Practical Measures of Integrated Information for Time-Series Data
Open accessAbstract
A recent measure of 'integrated information', Φ(DM), quantifies the extent to which a system generates more information than the sum of its parts as it transitions between states, possibly reflecting levels of consciousness generated by neural systems. However, Φ(DM) is defined only for discrete Markov systems, which are unusual in biology; as a result, Φ(DM) can rarely be measured in practice. Here, we describe two new measures, Φ(E) and Φ(AR), that overcome these limitations and are easy to apply to time-series data. We use simulations to demonstrate the in-practice applicability of our measures, and to explore their properties. Our results provide new opportunities for examining information integration in real and model systems and carry implications for relations between integrated information, consciousness, and other neurocognitive processes. However, our findings pose challenges for theories that ascribe physical meaning to the measured quantities.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060 · see citing works
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2001) · Wiley eBooks · doi:10.1002/0471200611 · Cited by 37,139 · see citing works
Investigating causal relations by econometric models and cross-spectral methods
Granger, C. W. J. (1969) · Econometrica · doi:10.2307/1912791 · Cited by 22,989 · see citing works
An Introduction to Genetic Algorithms
Mitchell, M. (1996) · doi:10.7551/mitpress/3927.001.0001 · Cited by 11,340 · see citing works
Breitung, J., & Hamilton, J. D. (1995) · Contemporary Sociology A Journal of Reviews · doi:10.2307/2076916 · Cited by 11,104 · see citing works
Hamilton, J. D. (1994) · Princeton University Press eBooks · doi:10.1515/9780691218632 · Cited by 7,401 · see citing works
Buzsáki, G. (2006) · doi:10.1093/acprof:oso/9780195301069.001.0001 · Cited by 4,873 · see citing works
Investigating Causal Relations by Econometric Models and Cross-Spectral Methods
Granger, C. W. J. (2010) · Essays in Econometrics · doi:10.1017/cbo9780511753978.002 · Cited by 4,762 · see citing works
Kraskov, A., Stögbauer, H., & Grassberger, P. (2004) · Physical Review E · doi:10.1103/physreve.69.066138 · Cited by 4,157 · see citing works
Booth, D. E. (1997) · Technometrics · doi:10.1080/00401706.1997.10485448 · Cited by 3,210 · see citing works
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Dayan, P., & Abbott, L. F. (2001) · Cited by 3,153 · see citing works
Measurement of Linear Dependence and Feedback between Multiple Time Series
Geweke, J. (1982) · Journal of the American Statistical Association · doi:10.1080/01621459.1982.10477803 · Cited by 2,060 · see citing works
Organization, development and function of complex brain networks
SPORNS, O., CHIALVO, D., KAISER, M., & HILGETAG, C. (2004) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2004.07.008 · Cited by 2,055 · see citing works
An information integration theory of consciousness
Tononi, G. (2004) · BMC Neuroscience · doi:10.1186/1471-2202-5-42 · Cited by 1,757 · cited 3× · see citing works
“In this paper, we critically evaluate ‘integrated information’ (W) [10,11], a candidate measure that has received significant recent attention, especially in the domain of consciousness science [12,13,14,15].”
BackgroundNetwork structure of cerebral cortex shapes functional connectivity on multiple time scales
Honey, C. J., Kötter, R., Breakspear, M. J., & Sporns, O. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0701519104 · Cited by 1,683 · see citing works
Tononi, G., Sporns, O., & Edelman, G. M. (1994) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.91.11.5033 · Cited by 1,626 · see citing works
Tononi, G. (1998) · Science · doi:10.1126/science.282.5395.1846 · Cited by 1,561 · see citing works
Neural Mechanisms for Interacting with a World Full of Action Choices
Cisek, P., & Kalaska, J. F. (2010) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.051508.135409 · Cited by 1,543 · see citing works
Consciousness as integrated information: a provisional manifesto
Tononi, G. (2008) · The Biological Bulletin · doi:10.2307/25470707 · Cited by 1,529 · see citing works
Estimation of entropy and mutual information
Paninski, L. (2003) · Neural Computation · doi:10.1162/089976603321780272 · Cited by 1,442 · see citing works
Nonlinear Time Series: Nonparametric and Parametric Methods
Fan, J., & Yao, Q. (2003) · Springer eBooks · doi:10.1007/b97702 · Cited by 1,225 · see citing works
Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables
Barnett, L., Barrett, A. B., & Seth, A. K. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.238701 · Cited by 1,152 · see citing works
Self-citationCERTAIN GENERALIZATIONS IN THE ANALYSIS OF VARIANCE
Wilks, S. S. (1932) · Biometrika · doi:10.1093/biomet/24.3-4.471 · Cited by 1,011 · see citing works
Cortical coordination dynamics and cognition
Bressler, S. L., & Kelso, J. A. S. (2001) · Trends in Cognitive Sciences · doi:10.1016/s1364-6613(00)01564-3 · Cited by 789 · see citing works
What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology
McDonnell, M. D., & Abbott, D. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000348 · Cited by 774 · see citing works
A MATLAB toolbox for Granger causal connectivity analysis
Seth, A. K. (2009) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2009.11.020 · Cited by 746 · see citing works
Self-citationGranger Causality: Basic Theory and Application to Neuroscience
Ding, M., Chen, Y., & Bressler, S. L. (2006) · doi:10.1002/9783527609970.ch17 · Cited by 669 · see citing works
Spatial EEG patterns, non-linear dynamics and perception: the neo-sherringtonian view
Freeman, W. J., & Skarda, C. A. (1985) · Brain Research Reviews · doi:10.1016/0165-0173(85)90022-0 · Cited by 574 · see citing works
James, W. (1904) · The Journal of Philosophy, Psychology and Scientific Methods · doi:10.2307/2011942 · Cited by 519 · see citing works
Complexity as thermodynamic depth
Lloyd, S., & Pagels, H. R. (1988) · Annals of Physics · doi:10.1016/0003-4916(88)90094-2 · Cited by 504 · see citing works
Measuring consciousness: relating behavioural and neurophysiological approaches
Seth, A. K., Dienes, Z., Cleeremans, A., Overgaard, M., & Pessoa, L. (2008) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2008.04.008 · Cited by 458 · cited 1× · see citing works
“, with locally stationary periods corresponding to a conscious state with a particular level and content. Our results now make it possible to measure the integrated information corresponding to these various states and to compare these values with other indices of consciousness, both subjective (e.g., verbal reports,…”
ResultSelf-citationNaturalizing consciousness: a theoretical framework.
Edelman, G. M. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0931349100 · Cited by 440 · see citing works
An Introduction to Genetic Algorithms.
Heiss-Czedik, D. (1997) · Artificial Life · doi:10.1162/artl.1997.3.1.63 · Cited by 437 · see citing works
Integrated information in discrete dynamical systems: motivation and theoretical framework
Balduzzi, D., & Tononi, G. (2008) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000091 · Cited by 419 · see citing works
Nonparametric Statistics for Stochastic Processes
Bosq, D. (1998) · Lecture notes in statistics · doi:10.1007/978-1-4612-1718-3 · Cited by 392 · see citing works
Handbook of Time Series Analysis
(2006) · Wiley eBooks · doi:10.1002/9783527609970 · Cited by 362 · see citing works
Criteria for consciousness in humans and other mammals
Seth, A. K., Baars, B. J., & Edelman, D. B. (2004) · Consciousness and Cognition · doi:10.1016/j.concog.2004.08.006 · Cited by 326 · see citing works
Self-citationNonparametric Statistics for Stochastic Processes: Estimation and Prediction
Odencrantz, J. R., & Bosq, D. (2000) · Technometrics · doi:10.2307/1270958 · Cited by 322 · see citing works
Theories and measures of consciousness: An extended framework
Seth, A. K., Izhikevich, E. M., Reeke, G. N., & Edelman, G. M. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0604347103 · Cited by 320 · see citing works
Self-citationMeasuring information integration
Tononi, G., & Sporns, O. (2003) · BMC Neuroscience · doi:10.1186/1471-2202-4-31 · Cited by 294 · see citing works
Mapping Information Flow in Sensorimotor Networks
Lungarella, M., & Sporns, O. (2006) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0020144 · Cited by 294 · see citing works
The Noisy BrainStochastic Dynamics as a Principle of Brain Function
Rolls, E. T., & Deco, G. (2010) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199587865.001.0001 · Cited by 289 · see citing works
Nonlinear Time Series: Nonparametric and Parametric Methods
Lu, Z. (2004) · Technometrics · doi:10.1198/tech.2004.s746 · Cited by 274 · see citing works
Qualia: The Geometry of Integrated Information
Balduzzi, D., & Tononi, G. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000462 · Cited by 269 · see citing works
Operational principles of neurocognitive networks
Bressler, S. L., & Tognoli, E. (2006) · International Journal of Psychophysiology · doi:10.1016/j.ijpsycho.2005.12.008 · Cited by 259 · see citing works
Multivariate Granger causality and generalized variance
Barrett, A. B., Barnett, L., & Seth, A. K. (2010) · Physical Review E · doi:10.1103/physreve.81.041907 · Cited by 259 · see citing works
Self-citationArthuis, M., Valton, L., Régis, J. M., Chauvel, P., Wendling, F., Naccache, L., Bernard, C., & Bartoloméi, F. (2009) · Brain · doi:10.1093/brain/awp086 · Cited by 257 · see citing works
Causal connectivity of evolved neural networks during behavior
Seth, A. K. (2005) · Network Computation in Neural Systems · doi:10.1080/09548980500238756 · Cited by 242 · see citing works
Self-citationConsciousness, information integration, and the brain
Tononi, G. (2005) · Progress in brain research · doi:10.1016/s0079-6123(05)50009-8 · Cited by 172 · see citing works
Metastability, criticality and phase transitions in brain and its models
Werner, G. (2006) · Biosystems · doi:10.1016/j.biosystems.2006.12.001 · Cited by 154 · see citing works
Explanatory correlates of consciousness: theoretical and computational challenges.
Seth, A. (2009) · Cognitive Computation · doi:10.1007/s12559-009-9007-x · Cited by 146 · see citing works
Self-citationThe Noisy Brain: Stochastic Dynamics as a Principle of Brain Function
Dawkins, M. S. (2010) · Animal Behaviour · doi:10.1016/j.anbehav.2010.04.019 · Cited by 118 · see citing works
Visual Binding Through Reentrant Connectivity and Dynamic Synchronization in a Brain-based Device
Seth, A. K. (2004) · Cerebral Cortex · doi:10.1093/cercor/bhh079 · Cited by 108 · see citing works
Self-citationInformation Geometry on Complexity and Stochastic Interaction
Ay, N. (2015) · Entropy · doi:10.3390/e17042432 · Cited by 100 · see citing works
Dynamical complexity in small-world networks of spiking neurons
Shanahan, M. (2008) · Physical Review E · doi:10.1103/physreve.78.041924 · Cited by 72 · see citing works
Neural complexity and structural connectivity
Barnett, L., Buckley, C. L., & Bullock, S. (2009) · Physical Review E · doi:10.1103/physreve.79.051914 · Cited by 69 · see citing works
Nonlinear Time Series—Nonparametric and Parametric Methods
Kreiß, J. (2006) · Biometrics · doi:10.1111/j.1541-0420.2006.00589_7.x · Cited by 46 · see citing works
Environment and Behavior Influence the Complexity of Evolved Neural Networks
Seth, A. K., & Edelman, G. M. (2004) · Adaptive Behavior · doi:10.1177/105971230401200103 · Cited by 45 · see citing works
Self-citationDynamical properties of strongly interacting Markov chains
Ay, N., & Wennekers, T. (2003) · Neural Networks · doi:10.1016/s0893-6080(03)00190-4 · Cited by 42 · see citing works
Measuring Shared Information and Coordinated Activity in Neuronal NetworksPreprint
Klinkner, K. L., Shalizi, C. R., & Camperi, M. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.q-bio/0506009 · Cited by 10 · see citing works
Flagged first, then by citations
1 of the 61 references couldn’t be matched to a known paper.
Research works printed but not linked: 3
- [24]Watts DJ 2004 Small worlds: The dynamics of networks between order and randomness (Princeton studies in complexity) Princeton Princeton University Press 264
- [28]Davidson J 2000 Econometric theory. Oxford Wiley-Blackwell 528
- [48]Ay N Olbrich E Bertschinger N Jost J 2001 A unifying framework for complexity measures of finite systems. Proceedings of ECCS'06, Santa Fe Institute Working Paper 06-08-028 Available: http://www.santafe.edu/media/workingpapers/06-08-028.pdf.
Cited by
Sorted by citations
Integrated information theory: from consciousness to its physical substrate
Tononi, G., Boly, M., Massimini, M., & Koch, C. (2016) · Nature Reviews Neuroscience · doi:10.1038/nrn.2016.44 · Cited by 1,727 · see citing works
From the phenomenology to the mechanisms of consciousness: integrated information theory 3.0
Oizumi, M., Albantakis, L., & Tononi, G. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003588 · Cited by 1,128 · see citing works
Rethinking segregation and integration: contributions of whole-brain modelling
Deco, G., Tononi, G., Boly, M., & Kringelbach, M. L. (2015) · Nature reviews. Neuroscience · doi:10.1038/nrn3963 · Cited by 658 · see citing works
No-Report Paradigms: Extracting the True Neural Correlates of Consciousness
Tsuchiya, N., Wilke, M., Frässle, S., & Lamme, V. A. F. (2015) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2015.10.002 · Cited by 551 · see citing works
Toward a computational theory of conscious processing
Dehaene, S., Charles, L., King, J.-R., & Marti, S. (2014) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2013.12.005 · Cited by 404 · see citing works
Integrated information theory of consciousness: an updated account.
