The non-random brain: Efficiency, economy, and complex dynamics

Frontiers in Computational Neuroscience

Volumn 5, Issue , 2011, Pages

  Sporns, Olaf ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Complex systems; Connectome; Networks; Neural dynamics; Neuroanatomy; Neuroimaging

Indexed keywords

DYNAMICS; GRAPH THEORY; IMAGING TECHNIQUES; LARGE SCALE SYSTEMS; MAMMALS; NETWORKS (CIRCUITS); NEUROIMAGING; RANDOM PROCESSES;

CONNECTOME; EXTERNAL STIMULATION; FUNCTIONAL PERFORMANCE; MAMMALIAN CEREBRAL CORTEX; NEURAL DYNAMICS; NEUROANATOMY; SPONTANEOUS ACTIVITY; TOPOLOGICAL FEATURES;

COMPLEX NETWORKS;

BRAIN CORTEX; BRAIN DEPTH STIMULATION; BRAIN FUNCTION; BRAIN MAPPING; BRAIN NERVE CELL; BRAIN REGION; CONNECTOME; HUMAN; NEUROANATOMY; NONHUMAN; REVIEW; SIGNAL TRANSDUCTION; SYNAPTIC POTENTIAL; TASK PERFORMANCE;

EID: 84892566412     PISSN: None     EISSN: 16625188     Source Type: Journal    
DOI: 10.3389/fncom.2011.00005     Document Type: Review

References (131)

