In recent decades, neuroscience has advanced with increasingly sophisticated strategies for recording and analysing brain activity, enabling detailed investigations into the roles of functional units, such as individual neurons, brain regions and their interactions. Recently, new strategies for the investigation of cognitive functions regard the study of higher order interactions-that is, the interactions involving more than two brain regions or neurons. Although methods focusing on individual units and their interactions at various levels offer valuable and often complementary insights, each approach comes with its own set of limitations. In this context, a conceptual map to categorize and locate diverse strategies could be crucial to orient researchers and guide future research directions. To this end, we define the spectrum of orders of interaction, namely, a framework that categorizes the interactions among neurons or brain regions based on the number of elements involved in these interactions. We use a simulation of a toy model and a few case studies to demonstrate the utility and the challenges of the exploration of the spectrum. We conclude by proposing future research directions aimed at enhancing our understanding of brain function and cognition through a more nuanced methodological framework.

Center for Psychedelic Research and Centre for Complexity Science Department of Brain Science Imperial College London London UK

Centre for Eudaimonia and Human Flourishing University of Oxford Oxford UK

Department of Computing Imperial College London London UK

Department of Philosophy Communication and Performing Arts Roma Tre University Rome Italy

Department of Physics Northeastern University Boston Massachusetts USA

Department of Psychology School of Biological and Behavioural Sciences Queen Mary University of London London UK

Department of Psychology University of Cambridge Cambridge UK

Division of Psychology and Language Sciences University College London London UK

DreamTeam Paris Brain Institute Paris France

Institut de Neurosciences de la Timone Aix Marseille Université UMR 7289 CNRS Marseille France

Institut de Neurosciences Des Systèmes Aix Marseille Université UMR 1106 Marseille France

Institute for Advanced Study Aix Marseille University Marseille France

Laboratoire de Neurosciences Cognitives et Adaptatives UMR 7364 Strasbourg France

NPLab CENTAI Institute Turin Italy

NPLab Network Science Institute Northeastern University London London UK

PICNIC lab Paris Brain Institute Paris France

Principles of Intelligent Behavior in Biological and Social Systems Prague Czechia

Sussex Centre for Consciousness Science and Sussex AI Department of Informatics University of Sussex Brighton UK

Zobrazit více v PubMed

Abeles, M., and G. L. Gerstein. 1988. “Detecting Spatiotemporal Firing Patterns Among Simultaneously Recorded Single Neurons.” Journal of Neurophysiology 60, no. 3: 909–924.

Akarca, D., A. W. E. Dunn, P. J. Hornauer, et al. 2022. Homophilic Wiring Principles Underpin Neuronal Network Topology In Vitro. bioRxiv.

Albantakis, L., and G. Tononi. 2019. “Causal Composition: Structural Differences Among Dynamically Equivalent Systems.” Entropy 21, no. 10: 989.

Anderson, J. S., J. A. Nielsen, A. L. Froehlich, et al. 2011. “Functional Connectivity Magnetic Resonance Imaging Classification of Autism.” Brain: A Journal of Neurology 134, no. Pt 12: 3742–3754.

Anderson, M. L., J. Kinnison, and L. Pessoa. 2013. “Describing Functional Diversity of Brain Regions and Brain Networks.” NeuroImage 73: 50–58.

Baeg, E. H., Y. B. Kim, J. Kim, J.‐W. Ghim, J. J. Kim, and M. W. Jung. 2007. “Learning‐Induced Enduring Changes in Functional Connectivity Among Prefrontal Cortical Neurons.” Journal of Neuroscience 27, no. 4: 909–918.

Barabási, A.‐L. 2011. “The Network Takeover.” Nature Physics 8, no. 1: 14–16.

Barlow, H. B. 1972. “Single Units and Sensation: A Neuron Doctrine for Perceptual Psychology?” Perception 1, no. 4: 371–394.

Bassett, D. S., and O. Sporns. 2017. “Network Neuroscience.” Nature Neuroscience 20, no. 3: 353–364.

Bassett, D. S., and E. Bullmore. 2006. “Small‐World Brain Networks.” Neuroscientist 12, no. 6: 512–523.

