The Erdos – Vershik Problem for the Golden Ratio
Functional Analysis and Its Applications. 2010. Vol. 44. No. 2. P. 83-91.
Bezhaeva Z., Oseledets V. I.
Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. An effective algorithm for calculating the entropy of an invariant Erdos measure is proposed. It is shown that, for certain values of the Bernulli parameter, the algorithm gives the Hausdorff dimension of an Erdos measure to 15 decimal places.
, , Функциональный анализ и его приложения 2010 Т. 44 № 2 С. 3-13
Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. An effective algorithm for ...
Added: April 12, 2012
, , / The Erwin Schrodinger International Institute for Mathematical Physics. Series "ESI preprints". 2008. No. 2087.
Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. ...
Added: April 12, 2012
, , Grazer Mathematische Berichte 2009 Vol. 354 P. 15-25
We study the ergodic properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter. We provide an new effective algorithm for the calculate of entropy of the Erdos measure. ...
Added: April 12, 2012
, , Theory of Probability and Its Applications 2013 Vol. 57 No. 1 P. 135-144
The formula for calculating the entropy and the Hausdorff dimension of an invariant Erdos measure for the pseudogolden ratio and all values Bernoulli parameter is obtained. This formula make possible calculating the entropy and the Hausdorff dimension with high accuracy. ...
Added: February 15, 2014
, , Journal of Dynamical and Control Systems 2013 Vol. 19 No. 4 P. 569-573
Algorithm is given for computation of the Hausdorff dimension of the support of the Erdos measure for a Pisot number. ...
Added: November 11, 2013
, , Journal of Dynamical and Control Systems 2013 Vol. 19 No. 2 P. 301-308
Consider a sofic dynamical system. We obtain an explcit formula for the KS-entropy of sofic dynamicsl system of Blackwell's type. ...
Added: August 22, 2013
, Physica A: Statistical Mechanics and its Applications 2012 Vol. 391 No. 1-2 P. 62-77
We present a possible approach to the study of the renormalization group (RG) flow based entirely on the information theory. The average information loss under a single step of Wilsonian RG transformation is evaluated as a conditional entropy of the fast variables, which are integrated out, when the slow ones are held fixed. Its positivity results in the monotonic ...
Added: October 23, 2014
, Информационные технологии и вычислительные системы 2018 № 2 С. 60-69
The paper considers the problem of reducing the dimension of the feature space for describing objects in data analysis problems using the example of binary classification. The article provides a detailed overview of existing approaches to solving this problem and proposes several modifications. In which the dimensionality reduction is considered as the problem of extracting the most relevant ...
Added: July 4, 2018
, , et al., Journal of Statistical Physics 2013 Vol. 152 No. 1 P. 1-14
We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles. ...
Added: March 13, 2014
, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2013 Vol. 87 P. 024101-024101-4
We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam’s redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving ...
Added: October 23, 2014
, , / Cornell University. Series math "arxiv.org". 2015. No. 1501.04584.
We prove that a polygonal billiard with one-sided mirrors has zero topological entropy. In certain cases we show sub exponential and for other polynomial estimates on the complexity. ...
Added: January 26, 2015
, , et al., В кн. : Материалы конференции «Современная математика и концепции инновационного математического образования». : М. : ООО "Издательский дом МФО", 2017. С. 15-23.
Рассматривается новый подход к получению общего вида автоморфизма группы Гейзенберга. Определена мера Эрдеша на группе Гейзенберга. Дано определение инвариантной меры Эрдеша и получен критерий абсолютной непрерывности меры Эрдеша. ...
Added: July 14, 2017
On the Vershik-Kerov Conjecture Concerning the Shannon-McMillan-Breiman Theorem for the Plancherel Family of Measures on the Space of Young Diagrams
, Geometric and Functional Analysis 2012 Vol. 22 No. 4 P. 938-975
Vershik and Kerov conjectured in 1985 that dimensions of irreducible representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to the Plancherel family of measures on the space of Young diagrams. The statement of the Vershik-Kerov conjecture can be seen as an analogue of the Shannon-McMillan-Breiman Theorem for the non-stationary ...
