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A Mathematical Theory of Communication
Open accessAbstract
In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.
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Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
Self-citation
Cited by
Coefficient Alpha and the Internal Structure of Tests
Cronbach, L. J. (1951) · Psychometrika · doi:10.1007/bf02310555 · Cited by 43,931
A Dynamic Theory of Organizational Knowledge Creation
Nonaka, I. (1994) · Organization Science · doi:10.1287/orsc.5.1.14 · Cited by 17,809
Information theory and statistical mechanics
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.106.620 · Cited by 12,931
The DeLone and McLean Model of Information Systems Success: A Ten-Year Update
(2003) · Journal of Management Information Systems · doi:10.1080/07421222.2003.11045748 · Cited by 11,791
An introduction to cybernetics
Ashby, W. R. (1956) · doi:10.5962/bhl.title.5851 · Cited by 7,578
Newman (2005) · doi:10.1080/00107510500052444 · Cited by 5,749
Defining virtual reality: Dimensions determining telepresence
Steuer, J. (1992) · Journal of Communication · doi:10.1111/j.1460-2466.1992.tb00812.x · Cited by 5,459
Gut microbiome modulates response to anti-PD-1 immunotherapy in melanoma patients
Gopalakrishnan, V., Spencer, C. N., Nezi, L., Reuben, A., Andrews, M. C., Karpinets, T. V., Prieto, P. A., Vicente, D., Hoffman, K., Wei, S. C., et al. (2018) · Science · doi:10.1126/science.aan4236 · Cited by 4,812
Jost, L. (2006) · Oikos · doi:10.1111/j.2006.0030-1299.14714.x · Cited by 4,669
Maps of random walks on complex networks reveal community structure
Rosvall, M., & Bergstrom, C. T. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0706851105 · Cited by 4,583
Genome-wide methylation profiles reveal quantitative views of human aging rates
Hannum, G., Guinney, J., Zhao, L., Zhang, L., Hughes, G., Sadda, S., Klotzle, B., Bibikova, M., Fan, J.-B., Gao, Y., et al. (2013) · Molecular Cell · doi:10.1016/j.molcel.2012.10.016 · Cited by 4,270
The interdisciplinary study of coordination
Malone, T. W., & Crowston, K. (1994) · ACM Computing Surveys · doi:10.1145/174666.174668 · Cited by 3,504
Information Theory and Statistical Mechanics. II
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.108.171 · Cited by 3,253
Information Theory and an Extension of the Maximum Likelihood Principle
Akaike, H. (1992) · Springer Series in Statistics · doi:10.1007/978-1-4612-0919-5_38 · Cited by 3,028
Environment dominates over host genetics in shaping human gut microbiota
Rothschild, D., Weissbrod, O., Barkan, E., Kurilshikov, A., Korem, T., Zeevi, D., Costea, P. I., Godneva, A., Kalka, I. N., Bar, N., et al. (2018) · Nature · doi:10.1038/nature25973 · Cited by 2,859
Toward a Universal Law of Generalization for Psychological Science
Shepard, R. N. (1987) · Science · doi:10.1126/science.3629243 · Cited by 2,416
Is working memory capacity task dependent?
Turner, M. L., & Engle, R. W. (1989) · Journal of Memory and Language · doi:10.1016/0749-596x(89)90040-5 · Cited by 2,299
Ritual and Religion in the Making of Humanity
Rappaport, R. A. (1999) · doi:10.1017/cbo9780511814686 · Cited by 2,295
On the Rate of Gain of Information
Hick, W. E. (1952) · Quarterly Journal of Experimental Psychology · doi:10.1080/17470215208416600 · Cited by 2,279
Using mutual information for selecting features in supervised neural net learning
Battiti, R. (1994) · IEEE Transactions on Neural Networks · doi:10.1109/72.298224 · Cited by 2,148
Probabilistic machine learning and artificial intelligence
Ghahramani, Z. (2015) · Nature · doi:10.1038/nature14541 · Cited by 1,995
Wehrl, A. (1978) · Reviews of Modern Physics · doi:10.1103/revmodphys.50.221 · Cited by 1,963
Facing up to the problem of consciousness
Chalmers, D. J. (1996) · Toward a Science of Consciousness · doi:10.7551/mitpress/6860.003.0003 · Cited by 1,966
Language-based information-flow security
Sabelfeld, A., & Myers, A. C. (2003) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2002.806121 · Cited by 1,907
A tissue-specific atlas of mouse protein phosphorylation and expression
Huttlin, E. L., Jedrychowski, M. P., Elias, J. E., Goswami, T., Rad, R., Beausoleil, S. A., Villén, J., Haas, W., Sowa, M. E., & Gygi, S. P. (2010) · Cell · doi:10.1016/j.cell.2010.12.001 · Cited by 1,778
Fredkin, E., & Toffoli, T. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf01857727 · Cited by 1,896
Consequences of individual feedback on behavior in organizations.
