Un lien entre réseaux de neurones et systèmes de particules : un modèle de rétinotopie
Unique positive almost periodic solution for discrete nonlinear delay survival red blood cells model.
Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model
In the present paper, we consider an approximate system of one-dimensional simplified tumor invasion model, which was originally proposed by Chaplain and Anderson in [chaplain-anderson-03]. The simplified tumor invasion model is composed of PDE and ODE. Actually, the PDE is the balance equation of the density of tumor cells and the ODE describes the dynamics of concentration of extracellular matrix. In this model, we take into account that the random motility of the density of tumor cells is given...
Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair
How does DNA, the molecule containing genetic information, change its three-dimensional shape during the complex cellular processes of replication, recombination and repair? This is one of the core questions in molecular biology which cannot be answered without help from mathematical modeling. Basic concepts of topology and geometry can be introduced in undergraduate teaching to help students understand counterintuitive complex structural transformations...
Use of fuzzy techniques for detection of multiple sclerosis small lesions.
This work shows an application of algorithms in which fuzzy techniques are used. It is focused on the automation of image analysis for use with a non-invasive technique, as magnetic resonance, in multiple sclerosis patients, and specifically in detection of the smallest lesions. The typical uncertainty in the definition of these lesions lead us to consider that a fuzzy approach is a good solution to the problem.The design of the algorithm is based on the definition of a rule set, which enable feature...
Using normal mode analysis in teaching mathematical modeling to biology students
Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many learning...
Using R to Build and Assess Network Models in Biology
In this paper we build and analyze networks using the statistical and programming environment R and the igraph package. We investigate random, small-world, and scale-free networks and test a standard problem of connectivity on a random graph. We then develop a method to study how vaccination can alter the structure of a disease transmission network. We also discuss a variety of other uses for networks in biology.