Battiston, F., E. Amico, A. Barrat, et al. 2021. “The Physics of Higher‐Order Interactions in Complex Systems.” Nature Physics 17, no. 10: 1093–1098.

Battiston, F., G. Cencetti, I. Iacopini, et al. 2020. “Networks Beyond Pairwise Interactions: Structure and Dynamics.” Physics Reports 874: 1–92.

Baudot, P., M. Tapia, D. Bennequin, and J.‐M. Goaillard. 2019. “Topological Information Data Analysis.” Entropy 21, no. 9: 869.

Beisteiner, R., E. Matt, C. Fan, et al. 2020. “Transcranial Pulse Stimulation With Ultrasound in Alzheimer's Disease—A New Navigated Focal Brain Therapy.” Advanced Science 7, no. 3: 1902583.

Berlim, M. T., F. van den Eynde, S. Tovar‐Perdomo, and Z. J. Daskalakis. 2014. “Response, Remission and Drop‐Out Rates Following High‐Frequency Repetitive Transcranial Magnetic Stimulation (rTMS) for Treating Major Depression: A Systematic Review and Meta‐Analysis of Randomized, Double‐Blind and Sham‐Controlled Trials.” Psychological Medicine 44, no. 2: 225–239.

Berlim, M. T., F. Van den Eynde, and Z. Jeff Daskalakis. 2013. “Clinically Meaningful Efficacy and Acceptability of Low‐Frequency Repetitive Transcranial Magnetic Stimulation (rTMS) for Treating Primary Major Depression: A Meta‐Analysis of Randomized, Double‐Blind and Sham‐Controlled Trials.” Neuropsychopharmacology 38, no. 4: 543–551.

Bickle, J. 2006. “Reducing Mind to Molecular Pathways: Explicating the Reductionism Implicit in Current Cellular and Molecular Neuroscience.” Synthese 151, no. 3: 411–434.

Bickle, J. 2015. “Marr and Reductionism.” Topics in Cognitive Science 7, no. 2: 299–311.

Boggio, P. S., C. A. Valasek, C. Campanhã, et al. 2011. “Non‐Invasive Brain Stimulation to Assess and Modulate Neuroplasticity in Alzheimer's Disease.” Neuropsychological Rehabilitation 21, no. 5: 703–716.

Brinker, S. T., F. Preiswerk, P. J. White, T. Y. Mariano, N. J. McDannold, and E. J. Bubrick. 2020. “Focused Ultrasound Platform for Investigating Therapeutic Neuromodulation Across the Human Hippocampus.” Ultrasound in Medicine & Biology 46, no. 5: 1270–1274.

Brown, S. D., & Vranesic, Z. G. (2000). Fundamentals of Digital Logic With VHDL Design.

Buzsáki, G. 2010. “Neural Syntax: Cell Assemblies, Synapsembles, and Readers.” Neuron 68, no. 3: 362–385.

Chambers, B., and J. N. MacLean. 2016. “Higher‐Order Synaptic Interactions Coordinate Dynamics in Recurrent Networks.” PLoS Computational Biology 12, no. 8: e1005078.

Chung, M. K., J. L. Hanson, J. Ye, R. J. Davidson, and S. D. Pollak. 2015. “Persistent Homology in Sparse Regression and Its Application to Brain Morphometry.” IEEE Transactions on Medical Imaging 34, no. 9: 1928–1939.

Craver, C. F. 2016. “The Explanatory Power of Network Models.” Philosophy of Science 83, no. 5: 698–709.

Curto, C., and V. Itskov. 2008. “Cell Groups Reveal Structure of Stimulus Space.” PLoS Computational Biology 4, no. 10: e1000205.

Damoiseaux, J. S., and M. D. Greicius. 2009. “Greater Than the Sum of Its Parts: A Review of Studies Combining Structural Connectivity and Resting‐State Functional Connectivity.” Brain Structure & Function 213, no. 6: 525–533.

Darmani, G., T. O. Bergmann, K. Butts Pauly, et al. 2022. “Non‐Invasive Transcranial Ultrasound Stimulation for Neuromodulation.” Clinical Neurophysiology 135: 51–73.

