- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Maximal dispersion of adaptive random walks

Gabriele Di Bona1, Leonardo Di Gaetano2, Vito Latora1,3,4, and Francesco Coghi5,*

  • 1School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, England
  • 2Department of Network and Data Science, Central European University, 1100 Vienna, Austria
  • 3Dipartimento di Fisica ed Astronomia, Università di Catania and INFN, I-95123 Catania, Italy
  • 4Complexity Science Hub Vienna (CSHV), Josefstädter Straße 39, 1080 Vienna, Austria
  • 5Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden

  • *francesco.coghi@su.se
PDF

Phys. Rev. Research 4, L042051 – Published 30 December, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042051

Abstract

Maximum entropy random walks (MERWs) are maximally dispersing and play a key role in optimizing information spreading in various contexts. However, building MERWs comes at the cost of knowing beforehand the global structure of the network, a requirement that makes them totally inadequate in real-case scenarios. Here, we propose an adaptive random walk (ARW), which instead maximizes dispersion by updating its transition rule on the local information collected while exploring the network. We show how to derive ARW via a large-deviation representation of MERW and study its dynamics on synthetic and real-world networks.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (64)

  1. S. Albeverio, V. Jentsch, and H. Kantz (Eds.), Extreme Events in Nature and Society, The Frontiers Collection (Springer, Berlin Heidelberg, 2006).
  2. V. Kishore, M. S. Santhanam, and R. E. Amritkar, Extreme Events on Complex Networks, Phys. Rev. Lett. 106, 188701 (2011).
  3. V. Kishore, M. S. Santhanam, and R. E. Amritkar, Extreme events and event size fluctuations in biased random walks on networks, Phys. Rev. E 85, 056120 (2012).
  4. Y. Z. Chen, Z. G. Huang, and Y. C. Lai, Controlling extreme events on complex networks, Sci. Rep. 4, 6121 (2014).
  5. Y. Z. Chen, Z. G. Huang, H. F. Zhang, D. Eisenberg, T. P. Seager, and Y. C. Lai, Extreme events in multilayer, interdependent complex networks and control, Sci. Rep. 5, 17277 (2015).
  6. J. Hindes and I. B. Schwartz, Epidemic Extinction and Control in Heterogeneous Networks, Phys. Rev. Lett. 117, 028302 (2016).
  7. C. De Bacco, A. Guggiola, R. Kühn, and P. Paga, Rare events statistics of random walks on networks: localisation and other dynamical phase transitions, J. Phys. A: Math. Theor. 49, 184003 (2016).
  8. J. Hindes and I. B. Schwartz, Large order fluctuations, switching, and control in complex networks, Sci. Rep. 7, 10663 (2017).
  9. G. Bianconi, Rare events and discontinuous percolation transitions, Phys. Rev. E 97, 022314 (2018).
  10. F. Coghi, F. Radicchi, and G. Bianconi, Controlling the uncertain response of real multiplex networks to random damage, Phys. Rev. E 98, 062317 (2018).
  11. W. Staffeldt and A. K. Hartmann, Rare-event properties of the Nagel-Schreckenberg model, Phys. Rev. E 100, 062301 (2019).
  12. F. Coghi, J. Morand, and H. Touchette, Large deviations of random walks on random graphs, Phys. Rev. E 99, 022137 (2019).
  13. R. Gutiérrez and C. Pérez-Espigares, Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks, Phys. Rev. E 103, 022319 (2021).
  14. G. Carugno, P. Vivo, and F. Coghi, Delocalization-localization dynamical phase transition of random walks on graphs [Phys. Rev. E (to be published)], arXiv:2206.09866 (2022).
