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Entropy, Volume 16, Issue 12 (December 2014), Pages 6195-6738

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Open AccessArticle A Large Deviation Principle and an Expression of the Rate Function for a Discrete Stationary Gaussian Process
Entropy 2014, 16(12), 6722-6738; https://doi.org/10.3390/e16126722
Received: 3 November 2014 / Revised: 17 December 2014 / Accepted: 18 December 2014 / Published: 22 December 2014
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Abstract
We prove a large deviation principle for a stationary Gaussian process over Rb,indexed by Ζd (for some positive integers d and b), with positive definite spectral density, andprovide an expression of the corresponding rate function in terms of the
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We prove a large deviation principle for a stationary Gaussian process over Rb,indexed by Ζd (for some positive integers d and b), with positive definite spectral density, andprovide an expression of the corresponding rate function in terms of the mean of the processand its spectral density. This result is useful in applications where such an expression isneeded. Full article
(This article belongs to the Section Statistical Mechanics)
Open AccessArticle A Representation of the Relative Entropy with Respect to a Diffusion Process in Terms of Its Infinitesimal Generator
Entropy 2014, 16(12), 6705-6721; https://doi.org/10.3390/e16126705
Received: 23 October 2014 / Revised: 17 December 2014 / Accepted: 18 December 2014 / Published: 22 December 2014
Cited by 1 | PDF Full-text (304 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback–Leibler Divergence) R(μ||P), where μ and P are measures on C([0,T];Rd). The underlying measure P is a weak solution to a martingale problem with
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In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback–Leibler Divergence) R(μ||P), where μ and P are measures on C([0,T];Rd). The underlying measure P is a weak solution to a martingale problem with continuous coefficients. Our representation is in the form of an integral with respect to its infinitesimal generator. This representation is of use in statistical inference (particularly involving medical imaging). Since R(μ||P) governs the exponential rate of convergence of the empirical measure (according to Sanov’s theorem), this representation is also of use in the numerical and analytical investigation of finite-size effects in systems of interacting diffusions. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Effect of the Postural Challenge on the Dependence of the Cardiovascular Control Complexity on Age
Entropy 2014, 16(12), 6686-6704; https://doi.org/10.3390/e16126686
Received: 28 October 2014 / Revised: 8 December 2014 / Accepted: 18 December 2014 / Published: 22 December 2014
Cited by 13 | PDF Full-text (1699 KB) | HTML Full-text | XML Full-text
Abstract
Short-term complexity of heart period (HP) and systolic arterial pressure (SAP) was computed to detect age and gender influences over cardiovascular control in resting supine condition (REST) and during standing (STAND). Healthy subjects (n = 110, men = 55) were equally divided
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Short-term complexity of heart period (HP) and systolic arterial pressure (SAP) was computed to detect age and gender influences over cardiovascular control in resting supine condition (REST) and during standing (STAND). Healthy subjects (n = 110, men = 55) were equally divided into five groups (21–30; 31–40; 41–50; 51–60; and 61–70 years of age). HP and SAP series were recorded for 15 min at REST and during STAND. A normalized complexity index (NCI) based on conditional entropy was assessed. At REST we found that both NCIHP and NCISAP decreased with age in the overall population, but only women were responsible for this trend. During STAND we observed that both NCIHP and NCISAP were unrelated to age in the overall population, even when divided by gender. When the variation of NCI in response to STAND (ΔNCI = NCI at REST-NCI during STAND) was computed individually, we found that ΔNCIHP progressively decreased with age in the overall population, and women were again responsible for this trend. Conversely, ΔNCISAP was unrelated to age and gender. This study stresses that the complexity of cardiovascular control and its ability to respond to stressors are more importantly lost with age in women than in men. Full article
(This article belongs to the Special Issue Entropy and Cardiac Physics)
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Open AccessArticle Fast Rate Estimation for RDO Mode Decision in HEVC
Entropy 2014, 16(12), 6667-6685; https://doi.org/10.3390/e16126667
