Integrate-and-Fire Neuronal Model With Correlated Stochastic Inputs

Although single neuron models with random inputs have been widely studied in theory and experiment, most such studies are done under the assumption that inputs are Poisson processes. Because spike trains which neuron fire and receive are commoly renewal processes. The assumption is a very rough approximation of physiological data. We will consider the case of renewal process inputs, which represents a more accurate approximation of synaptic inputs.In this paper, the issue how to approximate the integrate-and-fire(IF) with renewal inputs is studied, The effects of correlation between renewal process synaptic inputs are examined and the correlation relationship between two point processes is studied. A series of new results are obtained.Chapter 1 introduces the background of the problem-researching , the recent development of the neuron model and some research results we have obtained in this field.Chapter 2 focuses on the issue how to approximate the integrate-and-fire model with stochastic renewal inputs, two novel approximation schemes are proposed.Chapter 3 concerns the effect low correlation between renewal process synaptic inputs impacts on the output of the integrate-and-fire model. For low positive correlations, mean firing time is a decreasing function of input correlation . For low negative correlations, mean firing time is almost independent of input correlation.Chapter 4 concerns the correlation relationship between two point processes. We conclude: when the point process is Poisson, a single cofficient is enough to descibe the correlation relationship. However, for renewal processes, The correlation cofficient is a increasing function of time binsize. So we introduce the correlation coefficient curve to characterize the correlation relationship.Chapter 5 discusses optimally decoding the inputs of integrate-and-fire neuron model with correlated inputs. Using the Fisher information,we theoretically solve the issue: what is the rate(r) between inhibitory and exicitatory inputs so that the neuron can most accurately decode input rate. Besides, we argue that correlation input in general reduces the accutacy. The conclusions should be useful for the design of neural networks.