The Temporal Structures and Functional Significance of Scale-free Brain Activity
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Scale-free dynamics, with a power spectrum following P proportional to f(-beta), are an intrinsic feature of many complex processes in nature. In neural systems, scale-free activity is often neglected in electrophysiological research. Here, we investigate scale-free dynamics in human brain and show that it contains extensive nested frequencies, with the phase of lower frequencies modulating the amplitude of higher frequencies in an upward progression across the frequency spectrum. The functional significance of scale-free brain activity is indicated by task performance modulation and regional variation, with beta being larger in default network and visual cortex and smaller in hippocampus and cerebellum. The precise patterns of nested frequencies in the brain differ from other scale-free dynamics in nature, such as earth seismic waves and stock market fluctuations, suggesting system-specific generative mechanisms. Our findings reveal robust temporal structures and behavioral significance of scale-free brain activity and should motivate future study on its physiological mechanisms and cognitive implications.
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Several lines of evidence point to fractal-like (1/f) self-similarity over different spatio-temporal scales in brain dynamics and structure.
“Several lines of evidence point to fractal-like (1/f) self-similarity over different spatio-temporal scales in brain dynamics and structure [76,77].”
From Consciousness in the universe (2014) · cites this paper as [76]
There is evidence for scale-invariance in neurophysiological processes.
“there does appear to be evidence for some kind of scale-invariance in neurophysiological processes (Section 3.2 [76,77]).”
From Consciousness in the universe (2014) · cites this paper as [76]
EEG and its underlying neural activity almost never consist of a single-frequency rhythm; they include a mixture of rhythms and an arrhythmic component with a 1/f power-law distribution over a broad band.
“This is because EEG, or its underlying neural activity, nearly never manifests itself as a single-frequency rhythm; instead, it always contains a mixture of rhythms, and an arrhythmic component that follows a power-law (1/f) distribution across a broadband (168).”
From Electrophysiological source imaging: A noninvasive window to brain dynamics (2018) · cites this paper as [168]
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Cites
Complex brain networks: graph theoretical analysis of structural and functional systems
Bullmore, E., & Sporns, O. (2009) · Nature Reviews Neuroscience · doi:10.1038/nrn2575 · Cited by 11,820 · see citing works
Fractional Brownian Motions, Fractional Noises and Applications
Mandelbrot, B. B., & Ness, J. W. V. (1968) · SIAM Review · doi:10.1137/1010093 · Cited by 7,815 · see citing works
Self-organized criticality: An explanation of the 1/ f noise
Bak, P., Tang, C., & Wiesenfeld, K. A. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.381 · Cited by 7,644 · see citing works
Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging
Fox, M. D., & Raichle, M. E. (2007) · Nature Reviews Neuroscience · doi:10.1038/nrn2201 · Cited by 6,700 · see citing works
Self-citationBuzsáki, G. (2006) · doi:10.1093/acprof:oso/9780195301069.001.0001 · Cited by 4,873 · see citing works
Über das Elektrenkephalogramm des Menschen
Berger, H. (1929) · European Archives of Psychiatry and Clinical Neuroscience · doi:10.1007/bf01797193 · Cited by 4,266 · see citing works
Faisal, A. A., Selen, L. P. J., & Wolpert, D. M. (2008) · Nature Reviews Neuroscience · doi:10.1038/nrn2258 · Cited by 2,883 · see citing works
Bak, P. (1996) · Springer eBooks · doi:10.1007/978-1-4757-5426-1 · Cited by 2,826 · see citing works
High Gamma Power Is Phase-Locked to Theta Oscillations in Human Neocortex
Canolty, R. T., Edwards, E., Dalal, S. S., Soltani, M., Nagarajan, S. S., Kirsch, H. E., Berger, M. S., Barbaro, N. M., & Knight, R. T. (2006) · Science · doi:10.1126/science.1128115 · Cited by 2,650 · see citing works
Driving fast-spiking cells induces gamma rhythm and controls sensory responses
