Probability of neuronal spike initiation was considered within the framework of a simple stochastic model. The time of spike occurrence was defined as the first time of crossing of a stochastic process and a determined time function. This problem has been investigated in the case of a stationary Gaussian stochastic process and a linear time function. An integral equation obtained for the probability density function of the first time crossing was numerically solved by means of computer calculations. The model was applied to the analysis of temporal pattern of spike activity evoked in the cat spinal motoneurones by depolarizing current injected through the recording microelectrode.
We propose a domain model of a neural network, in which individual spin-neurons are joined into larger-scale aggregates, the so-called domains. The updating rule in the domain model is defined by analogy with the usual spin dynamics: if the state of a domain in an inhomogeneous local field is unstable, then it flips, in the opposite case its state undergoes no changes. The number of stable states of the domain network grows linearly with the domain's size k , where k is the number of spins in the domain. We show that the proposed model is effective for optimization problems, since the use of domain dynamics lowers the number of calculations in 2k times and allows one to find deeper minima than the standard Hopfield model does.
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