to be equally probable, or in other words: for every two vertexes, each path of given length is equally probable. This random walk has much stronger localization properties.


title: Random walk

text: There are a number of interesting models of random paths in which each step depends on the past in a complicated manner. All are more complex for solving analytically than the usual random walk; still, the behavior of any model of a random walker is obtainable using computers. Examples include:


title: Random walk

text: The self-avoiding walk of length "n" on formula_75 is the random "n"-step path which starts at the origin, makes transitions only between adjacent sites in formula_75, never revisit a site, and is chosen uniformly among all such paths. In two dimensions, due to self-trapping, a typical self-avoiding walk is very short, while in higher dimension it grows beyond all bounds.


title: Random walk

text: Random walks where the direction of movement at one time is correlated with the direction of movement at the next time. It is used to model animal movements.


title: Trusted Platform Module

text: Trusted Platform Module (TPM, also known as ISO/IEC 11889) is an international standard for a secure cryptoprocessor, a dedicated microcontroller designed to secure hardware through integrated cryptographic keys. The term can also refer to a chip conforming to the standard.


title: Trusted Platform Module

text: TPM is used for digital rights management (DRM), Windows Defender, Windows Domain logon, protection and enforcement of software licenses, and prevention of cheating in online games.


title: Trusted Platform Module

text: One of Windows 11's system requirements is TPM 2.0. Microsoft has stated that this is to help increase security against firmware and ransomware attacks.


title: Trusted Platform Module

text: Trusted Platform Module (TPM) was conceived by a computer industry consortium called Trusted Computing Group (TCG). It evolved into "TPM Main Specification Version 1.2" which was standardized by International Organization for Standardization (ISO) and International Electrotechnical Commission (IEC) in 2009 as ISO/IEC 11889:2009. "TPM Main Specification Version 1.2" was finalized on March 3, 2011, completing its revision.


title: Trusted Platform Module

text: On April 9, 2014 the Trusted Computing Group announced a major upgrade to their specification entitled "TPM Library Specification 2.0". The group continues work on the standard incorporating errata, algorithmic additions and new commands, with its most recent edition published as 2.0 in November 2019. This version became ISO/IEC 11889:2015.


title: Trusted Platform Module

text: When a new revision is released it is divided into multiple parts by the Trusted Computing Group. Each part consists of a document that makes up the whole of the new TPM specification.


title: Trusted Platform Module

text: Computer programs can use a TPM to authenticate hardware devices, since each TPM chip has a unique and secret Endorsement Key (EK) burned in as it is produced. Security embedded in hardware provides more protection than a software-only solution. Its use is restricted in some countries.


title: Trusted Platform Module

text: The primary scope of TPM is to ensure the integrity of a platform. In this context, "integrity" means "behave as intended", and a "platform" is any computer device regardless of its operating system. This is to ensure that the boot process starts from a trusted combination of hardware and software, and continues until the operating system has fully booted and applications are running.


title: Trusted Platform Module

text: For example, Unified Extensible Firmware Interface (UEFI) can use TPM to form a root of trust: The TPM contains several Platform Configuration Registers (PCRs) that allow secure storage and reporting of security-relevant metrics. These metrics can be used to detect changes to previous configurations and decide how to proceed. Examples of such use can be found in Linux Unified Key Setup (LUKS), BitLocker and PrivateCore vCage memory encryption. (See below.)


title: Trusted Platform Module

text: Another example of platform integrity via TPM is in the use of Microsoft Office 365 licensing and Outlook Exchange.


title: Trusted Platform Module

text: An example of TPM use for platform integrity is the Trusted Execution Technology (TXT), which creates a chain of trust. It could remotely attest that a computer is using the specified hardware and software.


title: Trusted Platform Module

text: Full disk encryption utilities, such as dm-crypt and BitLocker, can use this technology to protect the keys used to encrypt the computer's storage devices and provide integrity authentication for a trusted boot pathway that includes firmware and boot sector.


title: Trusted Platform Module

text: Other uses exist, some of which give rise to privacy concerns. The "physical presence" feature of TPM addresses some of these concerns by requiring BIOS-level confirmation for operations such as activating, deactivating, clearing or changing ownership of TPM by someone who is physically present at the console of the machine.


title: Trusted Platform Module

text: The United States Department of Defense (DoD) specifies that "new computer assets (e.g., server, desktop, laptop, thin client, tablet, smartphone, personal digital assistant, mobile phone) procured to support DoD will include a TPM version 1.2 or higher where required by Defense Information Systems Agency (DISA) Security Technical Implementation Guides (STIGs) and where such technology is available." DoD anticipates that TPM is to be used for device identification, authentication, encryption, and device integrity verification.


