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In this paper, it is considered linear discrete control and pursuit game problems. Control vectors are subjected to total constraints those are a discrete analogue of the integral constraints. Necessary and sufficient conditions of solvability of the 0-controllability problem are obtained. The connection between 0-controllability and solvability of the pursuit problem is studied.

Tumor clustering is a powerful approach for cancer class discovery which is crucial to the effective treatment of cancer. Many traditional clustering methods such as NMF-based models, have been widely used to identify tumors. However, they cannot achieve satisfactory results. Recently, subspace clustering approaches have been proposed to improve the performance by dividing the original space into multiple low-dimensional subspaces. Among them, low rank representation is becoming a popular approach to attain subspace clustering. In this paper, we propose a novel Low Rank Subspace Clustering model via Discrete Constraint and Hypergraph Regularization (DHLRS). The proposed method learns the cluster indicators directly by using discrete constraint, which makes the clustering task simple. For each subspace, we adopt Schatten $p$ -norm to better approximate the low rank constraint. Moreover, Hypergraph Regularization is adopted to infer the complex relationship between genes and intrinsic geometrical structure of gene expression data in each subspace. Finally, the molecular pattern of tumor gene expression data sets is discovered according to the optimized cluster indicators. Experiments on both synthetic data and real tumor gene expression data sets prove the effectiveness of proposed DHLRS. [ABSTRACT FROM AUTHOR]

The method overcomes local optima pitfalls in discrete structural optimizations. First-phase ESO fast eliminates ineffective sections from initial design spaces. Smaller swarm populations are constructed on the reducing sets of section domains. Second-phase processes a comprehensive learning PSO to minimize the design weight. This enhances a standard PSO for the cooperative responses among swarm populations. This paper proposes the novel two-phase metaheuristic method that combines the distinctive features provided by evolutionary structural optimization (ESO) and comprehensive learning particle swarm optimization (CLPSO) for the design of steel structures with standard sections. The approach overcomes the challenges associated with local optima pitfalls in processing the mixed integer nonlinear programming problem, and hence determines the accurate solutions at modest computing efforts. In essence, the first-phase ESO design incorporates the constraint relaxations to fast eliminate the ineffective (infeasible) sections from initial discrete variable domains. This advantageously provides a significant reduction in the search spaces performed in the second-phase CLPSO scheme. The comprehensive learning technique enhances a standard particle swarm optimization algorithm by enabling the cooperative responses among swarm populations. The learning probability function defines the comprehensive cross-positions between the sets of best particles constructed from the reducing sets of steel sections specified in the preliminary ESO phase leading to the computation of optimal solutions. Various benchmarks (subjected to infinite design combinations) illustrate robustness and accuracy of the proposed design method (viz., generating the smaller number of particles) as compared to conventional metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

• A graph matching method based on fast normalized cut and multiplicative update mapping is proposed. • The discrete constraint is incorporated into the optimization step and the multiplicative update algorithm is utilized in the mapping process. • Both synthetic points and real-world images comparisons with the state-of-the-art methods validate the effectiveness of the proposed method. Point correspondence is a fundamental problem in pattern recognition and computer vision, which can be tackled by graph matching. Since graph matching is basically an NP-complete problem, some approximate methods are proposed to solve it. Continuous relaxation offers an effective approximate method for graph matching problem. However, the discrete constraint is not taken into consideration in the optimization step. In this paper, a fast normalized cut based graph matching method is proposed, where the discrete constraint is introduced into the optimization step. Specifically, first a semidefinite positive affinity matrix based form objective function is constructed by introducing a regularization term which is related to the discrete constraint. Then the fast normalized cut algorithm is utilized to find the continuous solution. Last, the discrete solution of graph matching is obtained by a multiplicative update algorithm. Experiments on both synthetic points and real-world images validate the effectiveness of the proposed method by comparing it with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]