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Model and structure of locally linearly approximated signal in application to heliobiology


V.A. Ozheredov – Ph. (Phys.-Mat.), Leading Mathematician, Space Research Institute Russian Academy of Sciences (Moscow) E-mail: T.K. Breus – Dr.Sc. (Phys.-Mat.), Chief Research Scientist, Space Research Institute Russian Academy of Sciences (Moscow) E-mail:

Whether the nonlinear relationship of physiological and helio-geomagnetic parameters possesses by properties that allow detecting them by linear methods remains an open question in heliobiology. In order to verify whether the linear methodological approaches to the task of processing the changing helio-biological database are legitimate, this paper attempting to answer on this question. The object of locally linear approximation (smooth multi-dimensional relationship) - irrespective of the particular approximating algorithm that allows us to generalize some properties of such dependencies, as well as a means to get their modeling for numerical experiment are considered. We prove a key theorem for the application of a significant number of statistical approaches to helio-biological studies on obligatory presence of a linear component in sufficiently smooth required dependencies .Smoothness depending is formalized through a radius of planarity, which determines the minimum resolution algorithm of locally linear approximation. For the purposes of the numerical experiment a method of creating an artificial database, an adaptor part of which is a collection noise free realization of the dependent variables of a random function with a given radius of planarity is developed. Introduced analysis justifies many of the previous studies, as well as allowing to solve in a large extent the pre-existing doubts and contradictions in heliobiological researches.


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