Last issue
2016 (vol. 26) - Number 4


Andrzej Ruszewski:

Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model



D. Krokavec, A. Filasova, P. Liscinsky:

On fault tolerant control structures incorporating fault estimation



Sundarapandian Vaidyanathan:

Hyperchaos, adaptive control and synchronization of a novel 4-D  hyperchaotic system with two quadratic nonlinearities



H. Górecki, M. Zaczyk:

Analytic solutions of transcendental equations with application to automatics



F. Mnif:

Predictor-based stabilization for chained form systems with input time delay



S. Daniar, R. Aazami, M. Shiroei:

Multivariable predictive control considering time delay for load-frequency control in multi-area power systems



T. Kaczorek:

Analysis and comparison of the stability of discrete-time and continuous-time linear systems



M. Rachik, M. Lhous:

An observer-based control of linear systems with uncertain parameters



L. Malinski:

Identification of stable elementary bilinear time-series model



V.V. Huynh:

New observer-based control design for mismatched uncertain systems with time-delay




ACS Abstract:

1999 (Volume 9)
Number 1/2
1. Some Identification Problems for an Anchovy Larva Model with Diffusion
2. Predicting the Development of Pre-invasive Neoplastic Bronchial Epithelial Lesions from Biopsies
3. A Model for estimating cell kinetic parameters of experimental tumours studied by BrdUrd labelling and flow cytometry
4. Dynamics of the life history of a DNA-repeat sequence
5. HIV Testing as an Effective Control Strategy against the Spread of AIDS among Intravenous Drug Users
6. Singling out ill-fit items in a classification. Application to the taxonomy of Enterobacteriaceae
7. A Neuro-Fuzzy System Using Logical Interpretation of If-Then Rules and its Application to Diabetes Mellitus Forecasting
8. Dynamic properties of chain systems with applications to biological models
9. Mathematical Modeling of Telomere Shortening: an Overview
10. Upper and lower bounds to linear compartmental model output
11. Statistical Analysis of DNA Sequence Data: A Brief Review
12. A maturity structured model of a population of proliferating and quiescent cells
13. Modelling the Dynamics of the Cytoskeleton's Protein Filaments
14. A model of dynamics of mutation, genetic drift and recombination in DNA-repeat genetic loci


Some Identification Problems for an Anchovy Larva Model with DiffusionDownload full PDF article
Sebastian Anita
(University 'A1.I Cuza', Romania )
Ahmed Boussouar
(Université de Pau, France )

We study some identification problems for an anchovy larva model with diffusion. Existence of the optimal control for an abstract identification problem is demonstrated and necessary and sufficient optimality conditions are established. Applications for the anchovy larva model with diffusion are indicated. The uniqueness of the optimal control is discussed.

keywords: anchovy larva model, identification problem, optimality conditions, gradient type algorithm.

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Predicting the Development of Pre-invasive Neoplastic Bronchial Epithelial Lesions from BiopsiesDownload full PDF article
Alma Barranco-Mendoza and Arvind Gupta
(Simon Fraser University, Canada )
Carole Clem and Martial Guillaud
(British Columbia Cancer Research Centre, Canada )
Perry Fizzano
(University of Puget Sound, USA )

Lung cancer accounts for 28% of all cancer deaths in North America. However current treatment options lead to a cure in only 10% of these cases. It is well known that the survival rates can be improved by the early detection of pre-invasive lesions which are believed to be the possible precursors of malignant tumors. Although new technology is allowing numerous early lesions to be detected, it is becoming clear that only a small percentage of these will progress to cancer. A fundamental problem in the analysis of biopsies, i.e., longitudinal two-dimensional (2-D) sections of the central area of the lesions, is the quantification of tissue heterogeneity. One can distinguish abnormal cells from normal cells and analyse their spatial arrangement, but it is currently impossible in the case of pre-invasive lesions in the early stages, that is, when just a few abnormal cells are present in the biopsy, to tell if one observed pattern is more aggressive than another one. In this paper a stochastic model for the growth of pre-invasive neoplastic bronchial epithelial cells is presented. The results are analysed to differentiate progressive lesions from regressive ones given a particular biopsy. The problem is initially simplified to taking a one-dimensional (1-D) cross-section from a 2-D process and estimating the maximum likelihood rate of growth based on this limited information. We propose a number of extensions to eventually extend this approach to the higher dimension model by analysing 2-D sections and estimating their growth rates in a three-dimensional (3-D) process.

keywords: interacting particle system, contact process, lung cancer, computer model.

