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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...

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...

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...

Adaptive control scheme based on the least squares support vector machine network

Tarek A. Mahmoud (2011)

International Journal of Applied Mathematics and Computer Science

Recently, a new type of neural networks called Least Squares Support Vector Machines (LS-SVMs) has been receiving increasing attention in nonlinear system identification and control due to its generalization performance. This paper develops a stable adaptive control scheme using the LS-SVM network. The developed control scheme includes two parts: the identification part that uses a modified structure of LS-SVM neural networks called the multi-resolution wavelet least squares support vector machine...

Adaptive predictions of the euro/złoty currency exchange rate using state space wavelet networks and forecast combinations

Mietek A. Brdyś, Marcin T. Brdyś, Sebastian M. Maciejewski (2016)

International Journal of Applied Mathematics and Computer Science

The paper considers the forecasting of the euro/Polish złoty (EUR/PLN) spot exchange rate by applying state space wavelet network and econometric forecast combination models. Both prediction methods are applied to produce one-trading-dayahead forecasts of the EUR/PLN exchange rate. The paper presents the general state space wavelet network and forecast combination models as well as their underlying principles. The state space wavelet network model is, in contrast to econometric forecast combinations,...

Advances in model-based fault diagnosis with evolutionary algorithms and neural networks

Marcin Witczak (2006)

International Journal of Applied Mathematics and Computer Science

Challenging design problems arise regularly in modern fault diagnosis systems. Unfortunately, the classical analytical techniques often cannot provide acceptable solutions to such difficult tasks. This explains why soft computing techniques such as evolutionary algorithms and neural networks become more and more popular in industrial applications of fault diagnosis. The main objective of this paper is to present recent developments regarding the application of evolutionary algorithms and neural...

Algebraic Methods for Studying Interactions Between Epidemiological Variables

F. Ricceri, C. Fassino, G. Matullo, M. Roggero, M.-L. Torrente, P. Vineis, L. Terracini (2012)

Mathematical Modelling of Natural Phenomena

BackgroundIndependence models among variables is one of the most relevant topics in epidemiology, particularly in molecular epidemiology for the study of gene-gene and gene-environment interactions. They have been studied using three main kinds of analysis: regression analysis, data mining approaches and Bayesian model selection. Recently, methods of algebraic statistics have been extensively used for applications to biology. In this paper we present...

An automatic segmentation method for scanned images of wheat root systems with dark discolourations

Jarosław Gocławski, Joanna Sekulska-Nalewajko, Ewa Gajewska, Marzena Wielanek (2009)

International Journal of Applied Mathematics and Computer Science

The analysis of plant root system images plays an important role in the diagnosis of plant health state, the detection of possible diseases and growth distortions. This paper describes an initial stage of automatic analysis-the segmentation method for scanned images of Ni-treated wheat roots from hydroponic culture. The main roots of a wheat fibrous system are placed separately in the scanner view area on a high chroma background (blue or red). The first stage of the method includes the transformation...

An epidemic model with a time delay in transmission

Q. J. A. Khan, E. V. Krishnan (2003)

Applications of Mathematics

We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.

An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control

T. Dumrongpokaphan, Y. Lenbury, R. Ouncharoen, Y. Xu (2010)

Mathematical Modelling of Natural Phenomena

Previous work has shown that intracellular delay needs to be taken into account to accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay also effects the estimated value for the infected T-cell loss rate when we assume that the drug is not completely effective [19]. Models of virus infection that include intracellular delay are more accurate representations of the biological data.
We analyze a non-linear model of the human immunodeficiency virus (HIV)...

An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection

Marcin Mrugalski (2013)

International Journal of Applied Mathematics and Computer Science

This paper presents an identification method of dynamic systems based on a group method of data handling approach. In particular, a new structure of the dynamic multi-input multi-output neuron in a state-space representation is proposed. Moreover, a new training algorithm of the neural network based on the unscented Kalman filter is presented. The final part of the work contains an illustrative example regarding the application of the proposed approach to robust fault detection of a tunnel furnace....

Analysis of a Mathematical Model for the Molecular Mechanism of Fate Decision in Mammary Stem Cells

O. U. Kirnasovsky, Y. Kogan, Z. Agur (2008)

Mathematical Modelling of Natural Phenomena

Recently, adult stem cells have become a focus of intensive biomedical research, but the complex regulation that allows a small population of stem cells to replenish depleted tissues is still unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that a feedback control of stem cells on their own proliferation and differentiation (denoted Quorum Sensing) suffices...

Analysis of Space-Temporal Symmetry in the Early Embryogenesis of Calla palustris L., Araceae

I.V. Rudskiy, G.E. Titova, T.B. Batygina (2010)

Mathematical Modelling of Natural Phenomena

Plants and animals have highly ordered structure both in time and in space, and one of the main questions of modern developmental biology is the transformation of genetic information into the regular structure of organism. Any multicellular plant begins its development from the universal unicellular state and acquire own species-specific structure in the course of cell divisions, cell growth and death, according to own developmental program. However the cellular mechanisms of plant development are...

Analysis of the Growth Control Network Specific for Human Lung Adenocarcinoma Cells

G. Pinna, A. Zinovyev, N. Araujo, N. Morozova, A. Harel-Bellan (2012)

Mathematical Modelling of Natural Phenomena

Many cancer-associated genes and pathways remain to be identified in order to clarify the molecular mechanisms underlying cancer progression. In this area, genome-wide loss-of-function screens appear to be powerful biological tools, allowing the accumulation of large amounts of data. However, this approach currently lacks analytical tools to exploit the data with maximum efficiency, for which systems biology methods analyzing complex cellular networks...

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