title: Pramod Sawant

text: After the demise of Manohar Parrikar, the seat of the Chief Minister of Goa fell vacant. Pramod Sawant was elected by the Legislative Assembly afterwards and later he was sworn in as the 13th Chief Minister of Goa on 19 March 2019.


title: Pramod Sawant

text: Sawant is a Kunbi-Maratha by caste. He is married to Sulakshana, who is a teacher of chemistry at the Shri Shantadurga Higher Secondary School in Bicholim. She is also a leader of the Bharatiya Janata Party and currently the President of the Goa unit of the BJP Mahila Morcha.


title: Resolution (film)

text: Resolution is a 2012 American horror film directed by Justin Benson and Aaron Scott Moorhead, written by Benson, and starring Peter Cilella and Vinny Curran. Cilella plays a graphic designer and father-to-be named Michael who, after receiving a troubling email video of his drug-addicted best friend Chris (played by Curran), travels to a remote cabin to save him. The 2017 film "The Endless" shares the same creative universe as "Resolution", and may be interpreted as a partial sequel.


title: Resolution (film)

text: Michael Danube, a graphic designer living in the city with his pregnant wife, receives an email containing a video of Chris Daniels, his best friend. Chris, a drug addict, has retreated to a remote rural area and has become delusional and erratic. A map is included with the video. Despite his wife's objections, Michael makes one last attempt to save Chris. He promises to return after one week and follows the map.


title: Resolution (film)

text: At his destination, Michael hears Chris ranting and shooting a pistol. Chris invites Michael in and starts ranting about various subjects. When Chris refuses to go into rehab, Michael subdues him with a stun gun, handcuffs him and goes to a nearby town to shop for supplies. In the morning, Michael staves off an attempted attack from Chris.


title: Resolution (film)

text: Later, Micah and Billy, Michael and Chris' old acquaintances, arrive and ask for their drug, which Chris is holding. After Michael drives them off, Chris warns him against messing with them, as they have become violent and unpredictable. As he takes a walk, Michael meets members of a UFO religion, then returns to the house and finds a set of strange photographs. Micah and Billy return, but Charles, a tribal security guard chases them off. Charles tells Michael that Chris is squatting on reservation land, but accepts Michael's bribe in exchange for letting them stay for five days.


title: Resolution (film)

text: After they discover creepy film footage, Chris denies sending any emails or videos. Michael finds a book full of creepy campfire stories on their doorstep, and, when he returns the book to the library, finds film slides. Confused by the items that seem purposefully left for them to find, Michael suggests that it is a prank by Billy and Micah, which Chris dismisses.


title: Resolution (film)

text: Michael continues to find clues strewn about the area. When he bribes Charles for information, Charles warns him against digging into the past, only saying French students used the area for research. They encounter a con artist who offers to buy the house and leaves after Michael says that they are only "renting." Michael re-watches the video he received in the e-mail and finds it has changed, it now shows an argument that Michael and Chris had moments before. Billy and Micah return and kill a dog that Chris had adopted, and Chris reveals that he is suicidal.


title: Resolution (film)

text: Michael tracks down the dog's original owner, an archeologist named Byron, a member of the original French research team. Byron, who smokes a hallucinogenic drug that is red in colour, suggests that the two other students researchers were looking for monsters and found themselves. Byron believes the area is not haunted; instead, "something" there desires stories. While reflecting a small mirror into a large one, creating an infinity of reflections of himself and Michael, Byron stresses the need for a beginning, middle, and end. Unnerved by Byron's eccentricity, Michael leaves.


title: Resolution (film)

text: As more clues appear from nowhere, the film projector Michael has been using turns on and projects the gruesome deaths and funeral photos of himself and Chris. Michael's laptop plays a video depicting their deaths at the hands of Micah and Billy. The two flee the house, only to find a CD that has a recording of Charles murdering them and burning down the house. Chris wants to leave the property immediately; Michael, however, does not want to bring the curse home and wants to appease the entity instead. Upon returning to the house, they witness Charles and a companion from the reservation killing Micah and Billy, after which Charles and his companion set the house on fire. Chris and Michael panic; Chris breaks down and finally agrees to go to rehab. Their joy over achieving a happy ending to their story is abruptly cut short when the entity angrily confronts them. Chris kneels before it and apologizes profusely, and Michael asks the entity, "Can we try it another way?" The only reply he gets is an explosive roar from the creature.


title: Resolution (film)

text: Although the film is often described as "genre-bending", this was not an intentional concept; it was always meant as a horror film about an unseen antagonist that manipulates reality to create interesting stories. The detox plotline was introduced to give the story more structure, as the directors needed a plot device to have the story unfold over seven days. The script was written in six months. The main parts of the film were shot in 17 days, but the side plots were shot over the course of several months on weekends. The directors were specifically interested in avoiding overt homage, and, instead, focused on parodying independent film tropes. The film was shot in East County, San Diego. The directors have no direct experience with detox; to perform research, they searched Google for information. Benson was acquainted with a crack addict, however, and he used some of the addict's ramblings as inspiration for Chris' dialog.


title: Resolution (film)

text: "Resolution" had its world premiere at the Tribeca Film Festival April 20, 2012. Tribeca Film gave the film an initial limited theatrical release on January 25, 2013. Cinedigm and Tribeca Film released "Resolution" on DVD, Blu-ray, and video-on-demand October 8, 2013.


title: Resolution (film)

text: Rotten Tomatoes, a review aggregator, reports that "Resolution" received positive reviews from 80% of 15 critics surveyed. Metacritic scored it 80/100 based on 5 reviews, which indicates "generally favorable reviews". Mark Adams of Screen Daily called it "a clever, twisted and very impressive slow-burner of a chiller". Rod Lott of the "Oklahoma Gazette" called it suspenseful and singled out the last 20 minutes as "seriously unnerving." Jason Jenkins of Dread Central rated the film 4.5/5 stars and wrote, "With its great cast, unique concept, and its sharply written script, "Resolution" is one of the very best films I’ve seen this year." Peter Gutierrez of Twitch Film said that the film has a "quietly mythic power" and takes many big risks that pay off. Adam Tyner of DVD Talk rated the film 5/5 stars and wrote, "There's a sense of unease that pervades almost every frame in Resolution, and a key part of it is not knowing what's lurking around the next bend. This is what horror movies are supposed to do, but it hardly ever really works in practice. "Resolution" not only nails it, but it does so without leaning on any jump scares, stings in the score, or cheap gore as a crutch."


title: Resolution (film)

text: Michael Nazarewycz of DVD Verdict said that "Resolution" is "a very good film" that gives new life to old tropes. Dennis Harvey of "Variety" wrote, "There are long buildups, and then there's "Resolution", a movie that's virtually all nothing-much-happening setup until a still-teasing titular event that occupies just a few final seconds." Lonnie Nadler of Bloody Disgusting rated the film 4/5 stars and wrote that it "delivers a dashingly intelligent commentary on the horror genre, the nature of cinema, and the relationship viewers have to on-screen victims." Serena Whitney of Dread Central rated the film 5/5 stars and called it "a remarkable achievement" and "an inventive, character-based story" that "provides be the breath of fresh air the genre sorely needs". Robert Abele of the "Los Angeles Times" wrote that it offers "a strangely tense and humorous meta-narrative" that "manages to keep its eerier moments surprising and its emotional life arresting."


title: Resolution (film)

text: Many reviews compared it to "The Cabin in the Woods". "SFX" rated it 3.5/5 stars and described it as "clever, creepy meta-horror" that is like a lo-fi version of "The Cabin in the Woods". Kurt Halfyard of Twitch Film wrote, "Unlike the smug, offhand silliness of Joss Whedon and Drew Goddard's "Cabin in the Woods", this one makes you give a damn; as much about the films building "Lost"-type puzzlebox, but moreso the two exceptionally well realized characters." Scott Weinberg of Fearnet called the film "a smart and subversive take" that is less entertaining than "Cabin in the Woods". Nick Schager of "The Village Voice" wrote that it puts "Cabin in the Woods" "to shame on a fraction of the budget". Ian Buckwalter of NPR wrote, ""Resolution" is really a less self-conscious cousin to last year's "Cabin in the Woods"; both are hugely satisfying exercises in examining the way in which stories are told." Scott Tobias of The A.V. Club rated it B and called it "an indie analog to "The Cabin In The Woods"" that "gets further in its conceit than its execution".


title: Resolution (film)

text: At Macabro 2013, the directors were awarded Best Director. At the Toronto After Dark Film Festival, the film won four awards, including best screenplay and most innovative film. The directors won Best Director at the 2013 Fantastic Planet film festival.


title: Etch A Sketch

text: Etch A Sketch is a mechanical drawing toy invented by André Cassagnes of France and subsequently manufactured by the Ohio Art Company. It is now owned by Spin Master of Toronto, Ontario, Canada.


title: Etch A Sketch

text: An Etch A Sketch has a thick, flat gray screen in a red plastic frame. There are two white knobs on the front of the frame in the lower corners. Twisting the knobs moves a stylus that displaces aluminum powder on the back of the screen, leaving a solid line. The knobs create lineographic images. The left control moves the stylus horizontally, and the right one moves it vertically.


title: Etch A Sketch

text: The Etch A Sketch was introduced near the peak of the Baby Boom on 12 July 1960 for $2.99 (). It went on to sell 600,000 units that year and is one of the best known toys of that era. In 1998, it was inducted into the National Toy Hall of Fame at The Strong, in Rochester, New York. In 2003, the Toy Industry Association named Etch A Sketch one of the 100 most memorable toys of the 20th century. The Etch A Sketch has since sold over 100 million units worldwide.


title: Etch A Sketch

text: The toy is a kind of plotter. The inside surface of the glass screen is coated with aluminium powder, which is then scraped off by a movable stylus, leaving a dark line on the light gray screen. The stylus is controlled by the two large knobs, one of which moves it vertically and the other horizontally. Turning both knobs simultaneously makes diagonal lines. To erase the picture, the user turns the toy upside down and shakes it. Doing this causes polystyrene beads to smooth out and re-coat the inside surface of the screen with aluminum powder. The "black" line merely exposes the darkness inside the toy. Scraping out large "black" areas allows enough light through to expose parts of the interior.


title: Etch A Sketch

text: The Etch A Sketch toy was invented in the late 1950s by André Cassagnes, an electrician with Lincrusta Co, who named the toy "L'Écran Magique" (The Magic Screen). In 1959, he took his drawing toy to the International Toy Fair in Nuremberg, Germany. The Ohio Art Company saw it but had no interest in the toy. When Ohio Art saw the toy a second time, they decided to take a chance on the product. "L'Écran Magique" was soon renamed the Etch A Sketch and became the most popular drawing toy in the business. After a complex series of negotiations, the Ohio Art Company launched the toy in the United States in time for the 1960 Christmas season with the name "Etch A Sketch". Ohio Art supported the toy with a televised advertising campaign.


