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Topic: Andrey Markov

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Andrei Andreevich Markov

Markov property

Markov chain

Post correspondence problem

Inequality

Examples of Markov chains

Emil Post

1856

John von Neumann

Entscheidungsproblem

Halting problem

Post machine

Jessamyn West

Cap

Decision problem

	Andrey Markov Summary
		Markov involved himself in anti-Czarist, liberal politics and protested Czar Nicholas II (1868-1918) refusal to elect writer Maxim Gorky (1868-1936) to the St. Petersburg Academy in 1902.
		Markov was born in Ryazan, Russia, on June 14, 1856.
		Markov received his bachelor's degree in 1878 for a thesis on differential equations and continuing fractions, for which he was also awarded a gold medal.
	www.bookrags.com /Andrey_Markov (1675 words)

	Markov's inequality
		In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant.
		Markov's inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently) loose but still useful bounds for the distribution function of a random variable.
		Markov's inequality is actually just one of a wider class of inequalities relating probabilities and expectations, that are all examples of a single theorem.
	www.ebroadcast.com.au /lookup/encyclopedia/ma/Markov's_inequality.html (177 words)

	Markov biography
		Andrei Andreyevich Markov's mother was Nadezhda Petrovna, who was the daughter of a state worker, and his father was Andrei Grigorievich Markov, the son of a country deacon.
		Markov had known Maria Ivanova Valvatyeva since they were children for she was the daughter of the owner of the estate which his father was managing.
		Markov is particularly remembered for his study of Markov chains, sequences of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors.
	www-history.mcs.st-andrews.ac.uk /Biographies/Markov.html (1485 words)

	Wikidpedia - The free online encyclopedia - Markov chain (Site not responding. Last check: 2007-10-26)
		The Markov property means that the conditional probability distribution of the state in the future, given the state of the process currently and in the past, depends only on its current state and not on its state in the past.
		Markov chains are often described by a directed graph, where the edges are labeled by the probabilities of going from one state to the other states.
		Markov chains are related to Brownian motion and the ergodic hypothesis, two topics in physics which were important in the early years of the twentieth century, but Markov appears to have pursued this out of a mathematical motivation, namely the extension of the law of large numbers to dependent events.
	www.pagerank10.co.uk /wiki/?title=Markov_chain (2382 words)

	Andrey Markov - Wikipedia, the free encyclopedia
		Andrey (Andrei) Andreyevich Markov (Russian: Андрей Андреевич Марков) (June 14, 1856 N.S. July 20, 1922) was a Russian mathematician.
		Markov, an atheist, proved that Central Limit Theorem works also for random variables that are not independent, discrediting the ideas from Moscow school.
		Andrej Andreevich Markov was born in Ryazan as the son of the secretretary of the public forest management of Ryazan, Andrey Grigorevich Markov, and his first wife, Nadezhda Petrovna Markova.
	en.wikipedia.org /wiki/Andrey_Markov (786 words)

	Andrey Andreevich Markov
		Markov's School (currently available only in Russian, the English version is due in May)
		Andrey Andreevich Markov (1903-1979) was a Russian mathematician, a founder of the Russian school of constructive mathematics and logic.
		The major areas of Markov's mathematical achievement are topology, topological algebra, dynamical systems, theory of algorithms and constructive mathematics.
	logic.pdmi.ras.ru /Markov (189 words)

	Hidden Markov Model Encyclopedia Article @ Dictated.org (Site not responding. Last check: 2007-10-26)
		A hidden Markov model (HMM) is a statistical model in which the system being modeled is assumed to be a Markov process with unknown parameters, and the challenge is to determine the hidden parameters from the observable parameters.
		Hidden Markov models are especially known for their application in temporal pattern recognition such as speech, handwriting, gesture recognition, musical score following and bioinformatics.
		Hidden Markov Models were first described in a series of statistical papers by Leonard E. Baum and other authors in the second half of the 1960s.
	www.dictated.org /encyclopedia/Hidden_Markov_Model (1323 words)

	Andrey Markov
		Andrei Andreevich Markov (June 2, 1856-July 20, 1922) was a Russian mathematician.
		He studied at Petersburg University[?] in 1874 under the tutelage of Chebyshev and later in 1886 became a member of the St.
		He is best known for his work on Markov chains.
	ebroadcast.com.au /lookup/encyclopedia/an/Andrei_Andreevich_Markov.html (44 words)

	Andrey Markov (Site not responding. Last check: 2007-10-26)
		In statistics, the Gauss—Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimators of the coefficients are the least-squares estimators.
		Markov numbers are not always prime; but members of a Markov triple are always coprime.
		In machine learning, the Markov blanket for a node A in a Bayesian network is the set of nodes MB(A) composed of A's parents, its children, and its children's parents.
	libraryoflibrary.com /E_n_c_p_d_Andrei_Markov.html (4174 words)

	Markov Chains
		A Markov chain, named in honor of Russian mathematician Andrei Markov, is a stochastic process.
		Markov chain is said to be irreducible, if there is only one class, that is, all states
		Markov chains also have many biological applications, particularly population processes, which are useful in modelling processes that are, at least, analogous to biological populations.
	cs.bilgi.edu.tr /~bulent/MarkovChains.html (1400 words)

