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Entropy, Volume 14, Issue 6 (June 2012), Pages 978-1126

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Research

Open AccessArticle Adaptive Computation of Multiscale Entropy and Its Application in EEG Signals for Monitoring Depth of Anesthesia During Surgery
Entropy 2012, 14(6), 978-992; doi:10.3390/e14060978
Received: 29 March 2012 / Revised: 9 May 2012 / Accepted: 21 May 2012 / Published: 25 May 2012
Cited by 22 | PDF Full-text (471 KB) | HTML Full-text | XML Full-text
Abstract
Entropy as an estimate of complexity of the electroencephalogram is an effective parameter for monitoring the depth of anesthesia (DOA) during surgery. Multiscale entropy (MSE) is useful to evaluate the complexity of signals over different time scales. However, the limitation of the [...] Read more.
Entropy as an estimate of complexity of the electroencephalogram is an effective parameter for monitoring the depth of anesthesia (DOA) during surgery. Multiscale entropy (MSE) is useful to evaluate the complexity of signals over different time scales. However, the limitation of the length of processed signal is a problem due to observing the variation of sample entropy (SE) on different scales. In this study, the adaptive resampling procedure is employed to replace the process of coarse-graining in MSE. According to the analysis of various signals and practical EEG signals, it is feasible to calculate the SE from the adaptive resampled signals, and it has the highly similar results with the original MSE at small scales. The distribution of the MSE of EEG during the whole surgery based on adaptive resampling process is able to show the detailed variation of SE in small scales and complexity of EEG, which could help anesthesiologists evaluate the status of patients. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
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Open AccessArticle Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics
Entropy 2012, 14(6), 993-1010; doi:10.3390/e14060993
Received: 30 April 2012 / Revised: 31 May 2012 / Accepted: 31 May 2012 / Published: 5 June 2012
Cited by 2 | PDF Full-text (3051 KB) | HTML Full-text | XML Full-text
Abstract
Cellular automata (CA) are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile [...] Read more.
Cellular automata (CA) are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile tool for exploring dynamical processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER) graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution. Full article
(This article belongs to the Special Issue Emergence of Information in Evolutionary Processes)
Open AccessArticle Deterministic Thermal Reservoirs
Entropy 2012, 14(6), 1011-1027; doi:10.3390/e14061011
Received: 21 March 2012 / Revised: 16 May 2012 / Accepted: 5 June 2012 / Published: 8 June 2012
Cited by 4 | PDF Full-text (6645 KB) | HTML Full-text | XML Full-text
Abstract
We explore the consequences of a deterministic microscopic thermostat-reservoir contact mechanism for hard disks where the collision rule at the boundary is modified. Numerical evidence and theoretical argument is given that suggests that an energy balance is achieved for a system of [...] Read more.
We explore the consequences of a deterministic microscopic thermostat-reservoir contact mechanism for hard disks where the collision rule at the boundary is modified. Numerical evidence and theoretical argument is given that suggests that an energy balance is achieved for a system of hard disks in contact with two reservoirs at equal temperatures. This system however produces entropy near the the system-reservoir boundaries and this entropy flows into the two reservoirs. Thus rather than producing an equilibrium state, the system is at a steady state with a steady entropy flow without any associated energy flux. The microscopic mechanisms associated with energy and entropy fluxes for this system are examined in detail. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
Open AccessArticle Combined Effect of Buoyancy Force and Navier Slip on Entropy Generation in a Vertical Porous Channel
Entropy 2012, 14(6), 1028-1044; doi:10.3390/e14061028
Received: 18 May 2012 / Revised: 2 June 2012 / Accepted: 2 June 2012 / Published: 12 June 2012
Cited by 12 | PDF Full-text (881 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we investigate the combined effects of buoyancy force and Navier slip on the entropy generation rate in a vertical porous channel with wall suction/injection. The nonlinear model problem is tackled numerically using Runge–Kutta–Fehlberg method with shooting technique. Both the [...] Read more.
In this paper, we investigate the combined effects of buoyancy force and Navier slip on the entropy generation rate in a vertical porous channel with wall suction/injection. The nonlinear model problem is tackled numerically using Runge–Kutta–Fehlberg method with shooting technique. Both the velocity and temperature profiles are obtained and utilized to compute the entropy generation number. The effects of slip parameter, Brinkmann number, the Peclet number and suction/injection Reynolds number on the fluid velocity, temperature profile, Nusselt number, entropy generation rate and Bejan number are depicted graphically and discussed quantitatively. Full article
