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www.sbg.org.br A.N. Kolmogorov’s defence of Mendelism
"... In 1939 N.I. Ermolaeva published the results of an experiment which repeated parts of Mendel’s classical experiments. On the basis of her experiment she concluded that Mendel’s principle that selfpollination of hybrid plants gave rise to segregation proportions 3:1 was false. The great probability ..."
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theorist A.N. Kolmogorov reviewed Ermolaeva’s data using a test, now referred to as Kolmogorov’s, or KolmogorovSmirnov, test, which he had proposed in 1933. He found, contrary to Ermolaeva, that her results clearly confirmed Mendel’s principle. This paper shows that there were methodological flaws
ArelatedmaterialiscontainedalsoinArnold’srecollections“OnA.N.Kolmogorov”. Slightly
, 1937
"... superpositions to KAM theory ..."
An introduction to Kolmogorov Complexity and its Applications: Preface to the First Edition
, 1997
"... This document has been prepared using the L a T E X system. We thank Donald Knuth for T E X, Leslie Lamport for L a T E X, and Jan van der Steen at CWI for online help. Some figures were prepared by John Tromp using the xpic program. The London Mathematical Society kindly gave permission to reproduc ..."
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to reproduce a long extract by A.M. Turing. The Indian Statistical Institute, through the editor of Sankhy¯a, kindly gave permission to quote A.N. Kolmogorov. We gratefully acknowledge the financial support by NSF Grant DCR8606366, ONR Grant N0001485k0445, ARO Grant DAAL0386K0171, the Natural Sciences
The Kolmogorov sampler
, 2002
"... iid 2 Given noisy observations Xi = θi + Zi, i =1,...,n, with noise Zi ∼ N(0,σ), we wish to recover the signal θ with small meansquared error. We consider the Minimum Kolmogorov Complexity Estimator (MKCE), defined roughly as the nvector ˆ θ(X) solving the problem min Y K(Y) subject to �X − Y �2 l ..."
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iid 2 Given noisy observations Xi = θi + Zi, i =1,...,n, with noise Zi ∼ N(0,σ), we wish to recover the signal θ with small meansquared error. We consider the Minimum Kolmogorov Complexity Estimator (MKCE), defined roughly as the nvector ˆ θ(X) solving the problem min Y K(Y) subject to �X − Y �2
Kolmogorov complexity and the Recursion Theorem
, 2005
"... Several classes of diagonally nonrecursive (DNR) functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A can wttcompute a DNR function iff there is a nontrivial recursive lower bound on the Kolmogorov complexity of the initial segments of A. Furth ..."
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Cited by 54 (16 self)
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. Furthermore, A can Turing compute a DNR function iff there is a nontrivial Arecursive lower bound on the Kolmogorov complexity of the initial segements of A. A is PAcomplete, that is, A can compute a {0, 1}valued DNR function, iff A can compute a function F such that F (n) is a string of length n
Evaluating Kolmogorov’s Distribution
 Journal of Statistical Software
"... Kolmogorov’s goodnessoffit measure, Dn, for a sample CDF has consistently been set aside for methods such as the D+n or D n of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of Dn. As far as we know, no easy way to compute that distribution has ever been prov ..."
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Kolmogorov’s goodnessoffit measure, Dn, for a sample CDF has consistently been set aside for methods such as the D+n or D n of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of Dn. As far as we know, no easy way to compute that distribution has ever been
An Excursion to the Kolmogorov Random Strings
 In Proceedings of the 10th IEEE Structure in Complexity Theory Conference
, 1995
"... We study the set of resource bounded Kolmogorov random strings: R t = fx j K t (x) jxjg for t a time constructible function such that t(n) 2 n 2 and t(n) 2 2 n O(1) . We show that the class of sets that Turing reduce to R t has measure 0 in EXP with respect to the resourcebounded measure ..."
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We study the set of resource bounded Kolmogorov random strings: R t = fx j K t (x) jxjg for t a time constructible function such that t(n) 2 n 2 and t(n) 2 2 n O(1) . We show that the class of sets that Turing reduce to R t has measure 0 in EXP with respect to the resourcebounded measure
THE LANDAU–KOLMOGOROV INEQUALITY REVISITED
"... Abstract. We consider the Landau–Kolmogorov problem on a finite interval which is to find an exact bound for ‖f (k) ‖, for 0 < k < n, given bounds ‖f ‖ ≤ 1 and ‖f (n) ‖ ≤ σ, with ‖ · ‖ being the maxnorm on [−1, 1]. In 1972, Karlin conjectured that this bound is attained at the endpoint ..."
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Abstract. We consider the Landau–Kolmogorov problem on a finite interval which is to find an exact bound for ‖f (k) ‖, for 0 < k < n, given bounds ‖f ‖ ≤ 1 and ‖f (n) ‖ ≤ σ, with ‖ · ‖ being the maxnorm on [−1, 1]. In 1972, Karlin conjectured that this bound is attained at the end
Strong separations and Kolmogorov complexity
, 2013
"... A string is a finite or infinite sequence of 0’s and 1’s. The set of all finite strings is {0, 1} <N; elements are usually denoted as σ or τ. The set of all infinite strings is {0, 1} N, also known as Cantor space; elements are usually denoted as X or Y. A function ϕ ∶ ⊆ {0, 1} <N → {0, 1} < ..."
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} <N is partial recursive if it can be emulated by a Turing machine, and recursive if it is partial recursive and total. A set A ⊆ {0, 1} <N is recursively enumerable (r.e.) if there is a partial recursive ϕ such that A = rng(ϕ). Phil Hudelson Strong separations and Kolmogorov complexity 2 / 14
Enumerations of the Kolmogorov Function
"... We consider the hardness of enumerating k possible values for the Kolmogorov complexity function C(x) so that one of them is correct. We show several results including Any computable enumerator for C(x) must enumerate n) possibilities. If a kenumerator (fixed k) for C is reducible to an r.e. ..."
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We consider the hardness of enumerating k possible values for the Kolmogorov complexity function C(x) so that one of them is correct. We show several results including Any computable enumerator for C(x) must enumerate n) possibilities. If a kenumerator (fixed k) for C is reducible to an r
Results 1  10
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