Entropy

14 pages, 375 KiB

Open AccessArticle

Application of the Permutation Entropy over the Heart Rate Variability for the Improvement of Electrocardiogram-based Sleep Breathing Pause Detection

by Antonio G. Ravelo-García^1,*, Juan L. Navarro-Mesa¹

, Ubay Casanova-Blancas¹, Sofia Martin-Gonzalez¹, Pedro Quintana-Morales¹, Iván Guerra-Moreno¹, José M. Canino-Rodríguez² and Eduardo Hernández-Pérez¹

¹ Institute for Technological Development and Innovation in Communications, Universidad de Las Palmas de Gran Canaria, Las Palmas de Gran Canaria 35017, Spain

² Institute of Oceanography and Global Change, Universidad de Las Palmas de Gran Canaria, Las Palmas de Gran Canaria 35017, Spain

Entropy 2015, 17(3), 914-927; https://doi.org/10.3390/e17030914 - 20 Feb 2015

Cited by 46 | Viewed by 8472

Abstract

In this paper the permutation entropy (PE) obtained from heart rate variability (HRV) is analyzed in a statistical model. In this model we also integrate other feature extraction techniques, the cepstrum coefficients derived from the same HRV and a set of band powers [...] Read more.

In this paper the permutation entropy (PE) obtained from heart rate variability (HRV) is analyzed in a statistical model. In this model we also integrate other feature extraction techniques, the cepstrum coefficients derived from the same HRV and a set of band powers obtained from the electrocardiogram derived respiratory (EDR) signal. The aim of the model is detecting obstructive sleep apnea (OSA) events. For this purpose, we apply two statistical classification methods: Logistic Regression (LR) and Quadratic Discriminant Analysis (QDA). For testing the models we use seventy ECG recordings from the Physionet database which are divided into equal-size learning and testing sets. Both sets consist of 35 recordings, each containing a single ECG signal. In our experiments we have found that the features extracted from the EDR signal present a sensitivity of 65.6% and specificity of 87.7% (auc = 85) in the LR classifier, and sensitivity of 59.4% and specificity of 90.3% (auc = 83.9) in the QDA classifier. The HRV-based cepstrum coefficients present a sensitivity of 63.8% and specificity of 89.2% (auc = 86) in the LR classifier, and sensitivity of 67.2% and specificity of 86.8% (auc = 86.9) in the QDA. Subsequent tests show that the contribution of the permutation entropy increases the performance of the classifiers, implying that the complexity of RR interval time series play an important role in the breathing pauses detection. Particularly, when all features are jointly used, the quantification task reaches a sensitivity of 71.9% and specificity of 92.1% (auc = 90.3) for LR. Similarly, for QDA the sensitivity is 75.1% and the specificity is 90.5% (auc = 91.7). Full article

(This article belongs to the Special Issue Entropy in Bioinspired Intelligence)

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22 pages, 1557 KiB

Open AccessArticle

Instantaneous 3D EEG Signal Analysis Based on Empirical Mode Decomposition and the Hilbert–Huang Transform Applied to Depth of Anaesthesia

by Mu-Tzu Shih¹, Faiyaz Doctor², Shou-Zen Fan³

, Kuo-Kuang Jen⁴ and Jiann-Shing Shieh^1,5,*

¹ Department of Mechanical Engineering, and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Taoyuan, Chung-Li 32003, Taiwan

² Department of Computing, Faculty of Engineering & Computing, Coventry University, Coventry, CV15FB, UK

³ Department of Anesthesiology, College of Medicine, National Taiwan University, Taipei 100, Taiwan

⁴ National Chung-Shan Institute of Science and Technology, Taoyuan, Longtan 32500, Taiwan

⁵ Center for Dynamical Biomarkers and Translational Medicine, National Central University, Chung-Li 32001, Taiwan

Entropy 2015, 17(3), 928-949; https://doi.org/10.3390/e17030928 - 20 Feb 2015

Cited by 20 | Viewed by 10108

Abstract

Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We can [...] Read more.

Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We can monitor the DoA by observing the patient’s electroencephalography (EEG) signals during the surgical procedure. Typically high frequency EEG signals indicates the patient is conscious, while low frequency signals mean the patient is in a general anaesthetic state. If the anaesthetist is able to observe the instantaneous frequency changes of the patient’s EEG signals during surgery this can help to better regulate and monitor DoA, reducing surgical and post-operative risks. This paper describes an approach towards the development of a 3D real-time visualization application which can show the instantaneous frequency and instantaneous amplitude of EEG simultaneously by using empirical mode decomposition (EMD) and the Hilbert–Huang transform (HHT). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions (IMFs). The Hilbert spectral analysis method is then used to obtain instantaneous frequency data. The HHT provides a new method of analyzing non-stationary and nonlinear time series data. We investigate this approach by analyzing EEG data collected from patients undergoing surgical procedures. The results show that the EEG differences between three distinct surgical stages computed by using sample entropy (SampEn) are consistent with the expected differences between these stages based on the bispectral index (BIS), which has been shown to be quantifiable measure of the effect of anaesthetics on the central nervous system. Also, the proposed filtering approach is more effective compared to the standard filtering method in filtering out signal noise resulting in more consistent results than those provided by the BIS. The proposed approach is therefore able to distinguish between key operational stages related to DoA, which is consistent with the clinical observations. SampEn can also be viewed as a useful index for evaluating and monitoring the DoA of a patient when used in combination with this approach. Full article

(This article belongs to the Special Issue Entropy and Electroencephalography)

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Graphical abstract

18 pages, 2371 KiB

Open AccessArticle

Entropy Rate Maps of Complex Excitable Dynamics in Cardiac Monolayers

by Alexander Schlemmer^1,2, Sebastian Berg^1,2, T. K. Shajahan¹, Stefan Luther^1,2 and Ulrich Parlitz^1,2,*

¹ Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany

² Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17,37077 Göttingen, Germany

Entropy 2015, 17(3), 950-967; https://doi.org/10.3390/e17030950 - 26 Feb 2015

Cited by 5 | Viewed by 7242

Abstract

The characterization of spatiotemporal complexity remains a challenging task. This holds in particular for the analysis of data from fluorescence imaging (optical mapping), which allows for the measurement of membrane potential and intracellular calcium at high spatial and temporal resolutions and, therefore, allows [...] Read more.

The characterization of spatiotemporal complexity remains a challenging task. This holds in particular for the analysis of data from fluorescence imaging (optical mapping), which allows for the measurement of membrane potential and intracellular calcium at high spatial and temporal resolutions and, therefore, allows for an investigation of cardiac dynamics. Dominant frequency maps and the analysis of phase singularities are frequently used for this type of excitable media. These methods address some important aspects of cardiac dynamics; however, they only consider very specific properties of excitable media. To extend the scope of the analysis, we present a measure based on entropy rates for determining spatiotemporal complexity patterns of excitable media. Simulated data generated by the Aliev–Panfilov model and the cubic Barkley model are used to validate this method. Then, we apply it to optical mapping data from monolayers of cardiac cells from chicken embryos and compare our findings with dominant frequency maps and the analysis of phase singularities. The studies indicate that entropy rate maps provide additional information about local complexity, the origins of wave breakup and the development of patterns governing unstable wave propagation. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics)

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16 pages, 6666 KiB

Open AccessArticle

Do Transitive Preferences Always Result in Indifferent Divisions?

by Marcin Makowski^1,*, Edward W. Piotrowski¹ and Jan Sładkowski²

¹ Institute of Mathematics, University of Bialystok, Ciołkowskiego 1M, Pl-15245 Białystok, Poland

² Institute of Physics, University of Silesia, Uniwersytecka 4, Pl-40007 Katowice, Poland

Entropy 2015, 17(3), 968-983; https://doi.org/10.3390/e17030968 - 2 Mar 2015

Cited by 12 | Viewed by 6320

Abstract

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with the rationality of choice and is considered useful in building rankings. Intransitive preferences are considered paradoxical and undesirable. This problem [...] Read more.

