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

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 characterization 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.

A Mathematical Methodology for the Preventive Study of the Failure Rate to Optimize the Maintenance Program of a Public Work: Economic-Management Aspects for Safety and Quality

In this paper we analyze the problem of the assessment of the failure rate of the complex public work system and the engineering part of it (bridge, tunnel, etc.), examining the case of serious maintenance problems, such as those which occurred in the recent disaster of the "Morandi bridge". The original mathematical methodology envisaged makes it possible to optimize the safety and quality scenarios of the operation and infrastructure in question, also from an economic-management point of view, evaluating every aspect in an integrated way and for the entire period life. The scientific results obtained are of particular interest for the study of maximization of the planning protocols of "terotechnological" interventions, providing a contribution to the science of programmed maintenance for the mobility networks and for more complex parts such as bridges and tunnels.

Road Network Analysis with GIS and GRASS-GIS:A Probabilistic Approach

In this paper we show how it can be useful to the probability of intersections in the determination of a classification rule for raster conversions in Geographical Information System(GIS)and GRASS GIS for the Road Network Analysis(RNA).We use a geometric probabilities approach for irregular path considering these results for transportation planning operations.We study two particular problems with irregular tessellations,in order to have a situation more realistic respect to map GIS and considering also the maximum value of probability to narrow the range of possible probability values.