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Physicist’s approach to public transportation networks: between data processing and statistical physics

100%
Korduba Y., Holovatch Y., de Regt R.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2019
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tom 73
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nr 2
EN
In this paper we aim to demonstrate how physical perspective enriches statistical analysis when dealing with a complex system of many interacting agents of non-physical origin. To this end, we discuss analysis of urban public transportation networks viewed as complex systems. In such studies, a multi-disciplinary approach is applied by integrating methods in both data processing and statistical physics to investigate the correlation between public transportation network topological features and their operational stability. These studies incorporate concepts of coarse graining and clusterization, universality and scaling, stability and percolation behavior, diffusion and fractal analysis.
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Nanonetworks: The graph theory framework for modeling nanoscale systems

63%
Živkovic J., Tadic B.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
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2013
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tom 2
30-48
EN
Nanonetwork is defined as a mathematical model of nanosize objects with biological, physical and chemical attributes, which are interconnected within certain dynamical process. To demonstrate the potentials of this modeling approach for quantitative study of complexity at nanoscale, in this survey, we consider three kinds of nanonetworks: Genes of a yeast are connected by weighted links corresponding to their coexpression along the cell cycle; Gold nanoparticles, arranged on a substrate, are linked via quantum tunneling junctions which enable single-electron conduction; A network of similar profiles of force–distance curves consists of sequences of states of a molecular complex from HIV–1 virus observed in repeated single-molecule force spectroscopy experiments. The graph-theory analysis of these systems reveals their organizational principles, quantifies the relation between the function of nanostructured materials and their architecture, and helps understand the character of fluctuations at nanoscale.
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