Received: 19 August 2014 / Revised: 3 December 2014 / Accepted: 17 December 2014 / Published: 19 December 2014
Cited by 4 | PDF Full-text (830 KB) | HTML Full-text | XML Full-text
Abstract
The latter-day H.265/HEVC video compression standard is able to provide two-times higher compression efficiency compared to the current industrial standard, H.264/AVC. However, coding complexity also increased. The main bottleneck of the compression process is the rate-distortion optimization (RDO) stage, as it involves numerous
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The latter-day H.265/HEVC video compression standard is able to provide two-times higher compression efficiency compared to the current industrial standard, H.264/AVC. However, coding complexity also increased. The main bottleneck of the compression process is the rate-distortion optimization (RDO) stage, as it involves numerous sequential syntax-based binary arithmetic coding (SBAC) loops. In this paper, we present an entropy-based RDO estimation technique for H.265/HEVC compression, instead of the common approach based on the SBAC. Our RDO implementation reduces RDO complexity, providing an average bit rate overhead of 1.54%. At the same time, elimination of the SBAC from the RDO estimation reduces block interdependencies, thus providing an opportunity for the development of the compression system with parallel processing of multiple blocks of a video frame. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle The Effects of Spontaneous Random Activity on Information Transmission in an Auditory Brain Stem Neuron Model
Entropy 2014, 16(12), 6654-6666; https://doi.org/10.3390/e16126654
Received: 30 April 2014 / Revised: 8 December 2014 / Accepted: 15 December 2014 / Published: 19 December 2014
Cited by 2 | PDF Full-text (312 KB) | HTML Full-text | XML Full-text
Abstract
This paper presents the effects of spontaneous random activity on information transmission in an auditory brain stem neuron model. In computer simulations, the supra-threshold synaptic current stimuli ascending from auditory nerve fibers (ANFs) were modeled by a filtered inhomogeneous Poisson process modulated by
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This paper presents the effects of spontaneous random activity on information transmission in an auditory brain stem neuron model. In computer simulations, the supra-threshold synaptic current stimuli ascending from auditory nerve fibers (ANFs) were modeled by a filtered inhomogeneous Poisson process modulated by sinusoidal functions at a frequency of 220–3520 Hz with regard to the human speech spectrum. The stochastic sodium and stochastic high- and low-threshold potassium channels were incorporated into a single compartment model of the soma in spherical bushy neurons, so as to realize threshold fluctuations or a variation of spike firing times. The results show that the information rates estimated from the entropy of inter-spike intervals of spike trains tend toward a convex function of the spontaneous rates when the intensity of sinusoidal functions decreases. Furthermore, the results show that a convex function of the spontaneous rates tends to disappear as the frequency of the sinusoidal function increases, such that the phase-locked response can be unobserved. It is concluded that this sort of stochastic resonance (SR) phenomenon, which depends on the spontaneous rates with supra-threshold stimuli, can better enhance information transmission in a smaller intensity of sinusoidal functions within the human speech spectrum, like the situation in which the regular SR can enhance weak signals. Full article
(This article belongs to the Special Issue Entropy in Human Brain Networks)
Open AccessArticle The McMillan Theorem for Colored Branching Processes and Dimensions of Random Fractals
Entropy 2014, 16(12), 6624-6653; https://doi.org/10.3390/e16126624
Received: 16 September 2014 / Revised: 18 November 2014 / Accepted: 12 December 2014 / Published: 19 December 2014
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Abstract
For the simplest colored branching process, we prove an analog to the McMillan theorem and calculate the Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting, the role of
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For the simplest colored branching process, we prove an analog to the McMillan theorem and calculate the Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting, the role of Shannon’s entropy is played by the Kullback–Leibler divergence, and the Hausdorff dimensions are computed by means of the so-called Billingsley–Kullback entropy, defined in the paper. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Detection and Modeling of Cyber Attacks with Petri Nets
