{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T23:34:46Z","timestamp":1772494486752,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012934","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T00:00:00Z","timestamp":1745971200000}}],"reference-count":105,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T00:00:00Z","timestamp":1744675200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["982347"],"award-info":[{"award-number":["982347"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NextgenerationEU FAIR","award":["PE0000013"],"award-info":[{"award-number":["PE0000013"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    Information theory has deeply influenced the conceptualization of brain information processing and is a mainstream framework for analyzing how neural networks in the brain process information to generate behavior. Information theory tools have been initially conceived and used to study how information about sensory variables is encoded by the activity of small neural populations. However, recent multivariate information theoretic advances have enabled addressing how information is exchanged across areas and used to inform behavior. Moreover, its integration with dimensionality-reduction techniques has enabled addressing information encoding and communication by the activity of large neural populations or many brain areas, as recorded by multichannel activity measurements in functional imaging and electrophysiology. Here, we provide a Multivariate Information in Neuroscience Toolbox (MINT) that combines these new methods with statistical tools for robust estimation from limited-size empirical datasets. We demonstrate the capabilities of MINT by applying it to both simulated and real neural data recorded with electrophysiology or calcium imaging, but all MINT functions are equally applicable to other brain-activity measurement modalities. We highlight the synergistic opportunities that combining its methods afford for reverse engineering of specific information processing and flow between neural populations or areas, and for discovering how information processing functions emerge from interactions between neurons or areas. MINT works on Linux, Windows and macOS operating systems, is written in MATLAB (requires MATLAB version 2018b or newer) and depends on 4 native MATLAB toolboxes. The calculation of one possible way to compute information redundancy requires the installation and compilation of C files (made available by us also as pre-compiled files). MINT is freely available at\n                    <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/github.com\/panzerilab\/MINT\" xlink:type=\"simple\">https:\/\/github.com\/panzerilab\/MINT<\/jats:ext-link>\n                    with DOI doi.org\/10.5281\/zenodo.13998526 and operates under a GNU GPLv3 license.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1012934","type":"journal-article","created":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T13:34:58Z","timestamp":1744724098000},"page":"e1012934","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["MINT: A toolbox for the analysis of multivariate neural information coding and transmission"],"prefix":"10.1371","volume":"21","author":[{"given":"Gabriel Mat\u00edas","family":"Lorenz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicola Marie","family":"Engel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0890-0703","authenticated-orcid":true,"given":"Marco","family":"Celotto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Loren","family":"Ko\u00e7illari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4490-6835","authenticated-orcid":true,"given":"Sebastiano","family":"Curreli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tommaso","family":"Fellin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1700-8909","authenticated-orcid":true,"given":"Stefano","family":"Panzeri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,4,15]]},"reference":[{"issue":"9","key":"pcbi.1012934.ref001","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1038\/s41583-022-00606-4","article-title":"The structures and functions of correlations in neural population codes","volume":"23","author":"S Panzeri","year":"2022","journal-title":"Nat Rev Neurosci"},{"key":"pcbi.1012934.ref002","first-page":"1","article-title":"Large-scale neural recordings call for new insights to link brain and behavior","author":"A Urai","year":"2022;25(1)","journal-title":"Nat Neurosci"},{"issue":"3","key":"pcbi.1012934.ref003","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"CE Shannon","year":"1948","journal-title":"Bell Syst.