Related papers: Time-dependent branching processes: a model of osc…
We use mean field theory to study the response properties of a simple randomly-connected model cortical network of leaky integrate-and-fire neurons with balanced excitation and inhibition. The formulation permits arbitrary temporal…
Observations of power laws in neural activity data have raised the intriguing notion that brains may operate in a critical state. One example of this critical state is "avalanche criticality," which has been observed in various systems,…
Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes…
Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Moreover, experimental studies of morphology indicate that neurons develop a network of small-world-like connections, with the…
Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that…
Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex…
Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new…
We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of…
The temporal activity of many biological systems, including neural circuits, exhibits fluctuations simultaneously varying over a large range of timescales. The mechanisms leading to this temporal heterogeneity are yet unknown. Here we show…
Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
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…
Neural activity fluctuates over a wide range of timescales within and across brain areas. Experimental observations suggest that diverse neural timescales reflect information in dynamic environments. However, how timescales are defined and…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
Network theory provides novel concepts that promise an improved characterization of interacting dynamical systems. Within this framework, evolving networks can be considered as being composed of nodes, representing systems, and of…
We explore statistical characteristics of avalanches associated with the dynamics of a complex-network model, where two modules corresponding to sensorial and symbolic memories interact, representing unconscious and conscious mental…
Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their domains of attraction and…
We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given…