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Entropy, Volume 19, Issue 12 (December 2017)

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Cover Story (view full-size image) The combined application of the Bayesian Model Selection and Maximum Entropy sharply differentiates [...] Read more.
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Open AccessArticle A Geodesic-Based Riemannian Gradient Approach to Averaging on the Lorentz Group
Entropy 2017, 19(12), 698; https://doi.org/10.3390/e19120698
Received: 19 November 2017 / Revised: 16 December 2017 / Accepted: 17 December 2017 / Published: 20 December 2017
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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
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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. Full article
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Open AccessArticle Normalised Mutual Information of High-Density Surface Electromyography during Muscle Fatigue
Entropy 2017, 19(12), 697; https://doi.org/10.3390/e19120697
Received: 15 September 2017 / Revised: 8 December 2017 / Accepted: 18 December 2017 / Published: 20 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Information Theory Applied to Physiological Signals)
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Open AccessArticle Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions
Entropy 2017, 19(12), 696; https://doi.org/10.3390/e19120696
Received: 31 August 2017 / Revised: 18 December 2017 / Accepted: 18 December 2017 / Published: 20 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
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Open AccessLetter Molecular Conformational Manifolds between Gas-Liquid Interface and Multiphasic
Entropy 2017, 19(12), 695; https://doi.org/10.3390/e19120695
Received: 27 October 2017 / Revised: 11 December 2017 / Accepted: 12 December 2017 / Published: 19 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Nonequilibrium Thermodynamics of Interfaces)
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Open AccessArticle Combined Forecasting of Rainfall Based on Fuzzy Clustering and Cross Entropy
Entropy 2017, 19(12), 694; https://doi.org/10.3390/e19120694
Received: 31 August 2017 / Revised: 5 December 2017 / Accepted: 14 December 2017 / Published: 19 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
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Open AccessArticle Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law
Entropy 2017, 19(12), 681; https://doi.org/10.3390/e19120681
Received: 1 November 2017 / Revised: 3 December 2017 / Accepted: 6 December 2017 / Published: 19 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
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Open AccessArticle Stochastic Thermodynamics: A Dynamical Systems Approach
Entropy 2017, 19(12), 693; https://doi.org/10.3390/e19120693
Received: 16 October 2017 / Revised: 13 December 2017 / Accepted: 13 December 2017 / Published: 17 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Open AccessArticle Permutation Entropy: Too Complex a Measure for EEG Time Series?
Entropy 2017, 19(12), 692; https://doi.org/10.3390/e19120692
Received: 16 November 2017 / Revised: 11 December 2017 / Accepted: 13 December 2017 / Published: 16 December 2017
Cited by 1 | PDF Full-text (1364 KB) | HTML Full-text | XML Full-text | Supplementary Files
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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Permutation Entropy & Its Interdisciplinary Applications)
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Open AccessArticle Spin Interaction under the Collision of Two Kerr-(Anti-)de Sitter Black Holes
Entropy 2017, 19(12), 691; https://doi.org/10.3390/e19120691
Received: 8 November 2017 / Revised: 8 December 2017 / Accepted: 14 December 2017 / Published: 15 December 2017
Cited by 4 | PDF Full-text (476 KB) | HTML Full-text | XML Full-text
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
[...] Read more.
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. Full article
(This article belongs to the Section Astrophysics and Cosmology)
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Open AccessArticle Non-Equilibrium Thermodynamic Analysis of Double Diffusive, Nanofluid Forced Convection in Catalytic Microreactors with Radiation Effects
Entropy 2017, 19(12), 690; https://doi.org/10.3390/e19120690
Received: 11 October 2017 / Revised: 27 November 2017 / Accepted: 14 December 2017 / Published: 15 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Non-Equilibrium Thermodynamics of Micro Technologies)
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Open AccessArticle Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector
Entropy 2017, 19(12), 689; https://doi.org/10.3390/e19120689
Received: 19 October 2017 / Revised: 5 December 2017 / Accepted: 11 December 2017 / Published: 14 December 2017
Cited by 1 | PDF Full-text (233 KB) | HTML Full-text | XML Full-text
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,
[...] Read more.
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. Full article
(This article belongs to the Section Thermodynamics)
Open AccessArticle Entropy and Compression Capture Different Complexity Features: The Case of Fetal Heart Rate
Entropy 2017, 19(12), 688; https://doi.org/10.3390/e19120688
Received: 21 September 2017 / Revised: 28 November 2017 / Accepted: 11 December 2017 / Published: 14 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Information Theory Applied to Physiological Signals)
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Open AccessArticle Choosing between Higher Moment Maximum Entropy Models and Its Application to Homogeneous Point Processes with Random Effects
Entropy 2017, 19(12), 687; https://doi.org/10.3390/e19120687
Received: 29 August 2017 / Revised: 7 December 2017 / Accepted: 9 December 2017 / Published: 14 December 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
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Open AccessArticle Extremal Matching Energy of Random Polyomino Chains
Entropy 2017, 19(12), 684; https://doi.org/10.3390/e19120684
Received: 21 October 2017 / Revised: 9 December 2017 / Accepted: 11 December 2017 / Published: 14 December 2017
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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
[...] Read more.
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. Full article
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Open AccessArticle Do We Really Need to Catch Them All? A New User-Guided Social Media Crawling Method
Entropy 2017, 19(12), 686; https://doi.org/10.3390/e19120686
Received: 18 October 2017 / Revised: 28 November 2017 / Accepted: 11 December 2017 / Published: 13 December 2017
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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
[...] Read more.
[-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. Full article
(This article belongs to the Special Issue Entropy and Complexity of Data)
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