Related papers: Characterizing variability in nonlinear recurrent …
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate-and-fire neurons, we can show how the firing irregularity,…
We investigate the synchronization between two neurons using the stochastic version of the map-based Chialvo model. To simulate non-identical neurons, a mismatch is introduced in one of the main parameters of the model. Subsequently, the…
This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
We consider the probabilistic analogue to neural network matrix factorization (Dziugaite & Roy, 2015), which we construct with Bayesian neural networks and fit with variational inference. We find that a linear model fit with variational…
Rapid experimental advances now enable simultaneous electrophysiological recording of neural activity at single-cell resolution across large regions of the nervous system. Models of this neural network activity will necessarily increase in…
The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of…
Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…
It is becoming increasingly appreciated that the signal transduction systems used by eukaryotic cells to achieve a variety of essential responses represent highly complex networks rather than simple linear pathways. While significant effort…
Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex…
The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual…
Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we briefly discuss their derivations and then review the…
Animals rely on different decision strategies when faced with ambiguous or uncertain cues. Depending on the context, decisions may be biased towards events that were most frequently experienced in the past, or be more explorative. A…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differential equations in discrete time. The neurons interact…
Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation slows and diversifies inhibitory timescales, leading to improved task performance that is…
Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…
We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables - synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these…
This paper studies a stochastic neural field model that is extended from our previous paper [14]. The neural field model consists of many heterogeneous local populations of neurons. Rigorous results on the stochastic stability are proved,…
We introduce a method for computing probabilities for spontaneous activity and propagation fail- ure of the action potential in spatially extended, conductance-based neuronal models subject to channel noise, based on statistical properties…