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with the rationality of choice and is considered useful in building rankings. Intransitive preferences are considered paradoxical and undesirable. This problem is discussed by many social and natural scientists. A simple model of a sequential game in which two players choose one of the two elements in each iteration is discussed in this paper. The players make their decisions in different contexts defined by the rules of the game. It appears that the optimal strategy of one of the players can only be intransitive (the so-called relevant intransitive strategy)! On the other hand, the optimal strategy for the second player can be either transitive or intransitive. A quantum model of the game using pure one-qubit strategies is considered. In this model, an increase in the importance of intransitive strategies is observed: there is a certain course of the game where intransitive strategies are the only optimal strategies for both players. The study of decision-making models using quantum information theory tools may shed some new light on the understanding of mechanisms that drive the formation of types of preferences. Full article

(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)

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23 pages, 5812 KiB

Open AccessArticle

Phytotoponyms, Geographical Features and Vegetation Coverage in Western Hubei, China

by Guanghui Shi¹, Fu Ren^1,2,*, Qingyun Du^1,2

and Nan Gao¹

¹ School of Resource and Environmental Science, Wuhan University, 129 Luoyu Road, Wuhan, 430079, China

² Key Laboratory of GIS, Ministry of Education, Wuhan University, 129 Luoyu Road, Wuhan, 430079, China

Entropy 2015, 17(3), 984-1006; https://doi.org/10.3390/e17030984 - 2 Mar 2015

Cited by 12 | Viewed by 6654

Abstract

The purpose of this paper is to present and exploit fundamental information, such as semantic meanings and geographical features, of phytotoponyms (a type of toponym that includes plant names) in Western Hubei (China). Long-term vegetation degradation is also estimated. Toponym data for this [...] Read more.

The purpose of this paper is to present and exploit fundamental information, such as semantic meanings and geographical features, of phytotoponyms (a type of toponym that includes plant names) in Western Hubei (China). Long-term vegetation degradation is also estimated. Toponym data for this study were obtained from the place names database of Hubei Province at the Civil Affairs Department of Hubei. In total, 1259 instances of phytotoponyms were recognised; 898 (71.3%) were woody plant toponyms, and 361 (28.7%) were herbaceous plant toponyms. Subsequently, we randomly selected a similar number (1250) of non-phytotoponyms to compare with the phytotoponyms. All toponyms were localised and geo-referenced. The results showed that the most common plant names recognisable in place names are common plants that have a close connection with daily life and positive morals in Chinese culture and literature. The occurrence of plant names can reflect the characteristic plants of a city. The vegetation coverage rate where phytotoponyms are located is higher than that in non-phytotoponym areas. Altitude has a stronger correlation with the number of phytotoponyms than slope and vegetation coverage degree. The identification of long-term vegetation degradation based on phytotoponyms is presented for reference only, and other methods and materials are needed to validate these results. Full article

(This article belongs to the Special Issue Entropy and Space-Time Analysis in Environment and Health)

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16 pages, 288 KiB

Open AccessArticle

Entropy Measures in the Assessment of Heart Rate Variability in Patients with Cardiodepressive Vasovagal Syncope

by Beata Graff¹, Grzegorz Graff^2,*, Danuta Makowiec³, Agnieszka Kaczkowska², Dorota Wejer³, Szymon Budrejko⁴, Dariusz Kozłowski⁴ and Krzysztof Narkiewicz¹

¹ Hypertension Unit, Department of Hypertension and Diabetology, Medical University of Gdańsk, Dębinki 7c, 80-952 Gdańsk, Poland

² Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12,80-233 Gdańsk, Poland

³ Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952Gdańsk, Poland

⁴ Department of Cardiology and Electrotherapy, Medical University of Gdańsk, Dębinki 7, 80-952Gdańsk, Poland

Entropy 2015, 17(3), 1007-1022; https://doi.org/10.3390/e17031007 - 2 Mar 2015

Cited by 20 | Viewed by 6390

Abstract

Sample entropy (SampEn) was reported to be useful in the assessment of the complexity of heart rate dynamics. Permutation entropy (PermEn) is a new measure based on the concept of order and was previously shown to be accurate for short, non-stationary datasets. The [...] Read more.

Sample entropy (SampEn) was reported to be useful in the assessment of the complexity of heart rate dynamics. Permutation entropy (PermEn) is a new measure based on the concept of order and was previously shown to be accurate for short, non-stationary datasets. The aim of the present study is to assess if SampEn and PermEn obtained from baseline recordings might differentiate patients with various outcomes of the head-up tilt test (HUTT). Time-domain heart rate variability (HRV) indices and several nonlinear parameters were calculated using 500 RR interval-long ECG recordings done before tilting in patients with a history suggesting vasovagal syncope. Groups of patients with so-called cardiodepressive vasovagal syncope (VVS_2) during HUTT and patients who did not faint during the test were compared. Two types of HUT tests were analyzed: with spontaneous (SB) or controlled breathing (CB). In our study, SampEn was higher in VVS_2 patients during SB, and PermEn was higher in VVS_2 patients during CB. Irrespective of the type of breathing during the test, SampEn and PermEn were similar in patients with the same type of reaction during HUTT. The use of several entropy-based parameters seems to be useful in HRV assessment in patients with vasovagal fainting. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics)

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19 pages, 1546 KiB

Open AccessArticle

Mining Informative Hydrologic Data by Using Support Vector Machines and Elucidating Mined Data according to Information Entropy

by Shien-Tsung Chen

Department of Water Resources Engineering and Conservation, Feng Chia University, No. 100, Wenhua Road, Taichung City 40724, Taiwan

Entropy 2015, 17(3), 1023-1041; https://doi.org/10.3390/e17031023 - 2 Mar 2015

Cited by 16 | Viewed by 5749

Abstract

The support vector machine is used as a data mining technique to extract informative hydrologic data on the basis of a strong relationship between error tolerance and the number of support vectors. Hydrologic data of flash flood events in the Lan-Yang River basin [...] Read more.

