Related papers: Before and beyond the Wilson-Cowan equations
In this study we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in probability on compacts for a sequence of microscopic models when the number…
Homogenization of Wilson-Cowan type of nonlocal neural field models is investigated. Motivated by the presence of a convolution terms in this type of models, we first prove some general convergence results related to convolution sequences.…
Neuroscience has long informed the development of artificial neural networks, but the success of modern architectures invites, in turn, the converse: can modern networks teach us lessons about brain function? Here, we examine the structure…
Dynamics play a critical role in computation. The principled evolution of states over time enables both biological and artificial networks to represent and integrate information to make decisions. In the past few decades, significant…
Connectomics and network neuroscience offer quantitative scientific frameworks for modeling and analyzing networks of structurally and functionally interacting neurons, neuronal populations, and macroscopic brain areas. This shift in…
Humans and animals exhibit a range of interesting behaviors in dynamic environments, and it is unclear how our brains actively reformat this dense sensory information to enable these behaviors. Experimental neuroscience is undergoing a…
Elucidating the language-brain relationship requires bridging the methodological gap between the abstract theoretical frameworks of linguistics and the empirical neural data of neuroscience. Serving as an interdisciplinary cornerstone,…
Two transformative waves of computing have redefined the way we approach science. The first wave came with the birth of the digital computer, which enabled scientists to numerically simulate their models and analyze massive datasets. This…
We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the…
Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a…
This paper gives an introduction to \textit{Cognidynamics}, that is to the dynamics of cognitive systems driven by optimal objectives imposed over time when they interact either with a defined virtual or with a real-world environment. The…
AI's significant recent advances using general-purpose circuit computations offer a potential window into how the neocortex and cerebellum of the brain are able to achieve a diverse range of functions across sensory, cognitive, and motor…
Learning and interpreting the structure of the environment is an innate feature of biological systems, and is integral to guiding flexible behaviours for evolutionary viability. The concept of a cognitive map has emerged as one of the…
The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural…
Understanding neurocognitive computations will require not just localizing cognitive information distributed throughout the brain but also determining how that information got there. We review recent advances in linking empirical and…
We consider a stochastic version of the Wilson-Cowan model which accommodates for discrete populations of excitatory and inhibitory neurons. The model assumes a finite carrying capacity with the two populations being constant in size. The…
We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us…
Mathematical modelling of the macroscopic electrical activity of the brain is highly non-trivial and requires a detailed understanding of not only the associated mathematical techniques, but also the underlying physiology and anatomy.…
Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of biological information processing to mean-field results. These…
Neuroscientists today can measure activity from more neurons than ever before, and are facing the challenge of connecting these brain-wide neural recordings to computation and behavior. Here, we first describe emerging tools and…