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Empirical Variance Minimization with Applications in Variance Reduction and Optimal Control
Bernoulli: a journal of mathematical statistics and probability. 2022. Vol. 28. No. 2. P. 1382–1407.
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some restrictions imposed on the functional class fast convergence rates can be achieved including the optimal non-parametric rates for expressive classes in the non-Donsker regime under some additional assumptions. Our main applications include variance reduction and optimal control.
Publication based on the results of:
Guterman A., Jonoska N., Kreines E. et al., Proceedings of the Edinburgh Mathematical Society 2026 Vol. 69 No. 3 P. 1041–1057
We provide four equivalent combinatorial conditions for a simple assembly graph (rigid vertex graph where all vertices are of degree 1 or 4) to have the largest number of Hamiltonian sets of polygonal paths relative to its size. These conditions serve to prove the conjecture that such a maximum, which is equal to 𝐹_(2𝑛+1) −1, ...
Added: September 27, 2026
Qian X., Guan X., Zhang B. et al., Journal of Global Optimization 2026
Inverse quickest path problem on networks ...
Added: September 27, 2026
Shishkina E., Современная математика. Фундаментальные направления 2026 Т. 72 № 1 С. 52–67
In this paper, we construct a weighted Sobolev space of fractional order based on the
generalized Bessel potential.We apply these results to the analysis of the singular fractional Schr¨odinger
equation. To solve the Cauchy problem for this equation, we prove an estimate that relates the norm of
the solution to the norm of the initial condition in the ...
Added: September 26, 2026
Shishkina E., Computational Mathematics and Mathematical Physics 2026 Vol. 66 No. 5 P. 804–815
This article demonstrates that the Laplace–Bessel operator generates a strongly continuous
semigroup on a weighted Lebesgue space. Using this semigroup, we define the fractional Laplace–
Bessel operator via Balakrishnan’s formula. Furthermore, we derive three distinct representations for
fractional powers of the negative Laplace–Bessel operator. ...
Added: September 26, 2026
Kolokoltsov V., Shishkina E., Journal of Theoretical Probability 2026 P. 39–83
In this paper, we introduce a new construction of fractional derivatives and integrals
with respect to a function, based on a matrix approach. We believe that this is a powerful
tool in both analytical and numerical calculations.We begin with the differential
operator with respect to a function that generates a semigroup. By discretizing this
operator, we obtain a matrix ...
Added: September 26, 2026
Switzerland: Springer Cham, 2026.
This volume gathers selected, peer-reviewed contributions presented at the 19th Conference of the International Federation of Classification Societies (IFCS 2026), held on 14–16 July 2026 in Milan, Italy. Reflecting the volume’s motto, Navigating Complexity – Statistical Methods, Data Analysis, and Machine Learning for Actionable Insights, the papers showcase modern methodologies and real-world applications designed to extract ...
Added: September 25, 2026
Petr Kucheriaviy, Bulletin of the Australian Mathematical Society 2026
We prove that an analogue of Rogers’ theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals. ...
Added: September 25, 2026
Kraevskiy A., Sokolovskiy E., Prokhorov A., Emerging Markets Review 2026 No. 74 P. 1–19
Financial markets of emerging economies are vulnerable to extreme and cascading information spillovers, surges, sudden stops and reversals. With this in mind, we develop a new online early warning system (EWS) to detect what is referred to as ‘concept drift’ in machine learning, as a ‘regime shift’ in economics and as a ‘change-point’ in statistics. ...
Added: September 25, 2026
Пелевин Ф. Е., Математические заметки 2026 Т. 120 № 1 С. 159–163
Две не равные тождественно нулю функции (последовательности элементов некоторого поля) будем называть эквивалентными, если они удовлетворяют функциональному уравнению типа теорем сложения тэта-функций. Основной результат работы состоит в том, что рассматриваемое отношение действительно является отношением эквивалентности. ...
Added: September 25, 2026
Shimanogov I. N., Vyalyi M., Siberian Mathematical Journal 2026 Vol. 67 No. 5 P. 1203–1212
We consider a class of Boolean algebras formed by intersections of regular languages with
a given language. In the case where such an algebra is isomorphic to the algebra of regular languages,
we prove the existence of an isomorphism that is computable using oracles for the regular realizability
problem and the infinite regular realizability problem. This result yields ...
Added: September 25, 2026
Дубич Е. В., Schagin D., Славянский форум 2026 № 2 (52) С. 560–565
The paper compares HTTP/2 and HTTP/3 for static resource transfer under software-simulated network degradation. The experiment shows that HTTP/3 is not universally faster, but it is more stable as latency and packet loss increase. ...
Added: September 25, 2026
Ramazanov I., Bukh A., Shepelev Igor A., Chaos 2026 No. 36 P. 083150–083150
We investigate how stochastic Poisson impulsive forcing influences the spatiotemporal dynamics of a two-dimensional network of Hindmarsh–Rose neurons. Unlike continuous noise, impulsive forcing introduces discrete, state-dependent perturbations, making the system response highly sensitive to both the statistics and the spatial structure of the input. In most of the parameter space, stochastic impulses destabilize the initial ...
