Biomathematics Seminar: Stochastic Matrices as a tool for modelling of Biological processes
20 November 2012 14:00 in CM105
In this lecture we present a method of statistical analysis of dynamical changes and evolutionary trends in biological systems. When dealing with a great number of similar events or objects, we turn naturally to statistical analysis and probability distributions. It is often impossible, (and useless) to keep track of all characteristics of single items in the swarm of data. The precise knowledge of the exact numbers of items found in a given state at a given time is often out of reach experimentally.
On the contrary, the average values given by statistical analysis of data, are often the only useful experimental information available. The analysis of dynamical changes and evolutionary trends in biological systems are given then in terms of probabilities of finding a given state or configuration. Stochastic matrices transform a probability distribution into another one, keeping the normalization to 1.They display at least one asymptotic regime which can be considered as stable final configuration.
Several examples and applications are presented, from stochastic growth and agglomeration to viral capsid construction and development and transmission of hereditary features.
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