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  • Review
  • Open Access
2,759 Citations
186,902 Views
45 Pages

Explainable AI: A Review of Machine Learning Interpretability Methods

  • Pantelis Linardatos,
  • Vasilis Papastefanopoulos and
  • Sotiris Kotsiantis

25 December 2020

Recent advances in artificial intelligence (AI) have led to its widespread industrial adoption, with machine learning systems demonstrating superhuman performance in a significant number of tasks. However, this surge in performance, has often been ac...

(This article belongs to the Special Issue Theory and Applications of Information Theoretic Machine Learning)
  • Article
  • Open Access
948 Citations
43,931 Views
32 Pages

Exploration and Development of High Entropy Alloys for Structural Applications

  • Daniel B. Miracle,
  • Jonathan D. Miller,
  • Oleg N. Senkov,
  • Christopher Woodward,
  • Michael D. Uchic and
  • Jaimie Tiley

10 January 2014

We develop a strategy to design and evaluate high-entropy alloys (HEAs) for structural use in the transportation and energy industries. We give HEA goal properties for low (≤150 °C), medium (≤450 °C) and high (≥1,100 °C) use temperatures. A systemati...

(This article belongs to the Special Issue High Entropy Alloys)
  • Review
  • Open Access
721 Citations
39,861 Views
29 Pages

29 May 2013

Quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. The viewpoint advocated is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dyna...

(This article belongs to the Special Issue Quantum Information 2012)
  • Review
  • Open Access
691 Citations
32,743 Views
13 Pages

16 November 2009

Maximum entropy (Maxent) modeling has great potential for identifying distributions and habitat selection of wildlife given its reliance on only presence locations. Recent studies indicate Maxent is relatively insensitive to spatial errors associated...

(This article belongs to the Special Issue Maximum Entropy)
  • Article
  • Open Access
681 Citations
34,191 Views
28 Pages

4 June 2013

Understanding maritime traffic patterns is key to Maritime Situational Awareness applications, in particular, to classify and predict activities. Facilitated by the recent build-up of terrestrial networks and satellite constellations of Automatic Ide...

  • Review
  • Open Access
622 Citations
44,978 Views
37 Pages

Approximate Entropy and Sample Entropy: A Comprehensive Tutorial

  • Alfonso Delgado-Bonal and
  • Alexander Marshak

28 May 2019

Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored...

  • Review
  • Open Access
605 Citations
30,865 Views
20 Pages

26 August 2014

This paper describes some underlying principles of multicomponent and high entropy alloys, and gives some examples of these materials. Different types of multicomponent alloy and different methods of accessing multicomponent phase space are discusse...

(This article belongs to the Special Issue High Entropy Alloys)
  • Article
  • Open Access
594 Citations
32,392 Views
25 Pages

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

  • Massimiliano Zanin,
  • Luciano Zunino,
  • Osvaldo A. Rosso and
  • David Papo

23 August 2012

Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also...

(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
  • Article
  • Open Access
508 Citations
71,053 Views
34 Pages

21 August 2001

Energy, entropy and exergy concepts come from thermodynamics and are applicable to all fields of science and engineering. Therefore, this article intends to provide background for better understanding of these concepts and their differences among var...

  • Article
  • Open Access
458 Citations
22,677 Views
16 Pages

5 August 2016

The electrocardiogram (ECG) is one of the most important techniques for heart disease diagnosis. Many traditional methodologies of feature extraction and classification have been widely applied to ECG analysis. However, the effectiveness and efficien...

(This article belongs to the Special Issue Entropy on Biosignals and Intelligent Systems)
  • Article
  • Open Access
456 Citations
23,732 Views
13 Pages

The Prior Can Often Only Be Understood in the Context of the Likelihood

  • Andrew Gelman,
  • Daniel Simpson and
  • Michael Betancourt

19 October 2017

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys’ priors, reference priors, maximum entropy priors, and weakly informative priors. T...

(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
  • Article
  • Open Access
417 Citations
20,171 Views
15 Pages

On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests

  • Aaditya Ramdas,
  • Nicolás García Trillos and
  • Marco Cuturi

26 January 2017

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and r...

