On the exterior magnetic field and silent sources in magnetoencephalography.
On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion
Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as models of biological phenomena. This paper begins with a survey of applications to ecology, cell biology and bacterial colony patterns. The author then reviews mathematical results on the existence of travelling wave front solutions of these equations, and their generation from given initial data. A detailed study is then presented of the form of smooth-front...
On the fractality of the biological tree-like structures.
On the global dynamics of the cancer AIDS-related mathematical model
In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive...
On the heat impulse method for deducing sap flow.
On the identification of diffusion coefficients
On the Influence of Discrete Adhesive Patterns for Cell Shape and Motility: A Computational Approach
In this paper, we propose a computational model to investigate the coupling between cell’s adhesions and actin fibres and how this coupling affects cell shape and stability. To accomplish that, we take into account the successive stages of adhesion maturation from adhesion precursors to focal complexes and ultimately to focal adhesions, as well as the actin fibres evolution from growing filaments, to bundles and finally contractile stress fibres.We use substrates with discrete patterns of adhesive...
On the linearized stability of age-structured multispecies populations.
On the Mathematical Modelling of Microbial Growth: Some Computational Aspects
We propose a new approach to the mathematical modelling of microbial growth. Our approach differs from familiar Monod type models by considering two phases in the physiological states of the microorganisms and makes use of basic relations from enzyme kinetics. Such an approach may be useful in the modelling and control of biotechnological processes, where microorganisms are used for various biodegradation purposes and are often put under extreme inhibitory conditions. Some computational experiments are...
On the Mathematics of EEG and MEG in Spheroidal Geometry
On the measurement of the activity of a radioactive source and a related stochastic process.
A method is presented to compute the activity of a radioactive source. The principle of the method is based on the tuning of b, the time constant of the RC circuit of the detector with l being the rate of emission of the source, using a statistical argument.The stochastical process involved refers to the distribution of the following random voltage:Vt = ∑(0 < ti ≤ t) Yi c-b(t - ti)where the ti are Poisson dates of emission and the Yi are random or deterministic pulse heights. The case of...
On the nonlinear mechanical response of an arterial wall.
On the number of permutations arising from a problem in cell-biology.
On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis
We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.
On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
This review is dedicated to recent results on the 2d parabolic-elliptic Patlak-Keller-Segel model, and on its variant in higher dimensions where the diffusion is of critical porous medium type. Both of these models have a critical mass such that the solutions exist globally in time if the mass is less than and above which there are solutions which blowup in finite time. The main tools, in particular the free energy, and the idea of the methods are set out. A number of open questions are also...
On the real-time emission control - case study application
On the Relations Between 2D and 3D Fractal Dimensions: Theoretical Approach and Clinical Application in Bone Imaging
The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The question which arises however is to know to which extent it is possible to get an exact determination of the...
On the semigroups of age-size dependent population dynamcis with spatial diffusion.
On the Short Term Behaviour of Genetic Algorithms
On the speed of coming down from infinity for -coalescent processes.