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A Model for estimating cell kinetic parameters of experimental tumours studied by BrdUrd labelling and flow cytometryDownload full PDF article
Alessandro Bertuzzi and Alberto Gandolfi
(CNR, Italy )

A mathematical model that describes the time evolution of the DNA-BrdUrd distribution, as measured in experimental tumours after labelling with BrdUrd, is proposed in this paper. Cell-to-cell heterogeneity within the tumour of the rate of progression across cell cycle phases is taken into account, and a strict correlation between the durations of S and G2M phases is assumed. The model relates observable quantities to the parameters that characterize the cell population kinetics (such as the potential doubling time, Tpot), and appears thus to be suitable for parameter estimation. Simulations that illustrate the dependence of model response on the kinetic parameters are presented.

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Dynamics of the life history of a DNA-repeat sequenceDownload full PDF article
Adam Bobrowski
(University of Houston, USA )
Marek Kimmel
(Rice University, USA)

We consider a model of evolution of a DNA-repeat sequence, which takes into account stepwise extension/contraction events occurring with intensities proportional to the sequence length and the possibility of catastrophic breakdowns. The model was originally introduced by Kruglyak et al. [Proc. Natl. Acad. Sci. USA, 1998, 95: 10774-10778], in a slightly different form, and used for between-species comparisons of short DNA-repeat data. In the present paper, we investigate the dynamics of absorption in the model, which is equivalent to the elimination of the DNA-repeat sequence. Using the theory of Markov chains and stochastic semigroups, we obtain explicit expressions for the distributions of the process and for the time to absorption. We estimate median times to absorption for a range of coefficient values and discuss their relevance in view of known data for human and chimpanzee DNA-repeat sequences.

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HIV Testing as an Effective Control Strategy against the Spread of AIDS among Intravenous Drug UsersDownload full PDF article
Fraser Lewis and David Greenhalgh
(University of Strathclyde, UK)

In this article we examine the impact on the spread of HIV caused by regularly testing members of a needle sharing population for the presence of disease. We develop a model of injecting drug use which contains two classes of addicts, a class who are unaware of their infectious status and a class who are aware that they are infectious through having had an HIV test. We expect addicts in the latter class to participate in needle sharing far less frequently than other addicts. We begin the paper with a brief review and literature survey followed by the derivation of a model which includes both needle exchange and HIV testing control measures. We perform an equilibrium and stability analysis on our model and find that there is a critical threshold parameter R0 which determines the behaviour of the model. If R0≤0 then irrespective of the initial conditions of the system HIV will die out in all addicts and all needles. If R0>1 then this disease free equilibrium becomes unstable and if initialy present disease will now persist indefinitely, moreover there now exists a unique endemic equilibrum solution which is locally stable.

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Singling out ill-fit items in a classification. Application to the taxonomy of EnterobacteriaceaeDownload full PDF article
Helge G. Gyllenberg
(University of Helsinki, Finland)
Mats Gyllenberg, Timo Koski and Tatu Lund
(University of Turku, Finland)
Heikki Mannila and Christopher Meek
(Helsinki University of Technology, Finland )

We address the problem of evaluating the quality of cluster assignment of individual items in a classification. The problem can also be viewed as outlier detection in classifications. We describe simple methods for this task based on the use of Naive Bayes classification. Applied to two existing classifications of 5313 strains of bacteria the method indicated that one classification is far more robust than the other. The observations that fit badly to their clusters are typically items whose classification is suspect also from other considerations. Removing these elements from the data set, performing clustering on the reduced data set, and adding the outliers back one-by-one yielded a clustering that has a higher likelihood than the previous accepted classifications. Investigation of this new clustering lead to suggested changes in the classification of 69 strains in the material.

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A Neuro-Fuzzy System Using Logical Interpretation of If-Then Rules and its Application to Diabetes Mellitus ForecastingDownload full PDF article
J. Łęski and N. Henzel
(Technical University of Silesia, Poland )

Initially, an axiomatic definition of fuzzy implication has been recalled. Next, several important fuzzy implications and their properties have been described. Then, the idea of approximate reasoning using generalized modus ponens and fuzzy implication are considered. After reviewing well-known fuzzy systems, a new Artificial Neural network Based on Logical Interpretation of if-then Rules (ANBLIR) is introduced. The elimination of non-informative part of final fuzzy set before defuzzification plays the pivotal role in this system. The application of ANBLIR to recognition of non-insulin-dependent diabetes mellitus in Pima Indians is shown.