title: Etch A Sketch

text: Originally, the toy used a plate glass screen, which was criticized by safety advocates for being easily broken and a danger to children. In November 1970, Consumers Union filed a petition with the Department of Health, Education and Welfare, asking for emergency action under the 1969 Child Protection and Toy Safety Act. The Food and Drug Administration responded that the toy had been redesigned, replacing the glass plate with plastic.


title: Etch A Sketch

text: The Etch A Sketch toy was featured in the 1995 Disney/Pixar animated film "Toy Story", in a scene where a sentient one performs a "quick draw" duel with Sheriff Woody. This 12-second feature had been enough to give a significant sales boost, requiring the production line to work overtime to meet demand. By 1999, the company had again fallen into severe financial trouble from canceled orders of various products, reaching a point where the solvency of the company was in question. However, the company recovered with the prudent decision to agree to again have an Etch A Sketch appear in an animated feature film – this time in 1999 sequel "Toy Story 2". This scene featured an Etch A Sketch being used to present sketches related to the investigation of Sheriff Woody's kidnapping by Al McWhiggin the toy collector and the owner of Al's Toy Barn. At 45 seconds, the scene in question was much longer than the scene in the original movie. The exposure from the highly successful Pixar movie resulted in sales of the toy increasing by 20 percent and ensured the survival of the company.


title: Etch A Sketch

text: Etch A Sketch was manufactured in Bryan, Ohio until the company moved the manufacturing plant to Shenzhen, China in 2001.


title: Etch A Sketch

text: In France, its country of origin, Etch A Sketch was sold under the name of "Télécran", rather than "L'Écran Magique".


title: Etch A Sketch

text: In February 2016, the rights to the Etch A Sketch name and design were acquired by Toronto-based Spin Master Corporation.


title: Etch A Sketch

text: The Etch A Sketch Animator (known simply as "The Animator" in Canada and Europe), debuted in 1986, and featured a 40x30 dot matrix display and used two knobs for drawing, like a regular Etch A Sketch, with several buttons to manipulate the drawings. The initial price was . It had two kilobytes of memory, capable of storing 12 frames of pictures in any combination up to 96 times. It contained a speaker, which made static-like sounds when the knobs were moved and during animations.


title: Etch A Sketch

text: With the return of the home video game market in the mid 80s and the relative success of the Etch A Sketch Animator, Ohio Art decided to release a high-tech sequel to the Animator, known as the Animator 2000. Ohio Art released the system in 1987, at a suggested retail price of . The unit itself doesn't resemble a traditional Etch A Sketch at all: The classic knobs are replaced with "The Magic Touchpad", the system's form-factor resembles a laptop computer, and the unit features a large 6040 LCD screen. The unit contains 196KB of "powerful computer memory" which is a significant upgrade over the roughly 2KB of the original Animator. This memory upgrade allowed the system to have 22 frames in which to store drawings, and these frames could be animated in sequence up to 99 times. This memory upgrade combined with the relatively powerful custom processor was also important since the Animator 2000 was designed to be a portable entertainment/games system instead of simply an electronic drawing toy. The unit features a cartridge slot, and four cartridges were available: "Fly By", a flight simulator game; "Overdrive", a road racing game; "Putt-Nuts", a miniature golf game; and "Memory", a memory expansion cartridge. The price for one cartridge was .


title: Etch A Sketch

text: In 1993, Ohio launched a color Etch A Sketch. Similar to the original Etch A Sketch, it used the traditional two-knob interface to draw, but also featured six colors. It also had the ability to produce a color copy of each picture drawn.


title: Etch A Sketch

text: These are basically hand-held controllers that connect to a television-like handheld TV games and work like a regular Etch A Sketch, except on the television screen and with the addition of colors and sound effects.


title: Etch A Sketch

text: There are a few practicing artists who use the Etch A Sketch to produce professional lineographic work. The artists make their work permanent by removing the aluminum powder. This is done either by drilling holes in the bottom of the toy or by removing the entire plastic backing. It is then resealed as a permanent, shake-resistant piece of art.


title: Check digit

text: A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary parity bit used to check for errors in computer-generated data. It consists of one or more digits (or letters) computed by an algorithm from the other digits (or letters) in the sequence input.


title: Check digit

text: With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit or some permutations of two successive digits.


title: Check digit

text: Check digit algorithms are generally designed to capture "human" transcription errors. In order of complexity, these include the following:


title: Check digit

text: In choosing a system, a high probability of catching errors is traded off against implementation difficulty; simple check digit systems are easily understood and implemented by humans but do not catch as many errors as complex ones, which require sophisticated programs to implement.


title: Check digit

text: A desirable feature is that left-padding with zeros should not change the check digit. This allows variable length numbers to be used and the length to be changed.


title: Check digit

text: If there is a single check digit added to the original number, the system will not always capture "multiple" errors, such as two replacement errors (12 → 34) though, typically, double errors will be caught 90% of the time (both changes would need to change the output by offsetting amounts).


title: Check digit

text: A very simple check digit method would be to take the sum of all digits (digital sum) modulo 10. This would catch any single-digit error, as such an error would always change the sum, but does not catch any transposition errors (switching two digits) as re-ordering does not change the sum.


title: Check digit

text: A slightly more complex method is to take the weighted sum of the digits, modulo 10, with different weights for each number position.


title: Check digit

text: To illustrate this, for example if the weights for a four digit number were 5, 3, 2, 7 and the number to be coded was 4871, then one would take 5×4 + 3×8 + 2×7 + 7×1 = 65, i.e. 65 modulo 10, and the check digit would be 5, giving 48715.


title: Check digit

text: Systems with weights of 1, 3, 7, or 9, with the weights on neighboring numbers being different, are widely used: for example, 31 31 weights in UPC codes, 13 13 weights in EAN numbers (GS1 algorithm), and the 371 371 371 weights used in United States bank routing transit numbers. This system detects all single-digit errors and around 90% of transposition errors. 1, 3, 7, and 9 are used because they are coprime with 10, so changing any digit changes the check digit; using a coefficient that is divisible by 2 or 5 would lose information (because 5×0 = 5×2 = 5×4 = 5×6 = 5×8 = 0 modulo 10) and thus not catch some single-digit errors. Using different weights on neighboring numbers means that most transpositions change the check digit; however, because all weights differ by an even number, this does not catch transpositions of two digits that differ by 5 (0 and 5, 1 and 6, 2 and 7, 3 and 8, 4 and 9), since the 2 and 5 multiply to yield 10.


title: Check digit

text: The code instead uses modulo 11, which is prime, and all the number positions have different weights 1, 2, ... 10. This system thus detects all single-digit substitution and transposition errors (including jump transpositions), but at the cost of the check digit possibly being 10, represented by "X". (An alternative is simply to avoid using the serial numbers which result in an "X" check digit.) instead uses the GS1 algorithm used in EAN numbers.


title: Check digit

text: More complicated algorithms include the Luhn algorithm (1954), which captures 98% of single-digit transposition errors (it does not detect 90 ↔ 09) and the still more sophisticated Verhoeff algorithm (1969), which catches all single-digit substitution and transposition errors, and many (but not all) more complex errors. Similar is another abstract algebra-based method, the Damm algorithm (2004), that too detects all single-digit errors and all adjacent transposition errors. These three methods use a single check digit and will therefore fail to capture around 10% of more complex errors. To reduce this failure rate, it is necessary to use more than one check digit (for example, the modulo 97 check referred to below, which uses two check digits—for the algorithm, see International Bank Account Number) and/or to use a wider range of characters in the check digit, for example letters plus numbers.


title: Check digit

text: For instance, the UPC-A barcode for a box of tissues is "036000241457". The last digit is the check digit "7", and if the other numbers are correct then the check digit calculation must produce 7.


title: Check digit

text: The final character of a ten-digit International Standard Book Number is a check digit computed so that multiplying each digit by its position in the number (counting from the right) and taking the sum of these products modulo 11 is 0. The digit the farthest to the right (which is multiplied by 1) is the check digit, chosen to make the sum correct. It may need to have the value 10, which is represented as the letter X. For example, take the : The sum of products is 0×10 + 2×9 + 0×8 + 1×7 + 5×6 + 3×5 + 0×4 + 8×3 + 2×2 + 1×1 = 99 ≡ 0 (mod 11). So the ISBN is valid. Note that positions can also be counted from left, in which case the check digit is multiplied by 10, to check validity: 0×1 + 2×2 + 0×3 + 1×4 + 5×5 + 3×6 + 0×7 + 8×8 + 2×9 + 1×10 = 143 ≡ 0 (mod 11).


title: Check digit

text: <nowiki>ISBN</nowiki> 13 (in use January 2007) is equal to the EAN-13 code found underneath a book's barcode. Its check digit is generated the same way as the UPC except that the even digits are multiplied by 3 instead of the odd digits.


title: Check digit

text: EAN (European Article Number) check digits (administered by GS1) are calculated by summing each of the odd position numbers multiplied by 3 and then by adding the sum of the even position numbers. Numbers are examined going from right to left, so the first odd position is the last digit in the code. The final digit of the result is subtracted from 10 to calculate the check digit (or left as-is if already zero).


title: Check digit

text: Another official calculator page shows that the mechanism for GTIN-13 is the same for Global Location Number/GLN.


title: Check digit

text: The NOID Check Digit Algorithm (NCDA), in use since 2004, is designed for application in persistent identifiers and works with variable length strings of letters and digits, called extended digits. It is widely used with the ARK identifier scheme and somewhat used with schemes, such as the Handle System and DOI. An extended digit is constrained to betanumeric characters, which are alphanumerics minus vowels and the letter 'l' (ell). This restriction helps when generating opaque strings that are unlikely to form words by accident and will not contain both O and 0, or l and 1. Having a prime radix of R=29, the betanumeric repertoire permits the algorithm to guarantee detection of single-character and transposition errors for strings less than R=29 characters in length (beyond which it provides a slightly weaker check). The algorithm generalizes to any character repertoire with a prime radix R and strings less than R characters in length.


title: Natalia Sánchez (actress)

text: Natalia Sánchez Molina (born March 27, 1990) is a Spanish actress and singer, who is best known of portraying María Teresa "Teté" Capdevila Gómez on hit television "Los Serrano".


title: Natalia Sánchez (actress)

text: Natalia Sánchez Molina was born on March 27, 1990 in Madrid. She has one older sister, named Sandra. Sánchez speaks Spanish, English, Catalan and French.


