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Huffman coding

In computer science and information theory, a Huffman code is a particular type of optimal prefix code, used for lossless data compression. The process of finding or using such a code proceeds by means of Huffman coding, an algorithm developed by David A. Huffman while he was a Sc. D. Student at MIT, published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes"; the output from Huffman's algorithm can be viewed as a variable-length code table for encoding a source symbol. The algorithm derives this table from the estimated probability or frequency of occurrence for each possible value of the source symbol; as in other entropy encoding methods, more common symbols are represented using fewer bits than less common symbols. Huffman's method can be efficiently implemented, finding a code in time linear to the number of input weights if these weights are sorted. However, although optimal among methods encoding symbols separately, Huffman coding is not always optimal among all compression methods - it is replaced with arithmetic coding or asymmetric numeral systems if better compression ratio is required.

In 1951, David A. Huffman and his MIT information theory classmates were given the choice of a term paper or a final exam; the professor, Robert M. Fano, assigned a term paper on the problem of finding the most efficient binary code. Huffman, unable to prove any codes were the most efficient, was about to give up and start studying for the final when he hit upon the idea of using a frequency-sorted binary tree and proved this method the most efficient. In doing so, Huffman outdid Fano, who had worked with information theory inventor Claude Shannon to develop a similar code. Building the tree from the bottom up guaranteed optimality, unlike top-down Shannon–Fano coding. Huffman coding uses a specific method for choosing the representation for each symbol, resulting in a prefix code. Huffman coding is such a widespread method for creating prefix codes that the term "Huffman code" is used as a synonym for "prefix code" when such a code is not produced by Huffman's algorithm. Given A set of symbols and their weights.

Find A prefix-free binary code with minimum expected codeword length. Input. Alphabet A =, the symbol alphabet of size n. Tuple W =, the tuple of the symbol weights, i.e. w i = w e i g h t, 1 ≤ i ≤ n. Output. Code C =, the tuple of codewords, where c i is the codeword for a i, 1 ≤ i ≤ n. Goal. Let L = ∑ i = 1 n w i × l e n g t h be the weighted path length of code C. Condition: L ≤ L for any code T. We give an example of the result of Huffman coding for a code with five characters and given weights. We will not verify that it minimizes L over all codes, but we will compute L and compare it to the Shannon entropy H of the given set of weights. For any code, biunique, meaning that the code is uniquely decodeable, the sum of the probability budgets across all symbols is always less than or equal to one. In this example, the sum is equal to one. If this is not the case, you can always derive an equivalent code by adding extra symbols, to make the code complete while keeping it biunique; as defined by Shannon, the information content h of each symbol ai with non-null probability is h = log 2 ⁡

Aston Martin Rapide

The Aston Martin Rapide is a 5-door, 4-seater, high-performance sports saloon, which the British luxury marque Aston Martin introduced in early 2010. It was first presented as a concept car at the North American International Auto Show in 2006 and the production version was shown at the 2009 Frankfurt Motor Show; the Rapide name is a reference to the Lagonda Rapide, a five-door, four-seater saloon produced by Lagonda, now a part of Aston Martin. The new Rapide is the company's first 5-door fastback saloon since the Lagonda, discontinued in 1990; the Rapide is underpinned by the VH Generation III platform. The first cars rolled off the production line in May 2010 built at a dedicated plant at the Magna Steyr facility in Graz, Austria; the factory planned to build 2,000 cars per year, but production was relocated to England in 2012 after sales did not meet production targets. The Rapide is powered by a 5,935 cc V12 engine, generating a maximum power output 477 PS and torque of 600 N⋅m; the car has a 6-speed Touchtronic II automatic transmission.

