{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T02:18:40Z","timestamp":1777342720434,"version":"3.51.4"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1005893","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2017,12,21]],"date-time":"2017-12-21T00:00:00Z","timestamp":1513814400000}}],"reference-count":97,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2017,12,11]],"date-time":"2017-12-11T00:00:00Z","timestamp":1512950400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Research Council (BE)","award":["ERC-YStG-676943"],"award-info":[{"award-number":["ERC-YStG-676943"]}]},{"name":"European Research Council (BE)","award":["ERC-YStG-263584"],"award-info":[{"award-number":["ERC-YStG-263584"]}]},{"name":"Agence Nationale de la Recherche (FR)","award":["ANR-16-CE37-0004-04"],"award-info":[{"award-number":["ANR-16-CE37-0004-04"]}]},{"DOI":"10.13039\/501100007241","name":"Universit\u00e9 Paris-Saclay","doi-asserted-by":"publisher","award":["IDEX NoTime"],"award-info":[{"award-number":["IDEX NoTime"]}],"id":[{"id":"10.13039\/501100007241","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1005893","type":"journal-article","created":{"date-parts":[[2017,12,11]],"date-time":"2017-12-11T13:36:22Z","timestamp":1512999382000},"page":"e1005893","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":70,"title":["Non-linear auto-regressive models for cross-frequency coupling in neural time series"],"prefix":"10.1371","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2674-1670","authenticated-orcid":true,"given":"Tom","family":"Dupr\u00e9 la Tour","sequence":"first","affiliation":[]},{"given":"Lucille","family":"Tallot","sequence":"additional","affiliation":[]},{"given":"Laetitia","family":"Grabot","sequence":"additional","affiliation":[]},{"given":"Val\u00e9rie","family":"Doy\u00e8re","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2569-5502","authenticated-orcid":true,"given":"Virginie","family":"van Wassenhove","sequence":"additional","affiliation":[]},{"given":"Yves","family":"Grenier","sequence":"additional","affiliation":[]},{"given":"Alexandre","family":"Gramfort","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2017,12,11]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780195301069.001.0001","article-title":"Rhythms of the Brain","author":"G Buzs\u00e1ki","year":"2006"},{"issue":"1","key":"ref2","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.neuron.2015.09.034","article-title":"Rhythms for cognition: communication through coherence","volume":"88","author":"P Fries","year":"2015","journal-title":"Neuron"},{"issue":"3","key":"ref3","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.neuron.2010.09.023","article-title":"Neural syntax: cell assemblies, synapsembles, and readers","volume":"68","author":"G Buzs\u00e1ki","year":"2010","journal-title":"Neuron"},{"issue":"7","key":"ref4","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.tics.2007.05.003","article-title":"Cross-frequency coupling between neuronal oscillations","volume":"11","author":"O Jensen","year":"2007","journal-title":"Trends in cognitive sciences"},{"issue":"6","key":"ref5","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1016\/j.neuron.2013.03.007","article-title":"The theta-gamma neural code","volume":"77","author":"JE Lisman","year":"2013","journal-title":"Neuron"},{"issue":"5793","key":"ref6","doi-asserted-by":"crossref","first-page":"1626","DOI":"10.1126\/science.1128115","article-title":"High gamma power is phase-locked to theta oscillations in human neocortex","volume":"313","author":"RT Canolty","year":"2006","journal-title":"Science"},{"issue":"11","key":"ref7","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.tics.2010.09.001","article-title":"The functional role of cross-frequency coupling","volume":"14","author":"RT Canolty","year":"2010","journal-title":"Trends in cognitive sciences"},{"issue":"11","key":"ref8","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1016\/j.tins.2015.09.001","article-title":"Neural Cross-Frequency Coupling: Connecting Architectures, Mechanisms, and Functions","volume":"38","author":"A Hyafil","year":"2015","journal-title":"Trends in