  15. A. Kumar, S. Kulkarni, and M. S. Santhanam, Extreme events in stochastic transport on networks, Chaos 30, 043111 (2020).
  16. K. Gupta and M. S. Santhanam, Extreme events in NagelSchreckenberg model of traffic flow on complex networks, Eur. Phys. J.: Spec. Top. 230, 3201 (2021).
  17. G. Gandhi and M. Santhanam, Biased random walkers and extreme events on the edges of complex networks, Phys. Rev. E 105, 014315 (2022).
  18. J. D. Noh and H. Rieger, Random Walks on Complex Networks, Phys. Rev. Lett. 92, 118701 (2004).
  19. V. Colizza, R. Pastor-Satorras, and A. Vespignani, Reactiondiffusion processes and metapopulation models in heterogeneous networks, Nat. Phys. 3, 276 (2007).
  20. J. Gómez-Gardeñes and V. Latora, Entropy rate of diffusion processes on complex networks, Phys. Rev. E 78, 065102 (2008).
  21. R. Sinatra, J. Gómez-Gardeñes, R. Lambiotte, V. Nicosia, and V. Latora, Maximal-entropy random walks in complex networks with limited information, Phys. Rev. E 83, 030103 (2011).
  22. C. Toh, Ad Hoc Mobile Wireless Networks: Protocols and Systems (Prentice Hall PTR, 2002).
  23. Z. Burda, J. Duda, J. M. Luck, and B. Waclaw, Localization of the Maximal Entropy Random Walk, Phys. Rev. Lett. 102, 160602 (2009).
  24. L. Demetrius and T. Manke, Robustness and network evolution - an entropic principle, Physica A 346, 682 (2005).
  25. J.-C. Delvenne and A.-S. Libert, Centrality measures and thermodynamic formalism for complex networks, Phys. Rev. E 83, 046117 (2011).
  26. Y. Lin and Z. Zhang, Mean first-passage time for maximal-entropy random walks in complex networks, Sci. Rep. 4, 5365 (2014).
  27. F. Battiston, V. Nicosia, and V. Latora, Efficient exploration of multiplex networks, New J. Phys. 18, 043035 (2016).
  28. E. Estrada, Informational cost and networks navigability, Applied Mathematics and Computation 397, 125914 (2021).
  29. Y. Wang, X. Cao, T. Weng, H. Yang, and C. Gu, Lowest-degree preference random walks on complex networks, Physica A 577, 126075 (2021).
  30. J. K. Ochab and Z. Burda, Maximal entropy random walk in community finding, Eur. Phys. J.: Spec. Top. 216, 73 (2013).
  31. J. K. Ochab, Maximal-entropy random walk unifies centrality measures, Phys. Rev. E 86, 066109 (2012).
  32. Z. Xu, C. Pu, and J. Yang, Link prediction based on path entropy, Physica A 456, 294 (2016).
  33. I. Adam, D. Fanelli, T. Carletti, and G. Innocenti, Reactive explorers to unravel network topology, Eur. Phys. J. B 92, 99 (2019).
  34. Y. W. Niu, H. Liu, G. H. Wang, and G. Y. Yan, Maximal entropy random walk on heterogenous network for MIRNA-disease association prediction, Math. Biosci. 306, 1 (2018).
  35. M. Smerlak, Neutral quasispecies evolution and the maximal entropy random walk, Sci. Adv. 7, eabb2376 (2021).
  36. R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47 (2002).
  37. P. Holme and J. Saramäki, Temporal networks, Phys. Rep. 519, 97 (2012).
  38. N. Masuda and R. Lambiotte, A Guide to Temporal Networks, Series on Complexity Science, Vol. 4 (World Scientific, Europe, 2016).
  39. F. Coghi, Large deviation methods for the study of nonequilibrium systems: variational and spectral approaches, Ph.D. thesis, Queen Mary, University of London (2021).
  40. F. Coghi and H. Touchette, Adaptive power method for estimating large deviations in Markov chains, arXiv:2211.00060 (2022).
  41. T. M. Cover and J. A. Thomas, Elements of Information Theory, Vol. 2 (Wiley, New York, 2006) p. 748.
