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

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Open AccessArticle
Clustering Heterogeneous Data with k-Means by Mutual Information-Based Unsupervised Feature Transformation
Entropy 2015, 17(3), 1535-1548; https://doi.org/10.3390/e17031535 - 23 Mar 2015
Cited by 14 | Viewed by 3320
Abstract
Traditional centroid-based clustering algorithms for heterogeneous data with numerical and non-numerical features result in different levels of inaccurate clustering. This is because the Hamming distance used for dissimilarity measurement of non-numerical values does not provide optimal distances between different values, and problems arise [...] Read more.
Traditional centroid-based clustering algorithms for heterogeneous data with numerical and non-numerical features result in different levels of inaccurate clustering. This is because the Hamming distance used for dissimilarity measurement of non-numerical values does not provide optimal distances between different values, and problems arise from attempts to combine the Euclidean distance and Hamming distance. In this study, the mutual information (MI)-based unsupervised feature transformation (UFT), which can transform non-numerical features into numerical features without information loss, was utilized with the conventional k-means algorithm for heterogeneous data clustering. For the original non-numerical features, UFT can provide numerical values which preserve the structure of the original non-numerical features and have the property of continuous values at the same time. Experiments and analysis of real-world datasets showed that, the integrated UFT-k-means clustering algorithm outperformed others for heterogeneous data with both numerical and non-numerical features. Full article
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Open AccessArticle
Space-Time Quantum Imaging
Entropy 2015, 17(3), 1508-1534; https://doi.org/10.3390/e17031508 - 23 Mar 2015
Cited by 3 | Viewed by 3035
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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Open AccessArticle
Application of Divergence Entropy to Characterize the Structure of the Hydrophobic Core in DNA Interacting Proteins
Entropy 2015, 17(3), 1477-1507; https://doi.org/10.3390/e17031477 - 23 Mar 2015
Cited by 39 | Viewed by 3995
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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Open AccessArticle
The Solute-Exclusion Zone: A Promising Application for Mirofluidics
Entropy 2015, 17(3), 1466-1476; https://doi.org/10.3390/e17031466 - 23 Mar 2015
Cited by 2 | Viewed by 2639
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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Open AccessArticle
Thermodynamic Analysis of a Waste Heat Driven Vuilleumier Cycle Heat Pump
Entropy 2015, 17(3), 1452-1465; https://doi.org/10.3390/e17031452 - 20 Mar 2015
Cited by 5 | Viewed by 3503
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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Open AccessArticle
Approximated Information Analysis in Bayesian Inference
Entropy 2015, 17(3), 1441-1451; https://doi.org/10.3390/e17031441 - 20 Mar 2015
Cited by 3 | Viewed by 2380
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)
Open AccessArticle
A Comparison of Nonlinear Measures for the Detection of Cardiac Autonomic Neuropathy from Heart Rate Variability
Entropy 2015, 17(3), 1425-1440; https://doi.org/10.3390/e17031425 - 19 Mar 2015
Cited by 23 | Viewed by 4490
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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Open AccessArticle
Entropy Generation Analysis for a CNT Suspension Nanofluid in Plumb Ducts with Peristalsis
Entropy 2015, 17(3), 1411-1424; https://doi.org/10.3390/e17031411 - 19 Mar 2015
Cited by 37 | Viewed by 2729
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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Open AccessReview
Applied Cryptography Using Chaos Function for Fast Digital Logic-Based Systems in Ubiquitous Computing
Entropy 2015, 17(3), 1387-1410; https://doi.org/10.3390/e17031387 - 19 Mar 2015
Cited by 30 | Viewed by 4593
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
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Open AccessArticle
The Optimal Fix-Free Code for Anti-Uniform Sources
Entropy 2015, 17(3), 1379-1386; https://doi.org/10.3390/e17031379 - 19 Mar 2015
Viewed by 2078
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)
Open AccessArticle
Hidden State Conditional Random Field for Abnormal Activity Recognition in Smart Homes
Entropy 2015, 17(3), 1358-1378; https://doi.org/10.3390/e17031358 - 18 Mar 2015
Cited by 19 | Viewed by 2917
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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Open AccessArticle
Geometric Shrinkage Priors for Kählerian Signal Filters
Entropy 2015, 17(3), 1347-1357; https://doi.org/10.3390/e17031347 - 17 Mar 2015
Cited by 1 | Viewed by 2082
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)