Ilgen, D. R., Fisher, C. D., & Taylor, M. S. (1979) · Journal of Applied Psychology · doi:10.1037/0021-9010.64.4.349 · Cited by 1,822
Stochastic geometry and random graphs for the analysis and design of wireless networks
Haenggi, M., Andrews, J. G., Baccelli, F., Dousse, O., & Franceschetti, M. (2009) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2009.090902 · Cited by 1,719
A principle of natural self-organization: Part A: Emergence of the hypercycle
Eigen, M., & Schuster, P. (1977) · Naturwissenschaften · doi:10.1007/bf00450633 · Cited by 1,752
Neural correlations, population coding and computation
Averbeck, B. B., Latham, P. E., & Pouget, A. (2006) · Nature reviews. Neuroscience · doi:10.1038/nrn1888 · Cited by 1,743
Janssen, M. F., Pickard, A. S., Golicki, D., Gudex, C., Niewada, M., Scalone, L., Swinburn, P., & Busschbach, J. (2013) · Quality of Life Research · doi:10.1007/s11136-012-0322-4 · Cited by 1,582
The World’s Technological Capacity to Store, Communicate, and Compute Information
Hilbert, M., & López, P. (2011) · Science · doi:10.1126/science.1200970 · Cited by 1,643
Fitts' Law as a Research and Design Tool in Human-Computer Interaction
MacKenzie, I. S. (1992) · Human–Computer Interaction · doi:10.1207/s15327051hci0701_3 · Cited by 1,637
Assessing the Validity of IS Success Models: An Empirical Test and Theoretical Analysis
Rai, A., Lang, S. S., & Welker, R. B. (2002) · Information Systems Research · doi:10.1287/isre.13.1.50.96 · Cited by 1,611
Deep Learning Enabled Semantic Communication Systems
Xie, H., Qin, Z., Li, G. Y., & Juang, B.-H. (2021) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2021.3071210 · Cited by 1,602
Guadagnoli, M. A., & Lee, T. D. (2004) · Journal of Motor Behavior · doi:10.3200/jmbr.36.2.212-224 · Cited by 1,534
Media, Tasks, and Communication Processes: A Theory of Media Synchronicity1
Dennis, A. R., Fuller, R. M., & Valacich, J. S. (2008) · MIS Quarterly · doi:10.2307/25148857 · Cited by 1,511
Anchoring Data Quality Dimensions in Ontological Foundations
Wand, Y., & Wang, R. Y. (1996) · Communications of the ACM · doi:10.1145/240455.240479 · Cited by 1,479
Stimulus information as a determinant of reaction time.
Hyman, R. (1953) · Journal of Experimental Psychology · doi:10.1037/h0056940 · Cited by 1,443
Estimation of entropy and mutual information
Paninski, L. (2003) · Neural Computation · doi:10.1162/089976603321780272 · Cited by 1,442
Statistics and Partitioning of Species Diversity, and Similarity among Multiple Communities
Lande, R. (1996) · Oikos · doi:10.2307/3545743 · Cited by 1,409
Steane, A. (1998) · Reports on Progress in Physics · doi:10.1088/0034-4885/61/2/002 · Cited by 1,391
Optimality in human motor performance: Ideal control of rapid aimed movements.
Meyer, D. E., Abrams, R. A., Kornblum, S., Wright, C. E., & Keith Smith, J. E. (1988) · Psychological Review · doi:10.1037/0033-295x.95.3.340 · Cited by 1,406
Feedback as an individual resource: Personal strategies of creating information
Ashford, S. J., & Cummings, L. L. (1983) · Organizational Behavior and Human Performance · doi:10.1016/0030-5073(83)90156-3 · Cited by 1,309
Communication of emotions in vocal expression and music performance: different channels, same code?