Neurosciences"},{"issue":"33","key":"ref9","doi-asserted-by":"crossref","first-page":"13490","DOI":"10.1073\/pnas.0705708104","article-title":"On the formation of gamma-coherent cell assemblies by oriens lacunosum-moleculare interneurons in the hippocampus","volume":"104","author":"AB Tort","year":"2007","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"ref10","first-page":"1","article-title":"Phase resetting reduces theta\u2013gamma rhythmic interaction to a one-dimensional map","author":"P Malerba","year":"2013","journal-title":"Journal of mathematical biology"},{"issue":"2","key":"ref11","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.ijpsycho.2003.07.001","article-title":"Task-related coupling from high-to low-frequency signals among visual cortical areas in human subdural recordings","volume":"51","author":"A Bruns","year":"2004","journal-title":"International Journal of Psychophysiology"},{"issue":"15","key":"ref12","doi-asserted-by":"crossref","first-page":"7054","DOI":"10.1073\/pnas.0911184107","article-title":"Bidirectional changes to hippocampal theta\u2013gamma comodulation predict memory for recent spatial episodes","volume":"107","author":"PR Shirvalkar","year":"2010","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"1","key":"ref13","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1523\/JNEUROSCI.15-01-00047.1995","article-title":"Gamma (40\u2013100 Hz) oscillation in the hippocampus of the behaving rat","volume":"15","author":"A Bragin","year":"1995","journal-title":"The Journal of Neuroscience"},{"issue":"51","key":"ref14","doi-asserted-by":"crossref","first-page":"20517","DOI":"10.1073\/pnas.0810524105","article-title":"Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during performance of a T-maze task","volume":"105","author":"AB Tort","year":"2008","journal-title":"Proc Natl Acad Sci"},{"issue":"1","key":"ref15","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.brainresrev.2006.01.007","article-title":"Memory formation by neuronal synchronization","volume":"52","author":"N Axmacher","year":"2006","journal-title":"Brain research reviews"},{"issue":"4","key":"ref16","doi-asserted-by":"crossref","first-page":"e2000219","DOI":"10.1371\/journal.pbio.2000219","article-title":"Sequence learning modulates neural responses and oscillatory coupling in human and monkey auditory cortex","volume":"15","author":"Y Kikuchi","year":"2017","journal-title":"PLoS biology"},{"issue":"7","key":"ref17","doi-asserted-by":"crossref","first-page":"3228","DOI":"10.1073\/pnas.0911531107","article-title":"Cross-frequency coupling supports multi-item working memory in the human hippocampus","volume":"107","author":"N Axmacher","year":"2010","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"ref18","article-title":"Episodic sequence memory is supported by a theta- gamma phase code","author":"AC Heusser","year":"2016","journal-title":"Nature neuroscience"},{"key":"ref19","article-title":"Local and long-range functional connectivity is reduced in concert in autism spectrum disorders","author":"S Khan","year":"2013","journal-title":"Proc Natl Acad Sci"},{"issue":"2","key":"ref20","doi-asserted-by":"crossref","DOI":"10.1523\/ENEURO.0153-16.2017","article-title":"Communication between Brain Areas Based on Nested Oscillations","volume":"4","author":"M Bonnefond","year":"2017","journal-title":"eNeuro"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"e05352","DOI":"10.7554\/eLife.05352","article-title":"Corticothalamic phase synchrony and cross-frequency coupling predict human memory formation","volume":"3","author":"CM Sweeney-Reed","year":"2014","journal-title":"Elife"},{"issue":"1","key":"ref22","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.jneumeth.2008.06.035","article-title":"Testing for nested oscillation","volume":"174","author":"W Penny","year":"2008","journal-title":"Journal of Neuroscience methods"},{"issue":"2","key":"ref23","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1152\/jn.00106.2010","article-title":"Measuring phase-amplitude coupling between neuronal oscillations of different frequencies","volume":"104","author":"AB Tort","year":"2010","journal-title":"J Neurophysiol"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.conb.2014.08.002","article-title":"Untangling cross-frequency coupling in neuroscience","volume":"31","author":"J Aru","year":"2015","journal-title":"Current opinion in neurobiology"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.jneumeth.2015.01.032","article-title":"Parametric estimation of cross-frequency coupling","volume":"243","author":"B van Wijk","year":"2015","journal-title":"Journal of neuroscience methods"},{"issue":"2","key":"ref26","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.jneumeth.2011.08.014","article-title":"A critical note on the definition of phase\u2013 amplitude cross-frequency coupling","volume":"201","author":"TE \u00d6zkurt","year":"2011","journal-title":"Journal of Neuroscience methods"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.jneumeth.2014.01.002","article-title":"Toward a proper estimation of phase\u2013amplitude coupling in neural oscillations","volume":"225","author":"D Dvorak","year":"2014","journal-title":"Journal of Neuroscience methods"},{"issue":"1","key":"ref28","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.jneumeth.2005.12.009","article-title":"Towards a proper estimation of phase synchronization from time series","volume":"154","author":"M Chavez","year":"2006","journal-title":"Journal of Neuroscience methods"},{"key":"ref29","doi-asserted-by":"crossref","DOI":"10.3389\/fnins.2015.00370","article-title":"Misidentifications of specific forms of cross- frequency coupling: three warnings","volume":"9","author":"A Hyafil","year":"2015","journal-title":"Frontiers in Neuroscience"},{"issue":"2","key":"ref30","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.jneumeth.2008.01.020","article-title":"Sharp edge artifacts and spurious coupling in EEG frequency comodulation measures","volume":"170","author":"MA Kramer","year":"2008","journal-title":"Journal of Neuroscience methods"},{"issue":"4","key":"ref31","doi-asserted-by":"crossref","first-page":"e0173776","DOI":"10.1371\/journal.pone.0173776","article-title":"A neural mass model of cross frequency coupling","volume":"12","author":"M Chehelcheraghi","year":"2017","journal-title":"PLoS ONE"},{"key":"ref32","article-title":"Brain Oscillations and the Importance of Waveform Shape","author":"SR Cole","year":"2017","journal-title":"Trends in Cognitive Sciences"},{"issue":"1","key":"ref33","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0165-0270(98)00064-8","article-title":"A comparison of fast Fourier transform (FFT) and autoregressive (AR) spectral estimation techniques for the analysis of tremor data","volume":"83","author":"J Spyers-Ashby","year":"1998","journal-title":"Journal of neuroscience methods"},{"key":"ref34","doi-asserted-by":"crossref","unstructured":"Mahan MY, Chorn CR, Georgopoulos AP. White Noise Test: detecting autocorrelation and nonstationarities in long time series after ARIMA modeling. In: Proceedings 14th Python in Science Conference (Scipy 2015), Austin, TX; 2015.","DOI":"10.25080\/Majora-7b98e3ed-00f"},{"issue":"1","key":"ref35","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0304-4076(88)90045-0","article-title":"Some recent development in a concept of causality","volume":"39","author":"CW Granger","year":"1988","journal-title":"Journal of econometrics"},{"issue":"1457","key":"ref36","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1098\/rstb.2005.1654","article-title":"Estimating brain functional connectivity with sparse multivariate autoregression","volume":"360","author":"PA Vald\u00e9s-Sosa","year":"2005","journal-title":"Philosophical Transactions of the Royal Society of London B: Biological Sciences"},{"issue":"8","key":"ref37","doi-asserted-by":"crossref","first-page":"1954","DOI":"10.1109\/TBME.2010.2046325","article-title":"Modeling sparse connectivity between underlying brain sources for EEG\/MEG","volume":"57","author":"S Haufe","year":"2010","journal-title":"Bio Eng, IEEE Trans"},{"issue":"6","key":"ref38","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/PL00007990","article-title":"Partial directed coherence: a new concept in neural structure determination","volume":"84","author":"AL Baccal\u00e1","year":"2001","journal-title":"Biological Cybernetics"},{"key":"ref39","article-title":"Estimating an AR Model with Exogenous