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MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 28)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
Advances in Science and Research (ASR)     Open Access   (Followers: 5)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Entropy
  [SJR: 0.59]   [H-I: 30]   [5 followers]  Follow
  This is an Open Access Journal Open Access journal
   ISSN (Print) 1099-4300
   Published by MDPI Homepage  [202 journals]
  • Entropy, Vol. 20, Pages 7: Information Theoretic Approaches for
           Motor-Imagery BCI Systems: Review and Experimental Comparison

    • Authors: Rubén Martín-Clemente, Javier Olias, Deepa Thiyam, Andrzej Cichocki, Sergio Cruces
      First page: 7
      Abstract: Brain computer interfaces (BCIs) have been attracting a great interest in recent years. The common spatial patterns (CSP) technique is a well-established approach to the spatial filtering of the electroencephalogram (EEG) data in BCI applications. Even though CSP was originally proposed from a heuristic viewpoint, it can be also built on very strong foundations using information theory. This paper reviews the relationship between CSP and several information-theoretic approaches, including the Kullback–Leibler divergence, the Beta divergence and the Alpha-Beta log-det (AB-LD)divergence. We also revise other approaches based on the idea of selecting those features that are maximally informative about the class labels. The performance of all the methods will be also compared via experiments.
      Citation: Entropy
      PubDate: 2018-01-02
      DOI: 10.3390/e20010007
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 19: Thermodynamics-Based Evaluation of Various
           Improved Shannon Entropies for Configurational Information of Gray-Level

    • Authors: Peichao Gao, Zhilin Li, Hong Zhang
      First page: 19
      Abstract: The quality of an image affects its utility and image quality assessment has been a hot research topic for many years. One widely used measure for image quality assessment is Shannon entropy, which has a well-established information-theoretic basis. The value of this entropy can be interpreted as the amount of information. However, Shannon entropy is badly adapted to information measurement in images, because it captures only the compositional information of an image and ignores the configurational aspect. To fix this problem, improved Shannon entropies have been actively proposed in the last few decades, but a thorough evaluation of their performance is still lacking. This study presents such an evaluation, involving twenty-three improved Shannon entropies based on various tools such as gray-level co-occurrence matrices and local binary patterns. For the evaluation, we proposed: (a) a strategy to generate testing (gray-level) images by simulating the mixing of ideal gases in thermodynamics; (b) three criteria consisting of validity, reliability, and ability to capture configurational disorder; and (c) three measures to assess the fulfillment of each criterion. The evaluation results show only the improved entropies based on local binary patterns are invalid for use in quantifying the configurational information of images, and the best variant of Shannon entropy in terms of reliability and ability is the one based on the average distance between same/different-value pixels. These conclusions are theoretically important in setting a direction for the future research on improving entropy and are practically useful in selecting an effective entropy for various image processing applications.
      Citation: Entropy
      PubDate: 2018-01-02
      DOI: 10.3390/e20010019
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 20: Liouvillian of the Open STIRAP Problem

    • Authors: Thomas Mathisen, Jonas Larson
      First page: 20
      Abstract: With the corresponding Liouvillian as a starting point, we demonstrate two seemingly new phenomena of the STIRAP problem when subjected to irreversible losses. It is argued that both of these can be understood from an underlying Zeno effect, and in particular both can be viewed as if the environment assists the STIRAP population transfer. The first of these is found for relative strong dephasing, and, in the language of the Liouvillian, it is explained from the explicit form of the matrix generating the time-evolution; the coherence terms of the state decay off, which prohibits further population transfer. For pure dissipation, another Zeno effect is found, where the presence of a non-zero Liouvillian gap protects the system’s (adiabatic) state from non-adiabatic excitations. In contrast to full Zeno freezing of the evolution, which is often found in many problems without explicit time-dependence, here, the freezing takes place in the adiabatic basis such that the system still evolves but adiabatically.
      Citation: Entropy
      PubDate: 2018-01-03
      DOI: 10.3390/e20010020
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 21: Fuzzy Entropy Analysis of the
           Electroencephalogram in Patients with Alzheimer’s Disease: Is the Method
           Superior to Sample Entropy'

    • Authors: Samantha Simons, Pedro Espino, Daniel Abásolo
      First page: 21
      Abstract: Alzheimer’s disease (AD) is the most prevalent form of dementia in the world, which is characterised by the loss of neurones and the build-up of plaques in the brain, causing progressive symptoms of memory loss and confusion. Although definite diagnosis is only possible by necropsy, differential diagnosis with other types of dementia is still needed. An electroencephalogram (EEG) is a cheap, portable, non-invasive method to record brain signals. Previous studies with non-linear signal processing methods have shown changes in the EEG due to AD, which is characterised reduced complexity and increased regularity. EEGs from 11 AD patients and 11 age-matched control subjects were analysed with Fuzzy Entropy (FuzzyEn), a non-linear method that was introduced as an improvement over the frequently used Approximate Entropy (ApEn) and Sample Entropy (SampEn) algorithms. AD patients had significantly lower FuzzyEn values than control subjects (p < 0.01) at electrodes T6, P3, P4, O1, and O2. Furthermore, when diagnostic accuracy was calculated using Receiver Operating Characteristic (ROC) curves, FuzzyEn outperformed both ApEn and SampEn, reaching a maximum accuracy of 86.36%. These results suggest that FuzzyEn could increase the insight into brain dysfunction in AD, providing potentially useful diagnostic information. However, results depend heavily on the input parameters that are used to compute FuzzyEn.
      Citation: Entropy
      PubDate: 2018-01-03
      DOI: 10.3390/e20010021
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 22: Thermodynamic Fluid Equations-of-State

    • Authors: Leslie Woodcock
      First page: 22
      Abstract: As experimental measurements of thermodynamic properties have improved in accuracy, to five or six figures, over the decades, cubic equations that are widely used for modern thermodynamic fluid property data banks require ever-increasing numbers of terms with more fitted parameters. Functional forms with continuity for Gibbs density surface ρ(p,T) which accommodate a critical-point singularity are fundamentally inappropriate in the vicinity of the critical temperature (Tc) and pressure (pc) and in the supercritical density mid-range between gas- and liquid-like states. A mesophase, confined within percolation transition loci that bound the gas- and liquid-state by third-order discontinuities in derivatives of the Gibbs energy, has been identified. There is no critical-point singularity at Tc on Gibbs density surface and no continuity of gas and liquid. When appropriate functional forms are used for each state separately, we find that the mesophase pressure functions are linear. The negative and positive deviations, for both gas and liquid states, on either side of the mesophase, are accurately represented by three or four-term virial expansions. All gaseous states require only known virial coefficients, and physical constants belonging to the fluid, i.e., Boyle temperature (TB), critical temperature (Tc), critical pressure (pc) and coexisting densities of gas (ρcG) and liquid (ρcL) along the critical isotherm. A notable finding for simple fluids is that for all gaseous states below TB, the contribution of the fourth virial term is negligible within experimental uncertainty. Use may be made of a symmetry between gas and liquid states in the state function rigidity (dp/dρ)T to specify lower-order liquid-state coefficients. Preliminary results for selected isotherms and isochores are presented for the exemplary fluids, CO2, argon, water and SF6, with focus on the supercritical mesophase and critical region.
      Citation: Entropy
      PubDate: 2018-01-04
      DOI: 10.3390/e20010022
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 23: Asymmetric Bimodal Exponential Power
           Distribution on the Real Line

    • Authors: Mehmet Çankaya
      First page: 23
      Abstract: The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters that fit the shape of peakedness in bimodality on the real line. The special values of peakedness parameters of the distribution are a combination of half Laplace and half normal distributions on the real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and other distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data. A brief simulation study is presented.
      Citation: Entropy
      PubDate: 2018-01-03
      DOI: 10.3390/e20010023
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 24: High Density Nodes in the Chaotic Region of 1D
           Discrete Maps

    • Authors: George Livadiotis
      First page: 24
      Abstract: We report on the definition and characteristics of nodes in the chaotic region of bifurcation diagrams in the case of 1D mono-parametrical and S-unimodal maps, using as guiding example the logistic map. We examine the arrangement of critical curves, the identification and arrangement of nodes, and the connection between the periodic windows and nodes in the chaotic zone. We finally present several characteristic features of nodes, which involve their convergence and entropy.
      Citation: Entropy
      PubDate: 2018-01-04
      DOI: 10.3390/e20010024
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 25: Exact Renormalization Groups As a Form of
           Entropic Dynamics

    • Authors: Pedro Pessoa, Ariel Caticha
      First page: 25
      Abstract: The Renormalization Group (RG) is a set of methods that have been instrumental in tackling problems involving an infinite number of degrees of freedom, such as, for example, in quantum field theory and critical phenomena. What all these methods have in common—which is what explains their success—is that they allow a systematic search for those degrees of freedom that happen to be relevant to the phenomena in question. In the standard approaches the RG transformations are implemented by either coarse graining or through a change of variables. When these transformations are infinitesimal, the formalism can be described as a continuous dynamical flow in a fictitious time parameter. It is generally the case that these exact RG equations are functional diffusion equations. In this paper we show that the exact RG equations can be derived using entropic methods. The RG flow is then described as a form of entropic dynamics of field configurations. Although equivalent to other versions of the RG, in this approach the RG transformations receive a purely inferential interpretation that establishes a clear link to information theory.
      Citation: Entropy
      PubDate: 2018-01-04
      DOI: 10.3390/e20010025
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 26: Polyadic Entropy, Synergy and Redundancy among
           Statistically Independent Processes in Nonlinear Statistical Physics with
           Microphysical Codependence

    • Authors: Rui Perdigão
      First page: 26
      Abstract: The information shared among observables representing processes of interest is traditionally evaluated in terms of macroscale measures characterizing aggregate properties of the underlying processes and their interactions. Traditional information measures are grounded on the assumption that the observable represents a memoryless process without any interaction among microstates. Generalized entropy measures have been formulated in non-extensive statistical mechanics aiming to take microphysical codependence into account in entropy quantification. By taking them into consideration when formulating information measures, the question is raised on whether and if so how much information permeates across scales to impact on the macroscale information measures. The present study investigates and quantifies the emergence of macroscale information from microscale codependence among microphysics. In order to isolate the information emergence coming solely from the nonlinearly interacting microphysics, redundancy and synergy are evaluated among macroscale variables that are statistically independent from each other but not necessarily so within their own microphysics. Synergistic and redundant information are found when microphysical interactions take place, even if the statistical distributions are factorable. These findings stress the added value of nonlinear statistical physics to information theory in coevolutionary systems.
      Citation: Entropy
      PubDate: 2018-01-04
      DOI: 10.3390/e20010026
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 27: Strategic Information Processing from
           Behavioural Data in Iterated Games

    • Authors: Michael Harré
      First page: 27
      Abstract: Iterated games are an important framework of economic theory and application, at least since the original work of Axelrod’s computational tournaments of the early 80’s. Recent theoretical results have shown that games (the economic context) and game theory (the decision-making process) are both formally equivalent to computational logic gates. Here these results are extended to behavioural data obtained from an experiment in which rhesus monkeys sequentially played thousands of the “matching pennies” game, an empirical example similar to Axelrod’s tournaments in which algorithms played against one another. The results show that the monkeys exhibit a rich variety of behaviours, both between and within subjects when playing opponents of varying complexity. Despite earlier suggestions, there is no clear evidence that the win-stay, lose-switch strategy is used, however there is evidence of non-linear strategy-based interactions between the predictors of future choices. It is also shown that there is consistent evidence across protocols and across individuals that the monkeys extract non-markovian information, i.e., information from more than just the most recent state of the game. This work shows that the use of information theory in game theory can test important hypotheses that would otherwise be more difficult to extract using traditional statistical methods.
      Citation: Entropy
      PubDate: 2018-01-04
      DOI: 10.3390/e20010027
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 29: Influences of the Thomson Effect on the
           Performance of a Thermoelectric Generator-Driven Thermoelectric Heat Pump
           Combined Device

    • Authors: Yuanli Feng, Lingen Chen, Fankai Meng, Fengrui Sun
      First page: 29
      Abstract: A thermodynamic model of a thermoelectric generator-driven thermoelectric heat pump (TEG-TEH) combined device is established considering the Thomson effect and the temperature dependence of the thermoelectric properties based on non-equilibrium thermodynamics. Energy analysis and exergy analysis are performed. New expressions for heating load, maximum working temperature difference, coefficient of performance (COP), and exergy efficiency are obtained. The performance is analyzed and optimized using numerical calculations. The general performance, optimal performance, optimum variables, optimal performance ranges, and optimum variable ranges are obtained. The results show that the Thomson effect decreases the general performance and optimal performance, and narrows the optimal operating ranges and optimum variable ranges. Considering the Thomson effect, more thermoelectric elements should be allocated to the thermoelectric generator when designing the devices. The optimum design variables for the maximum exergy efficiency are different from those for the maximum COP. The results can provide more scientific guidelines for designing TEG-TEH devices.
      Citation: Entropy
      PubDate: 2018-01-05
      DOI: 10.3390/e20010029
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 30: Human Postural Control: Assessment of Two
           Alternative Interpretations of Center of Pressure Sample Entropy through a
           Principal Component Factorization of Whole-Body Kinematics

    • Authors: Thomas Haid, Peter Federolf
      First page: 30
      Abstract: Sample entropy (SaEn), calculated for center of pressure (COP) trajectories, is often distinct for compromised postural control, e.g., in Parkinson, stroke, or concussion patients, but the interpretation of COP-SaEn remains subject to debate. The purpose of this paper is to test the hypotheses that COP-SaEn is related (Hypothesis 1; H1) to the complexity of the postural movement structures, i.e., to the utilization and coordination of the mechanical degrees of freedom; or (Hypothesis 2; H2) to the irregularity of the individual postural movement strategies, i.e., to the neuromuscular control of these movements. Twenty-one healthy volunteers (age 26.4 ± 2.4; 10 females), equipped with 27 reflective markers, stood on a force plate and performed 2-min quiet stances. Principal movement strategies (PMs) were obtained from a principal component analysis (PCA) of the kinematic data. Then SaEn was calculated for the COP and PM time-series. H1 was tested by correlating COP-SaEn to the relative contribution of the PMs to the subject specific overall movement and H2 by correlating COP-SaEn and PM-SaEn. Both hypotheses were supported. This suggests that in a healthy population the COP-SaEn is linked to the complexity of the coordinative structure of postural movements, as well as to the irregularity of the neuromuscular control of specific movement components.
      Citation: Entropy
      PubDate: 2018-01-05
      DOI: 10.3390/e20010030
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 32: Searching for Chaos Evidence in Eye Movement