Juslin, P. N., & Laukka, P. (2003) · Psychological Bulletin · doi:10.1037/0033-2909.129.5.770 · Cited by 1,273
Postural Hand Synergies for Tool Use
Santello, M., Flanders, M., & Soechting, J. F. (1998) · The Journal of Neuroscience · doi:10.1523/jneurosci.18-23-10105.1998 · Cited by 1,215
Appealing to fear: A meta-analysis of fear appeal effectiveness and theories
Tannenbaum, M. B., Hepler, J., Zimmerman, R. S., Saul, L., Jacobs, S., Wilson, K., & Albarracín, D. (2015) · Psychological Bulletin · doi:10.1037/a0039729 · Cited by 1,315
Putnam, C. D., Hammel, M., Hura, G. L., & Tainer, J. A. (2007) · Quarterly Reviews of Biophysics · doi:10.1017/s0033583507004635 · Cited by 1,184
An information theoretical approach to prefrontal executive function
Koechlin, E., & Summerfield, C. (2007) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2007.04.005 · Cited by 1,183
Darwin's mistake: Explaining the discontinuity between human and nonhuman minds
Penn, D. C., Holyoak, K. J., & Povinelli, D. J. (2008) · Behavioral and Brain Sciences · doi:10.1017/s0140525x08003543 · Cited by 1,174
Long-term dynamics of CA1 hippocampal place codes
Ziv, Y., Burns, L. D., Cocker, E. D., Hamel, E. O., Ghosh, K. K., Kitch, L. J., Gamal, A. E., & Schnitzer, M. J. (2013) · Nature Neuroscience · doi:10.1038/nn.3329 · Cited by 1,155
A Survey of Quantization Methods for Efficient Neural Network Inference
Gholami, A., Kim, S., Dong, Z., Yao, Z., Mahoney, M. W., & Keutzer, K. (2022) · Low-Power Computer Vision · doi:10.1201/9781003162810-13 · Cited by 1,219
Incentive contracts and performance measurement
Baker, G. P. (1992) · Journal of Political Economy · doi:10.1086/261831 · Cited by 1,085
The effects of a visual fidelity criterion of the encoding of images
Mannos, J., & Sakrison, D. (1974) · IEEE Transactions on Information Theory · doi:10.1109/tit.1974.1055250 · Cited by 1,063
Quantum discord for two-qubit systems
Luo, S. (2008) · Physical Review A · doi:10.1103/physreva.77.042303 · Cited by 1,060
DeYoung, C. G. (2015) · Journal of Research in Personality · doi:10.1016/j.jrp.2014.07.004 · Cited by 1,057
EEG-correlated fMRI of human alpha activity
Laufs, H., Kleinschmidt, A., Beyerle, A., Eger, E., Salek-Haddadi, A., Preibisch, C., & Krakow, K. (2003) · NeuroImage · doi:10.1016/s1053-8119(03)00286-6 · Cited by 1,025
A note on the evaluation of generative models
Theis, L., Oord, A. V. D., & Bethge, M. (2015) · arXiv · doi:10.48550/arxiv.1511.01844 · Cited by 1,026
NELSON, R. R., TODD, P. A., & WIXOM, B. H. (2005) · Journal of Management Information Systems · doi:10.1080/07421222.2005.11045823 · Cited by 998
Working Memory and Intelligence: The Same or Different Constructs?