title: Natalia Sánchez (actress)

text: In 2004, Sánchez filmed a television commercial for El Corte Inglés with the rest of the main actors of "Los Serrano".


title: Natalia Sánchez (actress)

text: Since 2013, she has been in a relationship with Spanish actor, Marc Clotet. On January 8, 2019, she gave birth to the couple's first child, daughter Lia Clotet Sánchez, in Barcelona, Spain. On May 19, 2020, she gave birth to the couple's second child, son Neo Clotet Sánchez, also born in Barcelona.


title: 2015 NBA playoffs

text: The 2015 NBA playoffs was the postseason tournament of the National Basketball Association's 2014–15 season. The tournament concluded with the Western Conference champion Golden State Warriors defeating the Eastern Conference champion Cleveland Cavaliers 4 games to 2 in the NBA Finals. Andre Iguodala was named NBA Finals MVP.


title: 2015 NBA playoffs

text: For the first time since 2005–06, all teams from a particular division made the playoffs (in this case, all five teams from the Southwest Division).


title: 2015 NBA playoffs

text: The San Antonio Spurs made their 18th straight playoff appearance, while the Atlanta Hawks (eighth straight playoff appearance) and the Golden State Warriors (third straight playoff appearance) entered the playoffs as the first seeds of their respective conferences. The Warriors and Hawks advanced to the Conference Finals for the first time since 1976 and 1970, respectively.


title: 2015 NBA playoffs

text: The Cleveland Cavaliers made their first postseason appearance since 2010, the final season of LeBron James' first stint with the Cavaliers. They also made their first Conference Finals appearance since 2009, where they lost 4–2 to the Orlando Magic, and their first Finals appearance since 2007, when they were swept by the San Antonio Spurs. On the other hand, James' former team, the Miami Heat, missed the playoffs after making the previous year's Finals, becoming the first team to do so since the 2005 Lakers. Miami had qualified for the playoffs for six consecutive seasons before missing this year, also reaching the NBA Finals four consecutive times. The Heat and their in-state rivals, the Orlando Magic, both missed the playoffs in the same season for the first time since 1993.


title: 2015 NBA playoffs

text: The Oklahoma City Thunder and the Indiana Pacers were conference finalists a year ago but failed to make the playoffs. Oklahoma City and Indiana were tied with the New Orleans Pelicans and the Brooklyn Nets with 45 and 38 wins, respectively, but missed the playoffs due to tiebreakers.


title: 2015 NBA playoffs

text: Despite starting their respective seasons in a rebuilding mode, both the Milwaukee Bucks and the Boston Celtics returned to the playoffs after a one-year absence. Bucks head coach Jason Kidd became the first head coach to lead two teams to the playoffs in his first two seasons, having led the Nets to the playoffs the previous season.


title: 2015 NBA playoffs

text: The first round of the playoffs saw a record six teams take a 3–0 lead in their respective series, the first time it had happened since the first round expanded to a best-of-seven series in 2003.


title: 2015 NBA playoffs

text: Game 7 between the Clippers and Spurs ensured a 16th straight postseason in which at least one Game 7 was played; 1999 was the last postseason to not feature a Game 7.


title: 2015 NBA playoffs

text: The San Antonio Spurs became the first defending champions to be eliminated in the first round since the 2011–12 Dallas Mavericks. This was only the second time it had happened since 2000.


title: 2015 NBA playoffs

text: With the Spurs being eliminated in the first round, none of the eight teams remaining at the beginning of the Conference Semifinals had previously won an NBA championship in the 21st century. After the first round of the playoffs, of the teams who had previously won an NBA championship, the Chicago Bulls had the shortest drought at 17 years, having most recently won an NBA championship in 1998, while the Atlanta Hawks had the longest overall drought at 57 years, having won their only previous championship in 1958 when the franchise was based in St. Louis.


title: 2015 NBA playoffs

text: For the first time since 1970, the Hawks made the Conference Finals (then called the Division Finals). Since 1970, they had lost all 15 Division or Conference Semifinal series they participated in. The Warriors made their first conference finals appearance since 1976, and the Houston Rockets made their first conference finals appearance since 1997. These three were the NBA teams which had been waiting for the longest time for a return to the conference finals.


title: 2015 NBA playoffs

text: For the second straight year, the No. 1 seed faced the No. 2 seed in the Conference Finals, and for the fourth time since 2000.


title: 2015 NBA playoffs

text: In the second round, all teams that held a 2–1 series lead within the first three games of their respective series had gone on to lose that series.


title: 2015 NBA playoffs

text: The Rockets became only the second franchise to twice come back from 3–1 series deficits to win the series by defeating the Los Angeles Clippers in the Semifinals. They had first achieved that goal 20 years ago against the Phoenix Suns. The Boston Celtics are the only other franchise to twice make this comeback, doing it in 1968 and 1981. Overall, eleven teams have achieved the feat, with the Warriors doing it in the Conference Finals and Cavaliers doing it in the NBA Finals the year after.


title: 2015 NBA playoffs

text: For the first time in NBA playoff history, both conference finals teams, the Warriors of the West and the Cavaliers of the East, held commanding 3–0 series leads. Cleveland went on to the finals, sweeping the Atlanta Hawks 4–0 while Golden State won their series 4–1 defeating the Houston Rockets.


title: 2015 NBA playoffs

text: For the first time since the inaugural Basketball Association of America season in 1946–47, two rookie coaches, David Blatt of the Cavaliers and Steve Kerr of the Warriors, met each other in the NBA finals.


title: 2015 NBA playoffs

text: Within each conference, the three division winners and the five non-division winners with the most wins qualified for the playoffs. The seedings are based on each team's record; however, a division winner is guaranteed to be ranked at least fourth, regardless of record.


title: 2015 NBA playoffs

text: Each conference's bracket is fixed; there is no reseeding. All rounds are best-of-seven series; the team that has four wins advances to the next round. As stated above, all rounds, including the NBA Finals, are in a 2–2–1–1–1 format. Home court advantage in any round does not necessarily belong to the higher-seeded team, but instead to the team with the better regular season record. If two teams with the same record meet in a round, standard tiebreaker rules are used. The rule for determining home court advantage in the NBA Finals is winning percentage, then head-to-head record, followed by record vs. opposite conference.


title: 2015 NBA playoffs

text: If there are more than two teams tied, the team that wins the tiebreaker gets the highest seed, while the other teams were "re-broken" from the first step until all ties were resolved. Since the three division winners were guaranteed a spot in the top four, ties to determine the division winners had to be broken before any other ties.


title: 2015 NBA playoffs

text: As the 2014–15 regular season proceeded into February 2015, the ninth-place team in the Western Conference had a better record than the eighth-place team in the East. This led NBA Commissioner Adam Silver to suggest changing the playoff format, where the top 16 teams throughout the entire league would qualify, regardless of division or conference. Silver then stated that the league might not be able to implement such changes until the 2016–17 season at the earliest.


title: 2015 NBA playoffs

text: On March 3, the Atlanta Hawks became the first team to clinch a playoff spot. This was the earliest a team had clinched a playoff spot since the 1995–96 Chicago Bulls clinched on March 2. The Golden State Warriors became the first Western Conference team to clinch a playoff spot on March 16.


title: 2015 NBA playoffs

text: Memphis had home court advantage in the first round despite not being a higher seed as they had a better regular season record than their opponent, but did not have the best record of the non-division-champion playoff teams in the West. This rule was changed as a result of this season's playoffs. The southwest division, which the Grizzlies are a part of, also had all five teams make the playoffs this year. This had only happened 3 times before.


title: 2015 NBA playoffs

text: During the final minute of the game, Derrick Rose drove inside then passed to Pau Gasol who laid it in as he was fouled. Gasol would then make the free throw and tie the game at 90. Then, when Rose tried to win the series for Chicago, he crossed but then was stripped by Khris Middleton. He then attempted a half court shot, which was blocked by Jimmy Butler when timeout was called. With 1.3 seconds left, Jared Dudley found the lead pass for Jerryd Bayless, due to a defensive breakdown by Rose, who then hit the game-winning lay-up at the buzzer, allowing the Bucks to stave off elimination for at least one more game.


title: 2015 NBA playoffs

text: This was the fourth playoff meeting between these two teams, with the Bucks winning two out of the first three meeting.


title: 2015 NBA playoffs

text: After Anthony Davis split a pair of free throws, Curry missed an attempted game-tying three, but Marreese Speights grabbed the offensive rebound and Curry hit another three to tie the game at 108. The Warriors would win in OT.


title: 2015 NBA playoffs

text: This was the third playoff meeting between these two teams, with the Mavericks winning both previous meetings.


title: 2015 NBA playoffs

text: In Game 1, the Clippers had a dominant game. It was close in the first half, but the Clippers pulled away in the second half. Chris Paul scored 32 points, while Blake Griffin scored 27 points. This helped the Clippers win 107–92.


title: 2015 NBA playoffs

text: Game 2 was much closer, requiring overtime. The Spurs won 111–107 in the Staples Center, tying the series 1–1, lead by Tim Duncan's 27 points.


title: 2015 NBA playoffs

text: In Game 3, the Spurs completely controlled the offense, and never trailed. They won 100–73 with Kawhi Leonard scoring 32 points. In Game 4, the Clippers won 114–105. Chris Paul scored 34 points and 7 assists.


title: 2015 NBA playoffs

text: It was a tight game in Game 5 in the Staples Center, especially in the 4th quarter. At the end of the game, DeAndre Jordan tipped the ball in; however, the refs called goaltending. The Spurs prevailed 111–107, lead by Tim Duncan's 24 points and 11 rebounds.


title: 2015 NBA playoffs

text: In Game 6, Spurs Tim Duncan, Manu Ginóbili, Tony Parker, Kawhi Leonard along with Clippers Chris Paul and Blake Griffin struggled offensively. The Spurs gave up a 10-point lead, allowing the Clippers to win 102–96.


title: 2015 NBA playoffs

text: Game 7 was a very tight game, featuring 31 lead changes and 19 ties. In the first half, Chris Paul injured his hamstring, but returned in the third quarter, concluding that quarter with a buzzer beater 3-pointer, giving them a 79–78 lead. The fourth quarter was a nail-biter, with the Spurs leading in the beginning and the Clippers at the end. With 1 second left in the game, Chris Paul hit the game winner, and the Clippers moved on to the second round by a meager two-point margin. The final score was 111–109.


title: 2015 NBA playoffs

text: This was the second playoff meeting between these two teams, with the Spurs winning the only meeting.