Entropy 2014, 16(12), 6602-6623; https://doi.org/10.3390/e16126602
Received: 30 October 2014 / Revised: 4 December 2014 / Accepted: 16 December 2014 / Published: 19 December 2014
Cited by 12 | PDF Full-text (1300 KB) | HTML Full-text | XML Full-text
Abstract
The aim of this article is to present an approach to develop and verify a method of formal modeling of cyber threats directed at computer systems. Moreover, the goal is to prove that the method enables one to create models resembling the behavior
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The aim of this article is to present an approach to develop and verify a method of formal modeling of cyber threats directed at computer systems. Moreover, the goal is to prove that the method enables one to create models resembling the behavior of malware that support the detection process of selected cyber attacks and facilitate the application of countermeasures. The most common cyber threats targeting end users and terminals are caused by malicious software, called malware. The malware detection process can be performed either by matching their digital signatures or analyzing their behavioral models. As the obfuscation techniques make the malware almost undetectable, the classic signature-based anti-virus tools must be supported with behavioral analysis. The proposed approach to modeling of malware behavior is based on colored Petri nets. This article is addressed to cyber defense researchers, security architects and developers solving up-to-date problems regarding the detection and prevention of advanced persistent threats. Full article
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Open AccessArticle Depth Image Coding Using Entropy-Based Adaptive Measurement Allocation
Entropy 2014, 16(12), 6590-6601; https://doi.org/10.3390/e16126590
Received: 20 October 2014 / Revised: 7 December 2014 / Accepted: 12 December 2014 / Published: 17 December 2014
Cited by 1 | PDF Full-text (1435 KB) | HTML Full-text | XML Full-text
Abstract
Differently from traditional two-dimensional texture images, the depth images of three-dimensional (3D) video systems have significant sparse characteristics under the certain transform basis, which make it possible for compressive sensing to represent depth information efficiently. Therefore, in this paper, a novel depth image
[...] Read more.
Differently from traditional two-dimensional texture images, the depth images of three-dimensional (3D) video systems have significant sparse characteristics under the certain transform basis, which make it possible for compressive sensing to represent depth information efficiently. Therefore, in this paper, a novel depth image coding scheme is proposed based on a block compressive sensing method. At the encoder, in view of the characteristics of depth images, the entropy of pixels in each block is employed to represent the sparsity of depth signals. Then according to the different sparsity in the pixel domain, the measurements can be adaptively allocated to each block for higher compression efficiency. At the decoder, the sparse transform can be combined to achieve the compressive sensing reconstruction. Experimental results have shown that at the same sampling rate, the proposed scheme can obtain higher PSNR values and better subjective quality of the rendered virtual views, compared with the method using a uniform sampling rate. Full article
Open AccessArticle Automatic Sleep Stages Classification Using EEG Entropy Features and Unsupervised Pattern Analysis Techniques
Entropy 2014, 16(12), 6573-6589; https://doi.org/10.3390/e16126573
Received: 18 July 2014 / Revised: 28 November 2014 / Accepted: 9 December 2014 / Published: 17 December 2014
Cited by 21 | PDF Full-text (1157 KB) | HTML Full-text | XML Full-text
Abstract
Sleep is a growing area of research interest in medicine and neuroscience. Actually, one major concern is to find a correlation between several physiologic variables and sleep stages. There is a scientific agreement on the characteristics of the five stages of human sleep,
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Sleep is a growing area of research interest in medicine and neuroscience. Actually, one major concern is to find a correlation between several physiologic variables and sleep stages. There is a scientific agreement on the characteristics of the five stages of human sleep, based on EEG analysis. Nevertheless, manual stage classification is still the most widely used approach. This work proposes a new automatic sleep classification method based on unsupervised feature classification algorithms recently developed, and on EEG entropy measures. This scheme extracts entropy metrics from EEG records to obtain a feature vector. Then, these features are optimized in terms of relevance using the Q-α algorithm. Finally, the resulting set of features is entered into a clustering procedure to obtain a final segmentation of the sleep stages. The proposed method reached up to an average of 80% correctly classified stages for each patient separately while keeping the computational cost low. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Enhanced Automatic Wavelet Independent Component Analysis for Electroencephalographic Artifact Removal
