Search Results (158)

This study focuses on the formal verification of a parallel version of the minimax algorithm using the mCRL2 modeling language, applied to the game of Connect 4. The research aims to ensure that the algorithm behaves correctly in concurrent execution environments by providing a formal model and conducting rigorous verification. The parallel version of minimax distributes computations across multiple threads, with each thread evaluating different successor states concurrently. Using mCRL2, we specify the algorithm’s behavior, generate Labeled Transition Systems (LTSs), and verify critical properties such as the absence of deadlocks, liveness, and correctness of state transitions. The formal verification process demonstrates that the proposed model accurately represents the parallel minimax algorithm and ensures its reliability by verifying properties that guarantee unique and non-redundant actions throughout the execution. The findings highlight the value of formal methods in validating the correctness of parallel artificial intelligence algorithms, laying the foundation for future optimizations that focus on performance. Full article

This paper introduces a novel capped separable difference of two norms (CSDTN) method for sparse signal recovery, which generalizes the well-known minimax concave penalty (MCP) method. The CSDTN method incorporates two shape parameters and one scale parameter, with their appropriate selection being crucial for ensuring robustness and achieving superior reconstruction performance. We provide a detailed theoretical analysis of the method and propose an efficient iteratively reweighted ${\ell }_1$ (IRL1)-based algorithm for solving the corresponding optimization problem. Extensive numerical experiments, including electrocardiogram (ECG) and synthetic signal recovery tasks, demonstrate the effectiveness of the proposed CSDTN method. Our method outperforms existing methods in terms of recovery accuracy and robustness. These results highlight the potential of CSDTN in various signal-processing applications. Full article

Data-driven decision-making has become crucial across various domains. Randomization and re-randomization are standard techniques employed in controlled experiments to estimate causal effects in the presence of numerous pre-treatment covariates. This paper quantifies the worst-case mean squared error of the difference-in-means estimator as a generalized discrepancy of covariates between treatment and control groups. We demonstrate that existing randomized or re-randomized experiments utilizing Monte Carlo methods are sub-optimal in minimizing this generalized discrepancy. To address this limitation, we introduce a novel optimal deterministic experiment based on quasi-Monte Carlo techniques, which effectively minimizes the generalized discrepancy in a model-independent manner. We provide a theoretical proof indicating that the difference-in-means estimator derived from the proposed experiment converges more rapidly than those obtained from completely randomized or re-randomized experiments using Mahalanobis distance. Simulation results illustrate that the proposed experiment significantly reduces covariate imbalances and estimation uncertainties when compared to existing randomized and deterministic approaches. In summary, the proposed experiment serves as a reliable and effective framework for controlled experimentation in causal inference. Full article

We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate and the true underlying parameter value (i.e., the estimation error), whereas the second is more specifically oriented to the moments of the estimation error. The proposed bounds are relatively easy to calculate numerically (in the sense that their optimization is over relatively few auxiliary parameters), yet they turn out to be tighter (sometimes significantly so) than previously reported bounds that are associated with similar calculation efforts, across many application examples. In addition to their relative simplicity, they also have the following advantages: (i) Essentially no regularity conditions are required regarding the parametric family of distributions. (ii) The bounds are local (in a sense to be specified). (iii) The bounds provide the correct order of decay as functions of the number of observations, at least in all the examples examined. (iv) At least the first family of bounds extends straightforwardly to vector parameters. Full article

The choice of management strategy for companies operating in different sectors of the economy is of great importance for their sustainable development. In many cases, companies are in competition within the scope of the same activities, meaning that the profit of one company is at the expense of the other. The choice of strategies for each of the firms in this case can be optimized using game theory for a non-cooperative game case where the two players have antagonistic interests. The aim of this research is to develop a methodology which, in non-cooperative games, accounts for the benefits of different criteria for each of the strategies of the two participants. In this research a new integrated sequential interactive model for urban systems (SIMUS)–game theory technique for decision making in the case of non-cooperative games is proposed. The methodology includes three steps. The first step consists of a determination of the strategies of both players and the selection of criteria for their assessment. In the second step the SIMUS method for multi-criteria analysis is applied to identify the benefits of the strategies for both players according to the criteria. The model formation in game theory is drawn up in the third step. The payoff matrix of the game is formed based on the benefits obtained from the SIMUS method. The strategies of both players are solved by dual linear programming. Finally, to verify the results of the new approach we apply four criteria to make a decision—Laplace’s criterion, the minimax and maximin criteria, Savage’s criterion and Hurwitz’s criterion. The new integrated SIMUS–game theory approach is applied to a real example in the transport sector. The Bulgarian transport network is investigated regarding route and transport type selection for a carriage of containers between a starting point, Sofia, and a destination, Varna, in the case of competition between railway and road operators. Two strategies for a railway operator and three strategies for a road operator are examined. The benefits of the strategies for both operators are determined using the SIMUS method, based on seven criteria representing environmental, technological, infrastructural, economic, security and safety factors. The optimal strategies for both operators are determined using the game model and dual linear programming. It is discovered that the railway operator will apply their first strategy and that the road operator will also apply their first strategy. Both players will obtain a profit if they implement their optimal strategies. The new integrated SIMUS–game theory approach can be used in different areas of research, when the strategies for both players in non-cooperatives games need to be established. Full article