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Open AccessArticle Thermodynamic Geometry and Topological Einstein–Yang–Mills Black Holes
Entropy 2012, 14(6), 1045-1078; doi:10.3390/e14061045
Received: 25 April 2012 / Revised: 8 June 2012 / Accepted: 11 June 2012 / Published: 13 June 2012
Cited by 5 | PDF Full-text (1467 KB) | HTML Full-text | XML Full-text
Abstract
From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein–Yang–Mills black holes. In this paper, from the perspective of the state-space surface and chemical Weinhold surface of higher [...] Read more.
From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein–Yang–Mills black holes. In this paper, from the perspective of the state-space surface and chemical Weinhold surface of higher dimensional gravity, we provide the criteria for the local and global statistical stability of an ensemble of topological Einstein–Yang–Mills black holes in arbitrary spacetime dimensions D ≥ 5. Finally, as per the formulations of the thermodynamic geometry, we offer a parametric account of the statistical consequences in both the local and global fluctuation regimes of the topological extremal Einstein–Yang–Mills black holes. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
Open AccessArticle Case Studies and Benchmark Examples for the Use of Grading Entropy in Geotechnics
Entropy 2012, 14(6), 1079-1102; doi:10.3390/e14061079
Received: 15 March 2012 / Revised: 27 May 2012 / Accepted: 31 May 2012 / Published: 18 June 2012
Cited by 2 | PDF Full-text (388 KB) | HTML Full-text | XML Full-text
Abstract
The grading entropy concept can be adapted to the field of geotechnics, to establish criteria for phenomena such as particle packing, particle migration and filtering, through a quantified expression of the order/disorder in the grain size distribution, in terms of two entropy-based [...] Read more.
The grading entropy concept can be adapted to the field of geotechnics, to establish criteria for phenomena such as particle packing, particle migration and filtering, through a quantified expression of the order/disorder in the grain size distribution, in terms of two entropy-based parameters. In this paper, the grading entropy theory is applied in some geotechnical case studies, which serve as benchmark examples to illustrate its application to the characterisation of piping, softening and dispersive soils, and to filtering problems in the context of a leachate collection system for a landfill site. Further, since unstable cohesive (dispersive) soils are generally improved by lime, the effect of lime addition is also considered, on the basis of some measurements and a further application of the grading entropy concept, which allows evolutions in the entropy of a soil to be considered as its grading is modified. The examples described support the hypothesis that the potential for soil erosion and particle migration can be reliably identified using grading entropy parameters derived from grading curve data, and applied through an established soil structure stability criteria and a filtering rule. It is shown that lime modification is not necessarily helpful in stabilizing against particle migration. Full article
Open AccessArticle Minimum Mutual Information and Non-Gaussianity Through the Maximum Entropy Method: Theory and Properties
Entropy 2012, 14(6), 1103-1126; doi:10.3390/e14061103
Received: 20 May 2012 / Revised: 8 June 2012 / Accepted: 15 June 2012 / Published: 19 June 2012
Cited by 7 | PDF Full-text (663 KB) | HTML Full-text | XML Full-text
Abstract
The application of the Maximum Entropy (ME) principle leads to a minimum of the Mutual Information (MI), I(X,Y), between random variables X,Y, which is compatible with prescribed joint expectations and given ME marginal distributions. A sequence of sets [...] Read more.
The application of the Maximum Entropy (ME) principle leads to a minimum of the Mutual Information (MI), I(X,Y), between random variables X,Y, which is compatible with prescribed joint expectations and given ME marginal distributions. A sequence of sets of joint constraints leads to a hierarchy of lower MI bounds increasingly approaching the true MI. In particular, using standard bivariate Gaussian marginal distributions, it allows for the MI decomposition into two positive terms: the Gaussian MI (Ig), depending upon the Gaussian correlation or the correlation between ‘Gaussianized variables’, and a non‑Gaussian MI (Ing), coinciding with joint negentropy and depending upon nonlinear correlations. Joint moments of a prescribed total order p are bounded within a compact set defined by Schwarz-like inequalities, where Ing grows from zero at the ‘Gaussian manifold’ where moments are those of Gaussian distributions, towards infinity at the set’s boundary where a deterministic relationship holds. Sources of joint non-Gaussianity have been systematized by estimating Ing between the input and output from a nonlinear synthetic channel contaminated by multiplicative and non-Gaussian additive noises for a full range of signal-to-noise ratio (snr) variances. We have studied the effect of varying snr on Ig and Ing under several signal/noise scenarios. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)

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