scholarly journals Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure

2020 ◽  
Vol 16 (6) ◽  
pp. e1007265
Author(s):  
Yuxiu Shao ◽  
Jiwei Zhang ◽  
Louis Tao
Keyword(s):  
Maximum Entropy ◽  
Dimensional Reduction ◽  
Moment Closure ◽  
Cortical Dynamics

scholarly journals Dimensional Reduction of Emergent Spatiotemporal Cortical Dynamics via a Maximum Entropy Moment Closure

2019 ◽  
Author(s):  
Yuxiu Shao ◽  
Jiwei Zhang ◽  
Louis Tao
Keyword(s):  
Cognitive Processing ◽  
Traveling Waves ◽  
Dimensional Reduction ◽  
Network Architecture ◽  
Information Transfer ◽  
Large Scale ◽  
Moment Closure ◽  
Neural Population ◽  
Cortical Dynamics ◽  
Wide Range

AbstractModern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.

A Maximum Entropy Moment Closure Approach to Describing Spray Flows

1998 ◽  
Author(s):  
M. Archambault ◽  
R. W. MacCormack ◽  
C. F. Edwards
Keyword(s):  
Maximum Entropy ◽  
Moment Closure ◽  
Spray Flows

scholarly journals An Effective Approach for Reliability-Based Sensitivity Analysis with the Principle of Maximum Entropy and Fractional Moments

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 649 ◽  
Author(s):  
Xufang Zhang ◽  
Jiankai Liu ◽  
Ying Yan ◽  
Mahesh Pandey
Keyword(s):  
Sensitivity Analysis ◽  
Maximum Entropy ◽  
Failure Probability ◽  
Dimensional Reduction ◽  
Structural Model ◽  
Simulation Method ◽  
Reliability Estimation ◽  
Sensitivity Index ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

The reliability-based sensitivity analysis requires to recursively evaluate a multivariate structural model for many failure probability levels. This is in general a computationally intensive task due to irregular integrations used to define the structural failure probability. In this regard, the performance function is first approximated by using the multiplicative dimensional reduction method in this paper, and an approximation for the reliability-based sensitivity index is derived based on the principle of maximum entropy and the fractional moment. Three examples in the literature are presented to examine the performance of this entropy-based approach against the brute-force Monte-Carlo simulation method. Results have shown that the multiplicative dimensional reduction based entropy approach is rather efficient and able to provide reliability estimation results for the reliability-based sensitivity analysis of a multivariate structural model.

scholarly journals Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation

2010 ◽  
Vol 138 (8) ◽  
pp. 2997-3023 ◽  
Author(s):  
Marc Bocquet ◽  
Carlos A. Pires ◽  
Lin Wu
Keyword(s):  
Data Assimilation ◽  
Maximum Entropy ◽  
Statistical Modeling ◽  
Estimation Problem ◽  
Geophysical Data ◽  
Moment Closure ◽  
High Dimensional ◽  
Order Moment ◽  
Special Cases ◽  
Non Gaussian

Abstract This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from.

Multi-dimensional validation of a maximum-entropy-based interpolative moment closure

2016 ◽  
Author(s):  
Boone R. Tensuda ◽  
James G. McDonald ◽  
Clinton P. T. Groth
Keyword(s):  
Maximum Entropy ◽  
Moment Closure
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