Ackerman, P. L., Beier, M. E., & Boyle, M. O. (2005) · Psychological Bulletin · doi:10.1037/0033-2909.131.1.30 · Cited by 969
Application of a translational profiling approach for the comparative analysis of CNS cell types
Doyle, J. P., Dougherty, J. D., Heiman, M., Schmidt, E. F., Stevens, T. R., Ma, G., Bupp, S., Shrestha, P., Shah, R. D., Doughty, M. L., et al. (2008) · Cell · doi:10.1016/j.cell.2008.10.029 · Cited by 912
Johnson, R. (1986) · Psychophysiology · doi:10.1111/j.1469-8986.1986.tb00649.x · Cited by 960
Modelling and analysis of local field potentials for studying the function of cortical circuits
Einevoll, G. T., Kayser, C., Logothetis, N. K., & Panzeri, S. (2013) · Nature Reviews Neuroscience · doi:10.1038/nrn3599 · Cited by 857
Maximum entropy production principle in physics, chemistry and biology
Martyushev, L. M., & Seleznev, V. D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.12.001 · Cited by 943
Davoli, T., Xu, A. W., Mengwasser, K. E., Sack, L. M., Yoon, J. C., Park, P. J., & Elledge, S. J. (2013) · Cell · doi:10.1016/j.cell.2013.10.011 · Cited by 815
DNA Fountain enables a robust and efficient storage architecture
Erlich, Y., & Zielinski, D. (2017) · Science · doi:10.1126/science.aaj2038 · Cited by 898
Beyond Massive MIMO: The Potential of Data Transmission With Large Intelligent Surfaces
Hu, S., Rusek, F., & Edfors, O. (2018) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2018.2816577 · Cited by 892
Deep Learning Based Communication Over the Air
Dorner, S., Cammerer, S., Hoydis, J., & Brink, S. T. (2018) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2017.2784180 · Cited by 859
Hands-On Bayesian Neural Networks—A Tutorial for Deep Learning Users
Jospin, L. V., Laga, H., Boussaid, F., Buntine, W., & Bennamoun, M. (2022) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2022.3155327 · Cited by 879
Subjective organization in free recall of "unrelated" words.
Tulving, E. (1962) · Psychological Review · doi:10.1037/h0043150 · Cited by 867
Edge artificial intelligence for 6g: vision, enabling technologies, and applications
Letaief, K. B., Shi, Y., Lu, J., & Lu, J. (2022) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2021.3126076 · Cited by 829
Toward defining the autoimmune microbiome for type 1 diabetes
Giongo, A., Gano, K. A., Crabb, D. B., Mukherjee, N., Novelo, L. L., Casella, G., Drew, J. C., Ilonen, J., Knip, M., Hyöty, H., et al. (2011) · The ISME Journal · doi:10.1038/ismej.2010.92 · Cited by 806
Convolutional Neural Networks for P300 Detection with Application to Brain-Computer Interfaces
Cecotti, H., & Graser, A. (2011) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2010.125 · Cited by 778
Capacity of the noisy quantum channel
Lloyd, S. (1997) · Physical Review A · doi:10.1103/physreva.55.1613 · Cited by 783
Entropy and information in neural spike trains
Strong, S. P., Koberle, R., de Ruyter van Steveninck, R. R., & Bialek, W. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.197 · Cited by 791
The effects of remote work on collaboration among information workers
Yang, L., Holtz, D., Jaffe, S., Suri, S., Sinha, S., Weston, J., Joyce, C., Shah, N., Sherman, K., Hecht, B., et al. (2021) · Nature Human Behaviour · doi:10.1038/s41562-021-01196-4 · Cited by 789
Bai, B., Law, R., & Wen, I. (2008) · International Journal of Hospitality Management · doi:10.1016/j.ijhm.2007.10.008 · Cited by 749
Product lifecycle management: the new paradigm for enterprises
Grieves, M. W. (2005) · International Journal of Product Development · doi:10.1504/ijpd.2005.006669 · Cited by 741
Decision trees: An overview and their use in medicine
Podgorelec, V., Kokol, P., Stiglic, B., & Rozman, I. (2002) · Journal of Medical Systems · doi:10.1023/a:1016409317640 · Cited by 736
Local Shannon entropy measure with statistical tests for image randomness
Wu, Y., Zhou, Y., Saveriades, G., Agaian, S., Noonan, J. P., & Natarajan, P. (2013) · Information Sciences · doi:10.1016/j.ins.2012.07.049 · Cited by 722
On Defining Artificial Intelligence
Wang, P. (2019) · Journal of Artificial General Intelligence · doi:10.2478/jagi-2019-0002 · Cited by 740
Typologies of attentional networks
Raz, A., & Buhle, J. (2006) · Nature Reviews Neuroscience · doi:10.1038/nrn1903 · Cited by 706
Speculations Concerning the First Ultraintelligent Machine
Good, I. J. (1966) · Advances in Computers · doi:10.1016/s0065-2458(08)60418-0 · Cited by 703
A taxonomy of players and activities across the ERP project life cycle
Somers, T. M., & Nelson, K. G. (2004) · Information & Management · doi:10.1016/s0378-7206(03)00023-5 · Cited by 694
Could information theory provide an ecological theory of sensory processing?
