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Journal articles on the topic 'Kolmogorov'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 June 2025

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1

Semenov, A. L., A. Kh Shen, and N. K. Vereshchagin. "Kolmogorov's Last Discovery? (Kolmogorov and Algorithmic Statistics)." Theory of Probability & Its Applications 68, no. 4 (2024): 582–606. http://dx.doi.org/10.1137/s0040585x97t991647.

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2

RESCORLA, MICHAEL. "A DUTCH BOOK THEOREM AND CONVERSE DUTCH BOOK THEOREM FOR KOLMOGOROV CONDITIONALIZATION." Review of Symbolic Logic 11, no. 4 (2018): 705–35. http://dx.doi.org/10.1017/s1755020317000296.

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AbstractThis article discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios.

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3

Bienvenu, Laurent. "Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity." Theory of Computing Systems 46, no. 3 (2009): 598–617. http://dx.doi.org/10.1007/s00224-009-9232-4.

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4

Vitányi, Paul M. B. "Remembering Kolmogorov." Metascience 20, no. 3 (2011): 509–11. http://dx.doi.org/10.1007/s11016-011-9540-6.

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5

Rodin, Andrei V. "A.N. KOLMOGOROV’S CALCULUS OF PROBLEMS AND HOMOTOPY TYPE THEORY." Вестник Пермского университета. Философия. Психология. Социология, no. 3 (2022): 368–79. http://dx.doi.org/10.17072/2078-7898/2022-3-368-379.

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In 1932 A.N. Kolmogorov proposed an original version of mathematical intuitionism where the distinc-tion between problems and theorems plays a central role and which differs in its content from the versions of intuitionism developed by A. Heyting and other followers of L. Brouwer. In view of today’s historians and logicians, it remains a controversial point whether this distinction is to be treated as logical or Kol-mogorov’s «problems» should be regarded as propositions, provided the latter term is interpreted intui-tionistically. The popular BHK semantics of intuitionistic logic, so called after Brouwer, Heyting, and Kolmogorov and supposed to provide a synthesis of ideas of these authors, does not formally distinguish between problems and theorems and treats this distinction as contextual or purely linguistic. We argue that the distinction between problems and theorems is a crucial element of Kolmogorov’s approach and provide a logical interpretation of this distinction using homotopy type theory (HoTT). The notion of ho-motopy level of a given type in HoTT allows one to distinguish, after Kolmogorov, between problems re-duced to proving a sentence and problems that require realization of higher-order constructions. Thus, HoTT provides a support for Kolmogorov’s view on intuitionistic logic in his polemics with Heyting. At the same time, HoTT does not solve the problem of finding a constructive notion of negation applicable to general problems, which is raised by Kolmogorov in the same paper and still remains open.

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6

Tikhomirov, V. M. "The joy of mathematical discovery: To the 120th anniversary of Academician A.N. Kolmogorov." Вестник Российской академии наук 93, no. 4 (2023): 373–83. http://dx.doi.org/10.31857/s0869587323040126.

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This article is dedicated to the memory of the outstanding mathematician of the 20th century, Andrei Nikolaevich Kolmogorov, whose 120th birthday is celebrated this year. The author describes in detail the formation of Kolmogorov as a scientist, the significance of Moscow State University in the scientific life and pedagogical activity of the famous mathematician. Kolmogorov’s contribution to such branches of mathematics as classical analysis, topology, geometry, approximation theory, functional analysis, and probability theory is analyzed, and the contribution of his scientific school to Russian science, including not only mathematics and physics but also the humanities, is shown.

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7

Xu, Yifang, Andrew L. Krause, and Robert A. Van Gorder. "Generalist predator dynamics under kolmogorov versus non-Kolmogorov models." Journal of Theoretical Biology 486 (February 2020): 110060. http://dx.doi.org/10.1016/j.jtbi.2019.110060.

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8

Stoyanov, Jordan M. "Kolmogorov, stochastics in Bulgaria, and probabilistic problems with unexpected solutions." Mathematics and Education in Mathematics 53 (March 16, 2024): 180–97. http://dx.doi.org/10.55630/mem.2024.53.180-197.

