Related papers: Spike-Phase Coupling As an Order Parameter in a Le…
Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
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 extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find…
A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of…
Spike correlations between neurons are ubiquitous in the cortex, but their role is at present not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input…
Many experimental results, both in-vivo and in-vitro, support the idea that the brain cortex operates near a critical point, and at the same time works as a reservoir of precise spatio-temporal patterns. However the mechanism at the basis…
We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of…
Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general…
We show that a network of spiking neurons exhibits robust self-organized criticality if the synaptic efficacies follow realistic dynamics. Deriving analytical expressions for the average coupling strengths and inter-spike intervals, we…
Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii)…
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model…
The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as…
$k$-Core percolation has served as a paradigmatic model of discontinuous percolation for a long time. Recently it was revealed that the order parameter of $k$-core percolation of random networks additionally exhibits critical behavior. Thus…
The model of the current paper is an extension of a previous publication, wherein we used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine…
Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state.…
In this article, a correlation metric $\kappa_C$ is proposed for the inference of the dynamical state of neuronal networks. $\kappa_C$ is computed from the scaling of the correlation length with the size of the observation region, which…
Large networks of spiking neurons show abrupt changes in their collective dynamics resembling phase transitions studied in statistical physics. An example of this phenomenon is the transition from irregular, noise-driven dynamics to…
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…
Leaky integrate-and-fire (LIF) networks are standard reduced models for spike-based neural dynamics and a natural substrate for neuromorphic computation. We study time-driven Euler--Maruyama simulation of current-based LIF networks with…