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Gaussian limit theorem for posterior distribution in the problem of conflicting expert opinions
Mathematical Communications. 2023. Vol. 28. No. 2. P. 203–212.
Kasianova K., Kelbert M.
. Suppose we have n experts who have their prior opinions about the unknown probability q in the experiment with a binary outcome. It is known that expert opinions are in conflict with each other. To model “conflicting” expert opinions a prior distribution based on Selberg’s integral is constructed. We prove a theorem regarding the limiting properties of the posterior distribution. Also, differential entropy and the Kullback-Leibler (KL) divergence of such posterior are studied.
Lerman L. M., Turaev D. V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2025 Vol. 12 No. 1 P. 1–40
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., Sivkin V., Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
Белоусов Н. М., Черепанов Л. К., Деркачов С. Э. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
Муравьев М. Ю., Annales Mathematiques du Quebec 2025
Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Interpreting his approach in terms of differential forms permits to generalize these results to a much broader context. The spectrum of the absolute boundary problem for ...
Added: May 6, 2026
Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355
Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...
Added: May 5, 2026
Монахова Э. А., Монахов О. Г., Rzaev E. et al., Прикладная дискретная математика 2026 Т. 71 С. 112–127
В настоящей работе исследовано совместное конструирование топологий семейств оптимальных по диаметру циркулянтных сетей $C(N; \pm 1, \pm s_2)$ и реализуемых для них оптимальных алгоритмов маршрутизации сложности $O(1)$. Предлагаемый алгоритм маршрутизации основан на использовании масштабируемых параметров $L$-образных шаблонов плотной укладки графов на плоскости для семейств оптимальных сетей.
Определены аналитические формулы зависимости этих параметров от диаметра графов семейств ...
Added: May 4, 2026
Dudakov S., Lobachevskii Journal of Mathematics 2025 Vol. 46 No. 12 P. 6092–6102
We study the additive theory of arbitrary figures in linear spaces, that is, the theory of
addition extended to sets of vectors. Our main result is the following: if a linear space is infinite,
then the additive theory of figures admits interpreting second-order arithmetic and, therefore, it has
such or higher degree of undecidability. For countably infinite spaces, ...
Added: May 1, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Caglar U., Kolesnikov A., Werner E., Indiana University Mathematics Journal 2022 Vol. 71 No. 6 P. 2309–2333
In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant entropy inequalities. We obtain new inequalities on functional affine surface area and lower and upper bounds for the Kullback-Leibler divergence in terms of functional affine surface area. The functional inequalities ...
Added: June 23, 2023
Savchenko A., , in: International Joint Conference on Rough Sets, Springer, Cham.: Springer, 2017. P. 264–277.
In this paper it is proposed to improve performance of the automatic speech recognition by using sequential three-way decisions. At first, the largest piecewise quasi-stationary segments are detected in the speech signal. Every segment is classified using the maximum a-posteriori (MAP) method implemented with the Kullback-Leibler minimum information discrimination principle. The three-way decisions are taken ...
Added: October 26, 2018
Savchenko A., Belova N. S., / Series "Working papers by Cornell University". 2017.
The paper deals with the still-to-video face recognition for the small sample size problem based on computation of distances between high-dimensional deep bottleneck features. We present the novel statistical recognition method, in which the still-to-video recognition task is casted into Maximum A Posteriori estimation. In this method we maximize the joint probabilistic density of the ...
Added: August 29, 2017
Maslov V. P., Nazaikinskii V. E., Mathematical notes 2016 Vol. 99 No. 3 P. 616–618
Added: July 7, 2016
Mozgunov P., Kelbert M., , in: Proceedings of Information Technology and Systems 2015.: Sochi: ., 2015. P. 614–621.
Consider a Bayesian problem of estimating of probability of success in a series of trials with binary outcomes. We study the asymp- totic behaviour of weighted differential entropy for posterior probability density function (PDF) conditional on x successes after n trials, when n → ∞. Suppose that one is interested to know whether the coin is fair or not ...
Added: December 5, 2015
Mozgunov P., Kelbert M., Eurasian Mathematical Journal 2015 Vol. 6 No. 2 P. 6–17
Consider a Bayesian problem of success probability estimation in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of the weighted differential entropy for posterior probability density function conditional on x successes after n conditionally independent trials when n tends to infinity. Suppose that one is interested to know whether ...
Added: December 5, 2015
Savchenko A., Optimization Letters 2017 Vol. 11 No. 2 P. 329–341
This paper addresses the problem of insufficient performance of statistical classification with the medium-sized database (thousands of classes). Each object is represented as a sequence of independent segments. Each segment is defined as a random sample of independent features with the distribution of multivariate exponential type. To increase the speed of the optimal Kullback-Leibler minimum ...
Added: September 10, 2015