Edit Profile (opens in new tab) Shields, Paul C. Co-Author Distance Author ID: shields.paul-c Published as: Shields, Paul C.; Shields, P. C.; Shields, Paul; Shields, Paul G.; Shields, P. more...less External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 65 Publications since 1959, including 5 Books and 1 Additional arXiv Preprint Co-Authors: 17 Co-Authors with 39 Joint Publications 580 Co-Co-Authors all top 5 Co-Authors 26 single-authored 9 Neuhoff, David L. 5 Csiszár, Imre 5 Marton, Katalin 5 Ornstein, Donald Samuel 3 Adler, Roy Lee 2 Burton, Robert M. jun. 2 Gray, Robert Molten 2 Thouvenot, Jean-Paul 1 Aldous, David John 1 Davisson, Lee D. 1 Feldman, Jerome A. 1 Grillenberger, Christian 1 McCabe, Robert L. 1 Peres, Yuval 1 Pierce, Larry A. II 1 Smorodinsky, Meir 1 Weiss, Benjamin all top 5 Serials 14 IEEE Transactions on Information Theory 10 The Annals of Probability 5 Israel Journal of Mathematics 4 Advances in Mathematics 3 Monatshefte für Mathematik 2 Information and Control 2 Mathematical Systems Theory 2 Proceedings of the American Mathematical Society 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Ergodic Theory and Dynamical Systems 2 Journal of Theoretical Probability 1 American Mathematical Monthly 1 The Annals of Statistics 1 Mathematische Zeitschrift 1 Probability Theory and Related Fields 1 Problems of Control and Information Theory 1 Electronic Research Announcements of the American Mathematical Society 1 Bulletin of the American Mathematical Society 1 Graduate Studies in Mathematics 1 Foundations and Trends in Communications and Information Theory 1 Annals of Mathematical Statistics all top 5 Fields 28 Information and communication theory, circuits (94-XX) 25 Measure and integration (28-XX) 23 Probability theory and stochastic processes (60-XX) 9 Statistics (62-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Computer science (68-XX) 2 Operator theory (47-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functional analysis (46-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 53 Publications have been cited 632 times in 503 Documents Cited by ▼ Year ▼ The ergodic theory of discrete sample paths. Zbl 0879.28031 Shields, Paul C. 99 1996 Information theory and statistics: a tutorial. Zbl 1156.62300 Csiszár, Imre; Shields, Paul C. 84 2004 The theory of Bernoulli shifts. Zbl 0308.28011 Shields, Paul 76 1973 The consistency of the BIC Markov order estimator. Zbl 1105.62311 Csiszár, Imre; Shields, Paul C. 44 2000 An uncountable family of K-automorphisms. Zbl 0251.28004 Ornstein, Donald S.; Shields, Paul C. 28 1973 A diffusion limit for a class of randomly-growing binary trees. Zbl 0641.60026 Aldous, David; Shields, Paul 24 1988 A generalization of Ornstein’s \(\overline d\) distance with applications to information theory. Zbl 0304.94025 Gray, Robert M.; Neuhoff, David L.; Shields, Paul C. 18 1975 Skew products of Bernoulli shifts with rotations. Zbl 0246.28009 Adler, R. L.; Shields, P. C. 16 1972 Waiting times: Positive and negative results on the Wyner-Ziv problem. Zbl 0776.60082 Shields, Paul C. 14 1993 Mixing Markov shifts of kernel type are Bernoulli. Zbl 0252.28009 Ornstein, D. S.; Shields, P. C. 14 1973 Entropy and prefixes. Zbl 0765.28016 Shields, Paul