Driver","author":"Y Grenier","year":"2013"},{"key":"ref40","doi-asserted-by":"crossref","unstructured":"Dupr\u00e9 la Tour T, Grenier Y, Gramfort A. Parametric estimation of spectrum driven by an exogenous signal. In: Acoustics, Speech and Signal Processing (ICASSP), 2017 IEEE International Conference on. IEEE; 2017. p. 4301\u20134305.","DOI":"10.1109\/ICASSP.2017.7952968"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1111\/j.2517-6161.1980.tb01126.x","article-title":"Threshold autoregression, limit cycles and cyclical data","author":"H Tong","year":"1980","journal-title":"Journal of the Royal Statistical Society Series B (Methodological)"},{"issue":"3","key":"ref42","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/j.1467-9892.1986.tb00501.x","article-title":"On estimating thresholds in autoregressive models","volume":"7","author":"KS Chan","year":"1986","journal-title":"Journal of Time Series Analysis"},{"issue":"10","key":"ref43","doi-asserted-by":"crossref","first-page":"1602","DOI":"10.1109\/29.7548","article-title":"Autoregressive models with time-dependent log area ratios","volume":"36","author":"Y Grenier","year":"1988","journal-title":"Acoustics, Speech and Signal Processing, IEEE Transactions on"},{"issue":"3","key":"ref44","doi-asserted-by":"crossref","first-page":"1904","DOI":"10.1152\/jn.00263.2005","article-title":"An oscillatory hierarchy controlling neuronal excitability and stimulus processing in the auditory cortex","volume":"94","author":"P Lakatos","year":"2005","journal-title":"Journal of neurophysiology"},{"issue":"7271","key":"ref45","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1038\/nature08573","article-title":"Frequency of gamma oscillations routes flow of information in the hippocampus","volume":"462","author":"LL Colgin","year":"2009","journal-title":"Nature"},{"issue":"4","key":"ref46","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1002\/(SICI)1097-0193(1999)8:4<194::AID-HBM4>3.0.CO;2-C","article-title":"Measuring phase synchrony in brain signals","volume":"8","author":"JP Lachaux","year":"1999","journal-title":"Human brain mapping"},{"issue":"3","key":"ref47","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1089\/brain.2012.0085","article-title":"Variable bandwidth filtering for improved sensitivity of cross-frequency coupling metrics","volume":"2","author":"JI Berman","year":"2012","journal-title":"Brain connectivity"},{"issue":"4","key":"ref48","doi-asserted-by":"crossref","first-page":"041903","DOI":"10.1103\/PhysRevE.65.041903","article-title":"Performance of different synchronization measures in real data: a case study on EEG signals","volume":"65","author":"RQ Quiroga","year":"2002","journal-title":"Physical Review E"},{"issue":"2","key":"ref49","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.jneumeth.2004.03.002","article-title":"Fourier-, Hilbert-and wavelet-based signal analysis: are they really different approaches?","volume":"137","author":"A Bruns","year":"2004","journal-title":"Journal of Neuroscience methods"},{"issue":"7185","key":"ref50","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1038\/nature06713","article-title":"Identifying natural images from human brain activity","volume":"452","author":"KN Kay","year":"2008","journal-title":"Nature"},{"issue":"2","key":"ref51","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.neuroimage.2010.07.073","article-title":"Encoding and decoding in fMRI","volume":"56","author":"T Naselaris","year":"2011","journal-title":"Neuroimage"},{"issue":"7600","key":"ref52","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1038\/nature17637","article-title":"Natural speech reveals the semantic maps that tile human cerebral cortex","volume":"532","author":"AG Huth","year":"2016","journal-title":"Nature"},{"key":"ref53","doi-asserted-by":"crossref","first-page":"987","DOI":"10.2307\/1912773","article-title":"Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation","author":"RF Engle","year":"1982","journal-title":"Econometrica: Journal of the Econometric Society"},{"issue":"3","key":"ref54","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/0304-4076(86)90063-1","article-title":"Generalized autoregressive conditional