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On the entropy of coverable subshifts
[article]

2018
*
arXiv
*
pre-print

We also noticed that some

arXiv:1812.08022v1
fatcat:7i6td67ajreajmhqkjw3xi35n4
*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. ...##
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Algebraic entropy on strongly compactly covered groups
[article]

2018
*
arXiv
*
pre-print

For continuous endomorphisms ϕ:G→ G of these groups we compute the algebraic

arXiv:1805.09608v1
fatcat:kwzswnmxzfecfbraucz5g6xphu
*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 ...##
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Tight Results on Minimum Entropy Set Cover

2007
*
Algorithmica
*

In the minimum

doi:10.1007/s00453-007-9076-8
fatcat:2ch7capn7nfj5hqnep5criuvci
*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 ). ...##
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Tight Results on Minimum Entropy Set Cover
[chapter]

2006
*
Lecture Notes in Computer Science
*

In the minimum

doi:10.1007/11830924_8
fatcat:b5kyttpvi5awncuoiiykqhk55e
*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 ). ...##
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'Entropy' on Covers and Its Application on Decision TreeConstruction

2011
*
International Journal of Machine Learning and Computing
*

In parallel to the theory of generalized

doi:10.7763/ijmlc.2011.v1.31
fatcat:4we3qwyrcbgwdjhaxvpjlcybpa
*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. ...##
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Counting in Graph Covers: A Combinatorial Characterization of the Bethe Entropy Function

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-

doi:10.1109/tit.2013.2264715
fatcat:w6qat56jorbathzmerzqvrbfze
*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. ...##
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A remark on the topological entropies of covers and partitions

2007
*
Studia Mathematica
*

We study if the combinatorial

doi:10.4064/sm182-3-6
fatcat:5knqtpqhmfb6tehtpambveeif4
*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. ...##
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Entropy on Riemann surfaces and the Jacobians of finite covers

2013
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Commentarii Mathematici Helvetici
*

This paper characterizes those pseudo-Anosov mappings whose

doi:10.4171/cmh/308
fatcat:japlnyz5qndedpg2veddsdkoiu
*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. ...##
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The entropy of Markov trajectories

1993
*
IEEE Transactions on Information Theory
*

. • Depth of a state depends

doi:10.1109/18.243461
fatcat:jfmupufeg5dpvppdapjfe3qpom
*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 ? ...##
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Entropy/length profiles, bounds on the minimal covering of bipartite graphs, and trellis complexity of nonlinear codes

1998
*
IEEE Transactions on Information Theory
*

Additionally and independently, we use wellknown information-theoretic measures to derive novel bounds

doi:10.1109/18.661506
fatcat:uo65zcpytzdupkfubrkyrsqs6q
*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. ...##
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Entropy Change as Influenced by Anthropogenic Impact on a Boreal Land Cover - A Case Study

2006
*
Journal of Environmental Informatics
*

We hypothesize that this could be explained with the help of an

doi:10.3808/jei.200600069
fatcat:rpahbmqckfaynj2czokpe3g7im
*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. ...##
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Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy

2022
*
Applied Mathematics and Nonlinear Sciences
*

of traditional rough set theory,

doi:10.2478/amns.2021.1.00110
fatcat:3e5ilrdbcfahjop7fikzlu4wfa
*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*...##
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Maximum entropy and conditional probability

1981
*
IEEE Transactions on Information Theory
*

This distribution is the maximum

doi:10.1109/tit.1981.1056374
fatcat:tjbzibk4jramfi3oanea3fzche
*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 ...##
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The entropy of a randomly stopped sequence

1991
*
IEEE Transactions on Information Theory
*

Thus, the randomness in the stopped sequence X" is the expected number of "calls" for X times the

doi:10.1109/18.104324
fatcat:icy7z6icyvhsnhfkrwrhmp6fuu
*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]. ...##
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A convergent gambling estimate of the entropy of English

1978
*
IEEE Transactions on Information Theory
*

Abstmct-In his original paper

doi:10.1109/tit.1978.1055912
fatcat:qsulklzqgneybkoyeo7vj3ta5y
*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. ...
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