(2012) · PubMed · doi:10.4449/aib.v149i5.1388 · Cited by 370 · see citing works
A Synergistic Core for Human Brain Evolution and Cognition
Luppi, A. I., Mediano, P. A. M., Rosas, F. E., Holland, N., Fryer, T. D., O’Brien, J. T., Rowe, J. B., Menon, D. K., Bor, D., & Stamatakis, E. A. (2022) · Nature Neuroscience · doi:10.1038/s41593-022-01070-0 · Cited by 314 · see citing works
Consciousness in humans and non-human animals: recent advances and future directions
Boly, M., Seth, A. K., Wilke, M., Ingmundson, P., Baars, B., Laureys, S., Edelman, D. B., & Tsuchiya, N. (2013) · Frontiers in Psychology · doi:10.3389/fpsyg.2013.00625 · Cited by 291 · see citing works
Self-citationBarrett, A. B. (2015) · Physical Review E · doi:10.1103/physreve.91.052802 · Cited by 228 · see citing works
Self-citationQuantifying high-order interdependencies via multivariate extensions of the mutual information
Rosas, F. E., Mediano, P. A. M., Gastpar, M., & Jensen, H. J. (2019) · Physical review. E · doi:10.1103/physreve.100.032305 · Cited by 225 · see citing works
Measuring Integrated Information from the Decoding Perspective
Oizumi, M., Amari, S.-I., Yanagawa, T., Fujii, N., & Tsuchiya, N. (2016) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1004654 · Cited by 184 · see citing works
Volumetric Ca2+ Imaging in the Mouse Brain Using Hybrid Multiplexed Sculpted Light Microscopy
Weisenburger, S., Tejera, F., Demas, J., Chen, B., Manley, J., Sparks, F. T., Traub, F. M., Daigle, T. L., Zeng, H., Losonczy, A., et al. (2019) · Cell · doi:10.1016/j.cell.2019.03.011 · Cited by 188 · see citing works
Consciousness and complexity: a consilience of evidence
Sarasso, S., Casali, A. G., Casarotto, S., Rosanova, M., Sinigaglia, C., & Massimini, M. (2021) · Neuroscience of Consciousness · doi:10.1093/nc/niab023 · Cited by 171 · see citing works
Entropy and the Brain: An Overview
Keshmiri, S. (2020) · Entropy · doi:10.3390/e22090917 · Cited by 168 · see citing works
Unified framework for information integration based on information geometry
Oizumi, M., Tsuchiya, N., & Amari, S. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1603583113 · Cited by 156 · see citing works
Barrett, A. B., Murphy, M., Bruno, M., Noirhomme, Q., Boly, M., Laureys, S., & Seth, A. K. (2012) · PLoS ONE · doi:10.1371/journal.pone.0029072 · Cited by 149 · see citing works
Self-citationMeasuring integrated information: comparison of candidate measures in theory and simulation
Mediano, P., Seth, A., & Barrett, A. (2018) · Entropy · doi:10.3390/e21010017 · Cited by 145 · see citing works
Self-citationBor, D., & Seth, A. K. (2012) · Frontiers in Psychology · doi:10.3389/fpsyg.2012.00063 · Cited by 143 · see citing works
Self-citationCan the macro beat the micro? Integrated information across spatiotemporal scales
Hoel, E. P., Albantakis, L., Marshall, W., & Tononi, G. (2016) · Neuroscience of Consciousness · doi:10.1093/nc/niw012 · Cited by 140 · see citing works
The integrated information theory of consciousness: A case of mistaken identity
Merker, B. H., Williford, K., & Rudrauf, D. (2021) · Behavioral and Brain Sciences · doi:10.1017/s0140525x21000881 · Cited by 140 · see citing works
Causal density and integrated information as measures of conscious level
Seth, A. K., Barrett, A. B., & Barnett, L. (2011) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2011.0079 · Cited by 127 · see citing works
Self-citationImproved measures of integrated information
Tegmark, M. (2016) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1005123 · Cited by 128 · see citing works
Integrated Information Increases with Fitness in the Evolution of Animats
Edlund, J. A., Chaumont, N., Hintze, A., Koch, C., Tononi, G., & Adami, C. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002236 · Cited by 121 · see citing works
Measuring integrated information: comparison of \ncandidate measures in theory and simulation
Mediano, P. A. M., Seth, A. K., & Barrett, A. B. (2018) · Figshare · Cited by 114 · see citing works
Self-citationConsciousness and cognition in plants
Segundo‐Ortin, M., & Calvo, P. (2021) · Wiley Interdisciplinary Reviews Cognitive Science · doi:10.1002/wcs.1578 · Cited by 122 · see citing works
The strength of weak integrated information theory
Mediano, P. A. M., Rosas, F. E., Bor, D., Seth, A. K., & Barrett, A. B. (2022) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2022.04.008 · Cited by 115 · see citing works
Self-citationHoffman, D. D., & Prakash, C. (2014) · Frontiers in Psychology · doi:10.3389/fpsyg.2014.00577 · Cited by 103 · see citing works
Cortical mechanisms of loss of consciousness: insight from TMS/EEG studies.
