Prikladnaya Diskretnaya Matematika最新文献_第5页

О числе частиц из отмеченного множества ячеек в обобщенной схеме размещения 在广义位置图中注意到的细胞集合的数量

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.4213/dm1663

Алексей Николаевич Чупрунов, Alexej Nikolaevich Chuprunov

{"title":"О числе частиц из отмеченного множества ячеек в обобщенной схеме размещения","authors":"Алексей Николаевич Чупрунов, Alexej Nikolaevich Chuprunov","doi":"10.4213/dm1663","DOIUrl":"https://doi.org/10.4213/dm1663","url":null,"abstract":"В обобщенной схеме размещения $n$ частиц по $N$ ячейкам рассматривается случайная величина $eta_{n,N}(K)$ - число частиц, которые попали в ячейки заданного множества, состоящего из $K$ ячеек. Показано, что если $n, K, Ntoinfty$, то при одних условиях случайные величины $eta_{n,N}(K)$ асимптотически нормальны, а при других условиях случайные величины $eta_{n,N}(K)$ сходятся по распределению к пуассоновской случайной величине. В случае, когда $Ntoinfty$, а $n$ фиксировано, указаны условия, при которых случайные величины $eta_{n,N}(K)$ сходятся по распределению к биномиальной случайной величине с параметрами $n$ и $s=frac{K}{N}$, $0<K<N$, умноженной на целочисленный коэффициент. Показано, что если для обобщенной схемы размещения $n$ частиц по $N$ ячейкам со случайными величинами, имеющими распределение степенного ряда, определенное функцией $B(beta)=ln(1-beta)$, выполняются условия $n,N,Ktoinfty$, $frac{K}{N}to s$, $N=gammaln(n)+o(ln(n))$, где $0< s<1$, $0<gamma<infty$, то распределения случайных величин $frac{eta_{n,N}(K)}{n}$ сходятся к бета-распределению с параметрами $sgamma$, $(1-s)gamma$.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"52 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74945183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

О больших уклонениях момента достижения далекого уровня случайным блужданием в случайной среде 通过在随机环境中随机漫步来达到遥远水平的瞬间的大规避

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.4213/dm1726

Гавриил Андреевич Бакай, Gavriil Andreevich Bakai

引用次数: 1

Чистяков Владимир Павлович (19.04.1934-11.01.2022)

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.4213/dm1722

引用次数: 0

Локальная асимптотика вероятностей нижних уклонений строго надкритических ветвящихся процессов в случайной среде с геометрическими распределениями чисел потомков 在具有后代数字几何分布的随机环境中严格超临界分支过程的局部渐近线

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.4213/dm1725

Константин Евгеньевич Денисов, Konstantin Yurievich Denisov

{"title":"Локальная асимптотика вероятностей нижних уклонений строго надкритических ветвящихся процессов в случайной среде с геометрическими распределениями чисел потомков","authors":"Константин Евгеньевич Денисов, Konstantin Yurievich Denisov","doi":"10.4213/dm1725","DOIUrl":"https://doi.org/10.4213/dm1725","url":null,"abstract":"Рассматриваются вероятности нижних уклонений ветвящегося процесса $Z_{n} = X_{n, 1} + dotsb + X_{n, Z_{n-1}}$ в случайной среде $boldsymboleta$, представляющей собой последовательность независимых одинаково распределенных величин. В предположении, что случайные величины $X_{i,j}$ при фиксации среды имеют геометрические распределения, а приращения $xi_i$ сопровождающего случайного блуждания имеют среднее $mu > 0$ и удовлетворяют левостороннему условию Крамера ${{mathbf E}exp(hxi_i) < infty}$ при $h^{-}<h<0$ для некоторого $h^{-} < -1$, найдена асимптотика локальных вероятностей ${mathbf P}( Z_n = lfloorexp(theta n)rfloor )$, $ntoinfty$, при $theta in (max(m^{-},0);m(-1))$, а также в некоторой окрестности $m(-1)$, где $m^{-}$ и $m(-1)$ - некоторые константы.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80567170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Короткие условные полные диагностические тесты для схем при однотипных константных неисправностях элементов 单型常数问题电路的短条件全诊断测试

