Population rate codes carried by mean, fluctuation and synchrony of neuronal firings

Hasegawa, Hideo

doi:10.1016/j.physa.2008.10.033

Cited by 8 publications

(10 citation statements)

References 65 publications

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“…To estimate the network's statistics, we used the Augmented Moment Method (AMM) (24,25) that approximates deterministic dynamical equations for statistical moments of network activity (Methods and SI Methods). This reduces the number of variables and allows for parameter exploration that, otherwise, is unpractical as moments estimation would require many simulations of the entire stochastic system.…”

Section: Tuning Of the Noise Correlations Of Neurons With Similar Dirmentioning

confidence: 99%

“…We used the AMM (24,25) to express the system of stochastic differential Eqs. 1-3 in terms of means-that is, μ m ðtÞ = R m ðtÞ = N −1 P i r m i ðtÞ; variances-that is, γ m ðtÞ = N −1 P i ½r m i ðtÞ − μ m ðtÞ 2 ; and covariances of network activity-that is, ρ mn ðtÞ = N −2 P i P j ½r m i ðtÞ − μ m ðtÞ ½r n j ðtÞ − μ n ðtÞ .…”

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confidence: 99%

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Stimulus-dependent variability and noise correlations in cortical MT neurons

Ponce‐Alvarez

Thiele

Albright

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

124

152

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Population codes assume that neural systems represent sensory inputs through the firing rates of populations of differently tuned neurons. However, trial-by-trial variability and noise correlations are known to affect the information capacity of neural codes. Although recent studies have shown that stimulus presentation reduces both variability and rate correlations with respect to their spontaneous level, possibly improving the encoding accuracy, whether these second order statistics are tuned is unknown. If so, second-order statistics could themselves carry information, rather than being invariably detrimental. Here we show that rate variability and noise correlation vary systematically with stimulus direction in directionally selective middle temporal (MT) neurons, leading to characteristic tuning curves. We show that such tuning emerges in a stochastic recurrent network, for a set of connectivity parameters that overlaps with a single-state scenario and multistability. Information theoretic analysis shows that second-order statistics carry information that can improve the accuracy of the population code.C ortical activity is highly variable during spontaneous activity (1-4) and even when tested under constant experimental conditions (5-8). This variability is thought to limit the capacity of individual neurons to transmit information (9). Furthermore, variability is often correlated among neurons, and thus, it cannot be completely removed by averaging the population response (9-12). Recent experimental studies have examined the secondorder statistics of neural responses across a variety of species, cortical areas, tasks, and stimulus and/or attentional conditions (13-17). In particular, it has been shown that the Fano factor (FF)-that is, the ratio between the variance of the spike counts over trials and its mean-is reduced when a stimulus is applied (16), thus improving the encoding of the stimulus. Importantly, both preferred and nonpreferred stimuli reduced the FF. In addition, the evoked noise correlation-that is, the trial-to-trial covariance of stimulus induced activity between two simultaneously recorded neurons-is also reduced upon stimulus presentation (18), after stimulus adaptation (19) or perceptual learning (20), and under attention (14, 21), an effect that could, under certain conditions, lead to more reliable estimates of the mean population activity (22). Hence, there is a growing body of evidence suggesting that the encoding of a signal through cortical activity may be improved by minimizing both trialby-trial variability and noise correlations. However, it remains an open experimental and theoretical question, whether these statistics are themselves tuned to different stimulus features, an aspect that may be overlooked when only analyzing preferred and nonpreferred stimuli.Here, we examined the statistics of responses of area-middle temporal (MT) neurons in awake, fixating primates, to moving gratings and different plaid patterns of different directions, as well as moving gratings of differ...

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Section: Tuning Of the Noise Correlations Of Neurons With Similar Dirmentioning

confidence: 99%

mentioning

confidence: 99%

Stimulus-dependent variability and noise correlations in cortical MT neurons

Ponce‐Alvarez

Thiele

Albright

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

124

152

View full text Add to dashboard Cite

show abstract

“…The point (iii) shows that if input information is carried by synchrony within the population code hypothesis [50,51], its decoding accuracy may be improved either by small or large correlation, independently of q [the point (v)]. Our calculation concerns the long-standing controversy on a role of the synchrony in neuronal ensembles [5]- [12].…”

Section: Discussionmentioning

confidence: 99%

“…The calculated GFI is expected to provide us with a clear insight to the controversy on a role of the spatial correlation discussed above. Quite recently, we have pointed out the possibility that input information to neuronal ensembles may be carried not only by mean but also by variance and/or correlation in firing rate within the population code hypothesis [50,51]. The inverse of the calculated GFI matrix expresses an accuracy of decoding when input information is carried by such population codes.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Fisher information matrix in nonextensive systems with spatial correlation

Hasegawa

2009

Phys. Rev. E

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By using the q-Gaussian distribution derived by the maximum entropy method for spatiallycorrelated N -unit nonextensive systems, we have calculated the generalized Fisher information matrix of g θnθm for (θ 1 , θ 2 , θ 3 ) = (µ q , σ 2 q , s), where µ q , σ 2 q and s denote the mean, variance and degree of spatial correlation, respectively, for a given entropic index q. It has been shown from the Cramér-Rao theorem that (1) an accuracy of an unbiased estimate of µ q is improved (degraded)by a negative (positive) correlation s, (2) that of σ 2 q is worsen with increasing s, and (3) that of s is much improved for s ≃ −1/(N − 1) or s ≃ 1.0 though it is worst at s = (N − 2)/2(N − 1). Our calculation provides a clear insight to the long-standing controversy whether the spatial correlation is beneficial or detrimental to decoding in neuronal ensembles. We discuss also a calculation of the q-Gaussian distribution, applying the superstatistics to the Langevin model subjected to spatiallycorrelated inputs.

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Finite volume and asymptotic methods for stochastic neuron models with correlated inputs

Rosenbaum

Marpeau

et al. 2011

J. Math. Biol.

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We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting from the refractory period and firing threshold. We propose a finite volume method that is orders of magnitude faster than the Monte Carlo methods traditionally used to model such systems. The resulting numerical approximations are proved to be accurate, nonnegative and integrate to 1. We also approximate the transient evolution of the system using an Ornstein-Uhlenbeck process, and use the result to examine the properties of the joint output of cell pairs. The results suggests that the joint output of a cell pair is most sensitive to changes in input variance, and less sensitive to changes in input mean and correlation.

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Population rate codes carried by mean, fluctuation and synchrony of neuronal firings

Cited by 8 publications

References 65 publications

Stimulus-dependent variability and noise correlations in cortical MT neurons

Stimulus-dependent variability and noise correlations in cortical MT neurons

Generalized Fisher information matrix in nonextensive systems with spatial correlation

Finite volume and asymptotic methods for stochastic neuron models with correlated inputs

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