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In this talk, I am going to share with the readers my memories of personal meetings with Andrey Nikolaevich Kolmogorov (1903–1987), the content of our conversations, and the fruitful consequences. The reader is familiar with, or could read, the timely prepared recent comprehensive paper [34], presented by N.M. Yanev at the 52nd Spring Conference of the UBM. Included here are several new details about Andrey Nikolaevich and the great inﬂuence of the Moscow Probability School on the development of Stochastics in Bulgaria. I have used MathSciNet and introduced the ‘Kolmogorov number’, a ‘collaboration distance’ between a mathematician and Kolmogorov, with a focus on Bulgarian stochasticians. I am writing about Kolmogorov’s approach to doing mathematics in general and the role of counterexamples. Discussed are two speciﬁc probabilistic problems which, according to him, are with most unusual solutions, ‘Skitovich-Darmois theorem’ and ‘Plackett problem’. Several related short stories and not well-known facts are presented.

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9

Sinai, Ya G. "About A. N. Kolmogorov's work on the entropy of dynamical systems." Ergodic Theory and Dynamical Systems 8, no. 4 (1988): 501–2. http://dx.doi.org/10.1017/s0143385700004648.

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In the fall of 1957 A. N. Kolmogorov started lecturing on the theory of dynamical systems and supervised a seminar on the same theme at the Mechanical–Mathematical Department of Moscow State University. He began his lectures with the theory of systems with a pure point spectrum, which he approached from a probabilistic point of view. This approach, undoubtedly, has many advantages. In the seminar we studied Ito's theory of multiple stochastic integrals and, under the supervision of A. N. Kolmogorov, I. V. Girsanov constructed an example of a Gaussian dynamical system with a simple continuous spectrum. At one of the meetings of the seminar, still before the advent of entropy, Kolmogorov suggested a proof of an assertion, which today would read: the unitary operator induced by a K-automorphism has a countable Lebesgue spectrum. At this point Kolmogorov was studying Shannon's theory of information and the concept of the capacity of functional spaces. Judging by his well known article, we can say that the first of these, and all that is related to it, played a big role in the development of information theory in our country. The investigation of capacity is connected with Kolmogorov's work on Hilbert's 13th problem and was summarized in his well-known survey co-authored by V. M. Tihomirov.

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10

Dietz, Richard. "On Generalizing Kolmogorov." Notre Dame Journal of Formal Logic 51, no. 3 (2010): 323–35. http://dx.doi.org/10.1215/00294527-2010-019.

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11

Chanter, Dennis. "Kolmogorov-Smirnov tests." Teaching Statistics 12, no. 3 (1990): 90. http://dx.doi.org/10.1111/j.1467-9639.1990.tb00129.x.

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12

BALMFORTH, NEIL J., and YUAN-NAN YOUNG. "Stratified Kolmogorov flow." Journal of Fluid Mechanics 450 (January 9, 2002): 131–67. http://dx.doi.org/10.1017/s0022111002006371.

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In this study we investigate the Kolmogorov flow (a shear flow with a sinusoidal velocity profile) in a weakly stratified, two-dimensional fluid. We derive amplitude equations for this system in the neighbourhood of the initial bifurcation to instability for both low and high Péclet numbers (strong and weak thermal diffusion, respectively). We solve amplitude equations numerically and find that, for low Péclet number, the stratification halts the cascade of energy from small to large scales at an intermediate wavenumber. For high Péclet number, we discover diffusively spreading, thermal boundary layers in which the stratification temporarily impedes, but does not saturate, the growth of the instability; the instability eventually mixes the temperature inside the boundary layers, so releasing itself from the stabilizing stratification there, and thereby grows more quickly. We solve the governing fluid equations numerically to compare with the asymptotic results, and to extend the exploration well beyond onset. We find that the arrest of the inverse cascade by stratification is a robust feature of the system, occurring at higher Reynolds, Richards and Péclet numbers – the flow patterns are invariably smaller than the domain size. At higher Péclet number, though the system creates slender regions in which the temperature gradient is concentrated within a more homogeneous background, there are no signs of the horizontally mixed layers separated by diffusive interfaces familiar from doubly diffusive systems.

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13

Tihomirov, V. M. "Andrei Nikolaevich Kolmogorov." Ergodic Theory and Dynamical Systems 8, no. 4 (1988): 493–99. http://dx.doi.org/10.1017/s0143385700004636.

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14

Villanueva, Jordi. "Kolmogorov Theorem revisited." Journal of Differential Equations 244, no. 9 (2008): 2251–76. http://dx.doi.org/10.1016/j.jde.2008.02.010.

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15

Adomian, G. "Fisher-Kolmogorov equation." Applied Mathematics Letters 8, no. 2 (1995): 51–52. http://dx.doi.org/10.1016/0893-9659(95)00010-n.