Darrow, D. P. 2019. “Focused Ultrasound for Neuromodulation.” Neurotherapeutics 16, no. 1: 88–99.

de Jong, S., M. P. M. Boks, T. F. Fuller, et al. 2012. “A Gene Co‐Expression Network in Whole Blood of Schizophrenia Patients Is Independent of Antipsychotic‐Use and Enriched for Brain‐Expressed Genes.” PLoS ONE 7, no. 6: e39498.

Fisher, R. S., and A. L. Velasco. 2014. “Electrical Brain Stimulation for Epilepsy.” Nature Reviews. Neurology 10, no. 5: 261–270.

Folloni, D., L. Verhagen, R. B. Mars, et al. 2019. “Manipulation of Subcortical and Deep Cortical Activity in the Primate Brain Using Transcranial Focused Ultrasound Stimulation.” Neuron 101, no. 6: 1109–1116.e5.

Freedman, D. J., M. Riesenhuber, T. Poggio, and E. K. Miller. 2001. “Categorical Representation of Visual Stimuli in the Primate Prefrontal Cortex.” Science 291, no. 5502: 312–316.

Friston, K. J., A. P. Holmes, J. B. Poline, et al. 1995. “Analysis of fMRI Time‐Series Revisited.” NeuroImage 2, no. 1: 45–53.

Furman, D. J., J. P. Hamilton, and I. H. Gotlib. 2011. “Frontostriatal Functional Connectivity in Major Depressive Disorder.” Biology of Mood & Anxiety Disorders 1, no. 1: 11.

Gansel, K. S., and W. Singer. 2012. “Detecting Multineuronal Temporal Patterns in Parallel Spike Trains.” Frontiers in Neuroinformatics 6: 18.

Gardner, R. J., E. Hermansen, M. Pachitariu, et al. 2022. “Toroidal Topology of Population Activity in Grid Cells.” Nature 602, no. 7895: 123–128.

Gatica, M., C. Atkinson‐Clement, P. A. M. Mediano, et al. 2024. “Transcranial Ultrasound Stimulation Effect in the Redundant and Synergistic Networks Consistent Across Macaques.” Network Neuroscience 2024: 1032–1050. https://doi.org/10.1162/netn_a_00388.

Gatica, M., R. Cofré, P. A. M. Mediano, et al. 2021. “High‐Order Interdependencies in the Aging Brain.” Brain Connectivity 11, no. 9: 734–744.

Gatica, M., F. E. Rosas, A. M. Mediano P, et al. 2022. “High‐Order Functional Redundancy in Ageing Explained via Alterations in the Connectome in a Whole‐Brain Model.” PLoS Computational Biology 18, no. 9: e1010431.

Gelens, F., J. Äijälä, L. Roberts, et al. 2024. “Distributed Representations of Prediction Error Signals Across the Cortical Hierarchy Are Synergistic.” Nature Communications 15, no. 1: 3941.

Ghrist, R. 2007. “Barcodes: The Persistent Topology of Data.” Bulletin of the American Mathematical Society 45, no. 01: 61–76.

Giusti, C., R. Ghrist, and D. S. Bassett. 2016. “Two's Company, Three (or More) Is a Simplex: Algebraic‐Topological Tools for Understanding Higher‐Order Structure in Neural Data.” Journal of Computational Neuroscience 41, no. 1: 1–14.

Giusti, C., E. Pastalkova, C. Curto, and V. Itskov. 2015. “Clique Topology Reveals Intrinsic Geometric Structure in Neural Correlations.” Proceedings of the National Academy of Sciences of the United States of America 112, no. 44: 13455–13460.

Glickstein, M. 2006. “Golgi and Cajal: The Neuron Doctrine and the 100th Anniversary of the 1906 Nobel Prize.” Current Biology 16, no. 5: R147–R151.

Grasso, M., L. Albantakis, J. P. Lang, and G. Tononi. 2021. “Causal Reductionism and Causal Structures.” Nature Neuroscience 24, no. 10: 1348–1355.

