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39
InformationTheoretic Analysis of Neural Coding
 J. Comp. Neuroscience
, 1998
"... We describe an approach to analyzing single and multiunit (ensemble) discharge patterns based on informationtheoretic distance measures and on empirical theories derived from work in universal signal processing. In this approach, we quantify the difference between response patterns, be they tim ..."
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Cited by 58 (13 self)
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We describe an approach to analyzing single and multiunit (ensemble) discharge patterns based on informationtheoretic distance measures and on empirical theories derived from work in universal signal processing. In this approach, we quantify the difference between response patterns, be they timevarying or not, using informationtheoretic distance measures. We apply these techniques to single and multiple unit processing of sound amplitude and sound location. These examples illustrate that neurons can simultaneously represent at least two kinds of information with different levels of fidelity. The fidelity can persist through a transient and a subsequent steadystate response, indicating that it is possible for an evolving neural code to represent information with constant fidelity. 1 Johnson et al. Analysis of Neural Coding 1 Introduction Neural coding has been classified into two broadly defined types: rate codes the average rate of spike discharge and timing codes the t...
Noise in IntegrateandFire Neurons: From Stochastic Input to Escape Rates
 TO APPEAR IN NEURAL COMPUTATION.
, 1999
"... We analyze the effect of noise in integrateandfire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for timedependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard funct ..."
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Cited by 41 (6 self)
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We analyze the effect of noise in integrateandfire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for timedependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard function that has a Gaussian dependence upon the distance between the (noisefree) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.
A Method for Selecting the Bin Size of a Time Histogram
, 2007
"... The time histogram method is the most basic tool for capturing a timedependent rate of neuronal spikes. Generally in the neurophysiological literature, the bin size that critically determines the goodness of the fit of the time histogram to the underlying spike rate has been subjectively selected by ..."
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Cited by 24 (3 self)
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The time histogram method is the most basic tool for capturing a timedependent rate of neuronal spikes. Generally in the neurophysiological literature, the bin size that critically determines the goodness of the fit of the time histogram to the underlying spike rate has been subjectively selected by individual researchers. Here, we propose a method for objectively selecting the bin size from the spike count statistics alone, so that the resulting bar or line graph time histogram best represents the unknown underlying spike rate. For a small number of spike sequences generated from a modestly fluctuating rate, the optimal bin size may diverge, indicating that any time histogram is likely to capture a spurious rate. Given a paucity of data, the method presented here can nevertheless suggest how many experimental trials should be added in order to obtain a meaningful timedependent histogram with the required accuracy.
Trialtotrial variability and its effect on timevarying dependence between two neurons
 J. Neurophysiology
, 2005
"... The joint peristimulus time histogram (JPSTH) and crosscorrelogram provide a visual representation of correlated activity for a pair of neurons, and the way this activity may increase or decrease over time. In a companion paper (Cai et al. 2004a) we showed how a Bootstrap evaluation of the peaks in ..."
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Cited by 14 (7 self)
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The joint peristimulus time histogram (JPSTH) and crosscorrelogram provide a visual representation of correlated activity for a pair of neurons, and the way this activity may increase or decrease over time. In a companion paper (Cai et al. 2004a) we showed how a Bootstrap evaluation of the peaks in the smoothed diagonals of the JPSTH may be used to establish the likely validity of apparent timevarying correlation. As noted by Brody (1999a,b) and BenShaul et al. (2001), trialtotrial variation can confound correlation and synchrony effects. In this paper we elaborate on that observation, and present a method of estimating the timedependent trialtotrial variation in spike trains that may exceed the natural variation displayed by Poisson and nonPoisson point processes. The statistical problem is somewhat subtle because relatively few spikes per trial are available for estimating a firingrate function that fluctuates over time. The method developed here uses principal components of the trialtotrial variability in firing rate functions to obtain a small number of parameters (typically two or three) that characterize the deviation of each trial’s firing rate function from the acrosstrial average firing rate, represented by the
Power Spectra of Random Spike Fields & Related Processes
 Journal of Applied Probability
, 2003
"... This paper presents general methods for obtaining power spectra of a large class of signals and random fields driven by an underlying point processes, in particular spatial shot noises with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectrum, a ..."
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Cited by 11 (4 self)
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This paper presents general methods for obtaining power spectra of a large class of signals and random fields driven by an underlying point processes, in particular spatial shot noises with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectrum, and signals or fields sampled at random times or points, where again the sampling point process is quite general. The formulas obtained clearly show the interaction between the underlying counting process, the sampled process or the impulse response. We also obtain the Bartlett spectrum for the general linear Hawkes spatial branching point process with random fertility rate and general immigrant process described by its Bartlett spectrum. Finally we obtain the Cramr spectrum of general spatial birth and death processes.