\u00a0Tech.\u00a0J"},{"issue":"11","key":"pcbi.1012934.ref004","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1038\/14731","article-title":"Information theory and neural coding","volume":"2","author":"A Borst","year":"1999","journal-title":"Nat Neurosci"},{"issue":"3","key":"pcbi.1012934.ref005","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1038\/nrn2578","article-title":"Extracting information from neuronal populations: information theory and decoding approaches","volume":"10","author":"R Quian Quiroga","year":"2009","journal-title":"Nat Rev Neurosci"},{"issue":"4","key":"pcbi.1012934.ref006","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1016\/j.conb.2012.06.005","article-title":"Information theoretic approaches to understanding circuit function","volume":"22","author":"A Fairhall","year":"2012","journal-title":"Curr Opin Neurobiol"},{"key":"pcbi.1012934.ref007","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1146\/annurev-neuro-120320-082744","article-title":"The geometry of information coding in correlated neural populations","volume":"44","author":"R Azeredo da Silveira","year":"2021","journal-title":"Annu Rev Neurosci"},{"issue":"6849","key":"pcbi.1012934.ref008","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1038\/35090500","article-title":"Efficiency and ambiguity in an adaptive neural code","volume":"412","author":"AL Fairhall","year":"2001","journal-title":"Nature"},{"issue":"3","key":"pcbi.1012934.ref009","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1162\/neco.1990.2.3.308","article-title":"Towards a Theory of Early Visual Processing","volume":"2","author":"JJ Atick","year":"1990","journal-title":"Neural Comput"},{"issue":"3","key":"pcbi.1012934.ref010","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.tins.2009.12.001","article-title":"Sensory neural codes using multiplexed temporal scales","volume":"33","author":"S Panzeri","year":"2010","journal-title":"Trends Neurosci"},{"issue":"22","key":"pcbi.1012934.ref011","doi-asserted-by":"crossref","first-page":"5696","DOI":"10.1523\/JNEUROSCI.0009-08.2008","article-title":"Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information","volume":"28","author":"A Belitski","year":"2008","journal-title":"J Neurosci"},{"issue":"1","key":"pcbi.1012934.ref012","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1038\/s41467-024-46012-5","article-title":"Gamma oscillatory complexity conveys behavioral information in hippocampal networks","volume":"15","author":"V Douchamps","year":"2024","journal-title":"Nat Commun"},{"issue":"4","key":"pcbi.1012934.ref013","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.neuron.2009.01.008","article-title":"Spike-phase coding boosts and stabilizes information carried by spatial and temporal spike patterns","volume":"61","author":"C Kayser","year":"2009","journal-title":"Neuron"},{"issue":"5307","key":"pcbi.1012934.ref014","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1126\/science.275.5307.1805","article-title":"Reproducibility and variability in neural spike trains","volume":"275","author":"RR de Ruyter van Steveninck","year":"1997","journal-title":"Science"},{"issue":"3","key":"pcbi.1012934.ref015","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1162\/biot.2006.1.3.302","article-title":"Approaches to information-theoretic analysis of neural activity","volume":"1","author":"JD Victor","year":"2006","journal-title":"Biol Theory"},{"issue":"5866","key":"pcbi.1012934.ref016","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1126\/science.1149639","article-title":"Rapid neural coding in the retina with relative spike latencies","volume":"319","author":"T Gollisch","year":"2008","journal-title":"Science"},{"issue":"7","key":"pcbi.1012934.ref017","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1038\/s41593-021-00846-0","article-title":"Efficient and adaptive sensory codes","volume":"24","author":"WF M\u0142ynarski","year":"2021","journal-title":"Nat