1. Ahn, Y. Y., Jeong, H., and Kim, B. J. (2006). Wiring cost in the organization of a biological neuronal network. Physica A 367, 531-537.
2. Anderson, J. R., Jones, B. W., Yang, J. H., Shaw, M. V., Watt, C. B., Koshevoy, P., Spaltenstein, J., Jurrus, E., Uv, K., Whitaker, R. T., Mastronarde, D., Tasdizen, T., and Marc, R. E. (2009). A computational framework for ultrastructural mapping of neural circuitry. PLoS Biol. 7, e1000074. doi: 10.1371/journal.pbio.1000074
3. Arenas, A., Díaz-Guilera, A., and PérezVicente, C. (2006). Synchronization reveals topological scales in complex networks. Phys. Rev. Lett. 96, 114102.
4. Arenkiel, B. R., and Ehlers, M. D. (2009). Molecular genetics and imaging technologies for circuit-based neuroanatomy. Nature 461, 900-907.
5. Barabási, A. L., and Albert, R. (1999). Emergence of scaling in random networks. Science 286, 509-512.
6. Bassett, D. S., and Bullmore, E. T. (2006). Small world brain networks. Neuroscientist. 12, 512-523.
7. Bassett, D. S., and Bullmore, E. T. (2009). Human brain networks in health and disease. Curr. Opin. Neurol. 22, 340-347.
8. Bassett, D. S., Greenfield, D. L., MeyerLindenberg, A., Weinberger, D. R., Moore, S. W., and Bullmore, E. T. (2010). Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comput. Biol. 6, e1000748. doi: 10.1371/journal.pcbi.1000748
9. Bertschinger, N., and Natschläger, T. (2004). Real-time computation at the edge of chaos in recurrent neural networks. Neural. Comput. 16, 1413-1436.
10. Beurle, R. L. (1956). Properties of a mass of cells capable of regenerating pulses. Philos. Trans. R. Soc. Lond., B, Biol. Sci. 240, 55-94.
11. Binzegger, T., Bouglas, R. J., and Martin, K. A. C. (2004). A quantitative map of the circuit of cat primary visual cortex. J. Neurosci. 24, 8441-8453.
12. Binzegger, T., Douglas, R. J., and Martin, K. A. (2009). Topology and dynamics of the canonical circuit of cat V1. Neural. Netw. 22, 1071-1078.
13. Blondel, V. D., Guillaume, J. L., Lambiotte, R., and Lefebvre, E. (2008). Fast unfolding of communities in large networks. J. Stat. Mech. 10, P10008.
14. Bosking, W. H., Zhang, Y., Schofield, B., and Fitzpatrick, D. (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci. 17, 2112-2127.
15. Braitenberg, V., and Schüz, A. (1998). Statistics and Geometry of Neuronal Connectivity. Berlin: Springer.
16. Brandes, U., and Erlebach, T. (2005). Network Analysis. Berlin: Springer
17. Buckner, R. L., Sepulcre, J., Talukdar, T., Krienen, F. M., Liu, H., Hedden, T., Andrews-Hanna, J. R., Sperling, R. A., and Johnson, K. A. (2009). Cortical hubs revealed by intrinsic functional connectivity: mapping, assessment of stability, and relation to Alzheimer’s disease. J. Neurosci. 29, 1860-1873
18. Bullmore, E., and Sporns, O. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186-198.
19. Buzsáki, G., Geisler, C., Henze, D. A., and Wang, X. J. (2004). Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci. 27, 186-193
20. Cajal, S. R. (1995). Histology of the Nervous System of Man and Vertebrates. New York: Oxford University Press.
21. Callaway, D. S., Hopcroft, J. F., Kleinber, J. M., Newman, M. E. J., and Strogatz, S. H. (2001). Are randomly grown graphs really random? Phys. Rev. E 64, 041902.
22. Castellanos, F. X., Margulies, D. S., Kelly, A. M. C., Uddin, L. Q., Ghaffari, M., Kirsch, A., Shaw, D., Shezad, Z., Di Martino, A., Biswal, B., Sonuga-Barke, E. J. S., Rotrosen, J., Adler, L. A., and Milham, M. P. (2008). Cingulateprecuneus interactions: a new locus of dysfunction in adult attention-deficit/ hyperactivity disorder. Biol. Psychiatry 63, 332-337.
23. Chang, C., and Glover, G. H. (2010). Time-frequency dynamics of restingstate brain connectivity measured with fMRI. Neuroimage 50, 81-98.
24. Chen, B. L., Hall, D. H., and Chklovskii, D. B. (2006). Wiring optimization can relate neuronal structure and function. Proc. Natl. Acad. Sci. U.S.A. 103, 4723-4728.
25. Chen, Z. J., He, Y., Rosa-Neto, P., Germann, J., and Evans, A. C. (2008). Revealing modular architecture of human brain structural networks by using cortical thickness from MRI. Cereb. Cortex 18, 2374-2381.
26. Cherniak, C. (1995). Neural component placement. Trends Neurosci. 18, 522-527.
27. Chialvo, D. (2010). Emergent complex neural dynamics. Nature Phys. 6, 744-750.
