Theoretical computer science is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation. It is difficult to circumscribe the theoretical areas precisely; the ACM's Special Interest Group on Algorithms and Computation Theory provides the following description: TCS covers a wide variety of topics including algorithms, data structures, computational complexity and distributed computation, probabilistic computation, quantum computation, automata theory, information theory, program semantics and verification, machine learning, computational biology, computational economics, computational geometry, computational number theory and algebra. Work in this field is distinguished by its emphasis on mathematical technique and rigor. While logical inference and mathematical proof had existed in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved.
These developments have led to the modern study of logic and computability, indeed the field of theoretical computer science as a whole. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of neural networks and parallel distributed processing were established. In 1971, Stephen Cook and, working independently, Leonid Levin, proved that there exist relevant problems that are NP-complete – a landmark result in computational complexity theory. With the development of quantum mechanics in the beginning of the 20th century came the concept that mathematical operations could be performed on an entire particle wavefunction. In other words, one could compute functions on multiple states simultaneously; this led to the concept of a quantum computer in the latter half of the 20th century that took off in the 1990s when Peter Shor showed that such methods could be used to factor large numbers in polynomial time, which, if implemented, would render most modern public key cryptography systems uselessly insecure.
Modern theoretical computer science research is based on these basic developments, but includes many other mathematical and interdisciplinary problems that have been posed, as shown below: An algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, automated reasoning. An algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Starting from an initial state and initial input, the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states producing "output" and terminating at a final ending state; the transition from one state to the next is not deterministic. Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them, it is a theory in theoretical computer science, under Discrete mathematics. Automata comes from the Greek word αὐτόματα meaning "self-acting".
Automata Theory is the study of self-operating virtual machines to help in logical understanding of input and output process, without or with intermediate stage of computation. Coding theory is the study of their fitness for a specific application. Codes are used for data compression, error-correction and more also for network coding. Codes are studied by various scientific disciplines—such as information theory, electrical engineering and computer science—for the purpose of designing efficient and reliable data transmission methods; this involves the removal of redundancy and the correction of errors in the transmitted data. Computational biology involves the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological and social systems; the field is broadly defined and includes foundations in computer science, applied mathematics, statistics, chemistry, molecular biology, genomics, evolution, anatomy and visualization.
Computational biology is different from biological computation, a subfield of computer science and computer engineering using bioengineering and biology to build computers, but is similar to bioinformatics, an interdisciplinary science using computers to store and process biological data. Computational complexity theory is a branch of the theory of computation that focuses on classifying computational problems according to their inherent difficulty, relating those classes to each other. A computational problem is understood to be a task, in principle amenable to being solved by a computer, equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used; the theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage.
Other complexity measures are used, such as the amount of communication, the numbe
The Unimog 404 called the Unimog S and Unimog 404 S, is a vehicle of the Unimog-series by Mercedes-Benz, produced in the Unimog plant in Gaggenau from 1955 to 1980. Marketed as Unimog U82, Unimog U110, 64,242 units of the two Unimog 404 types 404.0 and 404.1 were built, which makes the 404 the Unimog model with the highest production figure of all Unimogs. Unlike the Unimog 401, the 404 is rather a small 1.5-tonne-offroad-truck than an agricultural vehicle. In Germany, it was a common military vehicle and fire engine, 36,000 Unimog 404 were made for the Bundeswehr; the first Unimog 404 concept-vehicle was made in 1953 and was smaller than the series production model, it had a track width of 1,600 mm and a wheelbase of 2,670 mm. Two prototypes for the French army followed in 1954, the first 1,100 series production models were purchased by the French army. Since the French army did not want the spare wheel to occupy space for soldiers on the bed, the Daimler-Benz engineers decided to build the Unimog 404 with a downswept frame so the spare wheel could be mounted underneath the bed.
This constructional feature allowed more torsional flexing and, improved the offroad capabilities of the Unimog. The downswept frame became a key constructional feature for the following Unimog types. At its introduction in 1955, the Unimog 404.1 was available as the 2,700 mm wheelbase model with the Otto engine M 180 producing 60 kW. In 1956, the 2,900 mm wheelbase model of the 404.1 available with the same engine. Both were sold as Unimog U82; the production of the U82 with the short wheelbase was stopped in 1971, while the long wheelbase model was built until 1980. Starting from 1971, the Unimog 404.0, sold as Unimog U110, was offered. It was fitted with the cab of the Unimog 406 and soon afterwards, with the model 404.012, it received the M 130 engine. However, only 1,791 404.0 were made. 81 Unimog 404 were made with the diesel engine OM 615 for the Portuguese market. The Unimog 404 is a small four-wheel offroad capable truck designed for a payload of 1,500 kg. Like other Unimogs, it has a ladder frame, two portal axles with reduction gears and coil springs with hydraulic shock absorbers for the rear and front axle.