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16

Yanin, V. L. "Kolmogorov as historian." Russian Mathematical Surveys 43, no. 6 (1988): 183–91. http://dx.doi.org/10.1070/rm1988v043n06abeh001994.

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17

Shiryaev, A. N. "Andrei Nikolaevich Kolmogorov." Russian Mathematical Surveys 59, no. 1 (2004): 1. http://dx.doi.org/10.1070/rm2004v059n01abeh000733.

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18

Sinai, Yakov. "Kolmogorov-Sinai entropy." Scholarpedia 4, no. 3 (2009): 2034. http://dx.doi.org/10.4249/scholarpedia.2034.

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19

Vitanyi, Paul. "Andrey Nikolaevich Kolmogorov." Scholarpedia 2, no. 2 (2007): 2798. http://dx.doi.org/10.4249/scholarpedia.2798.

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20

Taveneaux, Antoine. "Axiomatizing Kolmogorov Complexity." Theory of Computing Systems 52, no. 1 (2012): 148–61. http://dx.doi.org/10.1007/s00224-012-9395-2.

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21

Temlyakov, V. N. "Nonlinear Kolmogorov widths." Mathematical Notes 63, no. 6 (1998): 785–95. http://dx.doi.org/10.1007/bf02312773.

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22

Berthiaume, André, Wim van Dam, and Sophie Laplante. "Quantum Kolmogorov Complexity." Journal of Computer and System Sciences 63, no. 2 (2001): 201–21. http://dx.doi.org/10.1006/jcss.2001.1765.

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23

Meehan, Alexander, and Snow Zhang. "Jeffrey Meets Kolmogorov." Journal of Philosophical Logic 49, no. 5 (2020): 941–79. http://dx.doi.org/10.1007/s10992-019-09543-7.

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24

Parthasarathy, K. R. "Andrei Nikolaevich Kolmogorov." Resonance 3, no. 4 (1998): 54–63. http://dx.doi.org/10.1007/bf02834612.

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25

Yang, Wei, and Igor Zurbenko. "Kolmogorov-Zurbenko filters." Wiley Interdisciplinary Reviews: Computational Statistics 2, no. 3 (2010): 340–51. http://dx.doi.org/10.1002/wics.71.

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26

Baykal, Yahya, and Hamza Gerçekcioğlu. "Equivalence of structure constants in non-Kolmogorov and Kolmogorov spectra." Optics Letters 36, no. 23 (2011): 4554. http://dx.doi.org/10.1364/ol.36.004554.

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27

Toselli, Italo, Olga Korotkova, Xifeng Xiao, and David G. Voelz. "SLM-based laboratory simulations of Kolmogorov and non-Kolmogorov anisotropic turbulence." Applied Optics 54, no. 15 (2015): 4740. http://dx.doi.org/10.1364/ao.54.004740.

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28

Kupreenko, A. I., Kh M. Isaev, and S. M. Mikhaylichenko. "Solution of the Kolmogorov system of equations for the generalized graph of states of a mobile feed hopper." Traktory i sel hozmashiny 84, no. 7 (2017): 47–52. http://dx.doi.org/10.17816/0321-4443-66353.

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To determine the probabilistic time for feeding animals with mobile feeders on farms of cattle, it is required to solve the system of Kolmogorov equations. Because of the massive calculations, this work can be done only with the use of computer technology. However, a specific Kolmogorov system of equations is suitable only for a certain number of components in the feed mix. Depending on the chosen feeding ration, this amount can vary significantly. Solving the Kolmogorov equations for feed mixtures with a different number of components is a very laborious process. Therefore, it is required to develop a mathematical model that allows solving the problem of determining the probabilistic feeding time for multicomponent fodder mixtures. In the course of this work, the positions of the theory of random processes, the theory of graphs, and the foundations of mathematical modeling were used. To accomplish the task, Kolmogorov's system of equations for 2-, 3-, and 4-component fodder mixtures was compiled and solved. The combinations of intensities «L» were replaced by the coefficients introduced for visual perception of formulas and the possibility to reveal the patterns of their development with a change in the number of components. The observed regularities are reflected in the algorithm. The final solution of the Kolmogorov equations is also presented, and a general formula is obtained for calculating the probability of finding a mobile feed hopper in the state of distribution of feed. The formula consists of the coefficients which are calculated according to the developed algorithm. Thus, using the proposed algorithm, there is no need to compile and solve Kolmogorov's systems of equations to determine the probability of finding a mobile feed mill in the state of distribution of food. The observed regularities are conveniently implemented in an electronic environment, for example, MS Excel, which will allow modeling of the technological process of preparation and distribution of feed mixes with a different number of components.