Added: October 18, 2012
, , , Обозрение прикладной и промышленной математики 2016 Т. 23 № 1 С. 3-16
The tasks associated with finding some information characteristics (entropy, the distribution of m-grams, syllables and phrases), the using of which allows to build the predictive models for the development of natural languages, are considered. The texts in Russian, English, German, French and Georgian languages, as classified by time intervals and styles, are experimental studied. ...
Added: May 8, 2016
Элементы рандомизированного прогнозирования и его применение для предсказания суточной электрической нагрузки энергетической системы
, , , Автоматика и телемеханика 2020 № 7 С. 148-172
A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. ...
Added: October 31, 2020
, , Теория вероятностей и ее применения 2012 Т. 57 № 1 С. 1-10
В работе для псевдозолотого сечения и для произвольного параметра Бернулли получена формула для вычисления энтропии инвариантной меры Эрдеша. Формула позволяет производить вычисление энтропии и хаусдорфовой размерности инвариантной меры Эрдеша с высокой точностью. ...
Added: May 21, 2012
, , Дискретная математика 2012 Т. 24 № 1 С. 108-122
В работе изучается один из вариантов задачи Эрдеша. Определяется инвариантная мера Эрдеша на некотором компакте и соответствующая ей скрытая цепь Маркова. Получена формула для вычисления энтропии инвариантной меры Эрдеша. ...
Added: May 21, 2012
, , in : Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics. Vol. 197.: Springer, 2017. P. 127-152.
A new approach to network decomposition problems (and, hence, to classification problems, presented in network form) is suggested. Opposite to the conventional approach, consisting in construction of one, “the most correct” decomposition (classification), the suggested approach is focused on construction of a family of classifications. Basing on this family, two numerical indices are introduced and ...
Added: October 20, 2017
A Model of Classical Thermodynamics Based on the Partition Theory of Integers, Earth Gravitation, and Semiclassical Asymptotics. I
, Russian Journal of Mathematical Physics 2017 Vol. 24 No. 3 P. 354-372
In the paper, a new construction of the theory of partitions of integers is proposed. The author defines entropy as the natural logarithm of the number of partitions of a number M into natural summands with repetitions allowed p(M) and repetitions forbidden q(M). The passage from ln p(M) to lnq(M) through the mesoscopic values M → 0 is ...
Added: November 17, 2018
Methods of evaluating thermodynamic properties of landscape cover using multispectral reflected radiation measurements by the Landsat satellite
, , , Entropy 2013 Vol. 15 No. 9 P. 3970-3982
The paper discusses methods of evaluating thermodynamic properties of landscape cover based on multi-spectral measurements by the Landsat satellites. Authors demonstrate how these methods could be used for studying functionality of landscapes and for spatial interpolation of Flux NET system measurements. ...
Added: March 27, 2022
, , et al., Компетентность 2017 № 9-10 С. 46-57
We have examined the main new competencies that should be matched by the specialist — managers of complex techno-technological and socio-economic systems in the era of information (digital) and industrial revolutions. We have also investigated what kind of overprofessional competencies the expert should have and what the system of its preparation includes. Having outlined and ...
Added: January 29, 2018
, , , International Journal of Psychophysiology 2016 Vol. 108 P. 148-149
The approach and withdrawal behaviors can be superficially similar. Howether, they differ in a number of cognitive, neurological and physiological characteristics (Carver et al., 2000; Elliot, 2006; Brunia et al., 2011; Franzen et al., 2015). The critical assumption for the present study is that these two types of behaviour are supported by distinct asymmetric domains ...
Added: October 15, 2018
МО РФ, 2013
The transaction consisted from the paper devoted the different divisions of modern mathematics and its applications ...
Added: December 5, 2016
, , et al., Entropy 2017 Vol. 19(4) No. 178 P. 1-14
A proposal for a new method of classification of objects of various nature, named “2”-soft classification, which allows for referring objects to one of two types with optimal entropy probability for available collection of learning data with consideration of additive errors therein. A decision rule of randomized parameters and probability density function (PDF) is formed, ...
Added: May 26, 2017