Алексей Николаевич Чупрунов, Alexej Nikolaevich Chuprunov
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
{"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}
Рассматриваются локальные теоремы о больших уклонениях для момента $T_n$ достижения уровня $ninmathbb{N}$ случайным блужданием в случайной среде. Получены точные асимптотики вероятностей ${mathbf P}(T_n=k)$ в диапазоне параметра $k$, соответствующем зоне больших уклонений.
考虑到当地的大规避定理，当T_n美元达到n / n / mathbb时，随机漫步在随机环境中。我们得到了与大规避范围一致的美元(T_n=k)参数范围内的精确渐近线。
{"title":"О больших уклонениях момента достижения далекого уровня случайным блужданием в случайной среде","authors":"Гавриил Андреевич Бакай, Gavriil Andreevich Bakai","doi":"10.4213/dm1726","DOIUrl":"https://doi.org/10.4213/dm1726","url":null,"abstract":"Рассматриваются локальные теоремы о больших уклонениях для момента $T_n$ достижения уровня $ninmathbb{N}$ случайным блужданием в случайной среде. Получены точные асимптотики вероятностей ${mathbf P}(T_n=k)$ в диапазоне параметра $k$, соответствующем зоне больших уклонений.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"6 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75978508","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}
Константин Евгеньевич Денисов, Konstantin Yurievich Denisov
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 $h^{-}
在随机环境中，随机环境中，美元/ boldsymbol / eta是一系列独立分布的变量。在假设随机变量$ X_ {i、j} $固定环境下具有几何分布,增量美元/ xi_i伴随着美元的随机中学美元 mu > 0美元和满足左翼条件克雷默$ {{ mathbf E} xi_i exp (h) < / infty} $ 65 $ h ^ {-} < h < 0 $对于一些$ h ^{} < - 1美元,找到渐局部概率mathbf P (Z_n施工美元= / lfloor 员exp (n) / rfloor) $, $ n / to / infty $, $ /■员/ in (max (m ^{}, 0美元);m (- 1)),以及附近一些$ m (- 1) $, $ m ^{}美元和$ m(- 1)有些常数美元。
{"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}
Доказано, что любую (почти любую) булеву функцию от $n$ переменных можно реализовать схемой из функциональных элементов в базисе «конъюнкция, дизъюнкция, импликация, отрицание», допускающей условный полный диагностический тест глубины не более $n$ (соответственно не более $n-1$) относительно константных неисправностей типа $0$ на выходах элементов.
{"title":"Короткие условные полные диагностические тесты для схем при однотипных константных неисправностях элементов","authors":"Кирилл Андреевич Попков, K. A. Popkov","doi":"10.4213/dm1727","DOIUrl":"https://doi.org/10.4213/dm1727","url":null,"abstract":"Доказано, что любую (почти любую) булеву функцию от $n$ переменных можно реализовать схемой из функциональных элементов в базисе «конъюнкция, дизъюнкция, импликация, отрицание», допускающей условный полный диагностический тест глубины не более $n$ (соответственно не более $n-1$) относительно константных неисправностей типа $0$ на выходах элементов.","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":"89956149","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}
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.
{"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}
Если в выражении условия гомоморфизма многоосновной универсальной алгебры вместо равенства выполняется неравенство, то говорят о существовании инверсного гомоморфизма многоосновной универсальной алгебры. В работе исследуются методы построения нетривиальных инверсных гомоморфизмов конечных групп.
{"title":"Инверсные гомоморфизмы конечных групп","authors":"Игорь Гаврилович Шапошников, I. G. Shaposhnikov","doi":"10.4213/dm1716","DOIUrl":"https://doi.org/10.4213/dm1716","url":null,"abstract":"Если в выражении условия гомоморфизма многоосновной универсальной алгебры вместо равенства выполняется неравенство, то говорят о существовании инверсного гомоморфизма многоосновной универсальной алгебры. В работе исследуются методы построения нетривиальных инверсных гомоморфизмов конечных групп.","PeriodicalId":42607,"journal":{"name":"Prikladnaya Diskretnaya Matematika","volume":"45 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74326184","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}
The problem of constructing parsers from syntax diagrams with multiport components (SD) is solved. An algorithm for constructing a parser based on the GLL algorithm is proposed, which results in the compact representation of the input chain parse forest. The proposed algorithm makes it possible to build parsers based on the SD of an arbitrary structure and does not require preliminary SD transformations. We introduce the concepts of “inference tree” and “parsing forest” for SD and describe the data structures used by the parser, such as a graph-structured stack, a parser descriptor, and a compact representation of the parsing forest. The algorithm for constructing parsers based on SD is described and an example of parser constructing is given.
{"title":"Building parsers based on syntax diagrams with multiport components","authors":"Yuriy Ryazanov, S. V. Nazina","doi":"10.17223/20710410/55/8","DOIUrl":"https://doi.org/10.17223/20710410/55/8","url":null,"abstract":"The problem of constructing parsers from syntax diagrams with multiport components (SD) is solved. An algorithm for constructing a parser based on the GLL algorithm is proposed, which results in the compact representation of the input chain parse forest. The proposed algorithm makes it possible to build parsers based on the SD of an arbitrary structure and does not require preliminary SD transformations. We introduce the concepts of “inference tree” and “parsing forest” for SD and describe the data structures used by the parser, such as a graph-structured stack, a parser descriptor, and a compact representation of the parsing forest. The algorithm for constructing parsers based on SD is described and an example of parser constructing is given.","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":"67583131","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}
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).
{"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}
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