{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T18:46:12Z","timestamp":1791917172029,"version":"4.3.4"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1014820","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T00:00:00Z","timestamp":1791849600000}}],"reference-count":90,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000148","name":"Division of Electrical, Communications and Cyber Systems","doi-asserted-by":"publisher","award":["ECCS2032649"],"award-info":[{"award-number":["ECCS2032649"]}],"id":[{"id":"10.13039\/100000148","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000089","name":"Office of International Science and Engineering","doi-asserted-by":"publisher","award":["OISE2020624"],"award-info":[{"award-number":["OISE2020624"]}],"id":[{"id":"10.13039\/100000089","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000055","name":"National Institute on Deafness and Other Communication Disorders","doi-asserted-by":"publisher","award":["RO1DC017785"],"award-info":[{"award-number":["RO1DC017785"]}],"id":[{"id":"10.13039\/100000055","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000065","name":"National Institute of Neurological Disorders and Stroke","doi-asserted-by":"publisher","award":["U19NS107464"],"award-info":[{"award-number":["U19NS107464"]}],"id":[{"id":"10.13039\/100000065","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000065","name":"National Institute of Neurological Disorders and Stroke","doi-asserted-by":"publisher","award":["U19NS107464"],"award-info":[{"award-number":["U19NS107464"]}],"id":[{"id":"10.13039\/100000065","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    Understanding how neuronal populations interact to encode and transform sensory information is a fundamental challenge in computational neuroscience. Most existing studies, however, study neural encoding, behavioral readout, and functional connectivity as disjoint problems. Two-photon calcium imaging enables simultaneous recording of large neuronal ensembles\n                    <jats:italic>in vivo<\/jats:italic>\n                    , driven by diverse stimuli and eliciting distinct behaviors. However, extracting directional functional connectivity metrics as well as encoding and readout properties of neurons from such data remains difficult due to indirect and noisy observations of spiking activity, slow temporal dynamics, and the latent interplay between external stimuli and endogenous neural processes. Here, we introduce a unified conceptual and operational modeling and inference framework for\n                    <jats:italic>directly<\/jats:italic>\n                    extracting functional Granger causal (GC) effects between neurons, from external stimuli to neurons, and from neurons to behavior, from two-photon imaging data, in the sense of Granger\u2019s temporal predictability. Inspired by the intersection information framework, we also identify neurons that encode features of sensory stimuli that inform behavioral readout. The resulting GC networks together with the taxonomy of functional sensori-behavioral relevance, which we call G-taxonomy, provides a powerful statistical analysis framework, enabled by the integration of several techniques including state-space modeling and inference, variational inference, and point processes. We applied the proposed framework to simulated and experimentally-recorded two-photon imaging from the mouse auditory cortex (A1) during both passive listening and active tone discrimination. Our simulation studies reveal significant improvement of our proposed methodology over existing techniques. Analysis of experimental data from the mouse A1 identifies distinct groups of cells with diverse sensori-behavioral relevance, as well as changes in functional connectivity associated with correct vs. incorrect behavior. In summary, this work provides a principled and data-driven methodology for uncovering directional interactions among the neurons, sensory stimuli, and behavior, all within the same statistical framework, offering new insights into how distributed cortical populations transform sensory inputs into behaviorally relevant representations.