Greenblatt, S. H. 1995. “Phrenology in the Science and Culture of the 19th Century.” Neurosurgery 37, no. 4: 790–804.

Greicius, M. D., B. Krasnow, A. L. Reiss, and V. Menon. 2003. “Functional Connectivity in the Resting Brain: A Network Analysis of the Default Mode Hypothesis.” Proceedings of the National Academy of Sciences of the United States of America 100, no. 1: 253–258.

Gütig, R., A. Aertsen, and S. Rotter. 2003. “Analysis of Higher‐Order Neuronal Interactions Based on Conditional Inference.” Biological Cybernetics 88, no. 5: 352–359.

Han, Y., H. Zhu, Y. Zhao, et al. 2019. “The Effect of Acute Glutamate Treatment on the Functional Connectivity and Network Topology of Cortical Cultures.” Medical Engineering & Physics 71: 91–97.

Harris, K. D., J. Csicsvari, H. Hirase, G. Dragoi, and G. Buzsáki. 2003. “Organization of Cell Assemblies in the Hippocampus.” Nature 424, no. 6948: 552–556.

Hebart, M. N., and C. I. Baker. 2018. “Deconstructing Multivariate Decoding for the Study of Brain Function.” NeuroImage 180, no. Pt A: 4–18.

Hebb, D. O. 1949. “The Organization of Behavior: A Neuropsychological Theory.” American Journal of Psychology 63, no. 4: 633.

Herzog, R., P. A. M. Mediano, F. E. Rosas, et al. 2023. “A Whole‐Brain Model of the Neural Entropy Increase Elicited by Psychedelic Drugs.” Scientific Reports 13, no. 1: 6244.

Herzog, R., F. E. Rosas, R. Whelan, et al. 2022. “Genuine High‐Order Interactions in Brain Networks and Neurodegeneration.” Neurobiology of Disease 175: 105918.

Hong, S.‐B., A. Zalesky, L. Cocchi, et al. 2013. “Decreased Functional Brain Connectivity in Adolescents With Internet Addiction.” PLoS ONE 8, no. 2: e57831.

Hubel, D. H., and T. N. Wiesel. 1959. “Receptive Fields of Single Neurones in the Cat's Striate Cortex.” Journal of Physiology 148: 574–591.

Ince, R. A. A., F. Montani, E. Arabzadeh, M. E. Diamond, and S. Panzeri. 2009. “On the Presence of High‐Order Interactions Among Somatosensory Neurons and Their Effect on Information Transmission.” Journal of Physics: Conference Series 197: 012013.

Jorgenson, L. A., W. T. Newsome, D. J. Anderson, et al. 2015. “The BRAIN Initiative: Developing Technology to Catalyse Neuroscience Discovery.” Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 370, no. 1668.

Keene, A. C., and S. Waddell. 2007. “Drosophila Olfactory Memory: Single Genes to Complex Neural Circuits.” Nature Reviews. Neuroscience 8, no. 5: 341–354.

Kennedy, B. W., M. Quinton, and J. A. van Arendonk. 1992. “Estimation of Effects of Single Genes on Quantitative Traits.” Journal of Animal Science 70, no. 7: 2000–2012.

Levelt, W. J. M. 2016. “Localism Versus Holism. Historical Origins of Studying Language in the Brain.” Sartoniana 29: 37–60.

Liao, X., A. V. Vasilakos, and Y. He. 2017. “Small‐World Human Brain Networks: Perspectives and Challenges.” Neuroscience and Biobehavioral Reviews 77: 286–300.

Luppi, A. I., P. A. M. Mediano, F. E. Rosas, et al. 2022. “A Synergistic Core for Human Brain Evolution and Cognition.” Nature Neuroscience 25, no. 6: 771–782.

Luppi, A. I., F. E. Rosas, P. A. M. Mediano, D. K. Menon, and E. A. Stamatakis. 2024. “Information Decomposition and the Informational Architecture of the Brain.” Trends in Cognitive Sciences 28, no. 4: 352–368.