C. 13 1992 Cutting and independent stacking of intervals. Zbl 0255.28017 Shields, Paul 13 1973 The positive-divergence and blowing-up properties. Zbl 0797.60044 Marton, Katalin; Shields, Paul C. 12 1994 Cutting and stacking: A method for constructing stationary processes. Zbl 0741.94007 Shields, Paul C. 12 1991 Information theory and statistics: a tutorial. Zbl 1157.62300 Csiszár, Imre; Shields, Paul C. 12 2004 Irreducible Markov shifts. Zbl 0244.60053 Adler, R. L.; Shields, P.; Smorodinsky, M. 10 1972 Entropy and the consistent estimation of joint distributions. Zbl 0806.28014 Marton, Katalin; Shields, Paul C. 9 1994 Skew products of Bernoulli shifts with rotations. II. Zbl 0307.28014 Adler, R. L.; Shields, P. C. 9 1975 Almost block independence. Zbl 0393.60031 Shields, Paul C. 9 1979 Almost-sure waiting time results for weak and very weak Bernoulli processes. Zbl 0830.60023 Marton, Katalin; Shields, Paul C. 8 1995 Entropy zero \(\times\) Bernoulli processes are closed in the \(d\)-metric. Zbl 0333.28007 Shields, Paul; Thouvenot, J.-P. 8 1975 Weak and very weak Bernoulli partitions. Zbl 0388.28017 Shields, Paul C. 8 1977 Universal almost sure data compression. Zbl 0699.94004 Ornstein, Donald S.; Shields, Paul C. 7 1990 The interactions between ergodic theory and information theory. Zbl 0953.94009 Shields, Paul C. 7 1998 Two divergence-rate counterexamples. Zbl 0799.60046 Shields, Paul C. 7 1993 Universal redundancy rates do not exist. Zbl 0777.94009 Shields, Paul C. 6 1993 A class of Markov shifts which are Bernoulli shifts. Zbl 0223.28015 McCabe, Robert; Shields, Paul 6 1971 Stationary coding of processes. Zbl 0401.94018 Shields, Paul C. 6 1979 Charles S. Peirce ‘On the logic of number’. Zbl 1280.03003 Shields, Paul 5 2012 A skew-product which is Bernoulli. Zbl 0388.28026 Shields, Paul C.; Burton, Robert 5 1978 String matching bounds via coding. Zbl 0873.60029 Shields, Paul C. 4 1997 The \(\bar d\)-recognition of processes. Zbl 0801.60033 Ornstein, Donald S.; Shields, Paul C. 4 1994 String matching: The ergodic case. Zbl 0753.92021 Shields, Paul C. 4 1992 Linear algebra. Zbl 0125.28301 Shields, P. C. 3 1964 A mixing \(T\) for which \(T-T^{-1}\) is Bernoulli. Zbl 0498.28016 Burton, Robert M.; Shields, Paul C. 2 1983 How many future measures can there be? Zbl 1021.37003 Marton, Katalin; Shields, Paul C. 2 2002 Correction to: Entropy and the consistent estimation of joint distributions. Zbl 0861.28015 Marton, Katalin; Shields, Paul C. 2 1996 Sequences incompressible by SLZ (LZW), yet fully compressible by ULZ. Zbl 0955.68033 Pierce, Larry A. II; Shields, Paul C. 2 2000 Construction of strictly ergodic systems. III: Bernoulli systems. Zbl 0348.60046 Grillenberger, Christian; Shields, Paul 2 1975 Block and sliding-block source coding. Zbl 0383.94018 Shields, Paul C.; Neuhoff, David L. 2 1977 Channels with almost finite memory. Zbl 0409.94011 Neuhoff, David L.; Shields, Paul C. 2 1979 Fixed-rate universal codes for Markov sources. Zbl 0404.94006 Neuhoff, David L.; Shields, Paul C. 2 1978 Ergodic and entropy theorems revisited. Zbl 0633.94004 Shields, Paul C. 2 1987 Indecomposable finite state channels and primitive approximation. Zbl 0483.94011 Neuhoff, David L.; Shields, Paul C. 1 1982 Universal