heteroskedasticity","volume":"31","author":"T Bollerslev","year":"1986","journal-title":"Journal of econometrics"},{"issue":"1","key":"ref55","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1093\/biomet\/68.1.189","article-title":"Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model","volume":"68","author":"V Haggan","year":"1981","journal-title":"Biometrika"},{"issue":"1","key":"ref56","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0304-4149(95)00090-9","article-title":"On the Kullback-Leibler information divergence of locally stationary processes","volume":"62","author":"R Dahlhaus","year":"1996","journal-title":"Stochastic Processes and their Applications"},{"issue":"4","key":"ref57","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1109\/TASSP.1983.1164152","article-title":"Time-dependent ARMA modeling of nonstationary signals","volume":"31","author":"Y Grenier","year":"1983","journal-title":"Acoustics, Speech and Signal Processing, IEEE Transactions on"},{"key":"ref58","article-title":"Digital signal processing","author":"JG Proakis","year":"1996"},{"key":"ref59","doi-asserted-by":"crossref","unstructured":"Akaike H. Information theory and an extension of the maximum likelihood principle. In: Selected Papers of Hirotugu Akaike. Springer; 1998. p. 199\u2013213.","DOI":"10.1007\/978-1-4612-1694-0_15"},{"issue":"2","key":"ref60","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"G Schwarz","year":"1978","journal-title":"Ann Stat"},{"key":"ref61","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1214\/09-SS054","article-title":"A survey of cross-validation procedures for model selection","volume":"4","author":"S Arlot","year":"2010","journal-title":"Statistics surveys"},{"issue":"11","key":"ref62","doi-asserted-by":"crossref","first-page":"1380","DOI":"10.1109\/PROC.1981.12184","article-title":"Spectrum analysis\u2014a modern perspective","volume":"69","author":"SM Kay","year":"1981","journal-title":"Proceedings of the IEEE"},{"issue":"3","key":"ref63","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1111\/j.1365-246X.1973.tb03424.x","article-title":"The retrieval of harmonics from a covariance function","volume":"33","author":"VF Pisarenko","year":"1973","journal-title":"Geophysical Journal International"},{"issue":"3","key":"ref64","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"R Schmidt","year":"1986","journal-title":"IEEE transactions on antennas and propagation"},{"key":"ref65","doi-asserted-by":"crossref","unstructured":"Marple L. Resolution of conventional Fourier, autoregressive, and special ARMA methods of spectrum analysis. In: Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP\u201977. vol. 2. IEEE; 1977. p. 74\u201377.","DOI":"10.1109\/ICASSP.1977.1170219"},{"key":"ref66","first-page":"383","article-title":"Maximum entropy spectral analysis","volume":"15","author":"J Ables","year":"1974","journal-title":"Astronomy and Astrophysics Supplement Series"},{"key":"ref67","doi-asserted-by":"crossref","first-page":"16","DOI":"10.3389\/fninf.2015.00016","article-title":"The PREP pipeline: standardized preprocessing for large-scale EEG analysis","volume":"9","author":"N Bigdely-Shamlo","year":"2015","journal-title":"Frontiers in neuroinformatics"},{"key":"ref68","doi-asserted-by":"crossref","unstructured":"Cole SR, Peterson EJ, van der Meij R, de Hemptinne C, Starr PA, Voytek B. Nonsinusoidal oscillations underlie pathological phase-amplitude coupling in the motor cortex in Parkinson\u2019s disease. bioRxiv. 2016; p. 049304.","DOI":"10.1101\/049304"},{"issue":"2","key":"ref69","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1103\/PhysRevLett.85.461","article-title":"Measuring information transfer","volume":"85","author":"T Schreiber","year":"2000","journal-title":"Physical review letters"},{"issue":"2","key":"ref70","doi-asserted-by":"crossref","first-page":"e55809","DOI":"10.1371\/journal.pone.0055809","article-title":"Measuring information-transfer delays","volume":"8","author":"M Wibral","year":"2013","journal-title":"PloS one"},{"issue":"12","key":"ref71","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1016\/j.cub.2015.04.049","article-title":"Frontal top-down signals increase coupling of auditory low-frequency