Thermodynamic Characterization of Temporal Networks

详细信息    查看全文

• 关键词：Complex networks ; Quantum thermodynamics ; Graphs
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：10029
• 期：1
• 页码：49-59
• 全文大小：586 KB
• 参考文献：1.Arbeitman, M.N., Furlong, E.E., Imam, F., Johnson, E., Null, B.H., Baker, B.S., Krasnow, M.A., Scott, M.P., Davis, R.W., White, K.P.: Gene expression during the life cycle of drosophila melanogaster. Science 297(5590), 2270–2275 (2002)CrossRef
  2.Escolano, F., Hancock, E.R., Lozano, M.A.: Heat diffusion: thermodynamic depth complexity of networks. Phys. Rev. E 85(3), 036206 (2012)CrossRef
  3.Estrada, E.: The Structure of Complex Networks: Theory and Applications. OUP, Oxford (2011)CrossRef
  4.Estrada, E.: Introduction to complex networks: structure and dynamics. In: Banasiak, J., Mokhtar-Kharroubi, M. (eds.) Evolutionary Equations with Applications in Natural Sciences. LNM, vol. 2126, pp. 93–131. Springer, Heidelberg (2015). doi:10.​1007/​978-3-319-11322-7_​3
  5.Farhi, E., Gutmann, S.: Quantum computation and decision trees. Phys. Rev. A 58(2), 915 (1998)MathSciNet CrossRef
  6.Huang, K.: Statistical Mechanics. Wiley, New York (1987)MATH
  7.Javarone, M.A., Armano, G.: Quantum-classical transitions in complex networks. J. Stat. Mech.: Theor. Exp. 2013(04), P04019 (2013)
  8.Mikulecky, D.C.: Network thermodynamics and complexity: a transition to relational systems theory. Comput. Chem. 25(4), 369–391 (2001)CrossRef
  9.Newman, M.E.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)MathSciNet CrossRef MATH
  10.Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)CrossRef MATH
  11.Passerini, F., Severini, S.: Quantifying complexity in networks: the Von Neumann entropy. Int. J. Agent Technol. Syst. (IJATS) 1(4), 58–67 (2009)CrossRef
  12.Peron, T.D., Rodrigues, F.A.: Collective behavior in financial markets. EPL (Europhys. Lett.) 96(4), 48004 (2011)CrossRef
  13.Song, L., Kolar, M., Xing, E.P.: Keller: estimating time-varying interactions between genes. Bioinformatics 25(12), i128–i136 (2009)CrossRef
  14.Ye, C., Comin, C.H., Peron, T.K.D., Silva, F.N., Rodrigues, F.A., Costa, L.D.F., Torsello, A., Hancock, E.R.: Thermodynamic characterization of networks using graph polynomials. Phys. Rev. E 92(3), 032810 (2015)CrossRef
  15.Ye, C., Torsello, A., Wilson, R.C., Hancock, E.R.: Thermodynamics of time evolving networks. In: Liu, C.-L., Luo, B., Kropatsch, W.G., Cheng, J. (eds.) GbRPR 2015. LNCS, vol. 9069, pp. 315–324. Springer, Heidelberg (2015). doi:10.​1007/​978-3-319-18224-7_​31
  
• 作者单位：Giorgia Minello (18)
  Andrea Torsello (18)
  Edwin R. Hancock (19)
  
  18. DAIS, Università Ca’ Foscari Venezia, Venice, Italy
  19. Department of Computer Science, University of York, York, UK
  
• 丛书名：Structural, Syntactic, and Statistical Pattern Recognition
• ISBN：978-3-319-49055-7
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：10029

文摘

Time-evolving networks have proven to be an efficient and effective means of concisely characterising the behaviour of complex systems over time. However, the analysis of such networks and the identification of the underlying dynamical process has proven to be a challenging problem, particularly trying to model the large-scale properties of graphs. In this paper we present a novel method to characterize the behaviour of the evolving systems based on a thermodynamic framework for graphs. This framework aims at relating the major structural changes in time evolving networks to thermodynamic phase transitions. This is achieved by relating the thermodynamics variables to macroscopic changes in network topology. First, by considering a recent quantum-mechanical characterization of the structure of a network, we derive the network entropy. Then we adopt a Schrödinger picture of the dynamics of the network, in order to obtain a measure of energy exchange through the estimation of a hidden time-varying Hamiltonian from the data. Experimental evaluations on real-world data demonstrate how the estimation of this time-varying energy operator strongly characterizes the different states of time evolving networks.