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Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
Open accessAbstract
The human brain spontaneously generates neural oscillations with a large variability in frequency, amplitude, duration, and recurrence. Little, however, is known about the long-term spatiotemporal structure of the complex patterns of ongoing activity. A central unresolved issue is whether fluctuations in oscillatory activity reflect a memory of the dynamics of the system for more than a few seconds. We investigated the temporal correlations of network oscillations in the normal human brain at time scales ranging from a few seconds to several minutes. Ongoing activity during eyes-open and eyes-closed conditions was recorded with simultaneous magnetoencephalography and electroencephalography. Here we show that amplitude fluctuations of 10 and 20 Hz oscillations are correlated over thousands of oscillation cycles. Our analyses also indicated that these amplitude fluctuations obey power-law scaling behavior. The scaling exponents were highly invariant across subjects. We propose that the large variability, the long-range correlations, and the power-law scaling behavior of spontaneous oscillations find a unifying explanation within the theory of self-organized criticality, which offers a general mechanism for the emergence of correlations and complex dynamics in stochastic multiunit systems. The demonstrated scaling laws pose novel quantitative constraints on computational models of network oscillations. We argue that critical-state dynamics of spontaneous oscillations may lend neural networks capable of quick reorganization during processing demands.
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“The power spectra of neural signals typically follow a power-law form (), indicating temporal correlations that persist across multiple timescales (He et al. 2010; Miller et al. 2009; Linkenkaer-Hansen et al. 2001; Touboul and Destexhe 2010).”
From The myth of the Bayesian brain (2025) · cites this paper as Linkenkaer-Hansen et al. 2001
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Citations
Cites
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
Mosaic organization of DNA nucleotides
Peng, C., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, E., & Goldberger, A. L. (1994) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.49.1685 · Cited by 5,002 · cited 1×
“…fluctuation analysis has been developed for quantifying correlation properties in nonstationary signals, e.g., in physiological time series, because long-range correlations—revealed by an ACF analysis—can arise also as an artifact of the “patchiness” of nonstationary data (Peng et al., 1994, 1995).”
BackgroundBak, P., Tang, C., & Wiesenfeld, K. A. (1988) · Physical Review A · doi:10.1103/physreva.38.364 · Cited by 4,744 · cited 6×
“Unlike deterministic approaches aimed at finding low-dimensional chaos, the SOC framework allows for a highdimensional character of the dynamics and for the presence of stochastic effects.”
BackgroundInfluentialÜber das Elektrenkephalogramm des Menschen
Berger, H. (1929) · European Archives of Psychiatry and Clinical Neuroscience · doi:10.1007/bf01797193 · Cited by 4,266
Fractal Concepts in Surface Growth
Barabási, A. L., & Stanley, H. E. (1995) · doi:10.1017/cbo9780511599798 · Cited by 3,925
Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series
Peng, C., Havlin, S., Stanley, E., & Goldberger, A. L. (1995) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166141 · Cited by 3,865 · cited 4×
“and Marchesi, 1999), heartbeats (Peng et al., 1995), and human”
BackgroundInfluentialThalamocortical oscillations in the sleeping and aroused brain
Steriade, M., McCormick, D. A., & Sejnowski, T. J. (1993) · Science · doi:10.1126/science.8235588 · Cited by 3,564 · cited 3×
“…frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996; Herculano-Houzel et al., 1999; Tsodyks et al., 1999).”
BackgroundFractal Concepts in Surface Growth
Barabási, A.-Ĺ., Stanley, H. E., & Sander, L. M. (1995) · Physics Today · doi:10.1063/1.2808215 · Cited by 3,328
Bak, P. (1996) · Springer eBooks · doi:10.1007/978-1-4757-5426-1 · Cited by 2,830
Llinás, R. R. (1988) · Science · doi:10.1126/science.3059497 · Cited by 2,285 · cited 4×
“…frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996; Herculano-Houzel et al., 1999; Tsodyks et al., 1999).”
BackgroundInfluential
Cited by
Sorted by citations
Items 701–800 of 1,000
Optimally fuzzy scale-free memoryPreprint
Shankar, K. H., & Howard, M. W. (2012) · arXiv (Cornell University) · Cited by 10
Kramer, M., & Chu, C. J. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.03.10.532077 · Cited by 10
“, avalanches of population voltage discharges [68], amplitudes of narrowband oscillations [69]).”
