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Regulation of p53 by siRNA in radiation treated cells: Simulation studies

Krzysztof Puszyński, Roman Jaksik, Andrzej Świerniak (2012)

International Journal of Applied Mathematics and Computer Science

Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive...

Regulatory network of drug-induced enzyme production: parameter estimation based on the periodic dosing response measurement

Papáček, Štěpán, Lynnyk, Volodymyr, Rehák, Branislav (2021)

Programs and Algorithms of Numerical Mathematics

The common goal of systems pharmacology, i.e. systems biology applied to the field of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens et al. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system...

Relationship between the selection pressure and the rate of mutation accumulation

Katarzyna Bońkowska, Przemysław Biecek, Agnieszka Łaszkiewicz, Stanisław Cebrat (2008)

Banach Center Publications

We use the diploid, sexual Penna ageing model and its modification with noise and environment fluctuations to analyse the influence of random death on the accumulation of defective genes in the genetic pool of populations evolving under different environmental conditions.

Reliable numerical modelling of malaria propagation

István Faragó, Miklós Emil Mincsovics, Rahele Mosleh (2018)

Applications of Mathematics

We investigate biological processes, particularly the propagation of malaria. Both the continuous and the numerical models on some fixed mesh should preserve the basic qualitative properties of the original phenomenon. Our main goal is to give the conditions for the discrete (numerical) models of the malaria phenomena under which they possess some given qualitative property, namely, to be between zero and one. The conditions which guarantee this requirement are related to the time-discretization...

Repeat distributions from unequal crossovers

Michael Baake (2008)

Banach Center Publications

It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibrium distributions of this type. Due to the nonlinear and infinite-dimensional nature of these models, their analysis requires some nontrivial tools from measure theory and functional analysis, which makes them interesting...

Rings of constants of generic 4D Lotka-Volterra systems

Janusz Zieliński, Piotr Ossowski (2013)

Czechoslovak Mathematical Journal

We show that the rings of constants of generic four-variable Lotka-Volterra derivations are finitely generated polynomial rings. We explicitly determine these rings, and we give a description of all polynomial first integrals of their corresponding systems of differential equations. Besides, we characterize cofactors of Darboux polynomials of arbitrary four-variable Lotka-Volterra systems. These cofactors are linear forms with coefficients in the set of nonnegative integers. Lotka-Volterra systems...

Robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle

Yuan Jiang, Jiyang Dai (2011)

Kybernetika

This paper treats the question of robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output...

Robust Feedback Control Design for a Nonlinear Wastewater Treatment Model

M. Serhani, N. Raissi, P. Cartigny (2009)

Mathematical Modelling of Natural Phenomena

In this work we deal with the design of the robust feedback control of wastewater treatment system, namely the activated sludge process. This problem is formulated by a nonlinear ordinary differential system. On one hand, we develop a robust analysis when the specific growth function of the bacterium μ is not well known. On the other hand, when also the substrate concentration in the feed stream sin is unknown, we provide an observer of system and propose a design of robust feedback control in...

Robust numerical approximation of coupled Stokes' and Darcy's flows applied to vascular hemodynamics and biochemical transport*

Carlo D'Angelo, Paolo Zunino (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

The fully coupled description of blood flow and mass transport in blood vessels requires extremely robust numerical methods. In order to handle the heterogeneous coupling between blood flow and plasma filtration, addressed by means of Navier-Stokes and Darcy's equations, we need to develop a numerical scheme capable to deal with extremely variable parameters, such as the blood viscosity and Darcy's permeability of the arterial walls. In this paper, we describe a finite element method for...

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