Neurosci"},{"issue":"21","key":"pcbi.1012934.ref018","doi-asserted-by":"crossref","first-page":"5195","DOI":"10.1523\/JNEUROSCI.5319-04.2005","article-title":"Synergy, redundancy, and independence in population codes, revisited","volume":"25","author":"PE Latham","year":"2005","journal-title":"J Neurosci"},{"issue":"37","key":"pcbi.1012934.ref019","doi-asserted-by":"crossref","first-page":"11539","DOI":"10.1523\/JNEUROSCI.23-37-11539.2003","article-title":"Synergy, redundancy, and independence in population codes","volume":"23","author":"E Schneidman","year":"2003","journal-title":"J Neurosci"},{"issue":"1423","key":"pcbi.1012934.ref020","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1098\/rspb.1999.0736","article-title":"Correlations and the encoding of information in the nervous system","volume":"266","author":"S Panzeri","year":"1999","journal-title":"Proc Biol Sci"},{"issue":"1","key":"pcbi.1012934.ref021","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1088\/0954-898X\/14\/1\/303","article-title":"An exact method to quantify the information transmitted by different mechanisms of correlational coding","volume":"14","author":"G Pola","year":"2003","journal-title":"Network"},{"issue":"2","key":"pcbi.1012934.ref022","doi-asserted-by":"crossref","first-page":"402-411.e4","DOI":"10.1016\/j.neuron.2019.07.006","article-title":"Synergistic coding of visual information in columnar networks","volume":"104","author":"S Nigam","year":"2019","journal-title":"Neuron"},{"issue":"6","key":"pcbi.1012934.ref023","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1038\/nn.3707","article-title":"Population code in mouse V1 facilitates readout of natural scenes through increased sparseness","volume":"17","author":"E Froudarakis","year":"2014","journal-title":"Nat Neurosci"},{"issue":"7665","key":"pcbi.1012934.ref024","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1038\/nature23020","article-title":"Distinct timescales of population coding across cortex","volume":"548","author":"CA Runyan","year":"2017","journal-title":"Nature"},{"issue":"11","key":"pcbi.1012934.ref025","doi-asserted-by":"crossref","first-page":"e1005189","DOI":"10.1371\/journal.pcbi.1005189","article-title":"Using matrix and tensor factorizations for the single-trial analysis of population spike trains","volume":"12","author":"A Onken","year":"2016","journal-title":"PLoS Comput Biol"},{"issue":"5","key":"pcbi.1012934.ref026","first-page":"963-976.e7","article-title":"Activity correlations between direction-selective retinal ganglion cells synergistically enhance motion decoding from complex visual scenes","volume":"101","author":"NK K\u00fchn","year":"2019","journal-title":"Neuron"},{"issue":"3","key":"pcbi.1012934.ref027","doi-asserted-by":"crossref","first-page":"e3001530","DOI":"10.1371\/journal.pbio.3001530","article-title":"Complementary encoding of spatial information in hippocampal astrocytes","volume":"20","author":"S Curreli","year":"2022","journal-title":"PLoS Biol"},{"key":"pcbi.1012934.ref028","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.cobeha.2019.03.004","article-title":"Linking neural responses to behavior with information-preserving population vectors","volume":"29","author":"TO Sharpee","year":"2019","journal-title":"Curr Opin Behav Sci"},{"issue":"5","key":"pcbi.1012934.ref029","doi-asserted-by":"crossref","first-page":"1180-1197.e7","DOI":"10.1016\/j.neuron.2017.02.010","article-title":"Population coding in an innately relevant olfactory area","volume":"93","author":"G Iurilli","year":"2017","journal-title":"Neuron"},{"issue":"1","key":"pcbi.1012934.ref030","doi-asserted-by":"crossref","first-page":"2121","DOI":"10.1038\/s41467-023-37804-2","article-title":"A distributed and efficient population code of mixed selectivity neurons for flexible navigation decisions","volume":"14","author":"S Kira","year":"2023","journal-title":"Nat Commun"},{"key":"pcbi.1012934.ref031","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-54474-3","volume-title":"Directed information measures in neuroscience","author":"M Wibral","year":"2014"},{"issue":"1","key":"pcbi.1012934.ref032","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10827-010-0262-3","article-title":"Transfer entropy--a model-free measure of effective connectivity for the neurosciences","volume":"30","author":"R