title: Trusted Platform Module

text: In 2006, new laptops began being sold with a built-in TPM chip. In the future, this concept could be co-located on an existing motherboard chip in computers, or any other device where the TPM facilities could be employed, such as a cellphone. On a PC, either the LPC bus or the SPI bus is used to connect to the TPM chip.


title: Trusted Platform Module

text: The Trusted Computing Group (TCG) has certified TPM chips manufactured by Infineon Technologies, Nuvoton, and STMicroelectronics, having assigned TPM vendor IDs to Advanced Micro Devices, Atmel, Broadcom, IBM, Infineon, Intel, Lenovo, National Semiconductor, Nationz Technologies, Nuvoton, Qualcomm, Rockchip, Standard Microsystems Corporation, STMicroelectronics, Samsung, Sinosun, Texas Instruments, and Winbond.


title: Trusted Platform Module

text: There are five different types of TPM 2.0 implementations (listed in order from most to least secure):


title: Trusted Platform Module

text: The official TCG reference implementation of the TPM 2.0 Specification has been developed by Microsoft. It is licensed under BSD License and the source code is available on GitHub.


title: Trusted Platform Module

text: In 2018, Intel open-sourced its Trusted Platform Module 2.0 (TPM2) software stack with support for Linux and Microsoft Windows. The source code is hosted on GitHub and licensed under BSD License.


title: Trusted Platform Module

text: Infineon funded the development of an open source TPM middleware that complies with the Software Stack (TSS) Enhanced System API (ESAPI) specification of the TCG. It was developed by Fraunhofer Institute for Secure Information Technology (SIT).


title: Trusted Platform Module

text: IBM's Software TPM 2.0 is an implementation of the TCG TPM 2.0 specification. It is based on the TPM specification Parts 3 and 4 and source code donated by Microsoft. It contains additional files to complete the implementation. The source code is hosted on SourceForge and GitHub and licensed under BSD License.


title: Trusted Platform Module

text: In 2022, AMD announced that under certain circumstances their fTPM implementation causes performance problems. A fix is available in form of a BIOS-Update.


title: Trusted Platform Module

text: While TPM 2.0 addresses many of the same use cases and has similar features, the details are different. TPM 2.0 is not backward compatible with TPM 1.2.


title: Trusted Platform Module

text: The TPM 2.0 policy authorization includes the 1.2 HMAC, locality, physical presence, and PCR. It adds authorization based on an asymmetric digital signature, indirection to another authorization secret, counters and time limits, NVRAM values, a particular command or command parameters, and physical presence. It permits the ANDing and ORing of these authorization primitives to construct complex authorization policies.


title: Trusted Platform Module

text: TCG has faced resistance to the deployment of this technology in some areas, where some authors see possible uses not specifically related to Trusted Computing, which may raise privacy concerns. The concerns include the abuse of remote validation of software (where the manufacturerand not the user who owns the computer systemdecides what software is allowed to run) and possible ways to follow actions taken by the user being recorded in a database, in a manner that is completely undetectable to the user.


title: Trusted Platform Module

text: The TrueCrypt disk encryption utility, as well as its derivative VeraCrypt, do not support TPM. The original TrueCrypt developers were of the opinion that the exclusive purpose of the TPM is "to protect against attacks that require the attacker to have administrator privileges, or physical access to the computer". The attacker who has physical or administrative access to a computer can circumvent TPM, e.g., by installing a hardware keystroke logger, by resetting TPM, or by capturing memory contents and retrieving TPM-issued keys. The condemning text goes so far as to claim that TPM is entirely redundant. The VeraCrypt publisher has reproduced the original allegation with no changes other than replacing "TrueCrypt" with "VeraCrypt". The author is right that, after achieving either unrestricted physical access or administrative privileges, it is only a matter of time before other security measures in place are bypassed. However, stopping an attacker in possession of administrative privileges has never been one of the goals of TPM (see for details), and TPM can stop some physical tampering.


title: Trusted Platform Module

text: In 2015, Richard Stallman suggested to replace the term "Trusted computing" with the term "Treacherous computing" due to the danger that the computer can be made to systematically disobey its owner if the cryptographical keys are kept secret from them. He also considers that TPMs available for PCs are not currently dangerous and that there is no reason not to include one in a computer or support it in software due to failed attempts from the industry to use that technology for DRM.


title: Trusted Platform Module

text: In 2010, Christopher Tarnovsky presented an attack against TPMs at Black Hat Briefings, where he claimed to be able to extract secrets from a single TPM. He was able to do this after 6 months of work by inserting a probe and spying on an internal bus for the Infineon SLE 66 CL PC.


title: Trusted Platform Module

text: In 2015, as part of the Snowden revelations, it was revealed that in 2010 a US CIA team claimed at an internal conference to have carried out a differential power analysis attack against TPMs that was able to extract secrets.