    • Authors: Katarzyna Harezlak, Pawel Kasprowski
      First page: 32
      Abstract: Most naturally-occurring physical phenomena are examples of nonlinear dynamic systems, the functioning of which attracts many researchers seeking to unveil their nature. The research presented in this paper is aimed at exploring eye movement dynamic features in terms of the existence of chaotic nature. Nonlinear time series analysis methods were used for this purpose. Two time series features were studied: fractal dimension and entropy, by utilising the embedding theory. The methods were applied to the data collected during the experiment with “jumping point” stimulus. Eye movements were registered by means of the Jazz-novo eye tracker. One thousand three hundred and ninety two (1392) time series were defined, based on the horizontal velocity of eye movements registered during imposed, prolonged fixations. In order to conduct detailed analysis of the signal and identify differences contributing to the observed patterns of behaviour in time scale, fractal dimension and entropy were evaluated in various time series intervals. The influence of the noise contained in the data and the impact of the utilized filter on the obtained results were also studied. The low pass filter was used for the purpose of noise reduction with a 50 Hz cut-off frequency, estimated by means of the Fourier transform and all concerned methods were applied to time series before and after noise reduction. These studies provided some premises, which allow perceiving eye movements as observed chaotic data: characteristic of a space-time separation plot, low and non-integer time series dimension, and the time series entropy characteristic for chaotic systems.
      Citation: Entropy
      PubDate: 2018-01-07
      DOI: 10.3390/e20010032
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 34: Information Entropy Production of Maximum
           Entropy Markov Chains from Spike Trains

    • Authors: Rodrigo Cofré, Cesar Maldonado
      First page: 34
      Abstract: The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.
      Citation: Entropy
      PubDate: 2018-01-09
      DOI: 10.3390/e20010034
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 35: Automated Multiclass Classification of
           Spontaneous EEG Activity in Alzheimer’s Disease and Mild Cognitive

    • Authors: Saúl Ruiz-Gómez, Carlos Gómez, Jesús Poza, Gonzalo Gutiérrez-Tobal, Miguel Tola-Arribas, Mónica Cano, Roberto Hornero
      First page: 35
      Abstract: The discrimination of early Alzheimer’s disease (AD) and its prodromal form (i.e., mild cognitive impairment, MCI) from cognitively healthy control (HC) subjects is crucial since the treatment is more effective in the first stages of the dementia. The aim of our study is to evaluate the usefulness of a methodology based on electroencephalography (EEG) to detect AD and MCI. EEG rhythms were recorded from 37 AD patients, 37 MCI subjects and 37 HC subjects. Artifact-free trials were analyzed by means of several spectral and nonlinear features: relative power in the conventional frequency bands, median frequency, individual alpha frequency, spectral entropy, Lempel–Ziv complexity, central tendency measure, sample entropy, fuzzy entropy, and auto-mutual information. Relevance and redundancy analyses were also conducted through the fast correlation-based filter (FCBF) to derive an optimal set of them. The selected features were used to train three different models aimed at classifying the trials: linear discriminant analysis (LDA), quadratic discriminant analysis (QDA) and multi-layer perceptron artificial neural network (MLP). Afterwards, each subject was automatically allocated in a particular group by applying a trial-based majority vote procedure. After feature extraction, the FCBF method selected the optimal set of features: individual alpha frequency, relative power at delta frequency band, and sample entropy. Using the aforementioned set of features, MLP showed the highest diagnostic performance in determining whether a subject is not healthy (sensitivity of 82.35% and positive predictive value of 84.85% for HC vs. all classification task) and whether a subject does not suffer from AD (specificity of 79.41% and negative predictive value of 84.38% for AD vs. all comparison). Our findings suggest that our methodology can help physicians to discriminate AD, MCI and HC.
      Citation: Entropy
      PubDate: 2018-01-09
      DOI: 10.3390/e20010035
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 38: Information Entropy Suggests Stronger
           Nonlinear Associations between Hydro-Meteorological Variables and ENSO

    • Authors: Tue Vu, Ashok Mishra, Goutam Konapala
      First page: 38
      Abstract: Understanding the teleconnections between hydro-meteorological data and the El Niño–Southern Oscillation cycle (ENSO) is an important step towards developing flood early warning systems. In this study, the concept of mutual information (MI) was applied using marginal and joint information entropy to quantify the linear and non-linear relationship between annual streamflow, extreme precipitation indices over Mekong river basin, and ENSO. We primarily used Pearson correlation as a linear association metric for comparison with mutual information. The analysis was performed at four hydro-meteorological stations located on the mainstream Mekong river basin. It was observed that the nonlinear correlation information is comparatively higher between the large-scale climate index and local hydro-meteorology data in comparison to the traditional linear correlation information. The spatial analysis was carried out using all the grid points in the river basin, which suggests a spatial dependence structure between precipitation extremes and ENSO. Overall, this study suggests that mutual information approach can further detect more meaningful connections between large-scale climate indices and hydro-meteorological variables at different spatio-temporal scales. Application of nonlinear mutual information metric can be an efficient tool to better understand hydro-climatic variables dynamics resulting in improved climate-informed adaptation strategies.
      Citation: Entropy
      PubDate: 2018-01-09
      DOI: 10.3390/e20010038
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 39: Robust Macroscopic Quantum Measurements in the
           Presence of Limited Control and Knowledge

    • Authors: Marc-Olivier Renou, Nicolas Gisin, Florian Fröwis
      First page: 39
      Abstract: Quantum measurements have intrinsic properties that seem incompatible with our everyday-life macroscopic measurements. Macroscopic Quantum Measurement (MQM) is a concept that aims at bridging the gap between well-understood microscopic quantum measurements and macroscopic classical measurements. In this paper, we focus on the task of the polarization direction estimation of a system of N spins 1/2 particles and investigate the model some of us proposed in Barnea et al., 2007. This model is based on a von Neumann pointer measurement, where each spin component of the system is coupled to one of the three spatial component directions of a pointer. It shows traits of a classical measurement for an intermediate coupling strength. We investigate relaxations of the assumptions on the initial knowledge about the state and on the control over the MQM. We show that the model is robust with regard to these relaxations. It performs well for thermal states and a lack of knowledge about the size of the system. Furthermore, a lack of control on the MQM can be compensated by repeated “ultra-weak” measurements.
      Citation: Entropy
      PubDate: 2018-01-09
      DOI: 10.3390/e20010039
      Issue No: Vol. 20, No. 1 (2018)
  • Entropy, Vol. 20, Pages 1: Non-Equilibrium Relations for Bounded Rational
           Decision-Making in Changing Environments

    • Authors: Jordi Grau-Moya, Matthias Krüger, Daniel Braun
      First page: 1
      Abstract: Living organisms from single cells to humans need to adapt continuously to respond to changes in their environment. The process of behavioural adaptation can be thought of as improving decision-making performance according to some utility function. Here, we consider an abstract model of organisms as decision-makers with limited information-processing resources that trade off between maximization of utility and computational costs measured by a relative entropy, in a similar fashion to thermodynamic systems undergoing isothermal transformations. Such systems minimize the free energy to reach equilibrium states that balance internal energy and entropic cost. When there is a fast change in the environment, these systems evolve in a non-equilibrium fashion because they are unable to follow the path of equilibrium distributions. Here, we apply concepts from non-equilibrium thermodynamics to characterize decision-makers that adapt to changing environments under the assumption that the temporal evolution of the utility function is externally driven and does not depend on the decision-maker’s action. This allows one to quantify performance loss due to imperfect adaptation in a general manner and, additionally, to find relations for decision-making similar to Crooks’ fluctuation theorem and Jarzynski’s equality. We provide simulations of several exemplary decision and inference problems in the discrete and continuous domains to illustrate the new relations.
      Citation: Entropy
      PubDate: 2017-12-21
      DOI: 10.3390/e20010001
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 2: Rate-Distortion Region of a Gray–Wyner
           Model with Side Information

    • Authors: Meryem Benammar, Abdellatif Zaidi
      First page: 2
      Abstract: In this work, we establish a full single-letter characterization of the rate-distortion region of an instance of the Gray–Wyner model with side information at the decoders. Specifically, in this model, an encoder observes a pair of memoryless, arbitrarily correlated, sources ( S 1 n , S 2 n ) and communicates with two receivers over an error-free rate-limited link of capacity R 0 , as well as error-free rate-limited individual links of capacities R 1 to the first receiver and R 2 to the second receiver. Both receivers reproduce the source component S 2 n losslessly; and Receiver 1 also reproduces the source component S 1 n lossily, to within some prescribed fidelity level D 1 . In addition, Receiver 1 and Receiver 2 are equipped, respectively, with memoryless side information sequences Y 1 n and Y 2 n . Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair ( S 1 n , S 2 n ) ; and are not assumed to exhibit any particular ordering. Furthermore, by specializing the main result to two Heegard–Berger models with successive refinement and scalable coding, we shed light on the roles of the common and private descriptions that the encoder should produce and the role of each of the common and private links. We develop intuitions by analyzing the developed single-letter rate-distortion regions of these models, and discuss some insightful binary examples.
      Citation: Entropy
      PubDate: 2017-12-22
      DOI: 10.3390/e20010002
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 3: Polar Codes for Covert Communications over
           Asynchronous Discrete Memoryless Channels

    • Authors: Guillaume Frèche, Matthieu Bloch, Michel Barret
      First page: 3
      Abstract: This paper introduces an explicit covert communication code for binary-input asynchronous discrete memoryless channels based on binary polar codes, in which legitimate parties exploit uncertainty created by both the channel noise and the time of transmission to avoid detection by an adversary. The proposed code jointly ensures reliable communication for a legitimate receiver and low probability of detection with respect to the adversary, both observing noisy versions of the codewords. Binary polar codes are used to shape the weight distribution of codewords and ensure that the average weight decays as the block length grows. The performance of the proposed code is severely limited by the speed of polarization, which in turn controls the decay of the average codeword weight with the block length. Although the proposed construction falls largely short of achieving the performance of random codes, it inherits the low-complexity properties of polar codes.
      Citation: Entropy
      PubDate: 2017-12-22
      DOI: 10.3390/e20010003
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 4: Fog Computing: Enabling the Management and
           Orchestration of Smart City Applications in 5G Networks

    • Authors: José Santos, Tim Wauters, Bruno Volckaert, Filip De Turck
      First page: 4
      Abstract: Fog computing extends the cloud computing paradigm by placing resources close to the edges of the network to deal with the upcoming growth of connected devices. Smart city applications, such as health monitoring and predictive maintenance, will introduce a new set of stringent requirements, such as low latency, since resources can be requested on-demand simultaneously by multiple devices at different locations. It is then necessary to adapt existing network technologies to future needs and design new architectural concepts to help meet these strict requirements. This article proposes a fog computing framework enabling autonomous management and orchestration functionalities in 5G-enabled smart cities. Our approach follows the guidelines of the European Telecommunications Standards Institute (ETSI) NFV MANO architecture extending it with additional software components. The contribution of our work is its fully-integrated fog node management system alongside the foreseen application layer Peer-to-Peer (P2P) fog protocol based on the Open Shortest Path First (OSPF) routing protocol for the exchange of application service provisioning information between fog nodes. Evaluations of an anomaly detection use case based on an air monitoring application are presented. Our results show that the proposed framework achieves a substantial reduction in network bandwidth usage and in latency when compared to centralized cloud solutions.
      Citation: Entropy
      PubDate: 2017-12-23
      DOI: 10.3390/e20010004
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 5: State Estimation for General Complex Dynamical
           Networks with Incompletely Measured Information

    • Authors: Xinwei Wang, Guo-Ping Jiang, Xu Wu
      First page: 5
      Abstract: Estimating uncertain state variables of a general complex dynamical network with randomly incomplete measurements of transmitted output variables is investigated in this paper. The incomplete measurements, occurring randomly through the transmission of output variables, always cause the failure of the state estimation process. Different from the existing methods, we propose a novel method to handle the incomplete measurements, which can perform well to balance the excessively deviated estimators under the influence of incomplete measurements. In particular, the proposed method has no special limitation on the node dynamics compared with many existing methods. By employing the Lyapunov stability theory along with the stochastic analysis method, sufficient criteria are deduced rigorously to ensure obtaining the proper estimator gains with known model parameters. Illustrative simulation for the complex dynamical network composed of chaotic nodes are given to show the validity and efficiency of the proposed method.
      Citation: Entropy
      PubDate: 2017-12-23
      DOI: 10.3390/e20010005
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 6: Entropy Measures as Geometrical Tools in the
           Study of Cosmology

    • Authors: Gilbert Weinstein, Yosef Strauss, Sergey Bondarenko, Asher Yahalom, Meir Lewkowicz, Lawrence Horwitz, Jacob Levitan
      First page: 6
      Abstract: Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ ( x ) with χ ( x ) being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double-warped spacetime leads to the same entropy equation. By applying a Robertson–Walker metric for a flat three-dimensional Euclidean space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Riccati equation similar to the transformed entropy equation. Those Riccati-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of general relativity and cosmology. We suggest a refined entropy measure applicable in cosmology and defined by the average deviation of the geodesics in a congruence.
      Citation: Entropy
      PubDate: 2017-12-25
      DOI: 10.3390/e20010006
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 8: Paths of Cultural Systems