Vicente","year":"2011","journal-title":"J Comput Neurosci"},{"key":"pcbi.1012934.ref033","doi-asserted-by":"crossref","first-page":"116699","DOI":"10.1016\/j.neuroimage.2020.116699","article-title":"Disambiguating the role of blood flow and global signal with partial information decomposition","volume":"213","author":"N Colenbier","year":"2020","journal-title":"Neuroimage"},{"issue":"9","key":"pcbi.1012934.ref034","doi-asserted-by":"crossref","first-page":"e1002257","DOI":"10.1371\/journal.pbio.1002257","article-title":"Shifts of gamma phase across primary visual cortical sites reflect dynamic stimulus-modulated information transfer","volume":"13","author":"M Besserve","year":"2015","journal-title":"PLoS Biol"},{"issue":"6","key":"pcbi.1012934.ref035","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1038\/s41593-022-01070-0","article-title":"A synergistic core for human brain evolution and cognition","volume":"25","author":"AI Luppi","year":"2022","journal-title":"Nat Neurosci"},{"key":"pcbi.1012934.ref036","first-page":"64213","article-title":"An information-theoretic quantification of the content of communication between brain regions","volume":"36","author":"M Celotto","year":"2023","journal-title":"Adv Neural Inf Process Syst \u00b7\u00a0NeurIPS"},{"issue":"9","key":"pcbi.1012934.ref037","doi-asserted-by":"crossref","first-page":"1831","DOI":"10.1016\/j.cub.2024.03.023","article-title":"Information flow between motor cortex and striatum reverses during skill learning","volume":"34","author":"SM Lemke","year":"2024","journal-title":"Curr Biol"},{"issue":"7","key":"pcbi.1012934.ref038","doi-asserted-by":"crossref","first-page":"e1009196","DOI":"10.1371\/journal.pcbi.1009196","article-title":"Partial information decomposition reveals that synergistic neural integration is greater downstream of recurrent information flow in organotypic cortical cultures","volume":"17","author":"SP Sherrill","year":"2021","journal-title":"PLoS Comput Biol"},{"issue":"11","key":"pcbi.1012934.ref039","doi-asserted-by":"crossref","first-page":"1751","DOI":"10.1038\/s41593-019-0510-4","article-title":"Advancing functional connectivity research from association to causation","volume":"22","author":"AT Reid","year":"2019","journal-title":"Nat Neurosci"},{"issue":"6 Pt 2","key":"pcbi.1012934.ref040","doi-asserted-by":"crossref","first-page":"066211","DOI":"10.1103\/PhysRevE.86.066211","article-title":"Expanding the transfer entropy to identify information circuits in complex systems","volume":"86","author":"S Stramaglia","year":"2012","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"2","key":"pcbi.1012934.ref041","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":"pcbi.1012934.ref042","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1038\/s41593-020-00734-z","article-title":"Quantifying behavior to understand the brain","volume":"23","author":"TD Pereira","year":"2020","journal-title":"Nat Neurosci"},{"issue":"3","key":"pcbi.1012934.ref043","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/j.neuron.2016.12.036","article-title":"Cracking the neural code for sensory perception by combining statistics, intervention, and behavior","volume":"93","author":"S Panzeri","year":"2017","journal-title":"Neuron"},{"key":"pcbi.1012934.ref044","first-page":"3686","article-title":"Quantifying how much sensory information in a neural code is relevant for behavior","volume":"30","author":"G Pica","year":"2017","journal-title":"Adv Neural Inf Process Syst"},{"key":"pcbi.1012934.ref045","first-page":"4","article-title":"Python for information theoretic analysis of neural data","volume":"3","author":"RAA Ince","year":"2009","journal-title":"Front Neuroinform"},{"key":"pcbi.1012934.ref046","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1186\/1471-2202-10-81","article-title":"A toolbox for the fast information analysis of multiple-site LFP, EEG and spike train recordings","volume":"10","author":"C Magri","year":"2009","journal-title":"BMC Neurosci"},{"key":"pcbi.1012934.ref047","doi-asserted-by":"crossref","DOI":"10.3389\/frobt.2014.00011","article-title":"JIDT: an information-theoretic toolkit for studying the dynamics of complex systems","volume":"1","author":"JT Lizier","year":"2014","journal-title":"Front Robot