%0 Journal Article
%T Results on a Binding Neuron Model and Their Implications for Modified Hourglass Model for Neuronal Network
%A Viswanathan Arunachalam
%A Raha Akhavan-Tabatabaei
%A Cristina Lopez
%J Computational and Mathematical Methods in Medicine
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/374878
%X The classical models of single neuron like Hodgkin-Huxley point neuron or leaky integrate and fire neuron assume the influence of postsynaptic potentials to last till the neuron fires. Vidybida (2008) in a refreshing departure has proposed models for binding neurons in which the trace of an input is remembered only for a finite fixed period of time after which it is forgotten. The binding neurons conform to the behaviour of real neurons and are applicable in constructing fast recurrent networks for computer modeling. This paper develops explicitly several useful results for a binding neuron like the firing time distribution and other statistical characteristics. We also discuss the applicability of the developed results in constructing a modified hourglass network model in which there are interconnected neurons with excitatory as well as inhibitory inputs. Limited simulation results of the hourglass network are presented. 1. Introduction Several mathematical models of neurons have been developed so that the model neurons mimic biological neurons in various abstract biological features that make these neurons suitable for information processing. In this regard, models of temporal integrator, coincidence detector, and leaky integrate and fire (LIF) of the neuron are computed using the level crossing of the membrane potential. The leak of the membrane potential is at best accommodated using LIF models. However, for the problem of the level crossing of the LIF neuron with instant or curved boundaries, no closed form solution is available and this value can only be computed using numerical methods. Furthermore, the LIF models do not take into account the frequency of the inputs, thereby assuming that the membrane potential integrates the inputs, however large is the interval between them. But it has been observed that during the processing of sensory signals the spiking statistics of individual neurons changes substantially when the signal travels from periphery to more central areas. This aspect lends credence to the point of view of information condensation and supports the theory of finite lifetime of input signals. Inspired by the findings of numerical simulation of Hodgkin-Huxley [1] neurons as well as LIF models [2], Vidybida [3] proposed models of binding neurons with instantaneous feedback. These are model neurons which mimic real neurons in many biophysical mechanisms. In a binding neuron, any input impulse is stored for a fixed time period after which it is lost forever. When the number of stored inputs crosses a fixed threshold , the neuron sends
%U http://www.hindawi.com/journals/cmmm/2013/374878/