- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Measuring neuronal avalanches in disordered systems with absorbing states

M. Girardi-Schappo1,2 and M. H. R. Tragtenberg2,*

  • 1Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, McGill University, Montreal Neurological Institute and Hospital, H3A 2B4, Montreal, Quebec, Canada
  • 2Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil

  • *marcelotragtenberg@gmail.com
PDF

Phys. Rev. E 97, 042415 – Published 24 April, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.042415

Abstract

Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a system in which the separation of driving and relaxation time scales emerges from its structure. We apply both definitions of avalanche to our model. Both yield power-law-distributed avalanches that scale with system size in the critical point as expected. Nevertheless, we find restricted power-law-distributed avalanches outside of the critical region within the experimental procedure, which is not expected by the standard theoretical definition. We remark that these results are dependent on the model details.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (51)

  1. P. Bak, How Nature Works: The Science of Self-Organized Criticality (Copernicus Springer-Verlag, New York, 1996).
  2. H. J. Jensen, Self-Organized Criticality (Cambridge University Press, Cambridge, England, 1998).
  3. G. Pruessner, Self-Organised Criticality (Cambridge University Press, Cambridge, England, 2012).
  4. V. Frette, K. Christensen, A. Malthe-Sørenssen, J. Feder, T. Jøssang, and P. Meakin, Nature 379, 49 (1996).
  5. K. Christensen, H. Flyvbjerg, and Z. Olami, Phys. Rev. Lett. 71, 2737 (1993).
  6. B. D. Malamud, G. Morein, and D. L. Turcotte, Science 281, 1840 (1998).
  7. T. O. Richardson, E. J. H. Robinson, K. Christensen, H. J. Jensen, N. R. Franks, and A. B. Sendova-Franks, PLoS ONE 5, e9621 (2010).
  8. B. Gutenberg and C. F. Richter, Seismicity Of The Earth And Associated Phenomena (Princeton University Press, Princeton, NJ, 1949).
  9. F. Y. Wang and Z. G. Dai, Nat. Phys. 9, 465 (2013).
  10. X. Gabaix, P. Gopikrishnan, V. Plerou, and H. E. Stanley, Nature 423, 267 (2003).
  11. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).
  12. T. Gisiger, Biol. Rev. 76, 161 (2001).
  13. D. R. Chialvo, Nat. Phys. 6, 744 (2010).
  14. W. L. Shew and D. Plenz, Neuroscientist 19, 88 (2013).
  15. J. M. Beggs and N. Timme, Front. Physiol. 3, 163 (2012).
  16. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971).
  17. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
  18. J. P. Sethna, K. A. Dahmen, and C. R. Myers, Nature 410, 242 (2001).
  19. H. J. Jensen, K. Christensen, and H. C. Fogedby, Phys. Rev. B 40, 7425 (1989).
  20. D. Stassinopoulos and P. Bak, Phys. Rev. E 51, 5033 (1995).
  21. M. Usher, M. Stemmler, and Z. Olami, Phys. Rev. Lett. 74, 326 (1995).
  22. J. M. Beggs and D. Plenz, J. Neurosci. 23, 11167 (2003).
  23. O. Kinouchi and M. Copelli, Nat. Phys. 2, 348 (2006).
  24. L. de Arcangelis, C. Perrone-Capano, and H. J. Herrmann, Phys. Rev. Lett. 96, 028107 (2006).
  25. A. Levina, J. M. Herrmann, and T. Geisel, Nat. Phys. 3, 857 (2007).
  26. A. de Andrade Costa, M. Copelli, and O. Kinouchi, J. Stat. Mech. (2015) P06004.
  27. T. L. Ribeiro, M. Copelli, F. Caixeta, H. Belchior, D. R. Chialvo, M. A. L. Nicolelis, and S. Ribeiro, PLoS ONE 5, e14129 (2010).
  28. M. Girardi-Schappo, O. Kinouchi, and M. H. R. Tragtenberg, Phys. Rev. E 88, 024701 (2013).
  29. R. V. Williams-García, M. Moore, J. M. Beggs, and G. Ortiz, Phys. Rev. E 90, 062714 (2014).
  30. W. L. Shew, W. P. Clawson, J. Pobst, Y. Karimipanah, N. C. Wright, and R. Wessel, Nat. Phys. 11, 659 (2015).
  31. K. Linkenkaer-Hansen, V. V. Nikouline, J. M. Palva, and R. J. Ilmoniemi, J. Neurosci. 21, 1370 (2001).
  32. A. Haimovici, E. Tagliazucchi, P. Balenzuela, and D. R. Chialvo, Phys. Rev. Lett. 110, 178101 (2013).
  33. E. Novikov, A. Novikov, D. Shannahoff-Khalsa, B. Schwartz, and J. Wright, Phys. Rev. E 56, R2387 (1997).
  34. M. C. Teich, C. Heneghan, S. B. Lowen, T. Ozaki, and E. Kaplan, J. Opt. Soc. Am. A 14, 529 (1997).
  35. J. Andrew Henrie and R. Shapley, J. Neurophysiol. 94, 479 (2005).
  36. D. Hermes, K. J. Miller, B. A. Wandell, and J. Winawer, Cereb. Cortex 25, 2951 (2014).
  37. F. Lombardi, H. J. Herrmann, and L. de Arcangelis, Chaos 27, 047402 (2017).
  38. J. M. Beggs and D. Plenz, J. Neurosci. 24, 5216 (2004).
  39. V. Priesemann, M. H. J. Munk, and M. Wibral, BMC Neurosci. 10, 40 (2009).
  40. G. Hahn, T. Petermann, M. N. Havenith, S. Yu, W. Singer, D. Plenz, and D. Nikolić, J. Neurophysiol. 104, 3312 (2010).
  41. V. Priesemann, M. Wibral, M. Valderrama, R. Pröpper, M. Le Van Quyen, T. Geisel, J. Triesch, D. Nikolić, and M. H. J. Munk, Front Syst. Neurosci. 8, 108 (2014).
  42. S. Scarpetta and A. de Candia, PLoS One 8, e64162 (2013).
  43. S. Scarpetta and A. de Candia, Front. Syst. Neurosci. 8, 88 (2014).
  44. M. Martinello, J. Hidalgo, A. Maritan, S. di Santo, D. Plenz, and M. A. Muñoz, Phys. Rev. X 7, 041071 (2017).
  45. M. Girardi-Schappo, G. S. Bortolotto, J. J. Gonsalves, L. T. Pinto, and M. H. R. Tragtenberg, Sci. Rep. 6, 29561 (2016).
  46. T. D. Albright, T. M. Jessell, E. R. Kandel, and M. I. Posner, Neuron 25, S1 (2000).
  47. S. R. Williams and G. J. Stuart, Science 295, 1907 (2002).
  48. M. E. J. Newman, Contemp. Phys. 46, 323 (2005).
  49. G. S. Bortolotto, M. Girardi-Schappo, J. J. Gonsalves, L. T. Pinto, and M. H. R. Tragtenberg, J. Phys. Conf. Ser. 686, 012008 (2016).
  50. A. J. Bray and G. J. Rodgers, Phys. Rev. B 38, 11461 (1988).
  51. R. Juhász, I. A. Kovács, and F. Iglói, Phys. Rev. E 91, 032815 (2015).

Outline

Information

Phys. Rev. E 97, 042415– Published 24 April, 2018
  • Received 16 June 2017
Crossmark - Check for updates button

©2018 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation