Could condom stop the AIDS epidemic?
Countable representation for infinite dimensional diffusions derived from the two-parameter Poisson-Dirichlet process.
Counting number of cells and cell segmentation using advection-diffusion equations
We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical...
Coupled analytical and numerical approach to uncovering new regulatory mechanisms of intracellular processes
The paper deals with the analysis of signaling pathways aimed at uncovering new regulatory processes regulating cell responses. First, general issues of comparing simulation and experimental data are discussed, and various aspects of data normalization are covered. Then, a model of a particular signaling pathway, induced by Interferon-β, is briefly introduced. It serves as an example illustrating how mathematical modeling can be used for inferring the structure of a regulatory system governing the...
Coupling a branching process to an infinite dimensional epidemic process***
Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence...
Coupling of chemical reaction with flow and molecular transport
During the last years the interest in the numerical simulation of reacting flows has grown considerably. Numerical methods are available, which allow to couple chemical kinetics with flow and molecular transport. However, the use of detailed physical and chemical models, involving more than 100 chemical species, and thus more than 100 species conservation equations, is restricted to very simple flow configurations like one-dimensional systems or two-dimensional systems with very simple geometries,...
Coupling of transport and diffusion models in linear transport theory
This paper is concerned with the coupling of two models for the propagation of particles in scattering media. The first model is a linear transport equation of Boltzmann type posed in the phase space (position and velocity). It accurately describes the physics but is very expensive to solve. The second model is a diffusion equation posed in the physical space. It is only valid in areas of high scattering, weak absorption, and smooth physical coefficients, but its numerical solution is much cheaper...
Coupling of transport and diffusion models in linear transport theory
This paper is concerned with the coupling of two models for the propagation of particles in scattering media. The first model is a linear transport equation of Boltzmann type posed in the phase space (position and velocity). It accurately describes the physics but is very expensive to solve. The second model is a diffusion equation posed in the physical space. It is only valid in areas of high scattering, weak absorption, and smooth physical coefficients, but its numerical solution is...
Critical mass phenomenon for a chemotaxis kinetic model with spherically symmetric initial data
Critical points for reaction-diffusion system with one and two unilateral conditions
We show the location of so called critical points, i.e., couples of diffusion coefficients for which a non-trivial solution of a linear reaction-diffusion system of activator-inhibitor type on an interval with Neumann boundary conditions and with additional non-linear unilateral condition at one or two points on the boundary and/or in the interior exists. Simultaneously, we show the profile of such solutions.
Crop development model.
Curvature and absorption
Curvature Concentrations on the HIV-1 Capsid
It is known that the retrovirus capsids possess a fullerene-like structure. These caged polyhedral arrangements are built entirely from hexagons and exactly 12 pentagons according to the Euler theorem. Viral capsids are composed of capsid proteins, which create the hexagon and pentagon shapes by groups of six (hexamer) and five (pentamer) proteins. Different distributions of these 12 pentamers result in icosahedral, tubular, or conical shaped capsids. These pentamer clusters introduce declination...
Cyclic invariant sets for one class of maps.
Cyclical thrombocytopenia: Characterization by spectral analysis and a review.
Data mining methods for gene selection on the basis of gene expression arrays
The paper presents data mining methods applied to gene selection for recognition of a particular type of prostate cancer on the basis of gene expression arrays. Several chosen methods of gene selection, including the Fisher method, correlation of gene with a class, application of the support vector machine and statistical hypotheses, are compared on the basis of clustering measures. The results of applying these individual selection methods are combined together to identify the most often selected...
Decay and asymptotic behavior of solutions of the Keller-Segel system of degenerate and nondegenerate type
We classify the global behavior of weak solutions of the Keller-Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.
Defibrillation in models of cardiac muscle.
Degenerate diffusive SEIR model with logistic population control.
Delay dependent complex-valued bidirectional associative memory neural networks with stochastic and impulsive effects: An exponential stability approach
This paper investigates the stability in an exponential sense of complex-valued Bidirectional Associative Memory (BAM) neural networks with time delays under the stochastic and impulsive effects. By utilizing the contracting mapping theorem, the existence and uniqueness of the equilibrium point for the proposed complex-valued neural networks are verified. Moreover, based on the Lyapunov - Krasovskii functional construction, matrix inequality techniques and stability theory, some novel time-delayed...