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Entropy, Volume 14, Issue 8 (August 2012), Pages 1306-1605

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Research

Jump to: Review

Open AccessArticle A New Entropy Optimization Model for Graduation of Data in Survival Analysis
Entropy 2012, 14(8), 1306-1316; doi:10.3390/e14081306
Received: 7 March 2012 / Revised: 6 June 2012 / Accepted: 4 July 2012 / Published: 25 July 2012
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Abstract
Graduation of data is of great importance in survival analysis. Smoothness and goodness of fit are two fundamental requirements in graduation. Based on the instinctive defining expression for entropy in terms of a probability distribution, two optimization models based on the Maximum Entropy
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Graduation of data is of great importance in survival analysis. Smoothness and goodness of fit are two fundamental requirements in graduation. Based on the instinctive defining expression for entropy in terms of a probability distribution, two optimization models based on the Maximum Entropy Principle (MaxEnt) and Minimum Cross Entropy Principle (MinCEnt) to estimate mortality probability distributions are presented. The results demonstrate that the two approaches achieve the two basic requirements of data graduating, smoothness and goodness of fit respectively. Then, in order to achieve a compromise between these requirements, a new entropy optimization model is proposed by defining a hybrid objective function combining both principles of MaxEnt and MinCEnt models linked by a given adjustment factor which reflects the preference of smoothness and goodness of fit in the data graduation. The proposed approach is feasible and more reasonable in data graduation when both smoothness and goodness of fit are concerned. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
Open AccessArticle Equivalence of Partition Functions Leads to Classification of Entropies and Means
Entropy 2012, 14(8), 1317-1342; doi:10.3390/e14081317
Received: 24 April 2012 / Revised: 26 June 2012 / Accepted: 9 July 2012 / Published: 27 July 2012
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Abstract
We derive a two-parameter family of generalized entropies, Spq, and means mpq. To this end, assume that we want to calculate an entropy and a mean for n non-negative real numbers {x1,,xn
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We derive a two-parameter family of generalized entropies, Spq, and means mpq. To this end, assume that we want to calculate an entropy and a mean for n non-negative real numbers {x1,,xn}. For comparison, we consider {m1,,mk} where mi = m for all i = 1,,k and where m and k are chosen such that the lp and lq norms of {x1,,xn} and {m1,,mk} coincide. We formally allow k to be real. Then, we define k, log k, and m to be a generalized cardinality kpq, a generalized entropy Spq, and a generalized mean mpq respectively. We show that this family of entropies includes the Shannon and Rényi entropies and that the family of generalized means includes the power means (such as arithmetic, harmonic, geometric, root-mean-square, maximum, and minimum) as well as novel means of Shannon-like and Rényi-like forms. A thermodynamic interpretation arises from the fact that the lp norm is closely related to the partition function at inverse temperature β = p. Namely, two systems possess the same generalized entropy and generalized mean energy if and only if their partition functions agree at two temperatures, which is also equivalent to the condition that their Helmholtz free energies agree at these two temperatures. Full article
(This article belongs to the Special Issue Advances in Applied Thermodynamics)
Open AccessArticle Bearing Fault Diagnosis Based on Multiscale Permutation Entropy and Support Vector Machine
Entropy 2012, 14(8), 1343-1356; doi:10.3390/e14081343
Received: 31 May 2012 / Revised: 26 June 2012 / Accepted: 24 July 2012 / Published: 27 July 2012
Cited by 44 | PDF Full-text (292 KB) | HTML Full-text | XML Full-text
Abstract
Bearing fault diagnosis has attracted significant attention over the past few decades. It consists of two major parts: vibration signal feature extraction and condition classification for the extracted features. In this paper, multiscale permutation entropy (MPE) was introduced for feature extraction from faulty
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Bearing fault diagnosis has attracted significant attention over the past few decades. It consists of two major parts: vibration signal feature extraction and condition classification for the extracted features. In this paper, multiscale permutation entropy (MPE) was introduced for feature extraction from faulty bearing vibration signals. After extracting feature vectors by MPE, the support vector machine (SVM) was applied to automate the fault diagnosis procedure. Simulation results demonstrated that the proposed method is a very powerful algorithm for bearing fault diagnosis and has much better performance than the methods based on single scale permutation entropy (PE) and multiscale entropy (MSE). Full article
Open AccessArticle Impact of Interference in Coexisting Wireless Networks with Applications to Arbitrarily Varying Bidirectional Broadcast Channels
Entropy 2012, 14(8), 1357-1398; doi:10.3390/e14081357