almost sure data compression using Markov types. Zbl 0713.94006 Shields, P. C. 1 1990 Performance of LZ algorithms on individual sequences. Zbl 0957.94011 Shields, Paul C. 1 1999 Redundancy rates for renewal and other processes. Zbl 0874.94019 Csiszár, Imre; Shields, Paul C. 1 1996 Invariant elements for positive contractions on a Banach lattice. Zbl 0147.34101 Shields, P. C. 1 1967 Universal redundancy rates for the class of \(B\)-processes do not exist. Zbl 0827.94019 Shields, Paul; Weiss, Benjamin 1 1995 Une remarque sur les isomorphismes de schemas de Bernoulli qui preservent certains facteurs. Zbl 0324.28010 Shields, Paul; Thouvenot, Jean-Paul 1 1975 Weakly compact positive operators on summable functions. Zbl 0264.47033 Shields, Paul C. 1 1973 Bernoulli shifts are determined by their factor algebras. Zbl 0281.28007 Shields, Paul C. 1 1973 Total complexity and the inference of best programs. Zbl 0357.68044 Feldman, Jerome A.; Shields, Paul C. 1 1977 Charles S. Peirce ‘On the logic of number’. Zbl 1280.03003 Shields, Paul 5 2012 Information theory and statistics: a tutorial. Zbl 1156.62300 Csiszár, Imre; Shields, Paul C. 84 2004 Information theory and statistics: a tutorial. Zbl 1157.62300 Csiszár, Imre; Shields, Paul C. 12 2004 How many future measures can there be? Zbl 1021.37003 Marton, Katalin; Shields, Paul C. 2 2002 The consistency of the BIC Markov order estimator. Zbl 1105.62311 Csiszár, Imre; Shields, Paul C. 44 2000 Sequences incompressible by SLZ (LZW), yet fully compressible by ULZ. Zbl 0955.68033 Pierce, Larry A. II; Shields, Paul C. 2 2000 Performance of LZ algorithms on individual sequences. Zbl 0957.94011 Shields, Paul C. 1 1999 The interactions between ergodic theory and information theory. Zbl 0953.94009 Shields, Paul C. 7 1998 String matching bounds via coding. Zbl 0873.60029 Shields, Paul C. 4 1997 The ergodic theory of discrete sample paths. Zbl 0879.28031 Shields, Paul C. 99 1996 Correction to: Entropy and the consistent estimation of joint distributions. Zbl 0861.28015 Marton, Katalin; Shields, Paul C. 2 1996 Redundancy rates for renewal and other processes. Zbl 0874.94019 Csiszár, Imre; Shields, Paul C. 1 1996 Almost-sure waiting time results for weak and very weak Bernoulli processes. Zbl 0830.60023 Marton, Katalin; Shields, Paul C. 8 1995 Universal redundancy rates for the class of \(B\)-processes do not exist. Zbl 0827.94019 Shields, Paul; Weiss, Benjamin 1 1995 The positive-divergence and blowing-up properties. Zbl 0797.60044 Marton, Katalin; Shields, Paul C. 12 1994 Entropy and the consistent estimation of joint distributions. Zbl 0806.28014 Marton, Katalin; Shields, Paul C. 9 1994 The \(\bar d\)-recognition of processes. Zbl 0801.60033 Ornstein, Donald S.; Shields, Paul C. 4 1994 Waiting times: Positive and negative results on the Wyner-Ziv problem. Zbl 0776.60082 Shields, Paul C. 14 1993 Two divergence-rate counterexamples. Zbl 0799.60046 Shields, Paul C. 7 1993 Universal redundancy rates do not exist. Zbl 0777.94009 Shields, Paul C. 6 1993 Entropy and prefixes. Zbl 0765.28016 Shields, Paul C. 13 1992 String matching: The ergodic case. Zbl 0753.92021 Shields, Paul C. 4 1992 Cutting and stacking: A method for constructing stationary processes. Zbl 0741.94007 