Griffiths phases and the stretching of criticality in brain networks

Nature Communications

Volumn 4, Issue , 2013, Pages

  Moretti, Paolo ^a   Muñoz, Miguel A ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BRAIN; EVOLUTION; FUNCTIONAL ROLE; HIERARCHICAL SYSTEM; HOMINID; NATURAL SELECTION; NEMATODE; NEUROLOGY; PHYSIOLOGY; POWER LAW;

ARTICLE; BRAIN; BRAIN FUNCTION; CAENORHABDITIS ELEGANS; CONNECTOME; HUMAN; NONHUMAN; STEADY STATE;

ALGORITHMS; ANIMALS; CAENORHABDITIS ELEGANS; CEREBRAL CORTEX; COMPUTER SIMULATION; HUMANS; MODELS, NEUROLOGICAL; NERVE NET;

EID: 84885130654     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms3521     Document Type: Article

References (60)

1. Nykter, M. et al. Gene expression dynamics in the macrophage exhibit criticality. Proc. Natl Acad. Sci. USA 105, 1897-1900 (2008).
2. Furusawa, C. & Kaneko, K. Adaptation to optimal cell growth through selforganized criticality. Phys. Rev. Lett. 108, 208103 (2012).
3. Chen, X., Dong, X., Be?er, A., Swinney, H. & Zhang, H. Scale-invariant correlations in dynamic bacterial clusters. Phys. Rev. Lett. 108, 148101 (2012).
4. Bialek, W. et al. Statistical mechanics for natural flocks of birds. Proc. Natl Acad. Sci. USA 109, 4786-4791 (2012).
5. Kitzbichler, M. G., Smith, M. L., Christensen, S. R. & Bullmore, E. Broadband criticality of human brain network synchronization. PLoS Comput. Biol. 5, e1000314 (2009).
6. Beggs, J. M. & Plenz, D. Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167-11177 (2003).
7. Plenz, D. & Thiagarajan, T. C. The organizing principles of neuronal avalanches: Cell assemblies in the cortex? Trends. Neurosci. 30, 101-110 (2007).
8. Beggs, J. M. The criticality hypothesis: How local cortical networks might optimize information processing. Phil. Trans. R. Soc. A 366, 329-343 (2008).
9. Petermann, T. et al. Spontaneous cortical activity in awake monkeys composed of neuronal avalanches. Proc. Natl Acad. Sci. USA 106, 15921-15926 (2009).
10. Haimovici, A., Tagliazucchi, E., Balenzuela, P. & Chialvo, D. R. Brain organization into resting state networks emerges at criticality on a model of the human connectome. Phys. Rev. Lett. 110, 178101 (2013).
11. Chialvo, D. R. Emergent complex neural dynamics. Nat. Phys. 6, 744-750 (2010).
12. Bak, P. How Nature Works: The Science of Self-organized Criticality 1st edn (Copernicus Springer, 1996).
13. Jensen, H. J. Self-organized Criticality (Cambridge University Press, 1998).
14. Dickman, R., Munoz, M. A., Vespignani, A. & Zapperi, S. Paths to selforganized criticality. Braz. J. Phys. 30-45 (2000).
15. Mora, T. & Bialek, W. Are biological systems poised at criticality? J. Stat. Phys. 144, 268-302 (2011).
16. Langton, C. G. Computation at the edge of chaos: Phase transitions and emergent computation. Phys. D 42, 12-37 (1990).
17. Bertschinger, N. & Natschlager, T. Real-time computation at the edge of chaos in recurrent neural networks. Neural. Comput. 16, 1413-1436 (2004).
18. Haldeman, C. & Beggs, J. M. Critical branching captures activity in living neural networks and maximizes the number of metastable states. Phys. Rev. Lett. 94, 058101 (2005).
19. Legenstein, R. & Maass, W. Edge of chaos and prediction of computational performance for neural circuit models. Neural Networks 20, 323-334 (2007).
20. Beggs, J. M. & Plenz, D. Neuronal avalanches are diverse and precise activity patterns stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216-5229 (2004).
21. Kinouchi, O. & Copelli, M. Optimal dynamical range of excitable networks at criticality. Nat. Phys. 2, 348-351 (2006).
22. Tagliazucchi, E., Balenzuela, P., Fraiman, D. & Chialvo, D. R. Criticality in large-scale brain fMRI dynamics unveiled by a novel point process analysis. Front. Phys. 3, 15 (2012).
23. Mun?oz, M. A., Juhász, R., Castellano, C. & Ó dor, G. Griffiths phases on complex networks. Phys. Rev. Lett. 105, 128701 (2010).
24. Rubinov, M., Sporns, O., Thivierge, J. P. & Breakspear, M. Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons. PLoS Comput. Biol. 7, e1002038 (2011).
25. Wang, S. J. & Zhou, C. Hierarchical modular structure enhances the robustness of self-organized criticality in neural networks. New. J. Phys. 14, 023005 (2012).
26. Griffiths, R. B. Nonanalytic behavior above the critical point in a random ising ferromagnet. Phys. Rev. Lett. 23, 17-19 (1969).
27. Noest, A. J. New universality for spatially disordered cellular automata and directed percolation. Phys. Rev. Lett. 57, 90-93 (1986).
28. Vojta, T. Rare region effects at classical, quantum and nonequilibrium phase transitions. J. Phys. A 39, R143-r205 (2006).