Entropy 2014, 16(12), 6553-6572; https://doi.org/10.3390/e16126553
Received: 31 July 2014 / Revised: 4 December 2014 / Accepted: 5 December 2014 / Published: 17 December 2014
Cited by 5 | PDF Full-text (18016 KB) | HTML Full-text | XML Full-text
Abstract
Electroencephalography (EEG) is a fundamental diagnostic instrument for many neurological disorders, and it is the main tool for the investigation of the cognitive or pathological activity of the brain through the bioelectromagnetic fields that it generates. The correct interpretation of the EEG is
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Electroencephalography (EEG) is a fundamental diagnostic instrument for many neurological disorders, and it is the main tool for the investigation of the cognitive or pathological activity of the brain through the bioelectromagnetic fields that it generates. The correct interpretation of the EEG is misleading, both for clinicians’ visual evaluation and for automated procedures, because of artifacts. As a consequence, artifact rejection in EEG is a key preprocessing step, and the quest for reliable automatic processors has been quickly growing in the last few years. Recently, a promising automatic methodology, known as automatic wavelet-independent component analysis (AWICA), has been proposed. In this paper, a more efficient and sensitive version, called enhanced-AWICA (EAWICA), is proposed, and an extensive performance comparison is carried out by a step of tuning the different parameters that are involved in artifact detection. EAWICA is shown to minimize information loss and to outperform AWICA in artifact removal, both on simulated and real experimental EEG recordings. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Chaos Control and Synchronization of a Hyperchaotic Zhou System by Integral Sliding Mode control
Entropy 2014, 16(12), 6539-6552; https://doi.org/10.3390/e16126539
Received: 25 September 2014 / Revised: 25 November 2014 / Accepted: 3 December 2014 / Published: 12 December 2014
Cited by 8 | PDF Full-text (306 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, an adaptive integral sliding mode control scheme is proposed for synchronization of hyperchaotic Zhou systems. In the proposed scheme, an integral sliding mode control is designed to stabilize a hyperchaotic Zhou system with known parameters to its unstable equilibrium at
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In this paper, an adaptive integral sliding mode control scheme is proposed for synchronization of hyperchaotic Zhou systems. In the proposed scheme, an integral sliding mode control is designed to stabilize a hyperchaotic Zhou system with known parameters to its unstable equilibrium at the origin. The control is then applied to the synchronization of two identical systems, i.e., a slave and a master hyperchaotic Zhou system with unknown parameters. The adaptive control mechanism introduced synchronizes the systems by estimating the unknown parameters. Simulation results have shown that the proposed method has an excellent convergence from both speed and accuracy points of view, and it outperforms Vaidyanathan’s scheme, which is a well-recognized scheme in this area. Full article
(This article belongs to the Special Issue Complex Systems and Nonlinear Dynamics)
Open AccessArticle Consensus of Discrete Multiagent System with Various Time Delays and Environmental Disturbances
Entropy 2014, 16(12), 6524-6538; https://doi.org/10.3390/e16126524
Received: 4 October 2014 / Revised: 9 December 2014 / Accepted: 9 December 2014 / Published: 11 December 2014
Cited by 3 | PDF Full-text (209 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, the consensus problem of discrete multiagent systems with time varying sampling periods is studied. Firstly, with thorough analysis of various delays among agents, the control input of each agent is designed with consideration of sending delay and receiving delay. With
