Related papers: A Simple Noise Model with Memory for Biological Sy…
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…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…
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…
The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intensive activity followed by long times of no or reduced activity. The…
A method is proposed for obtaining the spectrum for noise that causes the phase decoherence of a qubit directly from experimentally available data. The method is based on a simple relationship between the spectrum and the coherence time of…
Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an…
We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system leave prescribed regions of the state…
Cells can utilize chemical communication to exchange information and coordinate their behavior in the presence of noise. Communication can reduce noise to shape a collective response, or amplify noise to generate distinct phenotypic…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
The measurement of data over time and/or space is of utmost importance in a wide range of domains from engineering to physics. Devices that perform these measurements therefore need to be extremely precise to obtain correct system…
An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…
Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system's behaviour changes over time. A key problem in time series modelling is \emph{inference}; determining properties of…
Modeling imaging sensor noise is a fundamental problem for image processing and computer vision applications. While most previous works adopt statistical noise models, real-world noise is far more complicated and beyond what these models…
In the field of medical image analysis, deep learning models have demonstrated remarkable success in enhancing diagnostic accuracy and efficiency. However, the reliability of these models is heavily dependent on the quality of training…
We investigate dynamics of recurrent neural networks with correlated noise to analyze the noise's effect. The mechanism of correlated firing has been analyzed in various models, but its functional roles have not been discussed in sufficient…
We present a simple stochastic mechanism which generates pulse trains exhibiting a power law distribution of the pulse intervals and a $1/f^\alpha$ power spectrum over several decades at low frequencies with $\alpha$ close to one. The…
The problem of estimating the delays and amplitudes of a positive stream of pulses appears in many applications, such as single-molecule microscopy. This paper suggests estimating the delays and amplitudes using a convex program, which is…