Cardin, J. A., Carlén, M., Meletis, K., Knoblich, U., Zhang, F., Deisseroth, K., Tsai, L.-H., & Moore, C. I. (2009) · Nature · doi:10.1038/nature08002 · Cited by 2,603 · see citing works
WALTER, W. G., COOPER, R., ALDRIDGE, V. J., McCALLUM, W. C., & WINTER, A. L. (1964) · Nature · doi:10.1038/203380a0 · Cited by 2,446 · see citing works
Scale-Free Networks: A Decade and Beyond
Barabási, A.-Ĺ. (2009) · Science · doi:10.1126/science.1173299 · Cited by 2,089 · see citing works
Kornhuber, H. H., & Deecke, L. (1965) · Pflügers Archiv - European Journal of Physiology · doi:10.1007/bf00412364 · Cited by 1,902 · see citing works
Entrainment of Neuronal Oscillations as a Mechanism of Attentional Selection
Lakatos, P., Karmos, G., Mehta, A. D., Ulbert, I., & Schroeder, C. E. (2008) · Science · doi:10.1126/science.1154735 · Cited by 1,719 · see citing works
Low-frequency neuronal oscillations as instruments of sensory selection
Schroeder, C. E., & Lakatos, P. (2009) · Trends in Neurosciences · doi:10.1016/j.tins.2008.09.012 · Cited by 1,528 · see citing works
Gamma (40-100 Hz) oscillation in the hippocampus of the behaving rat
Bragin, A., Jando, G., Nadasdy, Z., Hetke, J., Wise, K., & Buzsaki, G. (1995) · The Journal of Neuroscience · doi:10.1523/jneurosci.15-01-00047.1995 · Cited by 1,527 · see citing works
Long memory relationships and the aggregation of dynamic models
Granger, C. W. J. (1980) · Journal of Econometrics · doi:10.1016/0304-4076(80)90092-5 · Cited by 1,488 · see citing works
Scale-Free Brain Functional Networks
Eguı́luz, V. M., Chialvo, D. R., Cecchi, G., Baliki, M. N., & Apkarian, A. V. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.018102 · Cited by 1,464 · see citing works
1 f noise and other slow, nonexponential kinetics in condensed matter
Weissman, M. B. (1988) · Reviews of Modern Physics · doi:10.1103/revmodphys.60.537 · Cited by 1,370 · see citing works
Lakatos, P., Shah, A. S., Knuth, K. H., Ulbert, I., Karmos, G., & Schroeder, C. E. (2005) · Journal of Neurophysiology · doi:10.1152/jn.00263.2005 · Cited by 1,241 · see citing works
Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., & Ilmoniemi, R. J. (2001) · The Journal of Neuroscience · doi:10.1523/jneurosci.21-04-01370.2001 · Cited by 1,149 · see citing works
Slow potentials of the cerebral cortex and behavior.
Birbaumer, N., Elbert, T. R., Canavan, A. G. M., & Rockstroh, B. S. (1990) · Physiological Reviews · doi:10.1152/physrev.1990.70.1.1 · Cited by 1,099 · see citing works
Analysis of Dynamic Brain Imaging Data
Mitra, P. P., & Pesaran, B. (1999) · Biophysical Journal · doi:10.1016/s0006-3495(99)77236-x · Cited by 1,044 · see citing works
Cross-frequency coupling between neuronal oscillations
Jensen, O., & Colgin, L. L. (2007) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2007.05.003 · Cited by 991 · see citing works
Manning, J. R., Jacobs, J., Fried, I., & Kahana, M. J. (2009) · The Journal of Neuroscience · doi:10.1523/jneurosci.2041-09.2009 · Cited by 973 · see citing works
The neural basis of the blood–oxygen–level–dependent functional magnetic resonance imaging signal
Logothetis, N. K. (2002) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2002.1114 · Cited by 952 · see citing works
Analysis of Dynamic Brain Imaging Data
Mitra, P. P., & Pesaran, B. (1998) · Cold Spring Harbor Laboratory Institutional Repository (Cold Spring Harbor Laboratory) · Cited by 898 · see citing works
Tort, A. B. L., Kramer, M., Thorn, C. A., Gibson, D. J., Kubota, Y., Graybiel, A. M., & Kopell, N. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0810524105 · Cited by 842 · see citing works
Transient induced gamma-band response in EEG as a manifestation of miniature saccades
Yuval-Greenberg, S., Tomer, O., Keren, A. S., Nelken, I., & Deouell, L. Y. (2008) · Neuron · doi:10.1016/j.neuron.2008.03.027 · Cited by 776 · see citing works
Intrinsic Fluctuations within Cortical Systems Account for Intertrial Variability in Human Behavior
Fox, M., Snyder, A. Z., Vincent, J. L., & Raichle, M. E. (2007) · Neuron · doi:10.1016/j.neuron.2007.08.023 · Cited by 753 · see citing works
Self-citationPower-Law Scaling in the Brain Surface Electric Potential
Miller, K. J., Sorensen, L. B., Ojemann, J. G., & den Nijs, M. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000609 · Cited by 742 · see citing works
Cortical firing and sleep homeostasis