Shields, Paul C. 12 1991 Universal almost sure data compression. Zbl 0699.94004 Ornstein, Donald S.; Shields, Paul C. 7 1990 Universal almost sure data compression using Markov types. Zbl 0713.94006 Shields, P. C. 1 1990 A diffusion limit for a class of randomly-growing binary trees. Zbl 0641.60026 Aldous, David; Shields, Paul 24 1988 Ergodic and entropy theorems revisited. Zbl 0633.94004 Shields, Paul C. 2 1987 A mixing \(T\) for which \(T-T^{-1}\) is Bernoulli. Zbl 0498.28016 Burton, Robert M.; Shields, Paul C. 2 1983 Indecomposable finite state channels and primitive approximation. Zbl 0483.94011 Neuhoff, David L.; Shields, Paul C. 1 1982 Almost block independence. Zbl 0393.60031 Shields, Paul C. 9 1979 Stationary coding of processes. Zbl 0401.94018 Shields, Paul C. 6 1979 Channels with almost finite memory. Zbl 0409.94011 Neuhoff, David L.; Shields, Paul C. 2 1979 A skew-product which is Bernoulli. Zbl 0388.28026 Shields, Paul C.; Burton, Robert 5 1978 Fixed-rate universal codes for Markov sources. Zbl 0404.94006 Neuhoff, David L.; Shields, Paul C. 2 1978 Weak and very weak Bernoulli partitions. Zbl 0388.28017 Shields, Paul C. 8 1977 Block and sliding-block source coding. Zbl 0383.94018 Shields, Paul C.; Neuhoff, David L. 2 1977 Total complexity and the inference of best programs. Zbl 0357.68044 Feldman, Jerome A.; Shields, Paul C. 1 1977 A generalization of Ornstein’s \(\overline d\) distance with applications to information theory. Zbl 0304.94025 Gray, Robert M.; Neuhoff, David L.; Shields, Paul C. 18 1975 Skew products of Bernoulli shifts with rotations. II. Zbl 0307.28014 Adler, R. L.; Shields, P. C. 9 1975 Entropy zero \(\times\) Bernoulli processes are closed in the \(d\)-metric. Zbl 0333.28007 Shields, Paul; Thouvenot, J.-P. 8 1975 Construction of strictly ergodic systems. III: Bernoulli systems. Zbl 0348.60046 Grillenberger, Christian; Shields, Paul 2 1975 Une remarque sur les isomorphismes de schemas de Bernoulli qui preservent certains facteurs. Zbl 0324.28010 Shields, Paul; Thouvenot, Jean-Paul 1 1975 The theory of Bernoulli shifts. Zbl 0308.28011 Shields, Paul 76 1973 An uncountable family of K-automorphisms. Zbl 0251.28004 Ornstein, Donald S.; Shields, Paul C. 28 1973 Mixing Markov shifts of kernel type are Bernoulli. Zbl 0252.28009 Ornstein, D. S.; Shields, P. C. 14 1973 Cutting and independent stacking of intervals. Zbl 0255.28017 Shields, Paul 13 1973 Weakly compact positive operators on summable functions. Zbl 0264.47033 Shields, Paul C. 1 1973 Bernoulli shifts are determined by their factor algebras. Zbl 0281.28007 Shields, Paul C. 1 1973 Skew products of Bernoulli shifts with rotations. Zbl 0246.28009 Adler, R. L.; Shields, P. C. 16 1972 Irreducible Markov shifts. Zbl 0244.60053 Adler, R. L.; Shields, P.; Smorodinsky, M. 10 1972 A class of Markov shifts which are Bernoulli shifts. Zbl 0223.28015 McCabe, Robert; Shields, Paul 6 1971 Invariant elements for positive contractions on a Banach lattice. Zbl 0147.34101 Shields, P. C. 1 1967 Linear algebra. Zbl 0125.28301 Shields, P. C. 3 1964 all cited Publications top 5 cited Publications all top 5 Cited by 701 Authors 21 Weiss, Benjamin 16 Shields, Paul C. 14 Morvai, Gusztáv 10 Rudolph, Daniel J. 7 Thouvenot, Jean-Paul 6 