Equilibrium Processes in Biomedical Data Analysis: The Wright–Fisher Model

The biological process of cooperative interaction with equilibrium state is described as a model of binary statistical experiments with the Wright–Fisher normalization, which sets the concentration of a certain characteristic. Such mathematical model is supposed to have the property of persistent re...

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Bibliographic Details
Published in:Cybernetics and systems analysis 2014-11, Vol.50 (6), p.890-897
Main Authors: Koroliouk, D. V., Koroliuk, V. S., Rosato, N.
Format: Article
Language:English
Subjects:
Approximation
Artificial Intelligence
Biological activity
Biomedical research
Control
Data analysis
Disturbances
Dynamic tests
Enzymes
Equilibrium
Experiments
Hypotheses
Ligands
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Parabolas
Probability
Processor Architectures
Random variables
Regression
Regression analysis
Software Engineering/Programming and Operating Systems
Statistical methods
Studies
Systems Theory
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Summary:The biological process of cooperative interaction with equilibrium state is described as a model of binary statistical experiments with the Wright–Fisher normalization, which sets the concentration of a certain characteristic. Such mathematical model is supposed to have the property of persistent regression, which means that all current elementary transitions depend on the mean concentration of the said characteristics in the previous state. Equilibrium state of the model is expressed in terms of the regression function given by a cubic parabola with three real roots. We construct the stochastic approximation of the model by autoregressive process with normal disturbances. Such an approach was developed for effective and calculable mathematical description of dynamic concentration for experiment planning, parameter evaluation, and verification of hypotheses of the mechanisms of action.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-014-9680-y