Related papers: A statistical model for in vivo neuronal dynamics
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…
Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and close states of ion channels. Although it has previously been shown that channel noise can nontrivially…
Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $\nu(t)$ scale with the…
In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of…
Neuronal dynamics is intrinsically unstable, producing activity fluctuations that are essentially scale-free. Here we show that while these scale-free fluctuations are independent of temporal input statistics, they can be entrained by input…
We introduce a method for computing probabilities for spontaneous activity and propagation fail- ure of the action potential in spatially extended, conductance-based neuronal models subject to channel noise, based on statistical properties…
In a stochastic reaction network setting we consider the problem of tracking the fate of individual molecules. We show that using the classical large volume limit results, we may approximate the dynamics of a single tracked molecule in a…
The response of a neural cell to an external stimulus can follow one of the two patterns: Nonresonant neurons monotonously relax to the resting state after excitation while resonant ones show subthreshold oscillations. We investigate how do…
Recent advances in computational neuroscience demand models that balance biophysical realism with scalability. We present a hybrid neuron model combining the biophysical fidelity of Hodgkin-Huxley (HH) dynamics for taste receptor cells with…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
The stochastic FitzHugh-Nagumo (FHN) model is a two-dimensional nonlinear stochastic differential equation with additive degenerate noise, whose first component, the only one observed, describes the membrane voltage evolution of a single…
Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity,…
In awake animals, the activity of the cerebral cortex is highly complex, with neurons firing irregularly with apparent Poisson statistics. One way to characterize this complexity is to take advantage of the high interconnectivity of…
Cortical neurons are subject to sustained and irregular synaptic activity which causes important fluctuations of the membrane potential (Vm). We review here different methods to characterize this activity and its impact on spike generation.…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
We consider a stochastic model describing the spiking activity of a countable set of neurons spatially organized into a homogeneous tree of degree $d$, $d \geq 2$; the degree of a neuron is just the number of connections it has. Roughly,…
We prove the existence of a phase transition for a stochastic model of interacting neurons. The spiking activity of each neuron is represented by a point process having rate $1 $ whenever its membrane potential is larger than a threshold…
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…
The Hodgkin and Huxley (H-H) model is a nonlinear system of four equations that describes how action potentials in neurons are initiated and propagated, and represents a major advance in the understanding of nerve cells. However, some of…