Advertisement

The Simplicial Characterisation of TS Networks: Theory and Applications

  • Neelima GupteEmail author
  • N. Nirmal Thyagu
  • Malayaja Chutani
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 6)

Abstract

We use the visibility algorithm to construct the time series networks obtained from the time series of different dynamical regimes of the logistic map. We define the simplicial characterisers of networks which can analyse the simplicial structure at both the global and local levels. These characterisers are used to analyse the TS networks obtained in different dynamical regimes of the logisitic map. It is seen that the simplicial characterisers are able to distinguish between distinct dynamical regimes. We also apply the simplicial characterisers to time series networks constructed from fMRI data, where the preliminary results indicate that the characterisers are able to differentiate between distinct TS networks.

Keywords

Simplicial Complex Dynamical Regime Hurst Exponent Reading Task Visibility Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We would like to thank Dr. Nandini Chatterjee Singh and Dr. Sarika Cherodath of NBRC, Manesar for the fMRI data, and N. Nithyanand Rao for earlier collaboration.

References

  1. 1.
    R.V. Donner, Y. Zou, J.F. Donges, N. Marwan, J. Kurths, Recurrence networks—a novel paradigm for nonlinear time series analysis. New J. Phys. 12(3), 033025 (2010)Google Scholar
  2. 2.
    L. Lacasa, B. Luque, F. Ballesteros, J. Luque, Juan Carlos Nuño, From time series to complex networks: the visibility graph. Proc. Natl. Acad. Sci. 105(13), 4972–4975 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    J.B. Elsner, T.H. Jagger, E.A. Fogarty, Visibility network of United States hurricanes. Geophys. Res. Lett. 36(16), L16702 (2009)CrossRefGoogle Scholar
  4. 4.
    Y. Yang, J. Wang, H. Yang, J. Mang, Visibility graph approach to exchange rate series. Phys. A: Stat. Mech. Appl. 388(20), 4431–4437 (2009)CrossRefGoogle Scholar
  5. 5.
    C. Bron, J. Kerbosch, Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16(9), 575–577 (1973)CrossRefzbMATHGoogle Scholar
  6. 6.
    J. Jonsson, Simplicial Complexes of Graphs (Springer, 2008)Google Scholar
  7. 7.
    M. Andjelković, B. Tadić, S. Maletić, M. Rajković, Hierarchical sequencing of online social graphs. Phys. A: Stat. Mech. Appl. 436, 582–595 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Andjelković, N. Gupte, B. Tadić, Hidden geometry of traffic jamming. Phys. Rev. E 91, 052817 (2015)CrossRefGoogle Scholar
  9. 9.
    B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: Exact results for random time series. Phys. Rev. E 80, 046103 (2009)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Neelima Gupte
    • 1
    Email author
  • N. Nirmal Thyagu
    • 2
  • Malayaja Chutani
    • 1
  1. 1.Department of PhysicsIndian Institute of TechnologyMadras, ChennaiIndia
  2. 2.Vellore Institute of TechnologyChennaiIndia

Personalised recommendations