The Effect of a Refractory Period on the Power Spectrum of Neuronal Discharge

The interspike intervals in steady-state neuron firing are assumed to be independently and identically distributed random variables. In the simplest model discussed, each interval is assumed to be the sum of a random neuron refractory period and a statistically independent interval due to a stationary external process, whose statistics are assumed known. The power spectral density (hence the autocorrelation) of the composite neuron-firing renewal process is derived from the known spectrum of the external process and from the unknown spectrum of the neuron-refraction process. The results are applied to spike trains recorded in a previous study [2] of single neurons in the visual cortex of an awake monkey. Two models are demonstrated that may produce peaks in the power spectrum near 40 Hz

Temporal Precision of Spike Trains in Extrastriate Cortex of the Behaving Macaque Monkey

How reliably do action potentials in cortical neurons encode information about a visual stimulus? Most physiological studies do not weigh the occurrences of particular action potentials as significant but treat them only as reflections of average neuronal excitation. We report that single neurons recorded in a previous study by Newsome et al. (1989; see also Britten et al. 1992) from cortical area MT in the behaving monkey respond to dynamic and unpredictable motion stimuli with a markedly reproducible temporal modulation that is precise to a few milliseconds. This temporal modulation is stimulus dependent, being present for highly dynamic random motion but absent when the stimulus translates rigidly

Real-time motion detection using an analog VLSI zero-crossing chip

The authors have designed and tested a one-dimensional 64 pixel, analog CMOS VLSI chip which localizes intensity edges in real-time. This device exploits on-chip photoreceptors and the natural filtering properties of resistive networks to implement a scheme similar to and motivated by the Difference of Gaussians (DOG) operator proposed by Marr and Hildreth (1980). The chip computes the zero-crossings associated with the difference of two exponential weighting functions and reports only those zero-crossings at which the derivative is above an adjustable threshold. A real-time motion detection system based on the zero- crossing chip and a conventional microprocessor provides linear velocity output over two orders of magnitude of light intensity and target velocity

Real-time motion detection using an analog VLSI zero-crossing chip

The authors have designed and tested a one-dimensional 64 pixel, analog CMOS VLSI chip which localizes intensity edges in real-time. This device exploits on-chip photoreceptors and the natural filtering properties of resistive networks to implement a scheme similar to and motivated by the Difference of Gaussians (DOG) operator proposed by Marr and Hildreth (1980). The chip computes the zero-crossings associated with the difference of two exponential weighting functions and reports only those zero-crossings at which the derivative is above an adjustable threshold. A real-time motion detection system based on the zero- crossing chip and a conventional microprocessor provides linear velocity output over two orders of magnitude of light intensity and target velocity

Power spectrum analysis of bursting cells in area MT in the behaving monkey

It is widely held that visual cortical neurons encode information primarily in their mean firing rates. Some proposals, however, emphasize the information potentially available in the temporal structure of spike trains (Optican and Richmond, 1987; Bialek et al., 1991), in particular with respect to stimulus-related synchronized oscillations in the 30–70 Hz range (Eckhorn et al., 1988; Gray et al., 1989; Kreiter and Singer, 1992) as well as via bursting cells (Cattaneo et al., 1981a; Bonds, 1992). We investigate the temporal fine structure of spike trains recorded in extrastriate area MT of the trained macaque monkey, a region that plays a major role in processing motion information. The data were recorded while the monkey performed a near- threshold direction discrimination task so that both physiological and psychophysical data could be obtained on the same set of trials (Britten et al., 1992). We identify bursting cells and quantify their properties, in particular in relation to the behavior of the animal. We compute the power spectrum and the distribution of interspike intervals (ISIs) associated with individual spike trains from 212 cells, averaging these quantities across similar trials. (1) About 33% of the cells have a relatively flat power spectrum with a dip at low temporal frequencies. We analytically derive the power spectrum of a Poisson process with refractory period and show that it matches the observed spectrum of these cells. (2) About 62% of the cells have a peak in the 20–60 Hz frequency band. In about 10% of all cells, this peak is at least twice the height of its base. The presence of such a peak strongly correlates with a tendency of the cell to respond in bursts, that is, two to four spikes within 2–8 msec. For 93% of cells, the shape of the power spectrum did not change dramatically with stimulus conditions. (3) Both the ISI distribution and the power spectrum of the vast majority of bursting cells are compatible with the notion that these cells fire Poisson-distributed bursts, with a burst-related refractory period. Thus, for our stimulus conditions, no explicitly oscillating neuronal process is required to yield a peak in the power spectrum. (4) We found no statistically significant relationship between the peak in the power spectrum and psychophysical measures of the monkeys' performance on the direction discrimination task

Modeling Shape Representation in Area V4

Our model builds on a convolutional-style neural network with hierarchical stages representing processing steps in the ventral visual pathway. It was designed to capture the translation-invariance and shape-selectivity of neurons in area V4. The model uses biologically plausible linear filters at the front end, normalization and sigmoidal nonlinear activation functions. The max() function is used to generate translation invariance

Correlated Neuronal Response: Time Scales and Mechanisms

We have analyzed the relationship between correlated spike count and the peak in the cross-correlation of spike trains for pairs of simultaneously recorded neurons from a previous study of area MT in the macaque monkey (Zohary et al., 1994). We conclude that common input, responsible for creating peaks on the order of ten milliseconds wide in the spike train cross-correlograms (CCGs), is also responsible for creating the correlation in spike count observed at the two second time scale of the trial. We argue that both common excitation and inhibition may play significant roles in establishing this correlation

Computing motion using analog VLSI vision chips: An experimental comparison among different approaches

We have designed, built and tested a number of analog CMOS VLSI circuits for computing 1-D motion from the time-varying intensity values provided by an array of on-chip phototransistors. We present experimental data for two such circuits and discuss their relative performance. One circuit approximates the correlation model while a second chip uses resistive grids to compute zero-crossings to be tracked over time by a separate digital processor. Both circuits integrate image acquisition with image processing functions and compute velocity in real time. For comparison, we also describe the performance of a simple motion algorithm using off-the-shelf digital components. We conclude that analog circuits implementing various correlation-like motion algorithms are more robust than our previous analog circuits implementing gradient-like motion algorithms

Numerical Solution of Differential Equations by the Parker-Sochacki Method

A tutorial is presented which demonstrates the theory and usage of the Parker-Sochacki method of numerically solving systems of differential equations. Solutions are demonstrated for the case of projectile motion in air, and for the classical Newtonian N-body problem with mutual gravitational attraction.Comment: Added in July 2010: This tutorial has been posted since 1998 on a university web site, but has now been cited and praised in one or more refereed journals. I am therefore submitting it to the Cornell arXiv so that it may be read in response to its citations. See "Spiking neural network simulation: numerical integration with the Parker-Sochacki method:" J. Comput Neurosci, Robert D. Stewart & Wyeth Bair and http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378