    • Authors: Paul Ballonoff
      First page: 8
      Abstract: A theory of cultural structures predicts the objects observed by anthropologists. We here define those which use kinship relationships to define systems. A finite structure we call a partially defined quasigroup (or pdq, as stated by Definition 1 below) on a dictionary (called a natural language) allows prediction of certain anthropological descriptions, using homomorphisms of pdqs onto finite groups. A viable history (defined using pdqs) states how an individual in a population following such history may perform culturally allowed associations, which allows a viable history to continue to survive. The vector states on sets of viable histories identify demographic observables on descent sequences. Paths of vector states on sets of viable histories may determine which histories can exist empirically.
      Citation: Entropy
      PubDate: 2017-12-25
      DOI: 10.3390/e20010008
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 9: Analysis and Optimization of Trapezoidal
           Grooved Microchannel Heat Sink Using Nanofluids in a Micro Solar Cell

    • Authors: Ruijin Wang, Wen Wang, Jiawei Wang, Zefei Zhu
      First page: 9
      Abstract: It is necessary to control the temperature of solar cells for enhancing efficiency with increasing concentrations of multiple photovoltaic systems. A heterogeneous two-phase model was established after considering the interacting between temperature, viscosity, the flow of nanofluid, and the motion of nanoparticles in the nanofluid, in order to study the microchannel heat sink (MCHS) using Al2O3-water nanofluid as coolant in the photovoltaic system. Numerical simulations were carried out to investigate the thermal performance of MCHS with a series of trapezoidal grooves. The numerical results showed us that, (1) better thermal performance of MCSH using nanofluid can be achieved from a heterogeneous two-phase model than that from single-phase model; (2) The effects of flow field, volume fraction, nanoparticle size on the heat transfer enhancement in MCHS were interpreted by a non-dimensional parameter NBT (i.e., ratio of Brownian diffusion and thermophoretic diffusion). In addition, the geometrical parameters of MCHS and the physical parameters of the nanofluid were optimized. This can provide a sound foundation for the design of MCHS.
      Citation: Entropy
      PubDate: 2017-12-25
      DOI: 10.3390/e20010009
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 10: A Novel Method for Multi-Fault Feature
           Extraction of a Gearbox under Strong Background Noise

    • Authors: Zhijian Wang, Junyuan Wang, Zhifang Zhao, Rijun Wang
      First page: 10
      Abstract: Strong background noise and complicated interfering signatures when implementing vibration-based monitoring make it difficult to extract the weak diagnostic features due to incipient faults in a multistage gearbox. This can be more challenging when multiple faults coexist. This paper proposes an effective approach to extract multi-fault features of a wind turbine gearbox based on an integration of minimum entropy deconvolution (MED) and multipoint optimal minimum entropy deconvolution adjusted (MOMEDA). By using simulated periodic transient signals with different noise to signal ratios (SNR), it evaluates the outstanding performance of MED in noise suppression and reveals the deficient in extract multiple impulses. On the other hand, MOMEDA can performs better in extracting multiple pulses but not robust to noise influences. To compromise the merits of them, therefore the diagnostic approach is formalized by extracting the multiple weak features with MOMEDA based on the MED denoised signals. Experimental verification based on vibrations from a wind turbine gearbox test bed shows that the approach allows successful identification of multiple faults occurring simultaneously on the shaft and bearing in the high speed transmission stage of the gearbox.
      Citation: Entropy
      PubDate: 2017-12-26
      DOI: 10.3390/e20010010
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 11: Remarks on the Maximum Entropy Principle with
           Application to the Maximum Entropy Theory of Ecology

    • Authors: Marco Favretti
      First page: 11
      Abstract: In the first part of the paper we work out the consequences of the fact that Jaynes’ Maximum Entropy Principle, when translated in mathematical terms, is a constrained extremum problem for an entropy function H ( p ) expressing the uncertainty associated with the probability distribution p. Consequently, if two observers use different independent variables p or g ( p ) , the associated entropy functions have to be defined accordingly and they are different in the general case. In the second part we apply our findings to an analysis of the foundations of the Maximum Entropy Theory of Ecology (M.E.T.E.) a purely statistical model of an ecological community. Since the theory has received considerable attention by the scientific community, we hope to give a useful contribution to the same community by showing that the procedure of application of MEP, in the light of the theory developed in the first part, suffers from some incongruences. We exhibit an alternative formulation which is free from these limitations and that gives different results.
      Citation: Entropy
      PubDate: 2017-12-27
      DOI: 10.3390/e20010011
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 12: A New Chaotic System with Multiple Attractors:
           Dynamic Analysis, Circuit Realization and S-Box Design

    • Authors: Qiang Lai, Akif Akgul, Chunbiao Li, Guanghui Xu, Ünal Çavuşoğlu
      First page: 12
      Abstract: This paper reports about a novel three-dimensional chaotic system with three nonlinearities. The system has one stable equilibrium, two stable equilibria and one saddle node, two saddle foci and one saddle node for different parameters. One salient feature of this novel system is its multiple attractors caused by different initial values. With the change of parameters, the system experiences mono-stability, bi-stability, mono-periodicity, bi-periodicity, one strange attractor, and two coexisting strange attractors. The complex dynamic behaviors of the system are revealed by analyzing the corresponding equilibria and using the numerical simulation method. In addition, an electronic circuit is given for implementing the chaotic attractors of the system. Using the new chaotic system, an S-Box is developed for cryptographic operations. Moreover, we test the performance of this produced S-Box and compare it to the existing S-Box studies.
      Citation: Entropy
      PubDate: 2017-12-27
      DOI: 10.3390/e20010012
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 13: Self-Organization of Genome Expression from
           Embryo to Terminal Cell Fate: Single-Cell Statistical Mechanics of
           Biological Regulation

    • Authors: Alessandro Giuliani, Masa Tsuchiya, Kenichi Yoshikawa
      First page: 13
      Abstract: A statistical mechanical mean-field approach to the temporal development of biological regulation provides a phenomenological, but basic description of the dynamical behavior of genome expression in terms of autonomous self-organization with a critical transition (Self-Organized Criticality: SOC). This approach reveals the basis of self-regulation/organization of genome expression, where the extreme complexity of living matter precludes any strict mechanistic approach. The self-organization in SOC involves two critical behaviors: scaling-divergent behavior (genome avalanche) and sandpile-type critical behavior. Genome avalanche patterns—competition between order (scaling) and disorder (divergence) reflect the opposite sequence of events characterizing the self-organization process in embryo development and helper T17 terminal cell differentiation, respectively. On the other hand, the temporal development of sandpile-type criticality (the degree of SOC control) in mouse embryo suggests the existence of an SOC control landscape with a critical transition state (i.e., the erasure of zygote-state criticality). This indicates that a phase transition of the mouse genome before and after reprogramming (immediately after the late 2-cell state) occurs through a dynamical change in a control parameter. This result provides a quantitative open-thermodynamic appreciation of the still largely qualitative notion of the epigenetic landscape. Our results suggest: (i) the existence of coherent waves of condensation/de-condensation in chromatin, which are transmitted across regions of different gene-expression levels along the genome; and (ii) essentially the same critical dynamics we observed for cell-differentiation processes exist in overall RNA expression during embryo development, which is particularly relevant because it gives further proof of SOC control of overall expression as a universal feature.
      Citation: Entropy
      PubDate: 2017-12-28
      DOI: 10.3390/e20010013
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 14: Leakage Evaluation by Virtual Entropy
           Generation (VEG) Method

    • Authors: Zhichao Zhang, Corina Drapaca, Zhifeng Zhang, Shuaifang Zhang, Shimei Sun, Hui Liu
      First page: 14
      Abstract: Leakage through microscale or nanoscale cracks is usually hard to observe, difficult to control, and causes significant economic loss. In the present research, the leakage in a pipe was evaluated by the virtual entropy generation (VEG) method. In virtual entropy generation method, the “measured entropy generation” is forced to follow the “experimental second law of thermodynamics”. Taking the leakage as the source virtual entropy generation, a new pipe leakage evaluation criterion was analytically derived, which indicates that the mass leakage rate should be smaller than the pressure drop rate inside a pipe. A numerical study based on computational fluid dynamics showed the existence of an unrealistic virtual entropy generation at a high mass leakage rate. Finally, the new criterion was used in the evaluation of leakage available in the literature. These results could be useful for leakage control or industry criteria design in the future.
      Citation: Entropy
      PubDate: 2017-12-29
      DOI: 10.3390/e20010014
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 15: Robust Consensus of Networked Evolutionary
           Games with Attackers and Forbidden Profiles †

    • Authors: Yalu Li, Xueying Ding, Haitao Li
      First page: 15
      Abstract: Using the algebraic state space representation, this paper studies the robust consensus of networked evolutionary games (NEGs) with attackers and forbidden profiles. Firstly, an algebraic form is established for NEGs with attackers and forbidden profiles. Secondly, based on the algebraic form, a necessary and sufficient condition is presented for the robust constrained reachability of NEGs. Thirdly, a series of robust reachable sets is constructed by using the robust constrained reachability, based on which a constructive procedure is proposed to design state feedback controls for the robust consensus of NEGs with attackers and forbidden profiles. Finally, an illustrative example is given to show that the main results are effective.
      Citation: Entropy
      PubDate: 2017-12-29
      DOI: 10.3390/e20010015
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 16: The Poincaré Half-Plane for
           Informationally-Complete POVMs

    • Authors: Michel Planat
      First page: 16
      Abstract: It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from the Poincaré upper half-plane model H . To do this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates, some of the eigenstates of which are the sought fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen–Specker theorem.
      Citation: Entropy
      PubDate: 2017-12-31
      DOI: 10.3390/e20010016
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 17: Nonlinear Multiscale Entropy and Recurrence
           Quantification Analysis of Foreign Exchange Markets Efficiency

    • Authors: Hongli Niu, Lin Zhang
      First page: 17
      Abstract: The regularity of price fluctuations in exchange rates plays a crucial role in foreign exchange (FX) market dynamics. In this paper, we quantify the multiply irregular fluctuation behaviors of exchange rates in the last 10 years (November 2006–November 2016) of eight world economies with two nonlinear approaches. One is a recently proposed multiscale weighted permutation entropy (MWPE) and another is the typical quantification recurrence analysis (RQA) technique. Furthermore, we utilize the RQA technique to study the different intrinsic mode functions (IMFs) that represents different frequencies and scales of the raw time series via the empirical mode decomposition algorithm. Complexity characteristics of abundance and distinction are obtained in the foreign exchange markets. The empirical results show that JPY/USD (followed by EUR/USD) implies a a higher complexity and indicates relatively higher efficiency of the Japanese FX market, while some economies like South Korea, Hong Kong and China show lower and weaker efficiency of their FX markets. Meanwhile, it is suggested that the financial crisis enhances the market efficiency in the FX markets.
      Citation: Entropy
      PubDate: 2017-12-31
      DOI: 10.3390/e20010017
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 20, Pages 18: Composite Likelihood Methods Based on Minimum
           Density Power Divergence Estimator

    • Authors: Elena Castilla, Nirian Martín, Leandro Pardo, Konstantinos Zografos
      First page: 18
      Abstract: In this paper, a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered, and the robustness is studied on the basis of a simulation study. The composite minimum density power divergence estimator is also introduced, and its asymptotic properties are studied.
      Citation: Entropy
      PubDate: 2017-12-31
      DOI: 10.3390/e20010018
      Issue No: Vol. 20, No. 1 (2017)
  • Entropy, Vol. 19, Pages 547: Bayesian Inference of Ecological Interactions
           from Spatial Data

    • Authors: Christopher Stephens, Victor Sánchez-Cordero, Constantino González Salazar
      First page: 547
      Abstract: The characterization and quantification of ecological interactions and the construction of species’ distributions and their associated ecological niches are of fundamental theoretical and practical importance. In this paper, we discuss a Bayesian inference framework, which, using spatial data, offers a general formalism within which ecological interactions may be characterized and quantified. Interactions are identified through deviations of the spatial distribution of co-occurrences of spatial variables relative to a benchmark for the non-interacting system and based on a statistical ensemble of spatial cells. The formalism allows for the integration of both biotic and abiotic factors of arbitrary resolution. We concentrate on the conceptual and mathematical underpinnings of the formalism, showing how, using the naive Bayes approximation, it can be used to not only compare and contrast the relative contribution from each variable, but also to construct species’ distributions and ecological niches based on an arbitrary variable type. We also show how non-linear interactions between distinct niche variables can be identified and the degree of confounding between variables accounted for.
      Citation: Entropy
      PubDate: 2017-11-25
      DOI: 10.3390/e19120547
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 627: Group Sparsity and Graph Regularized
           Semi-Nonnegative Matrix Factorization with Discriminability for Data

    • Authors: Peng Luo, Jinye Peng
      First page: 627
      Abstract: Semi-Nonnegative Matrix Factorization (Semi-NMF), as a variant of NMF, inherits the merit of parts-based representation of NMF and possesses the ability to process mixed sign data, which has attracted extensive attention. However, standard Semi-NMF still suffers from the following limitations. First of all, Semi-NMF fits data in a Euclidean space, which ignores the geometrical structure in the data. What’s more, Semi-NMF does not incorporate the discriminative information in the learned subspace. Last but not least, the learned basis in Semi-NMF is unnecessarily part based because there are no explicit constraints to ensure that the representation is part based. To settle these issues, in this paper, we propose a novel Semi-NMF algorithm, called Group sparsity and Graph regularized Semi-Nonnegative Matrix Factorization with Discriminability (GGSemi-NMFD) to overcome the aforementioned problems. GGSemi-NMFD adds the graph regularization term in Semi-NMF, which can well preserve the local geometrical information of the data space. To obtain the discriminative information, approximation orthogonal constraints are added in the learned subspace. In addition, ℓ 21 norm constraints are adopted for the basis matrix, which can encourage the basis matrix to be row sparse. Experimental results in six datasets demonstrate the effectiveness of the proposed algorithms.
      Citation: Entropy
      PubDate: 2017-11-27
      DOI: 10.3390/e19120627
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 633: Fault Diagnosis of Rolling Bearings Based on
           EWT and KDEC