Martignon, L., H. Von Hasseln, S. Grün, A. Aertsen, and G. Palm. 1995. “Detecting Higher‐Order Interactions Among the Spiking Events in a Group of Neurons.” Biological Cybernetics 73, no. 1: 69–81.

McKenzie, A. T., M. Wang, M. E. Hauberg, et al. 2018. “Brain Cell Type Specific Gene Expression and Co‐Expression Network Architectures.” Scientific Reports 8, no. 1: 8868.

Montangie, L., and F. Montani. 2017. “Higher‐Order Correlations in Common Input Shapes the Output Spiking Activity of a Neural Population.” Physica A: Statistical Mechanics and its Applications 471: 845–861.

Morowitz, H. J. 2018. “Near Decomposability and Complexity: How a Mind Resides in a Brain.” In The Mind, the Brain, and Complex Adaptive Systems, edited by H. Morowitz and J. L. Singer, 25–44. Oxfordshire: Routledge.

Nazarova, M., and E. Blagovechtchenski. 2015. “Modern Brain Mapping—What Do We Map Nowadays?” Frontiers in Psychiatry 6: 89.

Nelson, R. J., and K. A. Young. 1998. “Behavior in Mice With Targeted Disruption of Single Genes.” Neuroscience and Biobehavioral Reviews 22, no. 3: 453–462.

Neri, M., C. Runfola, N. A. G. te Rietmolen, et al 2023. Neuronal Avalanches in Naturalistic Speech and Music Listening. bioRxiv.

Northoff, G. 2014. Localization Versus Holism and Intrinsic Versus Extrinsic Views of the Brain: A Neurophilosophical Approach. Torino: Minerva Psichiatrica.

Nurisso, M., M. Morandini, M. Lucas, and F. Vaccarino. 2024. Higher‐Order Laplacian Renormalization. arXiv Preprint arXiv.

O'Doherty, J., M. L. Kringelbach, E. T. Rolls, J. Hornak, and C. Andrews. 2001. “Abstract Reward and Punishment Representations in the Human Orbitofrontal Cortex.” Nature Neuroscience 4, no. 1: 95–102.

O'Keefe, J., and J. Dostrovsky. 1971. “The Hippocampus as a Spatial Map: Preliminary Evidence From Unit Activity in the Freely‐Moving Rat.” Brain Research 34, no. 1: 171–175.

Panzeri, S., M. Moroni, H. Safaai, and C. D. Harvey. 2022. “The Structures and Functions of Correlations in Neural Population Codes.” Nature Reviews. Neuroscience 23, no. 9: 551–567.

Parastesh, F., M. Mehrabbeik, K. Rajagopal, S. Jafari, and M. Perc. 2022. “Synchronization in Hindmarsh–Rose Neurons Subject to Higher‐Order Interactions.” Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 1: 013125.

Patania, A., F. Vaccarino, and G. Petri. 2017. “Topological Analysis of Data.” EPJ Data Science 6, no. 1: 7.

Petri, G., P. Expert, F. Turkheimer, et al. 2014. “Homological Scaffolds of Brain Functional Networks.” Journal of the Royal Society, Interface 11, no. 101: 20140873.

Poli, D., V. P. Pastore, and P. Massobrio. 2015. “Functional Connectivity in In Vitro Neuronal Assemblies.” Frontiers in Neural Circuits 9: 57.

Priesemann, V., M. Valderrama, M. Wibral, and M. Le Van Quyen. 2013. “Neuronal Avalanches Differ From Wakefulness to Deep Sleep—Evidence From Intracranial Depth Recordings in Humans.” PLoS Computational Biology 9, no. 3: e1002985.

Quiroga, R. Q., L. Reddy, G. Kreiman, C. Koch, and I. Fried. 2005. “Invariant Visual Representation by Single Neurons in the Human Brain.” Nature 435, no. 7045: 1102–1107.

Ramasamy, M., S. Devarajan, S. Kumarasamy, and K. Rajagopal. 2022. “Effect of Higher‐Order Interactions on Synchronization of Neuron Models With Electromagnetic Induction.” Applied Mathematics and Computation 434: 127447.

