Related papers: Weak and strong connectivity regimes for a general…
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 investigate the relationship of resting-state fMRI functional connectivity estimated over long periods of time with time-varying functional connectivity estimated over shorter time intervals. We show that using Pearson's correlation to…
The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…
Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher order interactions among…
Pairs of neurons in brain networks often share much of the input they receive from other neurons. Due to essential non-linearities of neuronal dynamics, the consequences for the correlation of the output spike trains are not well understood…
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…
We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…
We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neutrons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition…
We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…
We suggest a new perspective of research towards understanding the relations between structure and dynamics of a complex network: Can we design a network, e.g. by modifying the features of units or interactions, such that it exhibits a…
One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link…
We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to…
This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…
We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…
Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…
Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
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…
In most social and information systems the activity of agents generates rapidly evolving time-varying networks. The temporal variation in networks' connectivity patterns and the ongoing dynamic processes are usually coupled in ways that…
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-…
Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks…