相关论文: Dynamic range of hypercubic stochastic excitable m…

We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomogeneous highly degenerate diffusion for…

Dynamical correlation functions for temperature T=0 are calculated for a Hubbard chain with infinite on-site repulsion. This chain contains three sites per unit cell and has a known resonating-valence-bond ground state for a filling of 2…

We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between the…

We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…

By use of a stochastic generalization of the Hodgkin-Huxley model we investigate both the phenomena of stochastic resonance (SR) and coherence resonance (CR) in variable size patches of an excitable cell membrane. Our focus is on the…

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…

The decay of the hysteresis loop area of the system, which is obeying a site diluted kinetic Ising model, is considered by the disorder parameter using the effective field theory analysis. The exhibition focuses on the understanding of…

A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…

Stochasticity plays a central role in nearly every biological process, and the noise power spectral density (PSD) is a critical tool for understanding variability and information processing in living systems. In steady-state, many such…

Biological and living systems process information across spatiotemporal scales, exhibiting the hallmark ability to constantly modulate their behavior to ever-changing and complex environments. In the presence of repeated stimuli, a…

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…

By designing the decentralized time-regularized (Zeno-free) event-triggered strategies for the state-feedback control law, this paper considers the stochastic stabilization of a class of networked control systems, where two sources of…

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly…

The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…

The simulation of human neurons and neurotransmission mechanisms has been realized in deep neural networks based on the theoretical implementations of activation functions. However, recent studies have reported that the threshold potential…

The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with help of the Dynamical Cluster Approximation (DCA). To solve the effective cluster problem we employ an…

Neuronal dynamics is driven by externally imposed or internally generated random excitations/noise, and is often described by systems of random or stochastic ordinary differential equations. Such systems admit a distribution of solutions,…

We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random…

Deep brain stimulation (DBS) is a surgical treatment for Parkinson's Disease. Static models based on quasi-static approximation are common approaches for DBS modeling. While this simplification has been validated for bioelectric sources,…

We study dynamical behaviors of one-dimensional stochastic lattice gases with repulsive interactions whose span can be arbitrary large. We endow the system with a zero-temperature dynamics, so that the hops to empty sites which would have…