28. Cohen, A. L., Fair, D. A., Dosenbach, N. U. F., Miezin, F. M., Dierker, D., Van Essen, D. C., Schlaggar, B. L., and Petersen, S. E. (2008). Defining functional areas in individual human brains using resting state functional connectivity MRI. Neuroimage 41, 45-57.
29. Costa, L. D. F., Kaiser, M., and Hilgetag, C. C. (2007). Predicting the connectivity of primate cortical networks from topological and spatial node properties. BMC Syst. Biol. 1, 16. doi: 10.1186/1752-0509-1-16
30. Da Costa, N. M., and Martin, K. A. C. (2010). Whose cortical column would that be? Front. Neuroanat. 4:16. doi: 10.3389/fnana.2010.00016
31. Damoiseaux, J. S., and Greicius, M. D. (2009). Greater than the sum of its parts: a review of studies combining structural connectivity and resting-state functional connectivity. Brain Struct. Funct. 213, 525-533.
32. Deco, G., Jirsa, V., McIntosh, A. R., Sporns, O., and Kötter, R. (2009). Key role of coupling, delay, and noise in resting brain fluctuations. Proc. Natl. Acad. Sci. U.S.A. 106, 10302-10307.
33. Erdös, P., and Rényi, A. (1960). On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17-61
34. Felleman, D. J., and van Essen, D. C. (1991). Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1-47.
35. Fortunato, S. (2010). Community detection in graphs. Phys. Rep. 486, 75-174.
36. Fortunato, S., and Barthelemy, M. (2007). Resolution limit in community detection. Proc. Natl. Acad. Sci. U.S.A. 104, 36-41.
37. Fox, M. D., and Greicius, M. (2010). Clinical applications of resting state functional connectivity. Front. Syst. Neurosci. 4:19. doi: 10.3389/fnsys.2010.00019
38. Fox, M. D., Snyder, A. Z., Vincent, J. L., Corbetta, M., Van Essen, D. C., and Raichle, M. E. (2005). The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proc. Natl. Acad. Sci. U.S.A. 102, 9673-9678.
39. Friston, K. J., and Frith, C. D. (1995). Schizophrenia: a disconnection syndrome? Clin. Neurosci. 3, 89-97
40. Galán, R. F. (2008). On how network architecture determines the dominant patterns of spontaneous neural activity. PLoS ONE 3, e2148. doi: 10.1371/journal.pone.0002148
41. Ghosh, A., Rho, Y., McIntosh, A. R., Kötter, R., and Jirsa, V. K. (2008). Noise during rest enables the exploration of the brain’s dynamic repertoire. PLoS Comput. Biol. 4, e1000196. doi: 10.1371/journal.pcbi.1000196
42. Gomes-Gardenes, J., Zamora-Lopez, G., Moreno, Y., and Arenas, A. (2010). From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex. PLoS ONE 5, e12313. doi: 10.1371/journal.pone.0012313
43. Gong, G., He, Y., Concha, L., Lebel, C., Gross, D. W., Evans, A. C., and Beaulieu, C. (2009). Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography. Cereb. Cortex 19, 524-536.
44. Greicius, M. D., Krasnow, B., Reiss, A. L., and Menon, V. (2003). Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. Proc. Natl. Acad. Sci. U.S.A. 100, 253-258.
45. Grenander, U., and Silverstein, J. W. (1977). Spectral analysis of networks with random topologies. SIAM J. Appl. Math. 32, 499-519.
46. Hagmann, P., Cammoun, L., Gigandet, X., Gerhard, S., Grant, P. E., Wedeen, V., Meuli, R., Thiran, J. P., Honey, C. J., and Sporns, O. (2010). MR connectomics: principles and challenges. J. Neurosci. Meth. 194, 34-45.
47. Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C. J., Wedeen, V. J., and Sporns, O. (2008). Mapping the structural core of human cerebral cortex. PLoS Biol. 6, e159. doi: 10.1371/journal.pbio.0060159
48. He, Y., Chen, Z. J., and Evans, A. C. (2007). Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. Cereb. Cortex 17, 2407-2419.
49. Hellwig, B. (2000). A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex. Biol. Cybern. 82, 111-121.
50. Helmstaedter, M., Briggman, K. L., and Denk, W. (2008). 3D structural imaging of the brain with photons and electrons. Curr. Opin. Neurobiol. 18, 633-641.
51. Hilgetag, C. C., Burns, G. A., O’Neill, M. A., Scannell, J. W., and Young, M. P. (2000). Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. Philos. Trans. R. Soc. B 355, 91-110.
52. Hilgetag, C. C., and Kaiser, M. (2004). Clustered organization of cortical connectivity. Neuroinformatics 2, 353-360.
53. Honey, C. J., Kötter, R., Breakspear, M., and Sporns, O. (2007). Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc. Natl. Acad. Sci. U.S.A. 104, 10240-10245.
54. Honey, C. J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J. P., Meuli, R., and Hagmann, P. (2009). Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl. Acad. Sci. U.S.A. 106, 2035-2040.
