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A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a...
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the...
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic
PDEs are examined. The schemes under consideration are discontinuous in time but
conforming in space and of arbitrary order. Stability estimates are presented in the
natural energy norms and at arbitrary times, under minimal regularity assumptions.
Space-time error estimates of arbitrary order are derived, provided that the natural
parabolic regularity is present....
This paper presents a survey of recent successful algorithms for blind separation of determined instantaneous linear mixtures of independent sources such as natural speech or biomedical signals. These algorithms rely either on non-Gaussianity, nonstationarity, spectral diversity, or on a combination of them. Performance of the algorithms will be demonstrated on separation of a linear instantaneous mixture of audio signals (music, speech) and on artifact removal in electroencephalogram (EEG).
Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation. In order to perform long–time simulations and still control the solid fraction,...
Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly.
Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation.
In order to perform long–time simulations and still control the solid fraction,...
The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and stably solve the nonlinear PB equation in a pseudo-transient continuation approach. The operator splitting...
HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic
mechanisms are manifold and mediated through a range of positive and negative feedback
regulations of immune and physiological processes engaged in virus-host interactions. The
fundamental questions towards understanding the pathogenesis of HIV infection are now
shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally
disrupted? (ii)...
We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...
We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...
We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...
Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental
tool which can be used in conjunction with mathematical modeling to quantify the dynamic
behavior of a population of lymphocytes. In this survey we begin by providing an overview
of the mathematically relevant aspects of the data collection procedure. We then present
an overview of the large body of mathematical models, along with their assumptions and
uses,...
In this paper, we consider a system of nonlinear delay-differential equations
(DDEs) which models the dynamics of the interaction between chronic myelogenous
leukemia (CML), imatinib, and the anti-leukemia immune response. Because of the
chaotic nature of the dynamics and the sparse nature of experimental data, we
look for ways to use computation to analyze the model without employing direct
numerical simulation. In particular, we develop several tools using
Lyapunov-Krasovskii analysis that allow...
The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart. However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features of this system. For this reason, a simplification of this model, called Monodomain problem is quite often adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in the presence of applied currents...
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