Periodic Solution for a Complex-valued Network Model with Discrete Delay

For a tridiagonal two-layer real six-neuron model, the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature. In the present paper, we extend this two-layer real six-neuron network model into a complex-valued delayed network model. Based on the mathematical analysis method, some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts. Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method. Computer simulation is provided to illustrate the correctness of the theoretical results

Bifurcation Analysis and Spatiotemporal Patterns of Nonlinear Oscillations in a Ring Lattice of Identical Neurons with Delayed Coupling

We investigate the dynamics of a delayed neural network model consisting of n identical neurons. We first analyze stability of the zero solution and then study the effect of time delay on the dynamics of the system. We also investigate the steady state bifurcations and their stability. The direction and stability of the Hopf bifurcation and the pitchfork bifurcation are analyzed by using the derived normal forms on center manifolds. Then, the spatiotemporal patterns of bifurcating periodic solutions are investigated by using the symmetric bifurcation theory, Lie group theory and S1-equivariant degree theory. Finally, two neural network models with four or seven neurons are used to verify our theoretical results

Reprogramming fibroblasts to neural-stem-like cells by structured overexpression of pallial patterning genes

In this study, we assayed the capability of four genes implicated in embryonic specification of the cortico-cerebral field, Foxg1, Pax6, Emx2 and Lhx2, to reprogramm mouse embryonic fibroblasts toward neural identities. Lentivirus-mediated, TetON-dependent overexpression of Pax6 and Foxg1 transgenes specifically activated the neural stem cell (NSC) reporter Sox1-EGFP in a substantial fraction of engineered cells. The efficiency of this process was enhanced up to ten times by simultaneous inactivation of Trp53 and co-administration of a specific drug mix inhibiting HDACs, H3K27-HMTase and H3K4m2-demethylase. Remarkably, a fraction of the reprogrammed population expressed other NSC markers and retained its new identity, even upon transgenes switching off. When transferred into a pro-differentiative environment, Pax6/Foxg1-overexpressing cells activated the neuronal marker Tau-EGFP. Frequency of Tau-EGFP cells was almost doubled upon delayed delivery of Emx2 and Lhx2 transgenes. A further improvement of the neuron-like cells output was achieved by tonic inhibition of BMP and TGFb pathways. These Tau-EGFP cells showed a negative resting potential and displayed active electric responses, following injection of depolarizing currents

Theory and applications of artificial neural networks

In this thesis some fundamental theoretical problems about artificial neural networks and their application in communication and control systems are discussed. We consider the convergence properties of the Back-Propagation algorithm which is widely used for training of artificial neural networks, and two stepsize variation techniques are proposed to accelerate convergence. Simulation results demonstrate significant improvement over conventional Back-Propagation algorithms. We also discuss the relationship between generalization performance of artificial neural networks and their structure and representation strategy. It is shown that the structure of the network which represent a priori knowledge of the environment has a strong influence on generalization performance. A Theorem about the number of hidden units and the capacity of self-association MLP (Multi-Layer Perceptron) type network is also given in the thesis. In the application part of the thesis, we discuss the feasibility of using artificial neural networks for nonlinear system identification. Some advantages and disadvantages of this approach are analyzed. The thesis continues with a study of artificial neural networks applied to communication channel equalization and the problem of call access control in broadband ATM (Asynchronous Transfer Mode) communication networks. A final chapter provides overall conclusions and suggestions for further work