Commande optimale hiérarchisée d'une population de chaînes de Markov
Compact attractors for time-periodic age-structured population models.
Comparing the suitability of two factors for stratification in estimating diversity
Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models
We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in mice endowed with intact or disrupted circadian clocks, known to exert their influence on the cell division cycle. We compare the growth rate of the model controlled by a time-periodic control on its coefficients with the growth rate of stationary models of the same nature, but with averaged coefficients....
Competition between plasmid-bearing and plasmid-free organisms in a chemostat with pulsed input and washout.
Competition of Species with Intra-Specific Competition
Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom....
Competitive Exclusion in a Discrete Stage-Structured Two Species Model
We develop a stage-structured model that describes the dynamics of two competing species each of which have sexual and clonal reproduction. This is typical of many plants including irises. We first analyze the dynamical behavior of a single species model. We show that when the inherent net reproductive number is smaller than one then the population will go to extinction and if it is larger than one then an interior equilibrium exists and it is globally asymptotically stable. Then we analyze...
Complete polynomial vector fields in simplexes with application to evolutionary dynamics.
Computer simulations of DNA packing inside bacteriophages: Elasticity, electrostatics and entropy.
Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi Limit
The nonlocal Fisher equation has been proposed as a simple model exhibiting Turing instability and the interpretation refers to adaptive evolution. By analogy with other formalisms used in adaptive dynamics, it is expected that concentration phenomena (like convergence to a sum of Dirac masses) will happen in the limit of small mutations. In the present work we study this asymptotics by using a change of variables that leads to a constrained Hamilton-Jacobi equation. We prove the convergence analytically...
Conditional differential equations
We introduce and study conditional differential equations, a kind of random differential equations. We give necessary and sufficient conditions for the existence of a solution of such an equation. We apply our main result to a Malthus type model.
Continuous host-macroparasite models with application to aquaculture.
Contributi delle Scienze Matematiche ed Informatiche al sequenziamento genomico su larga scala
Nel panorama della scienza contemporanea, la biologia molecolare ha recentemente assunto un ruolo di fondamentale importanza. Il bisognocrescente di conoscere intere sequenze genomiche e l’esigenza, ancora piùpressante, di analizzare e confrontare tali sequenze per poter dedurre funzionalità e discendenze comuni, ha reso necessaria l’integrazione delleusuali tecniche sperimentali, proprie della ricerca biologica, con le metodologie formali della matematica e dell’informatica. Queste motivazioni...
Contributions of Alan C. Lazer to mathematical population dynamics.
Could condom stop the AIDS epidemic?
Countable representation for infinite dimensional diffusions derived from the two-parameter Poisson-Dirichlet process.
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...
Crop development model.
Cyclic invariant sets for one class of maps.
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...