We have modified a spatio-temporal neural network model of the superior colliculus proposed by the authors. Noise was added to the superior colliculus neurons, and an eye position or velocity feedback signal was used for saccade eye movement control. Also we hypothesize that the output of the superior colliculus inhibits the pause neuron in the brainstem in order to generate saccade eye movements. In simulations our modified model succeeded in replicating accurate saccades of a variety of sizes. Simulation results and the model's relation to neurophysiological findings were discussed.

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This paper describes a phenotype genetic operation for determining the structure and connection weights for neural networks. This technique defines the network as a two-dimensional chromosome, performs crossover using two-dimensional substructures, and application of genetic operation to both determining the network structure and training the connection weights. Using problems which partially involve Exclusive-OR logic, or training data that is partly dynamically changing, the proposed method is shown to be more effective than the standard genetic algorithms with one-point, two-point, or uniform crossover in the synthesis of neural networks that have two-dimensional building blocks.

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One of the differences between the regression models using the function representation of 3-layered neural network and the traditional linear regression models is whether the nonlinear parameters associated with the basis functions exist or not, where these parameters play a role of varying the form of the basis so as to minimize the square error. In this study, we gave attention to this feature and defined the regression model using the function representation with step-type discrete variable basis. Then we obtained the bounds of the asymptotic expectations of the least square error and the prediction square error with respect to the sample distribution using the extreme value theory. These results will provide an effective approach to the statistical properties of 3-layered neural network.

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The Hodgkin-Huxley equations (Hodgkin & Huxley 1952) are a neuron model describing electrical excitation of the squid giant axon membrane. By examining the global bifurcation structure of these equations, we found a degenerate Hopf bifurcation point. Several stable periodic orbits coexist in the neighborhood of this point. We determined parameter ranges where such multistability occurs and delimited regions where either two stable periodic solutions, or two stable periodic solutions and a stable equilibrium point coexist. We argue that comparison between the global bifurcation structure experimental data provides insight into the domain of validity of the Hodgkin-Huxley equations.

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