title: Close Encounters of the Third Kind

text: At a rural home, three-year-old Barry Guiler wakes to find his toys operating on their own. He starts to follow something outside, forcing his mother, Jillian, to chase after him. Large-scale power outages begin rolling through the area, forcing electrician Roy Neary to investigate. While he gets his bearings, Roy experiences a close encounter with a UFO, and when it flies over his truck, it lightly burns the side of his face with its lights. The UFO takes off with three others in the sky, as Roy and three police cars give chase. The spacecraft fly off into the night sky but the metaphysical experience leaves Roy mesmerized. He becomes fascinated by UFOs to the dismay of his wife, Ronnie, and begins obsessing over subliminal images of a mountain-like shape, often making models of it. Jillian meanwhile also becomes obsessed, sketching the unique mountain image. Soon after, she is terrorized in her home by a UFO which descends from the clouds. She fights off violent attempts by the UFO and unseen beings to enter the home, but in the chaos, Barry is abducted.


title: Close Encounters of the Third Kind

text: Lacombe and Laughlin—along with a group of United Nations experts—continue to investigate increasing UFO activity and strange, related occurrences. Witnesses in Dharamsala, Northern India report that the UFOs make distinctive sounds: a five-tone musical phrase in a major scale. Scientists broadcast the phrase to outer space, but are mystified by the response: a seemingly meaningless series of numbers (104 44 30 40 36 10) repeated over and over until Laughlin, with his background in cartography, recognizes it as a set of geographical coordinates, which point to Devils Tower near Moorcroft, Wyoming. Lacombe and the U.S. military converge on Wyoming. The United States Army evacuates the area, planting false reports in the media that a train wreck has spilled a toxic nerve gas, all the while preparing a secret landing zone for the UFOs and their occupants.


title: Close Encounters of the Third Kind

text: Meanwhile, Roy becomes increasingly erratic and causes Ronnie to abandon him, taking their three children with her. When a news program about the train wreck near Devils Tower airs on television, Roy and Jillian see the same broadcast, recognizing the same mountain they have been seeing. They, along with other travelers experiencing the same visions, set out for Devils Tower in spite of the public warnings about nerve gas.


title: Close Encounters of the Third Kind

text: While most of the travelers are apprehended by the Army, Roy and Jillian persist and make it to the site just as UFOs appear in the night sky. The government specialists at the site begin to communicate with the UFOs, that gradually appear by the dozens, by use of light and sound on a large electrical billboard. Following this, an enormous mothership lands at the site, releasing the missing World War II pilots and "Cotopaxi" sailors, as well as over a dozen other abductees from long-missing adults to children (and even a few animals), all from different eras and all of whom have strangely not aged since their abductions. Barry also returns and reunites with a relieved Jillian. The government officials decide to include Roy in a group of people whom they had selected to be potential visitors to the mothership, hastily preparing him.


title: Close Encounters of the Third Kind

text: As the extraterrestrials finally emerge from the mothership, they select Roy to join them on their travels. As Roy enters the mothership, one of the extraterrestrials pauses for a few moments with the humans. Lacombe uses Curwen hand signs that correspond to the five-note extraterrestrial tonal phrase. The extraterrestrial replies with the same gestures, smiles, and returns to its ship, which ascends into space.


title: Close Encounters of the Third Kind

text: The film's origins can be traced to director Steven Spielberg's childhood, when he and his father watched a meteor shower in New Jersey. At age 18, Spielberg completed the full-length science fiction film "Firelight". Many scenes from "Firelight" were incorporated in "Close Encounters" on a shot-for-shot basis. In 1970 he wrote a short story entitled "Experiences" about a lovers' lane in a Midwestern farming community and the "light show" a group of teenagers see in the night sky. In late 1973, after completing work on "The Sugarland Express", Spielberg developed a deal with Columbia Pictures for a science-fiction film. 20th Century Fox had previously turned down the offer. Julia and Michael Phillips signed on as producers.


title: Close Encounters of the Third Kind

text: Spielberg first considered doing a documentary or low-budget feature film about people who believed in UFOs. He decided "a film that depended on state-of-the-art technology couldn't be made for $2.5 million." Borrowing a phrase from the ending of "The Thing from Another World", he retitled the film "Watch the Skies", rewriting the premise concerning Project Blue Book and pitching the concept to Willard Huyck and Gloria Katz. Katz remembered, "It had flying saucers from outer space landing on Robertson Boulevard [in West Hollywood, California]. I go, Steve, that's the worst idea I ever heard." Spielberg brought Paul Schrader to write the script in December 1973 with principal photography to begin in late 1974. To discuss the script, Spielberg visited the home where Schrader lived with his brother Leonard. However, Spielberg started work on "Jaws" in 1974, pushing "Watch the Skies" back.


title: Close Encounters of the Third Kind

text: With the financial and critical success of "Jaws", Spielberg was able to negotiate a vast amount of creative control from Columbia, including the right to make the film any way he wanted. Schrader turned in his script, which Spielberg called "one of the most embarrassing screenplays ever professionally turned in to a major film studio or director" and "a terribly guilt-ridden story not about UFOs at all." Titled "Kingdom Come", the script's protagonist was a 45-year-old Air Force officer named Paul Van Owen who worked with Project Blue Book. "[His] job for the government is to ridicule and debunk flying saucers." Schrader continued: "One day he has an encounter. He goes to the government, threatening to blow the lid off to the public. Instead, he and the government spend 15 years trying to make contact."


title: Close Encounters of the Third Kind

text: Spielberg and Schrader experienced creative differences, hiring John Hill to rewrite. At one point the main character was a police officer. Spielberg "[found] it hard to identify with men in uniform. I wanted to have Mr. Everyday Regular Fella." Spielberg rejected the Schrader/Hill script during post-production on "Jaws", reflecting that "they wanted to make it like a James Bond adventure".


title: Close Encounters of the Third Kind

text: David Giler performed a rewrite; Hal Barwood and Matthew Robbins, friends of Spielberg, suggested the plot device of a kidnapped child. Spielberg then began to write the script. The song "When You Wish upon a Star" from "Pinocchio" influenced Spielberg's writing style. "I hung my story on the mood the song created, the way it affected me personally." During pre-production, the title was changed from "Kingdom Come" to "Close Encounters of the Third Kind".


title: Close Encounters of the Third Kind

text: J. Allen Hynek, who worked with the United States Air Force on Project Blue Book, was hired as a scientific consultant. Hynek felt that "even though the film is fiction, it's based for the most part on the known facts of the UFO mystery, and it certainly catches the flavor of the phenomenon. Spielberg was under enormous pressure to make another blockbuster after "Jaws", but he decided to make a UFO film. He put his career on the line." USAF and NASA declined to cooperate on the film. In fact, NASA reportedly sent a twenty-page letter to Spielberg, telling him that releasing the film was dangerous. In an interview, he said: "I really found my faith when I heard that the Government was opposed to the film. If NASA took the time to write me a 20-page letter, then I knew there must be something happening."


title: Close Encounters of the Third Kind

text: Early in pre-production, Spielberg hired film title designer Dan Perri to design a logotype for "Close Encounters". Perri, who had previously worked on "The Exorcist" (1973) and "Taxi Driver" (1976), produced a logotype in Handel Gothic typeface, with only a script to work from. Delighted with the result, Spielberg applied the logo to all production stationery and crew shirts. Unusual in filmmaking, Spielberg carried enough influence to maintain creative control over the film's entire branding and asked Perri to design the advertising campaign and title sequence for "Close Encounters" based on his logo.


title: Close Encounters of the Third Kind

text: Perri later went on to design titles for many other major Hollywood pictures, including "Star Wars" (1977), "Raging Bull" (1980), and "Airplane!" (1980).


title: Close Encounters of the Third Kind

text: Principal photography began on May 16, 1976, though an Associated Press report in August 1975 had suggested filming would start in late 1975. Spielberg did not want to do any location shooting because of his negative experience on "Jaws" and wanted to shoot "Close Encounters" entirely on sound stages, but eventually dropped the idea.


title: Close Encounters of the Third Kind

text: Filming took place in Burbank, California; Devils Tower National Monument in Wyoming; two abandoned World War II airship hangars at the former Brookley Air Force Base in Mobile, Alabama; and the Louisville and Nashville Railroad depot in Bay Minette, Alabama. The home where Barry is abducted is located outside the town of Fairhope, Alabama. Roy Neary's home is on Carlisle Drive East in Mobile. The UFOs fly through the former toll booth at the Vincent Thomas Bridge, San Pedro, California. The Sonora Desert sequence was photographed at the Dumont Dunes, California, and the Dharmsala-India exteriors were filmed at the small village of Hal near Khalapur, 35 miles (56 km) outside Mumbai, India. The hangars in Alabama were six times larger than the biggest sound stage in the world. Various technical and budgetary problems occurred during filming. Spielberg called "Close Encounters" "twice as bad and twice as expensive [as "Jaws"]".


title: Close Encounters of the Third Kind

text: Matters worsened when Columbia Pictures experienced financial difficulties. Spielberg claimed the film would cost $2.7 million to make in his original 1973 pitch to Columbia, although he revealed to producer Julia Philips that he knew the budget would have to be much higher; the final budget came to $19.4 million. Columbia studio executive John Veich remembered, "If we knew it was going to cost that much, we wouldn't have greenlighted it because we didn't have the money." Spielberg hired Joe Alves, his collaborator on "Jaws", as production designer. In addition the 1976 Atlantic hurricane season brought tropical storms to Alabama. A large portion of the sound stage in Alabama was damaged because of a lightning strike. Columbia raised $7 million from three sources: Time Inc., EMI, and German tax shelters.


title: Close Encounters of the Third Kind

text: Cinematographer Vilmos Zsigmond said that, during the shooting for the film, Spielberg got more ideas by watching films every night which in turn extended the production schedule because he was continually adding new scenes to be filmed. Zsigmond previously turned down the chance to work on "Jaws". In her 1991 book "You'll Never Eat Lunch in This Town Again", producer Julia Phillips wrote highly profane remarks about Spielberg, Zsigmond, and Truffaut, because she was fired during post-production due to a cocaine addiction. Phillips blamed it on Spielberg being a perfectionist.


