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Abstract: The discrete delayed Hopfield neural networks is an extension of the discrete Hopfield neural networks. In this paper, the convergence of discrete delayed Hopfield neural networks is mainly studied, and some results on the convergence are obtained by using Lyapunov function. Several new sufficient conditions for the delayed networks converging towards a limit cycle with period at most 2 are proved in parallel updating mode. Also, some conditions for the delayed networks converging towards a limit cycle with 2-period are investigated in parallel updating mode. All results established in this paper extend the previous results on the convergence of both the discrete Hopfield neural networks, and the discrete delayed Hopfield neural networks in parallel updating mode. [Copyright &y& Elsevier]

Abstract: Employing the matrix measure approach and Lyapunov function, the author studies the global exponential stability of delayed neural networks with impulses in this paper. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses. Finally, three examples are given to show the effectiveness of the results obtained here. [Copyright &y& Elsevier]

Abstract: Minor component analysis (MCA) is an important statistical tool for signal processing and data analysis. Neural networks can be used to extract online minor component from input data. Compared with traditional algebraic approaches, a neural network method has a lower computational complexity. Stability of neural networks learning algorithms is crucial to practical applications. In this paper, we propose a stable MCA neural networks learning algorithm, which has a more satisfactory numerical stability than some existing MCA algorithms. Dynamical behaviors of the proposed algorithm are analyzed via deterministic discrete time (DDT) method and the conditions are obtained to guarantee convergence. Simulations are carried out to illustrate the theoretical results achieved. [Copyright &y& Elsevier]

Abstract: In this paper, we study simple algorithms for tracking objects in a video sequence, based on the selection of landmark points representative of the moving objects in the first frame of the sequence to be analyzed. The movement of these points is estimated using a sparse optical-flow method. Methods of this kind are fast, but they are not very robust. Particularly, they are not able to handle the occlusion of the moving objects in the video. To improve the performance of optical flow-based methods, we propose the use of adaptive filters and neural networks to predict the expected instantaneous velocities of the objects, using the predicted velocities as indicators of the performance of the tracking algorithm. The efficiency of these strategies in handling occlusion problems are tested with a set of synthetic and real video sequences. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of asymptotic synchronization for a class of neural networks with reaction-diffusion terms and time-varying delays is investigated. Using the drive-response concept, a control law is derived to achieve the state synchronization of two identical neural networks with reaction-diffusion terms. Moreover, we derive a sufficient asymptotic synchronization condition for the neural networks with reaction-diffusion terms if reaction-diffusion terms satisfy a weaker condition. The synchronization condition is easy to verify and relies on the connection matrix in the driven networks and the suitable designed controller gain matrix in the response networks. [Copyright &y& Elsevier]

This paper develops a general purpose numerical method to compute the feedback Nash equilibria in dynamic games. Players'' feedback strategies are first approximated by neural networks which are then trained online by parallel genetic algorithms to search over all time-invariant equilibrium strategies synchronously. To eliminate the dependence of training on the initial conditions of the game, the players use the same stationary feedback policies (the same networks), to repeatedly play the game from a number of initial states at any generation. The fitness of a given feedback strategy is then computed as the sum of payoffs over all initial states. The evolutionary equilibrium of the game between the genetic algorithms is the feedback Nash equilibrium of the dynamic game. An oligopoly model with investment is approximated as a numerical example. [Copyright &y& Elsevier]