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8.8 Continuous Neural EntropyReverting back to the situation wherein the subjective and objective targets merge, the spread space can be quantized into subspaces at the target center concentrically as shown in Figure 8.4 with a quantizing extent of spread space equal to δ.
Equation (8.20) predicts that in the limiting (continuous) case, Suppose the vector yi in the spread-space has an equal probability of occurrence at all subspaces Δyir measured from the target by the same distance | yir - yT| = Qir. Then, for δ → 0, the probability of finding the vector yir in the rth annular space can be written as: satisfying the total probability condition that: The corresponding position entropy is defined in a continuous form as: with 0 ≤ Q ≤ Qmax and Q = 0 elsewhere. The above expression is again identical to Shannon's entropy and represents the continuous version of Equation (8.13) with δ → 0. It can also be related functionally to Shannon's entropy 8.9 Differential Disorganization in the Neural ComplexThe difference in entropies at two locations, namely, The information or entropy pertinent to the disorganized ith locale can be specified either by an associated a priori probability of attaining the goal pai so that 8.10 Dynamic Characteristics of Neural InformaticsThe stochastical aspects of a neural complex are invariably dynamic rather than time-invariant. Due to the presence of intra- or extracellular disturbances, the associated information in the neural system may degrade with time; and proliferation of information across the network may also become obsolete or nonpragmatic due to the existence of synaptic delays or processing delays across the interconnections. That is, aging of neural information (or degenerative negentropy ) leads to a devalued (or value-weighted) knowledge with a reduced utility. The degeneration of neural information can be depicted in a simple form by an exponential decay function, namely: where Another form of degradation perceived in neural information pertains to the delays encountered. Suppose the control-loop error information is delayed when it arrives at the controlling section; it is of no pragmatic value as it will not reflect the true neural output state because the global state of the neural complex would have changed considerably by then. In other words, the delayed neural information is rather devalued of its usefullness (or attains nonpragmatic value) at the receiving node, though the input and output contents of syntactic information remained the same. In either case of information degradation, the value of information (devalued for different reasons) can be specified as The information aging and/or enhancement can occur when the neural dynamics goes through a nonaging or nonenhancement (quiescent) period. This quiescent period corresponds to the refractory effects in the neurocellular response. The property of neural information dynamics can be described by appropriate informational transfer functions. Depicting the time-dependency of information function as The loss of neuronal information due to degradation can be specified by an informational efficiency which is defined as: where
Copyright © CRC Press LLC
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