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Understanding the mechanisms of brain functions from the angle of synchronization and complex network

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Abstract

The human brain is the most complicated and fascinated system and executes various important brain functions, but its underlying mechanism is a long-standing problem. In recent years, based on the progress of complex network science, much attention has been paid to this problem and many important results have been achieved, thus it is the time to make a summary to help further studies. For this purpose, we here make a brief but comprehensive review on those results from the aspect of brain networks, i.e., from the angle of synchronization and complex network. First, we briefly discuss the main features of human brain and its cognitive functions through synchronization. Then, we discuss how to construct both the anatomical and functional brain networks, including the pathological brain networks such as epilepsy and Alzheimer’s diseases. Next, we discuss the approaches of studying brain networks. After that, we discuss the current progress of understanding the mechanisms of brain functions, including the aspects of chimera state, remote synchronization, explosive synchronization, intelligence quotient, and remote propagation. Finally, we make a brief discussion on the envision of future study.

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References

  1. G. Buzsaki, Rhythms of the Brain, Oxford University Press, New York, 2006

    Book  MATH  Google Scholar 

  2. P. Bak, How Nature Works: The Science of Self-Organized Criticality, Springer, New York, 1996

    Book  MATH  Google Scholar 

  3. L. de Arcangelis, C. Perrone-Capano, and H. J. Herrmann, Self-organized criticality model for brain plasticity, Phys. Rev. Lett. 96(2), 028107 (2006)

    Article  ADS  Google Scholar 

  4. T. K. Hensch, Critical period regulation, Annu. Rev. Neurosci. 27(1), 549 (2004)

    Article  Google Scholar 

  5. L. F. Abbott and S. B. Nelson, Synaptic plasticity: Taming the beast, Nat. Neurosci. 3(S11), 1178 (2000)

    Article  Google Scholar 

  6. D. O. Hebb, The Organization of Behavior, John Wiley, New York, 1949

    Google Scholar 

  7. S. J. Cooper, Hebb’s synapse and learning rule: A history and commentary, Neurosci. Biobehav. Rev. 28(8), 851 (2005)

    Article  Google Scholar 

  8. K. Bansal, J. O. Garcia, S. H. Tompson, T. Verstynen, J. M. Vettel, and S. F. Muldoon, Cognitive chimera states in human brain networks, Sci. Adv. 5(4), eaau8535 (2019)

    Article  ADS  Google Scholar 

  9. P. Fries, A mechanism for cognitive dynamics: Neuronal communication through neuronal coherence, Trends Cogn. Sci. 9(10), 474 (2005)

    Article  Google Scholar 

  10. J. F. Hipp, A. K. Engel, and M. Siegel, Oscillatory synchronization in large-scale cortical networks predicts perception, Neuron 69(2), 387 (2011)

    Article  Google Scholar 

  11. T. J. Buschman and E. K. Miller, Top-down versus bottomup control of attention in the prefrontal and posterior parietal cortices, Science 315(5820), 1860 (2007)

    Article  ADS  Google Scholar 

  12. J. Gross, F. Schmitz, I. Schnitzler, K. Kessler, K. Shapiro, B. Hommel, and A. Schnitzler, Modulation of long-range neural synchrony reflects temporal limitations of visual attention in humans, Proc. Natl. Acad. Sci. USA 101(35), 13050 (2004)

    Article  ADS  Google Scholar 

  13. F. Crick and C. Koch, Some reflections on visual awareness, Cold Spring Harb. Symp. Quant. Biol. 55(0), 953 (1990)

    Article  Google Scholar 

  14. M. Volgushev, S. Chauvette, M. Mukovski, and I. Timofecv, Precise long-range synchronization of activity and silence in neoconical neurons during slow-wave sleep, J. Neurosci. 26(21), 5665 (2006)

    Article  Google Scholar 

  15. L. M. Ward, Synchronous neural oscillations and cognitive processes, Trends Cogn. Sci. 7(12), 553 (2003)

    Article  Google Scholar 

  16. E. Bullmore and O. Sporns, The economy of brain network organization, Nat. Rev. Neurosci. 13(5), 336 (2012)

    Article  Google Scholar 

  17. K. Bansal, J. D. Medaglia, D. S. Bassett, J. M. Vettel, and S. F. Muldoon, Data-driven brain network models differentiate variability across language tasks, PLoS Comput. Biol. 14(10), e1006487 (2018)

