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Chernoff
Chernoff is a surname. Notable people with the surname include: * Herman Chernoff applied mathematician, statistician and physicist ** Chernoff bound, also called Chernoff's inequality ** Chernoff face ** Chernoff's distribution * Maxine Chernoff * Mike Chernoff (other), two people * Paul Chernoff (1942–2017), American mathematician See also * Chernov Chernov (russian: Чернов) is a Slavic surname formed from the Russian word ''Chyorny'' (russian: Чёрный) meaning ''black''. The feminine form of the surname is Chernova (or Tchernova). Some people with this name include: * Alex Chernov ... * Chernow {{surname, Chernoff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chernoff Bound
In probability theory, the Chernoff bound gives exponentially decreasing bounds on tail distributions of sums of independent random variables. Despite being named after Herman Chernoff, the author of the paper it first appeared in, the result is due to Herman Rubin. It is a sharper bound than the first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, the Chernoff bound requires the variates to be independent, a condition that is not required by either Markov's inequality or Chebyshev's inequality (although Chebyshev's inequality does require the variates to be pairwise independent). The Chernoff bound is related to the Bernstein inequalities, which were developed earlier, and to Hoeffding's inequality. The generic bound The generic Chernoff bound for a random variable is attained by applying Markov's inequality to . This gives a bound in terms of the moment-generating function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chernoff Face
Chernoff faces, invented by applied mathematician, statistician and physicist Herman Chernoff in 1973, display multivariate data in the shape of a human face. The individual parts, such as eyes, ears, mouth and nose represent values of the variables by their shape, size, placement and orientation. The idea behind using faces is that humans easily recognize faces and notice small changes without difficulty. Chernoff faces handle each variable differently. Because the features of the faces vary in perceived importance, the way in which variables are mapped to the features should be carefully chosen (e.g. eye size and eyebrow-slant have been found to carry significant weight). Detail Chernoff faces themselves can be plotted on a standard ''X''–''Y'' graph; the faces can be positioned ''X''–''Y'' based on the two most important variables, and then the faces themselves represent the rest of the dimensions for each item. Edward Tufte, presenting such a diagram, says that this kind of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herman Chernoff
Herman Chernoff (born July 1, 1923) is an American applied mathematician, statistician and physicist. He was formerly a professor at University of Illinois Urbana-Champaign, Stanford, and MIT, currently emeritus at Harvard University. Early life and education Herman Chernoff's parents were Pauline and Max Chernoff, Jewish immigrants from Russia. He studied at Townsend Harris High School and earned a B.S. in mathematics from the City College of New York in 1943. He attended graduate school at Brown University, earning an M.Sc. in applied mathematics in 1945, and a Ph.D. in applied mathematics in 1948 under the supervision of Abraham Wald. Recognition Chernoff became a fellow of the American Academy of Arts and Sciences in 1974, and was elected to the National Academy of Sciences in 1980. In 1987 he was selected for the Wilks Memorial Award by the American Statistical Association, and in 2012 he was made an inaugural fellow of the American Mathematical Society. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chernoff's Distribution
In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable : Z =\underset\ (W(s) - s^2), where ''W'' is a "two-sided" Wiener process (or two-sided "Brownian motion") satisfying ''W''(0) = 0. If : V(a,c) = \underset \ (W(s) - c(s-a)^2), then ''V''(0, ''c'') has density : f_c(t) = \frac g_c(t) g_c(-t) where ''g''''c'' has Fourier transform given by : \hat_c (s) = \frac, \ \ \ s \in \mathbf and where Ai is the Airy function. Thus ''f''''c'' is symmetric about 0 and the density ''ƒ''''Z'' = ''ƒ''1. Groeneboom (1989) shows that : f_Z (z) \sim \frac \frac \exp \left( - \frac , z, ^3 + 2^ \tilde_1 , z, \right) \textz \rightarrow \infty where \tilde_1 \approx -2.3381 is the largest zero of the Airy function Ai and where \operatorname' (\tilde_1 ) \approx 0.7022. In the same paper, Groeneboom also gives an analysis of the process \. The connection with the sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxine Chernoff
Maxine Chernoff (born 1952) is an American novelist, writer, poet, academic and literary magazine editor. Biography She was born and raised in Chicago, Illinois, and attended the University of Illinois at Chicago. Chernoff is a professor and Chair of the Creative Writing program at San Francisco State University. With her husband, Paul Hoover (poet), Paul Hoover, she edits the long-running literary journal ''New American Writing''. She is the author of six books of fiction and ten books of poetry, including ''The Turning'' (2008) and ''Among the Names'' (2005), both from Apogee Press. Chernoff's novel ''American Heaven'' and her book of short stories, ''Some of Her Friends That Year'', were finalists for the Bay Area Book Reviewers Award. With Paul Hoover, she has translated ''The Selected Poems of Friedrich Hölderlin'' (Omnidawn Press, 2008) which won the 2009 PEN Translation Prize. As of 2013, she lives in Mill Valley, California. Works Novels ''A Boy in Winter''(Crown ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Chernoff
Paul Robert Chernoff (21 June 1942, Philadelphia – 17 January 2017) was an American mathematician, specializing in functional analysis and the mathematical foundations of quantum mechanics. He is known for Chernoff's Theorem, a mathematical result in the Feynman path integral formulation of quantum mechanics. Education and career Chernoff graduated from Central High School in Philadelphia. He matriculated at Harvard University, where he received bachelor's degree ''summa cum laude'' in 1963, master's degree in 1965, and Ph.D. in 1968 under George Mackey with thesis ''Semigroup Product Formulas and Addition of Unbounded Operators''. At the University of California, Berkeley he became in 1969 a lecturer, in 1971 an assistant professor, and in 1980 a full professor. U. C. Berkeley awarded him multiple Distinguished Teaching Awards and the Lili Fabilli and Eric Hoffer Essay Prize. In 1986 he was a visiting professor at the University of Pennsylvania. Chernoff was elected in 1984 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mike Chernoff (other) (1946–2011), ice hockey left winger
{{hndis, Chernoff, Mike ...
Mike Chernoff may refer to: * Mike Chernoff (baseball), American baseball general manager of the Cleveland Indians * Mike Chernoff (curler), Canadian curler and geologist *Mike Chernoff (ice hockey) Michael Terence Chernoff (May 13, 1946 — November 13, 2011) was a Canadian ice hockey Winger (ice hockey), left winger. He played one game in the National Hockey League for the Minnesota North Stars, on December 15, 1968, and 39 games in the Wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chernov
Chernov (russian: Чернов) is a Slavic surname formed from the Russian word ''Chyorny'' (russian: Чёрный) meaning ''black''. The feminine form of the surname is Chernova (or Tchernova). Some people with this name include: * Alex Chernov (born 1938), an Australian judge, Chancellor of the University of Melbourne, and Governor of Victoria * Alexander Chernov (1877–1963), a Soviet geologist, paleonthologist, and Hero of Socialist Labor * Anatoly Chernov (1919–1953), a Soviet aircraft pilot and Hero of the Soviet Union * Andrei Chernov (1966–2017), a Russian programmer, one of the founders of Runet and the creator of the KOI8-R character encoding * Artyom Chernov (1982–2020), a Russian professional ice hockey centre * Boris Chernov, designer of a series of light flying boats such as the Gidroplan Che-22 Korvet and the Chernov Che-25 * Dmitry Chernov (1839–1921), a Russian metallurgist * Evgeniy Demitrievich Chernov, a Soviet admiral, former commander of Soviet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