In this paper, we consider a class of fractional Schrödinger–Poisson systems ${(-\mathsf{\Delta })}^{s}u+\lambda V(x)u+\varphi u=f(u)+{|u|}^{2_s^{*}-2}u$ and ${(-\mathsf{\Delta })}^t\varphi =u^2$ in ${\mathbb{R}}^3$, where $s,t\in (0,1)$ with $2s+2t>3$, $\lambda >0$ denotes a parameter, $V:{\mathbb{R}}^3\to \mathbb{R}$ admits a potential well $\mathsf{\Omega }\triangleq \mathrm{int}{V}^{-1}(0)$ and $2_s^{*}\triangleq {\displaystyle \frac{6}{3-2s}}$ is the fractional Sobolev critical exponent. Given some reasonable assumptions as to the potential V and the nonlinearity f, with the help of a constrained manifold argument, we conclude the existence of positive ground state solutions for some sufficiently large $\lambda$. Upon relaxing the restrictions on V and f, we utilize the minimax technique to show that the system has a positive mountain-pass type by introducing some analytic tricks. Moreover, we investigate the asymptotical behavior of the obtained solutions when $\lambda \to +\infty$. Full article

New epidemics encourage the development of new mathematical models of the spread and forecasting of infectious diseases. Statistical epidemiology data are characterized by incomplete and inexact time series, which leads to an unstable and non-unique forecasting of infectious diseases. In this paper, a model of a conditional generative adversarial neural network (CGAN) for modeling and forecasting COVID-19 in St. Petersburg is constructed. It takes 20 processed historical statistics as a condition and is based on the solution of the minimax problem. The CGAN builds a short-term forecast of the number of newly diagnosed COVID-19 cases in the region for 5 days ahead. The CGAN approach allows modeling the distribution of statistical data, which allows obtaining the required amount of training data from the resulting distribution. When comparing the forecasting results with the classical differential SEIR-HCD model and a recurrent neural network with the same input parameters, it was shown that the forecast errors of all three models are in the same range. It is shown that the prediction error of the bagging model based on three models is lower than the results of each model separately. Full article

The paper presents an approach to solving the problem of unknown motion parameters Bayesian identification for the stochastic dynamic system model with randomly delayed observations. The system identification and the object tracking tasks obtain solutions in the form of recurrent Bayesian relations for a posteriori probability density. These relations are not practically applicable due to the computational challenges they present. For practical implementation, we propose a conditionally minimax nonlinear filter that implements the concept of conditionally optimal estimation. The random delays model source is the area of autonomous underwater vehicle control. The paper discusses in detail a computational experiment based on a model that is closely aligned with this practical need. The discussion includes both a description of the filter synthesis features based on the geometric interpretation of the simulated measurements and an impact analysis of the effectiveness of model special factors, such as time delays and model unknown parameters. Furthermore, the paper puts forth a novel approach to the identification problem statement, positing a random jumping change in the motion parameters values. Full article

The role of combining neoadjuvant endocrine therapy with conventional chemotherapy remains unclear; therefore, we conducted an open-label, single-center, nonrandomized phase II trial to assess the effect of this combination. Patients with previously untreated stage II or III HR-positive, HER2-negative breast cancer received concurrent letrozole 2.5 mg with standard neoadjuvant chemotherapy. The primary endpoint was pathologic complete response (pCR) at the time of surgery. We used Simon’s minimax two-stage design; a pCR rate > 6% was necessary at the first stage to continue. Between November 2017 and November 2020, 53 women were enrolled in the first stage of the trial. Their median age was 49 years (range, 33–63), and 60% of them were premenopausal. Subsequently, 66% and 34% of patients with clinical stages II and III, respectively, were included; 93% had clinically node-positive disease. Two patients (4%) achieved pCR after neoadjuvant chemo–endocrine treatment, which did not satisfy the criteria for continuing to the second stage. The overall response rate was 83%. During the median follow-up of 53.7 months, the 3-year disease-free survival and overall survival rates were 87% and 98%, respectively. Neutropenia was the most common grade 3/4 adverse event (40%), but rarely led to febrile neutropenic episodes (4%). Myalgia (32%), nausea (19%), constipation (17%), heartburn (11%), oral mucositis (9%), and sensory neuropathy (9%) were frequently observed, but classified as grade 1 or 2. No deaths occurred during preoperative treatment. The addition of letrozole to standard neoadjuvant chemotherapy was safe and beneficial in terms of overall response rate, but did not provide a higher pCR rate in locally advanced HR-positive, HER2-negative breast cancer. Further research is needed to enhance neoadjuvant treatment strategies for this cancer subtype. Full article