Vyazovskiy, V. V., Olcese, U., Lazimy, Y. M., Faraguna, U., Esser, S. K., Williams, J. C., Cirelli, C., & Tononi, G. (2009) · Neuron · doi:10.1016/j.neuron.2009.08.024 · Cited by 740 · see citing works
van den Heuvel, M. P., Stam, C. J., Boersma, M., & Pol, H. E. H. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.08.010 · Cited by 720 · see citing works
Empirical Analyses of BOLD fMRI Statistics
Zarahn, E., Aguirre, G. K., & D’Esposito, M. (1997) · NeuroImage · doi:10.1006/nimg.1997.0263 · Cited by 695 · see citing works
Very Slow Activity Fluctuations in Monkey Visual Cortex: Implications for Functional Brain Imaging
Leopold, D. A. (2003) · Cerebral Cortex · doi:10.1093/cercor/13.4.422 · Cited by 675 · see citing works
Interaction of sensory responses with spontaneous depolarization in layer 2/3 barrel cortex
Petersen, C. C. H., Hahn, T. T. G., Mehta, M. R., Grinvald, A., & Sakmann, B. J. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2235811100 · Cited by 673 · see citing works
Electrophysiological correlates of the brain's intrinsic large-scale functional architecture
He, B. J., Snyder, A. Z., Zempel, J. M., Smyth, M. D., & Raichle, M. E. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0807010105 · Cited by 670 · see citing works
Self-citation‘1/fnoise’ in music and speech
Voss, R. F., & Clarke, J. H. (1975) · Nature · doi:10.1038/258317a0 · Cited by 622 · see citing works
Spontaneous cortical activity in awake monkeys composed of neuronal avalanches
Petermann, T., Thiagarajan, T. C., Lebedev, M., Nicolelis, M. A. L., Chialvo, D. R., & Plenz, D. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0904089106 · Cited by 572 · see citing works
Dynamical synapses causing self-organized criticality in neural networks
Levina, A., Herrmann, J. M., & Geisel, T. (2007) · Nature Physics · doi:10.1038/nphys758 · Cited by 570 · see citing works
Episodic multiregional cortical coherence at multiple frequencies during visual task performance
Bressler, S. L., Coppola, R., & Nakamura, R. (1993) · Nature · doi:10.1038/366153a0 · Cited by 533 · see citing works
Sensory neural codes using multiplexed temporal scales
Panzeri, S., Brunel, N., Logothetis, N. K., & Kayser, C. (2010) · Trends in Neurosciences · doi:10.1016/j.tins.2009.12.001 · Cited by 520 · see citing works
Vanhatalo, S., Palva, J. M., Holmes, M., Miller, J. W., Voipio, J., & Kaila, K. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0305375101 · Cited by 517 · see citing works
Cognitive emissions of 1/f noise.
Gilden, D. L. (2001) · Psychological Review · doi:10.1037/0033-295x.108.1.33 · Cited by 516 · see citing works
Monto, S., Palva, S., Voipio, J., & Palva, J. M. (2008) · The Journal of Neuroscience · doi:10.1523/jneurosci.1910-08.2008 · Cited by 453 · see citing works
In Vivo Measurement of Cortical Impedance Spectrum in Monkeys: Implications for Signal Propagation
Logothetis, N. K., Kayser, C., & Oeltermann, A. (2007) · Neuron · doi:10.1016/j.neuron.2007.07.027 · Cited by 447 · see citing works
LFP Power Spectra in V1 Cortex: The Graded Effect of Stimulus Contrast
Henrie, J. A., & Shapley, R. M. (2005) · Journal of Neurophysiology · doi:10.1152/jn.00919.2004 · Cited by 425 · see citing works
Belitski, A., Gretton, A., Magri, C., Murayama, Y., Montemurro, M. A., Logothetis, N. K., & Panzeri, S. (2008) · Journal of Neuroscience · doi:10.1523/jneurosci.0009-08.2008 · Cited by 420 · see citing works
The Human K-Complex Represents an Isolated Cortical Down-State
Cash, S. S., Halgren, E., Dehghani, N., Rossetti, A. O., Thesen, T., Wang, C., Devinsky, O., Kuzniecky, R., Doyle, W., Madsen, J. R., et al. (2009) · Science · doi:10.1126/science.1169626 · Cited by 394 · see citing works
Phase-of-Firing Coding of Natural Visual Stimuli in Primary Visual Cortex
Montemurro, M. A., Rasch, M. J., Murayama, Y., Logothetis, N. K., & Panzeri, S. (2008) · Current Biology · doi:10.1016/j.cub.2008.02.023 · Cited by 389 · see citing works
Brain activity relating to the contingent negative variation: An fMRI investigation
Nagai, Y., Critchley, H. D., Featherstone, E., Fenwick, P. B. C., Trimble, M. R., & Dolan, R. J. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2003.10.036 · Cited by 377 · see citing works
The organizing principles of neuronal avalanches: cell assemblies in the cortex?
