Entropy

3004 KiB

Open AccessArticle

A Robust Sparse Adaptive Filtering Algorithm with a Correntropy Induced Metric Constraint for Broadband Multi-Path Channel Estimation

by Yingsong Li, Zhan Jin, Yanyan Wang and Rui Yang

Entropy 2016, 18(10), 380; https://doi.org/10.3390/e18100380 - 24 Oct 2016

Cited by 23 | Viewed by 5951

Abstract

A robust sparse least-mean mixture-norm (LMMN) algorithm is proposed, and its performance is appraised in the context of estimating a broadband multi-path wireless channel. The proposed algorithm is implemented via integrating a correntropy-induced metric (CIM) penalty into the conventional LMMN algorithm to modify [...] Read more.

A robust sparse least-mean mixture-norm (LMMN) algorithm is proposed, and its performance is appraised in the context of estimating a broadband multi-path wireless channel. The proposed algorithm is implemented via integrating a correntropy-induced metric (CIM) penalty into the conventional LMMN algorithm to modify the basic cost function, which is denoted as the CIM-based LMMN (CIM-LMMN) algorithm. The proposed CIM-LMMN algorithm is derived in detail within the kernel framework. The updating equation of CIM-LMMN can provide a zero attractor to attract the non-dominant channel coefficients to zeros, and it also gives a tradeoff between the sparsity and the estimation misalignment. Moreover, the channel estimation behavior is investigated over a broadband sparse multi-path wireless channel, and the simulation results are compared with the least mean square/fourth (LMS/F), least mean square (LMS), least mean fourth (LMF) and the recently-developed sparse channel estimation algorithms. The channel estimation performance obtained from the designated sparse channel estimation demonstrates that the CIM-LMMN algorithm outperforms the recently-developed sparse LMMN algorithms and the relevant sparse channel estimation algorithms. From the results, we can see that our CIM-LMMN algorithm is robust and is superior to these mentioned algorithms in terms of both the convergence speed rate and the channel estimation misalignment for estimating a sparse channel. Full article

(This article belongs to the Special Issue Maximum Entropy and Its Application II)

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1170 KiB

Open AccessArticle

A Novel Sequence-Based Feature for the Identification of DNA-Binding Sites in Proteins Using Jensen–Shannon Divergence

by Truong Khanh Linh Dang, Cornelia Meckbach, Rebecca Tacke, Stephan Waack and Mehmet Gültas

Entropy 2016, 18(10), 379; https://doi.org/10.3390/e18100379 - 24 Oct 2016

Cited by 5 | Viewed by 6979

Abstract

The knowledge of protein-DNA interactions is essential to fully understand the molecular activities of life. Many research groups have developed various tools which are either structure- or sequence-based approaches to predict the DNA-binding residues in proteins. The structure-based methods usually achieve good results, [...] Read more.

The knowledge of protein-DNA interactions is essential to fully understand the molecular activities of life. Many research groups have developed various tools which are either structure- or sequence-based approaches to predict the DNA-binding residues in proteins. The structure-based methods usually achieve good results, but require the knowledge of the 3D structure of protein; while sequence-based methods can be applied to high-throughput of proteins, but require good features. In this study, we present a new information theoretic feature derived from Jensen–Shannon Divergence (JSD) between amino acid distribution of a site and the background distribution of non-binding sites. Our new feature indicates the difference of a certain site from a non-binding site, thus it is informative for detecting binding sites in proteins. We conduct the study with a five-fold cross validation of 263 proteins utilizing the Random Forest classifier. We evaluate the functionality of our new features by combining them with other popular existing features such as position-specific scoring matrix (PSSM), orthogonal binary vector (OBV), and secondary structure (SS). We notice that by adding our features, we can significantly boost the performance of Random Forest classifier, with a clear increment of sensitivity and Matthews correlation coefficient (MCC). Full article

(This article belongs to the Special Issue Entropy on Biosignals and Intelligent Systems)

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7083 KiB

Open AccessArticle

Second Law Analysis of Nanofluid Flow within a Circular Minichannel Considering Nanoparticle Migration

by Mehdi Bahiraei and Navid Cheraghi Kazerooni

Entropy 2016, 18(10), 378; https://doi.org/10.3390/e18100378 - 21 Oct 2016

Cited by 3 | Viewed by 4905

Abstract

In the current research, entropy generation for the water–alumina nanofluid flow is studied in a circular minichannel for the laminar regime under constant wall heat flux in order to evaluate irreversibilities arising from friction and heat transfer. To this end, simulations are carried [...] Read more.

In the current research, entropy generation for the water–alumina nanofluid flow is studied in a circular minichannel for the laminar regime under constant wall heat flux in order to evaluate irreversibilities arising from friction and heat transfer. To this end, simulations are carried out considering the particle migration effects. Due to particle migration, the nanoparticles incorporate non-uniform distribution at the cross-section of the pipe, such that the concentration is larger at central areas. The concentration non-uniformity increases by augmenting the mean concentration, particle size, and Reynolds number. The rates of entropy generation are evaluated both locally and globally (integrated). The obtained results show that particle migration changes the thermal and frictional entropy generation rates significantly, particularly at high Reynolds numbers, large concentrations, and coarser particles. Hence, this phenomenon should be considered in examinations related to energy in the field of nanofluids. Full article

(This article belongs to the Special Issue Limits to the Second Law of Thermodynamics: Experiment and Theory)

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17446 KiB

Open AccessArticle

Isothermal Oxidation of Aluminized Coatings on High-Entropy Alloys

by Che-Wei Tsai, Kuen-Cheng Sung, Kzauki Kasai and Hideyuki Murakami

Entropy 2016, 18(10), 376; https://doi.org/10.3390/e18100376 - 20 Oct 2016

Cited by 6 | Viewed by 5198

Abstract

The isothermal oxidation resistance of Al_0.2Co_1.5CrFeNi_1.5Ti_0.3 high-entropy alloy is analyzed and the microstructural evolution of the oxide layer is studied. The limited aluminum, about 3.6 at %, leads to the non-continuous alumina. The present alloy is [...] Read more.

