Related papers: Sensitivity to initial conditions in coherent nois…
We investigate the effect of initial system-environment correlations to improve the estimation of environment parameters. By employing various physical situations of interest, we present results for the environment temperature and…
We study the effect of noise on the evolution of the growth factor of density perturbations in the context of the LCDM model. Stochasticity is introduced as a Wiener process amplified by an intensity parameter alpha. By comparing the…
In spite of the large amount of existing neural models in the literature, there is a lack of a systematic review of the possible effect of choosing different initial conditions on the dynamic evolution of neural systems. In this short…
We have investigated the effect of the initial condition on the spreading exponents of the one-dimensional pair contact process (PCP) and threshold transfer process (TTP).The non-order field was found to exhibit critical fluctuations,…
The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would…
We investigate the emergent behavior of four types of generic dynamical systems under random environmental perturbations. Sufficient conditions for nearly-emergence in various scenarios are presented. Recent fundamental works of F. Cucker…
Using a set of high resolution simulations, we quantify the effect of species specific initial transfer functions on probes of the IGM via the Lyman-$\alpha$ forest. We focus on redshifts $2-6$, after H~{\sc i} reionization. We explore the…
Modeling and synthesizing image noise is an important aspect in many computer vision applications. The long-standing additive white Gaussian and heteroscedastic (signal-dependent) noise models widely used in the literature provide only a…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
Strongly nonlinear models of internal wave propagation for incompressible stratified Euler fluids are investigated numerically and analytically to determine the evolution of a class of initial conditions of interest in laboratory…
We numerically investigate the sensitivity to initial conditions of asymmetric unimodal maps $x_{t+1} = 1-a|x_t|^{z_i}$ ($i=1,2$ correspond to $x_t>0$ and $x_t<0$ respectively, $z_i >1$, $0<a\leq 2$, $t=0,1,2,...$) at the edge of chaos. We…
The dichotomy between noise-stable and (completely) noise-sensitive stochastic models is of recent interest in probability theory. Of particular interest is the study of lattice models coming from statistical physics. The Fourier transform…
Variability on external conditions has important consequences for the dynamics and the organization of biological systems. In many cases, the characteristic timescale of environmental changes as well as their correlations play a fundamental…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
The chapter presents some new approaches to describing the collective behavior of complex systems of mathematical biology based on the evolution equations of observables such as open systems. This representation of kinetic evolution has…
The governed equations for the order parameter, one-time and two-time correlators are obtained on the basis of the Langevin equation with the white multiplicative noise which amplitude $x^{a}$ is determined by an exponent $0<a<1$ ($x$ being…
The main goal of the paper is to define and use a condition sufficient to choose a unique solution to conservation law systems with a singular measure in initial data. Different approximations can lead to solutions with different…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two…
$1/f^\alpha$ noises are ubiquitous and affect many measurements. These noises are both a nuisance and a peculiarity of several physical systems; in dielectrics, glasses and networked liquids it is very common to study this noise to gather…