title: 2015 NBA playoffs

text: The Hawks rallied from a 19-point deficit heading into the final period to tie the score at 101 with a basket. On the ensuing possession, Paul Pierce, who was double-teamed, hit a fadeaway jumper off the backboard at the buzzer to give the Wizards a 103–101 victory and a 2–1 lead in the series. After the game, when ESPN analyst Chris Broussard asked Pierce if he called bank on that shot, he responded, "I called game!"


title: 2015 NBA playoffs

text: With 8.3 seconds left, Kyle Korver inbounded the ball to Dennis Schroder, who drives for the layup that was blocked by John Wall, then Al Horford gets the offensive rebound and hits the game-winning layup with 1.9 seconds left. John Wall then misses the half-court buzzer beater, and the Hawks take the 3–2 series lead.


title: 2015 NBA playoffs

text: The Hawks were up by 3, with 6.4 seconds to go. Bradley Beal's inbound pass went to John Wall, who tried to get open with time running down, then he passed to Paul Pierce who hit an off-balanced game-tying 3. But when officials reviewed the play, the clock reached 0:00 before Pierce released the ball and therefore the shot did not count. The Hawks won the series and advanced to the Eastern Conference Finals for the first time since 1970.


title: 2015 NBA playoffs

text: This was the fifth playoff meeting between these two teams, with the Wizards (formerly known as the Bullets) winning three out of the first four meetings.


title: 2015 NBA playoffs

text: The Bulls led wire to wire to go up 1–0 in the series, leading by as many as 16 points in the second quarter. The Cavs rallied to tie the game early in the third quarter. However, the Bulls went on a 15–0 run in the third quarter to regain control before holding off the Cavs late in the 4th quarter.


title: 2015 NBA playoffs

text: Facing the possibility of going down 2–0 heading to Chicago, the Cavaliers blew out the Bulls in Game 2, leading wire to wire as they evened the series 1–1. The Cavs outscored the Bulls by 20 points in the first quarter and never looked back. The Bulls got no closer than 11 for the rest of the game. LeBron led the Cavs with 33 points on 13/29 shooting while Irving chipped in 21 points.


title: 2015 NBA playoffs

text: J.R. Smith returned to the lineup after missing the first two games due to suspension. This was a very competitive game that saw neither team lead by more than 8 points. Trailing 94–93, LeBron James missed a go-ahead layup with under 24 seconds to play. Taj Gibson was fouled and made two free throws to make it 96–93 Bulls. James found Smith, who hit the game tying three to make it 96–96. The Bulls called timeout on their final possession of regulation. Rose shot a deep three that went off the backboard and into the basket, giving the Bulls a 99–96 win and a 2–1 series lead. Rose led the Bulls with 30 points. LeBron led the Cavs with 27, but he continued to struggle with his shot and Jimmy Butler's defense, going 8/25 for the game and 1/7 on threes.


title: 2015 NBA playoffs

text: Looking to go up 3–1 and take complete control of the series, the Bulls went up 37–29 early in the second quarter. However, the Cavs scored 16 unanswered points to go up 45–37 before settling for a 49–45 halftime lead. The Bulls dominated the third quarter, outscoring the Cavs 23–12. They led by as many as 11 points before settling for a 68–61 lead heading into the 4th quarter. Led by J.R. Smith and Timofey Mozgov, the Cavs would rally, opening the 4th quarter on a 19–5 run to take an 80–73 lead with just under 5 minutes to play. With just under 40 seconds to play, LeBron hit two consecutive free throws to put the Cavs up 84–79. Butler hit a three on the Bulls' next possession, cutting the deficit to 84–82. The Cavs were forced to burn three consecutive timeouts as they were unable to inbound the ball. Once they inbounded the ball, James tried to burn the clock down as he was double teamed by Rose and Dunleavy. However, James swung his arm at Dunleavy and committed an offensive foul, giving the ball back to the Bulls with 14 seconds remaining. Rose tied the game with a layup to even the game at 84–84 with 8 seconds remaining. James rushed down the court and tried to score the go-ahead layup but was blocked. The ball went out of bounds with 1.5 seconds remaining. On the Cavs' final possession, Matthew Dellavedova inbounded the ball to James. James fired a jumper over Butler that went through the hoop as the buzzer sounded, giving the Cavs an 86–84 win. The Cavs regained homecourt advantage as they evened up the series at 2–2. James led the team with 25 points (10/30 shooting) while Rose led the Bulls with 31 points on 11/23 shooting.


title: 2015 NBA playoffs

text: This game was particularly controversial due to a timeout that wasn't called late in the game. After Rose made the layup to tie the game at 84–84, Cavaliers head coach, David Blatt, attempted to call timeout. However, the Cavs were out of timeouts. Calling a timeout without having one would have resulted in a technical foul and possession of the ball would go to the Bulls. Tyron Lue held back Blatt and prevented him from getting that timeout. None of the officials noticed Blatt signaling timeout as James ran up the court for what would eventually lead to his game winning buzzer beater.


title: 2015 NBA playoffs

text: Following the game, the NBA officiating report revealed that Blatt should have been charged with a timeout that would have drawn a technical and Cavs turnover.


title: 2015 NBA playoffs

text: The Bulls scored the first 8 points of the contest and led 18–8 early in the first quarter. However, the Cavs closed the first quarter on a 17–6 run to take a 25–24 lead into the 2nd quarter. The Cavs' momentum carried over into the 2nd quarter as they built a 54–44 halftime lead. James, who had struggled mightily with his shooting throughout the series, scored 24 points on 10/12 shooting in the first half. The Cavaliers controlled the third quarter and led by 9 after three quarters. Early in the 4th quarter, Dellavedova fell down, and Gibson's legs got tangled up with his. Gibson, attempting to break free, kicked Dellavedova. Gibson was charged with a flagrant 2 and ejected. The Cavs went up by as many as 17 points in the 4th quarter and led 97–82 with just over 6 minutes to play. However, the Bulls would rally, going on a 17–4 run to make it 101–99 Cavs with just over one minute to play. Trailing by 2, Butler attempted a three that would have given the Bulls to lead. However, he missed. James ran the clock down and missed a shot on the Cavs' next possession. However, Shumpert grabbed the offensive rebound. With 20 seconds remaining, and trailing by 2, the Bulls were forced to foul. However, the Cavs made their free throws and closed the game out, winning 106–101 and taking a 3–2 series lead. James led the Cavaliers with 38 points and 12 rebounds to go along with 6 assists and 0 turnovers. Butler led the Bulls with 29 points. Rose scored 12 points in the first quarter on 5/9 shooting. He had only 5 points on 2/15 shooting in the final three quarters, including 0 made baskets in the second half.


title: 2015 NBA playoffs

text: After three consecutive contests came down to the final minute, the Cavaliers finally finished off the Bulls, eliminating them 94–73 at the United Center to win the series 4–2. The Bulls led 40–38 halfway through the second quarter. However, the Cavs closed the half on a 20–4 run, leading by 14 at halftime. The Cavs never relinquished control, leading by double digits for the entire second half and going up by as many as 27 points in the 4th quarter. Irving was forced out of the game after suffering an injury in the second quarter. However, Dellavedova led the way, scoring a playoff career high and season high 19 points to lead the Cavaliers. James had 15–9–11, one rebound shy of a triple double. Butler led the Bulls with 20 points. The Bulls scored 31 points in the 1st quarter. However, they were held to 42 points in the final three quarters, including 29 in the second half.


title: 2015 NBA playoffs

text: It was the 4th time in the last 6 seasons that the Bulls were eliminated by a team with LeBron James on its roster.


title: 2015 NBA playoffs

text: This was the seventh playoff meeting between these two teams, with the Bulls winning five out of the first six meetings.


title: 2015 NBA playoffs

text: The Rockets recovered from a 3–1 deficit for the first time since 1995. Game 6 was one for the books as the Rockets overcome a 19–point deficit, going on an incredible 49–18 run including a 40-15 run in the 4th quarter to end the game. The Clippers missed 14 straight shots as Josh Smith and Corey Brewer dominated much of the 4th quarter combining for 29 points. The 4th quarter spark led Houston to a decisive Game 7, and they completed one of the greatest comebacks in NBA playoff history. This was the ninth time in NBA history a team has come back from a 3–1 deficit to win a series.


title: 2015 NBA playoffs

text: The Clippers would ultimately suffer the same fate in 2020, in which they relinquished a 19-point lead in Game 6, and eventually blew a 3–1 series lead to the lower-seeded Denver Nuggets.


title: 2015 NBA playoffs

text: This was the second playoff meeting between these two teams, with the Rockets winning the only previous meeting.


title: 2015 NBA playoffs

text: The Cavaliers defeated the Hawks 97–89, stealing homecourt advantage and taking a 1–0 series lead. LeBron led the team with 31 points while J.R. Smith chipped in 28 points, going 8/12 on threes and setting a Cavaliers franchise record for made threes in a playoff game. The game was tied 63–63 in the 3rd quarter. However, the Cavs, led by Smith's hot shooting, went on a 22–4 run (including an 11–0 run to start the fourth quarter) as they went up 85–67 and seized control. The Hawks would attempt to mount a rally, cutting an 18-point deficit down to 4 with under 50 seconds remaining. However, James drove through the lane and made a dunk to put the Cavs up 6. After Paul Millsap missed a three that would have made it a one possession game with 23 seconds remaining, the Cavs made their free throws to close it out.


title: 2015 NBA playoffs

text: With Irving sitting out due to injury, the Hawks were in a great position to even up the series. However, the Cavaliers blew out the Hawks and took a commanding 2–0 series lead, winning 94–82. The Cavs led 54–49 at halftime. Coming out of halftime, the Cavs seized control, outscoring the Hawks 30–17 in the third quarter, leading by as many as 20 before settling for an 84–66 lead heading into the 4th quarter. The Cavs scored only 10 points in the final period, but the Hawks trailed by double digits for the entire quarter and failed to make a significant run, managing 16 points. LeBron James led the way for the Cavs, scoring 30 points while having 11 assists and 9 rebounds. Dennis Schroder led the Hawks in scoring with 13 points off the bench. It was the first time this season that the Hawks had lost consecutive home games. The game was memorable when Hawks' 3-point specialist Kyle Korver sprained his right ankle after the Cavs' Matthew Dellavedova fell on his right leg while attempting to dive for a loose ball. This injury kept Korver out for the rest of the postseason and would require surgery in the off-season along with an injured elbow that bothered him for most of the season.