BackgroundTime-dependent scale-free brain dynamics during naturalistic inputs
Klar, P., Çatal, Y., Jocham, G., Langner, R., & Northoff, G. (2025) · NeuroImage · doi:10.1016/j.neuroimage.2025.121255 · Cited by 9
Genetic contributions to brain criticality and its relationship with human cognitive functions
Xin, Y., Cui, Y. J., Yu, S., & Liu, N. (2025) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2417010122 · Cited by 10
“The temporal dynamics of brain criticality can also be assessed through LRTCs, which reflect high temporal correlations in signal amplitude over time ( 29 , 35 , 42 ).”
Pu, J., Xu, H., Wang, Y., Cui, H., & Hu, Y. S. (2016) · Cognitive Neurodynamics · doi:10.1007/s11571-016-9394-0 · Cited by 9
Long-range sequential dependencies precede complex syntactic production in language acquisition
Sainburg, T., Mai, A., & Gentner, T. Q. (2022) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2021.2657 · Cited by 9
“For 94 this reason, it has been argued that hierarchical organization is an inherent property of biological processes, 95 including human behavior [50, 71, 72] and that the hierarchical structure of behavior is inherited from the 96 lower-level organization of neurophysiological mechanisms that produce it [73–76], whi…”
BackgroundThe sleep EEG envelope is a novel, neuronal firing-based human biomarker
Ujma, P. P., Dresler, M., Simor, P., Fabó, D., Ulbert, I., Erőss, L., & Bódizs, R. (2022) · Scientific Reports · doi:10.1038/s41598-022-22255-4 · Cited by 10
Sihn, D., Kim, J. S., Kwon, O., & Kim, S.-P. (2023) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2023.1132996 · Cited by 9
“Correlations of amplitude fluctuations during rest have also been observed over long periods of time, namely, long-range temporal correlations, which represent correlations between amplitude fluctuations in different time periods at the same brain region (10).”
BackgroundMethodResultInfluentialAltered dynamical integration/segregation balance during anesthesia-induced loss of consciousness
Lord, L.-D., Carletti, T., Fernandes, H. M., Turkheimer, F., & Expert, P. (2023) · Frontiers in Network Physiology · doi:10.3389/fnetp.2023.1279646 · Cited by 8
“long-distance interactions between brain regions displaying scaling behaviour in time and space across a range of imaging modalities) (30, 31), as well as by the dynamic exploration of a diverse and flexible repertoire of functional brain configurations (32-34).”
BackgroundExplicit Modeling of Brain State Duration Using Hidden Semi Markov Models in EEG Data
Trujillo‐Barreto, N. J., Araya, D., Astudillo, A., & El‐Deredy, W. (2024) · IEEE Access · doi:10.1109/access.2024.3354711 · Cited by 9
“A Geometric duration is then not consistent with the long-range temporal dependency (‘‘long memory’’) and near scale-invariance (self-similarity) ubiquitous in real EEG data [29], [57], [58], [59], [60].”
BackgroundDetrended fluctuation analysis and Kolmogorov–Sinai entropy of electroencephalogram signals
Lim, J. H., Khang, E. J., Lee, T. H., Kim, I. H., Maeng, S. E., & Lee, J. W. (2013) · Physics Letters A · doi:10.1016/j.physleta.2013.07.034 · Cited by 9
Correlated microtiming deviations in jazz and rock music
Sogorski, M., Geisel, T., & Priesemann, V. (2018) · PLoS ONE · doi:10.1371/journal.pone.0186361 · Cited by 9
Alex, P., Carreras, B. A., Arumugam, S., & Sinha, S. K. (2018) · Physics of Plasmas · doi:10.1063/1.5019930 · Cited by 9
Inference on Long-Range Temporal Correlations in Human EEG Data
Smith, R. J., Ombao, H., Shrey, D. W., & Lopour, B. A. (2019) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2019.2936326 · Cited by 9
“eter due to its widespread application in current neuroscience literature [6], [9], [13], [18], [19].”
BackgroundLloyd, D. E. (2020) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2019.00098 · Cited by 10
Emergent scale invariance in neural networks
Katsnelson, M. I., Vanchurin, V., & Westerhout, T. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.128401 · Cited by 25
Interictal Infraslow Activity in Stereoelectroencephalography
Thompson, S. A., Krishnan, B., Gonzalez-Martinez, J. A., Bulacio, J. C., Jehi, L. E., Mosher, J. C., Alexopoulos, A. V., & Burgess, R. C. (2015) · Journal of Clinical Neurophysiology · doi:10.1097/wnp.0000000000000236 · Cited by 9
“This 1/f power spectrum is the mathematical signature of scale-free systems (Linkenkaer-Hansen et al., 2001).”