The Rapide can attain a top speed of 303 km/h, can accelerate from 0 to 100 km/h in 5.2 seconds. The Rapide's standard features include a tilt-telescoping steering wheel, bi-xenon headlamps and LED taillamps. Leather and walnut wood trim with metallic accents. Other standard features include a Bang & Olufsen 16-speaker sound system with two tweeters that rise from the dashboard on activation of the system; the Rapide was designed by stretching the design of the DB9 in order to accommodate an extra set of doors. Aston Martin design director, Marek Reichman has described a thoroughbred race horse as an inspiration, stating that he wanted muscles in the design to be visible through the skin; the side windows of the car were made to appear like a single unit by using a black B pillar. The roof was designed to be as low as possible so it would mimic the design language of Aston Martin's model lineup. Due to the usage of swan doors and a low roof, the car is difficult for the accommodation of tall people.

By comparison, the Porsche Panamera, a competitor of the Rapide, is 2.3 inches taller. The rear flanks of the car are wider than those on the DB9, thus smoothening the extended roof design; the rear fenders and a curvaceous design language prevent the car as being perceived as stretched. The car makes use of rear lights and diffusers from the Vantage while the front headlamps are unique to the model. Although they would find use on the Vanquish and the facelift DB9; as part of the 2014 facelift and revisions to the Rapide, the V12 engine is upgraded and now has a power output of 558 PS and torque of 620 N⋅m. Performance improvements include a top speed of 306 km/h and acceleration from 0 to 100 km/h reduced to 4.9 seconds. Carbon dioxide emissions are reduced by 23g/km to 332g/km; the Rapide S received further revisions in 2015, with a new 8-speed Touchtronic III automatic transmission and power increase to 560 PS and 630 N⋅m of torque, resulting in an acceleration of 0 to 100 km/h in 4.4 seconds and an increased top speed of 327 km/h.

In 2015, Aston Martin was reported to be working on an all-electric version of the Rapide. The model named RapidE was confirmed for production at the 2018 Frankfurt Motor Show, the company revealed that the RapidE would go into production in the fourth quarter of 2019; the RapidE is expected to rival Porsche's upcoming Taycan electric saloon. One hundred and fifty-five examples of the model would be produced at Aston Martin's dedicated production facility located in St Athan, Wales where future all-electric Lagonda models will be produced. Williams Advanced Engineering would be providing R&D assist in the protype building and testing process with close involvement from interested customers; the RapidE will be powered by a 65 kWh battery supplied by HyperBat Limited. The battery would be capable of 800-volt power transfers. Five thousand six hundred lithium-ion electric cells would be fitted in the engine bay along with two electric motors supplied by Integral Powertrain at the rear. Both of the motors will drive the car via an Xtrac transmission featuring a limited-slip differential.

A new suspension system will be implemented to better cope with the changes in the drive train. The two electric motors will have a combined power output of 949 N ⋅ m of torque; the car will have claimed acceleration figures of 0–97 km/h in sub-4.0 seconds' time and 80–113 km/h in 1.5 seconds, along with a top speed of 249 km/h. Maximum performance will be accessible regardless of battery charge. A prototype was tested at the Nurbürgring to ensure that the car delivers linear power despite hard usage; the car will have a projected range of 322 km and will charge up to 185 miles of range an hour on a 400-volt, 50 kW charger. The car can be charged on an 800-volt super charging station which increases the charging rate; the RapidE will be fitted with low-drag wheels and low-resistance Pirelli P Zero tyres for maximum efficiency. In June 2018, Aston Martin unveiled the high-performance iteration of the Rapide called the Rapide AMR; the 6.0-litre aspirated V12 engine has received a power increase to 603 PS and 630 N⋅m of torque, courtesy of better air flow to the engine and new calibration software.

The 8-speed automatic transmission has received recalibration for bette

Lankester Merrin

Father Lankester Merrin is a fictional character in the novel The Exorcist, one of the two main protagonists in the 1973 film adaptation, several sequel films. Merrin, an elderly priest and paleontologist on an archeological dig in Iraq, finds images of the demon Pazuzu and subsequently experiences other unusual phenomena, he had faced the demon many years before during an exorcism in Africa. The find. Merrin does not appear again until much in the novel, when he joins the protagonist, Father Damien Karras, in Washington, D. C. to exorcise the demon from the body of a young girl. Merrin, who has a heart condition for which he takes nitroglycerin, dies during the ritual, leaving the inexperienced Karras to complete the exorcism himself. Merrin's depiction in the 1973 film The Exorcist is faithful to the novel; the character of Merrin reappears in the sequel Exorcist II: The Heretic, in extended flashbacks detailing an exorcism he performed in Africa following the Second World War. He is portrayed in both films by Max von Sydow.

