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Entropy, Volume 19, Issue 3 (March 2017)

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Open AccessArticle Structure and Dynamics of Water at Carbon-Based Interfaces
Entropy 2017, 19(3), 135; https://doi.org/10.3390/e19030135
Received: 9 March 2017 / Revised: 19 March 2017 / Accepted: 19 March 2017 / Published: 21 March 2017
Cited by 1 | PDF Full-text (1619 KB) | HTML Full-text | XML Full-text
Abstract
Water structure and dynamics are affected by the presence of a nearby interface. Here, first we review recent results by molecular dynamics simulations about the effect of different carbon-based materials, including armchair carbon nanotubes and a variety of graphene sheets—flat and with corrugation—on
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Water structure and dynamics are affected by the presence of a nearby interface. Here, first we review recent results by molecular dynamics simulations about the effect of different carbon-based materials, including armchair carbon nanotubes and a variety of graphene sheets—flat and with corrugation—on water structure and dynamics. We discuss the calculations of binding energies, hydrogen bond distributions, water’s diffusion coefficients and their relation with surface’s geometries at different thermodynamical conditions. Next, we present new results of the crystallization and dynamics of water in a rigid graphene sieve. In particular, we show that the diffusion of water confined between parallel walls depends on the plate distance in a non-monotonic way and is related to the water structuring, crystallization, re-melting and evaporation for decreasing inter-plate distance. Our results could be relevant in those applications where water is in contact with nanostructured carbon materials at ambient or cryogenic temperatures, as in man-made superhydrophobic materials or filtration membranes, or in techniques that take advantage of hydrated graphene interfaces, as in aqueous electron cryomicroscopy for the analysis of proteins adsorbed on graphene. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Confined Systems)
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Open AccessArticle Permutation Entropy: New Ideas and Challenges
Entropy 2017, 19(3), 134; https://doi.org/10.3390/e19030134
Received: 17 February 2017 / Revised: 17 March 2017 / Accepted: 17 March 2017 / Published: 21 March 2017
Cited by 5 | PDF Full-text (2828 KB) | HTML Full-text | XML Full-text
Abstract
Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations,
[...] Read more.
Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography II)
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Open AccessArticle Spectral Entropy Parameters during Rapid Ventricular Pacing for Transcatheter Aortic Valve Implantation
Entropy 2017, 19(3), 133; https://doi.org/10.3390/e19030133
Received: 16 December 2016 / Revised: 3 March 2017 / Accepted: 15 March 2017 / Published: 20 March 2017
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Abstract
The time-frequency balanced spectral entropy of the EEG is a monitoring technique measuring the level of hypnosis during general anesthesia. Two components of spectral entropy are calculated: state entropy (SE) and response entropy (RE). Transcatheter aortic valve implantation (TAVI) is a less invasive
[...] Read more.
The time-frequency balanced spectral entropy of the EEG is a monitoring technique measuring the level of hypnosis during general anesthesia. Two components of spectral entropy are calculated: state entropy (SE) and response entropy (RE). Transcatheter aortic valve implantation (TAVI) is a less invasive treatment for patients suffering from symptomatic aortic stenosis with contraindications for open heart surgery. The goal of hemodynamic management during the procedure is to achieve hemodynamic stability with exact blood pressure control and use of rapid ventricular pacing (RVP) that result in severe hypotension. The objective of this study was to examine how the spectral entropy values respond to RVP and other critical events during the TAVI procedure. Twenty one patients undergoing general anesthesia for TAVI were evaluated. The RVP was used twice during the procedure at a rate of 185 ± 9/min with durations of 16 ± 4 s (range 8–22 s) and 24 ± 6 s (range 18–39 s). The systolic blood pressure during RVP was under 50 ± 5 mmHg. Spectral entropy values SE were significantly declined during the RVP procedure, from 28 ± 13 to 23 ± 13 (p < 0.003) and from 29 ± 12 to 24 ± 10 (p < 0.001). The corresponding values for RE were 29 ± 13 vs. 24 ± 13 (p < 0.006) and 30 ± 12 vs. 25 ± 10 (p < 0.001). Both SE and RE values returned to the pre-RVP values after 1 min. Ultra-short hypotension during RVP changed the spectral entropy parameters, however these indices reverted rapidly to the same value before application of RVP. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography II)
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Open AccessArticle Discrepancies between Conventional Multiscale Entropy and Modified Short-Time Multiscale Entropy of Photoplethysmographic Pulse Signals in Middle- and Old- Aged Individuals with or without Diabetes
Entropy 2017, 19(3), 132; https://doi.org/10.3390/e19030132
Received: 2 February 2017 / Revised: 6 March 2017 / Accepted: 16 March 2017 / Published: 18 March 2017
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Abstract
Multiscale entropy (MSE) of physiological signals may reflect cardiovascular health in diabetes. The classic MSE (cMSE) algorithm requires more than 750 signals for the calculations. The modified short-time MSE (sMSE) may have inconsistent outcomes compared with the cMSE at large time scales and
[...] Read more.
