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Population genetics models for the statistics of DNA samples under different demographic scenarios - Maximum likelihood versus approximate methods

Andrzej PolańskiMarek Kimmel — 2003

International Journal of Applied Mathematics and Computer Science

The paper reviews the basic mathematical methodology of modeling neutral genetic evolution, including the statistics of the Fisher-Wright process, models of mutation and the coalescence method under various demographic scenarios. The basic approach is the use of maximum likelihood techniques. However, due to computational problems, intuitive or approximate methods are also of great importance.

A general on-the-fly algorithm for modifying the kinematic tree hierarchy

Jakub StępieńAndrzej PolańskiKonrad Wojciechowski — 2012

International Journal of Applied Mathematics and Computer Science

When conducting a dynamic simulation of a multibody mechanical system, the model definition may need to be altered during the simulation course due to, e.g., changes in the way the system interacts with external objects. In this paper, we propose a general procedure for modifying simulation models of articulated figures, particularly useful when dealing with systems in time-varying contact with the environment. The proposed algorithm adjusts model connectivity, geometry and current state, producing...

Node assignment problem in Bayesian networks

Joanna PolanskaDamian BorysAndrzej Polanski — 2006

International Journal of Applied Mathematics and Computer Science

This paper deals with the problem of searching for the best assignments of random variables to nodes in a Bayesian network (BN) with a given topology. Likelihood functions for the studied BNs are formulated, methods for their maximization are described and, finally, the results of a study concerning the reliability of revealing BNs' roles are reported. The results of BN node assignments can be applied to problems of the analysis of gene expression profiles.

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