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29

Feinan Chen, Feinan Chen, Qi Zhao Qi Zhao, Jingjing Chen Jingjing Chen, et al. "Evolutions of polarization of quasi-homogeneous beams propagating in Kolmogorov and non-Kolmogorov atmosphere turbulence." Chinese Optics Letters 11, s2 (2013): S20102–320106. http://dx.doi.org/10.3788/col201311.s20102.

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30

GHAHRAMANYAN, T., S. MIRZOYAN, E. POGHOSIAN, and G. YEGORIAN. "PROBING THE STATISTIC IN THE COSMIC MICROWAVE BACKGROUND." Modern Physics Letters A 24, no. 15 (2009): 1187–92. http://dx.doi.org/10.1142/s021773230903076x.

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Kolmogorov's statistic is used for the analysis of properties of perturbations in the Cosmic Microwave Background signal. We obtain the maps of the Kolmogorov stochasticity parameter for W and V band temperature data of WMAP which are differently affected by the Galactic disk radiation and then model datasets with various statistics of perturbations. The analysis shows that the Kolmogorov's parameter can be an efficient tool for the separation of Cosmic Microwave Background from the contaminating radiations due to their different statistical properties.

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31

Rangi, Anshuka, and Massimo Franceschetti. "Kolmogorov Capacity with Overlap." Entropy 27, no. 5 (2025): 472. https://doi.org/10.3390/e27050472.

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The notion of δ-mutual information between non-stochastic uncertain variables is introduced as a generalization of Nair’s non-stochastic information functional. Several properties of this new quantity are illustrated and used in a communication setting to show that the largest δ-mutual information between received and transmitted codewords over ϵ-noise channels equals the (ϵ,δ)-capacity. This notion of capacity generalizes the Kolmogorov ϵ-capacity to packing sets of overlap at most δ and is a variation of a previous definition proposed by one of the authors. Results are then extended to more general noise models, including non-stochastic, memoryless, and stationary channels. The presented theory admits the possibility of decoding errors, as in classical information theory, while retaining the worst-case, non-stochastic character of Kolmogorov’s approach.

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32

ROGERS, CAROLINE, and VLATKO VEDRAL. "THE SECOND QUANTIZED QUANTUM TURING MACHINE AND KOLMOGOROV COMPLEXITY." Modern Physics Letters B 22, no. 12 (2008): 1203–10. http://dx.doi.org/10.1142/s021798490801464x.

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The Kolmogorov complexity of a physical state is the minimal physical resources required to reproduce that state. We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity. There are two advantages to our approach — our measure of the second quantized Kolmogorov complexity is closer to physical reality and unlike other quantum Kolmogorov complexities, it is continuous. We give examples where the second quantized and quantum Kolmogorov complexity differ.

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33

Dimitriadis, Panayiotis, Theano Iliopoulou, G. Fivos Sargentis, and Demetris Koutsoyiannis. "Spatial Hurst–Kolmogorov Clustering." Encyclopedia 1, no. 4 (2021): 1010–25. http://dx.doi.org/10.3390/encyclopedia1040077.

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The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale.

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34

Uspensky, Vladimir A. "Kolmogorov and mathematical logic." Journal of Symbolic Logic 57, no. 2 (1992): 385–412. http://dx.doi.org/10.2307/2275276.

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There are human beings whose intellectual power exceeds that of ordinary men. In my life, in my personal experience, there were three such men, and one of them was Andrei Nikolaevich Kolmogorov. I was lucky enough to be his immediate pupil. He invited me to be his pupil at the third year of my being student at the Moscow University. This talk is my tribute, my homage to my great teacher.Andrei Nikolaevich Kolmogorov was born on April 25, 1903. He graduated from Moscow University in 1925, finished his post-graduate education at the same University in 1929, and since then without any interruption worked at Moscow University till his death on October 20, 1987, at the age 84½.Kolmogorov was not only one of the greatest mathematicians of the twentieth century. By the width of his scientific interests and results he reminds one of the titans of the Renaissance. Indeed, he made prominent contributions to various fields from the theory of shooting to the theory of versification, from hydrodynamics to set theory. In this talk I should like to expound his contributions to mathematical logic.Here the term “mathematical logic” is understood in a broad sense. In this sense it, like Gallia in Caesarian times, is divided into three parts:(1) mathematical logic in the strict sense, i.e. the theory of formalized languages including deduction theory,(2) the foundations of mathematics, and(3) the theory of algorithms.