The support vector machine is used as a data mining technique to extract informative hydrologic data on the basis of a strong relationship between error tolerance and the number of support vectors. Hydrologic data of flash flood events in the Lan-Yang River basin in Taiwan were used for the case study. Various percentages (from 50% to 10%) of hydrologic data, including those for flood stage and rainfall data, were mined and used as informative data to characterize a flood hydrograph. Information on these mined hydrologic data sets was quantified using entropy indices, namely marginal entropy, joint entropy, transinformation, and conditional entropy. Analytical results obtained using the entropy indices proved that the mined informative data could be hydrologically interpreted and have a meaningful explanation based on information entropy. Estimates of marginal and joint entropies showed that, in view of flood forecasting, the flood stage was a more informative variable than rainfall. In addition, hydrologic models with variables containing more total information were preferable to variables containing less total information. Analysis results of transinformation explained that approximately 30% of information on the flood stage could be derived from the upstream flood stage and 10% to 20% from the rainfall. Elucidating the mined hydrologic data by applying information theory enabled using the entropy indices to interpret various hydrologic processes. Full article

(This article belongs to the Special Issue Entropy and Space-Time Analysis in Environment and Health)

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12 pages, 873 KiB

Open AccessArticle

Tone Entropy Analysis of Foetal Heart Rate Variability

by Ahsan Khandoker^1,2,*, Chandan Karmakar^1,5, Yoshitaka Kimura^3,4, Miyuki Endo³, Sayaka Oshio³ and Marimuthu Palaniswami¹

¹ Biomedical Engineering Department, Khalifa University of Science, Technology and Research, Abu Dhabi 127788, United Arab Emirates

² Department of Electrical & Electronic Engineering, University of Melbourne, Melbourne, VIC 3010, Australia

³ Institute of International Advanced Interdisciplinary Research, Tohoku University School of Medicine, Sendai 980-8577, Japan

⁴ Department of Gynecology and Obstetrics, Tohoku University Hospital, Sendai 980-8577, Japan

⁵ Centre for Pattern Recognition and Data Analytics, Deakin University, VIC 3216, Australia

Entropy 2015, 17(3), 1042-1053; https://doi.org/10.3390/e17031042 - 2 Mar 2015

Cited by 6 | Viewed by 6632

Abstract

Development of the foetal autonomic nervous system can be indirectly understood by looking at the changes in beat to beat variability in foetal heart rates. This study presents Tone-Entropy (T-E) analysis of foetal heart rate variability (HRV) at multiple lags (1–8) to understand [...] Read more.

Development of the foetal autonomic nervous system can be indirectly understood by looking at the changes in beat to beat variability in foetal heart rates. This study presents Tone-Entropy (T-E) analysis of foetal heart rate variability (HRV) at multiple lags (1–8) to understand the influence of gestational ages (early and late) on the development of the foetal autonomic nervous system (ANS). The analysis was based on foetal electrocardiograms (FECGs) of 46 healthy foetuses of 20–32 weeks (early group) and 22 foetuses of 35–41 weeks (late group). Tone represents sympatho-vagal balance and entropy the total autonomic activities. Results show that tone increases and entropy decreases at all lags for the late foetus group. On the other hand, tone decreases and entropy increases at lags 1–4 in the early foetus group. Increasing tone in late foetuses might represent significant maturation of sympathetic nervous systems because foetuses approaching to delivery period need increased sympathetic activity. T-E could be quantitative clinical index to determine the early foetuses from late ones on the basis of maturation of autonomic nervous system. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics)

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9 pages, 127 KiB

Open AccessArticle

The Hosoya Entropy of a Graph

by Abbe Mowshowitz^1,*

and Matthias Dehmer^2,3

¹ Department of Computer Science, The City College of New York (CUNY), 138th Street at Convent Avenue, New York, NY 10031, USA

² Department of Biomedical Computer Science and Mechatronics, UMIT, Eduard Wallnoefer Zentrum 1, A-6060, Hall in Tyrol, Austria

³ Department of Computer Science, Universität der Bundeswehr München, Werner Heisenberg Weg 39, D-85579 Neubiberg, Germany

Entropy 2015, 17(3), 1054-1062; https://doi.org/10.3390/e17031054 - 5 Mar 2015

Cited by 18 | Viewed by 5574

Abstract

This paper demonstrates properties of Hosoya entropy, a quantitative measure of graph complexity based on a decomposition of the vertices linked to partial Hosoya polynomials. Connections between the information content of a graph and Hosoya entropy are established, and the special case of [...] Read more.

This paper demonstrates properties of Hosoya entropy, a quantitative measure of graph complexity based on a decomposition of the vertices linked to partial Hosoya polynomials. Connections between the information content of a graph and Hosoya entropy are established, and the special case of Hosoya entropy of trees is investigated. Full article

(This article belongs to the Section Complexity)

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27 pages, 1233 KiB

Open AccessArticle

Fully Bayesian Experimental Design for Pharmacokinetic Studies

by Elizabeth G. Ryan^1,2,*, Christopher C. Drovandi¹ and Anthony N. Pettitt^1,3

¹ Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane 4001, Australia

² Biostatistics Department, Institute of Psychiatry, King's College London, London SE5 8AF, UK

³ ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane 4001, Australia

Entropy 2015, 17(3), 1063-1089; https://doi.org/10.3390/e17031063 - 5 Mar 2015

Cited by 35 | Viewed by 7637

Abstract

Utility functions in Bayesian experimental design are usually based on the posterior distribution. When the posterior is found by simulation, it must be sampled from for each future dataset drawn from the prior predictive distribution. Many thousands of posterior distributions are often required. [...] Read more.

Utility functions in Bayesian experimental design are usually based on the posterior distribution. When the posterior is found by simulation, it must be sampled from for each future dataset drawn from the prior predictive distribution. Many thousands of posterior distributions are often required. A popular technique in the Bayesian experimental design literature, which rapidly obtains samples from the posterior, is importance sampling, using the prior as the importance distribution. However, importance sampling from the prior will tend to break down if there is a reasonable number of experimental observations. In this paper, we explore the use of Laplace approximations in the design setting to overcome this drawback. Furthermore, we consider using the Laplace approximation to form the importance distribution to obtain a more efficient importance distribution than the prior. The methodology is motivated by a pharmacokinetic study, which investigates the effect of extracorporeal membrane oxygenation on the pharmacokinetics of antibiotics in sheep. The design problem is to find 10 near optimal plasma sampling times that produce precise estimates of pharmacokinetic model parameters/measures of interest. We consider several different utility functions of interest in these studies, which involve the posterior distribution of parameter functions. Full article

(This article belongs to the Special Issue Entropy in Experimental Design, Sensor Placement, Inquiry and Search)

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13 pages, 241 KiB

Open AccessArticle

Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies

by Alexander L. Fradkov^1,2 and Dmitry S. Shalymov^2,*

¹ Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy ave. V.O., 199178 Saint-Petersburg, Russia

² Mathematics and Mechanics Faculty, Saint-Petersburg State University, Universitetsky prospekt, 28, 198504 Saint-Petersburg, Russia

Entropy 2015, 17(3), 1090-1102; https://doi.org/10.3390/e17031090 - 6 Mar 2015

Cited by 21 | Viewed by 5672

Abstract

In this paper we consider dynamics of non-stationary processes that follow the MaxEnt principle. We derive a set of equations describing dynamics of a system for Shannon and Tsallis entropies. Systems with discrete probability distribution are considered under mass conservation and energy conservation [...] Read more.

In this paper we consider dynamics of non-stationary processes that follow the MaxEnt principle. We derive a set of equations describing dynamics of a system for Shannon and Tsallis entropies. Systems with discrete probability distribution are considered under mass conservation and energy conservation constraints. The existence and uniqueness of solution are established and asymptotic stability of the equilibrium is proved. Equations are derived based on the speed-gradient principle originated in control theory. Full article

(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)

20 pages, 905 KiB

Open AccessArticle

Weakest-Link Scaling and Extreme Events in Finite-Sized Systems

by Dionissios T. Hristopulos^1,*, Manolis P. Petrakis¹ and Giorgio Kaniadakis²

¹ School of Mineral Resources Engineering, Technical University of Crete, Chania 73100, Greece

² Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24,10129 Torino, Italy

Entropy 2015, 17(3), 1103-1122; https://doi.org/10.3390/e17031103 - 9 Mar 2015

Cited by 13 | Viewed by 6981

Abstract

Weakest-link scaling is used in the reliability analysis of complex systems. It is characterized by the extensivity of the hazard function instead of the entropy. The Weibull distribution is the archetypical example of weakest-link scaling, and it describes variables such as the fracture [...] Read more.