Bradley, Richard C. jun. 6 Ornstein, Donald Samuel 6 Park, Kyewon Koh 5 Dȩbowski, Łukasz 5 Gallo, Sandro 5 Hochman, Michael 5 Kieffer, John Cronan 5 Krüger, Tyll 5 Mcgoff, Kevin 5 Ryabko, Daniil 5 Steif, Jeffrey E. 4 Burton, Robert M. jun. 4 Dascaliuc, Radu 4 Downarowicz, Tomasz 4 Galatolo, Stefano 4 Nobel, Andrew B. 4 Ryabko, Boris Ya. 4 Siegmund-Schultze, Rainer 4 Smorodinsky, Meir 4 Spinka, Yinon 4 Stummer, Wolfgang 4 Szpankowski, Wojciech 4 Thomann, Enrique A. 4 Waymire, Edward C. 3 Abadi, Miguel Natalio 3 Astola, Jaakko T. 3 Benedetto, Dario 3 Bjelaković, Igor 3 Caglioti, Emanuele 3 Cénac, Peggy 3 Chazottes, Jean-René 3 Colbrook, Matthew J. 3 Cristadoro, Giampaolo 3 Csiszár, Imre 3 den Hollander, Frank 3 Feldman, Jacob 3 Goldstein, Sheldon 3 Haydn, Nicolai T. A. 3 Jacquet, Philippe 3 Jakšić, Vojkan 3 Kanigowski, Adam 3 Kim, Donghan 3 Kwietniak, Dominik 3 Li, Wuchen 3 Morris, Ian D. 3 Oprocha, Piotr 3 Raquépas, Renaud 3 Sadeh, Ilan 3 Schwarz, Gideon E. 3 Seiler, Ruedi 3 Soo, Terry 3 Šujan, Štefan 3 Szkoła, Arleta 3 Ugalde, Edgardo 2 Adams, Terrence M. 2 Anellis, Irving Henry 2 Austin, Tim D. 2 Azevedo de Amorim, Arthur 2 Behera, Abhishek 2 Bellucci, Francesco 2 Berbee, Henry 2 Birkner, Matthias 2 Blume, Frank 2 Boyle, Mike 2 Burguet, David 2 Cerqueti, Roy 2 Chambaz, Antoine 2 Chauvin, Brigitte 2 Chen, Minghui 2 Choe, Geon Ho 2 David, Karl 2 de la Rue, Thierry 2 Degli Esposti, Mirko 2 Deuschel, Jean-Dominique 2 Devroye, Luc P. J. A. 2 Dong, Changguang 2 Dukkipati, Ambedkar 2 Falbo, Paolo 2 Fisher, Albert Meads 2 Flajolet, Philippe 2 Gaboardi, Marco 2 Garivier, Aurélien 2 Gayen, Atin 2 Glasner, Eli 2 Gopalkrishnan, Manoj 2 Greven, Andreas 2 Gutman, Yonatan 2 Harremoës, Peter 2 Hoffman, Christopher 2 Hsu, Justin 2 Johnson, Oliver Thomas 2 Kalikow, Steven Arthur 2 Kaltchenko, Alexei 2 Kamae, Teturo 2 Keane, Michael S. ...and 601 more Authors all top 5 Cited in 183 Serials 45 Israel Journal of Mathematics 28 Ergodic Theory and Dynamical Systems 16 The Annals of Probability 11 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 10 Kybernetika 10 Statistics & Probability Letters 9 Communications in Mathematical Physics 9 Journal of Statistical Physics 9 Advances in Mathematics 9 The Annals of Statistics 7 Monatshefte für Mathematik 7 Theoretical Computer Science 7 Stochastic Processes and their Applications 7 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Journal d’Analyse Mathématique 6 Journal of Mathematical Analysis and Applications 6 Journal of Statistical Planning and Inference 6 Proceedings of the American Mathematical Society 6 Transactions of the American Mathematical Society 6 Probability Theory and Related Fields 6 Random Structures & Algorithms 6 Bernoulli 5 Inventiones Mathematicae 5 Journal of Theoretical Probability 5 The Annals of Applied Probability 4 Physica A 4 Problems of Information Transmission 4 Communications in Statistics. Theory and Methods 4 Journal of Modern Dynamics 4 Electronic Journal of Statistics 3 Nonlinearity 3 Chaos, Solitons and Fractals 3 Journal of Econometrics 3 Mathematische Zeitschrift 3 SIAM Journal on Computing 3 Neural Computation 3 European Journal of Operational Research 3 Bulletin of the American Mathematical Society. New Series 3 Electronic Journal