Added: September 24, 2026
Joulitov A.K., Lomazova I.A., Proceedings of the Institute for System Programming of the RAS 2026 Vol. 38 No. 4(2) P. 215–224
In process mining, DFG (Directly-Follows Graph) models are popular due to their simplicity and clarity. However, if a process is acyclic but contains concurrent events, standard algorithms for discovering DFG models can generate "fake" cycles that do not actually exist in the event log. These cycles hinder the analysis of information processes, significantly reducing the ...
Added: September 24, 2026
Добрина Д. Н., Nesterenko A., Прикладная дискретная математика. Приложение 2026 № 19 С. 151–159
Работа содержит результаты формального анализа криптографических механизмов, входящих в состав проекта методических рекомендаций «Защищенный универсальный протокол передачи данных и управления микросхемой интеллектуальной карты» (протокол SECUNDA). Получена формальная модель и перечень трудноразрешимых математических задач, трудоёмкостью решения которых можно оценить стойкость используемых криптографических механизмов. ...
Added: September 24, 2026
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
I.I. Sergeev, I.A. Lomazova, Modeling and Analysis of Information Systems 2026 Vol. 33 No. 3 P. 394–419
Object-centric process mining has emerged as a powerful paradigm for analyzing event data involving multiple interacting business objects. Existing discovery techniques often rely on object-centric Petri nets with fixed arc multiplicities, limiting their ability to represent parametric resource consumption and production patterns and to capture quantitative dependencies between interacting object types. In this paper, we ...
Added: September 24, 2026
Sokolov V., Adler V. E., Journal of Geometry and Physics 2026 Vol. 227 Article 105860
The group reduction procedure is applied to vector generalizations of the NLS, mKdV,
and KdV equations. The resulting ODE systems admit isomonodromic Lax representations
and are multicomponent generalizations of the Painlevé equations P 1, P 2, P 34, and P 4.
Some of them can be interpreted as nonautonomous deformations of well-known systems
integrable in the Liouville sense, in ...
Added: September 24, 2026
Sokolov V., BALAKHNEV M. Y., Ufa Mathematical Journal 2026 Vol. 18 No. №3 P. 85–93
A collection of miscellaneous continuous, semi-discrete, and discrete integrable
systems can be associated with each integrable evolution equation of the KdV type. We provide them for the Schwarz — KdV equation and generalize to the vector case. The existence
of these vector generalizations is a non-trivial found fact, no mathematical explanation of
which is known yet. ...
Added: September 24, 2026
Yakovlev E., Maksimov D. A., Mathematical notes 2026 Vol. 120 No. 3 P. 483–496
Smooth principal bundles whose total spaces and bases are time oriented Lorentzian manifolds and whose projections are Lorentzian submersions preserving time orientations are studied. Previously, the authors showed that the chronologicity, causality, and stable causality always lift from the base to the space of a Lorentzian bundle. For strong causality and global hyperbolicity, this holds ...
Added: September 24, 2026
Parfenyev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 No. 1 Article 015104
Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a floating drone or active particle -- that is advected by a two-dimensional flow, self-propels at a fixed speed smaller than or comparable to the characteristic flow velocity, ...
Added: July 17, 2026
Optimal Control for Stochastic Multi-agent Systems With the Use of Parallel Hybrid Genetic Algorithm
Akopov A. S., Beklaryan A., , in: Numerical Computations: Theory and Algorithms. 4th International Conference, NUMTA 2023, Pizzo Calabro, Italy, June 14–20, 2023, Revised Selected Papers, Part IVol. 14476.: Springer Publishing Company, 2025. P. 273–280.
In modern times, stochastic large-scale multi-agent systems (MAS) aimed at supporting socio-economic planning are being developed. There is a well known problem of a high computational complexity task of an optimal control for multiple agents’ behaviour in models of random interactions. In particular, agents (such as sellers and buyers) should make individualised decisions on establishing ...
Added: November 23, 2025
Ronzhina M., Manita L., , in: Systems Analysis: Modeling and Control: Materials of the International Conference in memory of Academician A.V. Kryazhimskiy, Moscow, January 23–24, 2024. Abstracts.: -, 2024. P. 25–26.
For some class of small-dimensional optimal control problems we found a family of extremals in the form of logarithmic spirals. These extremals reach the singular surface in a finite time, while the control performs an infinite number of rotations around the circle. ...
Added: October 8, 2025
Delev A., Semakov S., , in: 2025 8th International Conference on Artificial Intelligence and Big Data (ICAIBD).: IEEE, 2025. P. 318–322.
Profit is one of the most important economic indicators of a company’s performance, and for every company it is necessary to allocate resources in such a way as to obtain the maximum possible profit. The profit maximization problem is usually a dynamic optimization problem. This article discusses an approach to solving the production expansion problem ...
Added: August 25, 2025
Gladin E., Alkousa M., Gasnikov A., Automation and Remote Control 2021 Vol. 82 P. 1679–1691
The article deals with some approaches to solving convex problems of the min-min type with smoothness and strong convexity in only one of the two groups of variables. It is shown that the proposed approaches based on Vaidya’s method, the fast gradient method, and the accelerated gradient method with variance reduction have linear convergence. It ...
Added: November 29, 2024