BackgroundDelirium, Caffeine, and Perioperative Cortical Dynamics
Kim, H., McKinney, A., Brooks, J., Mashour, G. A., Lee, U., & Vlisides, P. E. (2021) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2021.744054 · Cited by 9
“The primary analysis focused on the alpha band (8 – 12 Hz), given that alpha oscillations are postulated to play a vital role in coordinating spatiotemporally distributed information in the brain during waking consciousness (Linkenkaer-Hansen et al., 2001; Palva et al., 2013; Vlisides et al., 2018).”
BackgroundShelhamer, M. (2005) · Biological Cybernetics · doi:10.1007/s00422-005-0584-9 · Cited by 9
“In a study of amplitude fluctuations in 10 and 20 Hz brain oscillations in humans (Linkenkaer-Hansen et al. 2001), the fluctuations were found to exhibit powerlaw scaling over several minutes.”
BackgroundPalva, J. M., & Palva, S. (2014) · Wiley eBooks · doi:10.1002/9783527651009.ch5 · Cited by 9
Self-citationSelf-organized criticality in neural networksPreprint
Katsnelson, M. I., Vanchurin, V., & Westerhout, T. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.03402 · Cited by 9
“Many astrophysical [1], geological [2], biological [3] and even neurobiological [4] systems exhibit a remarkable property of being dynamically attracted towards self-organized critical states described by scale-invariant distributions of fluctuations.”
BackgroundPre-Stimulus Power but Not Phase Predicts Prefrontal Cortical Excitability in TMS-EEG
Poorganji, M., Zomorrodi, R., Zrenner, C., Bansal, A., Hawco, C., Hill, A., Hadas, I., Rajji, T., Chen, R., Zrenner, B., et al. (2023) · Biosensors · doi:10.3390/bios13020220 · Cited by 11
dos Santos, F. P., & Verschure, P. F. M. J. (2025) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1012723 · Cited by 9
“…we suggest that future studies focus not only on the laminar differences in mean firing rates and levels of input, but also investigate signatures of edge-of-bifurcation dynamics, such as long-range temporal correlations [87, 88], in the slow and fast oscillations of deep and superficial layers.”
Ao, Y., Klar, P., Çatal, Y., Wang, Y., & Northoff, G. (2025) · Communications Biology · doi:10.1038/s42003-025-08448-3 · Cited by 8
“A key concept in understanding neural timescales is scale-free dynamics, which can be measured by the power-law exponent (PLE) 2,31 – 33 .”
A Virtual Clinical Trial of Psychedelics to Treat Patients With Disorders of Consciousness
Alnagger, N., Cardone, P., Martial, C., Perl, Y. S., Mindlin, I., Sitt, J. D., Roseman, L., Carhart-Harris, R. L., Nutt, D., Mallaroni, P., et al. (2025) · Advanced Science · doi:10.1002/advs.202511780 · Cited by 8
Guan, S., Jiang, R., Chen, D. Y., Michael, A., Meng, C., & Biswal, B. B. (2023) · Cerebral Cortex · doi:10.1093/cercor/bhad393 · Cited by 8
Fractal Analyses of Networks of Integrate-and-Fire Stochastic Spiking Neurons
Costa, A. D. A., Amon, M. J., Sporns, O., & Favela, L. H. (2018) · Springer proceedings in complexity · doi:10.1007/978-3-319-73198-8_14 · Cited by 8
“Windows were overlapped by 50% to provide better estimates of within-window variability [8,43,44].”
MethodA repetitive modular oscillation underlies human brain electric activity
Tozzi, A., Peters, J. F., & Jaušovec, N. (2017) · Neuroscience Letters · doi:10.1016/j.neulet.2017.05.051 · Cited by 8
Bandyopadhyay, A., & Basu, S. (2020) · Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics · doi:10.1016/j.bbapap.2020.140474 · Cited by 8
Temporal Structure in Sensorimotor Variability: A Stable Trait, But What For?
Perquin, M. N., van Vugt, M. K., Hedge, C., & Bompas, A. (2023) · Computational Brain & Behavior · doi:10.1007/s42113-022-00162-1 · Cited by 10
Quantum Entanglement of the Brain, Dynamics of Information, and Intelligent Finance
Njegovanović, A. (2023) · Financial Markets Institutions and Risks · doi:10.61093/fmir.7(3).12-30.2023 · Cited by 7
Proposed Renormalization Group Analysis of Nonlinear Brain Dynamics at Criticality
Freeman, W., & Cao, T. Y. (2008) · Springer eBooks · doi:10.1007/978-1-4020-8387-7_27 · Cited by 8
“The broad spectra document simultaneous genesis of activity densities at all frequencies and wavelengths [3, 10, 11, 15].”
BackgroundNaruse, Y., Takiyama, K., Okada, M., & Murata, T. (2010) · Physical Review E · doi:10.1103/physreve.82.011912 · Cited by 8
Dynamic scaling behavior of human brain electroencephalogram
Yuan, J., Zheng, B., Pan, C., Wu, Y., & Trimper, S. (2005) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.09.038 · Cited by 8
Analysis of signal fluctuations of Cortical Spreading Depression: Preliminary findings
do Nascimento, R. S., Dore, L. H., Moraes, R. B., Barbosa, C. T. F., Guedes, R. C. A., Nogueira, R. A., & Stošić, T. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.01.010 · Cited by 8
Gao, T., Wu, D., & Yao, D. (2008) · Springer eBooks · doi:10.1007/978-1-4020-8387-7_87 · Cited by 8
“But the scalp EEG arises from a large number of neurons whose interactions are generally nonlinear [ 1 ], so it could not be best described by linear analyses, and nonlinear analyses are needed.”
BackgroundRobinson, P. A. (2014) · Physical Review E · doi:10.1103/physreve.90.042712 · Cited by 8
Towards plasma-like collisionless trajectories in the brain
Tozzi, A., Peters, J. F., & Déli, É. (2017) · Neuroscience Letters · doi:10.1016/j.neulet.2017.10.016 · Cited by 6
R/S analysis of reaction time in Neuron Type Test for human activity in civil aviation
Zhang, H., Kang, M.-C., Li, J., & Hai-tao, L. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.11.054 · Cited by 8
Myers, M. H., Jolly, E. J., Li, Y., Curry, A. L. D. J., & Parfenova, H. (2017) · Annals of Neurosciences · doi:10.1159/000464418 · Cited by 8
Emotions from Hindustani Classical Music: An EEG based study including Neural Hysteresis
Ghosh, D. C., Sengupta, R., Sanyal, S., & Banerjee, A. (2017) · Signals and communication technology · doi:10.1007/978-981-10-6511-8_3 · Cited by 8
Raiesdana, S. (2018) · Australasian Physical & Engineering Sciences in Medicine · doi:10.1007/s13246-018-0624-0 · Cited by 8
“In these systems no characteristic scales dominate the dynamics of the underlying process [16].”
BackgroundTetereva, A., Kartashov, S., Ivanitsky, A. M., & Martynova, O. (2020) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2020.509075 · Cited by 8
Fang, G., Xia, Y., Lai, Y., You, Z., & Yao, D. (2010) · Physiological Measurement · doi:10.1088/0967-3334/31/6/005 · Cited by 8
The discrete logic of the Brain - Explicit modelling of Brain State durations in EEG and MEGPreprint
Trujillo‐Barreto, N. J., Araya, D., & El‐Deredy, W. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/635300 · Cited by 8
“periodicity), while a heavy-tailed right skewed PDF corresponds to a process showing long-term dependencies and temporal scaling law (Gschwind et al., 2015; Linkenkaer-Hansen et al., 2001; Roberts et al., 2015).”
BackgroundSooter, J. S., Fontenele, A. J., Ly, C., Barreiro, A. K., & Shew, W. L. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.05.29.596499 · Cited by 9
Enhanced scaling crossover detection in long-range correlated time series
Fujimoto, Y., Mangalam, M., & Kiyono, K. (2024) · Chaos Solitons & Fractals X · doi:10.1016/j.csfx.2024.100125 · Cited by 7
Schroeder, F., Fairclough, S. H., Dehais, F., & Richins, M. T. (2025) · Frontiers in Neuroergonomics · doi:10.3389/fnrgo.2025.1582724 · Cited by 7
Zhang, Y., Lu, J. Z., Chen, F., Du, H., Gao, X., & Lin, Z. (2025) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2025.3591819 · Cited by 7
“Recent studies have shown that trial-specific features in EEG signals significantly impacts DNN-based directional focus decoding models, often resulting in overestimated decoding accuracy [31], [34], [35], [44], [45], [46], [47].”