Weakest-link scaling is used in the reliability analysis of complex systems. It is characterized by the extensivity of the hazard function instead of the entropy. The Weibull distribution is the archetypical example of weakest-link scaling, and it describes variables such as the fracture strength of brittle materials, maximal annual rainfall, wind speed and earthquake return times. We investigate two new distributions that exhibit weakest-link scaling, i.e., a Weibull generalization known as the κ-Weibull and a modified gamma probability function that we propose herein. We show that in contrast with the Weibull and the modified gamma, the hazard function of the κ -Weibull is non-extensive, which is a signature of inter-dependence between the links. We also investigate the impact of heterogeneous links, modeled by means of a stochastic Weibull scale parameter, on the observed probability distribution. Full article

(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)

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Graphical abstract

12 pages, 1009 KiB

Open AccessArticle

Projective Synchronization for a Class of Fractional-Order Chaotic Systems with Fractional-Order in the (1, 2) Interval

by Ping Zhou^1,*, Rongji Bai² and Jiming Zheng¹

¹ Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

² Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Entropy 2015, 17(3), 1123-1134; https://doi.org/10.3390/e17031123 - 10 Mar 2015

Cited by 8 | Viewed by 7446

Abstract

In this paper, a projective synchronization approach for a class of fractional-order chaotic systems with fractional-order 1 < q < 2 is demonstrated. The projective synchronization approach is established through precise theorization. To illustrate the effectiveness of the proposed scheme, we discuss two [...] Read more.

In this paper, a projective synchronization approach for a class of fractional-order chaotic systems with fractional-order 1 < q < 2 is demonstrated. The projective synchronization approach is established through precise theorization. To illustrate the effectiveness of the proposed scheme, we discuss two examples: (1) the fractional-order Lorenz chaotic system with fractional-order q = 1.1; (2) the fractional-order modified Chua’s chaotic system with fractional-order q = 1.02. The numerical simulations show the validity and feasibility of the proposed scheme. Full article

(This article belongs to the Section Complexity)

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11 pages, 200 KiB

Open AccessArticle

Comparing Security Notions of Secret Sharing Schemes

by Songsong Dai

and Donghui Guo^*

Department of Electronic Engineering, Xiamen University, Xiamen 361005, China

Entropy 2015, 17(3), 1135-1145; https://doi.org/10.3390/e17031135 - 10 Mar 2015

Cited by 6 | Viewed by 5194

Abstract

Different security notions of secret sharing schemes have been proposed by different information measures. Entropies, such as Shannon entropy and min entropy, are frequently used in the setting security notions for secret sharing schemes. Different to the entropies, Kolmogorov complexity was also defined [...] Read more.

Different security notions of secret sharing schemes have been proposed by different information measures. Entropies, such as Shannon entropy and min entropy, are frequently used in the setting security notions for secret sharing schemes. Different to the entropies, Kolmogorov complexity was also defined and used in study the security of individual instances for secret sharing schemes. This paper is concerned with these security notions for secret sharing schemes defined by the variational measures, including Shannon entropy, guessing probability, min entropy and Kolmogorov complexity. Full article

(This article belongs to the Special Issue Entropy-Based Applied Cryptography and Enhanced Security for Ubiquitous Computing)

19 pages, 211 KiB

Open AccessArticle

Maximum Relative Entropy Updating and the Value of Learning

by Patryk Dziurosz-Serafinowicz

Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, Groningen, 9712 GL, The Netherlands

Entropy 2015, 17(3), 1146-1164; https://doi.org/10.3390/e17031146 - 11 Mar 2015

Cited by 2 | Viewed by 5314

Abstract

We examine the possibility of justifying the principle of maximum relative entropy (MRE) considered as an updating rule by looking at the value of learning theorem established in classical decision theory. This theorem captures an intuitive requirement for learning: learning should lead to [...] Read more.

We examine the possibility of justifying the principle of maximum relative entropy (MRE) considered as an updating rule by looking at the value of learning theorem established in classical decision theory. This theorem captures an intuitive requirement for learning: learning should lead to new degrees of belief that are expected to be helpful and never harmful in making decisions. We call this requirement the value of learning. We consider the extent to which learning rules by MRE could satisfy this requirement and so could be a rational means for pursuing practical goals. First, by representing MRE updating as a conditioning model, we show that MRE satisfies the value of learning in cases where learning prompts a complete redistribution of one’s degrees of belief over a partition of propositions. Second, we show that the value of learning may not be generally satisfied by MRE updates in cases of updating on a change in one’s conditional degrees of belief. We explain that this is so because, contrary to what the value of learning requires, one’s prior degrees of belief might not be equal to the expectation of one’s posterior degrees of belief. This, in turn, points towards a more general moral: that the justification of MRE updating in terms of the value of learning may be sensitive to the context of a given learning experience. Moreover, this lends support to the idea that MRE is not a universal nor mechanical updating rule, but rather a rule whose application and justification may be context-sensitive. Full article

(This article belongs to the Special Issue Maximum Entropy Applied to Inductive Logic and Reasoning)

16 pages, 311 KiB

Open AccessArticle

Distributed Consensus for Metamorphic Systems Using a GossipAlgorithm for CAT(0) Metric Spaces

by Anass Bellachehab

Telecom SudParis, Institut Mines-Télécom, UMR CNRS 5157 SAMOVAR, 9 Rue Charles Fourier, 91000 Évry, France

Entropy 2015, 17(3), 1165-1180; https://doi.org/10.3390/e17031165 - 12 Mar 2015

Viewed by 4845

Abstract

We present an application of distributed consensus algorithms to metamorphic systems. A metamorphic system is a set of identical units that can self-assemble to form a rigid structure. For instance, one can think of a robotic arm composed of multiple links connected by [...] Read more.

We present an application of distributed consensus algorithms to metamorphic systems. A metamorphic system is a set of identical units that can self-assemble to form a rigid structure. For instance, one can think of a robotic arm composed of multiple links connected by joints. The system can change its shape in order to adapt to different environments via reconfiguration of its constituting units. We assume in this work that several metamorphic systems form a network: two systems are connected whenever they are able to communicate with each other. The aim of this paper is to propose a distributed algorithm that synchronizes all of the systems in the network. Synchronizing means that all of the systems should end up having the same configuration. This aim is achieved in two steps: (i) we cast the problem as a consensus problem on a metric space; and (ii) we use a recent distributed consensus algorithm that only makes use of metrical notions. Full article

(This article belongs to the Special Issue Information, Entropy and Their Geometric Structures)

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16 pages, 231 KiB

Open AccessArticle

Entropy of Quantum Measurement

by Hanna Podsȩdkowska

Faculty of Mathematics and Computer Sciences, University of Łódź, ul. S. Banacha 22, 90-238 Łódź, Poland

Entropy 2015, 17(3), 1181-1196; https://doi.org/10.3390/e17031181 - 12 Mar 2015

Cited by 4 | Viewed by 4162

Abstract

A notion of entropy of a normal state on a finite von Neumann algebra in Segal’s sense is considered, and its superadditivity is proven together with a necessary and sufficient condition for its additivity. Bounds on the entropy of the state after measurement [...] Read more.