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1014820","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T17:46:09Z","timestamp":1790790369000},"page":"e1014820","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Granger sensori-behavioral functional taxonomy of neuronal ensemble activity from two-photon calcium imaging data"],"prefix":"10.1371","volume":"22","author":[{"given":"Sahar","family":"Khosravi","sequence":"first","affiliation":[{"name":"University of Maryland","place":["College Park, Maryland, United States of 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Ding","year":"2012","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"8","key":"pcbi.1014820.ref002","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1038\/nn.2598","article-title":"Adaptive, behaviorally gated, persistent encoding of task-relevant auditory information in ferret frontal cortex","volume":"13","author":"JB Fritz","year":"2010","journal-title":"Nat Neurosci"},{"issue":"5180","key":"pcbi.1014820.ref003","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1126\/science.265.5180.1872","article-title":"Encoding of olfactory information with oscillating neural assemblies","volume":"265","author":"G Laurent","year":"1994","journal-title":"Science"},{"issue":"6174","key":"pcbi.1014820.ref004","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1126\/science.1245994","article-title":"Phonetic feature encoding in human superior temporal gyrus","volume":"343","author":"N Mesgarani","year":"2014","journal-title":"Science"},{"key":"pcbi.1014820.ref005","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1146\/annurev.neuro.24.1.1193","article-title":"Natural image statistics and neural representation","volume":"24","author":"EP Simoncelli","year":"2001","journal-title":"Annu Rev Neurosci"},{"issue":"18","key":"pcbi.1014820.ref006","doi-asserted-by":"crossref","first-page":"7411","DOI":"10.1523\/JNEUROSCI.18-18-07411.1998","article-title":"A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells","volume":"18","author":"EN Brown","year":"1998","journal-title":"J Neurosci"},{"issue":"5","key":"pcbi.1014820.ref007","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1162\/089976604773135069","article-title":"Dynamic analysis of neural encoding by point process adaptive filtering","volume":"16","author":"UT Eden","year":"2004","journal-title":"Neural 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Quantifying how much sensory information in a neural code is relevant for behavior. In: Advances in Neural Information Processing Systems. 2017. p. 3686\u201396."},{"key":"pcbi.1014820.ref016","doi-asserted-by":"crossref","first-page":"104028","DOI":"10.1016\/j.biosystems.2019.104028","article-title":"Using intersection information to map stimulus information transfer within neural networks","volume":"185","author":"G Pica","year":"2019","journal-title":"Biosystems"},{"issue":"2","key":"pcbi.1014820.ref017","doi-asserted-by":"crossref","first-page":"71","DOI":"10.3390\/e19020071","article-title":"Synergy and Redundancy in Dual Decompositions of Mutual Information Gain and Information Loss","volume":"19","author":"D Chicharro","year":"2017","journal-title":"Entropy"},{"issue":"21","key":"pcbi.1014820.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.1014820.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"},{"key":"pcbi.1014820.ref020","unstructured":"Williams PL, Beer RD. Nonnegative decomposition of multivariate information. arXiv preprint arXiv:10042515. 2010."},{"issue":"2251","key":"pcbi.1014820.ref021","first-page":"20210110","article-title":"Bits and pieces: understanding information decomposition from part-whole relationships and formal logic","volume":"477","author":"AJ Gutknecht","year":"2021","journal-title":"Proc Math Phys Eng Sci"},{"issue":"9","key":"pcbi.1014820.ref022","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":"1","key":"pcbi.1014820.ref023","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1186\/s40708-023-00212-9","article-title":"Behavioural relevance of redundant and synergistic stimulus information between functionally connected neurons in mouse auditory cortex","volume":"10","author":"L Ko\u00e7illari","year":"2023","journal-title":"Brain Inform"},{"key":"pcbi.1014820.ref024","first-page":"45","article-title":"Measuring stimulus-related redundant and synergistic functional connectivity with single cell resolution in auditory cortex.","volume-title":"International Conference on Brain Informatics","author":"L Ko\u00e7illari","year":"2023"},{"key":"pcbi.1014820.ref025","doi-asserted-by":"crossref","unstructured":"Park H, Arazi A, Talluri BC, Celotto M, Panzeri S, Stocker AA, et al. 