The studio wanted Marlon Brando for the role of Father Merrin. Friedkin vetoed this by stating it would become a "Brando movie"; the character was featured again in both prequel films, Exorcist: The Beginning and Dominion: Prequel to the Exorcist. Both films revisit Merrin's experiences in Africa prior to his first exorcism, but each presents a different version of the events and neither agrees with the events as presented in Exorcist II, he is played in both films by Stellan Skarsgård. In the 2014 BBC Radio dramatisation, Merrin is voiced by Ian McDiarmid

Coral Creek Airport

Coral Creek Airport is a private-use airport located 2 miles northeast of Boca Grande, a community on Gasparilla Island in southwest Florida, United States. The airport itself is located in Placida in Charlotte County, about a mile north of the separately-owned Coral Creek Club; the airport is owned by BK IV AS, L. L. C; the airfield is composed of a single asphalt runway connected to a ramp and two hangars via a single taxiway. There is one FBO for the airport, known as Boca Grande Jet Center; the office is attached to the main hangar, connected to the public road by a private driveway. Services for the airport are restricted to members-only with limited guest accommodations. Permission is needed to land, the pattern is uncontrolled and there is no tower. Coral Creek Airport opened, it was purchased in 2003 and, made private. In 2012, under new ownership, the 6000 foot runway in place, was surfaced. In the late hours of May 20, 2013, a group of burglars cut through a section of wire fence along the perimeter to gain entry onto the property.

Using three large trucks, they left damage, stole a large quantity of diesel fuel, as well as a fuel pump. The group was unable to get inside the locked hangars. Upon leaving, one of the trucks had gotten stuck in mud caused by recent heavy rainfall and a front-end loader was used to free the vehicle. Repairs were made to the damaged areas of the airport and regular service was back underway, as was the expansion project taking place at the time; the expansion project saw the addition of a second hangar, now utilized for long-term car and plane storage. Total hangar area is 17,140 square feet; the runway is lit by pilot-controlled, medium intensity lights with PAPIs on the north and south ends. A rotating beacon light is located on the main hangar. Weather is reported via an AWOS III P/T station. Both of the hangars are capable of holding Gulfstream/Global aircraft. There are six GA tiedowns on the ramp. Boca Grande Jet Center is a full-service FBO that offers Jet-A, Jet-A w/ Prist, 100LL, GPU, LAV.

There are shower facilities on the property, as well as internet in the main FBO office. The FBO can arrange rental cars and catering. Due to the private nature of the airport and because it serves members on-demand, it is difficult to gather a consistent schedule or number of movements. Takeoffs and landings can range from few to several on any given day. Peak season occurs between October and June, the period of business for the nearby Gasparilla Inn. Neither the airport nor the airspace is used for training purposes. Common aircraft operating at the airport include: Beechcraft Super King Air Bombardier Challenger Global Learjet Cessna Citation Dassault Falcon Embraer Phenom Legacy Gulfstream Hawker Beechcraft North American Sabre 65 Piaggio AvantiThe runway can accommodate aircraft with a gross weight up to 100,000 lbs. While the airport does store aircraft when members fly in, there are none permanently based at the airport. All aircraft are owned or chartered by members. Boca Grande Causeway - vehicular access from Placida to Boca Grande about 2 miles south of the airport.