In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of generalized convex functions. Additionally, we formulate a dual problem to the primal one and examine duality relations between them. In our results, by using the obtained results, we obtain necessary and sufficient optimality conditions for a class of robust fractional multi-objective optimization problems. Full article

The optimization problems in a fluid catalytic cracking process with dynamic constraints and conflicting objectives are challenging due to the complicated constraints and dynamic environments. The decision variables need to be reoptimized to obtain the best objectives when dynamic environments arise. To solve these problems, we established a mathematical model and proposed a dynamic constrained multiobjective optimization evolution algorithm for the fluid catalytic cracking process. In this algorithm, we design an offspring generation strategy based on minimax solutions, which can explore more feasible regions and converge quickly. Additionally, a dynamic response strategy based on population feasibility is proposed to improve the feasible and infeasible solutions by different perturbations, respectively. To verify the effectiveness of the algorithm, we test the algorithm on ten instances based on the hypervolume metric. Experimental results show that the proposed algorithm is highly competitive with several state-of-the-art competitors. Full article

With the advent of large-scale data, the demand for information is increasing, which makes signal sampling technology and digital processing methods particularly important. The utilization of 1-bit compressive sensing in sparse recovery has garnered significant attention due to its cost-effectiveness in hardware implementation and storage. In this paper, we first leverage the minimax concave penalty equipped with the least squares to recover a high-dimensional true signal $\mathbf{x}\in {\mathbb{R}}^p$ with k-sparse from n-dimensional 1-bit measurements and discuss the regularization by combing the nonconvex sparsity-inducing penalties. Moreover, we give an analysis of the complexity of the method with minimax concave penalty in certain conditions and derive the general theory for the model equipped with the family of sparsity-inducing nonconvex functions. Then, our approach employs a data-driven Newton-type method with stagewise steps to solve the proposed method. Numerical experiments on the synthesized and real data verify the competitiveness of the proposed method. Full article

To solve the problem of aperture fill time (AFT) for wideband sparse arrays, variable fractional delay (VFD) FIR filters are applied to eliminate linear coupling between spatial and time domains. However, the large dimensions of the filter coefficient matrix result in high system complexity. To alleviate the computational burden of solving VFD filter coefficients, a novel multi–regultion minimax (MRMM) model utilizing the sparse representation technique has been presented. The error function is constrained by the introduction of L2–norm and L1–norm regularizations within the minimax criterion. The L2–norm effectively resolves the problems of overfitting and non–unique solutions that arise in the sparse optimization of traditional minimax (MM) models. Meanwhile, the use of multiple L1–norms enables the optimal design of the smallest sub–filter number and order of the VFD filter. To solve the established nonconvex model, an improved sequential–alternating direction method of multipliers (S–ADMM) algorithm for filter coefficients is proposed, which utilizes sequential alternation to iteratively update multiple soft–thresholding problems. The experimental results show that the optimized VFD filter reduces system complexity significantly and corrects AFT effectively in a wideband sparse array. Full article

In this paper, we apply the classical FKKM lemma to obtain the Ky Fan minimax inequality defined on nonempty non-compact convex subsets in reflexive Banach spaces, and then we apply it to game theory and obtain Nash’s existence theorem for non-compact strategy sets, which can be regarded as a new, simple but interesting application of the FKKM lemma and the Ky Fan minimax inequality, and we can also present another proof about the famous John von Neumann’s existence theorem in two-player zero-sum games. Due to the results of Li, Shi and Chang, the coerciveness in the conclusion can be replaced with the P.S. or G.P.S. conditions. Full article

Topic modeling is a widely utilized tool in text analysis. We investigate the optimal rate for estimating a topic model. Specifically, we consider a scenario with n documents, a vocabulary of size p, and document lengths at the order N. When $N\ge c·p$, referred to as the long-document case, the optimal rate is established in the literature at $\sqrt{p/\left(Nn\right)}$. However, when $N=o\left(p\right)$, referred to as the short-document case, the optimal rate remains unknown. In this paper, we first provide new entry-wise large-deviation bounds for the empirical singular vectors of a topic model. We then apply these bounds to improve the error rate of a spectral algorithm, Topic-SCORE. Finally, by comparing the improved error rate with the minimax lower bound, we conclude that the optimal rate is still $\sqrt{p/\left(Nn\right)}$ in the short-document case. Full article