    Article  ADS  Google Scholar 

  18. P. Hagmann, L. Cammoun, X. Gigandet, R. Meuli, C. J. Honey, J. V. Wedeen, and O. Sporns, Mapping the structural core of human cerebral cortex, PLoS Biol. 6(7), e159 (2008)

    Article  Google Scholar 

  19. S. B. Eickhoff, B. T. T. Yeo, and S. Genon, Imaging-based parcellations of the human brain, Nat. Rev. Neurosci. 19(11), 672 (2018)

    Article  Google Scholar 

  20. C. J. Honey, O. Sporns, L. Cammoun, X. Gigandet, J. P. Thiran, R. Meuli, and P. Hagmann, Predicting human resting-state functional connectivity from structural connectivity, Proc. Natl. Acad. Sci. USA 106(6), 2035 (2009)

    Article  ADS  Google Scholar 

  21. S. Huo, C. Tian, M. Zheng, S. Guan, C. Zhou, and Z. Liu, Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure dynamics relationship in human brain, Natl. Sci. Rev. 8(1), nwaa125 (2021)

    Article  Google Scholar 

  22. C. J. Stam, Characterization of anatomical and functional connectivity in the brain: A complex networks perspective, Int. J. Psychophysiol. 77(3), 186 (2010)

    Article  Google Scholar 

  23. O. Sporns, D. R. Chialvo, M. Kaiser, and C. C. Hilgetag, Organization, development and function of complex brain networks, Trends Cogn. Sci. 8(9), 418 (2004)

    Article  Google Scholar 

  24. V. M. Eguíluz, D. R. Chialvo, G. A. Cecchi, M. Baliki, and A. V. Apkarian, Scale-free brain functional networks, Phys. Rev. Lett. 94(1), 018102 (2005)

    Article  ADS  Google Scholar 

  25. D. S. Bassett, A. Meyer-Lindenberg, S. Achard, T. Duke, and E. Bullmore, Adaptive reconfiguration of fractal smallworld human brain functional networks, Proc. Natl. Acad. Sci. USA 103(51), 19518 (2006)

    Article  ADS  Google Scholar 

  26. A. K. Engel, P. Fries, and W. Singer, Dynamic predictions: Oscillations and synchrony in top-down processing, Nat. Rev. Neurosci. 2(10), 704 (2001)

    Article  Google Scholar 

  27. F. Varela, J. P. Lachaux, E. Rodriguez, and J. Martinerie, The Brainweb: Phase Synchronization and Large-Scale Integration, Nat. Rev. Neurosci. 2(4), 229 (2001)

    Article  Google Scholar 

  28. K. E. Stephan, C. C. Hilgetag, G. A. P. C. Burns, M. A. O’Neill, M. P. Young, and R. Kotter, Computational analysis of functional connectivity between areas of primate cerebral cortex, Philos. Trans. R. Soc. Lond. B 355(1393), 111 (2000)

    Article  Google Scholar 

  29. L. M. A. Bettencourt, G. J. Stephens, M. I. Ham, and G. W. Gross, Functional structure of cortical neuronal networks grown in vitro, Phys. Rev. E 75(2), 021915 (2007)

    Article  ADS  Google Scholar 

  30. M. Guye, G. Bettus, F. Bartolomei, and P. J. Cozzone, Graph theoretical analysis of structural and functional connectivity MRI in normal and pathological brain networks, MAGMA 23(5–6), 409 (2010)

    Article  Google Scholar 

  31. C. J. Stam, B. F. Jones, G. Nolte, M. Breakspear, and P. Scheltens, Small world networks and functional connectivity in Alzheimers disease, Cereb. Cortex 17(1), 92 (2006)

    Article  Google Scholar 

  32. M. Chavez, M. Valencia, V. Navarro, V. Latora, and J. Martinerie, Functional modularity of background activities in normal and epileptic brain networks, Phys. Rev. Lett. 104(11), 118701 (2010)

    Article  ADS  Google Scholar 

  33. M. Lynall, D. S. Bassett, R. Kerwin, P. J. McKenna, M. Kitzbichler, U. Muller, and E. Bullmore, Functional connectivity and brain networks in schizophrenia, J. Neurosci. 30(28), 9477 (2010)

    Article  Google Scholar 

  34. K. J. Friston, Functional and effective connectivity in neuroimaging: A synthesis, Hum. Brain Mapp. 2(1–2), 56 (1994)

    Article  Google Scholar 

  35. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, The synchronization of chaotic systems, Phys. Rep. 366(1–2), 1 (2002)