AI"},{"issue":"3","key":"pcbi.1012934.ref048","doi-asserted-by":"crossref","DOI":"10.1523\/ENEURO.0052-18.2018","article-title":"A tutorial for information theory in neuroscience","volume":"5","author":"NM Timme","year":"2018","journal-title":"eNeuro"},{"key":"pcbi.1012934.ref049","doi-asserted-by":"crossref","first-page":"119347","DOI":"10.1016\/j.neuroimage.2022.119347","article-title":"Group-level inference of information-based measures for the analyses of cognitive brain networks from neurophysiological data","volume":"258","author":"E Combrisson","year":"2022","journal-title":"Neuroimage"},{"issue":"3","key":"pcbi.1012934.ref050","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1002\/hbm.23471","article-title":"A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula","volume":"38","author":"RAA Ince","year":"2017","journal-title":"Hum Brain Mapp"},{"issue":"5","key":"pcbi.1012934.ref051","doi-asserted-by":"crossref","first-page":"ENEURO.0266-21.2021","DOI":"10.1523\/ENEURO.0266-21.2021","article-title":"Information theoretic approaches to deciphering the neural code with functional fluorescence imaging","volume":"8","author":"JR Climer","year":"2021","journal-title":"eNeuro"},{"issue":"4","key":"pcbi.1012934.ref052","doi-asserted-by":"crossref","first-page":"271","DOI":"10.3390\/e20040271","article-title":"BROJA-2PID: a robust estimator for bivariate partial information decomposition","volume":"20","author":"A Makkeh","year":"2018","journal-title":"Entropy (Basel)"},{"key":"pcbi.1012934.ref053","volume-title":"Inform: A toolkit for information-theoretic analysis of complex systems","author":"DG Moore","year":"2017"},{"issue":"10","key":"pcbi.1012934.ref054","doi-asserted-by":"crossref","first-page":"e109462","DOI":"10.1371\/journal.pone.0109462","article-title":"MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy","volume":"9","author":"A Montalto","year":"2014","journal-title":"PLoS One"},{"issue":"1","key":"pcbi.1012934.ref055","first-page":"283","article-title":"Information theoretical estimators toolbox","volume":"15","author":"Z Szab\u00f3","year":"2014","journal-title":"J. Mach.\u00a0Learn.\u00a0Res"},{"key":"pcbi.1012934.ref056","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1186\/1471-2202-12-119","article-title":"TRENTOOL: a Matlab open source toolbox to analyse information flow in time series data with transfer entropy","volume":"12","author":"M Lindner","year":"2011","journal-title":"BMC Neurosci"},{"issue":"11","key":"pcbi.1012934.ref057","doi-asserted-by":"crossref","first-page":"e27431","DOI":"10.1371\/journal.pone.0027431","article-title":"Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model","volume":"6","author":"S Ito","year":"2011","journal-title":"PLoS One"},{"issue":"3","key":"pcbi.1012934.ref058","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s12021-009-9049-y","article-title":"Spike train analysis toolkit: enabling wider application of information-theoretic techniques to neurophysiology","volume":"7","author":"DH Goldberg","year":"2009","journal-title":"Neuroinformatics"},{"issue":"103","key":"pcbi.1012934.ref059","doi-asserted-by":"crossref","first-page":"7360","DOI":"10.21105\/joss.07360","article-title":"HOI: A Python toolbox for high-performance estimation of Higher-Order Interactions from multivariate data","volume":"9","author":"M Neri","year":"2024","journal-title":"JOSS"},{"issue":"25","key":"pcbi.1012934.ref060","doi-asserted-by":"crossref","first-page":"738","DOI":"10.21105\/joss.00738","article-title":"dit: a Python package for discrete information theory","volume":"3","author":"R G. James","year":"2018","journal-title":"JOSS"},{"issue":"47","key":"pcbi.1012934.ref061","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.21105\/joss.01609","article-title":"infotheory: A C++\/Python package for multivariate information theoretic analysis","volume":"5","author":"M Candadai","year":"2020","journal-title":"JOSS"},{"issue":"7890","key":"pcbi.1012934.ref062","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1038\/s41586-021-04094-x","article-title":"Cortical responses to touch reflect subcortical integration of LTMR signals","volume":"600","author":"AJ Emanuel","year":"2021","journal-title":"Nature"},{"issue":"7087","key":"pcbi.1012934.ref063","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1038\/nature04701","article-title":"Weak