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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…
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…
Finite-sized populations of spiking elements are fundamental to brain function, but also used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasi-renewal…
We extend previous mean-field approaches for non-equilibrium neural network models to estimate correlations in the system. This offers a powerful tool for approximating the system dynamics as well as a fast method to infer network…
Tasks that require information about the world imply a trade-off between the time spent on observation and the variance of the response. In particular, fast decisions need to rely on uncertain information. However, standard estimates of…
We study the dynamics of networks with inhibitory and excitatory leaky-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a Heterogeneous…
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…
Heterogeneity of firing rate statistics is known to have severe consequences on neural coding. Recent experimental recordings in weakly electric fish indicate that the distribution-width of superficial pyramidal cell firing rates (trial-…
The counter-intuitive phenomenon of coherence resonance describes a non-monotonic behavior of the regularity of noise-induced oscillations in the excitable regime, leading to an optimal response in terms of regularity of the excited…
We study finite-size fluctuations in a network of spiking deterministic neurons coupled with non-uniform synaptic coupling. We generalize a previously developed theory of finite size effects for uniform globally coupled neurons. In the…
Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve…
Travelling waves of neural firing activity are observed in brain tissue as a part of various sensory, motor and cognitive processes. They represent an object of major interest in the study of excitable networks, with analysis conducted in…
Recurrently connected neuron populations play key roles in sensory perception and memory storage across various brain regions. While these populations are often assumed to encode information through firing rates, this method becomes…
How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been…
The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
Neural responses are highly variable, and some portion of this variability arises from fluctuations in modulatory factors that alter their gain, such as adaptation, attention, arousal, expected or actual reward, emotion, and local metabolic…
We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at differentctime scales. Using…
We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…
The construction of transfer functions in theoretical neuroscience plays an important role in determining the spiking rate behavior of neurons in networks. These functions can be obtained through various fitting methods, but the biological…