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NEUROENERGETIC CONCEPT OF INTELLIGENCE

3 Optimal spike generation frequency

The spike in the neuron is a probabilistic event: excitability of neuron l 0=1/P0 corresponds to the probability of a single spike appearance per unit of time. Besides q, excitability l 0 depends on other factors, and they together may cause l 0>>1, that turns neuron into the threshold element. Conditions of generation can be conveniently considered on the plot of dependence of the neuron's dynamic threshold Pd on time t , passed from the last spike instant. Dependence Pd(t ) is well known in neurophysiology and is shown in fig.2.

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Pd varies in broad limits on a very small time interval, during which the values of other factors, influencing the neuron's excitability, practically do not vary. Therefore, the second and succeeding spikes in the series of spikes may be considered as threshold events. The spike takes place at the fulfillment of condition

W ³ P0+Ps+Pd ,

where W is the excitation potential, that is the result of the spatio-temporal summation of influences on the neuron from excitatory and inhibitory links, and Ps is the static threshold, which accounts for the influence of preceding spikes. If potential W is equal to small value W1, then after the first random spike the neuron will begin to generate spikes with the time interval t 1, i.e., will generate at low frequency (LF) 1/t 1 in the exaltation phase. At the great potential value W2 the neuron will generate at high frequency (HF) 1/t 2 in the phase of deep refractoriness. Since every spike decreases neuron's age q , the variation of t will vary an energetic cost for decrease of q . We have shown earlier, that there is a certain optimal time topt, which provides a minimal energetic cost. Parameters of the model can be selected by such a way, that topt would situate in the region of deep refractoriness; this creates conditions for the self-organization of the automaton: the most natural and easy generation mode in the exaltation phase is energetically unprofitable, while the neuron cannot itself reach the frequency of generation uopt=1/topt and therefore must interact with other neurons. The tendency to generate at optimal frequency is provided by the optimal learning rule [2]. The key idea of this rule is expressed by formula

D r i j=ui(uopt-uj),

where r i j is the conductivity of an excitatory link from i-th to j-th neuron.

It is important for the completeness of the concept, that besides generation at uopt the neuron has another energetically profitable working mode: random spikes with intervals, much greater than time te, which corresponds to the minimum of Pd.

 




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Last updated: July 05, 1998