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

Korduba, Yaryna ; Holovatch, Yurij ; de Regt, Robin

Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 73 (2019) no. 2.

Résumé

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.

Détail

Keywords: Complex systems, complex networks, statistical physics, transportation networks

Bibliographie

[1] Albert, R., Barabasi, A.-L., Statistical mechanics of complex networks, Rev. Mod. Phys. 74 (2002), 47–97.

[2] Alessandretti, L., Karsai, M., Gauvin, L., User-based representation of time-resolved multimodal public transportation networks, Open Science 3 (2016), 160156.

[3] Anderson, P. W., More is different, Science 177 (1972), 393–396.

[4] Barabasi, A.-L., Albert, R., Emergence of scaling in random networks, Science 286 (1999), 509–512.

[5] Barabasi, A.-L., Albert, R., Jeong, H., Mean-field theory for scale-free random networks, Physica A 272 (1999), 173–187.

[6] Barthelemy, M., Spatial networks, Physics Reports 499 (1) (2011), 1–101.

[7] Benguigui, L., The fractal dimension of some railway networks, Journal de Physique 2 (1992), 385–388.

[8] Benguigui, L., Daoud, M., Is the suburban railway system a fractal?, Geographical Analysis 23 (1991), 362–368.

[9] Benguigui, L., A fractal analysis of the public transportation system of Paris, Environment and Planning A 27 (1995), 1147–1161.

[10] Benguigui, L., The fractal dimension of some railway networks, Journal de Physique I 2 (1992), 385–388.

[11] Berche, B., von Ferber, C., Holovatch, T., Network harness: bundles of routes in public transport networks, AIP Conference Proceedings, vol. 1198, AIP, 2009, 3–12.

[12] Berche, B., von Ferber, C., Holovatch, T., Holovatch, Yu., Resilience of public transport networks against attacks, The European Physical Journal B 71 (1) (2009), 125–137.

[13] Berche, B., von Ferber, C., Holovatch, T., Holovatch, Yu., Transportation network stability: a case study of city transit, Advances in Complex Systems 15 (supp01) (2012), 1250063.

[14] Bollobas, B., Random Graphs, 2 ed., Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2001.

[15] Chang, H., Su, B., Zhou, Y., He, D., Assortativity and act degree distribution of some collaboration networks, Physica A: Statistical Mechanics and its Applications 383 (2007), 687–702.

[16] Corominas-Murtra, B., Hanel, R., Thurner, S., Understanding scaling through historydependent processes with collapsing sample space, Proc. Nat. Acad. Sci. USA 112 (2015), 5348–5353.

[17] Daletskii, A., Kondratiev, Yu., Kozitsky, Yu., Pasurek, T., A phase transition in a quenched amorphous ferromagnet, Journal of Statistical Physics 156 (2014), 156–176.

[18] de Regt, R., Complex Networks: Topology, Shape and Spatial Embedding, Doctoral Thesis, Coventry University, Coventry, UK, 2017.

[19] de Regt, R., von Ferber, C., Holovatch, Yu., Lebovka, M., Public transportation in Great Britain viewed as a complex network, Transportmetrica A: Transport Science 15 (2) (2019), 722–748.

[20] Dorogovtsev, S. N., Mendes, J. F. F., Evolution of Networks, Oxford University Press, Oxford, 2003.

[21] Essam, J. W., Percolation theory, Reports on Progress in Physics 43 (7) (1980), 833–912.

[22] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., A density-based algorithm for discovering clusters a density-based algorithm for discovering clusters in large spatial databases with noise, in: Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, KDD’96, AAAI Press, 1996, 226–231.

[23] Feder, J., Evolution of Networks, Springer US, 1988.

[24] von Ferber, C., Holovatch, Yu., Fractal transit networks: self-avoiding walks and Levy flights, The European Physical Journal ST 216 (2013), 49–55.

[25] von Ferber, C., Berche, B., Holovatch, T., Holovatch, Y., A tale of two cities, Journal of Transportation Security 5 (2012), 199–216.

[26] von Ferber, C., Holovatch, T., Holovatch, Yu., Palchykov, V., Public transport networks: empirical analysis and modeling, The European Physical Journal B 68 (2) (2009), 261–275.