Statistical assessment of timevarying dependency between two neurons
 J Neurophysiol
, 2005
"... The joint peristimulus time histogram (JPSTH) provides a visual representation of the dynamics of correlated activity for a pair of neurons. There are many ways to adjust the JPSTH for the timevarying firingrate modulation of each neuron, and then to define a suitable measure of timevarying corre ..."
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Cited by 11 (3 self)
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The joint peristimulus time histogram (JPSTH) provides a visual representation of the dynamics of correlated activity for a pair of neurons. There are many ways to adjust the JPSTH for the timevarying firingrate modulation of each neuron, and then to define a suitable measure of timevarying correlated activity. Our approach is to introduce a statistical model for the timevarying joint spiking activity so that the joint firing rate can be estimated more efficiently. We have applied an adaptive smoothing method, which has been shown to be effective in capturing sudden changes in firing rate, to the ratio of joint firing probability to the probability of firing predicted by independence. A Bootstrap procedure, applicable to both Poisson and nonPoisson data, was used to define a statistical significance test of whether a large ratio could be due to chance alone. A numerical simulation showed that the Bootstrapbased significance test has very nearly the correct rejection probability, and can have markedly better power to detect departures from independence than does an approach based on testing contiguous bins in the JPSTH. In a companion paper (Cai et al. 2004b) we show how this formulation can accommodate latency and timevarying excitability effects, which can confound spike timing effects.
Testing for and Estimating Latency Effects for Poisson and NonPoisson Spike Trains
, 2004
"... Determining the variations in response latency of one or several neurons to a stimulus is of interest in different contexts. Two common problems concern correlating latency with a particular behavior, for example, the reaction time to a stimulus, and adjusting tools for detecting synchronization bet ..."
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Cited by 10 (6 self)
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Determining the variations in response latency of one or several neurons to a stimulus is of interest in different contexts. Two common problems concern correlating latency with a particular behavior, for example, the reaction time to a stimulus, and adjusting tools for detecting synchronization between two neurons. We use two such problems to illustrate the latency testing and estimation methods developed in this article. Our test for latencies is a formal statistical test that produces a pvalue. It is applicable for Poisson and nonPoisson spike trains via use of the bootstrap. Our estimation method is model free, it is fast and easy to implement, and its performance compares favorably to other methods currently available.
Optimal Stimulus Coding by Neural Populations using Rate Codes
 J COMPUT NEUROSCI
, 2002
"... We create a framework based on Fisher information for determining the most effective population coding scheme for representing a continuousvalued stimulus attribute over its entire range. Using this scheme, we derive optimal single and multineuron rate codes for homogeneous populations using se ..."
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Cited by 8 (3 self)
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We create a framework based on Fisher information for determining the most effective population coding scheme for representing a continuousvalued stimulus attribute over its entire range. Using this scheme, we derive optimal single and multineuron rate codes for homogeneous populations using several statistical models frequently used to describe neural data. We show that each neuron's discharge rate should increase quadratically with the stimulus and that statistically independent neural outputs provides optimal coding. Only cooperative populations can achieve this condition in an informationally effective way.
Estimating Instantaneous Irregularity of Neuronal Firing
, 2009
"... Cortical neurons in vivo had been regarded as Poisson spike generators that convey no information other than the rate of random firing. Recently, using a metric for analyzing local variation of interspike intervals, researchers have found that individual neurons express specific patterns in generati ..."
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Cited by 7 (4 self)
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Cortical neurons in vivo had been regarded as Poisson spike generators that convey no information other than the rate of random firing. Recently, using a metric for analyzing local variation of interspike intervals, researchers have found that individual neurons express specific patterns in generating spikes, which may symbolically be termed regular, random, or bursty, rather invariantly in time. In order to study the dynamics of firing patterns in greater detail, we propose here a Bayesian method for estimating firing irregularity and the firing rate simultaneously for a given spike sequence, and we implement an algorithm that may render the empirical Bayesian estimation practicable for data comprising a large number of spikes. Application of this method to electrophysiological data revealed a subtle correlation between the degree of firing irregularity and the firing rate for individual neurons. Irregularity of firing did not deviate greatly around the low degree of dependence on the firing rate and remained practically unchanged for individual neurons in the cortical areas V1 and MT, whereas it fluctuated greatly in the lateral geniculate nucleus of the thalamus. This indicates the presence and absence of autocontrolling mechanisms for maintaining patterns of firing in the cortex and thalamus, respectively.