55. Honey, C. J., Thivierge, J. P., and Sporns, O. (2010). Can structure predict function in the human brain? Neuroimage 52, 766-776.
56. Horwitz, B. (2003). The elusive concept of brain connectivity. Neuroimage 19, 466-470.
57. Iturria-Medina, Y., Canales-Rodriguez, E. J., Melie-Garcia, L., Valdes-Hernandez, P. A., Martinez-Montes, E., AlemanGomez, Y., and Sanchez-Bornot, J. M. (2007). Characterizing brain anatomical connections using diffusion weighted MRI and graph theory. Neuroimage 36, 645-660.
58. Iturria-Medina, Y., Sotero, R. C., CanalesRodriguez, E. J., Aleman-Gomez, Y., and Melie-Garcia, L. (2008). Studying the human brain anatomical network via diffusion-weighted MRI and graph theory. Neuroimage 40, 1064-1076.
59. Izhikevich, E. M., and Edelman, G. M. (2008). Large-scale model of mammalian thalamocortical systems. Proc. Natl. Acad. Sci. U.S.A. 105, 3593-3598.
60. Jain, V., Seung, H. S., and Turage, S. C. (2010). Machines that learn to segment images: a crucial technology for connectomics. Curr. Opin. Neurobiol. 20, 653-666.
61. Johansen-Berg, H., and Behrens, T. E. J. (eds). (2009). Diffusion MRI: From Quantitative Measurement to In Vivo Neuroanatomy. Amsterdam: Academic Press.
62. Just, M. A., Cherkassky, V. L., Keller, T. A., Kana, R. K., and Minshew, N. J. (2007). Functional and anatomical cortical underconnectivity in autism: evidence from an fMRI study of an executive function task and corpus callosum morphometry. Cereb. Cortex 17, 951-961.
63. Kaiser, M., and Hilgetag, C. C. (2006). Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. 2, e95. doi: 10.1371/journal.pcbi.0020095
64. Kaiser, M., and Hilgetag, C. C. (2010). Optimal hierarchical modular topologies for producing limited sustained activation in neural networks. Front. Neuroinformatics 4:8. doi: 10.3389/fninf.2010.00008
65. Kashtan, N., and Alon, U. (2005). Spontaneous evolution of modularity and network motifs. Proc. Natl. Acad. Sci. U.S.A. 102, 13773-13778.
66. Keller, T. A., Kana, R. K., and Just, M. A. (2007). A developmental study of the structural integrity of white matter in autism. Neuroreport 18, 23-27.
67. Kenet, T., Bibitchkov, D., Tsodyks, M., Grinvald, A., and Arieli, A. (2003). Spontaneously emerging cortical representations of visual attributes. Nature 425, 954-956.
68. Kirschner, M., and Gerhart, J. (2005). The Plausibility of Life: Resolving Darwin’s Dilemma. New Haven: Yale University Press.
69. Koch, M. A., Norris, D. G., and HundGeorgiadis, M. (2002). An investigation of functional and anatomical connectivity using magnetic resonance imaging. Neuroimage 16, 241-250
70. Konrad, K., and Eickhoff, S. B. (2010). Is the ADHD brain wired differently? A review on structural and functional connectivity in attention deficit hyperactivity disorder. Hum. Brain Mapp. 31, 904-916.
71. Kremkow, J., Kumar, A., Rotter, S., and Aertsen, A. (2007). Emergence of population synchrony in a layered network of the cat visual cortex. Neurocomputing 70, 2069-2073.
72. Lai, M. C., Lombardo, M. V., Chakrabarti, B., Sadek, S. A., Pasco, G., Wheelwright, S. J., Bullmore, E. T., Baron-Cohen, S., MRC AIMS Consortium, Suckling, J. (2010). A shift to randomness of brain oscillations in people with autism. Biol. Psychiatry 68, 1092-1099.
73. Laughlin, S. B., and Sejnowski, T. J. (2003). Communication in neuronal networks. Science 301, 1870-1874.
74. Lichtman, J. W., Livet, J., and Sanes, J. R. (2008). A technicolour approach to the connectome. Nat. Rev. Neurosci. 9, 417-422.
75. Lipson, H., Pollack, J. B., and Suh, N. P. (2002). On the origin of modular variation. Evolution 56, 1549-1556
76. Liu, Y., Liang, M., Zhou, Y., He, Y., Hao, Y., Song, M., Yu, C., Liu, H., Liu, Z., and Jiang, T. (2008). Disrupted small-world networks in schizophrenia. Brain 131, 945-961.
77. Lu, J., Fiala, J. C., and Lichtman, J. W. (2009). Semi-automated reconstruction of neural processes from large numbers of fluorescence images. PLoS ONE 4, e5655. doi: 10.1371/journal.pone.0005655
78. Lynall, M. E., Bassett, D. S., Kerwin, R., McKenna, P. J., Kitzbichler, M., Muller, U., and Bullmore, E. (2010). Functional connectivity and brain networks in schizophrenia. J. Neurosci. 30, 9477-9487
79. Maass, W., Natschläger, T., and Markram, H. (2002). Real-time computing with-out stable states: a new framework for neural computation based on perturbations. Neural. Comput. 14, 2531-2560
80. Maslov, S., and Sneppen, K. (2002). Specificity and stability in topology of protein networks. Science 296, 910-913
81. Meunier, D., Lambiotte, R., and Bullmore, E. (2010). Modular and hierarchically modular organization of brain networks. Front. Neurosci. 4:200. doi: 10.3389/fnins.2010.00200
82. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U. (2002). Network motifs: simple building blocks of complex networks. Science 298, 824-827
83. Mishchenko, Y., Hu, T., Spacek, J., Mendenhall, J., Harris, K. M., and Chklovsii, D. B. (2010). Ultrastructural analysis of hippocampal neuropil from the connectomics perspective. Neuron 67, 1009-1020
84. Mountcastle, V. B. (1997). The columnar organization of the neocortex. Brain 120, 701-722
85. Müller-Linow, M., Hilgetag, C. C., and Hütt, M. T. (2008). Organization of excitable dynamics in hierarchical biological networks. PLoS Comput. Biol. 4, e1000190. doi: 10.1371/journal.pcbi.1000190
86. Nelson, S. M., Cohen, A. L., Power, J. D., Wig, G. S., Miezin, F. M., Wheeler, M. E., Velanova, K., Donaldson, D. I., Phillips, J. S., Schlaggar, B. L., and Petersen, S. E. (2010). A parcellation scheme for human left lateral parietal cortex. Neuron 67, 156-170
87. Newman, M. E. J. (2002). Assortative mixing in networks. Phys. Rev. Lett. 89, 208701
88. Newman, M. E. J. (2006). Modularity and community structure in networks. Proc. Natl. Acad. Sci. U.S.A. 103, 8577-8582
89. Newman, M. E. J. (2010). Networks. New York: Oxford University Press
90. Newman, M. E. J., and Girvan, M. (2004). Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113
91. Ohki, K., Chung, S., Ch’ng, Y. H., Kara, P., and Reid, R. C. (2005). Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex. Nature 433, 597-603
92. Palm, C., Axer, M., Grassel, D., Dammers, J., Lindemeyer, J., Zilles, K., Pietrzyk, U., and Amunts, K. (2010). Towards ultra-high resolution fibre tract mapping of the human brain registration of polarized light images and reorientation of fibre vectors. Front. Hum. Neurosci. 4:9. doi: 10.3389/neuro.09.009.2010
93. Raichle, M. (2009). A paradigm shift in functional brain imaging. J. Neurosci. 29, 12729-12734.
94. Raichle, M. E., MacLeod, A. M., Snyder, A. Z., Powers, W. J., Gusnard, D. A., and Shulman, G. L. (2001). A default mode of brain function. Proc. Natl. Acad. Sci. U.S.A. 98, 676-682.
95. Reijneveld, J. C., Ponten, S. C., Berendse, H. W., and Stam, C. J. (2007). The application of graph theoretical analysis to complex networks in the brain. Clin. Neurophysiol. 118, 2317-2331
96. Rubinov, M., Knock, S. A., Stam, C. J., Micheloyannis, S., Harris, A. W. F., Williams, L. M., and Breakspear, M. (2009). Small-world properties of nonlinear brain activity in schizophrenia. Hum. Brain Mapp. 30, 403-416
97. Rubinov, M., and Sporns, O. (2010). Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059-1069.
98. Scannell, J. W., Blakemore, C., and Young, M. P. (1995). Analysis of connectivity in the cat cerebral cortex. J. Neurosci. 15, 1463-1483.
99. Scannell, J. W., Burns, G. A. P. C., Hilgetag, C. C., O’Neil, M. A., and Young, M. P. (1999). The connectional organization of the cortico-thalamic system of the cat. Cereb. Cortex 9, 277-299.
100. Schmahmann, J. D., Pandya, D. N., Wang, R., Dai, G., D’Arceuil, H. E., de Crespigny, A. J., and Wedeen, V. J. (2007). Association fibre pathways of the brain: parallel observations from diffusion spectrum imaging and autoradiography. Brain 130, 630-653.
101. Sholl, D. A. (1953). Dendritic organization in the neurons of the visual and motor cortices of the cat. J. Anat. 87, 387-406.
102. Sholl, D. A. (1955). The organization of the visual cortex in the cat. J. Anat. 89, 33-46.
103. Smith, S. M., Fox, P. T., Miller, K. L., Glahn, D. C., Fox, P. M., Mackay, C. E., Filippini, N., Watkins, K. E., Toro, R., Laird, A., and Beckmann, C. F. (2009). Correspondence of the brain’s functional architecture during activation and rest. Proc. Natl. Acad. Sci. U.S.A. 106, 13040-13045.
104. Song, S., Sjöström, P. J., Reigl, M., Nelson, S., and Chklovskii, D. B. (2005). Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol. 3, e68. doi: 10.1371/journal.pbio.0030068
105. Sporns, O. (2011). Networks of the Brain. Cambridge: MIT Press.