Received: 31 May 2012 / Revised: 26 July 2012 / Accepted: 26 July 2012 / Published: 2 August 2012
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Abstract
The paradigm shift from an exclusive allocation of frequency bands, one for each system, to a shared use of frequencies comes along with the need of new concepts since interference will be an ubiquitous phenomenon. In this paper, we use the concept of
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The paradigm shift from an exclusive allocation of frequency bands, one for each system, to a shared use of frequencies comes along with the need of new concepts since interference will be an ubiquitous phenomenon. In this paper, we use the concept of arbitrarily varying channels to model the impact of unknown interference caused by coexisting wireless systems which operate on the same frequencies. Within this framework, capacity can be zero if pre-specified encoders and decoders are used. This necessitates the use of more sophisticated coordination schemes where the choice of encoders and decoders is additionally coordinated based on common randomness. As an application we study the arbitrarily varying bidirectional broadcast channel and derive the capacity regions for different coordination strategies. This problem is motivated by decode-and-forward bidirectional or two-way relaying, where a relay establishes a bidirectional communication between two other nodes while sharing the resources with other coexisting wireless networks. Full article
(This article belongs to the Special Issue Information Theory Applied to Communications and Networking)
Open AccessArticle An Integral Representation of the Relative Entropy
Entropy 2012, 14(8), 1469-1477; doi:10.3390/e14081469
Received: 15 June 2012 / Revised: 28 July 2012 / Accepted: 2 August 2012 / Published: 8 August 2012
Cited by 4 | PDF Full-text (91 KB) | HTML Full-text | XML Full-text
Abstract
Recently the identity of de Bruijn type between the relative entropy and the relative Fisher information with the reference moving has been unveiled by Verdú via MMSE in estimation theory. In this paper, we shall give another proof of this identity in more
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Recently the identity of de Bruijn type between the relative entropy and the relative Fisher information with the reference moving has been unveiled by Verdú via MMSE in estimation theory. In this paper, we shall give another proof of this identity in more direct way that the derivative is calculated by applying integrations by part with the heat equation. We shall also derive an integral representation of the relative entropy, as one of the applications of which the logarithmic Sobolev inequality for centered Gaussian measures will be given. Full article
Open AccessArticle Wavelet q-Fisher Information for Scaling Signal Analysis
Entropy 2012, 14(8), 1478-1500; doi:10.3390/e14081478
Received: 10 May 2012 / Revised: 13 June 2012 / Accepted: 28 June 2012 / Published: 8 August 2012
Cited by 2 | PDF Full-text (1274 KB) | HTML Full-text | XML Full-text
Abstract
Abstract: This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further
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Abstract: This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further analysis flexibility with the parameter q. In the limit of q → 1, wavelet q-Fisher information reduces to the standard wavelet Fisher information and for q > 2 it reverses its behavior. Experimental results on synthesized fGn signals validates the level-shift detection capabilities of wavelet q-Fisher information. A comparative study also shows that wavelet q-Fisher information locates structural changes in correlated and anti-correlated fGn signals in a way comparable with standard breakpoint location techniques but at a fraction of the time. Finally, the application of this quantifier to H.263 encoded video signals is presented. Full article
Open AccessArticle Potential and Evolution of Compressed Air Energy Storage: Energy and Exergy Analyses
Entropy 2012, 14(8), 1501-1521; doi:10.3390/e14081501
Received: 25 June 2012 / Revised: 8 August 2012 / Accepted: 8 August 2012 / Published: 10 August 2012
Cited by 37 | PDF Full-text (574 KB) | HTML Full-text | XML Full-text
Abstract
Energy storage systems are increasingly gaining importance with regard to their role in achieving load levelling, especially for matching intermittent sources of renewable energy with customer demand, as well as for storing excess nuclear or thermal power during the daily cycle. Compressed air
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Energy storage systems are increasingly gaining importance with regard to their role in achieving load levelling, especially for matching intermittent sources of renewable energy with customer demand, as well as for storing excess nuclear or thermal power during the daily cycle. Compressed air energy storage (CAES), with its high reliability, economic feasibility, and low environmental impact, is a promising method for large-scale energy storage. Although there are only two large-scale CAES plants in existence, recently, a number of CAES projects have been initiated around the world, and some innovative concepts of CAES have been proposed. Existing CAES plants have some disadvantages such as energy loss due to dissipation of heat of compression, use of fossil fuels, and dependence on geological formations. This paper reviews the main drawbacks of the existing CAES systems and presents some innovative concepts of CAES, such as adiabatic CAES, isothermal CAES, micro-CAES combined with air-cycle heating and cooling, and constant-pressure CAES combined with pumped hydro storage that can address such problems and widen the scope of CAES applications, by energy and exergy analyses. These analyses greatly help us to understand the characteristics of each CAES system and compare different CAES systems. Full article
