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More intriguingly, the interaction of the neurons (in the statistical sample space) corresponds vastly to the complicated dynamic interactions perceived in molecular or atomic ensembles. Therefore, an offshoot research on neuronal assembly had emerged historically to identify and correlate on a one-to-one basis the collective response of neurons against the physical characteristics of interacting molecules and/or atoms. In other words, the concepts of classical and statistical mechanics; the associated principles of thermodynamics; and the global functions such as the Lagrangian, the Hamiltonian, the total entropy, the action, and the entropy have also become the theoretical tools in the science of neural activity and neural networks. Thus from the times of Wiener [9], Gabor [10], and Griffith [11-14] to the current date, a host of publications has appeared in the relevant literature; however, there are many incomplete strategies in the formulations, several unexplained idealizations, and a few analogies with inconsistencies in the global modeling of neural activities vis-a-vis stochastical considerations associated with the interaction physics. Within the framework of depicting the neural assembly as a system of interconnected cells, the activities associated with the neurons can be viewed, in general, as a collective stochastical process characterized by a random proliferation of state transitions across the interconnected units. Whether the pertinent modeling of neuronal interaction(s) evolved (conventionally) as analogous to interacting magnetic spins is totally justifiable (if not what is the alternative approach) the question of considering the probabilistic progression of neuronal state by an analogy of momentum flow (in line with particle dynamics) or as being represented by an analog model of wave function, the stochastical modeling of noise-perturbed neural dynamics and informatic aspects considered in the entropy plane of neurocybernetics are the newer perspectives which can be viewed in an exploratory angle through statistical mechanics and cybernetic considerations. A streamline of relevant bases are as follows:
1.3 Neurocybernetic ConceptsModern information processing systems are neuromimetic and becoming more and more sophisticated as their functional capabilities are directed to emulate the diversified activities of complex neural systems. Naturally, the more we urge the functions of information processing systems to follow the complexities of the inner structure enclaved by the neural system, it becomes rather infeasible to realize a tangible representation of such information processing systems to mimic closely the neuronal activities. Hence, it calls for a shift of emphasis to project qualitatively a new viewpoint, in which the main aim is to investigate the control (and self-control) aspects of the neuronal system so as to develop information processing units emulating the image of the neural systems intact, probably with all its structural subtlety and complex control and communication protocols. The aforesaid emphasis could be realized by adopting the concept of universal nature for control of organizing a complex system (by lowering its entropy) by means of standard procedures. This approach was advocated by Wiener [9] as the method of cybernetics, which is thenceforth known as the science of the control and communication in complex systems, be they machines or living organisms. The cybernetic basis for modeling the neural complex is logical in that the neural structure and its activity are inherently stochastic; and the neuronal information and/or communication processing represents an activity that fights the associated randomness, thus emphasizing the idea of a control counteracting disorganization and destruction caused by (any) diverse random factors. The neural complex represents an entity wherein every activity is related essentially to the collection, conversion, transmission storage and retrieval of information. It represents a system in a state which allows certain functions to be carried out. It is the state normal, corresponding to a set of external conditions in which the system operates. Should these conditions change suddenly, the system departs from the normal state and the new conditions set forth correspond to a new normal state. The system then begs to be transferred to this new state. In the neural complex, this is achieved first by acquiring information on the new state, and second by ascertaining how the transition of the system to the new state can be carried out. Since the change in the neuronal environment is invariably random, neither the new normal state nor how to organize a transition to it is known a priori. The neural complex, therefore, advocates a random search. That is, the system randomly changes its parameters until it (randomly) matches the new normal state. Eventually, this matching is self-recognized as the system monitors its own behavior. Thus, the process of random search generates the information needed to transfer the system to the new normal state. This is an information-selection protocol with the criterion to change the system behavior approaching a new normal state, wherein the system settles down and functions normally a condition known as homeostasis.
Copyright © CRC Press LLC
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