The European Physical Journal Special Topics

, Volume 224, Issue 17–18, pp 3279–3293 | Cite as

A transfer entropy analysis of leader-follower interactions in flying bats

  • N. Orange
  • N. Abaid
Regular Article Physics of Social Interactions
Part of the following topical collections:
  1. Dynamics of Animal Systems


In this paper, we present a transfer entropy analysis applied to the 3D paths of bats flying in pairs. The 3D trajectories are one-dimensionally characterized as inverse curvature time series to allow for entropy calculations. In addition to a traditional formulation of information flow between pair members, a path coupling hypothesis is pursued with time-delay modifications implemented in such a way as to not change the Markovianity of the process. With this modification, we find trends that suggest a leader-follower interaction between the front bat and the rear bat, although statistical significance is not reached due in part to the small number of pairs considered.


Entropy European Physical Journal Special Topic Transfer Entropy Path Shape Tangential Acceleration 
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.


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  1. 1.
    F. Xiao, L. Wang, Int. J. Control 79, 1277 (2006)MathSciNetCrossRefGoogle Scholar
  2. 2.
    G. Dudek, M.R. Jenkin, E. Milios, D. Wilkes, Autonomous Robots 3, 375 (1996)CrossRefGoogle Scholar
  3. 3.
    A. Martinoli, K. Easton, W. Agassounon, The Int. J. Robotics Res. 23, 415 (2004)CrossRefGoogle Scholar
  4. 4.
    X.-S. Yang, Nature Inspired Cooperative Strategies for Optimization (NICSO, Springer, 2010), p. 65Google Scholar
  5. 5.
    A.R. Jordehi, Appl. Soft Computing 26, 523 (2015)CrossRefGoogle Scholar
  6. 6.
    N. Ulanovsky, M.B. Fenton, A. Tsoar, C. Korine, Proc. R. Soc. London B: Biol. Sci. 271, 1467 (2004)CrossRefGoogle Scholar
  7. 7.
    M.E. Bates, S.A. Stamper, J.A. Simmons, J. Exp. Bio. 211, 106 (2008)CrossRefGoogle Scholar
  8. 8.
    C. Chiu, W. Xian, C.F. Moss, Proc. Natl. Acad. Sci. 105, 13116 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    A.J. Corcoran, W.E. Conner, Sci. 346, 745 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    A. Getchell, Phys. 22, 757 (2008)Google Scholar
  11. 11.
    F. Xiao, L. Wang, A. Wang, J. Math. Anal. Appl. 322, 587 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    C. Shannon, W. Weaver, The Mathematical Theory of Information (University of Illinois Press, 1949)Google Scholar
  13. 13.
    A. Rényi, In Fourth Berkeley Symp. Math. Stat. Probab. 1, 547 (1961)Google Scholar
  14. 14.
    H. Marko, IEEE Trans. Commun. 21, 1345 (1973)CrossRefGoogle Scholar
  15. 15.
    A. Kaiser, T. Schreiber, Physica D: Nonlinear Phenomena 166, 43 (2002)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    T. Schreiber, Phys. Rev. Lett. 85, 461 (2000)ADSCrossRefGoogle Scholar
  17. 17.
    A.G. Dimitrov, A.A. Lazar, J.D. Victor, J. Computational Neurosci. 30, 1 (2011)CrossRefGoogle Scholar
  18. 18.
    O. Kwon, J.-S. Yang, Phys. A: Statistical Mech. Appl. 387, 2851 (2008)ADSCrossRefGoogle Scholar
  19. 19.
    G. Ver Steeg, A. Galstyan, In Proc. 21st Int. Conf. on World Wide Web, ACM, 509 (2012)Google Scholar
  20. 20.
    S. Butail, F. Ladu, D. Spinello, M. Porfiri, Entropy 16, 1315 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    M. Kadota, E.J. White, S. Torisawa, K. Komeyama, T. Takagi, PloS One 6, e28241 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    M.P. Paulus, M.A. Geyer, L.H. Gold, A.J. Mandell, Proc. Natl. Acad. Sci. 87, 723 (1990)ADSCrossRefGoogle Scholar
  23. 23.
    F. Ladu, V. Mwaffo, J. Li, S. Macrì, M. Porfiri, Behav. Brain Res. 289, 48 (2015)CrossRefGoogle Scholar
  24. 24.
    X.R. Wang, J.M. Miller, J.T. Lizier, M. Prokopenko, L.F. Rossi, PloS One 7, e40084 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    J.-Y. Bouguet, Camera calibration toolbox for MATLAB, (2013)
  26. 26.
    T. Svoboda, Multi-camera self-calibration,∼svoboda/SelfCal∼svoboda/SelfCal (2011)
  27. 27.
    N. Orange, Master’s thesis, Virginia Polytechnic Institute and State University (yr2015)Google Scholar
  28. 28.
    J.G. Puckett, D.H. Kelley, N.T. Ouellette, Scientific Reports 4 (2014)Google Scholar
  29. 29.
    M. Bergou, M. Wardetzky, S. Robinson, B. Audoly, E. Grinspun, In ACM Transactions on Graphics (TOG), ACM 27, 63 (2008)Google Scholar
  30. 30.
    H. Choi, Neurocomputing 139, 408 (2014)CrossRefGoogle Scholar
  31. 31.
    D.A. Smirnov, Phys. Rev. E 87, 042917 (2013)ADSCrossRefGoogle Scholar
  32. 32.
    M. Breslav, N.W. Fuller, M. Betke, In Proc. Workshop on Visual Observation and Analysis of Animal and Insect Behavior (VAIB 2012), Citeseer (2012)Google Scholar
  33. 33.
    J. Wong, D. Waters, J. Exp. Bio. 204, 575 (2001)Google Scholar
  34. 34.
    J. Runge, J. Heitzig, N. Marwan, J. Kurths, J. Exp. Bio. 86, 061121 (2012)Google Scholar
  35. 35.
    B.L. Ruddell, P. Kumar, Water Resources Res. 45 (2009)Google Scholar
  36. 36.
    B. Rosner, Fundamentals of Biostatistics (Brooks/Cole, 2011)Google Scholar
  37. 37.
    D. Endres, P. Foldiak, IEEE Trans. Information Theory 51, 3766 (2005)MathSciNetCrossRefGoogle Scholar

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© EDP Sciences and Springer 2015

Authors and Affiliations

  • N. Orange
    • 1
  • N. Abaid
    • 1
  1. 1.Department of Biomedical Engineering and MechanicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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