title: Close Encounters of the Third Kind

text: Douglas Trumbull was the visual effects supervisor, while Carlo Rambaldi designed the extraterrestrials. Trumbull joked that the visual effects budget, at $3.3 million, could have been used to produce an additional film. His work helped lead to advances in motion control photography. The mothership was designed by Ralph McQuarrie and built by Greg Jein. The look of the ship was inspired by an oil refinery Spielberg saw at night in India. Instead of the metallic hardware look used in "Star Wars", the emphasis was on a more luminescent look for the UFOs. One of the UFO models was an oxygen mask with lights attached to it, used because of its irregular shape. As a subtle in-joke, Dennis Muren (who had just finished working on "Star Wars") put a small R2-D2 model onto the underside of the mothership. The model of the mothership is now on display in the Smithsonian Institution's Air and Space Museum Udvar-Hazy Annex at Washington Dulles Airport in Chantilly, Virginia.


title: Close Encounters of the Third Kind

text: "Close Encounters" was filmed anamorphically and the visual effects sequences were shot on 70 mm film, which has greater resolution than the 35 mm film used for the rest of the production, so that when the miniature effects were combined with full-sized elements through an optical printer, the effects footage would still appear clear and sharp despite having lost a generation's worth of visual data. A test reel using computer-generated imagery was created for the UFOs, but Spielberg found it would be too expensive and ineffective since CGI was in its infancy in the mid-1970s.


title: Close Encounters of the Third Kind

text: The small extraterrestrials in the final scenes were played by fifty local six-year-old girls in Mobile, Alabama. That decision was requested by Spielberg because he felt "girls move more gracefully than boys". Puppetry was attempted for the extraterrestrials, but the idea failed. However, Rambaldi successfully used puppetry to depict two of the extraterrestrials, the first being a marionette (for the tall extraterrestrial that is the first to be seen emerging from the mothership in what was originally a test shot but eventually used in the final film) and an articulated puppet for the extraterrestrial that communicates via hand signals near the end of the film.


title: Close Encounters of the Third Kind

text: "Close Encounters" is the first collaboration between film editor Michael Kahn and Spielberg. Their working relationship has continued for the rest of Spielberg's films. Spielberg said that no film he has ever made since has been as hard to edit as the last 25 minutes of "Close Encounters" and that he and Kahn went through thousands of feet of footage to find the right shots for the end sequence. When Kahn and Spielberg completed the first cut of the film, Spielberg was dissatisfied, feeling "there wasn't enough wow-ness". Pick-ups were commissioned but cinematographer Vilmos Zsigmond could not participate due to other commitments. John A. Alonzo, László Kovács, and Douglas Slocombe worked on the pick-ups. Lacombe was originally to find Flight 19 hidden in the Amazon rainforest, but the idea was changed to the Sonoran Desert. Spielberg also took 7.5 minutes out from the preview.


title: Close Encounters of the Third Kind

text: The score for the film was composed, conducted and produced by John Williams, who had previously worked on Spielberg's "Jaws". Williams wrote over 300 examples of the iconic five-tone motif for "Close Encounters"—the five tones are used by scientists to communicate with the visiting spaceship as a mathematical language—before Spielberg chose the one incorporated into the film's signature theme. Spielberg called Williams' work "When You Wish Upon a Star meets science fiction". Incidentally, Williams briefly included the song's signature melody in the score at Spielberg's behest, just before Roy Neary turns to board the mothership. The synthesizer used to play the five notes is an ARP 2500. ARP Instruments' Vice President of Engineering, Phillip Dodds, was sent to install the unit on the film set and was subsequently cast as Jean Claude, the musician who plays the sequence on the huge synthesizer in an attempt to communicate with the extraterrestrial mothership. Spielberg initially included Cliff Edwards' original "When You Wish upon a Star" from "Pinocchio" in the closing credits, but after a Dallas preview where several members of the audience audibly snickered at the inclusion, the song was dropped and replaced with Williams' orchestral version. It was included in the special edition of the end titles on the 1998 Collector's Edition of the soundtrack.


title: Close Encounters of the Third Kind

text: The score was recorded at Warner Bros. Studios in Burbank, California. Williams was nominated for two Academy Awards in 1978, one for his score to "Star Wars" and one for his score to "Close Encounters". He won for "Star Wars", though he later won two Grammy Awards in 1979 for his "Close Encounters" score (one for Best Original Film Score and one for Best Instrumental Composition for "Theme from Close Encounters").


title: Close Encounters of the Third Kind

text: Film critic Charlene Engel observed "Close Encounters" "suggests that humankind has reached the point where it is ready to enter the community of the cosmos. While it is a computer which makes the final musical conversation with the extraterrestrial guests possible, the characteristics bringing Neary to make his way to Devils Tower have little to do with technical expertise or computer literacy. These are virtues taught in schools that will be evolved in the 21st century." The film also evokes typical science fiction archetypes and motifs. The film portrays new technologies as a natural and expected outcome of human development and indication of health and growth.


title: Close Encounters of the Third Kind

text: Other critics found a variety of Judeo-Christian analogies. Devils Tower parallels Mount Sinai, the extraterrestrials as God and Roy Neary as Moses. Cecil B. DeMille's "The Ten Commandments" is seen on television at the Neary household. Some found close relations between Elijah and Roy; Elijah was taken into a "chariot of fire", akin to Roy going in the UFO. Climbing Devils Tower behind the faltering Jillian, Neary exhorts Jillian to keep moving and not to look back, similar to Lot's wife who looked back at Sodom and turned into a pillar of salt. Spielberg explained, "I wanted to make "Close Encounters" a very accessible story about the everyday individual who has a sighting that overturns his life, and throws it into complete upheaval as he starts to become more and more obsessed with this experience."


title: Close Encounters of the Third Kind

text: Roy's wife Ronnie attempts to hide the sunburn caused by Roy's exposure to the UFOs and wants him to forget his encounter with them. She is embarrassed and bewildered by what has happened to him and desperately wants her ordinary life back. The expression of his lost life is seen when he is sculpting a huge model of Devils Tower in his living room, with his family deserting him. Roy's obsession with an idea implanted by an extraterrestrial intelligence, his construction of the model, and his gradual loss of contact with his wife, mimic the events in the short story "Dulcie and Decorum" (1955) by Damon Knight.


title: Close Encounters of the Third Kind

text: "Close Encounters" also studies the form of "youth spiritual yearning". Barry Guiler, the unfearing child who refers to the UFOs and their paraphernalia as "toys" (although that was unscripted, with the child being drawn to smile by being shown toys offstage), serves as a motif for childlike innocence and openness in the face of the unknown. Spielberg also compared the theme of communication as highlighting that of tolerance. "If we can talk to extraterrestrials in "Close Encounters of the Third Kind"", he said, "why not with the Reds in the Cold War?" Sleeping is the final obstacle to overcome in the ascent of Devils Tower. Roy, Jillian and a third invitee, Larry Butler, climb the mountain pursued by government helicopters spraying sleeping gas. Larry stops to rest, is gassed, and falls into a deep sleep.


title: Close Encounters of the Third Kind

text: In his interview with Spielberg on "Inside the Actors Studio", James Lipton suggested "Close Encounters" has another, more personal theme for Spielberg: "Your father was a computer engineer; your mother was a concert pianist, and when the spaceship lands, they make music together on the computer", suggesting that Roy Neary's boarding the spaceship is Spielberg's wish to be reunited with his parents. In a 2005 interview, Spielberg stated that he made "Close Encounters" when he did not have children, and if he were making it today, he would never have had Neary leave his family and board the mothership.


title: Close Encounters of the Third Kind

text: Communication and language issues constitute additional themes as noted by Andrew Johnston in "Time Out New York": "Throughout the film, there are many scenes that anticipate themes Spielberg would explore in subsequent projects, but his execution of these ideas here is usually more interesting and subtle. In "Amistad", for example, he devotes much time to illustrating the language barrier separating Africans from both their captors and their potential saviors. It's an essential plot point, but it's so belabored that the story gets bogged down. In "CE3K", the language problem is illustrated concisely by a quick scene in which an interpreter translates Spanish into English for Laughlin so he can turn around and translate it into French for Lacombe. Since Spielberg doesn't ram the language problem down our throats, the extraterrestrials' solution—using music to communicate with humanity—seems more elegant and natural."


title: Close Encounters of the Third Kind

text: The film was to be released in summer 1977 but was pushed back to November because of the various problems during production.


title: Close Encounters of the Third Kind

text: "Close Encounters" premiered at the Ziegfeld Theatre in New York City on November 16, 1977, and played there and at the Cinerama Dome in Los Angeles, grossing $1,077,000 prior to its national release on December 14, when it opened in 270 theatres grossing $10,115,000 in a week with a per-screen average of $37,460. It added 301 more theatres on December 21. By the end of the second week of national release it had grossed $24,695,317.


title: Close Encounters of the Third Kind

text: It made a record $3,026,558 on December 26, 1977, and set a one-week record of $17,393,654 from December 26 to January 1. The film opened overseas on February 24, 1978, and grossed $27 million internationally by the end of March from 19 countries. "Close Encounters" received mostly positive reviews and became a certified box office success, grossing $116.39 million in the United States and Canada, and $171.7 million in foreign countries, for $288 million worldwide.


title: Close Encounters of the Third Kind

text: Jonathan Rosenbaum refers to the film as "the best expression of Spielberg's benign, dreamy-eyed vision". A.D. Murphy of "Variety" magazine gave a positive review but wrote that "Close Encounters" "lacks the warmth and humanity" of George Lucas's "Star Wars". Murphy found most of the film slow-paced, but praised the climax. On Sneak Previews, Gene Siskel and Roger Ebert highly recommended the film. Siskel praised the film's message about not being "afraid of the unknown," said Dreyfuss was "perfectly cast" and described the ending as "a wonderful scene, combining fantasy, adventure and mystery." He mentioned, however, that the picture got "bogged down" by a subplot in the middle. Ebert said "the last 30 minutes are among the most marvelous things I've ever seen on the screen" and that the film was "like a kid's picture...in its innocence." Pauline Kael similarly called it "a kid's film in the best sense". Jean Renoir compared Spielberg's storytelling to Jules Verne and Georges Méliès. Ray Bradbury declared it the greatest science fiction film ever made.


title: Close Encounters of the Third Kind

text: On the final cut privilege, Spielberg was dissatisfied with the film. Columbia Pictures was experiencing financial problems, and they were depending on this film to save their company. "I wanted to have another six months to finish off this film, and release it in summer 1978. They told me they needed this film out immediately", Spielberg explained. "Anyway, "Close Encounters" was a huge financial success and I told them I wanted to make my own director's cut. They agreed on the condition that I show the inside of the mothership so they could have something to hang a [reissue marketing] campaign on. I never should have shown the inside of the mothership."


title: Close Encounters of the Third Kind

text: In 1979, Columbia gave Spielberg $1.5 million to produce what became the "Special Edition" of the film. Spielberg added seven minutes of new footage, but also deleted or shortened various existing scenes by ten minutes, so that the Special Edition was three minutes shorter than the original 1977 release, running 132 minutes. The Special Edition featured several new character development scenes, the discovery of the SS "Cotopaxi" in the Gobi Desert, and a view of the inside of the mothership. "Close Encounters of the Third Kind: The Special Edition" was released in August 1980, making a further $15.7 million, accumulating a final $303.7 million box office gross. Roger Ebert "thought the original film was an astonishing achievement, capturing the feeling of awe and wonder we have when considering the likelihood of life beyond the Earth. ... This new version ... is, quite simply, a better film ... Why didn't Spielberg make it this good the first time?"


title: Close Encounters of the Third Kind

text: The 1980 Special Edition was the only version officially available for many years on VHS. Then, in 1990, The Criterion Collection offered two versions for LaserDisc, one a variant of the original 1977 edition (with subtle edits made by Spielberg—this became the syndicated television version), the other the Special Edition (programmed by the viewer using their LaserDisc player's remote features that predated the seamless branching of DVDs). This triple-disc LaserDisc set also included an interactive "Making Close Encounters" documentary featuring interviews with Spielberg and other cast and crew involved with the film, as well as stills and script excerpts. In 1993, the Special Edition was released on VHS and LaserDisc and did not see a further release for 14 years.


title: Close Encounters of the Third Kind

text: Vincent Misiano reviewed "Close Encounters: The Special Edition" in "Ares Magazine" #5 and commented that "Artists in other media have always had the luxury of returning to a piece, reworking and refining it. For various reasons, money first among them, this opportunity has rarely been afforded to filmmakers. Steven Spielberg has been given the chance and used it well."


title: Close Encounters of the Third Kind

text: On May 12, 1998, Spielberg recut "Close Encounters" again for the "Director's Cut", released as simply the "Collector's Edition" on VHS. This version of the film is a re-edit of the original 1977 release with some elements of the 1980 Special Edition, but omits the mothership interior scenes as Spielberg felt they should have remained a mystery. The director's cut is the longest release of the film, running at 137 minutes, two minutes longer than the theatrical version and five minutes longer than the special edition. A LaserDisc release of the Collector's Edition, released on July 14, 1998, includes a new 101-minute documentary, "The Making of Close Encounters", which was produced in 1997 and features interviews with Spielberg, the main cast and notable crew members. There have also been many other alternative versions of the film for network and syndicated television, as well as the aforementioned Criterion LaserDisc version. Some of these combined all released material from the 1977 and 1980 versions. However, most of these versions were not edited by Spielberg, who regards the "Collector's Edition" as his definitive version of "Close Encounters". The Collector's Edition was given a limited release as part of a roadshow featuring select films to celebrate Columbia Pictures' 75th anniversary in 1999. It was the first time this version of the film had been shown theatrically. The director's cut was once again released in theaters on September 1, 2017 in tribute to the film's 40th anniversary. It made $1.8 million in the weekend ($2.3 million over the four-day Labor Day holiday), pushing its career global gross to over $306 million worldwide.


title: Close Encounters of the Third Kind

text: "Close Encounters" was released on DVD on May 29, 2001, in a two-disc "Collector's Edition" set that contained only the director's cut. This set contained several extra features, including the 1997 "making of" documentary, a featurette from 1977, trailers and deleted scenes that included the mothership interior from the 1980 Special Edition. A single-disc DVD edition of the film was released on August 27, 2002. In tribute to the film's 30th anniversary, Sony Pictures released the film on DVD and Blu-ray in 2007. For the first time, all three versions were packaged together. Then in 2017, in honor of its 40th anniversary, the film was given a 4K restoration of the original camera negative. Following its theatrical re-release of the director's cut, the film was released in 4K and Blu-ray with all three versions given the same 4K treatment.


title: Close Encounters of the Third Kind

text: Shortly after the film's release in late 1977, Spielberg desired to do either a sequel or prequel, before deciding against it. He explained, "The army's knowledge and ensuing cover-up is so subterranean that it would take a creative screen story, perhaps someone else making the picture and giving it the equal time it deserves."


title: Close Encounters of the Third Kind

text: When asked in 1980 to select a single "master image" that summed up his film career, Spielberg chose the shot of Barry opening his living room door to see the blazing orange light from the UFO. "That was beautiful but awful light, just like fire coming through the doorway. [Barry's] very small, and it's a very large door, and there's a lot of promise or danger outside that door." In 2007, "Close Encounters" was deemed "culturally, historically, or aesthetically significant" by the United States Library of Congress and was added to the National Film Registry for preservation. In American Film Institute polls, "Close Encounters" has been voted the 64th-greatest American film, the 31st-most thrilling, and the 58th-most inspiring. It was also nominated for the top 10 science fiction films in AFI's 10 Top 10 and the tenth-anniversary edition of the 100 Movies list. The score by John Williams was nominated for AFI's 100 Years of Film Scores.


title: Close Encounters of the Third Kind

text: Alongside "Star Wars" and "Superman", "Close Encounters" led to the reemergence of science fiction films. In 1985 Spielberg donated $100,000 to the Planetary Society for Megachannel ExtraTerrestrial Assay. In the 1979 James Bond film "Moonraker" the five-note sequence is heard when a scientist punches the combination into an electronic door lock. In the 2009 comedy film "Monsters vs. Aliens", the president of the United States plays the five-note sequence on a synthesizer while attempting "first contact" with an extraterrestrial robot. In the "South Park" episode "Imaginationland", a government scientist uses the five-note sequence to try to open a portal. In "Over Logging", a government scientist uses the five-note sequence to try to get the central Internet router working. The "mashed potato" sculpture was parodied in the films "UHF", and "Canadian Bacon", and episodes of "Spaced", "The X-Files", "That '70s Show", "The IT Crowd", and "The Simpsons". It was satirized in the 200th issue of "Mad", July 1978, by Stan Hart and Mort Drucker as "Clod Encounters of the Absurd Kind".


title: Close Encounters of the Third Kind

text: In 2011, ABC aired a primetime special, "", that counted down the best films chosen by fans based on results of a poll conducted by ABC and "People" magazine. "Close Encounters of the Third Kind" was selected as the #5 Best Sci-Fi Film. "The Guardian" also selected the film as the 11th best Sci-Fi and fantasy film of all-time.


title: Close Encounters of the Third Kind

text: Many prominent film directors have cited "Close Encounters of the Third Kind" as one of their favorites including Stanley Kubrick, Edgar Wright, Spike Lee, Denis Villeneuve, and Andrew Stanton.


title: Entropy (information theory)

text: In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable formula_1, which takes values in the alphabet formula_2 and is distributed according to formula_3:


title: Entropy (information theory)

text: where formula_5 denotes the sum over the variable's possible values. The choice of base for formula_6, the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannons"), while base "e" gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys". An equivalent definition of entropy is the expected value of the self-information of a variable.


title: Entropy (information theory)

text: The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", and is also referred to as Shannon entropy. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel, and a receiver. The "fundamental problem of communication" – as expressed by Shannon – is for the receiver to be able to identify what data was generated by the source, based on the signal it receives through the channel. Shannon considered various ways to encode, compress, and transmit messages from a data source, and proved in his famous source coding theorem that the entropy represents an absolute mathematical limit on how well data from the source can be losslessly compressed onto a perfectly noiseless channel. Shannon strengthened this result considerably for noisy channels in his noisy-channel coding theorem.


title: Entropy (information theory)

text: Entropy in information theory is directly analogous to the entropy in statistical thermodynamics. The analogy results when the values of the random variable designate energies of microstates, so Gibbs formula for the entropy is formally identical to Shannon's formula. Entropy has relevance to other areas of mathematics such as combinatorics and machine learning. The definition can be derived from a set of axioms establishing that entropy should be a measure of how "surprising" the average outcome of a variable is. For a continuous random variable, differential entropy is analogous to entropy.


title: Entropy (information theory)

text: The core idea of information theory is that the "informational value" of a communicated message depends on the degree to which the content of the message is surprising. If a highly likely event occurs, the message carries very little information. On the other hand, if a highly unlikely event occurs, the message is much more informative. For instance, the knowledge that some particular number "will not" be the winning number of a lottery provides very little information, because any particular chosen number will almost certainly not win. However, knowledge that a particular number "will" win a lottery has high informational value because it communicates the outcome of a very low probability event.


title: Entropy (information theory)

text: The "information content," also called the "surprisal" or "self-information," of an event formula_7 is a function which increases as the probability formula_8 of an event decreases. When formula_8 is close to 1, the surprisal of the event is low, but if formula_8 is close to 0, the surprisal of the event is high. This relationship is described by the function


title: Entropy (information theory)

text: where formula_6 is the logarithm, which gives 0 surprise when the probability of the event is 1. In fact, the formula_6 is the only function that satisfies this specific set of characterization.


title: Entropy (information theory)

text: Entropy measures the expected (i.e., average) amount of information conveyed by identifying the outcome of a random trial. This implies that casting a die has higher entropy than tossing a coin because each outcome of a die toss has smaller probability (about formula_17) than each outcome of a coin toss (formula_18).


