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Bella Subbotovskaya
Bella Abramovna Subbotovskaya (17 December 1937 – 23 September 1982) was a Soviet mathematician who founded the short-lived Jewish People's University (1978–1983) in Moscow. Szpiro, G. (2007),Bella Abramovna Subbotovskaya and the Jewish People's University, ''Notices of the American Mathematical Society'', 54(10), 1326–1330.Zelevinsky, A. (2005), "Remembering Bella Abramovna", ''You Failed Your Math Test Comrade Einstein'' (M. Shifman, ed.), World Scientific, 191–195. The school's purpose was to offer free education to those affected by structured anti-Semitism within the Soviet educational system. Its existence was outside Soviet authority and it was investigated by the KGB. Subbotovskaya herself was interrogated a number of times by the KGB and shortly thereafter was hit by a truck and died, in what has been speculated was an assassination. Academic work Prior to founding the Jewish People's University, Subbotovskaya published papers in mathematical logic. Her results ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents within the city limits, over 19.1 million residents in the urban area, and over 21.5 million residents in Moscow metropolitan area, its metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's List of largest cities, largest cities, being the List of European cities by population within city limits, most populous city entirely in Europe, the largest List of urban areas in Europe, urban and List of metropolitan areas in Europe, metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow became the capital of the Grand Principality of Moscow, which led the unification of the Russian lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\^k \to \, where \ is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0, the function is a constant element of \. A Boolean function with multiple outputs, f:\^k \to \^m with m>1 is a vectorial or ''vector-valued'' Boolean function (an S-box in symmetric cryptography). There are 2^ different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k-ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k, and two propositional formulas a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1938 Births
Events January * January 1 – state-owned enterprise, State-owned railway networks are created by merger, in France (SNCF) and the Netherlands (Nederlandse Spoorwegen – NS). * January 20 – King Farouk of Egypt marries Safinaz Zulficar, who becomes Farida of Egypt, Queen Farida, in Cairo. * January 27 – The Honeymoon Bridge (Niagara Falls), Honeymoon Bridge at Niagara Falls, New York, collapses as a result of an ice jam. February * February 4 ** Adolf Hitler abolishes the War Ministry and creates the Oberkommando der Wehrmacht (High Command of the Armed Forces), giving him direct control of the German military. In addition, he dismisses political and military leaders considered unsympathetic to his philosophy or policies. General Werner von Fritsch is forced to resign as Commander of Chief of the German Army following accusations of homosexuality, and replaced by General Walther von Brauchitsch. Foreign Minister Baron Konstantin von Neurath is dismi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Circuits
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length. Boolean circuits are defined in terms of the logic gates they contain. For example, a circuit might contain binary AND and OR gates and unary NOT gates, or be entirely described by binary NAND gates. Each gate corresponds to some Boolean function that takes a fixed number of bits as input and outputs a single bit. Boolean circuits provide a model for many digital components used in computer engineering, including multiplexers, adders, and arithmetic logic units, but they exclude sequential logic. They are an abstraction that omits many aspects relevant to designing real digital logic circuits, such as metastability, fanout, glitches, power consumption, and propagation delay variability. Formal definition In giving a formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Switching Lemma
In computational complexity theory, Håstad's switching lemma is a key tool for proving lower bounds on the size of constant-depth Boolean circuits. It was first introduced by Johan Håstad to prove that AC0, AC0 Boolean circuits of depth ''k'' require size \exp(\Omega(n^)) to compute the parity function on n bits. He was later awarded the Gödel Prize for this work in 1994. The switching lemma describes the behavior of a depth-2 circuit under ''random restriction'', i.e. when randomly fixing most of the coordinates to 0 or 1. Specifically, from the lemma, it follows that a formula in conjunctive normal form (that is, an AND of ORs) becomes a formula in disjunctive normal form (an OR of ANDs) under random restriction, and vice versa. This "switching" gives the lemma its name. Statement Consider a width-w formula in disjunctive normal form F = C_1 \vee C_2 \vee \cdots \vee C_m , the Logical disjunction, OR of clauses C_\ell which are the Logical conjunction, AND of ''w'' literals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johan Håstad
