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Modelling the system of agents in the presence of random moments of transactions
P. 1111–1116.
Zhukova A., Pospelov I. G.
This paper presents the approach to modelling the system of agents making transactions at random time. The two main ideas are, to obtain the agents' optimal control in the form of synthesis (feedback) and, secondly, to make the aggregate dynamics stock-flow consistent on the average, not strictly at any moment of time. We present a model of a large number of consumers and producers that take loans from the bank to buy consumption goods or investment. The moments of deals form described the Poisson flow. Consumers and producers optimally solve their stochastic optimal control problems. The solution to the OC problems are in the closed-loop form, obtained using asymptotic methods for large frequency of transactions. The optimal policy functions appear to be linear in the state variables, if time is far from the planning horizon. This enables aggregation across a large population of consumers or producers. As a result, the description of the dynamics of their aggregate state might be substituted by deterministic dynamics. The system of equations for the aggregate dynamics is reduced to one differential equation. The equation is studied numerically and the results are presented.
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
Surkov A., Ignatenko V., Koltsov S., Computers, Materials and Continua 2026 Vol. 88 No. 3 Article 74
Large language models have recently demonstrated promising capabilities in mathematical reasoning; however, their performance on tasks requiring strict symbolic manipulation, such as solving differential equations, remains limited, especially for compact models. In this work, we investigate whether activation steering combined with reinforcement learning can improve the quality of solutions generated by pretrained language models without ...
Added: July 8, 2026
Androsov I., Proceedings of the Institute for System Programming of the RAS 2026 Vol. 38 No. 3 P. 87–114
This paper examines echo state networks (ESNs), one of the most prevalent approaches to
implementing reservoir computing. An ESN consists of a recurrent neural network with fixed (untrained)
weights and a readout layer that is typically linear and trainable. This approach enables the creation of energyefficient and computationally efficient neural networks capable of real-time learning. However, since ...
Added: May 26, 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
Belan S., JETP Letters 2024 Vol. 120 No. 9 P. 705–712
Both Markovian and arbitrary residence time distributions are considered. The comparison of analytical predictions with the case of a time-decorrelated process shows that correlations can both decrease and increase the corresponding expected waiting time. Besides, the comparison of exponential, subexponential, and heavy-tailed models characterized by equal probabilities to observe the event of interest demonstrates that ...
Added: March 1, 2025
Sametov E., Kolotinskii D., Lisin E. et al., Physics of Plasmas 2024 Vol. 31 No. 12 Article 123705
A charged colloidal (dust) particle immersed in a plasma with an ion flow creates a disturbed region behind it, known as a wake. The paper considers a system of two charged and strongly coupled microparticles aligned along the ion flow in a weakly ionized plasma (e.g., in the plasma sheath of a ground-based RF discharge) ...
Added: February 24, 2025
-, 2024.
This collection of articles contains materials of the talks presented at the International Conference «Systems Analysis: Modeling and Control» in memory of Academician A.V. Kryazhimskiy, Moscow, January 23–24, 2024. ...
Added: June 24, 2024
Воронеж: Издательский дом ВГУ, 2024.
В сборнике представлены материалы докладов и лекций, включенных в программу Воронежской зимней математической школы С. Г. Крейна, проводимой Воронежским госуниверситетом совместно с Московским
государственным университетом им. М. В. Ломоносова, Математическим
институтом им. В. А. Стеклова РАН. Тематика охватывает широкий
спектр проблем теорий функций, функционального анализа, дифференциальных уравнений, уравнений математической физики, нелинейного анализа, геометрии, топологии, математического моделирования и истории
математики. ...
Added: May 3, 2024
Dmitry Starkov, Belan S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2023 Vol. 107 No. 6 Article L062101
As has long been known to computer scientists, the performance of probabilistic algorithms characterized by relatively large runtime fluctuations can be improved by applying a restart, i.e., episodic interruption of a randomized computational procedure followed by initialization of its new statistically independent realization. A similar effect of restart-induced process acceleration could potentially be possible in ...
Added: January 29, 2024
Mariani M., Pardoux E., Velleret A., Probability Theory and Related Fields 2025 Vol. 192 P. 721–802
We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller’s ratchet. This model was invented with the aim of evaluating the limitations of an asexual reproduction mode in preventing the accumulation of deleterious mutations through natural selection alone. The main considered model is non-classical, as ...
Added: November 27, 2023
Aksiotis V., Voskoboynikov A., Ossadtchi A. et al., , in: 2023 Fifth International Conference Neurotechnologies and Neurointerfaces (CNN) 18-20 Sept. 2023.: IEEE, 2023. P. 4–7.
Decision-making is a complex and prolonged process. In this study, we present an adaptive algorithm designed to explicitly estimate the duration of perceptual decision-making in the Random Dot Motion Task. The algorithm effectively disentangles the duration of the preparation period for the subject's decision on the direction of movement of the dots from the period ...
Added: November 9, 2023
Pleiades Publishing, Ltd. (Плеадес Паблишинг, Лтд), 2023.
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas:
mathematics
mathematical physics
computer science
control theory, and computers
It publishes brief ...
Added: June 9, 2023
Parfenyev V., Mogilevskiy E., Falkovich G., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2023 Vol. 107 No. 5 Article 054114
We suggest a new computer-assisted approach to the development of turbulence theory. It allows one to impose lower and upper bounds on correlation functions using sum-of-squares polynomials. We demonstrate it on the minimal cascade model of two resonantly interacting modes when one is pumped and the other dissipates. We show how to present correlation functions ...
Added: May 16, 2023
T. A. Alexeeva, Kuznetsov N. V., Lobachev M. et al., IFAC-PapersOnLine 2022 Vol. 55 No. 40 P. 157–162
One of the central tasks of macroeconomic analysis is forecasting and control of economic agents’ expectations for key macroeconomic indicators such as inflation, gross domestic product (GDP), prices and others, etc., so that to achieve maximum level of their welfare through monetary and fiscal policy. This problem is solved within the framework of the optimal ...
Added: April 8, 2023
Шагай М. А., Флегонтов А. В., В кн.: Некоторые актуальные проблемы современной математики и математического образования. Материалы научной конференции "Герценовские чтения - 2022".: СПб.: РГПУ им. А.И. Герцена, 2022.
This article deals with classes of equations - the Weierstrass orbit, the tangent orbit, and the elliptic integral orbit, - whose solutions have a special structure. Through a finite set of special functions, all solutions are constructed by the method of differential "puzzles" after applying the algorithmic direct method. ...
Added: February 6, 2023
Шагай М. А., Флегонтов А. В., Дифференциальные уравнения и процессы управления 2022 Т. 2 С. 23–40
A narrowing of the differential algebra of basic functions on solutions of the generalized homogeneous Emden-Fowler differential equation is considered. The basic finite elements are selected from the classes of trigonometric and special elliptic functions. According to the method of differential "puzzles", all solutions are constructed by applying the direct algorithmic method. ...
Added: January 9, 2023
Springer, 2022.
This book constitutes selected and revised papers from the 22nd International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2022, held in Nizhny Novgorod, Russia, in November 2022.
The 20 full papers and 5 short papers presented in the volume were thoroughly reviewed and selected from the 48 submissions. They are organized in topical secions on computational methods ...
Added: December 26, 2022