title: Entropy (information theory)

text: Consider a biased coin with probability of landing on heads and probability of landing on tails. The maximum surprise is when , for which one outcome is not expected over the other. In this case a coin flip has an entropy of one bit. (Similarly, one trit with equiprobable values contains formula_19 (about 1.58496) bits of information because it can have one of three values.) The minimum surprise is when or , when the event outcome is known ahead of time, and the entropy is zero bits. When the entropy is zero bits, this is sometimes referred to as unity, where there is no uncertainty at all - no freedom of choice - no information. Other values of "p" give entropies between zero and one bits.


title: Entropy (information theory)

text: Information theory is useful to calculate the smallest amount of information required to convey a message, as in data compression. For example, consider the transmission of sequences comprising the 4 characters 'A', 'B', 'C', and 'D' over a binary channel. If all 4 letters are equally likely (25%), one can't do better than using two bits to encode each letter. 'A' might code as '00', 'B' as '01', 'C' as '10', and 'D' as '11'. However, if the probabilities of each letter are unequal, say 'A' occurs with 70% probability, 'B' with 26%, and 'C' and 'D' with 2% each, one could assign variable length codes. In this case, 'A' would be coded as '0', 'B' as '10', 'C' as '110', and D as '111'. With this representation, 70% of the time only one bit needs to be sent, 26% of the time two bits, and only 4% of the time 3 bits. On average, fewer than 2 bits are required since the entropy is lower (owing to the high prevalence of 'A' followed by 'B' – together 96% of characters). The calculation of the sum of probability-weighted log probabilities measures and captures this effect. English text, treated as a string of characters, has fairly low entropy, i.e., is fairly predictable. We can be fairly certain that, for example, 'e' will be far more common than 'z', that the combination 'qu' will be much more common than any other combination with a 'q' in it, and that the combination 'th' will be more common than 'z', 'q', or 'qu'. After the first few letters one can often guess the rest of the word. English text has between 0.6 and 1.3 bits of entropy per character of the message.


title: Entropy (information theory)

text: Named after Boltzmann's Η-theorem, Shannon defined the entropy (Greek capital letter eta) of a discrete random variable formula_20, which takes values in the alphabet formula_2 and is distributed according to formula_22 such that formula_23:


title: Entropy (information theory)

text: where is the base of the logarithm used. Common values of are 2, Euler's number, and 10, and the corresponding units of entropy are the bits for , nats for , and bans for .


title: Entropy (information theory)

text: In the case of formula_28 for some formula_29, the value of the corresponding summand is taken to be , which is consistent with the limit:


title: Entropy (information theory)

text: One may also define the conditional entropy of two variables formula_1 and formula_32 taking values from sets formula_2 and formula_34 respectively, as:


title: Entropy (information theory)

text: where formula_36 and formula_37. This quantity should be understood as the remaining randomness in the random variable formula_1 given the random variable formula_32.


title: Entropy (information theory)

text: Entropy can be formally defined in the language of measure theory as follows: Let formula_40 be a probability space. Let formula_41 be an event. The surprisal of formula_42 is


title: Entropy (information theory)

text: A formula_46-almost partition is a set family formula_47 such that formula_48 and formula_49 for all distinct formula_50. (This is a relaxation of the usual conditions for a partition.) The entropy of formula_51 is


title: Entropy (information theory)

text: Finally, the entropy of the probability space is formula_57, that is, the entropy with respect to formula_46 of the sigma-algebra of "all" measurable subsets of formula_1.


title: Entropy (information theory)

text: David Ellerman wanted to explain why conditional entropy and other functions had properties similar to functions in probability theory. He claims that previous definitions based on measure theory only worked with powers of 2.


title: Entropy (information theory)

text: Ellerman created a "logic of partitions" that is the dual of subsets of a universal set. Information is quantified as "dits" (distinctions), a measure on partitions. "Dits" can be converted into Shannon's bits, to get the formulas for conditional entropy, etc..


title: Entropy (information theory)

text: Consider tossing a coin with known, not necessarily fair, probabilities of coming up heads or tails; this can be modelled as a Bernoulli process.


title: Entropy (information theory)

text: The entropy of the unknown result of the next toss of the coin is maximized if the coin is fair (that is, if heads and tails both have equal probability 1/2). This is the situation of maximum uncertainty as it is most difficult to predict the outcome of the next toss; the result of each toss of the coin delivers one full bit of information. This is because


title: Entropy (information theory)

text: However, if we know the coin is not fair, but comes up heads or tails with probabilities and , where , then there is less uncertainty. Every time it is tossed, one side is more likely to come up than the other. The reduced uncertainty is quantified in a lower entropy: on average each toss of the coin delivers less than one full bit of information. For example, if = 0.7, then


title: Entropy (information theory)

text: Uniform probability yields maximum uncertainty and therefore maximum entropy. Entropy, then, can only decrease from the value associated with uniform probability. The extreme case is that of a double-headed coin that never comes up tails, or a double-tailed coin that never results in a head. Then there is no uncertainty. The entropy is zero: each toss of the coin delivers no new information as the outcome of each coin toss is always certain.


title: Entropy (information theory)

text: Entropy can be normalized by dividing it by information length. This ratio is called metric entropy and is a measure of the randomness of the information.


title: Entropy (information theory)

text: To understand the meaning of , first define an information function in terms of an event with probability . The amount of information acquired due to the observation of event follows from Shannon's solution of the fundamental properties of information:


title: Entropy (information theory)

text: Given two independent events, if the first event can yield one of equiprobable outcomes and another has one of equiprobable outcomes then there are equiprobable outcomes of the joint event. This means that if bits are needed to encode the first value and to encode the second, one needs to encode both.


title: Entropy (information theory)

text: In fact, the only possible values of formula_62 are formula_65 for formula_66. Additionally, choosing a value for is equivalent to choosing a value formula_67 for formula_68, so that corresponds to the base for the logarithm. Thus, entropy is characterized by the above four properties.


title: Entropy (information theory)

text: The different units of information (bits for the binary logarithm , nats for the natural logarithm , bans for the decimal logarithm and so on) are constant multiples of each other. For instance, in case of a fair coin toss, heads provides bit of information, which is approximately 0.693 nats or 0.301 decimal digits. Because of additivity, tosses provide bits of information, which is approximately nats or decimal digits.


title: Entropy (information theory)

text: The "meaning" of the events observed (the meaning of "messages") does not matter in the definition of entropy. Entropy only takes into account the probability of observing a specific event, so the information it encapsulates is information about the underlying probability distribution, not the meaning of the events themselves.


title: Entropy (information theory)

text: Choosing , this implies that the entropy of a certain outcome is zero: . This implies that the efficiency of a source alphabet with symbols can be defined simply as being equal to its -ary entropy. See also Redundancy (information theory).


title: Entropy (information theory)

text: The Shannon entropy satisfies the following properties, for some of which it is useful to interpret entropy as the expected amount of information learned (or uncertainty eliminated) by revealing the value of a random variable :


title: Entropy (information theory)

text: The inspiration for adopting the word "entropy" in information theory came from the close resemblance between Shannon's formula and very similar known formulae from statistical mechanics.


title: Entropy (information theory)

text: In statistical thermodynamics the most general formula for the thermodynamic entropy of a thermodynamic system is the Gibbs entropy,


title: Entropy (information theory)

text: where is the Boltzmann constant, and is the probability of a microstate. The Gibbs entropy was defined by J. Willard Gibbs in 1878 after earlier work by Boltzmann (1872).


title: Entropy (information theory)

text: The Gibbs entropy translates over almost unchanged into the world of quantum physics to give the von Neumann entropy, introduced by John von Neumann in 1927,


title: Entropy (information theory)

text: At an everyday practical level, the links between information entropy and thermodynamic entropy are not evident. Physicists and chemists are apt to be more interested in "changes" in entropy as a system spontaneously evolves away from its initial conditions, in accordance with the second law of thermodynamics, rather than an unchanging probability distribution. As the minuteness of the Boltzmann constant indicates, the changes in for even tiny amounts of substances in chemical and physical processes represent amounts of entropy that are extremely large compared to anything in data compression or signal processing. In classical thermodynamics, entropy is defined in terms of macroscopic measurements and makes no reference to any probability distribution, which is central to the definition of information entropy.


title: Entropy (information theory)

text: The connection between thermodynamics and what is now known as information theory was first made by Ludwig Boltzmann and expressed by his famous equation:


title: Entropy (information theory)

text: where formula_96 is the thermodynamic entropy of a particular macrostate (defined by thermodynamic parameters such as temperature, volume, energy, etc.), is the number of microstates (various combinations of particles in various energy states) that can yield the given macrostate, and is the Boltzmann constant. It is assumed that each microstate is equally likely, so that the probability of a given microstate is . When these probabilities are substituted into the above expression for the Gibbs entropy (or equivalently times the Shannon entropy), Boltzmann's equation results. In information theoretic terms, the information entropy of a system is the amount of "missing" information needed to determine a microstate, given the macrostate.


title: Entropy (information theory)

text: In the view of Jaynes (1957), thermodynamic entropy, as explained by statistical mechanics, should be seen as an "application" of Shannon's information theory: the thermodynamic entropy is interpreted as being proportional to the amount of further Shannon information needed to define the detailed microscopic state of the system, that remains uncommunicated by a description solely in terms of the macroscopic variables of classical thermodynamics, with the constant of proportionality being just the Boltzmann constant. Adding heat to a system increases its thermodynamic entropy because it increases the number of possible microscopic states of the system that are consistent with the measurable values of its macroscopic variables, making any complete state description longer. (See article: "maximum entropy thermodynamics"). Maxwell's demon can (hypothetically) reduce the thermodynamic entropy of a system by using information about the states of individual molecules; but, as Landauer (from 1961) and co-workers have shown, to function the demon himself must increase thermodynamic entropy in the process, by at least the amount of Shannon information he proposes to first acquire and store; and so the total thermodynamic entropy does not decrease (which resolves the paradox). Landauer's principle imposes a lower bound on the amount of heat a computer must generate to process a given amount of information, though modern computers are far less efficient.