A notion of entropy of a normal state on a finite von Neumann algebra in Segal’s sense is considered, and its superadditivity is proven together with a necessary and sufficient condition for its additivity. Bounds on the entropy of the state after measurement are obtained, and it is shown that a weakly repeatable measurement gives minimal entropy and that a minimal state entropy measurement satisfying some natural additional conditions is repeatable. Full article

7 pages, 2669 KiB

Open AccessCommunication

Generalized Multiscale Entropy Analysis: Application to Quantifying the Complex Volatility of Human Heartbeat Time Series

by Madalena D. Costa^1,* and Ary L. Goldberger^1,2

¹ Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA 02215, USA

² Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA 02215, USA

Entropy 2015, 17(3), 1197-1203; https://doi.org/10.3390/e17031197 - 12 Mar 2015

Cited by 143 | Viewed by 12592

Abstract

We introduce a generalization of multiscale entropy (MSE) analysis. The method is termed MSEn, where the subscript denotes the moment used to coarse-grain a time series. MSEμ, described previously, uses the mean value (first moment). Here, we focus on MSEσ2 , which uses [...] Read more.

We introduce a generalization of multiscale entropy (MSE) analysis. The method is termed MSEn, where the subscript denotes the moment used to coarse-grain a time series. MSEμ, described previously, uses the mean value (first moment). Here, we focus on MSEσ2 , which uses the second moment, i.e., the variance. MSEσ2 quantifies the dynamics of the volatility (variance) of a signal over multiple time scales. We use the method to analyze the structure of heartbeat time series. We find that the dynamics of the volatility of heartbeat time series obtained from healthy young subjects is highly complex. Furthermore, we find that the multiscale complexity of the volatility, not only the multiscale complexity of the mean heart rate, degrades with aging and pathology. The “bursty” behavior of the dynamics may be related to intermittency in energy and information flows, as part of multiscale cycles of activation and recovery. Generalized MSE may also be useful in quantifying the dynamical properties of other physiologic and of non-physiologic time series. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics)

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14 pages, 241 KiB

Open AccessArticle

Information Geometry on the \(\kappa\)-Thermostatistics

by Tatsuaki Wada^1,* and Antonio M. Scarfone²

¹ Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan

² Istituto dei Sistemi Complessi (ISC-CNR) c/o Politecnico di Torino, Corso Duca degli Abruzzi 24,I-10129 Torino, Italy

Entropy 2015, 17(3), 1204-1217; https://doi.org/10.3390/e17031204 - 12 Mar 2015

Cited by 14 | Viewed by 5723

Abstract

We explore the information geometric structure of the statistical manifold generated by the \(\kappa\)-deformed exponential family. The dually-flat manifold is obtained as a dualistic Hessian structure by introducing suitable generalization of the Fisher metric and affine connections. As a byproduct, we obtain the [...] Read more.

We explore the information geometric structure of the statistical manifold generated by the \(\kappa\)-deformed exponential family. The dually-flat manifold is obtained as a dualistic Hessian structure by introducing suitable generalization of the Fisher metric and affine connections. As a byproduct, we obtain the fluctuation-response relations in the \(\kappa\)-formalism based on the \(\kappa\)-generalized exponential family. Full article

(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)

18 pages, 4221 KiB

Open AccessArticle

Information Hiding Method Using Best DCT and Wavelet Coefficients and Its Watermark Competition

by Hyunho Kang^* and Keiichi Iwamura

Department of Electrical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, 125-8585 Tokyo, Japan

Entropy 2015, 17(3), 1218-1235; https://doi.org/10.3390/e17031218 - 12 Mar 2015

Cited by 10 | Viewed by 6684

Abstract

In recent years, information hiding and its evaluation criteria have been developed by the IHC (Information Hiding and its Criteria) Committee of Japan. This committee was established in 2011 with the aim of establishing standard evaluation criteria for robust watermarks. In this study, [...] Read more.

In recent years, information hiding and its evaluation criteria have been developed by the IHC (Information Hiding and its Criteria) Committee of Japan. This committee was established in 2011 with the aim of establishing standard evaluation criteria for robust watermarks. In this study, we developed an information hiding method that satisfies the IHC evaluation criteria. The proposed method uses the difference of the frequency coefficients derived from a discrete cosine transform or a discrete wavelet transform. The algorithm employs a statistical analysis to find the best positions in the frequency domains for watermark insertion. In particular, we use the BCH (Bose-Chaudhuri-Hocquenghem) (511,31,109) code to error correct the watermark bits and the BCH (63,16,11) code as the sync signal to withstand JPEG (Joint Photographic Experts Group) compression and cropping attacks. Our experimental results showed that there were no errors in 10 HDTV-size areas after the second decompression. It should be noted that after the second compression, the file size should be less than 1 25 of the original size to satisfy the IHC evaluation criteria. Full article

(This article belongs to the Special Issue Entropy-Based Applied Cryptography and Enhanced Security for Ubiquitous Computing)

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17 pages, 531 KiB

Open AccessArticle

Analysis of the Magnetocaloric Effect in Heusler Alloys: Study of Ni50CoMn36Sn13 by Calorimetric Techniques

by Elias Palacios¹, Juan Bartolomé¹, Gaofeng Wang¹, Ramon Burriel^1,*, Konstantin Skokov², Sergey Taskaev^3,4 and Vladimir Khovaylo^4,5

¹ Instituto de Ciencia de Materiales de Aragón (ICMA) and Dep. de Física de la Materia Condensada, CSIC - University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain

² Faculty of Physics, Tver State University, Tver 170000, Russia

³ Faculty of Physics, Chelyabinsk State University, Chelyabinsk 454001, Russia

⁴ National University of Science and Technology "MISiS", Moscow 119049, Russia

⁵ ITMO University, 49 Kronverksky Ave., St. Petersburg 197101, Russia

Entropy 2015, 17(3), 1236-1252; https://doi.org/10.3390/e17031236 - 12 Mar 2015

Cited by 14 | Viewed by 6541

Abstract

Direct determinations of the isothermal entropy increment, \(-\Delta S_T\), in the Heusler alloy Ni\(_{50}\)CoMn\(_{36}\)Sn\(_{13}\) on demagnetization gave positive values, corresponding to a normal magnetocaloric effect. These values contradict the results derived from heat-capacity measurements and also previous results obtained from magnetization measurements, which [...] Read more.

Direct determinations of the isothermal entropy increment, \(-\Delta S_T\), in the Heusler alloy Ni\(_{50}\)CoMn\(_{36}\)Sn\(_{13}\) on demagnetization gave positive values, corresponding to a normal magnetocaloric effect. These values contradict the results derived from heat-capacity measurements and also previous results obtained from magnetization measurements, which indicated an inverse magnetocaloric effect, but showing different values depending on the technique employed. The puzzle is solved, and the apparent incompatibilities are quantitatively explained considering the hysteresis, the width of the martensitic transition and the detailed protocol followed to obtain each datum. The results show that these factors should be analyzed in detail when dealing with Heusler alloys. Full article

(This article belongs to the Section Thermodynamics)

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20 pages, 9041 KiB

Open AccessArticle

Entropic Measures of Complexity of Short-Term Dynamics of Nocturnal Heartbeats in an Aging Population

by Danuta Makowiec^1,*, Agnieszka Kaczkowska², Dorota Wejer¹, Marta Żarczyńska-Buchowiecka³ and Zbigniew R. Struzik^1,4,5

¹ Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, ul. Wita Stwosza 57, Poland

² Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, 80-233 Gdańsk, ul. Narutowicza 11/12, Poland

³ Chair & Clinic of Cardiology, Medical University of Gdańsk, 80-211 Gdańsk, ul. Dȩbinki 7, Poland

⁴ RIKEN Brain Science Institute, 2-1 Hirosawa, 351-0198 Wako-shi, Japan

⁵ Graduate School of Education, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-0033 Tokyo, Japan

Entropy 2015, 17(3), 1253-1272; https://doi.org/10.3390/e17031253 - 13 Mar 2015

Cited by 20 | Viewed by 6435

Abstract

Two entropy-based approaches are investigated to study patterns describing differences in time intervals between consecutive heartbeats. The first method explores matrices arising from networks of transitions constructed following events represented by a time series. The second method considers distributions of ordinal patterns of [...] Read more.