Plenz, D., & Thiagarajan, T. C. (2007) · Trends in Neurosciences · doi:10.1016/j.tins.2007.01.005 · Cited by 373 · see citing works
Long Memory Relationships and the Aggregation of Dynamic Models
Granger, C. W. J. (2008) · Cambridge University Press eBooks · doi:10.1017/ccol052179207x.019 · Cited by 360 · see citing works
Coarse-graining spectral analysis: new method for studying heart rate variability
Yamamoto, Y., & Hughson, R. L. (1991) · Journal of Applied Physiology · doi:10.1152/jappl.1991.71.3.1143 · Cited by 357 · see citing works
Miller, K. J., Zanos, S. P., Fetz, E. E., den Nijs, M., & Ojemann, J. G. (2009) · Journal of Neuroscience · doi:10.1523/jneurosci.5506-08.2009 · Cited by 350 · see citing works
Mandelbrot, B. B. (1999) · Springer eBooks · doi:10.1007/978-1-4612-2150-0 · Cited by 329 · see citing works
The fMRI signal, slow cortical potential and consciousness
He, B. J., & Raichle, M. E. (2009) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2009.04.004 · Cited by 324 · see citing works
Self-citationScale invariance in biology: coincidence or footprint of a universal mechanism?
Gisiger, T. (2001) · Biological reviews/Biological reviews of the Cambridge Philosophical Society · doi:10.1017/s1464793101005607 · Cited by 322 · see citing works
Estimation and interpretation of 1/fα noise in human cognition
Wagenmakers, E., Farrell, S., & Ratcliff, R. (2004) · Psychonomic Bulletin & Review · doi:10.3758/bf03196615 · Cited by 305 · see citing works
Maÿe, A., Hsieh, C., Sugihara, G., & Brembs, B. (2007) · PLoS ONE · doi:10.1371/journal.pone.0000443 · Cited by 275 · see citing works
Reliability, synchrony and noise
Ermentrout, G. B., Galán, R. F., & Urban, N. N. (2008) · Trends in Neurosciences · doi:10.1016/j.tins.2008.06.002 · Cited by 266 · see citing works
Self-Organized Criticality Model for Brain Plasticity
de Arcangelis, L., Perrone‐Capano, C., & Herrmann, H. J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.028107 · Cited by 252 · see citing works
Scale‐free dynamics of global functional connectivity in the human brain
Stam, C. J., & de Bruin, E. A. (2004) · Human Brain Mapping · doi:10.1002/hbm.20016 · Cited by 242 · see citing works
Ward, L. M. (2001) · The MIT Press eBooks · doi:10.7551/mitpress/2525.001.0001 · Cited by 231 · see citing works
Beyond Poisson: Increased Spike-Time Regularity across Primate Parietal Cortex
Maimon, G., & Assad, J. A. (2009) · Neuron · doi:10.1016/j.neuron.2009.03.021 · Cited by 228 · see citing works
Simulated power spectral density (PSD) of background electrocorticogram (ECoG)
Freeman, W. J., & Zhai, J. (2008) · Cognitive Neurodynamics · doi:10.1007/s11571-008-9064-y · Cited by 221 · see citing works
FRANK, S. A. (2009) · Journal of Evolutionary Biology · doi:10.1111/j.1420-9101.2009.01775.x · Cited by 220 · see citing works
Histonomy of the Cerebral Cortex.
