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About the Power Law of the PageRank Vector Component Distribution. Part 2. The Buckley–Osthus Model, Verification of the Power Law for This Model, and Setup of Real Search Engines
Сибирский журнал вычислительной математики. 2018. Т. 21. № 1. С. 23–45.
Gasnikov A., Dvurechensky P., Жуковский М. Е., Ким С. В., Плаунов С. С., Смирнов Д. А., Носков Ф. А.
This paper continues article [13]. Here we consider the Buckley–Osthus model for formation of an Internet network. We numerically calculate the PageRank vector for networks generated by this model.We show that the components of this vector are distributed according to a power law. We also discuss the computational aspects of this model with respect to the numerical methods for calculation of the PageRank vector, which were presented in the first part of the work. Finally, we describe a more general model for web-page ranking and some approaches to solve the optimization problem arising in this model learning.
Магазев А. А., Касенов А. А., Трапезников Е. В., Моделирование, оптимизация и информационные технологии 2024 Т. 12 № 2 (45)
The paper presents a description of the Markov model of cyber attacks as a method for analyzing information security in automated systems. Based on the presented model, the work provides a description of two safety metrics - the average time to safety failure (the average number of transitions between states in the corresponding Markov chain ...
Added: September 26, 2025
Канель-Белов А., Kirova V., Чебышевский сборник 2024 Т. 25 № 2 С. 102–126
To study a block array, it is important to be able to determine the relative number of blocks
that satisfy a given property. Thus, when developing a deposit of facing stone, it becomes
necessary to determine the distribution of blocks by volume based on data on fracturing. We
will assume (unless otherwise stated) that the cracks are modeled ...
Added: December 28, 2024
Bufetov A., Klimenko A. V., Series C., Commentarii Mathematici Helvetici 2023 Vol. 98 No. 1 P. 41–134
We prove pointwise convergence of spherical averages for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen–Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving ...
Added: February 29, 2024
Федотов И. А., Хританков А. С., Обидаре М. Д., Программная инженерия 2022 № 4 С. 200–208
Многосторонние соглашения используются в системах распределенного реестра и блокчейн-сетях для согласования изменений в системе. Если один из участников сети предлагает транзакцию на запись, то сначала ее должны подтвердить определенные участники сети. Многостороннее соглашение, или консенсус, определяет состав этих участников. На основе предыдущих ответов можно посчитать вероятность подтверждения транзакции для каждого из участников. В настоящей работе ...
Added: September 20, 2022
Lyulko Y., Теория вероятностей и ее применения 2011 Т. 56 № 1 С. 167–176
Работа состоит из двух частей. В первой части с помощью строго марковского свойства показано, что в общем случае распределение времени пребывания будет геометрическим (с массой в нуле). В качестве примера рассмотрено скошенное случайное блуждание Sα=(Sαk)k≥0 с параметром α∈[0,1], для которого распределение времени пребывания найдено в явном виде.
Во второй части работы делается предельный переход от времени пребывания скошенного случайного блуждания к ...
Added: May 19, 2022
Moltchanov D., Ometov A., Koucheryavy E., Computer Communications 2019 No. 146 P. 110–120
One of the recent major steps towards 5G cellular systems is standardization of 5G New Radio (NR) operatingin the millimeter wave (mmWave) frequency band. This radio access technology (RAT) will potentially provideextraordinary rates at the access interface enabling the set of new bandwidth-greedy applications. However,the blockage of the line-of-sight (LoS) path between 3GPP NR access ...
Added: October 31, 2019
Klimenko A. V., Bufetov A., Series C., / Series math "arxiv.org". 2018. No. 1805.11743.
Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving ...
Added: September 18, 2018
Blank M., Nonlinearity 2017 Vol. 30 No. 12 P. 4649–4664
The classical Birkhoff ergodic theorem in its most popular version says that the
time average along a single typical trajectory of a dynamical system is equal
to the space average with respect to the ergodic invariant distribution. This
result is one of the cornerstones of the entire ergodic theory and its numerous
applications. Two questions related to this subject ...
Added: July 16, 2018
Blank M., [б.и.], 2017.
We study typical points with respect to ergofic averaging of a general dynamical system. ...
Added: February 10, 2018
M. A. Fadeeva, Shchur L., Journal of Physics: Conference Series 2018 Vol. 955 No. 1 Article 012028
We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the ...
Added: February 1, 2018
Kashtanov V., Enatskaya N., Юрайт, 2017.
The textbook has passed practical tests and written on the basis of the readable authors for many years. Presented in textbook materials give students orientation in the solution of many practical problems in a number of areas, constitute the initial level to obtain a broader and deeper education in the field of probability theory. The ...
Added: December 17, 2017
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2016 Т. 448 С. 177–200
We prove existence of limiting curves (describing deviations in ergodic theorem) for cylindrical functions for Polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function we give necessary condition of a limiting curve to exist. Our work generalizes results by E'. Janvresse, T. de la Rue and Y. Velenik. ...
Added: October 14, 2016
Minabutdinov A., Лодкин А. А., Записки научных семинаров ПОМИ РАН 2015 Т. 437 С. 145–183
The paper generalizes the results by E. Janvresse, T. de la Rue and Y. Velenik on fluctuations in ergodic sums for the Pascal adic transformation in the case of any ergodic invariant measure and cylindric function. The result on non-discreteness of the spectrum of the Pascal adic is stated. ...
Added: October 14, 2015
Konakov V., Kozhina A., Menozzi S., / Series arXiv "math". 2016. No. 1506.08758v2.
We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients. As an important application, we give a first order expansion for the difference of the densities of a diffusion with H¨older coefficients and its approximation by the Euler scheme. ...
Added: July 1, 2015
V'yugin V., Theory of Computing Systems 2016 P. 403–423
We study a stability property of probability laws with respect to small violations of algorithmic randomness. Some sufficient
condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like the
strong law of large numbers, the law of iterated logarithm, and even Birkhoff's pointwise ergodic theorem for ergodic
transformations, are stable in ...
Added: May 16, 2015
Minabutdinov A., Лодкин А. А., Манаев И. Е., / Санкт-Петербургское математическое общество. Серия MSP "Preprints of the St. Petersburg Mathematical Society". 2014. № 11.
The paper generalizes the results by \'E. Janvresse, T. de la Rue and Y. Velenik [22] and the work [9] of the third author on fluctuations in ergodic sums for the Pascal adic in the case of arbitrary ergodic invariant measures. In particular, we answer several questions from [22] and [9]. ...
Added: March 28, 2015
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2015 Т. 432 С. 224–260
The paper generalizes the results by E. Janvresse, T. de la Rue and Y. Velenik [18] on fluctuations in ergodic sums for the Pascal adic transformation in the case of Lebesgue measure for a wide class of functions. In particular, we answer several questions from [18]. ...
Added: March 15, 2015
Bezhaeva Z., Oseledets V. I., Обозрение прикладной и промышленной математики 2011 Т. 18 № 4 С. 622–623
Рассматривается стационарная марковская цепь с конечным алфавитом и неприводимой переходной матрицей. Скрытая марковская цепь возникает из марковской цепи при передаче через канал. Получена формула для энтропии скрытой марковской цепи. Эффективность формулы продемонстрирована на конкретных примерах. ...
Added: March 22, 2013
Andreeva A. V., Аудит и финансовый анализ 2011 Т. 6 С. 104–108
This article concerns the problem of predicting the size of company's customer base in case of solving the task of managing its clients. The author purposes a new approach to segment-oriented predicting the size of clients based on adopting the Staroverov's employees moving model. Besides the article includes the limitations of using this model and ...
Added: September 19, 2012