oscillations to continuous speech in human listeners","volume":"25","author":"H Park","year":"2015","journal-title":"Current Biology"},{"issue":"3","key":"ref72","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s10827-010-0236-5","article-title":"Causal relationships between frequency bands of extracellular signals in visual cortex revealed by an information theoretic analysis","volume":"29","author":"M Besserve","year":"2010","journal-title":"Journal of computational neuroscience"},{"key":"ref73","doi-asserted-by":"crossref","first-page":"424","DOI":"10.2307\/1912791","article-title":"Investigating causal relations by econometric models and cross-spectral methods","author":"CW Granger","year":"1969","journal-title":"Econometrica: Journal of the Econometric Society"},{"issue":"23","key":"ref74","doi-asserted-by":"crossref","first-page":"238701","DOI":"10.1103\/PhysRevLett.103.238701","article-title":"Granger causality and transfer entropy are equivalent for Gaussian variables","volume":"103","author":"L Barnett","year":"2009","journal-title":"Physical review letters"},{"key":"ref75","unstructured":"Nolte G, Ziehe A, Kr\u00e4mer N, Popescu F, M\u00fcller KR. Comparison of Granger Causality and Phase Slope Index. In: NIPS Causality: Objectives and Assessment; 2010. p. 267\u2013276."},{"key":"ref76","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.neuroimage.2015.05.044","article-title":"Measuring directionality between neuronal oscillations of different frequencies","volume":"118","author":"H Jiang","year":"2015","journal-title":"Neuroimage"},{"key":"ref77","doi-asserted-by":"crossref","first-page":"234101","DOI":"10.1103\/PhysRevLett.100.234101","article-title":"Robustly Estimating the Flow Direction of Information in Complex Physical Systems","volume":"100","author":"G Nolte","year":"2008","journal-title":"Physical Review Letters"},{"key":"ref78","doi-asserted-by":"crossref","first-page":"13920","DOI":"10.1038\/ncomms13920","article-title":"Updating temporal expectancy of an aversive event engages striatal plasticity under amygdala control","volume":"8","author":"G Dall\u00e9rac","year":"2017","journal-title":"Nature Communications"},{"issue":"2","key":"ref79","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1038\/nn.3905","article-title":"NeuroGrid: recording action potentials from the surface of the brain","volume":"18","author":"D Khodagholy","year":"2015","journal-title":"Nature neuroscience"},{"key":"ref80","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1214\/aos\/1176350057","article-title":"The use of subseries values for estimating the variance of a general statistic from a stationary sequence","author":"E Carlstein","year":"1986","journal-title":"The Annals of Statistics"},{"issue":"2","key":"ref81","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1038\/nrn2979","article-title":"The role of phase synchronization in memory processes","volume":"12","author":"J Fell","year":"2011","journal-title":"Nature reviews Neuroscience"},{"issue":"6","key":"ref82","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/hipo.22255","article-title":"Medial prefrontal theta phase coupling during spatial memory retrieval","volume":"24","author":"R Kaplan","year":"2014","journal-title":"Hippocampus"},{"key":"ref83","doi-asserted-by":"crossref","first-page":"78","DOI":"10.3389\/fncom.2013.00078","article-title":"Cross-frequency coupling in real and virtual brain networks","volume":"7","author":"V Jirsa","year":"2013","journal-title":"Frontiers in computational neuroscience"},{"key":"ref84","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.neuroimage.2015.01.054","article-title":"The brain\u2019s resting-state activity is shaped by synchronized cross-frequency coupling of neural oscillations","volume":"111","author":"E Florin","year":"2015","journal-title":"NeuroImage"},{"key":"ref85","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.neuroimage.2014.01.049","article-title":"Inter-and intra-individual variability in alpha peak frequency","volume":"92","author":"S Haegens","year":"2014","journal-title":"Neuroimage"},{"issue":"12","key":"ref86","doi-asserted-by":"crossref","first-page":"e3990","DOI":"10.1371\/journal.pone.0003990","article-title":"Gamma