Measuring complexity with zippers

Baronchelli, Andrea; Caglioti, Emanuele; Loreto, Vittorio

doi:10.1088/0143-0807/26/5/s08

Cited by 17 publications

(23 citation statements)

References 27 publications

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“…As ǫ decreases, more detailed information is described by the symbols. Although c is not a reliable estimate of h at the finer partitions, it is still an indicator of the information content of the data streams and also shows the same decrease with Re [36]. The important point is that the general behavior of c and h * is the same for partitions of all sizes.…”

Section: Turbulencementioning

confidence: 92%

“…In order to account for the "overhead" (file headers, etc. ), a random data set is compressed and that compression ratio is used to normalize the real data [36].…”

Section: Entropy and Entropy Estimationmentioning

confidence: 99%

“…This is a measure of the computational complexity of the data set in question. Even if c is not equal to h, it is still a measure of the information content of the data [36][37][38]. It is important to recognize the many limitations involved in calculating information content.…”

Section: Entropy and Entropy Estimationmentioning

confidence: 99%

See 2 more Smart Citations

Information content of turbulence

Cerbus

Goldburg

2013

Phys. Rev. E

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We treat a turbulent velocity field as a message in the same way as a book or a picture. All messages can be described by their entropy per symbol h, defined as in Shannon's theory of communication. In a turbulent flow, as the Reynolds number Re increases, more correlated degrees of freedom are excited and participate in the turbulent cascade. Experiments in a turbulent soap film suggest that the spatial entropy density h is a decreasing function of Re, namely h[proportionality]-logRe + const. In the logistic map, also analyzed here, increasing the control parameter r increases h. A modified logistic map with additional coupling to past iterations suggests the significance of correlations.

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Section: Turbulencementioning

confidence: 92%

“…In order to account for the "overhead" (file headers, etc. ), a random data set is compressed and that compression ratio is used to normalize the real data [36].…”

Section: Entropy and Entropy Estimationmentioning

confidence: 99%

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Information content of turbulence

Cerbus

Goldburg

2013

Phys. Rev. E

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“…For equilibrium systems, a time series of the spin or the Edwards-Anderson autocorrelation parameter at a given site, obtained by Monte Carlo simulation, was used to locate the critical points of the 3D Edwards-Anderson spin glass [17] and the 2D and 3D Ising models [18,19], and to approximate the entropy of the 2D Ising model [19]. Data compression has also proven to be a useful tool in the definition and characterization of complexity of (mostly one-dimensional) dynamical models, such as cellular automata and dynamical systems [20][21][22][23][24][25][26], as well as for turbulence [27]. Methods based on data compression have also been used to estimate the entropy production of a nonequilibrium stationary state [28,29] and to detect the onset of chaos in biological systems [30][31][32].…”

Section: A Computable Information Densitymentioning

confidence: 99%

Quantifying Hidden Order out of Equilibrium

2019

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While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of nonequilibrium phenomena in diverse settings, from glasses to driven systems to biology. The length of a losslessly compressed data file is a direct measure of its information content: The more ordered the data file is, the lower its information content and the shorter the length of its encoding can be made. Here, we describe how data compression enables the quantification of order in nonequilibrium and equilibrium many-body systems, both discrete and continuous, even when the underlying form of order is unknown. We consider absorbing state models on and off lattice, as well as a system of active Brownian particles undergoing motility-induced phase separation. The technique reliably identifies nonequilibrium phase transitions, determines their character, quantitatively predicts certain critical exponents without prior knowledge of the order parameters, and reveals previously unknown ordering phenomena. This technique should provide a quantitative measure of organization in condensed matter and other systems exhibiting collective phase transitions in and out of equilibrium.

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“…On the other hand one can construct AT by merging dictionaries coming from different original texts: merging dictionaries extracted from different texts all about the same subject or all written by the same author. In this way the AT would play the role of an archetypal text of that specific subject or that specific author [63]. The possibility to construct many different AT all representative of the same original sequence (or of a given source) allows for an alternative way to estimate the selfentropy of a source (and consequently the relative entropy between two sources as mentioned above).…”

Section: Dictionaries and Artificial Textsmentioning

confidence: 99%

Artificial sequences and complexity measures

2005

Self Cite

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In this paper we exploit concepts of information theory to address the fundamental problem of identifying and defining the most suitable tools to extract, in a automatic and agnostic way, information from a generic string of characters. We introduce in particular a class of methods which use in a crucial way data compression techniques in order to define a measure of remoteness and distance between pairs of sequences of characters (e.g. texts) based on their relative information content. We also discuss in detail how specific features of data compression techniques could be used to introduce the notion of dictionary of a given sequence and of Artificial Text and we show how these new tools can be used for information extraction purposes. We point out the versatility and generality of our method that applies to any kind of corpora of character strings independently of the type of coding behind them. We consider as a case study linguistic motivated problems and we present results for automatic language recognition, authorship attribution and self consistentclassification.

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Measuring complexity with zippers

Cited by 17 publications

References 27 publications

Information content of turbulence

Information content of turbulence

Quantifying Hidden Order out of Equilibrium

Artificial sequences and complexity measures

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