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The bases of inculcating an informatic approach to neural cybernetics are the complexity of the system (in spatiotemporal domains), orderliness (alternatively randomness) associated with the system due to the presence of inevitable intra- and extracellular disturbances, degree of organization (of self-control) effected by feedback control strategies, and the entropy of the system [111].

The complexity of the neural system is decided basically by the number of units (cells), the variety of the functional events (state variables such as the energy levels), and the complexity of occurrence of such events in the time domain. An algorithmic description of the neural complexity in the informational plane should therefore include all the aforesaid considerations summarized by MacGregor [109] as beds and realizations.

Neural complexity is a generalized estimate functionally related to the number variety (composition), structure, and properties of the cellular units considered in space or time or both. The overall complexity could be nonadditive of the influences arising from the number of cellular units participating in the neural activity and their variety. For example, the excitatory neurons, the inhibiting neurons, the neurons with different threshold levels, the neurons with varying extents of synaptic inputs, etc. constitute the “variety” features indicated above. In other words, variety is an implicit attribution of diversed nature of beds and realizations constituting the items of neural informatic domain.

8.4 Informatics of Neurocybernetic Processes

The essential parameters deciding the informatic aspects of self-control functions in a neural network viewed in cybernetic perspective are:

  Complexity of neural architecture.
  Spatiotemporal randomness (disorder of the system) of neural state transitions.
  Self-organization efficiency of the interconnected cells.
  System entropy associated with the spatiotemporal neural events.

Corresponding informational analysis pertinent to the self-controlling or organizing characteristics of the neural system can be specified in terms of the following entities:

  Information processing algorithms at three stages of neural information traffic depicted in Figure 8.1
  Information utility or the value of neural information.
  Information efficiency resulting from loss of information due to intra- and/or extracellular disturbances.
  Steady and transient (dynamic) states of neural information flow.

A major function of a complex neurocybernetic system is a goal-related (dictated by an objective function), self-organizing (or self-regulating) effort viewed within a set of bounds. The associated randomness or disorderliness causes the system parameters (specified by a vector set) to veer from the system objective. The corresponding deviatory response in a neural network can be quantified by an ensemble of diversion factors pertinent to the neural environment which can be subdivided as follows:

  External (extraneural) diversion subset (due to disturbances or randomness introduced by external influences such as extracellular disturbances).
  Internal (intraneural) diversion subset (due to causes arising from internal randomness or cellular noise).

8.5 Disorganization in the Neural System

The task of self-control through adaptive feedback in the neural complex is to achieve a self-organization overcoming the influence of randomness which otherwise would promote a deviatory response from the objective or target response. The extent of disorganization so promoted can be generalized in terms of a self-organization deficiency parameter. That is, any disorganization perceived can be correlated to the randomness and the system complexity. Accordingly, the self-organization deficiency of a neural complex is defined as:

where represents the union operation in the spatiotemporal domains over instants of time, m situations (or realizations), and N cellular units (with τ, r, and W being the corresponding weights, respectively); and d(Yγ) denotes the randomness or disorderliness function associated with the γth neural unit as explained below.

Disorderliness is a measure of deviation of a selected variable, say yj, with reference to a specified standard of order, yT. Geometrically, if yT refers to the target vector pinpointing the center of a region of orderliness, around this center a quasi-ordered region can be considered wherein the orderliness is maintained within a bound constrained by a (statistical) standard deviatory limit (Figure 8.2). The disorderliness can be assessed in terms of D(yj), the distance from the center of orderliness to the boundary of the quasi-ordered region. Therefore, the disorderliness can be written as [111]:

where |yj - yT| = Qj is the magnitude of the error vector. Yj can be rendered dimensionless by normalizing it in terms of a reference (disorderliness) value. The disorganization function d(Yj) refers explicitly to the effect of disorderliness perceived at jth unit of the neural system.


Figure 8.2  Parameter spread-space and entropy-space of the neural complex
HST: Hartley-Shannon transform; INT: Inverse transform; OB: Locale of the objective function; BPS: Boundary of the quasi-order of parameter spread space; BES: Boundary of the quasi-order region of entropy space

The orderliness (or the disorderliness) of the neural system is also influenced by the system complexity Cs which as observed from the system exterior refers to the variety of the system subsets and/or microsubsets. Pertinent to the neural complex, the mixture of cells with excitatory and inhibitory states and individual synaptic (physiochemical and/or anatomical) properties considered in the spatiotemporal domains (as beds and realizations) constitute typically the universe of system complexity. Mathematically, it can be represented by:


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