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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.