von Bonin, G. (1960) · Archives of Neurology · doi:10.1001/archneur.1960.00450040126026 · Cited by 200 · see citing works
Sharp edge artifacts and spurious coupling in EEG frequency comodulation measures
Kramer, M. A., Tort, A. B. L., & Kopell, N. J. (2008) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2008.01.020 · Cited by 195 · see citing works
Histonomy of the Cerebral Cortex
(1961) · The Medical Journal of Australia · doi:10.5694/j.1326-5377.1961.tb69199.x · Cited by 188 · see citing works
Computation and the single neuron
Christof Koch, A. (1997) · Nature · doi:10.1038/385207a0 · Cited by 188 · see citing works
Temporal fluctuations in coherence of brain waves.
Bullock, T. H., McClune, M. C., Achimowicz, J. Z., Iragui‐Madoz, V., Duckrow, R. B., & Spencer, S. S. (1995) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.92.25.11568 · Cited by 163 · see citing works
Neuronal Shot Noise and Brownian 1/f2 Behavior in the Local Field Potential
Milstein, J. N., Mormann, F., Fried, I., & Christof Koch, A. (2009) · PLoS ONE · doi:10.1371/journal.pone.0004338 · Cited by 156 · see citing works
On oscillating neuronal responses in the visual cortex of the monkey
Young, M., Tanaka, K., & Yamane, S. (1992) · Journal of Neurophysiology · doi:10.1152/jn.1992.67.6.1464 · Cited by 155 · see citing works
High-frequency broadband modulation of electroencephalographic spectra
Onton, J. (2009) · Frontiers in Human Neuroscience · doi:10.3389/neuro.09.061.2009 · Cited by 155 · see citing works
Siegel, M., & Peter König, B. (2003) · Journal of Neuroscience · doi:10.1523/jneurosci.23-10-04251.2003 · Cited by 150 · see citing works
Stewart, C. V., & Plenz, D. (2006) · Journal of Neuroscience · doi:10.1523/jneurosci.0723-06.2006 · Cited by 145 · see citing works
Eckhorn, R. (1994) · Progress in brain research · doi:10.1016/s0079-6123(08)60556-7 · Cited by 134 · see citing works
Quantal Neurotransmitter Secretion Rate Exhibits Fractal Behavior
Lowen, S. B., Cash, S. S., Poo, M., & Teich, M. C. (1997) · Journal of Neuroscience · doi:10.1523/jneurosci.17-15-05666.1997 · Cited by 131 · see citing works
Extracting fractal components from time series
Yamamoto, Y., & Hughson, R. L. (1993) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(93)90083-d · Cited by 127 · see citing works
The Processing of Temporal Intervals Reflected by CNV‐Like Brain Potentials
Elbert, T. R., Ulrich, R., Rockstroh, B. S., & Lutzenberger, W. (1991) · Psychophysiology · doi:10.1111/j.1469-8986.1991.tb01009.x · Cited by 121 · see citing works
Ward, L. M., & Greenwood, P. E. (2007) · Scholarpedia · doi:10.4249/scholarpedia.1537 · Cited by 120 · see citing works
Power spectra and distribution of contrasts of natural images from different habitats
Balboa, R. M., & Grzywacz, N. M. (2003) · Vision Research · doi:10.1016/s0042-6989(03)00471-1 · Cited by 104 · see citing works
Self-organized criticality and scale-free properties in emergent functional neural networks
Shin, C.-W., & Kim, S. (2006) · Physical Review E · doi:10.1103/physreve.74.045101 · Cited by 102 · see citing works
(Micro)Saccades, corollary activity and cortical oscillations
Melloni, L., Schwiedrzik, C. M., Rodríguez, E., & Singer, W. (2009) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2009.03.007 · Cited by 101 · see citing works
On the relationship between slow cortical potentials and BOLD signal changes in humans
Khader, P., Schicke, T., Röder, B., & Rösler, F. (2008) · International Journal of Psychophysiology · doi:10.1016/j.ijpsycho.2007.05.018 · Cited by 99 · see citing works
Comparison of ongoing compound field potentials in the brains of invertebrates and vertebrates
Bullock, T. H., & Başar, E. (1988) · Brain Research Reviews · doi:10.1016/0165-0173(88)90005-7 · Cited by 98 · see citing works
Scale-invariance as a unifying psychological principle
Nick Chater, A., & Brown, G. D. A. (1999) · Cognition · doi:10.1016/s0010-0277(98)00066-3 · Cited by 90 · see citing works
Are the electroencephalograms mainly rhythmic? Assessment of periodicity in wide-band time series
Bullock, T. H., McClune, M. C., & Enright, J. T. (2003) · Neuroscience · doi:10.1016/s0306-4522(03)00208-2 · Cited by 89 · see citing works
Self-similarity of the "1/f noise" called music.
