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We prove lower semicontinuity, concavity, and a formula for the ergodic decomposition of statistical complexity. ... We also prove that, given the past output of a partially deterministic hidden Markov model (HMM), the uncertainty of the internal state is constant over time and knowledge of the internal state gives no ... Acknowledgements I am thankful to Nihat Ay for introducing me to computational mechanics, discussions, and all kinds of scientific support. ...doi:10.3390/e110300385 fatcat:n6hc5jxcofderoqgy2nqxw2dsu
Specifically, we evaluate (a) the number of the missing ordinal patterns, (b) the rate of missing ordinal pattern decay for increased length of the time series, and (c) the causal-entropy complexity plane ... Specifically, it remains unclear whether human AF dynamics are a deterministic or a stochastic process. ... The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. ...doi:10.1063/1.5023588 pmid:29960392 fatcat:n3s23pbf2fgkta4qsglxkok26y
Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252)
From the maximal bound we deduce a relationship between complexity and total information content. ... A new measure of string complexity  for finite strings is presented based on a specific recursive hierarchical string production process (c. f.  ). ... complexity, we write C T ( Z ) = li(& (x) x 1x1) where E is the expected entropy for the string x in nats/symbol. ...doi:10.1109/isit.1998.708931 fatcat:ng6qxbgconecjmfhin6nlxfgai
2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC)
Deterministic (chaos) dynamics dominate for intermediate values of the permutation entropy and the statistical complexity (τ = 10-70 samples). ... For large values of the permutation entropy and small ones of the statistical complexity the dynamics can be considered to be non-deterministic (τ = 0-10 and 70-200 samples). ... Deterministic (chaos) dynamics dominate for intermediate values of the permutation entropy and the statistical complexity (τ = 10-70 samples). ...doi:10.1109/cleoe.2011.5943565 fatcat:xef4colyrvaxzhwsu3ufbm3x6i
concerned variable, described by the contour map of a certain entropy measure, such as Shannon entropy, relative entropy, and mutual entropy [Koutsoyiannis, 2005; Brunsell, 2010; Mishra et al., 2009; Chou ... We conclude that the three ranks (low, middle, and high) approximately correspond to deterministic, stochastic, and random hydrological systems, respectively. ... Acknowledgments The authors gratefully acknowledged the valuable comments and suggestions on earlier version of the manuscript given by the Editor, L. Ruby Leung, and three reviewers. ...doi:10.1002/2014jd022844 fatcat:mpfaw7a7uff5jhtuv5ro3uk5w4
This is a paper in the intersection of time series analysis and complexity theory that presents new results on permutation complexity in general and permutation entropy in particular. ... Z-entropies are a family of group entropies, each of them extensive on a given complexity class. ... Acknowledgements J.M.A. and R.D. were financially supported by Agencia Estatal de Investigación, PID2019-108654GB-I00, Spain. ...arXiv:2103.11762v2 fatcat:2x4h3uksynbd7ol4rsct2lqgga
We then calculate the permutation entropy-a temporal entropy metric that uses ordinal analysis-of those traces and correlate those values against the prediction success ... The memory and processor loads of some simple programs are easy to predict, for example, but those of more-complex programs like compilers are not. ... ACKNOWLEDGMENT This work was partially supported by NSF grant #CMMI-1245947 and ARO grant #W911NF-12-1-0288. ...arXiv:1305.5408v1 fatcat:nbrm52o5trdo5eossl5biam6v4
The predictive information and the excess entropy are such complexity measures. ... We therefore propose a new decomposition of the excess entropy in resolution dependent and resolution independent parts and discuss how they depend on the dimensionality of the dynamics, correlations and ... Presented are the unrefined constant and dimension of the excess entropy, the state-, memory-, and core complexity (in nats) determined in the deterministic scaling range, see Figure 3 . ...doi:10.3390/e17107266 fatcat:6j2da3u2m5d7xlqmtlehwu7cfi
These are generated within the framework of a deterministic theory of string complexity . ... The average entropy is HZ= I,/jxI, i.e.: ... Titchener, "Deterministic com- putation of string complexity, informa tion and entropy", IEEE-ISIT. 106%0314/99 $10.00 0 1999 IEEE ...doi:10.1109/dcc.1999.785711 dblp:conf/dcc/TitchenerFC99 fatcat:aib5xbk54ncsbjnliyd4j5mffy
Insights pertaining to the deterministic component of the original time series are obtained with the help of the causal entropy-complexity plane [Rosso et al. Phys. Rev. Lett. 99 (2007) 154102]. ... Lett. 88 (2002) 174102] and ii) the so-called Amig\'o paradigm of forbidden/missing patterns [Amig\'o, Zambrano, Sanju\'an, Europhys. ... Martín Gómez Ravetti acknowledges support from FAPEMIG and CNPq, Brazil. ...doi:10.1140/epjb/e2012-30307-8 fatcat:ybwcs7tscfh3tb3wzdwqhjqbxe
deterministic uncertainty to deterministic complexity (Phillips 1994). ... Chaos is the most commonly discussed form of deterministic complexity (Marzocchi et al. 1997). ...
This result is extended to time complexities in the range between real time and linear time, and is generalized to arbitrary dimensions. ... Both of these constructions use fewer truly random bits than any previous construction which works for all min-entropies and extracts a constant fraction of the min-entropy. ...
We find that in the entropy-complexity plane this goal can be achieved without additional computations. ... Two different tools have been advanced in the literature to such effect, namely, i) the "causal" entropy-complexity plane [Rosso et al. Phys. Rev. ... Martín Gómez Ravetti acknowledges support from FAPEMIG and CNPq, Brazil. ...doi:10.1016/j.physa.2011.07.030 fatcat:gnozbpo4b5av3pou3gqx3xsbna
Complexity was equated with the amount of randomness within an ordered molecular structure and measured by the entropy of a posteriori probabilities for discrete (monomer sequences, atomic bonds) and continuous ... The transmission of complexity during DNA replication has been investigated to clarify the significance of this molecular property in a deterministic process. ... Peter Elias for his advice and to Paul Cantrell, who performed many of the calculations in this work. Financial support was received from National Institutes of Health Grant 7R01-HD-12998-01. ...doi:10.1073/pnas.76.5.2288 pmid:287070 pmcid:PMC383584 fatcat:2fucmvneuvbybmg43olyo3buie
The Kolmogorov–Sinai entropy for events and the Kolmogorov–Chaitin complexity for strings of numbers both approximate Shannon's entropy (an indicator for the removal of uncertainty), indicating that information ... Nevertheless, their information evolution and degree of complexity are amenable to measurement and can meaningfully replace the dichotomy of chance versus necessity. ... A distinction between a "random" occurrence and a complex "deterministic" occurrence is impossible to make as it has no correlate in nature. ...doi:10.3390/info11050245 fatcat:iz6xabfvjjddfn3hrcs62gitl4
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