(This article belongs to the Special Issue Exergy: Analysis and Applications)
Open AccessArticle The Entropy of a Discrete Real Variable
Entropy 2012, 14(8), 1522-1538; doi:10.3390/e14081522
Received: 12 June 2012 / Revised: 3 August 2012 / Accepted: 6 August 2012 / Published: 17 August 2012
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Abstract
The discrete Shannon entropy H was formulated only to measure indeterminacy effected through a set of probabilities, but the indeterminacy in a real-valued discrete variable depends on both the allowed outcomes x and the corresponding probabilities Þ. A fundamental measure that is sensitive
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The discrete Shannon entropy H was formulated only to measure indeterminacy effected through a set of probabilities, but the indeterminacy in a real-valued discrete variable depends on both the allowed outcomes x and the corresponding probabilities Þ. A fundamental measure that is sensitive to both x and p is derived here from the total differential entropy of a continuous real variable and its conjugate in the discrete limit, where the conjugate is universally eliminated. The asymptotic differential entropy recovers H plus the new measure, named ≡, which provides a novel probe of intrinsic organization in sequences of real numbers. Full article
Open AccessArticle Optimization of Two-Stage Peltier Modules: Structure and Exergetic Efficiency
Entropy 2012, 14(8), 1539-1552; doi:10.3390/e14081539
Received: 27 June 2012 / Revised: 4 August 2012 / Accepted: 16 August 2012 / Published: 21 August 2012
Cited by 5 | PDF Full-text (346 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we undertake the theoretical analysis of a two-stage semiconductor thermoelectric module (TEM) which contains an arbitrary and different number of thermocouples, n1 and n2, in each stage (pyramid-styled TEM). The analysis is based on a dimensionless entropy
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In this paper we undertake the theoretical analysis of a two-stage semiconductor thermoelectric module (TEM) which contains an arbitrary and different number of thermocouples, n1 and n2, in each stage (pyramid-styled TEM). The analysis is based on a dimensionless entropy balance set of equations. We study the effects of n1 and n2, the flowing electric currents through each stage, the applied temperatures and the thermoelectric properties of the semiconductor materials on the exergetic efficiency. Our main result implies that the electric currents flowing in each stage must necessarily be different with a ratio about 4.3 if the best thermal performance and the highest temperature difference possible between the cold and hot side of the device are pursued. This fact had not been pointed out before for pyramid-styled two stage TEM. The ratio n1/n2 should be about 8. Full article
(This article belongs to the Special Issue Exergy: Analysis and Applications)
Open AccessArticle Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review
Entropy 2012, 14(8), 1553-1577; doi:10.3390/e14081553
Received: 1 July 2012 / Revised: 10 August 2012 / Accepted: 21 August 2012 / Published: 23 August 2012
Cited by 104 | PDF Full-text (365 KB) | HTML Full-text | XML Full-text
Abstract
Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics,
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Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
Open AccessArticle Stability of Accelerating Cosmology in Two Scalar-Tensor Theory: Little Rip versus de Sitter
Entropy 2012, 14(8), 1578-1605; doi:10.3390/e14081578
Received: 21 July 2012 / Revised: 14 August 2012 / Accepted: 16 August 2012 / Published: 23 August 2012
Cited by 28 | PDF Full-text (314 KB) | HTML Full-text | XML Full-text
Abstract
We develop the general reconstruction scheme in two scalar model. The quintom-like theory which may describe (different) non-singular Little Rip or de Sitter cosmology is reconstructed. The number of scalar phantom dark energy models (with Little Rip cosmology or asymptotically de Sitter evolution)
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We develop the general reconstruction scheme in two scalar model. The quintom-like theory which may describe (different) non-singular Little Rip or de Sitter cosmology is reconstructed. The number of scalar phantom dark energy models (with Little Rip cosmology or asymptotically de Sitter evolution) is presented. Stability issue of such dark energy cosmologies as well as the flow to fixed points are studied. The stability of Little Rip universe which leads to dissolution of bound objects sometime in future indicates that no classical transition to de Sitter space occurs. The possibility of unification of inflation with Little Rip dark energy in two scalar theory is briefly mentioned. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