    Article  ADS  MATH  Google Scholar 

  36. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, Cambridge, UK, 2001

    Book  MATH  Google Scholar 

  37. A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Synchronization in complex networks, Phys. Rep. 469(3), 93 (2008)

    Article  ADS  Google Scholar 

  38. J. Fell and N. Axmacher, The role of phase synchronization in memory processes, Nat. Rev. Neurosci. 12(2), 105 (2011)

    Article  Google Scholar 

  39. P. Sauseng, W. Klimesch, M. Doppelmayr, S. Hanslmayr, M. Schabus, and W. R. Gruber, Theta coupling in the human electroencephalogram during a working memory task, Neurosci. Lett. 354(2), 123 (2004)

    Article  Google Scholar 

  40. J. Sarnthein, H. Petsche, P. Rappelsberger, G. L. Shaw, and A. von Stein, Synchronization between prefrontal and posterior association cortex during human working memory, Proc. Natl. Acad. Sci. USA 95(12), 7092 (1998)

    Article  ADS  Google Scholar 

  41. N. Axmacher, D. P. Schmitz, T. Wagner, C. E. Elger, and J. Fell, Interactions between medial temporal lobe, pre-frontal cortex, and inferior temporal regions during visual working memory, a combined intracranial EEG and functional magnetic resonance imaging study, J. Neurosci. 28(29), 7304 (2008)

    Article  Google Scholar 

  42. P. Sauseng, W. Klimesch, K. F. Heise, W. R. Gruber, E. Holz, A. A. Karim, M. Glennon, C. Gerloff, N. Birbaumer, and F. C. Hummel, Brain oscillatory substrates of visual shortterm memory capacity, Curr. Biol. 19(21), 1846 (2009)

    Article  Google Scholar 

  43. M. I. Rabinovich, A. N. Simmons, and P. Varona, Dynamical bridge between brain and mind, Trends Cogn. Sci. 19(8), 453 (2015)

    Article  Google Scholar 

  44. H. R. Wilson and J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons, Biophys. J. 12(1), 1 (1972)

    Article  ADS  Google Scholar 

  45. S. F. Muldoon, F. Pasqualetti, S. Gu, M. Cieslak, S. T. Grafton, J. M. Vettel, and D. S. Bassett, Stimulation-based control of dynamic brain networks, PLoS Comput. Biol. 12(9), e1005076 (2016)

    Article  ADS  Google Scholar 

  46. F. Wendling, J. J. Bellanger, F. Bartolomei, and P. Chauvel, Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals, Biol. Cybern. 83(4), 367 (2000)

    Article  Google Scholar 

  47. C. Zhou, L. Zemanova, G. Zamora-Lopez, C. C. Hilgetag, and J. Kurths, StructureCfunction relationship in complex brain networks expressed by hierarchical synchronization, New J. Phys. 9(6), 178 (2007)

    Article  ADS  Google Scholar 

  48. O. David, L. Harrison, and K. J. Friston, Modelling even-trelated responses in the brain, Neuroimage 25(3), 756 (2005)

    Article  Google Scholar 

  49. J. M. Huntenburg, P. L. Bazin, and D. S. Margulies, Large-scale gradients in human cortical organization, Trends Cogn. Neurosci. 22, 21 (2018)

    Article  Google Scholar 

  50. T. Ito, K. R. Kulkarni, D. H. Schultz, R. D. Mill, R. H. Chen, L. I. Solomyak, and M. W. Cole, Cognitive task information is transferred between brain regions via resting-state network topology, Nat. Commun. 8(1), 1027 (2017)

    Article  ADS  Google Scholar 

  51. X. G. Wang, Synchronous patterns in complex networks, Sci. Sin. Phys. Mech. & Astron. 50, 010503 (2020)

    Article  Google Scholar 

  52. M. L. Kelly, R. A. Peters, R. K. Tisdale, and J. A. Lesku, Unihemispheric sleep in crocodilians? J. Exp. Biol. 218(20), 3175 (2015)

    Article  Google Scholar 

  53. N. C. Rattenborg, S. L. Lima, and C. J. Amlaner, Half-awake to the risk of predation, Nature 397(6718), 397 (1999)

    Article  ADS  Google Scholar 

  54. N. C. Rattenborg, C. J. Amlaner, and S. L. Lima, Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep, Neurosci. Biobehav. Rev. 24(8), 817 (2000)

    Article  Google Scholar 

  55. M. Tamaki, J. W. Bang, T. Watanabe, and Y. Sasaki, Night watch in one brain hemisphere during sleep associated with the first-night effect in humans, Curr. Biol. 26(9), 1190 (2016)