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In this paper, the consensus problem of discrete multiagent systems with time varying sampling periods is studied. Firstly, with thorough analysis of various delays among agents, the control input of each agent is designed with consideration of sending delay and receiving delay. With construction of discrete dynamics of state error vector, it is proved by applying Halanay inequality that consensus of the system can be reached. Further, the definition of bounded consensus is proposed in the situation where environmental disturbances exist. In order to handle this problem, the Halanay inequality is extended into a more general one with boundedness property. Based on the new Halanay inequality obtained, the boundedness of consensus error is guaranteed. At last, simulation examples are presented to demonstrate the theoretical conclusions. Full article
(This article belongs to the Special Issue Complex Systems and Nonlinear Dynamics)
Open AccessArticle Geometric Thermodynamics: Black Holes and the Meaning of the Scalar Curvature
Entropy 2014, 16(12), 6515-6523; https://doi.org/10.3390/e16126515
Received: 9 October 2014 / Revised: 2 December 2014 / Accepted: 4 December 2014 / Published: 11 December 2014
Cited by 11 | PDF Full-text (199 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions in the underlying
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In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions in the underlying microscopic model of a thermodynamic system, which poses a limitation on the usefulness of Ruppeiner’s metric and conjecture. Finally, we address the problem of the choice of coordinates in black hole thermodynamics. We propose an alternative energy representation for Kerr-Newman black holes that mimics fully Weinhold’s approach. The corresponding Ruppeiner’s metrics become degenerate only at absolute zero and have non-vanishing scalar curvatures. Full article
(This article belongs to the Special Issue Entropy and Spacetime)
Open AccessArticle Statistical Power Law due to Reservoir Fluctuations and the Universal Thermostat Independence Principle
Entropy 2014, 16(12), 6497-6514; https://doi.org/10.3390/e16126497
Received: 3 November 2014 / Revised: 26 November 2014 / Accepted: 2 December 2014 / Published: 9 December 2014
Cited by 21 | PDF Full-text (224 KB) | HTML Full-text | XML Full-text
Abstract
Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and
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Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and \(q=1-1/\langle n \rangle + \Delta n^2/\langle n \rangle^2\). For the binomial distribution of \(n\) one obtains \(q=1-1/k\), for the negative binomial \(q=1+1/(k+1)\). These results also represent an approximation for general particle number distributions in the reservoir up to second order in the canonical expansion \(\omega \ll E\). For general systems the average phase-space volume ratio \(\langle e^{S(E-\omega)}/e^{S(E)}\rangle\) to second order delivers \(q=1-1/C+\Delta \beta^2/\langle \beta \rangle^2\) with \(\beta=S^{\prime}(E)\) and \(C=dE/dT\) heat capacity. However, \(q \ne 1\) leads to non-additivity of the Boltzmann–Gibbs entropy, \(S\). We demonstrate that a deformed entropy, \(K(S)\), can be constructed and used for demanding additivity, i.e., \(q_K=1\). This requirement leads to a second order differential equation for \(K(S)\). Finally, the generalized \(q\)-entropy formula, \(K(S)=\sum p_i K(-\ln p_i)\), contains the Tsallis, Rényi and Boltzmann–Gibbs–Shannon expressions as particular cases. For diverging variance, \(\Delta\beta^2\) we obtain a novel entropy formula. Full article
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
Open AccessArticle An Evolutionary Algorithm for the Texture Analysis of Cubic System Materials Derived by the Maximum Entropy Principle
Entropy 2014, 16(12), 6477-6496; https://doi.org/10.3390/e16126477
Received: 25 July 2014 / Revised: 15 October 2014 / Accepted: 12 November 2014 / Published: 9 December 2014
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Abstract
Based on the principle of maximum entropy method (MEM) for quantitative texture analysis, the differential evolution (DE) algorithm was effectively introduced. Using a DE-optimized algorithm with a faster but more stable convergence rate of iteration reliable complete orientation distributions (C-ODF) have
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Based on the principle of maximum entropy method (MEM) for quantitative texture analysis, the differential evolution (DE) algorithm was effectively introduced. Using a DE-optimized algorithm with a faster but more stable convergence rate of iteration reliable complete orientation distributions (C-ODF) have been obtained for deep-drawn IF steel sheets and the recrystallized aluminum foils after cold-rolling, which are designated as showing a macroscopic cubic-orthogonal symmetry. With special reference to the data processing, no more other assumptions are required for DE-optimized MEM except that the system entropy approach the maximum. Full article
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