[27] von Ferber, C., Holovatch, T., Holovatch, Yu., Palchykov, V., Network harness: Metropolis public transport, Physica A: Statistical Mechanics and its Applications 380 (2007), 585–591.

[28] von Ferber, C., Holovatch, T., Holovatch, Yu., Attack vulnerability of public transport networks, in: Traffic and Granular Flow07, Springer, 2009, 721–731.

[29] von Ferber, C., Holovatch, T., Holovatch, Yu., Palchykov, V., Modeling metropolis public transport, in: Traffic and Granular Flow07, Springer, 2009, 709–719.

[30] Frankhauser, P., Aspects fractals des structures urbaines, L’Espace Geographique 19 (1990), 45–69.

[31] Gallotti, R., Barthelemy, M., The multilayer temporal network of public transport in Great Britain, Scientific Data 2 (2015), 140056.

[32] Ghosh, S., Banerjee, A., Sharma, N., Agarwal, S., Mukherjee, A., Ganguly, N., Structure and evolution of the Indian railway network, in: Summer Solstice International Conference on Discrete Models of Complex Systems (SOLSTICE), 2010.

[33] Goldenfeld, N., Kadanoff, L. P., Simple lessons from complexity, Science 284 (1999), 87–89.

[34] Guida, M., Maria, F., Topology of the Italian airport network: A scale-free small-world network with a fractal structure?, Chaos, Solitons Fractals 31 (2007), 527–536.

[35] Guimera, R., Nunes Amaral, L. A., Modeling the world-wide airport network, The European Physical Journal B-Condensed Matter and Complex Systems 38 (2004), 381–385.

[36] Guimera, R., Mossa, S., Turtschi, A., Nunes Amaral, L., The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles, Proc. Nat. Acad. Sci. USA 102 (2005), 7794–7799.

[37] Guo, L., Zhu, Y., Luo, Z., Li, W., The scaling of several public transport networks in China, Fractals 21 (2013), 1350010.

[38] Holovatch, T., Complex Transportation Networks: Resilience, Modelling and Optimization, Doctoral Thesis, Universite Henri Poincare – Nancy 1 and Coventry University, 2011.

[39] Holovatch, Yu., von Ferber, C., Olemskoi, A., Holovatch, T., Mryglod, O., Olemskoi, I., Palchykov, V., Complex networks, Journ. Phys. Stud. 10 (2006), 247–291 (Ukrainian).

[40] Holovatch, Yu., (ed.), Order, Disorder and Criticality. Advanced Problems of Phase Transition Theory, Vol. I–V, World Scientific, Singapore, 2004–2018.

[41] Holovatch, Yu., Kenna, R., Thurner, S., Complex systems: physics beyond physics, European Journal of Physics 314 (2017), 023002.

[42] Kadanoff, L. P., Scaling laws for Ising models near tc, Physics Physique Fizika 2 (1966), 263–272.

[43] Kim, K. S., Kwan, S. K., Benguigui, L., Marinov, M., The fractal structure of Seoul’s public transportation system, Cities 20 (2003), 31–39.

[44] Korduba, Ya., Public transport networks: Topological features and stability analysis, Bachelor Thesis, Ukrainian Catholic University, Lviv, 2019.

[45] Kozitsky, Yu., Mathematical theory of the Ising model and its generalizations: an introduction, in: Order, Disorder and Criticality. Advanced Problems of Phase Transition Theory (Yu. Holovatch, ed.), World Scientific, 2004, 1–66.

[46] Kozitsky, Yu., Pilorz, K., Random jumps and coalescence in the continuum: evolution of states of an infinite system, preprint arXiv:1807.07310 [math.DS] (2018).

[47] Kozitsky, Yu. V., Hierarchical model of a vector ferromagnet – self-similar block-spin distributions and the Lee-Yang theorem, Reports on Mathematical Physics 26 (3) (1988), 429–445.

[48] Ladyman, J., Lambert, J., Wiesner, K., What is a complex system?, Eur. Journ. Philos. Sci. 3 (2013), 33–67.

[49] Latora, V., Marchiori, M., Is the Boston subway a small-world network?, Physica A: Statistical Mechanics and its Applications 314 (1–4) (2002), 109–113.