Role of criticality in the structure-function relationship in the human brain
Angiolelli, M., Scarpetta, S., Sorrentino, P., Lopez, E. T., Quarantelli, M., Granata, C., Sorrentino, G., Palmieri, V., Messuti, G., Stefano, M., et al. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.043153 · Cited by 7
Computational EEG attributes predict response to therapy for epileptic spasms
Rajaraman, R. R., Smith, R. J., Oana, S., Daida, A., Shrey, D. W., Nariai, H., Lopour, B. A., & Hussain, S. A. (2024) · Clinical Neurophysiology · doi:10.1016/j.clinph.2024.03.035 · Cited by 7
Neurodynamics of Intentional Behavior Generation
Kozma, R. (2007) · Springer eBooks · doi:10.1007/978-3-540-73267-9_7 · Cited by 7
“The importance of long-distance correlations has been emphasized by numerous brain theorists [57, 58, 59, 60, 61, 62, 63].”
BackgroundAge-dependent complex noise fluctuations in the brain
Mareš, J., Vyšata, O., Procházka, A., & Vališ, M. (2013) · Physiological Measurement · doi:10.1088/0967-3334/34/10/1269 · Cited by 6
“Current research has suggested the possibility of scale-free avalanche brain activity and scale-free electroencephalographic (EEG) spectra (Linkenkaer-Hansen et al 2001, Goh et al 2005).”
BackgroundBalasubramaniam, R., Hove, M. J., & Médé, B. (2017) · Topics in Cognitive Science · doi:10.1111/tops.12301 · Cited by 7
Soft-assembled human–machine perceptual systems
Favela, L. H. (2019) · Adaptive Behavior · doi:10.1177/1059712319847129 · Cited by 7
Temporal fluctuation scaling in nonstationary time series using the path integral formalism
Abril, F. S., & Quimbay, C. J. (2021) · Physical review. E · doi:10.1103/physreve.103.042126 · Cited by 7
Zinchenko, O. O., Nikulin, V. V., & Klucharev, V. A. (2021) · Neuroscience · doi:10.1016/j.neuroscience.2021.07.012 · Cited by 7
Psychological and Electrophysiological Correlates of Word Learning Success
Mkrtychian, N. A., Николаевна, К. С., Gnedykh, D., Tsvetova, D., Blagovechtchenski, E., & Юрьевич, Ш. Ю. (2021) · Psychology in Russia State of Art · doi:10.11621/pir.2021.0211 · Cited by 8
Carstens, N., Strunskus, T., Faupel, F., Hassanien, A., & Vahl, A. (2022) · Particle & Particle Systems Characterization · doi:10.1002/ppsc.202200131 · Cited by 7
Dynamical Nonstationarity Analysis of Resting EEGs in Alzheimer’s Disease
Latchoumane, C.-F. V., Ifeachor, E., Hudson, N. R., Wimalaratna, S., & Jeong, J. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-69162-4_96 · Cited by 7
“It was demonstrated that EEGs at rest present a long range correlation and a scale-free set of properties within the alpha and beta bands [18], which is thought to be a hallmark of complex systems with plasticity and multi-time scale correlations (i.”
BackgroundTransmission efficiency in ring, brain inspired neuronal networks. Information and energetic aspects
Paprocki, B., & Szczepański, J. (2013) · Brain Research · doi:10.1016/j.brainres.2013.07.024 · Cited by 7
“Understanding the role of the connections is recently subject to increased neuroscientists effort, primarily in context of synchronization and correlations (Linkenkaer-Hansen et al., 2001, 2004; De la Fuente et al., 2006; Uhlhaas et al., 2009; Nikulin et al., 2012; Steinbeck et al., 2012).”
Plasticity, Learning, and Complexity in Spiking Networks
Kello, C. T., Rodny, J., Warlaumont, A. S., & Noelle, D. C. (2012) · Critical Reviews in Biomedical Engineering · doi:10.1615/critrevbiomedeng.2013006724 · Cited by 7
Characteristic time scales of electroencephalograms of narcoleptic patients and healthy controls
Kim, J. W., Shin, H.-B., Kim, E.-J., Koo, Y.-J., Choi, B., Park, K. S., & Jeong, D. (2010) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2010.09.001 · Cited by 7
“[11].”
