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Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping
Discrete Mathematics and Applications. 2021. Vol. 31. No. 4. P. 259-269.
Mironkin V.
The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.
Mironkin V., Дискретная математика 2019 Т. 31 № 4 С. 38-52
The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of a arbitrary vertex with some restrictions are calculated. Exact expressions for the probability of belonging of two arbitrary vertices to a single connected component, of hitting by a ...
Added: December 8, 2019
Mironkin V., Прикладная дискретная математика 2018 № 42 С. 6-17
The paper is devoted to research of a random variable equal to the length of aperiodicity segment of an arbitrary vertex x of a finite set S in the k-fold iteration graph of an equiprobable random mapping f: S --> S. The behavior of the local probability of aperiodicity is studied. Its two-sided estimates are obtained ...
Added: March 15, 2019
Mironkin V., Математические вопросы криптографии 2019 Т. 10 № 3 С. 89-99
We consider graph of independent uniform random mappings composition. The distribution of the length of aperiodicity segment in such graph is studied. Exact and asymptotic expressions as well as inequalities for the probability distribution, mathematical expectation of the length of aperiodicity segment, the number of vertices with aperiodicity segment of given length are obtained. ...
Added: October 31, 2019
Mironkin V., Прикладная дискретная математика 2020 № 49 С. 5-17
We study the probability characteristics of the random mapping graph $ f_{\left[k\right]} $ --- the composition $k\in \mathbb{N}$ of independent equiprobable random mappings $ f_1, \ldots, f_k $, where $f_i\colon \left\{1,\ldots,n\right\}\to \left\{1,\ldots,n\right\}$, $n\in\mathbb{N}$, $i=1,\ldots,n$. The following results are obtained.
Let $k\in \mathbb{N}$ and random mappings $f_1,\ldots,f_k$ be independent with the equiprobable distribution on $\mathfrak{S}$. Then for ...
Added: September 20, 2020
Mironkin V., Математические вопросы криптографии 2019 Т. 10 № 1 С. 73-82
The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Exact and estimated expressions for the probability of belonging of one and several random vertices to the layers of cycles of a fixed and arbitrary length are obtained. Formulas for the distribution function of the height of a random vertex ...
Added: May 13, 2019
Mironkin V., Математические вопросы криптографии 2020 Т. 11 № 1 С. 101-114
The probabilistic characteristics of graph corresponding to the
composition of independent uniform random mappings are studied. Exact expressions and estimates for the distribution
of distances from vertices to cycles are obtained. Formulas for expected
mean values of numbers of vertices lying on
at the given distance from cycles and
for the distribution function of the height of a random vertex ...
Added: May 31, 2020
Béal S., Deschamps M., Moulin H., Acta Astronautica 2020 Vol. 177 P. 313-319
Satellites launched by independent spacefaring agencies and firms create space congestion and collision risk. Taking as benchmark the cost of a marginal reduction of the congestion rate, we discuss tax mechanisms financing a debris removal effort. We compare the non-cooperative equilibrium traffic when there is a tax on each new launch to recover cleanup costs, ...
Added: August 25, 2020
Дали Ф. А., Mironkin V., Проблемы информационной безопасности. Компьютерные системы 2018 № 1 С. 113-121
Two models of the tree modes of hash functions are introduced. For each model algorithms of computing of the hash code are formulated and their numerical characteristics are obtained. In terms of the constructed models we classify some existing algorithms for parallel hashing and identify some weaknesses of corresponding primitives. ...
Added: May 28, 2018
Shabanov D. A., Zakharov P., Труды Московского физико-технического института 2023 Т. 15 № 1 С. 23-32
The paper deals with the study of the size of the giant component in the random bipartite graph 𝐺(𝑛, 𝑛, 𝑝) in the sparse case, when 𝑝 = 𝑐/𝑛 for some fixed 𝑐 > 1. We prove that the distribution of size of the giant component is asymptotically normal. ...
Added: April 26, 2023
Mironkin V., Chukhno A., Проблемы информационной безопасности. Компьютерные системы 2018 № 2 С. 69-73
In this paper a generalization of the classical birthday problem for the case of several independent samples of arbitrary power is considered. Exact and asymptotic expressions describing the probability of the intersection of these samples are obtained. ...
Added: July 26, 2018
Mironkin V., Михайлов В. Г., Математические вопросы криптографии 2018 Т. 9 № 3 С. 99-108
The properties of the graph of $k$-fold iteration of uniform random mapping f: {1,...,n} to {1,...,n}. are being studied. Some recurrence formulas for the probabilities for a random vertex to belong to the set of images f^k({1,...,n}) and to the set of the initial vertices in the graph of f^k are obtained. ...
Added: September 14, 2018
Mironkin V., Обозрение прикладной и промышленной математики 2018 Т. 25 № 1 С. 3-8
The graph of internal states of Sponge construction and the relationship between internal states and elements of the output sequence are investigated. The methods of constructing collisions which use features of the cyclic structure of Sponge construction’s substitution are proposed. The general form of the corresponding collisions is described. ...
Added: April 27, 2018
Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016
The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...
Added: November 2, 2016
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253
Added: December 22, 2016
Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.
We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...
Added: September 29, 2019
Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.
We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...
Added: March 9, 2014
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291
The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...
Added: December 7, 2013
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293
Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...
Added: September 29, 2014
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Турунцева М., Астафьева Е., Баева М. et al., Научный вестник ИЭП им. Гайдара.ру (электронный журнал) 2015 № 3(85) С. 3-33
В статье представлены расчеты прогнозных значений различных экономических показателей Российской Федерации во II–III кварталах 2015 г., построенные на основе моделей временных рядов, структурных эконометрических уравнений и моделей, построенных с использованием результатов конъюнктурных опросов. ...
Added: June 18, 2015