Mathematical study on coding and ergodicity in a model brain

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In most electrophysiological experiments, it is often the case that experimenters present the same stimulation repeatedly and investigates trial average of activities of one or a few neurons. One important research topic to understain the brain function mechanism from such experiments is the "physiological ergodicity problem", which pursues conditions that "trial average of a single neuron" and "ensemble average of the responses of neurons to a single input" are equivalent. In this research, we analyzed the spatio-temporal spike coding and the ergodicity with mathematical models.First, we analysed dynamics of network that models the cerebral cortex, to clarify nonlinear interactions of the neurons, which influence the reproducibility of neuronal responses. As a result, we should that the firing sequence is highly reproducible in cases of shorter internal memory and smaller influence of internal connections than external inputs. In addition, we studied dynamics of the cluster state betw … More een synchronous and asynchronous states the connection structure of the cluster generation, and dependency to synaptic learning.Next, we investigated relations among nonlinear spatio-temporal dynamics of the neural network model, noise, network structure, and learning. Based on the STDP (Spike Timing Dependent Plasticity) learning rule and the network architecture, we clarified that coexistence of various coding and cluster formation can be self-organized when there are two or more input sources. Further, by introducing Mexican-hat type connections to Synfire-Chain models, we showed the possibility of coding the stimulus strength into the size of the activated area and the existence of two non-trivial stable states of the isolated local excitation and the uniform excitation. We also studied the relation between the small-world network structure and spatio-temporal dynamics. In addition, we examined relations between ergodicity and noise in terms of synchronous firing and possible functions of depolarizing GABA in information coding. Less