Massimini, M., Ferrarelli, F., Sarasso, S., & Tononi, G. (2012) · PubMed · doi:10.4449/aib.v150i2.1361 · Cited by 101 · see citing works
Information Geometry on Complexity and Stochastic Interaction
Ay, N. (2015) · Entropy · doi:10.3390/e17042432 · Cited by 100 · see citing works
Consciousness depends on integration between parietal cortex, striatum, and thalamus
Afrasiabi, M., Redinbaugh, M. J., Phillips, J. M., Kambi, N. A., Mohanta, S., Raz, A., Haun, A., & Saalmann, Y. B. (2021) · Cell Systems · doi:10.1016/j.cels.2021.02.003 · Cited by 93 · see citing works
Kim, H., Hudetz, A. G., Lee, J., Mashour, G. A., Lee, U., & the ReCCognition Study Group (2018) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2018.00042 · Cited by 82 · see citing works
An integration of integrated information theory with fundamental physics
Barrett, A. B. (2014) · Frontiers in Psychology · doi:10.3389/fpsyg.2014.00063 · Cited by 76 · see citing works
Self-citationInformation integration in large brain networks
Toker, D., & Sommer, F. T. (2019) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006807 · Cited by 73 · see citing works
Integrated information as a common signature of dynamical and information-processing complexity
Mediano, P. A. M., Rosas, F. E., Farah, J. C., Shanahan, M., Bor, D., & Barrett, A. B. (2022) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0063384 · Cited by 63 · see citing works
Self-citationSuperconducting optoelectronic loop neurons
Shainline, J. M., Buckley, S. M., McCaughan, A. N., Chiles, J. T., Salim, A. J., Castellanos-Beltran, M. A., Donnelly, C. A., Schneider, M. L., Mirin, R. P., & Nam, S. W. (2019) · Journal of Applied Physics · doi:10.1063/1.5096403 · Cited by 64 · see citing works
Boly, M., Sasai, S., Gosseries, O., Oizumi, M., Casali, A. G., Massimini, M., & Tononi, G. (2015) · PLoS ONE · doi:10.1371/journal.pone.0125337 · Cited by 60 · see citing works
Tagliazucchi, E. (2017) · Consciousness and Cognition · doi:10.1016/j.concog.2017.08.008 · Cited by 55 · see citing works
Jang, H., Mashour, G. A., Hudetz, A. G., & Huang, Z. (2024) · Nature Communications · doi:10.1038/s41467-024-53299-x · Cited by 54 · see citing works
Growing evidence for separate neural mechanisms for attention and consciousness
Maier, A., & Tsuchiya, N. (2020) · Attention Perception & Psychophysics · doi:10.3758/s13414-020-02146-4 · Cited by 45 · see citing works
A synergistic workspace for human consciousness revealed by Integrated Information Decomposition
Luppi, A. I., Mediano, P. A. M., Rosas, F. E., Allanson, J. E., Pickard, J. D., Carhart-Harris, R. L., Williams, G. B., Craig, M. M., Finoia, P., Owen, A. M., et al. (2023) · eLife · doi:10.7554/elife.88173 · Cited by 111 · see citing works
A Deeper Look at the “Neural Correlate of Consciousness”
Fink, F. (2016) · Frontiers in Psychology · doi:10.3389/fpsyg.2016.01044 · Cited by 48 · see citing works
Conscious perception as integrated information patterns in human electrocorticography
Haun, A. M., Oizumi, M., Kovach, C. K., Kawasaki, H., Oya, H., Howard, M. A., Adolphs, R., & Tsuchiya, N. (2017) · eneuro · doi:10.1523/eneuro.0085-17.2017 · Cited by 47 · see citing works
Redinbaugh, M. J., Afrasiabi, M., Phillips, J. M., Kambi, N. A., Mohanta, S., Raz, A., & Saalmann, Y. B. (2022) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010294 · Cited by 44 · see citing works
The Mathematical Structure of Integrated Information Theory
Kleiner, J., & Tull, S. (2021) · Frontiers in Applied Mathematics and Statistics · doi:10.3389/fams.2020.602973 · Cited by 46 · see citing works
An Integrated Information Theory of Consciousness
Tononi, G. (2009) · Wiley eBooks · doi:10.1002/9781119132363.ch17 · Cited by 46 · see citing works
Criticality as a determinant of integrated information Φ in human brain networks
Kim, H., & Lee, U. (2019) · Entropy · doi:10.3390/e21100981 · Cited by 45 · see citing works
Astrocyte-induced positive integrated information in neuron-astrocyte ensembles
Игоревич, К. О., Gordleeva, S., Ermolaeva, A. V., Jalan, S., & Zaikin, A. A. (2019) · Physical review. E · doi:10.1103/physreve.99.012418 · Cited by 44 · see citing works