title: 2015 NBA playoffs

text: In a pivotal Game 3, LeBron James got off to an awful start, going 0/9 in the first quarter as the Hawks led 24–21. Near the end of the second quarter, Al Horford and Matthew Dellavedova got tangled up on the floor. Horford, who had scored 15 points on 7/10 shooting in the first half, swung his elbow at Dellavedova. He received a Flagrant 2 foul and was ejected. The Hawks led 49–48 at halftime. However, the Cavs would dominate the third quarter again, outscoring the Hawks 33–27 to take a 5-point lead into the 4th quarter. The Cavs led by as many 10 in the 4th quarter, leading 88–78. However, the Hawks, led by Jeff Teague, would go on a 26–12 run, taking a four-point lead with just under 1:45 to play. The Cavs scored the final four points of regulation to tie up the game. The Hawks had the final possession of regulation. However, Teague's potential game winning three missed at the buzzer, and the game went into overtime. With just under one minute to play in overtime, the Hawks trailed 109–108. Teague hit a three pointer over Thompson to put the Hawks up 111–109. On the Cavs' next possession, James attempted a jumper that rimmed out. However, Thompson grabbed the offensive rebound and passed it back to James. James went behind the three point line and shot a three that went down, putting the Cavs back ahead 112–111. Out of the timeout, the Hawks turned it over on their next possession. On the Cavs' next possession, James ran the shot clock down before driving into the paint and making a layup to put the Cavs up 114–111. The Hawks had two chances to tie the game and potentially force a second overtime, but Shelvin Mack missed both game tying three point attempts, sending the Hawks to their third straight loss as the Cavs went up 3–0 in the series. James recorded his 51st career triple-double (12th of the postseason) with 37 points, 18 rebounds, and 13 assists. Teague led the Hawks with 30 points.


title: 2015 NBA playoffs

text: The Cavaliers routed the Hawks by 30 points, dominating from start to finish. The Cavs led 32–20 after the first quarter and never looked back. After leading by 17 at halftime, the Cavs controlled the entire second half. The Cavs led 85–60 heading into the fourth quarter, a quarter where very few starters logged minutes. The Cavaliers went on to win 118–88 as the franchise clinched their second Eastern Conference Championship in franchise history and returned to the Finals for the first time since 2007. The Atlanta Hawks became the first #1 seed to be swept in the Conference Finals since the Nets swept the Pistons in the 2003 Conference Finals. LeBron James and James Jones also became the first non-Celtics to appear in five consecutive NBA Finals series.


title: 2015 NBA playoffs

text: This was the second playoff meeting between these two teams, with the Cavaliers winning the only prior meeting.


title: 2015 NBA playoffs

text: In Game 5, James Harden set an NBA playoff record for turnovers, with 12. The record was previously held by John Williamson of the New Jersey Nets with 11 in 1979.


title: 2015 NBA playoffs

text: ESPN, TNT, ABC, ESPN2 and NBA TV broadcast the NBA Playoffs nationally. In the first round the regional sports networks affiliated with the teams can also broadcast the games. Throughout the first two rounds, TNT televises games Saturday through Thursday, ESPN televises games on Friday and Sunday, and ABC televises select games on Saturday and Sunday, usually in the afternoon. NBA TV and ESPN2 televises select games in the first round. TNT televises the Eastern Conference Finals and ESPN the Western Conference Finals. ABC televises the NBA Finals for the 13th consecutive year.


title: 2015 NBA playoffs

text: ESPN Radio has exclusive national radio rights to broadcast the playoffs in the United States. They broadcast mostly ABC games during the first two rounds, all of the conference finals, and the NBA Finals.


title: Amazing Stories (1985 TV series)

text: Amazing Stories is an American anthology television series created by Steven Spielberg, that originally ran on NBC in the United States from September 29, 1985 to April 10, 1987.


title: Amazing Stories (1985 TV series)

text: The series was nominated for 12 Emmy Awards and won five. The first season episode "The Amazing Falsworth" earned writer Mick Garris an Edgar Award for Best Episode in a TV Series. It was not a ratings hit (ranking 40th in Season 1 and 52nd in Season 2), however, and the network did not renew it after the two-year contract expired. The 1987 science fiction film "Batteries Not Included" was originally intended as a story for "Amazing Stories", but Spielberg liked the idea so much that he decided to make it a theatrical release.


title: Amazing Stories (1985 TV series)

text: The series title licensed the name of "Amazing Stories", the first dedicated science fiction magazine created by Hugo Gernsback in April 1926.


title: Amazing Stories (1985 TV series)

text: All episodes have a running time of around 24 minutes, with the exceptions of "The Mission" and "Go to the Head of the Class" (both running 46 minutes).


title: Amazing Stories (1985 TV series)

text: In 1999, Varèse Sarabande released a CD containing a rerecording of the scores for the episodes "The Mission" and "Dorothy and Ben" (John Williams and Georges Delerue respectively) plus Williams' opening and closing themes, performed by the Royal Scottish National Orchestra and conducted by Joel McNeely.


title: Amazing Stories (1985 TV series)

text: In 2006–2007, Intrada released three volumes of original music from the series, covering the impressive lineup of composers who worked on it and featuring all of the most noteworthy scores (with the exception of Danny Elfman and Steve Bartek's "The Family Dog," because the masters could not be found – a brief suite is on "Music for a Darkened Theatre: Vol. 2", however), as well as two alternate versions of Williams' main title theme, one used just once (Alternate #1, on "Alamo Jobe") and the other never used. The album is also notable for the premiere release of the music Williams composed for the Amblin Entertainment logo (although the logo music is not heard on the show itself).


title: Amazing Stories (1985 TV series)

text: Other than Williams, Bruce Broughton and Billy Goldenberg are the only composers to be represented on all three volumes. The running times below indicate the cumulative time for each score rather than the time of each track. (The series theme is not quoted in any of the episode scores, with the exception of "Ghost Train.")


title: Amazing Stories (1985 TV series)

text: The series gained a number of positive reviews. However, some reviewers were unimpressed with the show, with Jeff Jarvis of "People" saying "Amazing Stories is one of the worst disappointments I've ever had watching TV."


title: Amazing Stories (1985 TV series)

text: One episode of the show, "Family Dog", was spun off into its own series. Six years after "Amazing Stories" finished its run, "Family Dog" ran on CBS for ten episodes before being pulled off the schedule.


title: Amazing Stories (1985 TV series)

text: The video game "The Dig" originated as an idea Spielberg had for "Amazing Stories", but decided it would be too expensive to film.


title: Amazing Stories (1985 TV series)

text: In 1986, Steven Bauer wrote two novelizations of the series which were both published by Charter Books in the US and Futura Books in the UK. The first book, "Steven Spielberg's Amazing Stories" (October 1986, ), adapted episodes 5, 12, 9, 2, 7 and 12, while the second book, "Volume II of Steven Spielberg's Amazing Stories" (December 1986, ), adapted episodes 7, 20, 8, 11, 18, 25, 4, 3, 21, 17 and 19.


title: Amazing Stories (1985 TV series)

text: In 1985–86, TSR published six tie-in novels under the "Amazing Stories" banner. They were branching ("Choose Your Own Adventure" style) books where the reader chose where to jump at key points.


title: Amazing Stories (1985 TV series)

text: The 1987 film "Batteries Not Included" was originally planned to be a segment for the series, but Spielberg thought the story would work better on the big screen instead of television.


title: Amazing Stories (1985 TV series)

text: On October 23, 2015, it was announced that NBC was developing a reboot of the series with Bryan Fuller writing the pilot episode and executive producing alongside Justin Falvey and Darryl Frank. Production companies involved with the series were set to include Universal Television. Steven Spielberg was not expected to be involved with the new series. On May 5, 2017, NBC and Universal Television were formally notified that their option rights to the "Amazing Stories" properties had been withdrawn. Rights for the development of a genre television series under the name "Amazing Stories" were subsequently sold to Experimenter Media LLC.


title: Amazing Stories (1985 TV series)

text: On October 10, 2017, it was announced that Apple Inc. made a deal with Steven Spielberg's Amblin Television and NBC Universal to develop a new, ten-episode series on Apple's streaming service, Apple TV+. On February 7, 2018, it was announced that Fuller had stepped down as showrunner of the series over creative differences. It was further reported that it was unclear whether he would have a different role on the project going forward. He had not delivered a script to Apple before his amicable departure. Later that day, it was also announced that executive producer Hart Hanson was exiting the series as well. On May 22, 2018, it was announced that "Once Upon a Time" creators Edward Kitsis and Adam Horowitz had joined the production as executive producers and showrunners.


title: Amazing Stories (1985 TV series)

text: A selection of the original series episodes were released in the VHS format in 1993; these were titled "Book One" through "Book Five" in the US. In Japan and Europe episodes were cut together as movies and released in 8 volumes during the late 1980s, early 1990s. A three-tape VHS (PAL) set was released in the UK in 2001.


title: Amazing Stories (1985 TV series)

text: Between 2006 and 2009, "The Complete First Season" was released on DVD in the US, UK, France, Holland, Italy, Scandinavia, Spain and Australia. In 2009, both seasons were released in Germany and Japan only. In Germany both seasons were released as 12 separate DVDs or a complete box set, which was also reissued in 2011. All countries' DVDs contain the original English soundtrack, while Italy, Germany, France, Spain and Japan have a second soundtrack, dubbed in their respective languages. The second season was never released in any video format in America despite much demand by collectors.


title: Amazing Stories (1985 TV series)

text: In 1992, the series was somewhat erratically screened in Britain by BBC1 and BBC2 – billed in the "Radio Times" as "Steven Spielberg's Amazing Stories" – with episodes airing at any time from early on Sunday morning (such as "The Family Dog") to weekday evenings (like "Such Interesting Neighbors") to very late at night (for instance "Mirror, Mirror"); it later received a more coherent run on Sci-Fi. Three of the episodes ("The Mission", "Mummy Daddy" and "Go to the Head of the Class") were packaged together as an anthology film and released theatrically in several European countries such as Spain, France (July 10, 1986) or Finland (June 26, 1987), and also in Australia on September 17, 1987. It later appeared on LaserDisc in Japan as "Amazing Stories: The Movie" shortly afterwards.


title: Amazing Stories (1985 TV series)

text: Until 2006, the Sci Fi Channel in the United States showed episodes on an irregular schedule. The MoviePlex channel also showed the series as a collection of "movies," which are blocks of three episodes.


title: 2022 European Men's Handball Championship

text: The 2022 EHF European Men's Handball Championship was the 15th edition of the tournament and the second to feature 24 national teams. It was co-hosted in two countries – Hungary and Slovakia – from 13 to 30 January 2022. It was won by Sweden.


text: The games in Hungary were played with full capacity, while the games in Slovakia were capped at 25% capacity, due to the COVID-19 pandemic.


text: On 4 May 2017 it was announced that the following nations had sent in an official expression of interest:


text: However, when the deadline for submitting the final bids was over, the following applications had been received:


text: On 20 June at the 14th ordinary EHF Congress held in Glasgow, Hungary and Slovakia were selected to host the competition.