    • Authors: Mingtao Ge, Jie Wang, Xiangyang Ren
      First page: 633
      Abstract: This study proposes a novel fault diagnosis method that is based on empirical wavelet transform (EWT) and kernel density estimation classifier (KDEC), which can well diagnose fault type of the rolling element bearings. With the proposed fault diagnosis method, the vibration signal of rolling element bearing was firstly decomposed into a series of F modes by EWT, and the root mean square, kurtosis, and skewness of the F modes were computed and combined into the feature vector. According to the characteristics of kernel density estimation, a classifier based on kernel density estimation and mutual information was proposed. Then, the feature vectors were input into the KDEC for training and testing. The experimental results indicated that the proposed method can effectively identify three different operative conditions of rolling element bearings, and the accuracy rates was higher than support vector machine (SVM) classifier and back-propagation (BP) neural network classifier.
      Citation: Entropy
      PubDate: 2017-12-05
      DOI: 10.3390/e19120633
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 634: An Extension to the Revised Approach in the
           Assessment of Informational Entropy

    • Authors: Turkay Baran, Nilgun Harmancioglu, Cem Cetinkaya, Filiz Barbaros
      First page: 634
      Abstract: This study attempts to extend the prevailing definition of informational entropy, where entropy relates to the amount of reduction of uncertainty or, indirectly, to the amount of information gained through measurements of a random variable. The approach adopted herein describes informational entropy not as an absolute measure of information, but as a measure of the variation of information. This makes it possible to obtain a single value for informational entropy, instead of several values that vary with the selection of the discretizing interval, when discrete probabilities of hydrological events are estimated through relative class frequencies and discretizing intervals. Furthermore, the present work introduces confidence limits for the informational entropy function, which facilitates a comparison between the uncertainties of various hydrological processes with different scales of magnitude and different probability structures. The work addresses hydrologists and environmental engineers more than it does mathematicians and statisticians. In particular, it is intended to help solve information-related problems in hydrological monitoring design and assessment. This paper first considers the selection of probability distributions of best fit to hydrological data, using generated synthetic time series. Next, it attempts to assess hydrometric monitoring duration in a netwrok, this time using observed runoff data series. In both applications, it focuses, basically, on the theoretical background for the extended definition of informational entropy. The methodology is shown to give valid results in each case.
      Citation: Entropy
      PubDate: 2017-11-29
      DOI: 10.3390/e19120634
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 636: Analyzing Information Distribution in Complex

    • Authors: Sten Sootla, Dirk Theis, Raul Vicente
      First page: 636
      Abstract: Information theory is often utilized to capture both linear as well as nonlinear relationships between any two parts of a dynamical complex system. Recently, an extension to classical information theory called partial information decomposition has been developed, which allows one to partition the information that two subsystems have about a third one into unique, redundant and synergistic contributions. Here, we apply a recent estimator of partial information decomposition to characterize the dynamics of two different complex systems. First, we analyze the distribution of information in triplets of spins in the 2D Ising model as a function of temperature. We find that while redundant information obtains a maximum at the critical point, synergistic information peaks in the disorder phase. Secondly, we characterize 1D elementary cellular automata rules based on the information distribution between neighboring cells. We describe several clusters of rules with similar partial information decomposition. These examples illustrate how the partial information decomposition provides a characterization of the emergent dynamics of complex systems in terms of the information distributed across their interacting units.
      Citation: Entropy
      PubDate: 2017-11-24
      DOI: 10.3390/e19120636
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 638: How Successful Are Wavelets in Detecting

    • Authors: Burak Eroğlu, Ramazan Gençay, M. Yazgan
      First page: 638
      Abstract: We evaluate the performances of wavelet jump detection tests by using simulated high-frequency data, in which jumps and some other non-standard features are present. Wavelet-based jump detection tests have a clear advantage over the alternatives, as they are capable of stating the exact timing and number of jumps. The results indicate that, in addition to those advantages, these detection tests also preserve desirable power and size properties even in non-standard data environments, whereas their alternatives fail to sustain their desirable properties beyond standard data features.
      Citation: Entropy
      PubDate: 2017-11-25
      DOI: 10.3390/e19120638
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 639: Magnetic Engine for the Single-Particle
           Landau Problem

    • Authors: Francisco Peña, Alejandro González, Alvaro Nunez, Pedro Orellana, René Rojas, Patricio Vargas
      First page: 639
      Abstract: We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic engine. The scheme of the cycle is composed of two adiabatic processes and two isomagnetic processes, driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.
      Citation: Entropy
      PubDate: 2017-11-25
      DOI: 10.3390/e19120639
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 640: Information Theory to Probe Intrapartum Fetal
           Heart Rate Dynamics

    • Authors: Carlos Granero-Belinchon, Stéphane Roux, Patrice Abry, Muriel Doret, Nicolas Garnier
      First page: 640
      Abstract: Intrapartum fetal heart rate (FHR) monitoring constitutes a reference tool in clinical practice to assess the baby’s health status and to detect fetal acidosis. It is usually analyzed by visual inspection grounded on FIGO criteria. Characterization of intrapartum fetal heart rate temporal dynamics remains a challenging task and continuously receives academic research efforts. Complexity measures, often implemented with tools referred to as approximate entropy (ApEn) or sample entropy (SampEn), have regularly been reported as significant features for intrapartum FHR analysis. We explore how information theory, and especially auto-mutual information (AMI), is connected to ApEn and SampEn and can be used to probe FHR dynamics. Applied to a large (1404 subjects) and documented database of FHR data, collected in a French academic hospital, it is shown that (i) auto-mutual information outperforms ApEn and SampEn for acidosis detection in the first stage of labor and continues to yield the best performance in the second stage; (ii) Shannon entropy increases as labor progresses and is always much larger in the second stage; (iii) babies suffering from fetal acidosis additionally show more structured temporal dynamics than healthy ones and that this progressive structuration can be used for early acidosis detection.
      Citation: Entropy
      PubDate: 2017-11-25
      DOI: 10.3390/e19120640
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 641: Tsallis Entropy Theory for Modeling in Water
           Engineering: A Review

    • Authors: Vijay Singh, Bellie Sivakumar, Huijuan Cui
      First page: 641
      Abstract: Water engineering is an amalgam of engineering (e.g., hydraulics, hydrology, irrigation, ecosystems, environment, water resources) and non-engineering (e.g., social, economic, political) aspects that are needed for planning, designing and managing water systems. These aspects and the associated issues have been dealt with in the literature using different techniques that are based on different concepts and assumptions. A fundamental question that still remains is: Can we develop a unifying theory for addressing these' The second law of thermodynamics permits us to develop a theory that helps address these in a unified manner. This theory can be referred to as the entropy theory. The thermodynamic entropy theory is analogous to the Shannon entropy or the information theory. Perhaps, the most popular generalization of the Shannon entropy is the Tsallis entropy. The Tsallis entropy has been applied to a wide spectrum of problems in water engineering. This paper provides an overview of Tsallis entropy theory in water engineering. After some basic description of entropy and Tsallis entropy, a review of its applications in water engineering is presented, based on three types of problems: (1) problems requiring entropy maximization; (2) problems requiring coupling Tsallis entropy theory with another theory; and (3) problems involving physical relations.
      Citation: Entropy
      PubDate: 2017-11-27
      DOI: 10.3390/e19120641
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 642: On Maximum Entropy and Inference

    • Authors: Luigi Gresele, Matteo Marsili
      First page: 642
      Abstract: Maximum entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords predictions on all other (dependent) variables. Conversely, maximum entropy can be invoked to retrieve the relevant variables (sufficient statistics) directly from the data, once a model is identified by Bayesian model selection. We explore this approach in the case of spin models with interactions of arbitrary order, and we discuss how relevant interactions can be inferred. In this perspective, the dimensionality of the inference problem is not set by the number of parameters in the model, but by the frequency distribution of the data. We illustrate the method showing its ability to recover the correct model in a few prototype cases and discuss its application on a real dataset.
      Citation: Entropy
      PubDate: 2017-11-28
      DOI: 10.3390/e19120642
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 643: Diagnosis of Combined Cycle Power Plant Based
           on Thermoeconomic Analysis: A Computer Simulation Study

    • Authors: Hoo-Suk Oh, Youngseog Lee, Ho-Young Kwak
      First page: 643
      Abstract: In this study, diagnosis of a 300-MW combined cycle power plant under faulty conditions was performed using a thermoeconomic method called modified productive structure analysis. The malfunction and dysfunction, unit cost of irreversibility and lost cost flow rate for each component were calculated for the cases of pre-fixed malfunction and the reference conditions. A commercial simulating software, GateCycleTM (version 6.1.2), was used to estimate the thermodynamic properties under faulty conditions. The relative malfunction (RMF) and the relative difference in the lost cost flow rate between real operation and reference conditions (RDLC) were found to be effective indicators for the identification of faulty components. Simulation results revealed that 0.5% degradation in the isentropic efficiency of air compressor, 2% in gas turbine, 2% in steam turbine and 2% degradation in energy loss in heat exchangers can be identified. Multi-fault scenarios that can be detected by the indicators were also considered. Additional lost exergy due to these types of faulty components, that can be detected by RMF or RDLC, is less than 5% of the exergy lost in the components in the normal condition.
      Citation: Entropy
      PubDate: 2017-11-28
      DOI: 10.3390/e19120643
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 644: Entropic Constitutive Relation and Modeling
           for Fourier and Hyperbolic Heat Conductions

    • Authors: Shu-Nan Li, Bing-Yang Cao
      First page: 644
      Abstract: Most existing phenomenological heat conduction models are expressed by temperature and heat flux distributions, whose definitions might be debatable in heat conductions with strong non-equilibrium. The constitutive relations of Fourier and hyperbolic heat conductions are here rewritten by the entropy and entropy flux distributions in the frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). The entropic constitutive relations are then generalized by Boltzmann–Gibbs–Shannon (BGS) statistical mechanics, which can avoid the debatable definitions of thermodynamic quantities relying on local equilibrium. It shows a possibility of modeling heat conduction through entropic constitutive relations. The applicability of the generalizations by BGS statistical mechanics is also discussed based on the relaxation time approximation, and it is found that the generalizations require a sufficiently small entropy production rate.
      Citation: Entropy
      PubDate: 2017-12-01
      DOI: 10.3390/e19120644
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 645: Quantum Information: What Is It All

    • Authors: Robert Griffiths
      First page: 645
      Abstract: This paper answers Bell’s question: What does quantum information refer to' It is about quantum properties represented by subspaces of the quantum Hilbert space, or their projectors, to which standard (Kolmogorov) probabilities can be assigned by using a projective decomposition of the identity (PDI or framework) as a quantum sample space. The single framework rule of consistent histories prevents paradoxes or contradictions. When only one framework is employed, classical (Shannon) information theory can be imported unchanged into the quantum domain. A particular case is the macroscopic world of classical physics whose quantum description needs only a single quasiclassical framework. Nontrivial issues unique to quantum information, those with no classical analog, arise when aspects of two or more incompatible frameworks are compared.
      Citation: Entropy
      PubDate: 2017-11-29
      DOI: 10.3390/e19120645
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 646: Statistical Measures to Quantify Similarity
           between Molecular Dynamics Simulation Trajectories

    • Authors: Jenny Farmer, Fareeha Kanwal, Nikita Nikulsin, Matthew Tsilimigras, Donald Jacobs
      First page: 646
      Abstract: Molecular dynamics simulation is commonly employed to explore protein dynamics. Despite the disparate timescales between functional mechanisms and molecular dynamics (MD) trajectories, functional differences are often inferred from differences in conformational ensembles between two proteins in structure-function studies that investigate the effect of mutations. A common measure to quantify differences in dynamics is the root mean square fluctuation (RMSF) about the average position of residues defined by C α -atoms. Using six MD trajectories describing three native/mutant pairs of beta-lactamase, we make comparisons with additional measures that include Jensen-Shannon, modifications of Kullback-Leibler divergence, and local p-values from 1-sample Kolmogorov-Smirnov tests. These additional measures require knowing a probability density function, which we estimate by using a nonparametric maximum entropy method that quantifies rare events well. The same measures are applied to distance fluctuations between C α -atom pairs. Results from several implementations for quantitative comparison of a pair of MD trajectories are made based on fluctuations for on-residue and residue-residue local dynamics. We conclude that there is almost always a statistically significant difference between pairs of 100 ns all-atom simulations on moderate-sized proteins as evident from extraordinarily low p-values.
      Citation: Entropy
      PubDate: 2017-11-29
      DOI: 10.3390/e19120646
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 647: Langevin Dynamics with Variable Coefficients
           and Nonconservative Forces: From Stationary States to Numerical Methods

    • Authors: Matthias Sachs, Benedict Leimkuhler, Vincent Danos
      First page: 647
      Abstract: Langevin dynamics is a versatile stochastic model used in biology, chemistry, engineering, physics and computer science. Traditionally, in thermal equilibrium, one assumes (i) the forces are given as the gradient of a potential and (ii) a fluctuation-dissipation relation holds between stochastic and dissipative forces; these assumptions ensure that the system samples a prescribed invariant Gibbs-Boltzmann distribution for a specified target temperature. In this article, we relax these assumptions, incorporating variable friction and temperature parameters and allowing nonconservative force fields, for which the form of the stationary state is typically not known a priori. We examine theoretical issues such as stability of the steady state and ergodic properties, as well as practical aspects such as the design of numerical methods for stochastic particle models. Applications to nonequilibrium systems with thermal gradients and active particles are discussed.
      Citation: Entropy
      PubDate: 2017-11-29
      DOI: 10.3390/e19120647
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 648: Maximum Correntropy Criterion Kalman Filter
           for α-Jerk Tracking Model with Non-Gaussian Noise