(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
  • Article
  • Open Access
387 Citations
32,875 Views
37 Pages

27 December 2013

We review a selection of methods for performing enhanced sampling in molecular dynamics simulations. We consider methods based on collective variable biasing and on tempering, and offer both historical and contemporary perspectives. In collective-var...

(This article belongs to the Special Issue Molecular Dynamics Simulation)
  • Article
  • Open Access
379 Citations
21,434 Views
10 Pages

Imprecise Shannon’s Entropy and Multi Attribute Decision Making

  • Farhad Hosseinzadeh Lotfi and
  • Reza Fallahnejad

5 January 2010

Finding the appropriate weight for each criterion is one of the main points in Multi Attribute Decision Making (MADM) problems. Shannon’s entropy method is one of the various methods for finding weights discussed in the literature. However, in many r...

  • Article
  • Open Access
376 Citations
48,415 Views
22 Pages

Deep Learning for Stock Market Prediction

  • M. Nabipour,
  • P. Nayyeri,
  • H. Jabani,
  • A. Mosavi,
  • E. Salwana and
  • Shahab S.

30 July 2020

The prediction of stock groups values has always been attractive and challenging for shareholders due to its inherent dynamics, non-linearity, and complex nature. This paper concentrates on the future prediction of stock market groups. Four groups na...

(This article belongs to the Special Issue Information Transfer in Multilayer/Deep Architectures)
  • Article
  • Open Access
372 Citations
24,736 Views
37 Pages

14 June 2010

In this paper, we extend and overview wide families of Alpha-, Beta- and Gamma-divergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) divergence is considered. We show in this pap...

  • Review
  • Open Access
365 Citations
22,125 Views
36 Pages

The Quantum Harmonic Otto Cycle

  • Ronnie Kosloff and
  • Yair Rezek

23 March 2017

The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a work...

(This article belongs to the Special Issue Quantum Thermodynamics)
  • Article
  • Open Access
356 Citations
22,896 Views
17 Pages

16 June 2021

Grouping the objects based on their similarities is an important common task in machine learning applications. Many clustering methods have been developed, among them k-means based clustering methods have been broadly used and several extensions have...

(This article belongs to the Special Issue Machine/Statistical Learning and Modeling with Potential Applications in Entropy, Information Theory, and Artificial Intelligence)
  • Review
  • Open Access
355 Citations
27,984 Views
8 Pages

3 December 2013

The majority of studies on high-entropy alloys are focused on their phase, microstructure, and mechanical properties. However, the physical properties of these materials are also encouraging. This paper provides a brief overview of the physical prope...

(This article belongs to the Special Issue High Entropy Alloys)
  • Review
  • Open Access
349 Citations
50,654 Views
31 Pages

Sleep Stage Classification Using EEG Signal Analysis: A Comprehensive Survey and New Investigation

  • Khald Ali I. Aboalayon,
  • Miad Faezipour,
  • Wafaa S. Almuhammadi and
  • Saeid Moslehpour

23 August 2016

Sleep specialists often conduct manual sleep stage scoring by visually inspecting the patient’s neurophysiological signals collected at sleep labs. This is, generally, a very difficult, tedious and time-consuming task. The limitations of manual sleep...

(This article belongs to the Special Issue Entropy and Electroencephalography II)
  • Article
  • Open Access
347 Citations
11,781 Views
54 Pages

18 September 2012

Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann–Lemaˆıtre–Robertson–Walker metrics. The...

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)
  • Article
  • Open Access
345 Citations
22,381 Views
23 Pages

24 February 2020

The type of criterion weight can be distinguished according to different decision methods. Subjective weights are given by decision makers based on their knowledge, experience, expertise, and other factors. Objective weights are obtained through mult...

(This article belongs to the Special Issue Information Theories Based on Belief Functions for Decision-Making Support)
  • Article
  • Open Access
340 Citations
19,939 Views
16 Pages

Time Series Analysis Using Composite Multiscale Entropy

  • Shuen-De Wu,
  • Chiu-Wen Wu,
  • Shiou-Gwo Lin,
  • Chun-Chieh Wang and
  • Kung-Yen Lee

18 March 2013

Multiscale entropy (MSE) was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been successfully applied in a number of different fields, it encounters a problem in that the statis...

