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Peter Gacs
Péter Gács (Hungarian pronunciation: pe:ter 'ga:tʃ born May 9, 1947), professionally also known as Peter Gacs, is a Hungarian-American mathematician and computer scientist, professor, and an external member of the Hungarian Academy of Sciences. He is well known for his work in reliable computation, randomness in computing, algorithmic complexity, algorithmic probability, and information theory. Career Peter Gacs attended high school in his hometown, then obtained a diploma (M.S.) at Loránd Eötvös University in Budapest in 1970. Gacs started his career as a researcher at the Applied Mathematics Institute of the Hungarian Academy of Science. He obtained his doctoral degree from the Goethe University Frankfurt in 1978. Throughout his studies he had the opportunity to visit Moscow State University and work with Andrey Kolmogorov and his student Leonid A Levin. Through 1979 he was a visiting research associate at Stanford University. He was an assistant professor at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population of 1,752,286 over a land area of about . Budapest, which is both a city and county, forms the centre of the Budapest metropolitan area, which has an area of and a population of 3,303,786; it is a primate city, constituting 33% of the population of Hungary. The history of Budapest began when an early Celtic settlement transformed into the Roman town of Aquincum, the capital of Lower Pannonia. The Hungarians arrived in the territory in the late 9th century, but the area was pillaged by the Mongols in 1241–42. Re-established Buda became one of the centres of Renaissance humanist culture by the 15th century. The Battle of Mohács, in 1526, was followed by nearly 150 years of Ottoman rule. After the reconquest of Buda in 1686, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity. Biography Early life Andrey Kolmogorov was born in Tambov, about 500 kilometers south-southeast of Moscow, in 1903. His unmarried mother, Maria Y. Kolmogorova, died giving birth to him. Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do nobleman. Little is known about Andrey's father. He was supposedly named Nikolai Matveevich Kataev and had been an agronomist. Kataev had been exiled from St. Petersburg to the Yaroslavl province after his participation in the revolutionary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rudolf Ahlswede
Rudolf F. Ahlswede (15 September 1938 – 18 December 2010) was a German mathematician. Born in Dielmissen, Germany, he studied mathematics, physics, and philosophy. He wrote his Ph.D. thesis in 1966, at the University of Göttingen, with the topic "Contributions to the Shannon information theory in case of non-stationary channels". He dedicated himself in his further career to information theory and became one of the leading representatives of this area worldwide. Life and work In 1977, he joined and held a Professorship at the University of Bielefeld, Bielefeld, Germany. In 1988, he received together with Imre Csiszár the Best Paper Award of the IEEE Information Theory Society for work in the area of the hypothesis testing as well as in 1990 together with Gunter Dueck for a new theory of message identification. He has been awarded this prize twice. As an emeritus of Bielefeld University, Ahlswede received the 2006 Claude E. Shannon Award, one of the first few non-US c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
János Körner
János Körner is a Hungarian mathematician who works on information theory and combinatorics. Körner studied Mathematics at the Eötvös Loránd University in Budapest with a degree in 1970 and was then at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences until 1992. From 1981 to 1983 he was at the Bell Labs, Bell Laboratories and in 1987–88 at Télécom Paris (ENST) in Paris. He has been a professor at the Sapienza University of Rome since 1993. Over his career, he frequently collaborated with fellow information theorists such as Rudolf Ahlswede, Katalin Marton, and Imre Csiszár. Together with Rudolf Ahlswede and Peter Gács he proved the blowing-up lemma.Ahlswede, Gacs, Körner ''Bounds on conditional probabilities with applications in multiuser communication'', Z. Wahrsch. und Verw. Gebiete 34, 1976, 157–177 Besides information theory, he also works on extremal graph theory. In 2014 he received the Claude E. Shannon Award. He served as Ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The Steklov Institute Of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Steklov, who in 1919 founded the Institute of Physics and Mathematics in Leningrad. In 1934, this institute was split into separate parts for physics and mathematics, and the mathematical part became the Steklov Institute. At the same time, it was moved to Moscow. The first director of the Steklov Institute was Ivan Matveyevich Vinogradov. From 19611964, the institute's director was the notable mathematician Sergei Chernikov. The old building of the Institute in Leningrad became its Department in Leningrad. Today, that department has become a separate institute, called the ''St. Petersburg Department of Steklov Institute of Mathematics of Russian Academ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Transactions On Information Theory