    • Authors: Bowen Hou, Zhangming He, Xuanying Zhou, Haiyin Zhou, Dong Li, Jiongqi Wang
      First page: 648
      Abstract: As one of the most critical issues for target track, α -jerk model is an effective maneuver target track model. Non-Gaussian noises always exist in the track process, which usually lead to inconsistency and divergence of the track filter. A novel Kalman filter is derived and applied on α -jerk tracking model to handle non-Gaussian noise. The weighted least square solution is presented and the standard Kalman filter is deduced firstly. A novel Kalman filter with the weighted least square based on the maximum correntropy criterion is deduced. The robustness of the maximum correntropy criterion is also analyzed with the influence function and compared with the Huber-based filter, and, moreover, the kernel size of Gaussian kernel plays an important role in the filter algorithm. A new adaptive kernel method is proposed in this paper to adjust the parameter in real time. Finally, simulation results indicate the validity and the efficiency of the proposed filter. The comparison study shows that the proposed filter can significantly reduce the noise influence for α -jerk model.
      Citation: Entropy
      PubDate: 2017-11-29
      DOI: 10.3390/e19120648
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 649: Entropy-Based Economic Denial of
           Sustainability Detection

    • Authors: Marco Monge, Jorge Vidal, Luis Villalba
      First page: 649
      Abstract: In recent years, an important increase in the amount and impact of Distributed Denial of Service (DDoS) threats has been reported by the different information security organizations. They typically target the depletion of the computational resources of the victims, hence drastically harming their operational capabilities. Inspired by these methods, Economic Denial of Sustainability (EDoS) attacks pose a similar motivation, but adapted to Cloud computing environments, where the denial is achieved by damaging the economy of both suppliers and customers. Therefore, the most common EDoS approach is making the offered services unsustainable by exploiting their auto-scaling algorithms. In order to contribute to their mitigation, this paper introduces a novel EDoS detection method based on the study of entropy variations related with metrics taken into account when deciding auto-scaling actuations. Through the prediction and definition of adaptive thresholds, unexpected behaviors capable of fraudulently demand new resource hiring are distinguished. With the purpose of demonstrate the effectiveness of the proposal, an experimental scenario adapted to the singularities of the EDoS threats and the assumptions driven by their original definition is described in depth. The preliminary results proved high accuracy.
      Citation: Entropy
      PubDate: 2017-11-29
      DOI: 10.3390/e19120649
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 650: On the Deposition Equilibrium of Carbon
           Nanotubes or Graphite in the Reforming Processes of Lower Hydrocarbon

    • Authors: Zdzisław Jaworski, Paulina Pianko-Oprych
      First page: 650
      Abstract: The modeling of carbon deposition from C-H-O reformates has usually employed thermodynamic data for graphite, but has rarely employed such data for impure filamentous carbon. Therefore, electrochemical data for the literature on the chemical potential of two types of purified carbon nanotubes (CNTs) are included in the study. Parameter values determining the thermodynamic equilibrium of the deposition of either graphite or CNTs are computed for dry and wet reformates from natural gas and liquefied petroleum gas. The calculation results are presented as the atomic oxygen-to-carbon ratio (O/C) against temperature (200 to 100 °C) for various pressures (1 to 30 bar). Areas of O/C for either carbon deposition or deposition-free are computed, and indicate the critical O/C values below which the deposition can occur. Only three types of deposited carbon were found in the studied equilibrium conditions: Graphite, multi-walled CNTs, and single-walled CNTs in bundles. The temperature regions of the appearance of the thermodynamically stable forms of solid carbon are numerically determined as being independent of pressure and the analyzed reactants. The modeling indicates a significant increase in the critical O/C for the deposition of CNTs against that for graphite. The highest rise in the critical O/C, of up to 290% at 30 bar, was found for the wet reforming process.
      Citation: Entropy
      PubDate: 2017-11-30
      DOI: 10.3390/e19120650
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 651: K-Dependence Bayesian Classifier Ensemble

    • Authors: Zhiyi Duan, Limin Wang
      First page: 651
      Abstract: To maximize the benefit that can be derived from the information implicit in big data, ensemble methods generate multiple models with sufficient diversity through randomization or perturbation. A k-dependence Bayesian classifier (KDB) is a highly scalable learning algorithm with excellent time and space complexity, along with high expressivity. This paper introduces a new ensemble approach of KDBs, a k-dependence forest (KDF), which induces a specific attribute order and conditional dependencies between attributes for each subclassifier. We demonstrate that these subclassifiers are diverse and complementary. Our extensive experimental evaluation on 40 datasets reveals that this ensemble method achieves better classification performance than state-of-the-art out-of-core ensemble learners such as the AODE (averaged one-dependence estimator) and averaged tree-augmented naive Bayes (ATAN).
      Citation: Entropy
      PubDate: 2017-11-30
      DOI: 10.3390/e19120651
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 652: Cosine Similarity Entropy:
           Self-Correlation-Based Complexity Analysis of Dynamical Systems

    • Authors: Theerasak Chanwimalueang, Danilo Mandic
      First page: 652
      Abstract: The nonparametric Sample Entropy (SE) estimator has become a standard for the quantification of structural complexity of nonstationary time series, even in critical cases of unfavorable noise levels. The SE has proven very successful for signals that exhibit a certain degree of the underlying structure, but do not obey standard probability distributions, a typical case in real-world scenarios such as with physiological signals. However, the SE estimates structural complexity based on uncertainty rather than on (self) correlation, so that, for reliable estimation, the SE requires long data segments, is sensitive to spikes and erratic peaks in data, and owing to its amplitude dependence it exhibits lack of precision for signals with long-term correlations. To this end, we propose a class of new entropy estimators based on the similarity of embedding vectors, evaluated through the angular distance, the Shannon entropy and the coarse-grained scale. Analysis of the effects of embedding dimension, sample size and tolerance shows that the so introduced Cosine Similarity Entropy (CSE) and the enhanced Multiscale Cosine Similarity Entropy (MCSE) are amplitude-independent and therefore superior to the SE when applied to short time series. Unlike the SE, the CSE is shown to yield valid entropy values over a broad range of embedding dimensions. By evaluating the CSE and the MCSE over a variety of benchmark synthetic signals as well as for real-world data (heart rate variability of three different cardiovascular pathologies), the proposed algorithms are demonstrated to be able to quantify degrees of structural complexity in the context of self-correlation over small to large temporal scales, thus offering physically meaningful interpretations and rigor in the understanding the intrinsic properties of the structural complexity of a system, such as the number of its degrees of freedom.
      Citation: Entropy
      PubDate: 2017-11-30
      DOI: 10.3390/e19120652
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 653: Coherent Processing of a Qubit Using One
           Squeezed State

    • Authors: Allan Tameshtit
      First page: 653
      Abstract: In a departure from most work in quantum information utilizing Gaussian states, we use a single such state to represent a qubit and model environmental noise with a class of quadratic dissipative equations. A benefit of this single Gaussian representation is that with one deconvolution, we can eliminate noise. In this deconvolution picture, a basis of squeezed states evolves to another basis of such states. One of the limitations of our approach is that noise is eliminated only at a privileged time. We suggest that this limitation may actually be used advantageously to send information securely: the privileged time is only known to the sender and the receiver, and any intruder accessing the information at any other time encounters noisy data.
      Citation: Entropy
      PubDate: 2017-11-30
      DOI: 10.3390/e19120653
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 654: Entropy Parameter M in Modeling a Flow
           Duration Curve

    • Authors: Yu Zhang, Vijay Singh, Aaron Byrd
      First page: 654
      Abstract: A flow duration curve (FDC) is widely used for predicting water supply, hydropower, environmental flow, sediment load, and pollutant load. Among different methods of constructing an FDC, the entropy-based method, developed recently, is appealing because of its several desirable characteristics, such as simplicity, flexibility, and statistical basis. This method contains a parameter, called entropy parameter M, which constitutes the basis for constructing the FDC. Since M is related to the ratio of the average streamflow to the maximum streamflow which, in turn, is related to the drainage area, it may be possible to determine M a priori and construct an FDC for ungauged basins. This paper, therefore, analyzed the characteristics of M in both space and time using streamflow data from 73 gauging stations in the Brazos River basin, Texas, USA. Results showed that the M values were impacted by reservoir operation and possibly climate change. The values were fluctuating, but relatively stable, after the operation of the reservoirs. Parameter M was found to change inversely with the ratio of average streamflow to the maximum streamflow. When there was an extreme event, there occurred a jump in the M value. Further, spatially, M had a larger value if the drainage area was small.
      Citation: Entropy
      PubDate: 2017-12-01
      DOI: 10.3390/e19120654
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 655: Bayesian Nonlinear Filtering via Information
           Geometric Optimization

    • Authors: Yubo Li, Yongqiang Cheng, Xiang Li, Hongqiang Wang, Xiaoqiang Hua, Yuliang Qin
      First page: 655
      Abstract: In this paper, Bayesian nonlinear filtering is considered from the viewpoint of information geometry and a novel filtering method is proposed based on information geometric optimization. Under the Bayesian filtering framework, we derive a relationship between the nonlinear characteristics of filtering and the metric tensor of the corresponding statistical manifold. Bayesian joint distributions are used to construct the statistical manifold. In this case, nonlinear filtering can be converted to an optimization problem on the statistical manifold and the adaptive natural gradient descent method is used to seek the optimal estimate. The proposed method provides a general filtering formulation and the Kalman filter, the Extended Kalman filter (EKF) and the Iterated Extended Kalman filter (IEKF) can be seen as special cases of this formulation. The performance of the proposed method is evaluated on a passive target tracking problem and the results demonstrate the superiority of the proposed method compared to various Kalman filter methods.
      Citation: Entropy
      PubDate: 2017-12-01
      DOI: 10.3390/e19120655
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 656: Context-Aware Generative Adversarial Privacy

    • Authors: Chong Huang, Peter Kairouz, Xiao Chen, Lalitha Sankar, Ram Rajagopal
      First page: 656
      Abstract: Preserving the utility of published datasets while simultaneously providing provable privacy guarantees is a well-known challenge. On the one hand, context-free privacy solutions, such as differential privacy, provide strong privacy guarantees, but often lead to a significant reduction in utility. On the other hand, context-aware privacy solutions, such as information theoretic privacy, achieve an improved privacy-utility tradeoff, but assume that the data holder has access to dataset statistics. We circumvent these limitations by introducing a novel context-aware privacy framework called generative adversarial privacy (GAP). GAP leverages recent advancements in generative adversarial networks (GANs) to allow the data holder to learn privatization schemes from the dataset itself. Under GAP, learning the privacy mechanism is formulated as a constrained minimax game between two players: a privatizer that sanitizes the dataset in a way that limits the risk of inference attacks on the individuals’ private variables, and an adversary that tries to infer the private variables from the sanitized dataset. To evaluate GAP’s performance, we investigate two simple (yet canonical) statistical dataset models: (a) the binary data model; and (b) the binary Gaussian mixture model. For both models, we derive game-theoretically optimal minimax privacy mechanisms, and show that the privacy mechanisms learned from data (in a generative adversarial fashion) match the theoretically optimal ones. This demonstrates that our framework can be easily applied in practice, even in the absence of dataset statistics.
      Citation: Entropy
      PubDate: 2017-12-01
      DOI: 10.3390/e19120656
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 657: Properties of Risk Measures of Generalized
           Entropy in Portfolio Selection

    • Authors: Rongxi Zhou, Xiao Liu, Mei Yu, Kyle Huang
      First page: 657
      Abstract: This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.
      Citation: Entropy
      PubDate: 2017-12-01
      DOI: 10.3390/e19120657
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 658: Assessment of Heart Rate Variability during
           an Endurance Mountain Trail Race by Multi-Scale Entropy Analysis

    • Authors: Montserrat Vallverdú, Aroa Ruiz-Muñoz, Emma Roca, Pere Caminal, Ferran A. Rodríguez, Alfredo Irurtia, Alexandre Perera
      First page: 658
      Abstract: The aim of the study was to analyze heart rate variability (HRV) response to high-intensity exercise during a 35-km mountain trail race and to ascertain whether fitness level could influence autonomic nervous system (ANS) modulation. Time-domain, frequency-domain, and multi-scale entropy (MSE) indexes were calculated for eleven mountain-trail runners who completed the race. Many changes were observed, mostly related to exercise load and fatigue. These changes were characterized by increased mean values and standard deviations of the normal-to-normal intervals associated with sympathetic activity, and by decreased differences between successive intervals related to parasympathetic activity. Normalized low frequency (LF) power suggested that ANS modulation varied greatly during the race and between individuals. Normalized high frequency (HF) power, associated with parasympathetic activity, varied considerably over the race, and tended to decrease at the final stages, whereas changes in the LF/HF ratio corresponded to intervals with varying exercise load. MSE indexes, related to system complexity, indicated the existence of many interactions between the heart and its neurological control mechanism. The time-domain, frequency-domain, and MSE indexes were also able to discriminate faster from slower runners, mainly in the more difficult and in the final stages of the race. These findings suggest the use of HRV analysis to study cardiac function mechanisms in endurance sports.
      Citation: Entropy
      PubDate: 2017-12-01
      DOI: 10.3390/e19120658
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 659: Quantum Minimum Distance Classifier

    • Authors: Enrica Santucci
      First page: 659
      Abstract: We propose a quantum version of the well known minimum distance classification model called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous works. First, a quantum counterpart of the NMC for two-dimensional problems was introduced, named Quantum Nearest Mean Classifier (QNMC), together with a possible generalization to any number of dimensions. Secondly, we studied the n-dimensional problem into detail and we showed a new encoding for arbitrary n-feature vectors into density operators. In the present paper, another promising encoding is considered, suggested by recent debates on quantum machine learning. Further, we observe a significant property concerning the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a meaningful difference between the NMC and the respective quantum version, allows us to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted: (i) to compare the NMC and QNMC performance on different datasets; and (ii) to study the effects of the non-invariance under uniform rescaling for the QNMC.
      Citation: Entropy
      PubDate: 2017-12-01
      DOI: 10.3390/e19120659
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 660: Entropy-Based Investigation on the
           Precipitation Variability over the Hexi Corridor in China

