2020 (vol. 30) - Number 4

*A.B. Malinowska, R. Kamocki, R. Almeida, T. Odzijewicz:*

On the existence of optimal consensus control for the fractional Cucker--Smale model

*R. Grymin, W. Bożejko, J. Pempera, M. Wodecki, Z. Chaczko:*

Algorithm for solving the Discrete-Continuous Inspection Problem

*T. Kaczorek, A. Ruszewski:*

Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

*R. Arora, K. Gupta:*

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

*P. Nowak, J. Czeczot, P. Grelewicz:*

Tuning rules for industrial use of the second-order Reduced Active Disturbance Rejection Controller

*M.I. Gomoyunov:*

Optimal control problems with a fixed terminal time in linear fractional-order systems

*Muhafzan, A. Nazra, L. Yulianti, Zulakmal, R. Revina:*

On LQ optimization problem subject to fractional order irregular singular systems

*M. Blizorukova, V. Maksimov:*

On one algorithm for reconstruction of an disturbance in a linear system of ordinary differential equations

ACS Abstract:

**1999 (Volume 9)**

Number 1/2

**Some Identification Problems for an Anchovy Larva Model with Diffusion**

Sebastian Anita(University 'A1.I Cuza', Romania ) | Ahmed Boussouar(Université de Pau, France ) |

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

**Predicting the Development of Pre-invasive Neoplastic Bronchial Epithelial Lesions from Biopsies**

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 ) |

*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.

**A Model for estimating cell kinetic parameters of experimental tumours studied by BrdUrd labelling and flow cytometry**

Alessandro Bertuzzi and Alberto Gandolfi(CNR, Italy ) |

*T*), and appears thus to be suitable for parameter estimation. Simulations that illustrate the dependence of model response on the kinetic parameters are presented.

_{pot}**Dynamics of the life history of a DNA-repeat sequence**

Adam Bobrowski (University of Houston, USA ) | Marek Kimmel (Rice University, USA) |

*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.

**HIV Testing as an Effective Control Strategy against the Spread of AIDS among Intravenous Drug Users**

Fraser Lewis and David Greenhalgh(University of Strathclyde, UK) |

*R*

_{0}which determines the behaviour of the model. If

*R*

_{0}≤0 then irrespective of the initial conditions of the system HIV will die out in all addicts and all needles. If

*R*

_{0}>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.

**Singling out ill-fit items in a classification. Application to the taxonomy of Enterobacteriaceae**

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 ) |

**A Neuro-Fuzzy System Using Logical Interpretation of If-Then Rules and its Application to Diabetes Mellitus Forecasting**

J. Łęski and N. Henzel(Technical University of Silesia, Poland ) |

**A**rtificial

**N**eural network

**B**ased on

**L**ogical

**I**nterpretation of if-then

**R**ules (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.

**Dynamic properties of chain systems with applications to biological models**

Wojciech Mitkowski(The University of Mining and Metallurgy, Poland) |

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

**Mathematical Modeling of Telomere Shortening: an Overview**

Peter Olofsson(Rice University, USA ) |

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

**Upper and lower bounds to linear compartmental model output**

Giuseppe Schinaia(Universita di Roma La Sapienza, Italy ) |

A general compartmental system is described by the following matrix form equations d**X**/dt=**A**’**X**+**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**)=sup_{i≠j}|a_{ij}-b_{ij|}, 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 À_{t}(**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.

**Statistical Analysis of DNA Sequence Data: A Brief Review**

Chad A. Shaw(Rice University, USA) |

*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.

**A maturity structured model of a population of proliferating and quiescent cells**

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.

**Modelling the Dynamics of the Cytoskeleton's Protein Filaments**

J.A. Brown and J.A. Tuszynski(University of Alberta, Canada ) |

**A model of dynamics of mutation, genetic drift and recombination in DNA-repeat genetic loci**

Joanna Polańska(Silesian University of Technology, Poland) | Marek Kimmel(Rice University, USA) |

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

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