Hsü, K. J., & Hsü, A. (1991) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.88.8.3507 · Cited by 80 · see citing works
Universal 1/f Noise from Dissipative Self-Organized Criticality Models
Rios, P. D. L., & Zhang, Y. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.472 · Cited by 78 · see citing works
Scale invariance in the retrieval of retrospective and prospective memories
Maylor, E. A., Nick Chater, A., & Brown, G. D. A. (2001) · Psychonomic Bulletin & Review · doi:10.3758/bf03196153 · Cited by 72 · see citing works
Nonperiodic Synchronization in Heterogeneous Networks of Spiking Neurons
Thivierge, J., & Cisek, P. (2008) · Journal of Neuroscience · doi:10.1523/jneurosci.0870-08.2008 · Cited by 65 · see citing works
Buiatti, M., Papo, D., Baudonnière, P.-M., & van Vreeswijk, C. (2007) · Neuroscience · doi:10.1016/j.neuroscience.2007.02.048 · Cited by 53 · see citing works
Scale-free neocortical dynamics
Freeman, W. (2007) · Scholarpedia · doi:10.4249/scholarpedia.1357 · Cited by 53 · see citing works
Self-organized criticality in a simple model of neurons based on small-world networks
Lin, M., & Chen, T. (2005) · Physical Review E · doi:10.1103/physreve.71.016133 · Cited by 49 · see citing works
Power-law for axon diameters at branch point
Chklovskii, D. B., & Stepanyants, A. (2003) · BMC Neuroscience · doi:10.1186/1471-2202-4-18 · Cited by 38 · see citing works
An interpretation of 1/f fluctuations in neuronal spike trains during dream sleep
Grüneis, F., Nakao, M., Yamamoto, M., et al. (1989) · Biological Cybernetics · doi:10.1007/bf00207284 · Cited by 34 · see citing works
Constructing 1∕ωα noise from reversible Markov chains
Erland, S., & Greenwood, P. E. (2007) · Physical Review E · doi:10.1103/physreve.76.031114 · Cited by 31 · see citing works
Econophysics: Still Controversial After All These Years
Cho, A. (2009) · Science · doi:10.1126/science.325_408 · Cited by 11 · see citing works
Takahashi, K., Koyama, Y., Kayama, Y., Nakamura, K., & Yamamoto, M. (2003) · Neuroscience Research · doi:10.1016/j.neures.2003.10.015 · Cited by 4 · see citing works
Fluctuations observed in biological time series signals and their functional significance.
Yamamoto, M. P. (1991) · PubMed · Cited by 4 · see citing works
Liddle (2001) · doi:10.1002/1097-0193(200102)12:2
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Research works printed but not linked: 1
- Kornhuber HH Deecke L 1965 Changes in the Brain Potential in Voluntary Movements and Passive Movements in Man: Readiness Potential and Reafferent Potentials Pflugers Arch Gesamte Physiol Menschen Tiere 284 1 17 14341490
Cited by
Sorted by citations
Different Origins of Gamma Rhythm and High-Gamma Activity in Macaque Visual Cortex
Ray, S., & Maunsell, J. H. R. (2011) · PLoS Biology · doi:10.1371/journal.pbio.1000610 · Cited by 1,012 · see citing works
Hameroff, S., & Penrose, R. (2014) · Physics of Life Reviews · doi:10.1016/j.plrev.2013.08.002 · Cited by 983 · see citing works
“Neurons have a rich and uniquely organized cytoskeleton, the major components being microtubules, well-positioned and uniquely arrayed (e.g. in dendrites and soma) to mediate consciousness and regulate firing.”
