scholarly journals On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 450 ◽  
Author(s):  
Antonio Dávalos ◽  
Meryem Jabloun ◽  
Philippe Ravier ◽  
Olivier Buttelli
Keyword(s):  
Time Scale ◽  
Real Life ◽  
Theoretical Background ◽  
Quadratic Growth ◽  
Permutation Entropy ◽  
Statistical Comparison ◽  
Pattern Distribution ◽  
Ordinal Pattern ◽  
Analysis Of Time Series

Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) have been extensively used in the analysis of time series searching for regularities. Although PE has been explored and characterized, there is still a lack of theoretical background regarding MPE. Therefore, we expand the available MPE theory by developing an explicit expression for the estimator’s variance as a function of time scale and ordinal pattern distribution. We derived the MPE Cramér–Rao Lower Bound (CRLB) to test the efficiency of our theoretical result. We also tested our formulation against MPE variance measurements from simulated surrogate signals. We found the MPE variance symmetric around the point of equally probable patterns, showing clear maxima and minima. This implies that the MPE variance is directly linked to the MPE measurement itself, and there is a region where the variance is maximum. This effect arises directly from the pattern distribution, and it is unrelated to the time scale or the signal length. The MPE variance also increases linearly with time scale, except when the MPE measurement is close to its maximum, where the variance presents quadratic growth. The expression approaches the CRLB asymptotically, with fast convergence. The theoretical variance is close to the results from simulations, and appears consistently below the actual measurements. By knowing the MPE variance, it is possible to have a clear precision criterion for statistical comparison in real-life applications.

scholarly journals On Rényi Permutation Entropy

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 37
Author(s):  
Tim Gutjahr ◽  
Karsten Keller
Keyword(s):  
Shannon Entropy ◽  
Permutation Entropy ◽  
Correlation Integral ◽  
System A ◽  
The Family ◽  
Rényi Entropies ◽  
Pattern Distribution ◽  
Ordinal Pattern ◽  
Negative Real Number ◽  
Renyi Entropies

Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers. This paper discusses the relatively new concept of Rényi permutation entropies in dependence of non-negative real number q parameterizing the family of Rényi entropies and providing the Shannon entropy for q=1. Its relationship to Kolmogorov–Sinai entropy and, for q=2, to the recently introduced symbolic correlation integral are touched.

scholarly journals Calculators as Facilitators of Understanding Computational and Mathematical Contexts

2019 ◽  
Vol 1 (1) ◽  
pp. 177-183
Author(s):  
Jan Guncaga ◽  
Lilla Korenova ◽  
Jozef Hvorecky
Keyword(s):  
Soft Skills ◽  
Real Life ◽  
Theoretical Background ◽  
Learning Processes ◽  
Complex Phenomenon ◽  
Learning To Learn ◽  
Life Problems ◽  
The Subject ◽  
The Relationship

AbstractLearning is a complex phenomenon. Contemporary theories of education underline active participation of learners in their learning processes. One of the key arguments supporting this approach is the learner’s simultaneous and unconscious development of their ability of “learning to learn”. This ability belongs to the soft skills highly valued by employers today.For Mathematics Education, it means that teachers have to go beyond making calculations and memorizing formulas. We have to teach the subject in its social context. When the students start understanding the relationship between real-life problems and the role of numbers and formulas for their solutions, their learning becomes a part of their tacit knowledge. Below we explain the theoretical background of our approach and provide examples of such activities.

scholarly journals On the characterization of glacier response by a single time-scale

2001 ◽  
Vol 47 (159) ◽  
pp. 659-664 ◽  
Author(s):  
W. D. Harrison ◽  
D. H. Elsberg ◽  
K. A. Echelmeyer ◽  
R. M. Krimmel
Keyword(s):  
Climate Change ◽  
Mass Balance ◽  
Time Constant ◽  
Time Scale ◽  
Response Models ◽  
Single Time ◽  
Glacier Changes ◽  
Major Increase ◽  
Effect Of Surface

AbstractGlacier response to climate can be characterized by a single time-scale when the glacier changes sufficiently slowly. Then the derivative of volume with respect to area defines a thickness scale similar to that of Jóhannesson and others, and the time-scale follows from it. Our version of the time-scale is different from theirs because it explicitly includes the effect of surface elevation on mass-balance rate, which can cause a major increase in the time-scale or even lead to unstable response. The time constant has a dual role, controlling both the rate and magnitude of response to a given climate change. Data from South Cascade Glacier, Washington, U.S.A., illustrate the ideas, some of the difficulty in obtaining accurate values for the thickness and time-scales, and the susceptibility of all response models to potentially large errors.

scholarly journals Patterns with Equal Values in Permutation Entropy: Do They Really Matter for Biosignal Classification?