[50] Mandelbrot, B., An informational theory of the statistical structure of languages, in: Communication Theory (Woburn, MA) (W. Jackson, ed.), Butterworth, 1953, 486–502.

[51] Mitzenmacher, M., A brief history of generative models for power law and lognormal distributions, Internet Mathematics 1 (2004), 226–251.

[52] Molloy, M., Reed, B., A critical point for random graphs with a given degree sequence, Random Structures Algorithms 6 (2–3) (1995), 161–180.

[53] Newman, M., Barabasi, A.-L., Watts, D. J., The Structure and Dynamics of Networks, Princeton University Press, Princeton, New Jersey, 2006.

[54] Newman, M. E. J., Power laws, Pareto distributions and Zipf’s law, Contemporary Physics 46 (2005), 323–351.

[55] Nienhuis, B., Exact critical point and critical exponents of O(n) models in two dimensions, Phys. Rev. Lett. 49 (1982), 1062–1065.

[56] Parisi, G., Complex systems: a physicist’s viewpoint, Physica A 263 (1999), 557–564.

[57] Russo, G., Nicosia, V., Latora, V., Complex Networks: Principles, Methods and Applications, Cambridge university press, Cambridge, 2017.

[58] Schneider, C. M., Moreira, A. A., Andrade, J. S., Havlin, S., and Hans J Herrmann, Mitigation of malicious attacks on networks, Proceedings of the National Academy of Sciences 108 (10) (2011), 3838–3841.

[59] Seaton, K., Hackett, L., Stations, trains and small-world networks, Physica A 339 (2004), 635–644.

[60] Sen, P., Dasgupta, S., Chatterjee, A., Sreeram, P., Mukherjee, G., Manna, S., Smallworld properties of the Indian railway network, Physical Review E 67 (3) (2003), 036106.

[61] Sengupta, A. (ed.), Chaos, Nonlinearity, Complexity: The Dynamical Paradigm of Nature, Sringer, 2006.

[62] Shanmukhappa, T., Ho, I. W. H., Tse, C. K., Bus transport network in Hong Kong: Scale-free or not?, in: 2016 International Symposium on Nonlinear Theory and Its Applications, NOLTA2016, Yugawara, Japan, November 27th–30th, 2016, 610–614.

[63] Sherrington, D., Physics and complexity, Phil. Trans. Roy. Soc. A 368 (2010), 1175–1189.

[64] Sienkiewicz, J., Hołyst, J., Statistical analysis of 22 public transport networks in Poland, Physical Review E 72 (2005), 46127.

[65] Simkin, M. V., Roychowdhury, V. P., Re-inventing Willis, Physics Reports 502 (2011), 1–35.

[66] Simon, H. A., On a class of skew distribution functions, Biometrika 42 (1955), 425–440.

[67] Soh, H., Lim, S., Zhang, T., Fu, X., Lee, G., Hung, T., Di, P., Prakasam, S., Wong, L., Weighted complex network analysis of travel routes on the Singapore public transportation system, Physica A: Statistical Mechanics and its Applications 389 (2010), 5852–5863.

[68] Stanley, H. E., Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, 1971.

[69] Stauffer, D., Aharony, A., Introduction to Percolation Theory, Taylor Francis, London, 1991.

[70] Sui, Y., Shao, F., Sun, R., Li, S., Space evolution model and empirical analysis of an urban public transport network, Physica A: Statistical Mechanics and its Applications 391 (2012), 3708–3717.

[71] Thibault, S., Marchand, A., (eds.), Reseaux et Topologie, Institut National des Sciences Appliquees de Lyon, Villeurbanne, 1987.

[72] Thurner, S., Hanel, R., Klimek, P., Introduction to the Theory of Complex Systems, Oxford University Press, 2018.

[73] Thurner, S., (ed.), Visions for Complexity, World Scientific, Singapore, 2016.

[74] Xu, X., Hu, J., Liu, F., Liu, L., Scaling and correlations in three bus-transport networks of China, Physica A: Statistical Mechanics and its Applications 374 (2007), 441–448.

[75] Yang, X. H., Chen, G., Sun, B., Chen, S. Y., Wang, W. L., Bus transport network model with ideal n-depth clique network topology, Physica A: Statistical Mechanics and its Applications 390 (2011), 4660–4672.