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




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.


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


[1] Adhikari A. (2007), Using Data Network Metrics, Graphics and Topology to Explore Network Characteristics, Networks and Beyond, Vol. 54, pp. 62-75.

[2] Armondi S. (2012), Gli insediamenti produttivi nella società-crescita. Riscrittura di politiche e progetti, in Atti della XV Conferenza Nazionale SIU, L'Urbanistica che cambia. Rischi e valori, Pescara, 10-11 maggio 2012.

[3] Barabasi A., Oltvai Z. L. (2004), Networks biology: understanding the cellsfunctional organization, Nature Reviews Genetics, vol. 5, n. 2, pp. 101-113.

[4] Bianchetti C. (2008), Urbanistica e sfera pubblica, Donzelli, Roma.

[5] Boscacci F. (2003), La nuova logistica. Una industria in formazione tra territorio, ambiente e sistema economico, Egea, Milano.

[6] Bruneau M.e Co. (2003) A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities, Earthquake Spectra, vol. 19, n. 4, pp. 733-752, November 2003.

[7] Caristi G. and Stoka M. (2010), A Laplace type problem for a regular lattice with obstacles (I), Atti Acc. Sci. Torino, vol. 144, pp. 65-74.

[8] Caristi G. and Stoka M. (2010), A Laplace type problem for a regular lattice

[9] with obstacles (II), Atti Acc. Sci. Torino, vol. 144, pp. 109-131.

[10] Jenelius E. (2009), Network structure and travel patterns explaining the geographical disparities of road network vulnerability, Journal of Transport Geography, 17(3), pp. 234-244.

[11] Husdal J. (2004), Reliability and vulnerability ? a non-issue in cost-benet analyses - Samferdsel (Journal of the Norwegian Institute for Transport Economics), 2/2004, pp. 28-30.

[12] Henry D., Ramirez-Marquez J. E. (2012), Generic metrics and quantitative approaches for system resilience as a function of time, Reliability Engineering and System Safety, n. 99, pp. 114-122, 2012.

[13] Leonardi G., Moretti M., Stoka M. (2003), L'analisi del funzionamento della rete. Un approccio metodologico. Argomenti, N. 1, R.F.I.

[14] Lin N., Cook K., Burt R. S. (2001), Social Capital. Theory and Research, Aldine De Gruyter, New York, cap. 1-2.

[15] Lo Bosco S e Altri (2019), Analysis of project variables in the process of optimizing the mobility-economy- environment trinomial: the acoustic impact in the railway case- IF Ingegneria Ferroviara, N. 11, Novembre 2019.

[16] Lo Bosco S e Altri (2019), Evaluation of Investments for Mobility: a Mathematical Model of Decision Aid, LaborEst n. 19/2019. doi: 10.19254/LaborEst.19.

[17] Pedroni P., Rotondi A. (2005), Probabilita, statistica e simulazione. Springer Verlag, Milano.

[18] Poincare H., (1912), Calcul des probabilities, ed. 2, Carre, Paris.

[19] Reggiani A. (2012), Network resilience for transport security: some methodological considerations, Transport policy.

[20] Salvo M. (2015), Metti il turbo alla tua mente con le mappe mentali. Per professionisti, manager e studenti che vogliono trovare la rotta verso risultati straordinari, Ed. Gribaudo, Milano.

[21] Stoka M. (1976), Probabilites geometriques de type Buon dans le plan euclidean, Atti Acc. Sci. Torino, T. 110, pp. 53-59, 1975-1976.

[22] Trobia A., Milia V. (2011), Social Network Analysis. Approcci, tecniche e nuove applicazioni, Carrocci, Roma.



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