Criticality in the brain: A synthesis of neurobiology, models and cognition

Progress in Neurobiology

Volumn 158, Issue , 2017, Pages 132-152

  Cocchi, Luca ^a   Gollo, Leonardo L ^a   Zalesky, Andrew ^b   Breakspear, Michael ^a,c  

^a QIMR BERGHOFER MEDICAL RESEARCH INSTITUTE   (Australia)

^b UNIVERSITY OF MELBOURNE   (Australia)

^c Metro North Mental Health Service   (Australia)

Author keywords

Bifurcations; Cognition; Dynamics; Metastability; Multistability; Power law

Indexed keywords

BRAIN; BRAIN FUNCTION; COGNITION; CRITICAL THINKING; CRITICALITY; DYNAMICS; FUNCTIONAL MAGNETIC RESONANCE IMAGING; HUMAN; MENTAL DISEASE; MOTOR COORDINATION; NERVE CELL; NEUROBIOLOGY; NEUROPHYSIOLOGY; NOISE; PHASE TRANSITION; PRIORITY JOURNAL; REVIEW; RHYTHM; SEIZURE; ANIMAL; BIOLOGICAL MODEL; NERVE TRACT; PHYSIOLOGY;

ANIMALS; BRAIN; COGNITION; HUMANS; MODELS, NEUROLOGICAL; NEURAL PATHWAYS;

EID: 85028500862     PISSN: 03010082     EISSN: 18735118     Source Type: Journal    
DOI: 10.1016/j.pneurobio.2017.07.002     Document Type: Review

References (254)

1. Arneodo, A., Coullet, P., Tresser, C., Occurence of strange attractors in three-dimensional Volterra equations. Phys. Lett. A 79 (1980), 259–263.
2. Arviv, O., Goldstein, A., Shriki, O., Near-critical dynamics in stimulus-evoked activity of the human brain and its relation to spontaneous resting-State activity. J. Neurosci. 35 (2015), 13927–13942.
3. Ashwin, P., Lavric, A., A low-dimensional model of binocular rivalry using winnerless competition. Phys. D 239 (2010), 529–536.
4. Ashwin, P., Burylko, O., Maistrenko, Y., Popovych, O., Extreme sensitivity to detuning for globally coupled phase oscillators. Phys. Rev. Lett., 96, 2006, 054102.
5. Assis, V.R., Copelli, M., Dynamic range of hypercubic stochastic excitable media. Phys. Rev. E, 77, 2008, 011923.
6. Bak, P., Tang, C., Wiesenfeld, K., Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59 (1987), 381–384.
7. Bak, P., Tang, C., Wiesenfeld, K., Self-organized criticality. Phys. Rev. A 38 (1988), 364–374.
8. Bak, P., Self-organized criticality. Phys. A 163 (1990), 403–409.
9. Baldassarri, A., Colaiori, F., Castellano, C., Average shape of a fluctuation: universality in excursions of stochastic processes. Phys. Rev. Lett., 90, 2003, 060601.
10. Bartolomei, F., Wendling, F., Bellanger, J.-J., Régis, J., Chauvel, P., Neural networks involving the medial temporal structures in temporal lobe epilepsy. Clin. Neurophysiol. 112 (2001), 1746–1760.
11. Bassett, D.S., Wymbs, N.F., Rombach, M.P., Porter, M.A., Mucha, P.J., Grafton, S.T., Task-based core-periphery organization of human brain dynamics. PLoS Comput. Biol., 9, 2013, e1003171.
12. Beggs, J.M., Plenz, D., Neuronal avalanches in neocortical circuits. J. Neurosci. Off. J. Soc. Neurosci. 23 (2003), 11167–11177.
13. Beggs, J.M., Timme, N., Being critical of criticality in the brain. Front. Physiol., 3, 2012, 163.
14. Beggs, J.M., Neuronal avalanche. Scholarpedia, 2, 2007, 1344.
15. Bellay, T., Klaus, A., Seshadri, S., Plenz, D., Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state. Elife, 4, 2015, e07224.
16. Berkes, P., Orbán, G., Lengyel, M., Fiser, J., Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment. Science 331 (2011), 83–87.
17. Berryman, A.A., The orgins and evolution of predator-Prey theory. Ecology 73 (1992), 1530–1535.
18. Bertschinger, N., Natschläger, T., Real-time computation at the edge of chaos in recurrent neural networks. Neural Comput. 16 (2004), 1413–1436.
19. Biswal, B.B., Mennes, M., Zuo, X.N., Gohel, S., Kelly, C., Smith, S.M., Beckmann, C.F., Adelstein, J.S., Buckner, R.L., Colcombe, S., Dogonowski, A.M., Ernst, M., Fair, D., Hampson, M., Hoptman, M.J., Hyde, J.S., Kiviniemi, V.J., Kotter, R., Li, S.J., Lin, C.P., Lowe, M.J., Mackay, C., Madden, D.J., Madsen, K.H., Margulies, D.S., Mayberg, H.S., McMahon, K., Monk, C.S., Mostofsky, S.H., Nagel, B.J., Pekar, J.J., Peltier, S.J., Petersen, S.E., Riedl, V., Rombouts, S.A., Rypma, B., Schlaggar, B.L., Schmidt, S., Seidler, R.D., Siegle, G.J., Sorg, C., Teng, G.J., Veijola, J., Villringer, A., Walter, M., Wang, L., Weng, X.C., Whitfield-Gabrieli, S., Williamson, P., Windischberger, C., Zang, Y.F., Zhang, H.Y., Castellanos, F.X., Milham, M.P., Toward discovery science of human brain function. Proc. Natl. Acad. Sci. U. S. A. 107 (2010), 4734–4739.
20. Boedecker, J., Obst, O., Lizier, J.T., Mayer, N.M., Asada, M., Information processing in echo state networks at the edge of chaos. Theory Biosci. 131 (2012), 205–213.
21. Bojak, I., Stoyanov, Z.V., Liley, D.T., Emergence of spatially heterogeneous burst suppression in a neural field model of electrocortical activity. Front. Syst. Neurosci., 2015, 9.
22. Bonachela, J.A., De Franciscis, S., Torres, J.J., Munoz, M.A., Self-organization without conservation: are neuronal avalanches generically critical?. J. Stat. Mech: Theory Exp., 2010, 2010, P02015.
23. Boonstra, T.W., He, B.J., Daffertshofer, A., Scale-free dynamics and critical phenomena in cortical activity. Front. Physiol., 2013, 4.
24. Breakspear, M., Roberts, J., Terry, J.R., Rodrigues, S., Mahant, N., Robinson, P., A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb. Cortex 16 (2006), 1296–1313.
25. Breakspear, M., Roberts, G., Green, M.J., Nguyen, V.T., Frankland, A., Levy, F., Lenroot, R., Mitchell, P.B., Network dysfunction of emotional and cognitive processes in those at genetic risk of bipolar disorder. Brain, 2015, awv261.