title: Entropy (information theory)

text: Shannon's definition of entropy, when applied to an information source, can determine the minimum channel capacity required to reliably transmit the source as encoded binary digits. Shannon's entropy measures the information contained in a message as opposed to the portion of the message that is determined (or predictable). Examples of the latter include redundancy in language structure or statistical properties relating to the occurrence frequencies of letter or word pairs, triplets etc. The minimum channel capacity can be realized in theory by using the typical set or in practice using Huffman, Lempel–Ziv or arithmetic coding. (See also Kolmogorov complexity.) In practice, compression algorithms deliberately include some judicious redundancy in the form of checksums to protect against errors. The entropy rate of a data source is the average number of bits per symbol needed to encode it. Shannon's experiments with human predictors show an information rate between 0.6 and 1.3 bits per character in English; the PPM compression algorithm can achieve a compression ratio of 1.5 bits per character in English text.


title: Entropy (information theory)

text: If a compression scheme is lossless – one in which you can always recover the entire original message by decompression – then a compressed message has the same quantity of information as the original but communicated in fewer characters. It has more information (higher entropy) per character. A compressed message has less redundancy. Shannon's source coding theorem states a lossless compression scheme cannot compress messages, on average, to have "more" than one bit of information per bit of message, but that any value "less" than one bit of information per bit of message can be attained by employing a suitable coding scheme. The entropy of a message per bit multiplied by the length of that message is a measure of how much total information the message contains. Shannon's theorem also implies that no lossless compression scheme can shorten "all" messages. If some messages come out shorter, at least one must come out longer due to the pigeonhole principle. In practical use, this is generally not a problem, because one is usually only interested in compressing certain types of messages, such as a document in English, as opposed to gibberish text, or digital photographs rather than noise, and it is unimportant if a compression algorithm makes some unlikely or uninteresting sequences larger.


title: Entropy (information theory)

text: A 2011 study in "Science" estimates the world's technological capacity to store and communicate optimally compressed information normalized on the most effective compression algorithms available in the year 2007, therefore estimating the entropy of the technologically available sources.


title: Entropy (information theory)

text: The authors estimate humankind technological capacity to store information (fully entropically compressed) in 1986 and again in 2007. They break the information into three categories—to store information on a medium, to receive information through one-way broadcast networks, or to exchange information through two-way telecommunication networks.


title: Entropy (information theory)

text: Entropy is one of several ways to measure biodiversity, and is applied in the form of the Shannon index. A diversity index is a quantitative statistical measure of how many different types exist in a dataset, such as species in a community, accounting for ecological richness, evenness, and dominance. Specifically, Shannon entropy is the logarithm of , the true diversity index with parameter equal to 1. The Shannon index is related to the proportional abundances of types.


title: Entropy (information theory)

text: There are a number of entropy-related concepts that mathematically quantify information content in some way:


title: Entropy (information theory)

text: (The "rate of self-information" can also be defined for a particular sequence of messages or symbols generated by a given stochastic process: this will always be equal to the entropy rate in the case of a stationary process.) Other quantities of information are also used to compare or relate different sources of information.


title: Entropy (information theory)

text: It is important not to confuse the above concepts. Often it is only clear from context which one is meant. For example, when someone says that the "entropy" of the English language is about 1 bit per character, they are actually modeling the English language as a stochastic process and talking about its entropy "rate". Shannon himself used the term in this way.


title: Entropy (information theory)

text: If very large blocks are used, the estimate of per-character entropy rate may become artificially low because the probability distribution of the sequence is not known exactly; it is only an estimate. If one considers the text of every book ever published as a sequence, with each symbol being the text of a complete book, and if there are published books, and each book is only published once, the estimate of the probability of each book is , and the entropy (in bits) is . As a practical code, this corresponds to assigning each book a unique identifier and using it in place of the text of the book whenever one wants to refer to the book. This is enormously useful for talking about books, but it is not so useful for characterizing the information content of an individual book, or of language in general: it is not possible to reconstruct the book from its identifier without knowing the probability distribution, that is, the complete text of all the books. The key idea is that the complexity of the probabilistic model must be considered. Kolmogorov complexity is a theoretical generalization of this idea that allows the consideration of the information content of a sequence independent of any particular probability model; it considers the shortest program for a universal computer that outputs the sequence. A code that achieves the entropy rate of a sequence for a given model, plus the codebook (i.e. the probabilistic model), is one such program, but it may not be the shortest.


title: Entropy (information theory)

text: The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, ... treating the sequence as a message and each number as a symbol, there are almost as many symbols as there are characters in the message, giving an entropy of approximately . The first 128 symbols of the Fibonacci sequence has an entropy of approximately 7 bits/symbol, but the sequence can be expressed using a formula [ for , , ] and this formula has a much lower entropy and applies to any length of the Fibonacci sequence.


title: Entropy (information theory)

text: In cryptanalysis, entropy is often roughly used as a measure of the unpredictability of a cryptographic key, though its real uncertainty is unmeasurable. For example, a 128-bit key that is uniformly and randomly generated has 128 bits of entropy. It also takes (on average) formula_97 guesses to break by brute force. Entropy fails to capture the number of guesses required if the possible keys are not chosen uniformly. Instead, a measure called "guesswork" can be used to measure the effort required for a brute force attack.


title: Entropy (information theory)

text: Other problems may arise from non-uniform distributions used in cryptography. For example, a 1,000,000-digit binary one-time pad using exclusive or. If the pad has 1,000,000 bits of entropy, it is perfect. If the pad has 999,999 bits of entropy, evenly distributed (each individual bit of the pad having 0.999999 bits of entropy) it may provide good security. But if the pad has 999,999 bits of entropy, where the first bit is fixed and the remaining 999,999 bits are perfectly random, the first bit of the ciphertext will not be encrypted at all.


title: Entropy (information theory)

text: A common way to define entropy for text is based on the Markov model of text. For an order-0 source (each character is selected independent of the last characters), the binary entropy is:


title: Entropy (information theory)

text: where is the probability of . For a first-order Markov source (one in which the probability of selecting a character is dependent only on the immediately preceding character), the entropy rate is:


title: Entropy (information theory)

text: where is a state (certain preceding characters) and formula_100 is the probability of given as the previous character.


title: Entropy (information theory)

text: A source alphabet with non-uniform distribution will have less entropy than if those symbols had uniform distribution (i.e. the "optimized alphabet"). This deficiency in entropy can be expressed as a ratio called efficiency:


title: Entropy (information theory)

text: Efficiency has utility in quantifying the effective use of a communication channel. This formulation is also referred to as the normalized entropy, as the entropy is divided by the maximum entropy formula_104. Furthermore, the efficiency is indifferent to choice of (positive) base , as indicated by the insensitivity within the final logarithm above thereto.


title: Entropy (information theory)

text: The Shannon entropy is restricted to random variables taking discrete values. The corresponding formula for a continuous random variable with probability density function with finite or infinite support formula_105 on the real line is defined by analogy, using the above form of the entropy as an expectation:


title: Entropy (information theory)

text: This is the differential entropy (or continuous entropy). A precursor of the continuous entropy is the expression for the functional in the H-theorem of Boltzmann.


title: Entropy (information theory)

text: Although the analogy between both functions is suggestive, the following question must be set: is the differential entropy a valid extension of the Shannon discrete entropy? Differential entropy lacks a number of properties that the Shannon discrete entropy has – it can even be negative – and corrections have been suggested, notably limiting density of discrete points.


title: Entropy (information theory)

text: In order to obtain a generally finite measure as the bin size goes to zero. In the discrete case, the bin size is the (implicit) width of each of the (finite or infinite) bins whose probabilities are denoted by . As the continuous domain is generalized, the width must be made explicit.


title: Entropy (information theory)

text: which is, as said before, referred to as the differential entropy. This means that the differential entropy "is not" a limit of the Shannon entropy for . Rather, it differs from the limit of the Shannon entropy by an infinite offset (see also the article on information dimension).


title: Entropy (information theory)

text: It turns out as a result that, unlike the Shannon entropy, the differential entropy is "not" in general a good measure of uncertainty or information. For example, the differential entropy can be negative; also it is not invariant under continuous co-ordinate transformations. This problem may be illustrated by a change of units when is a dimensioned variable. will then have the units of . The argument of the logarithm must be dimensionless, otherwise it is improper, so that the differential entropy as given above will be improper. If is some "standard" value of (i.e. "bin size") and therefore has the same units, then a modified differential entropy may be written in proper form as:


title: Entropy (information theory)

text: and the result will be the same for any choice of units for . In fact, the limit of discrete entropy as formula_115 would also include a term of formula_116, which would in general be infinite. This is expected: continuous variables would typically have infinite entropy when discretized. The limiting density of discrete points is really a measure of how much easier a distribution is to describe than a distribution that is uniform over its quantization scheme.


title: Entropy (information theory)

text: Another useful measure of entropy that works equally well in the discrete and the continuous case is the relative entropy of a distribution. It is defined as the Kullback–Leibler divergence from the distribution to a reference measure as follows. Assume that a probability distribution is absolutely continuous with respect to a measure , i.e. is of the form for some non-negative -integrable function with -integral 1, then the relative entropy can be defined as


title: Entropy (information theory)

text: In this form the relative entropy generalizes (up to change in sign) both the discrete entropy, where the measure is the counting measure, and the differential entropy, where the measure is the Lebesgue measure. If the measure is itself a probability distribution, the relative entropy is non-negative, and zero if as measures. It is defined for any measure space, hence coordinate independent and invariant under co-ordinate reparameterizations if one properly takes into account the transformation of the measure . The relative entropy, and (implicitly) entropy and differential entropy, do depend on the "reference" measure .


title: Entropy (information theory)

text: A simple example of this is an alternative proof of the Loomis–Whitney inequality: for every subset , we have


title: Entropy (information theory)

text: The proof follows as a simple corollary of Shearer's inequality: if are random variables and are subsets of } such that every integer between 1 and lies in exactly of these subsets, then


title: Entropy (information theory)

text: where formula_121 is the Cartesian product of random variables with indexes in (so the dimension of this vector is equal to the size of ).


title: Entropy (information theory)

text: We sketch how Loomis–Whitney follows from this: Indeed, let be a uniformly distributed random variable with values in and so that each point in occurs with equal probability. Then (by the further properties of entropy mentioned above) , where denotes the cardinality of . Let }. The range of formula_122 is contained in and hence formula_123. Now use this to bound the right side of Shearer's inequality and exponentiate the opposite sides of the resulting inequality you obtain.


