STOCHASTIC CANALIZATION OF PHENOTYPIC
DEFORMATIONS DURING ONTOGENESIS
Peter L. Antonelli1, C.G. Leandro2, Solange F. Rutz3
1,3U. Alberta, AB, CANADA, presently at:
DMAT - UFPE
Av. Prof. Moraes Rego, 1235 - Cidade Universitaria
Recife - PE - CEP: 50670-901, BRAZIL
2Department of Nutrition - UFPE
Av. Prof. Moraes Rego, 1235 - Cidade Universitaria
Recife - PE - CEP: 50670-901, BRAZIL

Abstract

This article presents a new application of the Stochastic Theory of Volterra-Hamilton Systems of Finsler class to growth and ontogeny and particularly to the study of noise effects on the deterministic model equations for interaction of muscle and adipose tissue in mammals introduced in our previous study. Both normal development and its phenotypic deformation, due to non-optimal nutrition or disease, are considered. Efficient energy (ATP) usage by the system as a whole is centrally important. Feynman-Kac solutions to the noisy perturbation equations and sojourn time probabilities for the Sasaki lift Riemannian diffusion are obtained, based on the Riemannian Embedding Theorem for Finslerian Diffusion. Stochastic canalization of development, after C. H. Waddington, is proved for this mathematical model.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 29
Issue: 6
Year: 2016

DOI: 10.12732/ijam.v29i6.2

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