text: The qualification for the final tournament took place between January 2019 and May 2021. The two host teams, Hungary and Slovakia, and the two best placed teams from the previous championship, Spain and Croatia, were automatically qualified, leaving a total of 40 national teams to compete for the remaining 20 places in the final tournament.


text: The competition consisted of three rounds: two qualification phases and a relegation round. The first qualification phase involved teams that did not participate in the second round of the 2020 qualification tournament. The two best teams advanced to a relegation round, where they were joined by the best European team from the 2019 IHF Emerging Nations Championship and the three worst ranked fourth-placed teams from the second round of the 2020 qualification. The three winners of the two-legged relegation round matches advanced to the second and last qualifying phase, joining the remaining 21 teams that participated in the 2020 championship and the remaining eight teams that were eliminated in the second round of the 2020 qualification. Those 32 teams were divided into eight groups by four teams, with top two teams and four best ranked third-teams qualifying.


text: The official logo and slogan was unveiled on 25 January 2020 at the EHF Extraordinary Congress In Stockholm. The logo includes the national colours of both host nations – red, green, white and blue, forming the handball and an eye, relates closely to the event's motto "Watch Games, See More", highlighting the many opportunities for fans around the six venues.


text: The seedings were announced on 3 May 2021. The organizing countries had the right to allocate one team to each of the groups they were hosting due to potential spectators' interest. Hungary (assigned to group B) selected Croatia (assigned to group C) and Slovenia (assigned to group A), while Slovakia (assigned to group F) selected Germany (assigned to group D) and the Czech Republic (assigned to group E).


text: The referee pairs were selected on 10 September 2021. Two more pairs were selected on 10 January 2022.


text: David Mandić received a blue card in the 47th minute for a punch against the head of Kentin Mahé. He received a one game suspension from the EHF and he missed the next game against Serbia.


text: Points and goals gained in the preliminary group against teams that advance will be transferred to the main round.


text: The teams ranked fourth in each group after the completion of the preliminary round matches are ranked 19 to 24, while teams ranked third in each group after the completion of the preliminary round matches are ranked 13 to 18 according to the number of points won in the preliminary round. Places seven and eight are attributed to the two teams ranked fourth in the groups, places nine and ten to the two teams ranked fifth in the groups and places eleven and twelve to the two teams ranked sixth in the group according to the number of points won by the respective teams after completion of the main round matches. Places five and six will be decided by a play-off, and the top four places by knock-out.


title: Candy corn

text: Candy corn is a type of small, pyramid-shaped candy, typically divided into three sections of different colors, with a waxy texture and a flavor based on honey, sugar, butter, and vanilla. It is a staple candy of the fall season and Halloween in North America.


title: Candy corn

text: Candy corn's traditional colors of yellow, orange, and white represent the colors of the fall harvest, or of corn on the cob, with the wide yellow end resembling a corn kernel.


title: Candy corn

text: Candy corn has a reputation for generating polarizing responses, with articles referring to it as "Halloween's most contentious sweet" which people either "love" or "hate."


title: Candy corn

text: "Chicken Feed" was the original name of the candy with production starting in the late 1880s. It was first invented in the 1880s by a Wunderle Candy Company employee, George Renninger. Wunderle Candy Company was the first to produce the candy in 1888. The Goelitz Confectionery Company (now called Jelly Belly) began manufacturing the product in 1898. While Jelly Belly still makes candy corn, the largest manufacturer of candy corn is Brach's Confections owned by the Ferrara Candy Company. Brach's makes approximately 7 billion pieces of candy corn per year and possesses 85 percent of the total share of the candy corn industry during the Halloween season.


title: Candy corn

text: Along with other agriculture-inspired treats at the time in the late 19th century, America's confectioners sought to market candy corn to a largely rural society. During the late 19th century, "butter cream" candies molded into many types of nature inspired shapes, including chestnuts, turnips, and clover leaves were quite popular but what made candy corn stand out was its bright and iconic tri-color layering.


title: Candy corn

text: Although it is currently most popular in the fall, candy corn was not always associated with the fall and Halloween season. For the first half of the 20th century, candy corn was a well-known "penny candy" or bulk confectionery, and it was advertised as an affordable and popular treat that could be eaten year-round.


title: Candy corn

text: Candy corn developed into a fall and Halloween staple around the 1950s when people began to hand out individually wrapped candy to trick-or-treaters. The harvest-themed colors and increased advertising in October also helped candy corn become a fall staple.


title: Candy corn

text: The National Confectioners Association has deemed October 30, the day before Halloween, "National Candy Corn Day."


title: Candy corn

text: The National Confectioners Association estimates that around 35 million pounds (over 15,000 metric tons) of candy corn are sold annually. , annual production in the United States was 35 million pounds, or almost 9 billion pieces of candy. The majority of candy corn sales occur during the Halloween season.


title: Candy corn

text: Originally the candy was made by hand. Manufacturers first combined sugar, corn syrup, carnauba wax, and water and cooked them to form a slurry. Fondant was added for texture and marshmallows were added to provide a soft bite. The final mixture was then heated and poured into shaped molds. Three passes, one for each colored section, were required during the pouring process.


title: Candy corn

text: The recipe is similar today. The production method, called "corn starch modeling," likewise remains the same, though tasks initially performed by hand were soon taken over by machines made for that purpose.


title: Candy corn

text: A popular variation called "harvest corn" adds cocoa powder; it features a chocolate brown wide end, orange center, and pointed white tip. It is often available around Thanksgiving. During the Halloween season, blackberry cobbler candy corn can be found in Eastern Canada, as well as candy corn shaped like pumpkins. Confectioners have introduced additional color variations suited to other holidays. The Christmas variant (sometimes called "reindeer corn") typically has a red end and a green center; the Valentine's Day variant (sometimes called "cupid corn") typically has a red end and a pink center; In the United States during Independence Day celebrations, corn with a blue end, white center, and red tip (named "freedom corn") can be found at celebratory cook outs and patriotic celebrations; the Easter variant (sometimes called "bunny corn") is typically only a two-color candy, and comes with a variety of pastel bases (pink, green, yellow, and purple) with white tips all in one package. There have also been caramel apple and green apple, s'mores and pumpkin spice, carrot corn (green and orange, with a carrot cake flavor) and birthday cake candy corn flavors. In 2022, Brach's released a tailgate variant with fruit punch, vanilla ice cream, popcorn, hotdog, and hamburger flavored pieces.


title: Candy corn

text: Candy corn flavored snacks have become more widely available with candy corn flavored variants of snack foods and candy including Oreos, M&M's, marshmallows, and more.


title: Fitch Ratings

text: Fitch Ratings Inc. is an American credit rating agency and is one of the "Big Three credit rating agencies", the other two being Moody's and Standard & Poor's. It is one of the three nationally recognized statistical rating organizations (NRSRO) designated by the U.S. Securities and Exchange Commission in 1975.551


title: Fitch Ratings

text: Fitch Ratings is dual headquartered in New York and London. Hearst owns 100 percent of the company following its acquisition of an additional 20 percent for $2.8 billion on April 12, 2018. Hearst had owned 80 percent of the company after increasing its ownership stake by 30 percent on December 12, 2014, in a transaction valued at $1.965 billion. Hearst's previous equity interest was 50 percent following expansions on an original acquisition in 2006.


title: Fitch Ratings

text: Hearst had jointly owned Fitch with FIMALAC SA, which held 20 percent of the company until the 2018 transaction. Fitch Ratings and Fitch Solutions are part of the Fitch Group.


title: Fitch Ratings

text: The firm was founded by John Knowles Fitch on December 24, 1914, in New York City as the Fitch Publishing Company. In 1989, the company was acquired by a group including Robert Van Kampen. In 1997, Fitch was acquired by FIMALAC and was merged with London-based IBCA Limited, a FIMALAC subsidiary. In 2000 Fitch acquired both Chicago-based Duff & Phelps Credit Rating Co. (April) and Thomson Financial BankWatch (December).


title: Fitch Ratings

text: Fitch Ratings is the third largest NRSRO rating agency, covering a more limited share of the market than S&P and Moody's, though it has grown with acquisitions and frequently positions itself as a "tie-breaker" when the other two agencies have ratings similar, but not equal, in scale.


title: Fitch Ratings

text: In September 2011, Fitch Group announced the sale of Algorithmics (risk analytics software) to IBM for $387 million. The deal closed on October 21, 2011.


title: Fitch Ratings

text: Fitch Ratings' long-term credit ratings are assigned on an alphabetic scale from 'AAA' to 'D', first introduced in 1924 and later adopted and licensed by S&P. Like S&P, Fitch also uses intermediate +/− modifiers for each category between AA and CCC (e.g., AA+, AA, AA−, A+, A, A−, BBB+, BBB, BBB−, etc.).


title: Fitch Ratings

text: Launched in 2008, Fitch Solutions offers a range of fixed-income products and professional development services for financial professionals. The firm also distributes Fitch Ratings' proprietary credit ratings, research, financial data, and analytical tools.


title: Fitch Ratings

text: The main credit rating agencies, including Fitch, were accused of misrepresenting the risks associated with mortgage-related securities, which included the CDO market. There were large losses in the collateralized debt obligation (CDO) market that occurred despite being assigned top ratings by the CRAs.


title: Fitch Ratings

text: For instance, losses on $340.7 million worth of collateralized debt obligations (CDO) issued by Credit Suisse Group added up to about $125 million, despite being rated AAA by Fitch.


title: Fitch Ratings

text: However, differently from the other agencies, Fitch has been warning the market on the constant proportion debt obligations (CPDO) with an early and pre-crisis report highlighting the dangers of CPDO's.


title: Venky Mama

text: Venky Mama () is a 2019 Indian Telugu-language action comedy film directed by K. S. Ravindra.}} It stars Venkatesh, Naga Chaitanya, Raashii Khanna, and Payal Rajput in the lead roles, while Nassar, Prakash Raj, and Rao Ramesh play supporting roles. The film was produced by D. Suresh Babu of Suresh Productions and T. G. Vishwa Prasad of People Media Factory, with music composed by Thaman.


title: Venky Mama

text: The film was released on 13 December 2019, coinciding with Venkatesh's birthday, to mixed reviews from critics but praise for Venkatesh's performance and ended up as a commercial success at the box office.


title: Venky Mama

text: The film begins at Draksharama where a well-known personality Ramanarayana, an astrologer, lives with his wife Lakshmi and son Venkatarathnam. Ramanarayana opposes his daughter's marriage, as he foresaw the couple's death, soon after, a year of their son Karthik's birth. Just like Ramanarayana predicted, Karthik loses his parents in a tragic accident. Here, Ramanarayana warns that the kid also brings bummer to his family and suggests handing him over to his paternal grandparents. However, Venkatarathnam / Venky Mama denies it and rears his infant nephew with care and affection, even omitting his goal of enrollment in the army.