    • Authors: Liang Cheng, Jun Niu, Dehai Liao
      First page: 660
      Abstract: The spatial and temporal variability of precipitation time series were investigated for the Hexi Corridor, in Northwest China, by analyzing the entropy information. The examinations were performed on monthly, seasonal, and annual timescales based on 29 meteorological stations for the period of 1961–2015. The apportionment entropy and intensity entropy were used to analyze the regional precipitation characteristics, including the intra-annual and decadal distribution of monthly and annual precipitation amounts, as well as the number of precipitation days within a year and a decade. The regions with high precipitation variability are found in the western part of the Hexi corridor and with less precipitation, and may have a high possibility of drought occurrence. The variability of the number of precipitation days decreased from the west to the east of the corridor. Higher variability, in terms of both of precipitation amount and intensity during crop-growing season, has been found in the recent decade. In addition, the correlation between entropy-based precipitation variability and the crop yield is also compared, and the crop yield in historical periods is found to be correlated with the precipitation intensity disorder index in the middle reaches of the Hexi corridor.
      Citation: Entropy
      PubDate: 2017-12-01
      DOI: 10.3390/e19120660
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 661: Label-Driven Learning Framework: Towards More
           Accurate Bayesian Network Classifiers through Discrimination of
           High-Confidence Labels

    • Authors: Yi Sun, Limin Wang, Minghui Sun
      First page: 661
      Abstract: Bayesian network classifiers (BNCs) have demonstrated competitive classification accuracy in a variety of real-world applications. However, it is error-prone for BNCs to discriminate among high-confidence labels. To address this issue, we propose the label-driven learning framework, which incorporates instance-based learning and ensemble learning. For each testing instance, high-confidence labels are first selected by a generalist classifier, e.g., the tree-augmented naive Bayes (TAN) classifier. Then, by focusing on these labels, conditional mutual information is redefined to more precisely measure mutual dependence between attributes, thus leading to a refined generalist with a more reasonable network structure. To enable finer discrimination, an expert classifier is tailored for each high-confidence label. Finally, the predictions of the refined generalist and the experts are aggregated. We extend TAN to LTAN (Label-driven TAN) by applying the proposed framework. Extensive experimental results demonstrate that LTAN delivers superior classification accuracy to not only several state-of-the-art single-structure BNCs but also some established ensemble BNCs at the expense of reasonable computation overhead.
      Citation: Entropy
      PubDate: 2017-12-03
      DOI: 10.3390/e19120661
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 662: Is an Entropy-Based Approach Suitable for an
           Understanding of the Metabolic Pathways of Fermentation and

    • Authors: Roberto Zivieri, Nicola Pacini
      First page: 662
      Abstract: Lactic fermentation and respiration are important metabolic pathways on which life is based. Here, the rate of entropy in a cell associated to fermentation and respiration processes in glucose catabolism of living systems is calculated. This is done for both internal and external heat and matter transport according to a thermodynamic approach based on Prigogine’s formalism. It is shown that the rate of entropy associated to irreversible reactions in fermentation processes is higher than the corresponding one in respiration processes. Instead, this behaviour is reversed for diffusion of chemical species and for heat exchanges. The ratio between the rates of entropy associated to the two metabolic pathways has a space and time dependence for diffusion of chemical species and is invariant for heat and irreversible reactions. In both fermentation and respiration processes studied separately, the total entropy rate tends towards a minimum value fulfilling Prigogine’s minimum dissipation principle and is in accordance with the second principle of thermodynamics. The applications of these results could be important for cancer detection and therapy.
      Citation: Entropy
      PubDate: 2017-12-04
      DOI: 10.3390/e19120662
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 663: Capturing Causality for Fault Diagnosis Based
           on Multi-Valued Alarm Series Using Transfer Entropy

    • Authors: Jianjun Su, Dezheng Wang, Yinong Zhang, Fan Yang, Yan Zhao, Xiangkun Pang
      First page: 663
      Abstract: Transfer entropy (TE) is a model-free approach based on information theory to capture causality between variables, which has been used for the modeling and monitoring of, and fault diagnosis in, complex industrial processes. It is able to detect the causality between variables without assuming any underlying model, but it is computationally burdensome. To overcome this limitation, a hybrid method of TE and the modified conditional mutual information (CMI) approach is proposed by using generated multi-valued alarm series. In order to obtain a process topology, TE can generate a causal map of all sub-processes and modified CMI can be used to distinguish the direct connectivity from the above-mentioned causal map by using multi-valued alarm series. The effectiveness and accuracy rate of the proposed method are validated by simulated and real industrial cases (the Tennessee-Eastman process) to capture process topology by using multi-valued alarm series.
      Citation: Entropy
      PubDate: 2017-12-04
      DOI: 10.3390/e19120663
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 664: Entropic Updating of Probabilities and
           Density Matrices

    • Authors: Kevin Vanslette
      First page: 664
      Abstract: We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probabilities and density matrices, respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.
      Citation: Entropy
      PubDate: 2017-12-04
      DOI: 10.3390/e19120664
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 665: An Improved Chaotic Optimization Algorithm
           Applied to a DC Electrical Motor Modeling

    • Authors: Simone Fiori, Ruben Di Filippo
      First page: 665
      Abstract: The chaos-based optimization algorithm (COA) is a method to optimize possibly nonlinear complex functions of several variables by chaos search. The main innovation behind the chaos-based optimization algorithm is to generate chaotic trajectories by means of nonlinear, discrete-time dynamical systems to explore the search space while looking for the global minimum of a complex criterion function. The aim of the present research is to investigate the numerical properties of the COA, both on complex optimization test-functions from the literature and on a real-world problem, to contribute to the understanding of its global-search features. In addition, the present research suggests a refinement of the original COA algorithm to improve its optimization performances. In particular, the real-world optimization problem tackled within the paper is the estimation of six electro-mechanical parameters of a model of a direct-current (DC) electrical motor. A large number of test results prove that the algorithm achieves an excellent numerical precision at a little expense in the computational complexity, which appears as extremely limited, compared to the complexity of other benchmark optimization algorithms, namely, the genetic algorithm and the simulated annealing algorithm.
      Citation: Entropy
      PubDate: 2017-12-04
      DOI: 10.3390/e19120665
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 666: Assessment of Component Selection Strategies
           in Hyperspectral Imagery

    • Authors: Edurne Ibarrola-Ulzurrun, Javier Marcello, Consuelo Gonzalo-Martin
      First page: 666
      Abstract: Hyperspectral imagery (HSI) integrates many continuous and narrow bands that cover different regions of the electromagnetic spectrum. However, the main challenge is the high dimensionality of HSI data due to the ’Hughes’ phenomenon. Thus, dimensionality reduction is necessary before applying classification algorithms to obtain accurate thematic maps. We focus the study on the following feature-extraction algorithms: Principal Component Analysis (PCA), Minimum Noise Fraction (MNF), and Independent Component Analysis (ICA). After a literature survey, we have observed a lack of a comparative study on these techniques as well as accurate strategies to determine the number of components. Hence, the first objective was to compare traditional dimensionality reduction techniques (PCA, MNF, and ICA) in HSI of the Compact Airborne Spectrographic Imager (CASI) sensor and to evaluate different strategies for selecting the most suitable number of components in the transformed space. The second objective was to determine a new dimensionality reduction approach by dividing the CASI HSI regarding the spectral regions covering the electromagnetic spectrum. The components selected from the transformed space of the different spectral regions were stacked. This stacked transformed space was evaluated to see if the proposed approach improves the final classification.
      Citation: Entropy
      PubDate: 2017-12-05
      DOI: 10.3390/e19120666
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 667: L1-Minimization Algorithm for Bayesian Online
           Compressed Sensing

    • Authors: Paulo Rossi, Renato Vicente
      First page: 667
      Abstract: In this work, we propose a Bayesian online reconstruction algorithm for sparse signals based on Compressed Sensing and inspired by L1-regularization schemes. A previous work has introduced a mean-field approximation for the Bayesian online algorithm and has shown that it is possible to saturate the offline performance in the presence of Gaussian measurement noise when the signal generating distribution is known. Here, we build on these results and show that reconstruction is possible even if prior knowledge about the generation of the signal is limited, by introduction of a Laplace prior and of an extra Kullback–Leibler divergence minimization step for hyper-parameter learning.
      Citation: Entropy
      PubDate: 2017-12-05
      DOI: 10.3390/e19120667
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 668: Thermoelectrics of Interacting

    • Authors: Jens Schulenborg, Angelo Di Marco, Joren Vanherck, Maarten R. Wegewijs, Janine Splettstoesser
      First page: 668
      Abstract: Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager’s results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems—deriving from the fundamental fermion-parity superselection principle of quantum many-particle systems—provides new insights into thermoelectric transport. Using a master equation, we analyze the stationary charge and heat currents through a weakly coupled, but strongly interacting single-level quantum dot subject to electrical and thermal bias. In linear transport, the fermion-parity duality shows that features of thermoelectric response coefficients are actually dominated by the average and fluctuations of the charge in a dual quantum dot system, governed by attractive instead of repulsive electron-electron interaction. In the nonlinear regime, the duality furthermore relates most transport coefficients to much better understood equilibrium quantities. Finally, we naturally identify the fermion-parity as the part of the Coulomb interaction relevant for both the linear and nonlinear Fourier heat. Altogether, our findings hence reveal that next to time-reversal, the duality imposes equally important symmetry restrictions on thermoelectric transport. As such, it is also expected to simplify computations and clarify the physical understanding for more complex systems than the simplest relevant interacting nanostructure model studied here.
      Citation: Entropy
      PubDate: 2017-12-06
      DOI: 10.3390/e19120668
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 669: Formation of Photo-Responsive Liquid
           Crystalline Emulsion by Using Microfluidics Device

    • Authors: Yoshiharu Dogishi, Shun Endo, Woon Sohn, Kenji Katayama
      First page: 669
      Abstract: Photo-responsive double emulsions made of liquid crystal (LC) were prepared by a microfluidic device, and the light-induced processes were studied. The phase transition was induced from the center of the topological defect for an emulsion made of (N-(4-methoxybenzylidene)-4-butylaniline (MBBA), and strange texture change was observed for an emulsion made of 4-cyano-4′-pentylbiphenyl (5CB) doped with azobenzene. The results suggest that there are defect-involved processes in the phase change of LC double emulsions.
      Citation: Entropy
      PubDate: 2017-12-06
      DOI: 10.3390/e19120669
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 670: Oscillations in Multiparticle Production

    • Authors: Grzegorz Wilk, Zbigniew Włodarczyk
      First page: 670
      Abstract: We discuss two examples of oscillations apparently hidden in some experimental results for high-energy multiparticle production processes: (i) the log-periodic oscillatory pattern decorating the power-like Tsallis distributions of transverse momenta; (ii) the oscillations of the modified combinants obtained from the measured multiplicity distributions. Our calculations are confronted with p p data from the Large Hadron Collider (LHC). We show that in both cases, these phenomena can provide new insight into the dynamics of these processes.
      Citation: Entropy
      PubDate: 2017-12-06
      DOI: 10.3390/e19120670
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 671: Inspecting Non-Perturbative Contributions to
           the Entanglement Entropy via Wavefunctions

    • Authors: Arpan Bhattacharyya, Ling-Yan Hung, Pak Lau, Si-Nong Liu
      First page: 671
      Abstract: In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with a toy model of multiple particles whose interaction potential admits multiple minima. We study the entanglement of the true ground state after taking the tunneling effects into account and find some simple patterns. Notably, in the case of multiple particle interactions, entanglement entropy generically decreases with increasing number of minima. The knowledge of the subsystem actually increases with the number of minima. The reduced density matrix can also be seen to have close connections with graph spectra. In a more careful study of the two-well tunneling system, we also extract the exponentially-suppressed tail contribution, the analogue of instantons. To understand the effects of multiple minima in a field theory, we are inspired to inspect wavefunctions in a toy model of a bosonic field describing quasi-particles of two different condensates related by Bogoliubov transformations. We find that the area law is naturally preserved. This is probably a useful set of perspectives that promise wider applications.
      Citation: Entropy
      PubDate: 2017-12-07
      DOI: 10.3390/e19120671
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 672: Association between Multiscale Entropy
           Characteristics of Heart Rate Variability and Ischemic Stroke Risk in
           Patients with Permanent Atrial Fibrillation

    • Authors: Ryo Matsuoka, Kohzoh Yoshino, Eiichi Watanabe, Ken Kiyono
      First page: 672
      Abstract: Multiscale entropy (MSE) profiles of heart rate variability (HRV) in patients with atrial fibrillation (AFib) provides clinically useful information for ischemic stroke risk assessment, suggesting that the complex properties characterized by MSE profiles are associated with ischemic stroke risk. However, the meaning of HRV complexity in patients with AFib has not been clearly interpreted, and the physical and mathematical understanding of the relation between HRV dynamics and the ischemic stroke risk is not well established. To gain a deeper insight into HRV dynamics in patients with AFib, and to improve ischemic stroke risk assessment using HRV analysis, we study the HRV characteristics related to MSE profiles, such as the long-range correlation and probability density function. In this study, we analyze the HRV time series of 173 patients with permanent AFib. Our results show that, although HRV time series in patients with AFib exhibit long-range correlation (1/f fluctuations)—as observed in healthy subjects—in a range longer than 90 s, these autocorrelation properties have no significant predictive power for ischemic stroke occurrence. Further, the probability density function structure of the coarse-grained times series at scales greater than 2 s is dominantly associated with ischemic stroke risk. This observation could provide valuable information for improving ischemic stroke risk assessment using HRV analysis.
      Citation: Entropy
      PubDate: 2017-12-07
      DOI: 10.3390/e19120672
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 673: Characterisation of the Effects of Sleep
           Deprivation on the Electroencephalogram Using Permutation Lempel–Ziv
           Complexity, a Non-Linear Analysis Tool