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Pachitariu","year":"2018","journal-title":"J Neurosci"},{"issue":"8","key":"pcbi.1014820.ref029","doi-asserted-by":"crossref","first-page":"3293","DOI":"10.1523\/JNEUROSCI.4399-14.2015","article-title":"Granger causality analysis in neuroscience and neuroimaging","volume":"35","author":"AK Seth","year":"2015","journal-title":"J Neurosci"},{"issue":"23","key":"pcbi.1014820.ref030","doi-asserted-by":"crossref","first-page":"238701","DOI":"10.1103\/PhysRevLett.103.238701","article-title":"Granger causality and transfer entropy are equivalent for Gaussian variables","volume":"103","author":"L Barnett","year":"2009","journal-title":"Phys Rev Lett"},{"issue":"1","key":"pcbi.1014820.ref031","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0313875","article-title":"VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics","volume":"20","author":"LC Parra","year":"2025","journal-title":"PLoS 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Manomaisaowapak","year":"2022","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"11","key":"pcbi.1014820.ref039","doi-asserted-by":"crossref","first-page":"7439","DOI":"10.1109\/TIT.2023.3296336","article-title":"Non-Asymptotic Guarantees for Reliable Identification of Granger Causality via the LASSO","volume":"69","author":"P Das","year":"2023","journal-title":"IEEE Trans Inf Theory"},{"key":"pcbi.1014820.ref040","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.68046","article-title":"Direct extraction of signal and noise corrections from two-photon calcium imaging of ensemble neuronal activity","volume":"10","author":"A Rupasinghe","year":"2021","journal-title":"eLife"},{"issue":"27","key":"pcbi.1014820.ref041","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2510012122","article-title":"Patchy harmonic functional connectivity of the mouse auditory cortex","volume":"122","author":"P Jendrichovsky","year":"2025","journal-title":"Proc Natl Acad Sci U S 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Anal"},{"issue":"3","key":"pcbi.1014820.ref048","first-page":"601","article-title":"Covariances for smoothed estimates in state space models","volume":"75","author":"J P","journal-title":"Biometrika"},{"issue":"1","key":"pcbi.1014820.ref049","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1002\/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3","article-title":"Index for rating diagnostic tests","volume":"3","author":"WJ Youden","year":"1950","journal-title":"Cancer"},{"issue":"4","key":"pcbi.1014820.ref050","doi-asserted-by":"crossref","DOI":"10.1214\/aos\/1013699998","article-title":"The control of the false discovery rate in multiple testing under dependency","volume":"29","author":"Y Benjamini","year":"2001","journal-title":"Ann Statist"},{"issue":"2","key":"pcbi.1014820.ref051","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1152\/jn.00697.2004","article-title":"A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects","volume":"93","author":"W Truccolo","year":"2005","journal-title":"J Neurophysiol"},{"key":"pcbi.1014820.ref052","unstructured":"Panzeri S, Harvey CD, Piasini E, Latham PE, Fellin T. Cracking the neural code for sensory perception by combining statistics, intervention, and behavior."},{"issue":"2","key":"pcbi.1014820.ref053","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.neuron.2015.11.037","article-title":"Simultaneous Denoising, Deconvolution, and Demixing of Calcium Imaging Data","volume":"89","author":"EA Pnevmatikakis","year":"2016","journal-title":"Neuron"},{"key":"pcbi.1014820.ref054","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.10989","article-title":"Demixed principal component analysis of neural population data","volume":"5","author":"D Kobak","year":"2016","journal-title":"Elife"},{"issue":"10","key":"pcbi.1014820.ref055","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1038\/s41593-019-0502-4","article-title":"Single-trial neural dynamics are dominated by richly varied movements","volume":"22","author":"S Musall","year":"2019","journal-title":"Nat Neurosci"},{"issue":"7864","key":"pcbi.1014820.ref056","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1038\/s41586-021-03628-7","article-title":"Representational drift in primary olfactory cortex","volume":"594","author":"CE Schoonover","year":"2021","journal-title":"Nature"},{"key":"pcbi.1014820.ref057","doi-asserted-by":"crossref","unstructured":"Rupasinghe A, Mukherjee S, Babadi B. Adaptive Frequency-domain Granger Causal Inference from Neuronal Ensemble Data. In: 2020 54th Asilomar Conference on Signals, Systems, and