Article Open Access http://dx.doi.org/10.26855/jamc.2018.05.005
Application of Graph Extension Function in Nature
Irakli Avalishvili
Vladimir Chavchanidze Institute of Cybernetics of the Georgian Technical University Zurab Anjafaridze str. 5, Tbilisi 0186, (GEORGIA)
*Corresponding author: Irakli Avalishvili
Published: May 24,2018
Abstract
Arbitrary systems, will it
be biological, physical, cybernetic, etc. may be described by a mathematical
function, namely by a graph extension function, which we also call hierarchical function (and
which mathematically shows hierarchical nature of science). This function can be also used to describe
mathematical objects themselves, which in the paper is shown on the example of
the action of the graph extension function on the set of integers.
A new theory of
graph extensions, similar to group extension theory, is outlined. A theorem
about the equivalence of different extension functions is proved. There exists
an isomorphism between the modified functional graph of the cell (functional
block-scheme) and the morphological graph of the cell (the graph expressing topological
membrane inter transformations of the cell) which expresses the most essential
features of the cell and captures one of the specific differences between
living and non-living systems.
It is shown that
the construction of the graph of a complex organism from the primordial graph
given by Rashevsky is nothing but an extension of the primordial graph by the
graph extension function.
It is described
that there exist morphisms from biological graphs described by various authors
to our functional graph.
References
[1] Avalishvili I.P. Isomorphism between morphological and functional graphs of the cell and classification of cells by the extension of graphs. J. Biol. Phys, Chem. 1(2001),5-9)
[2] Avalishvili I.P. and Berishvili G.D. Extensions of automata. Trudi IK AN GSSR (Prov. Inst. Cybernetic Acad. Sci. Georgia) 1977, 183-188. Tbilisi: Mecniereba.
[3] Avalishvili I.P. “Most significant function of Georgia”, (in Georgian)" საქართველოს უმნიშვნელოვანესი ფუნქცია “vol.7., 2001, 541-544.
[4] Xarary F. Graph theory, p. 225. Addison-Wesey(1969).
How to cite this paper
Application of Graph Extension Function in Nature
How to cite this paper: Irakli Avalishvili. (2018) Application of Graph Extension Function in Nature. Journal of Applied Mathematics and Computation, 2(5), 208-232.
DOI: http://dx.doi.org/10.26855/jamc.2018.05.005