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
David Cuesta–Frau ◽  
Manuel Varela–Entrecanales ◽  
Antonio Molina–Picó ◽  
Borja Vargas
Keyword(s):  
Body Temperature ◽  
Sensitivity And Specificity ◽  
Scientific Literature ◽  
Statistical Significance ◽  
Permutation Entropy ◽  
Limiting Factor ◽  
Embedding Dimension ◽  
Class Segmentation ◽  
Biosignal Classification

Two main weaknesses have been identified for permutation entropy (PE): the neglect of subsequence pattern differences in terms of amplitude and the possible ambiguities introduced by equal values in the subsequences. A number of variations or customizations to the original PE method to address these issues have been proposed in the scientific literature recently. Specifically for ties, methods have tried to remove the ambiguity by assigning different weighted or computed orders to equal values. Although these methods are able to circumvent such ambiguity, they can substantially increase the algorithm costs, and a general characterization of their practical effectiveness is still lacking. This paper analyses the performance of PE using several biomedical datasets (electroencephalogram, heartbeat interval, body temperature, and glucose records) in order to quantify the influence of ties on its signal class segmentation capability. This capability is assessed in terms of statistical significance of the PE differences between classes and classification sensitivity and specificity. Being obvious that ties modify the PE results, we hypothesize that equal values are intrinsic to the acquisition process, and therefore, they impact all the classes more or less equally. The experimental results confirm ties are often not the limiting factor for PE, even they can be beneficial as a sort of stochastic resonance, and it can be far more effective to focus on the embedding dimension instead.

scholarly journals A mixed thinning based geometric INAR(1) model

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4009-4022 ◽  
Author(s):  
Aleksandar Nastic ◽  
Miroslav Ristic ◽  
Ana Janjic
Keyword(s):  
Parameter Estimation ◽  
Method Of Moments ◽  
Negative Binomial ◽  
Real Life ◽  
Binomial Thinning ◽  
Conditional Least Squares ◽  
Counting Data ◽  
Parameter Estimators ◽  
Thinning Operator

In this article a geometrically distributed integer-valued autoregressive model of order one based on the mixed thinning operator is introduced. This new thinning operator is defined as a probability mixture of two well known thinning operators, binomial and negative binomial thinning. Some model properties are discussed. Method of moments and the conditional least squares are considered as possible approaches in model parameter estimation. Asymptotic characterization of the obtained parameter estimators is presented. The adequacy of the introduced model is verified by its application on a certain kind of real-life counting data, while its performance is evaluated by comparison with two other INAR(1) models that can be also used over the observed data.

UX Work in Libraries

2018 ◽  
pp. 1-36
Author(s):  
Houda El Mimouni ◽  
Jennifer Anderson ◽  
Nadaleen F Tempelman-Kluit ◽  
Alexandra Dolan-Mescal
Keyword(s):  
New York ◽  
User Satisfaction ◽  
Real Life ◽  
Public Library ◽  
Theoretical Background ◽  
University Of California ◽  
Library Services ◽  
New York University ◽  
New York Public Library ◽  
Library User

The application of UX expertise is beneficial in all the areas and aspects of library services and products. All what a librarian needs is an understanding of those principles and some tools with which to practice them. The goal of this chapter, therefore, is to provide a guide for librarians, whether they are specifically in charge of UX work at their library or aspire to integrate UX into their work on other library services and products. This chapter provides some theoretical background on the traditional goal of library user satisfaction and introduces UX as an approach that benefits libraries and their users. It gives an overview of popular UX methodologies and describes real-life UX in libraries through the stories from three librarians in their respective institutions: the New York Public Library, New York University, and University of California, Riverside.

scholarly journals A Note on a New General Family of Deterministic Hierarchical Networks

2019 ◽  
Vol 19 (02) ◽  
pp. 1950005
Author(s):  
C. DALFÓ ◽  
M. A. FIOL
Keyword(s):  
Real Life ◽  
Small Diameter ◽  
Stochastic Methods ◽  
Local Algorithm ◽  
Hierarchical Networks ◽  
Binomial Tree ◽  
Scale Free ◽  
Local Clustering ◽  
Specific Rule

It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of the models are based on stochastic methods, some deterministic constructions have been recently proposed, because this allows a better computation of their properties. Here a new deterministic family of hierarchical networks is presented, which generalizes most of the previous proposals, such as the so-called binomial tree. The obtained graphs can be seen as graphs on alphabets (where vertices are labeled with words of a given alphabet, and the edges are defined by a specific rule relating different words). This allows us the characterization of their main distance-related parameters, such as the radius and diameter. Moreover, as a by-product, an efficient shortest-path local algorithm is proposed.

scholarly journals Improving Entropy Estimates of Complex Network Topology for the Characterization of Coupling in Dynamical Systems

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 891 ◽  
Author(s):  
Teddy Craciunescu ◽  
Andrea Murari ◽  
Michela Gelfusa
Keyword(s):  
Dynamical Systems ◽  
Southern Oscillation ◽  
Geodesic Distance ◽  
Influenza Pandemic ◽  
Real Life ◽  
Coupled Model ◽  
Model Systems ◽  
Life Problems ◽  
Metric Distance

A new measure for the characterization of interconnected dynamical systems coupling is proposed. The method is based on the representation of time series as weighted cross-visibility networks. The weights are introduced as the metric distance between connected nodes. The structure of the networks, depending on the coupling strength, is quantified via the entropy of the weighted adjacency matrix. The method has been tested on several coupled model systems with different individual properties. The results show that the proposed measure is able to distinguish the degree of coupling of the studied dynamical systems. The original use of the geodesic distance on Gaussian manifolds as a metric distance, which is able to take into account the noise inherently superimposed on the experimental data, provides significantly better results in the calculation of the entropy, improving the reliability of the coupling estimates. The application to the interaction between the El Niño Southern Oscillation (ENSO) and the Indian Ocean Dipole and to the influence of ENSO on influenza pandemic occurrence illustrates the potential of the method for real-life problems.

scholarly journals Segmentation Method for Ship-Radiated Noise Using the Generalized Likelihood Ratio Test on an Ordinal Pattern Distribution

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 374
Author(s):  
Lei He ◽  
Xiao-Hong Shen ◽  
Mu-Hang Zhang ◽  
Hai-Yan Wang
Keyword(s):  
Likelihood Ratio ◽  
Real World ◽  
Change Point Detection ◽  
Change Points ◽  
Ratio Test ◽  
Segmentation Method ◽  
Generalized Likelihood Ratio ◽  
Radiated Noise ◽  
Pattern Distribution ◽  
Ordinal Pattern

Due to the diversity of ship-radiated noise (SRN), audio segmentation is an essential procedure in the ship statuses/categories identification. However, the existing segmentation methods are not suitable for the SRN because of the lack of prior knowledge. In this paper, by a generalized likelihood ratio (GLR) test on the ordinal pattern distribution (OPD), we proposed a segmentation criterion and introduce it into single change-point detection (SCPD) and multiple change-points detection (MCPD) for SRN. The proposed method is free from the acoustic feature extraction and the corresponding probability distribution estimation. In addition, according to the sequential structure of ordinal patterns, the OPD is efficiently estimated on a series of analysis windows. By comparison with the Bayesian Information Criterion (BIC) based segmentation method, we evaluate the performance of the proposed method on both synthetic signals and real-world SRN. The segmentation results on synthetic signals show that the proposed method estimates the number and location of the change-points more accurately. The classification results on real-world SRN show that our method obtains more distinguishable segments, which verifies its effectiveness in SRN segmentation.

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