Related papers: Correlated noise in a logistic growth model
The problem of a spatially correlated noise affecting a complex system is studied in this paper. We present a comprehensive analysis of a 2D model polymer chain, driven by the spatially correlated Gaussian noise, for which we have varied…
Correlated noise affects most astronomical datasets and to neglect accounting for it can lead to spurious signal detections, especially in low signal-to-noise conditions, which is often the context in which new discoveries are pursued. For…
We propose a multiscale chemo-mechanical model of cancer tumour development in an epithelial tissue. The model is based on transformation of normal cells into the cancerous state triggered by a local failure of spatial synchronisation of…
In this work, we present and analyze a system of PDEs, which models tumor growth by considering chemotaxis, active transport, and random effects. The stochasticity of the system is modelled by random initial data and Wiener noises that…
We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…
Primary tumors infrequently lead to demise of cancer patients; instead, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs (metastasis). It is well-known that malignant tumors induce…
Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…
We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized…
Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies…
Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe…
The influence of an external random field on the competition process in a nonlinear open spatially extended system is analyzed numerically. A three-component model is chosen as the competition model in which a "weak" species can move in…
Most biological systems are formed by component parts that to some degree are inter-related. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of…
We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise…
Tumor-immune interactions are shaped by both antigenic heterogeneity and stochastic perturbations in the tumor microenvironment, yet the mathematical mechanisms underlying immune phase transitions remain poorly understood. We propose a…
We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…
The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially…
Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology. Using an in vivo mammalian model, we show here that one can obtain useful…
The acid-mediated tumor invasion hypothesis proposes that altered glucose metabolism exhibited by the vast majority of tumors leads to increased acid (H+ ion) production which subsequently facilitates tumor invasion [1-3]. The…
Products of Gaussian noises often emerge as the result of non-linear detection techniques or as a parasitic effect, and their proper handling is important in many practical applications, including in fluctuation-enhanced sensing, indoor air…
The ability to quantify stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally…