Absolute exponential stability of recurrent neural networks with generalized activation function.

In this paper, the recurrent neural networks (RNNs) with a generalized activation function class is proposed. In this proposed model, every component of the neuron's activation function belongs to a convex hull which is bounded by two odd symmetric piecewise linear functions that are convex or concave over the real space. All of the convex hulls are composed of generalized activation function classes. The novel activation function class is not only with a more flexible and more specific description of the activation functions than other function classes but it also generalizes some traditional activation function classes. The absolute exponential stability (AEST) of the RNN with a generalized activation function class is studied through three steps. The first step is to demonstrate the global exponential stability (GES) of the equilibrium point of original RNN with a generalized activation function being equivalent to that of RNN under all vertex functions of convex hull. The second step transforms the RNN under every vertex activation function into neural networks under an array of saturated linear activation functions. Because the GES of the equilibrium point of three systems are equivalent, the next stability analysis focuses on the GES of the equilibrium point of RNN system under an array of saturated linear activation functions. The last step is to study both the existence of equilibrium point and the GES of the RNN under saturated linear activation functions using the theory of M-matrix. In the end, a two-neuron RNN with a generalized activation function is constructed to show the effectiveness of our results.

[Proteomic analysis of differentially expressed proteins in human hepatoma SMMC-7721 cells induced by Fufang Banmao capsule serum].

OBJECTIVE: To investigate the effects of Fufang Banmao capusle on the proteome of SMMC-7721 cells and discover potential molecular mechanism of anti-cancer at molecular level. METHOD: SMMC-7721 cells were treated by Fufang Banmao capusle serum prepared with serum pharmacological method; proteomic protocol involving 2-DE, image analysis and mass spectrometry were used to detect the proteins in cells influenced by Fufang Banmao capusle. RESULT: Approximately 450 protein spots in SMMC-7721 cells were resolved and detected in 2-D gel maps from pH3-10L IEF. 47 protein plots varied over 2-fold quantitively between treated sample and control sample were uncovered. 13 differentially expressed proteins spots were further identified by MALDI-TOF-MS analysis and four of them were successfully identified. Annexin A5, heatshock 70 x 10(3) protein 8 was significantly up-regulated in treated sample compared with control sample, while Eukaryotic translation initiation factor 5A and Peroxiredoxin-2 was significantly down-regulated in treated sample. CONCLUSION: 4 differently expressed proteins associated with the proliferation, apoptosis, immunity of tumor were detected and they might provide clues for the coming research. The protocol of proteomics combined with serum pharmacological method is an effective platform to research complicated formulas in that it is capable of laying out many proteins associated with Fufang Banmao capusle.

A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems.

In this paper, we consider the H/sub 2/ sampled-data control for uncertain linear systems by the impulse response interpretation of the H/sub 2/ norm. Two H/sub 2/ measures for sampled-data systems are considered. The robust optimal control procedures subject to these two H/sub 2/ criteria are proposed. The development is primarily concerned with a multirate treatment in which a periodic time-varying robust optimal control for uncertain linear systems is presented. To facilitate multirate control design, a new result of stability of hybrid system is established. Moreover, the single-rate case is also obtained as a special case. The sampling period is explicitly involved in the result which is superior to traditional methods. The solution procedures proposed in this paper are formulated as an optimization problem subject to linear matrix inequalities. Finally, we present a numerical example to demonstrate the proposed techniques.