The isothermal oxidation resistance of Al_0.2Co_1.5CrFeNi_1.5Ti_0.3 high-entropy alloy is analyzed and the microstructural evolution of the oxide layer is studied. The limited aluminum, about 3.6 at %, leads to the non-continuous alumina. The present alloy is insufficient for severe circumstances only due to chromium oxide that is 10 μm after 1173 K for 360 h. Thus, the aluminized high-entropy alloys (HEAs) are further prepared by the industrial packing cementation process at 1273 K and 1323 K. The aluminizing coating is 50 μm at 1273 K after 5 h. The coating growth is controlled by the diffusion of aluminum. The interdiffusion zone reveals two regions that are the Ti-, Co-, Ni-rich area and the Fe-, Cr-rich area. The oxidation resistance of aluminizing HEA improves outstandingly, and sustains at 1173 K and 1273 K for 441 h without any spallation. The alumina at the surface and the stable interface contribute to the performance of this Al_0.2Co_1.5CrFeNi_1.5Ti_0.3 alloy. Full article

(This article belongs to the Special Issue High-Entropy Alloys and High-Entropy-Related Materials)

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345 KiB

Open AccessArticle

Non-Asymptotic Confidence Sets for Circular Means

by Thomas Hotz, Florian Kelma and Johannes Wieditz

Entropy 2016, 18(10), 375; https://doi.org/10.3390/e18100375 - 20 Oct 2016

Cited by 3 | Viewed by 4779

Abstract

The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that [...] Read more.

The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and for a real data set. Full article

(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)

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4763 KiB

Open AccessArticle

On the Virtual Cell Transmission in Ultra Dense Networks

by Xiaopeng Zhu, Jie Zeng, Xin Su, Chiyang Xiao, Jing Wang and Lianfen Huang

Entropy 2016, 18(10), 374; https://doi.org/10.3390/e18100374 - 20 Oct 2016

Cited by 11 | Viewed by 5060

Abstract

Ultra dense networks (UDN) are identified as one of the key enablers for 5G, since they can provide an ultra high spectral reuse factor exploiting proximal transmissions. By densifying the network infrastructure equipment, it is highly possible that each user will have one [...] Read more.

Ultra dense networks (UDN) are identified as one of the key enablers for 5G, since they can provide an ultra high spectral reuse factor exploiting proximal transmissions. By densifying the network infrastructure equipment, it is highly possible that each user will have one or more dedicated serving base station antennas, introducing the user-centric virtual cell paradigm. However, due to irregular deployment of a large amount of base station antennas, the interference environment becomes rather complex, thus introducing severe interferences among different virtual cells. This paper focuses on the downlink transmission scheme in UDN where a large number of users and base station antennas is uniformly spread over a certain area. An interference graph is first created based on the large-scale fadings to give a potential description of the interference relationship among the virtual cells. Then, base station antennas and users in the virtual cells within the same maximally-connected component are grouped together and merged into one new virtual cell cluster, where users are jointly served via zero-forcing (ZF) beamforming. A multi-virtual-cell minimum mean square error precoding scheme is further proposed to mitigate the inter-cluster interference. Additionally, the interference alignment framework is proposed based on the low complexity virtual cell merging to eliminate the strong interference between different virtual cells. Simulation results show that the proposed interference graph-based virtual cell merging approach can attain the average user spectral efficiency performance of the grouping scheme based on virtual cell overlapping with a smaller virtual cell size and reduced signal processing complexity. Besides, the proposed user-centric transmission scheme greatly outperforms the BS-centric transmission scheme (maximum ratio transmission (MRT)) in terms of both the average user spectral efficiency and edge user spectral efficiency. What is more, interference alignment based on the low complexity virtual cell merging can achieve much better performance than ZF and MRT precoding in terms of average user spectral efficiency. Full article

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1337 KiB

Open AccessCorrection

Correction: Jacobsen, C.S., et al. Continuous Variable Quantum Key Distribution with a Noisy Laser. Entropy 2015, 17, 4654–4663

by Christian S. Jacobsen, Tobias Gehring and Ulrik L. Andersen

Entropy 2016, 18(10), 373; https://doi.org/10.3390/e18100373 - 20 Oct 2016

Viewed by 3265

Abstract

n/a Full article

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4329 KiB

Open AccessArticle

Point Information Gain and Multidimensional Data Analysis

by Renata Rychtáriková, Jan Korbel, Petr Macháček, Petr Císař, Jan Urban and Dalibor Štys

Entropy 2016, 18(10), 372; https://doi.org/10.3390/e18100372 - 19 Oct 2016

Cited by 14 | Viewed by 5953

Abstract

We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these [...] Read more.

We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data with the examples of several images and discuss further possible utilizations in other fields of data processing. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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7021 KiB

Open AccessArticle

Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two Delays

by Jing Wang and Yuling Wang

Entropy 2016, 18(10), 371; https://doi.org/10.3390/e18100371 - 19 Oct 2016

Cited by 5 | Viewed by 3881

Abstract

In this paper, we build a model of energy-savings and emission-reductions with two delays. In this model, it is assumed that the interaction between energy-savings and emission-reduction and that between carbon emissions and economic growth are delayed. We examine the local stability and [...] Read more.

In this paper, we build a model of energy-savings and emission-reductions with two delays. In this model, it is assumed that the interaction between energy-savings and emission-reduction and that between carbon emissions and economic growth are delayed. We examine the local stability and the existence of a Hopf bifurcation at the equilibrium point of the system. By employing System Complexity Theory, we also analyze the impact of delays and the feedback control on stability and entropy of the system are analyzed from two aspects: single delay and double delays. In numerical simulation section, we test the theoretical analysis by using means bifurcation diagram, the largest Lyapunov exponent diagrams, attractor, time-domain plot, Poincare section plot, power spectrum, entropy diagram, 3-D surface chart and 4-D graph, the simulation results demonstrating that the inappropriate changes of delays and the feedback control will result in instability and fluctuation of carbon emissions. Finally, the bifurcation control is achieved by using the method of variable feedback control. Hence, we conclude that the greater the value of the control parameter, the better the effect of the bifurcation control. The results will provide for the development of energy-saving and emission-reduction policies. Full article

(This article belongs to the Section Complexity)

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450 KiB

Open AccessFeature PaperArticle

From Tools in Symplectic and Poisson Geometry to J.-M. Souriau’s Theories of Statistical Mechanics and Thermodynamics

by Charles-Michel Marle

Entropy 2016, 18(10), 370; https://doi.org/10.3390/e18100370 - 19 Oct 2016

Cited by 34 | Viewed by 5890

Abstract

I present in this paper some tools in symplectic and Poisson geometry in view of their applications in geometric mechanics and mathematical physics. After a short discussion of the Lagrangian an Hamiltonian formalisms, including the use of symmetry groups, and a presentation of [...] Read more.

I present in this paper some tools in symplectic and Poisson geometry in view of their applications in geometric mechanics and mathematical physics. After a short discussion of the Lagrangian an Hamiltonian formalisms, including the use of symmetry groups, and a presentation of the Tulczyjew’s isomorphisms (which explain some aspects of the relations between these formalisms), I explain the concept of manifold of motions of a mechanical system and its use, due to J.-M. Souriau, in statistical mechanics and thermodynamics. The generalization of the notion of thermodynamic equilibrium in which the one-dimensional group of time translations is replaced by a multi-dimensional, maybe non-commutative Lie group, is fully discussed and examples of applications in physics are given. Full article

(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)

415 KiB

Open AccessArticle

Chemical Reactions Using a Non-Equilibrium Wigner Function Approach

by Ramón F. Álvarez-Estrada and Gabriel F. Calvo

Entropy 2016, 18(10), 369; https://doi.org/10.3390/e18100369 - 19 Oct 2016

Cited by 4 | Viewed by 4047

Abstract

A three-dimensional model of binary chemical reactions is studied. We consider an ab initio quantum two-particle system subjected to an attractive interaction potential and to a heat bath at thermal equilibrium at absolute temperature

T > 0

. Under the sole action of [...] Read more.

A three-dimensional model of binary chemical reactions is studied. We consider an ab initio quantum two-particle system subjected to an attractive interaction potential and to a heat bath at thermal equilibrium at absolute temperature

T > 0

. Under the sole action of the attraction potential, the two particles can either be bound or unbound to each other. While at

T = 0

, there is no transition between both states, such a transition is possible when

T > 0

(due to the heat bath) and plays a key role as

k_{B} T

approaches the magnitude of the attractive potential. We focus on a quantum regime, typical of chemical reactions, such that: (a) the thermal wavelength is shorter than the range of the attractive potential (lower limit on T) and (b)

(3 / 2) k_{B} T

does not exceed the magnitude of the attractive potential (upper limit on T). In this regime, we extend several methods previously applied to analyze the time duration of DNA thermal denaturation. The two-particle system is then described by a non-equilibrium Wigner function. Under Assumptions (a) and (b), and for sufficiently long times, defined by a characteristic time scale D that is subsequently estimated, the general dissipationless non-equilibrium equation for the Wigner function is approximated by a Smoluchowski-like equation displaying dissipation and quantum effects. A comparison with the standard chemical kinetic equations is made. The time τ required for the two particles to transition from the bound state to unbound configurations is studied by means of the mean first passage time formalism. An approximate formula for τ, in terms of D and exhibiting the Arrhenius exponential factor, is obtained. Recombination processes are also briefly studied within our framework and compared with previous well-known methods. Full article

(This article belongs to the Special Issue Recent Advances in Non-Equilibrium Statistical Mechanics and Its Application)

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Open AccessArticle

A Hydrodynamic Model for Silicon Nanowires Based on the Maximum Entropy Principle

by Orazio Muscato and Tina Castiglione

Entropy 2016, 18(10), 368; https://doi.org/10.3390/e18100368 - 19 Oct 2016

Cited by 14 | Viewed by 4444

Abstract

Silicon nanowires (SiNW) are quasi-one-dimensional structures in which the electrons are spatially confined in two directions, and they are free to move along the axis of the wire. The spatial confinement is governed by the Schrödinger–Poisson system, which must be coupled to the [...] Read more.

