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The EM algorithm and its implementation for the estimation of frequencies of SNP-haplotypes

Joanna Polańska (2003)

International Journal of Applied Mathematics and Computer Science

A haplotype analysis is becoming increasingly important in studying complex genetic diseases. Various algorithms and specialized computer software have been developed to statistically estimate haplotype frequencies from marker phenotypes in unrelated individuals. However, currently there are very few empirical reports on the performance of the methods for the recovery of haplotype frequencies. One of the most widely used methods of haplotype reconstruction is the Maximum Likelihood method, employing...

Time delays in proliferation and apoptosis for solid avascular tumour

Urszula Foryś, Mikhail Kolev (2003)

Banach Center Publications

The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the...

Towards prediction of HCV therapy efficiency.

Wasik, Szymon, Jackowiak, Paulina, Krawczyk, Jacek B., Kedziora, Paweł, Formanowicz, Piotr, Figlerowicz, Marek, Błażewicz, Jacek (2010)

Computational & Mathematical Methods in Medicine

Two algorithms based on Markov chains and their application to recognition of protein coding genes in prokaryotic genomes

Małgorzata Grabińska, Paweł Błażej, Paweł Mackiewicz (2013)

Applicationes Mathematicae

Methods based on the theory of Markov chains are most commonly used in the recognition of protein coding sequences. However, they require big learning sets to fill up all elements in transition probability matrices describing dependence between nucleotides in the analyzed sequences. Moreover, gene prediction is strongly influenced by the nucleotide bias measured by e.g. G+C content. In this paper we compare two methods: (i) the classical GeneMark algorithm, which uses a three-periodic non-homogeneous...

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