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35

Osborne. "CONVERGENCE AND KOLMOGOROV DIMENSION." Real Analysis Exchange 21, no. 1 (1995): 264. http://dx.doi.org/10.2307/44153914.

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36

Banjević, D. "On a Kolmogorov Inequality." Theory of Probability & Its Applications 29, no. 2 (1985): 391–94. http://dx.doi.org/10.1137/1129050.

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37

Binns, Stephen, and Marie Nicholson. "Compressibility and Kolmogorov Complexity." Notre Dame Journal of Formal Logic 54, no. 1 (2013): 105–23. http://dx.doi.org/10.1215/00294527-1731416.

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38

Muchnik, Andrej A. "Kolmogorov complexity and cryptography." Proceedings of the Steklov Institute of Mathematics 274, no. 1 (2011): 193–203. http://dx.doi.org/10.1134/s0081543811060125.

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39

ROGERS, CAROLINE, VLATKO VEDRAL, and RAJAGOPAL NAGARAJAN. "SECOND QUANTIZED KOLMOGOROV COMPLEXITY." International Journal of Quantum Information 06, no. 04 (2008): 907–28. http://dx.doi.org/10.1142/s021974990800375x.

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The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantized Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this complexity's basic properties. We define the corresponding prefix complexity and show that the inequalities obeyed by this prefix complexity are also obeyed by von Neumann entropy.

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40

DITZIAN, Z. "A Kolmogorov-type inequality." Mathematical Proceedings of the Cambridge Philosophical Society 136, no. 3 (2004): 657–63. http://dx.doi.org/10.1017/s0305004103007448.

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41

Parthasarathy, K. R. "Obituary: Andrei Nikolaevich Kolmogorov." Journal of Applied Probability 25, no. 2 (1988): 444–50. http://dx.doi.org/10.1017/s0021900200041115.

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42

Manca, Luigi. "Kolmogorov equations for measures." Journal of Evolution Equations 8, no. 2 (2008): 231–62. http://dx.doi.org/10.1007/s00028-008-0335-1.

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43

Vulpiani, Angelo. "Kam Kolmogorov — Arnold — Moser." Lettera Matematica Pristem 100, no. 1 (2017): 64–67. http://dx.doi.org/10.1007/s10031-017-0012-z.

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44

Pollett, P. K. "The generalized Kolmogorov criterion." Stochastic Processes and their Applications 33, no. 1 (1989): 29–44. http://dx.doi.org/10.1016/0304-4149(89)90064-1.

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45

Zhang, Hong, Guo-Hua Li, and Mao-Kang Luo. "Fractional backward Kolmogorov equations." Chinese Physics B 21, no. 6 (2012): 060201. http://dx.doi.org/10.1088/1674-1056/21/6/060201.

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46

Kendall, Wilfrid, and Catherine Price. "Coupling Iterated Kolmogorov Diffusions." Electronic Journal of Probability 9 (2004): 382–410. http://dx.doi.org/10.1214/ejp.v9-201.

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47

Andrews, Donald W. K. "A Conditional Kolmogorov Test." Econometrica 65, no. 5 (1997): 1097. http://dx.doi.org/10.2307/2171880.

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48

López-Gótnez, Angel, and Kaoru Hirota. "Fuzzification of Kolmogorov Theorem." Journal of Advanced Computational Intelligence and Intelligent Informatics 5, no. 2 (2001): 99–109. http://dx.doi.org/10.20965/jaciii.2001.p0099.

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The extension of the Kolmogorov’s theorem (1957) about the representation of continuous real extended functions with more than one variables as superpositions of extended functions of one variable is presented. The graphical analysis of its behavior with a function of two variables is showed. The representation of the theorem using a practical neural network is obtained.

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49

Chierchia, Luigi, and John Mather. "Kolmogorov-Arnold-Moser theory." Scholarpedia 5, no. 9 (2010): 2123. http://dx.doi.org/10.4249/scholarpedia.2123.

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50

Davie, George. "Kolmogorov Complexity and Noncomputability." MLQ 48, no. 4 (2002): 574–80. http://dx.doi.org/10.1002/1521-3870(200211)48:4<574::aid-malq574>3.0.co;2-o.

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