Related papers: Dynamics of stochastic integrate-and-fire networks
In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote…
We report a transition from asynchronous to oscillatory behaviour in balanced inhibitory networks for class I and II neurons with instantaneous synapses. Collective oscillations emerge for sufficiently connected networks. Their origin is…
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…
The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. Open questions surround the basic nature of these correlations. In particular, what leads to…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
Self-sustained activity in the brain is observed in the absence of external stimuli and contributes to signal propagation, neural coding, and dynamic stability. It also plays an important role in cognitive processes. In this work, by means…
Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal…
We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is…
We examine the stability and qualitative dynamics of stochastic neuronal networks specified as multivariate nonlinear Hawkes processes and related point-process generalized linear models that incorporate both auto- and cross-history…
Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However,…
Many biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability. In balanced networks, strong excitatory synaptic inputs are canceled by strong inhibitory inputs…
Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates…
The dynamics of spatially-structured networks of $N$ interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does…
In spiking neural networks, neuron dynamics are described by the biologically realistic integrate-and-fire model that captures membrane potential accumulation and above-threshold firing behaviors. Among the hardware implementations of…
A single neuron is known to generate almost identical spike trains when the same fluctuating input is repeatedly applied. Here, we study the reliability of spike firing in a pulse-coupled network of oscillator neurons receiving fluctuating…
In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate…
The apparent stochasticity of in-vivo neural circuits has long been hypothesized to represent a signature of ongoing stochastic inference in the brain. More recently, a theoretical framework for neural sampling has been proposed, which…
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network…
The population activity of random networks of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons has been studied extensively. In particular, a state of asynchronous activity with low firing rates and low pairwise correlations…
Recurrent neural networks with balanced excitation and inhibition exhibit irregular asynchronous dynamics, which is fundamental for cortical computations. Classical balance mechanisms require strong external inputs to sustain finite firing…