Boundedness and global exponential stability for generalized Cohen-Grossberg neural networks with variable delay
A generalized Halanay inequality is established, and the boundedness of generalized Cohen–Grossberg neural networks is investigated. By applying the generalized Halanay inequality and Lyapunov functional method, new sufficient conditions are obtained ensuring the global exponential stability of the solution of the generalized Cohen–Grossberg neural networks with variable delay. Three examples are also given for illustration.

title: Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-Varying Delays and Continuously Distributed Delays
abstract: In this paper, we investigate the global exponential stability for a class of Cohen-Grossberg neural networks (CGNN) with time-varying delays and continuously distributed delays. CGNN herein is a general neural networks model which includes some well-known neural networks as its special cases. Firstly, applying the homeomorphism theory, we establish the new sufficient condition of existence and uniqueness of the equilibrium point to CGNN. Then, the sufficient criteria of global exponential stability of CGNN, which are easy to verify, are given by M-matrix. Our results imply and generalize some existed ones in previous literature. Furthermore, it is convenient to estimate the exponential convergence rates of the neural networks by using the criteria. Compared with the previous methods, our method does not resort to any Lyapunov functions or functionals. Finally, a example is given to illustrate the effective of our results.

title: Improved Results on Solving Quadratic Programming Problems with Delayed Neural Network
abstract: In this paper, in terms of a linear matrix inequality (LMI), using a delayed Lagrangian network to solve quadratic programming problems, sufficient conditions on delay-dependent and delay-independent are given to guarantee the globally exponential stability of the delayed neural network at the optimal solution. In addition, exponential convergence rate is estimated by the equation in the paper. Furthermore, the results in this paper improved the ones reported in the existing literatures and the proposed sufficient condition can be checked easily by solving LMI. Two simulation examples are provided to show the effectiveness of the approach and applicability of the proposed criteria.

title: Asymptotic behavior of stochastic Cohen-Grossberg neural networks with variable delays
abstract: Using Chebyshev inequality and nonnegative semi-martingale convergence theorem, the paper investigates asymptotic behavior of stochastic Cohen-Grossberg neural networks with delay by constructing suitable Lyapunov functional. Algebraic criteria are given for stochastic ultimate bounded and almost exponential stability. The result in the paper extend the main conclusion. In the end, examples are given to verify the effective of our results.

title: Stochastic High-Order Hopfield Neural Networks
abstract: In 1984 Hopfield showed that the time evolution of a symmetric Hopfield neural networks are a motion in state space that seeks out minima in the energy function (i.e., equilibrium point set of Hopfield neural networks). Because high-order Hopfield neural networks have more extensive applications than Hopfield neural networks, and have been discussed on the convergence of the networks. In practice, a neural network is often subject to environmental noise. It is therefore useful and interesting to find out whether the high-order neural network system still approacher some limit set under stochastic perturbation. In this paper, we will give a number of useful bounds for the noise intensity under which the stochastic high-order neural network will approach its limit set. Our result cancels the requirement of symmetry of the connection weight matrix and includes the classic result on Hopfield neural networks, which is a special case of stochastic high-order Hopfield neural networks. In the end, A example is given to verify the effective of our results.

title: A Generalized LMI-Based Approach to the Global Exponential Stability of Recurrent Neural Networks with Delay
abstract: A new theoretical result on the global exponential stability of recurrent neural networks with delay is presented. It should be noted that the activation functions of recurrent neural network do not require to be bounded. The presented criterion, which has the attractive feature of possessing the structure of linear matrix inequality (LMI), is a generalization and improvement over some previous criteria. A example is given to illustrate our results.

title: Convergence of iterative algorithms for image reconstruction
abstract: We introduce a general iterative scheme for image reconstruction based on Landweber's method. Within our configuration, the block-iterative (BI) version can be formulated from its simultaneous version easily, and vice versa. This provides the mechanism to formulate new algorithms from known algorithms. It can be shown that some of the widely used iterative algorithms, such as the ART, SART, Cimmino's Algorithm and recently designed DWE and CAV, are special examples of the general scheme or its BI version. By applying the convergence results of the general scheme, the corresponding convergence in the consistent or inconsistent cases, for the block-iterative or simultaneous versions, of those specific algorithms can be established under mild conditions on the relaxation parameters.

title: The Hamiltonicity of Directed sigma - tao Cayley Graphs (or: A Tale of Backtracking)
abstract: Let τ be the 2-cycle (1 2) and σ the n-cycle (12 … n). These two cycles generate the symmetric group Sn. Let Gn denote the directed Cayley graph Cay(τ, σ: Sn). Based on erroneous computer calculations, Nijenhuis and Wilf (1975, p. 238; 1978, p. 288) give as an exercise to show that G5 does not have a Hamiltonian path. To the contrary, we show that G5 is Hamiltonian. Furthermore, we show that G6 has a Hamilton path. Our results illustrate how a little theory and some good luck can save a lot of time in backtracking searches.

title: A simple technique for estimating message lengths for additive noise steganography
abstract: We propose a practical steganalysis method to detect hidden information and estimate embedding rate. By modelling steganographic embedding as an additive noise process, we exploit the fact that the mean and variance of stegosignal is a function of embedding rate. This can be used to estimate the embedding rate without knowledge of the original cover object. We present simulation results to demonstrate that the proposed method can estimate embedding rate with reasonable accuracy. The technique we propose is general and can be used for steganalysis of images, video, and audio etc.

title: Determining the hamilton-connectedness of certain vertex-transitive graphs
abstract: Faber and Moore have proposed a class of vertex-transitive digraphs as a model of directed inconnection networks. These networks have attractive degree versus diameter properties. We show that these digraphs are Hamiltonian and provide necessary and sufficient conditions for the existence of a Hamilton path between any two vertices. Particular cases of these digraphs are the right rotation Cayley digraphs Cay ( X n : S n where X n is the set of right rotations (1 2 s i −1 i) for i=2,3,…,n . Another class of vertex-transitive graphs that have been proposed as models of inconnection networks are the arrangement graphs introduced by Day and Tripathi. They have the same vertex set as the Faber–Moore digraphs. We prove that arrangement graphs are Hamilton-connected.

title: Soft-Information Assisted Near-Optimum Nonlinear Detection for BLAST-type Space Division Multiplexing OFDM Systems
abstract: In this contribution, a nonlinear hybrid detection scheme based on a novel soft-information assisted genetic algorithm (GA) is proposed for a turbo convolutional (TC) coded space division multiplexing (SDM) aided orthogonal frequency division multiplexing (OFDM) system. Our numerical results show that the performance of the currently known GA-assisted system can be improved by about 2 dB with the aid of the GA's population-based soft solution, approaching the optimum performance of the soft-information assisted maximum likelihood (ML) detection, while exhibiting a lower complexity, especially in high-throughput scenarios. Furthermore, the proposed scheme is capable of achieving a good performance even in the so-called overloaded systems, where the number of transmit antennas is higher than the number of receiver antennas