Dimitriadis, S. I., & Linden, D. E. J. (2016) · Clinical Neurophysiology · doi:10.1016/j.clinph.2016.05.359 · Cited by 7
Smit, D. J. A., & Anokhin, A. P. (2016) · International Journal of Psychophysiology · doi:10.1016/j.ijpsycho.2016.07.498 · Cited by 7
Conde, V., Andreasen, S. H., Petersen, T. H., Larsen, K. B., Madsen, K., Andersen, K. W., Akopian, I., Madsen, K. H., Hansen, C. P., Poulsen, I., et al. (2017) · BMJ Open · doi:10.1136/bmjopen-2017-016286 · Cited by 8
Comparative approximations of criticality in a neural and quantum regime
Bettinger, J. S. (2017) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2017.09.007 · Cited by 6
Rosales-Lagarde, A., Rodríguez‐Torres, E. E., Itzá‐Ortiz, B. A., Miramóntes, P., Vázquez‐Tagle, G., Enciso-Alva, J. C., García-Muñoz, V., Cubero‐Rego, L., Sánchez, J. E. P., Martínez-Alcalá, C. I., et al. (2018) · Frontiers in Psychology · doi:10.3389/fpsyg.2018.01205 · Cited by 7
Cellular Automata and Artificial Brain Dynamics
Fraile, A., Panagiotakis, E., Christakis, N., & Acedo, L. (2018) · Mathematical and Computational Applications · doi:10.3390/mca23040075 · Cited by 7
“A second point is that the GoL presents a 1/f noise [30], a feature that is believed to be present in brain dynamics [31,32] in electro- and magneto-encephalogram spectra (EEG and MEG) [33], and in human cognition as well [34].”
BackgroundCarpena, P., Bernaola‐Galván, P., Gómez-Extremera, M., & Coronado, A. V. (2019) · Repositorio Institucional de la Universidad de Málaga (University of Málaga) · doi:10.1063/5.0013986 · Cited by 7
“Such time series can be found, for example, in Physiology (heartbeat dynamics [1], brain activity [2], respiration [3], postural control [4, 5]), Biology (DNA and protein sequences) [6, 7], Economics (stock market activity) [8], Music [9], Meteorology (temperature or rain precipitation) [10, 11], Geophysics (seismic s…”
BackgroundArtieda, J., Alegre, M., Valencia, M., Urrestarazu, E., Pérez-Alcázar, M., Nicolás, M. J., Azcárate, J. L. P., & Iriarte, J. (2010) · Anales del Sistema Sanitario de Navarra · doi:10.23938/assn.0150 · Cited by 7
Coey, C. A., Kallen, R. W., Chemero, A. P., & Richardson, M. J. (2018) · Human Movement Science · doi:10.1016/j.humov.2018.09.006 · Cited by 7
Hartley, C., Farmer, S. F., & Luc Berthouze, A. (2020) · PLoS ONE · doi:10.1371/journal.pone.0226772 · Cited by 7
“This approach has been used by a number of previous authors to determine the presence of LRTCs in data, including neurophysiological data sets [24,53–58].”
MethodRestless minds, wandering brains
van Leeuwen, C., & Smit, D. J. A. (2012) · Advances in consciousness research · doi:10.1075/aicr.88.06lee · Cited by 7
“More recently, the 1/f scaling behavior characteristic of complexity has been observed in amplitude fluctuations of 10 and 20 Hz oscillation (Linkenkaer-Hansen et al. 2001).”
BackgroundHu, Z., & Shi, P. (2006) · Proceedings - International Conference on Pattern Recognition/Proceedings/International Conference on Pattern Recognition · doi:10.1109/icpr.2006.990 · Cited by 7
“For example, several efforts have concentrated on the α and β peaks of the so-called o and p channels, and have discovered that the amplitude of the oscillations is long-range correlated [ 6 ].”
BackgroundMultifractal analysis of sentence lengths in English literary textsPreprint
Grabska-Gradzińska, I., Kulig, A., Kwapień, J., Oświȩcimka, P., & Drożdż, S. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1212.3171 · Cited by 7
“Especially the latter seems to be interesting as reflecting the principles of brain function which is known to be long-range temporally correlated at least in its certain aspects [11,12,13,14].”