title: Entropy (information theory)

text: A nice interpretation of this is that the number of binary strings of length with exactly many 1's is approximately formula_126.


title: Entropy (information theory)

text: Machine learning techniques arise largely from statistics and also information theory. In general, entropy is a measure of uncertainty and the objective of machine learning is to minimize uncertainty.


title: Entropy (information theory)

text: Decision tree learning algorithms use relative entropy to determine the decision rules that govern the data at each node. The Information gain in decision trees formula_127, which is equal to the difference between the entropy of formula_32 and the conditional entropy of formula_32 given formula_1, quantifies the expected information, or the reduction in entropy, from additionally knowing the value of an attribute formula_1. The information gain is used to identify which attributes of the dataset provide the most information and should be used to split the nodes of the tree optimally.


title: Entropy (information theory)

text: Bayesian inference models often apply the Principle of maximum entropy to obtain Prior probability distributions. The idea is that the distribution that best represents the current state of knowledge of a system is the one with the largest entropy, and is therefore suitable to be the prior.


title: Entropy (information theory)

text: Classification in machine learning performed by logistic regression or artificial neural networks often employs a standard loss function, called cross entropy loss, that minimizes the average cross entropy between ground truth and predicted distributions. In general, cross entropy is a measure of the differences between two datasets similar to the KL divergence (a.k.a. relative entropy).


title: Anil Ambani

text: Anil Dhirubhai Ambani (born 4 June 1959) is an Indian businessman. He was the chairman of Reliance Group (also known as Reliance ADA Group), which was created in July 2006 following a demerger from Reliance Industries Limited. He leads a number of stocks listed corporations including Reliance Capital, Reliance Infrastructure, Reliance Power and Reliance Communications. Ambani, once the sixth richest person in the world, declared before a UK court in February 2020 that his net worth is zero and he is bankrupt, although the veracity of that claim is in question. He served in the Rajya Sabha, the upper house of the Parliament of India from Uttar Pradesh as an Independent MP between 2004 and 2006.


title: Anil Ambani

text: Anil Ambani is the younger son of the founder of Reliance Industries, Dhirubhai Ambani and his wife Kokilaben.


title: Anil Ambani

text: Ambani has said that his father would lead the brothers on "incentive-oriented outings" where they would be rewarded a box of mangoes for a 10-km (6 mile) hike, but also punished them for acting out in front of guests. He earned his Bachelor of Science degree from Kishinchand Chellaram College and received a Master in Business Administration at the Wharton School of the University of Pennsylvania in 1983.


title: Anil Ambani

text: Ambani's father Dhirubhai died in 2002 without leaving a clear succession plan. After bickering between Anil and his brother Mukesh, their mother Kokilaben mediated and split the family owned businesses between the two brothers.


title: Anil Ambani

text: Anil Ambani received parts of Reliance Group with interests in telecom, entertainment, financial services, power and infrastructure. Ambani is also credited with India's largest IPO, that of Reliance Power, which in 2008 was subscribed in less than 60 seconds, the fastest in the history of Indian capital markets to date.


title: Anil Ambani

text: In 2005 Ambani made his debut in the entertainment industry with an acquisition of a majority stake in Adlabs Films, a company with interests in film processing, production, exhibition and digital cinema. The company was renamed Reliance MediaWorks in 2009.


title: Anil Ambani

text: In 2008 a joint venture worth US$1.2 billion with Steven Spielberg's production company DreamWorks cast Ambani's entertainment business on to a global platform. He has contributed to the production of several Spielberg films, including the Academy Award-winning "Lincoln".


title: Anil Ambani

text: Ambani gained notoriety as one of the fastest destroyers of shareholder wealth in the last 100 years with the combined group market cap declining by 90% since the formation of the Reliance ADA Group.


title: Anil Ambani

text: In early 2019, a court in Mumbai held Ambani in criminal contempt for non-payment of personally guaranteed debt Reliance Communications owed to Swedish gear maker Ericsson. Instead of jail time, the court gave him a month to come up with the funds. At the end of the month, Ambani was bailed out by his elder brother, Mukesh Ambani.


title: Anil Ambani

text: In April 2019, three ADAG Companies reached standstill agreement with Franklin Templeton after secured NCD default. This led to SEBI changing mutual fund regulation of reducing unlisted NCDs exposure to 10% and making standstill agreement void. In aftermath, FT India didn't sell the pledged securities and wound 6 debt funds affecting 300,000 investors.


title: Anil Ambani

text: In February 2020, Anil Ambani was locked in a legal battle with 3 Chinese banks. He was asked to set aside by the court which led him to make the statement that his net worth is currently zero after considering his liabilities. The dispute still rages on with the UK court ordering him to pay the 3 Chinese banks to the tune of .


title: Anil Ambani

text: Ambani belongs to the Gujarati community. He is married to Indian actress Tina Munim and they have two sons, Jai Anmol Ambani and Jai Anshul Ambani. Ambani is the younger brother to Mukesh Ambani and has two sisters, Nina Ambani Kothari and Dipti Ambani Salgaocar.


title: Anil Ambani

text: In 2018, India's principal opposition party, Indian National Congress, accused Prime Minister Narendra Modi of favouring Anil Ambani's defence manufacturing company over HAL, a public sector enterprise, in a fighter aircraft deal worth with French manufacturing firm Dassault. Ambani, several of whose companies are debt-ridden, has denied all charges of benefiting from crony capitalism. In factual terms, Reliance Defence stood to get just over 3 per cent of the Dassault Aviation offsets contract, contrary to the impression that it was to be the biggest beneficiary of the Rafale fighter jet deal.


title: Anil Ambani

text: In a possibly related controversy, one of his businesses partly financed a French film in which former French president Francois Hollande's then-partner had acted around the same time the aircraft deal was being negotiated.


title: RDFa

text: RDFa or Resource Description Framework in Attributes is a W3C Recommendation that adds a set of attribute-level extensions to HTML, XHTML and various XML-based document types for embedding rich metadata within Web documents. The Resource Description Framework (RDF) data-model mapping enables its use for embedding RDF subject-predicate-object expressions within XHTML documents. It also enables the extraction of RDF model triples by compliant user agents.


title: RDFa

text: RDFa was first proposed by Mark Birbeck in the form of a W3C note entitled "XHTML and RDF", which was then presented to the Semantic Web Interest Group at the W3C's 2004 Technical Plenary. Later that year the work became part of the sixth public Working Draft of XHTML 2.0.


title: RDFa

text: Although it is generally assumed that RDFa was originally intended only for XHTML 2, in fact the purpose of RDFa was always to provide a way to add a metadata to "any" XML-based language. Indeed, one of the earliest documents bearing the "RDF/A Syntax" name has the sub-title "A collection of attributes for layering RDF on XML languages". The document was written by Mark Birbeck and Steven Pemberton, and was made available for discussion on October 11, 2004.


title: RDFa

text: In April 2007 the XHTML 2 Working Group produced a module to support RDF annotation within the XHTML 1 family. As an example, it included an extended version of XHTML 1.1 dubbed XHTML+RDFa 1.0. Although described as not representing an intended direction in terms of a formal markup language from the W3C, limited use of the XHTML+RDFa 1.0 DTD did subsequently appear on the public Web.


title: RDFa

text: October 2007 saw the first public Working Draft of a document entitled "RDFa in XHTML: Syntax and Processing". This superseded and expanded upon the April draft; it contained rules for creating an RDFa parser, as well as guidelines for organizations wishing to make practical use of the technology.


title: RDFa

text: RDFa 1.1 reached recommendation status in June 2012. It differs from RDFa 1.0 in that it no longer relies on the XML-specific namespace mechanism. Therefore, it is possible to use RDFa 1.1 with non-XML document types such as HTML 4 or HTML 5. Details can be found in an appendix to HTML 5.


title: RDFa

text: An additional "RDFa 1.1 Primer" document was last updated 17 March 2015. (The first public Working Draft dates back to 10 March 2006.)


title: RDFa

text: There are some main well-defined variants of the basic concepts, that are used as reference and as abbreviation to the W3C standards.


title: RDFa

text: RDFa was defined in 2008 with the "RDFa in XHTML: Syntax and Processing" Recommendation. Its first application was to be a module of XHTML.


title: RDFa

text: The HTML applications remained, ""a collection of attributes and processing rules for extending XHTML to support RDF"" expanded to HTML5, are now expressed in a specialized standard, the "HTML+RDFa" (the last is ""HTML+RDFa 1.1 - Support for RDFa in HTML4 and HTML5"").


title: RDFa

text: The ""HTML+RDFa"" syntax of 2008 was also termed ""RDFa 1.0"", so, there are no "RDFa Core 1.0" standard.


title: RDFa

text: In general this 2008's "RDFa 1.0" is used with the old XHTML standards (as long as "RDFa 1.1" is used with XHTML5 and HTML5).


title: RDFa

text: Is the first generic (for HTML and XML) RDFa standard, now (2015) the "RDFa Core 1.1" is in the Third Edition.


title: RDFa

text: RDFa Lite is minimal subset of RDFa ... consisting of a few attributes that may be used to express machine-readable data in Web documents like HTML, SVG, and XML. While it is not a complete solution for advanced data markup tasks, it does work for most day-to-day needs and can be learned by most Web authors in a day.


title: RDFa

text: RDFa Lite consists of five attributes: vocab, typeof, property, resource, and prefix. RDFa 1.1 Lite is upwards compatible with RDFa 1.1.


title: RDFa

text: In 2009 the W3C was positioned to retain "RDFa Lite" as unique and definitive standard alternative to Microdata. The position was confirmed with the publication of the HTML5 Recommendation in 2014.


title: RDFa

text: The essence of RDFa is to provide a set of attributes that can be used to carry metadata in an XML language (hence the 'a' in RDFa).


title: RDFa

text: Additionally RDFa may benefit web accessibility as more information is available to assistive technology.