Two entropy-based approaches are investigated to study patterns describing differences in time intervals between consecutive heartbeats. The first method explores matrices arising from networks of transitions constructed following events represented by a time series. The second method considers distributions of ordinal patterns of length three, whereby patterns with repeated values are counted as different patterns. Both methods provide estimators of dynamical aspects of short-term heartbeat signals obtained from nocturnal Holter electrocardiogram (ECG) recordings of healthy people of different ages and genders. The deceleration capacity, arising from the adjacency matrix of the network, and the entropy rate, resulting from the transition matrix of the network, are also calculated, and both significantly decay with aging. As people age, the permutation entropy grows, due to the increase in patterns with repeated values. All of these estimators describe in a consistent way changes in the beat-to-beat heart period dynamics caused by aging. An overall slowing down of heart period changes is observed, and an increase of permutation entropy results from the progressive increase of patterns with repeated values. This result points to the sympathetic drive becoming dominant in cardiac regulation of nocturnal heart rate with age. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics)

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5 pages, 193 KiB

Open AccessMeeting Report

Symmetry, Probabiliy, Entropy: Synopsis of the Lecture at MAXENT 2014

by Misha Gromov

Institut Hautes Études Scientifiques, 35, Route de Chartres, F-91440 Bures-sur-Yvette, France

Entropy 2015, 17(3), 1273-1277; https://doi.org/10.3390/e17031273 - 13 Mar 2015

Cited by 3 | Viewed by 6289

Abstract

In this discussion, we indicate possibilities for (homological and non-homological) linearization of basic notions of the probability theory and also for replacing the real numbers as values of probabilities by objects of suitable combinatorial categories. Full article

(This article belongs to the Special Issue Information, Entropy and Their Geometric Structures)

31 pages, 315 KiB

Open AccessArticle

Ricci Curvature, Isoperimetry and a Non-additive Entropy

by Nikos Kalogeropoulos

Weill Cornell Medical College in Qatar, Education City, PO Box 24144, Doha, Qatar

Entropy 2015, 17(3), 1278-1308; https://doi.org/10.3390/e17031278 - 16 Mar 2015

Cited by 10 | Viewed by 5750

Abstract

Searching for the dynamical foundations of Havrda-Charvát/Daróczy/ Cressie-Read/Tsallis non-additive entropy, we come across a covariant quantity called, alternatively, a generalized Ricci curvature, an N-Ricci curvature or a Bakry-Émery-Ricci curvature in the configuration/phase space of a system. We explore some of the implications [...] Read more.

Searching for the dynamical foundations of Havrda-Charvát/Daróczy/ Cressie-Read/Tsallis non-additive entropy, we come across a covariant quantity called, alternatively, a generalized Ricci curvature, an N-Ricci curvature or a Bakry-Émery-Ricci curvature in the configuration/phase space of a system. We explore some of the implications of this tensor and its associated curvature and present a connection with the non-additive entropy under investigation. We present an isoperimetric interpretation of the non-extensive parameter and comment on further features of the system that can be probed through this tensor. Full article

(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)

20 pages, 773 KiB

Open AccessArticle

A Link between Nano- and Classical Thermodynamics: Dissipation Analysis (The Entropy Generation Approach in Nano-Thermodynamics)

by Umberto Lucia

Dipartimento Energia, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129 Torino, Italy

Entropy 2015, 17(3), 1309-1328; https://doi.org/10.3390/e17031309 - 16 Mar 2015

Cited by 27 | Viewed by 7654

Abstract

The interest in designing nanosystems is continuously growing. Engineers apply a great number of optimization methods to design macroscopic systems. If these methods could be introduced into the design of small systems, a great improvement in nanotechnologies could be achieved. To do so, [...] Read more.

The interest in designing nanosystems is continuously growing. Engineers apply a great number of optimization methods to design macroscopic systems. If these methods could be introduced into the design of small systems, a great improvement in nanotechnologies could be achieved. To do so, however, it is necessary to extend classical thermodynamic analysis to small systems, but irreversibility is also present in small systems, as the Loschmidt paradox highlighted. Here, the use of the recent improvement of the Gouy-Stodola theorem to complex systems (GSGL approach), based on the use of entropy generation, is suggested to obtain the extension of classical thermodynamics to nanothermodynamics. The result is a new approach to nanosystems which avoids the difficulties highlighted in the usual analysis of the small systems, such as the definition of temperature for nanosystems. Full article

(This article belongs to the Special Issue Nanothermodynamics)

18 pages, 755 KiB

Open AccessArticle

Metriplectic Algebra for Dissipative Fluids in Lagrangian Formulation

by Massimo Materassi

Istituto dei Sistemi Complessi ISC-CNR, via Madonna del Piano 10, 50019 Sesto Fiorentino (Florence), Italy

Entropy 2015, 17(3), 1329-1346; https://doi.org/10.3390/e17031329 - 16 Mar 2015

Cited by 7 | Viewed by 5368

Abstract

The dynamics of dissipative fluids in Eulerian variables may be derived from an algebra of Leibniz brackets of observables, the metriplectic algebra, that extends the Poisson algebra of the frictionless limit of the system via a symmetric semidefinite component, encoding dissipative forces. [...] Read more.

The dynamics of dissipative fluids in Eulerian variables may be derived from an algebra of Leibniz brackets of observables, the metriplectic algebra, that extends the Poisson algebra of the frictionless limit of the system via a symmetric semidefinite component, encoding dissipative forces. The metriplectic algebra includes the conserved total Hamiltonian H, generating the non-dissipative part of dynamics, and the entropy S of those microscopic degrees of freedom draining energy irreversibly, which generates dissipation. This S is a Casimir invariant of the Poisson algebra to which the metriplectic algebra reduces in the frictionless limit. The role of S is as paramount as that of H, but this fact may be underestimated in the Eulerian formulation because S is not the only Casimir of the symplectic non-canonical part of the algebra. Instead, when the dynamics of the non-ideal fluid is written through the parcel variables of the Lagrangian formulation, the fact that entropy is symplectically invariant clearly appears to be related to its dependence on the microscopic degrees of freedom of the fluid, that are themselves in involution with the position and momentum of the parcel. Full article

(This article belongs to the Special Issue Selected Papers from 1st International Electronic Conference on Entropy and its Applications)

11 pages, 201 KiB

Open AccessArticle

Geometric Shrinkage Priors for Kählerian Signal Filters

by Jaehyung Choi^* and Andrew P. Mullhaupt

Department of Applied Mathematics and Statistics, State University of New York (SUNY), StonyBrook, NY 11794, USA

Entropy 2015, 17(3), 1347-1357; https://doi.org/10.3390/e17031347 - 17 Mar 2015

Cited by 1 | Viewed by 4497

Abstract

We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristics of Kähler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ansätze for the Bayesian predictive priors are also suggested. In [...] Read more.