BackgroundA General, Noise-Driven Mechanism for the 1/f-Like Behavior of Neural Field Spectra
Kramer, M., & Chu, C. J. (2024) · Neural Computation · doi:10.1162/neco_a_01682 · Cited by 6
Murtaza, H., Ahmed, M., Murtaza, G., Zafar, S. N., & Nazir, T. (2025) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2025.107552 · Cited by 9
Balancing excitation and inhibition: The role of neural network dynamics in working memory gating
Herzog, N., Čėsnaitė, E., Steinfath, T. P., Kapralov, N., Fallon, S. J., Nikulin, V., Villringer, A., Janssen, L. K., & Horstmann, A. (2024) · Imaging Neuroscience · doi:10.1162/imag_a_00380 · Cited by 7
Inhibitory neurons and the asymmetric shape of neuronal avalanches
Zaccariello, R., Herrmann, H. J., Sarracino, A., Zapperi, S., & de Arcangelis, L. (2025) · Physical review. E · doi:10.1103/physreve.111.024133 · Cited by 6
Long-Interval Spatio-Temporal Graph Convolution for Brain Disease Diagnosis
Li, S., Zhu, Q., Guan, D., Shen, B., Zhang, L., Ji, Y., Qi, S., & Zhang, D. (2025) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2025.3551032 · Cited by 6
“Linkenkaer-Hansen et al. [8] studied the temporal correlation of oscillations in normal human brain networks on timescales ranging from seconds to minutes, and found that the correlation decays as a power-law function.”
Ghaderi, A., Wang, H., & Protzner, A. B. (2026) · Neural Computation · doi:10.1162/neco.a.1488 · Cited by 4
A distribution model of functional connectome based on criticality and energy constraints
Takagi, K. (2017) · PLoS ONE · doi:10.1371/journal.pone.0177446 · Cited by 6
Changes in functional connectivity preserve scale-free neuronal and behavioral dynamics
Rabus, A., Curic, D., Ivan, V. E., Esteves, I. M., Gruber, A. J., & Davidsen, J. (2023) · Physical review. E · doi:10.1103/physreve.108.l052301 · Cited by 7
EEG Power Spectral Measurements Comparing Normal and “Thatcherized” Faces
Gersenowies, J., Marosi, E., Cansino, S., & Rodriguez, M. E. (2010) · International Journal of Neuroscience · doi:10.3109/00207454.2010.487746 · Cited by 6
Corticonic models of brain mechanisms underlying cognition and intelligence
FARHAT, N. (2007) · Physics of Life Reviews · doi:10.1016/j.plrev.2007.08.001 · Cited by 6
“Several types of network have been proposed [107–110] to model the long-distance synchronization that is readily observed in scalp EEG [111–113].”
The origin of scientific neurology and its consequences for modern and future neuroscience
Steinberg, D. A. (2013) · Brain · doi:10.1093/brain/awt157 · Cited by 6
Rampp, S., Rensch, L., Simmermacher, S., Rahne, T., Strauß, C., & Prell, J. (2016) · Journal of Clinical Monitoring and Computing · doi:10.1007/s10877-016-9837-5 · Cited by 6
“In a typical recording environment, EEG power of both physiological oscillations and noise decreases with increasing frequency f according to the 1/f-law [23, 24].”
BackgroundBurgess, A. (2019) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2019.00212 · Cited by 6
Huang, J., Ahlers, E., Bogatsch, H., Böhme, P., Ethofer, T., Fallgatter, A. J., Gallinat, J., Hegerl, U., Heuser, I., Hoffmann, K., et al. (2022) · European Archives of Psychiatry and Clinical Neuroscience · doi:10.1007/s00406-022-01452-2 · Cited by 6
“This is a phenomenon called long-range temporal correlation (LRTC) and has been observed in several EEG studies [21, 22, 24].”
