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

Giuseppe Caristi (Department of Economics, University of Messina, Italy)
Sabrina Lo Bosco (Course of Studies in Civil Engineering, Faculty of Law, Pegaso University, Italy)

Abstract


A systematic approach is proposed to the theme of safety, reliability andglobal quality of complex networks (material and immaterial) by meansof special mathematical tools that allow an adequate geometric characterization and study of the operation, even in the presence of multipleobstacles along the path. To that end, applying the theory of graphs tothe problem under study and using a special mathematical model basedon stochastic geometry, in this article we consider some regular latticesin which it is possible to schematize the elements of the network, withthe fundamental cell with six, eight or 2(n+2) obstacles, calculating theprobability of Laplace. In this way it is possible to measure the “degree ofimpedance” exerted by the anomalies along the network by the obstaclesexamined. The method can be extended to other regular and / or irregulargeometric figures, whose union together constitutes the examined network, allowing to optimize the functioning of the complex system considered.

Keywords


Mathematical models, Tangible and intangible network infras- tructures, Safety, Reliability, Stochastic geometry, Random sets, Random convex sets and Integral geometry, Logistics and transport, Social Network Analysis, WEB, Resilience analysis, Critical

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

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