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Dynamic properties of chain systems with applications to biological modelsDownload full PDF article
Wojciech Mitkowski
(The University of Mining and Metallurgy, Poland)

Spectral properties of chain systems are considered. We combine finite dimensional and asymptotic techniques. The microsatellite DNA repeats model is presented as example of chain system. Numerical calculations were made using the MATLAB program.

keywords: tridiagonal matrices, chain systems, DNA model, asymptotic stability.

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Mathematical Modeling of Telomere Shortening: an OverviewDownload full PDF article
Peter Olofsson
(Rice University, USA )

Shortening of telomeres is one of the supposed mechanisms of aging and death. This paper reviews the attempts to model and analyze this process with mathematical methods. The emphasis is put on branching process models where the main features are irreducibility and polynomial growth.

keywords: branching process, population dynamics, cell population, telomeres.

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Upper and lower bounds to linear compartmental model outputDownload full PDF article
Giuseppe Schinaia
(Universita di Roma La Sapienza, Italy )

A general compartmental system is described by the following matrix form equations dX/dt=AX+Y, where A ii is a compartmental matrix with its elements being constant or functions of t and/or of X. With a distance function given by d(A,B)=supi≠j|aij-bij|, the space L of compartmental matrices is a complete metric space and some important properties, such as uniform continuity over L of the system solution Àt(A)=X(t), as a function of A, can be derived in the linear, autonomous, constant coefficient case. Using these properties, upper and lower bounds to the model output are thus obtained and some applications, including a linearized epidemic model, show the use of such bounds in correspondence of various level of accuracy of the model parameter estimates.

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Statistical Analysis of DNA Sequence Data: A Brief ReviewDownload full PDF article
Chad A. Shaw
(Rice University, USA)

Molecular biology and the Human Genome Project generate large amounts of nucleic acid sequence data. The volume of these data makes it imperative to develop statistical techniques to detect the inner organization of DNA sequences. We review several methodologies,including M-entropies and Hidden Markov Models. A number of recent references are discussed. The existing approaches proved to be of somewhat limited usefulness, except in the domain of sequence comparison, mainly because of simplistic assumptions of the models and complicated structure of the data. Further efforts are needed to improve this situation.

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A maturity structured model of a population of proliferating and quiescent cellsDownload full PDF article
Janet Dyson
(University of Oxford, England)
Rosanna Villella-Bressan
(Universita' di Padova, Italy)
Glenn Webb
(Vanderbilt University, USA)

keywords: population dynamics, semigroup of operators, hypercyclicity, chaos.

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Modelling the Dynamics of the Cytoskeleton's Protein FilamentsDownload full PDF article
J.A. Brown and J.A. Tuszynski
(University of Alberta, Canada )

Microtubules are one of the most important components of the cell's cytoskeleton. We review the modelling efforts in the investigations of microtubules and their properties. Polymerization, crystal structure, dipole ordering and their consequences are discussed.

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A model of dynamics of mutation, genetic drift and recombination in DNA-repeat genetic lociDownload full PDF article
Joanna Polańska
(Silesian University of Technology, Poland)
Marek Kimmel
(Rice University, USA)

We present a model of genetic dynamics of a population of chromosomes, involving mutation, drift and recombination at a pair of repeat-DNA sequences. Such sequences, known as microsatellites and VNTR's, are commonly used as markers in studies in forensics, molecular evolution and gene mapping. The model we use has the form of a time-continuous Markov chain. It is further transformed to the form of a differential equation for probability generating functions. This description allows to follow dynamics with a variety of initial conditions. It allows, among other, to model the so called linkage disequilibrium, i.e. the state in which, due to processes like newly arisen mutation, selection, or population admixture, there exists a dependence between alleles at two loci. Recombination gradually dissolves the linkage disequilibrium, with additional contributions from drift and mutation. The model, in its complete form, is rather involved, since it includes all possible occurrences related to three genetic forces: mutation, genetic drift and recombination. However, we find explicit solutions to special cases which allow to understand the dynamics of dissolution of linkage disequilibrium. Other special cases of the model include the previously known relationships involving mutations and genetic drift. Also, we derive equations for the moments of the random variables present in the model. The moments can be used to define distance measures between distributions of alleles.

keywords: genetic dynamics, Markov process, Differential equation, Wrigh-Fisher model, Recombination, Linkage disequilibrium.

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