    Article  Google Scholar 

  56. D. M. Abrams and S. H. Strogatz, Chimera states for coupled oscillators, Phys. Rev. Lett. 93(17), 174102 (2004)

    Article  ADS  Google Scholar 

  57. M. J. Panaggio and D. M. Abrams, Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators, Nonlinearity 28(3), R67 (2015)

    Article  ADS  MATH  Google Scholar 

  58. S. Majhi, B. K. Bera, D. Ghosh, and M. Perc, Chimera states in neuronal networks: A review, Phys. Life Rev. 28, 100 (2019)

    Article  ADS  Google Scholar 

  59. Z. Wang and Z. Liu, Partial synchronization in complex networks: Chimera state, remote synchronization, and cluster synchronization, Acta Physica Sinica 69(8), 088902 (2020)

    Article  Google Scholar 

  60. Z. Wang and Z. Liu, A brief review of chimera state in empirical brain networks, Front. Physiol. 11, 724 (2020)

    Article  Google Scholar 

  61. R. Ma, J. Wang, and Z. Liu, Robust features of chimera states and the implementation of alternating chimera states, Europhys. Lett. 91(4), 40006 (2010)

    Article  ADS  Google Scholar 

  62. Y. Zhu, Z. Zheng, and J. Yang, Chimera states on complex networks, Phys. Rev. E 89(2), 022914 (2014)

    Article  ADS  Google Scholar 

  63. T. Chouzouris, I. Omelchenko, A. Zakharova, J. Hlinka, P. Jiruska, and E. Schöll, Chimera states in brain networks: Empirical neural vs. modular fractal connectivity, Chaos 28(4), 045112 (2018)

    Article  ADS  Google Scholar 

  64. R. G. Andrzejak, C. Rummel, F. Mormann, and K. Schindler, All together now: Analogies between chimera state collapses and epileptic seizures, Sci. Rep. 6(1), 23000 (2016)

    Article  ADS  Google Scholar 

  65. L. Kang, C. Tian, S. Huo, and Z. Liu, A two-layered brain network model and its chimera state, Sci. Rep. 9(1), 14389 (2019)

    Article  ADS  Google Scholar 

  66. S. Huo, C. Tian, M. Zheng, S. Guan, C. S. Zhou, and Z. Liu, Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure-dynamics relationship in human brain, Natl. Sci. Rev. 8(1), nwaa125 (2021)

    Article  Google Scholar 

  67. R. Vicente, L. L. Gollo, C. R. Mirasso, I. Fischer, and G. Pipa, Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays, Proc. Natl. Acad. Sci. USA 105(44), 17157 (2008)

    Article  ADS  Google Scholar 

  68. P. R. Roelfsema, A. K. Engel, P. Konig, and W. Singer, Visuomotor integration is associated with zero time lag synchronization among cortical areas, Nature 385(6612), 157 (1997)

    Article  ADS  Google Scholar 

  69. E. Rodriguez, N. George, J. P. Lachaux, J. Martinerie, B. Renault, and F. J. Varela, Perception’s shadow: Longdistance synchronization of human brain activity, Nature 397(6718), 430 (1999)

    Article  ADS  Google Scholar 

  70. V. Vuksanović and P. Hovel, Functional connectivity of distant cortical regions: Role of remote synchronization and symmetry in interactions, Neuroimage 97, 1 (2014)

    Article  Google Scholar 

  71. A. Bergner, M. Frasca, G. Sciuto, A. Buscarino, E. J. Ngamga, L. Fortuna, and J. Kurths, Remote synchronization in star networks, Phys. Rev. E 85(2), 026208 (2012)

    Article  ADS  Google Scholar 

  72. L. Kang, Z. Wang, S. Huo, C. Tian, and Z. Liu, Remote synchronization in human cerebral cortex network with identical oscillators, Nonlinear Dyn. 99(2), 1577 (2020)

    Article  Google Scholar 

  73. M. A. Kramer and S. S. Cash, Epilepsy as a disorder of cortical network organization, Neuroscientist 18(4), 360 (2012)

    Article  Google Scholar 

  74. M. Guye, J. Regis, M. Tamura, F. Wendling, A. Mc Gonigal, P. Chauvel, and F. Bartolomei, The role of corticothalamic coupling in human temporal lobe epilepsy, Brain 129(7), 1917 (2006)