BackgroundVoytek, B., & Knight, R. T. (2015) · Biological Psychiatry · doi:10.1016/j.biopsych.2015.04.016 · Cited by 556 · see citing works
Slow cortical dynamics and the accumulation of information over long timescales
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. (2012) · Neuron · doi:10.1016/j.neuron.2012.08.011 · Cited by 532 · see citing works
Understanding complexity in the human brain
Bassett, D. S., & Gazzaniga, M. S. (2011) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2011.03.006 · Cited by 572 · see citing works
On the stability of BOLD fMRI correlations
Laumann, T. O., Snyder, A. Z., Mitra, A., Gordon, E. M., Gratton, C., Adeyemo, B., Gilmore, A. W., Nelson, S. M., Berg, J. J., Greene, D. J., et al. (2016) · Cerebral Cortex · doi:10.1093/cercor/bhw265 · Cited by 516 · see citing works
Self-citationSeparating Fractal and Oscillatory Components in the Power Spectrum of Neurophysiological Signal
Wen, H., & Liu, Z. (2016) · Brain Topography · doi:10.1007/s10548-015-0448-0 · Cited by 419 · see citing works
Intrinsic Coupling Modes: Multiscale Interactions in Ongoing Brain Activity
Engel, A. K., Gerloff, C., Hilgetag, C. C., & Nolte, G. (2013) · Neuron · doi:10.1016/j.neuron.2013.09.038 · Cited by 471 · see citing works
Electrophysiological source imaging: A noninvasive window to brain dynamics
He, B., Sohrabpour, A., Brown, E., & Liu, Z. (2018) · Annual Review of Biomedical Engineering · doi:10.1146/annurev-bioeng-062117-120853 · Cited by 297 · see citing works
Self-citationBarttfeld, P., Wicker, B., Cukier, S., Navarta, S., Lew, S., & Sigman, M. (2011) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2010.11.024 · Cited by 311 · see citing works
Spontaneous and Task-Evoked Brain Activity Negatively Interact
He, B. J. (2013) · The Journal of Neuroscience · doi:10.1523/jneurosci.2922-12.2013 · Cited by 272 · see citing works
Self-citationThe development of theta and alpha neural oscillations from ages 3 to 24 years
Cellier, D., Riddle, J., Petersen, I., & Hwang, K. (2021) · Developmental Cognitive Neuroscience · doi:10.1016/j.dcn.2021.100969 · Cited by 223 · see citing works
Gotts, S. J., Chow, C. C., & Martin, A. (2012) · Cognitive Neuroscience · doi:10.1080/17588928.2012.670617 · Cited by 213 · see citing works
Eroding the Boundaries of Cognition: Implications of Embodiment<sup>1</sup>
Anderson, M. L., Richardson, M. J., & Chemero, A. (2012) · Topics in Cognitive Science · doi:10.1111/j.1756-8765.2012.01211.x · Cited by 200 · see citing works
Electrophysiological correlates of the BOLD signal for EEG-informed fMRI
Murta, T., Leite, M., Carmichael, D. W., Figueiredo, P., & Lemieux, L. (2015) · Human Brain Mapping · doi:10.1002/hbm.22623 · Cited by 165 · see citing works
A place for time: The spatiotemporal structure of neural dynamics during natural audition
Stephens, G. J., Honey, C. J., & Hasson, U. (2013) · Journal of Neurophysiology · doi:10.1152/jn.00268.2013 · Cited by 141 · see citing works
Palva, J. M., & Palva, S. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2012.02.060 · Cited by 163 · see citing works
Cytoskeletal signaling: is memory encoded in microtubule lattices by CaMKII phosphorylation?