Computers. IEEE; 2020. p. 101\u20135.","DOI":"10.1109\/IEEECONF51394.2020.9443471"},{"issue":"6106","key":"pcbi.1014820.ref058","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1126\/science.1227079","article-title":"Detecting causality in complex ecosystems","volume":"338","author":"G Sugihara","year":"2012","journal-title":"Science"},{"key":"pcbi.1014820.ref059","doi-asserted-by":"crossref","first-page":"14750","DOI":"10.1038\/srep14750","article-title":"Distinguishing time-delayed causal interactions using convergent cross mapping","volume":"5","author":"H Ye","year":"2015","journal-title":"Sci Rep"},{"key":"pcbi.1014820.ref060","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1007\/BFb0091924","article-title":"Detecting strange attractors in turbulence.","volume-title":"Dynamical systems and turbulence, Warwick 1980. vol. 898 of Lecture Notes in Mathematics","author":"F. Takens","year":"1981"},{"issue":"1","key":"pcbi.1014820.ref061","doi-asserted-by":"crossref","first-page":"3183","DOI":"10.1038\/s41598-023-30224-8","article-title":"Assessing brain state and anesthesia level with two-photon calcium signals","volume":"13","author":"N Tort-Colet","year":"2023","journal-title":"Sci Rep"},{"key":"pcbi.1014820.ref062","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10827-009-0179-x","article-title":"A new look at state-space models for neural data","volume":"29","author":"L Paninski","year":"2010","journal-title":"J Comput Neurosci"},{"key":"pcbi.1014820.ref063","volume-title":"Generalized Linear Models","author":"P McCullagh","edition":"2"},{"key":"pcbi.1014820.ref064","volume-title":"Pattern Recognition and Machine Learning","author":"CM Bishop"},{"issue":"1","key":"pcbi.1014820.ref065","doi-asserted-by":"crossref","first-page":"018701","DOI":"10.1103\/PhysRevLett.100.018701","article-title":"Estimating Granger causality from fourier and wavelet transforms of time series data","volume":"100","author":"M Dhamala","year":"2008","journal-title":"Phys Rev Lett"},{"key":"pcbi.1014820.ref066","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1023\/A:1007665907178","article-title":"An introduction to variational methods for graphical models","volume":"37","author":"MI Jordan","year":"2000","journal-title":"Mach Learn"},{"issue":"518","key":"pcbi.1014820.ref067","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational inference: A review for statisticians","volume":"112","author":"DM Blei","year":"2017","journal-title":"J Am Stat Assoc"},{"key":"pcbi.1014820.ref068","author":"MJ Beal","year":"2003"},{"key":"pcbi.1014820.ref069","first-page":"1898","article-title":"Fully Bayesian inference for neural models with negative-binomial spiking.","volume-title":"Advances in Neural Information Processing Systems","author":"JW Pillow","year":"2012"},{"key":"pcbi.1014820.ref070","unstructured":"Linderman S, Adams RP, Pillow JW. Bayesian latent structure discovery from multi-neuron recordings. In: Advances in Neural Information Processing Systems. p. 2002\u201310."},{"key":"pcbi.1014820.ref071","author":"S Fr\u00fchwirth-Schnatter"},{"key":"pcbi.1014820.ref072","doi-asserted-by":"crossref","unstructured":"Soleimani B, Das P, Kulasingham J, Simon JZ, Babadi B. Granger Causal Inference from Indirect Low-Dimensional Measurements with Application to MEG Functional Connectivity Analysis. In: 2020 54th Annual Conference on Information Sciences and Systems (CISS). IEEE; 2020. p. 1\u20135.","DOI":"10.1109\/CISS48834.2020.1570617418"},{"issue":"2","key":"pcbi.1014820.ref073","first-page":"209","article-title":"The limiting distribution of the likelihood ratio statistic under a class of local alternatives","volume":"32","author":"RR Davidson","year":"1970","journal-title":"Sankh\u0101 A"},{"issue":"3","key":"pcbi.1014820.ref074","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1090\/S0002-9947-1943-0012401-3","article-title":"Tests of statistical hypotheses concerning several parameters when the number of observations is large","volume":"54","author":"A Wald","year":"1943","journal-title":"Trans Amer Math Soc"},{"issue":"1","key":"pcbi.1014820.ref075","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1214\/aoms\/1177732360","article-title":"The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses","volume":"9","author":"SS Wilks","year":"1938","journal-title":"Ann Math Statist"},{"key":"pcbi.1014820.ref076","volume-title":"Adaptive Filter Theory","author":"SS