Related papers: Fluctuation-Dissipation Relations in the imbalance…
The activity of neurons within brain circuits has been ubiquitously reported to be correlated. The impact of these correlations on brain function has been extensively investigated. Correlations can in principle increase or decrease the…
Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity,…
Recent experiments suggested that homeostatic regulation of synaptic balance leads the visual system to recover and maintain a regime of power-law avalanches. Here we study an excitatory/inhibitory (E/I) mean-field neuronal network that has…
Increasing evidence suggests that cortical dynamics during wake exhibits long-range temporal correlations suitable to integrate inputs over extended periods of time to increase the signal-to-noise ratio in decision-making and working memory…
We here study a network of synaptic relations mingling excitatory and inhibitory neuron nodes that displays oscillations quite similar to electroencephalogram (EEG) brain waves, and identify abrupt variations brought about by swift synaptic…
We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a…
A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including…
Many systems are modulated by unknown slow processes. This hinders analysis in highly non-linear systems, such as excitable systems. We show that for such systems, if the input matches the sparse `spiky' nature of the output, the spiking…
We investigate the influence of indirect connections, interregional distance and collective effects on the large-scale functional networks of the human cortex. We study topologies of empirically derived resting state networks (RSNs),…
Understanding how neural dynamics shape cognitive experiences remains a central challenge in neuroscience and psychiatry. Here, we present a novel framework leveraging state-to-output controllability from dynamical systems theory to model…
We consider a differential model describing neuro-physiological contrast perception phenomena induced by surrounding orientations. The mathematical formulation relies on a cortical-inspired modelling [10] largely used over the last years to…
This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting,…
The temporal activity of many biological systems, including neural circuits, exhibits fluctuations simultaneously varying over a large range of timescales. The mechanisms leading to this temporal heterogeneity are yet unknown. Here we show…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent…
A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. Because neural spiking is noisy, spiking patterns are often quantified via pairwise correlations, or the probability that two…
We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables.…
We devised a measure based on the distributions of relative event timings of two coupled units. The measure dynamically evaluates temporal interdependencies between the two coupled units. Using this we show that even in the event of…
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…
In this paper we prove the propagation of chaos property for an ensemble of interacting neurons subject to independent Brownian noise. The propagation of chaos property means that in the large network size limit, the neurons behave as if…