Analysis of the activity of single neurons in stochastic settings (Q1115368)

Activity of single neurons in stochastic setting has been the subject matter of numerous investigations in the past two decades. The models and methods of analysis use the continuous parameter Markov chains and their properties; the memory dependence is often introduced by modelling the membrane potential as some kind of a cumulative response due to a point process of events. There is a general feeling that the continuous stochastic process describing the membrane potential is only an idealization and it may be worthwhile to model the activity of single neurons by a discrete-valued process [see for example \textit{A. Rangan} and \textit{R. E. Grace}, Selective interactions within a point process and their applications, Stochastic Anal. Appl. 4, 357-365 (1986)]. The present paper is an attempt in this direction. It is in fact a departure from the usual models of firings of single neuron systems. It uses the broad features of single neuron systems such as low firing rates of cortical neurons, the renewal nature of the firing process and the independence nature of the interactions among cortical neurons. The main results of the model are the convex nature of the relation between input-output firing rates of low values and the occurrence of firing due to synchronous convergence of the excitatories at low firing rates. The main conclusion of the paper is that the activity of the cortical neurons is more or less independent of the details of the synaptic information entering as input to the system. The reviewer feels that further research is necessary to answer the question whether Markov models can also lead to the same conclusion.