title: Venky Mama

text: Years roll by, and now the scene shifts to Kashmir where Venkatarathnam is under the search of Karthik, who left home without informing. Immediately, Venkatarathnam steps into army protected area and get prosecuted when he tries to convince the army officers regarding Karthik. However, they affirm the absence of such a person in their regiment, but Venkatarathnam persists to meet him. So, he starts narrating their story. After completing engineering, Karthik disdains various jobs because he prefers to stay behind his uncle. Nevertheless, his grandfather always needles. Later, Karthik realizes that Venkatarathnam has forsaken his marital life for his nurture, so he determines to get a perfect match for him. Just as, he is acquainted with newly appointed Hindi teacher Vennela and strives to develop intimacy with her, which she misunderstands. Besides, Karthik's ex-lover Harika, daughter of malicious MLA Pasupathi arrives at the village. Thereupon, Venkatarathnam learns about their love affair and chases Harika to seek the reason behind their break up which too, misfires. Right now, Karthik succeeds to make Vennela fall for his uncle. Parallelly, Venkatarathnam also knows from Harika about their detachment is of Karthik's prioritization of his uncle over her and his life. Being cognizant of it, Venkatarathnam decides to disentangle with Karthik and send him to London. At that point, Karthik proclaims that nobody can divide him from his uncle, including him. Overhearing their conversation, Harika repents and understands Karthik's virtue.


title: Venky Mama

text: Afterward, Venkatarathnam approaches Pasupathi with the marriage proposal. At that moment, Pasupathi bids to aid Venkatarathnam in the upcoming election because his word is an ordinance to the public in the area. Anyhow, the plan back-pedals when Venkatarathnam spares and ignominies him. All at once, an enraged Pasupathi ploy slays out Karthik when Venkatarathnam shields him. During the interval, as a flabbergast, Ramanarayana asserts that according to Karthik's horoscope, he is born to kill his maternal uncle and the only redress is to split them. Listening to it, Venkatarathnam and Karthik refuse to accept it. But unfortunately, the word befalls several incidents which make Karthik realize and leaves the house for the protection of his uncle. After three years, Ramanarayana announces the actuality of Karthik's presence in the army to fulfill his uncle's ambition. Momentarily the story shifts to the present when Venkatarathnam ascertains that Karthik is seized as a hostage by the terrorist to stand off for their leader who is already dead. During that plight, Venkatarathnam determines to swap as the terrorist in the know that it is a suicide mission for him. By the time of hand-off, due to Karthik's horoscope, he fires Venkatarathnam oversight him as a blackguard. At last, Karthik saves his uncle from the deathbed with his idolization confronting the horoscope. Finally, the movie ends on a happy note with uncle & nephew pairing up with their love interests with an axiom that horoscope is just a belief but love is a reality.


title: Venky Mama

text: D. Ramanaidu, father of Venkatesh Daggubati and grandfather of Naga Chaitanya, wanted both actors to be seen together on screen, D. Suresh Babu, elder son of Ramanaidu and producer of the film said on the occasion of his father 83rd birth anniversary. So, when Suresh Babu was in search of the story, writer Janardhana Maharshi pitched a story to him which he liked and later writer and director KS Ravindra was joined to direct the film and developed of the storyline of Janardhana and he made major changes to it.


title: Venky Mama

text: Venkatesh after multi-starrers like "Seethamma Vakitlo Sirimalle Chettu" with Mahesh Babu, "Masala" with Ram Pothineni, "Gopala Gopala" with Pawan Kalyan, and "F2 – Fun and Frustration" with Varun Tej, is doing another multi-starrer, this time with his nephew Naga Chaitanya. Before this Venkatesh did a cameo role in Chaitanya's film "Premam", this is the first time they are doing a full-length role together in a film.


title: Venky Mama

text: The film was officially launched at Ramanaidu Studios by director VV Vinayak as chief guest. It is jointly produced by People Media Factory and Suresh Productions.


title: Venky Mama

text: Initially, it was reported that Shriya Saran and Rakul Preet Singh were cast in the lead roles. But they were subsequently replaced by Payal Rajput and Raashi Khanna, respectively.


title: Venky Mama

text: Principal photography began on the banks of Godavari River on 24 February 2019, and completed its first schedule in Rajahmundry. In March 2019, while shooting for an action sequence Venkatesh was injured and advised to take two weeks rest.


title: Venky Mama

text: The second schedule was started in April 2019 in Hyderabad. Filming was also done in Kashmir and Visakhapatnam, and was wrapped up in August 2019.


title: Venky Mama

text: The first song "Venky Mama" was released on 7 November 2019, Sung by Sri Krishna, Mohana Bhogaraju and lyrics penned by Ramajogayya Sastry, the song tells deep bond between uncle (Venkatesh) and his nephew (Chaitanya).


title: Venky Mama

text: The second song "Yennellako" was released on 16 November 2019, on the occasion of the music director S. Thaman birthday, Sung by Prudhvi Chandra, S. Thaman and lyrics penned by Sri Mani.


title: Venky Mama

text: The third song "Coca Cola Pepsi" mass-song was released on 4 December 2019, sung by Aditi Bhavaraju, Ramya Behara, Simha and Hanuman; its lyrics were written by Kasarla Shyam.


title: Venky Mama

text: "Venky Mama" was set to release on 4 October 2019, but the release was delayed until November. The film was released on 13 December 2019, on the occasion of "Venkatesh's" birthday.


title: Venky Mama

text: In December 2019, a pre-release event was held in Khammam, later followed by a musical night event where the soundtrack album was released. K. Raghavendra Rao attended as guest.


title: Venky Mama

text: The film is available for streaming on Amazon Prime video since 16 January 2020. The satellite rights of the film were bagged by Gemini TV


title: Venky Mama

text: "Venky Mama" on opening day collected 16.5 crore gross worldwide. On the second day, the film collected 14 crore gross worldwide. On the third day, the film collected 14.5 crore gross worldwide and despite mixed reviews the movie's first weekend worldwide gross was 45 crore. In 11 days, the movie collected a total gross of 54.90 crore and a share of 31.99 crore worldwide.


title: Venky Mama

text: "The Hans India" gave 3 out of 5 stars stating "Having a solid storyline became the biggest plus point for this movie. The entire movies revolve around the beautiful relationship between Naga Chaitanya and Venkatesh and the director has executed it in an engaging way". "Samayam" gave 3.5 out of 5 stars stating "Venky Mama will make you laugh, cry and please".


title: Venky Mama

text: "The Times of India" gave 2.5 out of 5 stars stating "Mediocre writing and crass humour let down this comic caper. The only saving grace for Venky Mama is the performance of its lead actors Venkatesh and Naga Chaitanya". "India Today" gave 2.5 out of 5 stars stating "Director had to include everything just to play to the gallery and make it please every age group. The result is nothing but a colossal disappointment and a wasted opportunity".


title: Venky Mama

text: "The News Minute" gave 2 out of 5 stars stating "Venky Mama is a crowd-pleaser. What they call a mass entertainer. Two songs. Two comedians. Two “double-meaning” scenes, one wasted brilliant actor (Prakash Raj), one adored-as-god village head and a silly looking interview panel. Not really boring". "Firstpost" gave 2.5 out of 5 stars stating "This isn’t a film where one can judge how well an actor has performed when the writing and treatment leaves a lot to be desired. The film rushes through some of its major set-pieces and there’s hardly a build-up to moments where you might end up crying. The film just doesn't deliver what it sets out to achieve, and we are left to be content with bits and pieces of emotional sequences between Venkatesh and Naga Chaitanya. Venky Mama could have been so much more than what it is, but it's a missed opportunity!".


title: Solos (TV series)

text: Solos is an American dramatic anthology streaming television miniseries created by David Weil and produced by Amazon Studios. It stars Morgan Freeman, Anne Hathaway, Helen Mirren, Uzo Aduba, Anthony Mackie, Constance Wu, Dan Stevens and Nicole Beharie. The seven-episode series premiered on May 21, 2021 on Amazon Prime Video in UK, United States, Australia, Canada, Ireland, India, New Zealand and later that year in additional territories.


title: Solos (TV series)

text: The series ponders what it means to be human, arguing that we are connected to others through shared experiences, even in our most isolated moments.


title: Solos (TV series)

text: Amazon Studios greenlighted the series in October 2020. In February 2021, the title was announced. Weil is executive producer, and Laura Lancaster, Sam Taylor-Johnson and Pixie Wespiser produced. Weil makes his directorial debut directing three episodes and Taylor-Johnson directs two. Other directors for the series include Zach Braff and Tiffany Johnson. The cast was announced in February 2021, and their characters' names were announced in April 2021. Principal photography took place in Manhattan Beach, California from October 9 to November 19, 2020.


title: Solos (TV series)

text: The series debuted on Amazon Prime Video on May 21, 2021, for the UK, United States, Australia, Canada, Ireland, India, New Zealand. Other territories debuted later that year.


title: Solos (TV series)

text: On Rotten Tomatoes, the miniseries holds an approval rating of 47% based on 30 critic reviews and an average rating of 5.85/10. The website's critical consensus reads, "A star-studded cast and a smattering of truly lovely moments can't save "Solos" from feeling stranded in space." On Metacritic, it has a weighted average score of 45 out of 100 based on 14 critic reviews, indicating "mixed or average reviews".


title: Itô calculus

text: Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations.


title: Itô calculus

text: The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes:


title: Itô calculus

text: where "H" is a locally square-integrable process adapted to the filtration generated by "X" , which is a Brownian motion or, more generally, a semimartingale. The result of the integration is then another stochastic process. Concretely, the integral from 0 to any particular "t" is a random variable, defined as a limit of a certain sequence of random variables. The paths of Brownian motion fail to satisfy the requirements to be able to apply the standard techniques of calculus. So with the integrand a stochastic process, the Itô stochastic integral amounts to an integral with respect to a function which is not differentiable at any point and has infinite variation over every time interval.


title: Itô calculus

text: The main insight is that the integral can be defined as long as the integrand "H" is adapted, which loosely speaking means that its value at time "t" can only depend on information available up until this time. Roughly speaking, one chooses a sequence of partitions of the interval from 0 to "t" and constructs Riemann sums. Every time we are computing a Riemann sum, we are using a particular instantiation of the integrator. It is crucial which point in each of the small intervals is used to compute the value of the function. The limit then is taken in probability as the mesh of the partition is going to zero. Numerous technical details have to be taken care of to show that this limit exists and is independent of the particular sequence of partitions. Typically, the left end of the interval is used.