of Probability 3 Chaos 3 Stochastics and Dynamics 3 Bulletin of the American Mathematical Society 2 The Canadian Journal of Statistics 2 Scandinavian Journal of Statistics 2 Annals of the Institute of Statistical Mathematics 2 Applied Mathematics and Computation 2 Bulletin de la Société Mathématique de France 2 Information Sciences 2 Journal of Applied Probability 2 Journal of Combinatorial Theory. Series A 2 Journal of Computational and Applied Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Journal of Multivariate Analysis 2 Journal of Soviet Mathematics 2 Topology and its Applications 2 Physica D 2 Statistics 2 Algorithmica 2 Information and Computation 2 International Journal of Approximate Reasoning 2 Machine Learning 2 Aequationes Mathematicae 2 Journal of Dynamics and Differential Equations 2 Test 2 Discrete and Continuous Dynamical Systems 2 Doklady Mathematics 2 Theory of Computing Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 2 Journal of the European Mathematical Society (JEMS) 2 Probability in the Engineering and Informational Sciences 2 Applied Stochastic Models in Business and Industry 2 Dynamical Systems 2 Entropy 2 Journal of Machine Learning Research (JMLR) 2 Journal of Statistical Mechanics: Theory and Experiment 2 Statistical Methodology 2 ALEA. Latin American Journal of Probability and Mathematical Statistics 2 Logica Universalis 2 Foundations and Trends in Communications and Information Theory 2 Information Geometry 1 Applicable Analysis 1 Artificial Intelligence 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Communications on Pure and Applied Mathematics 1 Discrete Applied Mathematics 1 Journal of Fluid Mechanics 1 Journal of the Franklin Institute 1 Journal of Mathematical Physics 1 Letters in Mathematical Physics 1 Linear and Multilinear Algebra 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Stochastics 1 Studia Mathematica 1 Arkiv för Matematik 1 Reviews in Mathematical Physics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Automatica ...and 83 more Serials all top 5 Cited in 42 Fields 189 Probability theory and stochastic processes (60-XX) 131 Dynamical systems and ergodic theory (37-XX) 130 Statistics (62-XX) 109 Measure and integration (28-XX) 87 Information and communication theory, circuits (94-XX) 65 Computer science (68-XX) 30 Statistical mechanics, structure of matter (82-XX) 18 Operator theory (47-XX) 13 Combinatorics (05-XX) 13 General topology (54-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Mathematical logic and foundations (03-XX) 12 Numerical analysis (65-XX) 12 Operations research, mathematical programming (90-XX) 11 Number theory (11-XX) 10 Functional analysis (46-XX) 10 Quantum theory (81-XX) 9 Biology and other natural sciences (92-XX) 8 Topological groups, Lie groups (22-XX) 7 History and biography (01-XX) 7 Systems theory; control (93-XX) 6 Partial differential equations (35-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 4 Differential geometry (53-XX) 3 Group theory and generalizations (20-XX) 3 Ordinary differential equations (34-XX) 3 Fluid mechanics (76-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Category theory; homological algebra (18-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.