Reznik, S. J., J. L. Sanguinetti, W. J. Tyler, C. Daft, and J. J. B. Allen. 2020. “A Double‐Blind Pilot Study of Transcranial Ultrasound (TUS) as a Five‐Day Intervention: TUS Mitigates Worry Among Depressed Participants.” Neurology, Psychiatry and Brain Research 37: 60–66.

Ritchie, J. B., D. M. Kaplan, and C. Klein. 2019. “Decoding the Brain: Neural Representation and the Limits of Multivariate Pattern Analysis in Cognitive Neuroscience.” British Journal for the Philosophy of Science 70, no. 2: 581–607.

Robiglio, T., Neri, M., Coppes, D., & Agostinelli, C. (2024). Synergistic Signatures of Group Mechanisms in Higher‐Order Systems. arXiv Preprint arXiv.

Rosas, F. E., P. A. M. Mediano, and M. Gastpar. 2024. Characterising Directed and Undirected Metrics of High‐Order Interdependence. arXiv Preprint arXiv:2404.07140.

Rosas, F. E., P. A. M. Mediano, M. Gastpar, and H. J. Jensen. 2019. “Quantifying High‐Order Interdependencies via Multivariate Extensions of the Mutual Information.” Physical Review E 100, no. 3–1: 032305.

Rosas, F. E., P. A. M. Mediano, A. I. Luppi, et al. 2022. “Disentangling High‐Order Mechanisms and High‐Order Behaviours in Complex Systems.” Nature Physics 18: 476–477.

Ross, L. N., and D. S. Bassett. 2024. “Causation in Neuroscience: Keeping Mechanism Meaningful.” Nature Reviews. Neuroscience 25, no. 2: 81–90.

Santoro, A., F. Battiston, G. Petri, and E. Amico. 2023. “Higher‐Order Organization of Multivariate Time Series.” Nature Physics 19, no. 2: 221–229.

Santos, F. A. N., P. K. B. Tewarie, P. Baudot, et al. 2023. Emergence of High‐Order Functional Hubs in the Human Brain. bioRxiv.

Sejnowski, T. J., P. S. Churchland, and J. A. Movshon. 2014. “Putting Big Data to Good Use in Neuroscience.” Nature Neuroscience 17, no. 11: 1440–1441.

Shannon, C. E. 1948. “A Mathematical Theory of Communication.” Bell System Technical Journal 27, no. 3: 379–423.

Shimazaki, H., S.‐I. Amari, E. N. Brown, and S. Grün. 2012. “State‐Space Analysis of Time‐Varying Higher‐Order Spike Correlation for Multiple Neural Spike Train Data.” PLoS Computational Biology 8, no. 3: e1002385.

Shimazaki, H., K. Sadeghi, T. Ishikawa, Y. Ikegaya, and T. Toyoizumi. 2015. “Simultaneous Silence Organizes Structured Higher‐Order Interactions in Neural Populations.” Scientific Reports 5: 9821.

Simon, H. A. 1962. “The Architecture of Complexity.” Proceedings of the American Philosophical Society 106, no. 6: 467–482.

Sporns, O. 2014. “Network Neuroscience.” In The Future of the Brain: Essays by the World's Leading Neuroscientists, edited by G. Marcus and J. Freeman, 90–99. Princeton, NJ: Princeton University Press. https://doi.org/10.1515/9781400851935‐012.

Sporns, O. 2016. Networks of the Brain. Cambridge, UK: MIT Press.

Sporns, O., and R. F. Betzel. 2016. “Modular Brain Networks.” Annual Review of Psychology 67: 613–640.

Stolz, B. J., T. Emerson, S. Nahkuri, M. A. Porter, and H. A. Harrington. 2021. “Topological Data Analysis of Task‐Based fMRI Data From Experiments on Schizophrenia.” Journal of Physics: Complexity 2, no. 3: 035006.

Stramaglia, S., T. Scagliarini, B. C. Daniels, and D. Marinazzo. 2020. “Quantifying Dynamical High‐Order Interdependencies From the O‐Information: An Application to Neural Spiking Dynamics.” Frontiers in Physiology 11: 595736.