Craddock, T. J. A., Tuszynski, J. A., & Hameroff, S. (2012) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002421 · Cited by 160 · see citing works
Ongoing physiological processes in the cerebral cortex
Leopold, D. A., & Maier, A. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2011.10.059 · Cited by 127 · see citing works
The Neural Correlates of Consciousness and Attention: Two Sister Processes of the Brain
Nani, A., Manuello, J., Mancuso, L., Liloia, D., Costa, T., & Cauda, F. (2019) · Frontiers in Neuroscience · doi:10.3389/fnins.2019.01169 · Cited by 119 · see citing works
Broadband Electrophysiological Dynamics Contribute to Global Resting-State fMRI Signal
Wen, H., & Liu, Z. (2016) · The Journal of Neuroscience · doi:10.1523/jneurosci.0187-16.2016 · Cited by 100 · see citing works
Veerakumar, A., Tiruvadi, V., Howell, B., Waters, A. C., Crowell, A. L., Voytek, B., Riva-Posse, P., Denison, L., Rajendra, J. K., Edwards, J. A., et al. (2019) · Journal of Neurophysiology · doi:10.1152/jn.00875.2018 · Cited by 89 · see citing works
How quantum brain biology can rescue conscious free will
Hameroff, S. (2012) · Frontiers in Integrative Neuroscience · doi:10.3389/fnint.2012.00093 · Cited by 95 · see citing works
The self and its prolonged intrinsic neural timescale in schizophrenia
Northoff, G., Sandsten, K. E., Nordgaard, J., Kjaer, T. W., & Parnas, J. (2021) · Schizophrenia Bulletin · doi:10.1093/schbul/sbaa083 · Cited by 91 · see citing works
The Fine-Scale Functional Correlation of Striate Cortex in Sighted and Blind People
Butt, O. H., Benson, N. C., Datta, R., & Aguirre, G. K. (2013) · The Journal of Neuroscience · doi:10.1523/jneurosci.0363-13.2013 · Cited by 84 · see citing works
Enhanced functional connectivity properties of human brains during in-situ nature experience
Chen, Z., He, Y., & Yu, Y. (2016) · PeerJ · doi:10.7717/peerj.2210 · Cited by 74 · see citing works
Critical branching neural networks.
Kello, C. T. (2013) · Psychological Review · doi:10.1037/a0030970 · Cited by 63 · see citing works
Palva, J. M., & Palva, S. (2011) · Progress in Brain Research · doi:10.1016/b978-0-444-53839-0.00022-3 · Cited by 63 · see citing works
Kraus, C., Ganger, S., Losak, J., Hahn, A., Savli, M., Kranz, G. S., Baldinger, P., Windischberger, C., Kasper, S., & Lanzenberger, R. (2014) · NeuroImage · doi:10.1016/j.neuroimage.2013.08.036 · Cited by 54 · see citing works
Wiese, W., & Friston, K. J. (2021) · Philosophy and the Mind Sciences · doi:10.33735/phimisci.2021.81 · Cited by 27 · see citing works
A measure centrality index for systematic empirical comparison of consciousness theories
Chis-Ciure, R., Melloni, L., & Northoff, G. (2024) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2024.105670 · Cited by 22 · see citing works
The myth of the Bayesian brain
Mangalam, M. (2025) · European Journal of Applied Physiology · doi:10.1007/s00421-025-05855-6 · Cited by 14 · see citing works
“Scale-free dynamics: The power spectra of neural signals typically follow a power-law form ( 1 ∕ f 𝛽 ), indicating temporal correlations that persist across multiple time-scales (He et al. 2010; Miller et al. 2009; Linkenkaer-Hansen et al. 2001; Touboul and Destexhe 2010).”
- Authors
- He, B. J., Zempel, J. M., Snyder, A. Z., & Raichle, M. E.
- Affiliations
- Washington University in St. Louis (US)
- Corresponding author
- He, Biyu J.
- Venue
- Neuron
- Publisher
- Elsevier BV
- Published
- 2010-05
- Volume
- 66
- Issue
- 3
- Pages
- 353-369
- ISSN
- 0896-6273 (ISSN-L)
- PMC
- PMC2878725
- OpenAlex
- W2148791497
- Cited by
- 990
- References
- 103
- Citations by year
- 2026: 55 · 2025: 74 · 2024: 100 · 2023: 66 · 2022: 100 · 2021: 70 · 2020: 66 · 2019: 51 · 2018: 63 · 2017: 53 · 2016: 57 · 2015: 52 · 2014: 47 · 2013: 44 · 2012: 48
- FWCI
- 26.38
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Neuron (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institutes of Health
- U.S. Public Health Service (06833)
- National Institute of Neurological Disorders and Stroke (P50NS006833)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Keywords
- scale-free dynamics, brain activity, power spectrum, frequency modulation, temporal structure, default mode network, visual cortex, hippocampus, cerebellum, task performance, regional variation, complex dynamics
- MeSH terms
- Action Potentials, Brain, Brain Mapping, Electrodes, Implanted, Electroencephalography, Humans, Magnetic Resonance Imaging, Models, Neurological, Nerve Net, Synaptic Transmission, Neurons, Signal Processing, Computer-Assisted
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