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Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation

R. Rudnicki, R. Wieczorek (2010)

Mathematical Modelling of Natural Phenomena

We present models of the dynamics of phytoplankton aggregates. We start with an individual-based model in which aggregates can grow, divide, joint and move randomly. Passing to infinity with the number of individuals, we obtain a model which describes the space-size distribution of aggregates. The density distribution function satisfies a non-linear transport equation, which contains terms responsible for the growth of phytoplankton aggregates, their fragmentation, coagulation, and diffusion.

Picture languages in automatic radiological palm interpretation

Ryszard Tadeusiewicz, Marek Ogiela (2005)

International Journal of Applied Mathematics and Computer Science

The paper presents a new technique for cognitive analysis and recognition of pathological wrist bone lesions. This method uses AI techniques and mathematical linguistics allowing us to automatically evaluate the structure of the said bones, based on palm radiological images. Possibilities of computer interpretation of selected images, based on the methodology of automatic medical image understanding, as introduced by the authors, were created owing to the introduction of an original relational description...

Plant Growth and Development - Basic Knowledge and Current Views

V. Brukhin, N. Morozova (2010)

Mathematical Modelling of Natural Phenomena

One of the most intriguing questions in life science is how living organisms develop and maintain their predominant form and shape via the cascade of the processes of differentiation starting from the single cell. Mathematical modeling of these developmental processes could be a very important tool to properly describe the complex processes of evolution and geometry of morphogenesis in time and space. Here, we summarize the most important biological knowledge on plant development, exploring the...

Population dynamical behavior of a single-species nonlinear diffusion system with random perturbation

Li Zu, Daqing Jiang, Donal O'Regan (2017)

Czechoslovak Mathematical Journal

We consider a single-species stochastic logistic model with the population's nonlinear diffusion between two patches. We prove the system is stochastically permanent and persistent in mean, and then we obtain sufficient conditions for stationary distribution and extinction. Finally, we illustrate our conclusions through numerical simulation.

Population Dynamics of Grayling: Modelling Temperature and Discharge Effects

S. Charles, J.-P. Mallet, H. Persat (2010)

Mathematical Modelling of Natural Phenomena

We propose a matrix population modelling approach in order to describe the dynamics of a grayling (Thymallus thymallus, L. 1758) population living in the Ain river (France). We built a Leslie like model, which integrates the climate changes in terms of temperature and discharge. First, we show how temperature and discharge can be related to life history traits like survival and reproduction. Second, we show how to use the population model to precisely examine the life cycle of grayling : estimated...

Population genetics models for the statistics of DNA samples under different demographic scenarios - Maximum likelihood versus approximate methods

Andrzej Polański, Marek Kimmel (2003)

International Journal of Applied Mathematics and Computer Science

The paper reviews the basic mathematical methodology of modeling neutral genetic evolution, including the statistics of the Fisher-Wright process, models of mutation and the coalescence method under various demographic scenarios. The basic approach is the use of maximum likelihood techniques. However, due to computational problems, intuitive or approximate methods are also of great importance.

Population Growth and Persistence in a Heterogeneous Environment: the Role of Diffusion and Advection

A. B. Ryabov, B. Blasius (2008)

Mathematical Modelling of Natural Phenomena

The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible we demonstrate...

Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies

Alexander Lorz, Tommaso Lorenzi, Michael E. Hochberg, Jean Clairambault, Benoît Perthame (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death...

Currently displaying 81 – 100 of 143