title: Trusted Platform Module

text: In 2018, a design flaw in the TPM 2.0 specification for the static root of trust for measurement (SRTM) was reported (). It allows an adversary to reset and forge platform configuration registers which are designed to securely hold measurements of software that are used for bootstrapping a computer. Fixing it requires hardware-specific firmware patches. An attacker abuses power interrupts and TPM state restores to trick TPM into thinking that it is running on non-tampered components.


title: Trusted Platform Module

text: Main Trusted Boot (tboot) distributions before November 2017 are affected by a dynamic root of trust for measurement (DRTM) attack , which affects computers running on Intel's Trusted eXecution Technology (TXT) for the boot-up routine.


title: Trusted Platform Module

text: In case of physical access, computers with TPM are vulnerable to cold boot attacks as long as the system is on or can be booted without a passphrase from shutdown or hibernation, which is the default setup for Windows computers with BitLocker full disk encryption.


title: Trusted Platform Module

text: In 2021, the Dolos Group showed an attack on a discrete TPM, where the TPM chip itself had some tamper resistance, but the other endpoints of its communication bus did not. They read a full-disk-encryption key as it was transmitted across the motherboard, and used it to decrypt the laptop's SSD.


title: Trusted Platform Module

text: In October 2017, it was reported that a code library developed by Infineon, which had been in widespread use in its TPMs, contained a vulnerability, known as ROCA, which generated weak RSA key pairs that allowed private keys to be inferred from public keys. As a result, all systems depending upon the privacy of such weak keys are vulnerable to compromise, such as identity theft or spoofing.


title: Trusted Platform Module

text: Cryptosystems that store encryption keys directly in the TPM without blinding could be at particular risk to these types of attacks, as passwords and other factors would be meaningless if the attacks can extract encryption secrets.


title: Trusted Platform Module

text: There are also hybrid types; for example, TPM can be integrated into an Ethernet controller, thus eliminating the need for a separate motherboard component.


title: Trusted Platform Module

text: Field upgrade is the TCG term for updating the TPM firmware. The update can be between TPM 1.2 and TPM 2.0, or between firmware versions. Some vendors limit the number of transitions between 1.2 and 2.0, and some restrict rollback to previous versions. Platform OEMs such as HP supply an upgrade tool.


title: Trusted Platform Module

text: Since July 28, 2016, all new Microsoft device models, lines, or series (or updating the hardware configuration of an existing model, line, or series with a major update, such as CPU, graphic cards) implement, and enable by default TPM 2.0.


title: Trusted Platform Module

text: While TPM 1.2 parts are discrete silicon components, which are typically soldered on the motherboard, TPM 2.0 is available as a discrete (dTPM) silicon component in a single semiconductor package, an integrated component incorporated in one or more semiconductor packages - alongside other logic units in the same package(s), and as a firmware (fTPM) based component running in a trusted execution environment (TEE) on a general purpose System-on-a-chip (SoC).


title: Trusted Platform Module

text: TPM endorsement keys (EKs) are asymmetric key pairs unique to each TPM. They use the RSA and ECC algorithms. The TPM manufacturer usually provisions endorsement key certificates in TPM non-volatile memory. The certificates assert that the TPM is authentic. Starting with TPM 2.0, the certificates are in X.509 DER format.


title: Trusted Platform Module

text: These manufacturers typically provide their certificate authority root (and sometimes intermediate) certificates on their web sites.


title: Trusted Platform Module

text: To utilize a TPM, the user needs a software library that communicates with the TPM and provides a friendlier API than the raw TPM communication. Currently, there are several such open-source TPM 2.0 libraries. Some of them also support TPM 1.2, but mostly TPM 1.2 chips are now deprecated and modern development is focused on TPM 2.0.


title: Trusted Platform Module

text: Typically, a TPM library provides an API with one-to-one mappings to TPM commands. The TCG specification calls this layer the System API(SAPI). This way the user has more control over the TPM operations, however the complexity is high. To hide some of the complexity most libraries also offer simpler ways to invoke complex TPM operations. The TCG specification call these two layers Enhanced System API(ESAPI) and Feature API(FAPI).


title: Trusted Platform Module

text: There is currently only one stack that follows the TCG specification. All the other available open-source TPM libraries use their own form of richer API.


title: Trusted Platform Module

text: (*) There is a separate project called "CHARRA" by Fraunhofer that uses the tpm2-tss library for Remote Attestation. The other stacks have accompanying attestation servers or directly include examples for attestation. IBM offer their open-source Remote Attestation Server called "IBM ACS" on SourceForge and Google have "Go-Attestation" available on GitHub, while "wolfTPM" offers time and local attestation examples directly in its open-source code, also on GitHub.


