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Информация, кодирование, статистика и машинное обучение. Часть I. Теория информации
M. :
MCCME, 2025.
Kelbert M., Сухов Ю. М.
Academic editor: Kabatiansky G. A.
Keywords: теория информации
Publication based on the results of:
Glutsyuk A., Inventiones Mathematicae 2026 Vol. 245 P. 977–1058
A caustic of a strictly convex planar bounded billiard is a smooth curve whose tangent lines are reflected from the billiard boundary to its tangent lines. The famous Birkhoff Conjecture, studied by many mathematicians, states that if the billiard boundary has an inner neighborhood foliated by closed caustics, then it is an ellipse. In the paper we study ...
Added: September 8, 2026
Prikhodko Artem, Kubrak D., Compositio Mathematica 2026 Vol. 162 No. 6 P. 1377–1438
In this follow-up paper we show that smooth Hodge-proper stacks over O𝐾 are ℚ𝑝-locally acyclic: namely the natural map between étale ℚ𝑝-cohomology of the algebraic and Raynaud generic fibers is an equivalence. This establishes the ℚ𝑝-case of general conjectures made in D. Kubrak and A. Prikhodko [p-adic Hodge theory for Artin stacks, Mem. Amer. Math. ...
Added: September 7, 2026
Ismailov A., Constructive Approximation 2026
The measure of the positivity set {x ∈ [0; 2π] | f (x) > 0} of a trigonometric polynomial f is bounded from below by the Motzkin density.
We generalize the bound to polynomials in several variables and almost periodic functions.
We then use these generalizations to extend known results on Taikov’s problem. ...
Added: September 7, 2026
Kucheryavyy P., Математические заметки 2026 Т. 2026 № 120 С. 380–401
В работе изучаются перестановки, возникающие при упорядочивании по возрастанию дробных долей произведений элементов фиксированной целочисленной последовательности на вещественный параметр. Исследуется количество различных перестановок, которые можно получить таким образом при изменении этого параметра от нуля до единицы. ...
Added: September 7, 2026
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Puzachenko A. Y., Sandlerskiy R., Biology Bulletin 2023 Vol. 50 No. 2 P. S119–S131
We tried to trace the stages of Puzachenko scientific path and highlight the key areas of his scientific interest: the organization and functioning of complex self-organizing nonequilibrium systems (biogeocenosis and landscapes) and different aspects of biodiversity and relationships between species and their environment. ...
Added: February 26, 2025
Los A., Nesterenko A., Rogacheva O., В кн.: Алгебра, теория чисел, дискретная математика и многомасштабное моделирование: современные проблемы, приложения и проблемы истории. Материалы XXII Международной конференции, посвящённой 120-летию со дня рождения академика Андрея Николаевича Колмогорова и 60-летию со дня открытия школы-интерната № 18 при Московском университете.: [б.и.], 2023. С. 151–157.
One of the requirements for the quality of cryptographic algorithms is the equiprobable distribution of the characters of the sequence obtained after applying the cryptographic transformation. This requirement is due to the fact that in the presence of unequal probability of signs of the output sequence, it becomes possible to construct an effective method for ...
Added: April 24, 2024
Kuralenok I., Starikova N., Khvorov A. et al., , in: Proceedings of the 27th ACM International Conference on Information and Knowledge Management.: Association for Computing Machinery (ACM), 2018. P. 1343–1352.
This paper presents a new method for constructing an optimal feature set from sequential data. It creates a dictionary of n-grams of variable length (we call them v-grams), based on the minimum description length principle. The proposed method is a dictionary coder and works simultaneously as both a compression algorithm and as unsupervised feature extraction. ...
Added: December 27, 2019
Российский университет дружбы народов (РУДН), 2019.
В научном издании представлены материалы XXII Международной научной конференции «Распределенные компьютерные и телекоммуникационные сети: управление, вычисление, связь» по следующим направлениям: • Алгоритмы и протоколы телекоммуникационных сетей • Управление в компьютерных и инфокоммуникационных системах • Анализ производительности, оценка QoS / QoE и эффективность сетей • Аналитическое и имитационное моделирование коммуникационных систем последующих поколений • Эволюция беспроводных ...
Added: December 25, 2019
Meniailo V. V., Билятдинов К. З., Красов А. В. et al., СПб.: Астерион, 2019.
В учебнике излагаются основы дисциплины «Теория информационных процессов и систем». В учебнике рассматриваются: теория систем, системы связи, основы теории кодирования, теория информации, а также модели динамического хаоса. Учебник предназначен для студентов высших учебных заведений, обучающихся по направлению подготовки бакалавров “Системный анализ и управление” и специальности “Информационные системы и технологии”. Также может быть использован при самостоятельном ...
Added: November 28, 2019
Kruglik Stanislav, Frolov A., , in: 2017 IEEE International Symposium on Information Theory (ISIT).: IEEE, 2017. P. 1023–1027.
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the shortening method and improves existing shortening bounds. To reduce the gap in between upper and lower bounds ...
Added: October 26, 2018
NY: Institute of Electrical and Electronics Engineers, 2016.
This is the landmark international conference of the IEEE Information Theory Society. The conference will seek original contributions in: Coding theory and practice, Communication theory, Compression, Cryptography and data security, Detection and estimation, Information theory and statistics, Information theory in networks, Multi-terminal information theory, Pattern recognition and learning, Quantum information theory, Sequences and complexity, Shannon ...
Added: March 11, 2018
Switzerland: Springer, 2017.
This book constitutes the refereed proceedings of the 5th International Castle Meeting on Coding Theory and Applications, ICMCTA 2017, held in Vihula, Estonia, in August 2017.
The 24 full papers presented were carefully reviewed and selected for inclusion in this volume. The papers cover relevant research areas in modern coding theory, including codes and combinatorial structures, ...
Added: March 11, 2018