Haykin","year":"2002","edition":"4"},{"key":"pcbi.1014820.ref077","doi-asserted-by":"crossref","DOI":"10.1017\/9781108231596","volume-title":"High-dimensional probability: an introduction with applications in data science","author":"R Vershynin","year":"2018"},{"issue":"4","key":"pcbi.1014820.ref078","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"},{"key":"pcbi.1014820.ref079","doi-asserted-by":"crossref","first-page":"64213","DOI":"10.52202\/075280-2806","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 Inform Process Syst"},{"issue":"5","key":"pcbi.1014820.ref080","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":"1","key":"pcbi.1014820.ref081","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.neuron.2019.09.045","article-title":"Excitatory and inhibitory subnetworks are equally selective during decision-making and emerge simultaneously during learning","volume":"105","author":"F Najafi","year":"2020","journal-title":"Neuron"},{"issue":"10","key":"pcbi.1014820.ref082","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004464","article-title":"Efficient \u201cShotgun\u201d Inference of Neural Connectivity from Highly Sub-sampled Activity Data","volume":"11","author":"D Soudry","year":"2015","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"pcbi.1014820.ref083","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004083","article-title":"Improved estimation and interpretation of correlations in neural circuits","volume":"11","author":"D Yatsenko","year":"2015","journal-title":"PLoS Comput Biol"},{"issue":"4","key":"pcbi.1014820.ref084","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1016\/j.neuron.2018.09.024","article-title":"Intermingled ensembles in visual association cortex encode stimulus identity or predicted outcome","volume":"100","author":"RN Ramesh","year":"2018","journal-title":"Neuron"},{"key":"pcbi.1014820.ref085","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.46966","article-title":"Functional clustering of dendritic activity during decision-making","volume":"8","author":"A Kerlin","year":"2019","journal-title":"eLife"},{"issue":"4","key":"pcbi.1014820.ref086","doi-asserted-by":"crossref","DOI":"10.1016\/j.neuron.2018.01.019","article-title":"Small Networks Encode Decision-Making in Primary Auditory Cortex","volume":"97","author":"NA Francis","year":"2018","journal-title":"Neuron"},{"key":"pcbi.1014820.ref087","doi-asserted-by":"crossref","unstructured":"Khosravi S, Jendrichovsky P, Maximov K, Kanold PO, Babadi B. Extracting two-dimensional signal correlation maps via Gaussian process regression with Zernike means. In: Proceedings of the 2025 Asilomar Conference on Signals, Systems, and Computers. IEEE.","DOI":"10.1109\/IEEECONF67917.2025.11443692"},{"issue":"3","key":"pcbi.1014820.ref088","doi-asserted-by":"crossref","first-page":"872","DOI":"10.1016\/j.celrep.2019.03.069","article-title":"Parallel Processing of Sound Dynamics across Mouse Auditory Cortex via Spatially Patterned Thalamic Inputs and Distinct Areal Intracortical Circuits","volume":"27","author":"J Liu","year":"2019","journal-title":"Cell Rep"},{"issue":"1","key":"pcbi.1014820.ref089","doi-asserted-by":"crossref","first-page":"10905","DOI":"10.1038\/s41598-020-67819-4","article-title":"Functional organization of mouse primary auditory cortex in adult C57BL\/6 and F1 (CBAxC57) mice","volume":"10","author":"Z Bowen","year":"2020","journal-title":"Sci Rep"},{"issue":"1","key":"pcbi.1014820.ref090","doi-asserted-by":"crossref","first-page":"3493","DOI":"10.1038\/s41598-018-21640-2","article-title":"FISSA: A neuropil decontamination toolbox for calcium imaging signals","volume":"8","author":"SW Keemink","year":"2018","journal-title":"Sci Rep"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1014820","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T00:00:00Z","timestamp":1791849600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014820","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T17:55:43Z","timestamp":1791914143000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014820"}},"subtitle":[],"editor":[{"given":"Alain","family":"Nogaret","sequence":"first","affiliation":[{"name":"University of Bath","place":["UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND"]}],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,9,30]]},"references-count":90,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9,30]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1014820","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,30]]}}}