{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:42Z","timestamp":1760242542444,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T00:00:00Z","timestamp":1508976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Information processing within neural systems often depends upon selective amplification of relevant signals and suppression of irrelevant signals. This has been shown many times by studies of contextual effects but there is as yet no consensus on how to interpret such studies. Some researchers interpret the effects of context as contributing to the selective receptive field (RF) input about which neurons transmit information. Others interpret context effects as affecting transmission of information about RF input without becoming part of the RF information transmitted. Here we use partial information decomposition (PID) and entropic information decomposition (EID) to study the properties of a form of modulation previously used in neurobiologically plausible neural nets. PID shows that this form of modulation can affect transmission of information in the RF input without the binary output transmitting any information unique to the modulator. EID produces similar decompositions, except that information unique to the modulator and the mechanistic shared component can be negative when modulating and modulated signals are correlated. Synergistic and source shared components were never negative in the conditions studied. Thus, both PID and EID show that modulatory inputs to a local processor can affect the transmission of information from other inputs. Contrary to what was previously assumed, this transmission can occur without the modulatory inputs becoming part of the information transmitted, as shown by the use of PID with the model we consider. Decompositions of psychophysical data from a visual contrast detection task with surrounding context suggest that a similar form of modulation may also occur in real neural systems.<\/jats:p>","DOI":"10.3390\/e19110560","type":"journal-article","created":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T06:48:14Z","timestamp":1509000494000},"page":"560","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Partial and Entropic Information Decompositions of a Neuronal Modulatory Interaction"],"prefix":"10.3390","volume":"19","author":[{"given":"Jim","family":"Kay","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Glasgow, Glasgow G12 8QQ, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8427-0507","authenticated-orcid":false,"given":"Robin","family":"Ince","sequence":"additional","affiliation":[{"name":"Institute of Neuroscience and Psychology, University of Glasgow, Glasgow G12 8QQ, UK"}]},{"given":"Benjamin","family":"Dering","sequence":"additional","affiliation":[{"name":"Faculty of Natural Sciences, University of Stirling, Stirling FK9 4LA, UK"}]},{"given":"William","family":"Phillips","sequence":"additional","affiliation":[{"name":"Faculty of Natural Sciences, University of Stirling, Stirling FK9 4LA, UK"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1016\/j.neuron.2007.05.019","article-title":"Brain States: Top-Down Influences in Sensory Processing","volume":"54","author":"Gilbert","year":"2007","journal-title":"Neuron"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1017\/S0140525X9700160X","article-title":"In search of common foundations for cortical computation","volume":"20","author":"Phillips","year":"1997","journal-title":"Behav. Brain Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1017\/S0140525X03000025","article-title":"Convergence of biological and psychological perspectives on cognitive coordination in schizophrenia","volume":"26","author":"Phillips","year":"2003","journal-title":"Behav. Brain Sci."},{"key":"ref_4","unstructured":"Werner, J.S., and Chalupa, L.M. (2004). Beyond the classical receptive field: Contextual modulation of V1 responses. The Visual Neurosciences, MIT Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/S0893-6080(97)00110-X","article-title":"Contextually guided unsupervised learning using local multivariate binary processors","volume":"11","author":"Kay","year":"1998","journal-title":"Neural Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.tins.2012.11.006","article-title":"A cellular mechanism for cortical associations: An organizing principle for the cerebral cortex","volume":"36","author":"Larkum","year":"2013","journal-title":"Trends Neurosci."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Phillips, W.A., Larkum, M.E., Harley, C.W., and Silverstein, S.M. (2016). The effects of arousal on apical amplification and conscious state. Neurosci. Conscious., 1\u201313.","DOI":"10.1093\/nc\/niw015"},{"key":"ref_8","unstructured":"Williams, P.L., and Beer, R.D. (arXiv, 2010). Nonnegative Decomposition of Multivariate Information, arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2161","DOI":"10.3390\/e16042161","article-title":"Quantifying Unique Information","volume":"16","author":"Bertschinger","year":"2014","journal-title":"Entropy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/978-3-642-53734-9_6","article-title":"Quantifying synergistic mutual information","volume":"Volume 9","author":"Griffith","year":"2014","journal-title":"Guided Self-Organization: Inception. Emergence, Complexity and Computation"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"James, R.G., Emenheiser, J., and Crutchfield, J.P. (arXiv, 2017). Unique Information via Dependency Constraints, arXiv.","DOI":"10.1088\/1751-8121\/aaed53"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ince, R.A.A. (2017). Measuring multivariate redundant information with pointwise common change in surprisal. Entropy, 19.","DOI":"10.3390\/e19070318"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ince, R.A.A. (arXiv, 2017). The Partial Entropy Decomposition: Decomposing multivariate entropy and mutual information via pointwise common surprisal, arXiv.","DOI":"10.3390\/e19070318"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1088\/0954-898X_6_2_005","article-title":"The discovery of structure by multi-stream networks of local processors with contextual guidance","volume":"6","author":"Phillips","year":"1995","journal-title":"Netw. Comput. Neural Syst."