pairwise correlations imply strongly correlated network states in a neural population","volume":"440","author":"E Schneidman","year":"2006","journal-title":"Nature"},{"issue":"50","key":"pcbi.1012934.ref064","doi-asserted-by":"crossref","first-page":"E11817","DOI":"10.1073\/pnas.1810701115","article-title":"Photoreceptive retinal ganglion cells control the information rate of the optic nerve","volume":"115","author":"N Milosavljevic","year":"2018","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"1","key":"pcbi.1012934.ref065","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/j.neuroimage.2009.07.038","article-title":"An information theoretic approach to EEG-fMRI integration of visually evoked responses","volume":"49","author":"D Ostwald","year":"2010","journal-title":"Neuroimage"},{"issue":"3","key":"pcbi.1012934.ref066","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1093\/cercor\/bhk020","article-title":"Decoding near-threshold perception of fear from distributed single-trial brain activation","volume":"17","author":"L Pessoa","year":"2007","journal-title":"Cereb Cortex"},{"issue":"25","key":"pcbi.1012934.ref067","doi-asserted-by":"crossref","first-page":"8005","DOI":"10.1523\/JNEUROSCI.4919-08.2009","article-title":"Spatial pattern coding of sensory information by climbing fiber-evoked calcium signals in networks of neighboring cerebellar Purkinje cells","volume":"29","author":"SR Schultz","year":"2009","journal-title":"J Neurosci"},{"issue":"6838","key":"pcbi.1012934.ref068","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1038\/35079612","article-title":"Retinal ganglion cells act largely as independent encoders","volume":"411","author":"S Nirenberg","year":"2001","journal-title":"Nature"},{"issue":"13","key":"pcbi.1012934.ref069","doi-asserted-by":"crossref","first-page":"4815","DOI":"10.1523\/JNEUROSCI.4360-09.2010","article-title":"Mismatched decoding in the brain","volume":"30","author":"M Oizumi","year":"2010","journal-title":"J Neurosci"},{"key":"pcbi.1012934.ref070","article-title":"Nonnegative decomposition of multivariate information","volume":"arXiv:10042515","author":"P Williams","year":"2010","journal-title":"arXiv preprint"},{"key":"pcbi.1012934.ref071","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.bandc.2015.09.004","article-title":"Partial information decomposition as a unified approach to the specification of neural goal functions","volume":"112","author":"M Wibral","year":"2017","journal-title":"Brain Cogn"},{"issue":"4","key":"pcbi.1012934.ref072","doi-asserted-by":"crossref","first-page":"2161","DOI":"10.3390\/e16042161","article-title":"Quantifying unique information","volume":"16","author":"N Bertschinger","year":"2014","journal-title":"Entropy"},{"issue":"5","key":"pcbi.1012934.ref073","doi-asserted-by":"crossref","first-page":"052802","DOI":"10.1103\/PhysRevE.91.052802","article-title":"Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems","volume":"91","author":"AB Barrett","year":"2015","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"2","key":"pcbi.1012934.ref074","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":"Phys Rev Lett"},{"issue":"1","key":"pcbi.1012934.ref075","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1103\/PhysRevLett.80.197","article-title":"Entropy and information in neural spike trains","volume":"80","author":"SP Strong","year":"1998","journal-title":"Phys Rev Lett"},{"issue":"12","key":"pcbi.1012934.ref076","doi-asserted-by":"crossref","first-page":"e1001752","DOI":"10.1371\/journal.pbio.1001752","article-title":"Speech rhythms and multiplexed oscillatory sensory coding in the human brain","volume":"11","author":"J Gross","year":"2013","journal-title":"PLoS Biol"},{"issue":"18","key":"pcbi.1012934.ref077","doi-asserted-by":"crossref","first-page":"3987-3999.e4","DOI":"10.1016\/j.cub.2022.07.049","article-title":"Look-up and look-down neurons in the mouse visual thalamus during freely moving exploration","volume":"32","author":"P Orlowska-Feuer","year":"2022","journal-title":"Curr Biol"},{"issue":"4","key":"pcbi.1012934.ref078","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1002\/wics.103","article-title":"Scott\u2019s rule","volume":"2","author":"DW Scott","year":"2010","journal-title":"WIREs Computational