Silicon nanowires (SiNW) are quasi-one-dimensional structures in which the electrons are spatially confined in two directions, and they are free to move along the axis of the wire. The spatial confinement is governed by the Schrödinger–Poisson system, which must be coupled to the transport in the free motion direction. For devices with the characteristic length of a few tens of nanometers, the transport of the electrons along the axis of the wire can be considered semiclassical, and it can be dealt with by the multi-sub-band Boltzmann transport equations (MBTE). By taking the moments of the MBTE, a hydrodynamic model has been formulated, where explicit closure relations for the fluxes and production terms (i.e., the moments on the collisional operator) are obtained by means of the maximum entropy principle of extended thermodynamics, including the scattering of electrons with phonons, impurities and surface roughness scattering. Numerical results are shown for a SiNW transistor. Full article

(This article belongs to the Special Issue Maximum Entropy Principle and Semiconductors)

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2100 KiB

Open AccessArticle

Methodology for Simulation and Analysis of Complex Adaptive Supply Network Structure and Dynamics Using Information Theory

by Joshua Rodewald, John Colombi, Kyle Oyama and Alan Johnson

Entropy 2016, 18(10), 367; https://doi.org/10.3390/e18100367 - 18 Oct 2016

Cited by 6 | Viewed by 5544

Abstract

Supply networks existing today in many industries can behave as complex adaptive systems making them more difficult to analyze and assess. Being able to fully understand both the complex static and dynamic structures of a complex adaptive supply network (CASN) are key to [...] Read more.

Supply networks existing today in many industries can behave as complex adaptive systems making them more difficult to analyze and assess. Being able to fully understand both the complex static and dynamic structures of a complex adaptive supply network (CASN) are key to being able to make more informed management decisions and prioritize resources and production throughout the network. Previous efforts to model and analyze CASN have been impeded by the complex, dynamic nature of the systems. However, drawing from other complex adaptive systems sciences, information theory provides a model-free methodology removing many of those barriers, especially concerning complex network structure and dynamics. With minimal information about the network nodes, transfer entropy can be used to reverse engineer the network structure while local transfer entropy can be used to analyze the network structure’s dynamics. Both simulated and real-world networks were analyzed using this methodology. Applying the methodology to CASNs allows the practitioner to capitalize on observations from the highly multidisciplinary field of information theory which provides insights into CASN’s self-organization, emergence, stability/instability, and distributed computation. This not only provides managers with a more thorough understanding of a system’s structure and dynamics for management purposes, but also opens up research opportunities into eventual strategies to monitor and manage emergence and adaption within the environment. Full article

(This article belongs to the Special Issue Transfer Entropy II)

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4742 KiB

Open AccessArticle

Intelligent Security IT System for Detecting Intruders Based on Received Signal Strength Indicators

by Yunsick Sung

Entropy 2016, 18(10), 366; https://doi.org/10.3390/e18100366 - 16 Oct 2016

Cited by 5 | Viewed by 5948

Abstract

Given that entropy-based IT technology has been applied in homes, office buildings and elsewhere for IT security systems, diverse kinds of intelligent services are currently provided. In particular, IT security systems have become more robust and varied. However, access control systems still depend [...] Read more.

Given that entropy-based IT technology has been applied in homes, office buildings and elsewhere for IT security systems, diverse kinds of intelligent services are currently provided. In particular, IT security systems have become more robust and varied. However, access control systems still depend on tags held by building entrants. Since tags can be obtained by intruders, an approach to counter the disadvantages of tags is required. For example, it is possible to track the movement of tags in intelligent buildings in order to detect intruders. Therefore, each tag owner can be judged by analyzing the movements of their tags. This paper proposes a security approach based on the received signal strength indicators (RSSIs) of beacon-based tags to detect intruders. The normal RSSI patterns of moving entrants are obtained and analyzed. Intruders can be detected when abnormal RSSIs are measured in comparison to normal RSSI patterns. In the experiments, one normal and one abnormal scenario are defined for collecting the RSSIs of a Bluetooth-based beacon in order to validate the proposed method. When the RSSIs of both scenarios are compared to pre-collected RSSIs, the RSSIs of the abnormal scenario are about 61% more different compared to the RSSIs of the normal scenario. Therefore, intruders in buildings can be detected by considering RSSI differences. Full article

(This article belongs to the Collection Entropy-Based Applied Cryptography and Enhanced Security for Future IT Environments)

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984 KiB

Open AccessArticle

Boltzmann Sampling by Degenerate Optical Parametric Oscillator Network for Structure-Based Virtual Screening

by Hiromasa Sakaguchi, Koji Ogata, Tetsu Isomura, Shoko Utsunomiya, Yoshihisa Yamamoto and Kazuyuki Aihara

Entropy 2016, 18(10), 365; https://doi.org/10.3390/e18100365 - 13 Oct 2016

Cited by 32 | Viewed by 8517

Abstract

A structure-based lead optimization procedure is an essential step to finding appropriate ligand molecules binding to a target protein structure in order to identify drug candidates. This procedure takes a known structure of a protein-ligand complex as input, and structurally similar compounds with [...] Read more.