Atick, J. J. (2011) · Network: Computation in Neural Systems · doi:10.3109/0954898x.2011.638888 · Cited by 679
Gastrointestinal microbiome signatures of pediatric patients with irritable bowel syndrome
Saulnier, D. M., Riehle, K., Mistretta, T., Diaz, M., Mandal, D., Raza, S., Weidler, E. M., Qin, X., Coarfa, C., Milosavljevic, A., et al. (2011) · Gastroenterology · doi:10.1053/j.gastro.2011.06.072 · Cited by 672
Langer, E. J., Blank, A., & Chanowitz, B. (1978) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.36.6.635 · Cited by 694
Representation in Cognitive Science
Shea, N. (2018) · doi:10.1093/oso/9780198812883.001.0001 · Cited by 676
Equitability, mutual information, and the maximal information coefficient
Kinney, J. B., & Atwal, G. S. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1309933111 · Cited by 667
Interactivity: a concept explication
Kiousis, S. (2002) · New Media & Society · doi:10.1177/146144480200400303 · Cited by 666
(2001) · PubMed · Cited by 662
Measures of degeneracy and redundancy in biological networks
Tononi, G., Sporns, O., & Edelman, G. M. (1999) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.96.6.3257 · Cited by 632
The communicative function of ambiguity in language
Piantadosi, S. T., Tily, H., & Gibson, E. (2012) · Cognition · doi:10.1016/j.cognition.2011.10.004 · Cited by 628
Big data in accounting: an overview
Vasarhelyi, M. A., Kogan, A., & Tuttle, B. M. (2015) · Accounting Horizons · doi:10.2308/acch-51071 · Cited by 641
Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spaces
Petersen, D. P., & Middleton, D. (1962) · Information and Control · doi:10.1016/s0019-9958(62)90633-2 · Cited by 614
A Framework and Guidelines for Context-Specific Theorizing in Information Systems Research
Hong, W., Chan, F. K. Y., Thong, J. Y. L., Chasalow, L. C., & Dhillon, G. (2014) · Information Systems Research · doi:10.1287/isre.2013.0501 · Cited by 609
LaFleur, K., Cassady, K., Doud, A., Shades, K., Rogin, E., & He, B. (2013) · Journal of Neural Engineering · doi:10.1088/1741-2560/10/4/046003 · Cited by 583
The role of bacteria in the pathogenesis and progression of idiopathic pulmonary fibrosis
Molyneaux, P. L., Cox, M. J., Willis-Owen, S. A. G., Mallia, P., Russell, K. E., Russell, A.-M., Murphy, E., Johnston, S. L., Schwartz, D. A., Wells, A. U., et al. (2014) · American Journal of Respiratory and Critical Care Medicine · doi:10.1164/rccm.201403-0541oc · Cited by 567
The entropic brain - revisited
Carhart-Harris, R. L. (2018) · Neuropharmacology · doi:10.1016/j.neuropharm.2018.03.010 · Cited by 522
Gene therapy for Wiskott-Aldrich syndrome–long-term efficacy and genotoxicity
Braun, C. J., Boztug, K., Paruzynski, A., Witzel, M., Schwarzer, A., Rothe, M., Modlich, U., Beier, R., Göhring, G., Steinemann, D., et al. (2014) · Science Translational Medicine · doi:10.1126/scitranslmed.3007280 · Cited by 562
Metadata
- Authors
- Shannon, C. E.
- Venue
- Bell System Technical Journal
- Published
- 1948-10
- Volume
- 27
- Issue
- 4
- Pages
- 623-656
- ISSN
- 0005-8580 (ISSN-L)
- OpenAlex
- W2041404167
- Cited by
- 48,949
- References
- 1
- FWCI
- 35.89
- Type
- journal article
- Language
- en
- Open access
- green
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