    • Authors: Pinar Tosun, Daniel Abásolo, Gillian Stenson, Raphaelle Winsky-Sommerer
      First page: 673
      Abstract: Specific patterns of brain activity during sleep and waking are recorded in the electroencephalogram (EEG). Time-frequency analysis methods have been widely used to analyse the EEG and identified characteristic oscillations for each vigilance state (VS), i.e., wakefulness, rapid-eye movement (REM) and non-rapid-eye movement (NREM) sleep. However, other aspects such as change of patterns associated with brain dynamics may not be captured unless a non-linear-based analysis method is used. In this pilot study, Permutation Lempel–Ziv complexity (PLZC), a novel symbolic dynamics analysis method, was used to characterise the changes in the EEG in sleep and wakefulness during baseline and recovery from sleep deprivation (SD). The results obtained with PLZC were contrasted with a related non-linear method, Lempel–Ziv complexity (LZC). Both measure the emergence of new patterns. However, LZC is dependent on the absolute amplitude of the EEG, while PLZC is only dependent on the relative amplitude due to symbolisation procedure and thus, more resistant to noise. We showed that PLZC discriminates activated brain states associated with wakefulness and REM sleep, which both displayed higher complexity, compared to NREM sleep. Additionally, significantly lower PLZC values were measured in NREM sleep during the recovery period following SD compared to baseline, suggesting a reduced emergence of new activity patterns in the EEG. These findings were validated using PLZC on surrogate data. By contrast, LZC was merely reflecting changes in the spectral composition of the EEG. Overall, this study implies that PLZC is a robust non-linear complexity measure, which is not dependent on amplitude variations in the signal, and which may be useful to further assess EEG alterations induced by environmental or pharmacological manipulations.
      Citation: Entropy
      PubDate: 2017-12-08
      DOI: 10.3390/e19120673
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 674: On the Statistical Mechanics of Alien Species

    • Authors: Michael Bowler, Colleen Kelly
      First page: 674
      Abstract: Many species of plants are found in regions to which they are alien. Their global distributions are characterised by a family of exponential functions of the kind that arise in elementary statistical mechanics (an example in ecology is MacArthur’s broken stick). We show here that all these functions are quantitatively reproduced by a model containing a single parameter—some global resource partitioned at random on the two axes of species number and site number. A dynamical model generating this equilibrium is a two-fold stochastic process and suggests a curious and interesting biological interpretation in terms of niche structures fluctuating with time and productivity, with sites and species highly idiosyncratic. Idiosyncrasy implies that attempts to identify a priori those species likely to become naturalised are unlikely to be successful. Although this paper is primarily concerned with a particular problem in population biology, the two-fold stochastic process may be of more general interest.
      Citation: Entropy
      PubDate: 2017-12-09
      DOI: 10.3390/e19120674
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 675: A General Symbolic Approach to
           Kolmogorov-Sinai Entropy

    • Authors: Inga Stolz, Karsten Keller
      First page: 675
      Abstract: It is popular to study a time-dependent nonlinear system by encoding outcomes of measurements into sequences of symbols following certain symbolization schemes. Mostly, symbolizations by threshold crossings or variants of it are applied, but also, the relatively new symbolic approach, which goes back to innovative works of Bandt and Pompe—ordinal symbolic dynamics—plays an increasing role. In this paper, we discuss both approaches novelly in one breath with respect to the theoretical determination of the Kolmogorov-Sinai entropy (KS entropy). For this purpose, we propose and investigate a unifying approach to formalize symbolizations. By doing so, we can emphasize the main advantage of the ordinal approach if no symbolization scheme can be found that characterizes KS entropy directly: the ordinal approach, as well as generalizations of it provide, under very natural conditions, a direct route to KS entropy by default.
      Citation: Entropy
      PubDate: 2017-12-09
      DOI: 10.3390/e19120675
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 676: Maximum Exergetic Efficiency Operation of a
           Solar Powered H2O-LiBr Absorption Cooling System

    • Authors: Camelia Stanciu, Dorin Stanciu, Adina-Teodora Gheorghian, Elena-Beatrice Tănase, Cătălina Dobre, Marius Spiroiu
      First page: 676
      Abstract: A solar driven cooling system consisting of a single effect H2O-LiBr absorbtion cooling module (ACS), a parabolic trough collector (PTC), and a storage tank (ST) module is analyzed during one full day operation. The pressurized water is used to transfer heat from PTC to ST and to feed the ACS desorber. The system is constrained to operate at the maximum ACS exergetic efficiency, under a time dependent cooling load computed on 15 July for a one storey house located near Bucharest, Romania. To set up the solar assembly, two commercial PTCs were selected, namely PT1-IST and PTC 1800 Solitem, and a single unit ST was initially considered. The mathematical model, relying on the energy balance equations, was coded under Engineering Equation Solver (EES) environment. The solar data were obtained from the Meteonorm database. The numerical simulations proved that the system cannot cover the imposed cooling load all day long, due to the large variation of water temperature inside the ST. By splitting the ST into two units, the results revealed that the PT1-IST collector only drives the ACS between 9 am and 4:30 pm, while the PTC 1800 one covers the entire cooling period (9 am–6 pm) for optimum ST capacities of 90 kg/90 kg and 90 kg/140 kg, respectively.
      Citation: Entropy
      PubDate: 2017-12-09
      DOI: 10.3390/e19120676
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 677: Automated Detection of Paroxysmal Atrial
           Fibrillation Using an Information-Based Similarity Approach

    • Authors: Xingran Cui, Emily Chang, Wen-Hung Yang, Bernard C. Jiang, Albert C. Yang, Chung-Kang Peng
      First page: 677
      Abstract: Atrial fibrillation (AF) is an abnormal rhythm of the heart, which can increase heart-related complications. Paroxysmal AF episodes occur intermittently with varying duration. Human-based diagnosis of paroxysmal AF with a longer-term electrocardiogram recording is time-consuming. Here we present a fully automated ensemble model for AF episode detection based on RR-interval time series, applying a novel approach of information-based similarity analysis and ensemble scheme. By mapping RR-interval time series to binary symbolic sequences and comparing the rank-frequency patterns of m-bit words, the dissimilarity between AF and normal sinus rhythms (NSR) were quantified. To achieve high detection specificity and sensitivity, and low variance, a weighted variation of bagging with multiple AF and NSR templates was applied. By performing dissimilarity comparisons between unknown RR-interval time series and multiple templates, paroxysmal AF episodes were detected. Based on our results, optimal AF detection parameters are symbolic word length m = 9 and observation window n = 150, achieving 97.04% sensitivity, 97.96% specificity, and 97.78% overall accuracy. Sensitivity, specificity, and overall accuracy vary little despite changes in m and n parameters. This study provides quantitative information to enhance the categorization of AF and normal cardiac rhythms.
      Citation: Entropy
      PubDate: 2017-12-10
      DOI: 10.3390/e19120677
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 678: Information Landscape and Flux, Mutual
           Information Rate Decomposition and Connections to Entropy Production

    • Authors: Qian Zeng, Jin Wang
      First page: 678
      Abstract: We explored the dynamics of two interacting information systems. We show that for the Markovian marginal systems, the driving force for information dynamics is determined by both the information landscape and information flux. While the information landscape can be used to construct the driving force to describe the equilibrium time-reversible information system dynamics, the information flux can be used to describe the nonequilibrium time-irreversible behaviors of the information system dynamics. The information flux explicitly breaks the detailed balance and is a direct measure of the degree of the nonequilibrium or time-irreversibility. We further demonstrate that the mutual information rate between the two subsystems can be decomposed into the equilibrium time-reversible and nonequilibrium time-irreversible parts, respectively. This decomposition of the Mutual Information Rate (MIR) corresponds to the information landscape-flux decomposition explicitly when the two subsystems behave as Markov chains. Finally, we uncover the intimate relationship between the nonequilibrium thermodynamics in terms of the entropy production rates and the time-irreversible part of the mutual information rate. We found that this relationship and MIR decomposition still hold for the more general stationary and ergodic cases. We demonstrate the above features with two examples of the bivariate Markov chains.
      Citation: Entropy
      PubDate: 2017-12-11
      DOI: 10.3390/e19120678
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 679: Second-Law Analysis: A Powerful Tool for
           Analyzing Computational Fluid Dynamics (CFD) Results

    • Authors: Yan Jin
      First page: 679
      Abstract: Second-law analysis (SLA) is an important concept in thermodynamics, which basically assesses energy by its value in terms of its convertibility from one form to another.[...]
      Citation: Entropy
      PubDate: 2017-12-11
      DOI: 10.3390/e19120679
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 680: Altered Brain Complexity in Women with
           Primary Dysmenorrhea: A Resting-State Magneto-Encephalography Study Using
           Multiscale Entropy Analysis

    • Authors: Intan Low, Po-Chih Kuo, Yu-Hsiang Liu, Cheng-Lin Tsai, Hsiang-Tai Chao, Jen-Chuen Hsieh, Li-Fen Chen, Yong-Sheng Chen
      First page: 680
      Abstract: How chronic pain affects brain functions remains unclear. As a potential indicator, brain complexity estimated by entropy-based methods may be helpful for revealing the underlying neurophysiological mechanism of chronic pain. In this study, complexity features with multiple time scales and spectral features were extracted from resting-state magnetoencephalographic signals of 156 female participants with/without primary dysmenorrhea (PDM) during pain-free state. Revealed by multiscale sample entropy (MSE), PDM patients (PDMs) exhibited loss of brain complexity in regions associated with sensory, affective, and evaluative components of pain, including sensorimotor, limbic, and salience networks. Significant correlations between MSE values and psychological states (depression and anxiety) were found in PDMs, which may indicate specific nonlinear disturbances in limbic and default mode network circuits after long-term menstrual pain. These findings suggest that MSE is an important measure of brain complexity and is potentially applicable to future diagnosis of chronic pain.
      Citation: Entropy
      PubDate: 2017-12-11
      DOI: 10.3390/e19120680
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 681: Chaos in a Cancer Model via Fractional
           Derivatives with Exponential Decay and Mittag-Leffler Law

    • Authors: José Gómez-Aguilar, María López-López, Victor Alvarado-Martínez, Dumitru Baleanu, Hasib Khan
      First page: 681
      Abstract: In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.
      Citation: Entropy
      PubDate: 2017-12-19
      DOI: 10.3390/e19120681
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 682: Channel Capacity of Coding System on Tsallis
           Entropy and q-Statistics

    • Authors: Tatsuaki Tsuruyama
      First page: 682
      Abstract: The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the channel capacity by maximization of the Tsallis entropy within a given condition of code length. As a result, we obtained a simple relational expression between code length and code appearance probability and, additionally, a generalized formula of the channel capacity on the basis of Tsallis entropy statistics. This theoretical framework may contribute to data processing techniques and other applications.
      Citation: Entropy
      PubDate: 2017-12-12
      DOI: 10.3390/e19120682
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 683: Entropy Conditions Involved in the Nonlinear
           Coupled Constitutive Method for Solving Continuum and Rarefied Gas Flows

    • Authors: Ke Tang, Hong Xiao
      First page: 683
      Abstract: The numerical study of continuum-rarefied gas flows is of considerable interest because it can provide fundamental knowledge regarding flow physics. Recently, the nonlinear coupled constitutive method (NCCM) has been derived from the Boltzmann equation and implemented to investigate continuum-rarefied gas flows. In this study, we first report the important and detailed issues in the use of the H theorem and positive entropy generation in the NCCM. Importantly, the unified nonlinear dissipation model and its relationships to the Rayleigh–Onsager function were demonstrated in the treatment of the collision term of the Boltzmann equation. In addition, we compare the Grad moment method, the Burnett equation, and the NCCM. Next, differences between the NCCM equations and the Navier–Stokes equations are explained in detail. For validation, numerical studies of rarefied and continuum gas flows were conducted. These studies include rarefied and/or continuum gas flows around a two-dimensional (2D) cavity, a 2D airfoil, a 2D cylinder, and a three-dimensional space shuttle. It was observed that the present results of the NCCM are in good agreement with those of the Direct Simulation Monte Carlo (DSMC) method in rarefied cases and are in good agreement with those of the Navier–Stokes equations in continuum cases. Finally, this study can be regarded as a theoretical basis of the NCCM for the development of a unified framework for solving continuum-rarefied gas flows.
      Citation: Entropy
      PubDate: 2017-12-12
      DOI: 10.3390/e19120683
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 684: Extremal Matching Energy of Random Polyomino

    • Authors: Tingzeng Wu, Huazhong Lü, Xuexin Zhang
      First page: 684
      Abstract: Polyomino graphs is one of the research objectives in statistical physics and in modeling problems of surface chemistry. A random polyomino chain is a subgraph of a polyomino graph. The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. In this paper, we characterize the graphs with the extremal matching energy among all random polyomino chains of a polyomino graph by the probability method.
      Citation: Entropy
      PubDate: 2017-12-14
      DOI: 10.3390/e19120684
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 685: Testing the Beta-Lognormal Model in Amazonian
           Rainfall Fields Using the Generalized Space q-Entropy

    • Authors: Hernán Salas, Germán Poveda, Oscar Mesa
      First page: 685
      Abstract: We study spatial scaling and complexity properties of Amazonian radar rainfall fields using the Beta-Lognormal Model (BL-Model) with the aim to characterize and model the process at a broad range of spatial scales. The Generalized Space q-Entropy Function (GSEF), an entropic measure defined as a continuous set of power laws covering a broad range of spatial scales, S q ( λ ) ∼ λ Ω ( q ), is used as a tool to check the ability of the BL-Model to represent observed 2-D radar rainfall fields. In addition, we evaluate the effect of the amount of zeros, the variability of rainfall intensity, the number of bins used to estimate the probability mass function, and the record length on the GSFE estimation. Our results show that: (i) the BL-Model adequately represents the scaling properties of the q-entropy, S q, for Amazonian rainfall fields across a range of spatial scales λ from 2 km to 64 km; (ii) the q-entropy in rainfall fields can be characterized by a non-additivity value, q s a t, at which rainfall reaches a maximum scaling exponent, Ω s a t; (iii) the maximum scaling exponent Ω s a t is directly related to the amount of zeros in rainfall fields and is not sensitive to either the number of bins to estimate the probability mass function or the variability of rainfall intensity; and (iv) for small-samples, the GSEF of rainfall fields may incur in considerable bias. Finally, for synthetic 2-D rainfall fields from the BL-Model, we look for a connection between intermittency using a metric based on generalized Hurst exponents, M ( q 1 , q 2 ), and the non-extensive order (q-order) of a system, Θ q, which relates to the GSEF. Our results do not exhibit evidence of such relationship.
      Citation: Entropy
      PubDate: 2017-12-13
      DOI: 10.3390/e19120685
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 686: Do We Really Need to Catch Them All' A
           New User-Guided Social Media Crawling Method