We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristics of Kähler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ansätze for the Bayesian predictive priors are also suggested. In particular, the ansätze related to Kähler potential are geometrically intrinsic priors to the information manifold of which the geometry is derived from the potential. The implication of the algorithm to time series models is also provided. Full article

(This article belongs to the Special Issue Information, Entropy and Their Geometric Structures)

21 pages, 945 KiB

Open AccessArticle

Hidden State Conditional Random Field for Abnormal Activity Recognition in Smart Homes

by Yu Tong, Rong Chen^*

and Jian Gao

College of Information Science and Technology, Dalian Maritime University, Dalian 116026, China

Entropy 2015, 17(3), 1358-1378; https://doi.org/10.3390/e17031358 - 18 Mar 2015

Cited by 23 | Viewed by 6598

Abstract

As the number of elderly people has increased worldwide, there has been a surge of research into assistive technologies to provide them with better care by recognizing their normal and abnormal activities. However, existing abnormal activity recognition (AAR) algorithms rarely consider sub-activity relations [...] Read more.

As the number of elderly people has increased worldwide, there has been a surge of research into assistive technologies to provide them with better care by recognizing their normal and abnormal activities. However, existing abnormal activity recognition (AAR) algorithms rarely consider sub-activity relations when recognizing abnormal activities. This paper presents an application of the Hidden State Conditional Random Field (HCRF) method to detect and assess abnormal activities that often occur in elderly persons’ homes. Based on HCRF, this paper designs two AAR algorithms, and validates them by comparing them with a feature vector distance based algorithm in two experiments. The results demonstrate that the proposed algorithms favorably outperform the competitor, especially when abnormal activities have same sensor type and sensor number as normal activities. Full article

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8 pages, 197 KiB

Open AccessArticle

The Optimal Fix-Free Code for Anti-Uniform Sources

by Ali Zaghian¹, Adel Aghajan² and T. Aaron Gulliver^3,*

¹ Department of Mathematics and Cryptography, Malek Ashtar University of Technology, Isfahan 83145/115, Iran

² Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran

³ Department of Electrical and Computer Engineering, University of Victoria, PO Box 1700, STN CSC, Victoria, BC V8W 2Y2, Canada

Entropy 2015, 17(3), 1379-1386; https://doi.org/10.3390/e17031379 - 19 Mar 2015

Cited by 1 | Viewed by 4576

Abstract

An \(n\) symbol source which has a Huffman code with codelength vector \(L_{n}=(1,2,3,\cdots,n-2,n-1,n-1)\) is called an anti-uniform source. In this paper, it is shown that for this class of sources, the optimal fix-free code and symmetric fix-free code is \(C_{n}^{*}=(0,11,101,1001,\cdots,1\overbrace{0\cdots0}^{n-2}1) \) Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

24 pages, 850 KiB

Open AccessReview

Applied Cryptography Using Chaos Function for Fast Digital Logic-Based Systems in Ubiquitous Computing

by Piyush Kumar Shukla^1,*, Ankur Khare², Murtaza Abbas Rizvi³, Shalini Stalin⁴ and Sanjay Kumar⁵

¹ Computer Science & Engineering, University Institute of Technology, RGPV, Bhopal, Airport Bypass Road, Gandhi Nagar, Bhopal 462033, India

² Computer Science, Government Women's Polytechnic College, Sehore 462033, India

³ National Institute of Technical Teachers' Training and research, Shamla Hills, Bhopal 462001, India

⁴ AISECT, Scope Campus, Nh-12, Near Misrod,Hoshangabad Road, Bhopal 462047, India

⁵ Department of Information Technology, National Institutes of Technology, Raipur 492010, India

Entropy 2015, 17(3), 1387-1410; https://doi.org/10.3390/e17031387 - 19 Mar 2015

Cited by 44 | Viewed by 11428

Abstract

Recently, chaotic dynamics-based data encryption techniques for wired and wireless networks have become a topic of active research in computer science and network security such as robotic systems, encryption, and communication. The main aim of deploying a chaos-based cryptosystem is to provide encryption [...] Read more.

Recently, chaotic dynamics-based data encryption techniques for wired and wireless networks have become a topic of active research in computer science and network security such as robotic systems, encryption, and communication. The main aim of deploying a chaos-based cryptosystem is to provide encryption with several advantages over traditional encryption algorithms such as high security, speed, and reasonable computational overheads and computational power requirements. These challenges have motivated researchers to explore novel chaos-based data encryption techniques with digital logics dealing with hiding information for fast secure communication networks. This work provides an overview of how traditional data encryption techniques are revised and improved to achieve good performance in a secure communication network environment. A comprehensive survey of existing chaos-based data encryption techniques and their application areas are presented. The comparative tables can be used as a guideline to select an encryption technique suitable for the application at hand. Based on the limitations of the existing techniques, an adaptive chaos based data encryption framework of secure communication for future research is proposed Full article

(This article belongs to the Special Issue Entropy-Based Applied Cryptography and Enhanced Security for Ubiquitous Computing)

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14 pages, 1116 KiB

Open AccessArticle

Entropy Generation Analysis for a CNT Suspension Nanofluid in Plumb Ducts with Peristalsis

by Noreen Sher Akbar

DBS&H, CEME, National University of Sciences and Technology, Islamabad 44000, Pakistan

Entropy 2015, 17(3), 1411-1424; https://doi.org/10.3390/e17031411 - 19 Mar 2015

Cited by 49 | Viewed by 5976

Abstract

The purpose of the current investigation was to discuss the entropy generation analysis for a carbon nanotube (CNT) suspension nanofluid in a plumb duct with peristalsis. The entropy generation number due to heat transfer and fluid friction is formulated. The velocity and temperature [...] Read more.

The purpose of the current investigation was to discuss the entropy generation analysis for a carbon nanotube (CNT) suspension nanofluid in a plumb duct with peristalsis. The entropy generation number due to heat transfer and fluid friction is formulated. The velocity and temperature distributions across the tube are presented along with pressure attributes. Exact analytical solution for velocity and temperature profile are obtained. It is found that the entropy generation number attains high values in the region close to the walls of the tube, while it attains low values near the center of the tube. Full article

(This article belongs to the Section Thermodynamics)

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16 pages, 816 KiB

Open AccessArticle

A Comparison of Nonlinear Measures for the Detection of Cardiac Autonomic Neuropathy from Heart Rate Variability

by David Cornforth^1,2,*, Herbert F. Jelinek^3,4 and Mika Tarvainen^5,6

¹ Applied Informatics Research Group, Faculty of Science and IT, University of Newcastle, Newcastle, NSW 2308, Australia

² School of Engineering and Information Technology, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2610, Australia

³ Centre for Research in Complex Systems, School of Community Health, Charles Sturt University, Albury, NSW 2640, Australia

⁴ Australian School of Advanced Medicine, Macquarie University, Sydney, NSW 2109, Australia

⁵ University of Eastern Finland, Kuopio 70210, Finland

⁶ Kuopio University Hospital, Kuopio 70210, Finland

Entropy 2015, 17(3), 1425-1440; https://doi.org/10.3390/e17031425 - 19 Mar 2015

Cited by 33 | Viewed by 9047

Abstract

In this work we compare three multiscale measures for their ability to discriminate between participants having cardiac autonomic neuropathy (CAN) and aged controls. CAN is a disease that involves nerve damage leading to an abnormal control of heart rate, so one would expect [...] Read more.

