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Andrei Nikolaevich Kolmogorov Uspensky -- Preliminaries for semiotic epistles of Andrei Nikolaevich Kolmogorov Kolmogorov's 1941 theory is presented in a novel fashion with emphasis on symmetries (including scaling transformations) which are broken by the mechanisms producing the turbulence and restored by the chaotic character of the cascade to small scales. Kolmogorov was President of the Moscow Mathematical Society from 1964 to 1966 and from 1973 to 1985. www.kolmogorov.com /Kolmogorov.html   (4215 words)

Kolmogorov conference The Conference will cover the main areas of A.N. Kolmogorov's scientific interests with an emphasis on his vision of Mathematics in its fundamental unity as well as recent developments in the fields: The exhibition of the main publication of A.N. Kolmogorov 3 volumes of the jubilee edition "Kolmogorov" (in Russian) kolmogorov-100.mi.ras.ru   (274 words)

[No title] Kolmogorov complexity is a modern notion of randomness dealing with the quantity of information in individual objects; that is, pointwise randomness rather than average randomness as produced by a random source. It was proposed by A.N. Kolmogorov in 1965 to quantify the randomness of individual objects in an objective and absolute manner. `Kolmogorov' complexity was earlier proposed by Ray Solomonoff in a Zator Technical Report in 1960 and in a long paper in Information and Control in 1964. homepages.cwi.nl /~paulv/kolmogorov.html   (824 words)

Andrey Kolmogorov Kolmogorov was one of the broadest of this century's mathematicians. Kolmogorov went on to study the motion of the planets and turbulent fluid flows, later publishing two papers in 1941 on turbulence that even today are of fundamental importance. Kolmogorov's notion of complexity is a measure of randomness, one that is closely related to Claude Shannon's entropy rate of an information source. www.exploratorium.edu /complexity/CompLexicon/kolmogorov.html   (330 words)

Andrey Kolmogorov Summary Kolmogorov was born in the town of Tambov in central Russia on April 25, 1903. Kolmogorov's father, a Russian agriculturist named Nikolai Kataev, was killed in World War I, and his mother, Mariya Kolmogorova—who was not married to Nikolai—died giving birth to their son in the town of Tambov on April 25, 1903. Kolmogorov, however, remained modest to the end, and, in line with his belief that a mathematician could no longer conduct valuable research after the age of 60, he retired in 1963, spending 20 years teaching high school. www.bookrags.com /Andrey_Kolmogorov   (2461 words)

Kolmogorov machine - Esolang A Kolmogorov machine (also known as a Kolmogorov-Uspenski machine) is similar to a Turing machine in most respects except that its storage unit, instead of an unbounded linear tape, is a particular kind of connected graph. This was done by Kolmogorov and Uspenski by inserting intermediate 'address' vertices in an undirected graph; an alternate technique is to use a directed graph and simply to label the edges of the graph, with a different label bestowed upon each out-edge of a vertex. Kolmogorov machines are in the same computational class as Turing machines; that is, they are Turing-complete. esoteric.voxelperfect.net /wiki/Kolmogorov_machine   (311 words)

Bibliografía sobre A. N. Kolmogorov Kolmogorov analizó en profundidad las afirmaciones y nuevas construcciones de la integral, buscando armonía y claridad a toda la teoría de integración, donde hasta ese momento los resultados habían sido generalizados sin ningún tipo de orden y conexión. Kolmogorov era una persona muy responsable y cuidadosa tanto en sus estudios como matemático puro, como en su aspecto práctico, de aplicaciones de sus investigaciones. Kolmogorov realiza una lista de los artículos que desea incluir agrupados por temas, escribe sus comentarios y completa sus trabajos con un comentario general sobre los artículos escritos por sus discípulos. thales.cica.es /rd/Recursos/rd97/Biografias/40-1-b-Kolmogorov.html   (3747 words)

Biographies Kolmogorov was doubtless the most important Russian mathematician of the twentieth century. Kolmogorov began his mathematical studies at the same time as the topologist Pavel Alexandrov, the two first meeting in the summer of 1929. Kolmogorov was an orphan who was raised by his sister. tulsagrad.ou.edu /statistics/biographies/kolmogorov.htm   (500 words)

Kolmogorov Kolmogorov may have told this story as a joke but never-the-less jokes are only funny if there is some truth in them and undoubtedly this is the case here. Kolmogorov graduated from Moscow State University in 1925 and began research under Luzin 's supervision in that year. If Kolmogorov made a major contribution to Hilbert 's sixth problem, he completely solved Hilbert 's Thirteenth Problem in 1957 when he showed that Hilbert was wrong in asking for a proof that there exist continuous functions of three variables which could not be represented by continuous functions of two variables. www.weizmann.ac.il /lvov/Lecture-Online/Bib/Kolmogorov.html   (2006 words)