    Article  Google Scholar 

  75. Z. Wang, C. Tian, M. Dhamala, and Z. Liu, A small change in neuronal network topology can induce explosive synchronization transition and activity propagation in the entire network, Sci. Rep. 7(1), 561 (2017)

    Article  ADS  Google Scholar 

  76. J. Gómez-Gardeñes, S. Gomez, A. Arenas, and Y. Moreno, Explosive synchronization transitions in scale-free networks, Phys. Rev. Lett. 106(12), 128701 (2011)

    Article  ADS  Google Scholar 

  77. I. Leyva, R. Sevilla-Escoboza, J. M. Buldú, I. Sendiña-Nadal, J. Gómez-Gardeñes, A. Arenas, Y. Moreno, S. Gómez, R. Jaimes-Reátegui, and S. Boccaletti, Explosive first-order transition to synchrony in networked chaotic oscillators, Phys. Rev. Lett. 108(16), 168702 (2012)

    Article  ADS  Google Scholar 

  78. P. Ji, T. K. D. M. Peron, P. J. Menck, F. A. Rodrigues, and J. Kurths, Cluster explosive synchronization in complex networks, Phys. Rev. Lett. 110(21), 218701 (2013)

    Article  ADS  Google Scholar 

  79. X. Zhang, X. Hu, J. Kurths, and Z. Liu, Explosive synchronization in a general complex network, Phys. Rev. E 88, 010802(R) (2013)

    Article  ADS  Google Scholar 

  80. Y. Zou, T. Pereira, M. Small, Z. Liu, and J. Kurths, Basin of attraction determines hysteresis in explosive synchronization, Phys. Rev. Lett. 112(11), 114102 (2014)

    Article  ADS  Google Scholar 

  81. X. Zhang, Y. Zou, S. Boccaletti, and Z. Liu, Explosive synchronization as a process of explosive percolation in dynamical phase space, Sci. Rep. 4(1), 5200 (2015)

    Article  Google Scholar 

  82. X. Zhang, S. Boccaletti, S. Guan, and Z. Liu, Explosive synchronization in adaptive and multilayer networks, Phys. Rev. Lett. 114(3), 038701 (2015)

    Article  ADS  Google Scholar 

  83. S. Boccaletti, J. A. Almendral, S. Guan, I. Leyva, Z. Liu, I. Sendiña-Nadal, Z. Wang, and Y. Zou, Explosive transitions in complex networks structure and dynamics: Percolation and synchronization, Phys. Rep. 660, 1 (2016)

    Article  ADS  MATH  Google Scholar 

  84. M. B. Kelz, Y. Sun, J. Chen, Q. Cheng Meng, J. T. Moore, S. C. Veasey, S. Dixon, M. Thornton, H. Funato, and M. Yanagisawa, An essential role for orexins in emergence from general anesthesia, Proc. Natl. Acad. Sci. USA 105(4), 1309 (2008)

    Article  ADS  Google Scholar 

  85. E. B. Friedman, Y. Sun, J. T. Moore, H. T. Hung, Q. C. Meng, P. Perera, W. J. Joiner, S. A. Thomas, R. G. Eckenhoff, A. Sehgal, and M. B. Kelz, A conserved behavioral state barrier impedes transitions between anesthetic-induced unconsciousness and wakefulness: Evidence for neural inertia, PLoS One 5(7), e11903 (2010)

    Article  ADS  Google Scholar 

  86. W. J. Joiner, E. B. Friedman, H. T. Hung, K. Koh, M. Sowcik, A. Sehgal, and M. B. Kelz, Genetic and anatomical basis of the barrier separatingwakefulness and anesthetic-induced unresponsiveness, PLoS Genet. 9(9), e1003605 (2013)

    Article  Google Scholar 

  87. M. Kim, G. A. Mashour, S. B. Moraes, G. Vanini, V. Tarnal, E. Janke, A. G. Hudetz, and U. Lee, Functional and topological conditions for explosive synchronization develop in human brain networks with the onset of anesthetic-induced unconsciousness, Front. Comput. Neurosci. 10, 1 (2016)

    Article  Google Scholar 

  88. A. C. Neubauer and A. Fink, Intelligence and neural efficiency, Neurosci. Biobehav. Rev. 33(7), 1004 (2009)

    Article  Google Scholar 

  89. E. Genç, C. Fraenz, C. Schlüter, P. Friedrich, R. Hossiep, M. C. Voelkle, J. M. Ling, O. Güntürkün, and R. E. Jung, Diffusion markers of dendritic density and arborization in gray matter predict differences in intelligence, Nat. Commun. 9(1), 1905 (2018)