    • Authors: Fredrik Erlandsson, Piotr Bródka, Martin Boldt, Henric Johnson
      First page: 686
      Abstract: [-15]With the growing use of popular social media services like Facebook and Twitter it is challenging to collect all content from the networks without access to the core infrastructure or paying for it. Thus, if all content cannot be collected one must consider which data are of most importance. In this work we present a novel User-guided Social Media Crawling method (USMC) that is able to collect data from social media, utilizing the wisdom of the crowd to decide the order in which user generated content should be collected to cover as many user interactions as possible. USMC is validated by crawling 160 public Facebook pages, containing content from 368 million users including 1.3 billion interactions, and it is compared with two other crawling methods. The results show that it is possible to cover approximately 75% of the interactions on a Facebook page by sampling just 20% of its posts, and at the same time reduce the crawling time by 53%. In addition, the social network constructed from the 20% sample contains more than 75% of the users and edges compared to the social network created from all posts, and it has similar degree distribution.
      Citation: Entropy
      PubDate: 2017-12-13
      DOI: 10.3390/e19120686
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 687: Choosing between Higher Moment Maximum
           Entropy Models and Its Application to Homogeneous Point Processes with
           Random Effects

    • Authors: Lotfi Khribi, Brenda MacGibbon, Marc Fredette
      First page: 687
      Abstract: In the Bayesian framework, the usual choice of prior in the prediction of homogeneous Poisson processes with random effects is the gamma one. Here, we propose the use of higher order maximum entropy priors. Their advantage is illustrated in a simulation study and the choice of the best order is established by two goodness-of-fit criteria: Kullback–Leibler divergence and a discrepancy measure. This procedure is illustrated on a warranty data set from the automobile industry.
      Citation: Entropy
      PubDate: 2017-12-14
      DOI: 10.3390/e19120687
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 688: Entropy and Compression Capture Different
           Complexity Features: The Case of Fetal Heart Rate

    • Authors: João Monteiro-Santos, Hernâni Gonçalves, João Bernardes, Luís Antunes, Mohammad Nozari, Cristina Costa-Santos
      First page: 688
      Abstract: Entropy and compression have been used to distinguish fetuses at risk of hypoxia from their healthy counterparts through the analysis of Fetal Heart Rate (FHR). Low correlation that was observed between these two approaches suggests that they capture different complexity features. This study aims at characterizing the complexity of FHR features captured by entropy and compression, using as reference international guidelines. Single and multi-scale approaches were considered in the computation of entropy and compression. The following physiologic-based features were considered: FHR baseline; percentage of abnormal long (%abLTV) and short (%abSTV) term variability; average short term variability; and, number of acceleration and decelerations. All of the features were computed on a set of 68 intrapartum FHR tracings, divided as normal, mildly, and moderately-severely acidemic born fetuses. The correlation between entropy/compression features and the physiologic-based features was assessed. There were correlations between compressions and accelerations and decelerations, but neither accelerations nor decelerations were significantly correlated with entropies. The %abSTV was significantly correlated with entropies (ranging between −0.54 and −0.62), and to a higher extent with compression (ranging between −0.80 and −0.94). Distinction between groups was clearer in the lower scales using entropy and in the higher scales using compression. Entropy and compression are complementary complexity measures.
      Citation: Entropy
      PubDate: 2017-12-14
      DOI: 10.3390/e19120688
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 689: Entropy Analysis for a Nonlinear Fluid with a
           Nonlinear Heat Flux Vector

    • Authors: Hyunjin Yang, Mehrdad Massoudi, A. Kirwan
      First page: 689
      Abstract: Flowing media in both industrial and natural processes are often characterized as assemblages of densely packed granular materials. Typically, the constitutive relations for the stress tensor and heat flux vector are fundamentally nonlinear. Moreover, these equations are coupled through the Clausius–Duhem inequality. However, the consequences of this coupling are rarely studied. Here we address this issue by obtaining constraints imposed by the Clausius–Duhem inequality on the constitutive relations for both the stress tensor and the heat flux vector in which the volume fraction gradient plays an important role. A crucial result of the analysis is the restriction on the dependency of phenomenological coefficients appearing in the constitutive equations on the model objective functions.
      Citation: Entropy
      PubDate: 2017-12-14
      DOI: 10.3390/e19120689
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 690: Non-Equilibrium Thermodynamic Analysis of
           Double Diffusive, Nanofluid Forced Convection in Catalytic Microreactors
           with Radiation Effects

    • Authors: Lilian Govone, Mohsen Torabi, Graeme Hunt, Nader Karimi
      First page: 690
      Abstract: This paper presents a theoretical investigation of the second law performance of double diffusive forced convection in microreactors with the inclusion of nanofluid and radiation effects. The investigated microreactors consist of a single microchannel, fully filled by a porous medium. The transport of heat and mass are analysed by including the thick walls and a first order, catalytic chemical reaction on the internal surfaces of the microchannel. Two sets of thermal boundary conditions are considered on the external surfaces of the microchannel; (1) constant temperature and (2) constant heat flux boundary condition on the lower wall and convective boundary condition on the upper wall. The local thermal non-equilibrium approach is taken to thermally analyse the porous section of the system. The mass dispersion equation is coupled with the transport of heat in the nanofluid flow through consideration of Soret effect. The problem is analytically solved and illustrations of the temperature fields, Nusselt number, total entropy generation rate and performance evaluation criterion (PEC) are provided. It is shown that the radiation effect tends to modify the thermal behaviour within the porous section of the system. The radiation parameter also reduces the overall temperature of the system. It is further demonstrated that, expectedly, the nanoparticles reduce the temperature of the system and increase the Nusselt number. The total entropy generation rate and consequently PEC shows a strong relation with radiation parameter and volumetric concentration of nanoparticles.
      Citation: Entropy
      PubDate: 2017-12-15
      DOI: 10.3390/e19120690
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 691: Spin Interaction under the Collision of Two
           Kerr-(Anti-)de Sitter Black Holes

    • Authors: Bogeun Gwak, Daeho Ro
      First page: 691
      Abstract: We investigate herein the spin interaction during collisions between Kerr-(anti-)de Sitter black holes. The spin interaction potential depends on the relative rotation directions of the black holes, and this potential can be released as gravitational radiation upon collision. The energy of the radiation depends on the cosmological constant and corresponds to the spin interaction potential in the limit that one of the black holes has negligibly small mass and angular momentum. We then determine the approximate overall behaviors of the upper bounds on the radiation using thermodynamics. The results indicate that the spin interaction can consistently contribute to the radiation. In addition, the radiation depends on the stability of the black hole produced by the collision.
      Citation: Entropy
      PubDate: 2017-12-15
      DOI: 10.3390/e19120691
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 692: Permutation Entropy: Too Complex a Measure
           for EEG Time Series'

    • Authors: Sebastian Berger, Gerhard Schneider, Eberhard Kochs, Denis Jordan
      First page: 692
      Abstract: Permutation entropy (PeEn) is a complexity measure that originated from dynamical systems theory. Specifically engineered to be robustly applicable to real-world data, the quantity has since been utilised for a multitude of time series analysis tasks. In electroencephalogram (EEG) analysis, value changes of PeEn correlate with clinical observations, among them the onset of epileptic seizures or the loss of consciousness induced by anaesthetic agents. Regarding this field of application, the present work suggests a relation between PeEn-based complexity estimation and spectral methods of EEG analysis: for ordinal patterns of three consecutive samples, the PeEn of an epoch of EEG appears to approximate the centroid of its weighted power spectrum. To substantiate this proposition, a systematic approach based on redundancy reduction is introduced and applied to sleep and epileptic seizure EEG. The interrelation demonstrated may aid the interpretation of PeEn in EEG, and may increase its comparability with other techniques of EEG analysis.
      Citation: Entropy
      PubDate: 2017-12-16
      DOI: 10.3390/e19120692
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 693: Stochastic Thermodynamics: A Dynamical
           Systems Approach

    • Authors: Tanmay Rajpurohit, Wassim M. Haddad
      First page: 693
      Abstract: In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time.
      Citation: Entropy
      PubDate: 2017-12-17
      DOI: 10.3390/e19120693
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 694: Combined Forecasting of Rainfall Based on
           Fuzzy Clustering and Cross Entropy

    • Authors: Baohui Men, Rishang Long, Yangsong Li, Huanlong Liu, Wei Tian, Zhijian Wu
      First page: 694
      Abstract: Rainfall is an essential index to measure drought, and it is dependent upon various parameters including geographical environment, air temperature and pressure. The nonlinear nature of climatic variables leads to problems such as poor accuracy and instability in traditional forecasting methods. In this paper, the combined forecasting method based on data mining technology and cross entropy is proposed to forecast the rainfall with full consideration of the time-effectiveness of historical data. In view of the flaws of the fuzzy clustering method which is easy to fall into local optimal solution and low speed of operation, the ant colony algorithm is adopted to overcome these shortcomings and, as a result, refine the model. The method for determining weights is also improved by using the cross entropy. Besides, the forecast is conducted by analyzing the weighted average rainfall based on Thiessen polygon in the Beijing–Tianjin–Hebei region. Since the predictive errors are calculated, the results show that improved ant colony fuzzy clustering can effectively select historical data and enhance the accuracy of prediction so that the damage caused by extreme weather events like droughts and floods can be greatly lessened and even kept at bay.
      Citation: Entropy
      PubDate: 2017-12-19
      DOI: 10.3390/e19120694
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 695: Molecular Conformational Manifolds between
           Gas-Liquid Interface and Multiphasic

    • Authors: Rasoul Nasiri, Kai Hong Luo
      First page: 695
      Abstract: The analysis of conformational changes of hydrocarbon molecules is imperative in the prediction of their transport properties in different phases, such as evaporation/condensation coefficients (β) in the gas-liquid interface and evaporation rates of fuel droplets (k) in multiphases. In this letter, we analyze the effects of entropic contributions ( T Δ S e v ( T ) ) to Δ G e v ( T ) during the evaporation/condensation of chain conformers at the interface with a modified version of the solvation model SMD/ωB97X-D/cc-pVTZ in which the temperature dependency of surface tension and the interfacial flow density of the conformers is taken into account. The evaporation/condensation coefficient (β) and evaporation rate (k) are respectively calculated using the statistical associating fluid theory (SAFT) and a combined quantum-classical reaction rate theory named quantum transition state theory-classical kinetic gas theory (QTST-CKGT). The detailed analyses show the importance of internal entropic states over the interfacial layer induced by meso-confinement phenomena in the very vicinity of fuel droplets surfaces.
      Citation: Entropy
      PubDate: 2017-12-19
      DOI: 10.3390/e19120695
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 696: Hypothesis Tests for Bernoulli Experiments:
           Ordering the Sample Space by Bayes Factors and Using Adaptive Significance
           Levels for Decisions

    • Authors: Carlos Pereira, Eduardo Nakano, Victor Fossaluza, Luís Esteves, Mark Gannon, Adriano Polpo
      First page: 696
      Abstract: The main objective of this paper is to find the relation between the adaptive significance level presented here and the sample size. We statisticians know of the inconsistency, or paradox, in the current classical tests of significance that are based on p-value statistics that are compared to the canonical significance levels (10%, 5%, and 1%): “Raise the sample to reject the null hypothesis” is the recommendation of some ill-advised scientists! This paper will show that it is possible to eliminate this problem of significance tests. We present here the beginning of a larger research project. The intention is to extend its use to more complex applications such as survival analysis, reliability tests, and other areas. The main tools used here are the Bayes factor and the extended Neyman–Pearson Lemma.
      Citation: Entropy
      PubDate: 2017-12-20
      DOI: 10.3390/e19120696
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 697: Normalised Mutual Information of High-Density
           Surface Electromyography during Muscle Fatigue

    • Authors: Adrian Bingham, Sridhar Arjunan, Beth Jelfs, Dinesh Kumar
      First page: 697
      Abstract: This study has developed a technique for identifying the presence of muscle fatigue based on the spatial changes of the normalised mutual information (NMI) between multiple high density surface electromyography (HD-sEMG) channels. Muscle fatigue in the tibialis anterior (TA) during isometric contractions at 40% and 80% maximum voluntary contraction levels was investigated in ten healthy participants (Age range: 21 to 35 years; Mean age = 26 years; Male = 4, Female = 6). HD-sEMG was used to record 64 channels of sEMG using a 16 by 4 electrode array placed over the TA. The NMI of each electrode with every other electrode was calculated to form an NMI distribution for each electrode. The total NMI for each electrode (the summation of the electrode’s NMI distribution) highlighted regions of high dependence in the electrode array and was observed to increase as the muscle fatigued. To summarise this increase, a function, M(k), was defined and was found to be significantly affected by fatigue and not by contraction force. The technique discussed in this study has overcome issues regarding electrode placement and was used to investigate how the dependences between sEMG signals within the same muscle change spatially during fatigue.
      Citation: Entropy
      PubDate: 2017-12-20
      DOI: 10.3390/e19120697
      Issue No: Vol. 19, No. 12 (2017)
  • Entropy, Vol. 19, Pages 698: A Geodesic-Based Riemannian Gradient Approach
           to Averaging on the Lorentz Group

    • Authors: Jing Wang, Huafei Sun, Didong Li
      First page: 698
      Abstract: In this paper, we propose an efficient algorithm to solve the averaging problem on the Lorentz group O ( n , k ) . Firstly, we introduce the geometric structures of O ( n , k ) endowed with a Riemannian metric where geodesic could be written in closed form. Then, the algorithm is presented based on the Riemannian-steepest-descent approach. Finally, we compare the above algorithm with the Euclidean gradient algorithm and the extended Hamiltonian algorithm. Numerical experiments show that the geodesic-based Riemannian-steepest-descent algorithm performs the best in terms of the convergence rate.
      Citation: Entropy
      PubDate: 2017-12-20
      DOI: 10.3390/e19120698
      Issue No: Vol. 19, No. 12 (2017)
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