  • Review
  • Open Access
322 Citations
32,909 Views
36 Pages

Particle Swarm Optimisation: A Historical Review Up to the Current Developments

  • Diogo Freitas,
  • Luiz Guerreiro Lopes and
  • Fernando Morgado-Dias

21 March 2020

The Particle Swarm Optimisation (PSO) algorithm was inspired by the social and biological behaviour of bird flocks searching for food sources. In this nature-based algorithm, individuals are referred to as particles and fly through the search space s...

(This article belongs to the Special Issue Intelligent Tools and Applications in Engineering and Mathematics)
  • Review
  • Open Access
322 Citations
17,754 Views
21 Pages

31 August 2015

The ability to distribute secret keys between two parties with information-theoretic security, that is regardless of the capacities of a malevolent eavesdropper, is one of the most celebrated results in the field of quantum information processing and...

(This article belongs to the Special Issue Quantum Cryptography)
  • Review
  • Open Access
320 Citations
19,931 Views
14 Pages

12 May 2015

Multiscale entropy (MSE) analysis was introduced in the 2002 to evaluate the complexity of a time series by quantifying its entropy over a range of temporal scales. The algorithm has been successfully applied in different research fields. Since its i...

(This article belongs to the Special Issue Multiscale Entropy and Its Applications in Medicine and Biology)
  • Review
  • Open Access
319 Citations
22,931 Views
28 Pages

High-Entropy Alloys for Advanced Nuclear Applications

  • Ed J. Pickering,
  • Alexander W. Carruthers,
  • Paul J. Barron,
  • Simon C. Middleburgh,
  • David E. J. Armstrong and
  • Amy S. Gandy

11 January 2021

The expanded compositional freedom afforded by high-entropy alloys (HEAs) represents a unique opportunity for the design of alloys for advanced nuclear applications, in particular for applications where current engineering alloys fall short. This rev...

(This article belongs to the Special Issue Future Directions of High Entropy Alloys)
  • Article
  • Open Access
314 Citations
22,923 Views
16 Pages

18 October 2013

There has been considerable technological interest in high-entropy alloys (HEAs) since the initial publications on the topic appeared in 2004. However, only several of the alloys investigated are truly single-phase solid solution compositions. These...

(This article belongs to the Special Issue High Entropy Alloys)
  • Article
  • Open Access
314 Citations
21,426 Views
13 Pages

Development of a Refractory High Entropy Superalloy

  • Oleg N. Senkov,
  • Dieter Isheim,
  • David N. Seidman and
  • Adam L. Pilchak

17 March 2016

Microstructure, phase composition and mechanical properties of a refractory high entropy superalloy, AlMo0.5NbTa0.5TiZr, are reported in this work. The alloy consists of a nano-scale mixture of two phases produced by the decomposition from a high tem...

(This article belongs to the Special Issue High-Entropy Alloys and High-Entropy-Related Materials)
  • Article
  • Open Access
308 Citations
18,186 Views
13 Pages

Automatic ECG Classification Using Continuous Wavelet Transform and Convolutional Neural Network

  • Tao Wang,
  • Changhua Lu,
  • Yining Sun,
  • Mei Yang,
  • Chun Liu and
  • Chunsheng Ou

18 January 2021

Early detection of arrhythmia and effective treatment can prevent deaths caused by cardiovascular disease (CVD). In clinical practice, the diagnosis is made by checking the electrocardiogram (ECG) beat-by-beat, but this is usually time-consuming and...

  • Article
  • Open Access
301 Citations
17,316 Views
23 Pages

3 February 2015

The brain is a complex structure made up of interconnected neurons, and its electrical activities can be evaluated using electroencephalogram (EEG) signals. The characteristics of the brain area affected by partial epilepsy can be studied using focal...

(This article belongs to the Special Issue Entropy and Electroencephalography)
  • Review
  • Open Access
292 Citations
32,495 Views
37 Pages

Thermodynamics of Thermoelectric Phenomena and Applications

  • Christophe Goupil,
  • Wolfgang Seifert,
  • Knud Zabrocki,
  • Eckhart Müller and
  • G. Jeffrey Snyder

15 August 2011

Fifty years ago, the optimization of thermoelectric devices was analyzed by considering the relation between optimal performances and local entropy production. Entropy is produced by the irreversible processes in thermoelectric devices. If these proc...

