Doklady Mathematics最新文献

The phenomenon of intransitivity of trading strategies with constant levels in the stock market is studied. By using Doob’s stopping theorem and basic concepts from probability theory, accurate estimates for the strength of intransitivity are derived for the case of strategies with constant levels.

The problem of optimal organization of state inspection with an honest head and rational auditors is considered. Audit schemes are investigated in which the honest behavior of taxpayers and auditors turns out to be resistant to coalition deviations. In addition to hierarchical structures, a three-stage scheme with cross-checking is considered. It is proved that cross-checking is never optimal. The minimum audit costs for two- and three-level structures are determined. The best option is specified depending on the model parameters.

The paper examines an infinite-horizon multistage game of renewable resource extraction with two types of players differing in the discount rates of future payoffs. Using the dynamic programming method, we construct a noncooperative solution—a subgame perfect Nash equilibrium in stationary feedback strategies—and a cooperative (Pareto optimal) solution for the case of complete cooperation of all players. The resulting solutions are analyzed for sensitivity to variations in model parameters. In particular, the range of the coefficient of natural resource renewal is found in which a noncooperative solution leads to complete depletion of the resource, while a cooperative scheme allows the players to avoid this negative scenario. A numerical example is given to demonstrate the theoretical results obtained.

The article provides an overview of the practice of using large language models (LLMs) in cyberattacks. Artificial intelligence models (machine learning and deep learning) are applied across various fields, with cybersecurity being no exception. One aspect of this usage is offensive artificial intelligence, specifically in relation to LLMs. Generative models, including LLMs, have been utilized in cybersecurity for some time, primarily for generating adversarial attacks on machine learning models. The analysis focuses on how LLMs, such as ChatGPT, can be exploited by malicious actors to automate the creation of phishing emails and malware, significantly simplifying and accelerating the process of conducting cyberattacks. Key aspects of LLM usage are examined, including text generation for social engineering attacks and the creation of malicious code. The article is aimed at cybersecurity professionals, researchers, and LLM developers, providing them with insights into the risks associated with the malicious use of these technologies and recommendations for preventing their exploitation as cyber weapons. The research emphasizes the importance of recognizing potential threats and the need for active countermeasures against automated cyberattacks.

Chess players’ positions in intransitive (rock-paper-scissors) relations are considered. Intransitivity of chess players’ positions means that: position A of White is preferable (it should be chosen if choice is possible) to position B of Black, if A and B are on a chessboard; position B of Black is preferable to position C of White, if B and C are on the chessboard; position C of White is preferable to position D of Black, if C and D are on the chessboard; but position D of Black is preferable to position A of White, if A and D are on the chessboard. Intransitivity of winningness of chess players’ positions is considered to be a consequence of complexity of the chess environment—in contrast with simpler games with transitive positions only. The space of relations between winningness of chess players’ positions is non-Euclidean. The Zermelo-von Neumann theorem is complemented by statements about possibility vs. impossibility of building pure winning strategies based on the assumption of transitivity of players’ positions. Questions about the possibility of intransitive players’ positions in other positional games are raised.

In 1984, Kaminsky, Luks, and Nelson formulated the gladiator game model of two teams with given strengths. Suppose that a team wants to maximize its expected strength at the end of a battle. We consider an optimization problem: how to distribute the team’s strength among its gladiators. In the above we suppose that the teams distribute their strengths at the beginning of a battle. We also consider Nash equilibria when the teams may change gladiators’ strengths before every fight. We consider two cases. In both, the first team wants to maximize its strength. The second team wants to maximize its strength too in the first case or wants to minimize the first team’s strength in the second case.

The basic model of the Cournot oligopoly taking into account competition-cooperation and environmental pollution as a differential game in a normal form is described. The numerical analysis for independent and cooperative behavior is carried out for an example used in the future. Games in the form of the characteristic von Neumann–Morgenstern, Petrosyan–Zaccour, and Gromova–Petrosyan functions are constructed, and the Shapley values are calculated. Hierarchical games with information regulations for direct and reverse Stackelberg games are analyzed, payoffs’ comparative analysis for all methods of organization is provided. All the results are presented for the dynamic game with three players.

The paper examines discrete-time network models of competition with a finite planning horizon. Firms produce a homogeneous product in constant quantities and sell it in a common market. In a nonterminal period, the behavior of each firm is characterized by a multicomponent profile that includes, among other things, the amount of investment and the structure of bilateral links with partner firms. The latter affects the technological state of the firm and allows it to reduce its current costs. The endogenous structure of partner firms is described by a network. For the models under study, an open-loop Nash equilibrium is characterized.

In this paper we consider a distributed optimization problem in the black-box formulation. This means that the target function   f is decomposed into the sum of (n) functions ({{f}_{i}}), where (n) is the number of workers, it is assumed that each worker has access only to the zero-order noisy oracle, i.e., only to the values of ({{f}_{i}}(x)) with added noise. In this paper, we propose a new method ZO-MARINA based on the state-of-the-art distributed optimization algorithm MARINA. In particular, the following modifications are made to solve the problem in the black-box formulation: (i) we use approximations of the gradient instead of the true value, (ii) the difference of two approximated gradients at some coordinates is used instead of the compression operator. In this paper, a theoretical convergence analysis is provided for non-convex functions and functions satisfying the PL condition. The convergence rate of the proposed algorithm is correlated with the results for the algorithm that uses the first-order oracle. The theoretical results are validated in computational experiments to find optimal hyperparameters for the Resnet-18 neural network, that is trained on the CIFAR-10 dataset and the SVM model on the LibSVM library dataset and on the Mnist-784 dataset.

In heterogeneous computing environments, efficiently scheduling tasks, especially those forming Directed Acyclic Graphs (DAGs), is critical. This is particularly true for various Cloud and Edge computing tasks, as well as training Large Language Models (LLMs). This paper introduces a new scheduling approach using an Adaptive Neural Hyper-heuristic. By integrating a neural network trained with genetic algorithms, our method aims to minimize makespan. The approach uses a two-level algorithm: the first level prioritizes tasks using adaptive heuristic and the second level assigns resources based on the Earliest Finish Time (EFT) algorithm. Our tests show that this method significantly improves over traditional scheduling heuristics and other machine learning-based approaches. It reduces the makespan by 6.7% for small-scale DAGs and 28.49% for large-scale DAGs compared to the leading DONF algorithm. Additionally, it achieves a proximity of 84.08% to 96.43% to the optimal solutions found using Mixed-Integer Linear Programming (MILP), demonstrating its effectiveness in diverse computational settings.