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Extremal Random Beta Polytopes
Journal of Mathematical Sciences. 2023. Vol. 273. P. 844–860.
Simarova E.
Translator: Simarova E.
The convex hull of several i.i.d. beta distributed random vectors in ℝd is called the random beta polytope. Recently, the expected values of their intrinsic volumes, number of faces, normal and tangent angles and other quantities have been calculated, explicitly and asymptotically. In the present paper, we aim to investigate the asymptotic behavior of the beta polytopes with extremal intrinsic volumes. We suggest a conjecture and solve it in dimension two. To this end, we obtain some general limit relation for a wide class of U-max statistics whose kernels include the perimeter and the area of the convex hull of the arguments.
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
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ООО "Издательство Юрайт ", 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
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Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
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Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
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Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
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Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
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Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
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Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
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Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
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Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
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Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
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Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
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Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
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Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
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Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
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Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
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Kulya M., Pusev R., Moskvitin D., , in: 2025 International Russian Smart Industry Conference (SmartIndustryCon).: Sochi: IEEE, 2025. P. 83–88.
We claim the method to obtain a reliable queuing one-way delay metric for the wireless computer networking systems. The method requires only a measurement of the timestamp series between packet departure and arrival events. These timestamps are included inside the packets with stream frames. Thus, the method does not need to involve any additional probe ...
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Yakov Nikitin, Simarova E., Journal of Applied Probability 2022 Vol. 59 No. 3 P. 825–848
U-max statistics were introduced by Lao and Mayer in 2008. Such statistics are natural
in stochastic geometry. Examples are the maximal perimeters and areas of polygons and
polyhedra formed by random points on a circle, ellipse, etc. The main method to study
limit theorems for U-max statistics is via a Poisson approximation. In this paper we
consider a general ...
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Magazinov A., Discrete and Computational Geometry 2013 Vol. 49 No. 2 P. 200–220
Let P_λ be a homogeneous Poisson point process of rate λ in the Clifford torus T^2⊂E^4. Let (f0,f1,f2,f3) be the f-vector of conv P_λ and let \bar{v} be the mean valence of a vertex of the convex hull. Asymptotic expressions for 𝖤 f_1, 𝖤 f_2, 𝖤 f_3 and 𝖤 \bar{v} as λ→∞ are proved in this paper. ...
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Фетисова Ю. А., Ермоленко Б. В., Ермоленко Г. В. et al., Thermal Engineering (English translation of Teploenergetika) 2017 Vol. 64 No. 4 P. 251–257
We studied the information basis for the assessment of wind power potential on the territory of Russia. We described the methodology to determine the parameters of the Weibull function, which reflects the density of distribution of probabilities of wind flow speeds at a defined basic height above the surface of the earth using the available ...
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Koroleva E. V., Nikitin Y. Y., Journal of Multivariate Analysis 2014 Vol. 127 No. 5 P. 98–111
Recently Lao and Mayer (2008) considered U-max-statistics, where the maximum of kernels over the set of indices is studied instead of the usual sums. Such statistics emerge frequently in stochastic geometry. The examples include the largest distance between random points in a ball, the maximal diameter of a random polygon, the largest scalar product within ...
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Shvedov A. S., / Высшая школа экономики. Серия WP2 "Количественный анализ в экономике". 2009. № 01.
This paper is concerned with a matrix variate beta distribution. Two vector parameters determine the distribution. It is applied to state space models. ...
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