Cape Haze Pioneer Trail - rail trail that comes near the beginning of runway 05. FlexJet - fractional carrier that flies into the airport. NetJets - another popular carrier at Coral Creek. Spirit of St. Louis Airport - BK IV AS, L. L. C. Office. Wheels Up - another popular carrier at Coral Creek. Official website

Wayne King (ice hockey)

Wayne Gordon King is a retired professional Winger of Ojibwe descent who played in the National Hockey League for the California Golden Seals. During the 1973-74 season, King piled up 34 goals and 34 assists, skating for the Salt Lake Golden Eagles of the Western Hockey League, the Seals' top farm team. A left-shot operating from the opposite wing, his performance earned him WHL Second Team All-Star Right Wing honours at season's end. King was born in Midland, about an hour north of Toronto, but raised in Port McNicoll, Ontario as the son of an engineer father and stay-at-home mother; the King's were the only Native family in Port McNicoll, the parents having both lived on reserves, but moving into the larger community in search of work. After spending the 1976-77 season back in Salt Lake City, King joined the OHA senior Barrie Flyers, not far from his hometown, he averaged a point per game in 1977-78 for the Flyers announced his retirement. Upon retiring from hockey in 1978, King returned to his hometown of Midland, Ontario to start a family with his wife Shirley.

The following year, 1979, they had their first child, a boy they named G. W. Four years in 1983, the Kings had another child, their daughter MaKala. King enjoyed playing hockey and fastball recreationally during his retirement, but due to a knee injury sustained during his professional career he no longer participates in these sports, but still golfs frequently. King reached the Ontario Hockey Association Finals while playing as a 17-year-old for the [[Midland Flyers Intermediate B team in 1968-69. In the same year, while trying out for the Junior B Owen Sound Greys, King was scouted by the owner and general manager of the Niagara Falls Flyers Junior A team, Hap Emms, spent the next two seasons playing for Niagara. King was signed by an expansion team in the National Hockey League; as a player he was known as a tough forward, an aggressive checker and an intrepid battler in the corners. He made his pro debut with the Columbus Seals of the International Hockey League during the 1971-72 season; the Seals were the initial farm team of the California Golden Seals, King played for the top farm team, the Salt Lake City Golden Seals in the Western Hockey League.

It was during his 1973-74 season with Salt Lake City that King put up the best statistical season of his professional career, compiling 34 goals and 34 assists in 76 games. King played 25 games with the California Golden Seals of the NHL during the 1974-75 season before suffering a devastating knee injury, tearing ligaments during a collision with Mike Marson of the Washington Capitals. Prior to this injury, King had amassed seven assists on the year; this injury slowed his pursuit of an NHL career, but King did not give up, returning to play for California in 1975-76. It was announced in 1976. King appeared 46 games in the 1976-77 season and retired at the end of the year after receiving little interest from the other professional teams. King worked in an auto body shop for two years starting in 1977. Following this, King began his post-hockey career, working as a mental health worker and security guard at the Penetanguishene Mental Health Centre, now known as the Waypoint Centre for Mental Health Care.

During this time, King became a Registered Practical Nurse, having completed a two-year program to receive the designation. As of 2004, King was employed by the Government of Ontario and enjoyed playing Golf in his free time. Wayne King career statistics at The Internet Hockey Database Wayne King's Profile with the Midland Ontario Sports Hall of Fame


A metaphosphate ion is an oxyanion that has the empirical formula PO−3. The structure of a metaphosphate ion can be described as being made up of PO4 structural units in which each unit shares two corners with another unit; this can come about in two ways. Formation of a ring, as in trimetaphosphate, illustrated. Formation of an infinite chain, with the same structure as in ammonium metavanadateMetaphosphates can be considered as salts of the corresponding metaphosphoric acids although none of these acids has been isolated; the metaphosphoric acids can be formulated as H2O·P2O5. In comparison, phosphoric acid, H3PO4 can be formulated as 3H2O·P2O5 and pyrophosphoric acid, H4P2O7, as 2H2O·P2O5. Metaphosphates can be used as an alternative of white phosphorus in organic syntheses. Sodium trimetaphosphate Sodium hexametaphosphate