Graeme Clark Collection
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ItemSynchronization of the neural response to noisy periodic synaptic input( 1999)The relationship between the timing of the synaptic inputs and the output spikes of leaky integrate and fire neurons with noisy periodic synaptic input is addressed using the recently developed integrated-input technique. The conditional output spike density in response to noisy periodic input is evaluated as a function of the initial phase of the inputs. This enables the phase transition matrix to be calculated, which relates the phase at which the output spike is generated to the initial phase of the inputs. The interspike interval histogram and the period histogram for the neural response to ongoing periodic input are then evaluated by using the leading eigenvector of this phase transition matrix. The dependence of the synchronization index of the neural response upon the number and amplitude of synaptic inputs, the membrane time constant, the average rate of inputs and their frequency of modulation is examined.
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ItemPeak-Splitting in the Response of the Leaky Integrate-and-Fire Neuron Model to Low-Frequency Periodic Inputs(Monash University Press, 2001)
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ItemModelling the response of neurons to auditory stimuli: differences between acoustical and electrical stimulation( 1999)There are significant differences in the responses of auditory nerves when they are stimulated acoustically (normal hearing situation) or electrically (with a cochlear implant). This paper addresses the underlying causes of these differences by studying the interspike interval histogram, the synchronization index, and the entrainment (degree of response to successive cycles of the stimulus). The new integrated-input technique is used to analyze the response to periodic synaptic input of integrate-and-fire neurons, in which the randomly arriving synaptic inputs are summed and an action potential is generated when the postsynaptic potential reaches threshold. The synaptic inputs in the model are a sinusoidally modulated inhomogeneous Poisson process, and each input generates a postsynaptic response that subsequently decays according to the membrane decay constant. The results provide a quantitative understanding of both the decrease of the synchronization index with increasing frequency of acoustical stimulation in the auditory pathway and the previously observed enhancement of synchronization in globular bushy cells of the cochlear nucleus. The differences in the responses of neurons in higher stages of the auditory pathway for acoustical and electrical stimulation may be accounted for by the differences in the degree of entrainment that they induce.
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ItemNew method for anlayzing the synchronization of synaptic input and spike output in neural systems( 1998)We present a new technique for analyzing the probability distribution of output spikes for the integrate and fire model. Using this method we investigate models with arbitrary synaptic response functions and the results, which are compared with numerical simulations, are exact in the limit of a large number of small amplitude inputs. We apply this method to the synchronization problem, in which the relationship between the spread in arrival times of the inputs (the temporal jitter of the synaptic input) and the resultant spread in the times at which the output spikes are generated (output jitter) is analyzed. The results indicate that the ratio of the output jitter to the input jitter is consistently less than one and that it decreases for increasing numbers of inputs, in agreement with earlier studies. We identify the variation in the spike generating thresholds of the neurons and the variation in the number of active inputs as being important factors that determine the timing jitter in layered networks, in addition to those identified previously.