Composition Operations of Generalized Entropies Applied to the Study of Numbers

Amelia Carolina Sparavigna

doi:10.18483/ijsci.2044

Detection and Classification of Anomalies in Network Traffic Using Generalized Entropies and OC-SVM with Mahalanobis Kernel

10.3390/ecea-1-b004 ◽

2014 ◽

Author(s):

Jayro Santiago-Paz ◽

Deni Torres-Roman ◽

Angel Figueroa-Ypiña

Keyword(s):

Network Traffic ◽

Generalized Entropies

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Comment on “Third law of thermodynamics as a key test of generalized entropies”

Physical Review E ◽

10.1103/physreve.92.016103 ◽

2015 ◽

Vol 92 (1) ◽

Cited By ~ 2

Author(s):

G. Baris Bagci ◽

Thomas Oikonomou

Keyword(s):

Third Law Of Thermodynamics ◽

Third Law ◽

Generalized Entropies

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Generalized entropies and the transformation group of superstatistics

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1103539108 ◽

2011 ◽

Vol 108 (16) ◽

pp. 6390-6394 ◽

Cited By ~ 80

Author(s):

R. Hanel ◽

S. Thurner ◽

M. Gell-Mann

Keyword(s):

Transformation Group ◽

Generalized Entropies

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When the Whole Is Not Greater Than the Combination of Its Parts: A “Decompositional” Look at Compositional Distributional Semantics

Computational Linguistics ◽

10.1162/coli_a_00215 ◽

2015 ◽

Vol 41 (1) ◽

pp. 165-173 ◽

Cited By ~ 3

Author(s):

Fabio Massimo Zanzotto ◽

Lorenzo Ferrone ◽

Marco Baroni

Keyword(s):

Distributional Semantics ◽

Important Class ◽

Strong Link ◽

Composition Methods ◽

Convolution Kernels ◽

Composition Operations ◽

Compositional Distributional Semantics

Distributional semantics has been extended to phrases and sentences by means of composition operations. We look at how these operations affect similarity measurements, showing that similarity equations of an important class of composition methods can be decomposed into operations performed on the subparts of the input phrases. This establishes a strong link between these models and convolution kernels.

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Extended properties of the class of Rényi Generalized Entropies in the discrete time domain

International Conference on Computer Networks and Information Technology ◽

10.1109/iccnit.2011.6020894 ◽

2011 ◽

Cited By ~ 1

Author(s):

Ismail A.M. Mohamed ◽

Demetres D. Kouvatsos

Keyword(s):

Discrete Time ◽

Time Domain ◽

Generalized Entropies

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A Brief Review of Generalized Entropies

Entropy ◽

10.3390/e20110813 ◽

2018 ◽

Vol 20 (11) ◽

pp. 813 ◽

Cited By ~ 25

Author(s):

José Amigó ◽

Sámuel Balogh ◽

Sergio Hernández

Keyword(s):

Diffusion Processes ◽

Complex Dynamics ◽

Probability Distributions ◽

Point Of View ◽

Scaling Exponent ◽

Scaling Exponents ◽

Physical Systems ◽

New Phenomena ◽

Generalized Entropies

Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon–Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances.

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Spatial Measures of Urban Systems: from Entropy to Fractal Dimension

Entropy ◽

10.3390/e20120991 ◽

2018 ◽

Vol 20 (12) ◽

pp. 991 ◽

Cited By ~ 8

Author(s):

Yanguang Chen ◽

Linshan Huang

Keyword(s):

Fractal Dimension ◽

Spatial Analysis ◽

Fractal Dimensions ◽

Scale Dependence ◽

Urban Systems ◽

Scale Free ◽

Spatial Entropy ◽

Spatial Systems ◽

Urban Patterns ◽

Generalized Entropies

One type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimensions can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connection between entropy and fractal dimensions, they have different application scopes and directions in urban studies. This paper focuses on exploring how to convert entropy measurements into fractal dimensions for the spatial analysis of scale-free urban phenomena using the ideas from scaling. Urban systems proved to be random prefractal and multifractal systems. The spatial entropy of fractal cities bears two properties. One is the scale dependence: the entropy values of urban systems always depend on the linear scales of spatial measurement. The other is entropy conservation: different fractal parts bear the same entropy value. Thus, entropy cannot reflect the simple rules of urban processes and the spatial heterogeneity of urban patterns. If we convert the generalized entropies into multifractal spectrums, the problems of scale dependence and entropy homogeneity can be solved to a degree for urban spatial analysis. Especially, the geographical analyses of urban evolution can be simplified. This study may be helpful for students in describing and explaining the spatial complexity of urban evolution.

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