Functional split brain in a driving/listening paradigm
Sasai, S., Boly, M., Mensen, A., & Tononi, G. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1613200113 · Cited by 43 · see citing works
Luppi, A. I., Mediano, P. A. M., Rosas, F. E., Harrison, D. J., Carhart-Harris, R. L., Bor, D., & Stamatakis, E. A. (2021) · Neuroscience of Consciousness · doi:10.1093/nc/niab027 · Cited by 45 · see citing works
Chang, J.-Y., Pigorini, A., Massimini, M., Tononi, G., Nobili, L., & Veen, B. D. V. (2012) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2012.00317 · Cited by 42 · see citing works
A synergistic workspace for human consciousness revealed by Integrated Information Decomposition
Luppi, A. I., Mediano, P. A. M., Rosas, F. E., Allanson, J. E., Pickard, J. D., Carhart-Harris, R. L., Williams, G. B., Craig, M. M., Finoia, P., Owen, A. M., et al. (2024) · eLife · doi:10.7554/elife.88173.4 · Cited by 41 · see citing works
Integrated information as a metric for group interaction
Engel, D., & Malone, T. W. (2018) · PLoS ONE · doi:10.1371/journal.pone.0205335 · Cited by 41 · see citing works
A Synergistic Workspace for Human Consciousness Revealed by Integrated Information DecompositionPreprint
Luppi, A. I., Mediano, P. A. M., Rosas, F. E., Allanson, J. E., Pickard, J. D., Carhart-Harris, R. L., Williams, G. B., Craig, M. M., Finoia, P., Owen, A. M., et al. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.11.25.398081 · Cited by 43 · see citing works
Aleksander, I. (2017) · doi:10.1002/9781119132363.ch7 · Cited by 41 · see citing works
Wong, W., Noreika, V., Móró, L., Revonsuo, A., Windt, J., Valli, K., & Tsuchiya, N. (2020) · Neuroscience of Consciousness · doi:10.1093/nc/niaa006 · Cited by 40 · see citing works
Leung, A., Cohen, D., van Swinderen, B., & Tsuchiya, N. (2021) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008722 · Cited by 39 · see citing works
Towards an extended taxonomy of information dynamics via Integrated Information DecompositionPreprint
Mediano, P. A. M., Rosas, F. E., Luppi, A. I., Carhart-Harris, R. L., Bor, D., Seth, A. K., & Barrett, A. B. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.13186 · Cited by 40 · see citing works
Self-citationIsler, J. R., Stark, R. I., Grieve, P. G., Welch, M. G., & Myers, M. M. (2018) · PLoS ONE · doi:10.1371/journal.pone.0206237 · Cited by 39 · see citing works
Integrated information and state differentiation
Marshall, W., Gomez-Ramirez, J., & Tononi, G. (2016) · Frontiers in Psychology · doi:10.3389/fpsyg.2016.00926 · Cited by 36 · see citing works
Measuring the Complexity of Consciousness
Arsiwalla, X. D., & Verschure, P. (2018) · Frontiers in Neuroscience · doi:10.3389/fnins.2018.00424 · Cited by 35 · see citing works
Integrated world modeling theory expanded: Implications for the future of consciousness
Safron, A. (2022) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2022.642397 · Cited by 43 · see citing works
Fast and exact search for the partition with minimal information loss
Hidaka, S., & Oizumi, M. (2018) · PLoS ONE · doi:10.1371/journal.pone.0201126 · Cited by 33 · see citing works
Accuracy and performance of the state-based Φ and liveliness measures of information integration
Gamez, D., & Aleksander, I. (2011) · Consciousness and Cognition · doi:10.1016/j.concog.2011.05.016 · Cited by 31 · see citing works
Four-dimensional graded consciousness
Jonkisz, J., Wierzchoń, M., & Binder, M. (2017) · Frontiers in Psychology · doi:10.3389/fpsyg.2017.00420 · Cited by 30 · see citing works
Causal composition: Structural differences among dynamically equivalent systems
Albantakis, L., & Tononi, G. (2019) · Entropy · doi:10.3390/e21100989 · Cited by 30 · see citing works
“Most proposed empirical measures of information integration [56,74–77] do not evaluate φ in a state-dependent manner, but rather as a difference in conditional entropies or mutual information under a (bidirectional) system partition (but see [78], which includes state-dependent measures).”
