Related papers: Transition densities for stochastic Hodgkin-Huxley…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a…
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…
We study a frequency-dependent damping model of hyper-diffusion within the generalized Langevin equation. The model allows for the colored noise defined by its spectral density, assumed to be proportional to $\omega^{\delta-1}$ at low…
We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material,…
Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of…
The binding neuron model is inspired by numerical simulation of Hodgkin-Huxley-type point neuron, as well as by the leaky integrate-and-fire model. In the binding neuron, the trace of an input is remembered for a fixed period of time after…
By means of the concept DE we analyze the responses of a HH neuron to two types of spike-train inputs. Two characteristic quantities can be extracted, which can reflect partially the dynamical process of a HH neuron.
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…
In this paper, we consider a stochastic version of the Cahn-Hilliard-Brinkman model in a smooth two- or three-dimensional domain with dynamical boundary conditions. The system describes creeping two-phase flows and is basically a coupling…
Ultrafast disordering observed after photo-excitation challenges the conventional picture of photo-induced transitions where symmetry-breaking takes place along a single collective coordinate. We propose that key spectroscopic signatures of…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
We study the response of a Hodgkin-Huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high frequency regime. In addition to the usual excitation threshold there is a smooth crossover…
This work focuses on a class of stochastic Hamiltonian type jump diffusion systems with state-dependent switching, in which the switching component has countably infinite many states. First,the existence and uniqueness of the underlying…
The random transitions of ion channels between conducting and non-conducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling fluctuations in the states of ion channels…
The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the…