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8.14 Dynamic State of Neural Organization

As indicated in Section 8.10, the neuronal informational flow has distinct dynamic characterizations dictated by synaptic delays and cellular disturbances. The consequence of this is a devaluation of the pragmatic values of the information content. The dynamic state of informational flow portrays the dynamic degradation of self-regulating performance of the neural complex assessed via disorganization parameters in terms of the devalued information parameters.

The neural complex is essentially a self-regulating automaton which maintains its stability without assistance from the control system. Opening the control loop in such systems causes goal-related disorganization to increase within, however, certain bounds.

Intra- and/or extracellular disturbances cause the vector y in the spread space ΩS to deviate from the system objective. Such diversions in the information plane refer to the spatial transient diversions. On opening the control-loop in a goal-seeking self-controlling system, the corresponding disorganization can be described symbolically as:

where Ro is a subset of the quasi-ordered region of ΩS and represents the well-ordered region or the region at which the goal is totally attained in the spread space, and CY is the constant as defined in Equation (8.5).

When the control-loop is closed, there is a net steady-state control information vis-a-vis disorganization OD. They are related by:

To let should converge , the control information. That is, an information invariance occurs when actions of the information processor and implicit organizational activities balance against each other so that the vector y converges to the objective locale. By the same token, there may be information invariance in each stage of information processing. Thus, information invariance is a relative indicator of the extent of the objective been achieved.

Considering the dynamic state of the neural system, the control information and the corresponding state of disorganization OD(t), the transient (time-varying) information state of the system can be written as:

The conditions for the invariancy of this disorganization control information under the dynamic state which stipulate the convergence towards the objective function cannot, however, be ascertained explicitly without approximations.

8.15 Concluding Remarks

The parallel theme of cybernetics and informatics as posed in this chapter is a coordinated approach in seeking a set of avenues to model the information processing in the neural complex via entropy of disorganization and semiotic considerations. In this endeavor, it is strived to provide relevant conceptual and mathematical foundations of the physical process involved supplemented by the host of definitions and terminologies of various quantifiable terms which dictate the neural functions in the informatic plane. The concepts of cybernetics are matched with functioning of the neural complex through the general principles of information theory. This admixture of analysis could possibly lead to the passage of viewing higher order, composite neural networks (interacting networks) which (unlike the simple interacting networks) are more involved at organizational and operational levels calling for new strategies of neural information handling.

The informatic structure of neural assembly is complex. It has hierarchical relationships between and within the control centers. The neural channels, in general, handle huge informational flows. There is an explicit dependence of neural information and the attainment of the objective function. In fact, the processing involved in the realization of the target (objective function) specifies the sematic and pragmatic aspects of the data proliferating across the network of neural cells. The neural information base with its hierarchical structure of control and goal has a system-wide domain enclosing memory locales and control centers with distinct functions warranting specific algorithmic executions. The relevant characteristics of information handled pertain to disorganization in the (mal)functioning of the neural complex with regard to its objective function. Such a disorganization, in general, is a dynamic (time-dependent) entity.

A neurocybernetic system attempts to self-regulate despite of it being informatically starved. That is, more often a neural complex is (self) controlled under conditions of incomplete information. This is due to the fact that a massive system like the neural assembly is only partly observable and controllable (by the C3I protocol), and consequently partly cognizable and predictable towards self-regulation (or in achieving the objective function). The variety features dictated by the extremely complex structure, composition and properties of the neural units and the limited time of operation involved (or available) in the control endeavor are responsible for the incomplete acquisition of the neural information. Nevertheless, analysis of the neurocybernetic system in the informatic plane permits a singular entity (namely, the entropy) to depict the functioning of the neural complex system (both in terms of memory considerations as well as control information processing) and provides a framework for alternative analytical strategies to study the neural complex.


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