BackgroundInfluentialHancock, F., Rosas, F. E., Mediano, P. A. M., Luppi, A. I., Cabral, J., Dipasquale, O., & Turkheimer, F. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0214 · Cited by 26 · see citing works
Finding continuity and discontinuity in fish schools via integrated information theory
Niizato, T., Sakamoto, K., Mototake, Y.-I., Murakami, H., Tomaru, T., Hoshika, T., & Fukushima, T. (2020) · PLoS ONE · doi:10.1371/journal.pone.0229573 · Cited by 29 · see citing works
Self-organized criticality as a framework for consciousness: A review study
Walter, N., & Hinterberger, T. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.911620 · Cited by 28 · see citing works
Quantifying information of intracellular signaling: progress with machine learning
Tang, Y., & Hoffmann, A. (2022) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac7a4a · Cited by 23 · see citing works
How Organisms Gained Causal Independence and How It Might Be Quantified
Farnsworth, K. D. (2018) · Biology · doi:10.3390/biology7030038 · Cited by 25 · see citing works
“What is it like to be a bat?”—a pathway to the answer from the integrated information theory
Tsuchiya, N. (2017) · Philosophy Compass · doi:10.1111/phc3.12407 · Cited by 25 · see citing works
Ito, S., & Oizumi, M. (2020) · Institutional Repositories DataBase (IRDB) · doi:10.1103/physrevresearch.2.033048 · Cited by 24 · see citing works
Are Information or Data Patterns Correlated with Consciousness?
Gamez, D. (2014) · Topoi · doi:10.1007/s11245-014-9246-7 · Cited by 24 · see citing works
Muñoz, R. N., Leung, A., Zecevik, A., Pollock, F. A., Cohen, D., van Swinderen, B., Tsuchiya, N., & Modi, K. K. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023219 · Cited by 23 · see citing works
Integrated information in the thermodynamic limit
Aguilera, M., & Paolo, E. A. D. (2019) · Neural Networks · doi:10.1016/j.neunet.2019.03.001 · Cited by 21 · 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
Toward a unified taxonomy of information dynamics via Integrated Information Decomposition
Mediano, P. A. M., Rosas, F. E., Luppi, A. I., Carhart-Harris, R. L., Bor, D., Seth, A. K., & Barrett, A. B. (2025) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2423297122 · Cited by 22 · see citing works
Self-citationIntegrated information for large complex networks
Arsiwalla, X. D., & Verschure, P. F. M. J. (2013) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2013.6706794 · Cited by 22 · see citing works
Modes and models in disorders of consciousness science.