A structure-based lead optimization procedure is an essential step to finding appropriate ligand molecules binding to a target protein structure in order to identify drug candidates. This procedure takes a known structure of a protein-ligand complex as input, and structurally similar compounds with the query ligand are designed in consideration with all possible combinations of atomic species. This task is, however, computationally hard since such combinatorial optimization problems belong to the non-deterministic nonpolynomial-time hard (NP-hard) class. In this paper, we propose the structure-based lead generation and optimization procedures by a degenerate optical parametric oscillator (DOPO) network. Results of numerical simulation demonstrate that the DOPO network efficiently identifies a set of appropriate ligand molecules according to the Boltzmann sampling law. Full article

(This article belongs to the Collection Quantum Information)

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833 KiB

Open AccessArticle

Entropy Rate Estimates for Natural Language—A New Extrapolation of Compressed Large-Scale Corpora

by Ryosuke Takahira, Kumiko Tanaka-Ishii and Łukasz Dębowski

Entropy 2016, 18(10), 364; https://doi.org/10.3390/e18100364 - 12 Oct 2016

Cited by 31 | Viewed by 9872

Abstract

One of the fundamental questions about human language is whether its entropy rate is positive. The entropy rate measures the average amount of information communicated per unit time. The question about the entropy of language dates back to experiments by Shannon in 1951, [...] Read more.

One of the fundamental questions about human language is whether its entropy rate is positive. The entropy rate measures the average amount of information communicated per unit time. The question about the entropy of language dates back to experiments by Shannon in 1951, but in 1990 Hilberg raised doubt regarding a correct interpretation of these experiments. This article provides an in-depth empirical analysis, using 20 corpora of up to 7.8 gigabytes across six languages (English, French, Russian, Korean, Chinese, and Japanese), to conclude that the entropy rate is positive. To obtain the estimates for data length tending to infinity, we use an extrapolation function given by an ansatz. Whereas some ansatzes were proposed previously, here we use a new stretched exponential extrapolation function that has a smaller error of fit. Thus, we conclude that the entropy rates of human languages are positive but approximately 20% smaller than without extrapolation. Although the entropy rate estimates depend on the script kind, the exponent of the ansatz function turns out to be constant across different languages and governs the complexity of natural language in general. In other words, in spite of typological differences, all languages seem equally hard to learn, which partly confirms Hilberg’s hypothesis. Full article

(This article belongs to the Section Complexity)

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330 KiB

Open AccessArticle

The Shell Collapsar—A Possible Alternative to Black Holes

by Trevor W. Marshall

Entropy 2016, 18(10), 363; https://doi.org/10.3390/e18100363 - 12 Oct 2016

Viewed by 5118

Abstract

This article argues that a consistent description is possible for gravitationally collapsed bodies, in which collapse stops before the object reaches its gravitational radius, the density reaching a maximum close to the surface and then decreasing towards the centre. The way towards such [...] Read more.

This article argues that a consistent description is possible for gravitationally collapsed bodies, in which collapse stops before the object reaches its gravitational radius, the density reaching a maximum close to the surface and then decreasing towards the centre. The way towards such a description was indicated in the classic Oppenheimer-Snyder (OS) 1939 analysis of a dust star. The title of that article implied support for a black-hole solution, but the present article shows that the final OS density distribution accords with gravastar and other shell models. The parallel Oppenheimer-Volkoff (OV) study of 1939 used the equation of state for a neutron gas, but could consider only stationary solutions of the field equations. Recently we found that the OV equation of state permits solutions with minimal rather than maximal central density, and here we find a similar topology for the OS dust collapsar; a uniform dust-ball which starts with large radius, and correspondingly small density, and collapses to a shell at the gravitational radius with density decreasing monotonically towards the centre. Though no longer considered central in black-hole theory, the OS dust model gave the first exact, time-dependent solution of the field equations. Regarded as a limiting case of OV, it indicates the possibility of neutron stars of unlimited mass with a similar shell topology. Progress in observational astronomy will distinguish this class of collapsars from black holes. Full article

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840 KiB

Open AccessArticle

Measures of Difference and Significance in the Era of Computer Simulations, Meta-Analysis, and Big Data

by Reinout Heijungs, Patrik J.G. Henriksson and Jeroen B. Guinée

Entropy 2016, 18(10), 361; https://doi.org/10.3390/e18100361 - 9 Oct 2016

Cited by 18 | Viewed by 5967

Abstract

In traditional research, repeated measurements lead to a sample of results, and inferential statistics can be used to not only estimate parameters, but also to test statistical hypotheses concerning these parameters. In many cases, the standard error of the estimates decreases (asymptotically) with [...] Read more.

In traditional research, repeated measurements lead to a sample of results, and inferential statistics can be used to not only estimate parameters, but also to test statistical hypotheses concerning these parameters. In many cases, the standard error of the estimates decreases (asymptotically) with the square root of the sample size, which provides a stimulus to probe large samples. In simulation models, the situation is entirely different. When probability distribution functions for model features are specified, the probability distribution function of the model output can be approached using numerical techniques, such as bootstrapping or Monte Carlo sampling. Given the computational power of most PCs today, the sample size can be increased almost without bounds. The result is that standard errors of parameters are vanishingly small, and that almost all significance tests will lead to a rejected null hypothesis. Clearly, another approach to statistical significance is needed. This paper analyzes the situation and connects the discussion to other domains in which the null hypothesis significance test (NHST) paradigm is challenged. In particular, the notions of effect size and Cohen’s d provide promising alternatives for the establishment of a new indicator of statistical significance. This indicator attempts to cover significance (precision) and effect size (relevance) in one measure. Although in the end more fundamental changes are called for, our approach has the attractiveness of requiring only a minimal change to the practice of statistics. The analysis is not only relevant for artificial samples, but also for present-day huge samples, associated with the availability of big data. Full article

(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)

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3548 KiB

Open AccessArticle

Metric for Estimating Congruity between Quantum Images

by Abdullah M. Iliyasu, Fei Yan and Kaoru Hirota

Entropy 2016, 18(10), 360; https://doi.org/10.3390/e18100360 - 9 Oct 2016

Cited by 23 | Viewed by 6006

Abstract

An enhanced quantum-based image fidelity metric, the QIFM metric, is proposed as a tool to assess the “congruity” between two or more quantum images. The often confounding contrariety that distinguishes between classical and quantum information processing makes the widely accepted peak-signal-to-noise-ratio (PSNR) ill-suited [...] Read more.