Stats"},{"issue":"4","key":"pcbi.1012934.ref079","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/BF01025868","article-title":"On the histogram as a density estimator:L 2 theory","volume":"57","author":"D Freedman","year":"1981","journal-title":"Z Wahrscheinlichkeitstheorie verw Gebiete"},{"issue":"1","key":"pcbi.1012934.ref080","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1080\/0954898X.1996.11978656","article-title":"Analytical estimates of limited sampling biases in different information measures","volume":"7","author":"S Panzeri","year":"1996","journal-title":"Network"},{"issue":"6","key":"pcbi.1012934.ref081","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1162\/089976603321780272","article-title":"Estimation of entropy and mutual information","volume":"15","author":"L Paninski","year":"2003","journal-title":"Neural Comput"},{"issue":"3","key":"pcbi.1012934.ref082","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1152\/jn.00559.2007","article-title":"Correcting for the sampling bias problem in spike train information measures","volume":"98","author":"S Panzeri","year":"2007","journal-title":"J Neurophysiol"},{"issue":"5","key":"pcbi.1012934.ref083","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/BF00216963","article-title":"Unbiased measures of transmitted information and channel capacity from multivariate neuronal data","volume":"65","author":"LM Optican","year":"1991","journal-title":"Biol Cybern"},{"issue":"11","key":"pcbi.1012934.ref084","doi-asserted-by":"crossref","first-page":"2913","DOI":"10.1162\/neco.2007.19.11.2913","article-title":"Tight data-robust bounds to mutual information combining shuffling and model selection techniques","volume":"19","author":"MA Montemurro","year":"2007","journal-title":"Neural Comput"},{"issue":"6","key":"pcbi.1012934.ref085","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/j.neunet.2010.05.008","article-title":"Information-theoretic methods for studying population codes","volume":"23","author":"RAA Ince","year":"2010","journal-title":"Neural Netw"},{"issue":"6 Pt 2","key":"pcbi.1012934.ref086","doi-asserted-by":"crossref","first-page":"066138","DOI":"10.1103\/PhysRevE.69.066138","article-title":"Estimating mutual information","volume":"69","author":"A Kraskov","year":"2004","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"2\u20131","key":"pcbi.1012934.ref087","doi-asserted-by":"crossref","first-page":"022404","DOI":"10.1103\/PhysRevE.100.022404","article-title":"Estimation of mutual information for real-valued data with error bars and controlled bias","volume":"100","author":"CM Holmes","year":"2019","journal-title":"Phys Rev E"},{"issue":"5 Pt 2","key":"pcbi.1012934.ref088","doi-asserted-by":"crossref","first-page":"056111","DOI":"10.1103\/PhysRevE.69.056111","article-title":"Entropy and information in neural spike trains: progress on the sampling problem","volume":"69","author":"I Nemenman","year":"2004","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"6755","key":"pcbi.1012934.ref089","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1038\/44565","article-title":"Learning the parts of objects by non-negative matrix factorization","volume":"401","author":"DD Lee","year":"1999","journal-title":"Nature"},{"issue":"3","key":"pcbi.1012934.ref090","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1961189.1961199","article-title":"Libsvm: a library for support vector machines","volume":"2","author":"C-C Chang","year":"2011","journal-title":"ACM Trans Intell Syst Technol"},{"issue":"1","key":"pcbi.1012934.ref091","doi-asserted-by":"crossref","DOI":"10.18637\/jss.v033.i01","article-title":"Regularization paths for generalized linear models via coordinate descent","volume":"33","author":"J Friedman","year":"2010","journal-title":"J Stat Soft"},{"issue":"2","key":"pcbi.1012934.ref092","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1038\/nn.2733","article-title":"Decoding the activity of neuronal populations in macaque primary visual cortex","volume":"14","author":"ABA Graf","year":"2011","journal-title":"Nat Neurosci"},{"issue":"5","key":"pcbi.1012934.ref093","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1038\/nrn1888","article-title":"Neural correlations, population coding and computation","volume":"7","author":"BB