29. Hagmann, P. et al. Mapping the structural core of human cerebral cortex. PLoS Biol. 6, e159 (2008).
30. Honey, C. J. et al. Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl Acad. Sci. 106, 2035-2040 (2009).
31. Sporns, O. Networks of the Brain (MIT Press, 2010).
32. Kaiser, M. A tutorial in connectome analysis: Topological and spatial features of brain networks. NeuroImage 57, 892-907 (2011).
33. Meunier, D., Lambiotte, R. & Bullmore, E. T. Modular and hierarchically modular organization of brain networks. Front. Neurosci. 4, 200 (2010).
34. Sporns, O., Chialvo, D. R., Kaiser, M. & Hilgetag, C. C. Organization, development and function of complex brain networks. Trends Cogn. Sci. 8, 418-425 (2004).
35. Wang, S. J., Hilgetag, C. C. & Zhou, C. Sustained activity in hierarchical modular neural networks: Self-organized criticality and oscillations. Front. Comput. Neurosci. 5, 30 (2011).
36. Albert, R. & Barabási, A. L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).
37. Gallos, L. K., Makse, H. A. & Sigman, M. A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. Proc. Natl Acad. Sci. USA 109, 2825-2830 (2012).
38. Binney, J., Dowrick, N., Fisher, A. & Newman, M. The Theory of Critical Phenomena (Oxford University Press, 1993).
39. Chatterjee, N. & Sinha, S. Understanding the mind of a worm: Hierarchical network structure underlying nervous system function in C. elegans. Prog. Brain. Res. 168, 145-153 (2007).
40. Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H. & Chklovskii, D. B. Structural properties of the C. Elegans neuronal network. PLoS Comput. Biol. 7, e1001066 (2011).
41. Zhou, C., Zemanova, L., Zamora, G., Hilgetag, C. C. & Kurths, J. Hierarchical organization unveiled by functional connectivity in complex brain networks. Phys. Rev. Lett. 97, 238103 (2006).
42. Bassett, D. S. et al. Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comput. Biol. 6, e1000748 (2010).
43. Chung, F. R. K. Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92) (American Mathematical Society, 1996).
44. Goltsev, A. V., Dorogovtsev, S. N., Oliveira, J. G. & Mendes, J. F. F. Localization and spreading of diseases in complex networks. Phys. Rev. Lett. 109, 128702 (2012).
45. Nieuwenhuizen, T. M. Griffiths singularities in two-Dimensional random-bond Ising models: Relation with Lifshitz band tails. Phys. Rev. Lett. 63, 1760-1763 (1989).
46. Khorunzhiy, O., Kirsch, W. & Muller, P. Lifshits tails for spectra of Erdos Rényi random graphs. Ann. Appl. Probab. 16, 295-309 (2006).
47. Kaiser, M., Gorner, M. & Hilgetag, C. Criticality of spreading dynamics in hierarchical cluster networks without inhibition. N. J. Phys. 9, 110 (2007).
48. Muller-Linow, M., Hilgetag, C. C. & Hutt, M. T. Organization of excitable dynamics in hierarchical biological networks. PLoS Comput. Biol. 4, 15 (2008).
49. Levina, A., Herrmann, J. M. & Geisel, T. Dynamical synapses causing selforganized criticality in neural networks. Nat. Phys. 3, 857-860 (2007).
50. Millman, D., Mihalas, S., Kirkwood, A. & Niebur, E. Self-organized criticality occurs in non-conservative neuronal networks during ?up? states. Nat. Phys. 6, 801-805 (2010).
51. Bonachela, J. A., De Franciscis, S., Torres, J. J. & Mun?oz, M. A. Self-organization without conservation: Are neuronal avalanches generically critical? J. Stat. Mech.. P02015 (2010).
52. Johnson, S., Marro, J. & Torres, J. J. Robust short-term memory without synaptic learning. PLoS One 8, e50276 (2013).
53. Wixted, J. T. & Ebbesen, E. B. Genuine power curves in forgetting: A quantitative analysis of individual subject forgetting functions. Mem. Cogn. 25, 731-739 (1997).
54. Trevin?o, III S., Sun, Y., Cooper, T. F. & Bassler, K. Robust detection of hierarchical communities from Escherichia Coli gene expression data. PLoS Comput. Biol. 8, e1002391 (2012).
55. Reese, T. M., Brzoska, A., Yott, D. T. & Kelleher, D. J. Analyzing self-similar and fractal properties of the C. Elegans neural network. PLoS One 7, e40483 (2012).
56. Mones, E., Vicsek, L. & Vicsek, T. Hierarchy measure for complex networks. PLoS One 7, e33799 (2012).
57. Pastor-satorras, R. & Vespignani, A. Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200-3203 (2001).
58. Grinstein, G. & Linsker, R. Synchronous neural activity in scale-free network models versus random network models. Proc. Natl Acad. Sci. USA 102, 9948-9953 (2005).
59. Clauset, A., Shalizi, C. R. & Newman, M. E. J. Power-Law distributions in empirical data. SIAM Rev. 51, 661-703 (2009).
60. Gantmacher, F. The Theory of Matrices Vol. 2 (AMS Chelsea Pub, 2000).