Johan Torkel Håstad (; born 19 November 1960) is a Swedish theoretical computer scientist most known for his work on computational complexity theory. He was the recipient of the Gödel Prize in 1994 and 2011 and the ACM Doctoral Dissertation Award in 1986, among other prizes. He has been a professor in theoretical computer science at KTH Royal Institute of Technology in Stockholm, Sweden since 1988, becoming a full professor in 1992. He is a member of the Royal Swedish Academy of Sciences since 2001. He received his B.S. in Mathematics at Stockholm University in 1981, his M.S. in Mathematics at Uppsala University in 1984 and his Ph.D. in Mathematics from MIT in 1986. Håstad's thesis and 1994 Gödel Prize concerned his work on lower bounds on the size of constant-depth Boolean circuits for the parity function. After Andrew Yao proved that such circuits require exponential size, Håstad proved nearly optimal lower bounds on the necessary size through his switching lemma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uri Zwick
Uri Zwick (Hebrew: אורי צוויק) is an Israeli computer scientist and mathematician known for his work on graph algorithms, in particular on distances in graphs and on the color-coding technique for subgraph isomorphism. With Howard Karloff, he is the namesake of the Karloff–Zwick algorithm for approximating the MAX-3SAT problem of Boolean satisfiability. He and his coauthors won the David P. Robbins Prize in 2011 for their work on the block-stacking problem. Zwick earned a bachelor's degree from the Technion – Israel Institute of Technology, and completed his doctorate at Tel Aviv University in 1989 under the supervision of Noga Alon Noga Alon (; born 1956) is an Israeli mathematician and a professor of mathematics at Princeton University noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of papers. Education and career .... He is currently a professor of computer science at Tel Aviv University. References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mike Paterson
Michael Stewart Paterson, is a British computer scientist, who was the director of the Centre for Discrete Mathematics and its Applications (DIMAP) at the University of Warwick until 2007, and chair of the department of computer science in 2005. He received his Doctor of Philosophy (Ph.D.) from the University of Cambridge in 1967, under the supervision of David Park. He spent three years at the Massachusetts Institute of Technology (MIT) and moved to the University of Warwick in 1971, where he remains Professor Emeritus. Paterson is an expert on theoretical computer science with more than 100 publications, especially in the design and analysis of algorithms and computational complexity. Paterson's distinguished career was recognised with the EATCS Award in 2006, and a workshop in honour of his 66th birthday in 2008, including contributions of several Turing Award and Gödel Prize laureates. A further workshop was held in 2017 in honour of his 75th birthday, co-located with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Method
In mathematics, the probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is strictly greater than zero. Although the proof uses probability, the final conclusion is determined for ''certain'', without any possible error. This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory. Introduction If every object in a collection of objects fails to have a certain property, then the probability that a random object chosen from the collection has that property is zero. Thus, by contraposition, if the probability that a random object chosen from the collection has that property is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity Function
In Boolean algebra, a parity function is a Boolean function whose value is one if and only if the input vector has an odd number of ones. The parity function of two inputs is also known as the XOR function. The parity function is notable for its role in theoretical investigation of circuit complexity of Boolean functions. The output of the parity function is the parity bit. Definition The n-variable parity function is the Boolean function f:\^n\to\ with the property that f(x)=1 if and only if the number of ones in the vector x\in\^n is odd. In other words, f is defined as follows: :f(x)=x_1\oplus x_2 \oplus \dots \oplus x_n where \oplus denotes exclusive or. Properties Parity only depends on the number of ones and is therefore a symmetric Boolean function. The ''n''-variable parity function and its negation are the only Boolean functions for which all disjunctive normal forms have the maximal number of 2 ''n'' − 1 monomials of length ''n'' and al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov's Inequality
In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some positive Constant (mathematics), constant. Markov's inequality is tight in the sense that for each chosen positive constant, there exists a random variable such that the inequality is in fact an equality. It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev (Markov's teacher), and many sources, especially in Mathematical analysis, analysis, refer to it as Chebyshev's inequality (sometimes, calling it the first Chebyshev inequality, while referring to Chebyshev's inequality as the second Chebyshev inequality) or Irénée-Jules Bienaymé, Bienaymé's inequality. Markov's inequality (and other similar inequalities) relate probabilities to expected value, expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