title: Itô calculus

text: Important results of Itô calculus include the integration by parts formula and Itô's lemma, which is a change of variables formula. These differ from the formulas of standard calculus, due to quadratic variation terms.


title: Itô calculus

text: In mathematical finance, the described evaluation strategy of the integral is conceptualized as that we are first deciding what to do, then observing the change in the prices. The integrand is how much stock we hold, the integrator represents the movement of the prices, and the integral is how much money we have in total including what our stock is worth, at any given moment. The prices of stocks and other traded financial assets can be modeled by stochastic processes such as Brownian motion or, more often, geometric Brownian motion (see Black–Scholes). Then, the Itô stochastic integral represents the payoff of a continuous-time trading strategy consisting of holding an amount "H" of the stock at time "t". In this situation, the condition that "H" is adapted corresponds to the necessary restriction that the trading strategy can only make use of the available information at any time. This prevents the possibility of unlimited gains through clairvoyance: buying the stock just before each uptick in the market and selling before each downtick. Similarly, the condition that "H" is adapted implies that the stochastic integral will not diverge when calculated as a limit of Riemann sums .


title: Itô calculus

text: is itself a stochastic process with time parameter "t", which is also sometimes written as "Y" = "H" · "X" . Alternatively, the integral is often written in differential form "dY = H dX", which is equivalent to "Y" − "Y" = "H" · "X". As Itô calculus is concerned with continuous-time stochastic processes, it is assumed that an underlying filtered probability space is given


title: Itô calculus

text: The σ-algebra "F" represents the information available up until time "t", and a process "X" is adapted if "X" is "F"-measurable. A Brownian motion "B" is understood to be an "F"-Brownian motion, which is just a standard Brownian motion with the properties that "B" is "F"-measurable and that "B" − "B" is independent of "F" for all "s","t" ≥ 0 .


title: Itô calculus

text: The Itô integral can be defined in a manner similar to the Riemann–Stieltjes integral, that is as a limit in probability of Riemann sums; such a limit does not necessarily exist pathwise. Suppose that "B" is a Wiener process (Brownian motion) and that "H" is a right-continuous (càdlàg), adapted and locally bounded process. If formula_4 is a sequence of partitions of [0, "t"] with mesh going to zero, then the Itô integral of "H" with respect to "B" up to time "t" is a random variable


title: Itô calculus

text: For some applications, such as martingale representation theorems and local times, the integral is needed for processes that are not continuous. The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes. If "H" is any predictable process such that ∫ "H" "ds" < ∞ for every "t" ≥ 0 then the integral of "H" with respect to "B" can be defined, and "H" is said to be "B"-integrable. Any such process can be approximated by a sequence "H" of left-continuous, adapted and locally bounded processes, in the sense that


title: Itô calculus

text: where, again, the limit can be shown to converge in probability. The stochastic integral satisfies the Itô isometry


title: Itô calculus

text: which holds when "H" is bounded or, more generally, when the integral on the right hand side is finite.


title: Itô calculus

text: An Itô process is defined to be an adapted stochastic process that can be expressed as the sum of an integral with respect to Brownian motion and an integral with respect to time,


title: Itô calculus

text: Here, "B" is a Brownian motion and it is required that σ is a predictable "B"-integrable process, and μ is predictable and (Lebesgue) integrable. That is,


title: Itô calculus

text: This is defined for all locally bounded and predictable integrands. More generally, it is required that "H"σ be "B"-integrable and "H"μ be Lebesgue integrable, so that


title: Itô calculus

text: An important result for the study of Itô processes is Itô's lemma. In its simplest form, for any twice continuously differentiable function "f" on the reals and Itô process "X" as described above, it states that "f"("X") is itself an Itô process satisfying


title: Itô calculus

text: This is the stochastic calculus version of the change of variables formula and chain rule. It differs from the standard result due to the additional term involving the second derivative of "f", which comes from the property that Brownian motion has non-zero quadratic variation.


title: Itô calculus

text: The Itô integral is defined with respect to a semimartingale "X". These are processes which can be decomposed as "X" = "M" + "A" for a local martingale "M" and finite variation process "A". Important examples of such processes include Brownian motion, which is a martingale, and Lévy processes. For a left continuous, locally bounded and adapted process "H" the integral "H" · "X" exists, and can be calculated as a limit of Riemann sums. Let π be a sequence of partitions of [0, "t"] with mesh going to zero,


title: Itô calculus

text: This limit converges in probability. The stochastic integral of left-continuous processes is general enough for studying much of stochastic calculus. For example, it is sufficient for applications of Itô's Lemma, changes of measure via Girsanov's theorem, and for the study of stochastic differential equations. However, it is inadequate for other important topics such as martingale representation theorems and local times.


title: Itô calculus

text: The integral extends to all predictable and locally bounded integrands, in a unique way, such that the dominated convergence theorem holds. That is, if "H" → ;"H" and |"H"| ≤ "J" for a locally bounded process "J", then


title: Itô calculus

text: in probability. The uniqueness of the extension from left-continuous to predictable integrands is a result of the monotone class lemma.


title: Itô calculus

text: In general, the stochastic integral "H" · "X" can be defined even in cases where the predictable process "H" is not locally bounded. If "K" = 1 / (1 + |"H"|) then "K" and "KH" are bounded. Associativity of stochastic integration implies that "H" is "X"-integrable, with integral "H" · "X" = "Y", if and only if "Y" = 0 and "K" · "Y" = ("KH") · "X". The set of "X"-integrable processes is denoted by "L"("X").


title: Itô calculus

text: As with ordinary calculus, integration by parts is an important result in stochastic calculus. The integration by parts formula for the Itô integral differs from the standard result due to the inclusion of a quadratic covariation term. This term comes from the fact that Itô calculus deals with processes with non-zero quadratic variation, which only occurs for infinite variation processes (such as Brownian motion). If "X" and "Y" are semimartingales then


title: Itô calculus

text: The result is similar to the integration by parts theorem for the Riemann–Stieltjes integral but has an additional quadratic variation term.


title: Itô calculus

text: Itô's lemma is the version of the chain rule or change of variables formula which applies to the Itô integral. It is one of the most powerful and frequently used theorems in stochastic calculus. For a continuous "n"-dimensional semimartingale "X" = ("X"...,"X") and twice continuously differentiable function "f" from R to R, it states that "f"("X") is a semimartingale and,


title: Itô calculus

text: This differs from the chain rule used in standard calculus due to the term involving the quadratic covariation ["X","X" ]. The formula can be generalized to include an explicit time-dependence in formula_20 and in other ways (see Itô's lemma).


title: Itô calculus

text: An important property of the Itô integral is that it preserves the local martingale property. If "M" is a local martingale and "H" is a locally bounded predictable process then "H" · "M" is also a local martingale. For integrands which are not locally bounded, there are examples where "H" · "M" is not a local martingale. However, this can only occur when "M" is not continuous. If "M" is a continuous local martingale then a predictable process "H" is "M"-integrable if and only if


title: Itô calculus

text: The most general statement for a discontinuous local martingale "M" is that if ("H" · ["M"]) is locally integrable then "H" · "M" exists and is a local martingale.


title: Itô calculus

text: For bounded integrands, the Itô stochastic integral preserves the space of "square integrable" martingales, which is the set of càdlàg martingales "M" such that E["M"] is finite for all "t". For any such square integrable martingale "M", the quadratic variation process ["M"] is integrable, and the Itô isometry states that


title: Itô calculus

text: This equality holds more generally for any martingale "M" such that "H" · ["M"] is integrable. The Itô isometry is often used as an important step in the construction of the stochastic integral, by defining "H" · "M" to be the unique extension of this isometry from a certain class of simple integrands to all bounded and predictable processes.


title: Itô calculus

text: For any "p" > 1, and bounded predictable integrand, the stochastic integral preserves the space of "p"-integrable martingales. These are càdlàg martingales such that E(|"M"|) is finite for all "t". However, this is not always true in the case where "p" = 1. There are examples of integrals of bounded predictable processes with respect to martingales which are not themselves martingales.


title: Itô calculus

text: The maximum process of a càdlàg process "M" is written as "M*" = sup |"M"|. For any "p" ≥ 1 and bounded predictable integrand, the stochastic integral preserves the space of càdlàg martingales "M" such that E[("M*")] is finite for all "t". If "p" > 1 then this is the same as the space of "p"-integrable martingales, by Doob's inequalities.


title: Itô calculus

text: The Burkholder–Davis–Gundy inequalities state that, for any given "p" ≥ 1, there exist positive constants "c", "C" that depend on "p", but not "M" or on "t" such that


title: Itô calculus

text: for all càdlàg local martingales "M". These are used to show that if ("M*") is integrable and "H" is a bounded predictable process then


title: Itô calculus

text: and, consequently, "H" · "M" is a "p"-integrable martingale. More generally, this statement is true whenever ("H" · ["M"]) is integrable.


title: Itô calculus

text: Proofs that the Itô integral is well defined typically proceed by first looking at very simple integrands, such as piecewise constant, left continuous and adapted processes where the integral can be written explicitly. Such "simple predictable" processes are linear combinations of terms of the form "H" = "A"1 for stopping times "T" and "F"-measurable random variables "A", for which the integral is


title: Itô calculus

text: For a Brownian motion "B", the property that it has independent increments with zero mean and variance Var("B") = "t" can be used to prove the Itô isometry for simple predictable integrands,


title: Itô calculus

text: By a continuous linear extension, the integral extends uniquely to all predictable integrands satisfying


title: Itô calculus

text: in such way that the Itô isometry still holds. It can then be extended to all "B"-integrable processes by localization. This method allows the integral to be defined with respect to any Itô process.


title: Itô calculus

text: For a general semimartingale "X", the decomposition "X" = "M" + "A" into a local martingale "M" plus a finite variation process "A" can be used. Then, the integral can be shown to exist separately with respect to "M" and "A" and combined using linearity, "H" · "X" = "H" · "M" + "H" · "A", to get the integral with respect to "X". The standard Lebesgue–Stieltjes integral allows integration to be defined with respect to finite variation processes, so the existence of the Itô integral for semimartingales will follow from any construction for local martingales.


title: Itô calculus

text: For a càdlàg square integrable martingale "M", a generalized form of the Itô isometry can be used. First, the Doob–Meyer decomposition theorem is used to show that a decomposition exists, where "N" is a martingale and is a right-continuous, increasing and predictable process starting at zero. This uniquely defines , which is referred to as the "predictable quadratic variation" of "M". The Itô isometry for square integrable martingales is then