(2012) · PubMed · doi:10.4449/aib.v150i2.1372 · Cited by 22 · see citing works
Self-citationSystem, Subsystem, Hive: Boundary Problems in Computational Theories of Consciousness
Fekete, T., van Leeuwen, C., & Edelman, S. (2016) · Frontiers in Psychology · doi:10.3389/fpsyg.2016.01041 · Cited by 22 · see citing works
Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines
Kanwal, M. S., Grochow, J. A., & Ay, N. (2017) · CU Scholar (University of Colorado Boulder) · Cited by 22 · see citing works
Information-Theoretic Neuro-Correlates Boost Evolution of Cognitive Systems
Schossau, J., Adami, C., & Hintze, A. (2015) · Entropy · doi:10.3390/e18010006 · Cited by 21 · see citing works
Evaluating Approximations and Heuristic Measures of Integrated Information
Nilsen, A. S., Juel, B. E., Marshall, W., & Storm, J. F. (2019) · Entropy · doi:10.3390/e21050525 · Cited by 19 · see citing works
Lou, W., Liu, P., Cheng, L., & Li, Z. (2021) · JAWRA Journal of the American Water Resources Association · doi:10.1111/1752-1688.12978 · Cited by 20 · see citing works
The Morphospace of ConsciousnessPreprint
Arsiwalla, X. D., Moulin-Frier, C., Herreros, I., Sánchez-Fibla, M., & Verschure, P. F. M. J. (2017) · doi:10.31234/osf.io/emhnp · Cited by 20 · see citing works
A novel perturbation based compression complexity measure for networks
Virmani, M., & Nagaraj, N. (2019) · Heliyon · doi:10.1016/j.heliyon.2019.e01181 · Cited by 19 · see citing works
Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines
Kanwal, M., Grochow, J. A., & Ay, N. (2017) · Entropy · doi:10.3390/e19070310 · Cited by 19 · see citing works
Aguilera, M., & Paolo, E. A. D. (2021) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2021.01.009 · Cited by 18 · see citing works
The global dynamical complexity of the human brain network
Arsiwalla, X. D., & Verschure, P. F. M. J. (2016) · Applied Network Science · doi:10.1007/s41109-016-0018-8 · Cited by 18 · see citing works
Efficient search for informational cores in complex systems: Application to brain networks
Kitazono, J., Ryota Kanai, C., & Oizumi, M. (2020) · Neural Networks · doi:10.1016/j.neunet.2020.08.020 · Cited by 18 · see citing works
Dong, K., Zhang, D., Wei, Q., Wang, G., Chen, X., Zhang, L., & Liu, J. (2022) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2022.106480 · Cited by 18 · see citing works
Dynamical complexity in the C.elegans neural network
Antonopoulos, C. G., FOKAS, A. S., & Bountis, T. (2016) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2016-02670-3 · Cited by 17 · see citing works
Advances in the Scientific Investigation of Consciousness
Bor, D. (2015) · Springer eBooks · doi:10.1007/978-3-319-21425-2_2 · Cited by 16 · see citing works
Information Theoretic Measures to Infer Feedback Dynamics in Coupled Logistic Networks
Goodwell, A. E., & Kumar, P. (2015) · Entropy · doi:10.3390/e17117468 · Cited by 16 · see citing works
Detecting direct associations in a network by information theoretic approaches
Shi, J., Zhao, J., Li, T., & Chen, L. (2018) · Science China Mathematics · doi:10.1007/s11425-017-9206-0 · Cited by 16 · see citing works
Multimodal fusion via cortical network inspired losses
Shankar, S. (2022) · Proceedings of the conference - Association for Computational Linguistics. Meeting · doi:10.18653/v1/2022.acl-long.83 · Cited by 16 · see citing works
High Integrated Information in Complex Networks Near Criticality
Arsiwalla, X. D., & Verschure, P. F. M. J. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-44778-0_22 · Cited by 16 · see citing works
Scaling Behaviour and Critical Phase Transitions in Integrated Information Theory
Aguilera, M. (2019) · Entropy · doi:10.3390/e21121198 · Cited by 15 · see citing works
An implementation of integrated information theory in resting-state fMRI
Nemirovsky, I. E., Popiel, N. J. M., Rudas, J., Caius, M., Naci, L., Schiff, N. D., Owen, A. M., & Soddu, A. (2023) · Communications Biology · doi:10.1038/s42003-023-05063-y · Cited by 15 · see citing works
Antonacci, Y., Barà, C., Sparacino, L., Pirovano, I., Mastropietro, A., Rizzo, G., & Faes, L. (2024) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2024.3516943 · Cited by 15 · see citing works
- Authors
- Barrett, A. B., & Seth, A. K.
- Affiliations
- University of Sussex (GB)
- Corresponding author
- Barrett, Adam B.
- Venue
- PLoS Computational Biology
- Publisher
- Public Library of Science (PLoS)
- Published
- 2011-01-20
- Volume
- 7
- Issue
- 1
- Pages
- e1001052
- ISSN
- 1553-734X (ISSN-L)
- 1553-7358
- PMC
- PMC3024259
- OpenAlex
- W2048013965
- Cited by
- 225
- References
- 61
- Citations by year
- 2026: 11 · 2025: 16 · 2024: 22 · 2023: 18 · 2022: 17 · 2021: 14 · 2020: 17 · 2019: 21 · 2018: 17 · 2017: 17 · 2016: 16 · 2015: 13 · 2014: 10 · 2013: 2 · 2012: 9
- FWCI
- 10.30
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS Computational Biology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Sussex Research Online (University of Sussex) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Figshare (submittedVersion, cc-by)
- Funders
- Engineering and Physical Sciences Research Council (EP/G007543/1)
- Topics
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Philosophy and Theoretical Science
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Keywords
- integrated information, information integration, time series, Markov systems, consciousness, neural systems, information measures
- MeSH terms
- Information Services, Markov Chains, Models, Theoretical
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.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
