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

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Abstract

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.

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Authors and Affiliations

  1. Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    D. V. Koroliouk

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. S. Koroliuk

  3. Tor Vergata University of Rome and NAST Centre for Nanoscience & Nanotechnology & Innovative Instrumentation, Rome, Italy

    N. Rosato

Authors
  1. D. V. Koroliouk
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  2. V. S. Koroliuk
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  3. N. Rosato
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Corresponding author

Correspondence to D. V. Koroliouk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2014, pp. 80–86.

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Koroliouk, D.V., Koroliuk, V.S. & Rosato, N. Equilibrium Processes in Biomedical Data Analysis: The Wright–Fisher Model. Cybern Syst Anal 50, 890–897 (2014). https://doi.org/10.1007/s10559-014-9680-y

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  • DOI: https://doi.org/10.1007/s10559-014-9680-y

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