An enhanced quantum-based image fidelity metric, the QIFM metric, is proposed as a tool to assess the “congruity” between two or more quantum images. The often confounding contrariety that distinguishes between classical and quantum information processing makes the widely accepted peak-signal-to-noise-ratio (PSNR) ill-suited for use in the quantum computing framework, whereas the prohibitive cost of the probability-based similarity score makes it imprudent for use as an effective image quality metric. Unlike the aforementioned image quality measures, the proposed QIFM metric is calibrated as a pixel difference-based image quality measure that is sensitive to the intricacies inherent to quantum image processing (QIP). As proposed, the QIFM is configured with in-built non-destructive measurement units that preserve the coherence necessary for quantum computation. This design moderates the cost of executing the QIFM in order to estimate congruity between two or more quantum images. A statistical analysis also shows that our proposed QIFM metric has a better correlation with digital expectation of likeness between images than other available quantum image quality measures. Therefore, the QIFM offers a competent substitute for the PSNR as an image quality measure in the quantum computing framework thereby providing a tool to effectively assess fidelity between images in quantum watermarking, quantum movie aggregation and other applications in QIP. Full article

(This article belongs to the Collection Quantum Information)

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Open AccessArticle

Tolerance Redistributing of the Reassembly Dimensional Chain on Measure of Uncertainty

by Conghu Liu

Entropy 2016, 18(10), 348; https://doi.org/10.3390/e18100348 - 9 Oct 2016

Cited by 15 | Viewed by 4626

Abstract

How to use the limited precision of remanufactured parts to assemble higher-quality remanufactured products is a challenge for remanufacturing engineering under uncertainty. On the basis of analyzing the uncertainty of remanufacturing parts, this paper takes tolerance redistributing of the reassembly (remanufactured assembly) dimensional [...] Read more.

How to use the limited precision of remanufactured parts to assemble higher-quality remanufactured products is a challenge for remanufacturing engineering under uncertainty. On the basis of analyzing the uncertainty of remanufacturing parts, this paper takes tolerance redistributing of the reassembly (remanufactured assembly) dimensional chain as the research object. An entropy model to measure the uncertainty of assembly dimensional is built, and we quantify the degree of the uncertainty gap between reassembly and assembly. Then, in order to make sure the uncertainty of reassembly is not lower than that of assembly, the tolerance redistribution optimization model of the reassembly dimensional chain is proposed which is based on the tolerance of the grading allocation method. Finally, this paper takes the remanufactured gearbox assembly dimension chain as an example. The redistribution optimization model saves 19.11% of the cost with the assembly precision of remanufactured products. It provides new technical and theoretical support to expand the utilization rate of remanufactured parts and improve reassembly precision. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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2043 KiB

Open AccessFeature PaperArticle

Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties

by Eduardo Jonathan Torres-Herrera, Jonathan Karp, Marco Távora and Lea F. Santos

Entropy 2016, 18(10), 359; https://doi.org/10.3390/e18100359 - 8 Oct 2016

Cited by 38 | Viewed by 6763

Abstract

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von [...] Read more.

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems. Full article

(This article belongs to the Special Issue Quantum Information 2016)

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1230 KiB

Open AccessArticle

Ordering Quantiles through Confidence Statements

by Cassio P. De Campos, Carlos A. De B. Pereira, Paola M. V. Rancoita and Adriano Polpo

Entropy 2016, 18(10), 357; https://doi.org/10.3390/e18100357 - 8 Oct 2016

Cited by 1 | Viewed by 4539

Abstract

Ranking variables according to their relevance to predict an outcome is an important task in biomedicine. For instance, such ranking can be used for selecting a smaller number of genes for then applying other sophisticated experiments only on genes identified as important. A [...] Read more.

Ranking variables according to their relevance to predict an outcome is an important task in biomedicine. For instance, such ranking can be used for selecting a smaller number of genes for then applying other sophisticated experiments only on genes identified as important. A nonparametric method called Quor is designed to provide a confidence value for the order of arbitrary quantiles of different populations using independent samples. This confidence may provide insights about possible differences among groups and yields a ranking of importance for the variables. Computations are efficient and use exact distributions with no need for asymptotic considerations. Experiments with simulated data and with multiple real -omics data sets are performed, and they show advantages and disadvantages of the method. Quor has no assumptions but independence of samples, thus it might be a better option when assumptions of other methods cannot be asserted. The software is publicly available on CRAN. Full article

(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)

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425 KiB

Open AccessArticle

Entropy Cross-Efficiency Model for Decision Making Units with Interval Data

by Lupei Wang, Lei Li and Ningxi Hong

Entropy 2016, 18(10), 358; https://doi.org/10.3390/e18100358 - 1 Oct 2016

Cited by 19 | Viewed by 5501

Abstract

The cross-efficiency method, as a Data Envelopment Analysis (DEA) extension, calculates the cross efficiency of each decision making unit (DMU) using the weights of all decision making units (DMUs). The major advantage of the cross-efficiency method is that it can provide a complete [...] Read more.

