فرایند براونی استاندارد متاثر از پرشیدگی زوایای دو سطحی
موسی گل علیزاده
دانشگاه تربیت مدرس
Describing the random change of proteins is of great importance from the probabilistic point of view. Although proteins have different geometrical structures, their second and third forms have received more attentions. It provided an opportunity for the probabilists to play a vital role in enriching the recent progress of bioinformatics. They have, initially, paid attention to the linear statistics due to those variables lying in some Euclidean space. However, they gradually realized that the non-linear statistics are better context to work because angles well describe the link between atoms. Notably, the dihedral angles are proved to, accurately, determine the molecular structure of proteins. Although many activities have been conducted on understanding the statistical analysis of these perspectives, to model their stochastic behaviors are rarely investigated. It might be due to the periodic properties of the dihedral angles. To define a standard Brownian motion on a torus, we utilize the connection between the tensor metric and the Laplace-Beltrami operator on a Riemannian manifold to derive the infinitesimal drift and diffusion coefficients. The algebraic manipulations are the key components on obtaining this important process, and it is shown how the symbolic notations are vital on tackling this procedure. The simulation studies will be performed to highlight the main achievements in this study.