Open AccessArticle
Metriplectic Algebra for Dissipative Fluids in Lagrangian Formulation
Entropy 2015, 17(3), 1329-1346; https://doi.org/10.3390/e17031329 - 16 Mar 2015
Cited by 5 | Viewed by 2263
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
Open AccessArticle
A Link between Nano- and Classical Thermodynamics: Dissipation Analysis (The Entropy Generation Approach in Nano-Thermodynamics)
Entropy 2015, 17(3), 1309-1328; https://doi.org/10.3390/e17031309 - 16 Mar 2015
Cited by 23 | Viewed by 3258
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)
Open AccessArticle
Ricci Curvature, Isoperimetry and a Non-additive Entropy
Entropy 2015, 17(3), 1278-1308; https://doi.org/10.3390/e17031278 - 16 Mar 2015
Cited by 9 | Viewed by 2542
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)
Open AccessMeeting Report
Symmetry, Probabiliy, Entropy: Synopsis of the Lecture at MAXENT 2014
Entropy 2015, 17(3), 1273-1277; https://doi.org/10.3390/e17031273 - 13 Mar 2015
Cited by 2 | Viewed by 3086
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)
Open AccessArticle
Entropic Measures of Complexity of Short-Term Dynamics of Nocturnal Heartbeats in an Aging Population
Entropy 2015, 17(3), 1253-1272; https://doi.org/10.3390/e17031253 - 13 Mar 2015
Cited by 16 | Viewed by 2857
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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Open AccessArticle
Analysis of the Magnetocaloric Effect in Heusler Alloys: Study of Ni50CoMn36Sn13 by Calorimetric Techniques
Entropy 2015, 17(3), 1236-1252; https://doi.org/10.3390/e17031236 - 12 Mar 2015
Cited by 10 | Viewed by 2816
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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Open AccessArticle
Information Hiding Method Using Best DCT and Wavelet Coefficients and Its Watermark Competition
Entropy 2015, 17(3), 1218-1235; https://doi.org/10.3390/e17031218 - 12 Mar 2015
Cited by 9 | Viewed by 2749
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
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Open AccessArticle
Information Geometry on the \(\kappa\)-Thermostatistics
Entropy 2015, 17(3), 1204-1217; https://doi.org/10.3390/e17031204 - 12 Mar 2015
Cited by 7 | Viewed by 2851
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)
Open AccessCommunication
Generalized Multiscale Entropy Analysis: Application to Quantifying the Complex Volatility of Human Heartbeat Time Series
Entropy 2015, 17(3), 1197-1203; https://doi.org/10.3390/e17031197 - 12 Mar 2015
Cited by 85 | Viewed by 5260
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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Open AccessArticle
Entropy of Quantum Measurement
Entropy 2015, 17(3), 1181-1196; https://doi.org/10.3390/e17031181 - 12 Mar 2015
Cited by 4 | Viewed by 1790
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
Open AccessArticle
Distributed Consensus for Metamorphic Systems Using a GossipAlgorithm for CAT(0) Metric Spaces
Entropy 2015, 17(3), 1165-1180; https://doi.org/10.3390/e17031165 - 12 Mar 2015
Viewed by 2076
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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Open AccessArticle
Maximum Relative Entropy Updating and the Value of Learning
Entropy 2015, 17(3), 1146-1164; https://doi.org/10.3390/e17031146 - 11 Mar 2015
Cited by 2 | Viewed by 2654
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)
Open AccessArticle
Comparing Security Notions of Secret Sharing Schemes
Entropy 2015, 17(3), 1135-1145; https://doi.org/10.3390/e17031135 - 10 Mar 2015
Cited by 5 | Viewed by 2338
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
Open AccessArticle
Projective Synchronization for a Class of Fractional-Order Chaotic Systems with Fractional-Order in the (1, 2) Interval
Entropy 2015, 17(3), 1123-1134; https://doi.org/10.3390/e17031123 - 10 Mar 2015
Cited by 8 | Viewed by 3456
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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Open AccessArticle
Weakest-Link Scaling and Extreme Events in Finite-Sized Systems
Entropy 2015, 17(3), 1103-1122; https://doi.org/10.3390/e17031103 - 09 Mar 2015
Cited by 4 | Viewed by 2544
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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Open AccessArticle
Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies
Entropy 2015, 17(3), 1090-1102; https://doi.org/10.3390/e17031090 - 06 Mar 2015
Cited by 15 | Viewed by 2633
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)
Open AccessArticle
Fully Bayesian Experimental Design for Pharmacokinetic Studies
Entropy 2015, 17(3), 1063-1089; https://doi.org/10.3390/e17031063 - 05 Mar 2015
Cited by 18 | Viewed by 3138
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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Open AccessArticle
The Hosoya Entropy of a Graph
Entropy 2015, 17(3), 1054-1062; https://doi.org/10.3390/e17031054 - 05 Mar 2015
Cited by 8 | Viewed by 2409
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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