Related papers: Generalized Wilson-Cowan model with short term syn…
Neurons in the brain show great diversity in their individual properties and their connections to other neurons. To develop an understanding of how neuronal diversity contributes to brain dynamics and function at large scales we start with…
A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of…
Normative models of synaptic plasticity use a combination of mathematics and computational simulations to arrive at predictions of behavioral and network-level adaptive phenomena. In recent years, there has been an explosion of theoretical…
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…
Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for general non-renewal processes to calculate the interval and…
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…
The relation between spontaneous and stimulated global brain activity is a fundamental problem in the understanding of brain functions. This question is investigated both theoretically and experimentally within the context of nonequilibrium…
The Wilson-Cowan equations represent a landmark in the history of computational neuroscience. Among the insights Wilson and Cowan offered for neuroscience, they crystallized an approach to modeling neural dynamics and brain function.…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
Neurons in early sensory areas rapidly adapt to changing sensory statistics, both by normalizing the variance of their individual responses and by reducing correlations between their responses. Together, these transformations may be viewed…
Theoretical models of neuronal function consider different mechanisms through which networks learn, classify and discern inputs. A central focus of these models is to understand how associations are established amongst neurons, in order to…
Slow waves (SWs) are spatio-temporal patterns of cortical activity that occur both during natural sleep and anesthesia and are preserved across species. Even though electrophysiological recordings have been largely used to characterize…
We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman, Perthame, and Salort (2010, 2014). In the first model, the structuring variable $s$ represents the time elapsed since its last…
We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitely, including network parameters dependence. This is done in a statistical physics-like approach where one…
This technical note introduces parametric dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow…
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…
How can we develop simple yet realistic models of the small neural circuits known as central pattern generators (CPGs), which contribute to generate complex multi-phase locomotion in living animals? In this paper we introduce a new model…
Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic…
We investigate the dynamics of large stochastic networks with different timescales and nonlinear mean-field interactions. After deriving the limit equations for a general class of network models, we apply our results to the celebrated…
We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time…