power is phase-locked to posterior alpha activity","volume":"3","author":"D Osipova","year":"2008","journal-title":"PloS one"},{"issue":"45","key":"ref87","doi-asserted-by":"crossref","first-page":"17827","DOI":"10.1523\/JNEUROSCI.5778-12.2013","article-title":"The phase of thalamic alpha activity modulates cortical gamma-band activity: evidence from resting- state MEG recordings","volume":"33","author":"F Roux","year":"2013","journal-title":"Journal of Neuroscience"},{"key":"ref88","doi-asserted-by":"crossref","first-page":"191","DOI":"10.3389\/fnhum.2010.00191","article-title":"Shifts in gamma phase\u2013amplitude coupling frequency from theta to alpha over posterior cortex during visual tasks","volume":"4","author":"B Voytek","year":"2010","journal-title":"Frontiers in human neuroscience"},{"issue":"5508","key":"ref89","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1126\/science.1055465","article-title":"Modulation of oscillatory neuronal synchronization by selective visual attention","volume":"291","author":"P Fries","year":"2001","journal-title":"Science"},{"issue":"10","key":"ref90","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.tics.2005.08.011","article-title":"A mechanism for cognitive dynamics: neuronal communication through neuronal coherence","volume":"9","author":"P Fries","year":"2005","journal-title":"Trends in cognitive sciences"},{"key":"ref91","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.conb.2014.11.001","article-title":"Communication through coherence with inter-areal delays","volume":"31","author":"AM Bastos","year":"2015","journal-title":"Current opinion in neurobiology"},{"key":"ref92","doi-asserted-by":"crossref","DOI":"10.3389\/fncom.2016.00087","article-title":"Neuronal oscillations with non-sinusoidal morphology produce spurious phase-to-amplitude coupling and directionality","volume":"10","author":"D Lozano-Soldevilla","year":"2016","journal-title":"Frontiers in Computational Neuroscience"},{"issue":"1","key":"ref93","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.clinph.2015.04.290","article-title":"High frequency oscillations and spikes: separating real HFOs from false oscillations","volume":"127","author":"M Amiri","year":"2016","journal-title":"Clinical Neurophysiology"},{"issue":"12","key":"ref94","doi-asserted-by":"crossref","first-page":"e0167351","DOI":"10.1371\/journal.pone.0167351","article-title":"Non-sinusoidal activity can produce cross-frequency coupling in cortical signals in the absence of functional interaction between neural sources","volume":"11","author":"EM Gerber","year":"2016","journal-title":"PloS one"},{"key":"ref95","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.neuroimage.2017.01.001","article-title":"Dual origins of measured phase-amplitude coupling reveal distinct neural mechanisms underlying episodic memory in the human cortex","volume":"148","author":"AP Vaz","year":"2017","journal-title":"Neuroimage"},{"key":"ref96","article-title":"Discriminating valid from spurious indices of phase- amplitude coupling","author":"O Jensen","year":"2016","journal-title":"eneuro"},{"key":"ref97","doi-asserted-by":"crossref","first-page":"e21792","DOI":"10.7554\/eLife.21792","article-title":"Multivariate cross-frequency coupling via generalized eigendecomposition","volume":"6","author":"MX Cohen","year":"2017","journal-title":"eLife"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1005893","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2017,12,21]],"date-time":"2017-12-21T00:00:00Z","timestamp":1513814400000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1005893","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,8]],"date-time":"2020-05-08T21:43:14Z","timestamp":1588974194000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1005893"}},"subtitle":[],"editor":[{"given":"Francesco P.","family":"Battaglia","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2017,12,11]]},"references-count":97,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2017,12,11]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1005893","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/159731","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,11]]}}}