    Article  ADS  Google Scholar 

  90. Y. Chen, S. Wang, C. C. Hilgetag, and C. Zhou, Trade-off between multiple constraints enables simultaneous formation of modules and hubs in neural systems, PLoS Comput. Biol. 9(3), e1002937 (2013)

    Article  ADS  Google Scholar 

  91. M. Kaiser and C. Hilgetag, Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems, PLoS Comput. Biol. 2(7), e95 (2006)

    Article  ADS  Google Scholar 

  92. J. Budd, K. Kovács, A. S. Ferecskó, P. Buzás, U. T. Eysel, and Z. F. Kisvárday, Neocortical axon arbors trade-off material and conduction delay conservation, PLoS Comput. Biol. 6(3), e1000711 (2010)

    Article  ADS  Google Scholar 

  93. S. Baron-Cohen, R. C. Knickmeyer, and M. K. Belmonte, Sex differences in the brain: Implications for explaining autism, Science 310(5749), 819 (2005)

    Article  ADS  Google Scholar 

  94. I. J. Deary, L. Penke, and W. Johnson, The neuroscience of human intelligence differences, Nat. Rev. Neurosci. 11(3), 201 (2010)

    Article  Google Scholar 

  95. L. Cao and Z. Liu, How IQ depends on the running mode of brain network? Chaos 30(7), 073111 (2020)

    Article  ADS  Google Scholar 

  96. J. Wang and Z. Liu, A chain model for signal detection and transmission, Europhys. Lett. 102(1), 10003 (2013)

    Article  ADS  Google Scholar 

  97. Z. Liu, Organization network enhanced detection and transmission of phase—locking, Europhys. Lett. 100(6), 60002 (2012)

    Article  ADS  Google Scholar 

  98. Q. Shen and Z. Liu, Remote firing propagation in the neural network of C. elegans, Phys. Rev. E 103(5), 052414 (2021)

    Article  ADS  Google Scholar 

  99. Z. Wang and Z. Liu, Effect of remote signal propagation in an empirical brain network, Chaos 31(6), 063126 (2021)

    Article  ADS  MATH  Google Scholar 

  100. I. Diez, A. Erramuzpe, I. Escudero, B. Mateos, A. Cabrera, D. Marinazzo, E. J. Sanz-Arigita, S. Stramaglia, and J. M. Cortes Diaz, Information flow between resting-state networks, Brain Connect. 5(9), 554 (2015)

    Article  Google Scholar 

  101. M. R. Brier, J. B. Thomas, A. Z. Snyder, T. L. Benzinger, D. Zhang, M. E. Raichle, D. M. Holtzman, J. C. Morris, and B. M. Ances, Loss of intranetwork and internetwork resting state functional connections with Alzheimer’s disease progression, J. Neurosci. 32(26), 8890 (2012)

    Article  Google Scholar 

  102. E. J. Sanz-Arigita, M. M. Schoonheim, J. S. Damoiseaux, S. A. R. B. Rombouts, E. Maris, F. Barkhof, P. Scheltens, and C. J. Stam, Loss of ‘small-world’ networks in Alzheimer’s disease: Graph analysis of fMRI resting-state functional connectivity, PLoS One 5(11), e13788 (2010)

    Article  ADS  Google Scholar 

  103. E. Başar, C. Basar-Eroglu, S. Karakas, and M. Schurmann, Gamma, alpha, delta, and theta oscillations govern cognitive processes, Int. J. Psychophysiol. 39(2–3), 241 (2001)

    Article  Google Scholar 

  104. E. Bullmore and O. Sporns, Complex brain networks: Graph theoretical analysis of structural and functional systems, Nat. Rev. Neurosci. 10(3), 186 (2009)

    Article  Google Scholar 

  105. R. Wang, P. Lin, M. Liu, Y. Wu, T. Zhou, and C. Zhou, Hierarchical connectome modes and critical state jointly maximize human brain functional diversity, Phys. Rev. Lett. 123(3), 038301 (2019)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 11835003, 82161148012, and 12175070, and the “Technology Innovation 2030-major Projects” on brain science and brain-like computing of the Ministry of Science & Tecknology of China (No. 2021ZD0202600).

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Wu, T., Zhang, X. & Liu, Z. Understanding the mechanisms of brain functions from the angle of synchronization and complex network. Front. Phys. 17, 31504 (2022). https://doi.org/10.1007/s11467-022-1161-6

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