The Fourth Annual Kolmogorov Lecture Each Kolmogorov Lecture is given by one of the leading figures in their field, who is presented with a medal in recognition of their own contribution to science. The lecture at the Fourth Annual Kolmogorov Lecture was given by Professor Jorma Rissanen, Professor Emeritus of Tampere University and was entitled "The Structure Function and Distinguishable Models of Data." Inspired by Kolmogorov's structure function for finite sets as models of data in the algorithmic theory of information we adapt the construct to probability models in a family of distributions to avoid the noncomputability problem. www.clrc.rhul.ac.uk /events/kl2006.htm   (437 words)

The Kolmogorov turbulence theory in the light of six-dimensional Navier-Stokes' equation   (Site not responding. Last check: 2007-11-05) The classical turbulence theory by Kolmogorov is reconsidered using Navier-Stokes' equation generalized to 6D physical-plus-eddy space. Strong pseudo-singularity is shown to reveal itself along the boundary `ridge' line separating the dissipation and inertial sub-ranges surrounding the origin of the eddy space. It is supported by the observation that the universal power spectrum calculated rediscovers the Kolmogorov's -5/3 power law as independent of the dimensional approach. www.ca-homes.com /science/tsuge-8   (107 words)

SSRN-Induction: From Kolmogorov and Solomonoff to De Finetti and back to Kolmogorov by John McCall Kolmogorov's best-known contribution was the axiomatization of probability in 1933. However, Kolmogorov was not satisfied by his treatment of the frequency aspect of his creation. The decisive connection between de Finetti and Kolmogorov was their lifelong interest in the frequency aspect of induction. papers.ssrn.com /sol3/papers.cfm?abstract_id=551214   (422 words)

GENERALIZED KOLMOGOROV COMPLEXITY The algorithmic information or Kolmogorov complexity of a bitstring x is the length of the shortest program that computes x and halts. This leads to generalizations of the concept of Kolmogorov complexity, and has consequences for Solomonoff's theory of algorithmic probability and universal prediction. We obtain a natural hierarchy of generalizations of algorithmic probability and Kolmogorov complexity, suggesting that the ``true'' information content of some (possibly infinite) bitstring x is the size of the shortest nonhalting program that converges to x and nothing but x on a Turing machine that can edit its previous outputs. www.idsia.ch /~juergen/kolmogorov.html   (580 words)

Schloss Dagstuhl : Seminar Homepage The Kolmogorov complexity of an object is the minimal number of bits required to effectively describe the object. Kolmogorov complexity (also known as algorithmic information theory) is widely applied in computer science and a plethora of other scientific disciplines. The seminar was meant to be cross-disciplinary and to connect through the common technique of Kolmogorov complexity the areas information theory, individual randomness, algorithmic probability, recursion theory, computational complexity, machine learning and statistics, pattern recognition, data mining, and knowledge discovery. www.dagstuhl.de /06051   (504 words)

Kolmogorov Complexity I   (Site not responding. Last check: 2007-11-05) Kolmogorov complexity allows us to describe the fact that some strings are more regular in some sense than are others. Kolmogorov Complexity tells us how compressible a string is. The higher the Kolmogorov complexity, the less we can squeeze it. A long string with low Kolmogorov complexity can be described by a smaller string -- therefore it could be replaced with a smaller string and we would still have the same information. www.oswego.edu /~delancey/309_DIR/LLT_LECTURES/13_kolmogorov_1_out.html   (616 words)

Algorithmic Information Theory Kolmogorov defined the complexity of a string x as the length of its shortest description p on a universal Turing machine U (K(x)=min{l(p):U(p)=x}). Kolmogorov complexity is a key concept in (algorithmic) information theory. Lecture notes on Kolmogorov complexity (in German), by J. Schmidhuber, TUM, Munich, Germany, 1994. www.hutter1.net /ait.htm   (1349 words)

Amazon.de: Elements of the Theory of Functions and Functional Analysis: English Books: A. N. Kolmogorov,S. V. Fomin   (Site not responding. Last check: 2007-11-05) This highly regarded book came out from the notes of Andrei Kolmogorov's lectures given at Moscow's Lomonosov University in the 1940's, and it still stands as one of the best introductions to real analysis available. It is a pleasure to find through every page of the book the great genious of Kolmogorov who not only mastered most areas of mathematics but who also had an almost unparalleled understanding of what the trends of future mathematics would be. In deed, Kolmogorov and Fomin did it again to co-author a wonderful math book as their "Introductory Real Analysis" (by Dover). www.amazon.de /Elements-Theory-Functions-Functional-Analysis/dp/0486406830   (856 words)

