Asymptotical mean square stability of Cohen-Grossberg neural networks with random delay.
Asymptotically self-similar solutions for the parabolic system modelling chemotaxis
We consider a nonlinear parabolic system modelling chemotaxis , in ℝ², t > 0. We first prove the existence of time-global solutions, including self-similar solutions, for small initial data, and then show the asymptotically self-similar behavior for a class of general solutions.
Atherosclerosis Initiation Modeled as an Inflammatory Process
In this work we study the inflammatory process resulting in the development of atherosclerosis. We develop a one- and two-dimensional models based on reaction-diffusion systems to describe the set up of a chronic inflammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic inflammatory reaction. Intermediate ox-LDL concentrations...
ATP Production and Necrosis Formation in a Tumour Spheroid Model
Mathematical models of tumour spheroids, proposed since the early seventies, have been generally formulated in terms of a single diffusive nutrient which is critical for cell replication and cell viability. Only recently, attempts have been made to incorporate in the models the cell energy metabolism, by considering the interplay between glucose, oxygen and lactate (or pH). By assuming glucose and lactate as the only fuel substrates, we propose a simple model for the cell ATP production which takes...
Automatic recognition of muscle-invasive T-lymphocytes expressing dipeptidyl-peptidase IV (CD26) and analysis of the associated cell surface phenotypes.
Automaty a mozek
Autoselection phenomenon in the normal cell clone undergoing differentiation: From cell population heterogeneity to cancer phenotype via nonmutational changes.
Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy
A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that the tumour...
Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural network
In this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if network combines an error backpropagation algorithm with the self-consistency paradigm widely used in physics....
Bacteriophage Infection Dynamics: Multiple Host Binding Sites
We construct a stochastic model of bacteriophage parasitism of a host bacteria that accounts for demographic stochasticity of host and parasite and allows for multiple bacteriophage adsorption to host. We analyze the associated deterministic model, identifying the basic reproductive number for phage proliferation, showing that host and phage persist when it exceeds unity, and establishing that the distribution of adsorbed phage on a host is binomial with slowly evolving mean. Not surprisingly,...
Baire classification and infinite perceptrons
Basic terms of the theory of compartmental systems
Berwald-moor metrics and structural stability of conformally-deformed geodesic SODE.
Bifurcation analysis for a two-dimensional discrete-time Hopfield neural network with delays.
Bifurcation analysis on a delayed SIS epidemic model with stage structure.
Bifurcation in a model of the population dynamics.
Bifurcation of reaction-diffusion systems related to epidemics.
Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination
Simple epidemiological models with information dependent vaccination functions can generate sustained oscillations via Hopf bifurcation of the endemic state. The onset of these oscillations depend on the shape of the vaccination function. A “global” approach is used to characterize the instability condition and identify classes of functions that always lead to stability/instability. The analysis allows the identification of an analytically determined “threshold vaccination function” having...
Bifurcations and biological observables
Bifurcations in a modulation equation for alternans in a cardiac fiber
While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either stationary or travelling, which is known as discordant alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by Echebarria-Karma. As shown in our previous paper, the zero solution of their equation may lose...