26. Breakspear, M., Perception of odors by a nonlinear model of the olfactory bulb. Int. J. Neural Syst. 11 (2001), 101–124.
27. Bressler, S.L., Kelso, J.S., Cortical coordination dynamics and cognition. Trends Cogn. Sci. 5 (2001), 26–36.
28. Brochini, L., de Andrade Costa, A., Abadi, M., Roque, A.C., Stolfi, J., Kinouchi, O., Phase transitions and self-organized criticality in networks of stochastic spiking neurons. Sci. Rep., 2016, 6.
29. Burridge, R., Knopoff, L., Model and theoretical seismicity. Bull. Seismol. Soc. Am. 57 (1967), 3411–3471.
30. Camalet, S., Duke, T., Jülicher, F., Prost, J., Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc. Natl. Acad. Sci. 97 (2000), 3183–3188.
31. Carlson, J., Langer, J., Mechanical model of an earthquake fault. Phys. Rev. A, 40, 1989, 6470.
32. Cavagna, A., Cimarelli, A., Giardina, I., Parisi, G., Santagati, R., Stefanini, F., Viale, M., Scale-free correlations in starling flocks. Proc. Natl. Acad. Sci. 107 (2010), 11865–11870.
33. Chapman, J.J., et al. Quantification of free-living activity patterns using accelerometry in adults with mental illness. Sci. Rep., 7, 2016, 43174.
34. Chialvo Dante, R., The brain near the edge., AIP AIP Conference Proceedings, vol. 887, 2007 No. 1.
35. Chialvo, D.R., Emergent complex neural dynamics. Nat. Phys. 6 (2010), 744–750.
36. Chialvo, D.R., 2012. Critical brain dynamics at large scale. arXiv preprint arXiv:1210.3632.
37. Ching, S., Cimenser, A., Purdon, P.L., Brown, E.N., Kopell, N.J., Thalamocortical model for a propofol-induced α-rhythm associated with loss of consciousness. Proc. Natl. Acad. Sci. 107 (2010), 22665–22670.
38. Churchland, M.M., Yu, B.M., Cunningham, J.P., Sugrue, L.P., Cohen, M.R., Corrado, G.S., Newsome, W.T., Clark, A.M., Hosseini, P., Scott, B.B., Bradley, D.C., Smith, M.A., Kohn, A., Movshon, J.A., Armstrong, K.M., Moore, T., Chang, S.W., Snyder, L.H., Lisberger, S.G., Priebe, N.J., Finn, I.M., Ferster, D., Ryu, S.I., Santhanam, G., Sahani, M., Shenoy, K.V., Stimulus onset quenches neural variability: a widespread cortical phenomenon. Nat. Neurosci. 13 (2010), 369–378.
39. Clauset, A., Shalizi, C.R., Newman, M.E., Power-law distributions in empirical data. SIAM Rev. 51 (2009), 661–703.
40. Cocchi, L., Zalesky, A., Fornito, A., Mattingley, J.B., Dynamic cooperation and competition between brain systems during cognitive control. Trends Cogn. Sci. 17 (2013), 493–501.
41. Cocchi, L., et al. Dissociable effects of local inhibitory and excitatory theta-burst stimulation on large-scale brain dynamics. J. Neurophysiol. 113:9 (2015), 3375–3385.
42. Cocchi, L., Sale, M.V., Gollo, L.L., Bell, P.T., Nguyen, V.T., Zalesky, A., Breakspear, M., Mattingley, J.B., A hierarchy of timescales explains distinct effects of local inhibition of primary visual cortex and frontal eye fields. Elife, 2016, 5.
43. Coombes, S., Terry, J.R., The dynamics of neurological disease: integrating computational, experimental and clinical neuroscience. Eur. J. Neurosci. 36 (2012), 2118–2120.
44. Copelli, M., Criticality at work: how do critical networks respond to stimuli?. Critic. Neural Syst., 2014, 347–364.
45. Cote, P., Meisel, L., Self-organized criticality and the Barkhausen effect. Phys. Rev. Lett., 67, 1991, 1334.
46. Cowan, J.D., Neuman, J., van Drongelen, W., Self-organized criticality and near criticality in neural networks. Critic. Neural Syst., 2014, 465–484.
47. Crutchfield, J.P., Young, K., Computation at the Onset of Chaos. 1988, The Santa Fe Institute, Westview, Citeseer.
48. Da Silva, F.L., Blanes, W., Kalitzin, S.N., Parra, J., Suffczynski, P., Velis, D.N., Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia 44 (2003), 72–83.
49. Damoiseaux, J.S., Rombouts, S.A., Barkhof, F., Scheltens, P., Stam, C.J., Smith, S.M., Beckmann, C.F., Consistent resting-state networks across healthy subjects. Proc. Natl. Acad. Sci. U. S. A. 103 (2006), 13848–13853.
50. Daunizeau, J., Friston, K.J., Kiebel, S.J., Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models. Physica D. Nonlinear Phenom. 238 (2009), 2089–2118.
51. de Andrade Costa, A., Copelli, M., Kinouchi, O., 2015. Can dynamical synapses produce true self-organized criticality?. J. Stat. Mech: Theory Exp., 2015, P06004.
52. de Arcangelis, L., Perrone-Capano, C., Herrmann, H.J., Self-organized criticality model for brain plasticity. Phys. Rev. Lett., 96, 2006, 028107.
53. de Arcangelis, L., Activity-Dependent model for neuronal avalanches. Aspects of Physical Biology, 2008, Springer, 215–230.
54. De Carvalho, J.X., Prado, C.P., Self-organized criticality in the Olami-Feder-Christensen model. Phys. Rev. Lett., 84, 2000, 4006.
55. Deco, G., Jirsa, V.K., Ongoing cortical activity at rest: criticality multistability, and ghost attractors. J. Neurosci. 32 (2012), 3366–3375.
56. Deco, G., Jirsa, V., McIntosh, A.R., Sporns, O., Kotter, R., Key role of coupling delay, and noise in resting brain fluctuations. Proc. Natl. Acad. Sci. U. S. A. 106 (2009), 10302–10307.
57. Deco, G., Jirsa, V.K., McIntosh, A.R., Emerging concepts for the dynamical organization of resting-state activity in the brain. Nat. Rev. Neurosci. 12 (2011), 43–56.
58. Deco, G., Jirsa, V.K., McIntosh, A.R., Resting brains never rest: computational insights into potential cognitive architectures. Trends Neurosci. 36 (2013), 268–274.
59. Destexhe, A., Terrence Sejnowski, J., Thalamocortical Assemblies: How Ion Channels, Single Neurons and Large-Scale Networks Organize Sleep Oscillations. 2001, Oxford University Press, USA, 2001.
60. Eguíluz, V.M., Ospeck, M., Choe, Y., Hudspeth, A., Magnasco, M.O., Essential nonlinearities in hearing. Phys. Rev. Lett., 84, 2000, 5232.
61. Eguiluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., Apkarian, A.V., Scale-free brain functional networks. Phys. Rev. Lett., 2005, 94.
62. Fagerholm, E.D., Lorenz, R., Scott, G., Dinov, M., Hellyer, P.J., Mirzaei, N., Leeson, C., Carmichael, D.W., Sharp, D.J., Shew, W.L., Leech, R., Cascades and cognitive state: focused attention incurs subcritical dynamics. J. Neurosci. Off. J. Soc. Neurosci. 35 (2015), 4626–4634.
63. Fagerholm, E.D., Scott, G., Shew, W.L., Song, C., Leech, R., Knöpfel, T., Sharp, D.J., Cortical entropy, mutual information and scale-Free dynamics in waking mice. Cereb. Cortex, 2016.
64. Farmer, S., Comment on broadband criticality of human brain network synchronization by Kitzbichler MG, Smith ML, Christensen SR, Bullmore E (2009). PLoS Comput. Biol., 5, 2015, e1000314.
65. Feyerabend, P., Against Method. 1993, Verso.
66. Field, D.J., Relations between the statistics of natural images and the response properties of cortical cells. JOSA A 4 (1987), 2379–2394.
67. Fiser, J., Berkes, P., Orbán, G., Lengyel, M., Statistically optimal perception and learning: from behavior to neural representations. Trends Cogn. Sci. 14 (2010), 119–130.
68. Fornito, A., Zalesky, A., Breakspear, M., The connectomics of brain disorders. Nat. Rev. Neurosci. 16 (2015), 159–172.
69. Fox, M.D., Snyder, A.Z., Vincent, J.L., Corbetta, M., Van Essen, D.C., Raichle, M.E., The human brain is intrinsically organized into dynamic: anticorrelated functional networks. Proc. Natl. Acad. Sci. U. S. A. 102 (2005), 9673–9678.
70. Fröhlich, F., Sejnowski, T.J., Bazhenov, M., Network bistability mediates spontaneous transitions between normal and pathological brain states. J. Neurosci. 30 (2010), 10734–10743.
71. Freeman, W.J., Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biol. Cybern. 56 (1987), 139–150.
72. Freeman, W.J., The physiology of perception. Sci. Am. 264 (1991), 78–85.
73. Freestone, D.R., Long, S.N., Frey, S., Stypulkowski, P.H., Giftakis, J.E., Cook, M.J., A method for actively tracking excitability of brain networks using a fully implantable monitoring system. Engineering in Medicine and Biology Society (EMBC), 2013 35th Annual International Conference of the IEEE, IEEE, 2013, 6151–6154.
74. Freyer, F., Aquino, K., Robinson, P.A., Ritter, P., Breakspear, M., Bistability and non-Gaussian fluctuations in spontaneous cortical activity. J. Neurosci. Off. J. Soc. Neurosci. 29 (2009), 8512–8524.
75. Freyer, F., Roberts, J.A., Becker, R., Robinson, P.A., Ritter, P., Breakspear, M., Biophysical mechanisms of multistability in resting-state cortical rhythms. J. Neurosci. Off. J. Soc. Neurosci. 31 (2011), 6353–6361.
76. Freyer, F., Roberts, J.A., Ritter, P., Breakspear, M., A canonical model of multistability and scale-invariance in biological systems. PLoS Comput. Biol., 8, 2012, e1002634.
77. Friedman, N., Ito, S., Brinkman, B.A., Shimono, M., DeVille, R.L., Dahmen, K.A., Beggs, J.M., Butler, T.C., Universal critical dynamics in high resolution neuronal avalanche data. Phys. Rev. Lett., 108, 2012, 208102.
78. Friston, K., Adams, R., Perrinet, L., Breakspear, M., Perceptions as hypotheses: saccades as experiments. Front. Psychol., 3, 2012, 151.
79. Friston, K., Breakspear, M., Deco, G., Perception and self-organized instability. Front. Comput. Neurosci., 2012, 6.
80. Friston, K.J., The labile brain. II. Transients: complexity and selection. Philos. Trans. R. Soc. Lond. B: Biol. Sci. 355 (2000), 237–252.
81. Gal, A., Marom, S., Self-organized criticality in single-neuron excitability. Phys. Rev. E, 2013, 88.
82. Garrett, D.D., Kovacevic, N., McIntosh, A.R., Grady, C.L., The importance of being variable. J. Neurosci. 31 (2011), 4496–4503.
83. Gatlin, L.L., Information Theory and the Living System. 1972, Columbia University Press, New York.
84. Gautam, S.H., Hoang, T.T., McClanahan, K., Grady, S.K., Shew, W.L., Maximizing sensory dynamic range by tuning the cortical state to criticality. PLoS Comput. Biol., 11, 2015, e1004576.
85. Gireesh, E.D., Plenz, D., Neuronal avalanches organize as nested theta-and beta/gamma-oscillations during development of cortical layer 2/3. Proc. Natl. Acad. Sci. 105 (2008), 7576–7581.
86. Gollo L.L., 2017. Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding. arXiv:1707.04484.
87. Gollo, L.L., Breakspear, M., The frustrated brain: from dynamics on motifs to communities and networks. Philos. Trans R. Soc. Lond. B Biol. Sci., 2014, 369.
88. Gollo, L.L., Mirasso, C., Eguíluz, V.M., Signal integration enhances the dynamic range in neuronal systems. Phys. Rev. E, 85, 2012, 040902.
89. Gollo, L.L., Kinouchi, O., Copelli, M., Single-neuron criticality optimizes analog dendritic computation. Sci. Rep., 2013, 3.
90. Gollo, L.L., Zalesky, A., Hutchison, R.M., van den Heuvel, M., Breakspear, M., Dwelling quietly in the rich club: brain network determinants of slow cortical fluctuations. Philos. Trans. R. Soc. Lond. B Biol. Sci., 2015, 370.
91. Gollo, L.L., Copelli, M., Roberts, J.A., Diversity improves performance in excitable networks. PeerJ, 4, 2016, e1912.
92. Gollo, L.L., Roberts, J.A., Cocchi, L., Mapping how local perturbations influence systems-level brain dynamics. NeuroImage, 2017.
93. Golubitsky, M., Stewart, I., Buono, P.L., Collins, J.J., Symmetry in locomotor central pattern generators and animal gaits. Nature 401 (1999), 693–695.
94. Greenfield, E., Lecar, H., Mutual information in a dilute, asymmetric neural network model. Phys. Rev. E, 63, 2001, 041905.
95. Greicius, M.D., Krasnow, B., Reiss, A.L., Menon, V., Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. Proc. Natl. Acad. Sci. U. S. A. 100 (2003), 253–258.
96. 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, 2013, 178101.
97. Haken, H., Kelso, J.S., Bunz, H., A theoretical model of phase transitions in human hand movements. Biol. Cybern. 51 (1985), 347–356.