''IEEE Transactions on Information Theory'' is a monthly peer-reviewed scientific journal published by the IEEE Information Theory Society. It covers information theory and the mathematics of communications. It was established in 1953 as ''IRE Transactions on Information Theory''. The editor-in-chief is Muriel Médard (Massachusetts Institute of Technology). As of 2007, the journal allows the posting of preprints on arXiv. According to Jack van Lint, it is the leading research journal in the whole field of coding theory. A 2006 study using the PageRank network analysis algorithm found that, among hundreds of computer science-related journals, ''IEEE Transactions on Information Theory'' had the highest ranking and was thus deemed the most prestigious. ''ACM Computing Surveys'', with the highest impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing-reducible
In computability theory, a Turing reduction from a decision problem A to a decision problem B is an oracle machine which decides problem A given an oracle for B (Rogers 1967, Soare 1987). It can be understood as an algorithm that could be used to solve A if it had available to it a subroutine for solving ''B''. The concept can be analogously applied to function problems. If a Turing reduction from A to B exists, then every algorithm for B can be used to produce an algorithm for A, by inserting the algorithm for B at each place where the oracle machine computing A queries the oracle for B. However, because the oracle machine may query the oracle a large number of times, the resulting algorithm may require more time asymptotically than either the algorithm for B or the oracle machine computing A. A Turing reduction in which the oracle machine runs in polynomial time is known as a polynomial-time reduction#Turing reductions, Cook reduction. The first formal definition of relative comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonid A
Leonid (russian: Леонид ; uk, Леонід ; be, Леанід, Ljeaníd ) is a Slavic version of the given name Leonidas. The French version is Leonide. People with the name include: *Leonid Andreyev (1871–1919), Russian playwright and short-story writer who led the Expressionist movement in the national literature *Leonid Brezhnev (1906–1982), leader of the USSR from 1964 to 1982 *Leonid Buryak (b. 1953), USSR/Ukraine-born Olympic-medal-winning soccer player and coach *Leonid Bykov (1928–1979), Soviet and Ukrainian actor, film director, and script writer *Leonid Desyatnikov (b. 1955), Soviet and Russian opera and film composer *Leonid Feodorov (1879–1935), a bishop and Exarch for the Russian Catholic Church, and survivor of the Gulag *Leonid Filatov (1946–2003), Soviet and Russian actor, director, poet, and pamphleteer *Leonid Gaidai, (1923–1993), Soviet comedy film director *Leonid Geishtor (b. 1936), USSR (Belarus)-born Olympic champion Canadian pairs spri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Problem (cellular Automaton)
The majority problem, or density classification task, is the problem of finding one-dimensional cellular automaton rules that accurately perform majority voting. Using local transition rules, cells cannot know the total count of all the ones in system. In order to count the number of ones (or, by symmetry, the number of zeros), the system requires a logarithmic number of bits in the total size of the system. It also requires the system send messages over a distance linear in the size of the system and for the system to recognize a non- regular language. Thus, this problem is an important test case in measuring the computational power of cellular automaton systems. Problem statement Given a configuration of a two-state cellular automaton with ''i'' + ''j'' cells total, ''i'' of which are in the zero state and ''j'' of which are in the one state, a correct solution to the voting problem must eventually set all cells to zero if ''i'' > ''j'' and must eventually set all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of '' states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that determines the new state ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sipser–Lautemann Theorem
In computational complexity theory, the Sipser–Lautemann theorem or Sipser–Gács–Lautemann theorem states that bounded-error probabilistic polynomial (BPP) time is contained in the polynomial time hierarchy, and more specifically Σ2 ∩ Π2. In 1983, Michael Sipser showed that BPP is contained in the polynomial time hierarchy. Péter Gács showed that BPP is actually contained in Σ2 ∩ Π2. Clemens Lautemann contributed by giving a simple proof of BPP’s membership in Σ2 ∩ Π2, also in 1983. It is conjectured that in fact BPP= P, which is a much stronger statement than the Sipser–Lautemann theorem. Proof Here we present the Lautemann's proof. Without loss of generality, a machine ''M'' ∈ BPP with error ≤ 2−, ''x'', can be chosen. (All BPP problems can be amplified to reduce the error probability exponentially.) The basic idea of the proof is to define a Σ2 sentence that is equivalent to stating that ''x'' is in the language, ''L'', defined by ''M'' by usi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (magazine)
''Science'', also widely referred to as ''Science Magazine'', is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival '' Nature'' cover the full ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