Averbeck","year":"2006","journal-title":"Nat Rev Neurosci"},{"issue":"5551","key":"pcbi.1012934.ref094","doi-asserted-by":"crossref","first-page":"2566","DOI":"10.1126\/science.1065839","article-title":"Independent and redundant information in nearby cortical neurons","volume":"294","author":"DS Reich","year":"2001","journal-title":"Science"},{"key":"pcbi.1012934.ref095","first-page":"1","article-title":"Group redundancy measures reveal redundancy reduction in the auditory pathway","volume":"14","author":"G Chechik","year":"2001","journal-title":"Adv Neural Inf Process Syst"},{"issue":"1","key":"pcbi.1012934.ref096","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/cogs.12142","article-title":"Information processing and dynamics in minimally cognitive agents","volume":"39","author":"RD Beer","year":"2015","journal-title":"Cogn Sci"},{"issue":"9","key":"pcbi.1012934.ref097","doi-asserted-by":"crossref","first-page":"110878","DOI":"10.1016\/j.celrep.2022.110878","article-title":"Sequential transmission of task-relevant information in cortical neuronal networks","volume":"39","author":"NA Francis","year":"2022","journal-title":"Cell Rep"},{"issue":"7","key":"pcbi.1012934.ref098","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1038\/s41593-021-00845-1","article-title":"Correlations enhance the behavioral readout of neural population activity in association cortex","volume":"24","author":"M Valente","year":"2021","journal-title":"Nat Neurosci"},{"issue":"13","key":"pcbi.1012934.ref099","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1167\/14.13.7","article-title":"Eye coding mechanisms in early human face event-related potentials","volume":"14","author":"GA Rousselet","year":"2014","journal-title":"J Vis"},{"issue":"11","key":"pcbi.1012934.ref100","doi-asserted-by":"crossref","first-page":"4123","DOI":"10.1093\/cercor\/bhw196","article-title":"The Deceptively Simple N170 reflects network information processing mechanisms involving visual feature coding and transfer across hemispheres","volume":"26","author":"RAA Ince","year":"2016","journal-title":"Cereb Cortex"},{"key":"pcbi.1012934.ref101","doi-asserted-by":"crossref","first-page":"156869","DOI":"10.1155\/2011\/156869","article-title":"FieldTrip: Open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data","volume":"2011","author":"R Oostenveld","year":"2011","journal-title":"Comput Intell Neurosci"},{"issue":"3","key":"pcbi.1012934.ref102","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1016\/j.neuroimage.2009.10.003","article-title":"Complex network measures of brain connectivity: uses and interpretations","volume":"52","author":"M Rubinov","year":"2010","journal-title":"Neuroimage"},{"issue":"5","key":"pcbi.1012934.ref103","doi-asserted-by":"crossref","first-page":"053302","DOI":"10.1103\/PhysRevE.98.053302","article-title":"Information estimation using nonparametric copulas","volume":"98","author":"H Safaai","year":"2018","journal-title":"Phys Rev E"},{"issue":"5 Pt 1","key":"pcbi.1012934.ref104","doi-asserted-by":"crossref","first-page":"051903","DOI":"10.1103\/PhysRevE.66.051903","article-title":"Binless strategies for estimation of information from neural data","volume":"66","author":"JD Victor","year":"2002","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"4","key":"pcbi.1012934.ref105","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.tics.2023.11.005","article-title":"Information decomposition and the informational architecture of the brain","volume":"28","author":"AI Luppi","year":"2024","journal-title":"Trends Cogn Sci"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1012934","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T00:00:00Z","timestamp":1745971200000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012934","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T14:06:08Z","timestamp":1746799568000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012934"}},"subtitle":[],"editor":[{"given":"Hugues","family":"Berry","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,4,15]]},"references-count":105,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4,15]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1012934","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2024.11.04.621910","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,15]]}}}