  • Article
  • Open Access
289 Citations
30,135 Views
22 Pages

31 October 2012

This paper describes a free energy principle that tries to explain the ability of biological systems to resist a natural tendency to disorder. It appeals to circular causality of the sort found in synergetic formulations of self-organization (e.g., t...

(This article belongs to the Special Issue The Information Bottleneck Method)
  • Article
  • Open Access
284 Citations
10,516 Views
15 Pages

23 June 2015

Using some investigations based on information theory, the model proposed by Keller and Segel was extended to the concept of fractional derivative using the derivative with fractional order without singular kernel recently proposed by Caputo and Fabr...

(This article belongs to the Special Issue Wavelets, Fractals and Information Theory I)
  • Article
  • Open Access
282 Citations
13,691 Views
14 Pages

Bearing Fault Diagnosis Based on Multiscale Permutation Entropy and Support Vector Machine

  • Shuen-De Wu,
  • Po-Hung Wu,
  • Chiu-Wen Wu,
  • Jian-Jiun Ding and
  • Chun-Chieh Wang

27 July 2012

Bearing fault diagnosis has attracted significant attention over the past few decades. It consists of two major parts: vibration signal feature extraction and condition classification for the extracted features. In this paper, multiscale permutation...

  • Article
  • Open Access
282 Citations
19,676 Views
21 Pages

Design of Light-Weight High-Entropy Alloys

  • Rui Feng,
  • Michael C. Gao,
  • Chanho Lee,
  • Michael Mathes,
  • Tingting Zuo,
  • Shuying Chen,
  • Jeffrey A. Hawk,
  • Yong Zhang and
  • Peter K. Liaw

13 September 2016

High-entropy alloys (HEAs) are a new class of solid-solution alloys that have attracted worldwide attention for their outstanding properties. Owing to the demand from transportation and defense industries, light-weight HEAs have also garnered widespr...

(This article belongs to the Special Issue High-Entropy Alloys and High-Entropy-Related Materials)
  • Article
  • Open Access
275 Citations
22,323 Views
36 Pages

Entropy Generation Analysis of Desalination Technologies

  • Karan H. Mistry,
  • Ronan K. McGovern,
  • Gregory P. Thiel,
  • Edward K. Summers,
  • Syed M. Zubair and
  • John H. Lienhard

30 September 2011

Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies. Entropy generation analysis, and specifically, Second Law efficiency, is an important tool for illustratin...

(This article belongs to the Special Issue Entropy Generation Minimization)
  • Article
  • Open Access
262 Citations
14,126 Views
23 Pages

An Efficient DenseNet-Based Deep Learning Model for Malware Detection

  • Jeyaprakash Hemalatha,
  • S. Abijah Roseline,
  • Subbiah Geetha,
  • Seifedine Kadry and
  • Robertas Damaševičius

15 March 2021

Recently, there has been a huge rise in malware growth, which creates a significant security threat to organizations and individuals. Despite the incessant efforts of cybersecurity research to defend against malware threats, malware developers discov...

  • Article
  • Open Access
261 Citations
36,572 Views
20 Pages

24 May 2017

Recent advances in Convolutional Neural Networks (CNNs) have obtained promising results in difficult deep learning tasks. However, the success of a CNN depends on finding an architecture to fit a given problem. A hand-crafted architecture is a challe...

(This article belongs to the Section Information Theory, Probability and Statistics)
  • Article
  • Open Access
255 Citations
19,249 Views
17 Pages

Multivariate Multi-Scale Permutation Entropy for Complexity Analysis of Alzheimer’s Disease EEG

  • Francesco Carlo Morabito,
  • Domenico Labate,
  • Fabio La Foresta,
  • Alessia Bramanti,
  • Giuseppe Morabito and
  • Isabella Palamara

4 July 2012

An original multivariate multi-scale methodology for assessing the complexity of physiological signals is proposed. The technique is able to incorporate the simultaneous analysis of multi-channel data as a unique block within a multi-scale framework....