  42. U. Seifert, Entropy Production along a Stochastic Trajectory and an Integral Fluctuation Theorem, Phys. Rev. Lett. 95, 040602 (2005).
  43. H. Touchette, The large deviation approach to statistical mechanics, Phys. Rep. 478, 1 (2009).
  44. F. den Hollander, Large Deviations (American Mathematical Society, Providence, 2000).
  45. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Stochastic Modelling and Applied Probability, Vol. 38 (Springer Berlin Heidelberg, 2010).
  46. R. Chetrite and H. Touchette, Nonequilibrium Microcanonical and Canonical Ensembles and Their Equivalence, Phys. Rev. Lett. 111, 120601 (2013).
  47. R. Chetrite and H. Touchette, Nonequilibrium Markov processes conditioned on large deviations, Ann. Henri Poincaré 16, 2005 (2015).
  48. R. Chetrite and H. Touchette, Variational and optimal control representations of conditioned and driven processes, J. Stat. Mech.: Theory Exp. (2015) P12001.
  49. H. Touchette, Legendre–Fenchel transforms in a nutshell, Research Report, Rockefeller University, New York, 2007, https://appliedmaths.sun.ac.za/∼htouchette/archive/notes/lfth2.pdf.
  50. V. S. Borkar, S. Juneja, and A. A. Kherani, Peformance analysis conditioned on rare events: an adaptive simulation scheme, Commun. inf. syst. 3, 259 (2003).
  51. T. P. Ahamed, V. S. Borkar, and S. Juneja, Adaptive importance sampling technique for Markov chains using stochastic approximation, Oper. Res. 54, 489 (2006).
  52. G. Ferré and H. Touchette, Adaptive sampling of large deviations, J. Stat. Phys. 172, 1525 (2018).
  53. G. Ferré and H. Touchette, Correction to: Adaptive sampling of large deviations, J. Stat. Phys. 173, 1547 (2018).
  54. J. A. Bucklew, Introduction to Rare Event Simulation, Springer Series in Statistics (Springer New York, 2004).
  55. V. S. Borkar, Asynchronous stochastic approximations, SIAM J. Control Optim. 36, 840 (1998).
  56. M. Benaïm, Dynamics of stochastic approximation algorithms, in Séminaire de Probabilités XXXIII (Springer, Berlin, Heidelberg, 1999) pp. 1–68.
  57. R. Guimera, S. Mossa, A. Turtschi, and L. N. Amaral, The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles, Proc. Natl. Acad. Sci. 102, 7794 (2005).
  58. L. Gao, W. Wang, L. Pan, M. Tang, and H. F. Zhang, Effective information spreading based on local information in correlated networks, Sci. Rep. 6, 1 (2016).
  59. T. P. Peixoto, Network Reconstruction and Community Detection from Dynamics, Phys. Rev. Lett. 123, 128301 (2019).
  60. P. Holme and J. Saramäki (eds.), Temporal Network Theory, Computational Social Sciences (Springer International Publishing, Cham, 2019).
  61. S. Manfredi, E. Di Tucci, and V. Latora, Mobility and Congestion in Dynamical Multilayer Networks with Finite Storage Capacity, Phys. Rev. Lett. 120, 068301 (2018).
  62. T. Carletti, M. Asllani, D. Fanelli, and V. Latora, Nonlinear walkers and efficient exploration of congested networks, Phys. Rev. Res. 2, 033012 (2020).
  63. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L042051 for analytical and numerical details..
  64. G. Di Bona, L. Di Gaetano, V. Latora, and F. Coghi, Data cite for “Maximal dispersion of adaptive random walks”, https://github.com/gabriele-di-bona/ARW (2022).

Outline

Information

Phys. Rev. Research 4, L042051– Published 30 December, 2022
  • Received 26 February 2022
  • Revised 27 May 2022
  • Accepted 10 November 2022
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation