Related papers: Characterizing variability in nonlinear recurrent …
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…
Plasticity is one of the most important properties of the nervous system, which enables animals to adjust their behavior to the ever-changing external environment. Changes in synaptic efficacy between neurons constitute one of the major…
We consider the problem of inferring the functional connectivity of a large-scale computer network from sparse time series of events emitted by its nodes. We do so under the following three domain-specific constraints: (a) non-stationarity…
We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
We propose a network structure discovery model for continuous observations that generalizes linear causal models by incorporating a Gaussian process (GP) prior on a network-independent component, and random sparsity and weight matrices as…
The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…
Leveraging advances in variational inference, we propose to enhance recurrent neural networks with latent variables, resulting in Stochastic Recurrent Networks (STORNs). The model i) can be trained with stochastic gradient methods, ii)…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with…
The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances raises the question how these models relate to each other. In particular it is hard to distinguish between…
A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…
We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…
Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since…
Individual neurons often produce highly variable responses over nominally identical trials, reflecting a mixture of intrinsic "noise" and systematic changes in the animal's cognitive and behavioral state. Disentangling these sources of…
Recent advancements in measurement techniques have resulted in an increasing amount of data on neural activities recorded in parallel, revealing largely heterogeneous correlation patterns across neurons. Yet, the mechanistic origin of this…
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…
The paper deals with non-linear Poisson neuron network models with bounded memory dynamics, that can include both Hebbian learning mechanisms and refractory periods. The state of a network is described by the times elapsed since its neurons…
A mathematical model is developed, to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random…