Optimization Processes of Tangible and Intangible Networks through the Laplace Problems for Regular Lattices with Multiple Obstacles along the Way

Updata:01-01-1970

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By:Giuseppe Caristi

DOI: https://doi.org/10.30564/jbar.v3i3.1898

Abstract:
A systematic approach is proposed to the theme of safety, reliability and
global quality of complex networks (material and immaterial) by means
of special mathematical tools that allow an adequate geometric charac
terization and study of the operation, even in the presence of multiple
obstacles along the path. To that end, applying the theory of graphs to
the problem under study and using a special mathematical model based
on stochastic geometry, in this article we consider some regular lattices
in which it is possible to schematize the elements of the network, with
the fundamental cell with six, eight or 2(n+2) obstacles, calculating the
probability of Laplace. In this way it is possible to measure the “degree of
impedance” exerted by the anomalies along the network by the obstacles
examined. The method can be extended to other regular and / or irregular
geometric figures, whose union together constitutes the examined network, allowing to optimize the functioning of the complex system considered.
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