98. Haldeman, C., Beggs, J.M., Critical branching captures activity in living neural networks and maximizes the number of metastable states. Phys. Rev. Lett., 94, 2005, 058101.
99. Harrison, B.J., Yucel, M., Pujol, J., Pantelis, C., Task-induced deactivation of midline cortical regions in schizophrenia assessed with fMRI. Schizophr. Res. 91 (2007), 82–86.
100. Hasson, U., Yang, E., Vallines, I., Heeger, D.J., Rubin, N., A hierarchy of temporal receptive windows in human cortex. J. Neurosci. Off. J. Soc. Neurosci. 28 (2008), 2539–2550.
101. Hasson, U., Chen, J., Honey, C.J., Hierarchical process memory: memory as an integral component of information processing. Trends Cogn. Sci. 19 (2015), 304–313.
102. He, B.J., Zempel, J.M., Snyder, A.Z., Raichle, M.E., The temporal structures and functional significance of scale-free brain activity. Neuron 66 (2010), 353–369.
103. Hearne, L., Cocchi, L., Zalesky, A., Mattingley, J.B., Interactions between default mode and control networks as a function of increasing cognitive reasoning complexity. Hum. Brain Mapp., 2015.
104. Heathcote, A., Popiel, S.J., Mewhort, D., Analysis of response time distributions: an example using the Stroop task. Psychol. Bull., 109, 1991, 340.
105. Heathcote, A., Brown, S., Mewhort, D., The power law repealed: the case for an exponential law of practice. Psychonom. Bull. Rev. 7 (2000), 185–207.
106. Hellyer, P.J., Shanahan, M., Scott, G., Wise, R.J., Sharp, D.J., Leech, R., The control of global brain dynamics: opposing actions of frontoparietal control and default mode networks on attention. J. Neurosci. Off. J. Soc. Neurosci. 34 (2014), 451–461.
107. Hesse, J., Gross, T., Self-organized criticality as a fundamental property of neural systems. Front. Syst. Neurosci., 2014, 8.
108. Hidalgo, J., Grilli, J., Suweis, S., Muñoz, M.A., Banavar, J.R., Maritan, A., Information-based fitness and the emergence of criticality in living systems. Proc. Natl. Acad. Sci. 111 (2014), 10095–10100.
109. Honey, C.J., Kotter, R., Breakspear, M., Sporns, O., Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc. Natl. Acad. Sci. U. S. A. 104 (2007), 10240–10245.
110. Honey, C.J., Thesen, T., Donner, T.H., Silbert, L.J., Carlson, C.E., Devinsky, O., Doyle, W.K., Rubin, N., Heeger, D.J., Hasson, U., Slow cortical dynamics and the accumulation of information over long timescales. Neuron 76 (2012), 423–434.
111. Houle, P.A., Sethna, J.P., Acoustic emission from crumpling paper. Phys. Rev. E, 54, 1996, 278.
112. Hudspeth, A., Making an effort to listen: mechanical amplification in the ear. Neuron 59 (2008), 530–545.
113. Hyett, M.P., Breakspear, M.J., Friston, K.J., Guo, C.C., Parker, G.B., Disrupted effective connectivity of cortical systems supporting attention and interoception in melancholia. JAMA Psychiatry 72 (2015), 350–358.
114. Hyett, M.P., Parker, G.B., Guo, C.C., Zalesky, A., Nguyen, V.T., Yuen, T., Breakspear, M., Scene unseen: disrupted neuronal adaptation in melancholia during emotional film viewing. NeuroImage: Clin. 9 (2015), 660–667.
115. Iyer, K.K., Roberts, J.A., Metsaranta, M., Finnigan, S., Breakspear, M., Vanhatalo, S., Novel features of early burst suppression predict outcome after birth asphyxia. Ann. Clin. Transl. Neurol. 1 (2014), 209–214.
116. Iyer, K.K., Roberts, J.A., Hellstrom-Westas, L., Wikstrom, S., Hansen Pupp, I., Ley, D., Breakspear, M., Vanhatalo, S., Early detection of preterm intraventricular hemorrhage from clinical electroencephalography. Crit. Care Med. 43 (2015), 2219–2227.
117. Iyer, K.K., Roberts, J.A., Hellstrom-Westas, L., Wikstrom, S., Hansen Pupp, I., Ley, D., Vanhatalo, S., Breakspear, M., Cortical burst dynamics predict clinical outcome early in extremely preterm infants. Brain 138 (2015), 2206–2218.
118. Jirsa, V.K., Friedrich, R., Haken, H., Kelso, J.S., A theoretical model of phase transitions in the human brain. Biol. Cybern. 71 (1994), 27–35.
119. Jirsa, V.K., Stacey, W.C., Quilichini, P.P., Ivanov, A.I., Bernard, C., On the nature of seizure dynamics. Brain 137 (2014), 2210–2230.
120. Jirsa, V.K., Proix, T., Perdikis, D., Woodman, M.M., Wang, H., Gonzalez-Martinez, J., Bernard, C., Bénar, C., Guye, M., Chauvel, P., The virtual epileptic patient: individualized whole-brain models of epilepsy spread. Neuroimage 145 (2017), 377–388.
121. Kastner, D.B., Baccus, S.A., Sharpee, T.O., Critical and maximally informative encoding between neural populations in the retina. Proc. Natl. Acad. Sci. 112 (2015), 2533–2538.
122. Kauffman, S.A., Johnsen, S., Coevolution to the edge of chaos: coupled fitness landscapes poised states, and coevolutionary avalanches. J. Theor. Biol. 149 (1991), 467–505.
123. Kello, C.T., Brown, G.D., Ferrer-i-Cancho, R., Holden, J.G., Linkenkaer-Hansen, K., Rhodes, T., Van Orden, G.C., Scaling laws in cognitive sciences. Trends Cogn. Sci. 14 (2010), 223–232.
124. Kelso, J.S., Clark, J.E., The Development of Movement Control and Coordination. 1982, John Wiley & Sons.
125. Kelso, J., Scholz, J., Schöner, G., Nonequilibrium phase transitions in coordinated biological motion: critical fluctuations. Phys. Lett. A 118 (1986), 279–284.
126. Kelso, J., Bressler, S., Buchanan, S., DeGuzman, G., Ding, M., Fuchs, A., Holroyd, T., A phase transition in human brain and behavior. Phys. Lett. A 169 (1992), 134–144.
127. Kelso, J., Phase transitions and critical behavior in human bimanual coordination. Am. J. Physiol.-Regul. Integr. Comparat. Physiol. 246 (1984), R1000–R1004.
128. Kelso, J., The dynamic brain in action: coordinative structures, criticality, and coordination dynamics. Critic. Neural Syst., 2014, 67–104.
129. Kim, S., Park, S.H., Ryu, C.S., Noise-enhanced multistability in coupled oscillator systems. Phys. Rev. Lett., 78, 1997, 1616.
130. Kinouchi, O., Copelli, M., Optimal dynamical range of excitable networks at criticality. Nat. Phys. 2 (2006), 348–351.
131. Kitzbichler, M.G., Smith, M.L., Christensen, S.R., Bullmore, E., Broadband criticality of human brain network synchronization. PLoS Comput. Biol., 5, 2009, e1000314.
132. Kosterlitz, J.M., Thouless, D.J., Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C: Solid State Phys., 6, 1973, 1181.
133. Kramer, E.M., Lobkovsky, A.E., Universal power law in the noise from a crumpled elastic sheet. Phys. Rev. E, 53, 1996, 1465.
134. Langlois, D., Cousineau, D., Thivierge, J.-P., Maximum likelihood estimators for truncated and censored power-law distributions show how neuronal avalanches may be misevaluated. Phys. Rev. E, 89, 2014, 012709.
135. Langton, C.G., Computation at the edge of chaos: phase transitions and emergent computation. Phys. D 42 (1990), 12–37.
136. Larremore, D.B., Shew, W.L., Restrepo, J.G., Predicting criticality and dynamic range in complex networks: effects of topology. Phys. Rev. Lett., 106, 2011, 058101.
137. Larremore, D.B., Shew, W.L., Ott, E., Sorrentino, F., Restrepo, J.G., Inhibition causes ceaseless dynamics in networks of excitable nodes. Phys. Rev. Lett., 112, 2014, 138103.
138. Leech, R., Braga, R., Sharp, D.J., Echoes of the brain within the posterior cingulate cortex. J. Neurosci. Off. J. Soc. Neurosci. 32 (2012), 215–222.
139. Legenstein, R., Maass, W., Edge of chaos and prediction of computational performance for neural circuit models. Neural Netw. 20 (2007), 323–334.
140. Levina, A., Herrmann, J.M., Geisel, T., Dynamical synapses causing self-organized criticality in neural networks. Nat. Phys., 3(12), 2007.
141. Levina, A., Herrmann, J.M., Geisel, T., Theoretical neuroscience of self-organized criticality: from formal approaches to realistic models. Critic. Neural Syst., 2014, 417–436.
142. Linkenkaer-Hansen, K., Nikouline, V.V., Palva, J.M., Ilmoniemi, R.J., Long-range temporal correlations and scaling behavior in human brain oscillations. J. Neurosci. Off. J. Soc. Neurosc. 21 (2001), 1370–1377.
143. Livi, L., Bianchi, F.M., Alippi, C., Determination of the edge of criticality in echo state networks through Fisher information maximization. IEEE Trans. Neural Netw. Learn. Syst.(Janurary), 2017, 16.
144. Loh, M., Rolls, E.T., Deco, G., A dynamical systems hypothesis of schizophrenia. PLoS Comput. Biol., 3(November (11)), 2007, e228.
145. Lu, E.T., Hamilton, R.J., McTiernan, J., Bromund, K.R., Solar flares and avalanches in driven dissipative systems. Astrophys. J. 412 (1993), 841–852.
146. Magnasco, M.O., Piro, O., Cecchi, G.A., Self-tuned critical anti-Hebbian networks. Phys. Rev. Lett., 102, 2009, 258102.
147. Maoiléidigh, D.Ó., Nicola, E.M., Hudspeth, A., The diverse effects of mechanical loading on active hair bundles. Proc. Natl. Acad. Sci. 109 (2012), 1943–1948.
148. Marković, D., Gros, C., Power laws and self-organized criticality in theory and nature. Phys. Rep. 536 (2014), 41–74.
149. Markram, H., Muller, E., Ramaswamy, S., Reimann, M.W., Abdellah, M., Sanchez, C.A., Ailamaki, A., Alonso-Nanclares, L., Antille, N., Arsever, S., Kahou, G.A., Berger, T.K., Bilgili, A., Buncic, N., Chalimourda, A., Chindemi, G., Courcol, J.D., Delalondre, F., Delattre, V., Druckmann, S., Dumusc, R., Dynes, J., Eilemann, S., Gal, E., Gevaert, M.E., Ghobril, J.P., Gidon, A., Graham, J.W., Gupta, A., Haenel, V., Hay, E., Heinis, T., Hernando, J.B., Hines, M., Kanari, L., Keller, D., Kenyon, J., Khazen, G., Kim, Y., King, J.G., Kisvarday, Z., Kumbhar, P., Lasserre, S., Le Be, J.V., Magalhaes, B.R., Merchan-Perez, A., Meystre, J., Morrice, B.R., Muller, J., Munoz-Cespedes, A., Muralidhar, S., Muthurasa, K., Nachbaur, D., Newton, T.H., Nolte, M., Ovcharenko, A., Palacios, J., Pastor, L., Perin, R., Ranjan, R., Riachi, I., Rodriguez, J.R., Riquelme, J.L., Rossert, C., Sfyrakis, K., Shi, Y., Shillcock, J.C., Silberberg, G., Silva, R., Tauheed, F., Telefont, M., Toledo-Rodriguez, M., Trankler, T., Van Geit, W., Diaz, J.V., Walker, R., Wang, Y., Zaninetta, S.M., DeFelipe, J., Hill, S.L., Segev, I., Schurmann, F., Reconstruction and simulation of neocortical microcircuitry. Cell 163 (2015), 456–492.
150. McClure, J.C. Jr, Schroder, K., The magnetic barkhausen effect. Crit. Rev. Solid State Mater. Sci. 6 (1976), 45–83.
151. McIntosh, A.R., Kovacevic, N., Lippe, S., Garrett, D., Grady, C., Jirsa, V., The development of a noisy brain. Arch. Ital. Biol. 148 (2010), 323–337.
152. Meisel, L., Cote, P., Power laws, flicker noise, and the Barkhausen effect. Phys. Rev. B, 46, 1992, 10822.
153. Meisel, C., Storch, A., Hallmeyer-Elgner, S., Bullmore, E., Gross, T., Failure of adaptive self-organized criticality during epileptic seizure attacks. PLoS Comput. Biol., 8, 2012, e1002312.
154. Melbourne, I., Chossat, P., Golubitsky, M., Heteroclinic cycles involving periodic solutions in mode interactions with O (2) symmetry. Proc. R. Soc. Edinburgh: Sec. A Math. 113 (1989), 315–345.
155. Meyer-Lindenberg, A., Poline, J.B., Kohn, P.D., Holt, J.L., Egan, M.F., Weinberger, D.R., Berman, K.F., Evidence for abnormal cortical functional connectivity during working memory in schizophrenia. Am. J. Psychiatry 158 (2001), 1809–1817.
156. Mihalas, S., Millman, D., Iyer, R., Kirkwood, A., Niebur, E., Nonconservative neuronal networks during up-States self-Organize near critical points. Critic. Neural Syst., 2014, 437–464.
157. Miller, K.J., Sorensen, L.B., Ojemann, J.G., den Nijs, M., Power-law scaling in the brain surface electric potential. PLoS Comput. Biol., 5, 2009, e1000609.
158. Millman, D., Mihalas, S., Kirkwood, A., Niebur, E., Self-organized criticality occurs in non-conservative neuronal networks during/up/'states. Nat. Phys. 6 (2010), 801–805.
159. Misic, B., Betzel, R.F., Nematzadeh, A., Goni, J., Griffa, A., Hagmann, P., Flammini, A., Ahn, Y.Y., Sporns, O., Cooperative and competitive spreading dynamics on the human connectome. Neuron 86 (2015), 1518–1529.
160. Mitchell M., Hraber P., Crutchfield J.P., 1993. Revisiting the edge of chaos: Evolving cellular automata to perform computations. arXiv preprint adap-org/9303003.
161. Mora, T., Bialek, W., Are biological systems poised at criticality?. J. Stat. Phys. 144 (2011), 268–302.
162. Moretti, P., Muñoz, M.A., Griffiths phases and the stretching of criticality in brain networks. Nat. Commun., 2013, 4.
163. Mosqueiro, T.S., Maia, L.P., Optimal channel efficiency in a sensory network. Phys. Rev. E, 88, 2013, 012712.
164. Murray, J.D., Bernacchia, A., Freedman, D.J., Romo, R., Wallis, J.D., Cai, X., Padoa-Schioppa, C., Pasternak, T., Seo, H., Lee, D., Wang, X.J., A hierarchy of intrinsic timescales across primate cortex. Nat. Neurosci. 17 (2014), 1661–1663.
165. Nagel, K., Herrmann, H.J., Deterministic models for traffic jams. Phys. A 199 (1993), 254–269.
166. Nakamura, T., Kiyono, K., Yoshiuchi, K., Nakahara, R., Struzik, Z.R., Yamamoto, Y., Universal scaling law in human behavioral organization. Phys. Rev. Lett., 99, 2007, 138103.
167. Nakamura, T., Takumi, T., Takano, A., Aoyagi, N., Yoshiuchi, K., Struzik, Z.R., Yamamoto, Y., Of mice and men–universality and breakdown of behavioral organization. PLoS One, 3, 2008, e2050.
168. Nejad, A.B., Ebdrup, B.H., Siebner, H.R., Rasmussen, H., Aggernaes, B., Glenthoj, B.Y., Baare, W.F., Impaired temporoparietal deactivation with working memory load in antipsychotic-naive patients with first-episode schizophrenia. World J. Biol. Psychiatry Off. J. World Fed. Soc. Biol. Psychiatry 12 (2011), 271–281.
169. Nelson, T.S., Suhr, C.L., Freestone, D.R., Lai, A., Halliday, A.J., Mclean, K.J., Burkitt, A.N., Cook, M.J., Closed-loop seizure control with very high frequency electrical stimulation at seizure onset in the GAERS model of absence epilepsy. Int. J. Neural Syst. 21 (2011), 163–173.
170. Nevado-Holgado, A.J., Marten, F., Richardson, M.P., Terry, J.R., Characterising the dynamics of EEG waveforms as the path through parameter space of a neural mass model: application to epilepsy seizure evolution. Neuroimage 59 (2012), 2374–2392.
171. Niedermeyer, E., Sherman, D.L., Geocadin, R.J., Hansen, H.C., Hanley, D.F., The burst-suppression electroencephalogram. Clin. EEG (Electroencephalogr.) 30 (1999), 99–105.
172. Nielson, D.M., Smith, T.A., Sreekumar, V., Dennis, S., Sederberg, P.B., Human hippocampus represents space and time during retrieval of real-world memories. Proc. Natl. Acad. Sci. 112 (2015), 11078–11083.
173. Nykter, M., Price, N.D., Larjo, A., Aho, T., Kauffman, S.A., Yli-Harja, O., Shmulevich, I., Critical networks exhibit maximal information diversity in structure-dynamics relationships. Phys. Rev. Lett., 100, 2008, 058702.
174. Palva, J.M., Palva, S., 22 Roles of multiscale brain activity fluctuations in shaping the variability and dynamics of psychophysical performance. Prog. Brain Res., 193, 2011, 335.
175. Palva, J.M., Zhigalov, A., Hirvonen, J., Korhonen, O., Linkenkaer-Hansen, K., Palva, S., Neuronal long-range temporal correlations and avalanche dynamics are correlated with behavioral scaling laws. Proc. Natl. Acad. Sci. 110 (2013), 3585–3590.
176. Papanikolaou, S., Bohn, F., Sommer, R.L., Durin, G., Zapperi, S., Sethna, J.P., Universality beyond power laws and the average avalanche shape. Nat. Phys. 7 (2011), 316–320.
177. Penny, W.D., Comparing dynamic causal models using AIC, BIC and free energy. Neuroimage 59 (2012), 319–330.
178. Perković, O., Dahmen, K., Sethna, J.P., Avalanches, Barkhausen noise, and plain old criticality. Phys. Rev. Lett., 75, 1995, 4528.
179. Petermann, T., Thiagarajan, T.C., Lebedev, M.A., Nicolelis, M.A., Chialvo, D.R., Plenz, D., Spontaneous cortical activity in awake monkeys composed of neuronal avalanches. Proc. Natl. Acad. Sci. U. S. A. 106 (2009), 15921–15926.
180. Petzschner, F.H., Weber, L.A., Gard, T., Stephan, K.E., Computational Psychosomatics and Computational Psychiatry: towards a joint framework for differential diagnosis. Biol. Psychiatry, 2017.
181. Plenz, D., Thiagarajan, T.C., The organizing principles of neuronal avalanches: cell assemblies in the cortex?. Trends Neurosci. 30 (2007), 101–110.
182. Ponce-Alvarez, A., He, B.J., Hagmann, P., Deco, G., Task-Driven activity reduces the cortical activity space of the brain: experiment and whole-Brain modeling. PLoS Comput. Biol., 11, 2015, e1004445.
183. Priesemann, V., Valderrama, M., Wibral, M., Le Van Quyen, M., Neuronal avalanches differ from wakefulness to deep sleep–evidence from intracranial depth recordings in humans. PLoS Comput. Biol., 9, 2013, e1002985.
184. Priesemann, V., Wibral, M., Valderrama, M., Propper, R., Le Van Quyen, M., Geisel, T., Triesch, J., Nikolic, D., Munk, M.H., Spike avalanches in vivo suggest a driven, slightly subcritical brain state. Front. Syst. Neurosci., 8, 2014, 108.
185. Publio, R., Ceballos, C.C., Roque, A.C., Dynamic range of vertebrate retina ganglion cells: importance of active dendrites and coupling by electrical synapses. PLoS One, 7, 2012, e48517.
186. Rabinovich, M., Volkovskii, A., Lecanda, P., Huerta, R., Abarbanel, H., Laurent, G., Dynamical encoding by networks of competing neuron groups: winnerless competition. Phys. Rev. Lett., 87, 2001, 068102.
187. Rabinovich, M.I., Huerta, R., Varona, P., Afraimovich, V.S., Transient cognitive dynamics, metastability, and decision making. PLoS Comput. Biol., 4, 2008, e1000072.
188. Razi, A., Kahan, J., Rees, G., Friston, K.J., Construct validation of a DCM for resting state fMRI. Neuroimage 106 (2015), 1–14.
189. Ribeiro, T.L., Copelli, M., Caixeta, F., Belchior, H., Chialvo, D.R., Nicolelis, M.A., Ribeiro, S., Spike avalanches exhibit universal dynamics across the sleep-wake cycle. PLoS One, 5, 2010, e14129.
190. Rice, J., Ruina, A., Stability of steady frictional slipping. J. Appl. Mech. 50 (1983), 343–349.
191. Roberts, D.C., Turcotte, D.L., Fractality and self-organized criticality of wars. Fractals 6 (1998), 351–357.
192. Roberts, J.A., Wallis, G., Breakspear, M., Fixational eye movements during viewing of dynamic natural scenes. Front. Psychol., 4, 2013, 797.
193. Roberts, J.A., Iyer, K.K., Finnigan, S., Vanhatalo, S., Breakspear, M., Scale-free bursting in human cortex following hypoxia at birth. J. Neurosci. 34 (2014), 6557–6572.
194. Roberts, J.A., Iyer, K.K., Vanhatalo, S., Breakspear, M., Critical role for resource constraints in neural models. Front. Syst. Neurosci., 8, 2014, 154.
195. Roberts, J.A., Boonstra, T.W., Breakspear, M., The heavy tail of the human brain. Curr. Opin. Neurobiol. 31 (2015), 164–172.
196. Roberts, J.A., Perry, A., Lord, A.R., Roberts, G., Mitchell, P.B., Smith, R.E., Calamante, F., Breakspear, M., The contribution of geometry to the human connectome. Neuroimage 124 (2016), 379–393.
197. Roberts, J.A., Friston, K.J., Breakspear, M., Clinical applications of stochastic dynamic models of the brain, part II: A review. Biol. Psychiatry Cogn. Neurosci. Neuroimaging, 2017.
198. Robinson, P., Rennie, C., Rowe, D., Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys. Rev. E, 65, 2002, 041924.
199. Romani, G.L., Williamson, S.J., Kaufman, L., Tonotopic organization of the human auditory cortex. Science 216 (1982), 1339–1340.
200. Rubinov, M., Sporns, O., van Leeuwen, C., Breakspear, M., Symbiotic relationship between brain structure and dynamics. BMC Neurosci., 10, 2009, 55.
201. 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, 2011, e1002038.
202. Ruderman, D.L., Bialek, W., Statistics of natural images: scaling in the woods. Phys. Rev. Lett. 73 (1994), 814–817.
203. Scarpetta, S., de Candia, A., Neural avalanches at the critical point between replay and non-replay of spatiotemporal patterns. PLoS One, 8, 2013, e64162.
204. Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V., Held, H., Van Nes, E.H., Rietkerk, M., Sugihara, G., Early-warning signals for critical transitions. Nature 461 (2009), 53–59.
205. Schrauwen, B., Büsing, L., Legenstein, R., On computational power and the order-chaos phase transition in reservoir computing. 22nd Annual Conference on Neural Information Processing Systems (NIPS 2008), NIPS Foundation, 2009, 1425–1432.
206. Schuster, H.G., Plenz, D., Niebur, E., Criticality in Neural Systems. 2014, John Wiley & Sons.
207. Scott, G., Fagerholm, E.D., Mutoh, H., Leech, R., Sharp, D.J., Shew, W.L., Knöpfel, T., Voltage imaging of waking mouse cortex reveals emergence of critical neuronal dynamics. J. Neurosci. 34 (2014), 16611–16620.
208. Sethna, J.P., Dahmen, K.A., Myers, C.R., Crackling noise. Nature 410 (2001), 242–250.
209. Shew, W.L., Plenz, D., The functional benefits of criticality in the cortex. Neuroscientist 19 (2013), 88–100.
210. Shew, W.L., Yang, H.D., Petermann, T., Roy, R., Plenz, D., Neuronal avalanches imply maximum dynamic range in cortical networks at criticality. J. Neurosci. 29 (2009), 15595–15600.
211. Shew, W.L., Yang, H., Yu, S., Roy, R., Plenz, D., Information capacity and transmission are maximized in balanced cortical networks with neuronal avalanches. J. Neurosci. 31 (2011), 55–63.
212. Shew, W.L., Clawson, W.P., Pobst, J., Karimipanah, Y., Wright, N.C., Wessel, R., Adaptation to sensory input tunes visual cortex to criticality. Nat. Phys. 11 (2015), 659–663.
213. Shew, W., Neuronal avalanches. Encyclopedia Comput. Neurosci., 2015, 2018–2024.
214. Shih, H.-Y., Hsieh, T.-L., Goldenfeld, N., Ecological collapse and the emergence of travelling waves at the onset of shear turbulence. Nat. Phys. 12 (2016), 245–248.
215. Shriki, O., Alstott, J., Carver, F., Holroyd, T., Henson, R.N., Smith, M.L., Coppola, R., Bullmore, E., Plenz, D., Neuronal avalanches in the resting MEG of the human brain. J. Neurosci. 33 (2013), 7079–7090.
216. Sreekumar, V., Dennis, S., Doxas, I., Zhuang, Y., Belkin, M., The geometry and dynamics of lifelogs: discovering the organizational principles of human experience. PLoS One, 9, 2014, e97166.
217. Sreekumar, V., Dennis, S., Doxas, I., The episodic nature of experience: a dynamical systems analysis. Cogn. Sci., 2016.
218. Stam, C.J., de Bruin, E.A., Scale-free dynamics of global functional connectivity in the human brain. Hum. Brain Mapp. 22 (2004), 97–109.
219. Stanley, H.E., Introduction to phase transitions and critical phenomena. Introduction to Phase Transitions and Critical Phenomena, by H Eugene Stanley, Pp. 336. Foreword by H Eugene Stanley. Oxford University Press, Jul 1987. ISBN-10: 0195053168. ISBN-13: 9780195053166, 1987, 1.
220. Stanley, H.E., Scaling, universality, and renormalization: three pillars of modern critical phenomena. Rev. Mod. Phys., 71, 1999, S358.
221. Stepp, N., Plenz, D., Srinivasa, N., Synaptic plasticity enables adaptive self-tuning critical networks. PLoS Comput. Biol., 11, 2015, e1004043.
222. Stevens, S.S., Psychophysics. 1975, Transaction Publishers.
223. Stewart, C.V., Plenz, D., Inverted-U profile of dopamine–NMDA-mediated spontaneous avalanche recurrence in superficial layers of rat prefrontal cortex. J. Neurosci. 26 (2006), 8148–8159.
224. Stramaglia S., Pellicoro M., Angelini L., Amico E., Aerts H., Cortés J., Laureys S., Marinazzo D., 2015. Conserved Ising Model on the Human Connectome. arXiv preprint arXiv:1509.02697.
225. Suffczynski, P., Kalitzin, S., Da Silva, F.L., Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience 126 (2004), 467–484.
226. Tagliazucchi, E., Balenzuela, P., Fraiman, D., Chialvo, D.R., Criticality in large-scale brain FMRI dynamics unveiled by a novel point process analysis. Front. Physiol., 3, 2012, 15.
227. Tagliazucchi, E., Chialvo, D.R., Siniatchkin, M., Amico, E., Brichant, J.-F., Bonhomme, V., Noirhomme, Q., Laufs, H., Laureys, S., Large-scale signatures of unconsciousness are consistent with a departure from critical dynamics. J. R. Soc. Interface, 13, 2016, 20151027.
228. Thornton, T.L., Gilden, D.L., Provenance of correlations in psychological data. Psychonom. Bull. Rev. 12 (2005), 409–441.
229. Tognoli, E., Kelso, J.A., The metastable brain. Neuron 81 (2014), 35–48.
230. Tononi, G., Sporns, O., Edelman, G.M., A measure for brain complexity: relating functional segregation and integration in the nervous system. Proc. Natl. Acad. Sci. 91 (1994), 5033–5037.
231. Touboul, J., Destexhe, A., Can power-law scaling and neuronal avalanches arise from stochastic dynamics. PLoS One, 5, 2010, e8982.
232. Touboul J., Destexhe A., 2015. Power-law statistics and universal scaling in the absence of criticality. arXiv preprint arXiv:1503.08033.
233. Van Kessenich, L.M., de Arcangelis, L., Herrmann, H., Synaptic plasticity and neuronal refractory time cause scaling behaviour of neuronal avalanches. Sci. Rep., 6, 2016, 32071.
234. Van Orden, G.C., Holden, J.G., Turvey, M.T., Human cognition and 1/f scaling. J. Exp. Psychol. Gen., 134, 2005, 117.
235. Van de Ville, D., Britz, J., Michel, C.M., EEG microstate sequences in healthy humans at rest reveal scale-free dynamics. Proc. Natl. Acad. Sci. U. S. A. 107 (2010), 18179–18184.
236. Vano, J., Wildenberg, J., Anderson, M., Noel, J., Sprott, J., Chaos in low-dimensional Lotka–Volterra models of competition. Nonlinearity, 19, 2006, 2391.
237. Vasa, F., Shanahan, M., Hellyer, P.J., Scott, G., Cabral, J., Leech, R., Effects of lesions on synchrony and metastability in cortical networks. Neuroimage, 2015.
238. Virkar, Y.S., Shew, W.L., Restrepo, J.G., Ott, E., Feedback control stabilization of critical dynamics via resource transport on multilayer networks: how glia enable learning dynamics in the brain. Phys. Rev. E, 94, 2016, 042310.
239. Vojta, T., Avella, A., Mancini, F., Phases and phase transitions in disordered quantum systems. AIP Conference Proceedings, AIP, 2013, 188–247.
240. Vuong, Q.H., Likelihood ratio tests for model selection and non-nested hypotheses. Econometr. J. Econometr. Soc., 1989, 307–333.
241. Wagenmakers, E.-J., Farrell, S., Ratcliff, R., Estimation and interpretation of 1/fα noise in human cognition. Psychonom. Bull. Rev. 11 (2004), 579–615.
242. Wendling, F., Bartolomei, F., Bellanger, J., Chauvel, P., Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur. J. Neurosci. 15 (2002), 1499–1508.
243. Wendling, F., Hernandez, A., Bellanger, J.-J., Chauvel, P., Bartolomei, F., Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral EEG. J. Clin. Neurophysiol., 22, 2005, 343.
244. Whitfield-Gabrieli, S., Thermenos, H.W., Milanovic, S., Tsuang, M.T., Faraone, S.V., McCarley, R.W., Shenton, M.E., Green, A.I., Nieto-Castanon, A., LaViolette, P., Wojcik, J., Gabrieli, J.D., Seidman, L.J., Hyperactivity and hyperconnectivity of the default network in schizophrenia and in first-degree relatives of persons with schizophrenia. Proc. Natl. Acad. Sci. U. S. A. 106 (2009), 1279–1284.
245. Yang, C.-N., Lee, T.-D., Statistical theory of equations of state and phase transitions. I. Theory of condensation. Phys. Rev., 87, 1952, 404.
246. Yang, H.D., Shew, W.L., Roy, R., Plenz, D., Maximal variability of phase synchrony in cortical networks with neuronal avalanches. J. Neurosci. 32 (2012), 1061–1072.
247. Yang, G.J., Murray, J.D., Repovs, G., Cole, M.W., Savic, A., Glasser, M.F., Pittenger, C., Krystal, J.H., Wang, X.-J., Pearlson, G.D., Altered global brain signal in schizophrenia. Proc. Natl. Acad. Sci. 111 (2014), 7438–7443.
248. Yang, D.P., Zhou, H.J., Zhou, C., Co-emergence of multi-scale cortical activities of irregular firing, oscillations and avalanches achieves cost-efficient information capacity. PLoS Comput. Biol., 13(Feburary (2)), 2017, e1005384.
249. Yeo, B.T., Krienen, F.M., Sepulcre, J., Sabuncu, M.R., Lashkari, D., Hollinshead, M., Roffman, J.L., Smoller, J.W., Zollei, L., Polimeni, J.R., Fischl, B., Liu, H., Buckner, R.L., The organization of the human cerebral cortex estimated by intrinsic functional connectivity. J. Neurophysiol. 106 (2011), 1125–1165.
250. Zalesky, A., Fornito, A., Cocchi, L., Gollo, L.L., Breakspear, M., Time-resolved resting-state brain networks. Proc. Natl. Acad. Sci. U. S. A. 111 (2014), 10341–10346.
251. Zapperi, S., Lauritsen, K.B., Stanley, H.E., Self-organized branching processes: mean-field theory for avalanches. Phys. Rev. Lett., 75, 1995, 4071.
252. Zapperi, S., Castellano, C., Colaiori, F., Durin, G., Signature of effective mass in crackling-noise asymmetry. Nat. Phys. 1 (2005), 46–49.
253. Zhou, C., Zemanová, L., Zamora, G., Hilgetag, C.C., Kurths, J., Hierarchical organization unveiled by functional connectivity in complex brain networks. Phys. Rev. Lett., 2006.
254. Zhigalov, A., Arnulfo, G., Nobili, L., Palva, S., Palva, J.M., Modular co-organization of functional connectivity and scale-free dynamics in the human brain. Netw. Neurosci., 2017.