Stochastic neural field model: multiple firing events and correlations

Li, Yao; Xu, Hui

doi:10.1007/s00285-019-01389-6

Cited by 7 publications

(16 citation statements)

References 31 publications

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“…We first present in detail our methods on a small, homogeneous network of 100 neurons (75 excitatory and 25 inhibitory), exhibiting gamma frequency oscillations. Inspired by Li et al ( 2019 ) and Li and Xu ( 2019 ), to achieve dimensional reduction, we assume that the spiking activities during gamma oscillations and their temporally organization are mainly governed by one simple variable, namely, which sub-threshold neurons are only a few postsynaptic spikes from firing. Thus, in terms of dynamical dimensions, the number of network states is drastically reduced (although still too large for any meaningful analytical work, since 2 n is astronomical even for n = 100).…”

Section: Introductionmentioning

confidence: 99%

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

Cai

Tao

et al. 2021

Front. Comput. Neurosci.

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Gamma frequency oscillations (25–140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong non-linearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and apply it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from nearly homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

Cai

Tao

et al. 2021

Front. Comput. Neurosci.

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“…The following assumptions are made in order to describe the neuronal activity of this population by a mathematically tractable Markov process. Note that the first three assumptions are identical to those in our earlier papers [16,18] • The membrane potential of a neuron takes finitely many discrete values.…”

Section: Structured Spiking Neural Network Modelmentioning

confidence: 88%

“…Both the configuration of neurons and the rule of interactions among neurons are simplified to make the model mathematically and computationally tractable. It was shown in [16] and [18] that this model is still able to produce a rich dynamics of spiking patterns. In particular, this model can produce multiple firing events (MFEs), which is a partially synchronized spiking activities that have been observed in other more realistic models [24,25,4,3].…”

Section: Introductionmentioning

confidence: 99%

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Entropy, mutual information, and systematic measures of structured spiking neural networks

2019

Preprint

Self Cite

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The aim of this paper is to investigate various information-theoretic measures, including entropy, mutual information, and some systematic measures that based on mutual information, for a class of structured spiking neuronal network. In order to analyze and compute these information-theoretic measures for large networks, we coarse-grained the data by ignoring the order of spikes that fall into the same small time bin. The resultant coarse-grained entropy mainly capture the information contained in the rhythm produced by a local population of the network. We first proved that these information theoretical measures are welldefined and computable by proving the stochastic stability and the law of large numbers. Then we use three neuronal network examples, from simple to complex, to investigate these information-theoretic measures. Several analytical and computational results about properties of these information-theoretic measures are given.

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“…We first present in detail our methods on a small, homogeneous network of 100 neurons (75 excitatory and 25 inhibitory), exhibiting gamma frequency oscillations. Inspired by [43,44], to achieve dimensional reduction, we assume that the spiking activities during gamma oscillations and their temporally organization are mainly governed by one simple variable, namely, which sub-threshold neurons are only a few postsynaptic spikes from firing. Thus, in terms of dynamical dimensions, the number of network states is drasticaly reduced (although still too large for any meaningful analytical work, since 2 n is astronomical even for n = 100).…”

Section: Introductionmentioning

confidence: 99%

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

Cai¹,

Wu²,

Tao³

et al. 2021

Preprint

View full text Add to dashboard Cite

Gamma frequency oscillations , observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong nonlinearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and apply it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from nearly homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.

show abstract

Stochastic neural field model: multiple firing events and correlations

Cited by 7 publications

References 31 publications

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

Entropy, mutual information, and systematic measures of structured spiking neural networks

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

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