Kolmogorov Complexity II One exciting feature of Kolmogorov complexity is that it has an incompleteness result as a relatively straightforward consequence. Consider for example a string S that is Chaitin random and is of Kolmogorov complexity k. Therefore, the Kolmogorov complexity of S is at most n (since a program P of size n can print S!). www.oswego.edu /~delancey/309_DIR/LLT_LECTURES/14_kolmogorov_2_out.html   (1219 words)

Kolmogorov Turbulence The velocity fluctuations occur on a wide range of space and time scales formed in a turbulent cascade. Kolmogorov turbulence model states that energy enters the flow at low frequencies at scale length This is the famous two-thirds power law derived by Kolmogorov from dimensional arguments for velocity grus.berkeley.edu /~jrg/SEEING/node3.html   (791 words)

Kolmogorov conference Kolmogorov interpretation of intuitionistic logic and Kolmogorov complexity Kolmogorov and Brouwer on constructive implication and the ex falso rule Kolmogorov’s structure functions with an application to the foundations of model selection kolmogorov-100.mi.ras.ru /info2.htm   (350 words)

Kolmogorov complexity   (Site not responding. Last check: 2007-11-05) Special issue of the Computer Journal on Kolmogorov Complexity (1999). Tributes to, pictures of, bibliography of, etc. Andrei Nikolaevich Kolmogorov. Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "Kolmogorov complexity", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. www.nist.gov /dads/HTML/kolmogorov.html   (152 words)

Kolmogorov-Smirnov Test Numbers in parentheses correspond to the numbered references in my publication list. In the 1930s, Kolmogorov and Smirnov developed a goodness of fit test for continuous data to determine if a sample comes from a given hypothesized distribution. Today it continues to be one of the best known and most widely used goodness of fit tests because of its simplicity and because it is based on the empirical distribution function (edf), which converges uniformly to the population cumulative distribution function (cdf) with probability measure one (Glivenko-Cantelli theorem). www.math.wright.edu /People/Harry_Khamis/pages_based_on_template/kolmogorov_smirnov_test/kolmogorov_smirnov_test.htm   (255 words)

Topics in Kolmogorov Complexity In this seminar we will cover the basics and some applications of Kolmogorov complexity. The main text for this seminar will be An introduction to Kolmogorov complexity and its applications by Li and Vitanyi. All section references in the list below are to the course book: An Introduction to Kolmogorov Complexity and its applications, by Li and Vitanyi, Second edition. www.cs.technion.ac.il /~tzach/Kolmogorov   (376 words)

Amazon.com: kolmogorov   (Site not responding. Last check: 2007-11-05) An Introduction to Kolmogorov Complexity and Its Applications (Texts in Computer Science) by Ming Li Price: $84.95 $72.21 Selected Works of A.N. Kolmogorov: Volume III: Information Theory and the Theory of Algorithms (Mathematics and its Applications) by A.N. Shiryayev No one has created a list or guide tagged "kolmogorov" yet. www.amazon.com /gp/tagging/glance/kolmogorov   (84 words)

Kolmogorov: Foundations of the Theory of Probability The book "Kolmogorov: Foundations of the Theory of Probability" by Andrey Nikolaevich Kolmogorov is historically very important. The book is out of print and can only be purchased on the (now often electronic) flea markets. Foundations of the Theory of Probability, By A.N. Kolmogorov, Chelsea Publishing Company, New Yori, 1956 www.mathematik.com /Kolmogorov   (192 words)

Vladimir Kolmogorov's homepage Antonio Criminisi, Geoffrey Cross, Andrew Blake and Vladimir Kolmogorov. Yuri Boykov, Vladimir Kolmogorov, Daniel Cremers and Andrew Delong. Vladimir Kolmogorov, Antonio Criminisi, Andrew Blake, Geoffrey Cross and Carsten Rother. www.adastral.ucl.ac.uk /~vladkolm   (486 words)

Kolmogorov-Smirnov Goodness of Fit Test The location and scale parameters default to 0 and 1 if not specified. normal kolmogorov smirnov goodness of fit test y Please email comments on this WWW page to alan.heckert@nist.gov. www.itl.nist.gov /div898/software/dataplot/refman1/auxillar/kstest.htm   (719 words)

The Mathematics Genealogy Project - Andrei Kolmogorov   (Site not responding. Last check: 2007-11-05) Click here to see the students listed in chronological order. According to our current on-line database, Andrei Kolmogorov has 77 students and 1197 descendants. If you have additional information or corrections regarding this mathematician, please use the update form. www.genealogy.ams.org /html/id.phtml?id=10480   (78 words)

SourceForge.net: Kolmogorov A collection of open source software and documents on machine perception and machine learning. Includes a state of the art face detector (MPISearch), video labeling tools (Score), and tutorials (Kolmogorov Tutorials). Support Requests : (1 open / 1 total) sourceforge.net /projects/kolmogorov   (133 words)

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