Timme, N. M., and C. Lapish. 2018. “A Tutorial for Information Theory in Neuroscience.” eNeuro 5, no. 3: ENEURO.0052‐18.2018.

Tramacere, A. 2024. “About Leaving the Neuroscience Lab.” In Advances in Neurophilosophy, 1–240. London: Bloomsbury Publishing.

Tramacere, A. 2021. “Triangulating Tools in the Messiness of Cognitive Neuroscience.” In The Tools of Neuroscience Experiment: Philosophical and Scientific Perspectives, 176–194. New York: Routledge.

Tramacere, A., and J. Bickle. 2024. “Neuroepigenetics in Philosophical Focus: A Critical Analysis of the Philosophy of Mechanisms.” Biological Theory 19, no. 1: 56–71.

Tufail, Y., A. Yoshihiro, S. Pati, M. M. Li, and W. J. Tyler. 2011. “Ultrasonic Neuromodulation by Brain Stimulation With Transcranial Ultrasound.” Nature Protocols 6, no. 9: 1453–1470.

Turkheimer, F. E., F. E. Rosas, O. Dipasquale, et al. 2022. “A Complex Systems Perspective on Neuroimaging Studies of Behavior and Its Disorders.” Neuroscientist 28, no. 4: 382–399.

Varley, T. F., M. Pope, J. Faskowitz, and O. Sporns. 2023. “Multivariate Information Theory Uncovers Synergistic Subsystems of the Human Cerebral Cortex.” Communications Biology 6, no. 1: 451.

Varley, T. F., M. Pope, M. G. Puxeddu, J. Faskowitz, and O. Sporns. 2023. “Partial Entropy Decomposition Reveals Higher‐Order Information Structures in Human Brain Activity.” Proceedings of the National Academy of Sciences of the United States of America 120, no. 30: e2300888120.

Varley, T. F., O. Sporns, S. Schaffelhofer, H. Scherberger, and B. Dann. 2023. “Information‐Processing Dynamics in Neural Networks of Macaque Cerebral Cortex Reflect Cognitive State and Behavior.” Proceedings of the National Academy of Sciences of the United States of America 120, no. 2: e2207677120.

Varley, T. F., O. Sporns, N. J. Stevenson, et al. 2024. Emergence of a Synergistic Scaffold in the Brains of Human Infants. bioRxiv.

Verhagen, L., C. Gallea, D. Folloni, et al. 2019. “Offline Impact of Transcranial Focused Ultrasound on Cortical Activation in Primates.” eLife 8.

Wang, K., M. Liang, L. Wang, et al. 2007. “Altered Functional Connectivity in Early Alzheimer's Disease: A Resting‐State fMRI Study.” Human Brain Mapping 28, no. 10: 967–978.

Wasserman, L. 2018. “Topological Data Analysis.” Annual Review of Statistics and Its Application 5, no. 1: 501–532.

Weaver, I. C. G., N. Cervoni, F. A. Champagne, et al. 2004. “Epigenetic Programming by Maternal Behavior.” Nature Neuroscience 7, no. 8: 847–854.

Williams, P. L., & Beer, R. D. 2010. Nonnegative Decomposition of Multivariate Information. arXiv Preprint arXiv:1004.2515.

Yu, S., H. Yang, H. Nakahara, G. S. Santos, D. Nikolić, and D. Plenz. 2011. “Higher‐Order Interactions Characterized in Cortical Activity.” Journal of Neuroscience 31, no. 48: 17514–17526.

Zednik, C. 2019. “Models and Mechanisms in Network Neuroscience.” Philosophical Psychology 32, no. 1: 23–51.

Zhou, X., N. Ma, B. Song, et al. 2021. “Optimal Organization of Functional Connectivity Networks for Segregation and Integration With Large‐Scale Critical Dynamics in Human Brains.” Frontiers in Computational Neuroscience 15: 641335.

Zomorodian, A., and G. Carlsson. 2004. “Computing Persistent Homology.” In Proceedings of the Twentieth Annual Symposium on Computational Geometry—SCG '04, 347. New York, New York, USA: ACM Press.