title: Trusted Platform Module

text: (**) There is an application note about an example project for the AURIX 32-bit SoC using the tpm2-tss library.


title: Trusted Platform Module

text: These TPM libraries are sometimes also called TPM stacks, because they provide the interface for the developer or user to interact with the TPM. As seen from the table, the TPM stacks abstract the operating system and transport layer, so the user could migrate one application between platforms. For example, by using TPM stack API the user would interact the same way with a TPM, regardless if the physical chip is connected over SPI, I2C or LPC interface to the Host system.


title: Consumer

text: A consumer is a person or a group who intends to order, or uses purchased goods, products, or services primarily for personal, social, family, household and similar needs, who is not directly related to entrepreneurial or business activities. The term most commonly refers to a person who purchases goods and services for personal use.


title: Consumer

text: “Consumers, by definition, include us all," said President John F. Kennedy, offering his definition to the United States Congress on March 15, 1962. This speech became the basis for the creation of World Consumer Rights Day, now celebrated on March 15. In his speech : John Fitzgerald Kennedy outlined the integral responsibility to consumers from their respective governments to help exercise consumers' rights, including:


title: Consumer

text: In an economy, a consumer buys goods or services primarily for consumption and not for resale or for commercial purposes. Consumers pay some amount of money (or equivalent) for goods or services.) then consume (use up). As such, consumers play a vital role in the economic system of a capitalist system


title: Consumer

text: Without consumer demand, producers would lack one of the key motivations to produce: to sell to consumers. The consumer also forms one end of the chain of distribution.


title: Consumer

text: Recently in marketing, instead of marketers generating broad demographic profiles and Fisio-graphic profiles of market segments, marketers have started to engage in personalized marketing, permission marketing, and mass customization to target potential consumers.


title: Consumer

text: Largely due to the rise of the Internet, consumers are shifting more and more towards becoming prosumers, consumers who are also producers (often of information and media on the social web) - they influence the products created (e.g. by customization, crowdfunding or publishing their preferences), actively participate in the production process, or use interactive products.


title: Consumer

text: The law primarily uses a notion of the consumer in relation to consumer protection laws, and the definition of consumer is often restricted to living persons (not corporations or businesses) and excludes commercial users. A typical legal rationale for protecting the consumer is based on the notion of policing market failures and inefficiencies, such as inequalities of bargaining power between a consumer and a business. As all potential voters are also consumers, consumer protection has a clear political significance.


title: Consumer

text: Concern over the interests of consumers has spawned consumer activism, where organized activists do research, education and advocacy to improve the offer of products and services. Consumer education has been incorporated into some school curricula. There are also various non-profit publications, such as "Which?", "Consumer Reports" and "Choice magazine", dedicated to assist in consumer education and decision making.


title: Consumer

text: In India, the Consumer Protection Act 1986 differentiates the consumption of a commodity or service for personal use or to earn a livelihood. Only consumers are protected per this act and any person, entity or organization purchasing a commodity for commercial reasons are exempted from any benefits of this act.


title: David Patrick Kelly

text: David Patrick Kelly (born January 23, 1951) is an American actor, musician and lyricist who has appeared in numerous films and television series. He is best known for his role as the main antagonist, Luther, in the cult film "The Warriors" (1979). Kelly is also known for his collaborations with Spike Lee, in the films "Malcolm X" (1992), "Crooklyn" (1994), and "Chi-Raq" (2015), and with David Lynch, appearing in "Wild at Heart" (1990) as well as "Twin Peaks" (1990–91) and its 2017 revival.


title: David Patrick Kelly

text: Kelly's other credits include roles in "48 Hrs." (1982), "Commando" (1985), "The Crow" (1994), "The Funeral" and "Last Man Standing" (both 1996), "The Longest Yard" (2005), as President Harry S. Truman in "Flags of Our Fathers" (2006), and a recurring role in "The Blacklist" (2015).


title: David Patrick Kelly

text: Kelly was born in Detroit, Michigan to Margaret Elizabeth (Murphy) and Robert Corby Kelly, an accountant. His father received a Bronze Star Medal for service during the Battle of the Bulge in World War II. His grandfather, Daniel Murphy, was from Lisnashearshane, Duhallow, County Cork, Ireland. His great-grand-uncle was Father William Corby, chaplain of the Irish Brigade at Gettysburg. As detailed in Corby's book, "Memoir of Chaplain Life: 3 Years With the Irish Brigade", Father Corby eventually became president of the University of Notre Dame.


title: David Patrick Kelly

text: Kelly was given a mandolin on Saint Patrick's Day 1964 by his mother and considers that to have been the greatest influence on his artistic life.