All four wheels and tyres are fitted with hydraulic ATE drum brakes. The 404 is a rear-wheel-drive vehicle with switchable all-wheel-drive and additional differential locks. A water-cooled straight-six Otto engine, type M 180 II-U, displacing 2,195 cc powers the 404.1. It is fitted with a Zenith 32 NDIX offroad-carburettor and transmits the torque to a synchronised manual Daimler-Benz-six-speed-gearbox with two additional reverse gears; as clutch, the Fichtel & Sachs K 16 Z single-disc-dry-clutch is used. The 404 was available both with a standard closed two-door-cab and as a two-door-cabriolet with a convertible top; the 404.1 has a divided windscreen, while the 404.0 with the cab of the Unimog model 406 has a single windscreen. Only the standard cab models have side windows in the doors. Special purpose vehicles, such as fire engines, were made with an extended four-door-cab. Carl-Heinz Vogler: Typenatlas Unimog. Alle Unimog-Klassiker seit 1946 bis 1993. GeraMond, München 2015, ISBN 978-3-86245-026-8, S. 41 ff
Fit for Life is a diet and lifestyle book series stemming from the principles of orthopathy. It is promoted by the American writers Harvey and Marilyn Diamond; the Fit for Life book series describes a fad diet which specifies eating only fruit in the morning, eating predominantly "live" and "high-water-content" food, if eating animal protein to avoid combining it with complex carbohydrates. While the diet has been praised for encouraging the consumption of raw fruits and vegetables, several other aspects of the diet have been disputed by dietitians and nutritionists, the American Dietetic Association and the American Academy of Family Physicians list it as a fad diet; the diet is based on Diamond's exploration of Herbert M. Shelton theories of food combining. Both authors claimed to be able to bring about weight loss without the need to count calories or undertake anything more than a reasonable exercise program. In the first version of the program, Diamond claimed that if one eats the foods in the wrong combination they "cause fermentation" in the stomach.
This in turns gives rise to the destruction of nutrients. Diamond categorized foods into two groups: "dead foods" that "clog" the body, "living foods" that "cleanse" it. According to Fit for Life principles, dead foods are those that have refined or processed origins; the basic points of Fit for Life are as follows: Fruits are best eaten fresh and raw. Where possible they should be eaten alone. Carbohydrates & Proteins should never be combined in the one meal. Water should never be drunk at meals. Dairy products are considered of limited value and because of their allergic capacity, should if be eaten. In the 2000s, the Fit for Life system added the Personalized FFL Weight Management Program, which employs proprietary protocols called Biochemical "Analyzation", Metabolic Typing and Genetic Predispositions; the Diamonds claim that these protocols allow the personalization of the diet, which thus customized is effective only for one individual, can be used for that person's entire life. This version of the diet puts less emphasis on "live" and "dead" foods, instead talks of "enzyme deficient foods".
The Diamonds posit that enzymes that digest proteins interfere with enzymes that digest carbohydrates, justifying some of the rules above. They began to sell nutritional supplements, advertised as enzyme supplements, many of which are recommended in the newest version of FFL; the diet came to public attention in the mid-1980s with the publication of Fit for Life, a New York Times best seller which sold millions of copies, over 12 million according to Harvey Diamond. Harvey Diamond has appeared on dozens of television talk shows promoting his theories. In Fit for Life II the Diamonds warned against eating artificial food additives such as hydrogenated vegetable oil, which at the time was being promoted by the food industry as a healthy alternative to saturated fat. Tony Robbins promoted the Fit for Life principles and veganism to increase energy levels in his book Unlimited Power. Fit for Life - by Harvey and Marilyn Diamond ISBN 0-446-30015-2 Living Health - by Harvey and Marilyn Diamond ISBN 0-446-51281-8 Fit for Life II - by Harvey and Marilyn Diamond ISBN 0-446-35875-4 Fit for Life: A New Beginning - by Harvey Diamond ISBN 1-57566-718-5 Fit for Life Not Fat For Life - by Harvey Diamond ISBN 978-0-7573-0113-1 Living Without Pain - by Harvey Diamond ISBN 0-9769961-0-3 A New Way of Eating from the Fit for Life Kitchen The American Vegetarian Cookbook from the Fit for Life Kitchen The Fit for Life Cookbook Fitonics for Life with Donald Burton Schnell Recipes for Life with Lisa Neurith Young For Life with Donald Burton Schnell Health experts and science writers have dismissed the book as quackery.
The rigor of study underlying Harvey Diamond's credentials have been disputed, which has drawn questions about his competence to write about nutrition, because his doctoral degree came from the American College of Life Science, a non-accredited correspondence school founded in 1982 by T. C. Fry, who did not graduate high school or undergo a formal accreditation process himself. FFL's personalized diet program has been criticized for providing a "Clinical Manual", infused with alternative medicine claims about how the body works, some of which may be scientifically inaccurate or not accepted by conventional medicine. Despite the fact that FFL web site mentioned "clinical trials", many of the proposed principles and benefits of FFL diet are not supported by citations to any scholarly research, some of the claims have been directly refuted by scientific research. For example, a dissociated diet as that advertised by FFL is no more effective for weight loss than a calorie-restricted diet. Raw veganism Dr. Hay diet Alkaline diet List of diets Harvey Diamond's official website Criticism by James J. Kenney, Ph.
D. R. D. ChaseFreedom's criticism by dietitian