Spectral properties of the temporal evolution of brain network structure.

The temporal evolution properties of the brain network are crucial for complex brain processes. In this paper, we investigate the differences in the dynamic brain network during resting and visual stimulation states in a task-positive subnetwork, task-negative subnetwork, and whole-brain network. The dynamic brain network is first constructed from human functional magnetic resonance imaging data based on the sliding window method, and then the eigenvalues corresponding to the network are calculated. We use eigenvalue analysis to analyze the global properties of eigenvalues and the random matrix theory (RMT) method to measure the local properties. For global properties, the shifting of the eigenvalue distribution and the decrease in the largest eigenvalue are linked to visual stimulation in all networks. For local properties, the short-range correlation in eigenvalues as measured by the nearest neighbor spacing distribution is not always sensitive to visual stimulation. However, the long-range correlation in eigenvalues as evaluated by spectral rigidity and number variance not only predicts the universal behavior of the dynamic brain network but also suggests non-consistent changes in different networks. These results demonstrate that the dynamic brain network is more random for the task-positive subnetwork and whole-brain network under visual stimulation but is more regular for the task-negative subnetwork. Our findings provide deeper insight into the importance of spectral properties in the functional brain network, especially the incomparable role of RMT in revealing the intrinsic properties of complex systems.

[1]  Sarika Jalan,et al.  Universality in complex networks: random matrix analysis. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  A. Edelman,et al.  Random matrix theory , 2005, Acta Numerica.

[3]  P. Sarnak,et al.  Number variance for arithmetic hyperbolic surfaces , 1994 .

[4]  Camellia Sarkar,et al.  Uncovering Randomness and Success in Society , 2014, PloS one.

[5]  Boris Podobnik,et al.  Systemic risk and spatiotemporal dynamics of the US housing market , 2013, Scientific Reports.

[6]  Scott T. Grafton,et al.  Dynamic reconfiguration of human brain networks during learning , 2010, Proceedings of the National Academy of Sciences.

[7]  Uzy Smilansky,et al.  Quantum Chaos on Graphs , 1997 .

[8]  Sarika Jalan,et al.  Randomness of random networks: A random matrix analysis , 2009 .

[9]  M. S. Santhanam,et al.  Statistics of atmospheric correlations. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  P. Seba,et al.  Random matrix analysis of human EEG data. , 2003, Physical review letters.

[11]  Peter J Hellyer,et al.  The Control of Global Brain Dynamics: Opposing Actions of Frontoparietal Control and Default Mode Networks on Attention , 2014, The Journal of Neuroscience.

[12]  R W Cox,et al.  AFNI: software for analysis and visualization of functional magnetic resonance neuroimages. , 1996, Computers and biomedical research, an international journal.

[13]  Sarika Jalan,et al.  Random matrix analysis of complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  D. Schacter,et al.  The Brain's Default Network , 2008, Annals of the New York Academy of Sciences.

[15]  V. Menon.  Large-scale brain networks and psychopathology: a unifying triple network model , 2011, Trends in Cognitive Sciences.

[16]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[17]  Feng Luo,et al.  Constructing gene co-expression networks and predicting functions of unknown genes by random matrix theory , 2007, BMC Bioinformatics.

[18]  Sarika Jalan,et al.  Random matrix analysis of network Laplacians , 2008 .

[19]  Hao He,et al.  Assessing dynamic brain graphs of time-varying connectivity in fMRI data: Application to healthy controls and patients with schizophrenia , 2015, NeuroImage.

[20]  U. Hasson,et al.  A Neuronal Basis for Task-Negative Responses in the Human Brain , 2010, Cerebral cortex.

[21]  M. Corbetta,et al.  Temporal dynamics of spontaneous MEG activity in brain networks , 2010, Proceedings of the National Academy of Sciences.

[22]  David A. Leopold,et al.  Dynamic functional connectivity: Promise, issues, and interpretations , 2013, NeuroImage.

[23]  D. L. Shepelyansky.  Quantum Diffusion Limitation at Excitation of Rydberg Atom in Variable Field , 1985 .

[24]  Eswar Damaraju,et al.  Tracking whole-brain connectivity dynamics in the resting state. , 2014, Cerebral cortex.

[25]  Danielle S Bassett,et al.  Dynamic network structure of interhemispheric coordination , 2012, Proceedings of the National Academy of Sciences.

[26]  SARIKA JALAN,et al.  Importance of randomness in biological networks: A random matrix analysis , 2015 .

[27]  Robert Leech,et al.  Dynamic Network Mechanisms of Relational Integration , 2015, The Journal of Neuroscience.

[28]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[29]  Maurizio Corbetta,et al.  The human brain is intrinsically organized into dynamic, anticorrelated functional networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Stephen P. Ficklin,et al.  Massive-Scale Gene Co-Expression Network Construction and Robustness Testing Using Random Matrix Theory , 2013, PloS one.

[31]  M. Corbetta,et al.  Individual variability in functional connectivity predicts performance of a perceptual task , 2012, Proceedings of the National Academy of Sciences.

[32]  H. Eugene Stanley,et al.  Identifying States of a Financial Market , 2012, Scientific Reports.

[33]  A. Soshnikov,et al.  Random matrices and quantum chaos , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[34]  S. Bressler,et al.  Large-scale brain networks in cognition: emerging methods and principles , 2010, Trends in Cognitive Sciences.

[35]  V. Plerou,et al.  Random matrix approach to cross correlations in financial data. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  M. Greicius,et al.  Decoding subject-driven cognitive states with whole-brain connectivity patterns. , 2012, Cerebral cortex.

[37]  Ying-Cheng Lai,et al.  A phase-synchronization and random-matrix based approach to multichannel time-series analysis with application to epilepsy. , 2011, Chaos.

[38]  Sepideh Sadaghiani,et al.  Ongoing dynamics in large-scale functional connectivity predict perception , 2015, Proceedings of the National Academy of Sciences.

[39]  M. Sigman,et al.  Signature of consciousness in the dynamics of resting-state brain activity , 2015, Proceedings of the National Academy of Sciences.

[40]  U. Stephani,et al.  Detection and characterization of changes of the correlation structure in multivariate time series. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  V. Menon,et al.  Saliency, switching, attention and control: a network model of insula function , 2010, Brain Structure and Function.

[42]  Emery N. Brown,et al.  Tracking brain states under general anesthesia by using global coherence analysis , 2011, Proceedings of the National Academy of Sciences.

[43]  Viviana Betti,et al.  Dynamic reorganization of human resting-state networks during visuospatial attention , 2015, Proceedings of the National Academy of Sciences.

[44]  Peter J Hellyer,et al.  Cognitive Flexibility through Metastable Neural Dynamics Is Disrupted by Damage to the Structural Connectome , 2015, The Journal of Neuroscience.