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.4213/dm1727

Кирилл Андреевич Попков, K. A. Popkov

引用次数: 0

Image stegoanalysis using deep neural networks and heteroassociative integral transformations 基于深度神经网络和异关联积分变换的图像隐写分析

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.17223/20710410/55/3

M. Dryuchenko, A. Sirota

{"title":"Image stegoanalysis using deep neural networks and heteroassociative integral transformations","authors":"M. Dryuchenko, A. Sirota","doi":"10.17223/20710410/55/3","DOIUrl":"https://doi.org/10.17223/20710410/55/3","url":null,"abstract":"The problem of steganalysis of digital images is considered. The proposed approach is based on the use of deep convolutional neural networks with a relatively simple architecture, distinguished by the use of additional layers of special processing. These networks are trained and used for steganalysis of small fragments of the original large images. For the analysis of full sized images, it is proposed to carry out secondary post-processing, which involves combining the obtained classification results in blocks as a sequence of binary features according to the scheme of a naive Bayesian classifier. We propose to use integral heteroassociative transformations that provide the selection of the estimated and stochastic (masking) components on the processed image fragment based on the forecast model of one part of the fragment in relation to another to identify violations of the structural and statistical image properties after message embedding. Such transformations are included in the architecture of trained neural networks as an additional layer. Alternative versions of deep neural network architectures (with and without an integral layer of heteroassociative transformation) are considered. The PPG-LIRMM-COLOR images base was used to create data sets. Experiments have been carried out for several well-known stego algorithms (including the classic block and block-spectral algorithms of Kutter, Koha - Zhao, modern algorithms EMD, MBEP and algorithms for adaptive spatial steganography WOW and S-UNIWARD) and for the stego algorithms based on the use of heteroassociative compression transformations. It is shown that the accuracy of steganalysis obtained when implementing the proposed information processing schemes for large images with relatively low computational costs is comparable to the results obtained by other authors, and in some cases even exceeds them.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67583028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Инверсные гомоморфизмы конечных групп

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.4213/dm1716

Игорь Гаврилович Шапошников, I. G. Shaposhnikov

引用次数: 0

Письмо в редакцию 给编辑部的信

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.4213/dm1735

Алексей Дмитриевич Яшунский, Aleksei Dmitrievich Yashunskii

引用次数: 0

Building parsers based on syntax diagrams with multiport components 基于带有多端口组件的语法图构建解析器

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.17223/20710410/55/8

Yuriy Ryazanov, S. V. Nazina

引用次数: 0

The construction of circulant matrices related to MDS matrices 与MDS矩阵相关的循环矩阵的构造

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Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI: 10.17223/20710410/56/2

S. S. Malakhov, M. I. Rozhkov

{"title":"The construction of circulant matrices related to MDS matrices","authors":"S. S. Malakhov, M. I. Rozhkov","doi":"10.17223/20710410/56/2","DOIUrl":"https://doi.org/10.17223/20710410/56/2","url":null,"abstract":"The objective of this paper is to suggest a method of the construction of circulant matrices, which are appropriate for being MDS (Maximum Distance Separable) matrices utilising in cryptography. Thus, we focus on designing so-called bi-regular circulant matrices, and furthermore, impose additional restraints on matrices in order that they have the maximal number of some element occurrences and the minimal number of distinct elements. The reason to construct bi-regular matrices is that any MDS matrix is necessarily the bi-regular one, and two additional restraints on matrix elements grant that matrix-vector multiplication for the samples constructed may be performed efficiently. The results obtained include an upper bound on the number of some element occurrences for which the circulant matrix is bi-regular. Furthermore, necessary and sufficient conditions for the circulant matrix bi-regularity are derived. On the basis of these conditions, we developed an efficient bi-regularity verification procedure. Additionally, several bi-regular circulant matrix layouts of order up to 31 with the maximal number of some element occurrences are listed. In particular, it appeared that there are no layouts of order 32 with more than 5 occurrences of any element which yield a bi-regular matrix (and hence an MDS matrix).","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67583178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0