	About us
		Andrey Markov, Russian born in 1978, has been in the circus since 10 years old.
		Andrey worked as an assistant to his mother, while at the same time, he took classes for juggling and dog training.
		Andrey Markov has performed his most unique animal acts in many countries around the world, including Russia, Ukraine, UAE, Puerto Rico, Canada, and USA.
	trainedcircusdogs.com /aboutus.aspx (180 words)

	PowerPoint Presentation (Site not responding. Last check: 2007-10-26)
		In mathematics, a (discrete-time) Markov chain is a discrete-time stochastic process with the Markov property named after Andrey Markov.
		The range of these variables, i.e., the set of their possible values, is called the state space, the value of Xn being the state of the process at time n.
		Markov chains are apparent in static physics and anything relevant to statistics.
	www2.nvnet.org /nvhs/dept/math/MathProject/Index_files/slide0044.htm (137 words)

	Circus Flora - Circus Stars - Andrey and Tanya Markov
		As a child, Andrey juggled and performed in his family’s dog act.
		For the last three years, Andrey has performed throughout the world in such places as the United Arab Emirates, Russia, Puerto Rico, the United States and was the Big Apple Circus’ 25th Anniversary hit.
		The marvelous mix of mutts are remarkable for their stamina and agility as they perform feats of skill and balance that would be unequaled...even for a two-legged human to accomplish.
	www.circusflora.org /troupe/andrey_markov.htm (161 words)

	Andrey Markov - Biocrawler (Site not responding. Last check: 2007-10-26)
		Andrey Andreyevich Markov (Андрей Андреевич Марков) (June 14, 1856 N.S. July 20, 1922) was a Russian mathematician.
		Andrey Andreevich Markov (1903-1979) (http://logic.pdmi.ras.ru/Markov/) (biography of Markov's son, located at the Steklov Institute of Mathematics at St.Petersburg)
		This biographical article about a mathematician is a stub.
	www.biocrawler.com /encyclopedia/Andrey_Markov (235 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		In short, Markov chains are the "next thing" after memoryless processes (i.e., a sequence of independent identically distributed random variables).
		Markov chain methods have also become very important for generating sequences of random numbers to accurately reflect very complicated desired probability distributions - a process called HYPERLINK "http://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo" \o "Markov chain Monte Carlo" Markov chain Monte Carlo or MCMC for short.
		Markov chains also have many applications in biological modelling, particularly HYPERLINK "http://en.wikipedia.org/wiki/Population_process" \o "Population process" population processes, which are useful in modelling processes that are (at least) analogous to biological populations.
	stat.berkeley.edu /users/hhuang/STAT141/stochastic-process-BLAST.doc (1084 words)

	Andrey Markov - Cleverpedia, the ultimate encyclopedia (Site not responding. Last check: 2007-10-26)
		Andrei A. Markow as dreissigjähriger one Andrei A. Markow
		June 1856 in Rjasan; † 20 July 1922 in Petrograd) was a Russian mathematician, who contributed substantial contributions to the probability theory and analysis.
		From this beginning developed a general statistic tool, which so-called stochastic Markow process, from which future developments on basis of the present knowledge can be determined.
	cleverpedia.com /Andrey_Markov (188 words)

	Software Helps Decipher Genomes Of Higher Organisms
		Therefore, the predictions of where eukaryotic genes lie on a strand of DNA must include predictions of the boundaries between the exons, which contain the genetic information, and introns, which are the non-coding regions.
		The Russian mathematician, Andrey Markov, introduced his models early in the 20th century.
		Borodovsky believed Markov models could portray genes by the frequency of certain combinations of bases in known genes, contrary to non-genes.
	www.eurekalert.org /pub_releases/1998-12/GIoT-SHDG-011298.php (877 words)

	Sestroretsk Athletic School of Olympic Reserve named after V. Korenkov
		This is the year when Andrey Markov, a Tae Kwon Do coach came to the Athletic School with a proposal to open the first in the district and in Saint-Petersburg department of martial arts.
		In 2000 Andrey Aronovich, graduate of the Saint-Petersburg State Academy of Physical Education named after P.F.Lesgaft, replaced Kyrillov who leaft his position; A. Aranovich has been heading the department up to the present moment.
		In 2005 Anna Subbotina, a judoist, having won the silver medal of the Russian national championship, received the honorary right to become a member of the Russian Olympic team and is currently preparing for 2008 Olympic Games in Beijing.
	sestroretsk.info /borbae.htm (833 words)

	cars - Hidden Markov model
		A hidden Markov model (HMM) is a statistical model where the system being modelled is assumed to be a Markov process with unknown parameters, and the challenge is to determine the hidden parameters, from the observable parameters, based on this assumption.
		A hidden Markov model adds outputs: each state has a probability distribution over the possible output tokens.
		The preceding diagram emphasizes the state transitions of a hidden Markov model.
	www.carluvers.com /cars/HMM (356 words)

