Doklady Mathematics最新文献

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.

This paper presents the development and evaluation of methods for detecting cyberattacks on industrial systems using neural network approaches. The focus is on the task of detecting anomalies in multivariate time series, where the diversity and complexity of potential attack scenarios require the use of advanced models. To address these challenges, a transformer-based autoencoder architecture was used, which was further enhanced by transitioning to a variational autoencoder (VAE) and integrating normalizing flows. These modifications allowed the model to better capture the data distribution, enabling effective anomaly detection, including those not present in the training set. As a result, high performance was achieved, with an F1 score of 0.93 and a ROC-AUC of 0.87. The results underscore the effectiveness of the proposed methodology and provide valuable contributions to the field of anomaly detection and cybersecurity in industrial systems.

Handwritten character recognition (HCR) is a challenging problem for machine learning researchers. Unlike printed text data, handwritten character datasets have more variation due to human-introduced bias. With numerous unique character classes present, some data, such as Logographic Scripts or Sino-Korean character sequences, bring new complications to the HCR problem. The classification task on such datasets requires the model to learn high-complexity details of the images that share similar features. With recent advances in computational resource availability and further computer vision theory development, some research teams have effectively addressed the arising challenges. Although known for achieving high accuracy while keeping the number of parameters small, many common approaches are still not generalizable and use dataset-specific solutions to achieve better results. Due to complex structure, existing methods frequently prevent the solutions from gaining popularity. This paper proposes a highly scalable approach for detailed character image classification by introducing the model architecture, data preprocessing steps, and testing design instructions. We also perform experiments to compare the performance of our method with that of existing ones to show the improvements achieved.

In this paper, we present a novel methodology we call MDS-ViTNet (Multi Decoder Saliency by Vision Transformer Network) for enhancing visual saliency prediction or eye-tracking. This approach holds significant potential for diverse fields, including marketing, medicine, robotics, and retail. We propose a network architecture that leverages the Vision Transformer, moving beyond the conventional ImageNet backbone. The framework adopts an encoder-decoder structure, with the encoder utilizing a Swin transformer to efficiently embed most important features. This process involves a Transfer Learning method, wherein layers from the Vision Transformer are converted by the Encoder Transformer and seamlessly integrated into a CNN Decoder. This methodology ensures minimal information loss from the original input image. The decoder employs a multi-decoding technique, utilizing dual decoders to generate two distinct attention maps. These maps are subsequently combined into a singular output via an additional CNN model. Our trained model MDS-ViTNet achieves state-of-the-art results across several benchmarks. Committed to fostering further collaboration, we intend to make our code, models, and datasets accessible to the public.

Coronary arterial dominance classification is essential for SYNTAX score estimation, which is a tool used to determine the complexity of coronary artery disease and guide patient selection toward optimal revascularization strategy. We developed coronary dominance classification algorithm based on the analysis of right coronary artery (RCA) angiograms using neural network.

We employed convolutional neural network ConvNext and Swin transformer for 2D image (frames) classification, along with a majority vote for cardio angiographic view classification. An auxiliary network was also used to detect irrelevant images which were then excluded from the data set.

5-fold cross validation gave the following dominance classification metrics (p = 95%): macro recall = 93.1% ± 4.3%, accuracy = 93.5% ± 3.8%, macro F1 = 89.2% ± 5.6%. The most common case in which the model regularly failed was RCA occlusion, as it requires utilization of left coronary artery (LCA) information.

The use of machine learning approaches to classify coronary dominance based on RCA alone has been shown to be successful with satisfactory accuracy. However, for higher accuracy, it is necessary to utilize LCA information in the case of an occluded RCA and detect cases where there is high uncertainty.