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On the entropy of coverable subshifts [article]

Guilhem Gamard
2018 arXiv   pre-print
We also noticed that some covers force subshifts to have zero topological entropy while not forcing them to be finite.  ...  In the current paper we work towards characterizing precisely covers which force a subshift to have zero entropy, but not necessarily periodicity.  ...  entropy coverable subshift.  ... 
arXiv:1812.08022v1 fatcat:7i6td67ajreajmhqkjw3xi35n4

Algebraic entropy on strongly compactly covered groups [article]

Anna Giordano Bruno, Menachem Shlossberg, Daniele Toller
2018 arXiv   pre-print
For continuous endomorphisms ϕ:G→ G of these groups we compute the algebraic entropy and study its properties. Also an Addition Theorem is available under suitable conditions.  ...  We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups G such that every element of G is contained in a compact open  ...  Another consequence of our Addition Theorem (see Corollary 7.7) is that, to compute the algebraic entropy of a topological automorphism φ of a strongly compactly covered group G, one can assume G to be  ... 
arXiv:1805.09608v1 fatcat:kwzswnmxzfecfbraucz5g6xphu

Tight Results on Minimum Entropy Set Cover

Jean Cardinal, Samuel Fiorini, Gwenaël Joret
2007 Algorithmica  
In the minimum entropy set cover problem, one is given a collection of k sets which collectively cover an n-element ground set.  ...  The goal is to find a partition minimizing the (binary) entropy of the corresponding probability distribution, i.e., the one found by dividing each part size by n.  ...  ., q i := | f −1 (S i )| n . (1) The minimum entropy set cover problem (MESC) asks to find a cover f minimizing the entropy of the distribution (q 1 , . . . , q k ).  ... 
doi:10.1007/s00453-007-9076-8 fatcat:2ch7capn7nfj5hqnep5criuvci

Tight Results on Minimum Entropy Set Cover [chapter]

Jean Cardinal, Samuel Fiorini, Gwenaël Joret
2006 Lecture Notes in Computer Science  
In the minimum entropy set cover problem, one is given a collection of k sets which collectively cover an n-element ground set.  ...  The goal is to find a partition minimizing the (binary) entropy of the corresponding probability distribution, i.e., the one found by dividing each part size by n.  ...  ., q i := | f −1 (S i )| n . (1) The minimum entropy set cover problem (MESC) asks to find a cover f minimizing the entropy of the distribution (q 1 , . . . , q k ).  ... 
doi:10.1007/11830924_8 fatcat:b5kyttpvi5awncuoiiykqhk55e

'Entropy' on Covers and Its Application on Decision TreeConstruction

Zhimin Wang
2011 International Journal of Machine Learning and Computing  
In parallel to the theory of generalized entropy, 'disconnectivity' is also generalized to a family of measures.  ...  To properly evaluate polymorphic attributes during tree construction, we propose the conditional form of a novel 'entropy' measure called 'disconnectivity' as the heuristic.  ...  Let U be a universe, Λ a cover on U.  ... 
doi:10.7763/ijmlc.2011.v1.31 fatcat:4we3qwyrcbgwdjhaxvpjlcybpa

Counting in Graph Covers: A Combinatorial Characterization of the Bethe Entropy Function

Pascal O. Vontobel
2013 IEEE Transactions on Information Theory  
The above findings are a natural backdrop for introducing a decoder for graph-based codes that we will call symbolwise graph-cover decoding, a decoder that extends our earlier work on blockwise graph-cover  ...  decoding with linear programming decoding, and symbolwise graph-cover decoding links sum-product algorithm decoding with Bethe free energy function minimization at temperature one.  ...  M -covers we get the Bethe entropy function, whereas when counting certain valid configurations in "nonintertwined" M -covers we get the Gibbs entropy function.  ... 
doi:10.1109/tit.2013.2264715 fatcat:w6qat56jorbathzmerzqvrbfze

A remark on the topological entropies of covers and partitions

Pierre-Paul Romagnoli
2007 Studia Mathematica  
We study if the combinatorial entropy of a finite cover can be computed using finite partitions finer than the cover. This relates to an unsolved question in [R] for open covers.  ...  We explicitly compute the topological entropy of a fixed clopen cover showing that it is smaller than the infimum of the topological entropy of all finer clopen partitions.  ...  The author would like to thank Bernard Host for suggesting this kind of covers a long time ago.  ... 
doi:10.4064/sm182-3-6 fatcat:5knqtpqhmfb6tehtpambveeif4

Entropy on Riemann surfaces and the Jacobians of finite covers

Curtis McMullen
2013 Commentarii Mathematici Helvetici  
This paper characterizes those pseudo-Anosov mappings whose entropy can be detected homologically using a limit over finite covers. The proof is via complex-analytic methods.  ...  The same methods show the natural map M g → A h sending a Riemann surface to Jacobians of all of its finite covers is a contraction in most directions.  ...  If we lift f to a map f : S → S on a finite cover of S, then its entropy stays the same but the spectral radius of the action on homology can increase.  ... 
doi:10.4171/cmh/308 fatcat:japlnyz5qndedpg2veddsdkoiu

The entropy of Markov trajectories

L. Ekroot, T.M. Cover
1993 IEEE Transactions on Information Theory  
. • Depth of a state depends on , the probability of the trajectory taken (starting at a given state). • Average Depth of a state d: • Computation of trajectories Entropy needed.  ...  Theorem If P is the transition matrix of an irreducible finite state Markov chain, then the matrix H of trajectory entropies is given by • What if we condition on an intermediary state ?  ... 
doi:10.1109/18.243461 fatcat:jfmupufeg5dpvppdapjfe3qpom

Entropy/length profiles, bounds on the minimal covering of bipartite graphs, and trellis complexity of nonlinear codes

I. Reuven, Y. Be'ery
1998 IEEE Transactions on Information Theory  
Additionally and independently, we use wellknown information-theoretic measures to derive novel bounds on the minimal covering of a bipartite graph by complete subgraphs.  ...  This elaboration of the DLP, the entropy/length profiles, appears to be suitable to the analysis of nonlinear codes.  ...  Entropy/Length Profiles, Bounds on the Minimal Covering of Bipartite Graphs, and Trellis Complexity of Nonlinear Codes I.  ... 
doi:10.1109/18.661506 fatcat:uo65zcpytzdupkfubrkyrsqs6q

Entropy Change as Influenced by Anthropogenic Impact on a Boreal Land Cover - A Case Study

J. Kumari
2006 Journal of Environmental Informatics  
We hypothesize that this could be explained with the help of an entropy parameter, based on vegetation related spectral characteristics.  ...  Landscape heterogeneity can be quantified based on the spectral heterogeneity.  ...  The authors are also thankful to Global Land Cover Facility (http://glcf.umiacs.umd.edu/ for the Landsat data). mote Sens. Environ., 25, 295-309.  ... 
doi:10.3808/jei.200600069 fatcat:rpahbmqckfaynj2czokpe3g7im

Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy

Xiuyun Xia, Hao Tian, Ye Wang
2022 Applied Mathematics and Nonlinear Sciences  
of traditional rough set theory, covers.  ...  In this article, we posit a method to reduce the attributes of covering decision systems, which are databases incarnated in the form of covers.  ...  Attribute reduction of consistent covering decision systems based on conditional information entropy In this section, we focus on investigating the basic concepts and key results of consistent covering  ... 
doi:10.2478/amns.2021.1.00110 fatcat:3e5ilrdbcfahjop7fikzlu4wfa

Maximum entropy and conditional probability

J. van Campenhout, T. Cover
1981 IEEE Transactions on Information Theory  
This distribution is the maximum entropy distribution when g is uniform. The proof of this and related results relies heavily on the work of Zabell and Lanford.  ...  It is well-known that maximum entropy distributions, subject to appropriate moment constraints, arise in physics and mathematics.  ...  Cover is with the Departments of Electrical Engineering and Statistics, Stanford University, Stanford, CA 94305. normal distribution of velocities in gases as a maximum entropy distribution under an energy  ... 
doi:10.1109/tit.1981.1056374 fatcat:tjbzibk4jramfi3oanea3fzche

The entropy of a randomly stopped sequence

L. Ekroot, T.M. Cover
1991 IEEE Transactions on Information Theory  
Thus, the randomness in the stopped sequence X" is the expected number of "calls" for X times the entropy per call plus the residual randomness in the stopping time conditioned on the nnstoppe4 sequence  ...  A Wald-like equation is proved for the entropy of a ran-db@y, stopped sequence of independent identically distributed discrete random variables XI, X2,. with a nonanticipating stopping time N.  ...  Some related results on the asymptotic entropy rate for channels without synchronization are developed in [5] and [l]. Related work on the entropy of rooted trees is presented by Massey in [3].  ... 
doi:10.1109/18.104324 fatcat:icy7z6icyvhsnhfkrwrhmp6fuu

A convergent gambling estimate of the entropy of English

T. Cover, R. King
1978 IEEE Transactions on Information Theory  
Abstmct-In his original paper on the subject, Shannon found upper and lower bounds for the entropy of printed English based on the number of trials required for a subject to guess subsequent symbols in  ...  ls an asymptotic upper bound for the true entropy. ff X is stationary, EH"(X)+H(X), H(X) bell the true entropy of the process.  ...  Table I shows the resulting entropy estimates. One disadvantage of this type of entropy estimate lies in the time necessary to perform the experiment.  ... 
doi:10.1109/tit.1978.1055912 fatcat:qsulklzqgneybkoyeo7vj3ta5y
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