	Официальный сайт Союза Биатлонистов России - Russia Cup 1 in Archery Biathlon is ... (Site not responding. Last check: 2007-10-26)
		Two athletes were fighting for the second position, Konstantin Pogorelov from Khimki and Andrey Markov from Yugra, both of them having 3 errors.
		But the former outran his rival on one of the ascends and finished 4 seconds ahead him (32:10, 3 errors).
		Markov finished at the 3rd place (32:14, 3 errors).
	rbu-biathlon.ru /content/view/188/31/lang,eng (228 words)

	Håkans Aviation page - Biplane Fighter Aces
		Andrey Danilov - 4 biplane victories / 9 total
		Markov - 1 shared biplane victory / 1 shared total
		More eminent biplane information from Black Cross/Red Star Volume I by Christer Bergström and Andrey Mikhailov.
	surfcity.kund.dalnet.se /soviet.htm (1360 words)

	MoreWriting - Viewing Work - The Moving Digit Writes II
		It’s now time to mention Andrey Markov, he was a Russian professor of mathematics, and yes he was poet too.
		Here is a sample of raw Markov generated poetry; the training text is ‘Alice in Wonderland’ by Lewis Carol and the pattern used was Shakespeare’s Sonnet 18.
		The Markov chain explanation will get a bit of a re-write soon as I may be able to describe it slightly better.
	www.morewriting.co.uk /work/13809 (3194 words)

	Andrey Markov (Site not responding. Last check: 2007-10-26)
		A student of Pafnuty Chebyshev, he worked on number theory and probability theory.
		His name is best known for the concept of the Markov chain, a series of events in which the probability of a given even occurring depends only on the immediately previous event.
		This has since found many applications in physics, biology, and linguistics.
	userwww.sfsu.edu /~rob/Markov.html (90 words)

	Technology Review: Enter the Dragon
		As an undergraduate, he had developed a mathematical technique for analyzing apparently random events, based on methods pioneered by the Russian mathematician Andrey Markov (1856-1922).
		Jim was the first person to realize that such "Hidden Markov Models" might be used to untangle the speech riddle.
		Most newlyweds collaborate to solve challenges such as what pattern to choose for their wedding china.
	www.technologyreview.com /InfoTech/11740/page2 (549 words)

	REVIEW: Big Apple Circus
		Andrey Markov of Russian puts his trained dogs through their tricks, returning later with a juggler's routine in which one of the dogs actually gets into the act.
		And Virgile Peyramaure and Andrey Mantchev perform some amazing hand to hand balancing.
		Music Director Rob Slowik gets more than he bargains for when he leaves the safety of the bandstand to join Grandma in the ring for some musical frivolity.
	www.onstageboston.com /Articles/2004/04/April/reviewbigapple.html (784 words)

	Highbeam Encyclopedia - Search Results for Andrey Markov (Site not responding. Last check: 2007-10-26)
		Highbeam Encyclopedia - Search Results for Andrey Markov
		Find newspaper and magazine articles plus images and maps related to "Andrey Markov" at HighBeam.
		Ethnology; 6/22/2005; Bondarenko, Dmitri Kazankov, Alexander Khaltourina, Daria Korotayev, Andrey; 12916 words
	www.encyclopedia.com /SearchResults.aspx?Q=Andrey+Markov (133 words)

	Amazon.com: "Andrey Andreyevich": Key Phrase page (Site not responding. Last check: 2007-10-26)
		That is the truth." D D W N THE HALL in his office, Rozhdestvenskiy drew up the brief dispatch for...
		Russian mathematician Andrey Andreyevich Markov studies random processes that are subsequently known as Markov chains.
		a concept named after the Russian mathematician Andrey Andreyevich Markov who invented a general theory of such things in the early 1900s.
	www.amazon.com /phrase/Andrey-Andreyevich (490 words)

	GT Research Horizons — Winter 1999
		"GeneMark marks genes, which appeals to biologists; it is based on the Markov model, which mathematicians appreciate; and since my name is Mark, it is meaningful to me personally," says Borodovsky, smiling.
		His next version, called GeneMark Genesis, became necessary when TIGR scientists wanted to sequence the genome of the bacterium Methanoccocus jannaschii, for which there were no experimentally studied segments available to train the Markov models.
		The new program developed by Borodovsky and graduate student William Hayes "learned Markov models from anonymous sequences based on the grammar of the genetic code," Borodovsky explains.
	gtresearchnews.gatech.edu /reshor/rh-win99/gen-main.html (2516 words)

	Mathematics in Latvia Through the Centuries, by Daina Taimina and Ingrida Henina
		While lecturing on probability theory Grinbergs became interested in Markov processes, and he with some co-authors developed methods which could be used in telephone wiring.
		He was collaborating with a well known Russian mathematician Professor Andrey Markov.
		In the 1960's J. Barzdins was investigating universality problems in the theory of growing automata, estimated the complexity of symmetry recognition by Turing machines, and explored the behavior of different type of automata depending on its topology.
	www.math.cornell.edu /~dtaimina/mathinlv.html (16065 words)

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