106. Sporns, O., Chialvo, D., Kaiser, M., and Hilgetag, C. C. (2004). Organization, development and function of complex brain networks. Trends Cogn. Sci. (Regul. Ed.) 8, 418-425.
107. Sporns, O., Honey, C. J., and Kötter, R. (2007). Identification and classification of hubs in brain networks. PLoS ONE 2, e1049. doi: 10.1371/journal.pone.0001049
108. Sporns, O., and Kötter, R. (2004). Motifs in brain networks. PLoS Biol. 2, 1910-1918. doi: 10.1371/journal.pbio.0020369
109. Sporns, O., Tononi, G., and Edelman, G. M. (2000). Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb. Cortex 10, 127-141.
110. Sporns, O., Tononi, G., and Kötter, R. (2005). The human connectome: a structural description of the human brain. PLoS Comput. Biol. 1, 245-251. doi: 10.1371/journal.pcbi.0010042
111. Stam, C. J., de Haan, W., Daffertshofer, A., Jones, B. F., Manshanden, I., van Cappellen van Walsum, A. M., Montez, T., Verbunt, J. P. A., de Munck, J. C., van Dijk, B. W., Berendse, H. W., and Scheltens, P. (2009). Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer’s disease. Brain 132, 213-224.
112. Stam, C. J., Jones, B. F., Nolte, G., Breakspear, M., and Scheltens, P. (2007). Small-world networks and functional connectivity in Alzheimer’s disease. Cereb. Cortex 17, 92-99.
113. Supekar, K., Menon, V., Rubin, D., Musen, M., and Greicius, M. D. (2008). Network analysis of intrinsic functional brain connectivity in Alzheimer’s disease. PLoS Comput. Biol. 4, e1000100. doi: 10.1371/journal.pcbi.1000100
114. Tononi, G., and Edelman, G. M. (2000). Schizophrenia and the mechanisms of conscious integration. Brain Res. Rev. 31, 391-400.
115. Tononi, G., Sporns, O., and Edelman, G. M. (1994). A measure for brain complexity: Relating functional segregation and integration in the nervous system. Proc. Natl. Acad. Sci. U.S.A. 91, 5033-5037.
116. Tuckwell, H. C. (1989). Stochastic Processes in the Neurosciences. Philadelphia: Society for Industrial and Applied Mathematics.
117. Turing, A. M. (1948). “Intelligent machinery, national physical laboratory report,” in Machine Intelligence, Vol. 5, eds B. Meltzer and D. Michie (Edinburgh: Edinburgh University Press), 3-23.
118. Uttley, A. M. (1955). The probability of neural connexions. Proc. R. Soc. B 144, 229-240.
119. Van den Heuvel, M. P., Mandl, R. C. W., Stam, C. J., Kahn, R. S., and Hulshoff Pol, H. E. (2010). Aberrant frontal and temporal complex network structure in schizophrenia: a graph theoretical analysis. J. Neurosci. 30, 15915-15926.
120. Vincent, J. L., Patel, G. H., Fox, M. D., Snyder, A. Z., Baker, J. T., Van Essen, D. C., Zempel, J. M., Snyder, L. H., Corbetta, M., and Raichle, M. E. (2007). Intrinsic functional architecture in the anaesthetized monkey brain. Nature 447, 83-86.
121. Wagner, G. P., Pavlicev, M., and Cheverud, J. M. (2007). The road to modularity. Nat. Rev. Genet. 8, 921-931.
122. Wang, L., Zhu, C., Zang, Y., Cao, Q., Zhang, H., Zhong, Q., and Wang, Y. (2009). Altered small-world brain functional networks in children with attention-deficit/hyperactivity disorder. Hum. Brain Mapp. 30, 638-649.
123. Wang, X. J. (2010). Neurophysiological and computational principles of cortical rhythms in cognition. Physiol. Rev. 90, 1195-1268.
124. Watts, D. J., and Strogatz, S. H. (1998). Collective dynamics of “small-world” networks. Nature 393, 440-442
125. White, J. G. (1985). Neuronal connectivity in Caenorhabditis elegans. Trends Neurosci. 8, 277-283.
126. 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. E., and Seidman, L. J. (2009). 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, 1279-1284.
127. Yoshimura, Y., Dantzker, J. L. M., and Callaway, E. M. (2005). Excitatory cortical neurons form fine-scale functional networks. Nature 433, 868-873.
128. Young, M. P. (1992). Objective analysis of the topological organization of the primate cortical visual system. Nature 358, 152-155.
129. Zamora-Lopez, G., Zhou, C., and Kurths, J. (2010). Cortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks. Front. Neuroinformatics 4:1. doi: 10.3389/neuro.11.001.2010
130. Zhang, K., and Sejnowski, T. J. (2000). A universal scaling law between gray matter and white matter of the cerebral cortex. Proc. Natl. Acad. Sci. U.S.A. 97, 5621-5626.
131. Zhou, C., Zemanová, L., Zamora, G., Hilgetag, C. C., and Kurths, J. (2007). Structure function relationship in complex brain networks expressed by hierarchical synchronization. New J. Phys. 9, 178