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A topological model of site-specific recombination that predicts the knot and link type of DNA products

Karin Valencia (2014)

Banach Center Publications

This is a short summary of a topological model of site-specific recombination, a cellular reaction that creates knots and links out of circular double stranded DNA molecules. The model is used to predict and characterise the topology of the products of a reaction on double stranded DNA twist knots. It is shown that all such products fall into a small family of Montesinos knots and links, meaning that the knot and link type of possible products is significantly reduced, thus aiding their experimental...

A viscoelastic model with non-local damping application to the human lungs

Céline Grandmont, Bertrand Maury, Nicolas Meunier (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses. The...

A weighted HP model for protein folding with diagonal contacts

Hans-Joachim Böckenhauer, Dirk Bongartz (2007)

RAIRO - Theoretical Informatics and Applications

The HP model is one of the most popular discretized models for attacking the protein folding problem, i.e., for the computational prediction of the tertiary structure of a protein from its amino acid sequence. It is based on the assumption that interactions between hydrophobic amino acids are the main force in the folding process. Therefore, it distinguishes between polar and hydrophobic amino acids only and tries to embed the amino acid sequence into a two- or three-dimensional grid lattice...

A within-host dengue infection model with immune response and nonlinear incidence rate

Hajar Ansari, Mahmoud Hesaaraki (2013)

Applicationes Mathematicae

A model of viral infection of monocytes population by the dengue virus is formulated as a system of four ordinary differential equations. The model takes into account the immune response and nonlinear incidence rate of susceptible and free virus particles. Global stability of the uninfected steady state is investigated. Such a steady state always exists. If it is the only steady state, then it is globally asymptotically stable. If any infected steady state exists, then the uninfected...

About the maximum information and maximum likelihood principles

Igor Vajda, Jiří Grim (1998)

Kybernetika

Neural networks with radial basis functions are considered, and the Shannon information in their output concerning input. The role of information- preserving input transformations is discussed when the network is specified by the maximum information principle and by the maximum likelihood principle. A transformation is found which simplifies the input structure in the sense that it minimizes the entropy in the class of all information-preserving transformations. Such transformation need not be unique...

Absorption in stochastic epidemics

Josef Štěpán, Jakub Staněk (2009)

Kybernetika

A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack–McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.

Acceleration of Le Bail fitting method on parallel platforms

Mařík, Ondřej, Šimeček, Ivan (2015)

Programs and Algorithms of Numerical Mathematics

Le Bail fitting method is procedure used in the applied crystallography mainly during the crystal structure determination. As in many other applications, there is a need for a great performance and short execution time. In this paper, we describe utilization of parallel computing for mathematical operations used in Le Bail fitting. We present an algorithm implementing this method with highlighted possible approaches to its aforementioned parallelization. Then, we propose a sample parallel version...

Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions

Tomáš Vejchodský (2014)

Mathematica Bohemica

Quasi-steady state assumptions are often used to simplify complex systems of ordinary differential equations in the modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original system and to have a small number of variables. This enables to use the stability and bifurcation analysis to reveal a deeper structure in the dynamics of the original system. This contribution shows that introducing delays to quasi-steady state assumptions...

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