title: RDFa

text: Simplified approaches to semantically annotate information items in webpages were greatly encouraged by the HTML+RDFa (released in 2008) and microformats (since ~2005) standards.


title: RDFa

text: The following is an example of adding Dublin Core metadata to an XML element in an XHTML file. Dublin Core data elements are data typically added to a book or article (title, author, subject etc.)


title: RDFa

text: The following is an example of a complete XHTML+RDFa 1.0 document. It uses Dublin Core and FOAF, an ontology for describing people and their relationships with other people and things:


title: RDFa

text: In the example above, the document URI can be seen as representing an HTML document, but the document URI plus the "#me" string codice_1 represents the actual person, as distinct from a document about them. The "foaf:primaryTopic" in the header tells us a URI of the person the document is about. The "foaf:nick" property (in the first codice_2 element) contains a nickname for this person, and the "dc:creator" property (in the codice_3 element) tells us who created the document. The hyperlink to the Einstürzende Neubauten website contains codice_4, suggesting that John Doe is interested in this band. The URI of their website is a resource.


title: RDFa

text: The "foaf:interest" inside the second codice_5 element is referring to a book by ISBN number. The codice_6 attribute defines a resource in a similar way to the codice_7 attribute, but without defining a hyperlink. Further into the paragraph, a codice_2 element containing an codice_9 attribute defines the book as another resource to specify metadata about. The book title and author are defined within the contents of this tag using the "dc:title" and "dc:creator" properties.


title: RDFa

text: Note how the prefix foaf is still used without declaration. RDFa 1.1 automatically includes prefixes for popular vocabularies such as FOAF.


title: RDFa

text: That is, it is recommended that all of these attributes are used: codice_10, codice_11, codice_12; not only one of them.


title: Lexus

text: Created at around the same time as Japanese rivals Honda and Nissan created their Acura and Infiniti luxury divisions respectively, Lexus originated from a corporate project to develop a new premium sedan, code-named F1, which began in 1983 and culminated in the launch of the Lexus LS in 1989. Subsequently, the division added sedan, coupé, convertible and SUV models. Lexus did not exist as a brand in its home market until 2005, and all vehicles marketed internationally as Lexus from 1989 to 2005 were released in Japan under the Toyota marque and an equivalent model name. In 2005, a hybrid version of the RX crossover debuted and additional hybrid models later joined the division's lineup. Lexus launched its own F marque performance division in 2007 with the debut of the IS F sport sedan, followed by the LFA supercar in 2009.


title: Lexus

text: Lexus vehicles are largely produced in Japan, with manufacturing centered in the Chūbu and Kyūshū regions, and in particular at Toyota's Tahara, Aichi, Chūbu and Miyata, Fukuoka, Kyūshū plants. Assembly of the first Lexus produced outside the country, the Canadian-built RX 330, began in 2003. Following a corporate reorganization from 2001 to 2005, Lexus began operating its own design, engineering and manufacturing centers.


title: Lexus

text: Since the 2000s, Lexus has increased sales outside its largest market, the United States. The division inaugurated dealerships in the Japanese domestic market in 2005, becoming the first Japanese premium car marque to launch in its country of origin. The brand has since debuted in Southeast Asia, Latin America, Europe and other regions, and has introduced hybrid vehicles in many markets.


title: Lexus

text: The Lexus brand was created around the same time as Japanese rivals Nissan and Honda developed their Infiniti and Acura premium brands. The Japanese government imposed voluntary export restraints for the U.S. market, so it was more profitable for Japanese automakers to export more expensive cars to the U.S.


title: Lexus

text: In 1983, Toyota chairman Eiji Toyoda issued a challenge to build the world's best car. The project, code-named F1 (“Flagship One”) developed the Lexus LS 400 to expand Toyota's product line in the premium segment. The F1 project followed the Toyota Supra sports car and the premium Toyota Mark II models. Both the Supra and Mark II were rear-wheel drive cars with a powerful 7M-GE or 7M-GTE inline-six engine. The largest sedan Toyota built at the time was the limited-production, 1960s-vintage Toyota Century, a domestic, hand-built limousine, and V8-powered model, followed by the inline-six-engined Toyota Crown premium sedan. The Century was conservatively styled for the Japanese market and along with the Crown not slated for export after a restyle in 1982. The F1 designers targeted their new sedan at international markets and began development on a new V8 engine.


title: Lexus

text: Japanese manufacturers exported more expensive models in the 1980s due to voluntary export restraints negotiated by the Japanese government and U.S. trade representatives that restricted mainstream car sales. In 1986, Honda launched its Acura marque in the U.S., influencing Toyota's plans for a luxury division. The initial Acura model was an export version of the Honda Legend, itself launched in Japan in 1985 as a rival to the Toyota Crown, Nissan Cedric/Gloria and Mazda Luce. In 1987, Nissan unveiled its plans for a premium brand, Infiniti, and revised its Nissan President sedan in standard wheelbase form for export as the Infiniti Q45, which it launched in 1990. Mazda began selling the Luce as the Mazda 929 in North America in 1988 and later began plans to develop an upscale marque to be called Amati, but its plans did not come to fruition.


title: Lexus

text: Toyota researchers visited the U.S. in May 1985 to conduct focus groups and market research on luxury consumers. During that time, several F1 designers rented a home in Laguna Beach, California, to observe the lifestyles and tastes of American upper class consumers. Meanwhile, F1 engineering teams conducted prototype testing on locations ranging from the German autobahn to U.S. roads. Toyota's market research concluded that a separate brand and sales channel were needed to present its new sedan, and plans were made to develop a new network of dealerships in the U.S. market.


title: Lexus

text: In 1986, Toyota's longtime advertising agency Saatchi & Saatchi formed a specialized unit, Team One, to handle marketing for the new brand. Image consulting firm Lippincott & Margulies was hired to develop a list of 219 prospective names; Vectre, Verone, Chaparel, Calibre and Alexis were chosen as top candidates. While Alexis quickly became the front runner, concerns were raised that the name applied to people more than cars (being associated with the Alexis Carrington character on the popular 1980s prime time drama "Dynasty"). As a result, the first letter was removed and the "i" replaced with a "u" to morph the name to Lexus.


title: Lexus

text: Theories of the etymology of the Lexus name have suggested it is the combination of the words "luxury" and "elegance," and that it is an acronym for "luxury exports to the U.S." According to Team One interviews, the brand name has no specific meaning and simply denotes a luxurious and technological image. Prior to the release of the first vehicles, database service LexisNexis obtained a temporary injunction forbidding the name Lexus from being used because it might cause product confusion. The injunction threatened to delay the division's launch and marketing efforts. The U.S. appeals court lifted the injunction, deciding that there was little likelihood of confusion between the two products.


title: Lexus

text: The original Lexus slogan, developed after Team One representatives visited Lexus designers in Japan and noted an obsessive attention to detail, became "The Relentless Pursuit of Perfection." Three firms were involved in the final phase of logo development: Saatchi & Saatchi, Molly Designs and Hunter/Korobkin, Inc. The finished logo was a combination of two firms’ final designs: the Lexus logo typeface came from Saatchi & Saatchi and the “L” was Hunter/Korobkin, Inc.’s design. According to Toyota, the automaker made some refinements so the logo would be easier to manufacture, rendering it using a mathematical formula. The first teaser ads featuring the Lexus name and logo appeared at the Chicago, Los Angeles and New York auto shows in 1988.


title: Lexus

text: The F1 project was completed in 1989, involving 60 designers, 24 engineering teams, 1,400 engineers, 2,300 technicians, 220 support workers, approximately 450 prototypes and more than $1 billion in costs. The resulting car, the Lexus LS 400, had a design that shared no major elements with previous Toyota vehicles, with a new 4.0 L V8 gasoline engine and rear-wheel drive. The car debuted in January 1989 at the North American International Auto Show in Detroit and official sales of the vehicle began the following September at a network of 81 new Lexus dealerships in the U.S. The LS 400 was sold along with the smaller ES 250, a rebadged version of the Japanese market Toyota Camry Prominent/Toyota Vista. The launch of Lexus was accompanied by a multimillion-dollar advertising campaign.


title: Lexus

text: The LS 400 was praised for its quietness, well-appointed and ergonomic interior, engine performance, build quality, aerodynamics, fuel economy and value. However, it was criticized by some automobile columnists for derivative styling and a suspension regarded as too compromising of handling for ride comfort. In some markets it was priced against mid-size, six-cylinder Mercedes-Benz and BMW models. It was rated by "Car and Driver" magazine as better than the higher-priced Mercedes-Benz 420 SEL and BMW 735i in terms of ride, handling and performance. The LS 400 also won motoring awards from automotive publications including "Automobile Magazine" and "Wheels Magazine". Lexus quickly established customer loyalty and its debut was generally regarded as a shock to existing luxury marques. BMW's and Mercedes-Benz's U.S. sales figures dropped 29 percent and 19 percent, respectively, with BMW executives accusing Lexus of dumping in that market, while 35 percent of Lexus buyers traded in a Lincoln or Cadillac.


title: Lexus

text: In December 1989, Lexus initiated a voluntary recall of all 8,000 LS 400s based upon two customer complaints over defective wiring and an overheated brake light. A 20-day operation to replace the parts on affected vehicles included technicians to pick up, repair and return cars to customers free of charge, and also flying personnel and renting garage space for owners in remote locations. This response was covered in media publications and helped establish the marque's early reputation for customer service.


title: Lexus

text: By the end of 1989, a total of 16,392 LS 400 and ES 250 sedans were sold in the four months following the U.S. launch. Although sales had begun at a slower pace than expected, the final tally matched the division's target of 16,000 units for that year. Following initial models, plans called for the addition of a sports coupe along with a redesigned ES sedan.


title: Lexus

text: In 1990, during its first full year of sales, Lexus sold 63,594 LS 400 and ES 250 sedans in the U.S., the majority being the LS model. That year, Lexus also began limited exports to the United Kingdom, Switzerland, Canada and Australia. In 1991, Lexus launched its first sports coupe, the SC 400, which shared the LS 400s V8 engine and rear-wheel drive design. This was followed by the second generation ES 300 sedan, which succeeded the ES 250 and became Lexus' top seller. At the conclusion of 1991, Lexus had become the top-selling premium car import in the U.S., with sales reaching 71,206 vehicles. That year, Lexus ranked highest in J.D. Power and Associates' studies on initial vehicle quality, customer satisfaction and sales satisfaction for the first time. The marque also began increasing U.S. model prices past those of comparable American premium makes, but still below high-end European models. By 1992, the LS 400's base price had risen 18 percent.