BackgroundResultCortical response variability is driven by local excitability changes with somatotopic organization
Stephani, T., Nierula, B., Villringer, A., Eippert, F., & Nikulin, V. V. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119687 · Cited by 6
Ouyang, G., Wang, S.-J., Liu, M., Zhang, M., & Zhou, C. (2022) · Cognitive Neurodynamics · doi:10.1007/s11571-022-09889-w · Cited by 7
“…of neurons with statistics close to Poisson random process (Softky and Koch 1993), the scale-free spectrum of cortical electrophysiological signals (Linkenkaer-Hansen et al. 2001; Miller et al. 2009; He 2014), the distinct oscillations amidst the background noise and scale-free activity (Buz-saki…”
BackgroundJanjarasjitt, S., & Loparo, K. A. (2015) · Journal of Medical and Biological Engineering · doi:10.1007/s40846-015-0020-0 · Cited by 6
Lin, D. C., Velázquez, J. L. P., & Nenadovic, V. (2012) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/97/40001 · Cited by 6
Vallone, F., Cintio, A., Mainardi, M., Caleo, M., & Garbo, A. D. (2015) · Physical Review E · doi:10.1103/physreve.91.012702 · Cited by 7
Weakened long-range correlation of renal sympathetic nerve activity in Wistar rats after anaesthesia
Li, Y.-T., Qiu, J., Yan, R., Yang, Z. R., & Zhang, T. (2008) · Neuroscience Letters · doi:10.1016/j.neulet.2007.12.038 · Cited by 6
“In neurophysiology, similar long-rang power–law correlations have been investigated from microscopic to macroscopic domains, ranging from medullary sympathetic neurons [10] and to human brain oscillations [12].”
Segmentation and Characterization of EEG During Mental tasks using Dynamical Nonstationarity
Latchoumane, C. F. V., Chung, D., Kim, S.-K., & Jeong, J. (2007) · Scholarworks@UNIST (Ulsan National Institute of Science and Technology) · Cited by 6
Brain criticality predicts individual synchronization levels in humansPreprint
Fuscà, M., Siebenhühner, F., Wang, S. H., Myrov, V. O., Arnulfo, G., Nobili, L., Palva, J. M., & Palva, S. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.11.24.517800 · Cited by 6
“Detrended Fluctuation Analysis We used Detrended Fluctuation Analysis (DFA) (Linkenkaer-Hansen et al., 2001) to estimate monofractal scaling exponents of neuronal LRTCs that typically vary between 0.5 and 1 (Linkenkaer-Hansen et al., 2001, 2005; Meisel et al., 2015; Monto et al., 2007; Nikulin &…”
BackgroundMethodInfluentialSelf-citationZhu, Y., Wei, Y., Yu, X., Liu, J., Lan, R., Guo, X., & Luo, Y. (2024) · Clinical Neurophysiology · doi:10.1016/j.clinph.2024.08.002 · Cited by 5
Marín-García, A., Arzate-Mena, J. D., Corsi‐Cabrera, M., Muñoz‐Torres, Z., Olguín-Rodríguez, P. V., Ríos-Herrera, W. A., Rivera, A., & Müller, M. (2024) · PLoS ONE · doi:10.1371/journal.pone.0307378 · Cited by 5
“It is to say, even at rest the brain is permanently active [55–59], producing the largest possible set of different spatio-temporal structures of synchronous neural activity [60–65] expressed by power laws [66, 67].”
Metadata
- Authors
- Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., & Ilmoniemi, R. J.
- Affiliations
- Helsinki University Hospital (FI)
- University of Helsinki (FI)
- Venue
- The Journal of Neuroscience
- Publisher
- Society for Neuroscience
- Published
- 2001-02-15
- Volume
- 21
- Issue
- 4
- Pages
- 1370-1377
- ISSN
- 0270-6474 (ISSN-L)
- 1529-2401
- PMC
- PMC6762238
- OpenAlex
- W2139852582
- Cited by
- 1,149
- References
- 50
- Citations by year
- 2026: 63 · 2025: 70 · 2024: 63 · 2023: 53 · 2022: 76 · 2021: 60 · 2020: 63 · 2019: 57 · 2018: 65 · 2017: 66 · 2016: 62 · 2015: 43 · 2014: 53 · 2013: 48 · 2012: 45
- FWCI
- 6.12
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of Neuroscience (publishedVersion, cc-by-nc-sa)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Funders
- Helsingin ja Uudenmaan Sairaanhoitopiiri
- Academy of Finland
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Keywords
- long-range temporal correlations, power-law scaling, neural oscillations, spontaneous neuronal activity, self-organized criticality, neural network reorganization, scaling exponents
- MeSH terms
- Adult, Biological Clocks, Brain, Computer Simulation, Electroencephalography, Female, Humans, Male, Models, Neurological, Nerve Net, Occipital Lobe, Parietal Lobe, Signal Processing, Computer-Assisted, Stochastic Processes, Time Factors, Visual Perception, Magnetoencephalography, Fractals
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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