In this work we compare three multiscale measures for their ability to discriminate between participants having cardiac autonomic neuropathy (CAN) and aged controls. CAN is a disease that involves nerve damage leading to an abnormal control of heart rate, so one would expect disease progression to manifest in changes to heart rate variability (HRV). We applied multiscale entropy (MSE), multi fractal detrended fluctuation analysis (MFDFA), and Renyi entropy (RE) to recorded datasets of RR intervals. The latter measure provided the best separation (lowest p-value in Mann–Whitney tests) between classes of participants having CAN, early CAN or no CAN (controls). This comparison suggests the efficacy of RE as a measure for diagnosis of CAN and its progression, when compared to the other multiscale measures. Full article

(This article belongs to the Special Issue Entropy and Cardiac Physics)

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Graphical abstract

11 pages, 231 KiB

Open AccessArticle

Approximated Information Analysis in Bayesian Inference

by Jung In Seo¹ and Yongku Kim^2,*

¹ Department of Statistics, Yeungnam University, Gyeongsan 712-749, Korea

² Department of Statistics, Kyungpook National University, Daegu 702-701, Korea

Entropy 2015, 17(3), 1441-1451; https://doi.org/10.3390/e17031441 - 20 Mar 2015

Cited by 4 | Viewed by 4702

Abstract

In models with nuisance parameters, Bayesian procedures based on Markov Chain Monte Carlo (MCMC) methods have been developed to approximate the posterior distribution of the parameter of interest. Because these procedures require burdensome computations related to the use of MCMC, approximation and convergence [...] Read more.

In models with nuisance parameters, Bayesian procedures based on Markov Chain Monte Carlo (MCMC) methods have been developed to approximate the posterior distribution of the parameter of interest. Because these procedures require burdensome computations related to the use of MCMC, approximation and convergence in these procedures are important issues. In this paper, we explore Gibbs sensitivity by using an alternative to the full conditional distribution of the nuisance parameter. The approximate sensitivity of the posterior distribution of interest is studied in terms of an information measure, including Kullback–Leibler divergence. As an illustration, we then apply these results to simple spatial model settings. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

14 pages, 768 KiB

Open AccessArticle

Thermodynamic Analysis of a Waste Heat Driven Vuilleumier Cycle Heat Pump

by Yingbai Xie^* and Xuejie Sun

Department of Power Engineering, North China Electric Power University, Baoding 07100, China

Entropy 2015, 17(3), 1452-1465; https://doi.org/10.3390/e17031452 - 20 Mar 2015

Cited by 7 | Viewed by 8116

Abstract

A Vuilleumier (VM) cycle heat pump is a closed gas cycle driven by heat energy. It has the highest performance among all known heat driven technologies. In this paper, two thermodynamic analyses, including energy and exergy analysis, are carried out to evaluate the [...] Read more.

A Vuilleumier (VM) cycle heat pump is a closed gas cycle driven by heat energy. It has the highest performance among all known heat driven technologies. In this paper, two thermodynamic analyses, including energy and exergy analysis, are carried out to evaluate the application of a VM cycle heat pump for waste heat utilization. For a prototype VM cycle heat pump, equations for theoretical and actual cycles are established. Under the given conditions, the exergy efficiency for the theoretical cycle is 0.23 compared to 0.15 for the actual cycle. This is due to losses taking place in the actual cycle. Reheat losses and flow friction losses account for almost 83% of the total losses. Investigation of the effect of heat source temperature, cycle pressure and speed on the exergy efficiency indicate that the low temperature waste heat is a suitable heat source for a VM cycle heat pump. The selected cycle pressure should be higher than 100 MPa, and 200–300 rpm is the optimum speed. Full article

(This article belongs to the Special Issue Exergy: Analysis and Applications)

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11 pages, 3049 KiB

Open AccessArticle

The Solute-Exclusion Zone: A Promising Application for Mirofluidics

by Chi-Shuo Chen¹, Erik Farr¹, Jesse M. Anaya¹, Eric Y-T Chen^1,2,3 and Wei-Chun Chin^1,*

¹ Bioengineering Department, University of California, Merced, CA 94343, USA

² MicroBase Technology Corp., Bade City, Taoyuan, 33464, Taiwan

³ Center for Biomedical Engineering, Chang Gung University, Taoyuan, 33302, Taiwan

Entropy 2015, 17(3), 1466-1476; https://doi.org/10.3390/e17031466 - 23 Mar 2015

Cited by 4 | Viewed by 6885

Abstract

While unique phenomena exist at fluid-solid phase intersections, many interfacial phenomena manifest solely on limited scales—i.e., the nm-mm ranges—which stifles their application potential. Here, we constructed microfluidic chips that utilize the unique long-distance interface effects of the Solute-Exclusion Zone (EZ) phenomenon [...] Read more.

While unique phenomena exist at fluid-solid phase intersections, many interfacial phenomena manifest solely on limited scales—i.e., the nm-mm ranges—which stifles their application potential. Here, we constructed microfluidic chips that utilize the unique long-distance interface effects of the Solute-Exclusion Zone (EZ) phenomenon to mix, separate, and guide samples in desired directions within microfluidic channels. On our “EZ Chip”, we utilized the interfacial force generated by EZs to transport specimens across streamlines without the need of an off-chip power source. The advantages of easy-integration, low fabrication cost, and no off-chip energy input make the EZ suitable for independent, portable lab-on-chip system applications. Full article

(This article belongs to the Special Issue Entropy and EZ-Water)

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31 pages, 1576 KiB

Open AccessArticle

Application of Divergence Entropy to Characterize the Structure of the Hydrophobic Core in DNA Interacting Proteins

by Barbara Kalinowska^1,2, Mateusz Banach^1,2

, Leszek Konieczny³ and Irena Roterman^1,*

¹ Department of Bioinformatics and Telemedicine, Collegium Medium, Jagiellonian University, Lazarza 16, 31-530 Krakow, Poland

² Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Łojasiewicza 11, Krakow, Poland

³ Chair of Medical Biochemistry, Collegium Medicum, Jagiellonian University, Kopernika 7, 31-034 Krakow, Poland

Entropy 2015, 17(3), 1477-1507; https://doi.org/10.3390/e17031477 - 23 Mar 2015

Cited by 55 | Viewed by 8111

Abstract

The fuzzy oil drop model, a tool which can be used to study the structure of the hydrophobic core in proteins, has been applied in the analysis of proteins belonging to the jumonji group—JARID2, JARID1A, JARID1B and JARID1D—proteins that share the property of [...] Read more.

The fuzzy oil drop model, a tool which can be used to study the structure of the hydrophobic core in proteins, has been applied in the analysis of proteins belonging to the jumonji group—JARID2, JARID1A, JARID1B and JARID1D—proteins that share the property of being able to interact with DNA. Their ARID and PHD domains, when analyzed in the context of the fuzzy oil drop model, are found to exhibit structural variability regarding the status of their secondary folds, including the β-hairpin which determines their biological function. Additionally, the structure of disordered fragments which are present in jumonji proteins (as confirmed by the DisProt database) is explained on the grounds of the hydrophobic core model, suggesting that such fragments contribute to tertiary structural stabilization. This conclusion is supported by divergence entropy measurements, expressing the degree of ordering in each protein’s hydrophobic core. Full article

(This article belongs to the Special Issue Entropy and RNA Structure, Folding and Mechanics)

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27 pages, 2748 KiB

Open AccessArticle

Space-Time Quantum Imaging

by Ronald E. Meyers^* and Keith S. Deacon

US Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783, USA

Entropy 2015, 17(3), 1508-1534; https://doi.org/10.3390/e17031508 - 23 Mar 2015

Cited by 5 | Viewed by 7113

Abstract

We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground [...] Read more.

We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time. Full article

(This article belongs to the Special Issue Entropy and Spacetime)

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Entropy, Volume 17, Issue 3 (March 2015) – 38 articles , Pages 914-1548

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