(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
  • Article
  • Open Access
253 Citations
18,433 Views
17 Pages

Automatic Epileptic Seizure Detection in EEG Signals Using Multi-Domain Feature Extraction and Nonlinear Analysis

  • Lina Wang,
  • Weining Xue,
  • Yang Li,
  • Meilin Luo,
  • Jie Huang,
  • Weigang Cui and
  • Chao Huang

27 May 2017

Epileptic seizure detection is commonly implemented by expert clinicians with visual observation of electroencephalography (EEG) signals, which tends to be time consuming and sensitive to bias. The epileptic detection in most previous research suffer...

(This article belongs to the Special Issue Information Theory Applied to Physiological Signals)
  • Article
  • Open Access
250 Citations
13,695 Views
15 Pages

29 August 2017

To determine the number of clusters in the clustering analysis that has a broad range of applied sciences, such as physics, chemistry, biology, engineering, economics etc., many methods have been proposed in the literature. The aim of this paper is t...

(This article belongs to the Section Information Theory, Probability and Statistics)
  • Article
  • Open Access
249 Citations
17,158 Views
23 Pages

Quantifying Unique Information

  • Nils Bertschinger,
  • Johannes Rauh,
  • Eckehard Olbrich,
  • Jürgen Jost and
  • Nihat Ay

15 April 2014

We propose new measures of shared information, unique information and synergistic information that can be used to decompose the mutual information of a pair of random variables (Y, Z) with a third random variable X. Our measures are motivated by an o...

  • Article
  • Open Access
244 Citations
6,349 Views
16 Pages

Optimization of Big Data Scheduling in Social Networks

  • Weina Fu,
  • Shuai Liu and
  • Gautam Srivastava

17 September 2019

In social network big data scheduling, it is easy for target data to conflict in the same data node. Of the different kinds of entropy measures, this paper focuses on the optimization of target entropy. Therefore, this paper presents an optimized met...

(This article belongs to the Special Issue Information Theories Based on Belief Functions for Decision-Making Support)
  • Article
  • Open Access
240 Citations
11,467 Views
19 Pages

New Results on Fractional Power Series: Theories and Applications

  • Ahmad El-Ajou,
  • Omar Abu Arqub,
  • Zeyad Al Zhour and
  • Shaher Momani

2 December 2013

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional de...

(This article belongs to the Special Issue Dynamical Systems)
  • Review
  • Open Access
239 Citations
492,584 Views
48 Pages

18 April 2013

Glyphosate, the active ingredient in Roundup®, is the most popular herbicide used worldwide. The industry asserts it is minimally toxic to humans, but here we argue otherwise. Residues are found in the main foods of the Western diet, comprised primar...

(This article belongs to the Special Issue Biosemiotic Entropy: Disorder, Disease, and Mortality)
  • Review
  • Open Access
239 Citations
19,766 Views
18 Pages

Additive Manufacturing of High-Entropy Alloys: A Review

  • Shuying Chen,
  • Yang Tong and
  • Peter K. Liaw

6 December 2018

Owing to the reduced defects, low cost, and high efficiency, the additive manufacturing (AM) technique has attracted increasingly attention and has been applied in high-entropy alloys (HEAs) in recent years. It was found that AM-processed HEAs posses...

(This article belongs to the Special Issue New Advances in High-Entropy Alloys)
  • Article
  • Open Access
236 Citations
10,368 Views
12 Pages

17 September 2018

The aim of this paper is to investigate the generalization of the Sierpinski gasket through the harmonic metric. In particular, this work presents an antenna based on such a generalization. In fact, the harmonic Sierpinski gasket is used as a geometr...

(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
  • Article
  • Open Access
235 Citations
19,445 Views
19 Pages

13 April 2011

This paper proposes a global multi-level thresholding method for image segmentation. As a criterion for this, the traditional method uses the Shannon entropy, originated from information theory, considering the gray level image histogram as a probabi...

(This article belongs to the Special Issue Tsallis Entropy)
  • Review
  • Open Access
231 Citations
15,390 Views
26 Pages

17 April 2019

Rotating machinery is widely applied in various types of industrial applications. As a promising field for reliability of modern industrial systems, early fault diagnosis (EFD) techniques have attracted increasing attention from both academia and ind...

(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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