},{"key":"ref_15","unstructured":"Cover, T.M., and Thomas, J.A. (1991). Elements of Information Theory, Wiley-Interscience."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11539","DOI":"10.1523\/JNEUROSCI.23-37-11539.2003","article-title":"Synergy, Redundancy, and Population Codes","volume":"23","author":"Schneidman","year":"2003","journal-title":"J. Neurosci."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kay, J.W., and Titterington, D.M. (1999). Neural networks for unsupervised learning based on information theory. Statistics and Neural Networks: Advances at the Interface, Oxford University Press.","DOI":"10.1093\/oso\/9780198524229.003.0002"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1162\/neco.1997.9.4.895","article-title":"Activation functions, computational goals and learning rules for local processors with contextual guidance","volume":"9","author":"Kay","year":"1997","journal-title":"Neural Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1007\/s11538-010-9564-x","article-title":"Coherent infomax as a computational goal for neural systems","volume":"73","author":"Kay","year":"2011","journal-title":"Bull. Math. Biol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"James, R.G., and Crutchfield, J.P. (2017). Multivariate Dependence beyond Shannon Information. Entropy, 19.","DOI":"10.3390\/e19100531"},{"key":"ref_21","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":"Wibral","year":"2017","journal-title":"Brain Cognit."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Harder, M., Salge, C., and Polani, D. (2013). Bivariate measure of redundant information. Phys. Rev. E, 87.","DOI":"10.1103\/PhysRevE.87.012130"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Pica, G., Piasini, E., Chicharro, D., and Panzeri, S. (2017). Invariant components of synergy, redundancy, and unique information. Entropy, 19.","DOI":"10.3390\/e19090451"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wibral, M., Lizier, J.T., V\u00f6gler, S., Priesemann, V., and Galuske, R. (2014). Local active information storage as a tool to understand distributed neural information processing. Front. Neuroinf., 8.","DOI":"10.3389\/fninf.2014.00001"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lizier, J.T., Prokopenko, M., and Zomaya, A. (2008). Local information transfer as a spatiotemporal filter for complex systems. Phys. Rev. E, 77.","DOI":"10.1103\/PhysRevE.77.026110"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wibral, M., Lizier, J.T., and Priesemann, V. (2015). Bits from brains for biologically inspired computing. Front. Robot. AI.","DOI":"10.3389\/frobt.2015.00005"},{"key":"ref_27","unstructured":"Van de Cruys, T. (2011, January 24). Two Multivariate Generalizations of Pointwise Mutual Information. Proceedings of the Workshop on Distributional Semantics and Compositionality, Portland, Oregon."},{"key":"ref_28","first-page":"22","article-title":"Word Association Norms, Mutual Information, and Lexicography","volume":"16","author":"Church","year":"1990","journal-title":"Comput. Linguist."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"James, R.G., Ellison, C.J., and Crutchfield, J.P. (2011). Anatomy of a bit: Information in a time series observation. Chaos, 037109.","DOI":"10.1063\/1.3637494"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3501","DOI":"10.3390\/e17053501","article-title":"Information decomposition and synergy","volume":"17","author":"Olbrich","year":"2015","journal-title":"Entropy"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"doi","DOI":"10.1103\/PhysRevE.91.052802","article-title":"An exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems","volume":"91","author":"Barrett","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1097\/00001756-200103260-00008","article-title":"Contrast response characteristics of long-range lateral interactions in cat striate cortex","volume":"12","author":"Chen","year":"2001","journal-title":"Neuroreport"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1038\/35372","article-title":"Collinear stimuli regulate visual responses depending on cell\u2019s contrast threshold","volume":"391","author":"Polat","year":"1998","journal-title":"Nature"},{"key":"ref_34","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":"Ince","year":"2017","journal-title":"Hum. Brain Mapp."},{"key":"ref_35","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":"Panzeri","year":"2007","journal-title":"J. Neurophys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.jneumeth.2011.11.013","article-title":"A Novel Test to Determine the Significance of Neural Selectivity to Single and Multiple Potentially Correlated Stimulus Features","volume":"210","author":"Ince","year":"2012","journal-title":"J. Neurosci. Methods"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2518","DOI":"10.1109\/TBME.2016.2559578","article-title":"Synergistic and redundant information flow detected by unnormalized Granger causality: Application to resting state fMRI","volume":"63","author":"Stramaglia","year":"2016","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Timme, N.M., Ito, S., Myroshnychenko, M., Nigam, S., Shimono, M., and Yeh, F.-C. (2016). High-Degree Neurons Feed Cortical Computations. PLoS Comput. Biol., 12.","DOI":"10.1371\/journal.pcbi.1004858"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neubiorev.2015.02.010","article-title":"On the functions, mechanisms, and malfunctions of intracortical contextual modulation","volume":"52","author":"Phillips","year":"2015","journal-title":"Neurosci. Biobehav. Rev."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/11\/560\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:48:32Z","timestamp":1760208512000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/11\/560"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,26]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2017,11]]}},"alternative-id":["e19110560"],"URL":"https:\/\/doi.org\/10.3390\/e19110560","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,10,26]]}}}