Thermodynamic formalism in neuronal dynamics and spike train statistics
The Thermodynamic Formalism provides a rigorous mathematical framework for studying
quantitative and qualitative aspects of dynamical systems. At its core, there is a variational …
quantitative and qualitative aspects of dynamical systems. At its core, there is a variational …
Large deviations for nonlocal stochastic neural fields
C Kuehn, MG Riedler - The Journal of Mathematical Neuroscience, 2014 - Springer
We study the effect of additive noise on integro-differential neural field equations. In
particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on …
particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on …
The complexity of dynamics in small neural circuits
Mean-field approximations are a powerful tool for studying large neural networks. However,
they do not describe well the behavior of networks composed of a small number of neurons …
they do not describe well the behavior of networks composed of a small number of neurons …
A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model
We introduce a new formalism for evaluating analytically the cross-correlation structure of a
finite-size firing-rate network with recurrent connections. The analysis performs a first-order …
finite-size firing-rate network with recurrent connections. The analysis performs a first-order …
Generalized entropy plane based on large deviations theory for financial time series
S Chen, P Shang, Y Wu - Applied Mathematics and Computation, 2020 - Elsevier
Complexity-entropy causality plane analysis and large deviations spectrums theory are
proposed to study time series. The entropy plane analysis depicts the complexity of a system …
proposed to study time series. The entropy plane analysis depicts the complexity of a system …
A multiscale study of stochastic spatially-extended conductance-based models for excitable systems
A Genadot - 2013 - theses.hal.science
The purpose of the present thesis is the mathematical study of probabilistic models for the
generation and propagation of an action potential in neurons and more generally of …
generation and propagation of an action potential in neurons and more generally of …
Context-dependent representation in recurrent neural networks
G Wainrib - arXiv preprint arXiv:1506.06602, 2015 - arxiv.org
In order to assess the short-term memory performance of non-linear random neural
networks, we introduce a measure to quantify the dependence of a neural representation …
networks, we introduce a measure to quantify the dependence of a neural representation …
A representation of the relative entropy with respect to a diffusion process in terms of its infinitesimal generator
O Faugeras, J MacLaurin - Entropy, 2014 - mdpi.com
In this paper we derive an integral (with respect to time) representation of the relative
entropy (or Kullback–Leibler Divergence) R (μ|| P), where μ and P are measures on C ([0, T]; …
entropy (or Kullback–Leibler Divergence) R (μ|| P), where μ and P are measures on C ([0, T]; …
On the form of the relative entropy between measures on the space of continuous functions
J MacLaurin, O Faugeras - arXiv preprint arXiv:1312.5888, 2013 - arxiv.org
In this paper we derive an integral (with respect to time) representation of the relative
entropy (or Kullback-Leibler Divergence) between measures mu and P on the space of …
entropy (or Kullback-Leibler Divergence) between measures mu and P on the space of …