title: Lexus

text: In 1993, Lexus launched the mid-size GS 300 sports sedan, based on the Toyota Aristo using the Toyota "S" platform from the Toyota Crown, which had sold for two years prior in Japan. The GS 300 was priced below the LS 400 in the marque's lineup. That same year, Lexus became one of the first marques to debut a certified pre-owned program, with the aim of improving trade-in model values. The marque introduced the second generation LS 400 in 1994. In May 1995, sales were threatened by the U.S. government's proposal of 100 percent tariffs on upscale Japanese cars in response to the widening U.S.-Japan trade deficit. SUVs were exempt from the proposed sanctions. Normal sales operations resumed by late 1995 when the Japanese auto manufacturers collectively agreed to greater American investments and the tariffs were not enacted.


title: Lexus

text: In 1996, Lexus debuted its first sport utility vehicle, the LX 450, followed by the third generation ES 300 sedan, and the second generation GS 300 and GS 400 sedans in 1997. The marque's plans for developing an SUV model had accelerated during the U.S.-Japan tariff discussions of 1995. Lexus added the first luxury-branded crossover SUV, the RX 300 in 1998. The RX crossover targeted suburban buyers who desired an upmarket SUV but did not need the LX's off-road capability. It was particularly successful, eventually becoming the marque's top-selling model ahead of the ES sedan. The same year, Lexus made its debut in South America's most populous country when it launched sales in Brazil. In 1999, the IS was introduced, an entry-level sport sedan. Lexus also recorded its 1 millionth vehicle sold in the U.S. market, being ranked as the top-selling premium car maker in the U.S. overall.


title: Lexus

text: In July 2000, Lexus introduced the IS 300 in North America, following global launch in 1999 (as the IS 200) and the third generation LS 430. In 2001, the first convertible was introduced, as well as the SC 430 and a redesigned ES 300. The GX 470 mid-size SUV debuted in 2002, followed by the second generation RX 330 in 2003. The following year, Lexus recorded its 2 millionth U.S. vehicle sale, and the first luxury-branded production hybrid SUV, the RX 400h. This vehicle used Toyota's Hybrid Synergy Drive system that combined gasoline and electric motors.


title: Lexus

text: In 2005, Lexus completed an organizational separation from parent company Toyota, with dedicated design, engineering, training, and manufacturing centers working exclusively for the division. This effort coincided with Lexus' launch in its home market of Japan and an expanded global launch of the brand in markets such as China. Executives aimed to increase Lexus sales outside of its largest market in the U.S. To accompany this expansion, next generation Lexus vehicles were redesigned as "global models" for international release. In the European market, where Lexus had long faced struggling sales owing to low brand recognition, few dedicated dealerships, and 1990s import quotas, the marque announced plans to introduce hybrid and diesel powertrains, increase the number of Lexus dealerships, and expand operations in emerging markets such as Russia.


title: Lexus

text: Lexus' arrival in the Japanese market in July 2005 marked the first introduction of a Japanese premium car marque in the domestic market. New generation LS, IS, ES, GS, and RX models subsequently became available in Japan along with the SC 430, ending domestic sales of Toyota-branded models under the Celsior, Altezza, Windom, Aristo, Harrier, and Soarer nameplates, respectively. The Altezza and Aristo were previously exclusive to Japanese Toyota retail sales channels called Toyota Vista Store, the Windom was exclusive to Toyota Corolla Store, the Celsior and Harrier were exclusive to Toyopet Store, and the Soarer was previously available at both Toyota Store and Toyopet Store locations. Lexus models sold in Japan featured higher specifications and a price premium compared with their discontinued Toyota counterparts. Sales for the first half-year were slower than expected, affected by the contraction of the domestic auto market and price increases, but improved in subsequent months with an expanded lineup.


title: Lexus

text: Through the mid-2000s, Lexus experienced sales successes in South Korea and Taiwan, becoming the top-selling import make in both markets in 2005; the marque also sold well in the Middle East, where it ranked first or second among rivals in multiple countries, and in Australia, where Lexus reached third in luxury car sales in 2006. Division executives in 2006 announced an expansion goal from 68 countries to 76 worldwide by 2010. By the end of the decade, this expansion resulted in official launches in Malaysia and South Africa in 2006, Indonesia in 2007, Chile in 2008, and the Philippines in 2009.


title: Lexus

text: In 2006, Lexus began sales of the GS 450h, a V6 hybrid performance sedan, and launched the fourth generation LS line, comprising both standard- and long-wheelbase V8 (LS 460 and LS 460 L) and hybrid (LS 600h and LS 600h L) versions. The fifth generation ES 350 also debuted in the same year. The LS 600h L subsequently went on sale as the most expensive sedan ever produced in Japan. By the end of 2006, Lexus' annual sales had reached 475,000 vehicles worldwide. In January 2007, Lexus announced a new F marque performance division, which would produce racing-inspired versions of its performance models. The IS F, made its debut at the 2007 North American International Auto Show, accompanied by a concept car, the LF-A.


title: Lexus

text: In October 2007, Lexus entered the Specialty Equipment Market Association show in the U.S. for the first time with the IS F, and announced its F-Sport performance trim level and factory-sanctioned accessory line. Increased emphasis on sporty models was an effort to target rivals from Mercedes-Benz's AMG and BMW's M divisions. Models such as the SC 400 and GS 400 had received favorable reactions from sport luxury buyers, most Lexus models had been characterized as favoring comfort over sporty road feel and handling, compared with European rivals. By the end of 2007, Lexus annual worldwide sales had surpassed 500,000 vehicles, and the marque ranked as the top-selling premium import in China for the first time. The largest sales markets in order of size for 2007 were the U.S., Japan, the UK, China, Canada, and Russia.


title: Lexus

text: In 2008, amidst the late-2000s recession and a weakened world car market, global sales fell 16 percent to 435,000, with declines in markets such as the U.S. and Europe where deliveries fell by 21 percent and 27.5 percent, respectively. In 2009, the marque launched the HS 250h, a dedicated hybrid sedan for North America and Japan, the RX 450h, the second generation hybrid SUV replacing the earlier RX 400h, and later that year debuted the production LFA exotic coupe. In late 2009, citing higher sales of hybrid models over their petrol counterparts, Lexus announced plans to become a hybrid-only marque in Europe. By the end of the decade, Lexus ranked as the fourth-largest premium car make in the world by volume, and was the number one selling premium car marque in the U.S. for 10 consecutive years.


title: Lexus

text: In 2010, Lexus underwent a gradual sales recovery in North America and Asia as the marque focused on adding hybrids and new model derivatives. Sales in the U.S. held steady despite the 2009–2010 Toyota vehicle recalls, several of which included Lexus models. The ES 350 and certain IS models were affected by a recall for potentially jamming floor mats, while parent company Toyota bore the brunt of negative publicity amid investigations over its series of product recalls and problem rates per-vehicle. The redesigned GX 460 was also voluntarily recalled in April 2010 for a software update, one week after "Consumer Reports" issued a recommendation not to buy the SUV, citing a possible rollover risk following the slow stability control response to a high-speed emergency turn. Although the publication knew of no reported incidents, the GX 460 received updated stability control software.


title: Lexus

text: In late 2010 and early 2011, Lexus began sales of the CT 200h, a compact four-door hybrid hatchback designed for Europe, in multiple markets. Sales of lower-displacement regional models were also expanded, beginning with the ES 240 in China followed by the RX 270; Japan, Russia, and Taiwan were among markets which received model variants intended for reduced emissions or import taxes. In March 2011, the Tōhoku earthquake and tsunami caused severe disruption to Lexus' Japan-based production lines, hindering the marque's near-term sales prospects. Lexus' U.S. executives stated that due to vehicle shortages amidst close competition from BMW, Mercedes-Benz, and Audi, the marque would not remain the country's top-selling premium car brand.


title: Lexus

text: Cumulative sales results for 2011 indicated a 14 percent sales drop in the U.S. market, along with sales increases of 40 percent and 27 percent in Europe and Japan respectively, for a global sales total of 410,000 units. Lexus' streak of 11 consecutive years as the best-selling luxury marque in the U.S. ended that year, with the title going to BMW followed by Mercedes-Benz. While 45 percent of Lexus sales in the U.S. in 2011 relied upon the RX luxury crossover SUV, rival Mercedes-Benz's best-selling offering was the E-Class mid-luxury sedan, which commands considerably higher prices. Subsequently, Toyota chairman Akio Toyoda vowed to restore passion to the marque and further increase its organizational independence, admitting that "...back then we did not regard Lexus as a brand, but as a distribution channel". As a result of Toyoda's organizational changes, Lexus senior managers report directly to the chairman for the first time in the marque's history.


title: Lexus

text: In January 2012, the marque began sales of the fourth generation GS line, including GS 350 and GS 450h variants, as well as a lower-displacement GS 250 model for select markets. In April 2012, the sixth generation ES line, including ES 350 and ES 300h variants, debuted at the New York International Auto Show.


title: Lexus

text: In April 2014, Lexus unveiled the five-seater NX crossover. The vehicle features a very first for a Lexus vehicle: a turbocharger. Its nomenclature is denoted as the 200t. In August 2014, Toyota announced it would be cutting its Lexus spare parts prices in China by up to 35 percent. The company admitted the move was in response to a probe foreshadowed earlier in the month by China's National Development and Reform Commission of Lexus spare parts policies, as part of an industry-wide investigation into what the Chinese regulator considers exorbitantly high prices being charged by automakers for spare parts and after-sales servicing.


title: Lexus

text: In March 2016, Lexus announced that it will be producing a new flagship vehicle: the two-door LC 500. The vehicle will be produced for late 2017 in a V8 version putting out 467 horsepower. The LC 500h, a V6 hybrid variant, could potentially become available in late 2017 or early 2018.