Multiscale entropy (MSE) of physiological signals may reflect cardiovascular health in diabetes. The classic MSE (cMSE) algorithm requires more than 750 signals for the calculations. The modified short-time MSE (sMSE) may have inconsistent outcomes compared with the cMSE at large time scales and in a disease status. Therefore, we compared the cMSE of 1500 (cMSE1500) consecutive and 1000 photoplethysmographic (PPG) pulse amplitudes with the sMSE of 500 PPG (sMSE500) pulse amplitudes of bilateral fingertips among middle- to old-aged individuals with or without type 2 diabetes. We discovered that cMSE1500 had the smallest value across scale factors 1–10, followed by cMSE1000, and then sMSE500 in both hands. The cMSE1500, cMSE1000 and sMSE500 did not differ at each scale factor in both hands of persons without diabetes and in the dominant hand of those with diabetes. In contrast, the sMSE500 differed at all scales 1–10 in the non-dominant hand with diabetes. In conclusion, autonomic dysfunction, prevalent in the non-dominant hand which had a low local physical activity in the person with diabetes, might be imprecisely evaluated by the sMSE; therefore, using more PPG signal numbers for the cMSE is preferred in such a situation. Full article
(This article belongs to the Special Issue Entropy and Cardiac Physics II)
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Open AccessArticle Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks
Entropy 2017, 19(3), 131; https://doi.org/10.3390/e19030131
Received: 30 December 2016 / Revised: 1 March 2017 / Accepted: 16 March 2017 / Published: 17 March 2017
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Abstract
In this paper, firstly, manifoldPD(n)consisting of alln×nsymmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold ofPD(n)are presented including metric,
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In this paper, firstly, manifoldPD(n)consisting of alln×nsymmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold ofPD(n)are presented including metric, geodesic and geodesic distance; Thirdly, the information resolution with sensor networks is presented by three classical measurement models based on information submanifold; Finally, the bearing-only tracking by single sensor is introduced by the Fisher information matrix. The preliminary analysis results introduced in this paper indicate that information submanifold is able to offer consistent and more comprehensive means to understand and solve sensor network problems for targets resolution and tracking, which are not easily handled by some conventional analysis methods. Full article
(This article belongs to the Special Issue Information Geometry II)
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Open AccessArticle Quantitative EEG Markers of Entropy and Auto Mutual Information in Relation to MMSE Scores of Probable Alzheimer’s Disease Patients
Entropy 2017, 19(3), 130; https://doi.org/10.3390/e19030130
Received: 17 December 2016 / Revised: 28 February 2017 / Accepted: 3 March 2017 / Published: 17 March 2017
Cited by 2 | PDF Full-text (4315 KB) | HTML Full-text | XML Full-text
Abstract
Analysis of nonlinear quantitative EEG (qEEG) markers describing complexity of signal in relation to severity of Alzheimer’s disease (AD) was the focal point of this study. In this study, 79 patients diagnosed with probable AD were recruited from the multi-centric Prospective Dementia Database
[...] Read more.