Review

Jump to: Research

Open AccessReview The Initial Common Pathway of Inflammation, Disease, and Sudden Death
Entropy 2012, 14(8), 1399-1442; doi:10.3390/e14081399
Received: 29 June 2012 / Revised: 19 July 2012 / Accepted: 20 July 2012 / Published: 2 August 2012
Cited by 11 | PDF Full-text (1223 KB) | HTML Full-text | XML Full-text
Abstract
In reviewing the literature pertaining to interfacial water, colloidal stability, and cell membrane function, we are led to propose that a cascade of events that begins with acute exogenous surfactant-induced interfacial water stress can explain the etiology of sudden death syndrome (SDS), as
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In reviewing the literature pertaining to interfacial water, colloidal stability, and cell membrane function, we are led to propose that a cascade of events that begins with acute exogenous surfactant-induced interfacial water stress can explain the etiology of sudden death syndrome (SDS), as well as many other diseases associated with modern times. A systemic lowering of serum zeta potential mediated by exogenous cationic surfactant administration is the common underlying pathophysiology. The cascade leads to subsequent inflammation, serum sickness, thrombohemorrhagic phenomena, colloidal instability, and ultimately even death. We propose that a sufficient precondition for sudden death is lowered bioavailability of certain endogenous sterol sulfates, sulfated glycolipids, and sulfated glycosaminoglycans, which are essential in maintaining biological equipose, energy metabolism, membrane function, and thermodynamic stability in living organisms. Our literature review provides the basis for the presentation of a novel hypothesis as to the origin of endogenous bio-sulfates which involves energy transduction from sunlight. Our hypothesis is amply supported by a growing body of data showing that parenteral administration of substances that lower serum zeta potential results in kosmotropic cationic and/or chaotropic anionic interfacial water stress, and the resulting cascade. Full article
(This article belongs to the Special Issue Biosemiotic Entropy: Disorder, Disease, and Mortality)
Open AccessReview Application of Hydration Thermodynamics to the Evaluation of Protein Structures and Protein-Ligand Binding
Entropy 2012, 14(8), 1443-1468; doi:10.3390/e14081443
Received: 28 June 2012 / Revised: 18 July 2012 / Accepted: 2 August 2012 / Published: 7 August 2012
Cited by 5 | PDF Full-text (824 KB) | HTML Full-text | XML Full-text
Abstract
Discovering the mechanism that controls the three-dimensional structures of proteins, which are closely related to their biological functions, remains a challenge in modern biological science, even for small proteins. From a thermodynamic viewpoint, the native structure of a protein can be understood as
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Discovering the mechanism that controls the three-dimensional structures of proteins, which are closely related to their biological functions, remains a challenge in modern biological science, even for small proteins. From a thermodynamic viewpoint, the native structure of a protein can be understood as the global minimum of the free energy landscape of the protein-water system. However, it is still difficult to describe the energetics of protein stability in an effective manner. Recently, our group developed a free energy function with an all-atomic description for a protein that focuses on hydration thermodynamics. The validity of the function was examined using structural decoy sets that provide numerous misfolded “non-native” structures. For all targeted sets, the function was able to identify the experimentally determined native structure as the best structure. The energy function can also be used to calculate the binding free energy of a protein with ligands. I review the physicochemical theories employed in the development of the free energy function and recent studies evaluating protein structure stability and protein-ligand binding affinities that use this function. Full article

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