scholarly journals Sparse balance: excitatory-inhibitory networks with small bias currents and broadly distributed synaptic weights

2021 ◽  
Author(s):  
Ramin Khajeh ◽  
Francesco Fumarola ◽  
LF Abbott
Keyword(s):  
Mean Field ◽  
Field Analysis ◽  
Cortical Circuits ◽  
Recurrent Excitation ◽  
Nonlinear Responses ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Sparse Set ◽  
Balanced Networks ◽  
Inhibitory Networks

Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian statistics. In addition to simulations, we present a mean-field analysis to illustrate the properties of these networks.

scholarly journals Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part II: Applications

2013 ◽  
Vol 141 (6) ◽  
pp. 1761-1785 ◽  
Author(s):  
Thomas Sondergaard ◽  
Pierre F. J. Lermusiaux
Keyword(s):  
Gaussian Mixture Models ◽  
Mean Field ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Sudden Expansion ◽  
Test Case ◽  
Field Equations ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Orthogonal Field

Abstract The properties and capabilities of the Gaussian Mixture Model–Dynamically Orthogonal filter (GMM-DO) are assessed and exemplified by applications to two dynamical systems: 1) the double well diffusion and 2) sudden expansion flows; both of which admit far-from-Gaussian statistics. The former test case, or twin experiment, validates the use of the Expectation-Maximization (EM) algorithm and Bayesian Information Criterion with GMMs in a filtering context; the latter further exemplifies its ability to efficiently handle state vectors of nontrivial dimensionality and dynamics with jets and eddies. For each test case, qualitative and quantitative comparisons are made with contemporary filters. The sensitivity to input parameters is illustrated and discussed. Properties of the filter are examined and its estimates are described, including the equation-based and adaptive prediction of the probability densities; the evolution of the mean field, stochastic subspace modes, and stochastic coefficients; the fitting of GMMs; and the efficient and analytical Bayesian updates at assimilation times and the corresponding data impacts. The advantages of respecting nonlinear dynamics and preserving non-Gaussian statistics are brought to light. For realistic test cases admitting complex distributions and with sparse or noisy measurements, the GMM-DO filter is shown to fundamentally improve the filtering skill, outperforming simpler schemes invoking the Gaussian parametric distribution.

scholarly journals Reconciling contrast invariance and non-linear computation in cortical circuits

2021 ◽  
Author(s):  
L. Bernáez Timón ◽  
P. Ekelmans ◽  
S. Konrad ◽  
A. Nold ◽  
T. Tchumatchenko
Keyword(s):  
Synaptic Plasticity ◽  
Piriform Cortex ◽  
Mean Field ◽  
Dependent Manner ◽  
Cortical Circuits ◽  
Stimulus Contrast ◽  
Spiking Network ◽  
Network Simulations ◽  
Contrast Invariance ◽  
Balanced Networks

AbstractNetwork selectivity for orientation is invariant to changes in the stimulus contrast in the primary visual cortex. Similarly, the selectivity for odor identity is invariant to changes in odorant concentration in the piriform cortex. Interestingly, invariant network selectivity appears robust to local changes in synaptic strength induced by synaptic plasticity, even though: i) synaptic plasticity can potentiate or depress connections between neurons in a feature-dependent manner, and ii) in networks with balanced excitation and inhibition, synaptic plasticity is a determinant for the network non-linearity. In this study, we investigate whether network contrast invariance is consistent with a variety of synaptic states and connectivities in balanced networks. By using mean-field models and spiking network simulations, we show how the synaptic state controls the non-linearity in the network response to contrast and how it can lead to the emergence of contrast-invariant or contrast-dependent selectivity. Different forms of synaptic plasticity sharpen or broaden the network selectivity, while others do not affect it. Our results explain how the physiology of individual synapses is linked to contrast-invariant selectivity at the network level.

scholarly journals Imbalanced amplification: A mechanism of amplification and suppression from local imbalance of excitation and inhibition in cortical circuits

2017 ◽  
Author(s):  
Christopher Ebsch ◽  
Robert Rosenbaum
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Cortical Circuits ◽  
Response Properties ◽  
Biologically Relevant ◽  
Linear Correction ◽  
External Stimuli ◽  
The Relationship ◽  
Balanced Networks

AbstractUnderstanding the relationship between external stimuli and the spiking activity of cortical populations is a central problem in neuroscience. Dense recurrent connectivity in local cortical circuits can lead to counterintuitive response properties, raising the question of whether there are simple arithmetical rules for relating circuits’ connectivity structure to their response properties. One such arithmetic is provided by the mean field theory of balanced networks, which is derived in a limit where excitatory and inhibitory synaptic currents precisely balance on average. However, balanced network theory is not applicable to some biologically relevant connectivity structures. We show that cortical circuits with such structure are susceptible to an amplification mechanism arising when excitatory-inhibitory balance is broken at the level of local subpopulations, but maintained at a global level. This amplification, which can be quantified by a linear correction to the classical mean field theory of balanced networks, explains several response properties observed in cortical recordings.

scholarly journals Mean Field Analysis of Orientation Selective Grain Growth Driven By Interface-Energy Anisotropy

1994 ◽  
Vol 343 ◽  
Author(s):  
J. A. Floro ◽  
C. V. Thompson
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Growth ◽  
Texture Evolution ◽  
Mean Field ◽  
Orientation Distribution ◽  
Interface Energy ◽  
Abnormal Grain Growth ◽  
Field Analysis ◽  
Energy Anisotropy

ABSTRACTAbnormal grain growth is characterized by the lack of a steady state grain size distribution. In extreme cases the size distribution becomes transiently bimodal, with a few grains growing much larger than the average size. This is known as secondary grain growth. In polycrystalline thin films, the surface energy γs and film/substrate interfacial energy γi vary with grain orientation, providing an orientation-selective driving force that can lead to abnormal grain growth. We employ a mean field analysis that incorporates the effect of interface energy anisotropy to predict the evolution of the grain size/orientation distribution. While abnormal grain growth and texture evolution always result when interface energy anisotropy is present, whether secondary grain growth occurs will depend sensitively on the details of the orientation dependence of γi.

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