Analysis of nonlinear quantitative EEG (qEEG) markers describing complexity of signal in relation to severity of Alzheimer’s disease (AD) was the focal point of this study. In this study, 79 patients diagnosed with probable AD were recruited from the multi-centric Prospective Dementia Database Austria (PRODEM). EEG recordings were done with the subjects seated in an upright position in a resting state with their eyes closed. Models of linear regressions explaining disease severity, expressed in Mini Mental State Examination (MMSE) scores, were analyzed by the nonlinear qEEG markers of auto mutual information (AMI), Shannon entropy (ShE), Tsallis entropy (TsE), multiscale entropy (MsE), or spectral entropy (SpE), with age, duration of illness, and years of education as co-predictors. Linear regression models with AMI were significant for all electrode sites and clusters, where R 2 is 0.46 at the electrode site C3, 0.43 at Cz, F3, and central region, and 0.42 at the left region. MsE also had significant models at C3 with R 2 > 0.40 at scales τ = 5 and τ = 6 . ShE and TsE also have significant models at T7 and F7 with R 2 > 0.30 . Reductions in complexity, calculated by AMI, SpE, and MsE, were observed as the MMSE score decreased. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography II)
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Open AccessArticle Distance-Based Lempel–Ziv Complexity for the Analysis of Electroencephalograms in Patients with Alzheimer’s Disease
Entropy 2017, 19(3), 129; https://doi.org/10.3390/e19030129
Received: 9 February 2017 / Revised: 13 March 2017 / Accepted: 15 March 2017 / Published: 17 March 2017
Cited by 1 | PDF Full-text (889 KB) | HTML Full-text | XML Full-text
Abstract
The analysis of electroencephalograms (EEGs) of patients with Alzheimer’s disease (AD) could contribute to the diagnosis of this dementia. In this study, a new non-linear signal processing metric, distance-based Lempel–Ziv complexity (dLZC), is introduced to characterise changes between pairs of electrodes in EEGs
[...] Read more.
The analysis of electroencephalograms (EEGs) of patients with Alzheimer’s disease (AD) could contribute to the diagnosis of this dementia. In this study, a new non-linear signal processing metric, distance-based Lempel–Ziv complexity (dLZC), is introduced to characterise changes between pairs of electrodes in EEGs in AD. When complexity in each signal arises from different sub-sequences, dLZC would be greater than when similar sub-sequences are present in each signal. EEGs from 11 AD patients and 11 age-matched control subjects were analysed. The dLZC values for AD patients were lower than for control subjects for most electrode pairs, with statistically significant differences (p < 0.01, Student’s t-test) in 17 electrode pairs in the distant left, local posterior left, and interhemispheric regions. Maximum diagnostic accuracies with leave-one-out cross-validation were 77.27% for subject-based classification and 78.25% for epoch-based classification. These findings suggest not only that EEGs from AD patients are less complex than those from controls, but also that the richness of the information contained in pairs of EEGs from patients is also lower than in age-matched controls. The analysis of EEGs in AD with dLZC may increase the insight into brain dysfunction, providing complementary information to that obtained with other complexity and synchrony methods. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications
Entropy 2017, 19(3), 128; https://doi.org/10.3390/e19030128
Received: 31 January 2017 / Revised: 11 March 2017 / Accepted: 15 March 2017 / Published: 17 March 2017
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Abstract
In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in
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In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoretical model, such as the scale relativity theory or the extended scale relativity theory. Thus, using the last theory, fractal entropy through non-differentiable Lie groups was established and, moreover, the pairs generating mechanisms through fractal entanglement states were explained. Our model has implications in the dynamics of biological structures, in the form of the “chameleon-like” behavior of cholesterol. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle Fractional Jensen–Shannon Analysis of the Scientific Output of Researchers in Fractional Calculus
Entropy 2017, 19(3), 127; https://doi.org/10.3390/e19030127
Received: 9 March 2017 / Revised: 14 March 2017 / Accepted: 15 March 2017 / Published: 17 March 2017
Cited by 3 | PDF Full-text (359 KB) | HTML Full-text | XML Full-text
Abstract
This paper analyses the citation profiles of researchers in fractional calculus. Different metrics are used to quantify the dissimilarities between the data, namely the Canberra distance, and the classical and the generalized (fractional) Jensen–Shannon divergence. The information is then visualized by means of
[...] Read more.
This paper analyses the citation profiles of researchers in fractional calculus. Different metrics are used to quantify the dissimilarities between the data, namely the Canberra distance, and the classical and the generalized (fractional) Jensen–Shannon divergence. The information is then visualized by means of multidimensional scaling and hierarchical clustering. The mathematical tools and metrics allow for direct comparison and visualization of researchers based on their relative positioning and on patterns displayed in two- or three-dimensional maps. Full article
(This article belongs to the Special Issue Complex Systems and Fractional Dynamics)
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Open AccessArticle Friction, Free Axes of Rotation and Entropy
Entropy 2017, 19(3), 123; https://doi.org/10.3390/e19030123
Received: 16 February 2017 / Revised: 13 March 2017 / Accepted: 14 March 2017 / Published: 17 March 2017
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Abstract
Friction forces acting on rotators may promote their alignment and therefore eliminate degrees of freedom in their movement. The alignment of rotators by friction force was shown by experiments performed with different spinners, demonstrating how friction generates negentropy in a system of rotators.
[...] Read more.
Friction forces acting on rotators may promote their alignment and therefore eliminate degrees of freedom in their movement. The alignment of rotators by friction force was shown by experiments performed with different spinners, demonstrating how friction generates negentropy in a system of rotators. A gas of rigid rotators influenced by friction force is considered. The orientational negentropy generated by a friction force was estimated with the Sackur-Tetrode equation. The minimal change in total entropy of a system of rotators, corresponding to their eventual alignment, decreases with temperature. The reported effect may be of primary importance for the phase equilibrium and motion of ubiquitous colloidal and granular systems. Full article
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Open AccessArticle Identity Based Generalized Signcryption Scheme in the Standard Model
Entropy 2017, 19(3), 121; https://doi.org/10.3390/e19030121
Received: 10 January 2017 / Revised: 7 March 2017 / Accepted: 13 March 2017 / Published: 17 March 2017
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Abstract
Generalized signcryption (GSC) can adaptively work as an encryption scheme, a signature scheme or a signcryption scheme with only one algorithm. It is more suitable for the storage constrained setting. In this paper, motivated by Paterson–Schuldt’s scheme, based on bilinear pairing, we first
[...] Read more.
Generalized signcryption (GSC) can adaptively work as an encryption scheme, a signature scheme or a signcryption scheme with only one algorithm. It is more suitable for the storage constrained setting. In this paper, motivated by Paterson–Schuldt’s scheme, based on bilinear pairing, we first proposed an identity based generalized signcryption (IDGSC) scheme in the standard model. To the best of our knowledge, it is the first scheme that is proven secure in the standard model. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Nonequilibrium Thermodynamics and Scale Invariance
Entropy 2017, 19(3), 126; https://doi.org/10.3390/e19030126
Received: 30 January 2017 / Revised: 7 March 2017 / Accepted: 14 March 2017 / Published: 16 March 2017
Cited by 1 | PDF Full-text (244 KB) | HTML Full-text | XML Full-text
Abstract
A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces is proposed here. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic
[...] Read more.
A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces is proposed here. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It is shown here that such a modification not only makes it possible to deductively obtain the main results of classical linear nonequilibrium thermodynamics, but also provides evidence for a number of statements for a nonlinear case (the maximum entropy production principle, the macroscopic reversibility principle, and generalized reciprocity relations) that are under discussion in the literature. Full article
(This article belongs to the Section Thermodynamics)
Open AccessArticle Packer Detection for Multi-Layer Executables Using Entropy Analysis
Entropy 2017, 19(3), 125; https://doi.org/10.3390/e19030125
Received: 31 January 2017 / Revised: 9 March 2017 / Accepted: 13 March 2017 / Published: 16 March 2017
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Abstract
Packing algorithms are broadly used to avoid anti-malware systems, and the proportion of packed malware has been growing rapidly. However, just a few studies have been conducted on detection various types of packing algorithms in a systemic way. Following this understanding, we elaborate
[...] Read more.
Packing algorithms are broadly used to avoid anti-malware systems, and the proportion of packed malware has been growing rapidly. However, just a few studies have been conducted on detection various types of packing algorithms in a systemic way. Following this understanding, we elaborate a method to classify packing algorithms of a given executable into three categories: single-layer packing, re-packing, or multi-layer packing. We convert entropy values of the executable file loaded into memory into symbolic representations, for which we used SAX (Symbolic Aggregate Approximation). Based on experiments of 2196 programs and 19 packing algorithms, we identify that precision (97.7%), accuracy (97.5%), and recall ( 96.8%) of our method are respectively high to confirm that entropy analysis is applicable in identifying packing algorithms. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle Witnessing Multipartite Entanglement by Detecting Asymmetry
Entropy 2017, 19(3), 124; https://doi.org/10.3390/e19030124
Received: 4 February 2017 / Revised: 8 March 2017 / Accepted: 12 March 2017 / Published: 16 March 2017
Cited by 7 | PDF Full-text (817 KB) | HTML Full-text | XML Full-text
Abstract
The characterization of quantum coherence in the context of quantum information theory and its interplay with quantum correlations is currently subject of intense study. Coherence in a Hamiltonian eigenbasis yields asymmetry, the ability of a quantum system to break a dynamical symmetry generated
[...] Read more.
The characterization of quantum coherence in the context of quantum information theory and its interplay with quantum correlations is currently subject of intense study. Coherence in a Hamiltonian eigenbasis yields asymmetry, the ability of a quantum system to break a dynamical symmetry generated by the Hamiltonian. We here propose an experimental strategy to witness multipartite entanglement in many-body systems by evaluating the asymmetry with respect to an additive Hamiltonian. We test our scheme by simulating asymmetry and entanglement detection in a three-qubit Greenberger–Horne–Zeilinger (GHZ) diagonal state. Full article
(This article belongs to the Special Issue Information Geometry II)
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Open AccessArticle On Hölder Projective Divergences
Entropy 2017, 19(3), 122; https://doi.org/10.3390/e19030122
Received: 20 January 2017 / Revised: 8 March 2017 / Accepted: 10 March 2017 / Published: 16 March 2017
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Abstract
We describe a framework to build distances by measuring the tightness of inequalities and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the Hölder ordinary and reverse inequalities and present two novel classes of Hölder divergences and pseudo-divergences
[...] Read more.
We describe a framework to build distances by measuring the tightness of inequalities and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the Hölder ordinary and reverse inequalities and present two novel classes of Hölder divergences and pseudo-divergences that both encapsulate the special case of the Cauchy–Schwarz divergence. We report closed-form formulas for those statistical dissimilarities when considering distributions belonging to the same exponential family provided that the natural parameter space is a cone (e.g., multivariate Gaussians) or affine (e.g., categorical distributions). Those new classes of Hölder distances are invariant to rescaling and thus do not require distributions to be normalized. Finally, we show how to compute statistical Hölder centroids with respect to those divergences and carry out center-based clustering toy experiments on a set of Gaussian distributions which demonstrate empirically that symmetrized Hölder divergences outperform the symmetric Cauchy–Schwarz divergence. Full article
(This article belongs to the Special Issue Information Geometry II)
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