Stochastical aspects of neuronal activity, neural networks, and communication

By revisiting the popular framework of depicting neuronal (collective) activities as analogous to Ising's spin-glass theory of interacting magnetic spins, the contradictions that coexist with such an analogy are extracted and discussed. To alleviate such contradictions, an alternative strategy of equating the neuronal interactions to the partially anisotropic nematic phase of disorder pertaining to liquid crystals is proposed. Hence, the extent of anisotropy in the neuronal system, quantified in terms of an order-function, is specified to elucidate the nonlinear squashing action of the input-output relations in a neuronal cell. The relevant approach thereof, is based on Langevin's theory considerations as applied to dipole molecules. Further, in view of the stochastical properties due to the inherent disorder associated with the neuronal assembly, the progression of state-transitions across the interconnected cells is modeled as a momentum flow relevant to particle dynamics. Hence, corresponding wave mechanics attributions of such a collective movement of state-transition activity are described in terms of a probabilistic wave function. Lastly, the stochastical aspects of noise-perturbed neuronal dynamics are studied via Fokker-Planck equation representing the Langevin-type relaxational (nonlinear) process associated with the neuronal states. On each of these topics portraying the stochastical characteristics of the neuronal assembly and its activities, newer and/or more exploratory inferences are made, logical conclusions are enumerated and relevant discussions are presented along with the scope for future research to be pursued.