The cross-efficiency method, as a Data Envelopment Analysis (DEA) extension, calculates the cross efficiency of each decision making unit (DMU) using the weights of all decision making units (DMUs). The major advantage of the cross-efficiency method is that it can provide a complete ranking for all DMUs. In addition, the cross-efficiency method could eliminate unrealistic weight results. However, the existing cross-efficiency methods only evaluate the relative efficiencies of a set of DMUs with exact values of inputs and outputs. If the input or output data of DMUs are imprecise, such as the interval data, the existing methods fail to assess the efficiencies of these DMUs. To address this issue, we propose the introduction of Shannon entropy into the cross-efficiency method. In the proposed model, intervals of all cross-efficiency values are firstly obtained by the interval cross-efficiency method. Then, a distance entropy model is proposed to obtain the weights of interval efficiency. Finally, all alternatives are ranked by their relative Euclidean distance from the positive solution. Full article

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2218 KiB

Open AccessArticle

Entropy-Based Application Layer DDoS Attack Detection Using Artificial Neural Networks

by Khundrakpam Johnson Singh, Khelchandra Thongam and Tanmay De

Entropy 2016, 18(10), 350; https://doi.org/10.3390/e18100350 - 1 Oct 2016

Cited by 69 | Viewed by 13282

Abstract

Distributed denial-of-service (DDoS) attack is one of the major threats to the web server. The rapid increase of DDoS attacks on the Internet has clearly pointed out the limitations in current intrusion detection systems or intrusion prevention systems (IDS/IPS), mostly caused by application-layer [...] Read more.

Distributed denial-of-service (DDoS) attack is one of the major threats to the web server. The rapid increase of DDoS attacks on the Internet has clearly pointed out the limitations in current intrusion detection systems or intrusion prevention systems (IDS/IPS), mostly caused by application-layer DDoS attacks. Within this context, the objective of the paper is to detect a DDoS attack using a multilayer perceptron (MLP) classification algorithm with genetic algorithm (GA) as learning algorithm. In this work, we analyzed the standard EPA-HTTP (environmental protection agency-hypertext transfer protocol) dataset and selected the parameters that will be used as input to the classifier model for differentiating the attack from normal profile. The parameters selected are the HTTP GET request count, entropy, and variance for every connection. The proposed model can provide a better accuracy of 98.31%, sensitivity of 0.9962, and specificity of 0.0561 when compared to other traditional classification models. Full article

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4063 KiB

Open AccessArticle

Analysis of Entropy Generation in Mixed Convective Peristaltic Flow of Nanofluid

by Tasawar Hayat, Sadaf Nawaz, Ahmed Alsaedi and Maimona Rafiq

Entropy 2016, 18(10), 355; https://doi.org/10.3390/e18100355 - 30 Sep 2016

Cited by 18 | Viewed by 6213

Abstract

This article examines entropy generation in the peristaltic transport of nanofluid in a channel with flexible walls. Single walled carbon nanotubes (SWCNT) and multiple walled carbon nanotubes (MWCNT) with water as base fluid are utilized in this study. Mixed convection is also considered [...] Read more.

This article examines entropy generation in the peristaltic transport of nanofluid in a channel with flexible walls. Single walled carbon nanotubes (SWCNT) and multiple walled carbon nanotubes (MWCNT) with water as base fluid are utilized in this study. Mixed convection is also considered in the present analysis. Viscous dissipation effect is present. Moreover, slip conditions are encountered for both velocity and temperature at the boundaries. Analysis is prepared in the presence of long wavelength and small Reynolds number assumptions. Two phase model for nanofluids are employed. Nonlinear system of equations for small Grashof number is solved. Velocity and temperature are examined for different parameters via graphs. Streamlines are also constructed to analyze the trapping. Results show that axial velocity and temperature of the nanofluid decrease when we enhance the nanoparticle volume fraction. Moreover, the wall elastance parameter shows increase in axial velocity and temperature, whereas decrease in both quantities is noticed for damping coefficient. Decrease is notified in Entropy generation and Bejan number for increasing values of nanoparticle volume fraction. Full article

(This article belongs to the Special Issue Advances in Applied Thermodynamics II)

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11845 KiB

Open AccessArticle

Exergetic Analysis of a Novel Solar Cooling System for Combined Cycle Power Plants

by Francesco Calise, Luigi Libertini and Maria Vicidomini

Entropy 2016, 18(10), 356; https://doi.org/10.3390/e18100356 - 29 Sep 2016

Cited by 11 | Viewed by 5622

Abstract

This paper presents a detailed exergetic analysis of a novel high-temperature Solar Assisted Combined Cycle (SACC) power plant. The system includes a solar field consisting of innovative high-temperature flat plate evacuated solar thermal collectors, a double stage LiBr-H₂O absorption chiller, pumps, [...] Read more.

This paper presents a detailed exergetic analysis of a novel high-temperature Solar Assisted Combined Cycle (SACC) power plant. The system includes a solar field consisting of innovative high-temperature flat plate evacuated solar thermal collectors, a double stage LiBr-H₂O absorption chiller, pumps, heat exchangers, storage tanks, mixers, diverters, controllers and a simple single-pressure Combined Cycle (CC) power plant. Here, a high temperature solar cooling system is coupled with a conventional combined cycle, in order to pre-cool gas turbine inlet air in order to enhance system efficiency and electrical capacity. In this paper, the system is analyzed from an exergetic point of view, on the basis of an energy-economic model presented in a recent work, where the obtained main results show that SACC exhibits a higher electrical production and efficiency with respect to the conventional CC. The system performance is evaluated by a dynamic simulation, where detailed simulation models are implemented for all the components included in the system. In addition, for all the components and for the system as whole, energy and exergy balances are implemented in order to calculate the magnitude of the irreversibilities within the system. In fact, exergy analysis is used in order to assess: exergy destructions and exergetic efficiencies. Such parameters are used in order to evaluate the magnitude of the irreversibilities in the system and to identify the sources of such irreversibilities. Exergetic efficiencies and exergy destructions are dynamically calculated for the 1-year operation of the system. Similarly, exergetic results are also integrated on weekly and yearly bases in order to evaluate the corresponding irreversibilities. The results showed that the components of the Joule cycle (combustor, turbine and compressor) are the major sources of irreversibilities. System overall exergetic efficiency was around 48%. Average weekly solar collector exergetic efficiency ranged from 6.5% to 14.5%, significantly increasing during the summer season. Conversely, absorption chiller exergy efficiency varies from 7.7% to 20.2%, being higher during the winter season. Combustor exergy efficiency is stably close to 68%, whereas the exergy efficiencies of the remaining components are higher than 80%. Full article

(This article belongs to the Special Issue Thermoeconomics for Energy Efficiency)

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378 KiB

Open AccessArticle

A Langevin Canonical Approach to the Study of Quantum Stochastic Resonance in Chiral Molecules

by Germán Rojas-Lorenzo, Helen Clara Peñate-Rodríguez, Anais Dorta-Urra, Pedro Bargueño and Salvador Miret-Artés

Entropy 2016, 18(10), 354; https://doi.org/10.3390/e18100354 - 29 Sep 2016

Cited by 1 | Viewed by 4442

Abstract

A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification [...] Read more.

A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules. Full article

(This article belongs to the Section Statistical Physics)

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13147 KiB

Open AccessReview

Generalized Thermodynamic Optimization for Iron and Steel Production Processes: Theoretical Exploration and Application Cases

by Lingen Chen, Huijun Feng and Zhihui Xie

Entropy 2016, 18(10), 353; https://doi.org/10.3390/e18100353 - 29 Sep 2016

Cited by 128 | Viewed by 16895

Abstract

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is [...] Read more.

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries. Full article

(This article belongs to the Special Issue Advances in Applied Thermodynamics II)

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346 KiB

Open AccessArticle

Propositions for Confidence Interval in Systematic Sampling on Real Line

by Mehmet Niyazi Çankaya

Entropy 2016, 18(10), 352; https://doi.org/10.3390/e18100352 - 28 Sep 2016

Cited by 2 | Viewed by 4756

Abstract

Systematic sampling is used as a method to get the quantitative results from tissues and radiological images. Systematic sampling on a real line (

R

) is a very attractive method within which biomedical imaging is consulted by practitioners. For the systematic sampling [...] Read more.

Systematic sampling is used as a method to get the quantitative results from tissues and radiological images. Systematic sampling on a real line (

R

) is a very attractive method within which biomedical imaging is consulted by practitioners. For the systematic sampling on

R

, the measurement function (

M F

) occurs by slicing the three-dimensional object equidistant systematically. The currently-used covariogram model in variance approximation is tested for the different measurement functions in a class to see the performance on the variance estimation of systematically-sampled

R

. An exact calculation method is proposed to calculate the constant

λ (q, N)

of the confidence interval in the systematic sampling. The exact value of constant

λ (q, N)

is examined for the different measurement functions, as well. As a result, it is observed from the simulation that the proposed

M F

should be used to check the performances of the variance approximation and the constant

λ (q, N)

. Synthetic data can support the results of real data. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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8854 KiB

Open AccessArticle

Influence of the Aqueous Environment on Protein Structure—A Plausible Hypothesis Concerning the Mechanism of Amyloidogenesis

by Irena Roterman, Mateusz Banach, Barbara Kalinowska and Leszek Konieczny

Entropy 2016, 18(10), 351; https://doi.org/10.3390/e18100351 - 28 Sep 2016

Cited by 17 | Viewed by 6391

Abstract

The aqueous environment is a pervasive factor which, in many ways, determines the protein folding process and consequently the activity of proteins. Proteins are unable to perform their function unless immersed in water (membrane proteins excluded from this statement). Tertiary conformational stabilization is [...] Read more.

The aqueous environment is a pervasive factor which, in many ways, determines the protein folding process and consequently the activity of proteins. Proteins are unable to perform their function unless immersed in water (membrane proteins excluded from this statement). Tertiary conformational stabilization is dependent on the presence of internal force fields (nonbonding interactions between atoms), as well as an external force field generated by water. The hitherto the unknown structuralization of water as the aqueous environment may be elucidated by analyzing its effects on protein structure and function. Our study is based on the fuzzy oil drop model—a mechanism which describes the formation of a hydrophobic core and attempts to explain the emergence of amyloid-like fibrils. A set of proteins which vary with respect to their fuzzy oil drop status (including titin, transthyretin and a prion protein) have been selected for in-depth analysis to suggest the plausible mechanism of amyloidogenesis. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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