Entropy doi: 10.3390/e20050309

Authors: Qinglin Cheng Anbo Zheng Shuang Song Hao Wu Lili Lv Yang Liu

With the increasing demand of oil products in China, the energy consumption of pipeline operation will continue to rise greatly, as well as the cost of oil transportation. In the field of practical engineering, saving energy, reducing energy consumption and adapting to the international oil situation are the development trends and represent difficult problems. Based on the basic principle of non-equilibrium thermodynamics, this paper derives the field equilibrium equations of non-equilibrium thermodynamic process for pipeline transportation. To seek the bilinear form of “force” and “flow” in the non-equilibrium thermodynamics of entropy generation rate, the oil pipeline exergy balance equation and the exergy transfer pipeline dynamic equation of the irreversibility were established. The exergy balance equation was applied to energy balance evaluation system, which makes the system more perfect. The exergy flow transfer law of the waxy oil pipeline were explored deeply from the directions of dynamic exergy, pressure exergy, thermal exergy and diffusion exergy. Taking an oil pipeline as an example, the influence factors of exergy transfer coefficient and exergy flow density were analyzed separately.

]]>Entropy doi: 10.3390/e20050308

Authors: Marco Favretti

In a paper published in this journal, I addressed the following problem: under which conditions will two scientists, observing the same system and sharing the same initial information, reach the same probabilistic description upon the application of the Maximum Entropy inference principle (MaxEnt) independent of the probability distribution chosen to set up the MaxEnt procedure. This is a minimal objectivity requirement which is generally asked for scientific investigation. In the same paper, I applied the findings to a critical examination of the application of MaxEnt made in Harte&rsquo;s Maximum Entropy Theory of Ecology (METE). Prof. Harte published a comment to my paper and this is my reply. For the sake of the reader who may be unaware of the content of the papers, I have tried to make this reply self-contained and to skip technical details. However, I invite the interested reader to consult the previously published papers.

]]>Entropy doi: 10.3390/e20040307

Authors: Joseph Lizier Nils Bertschinger Jürgen Jost Michael Wibral

The formulation of the Partial Information Decomposition (PID) framework by Williams and Beer in 2010 attracted a significant amount of attention to the problem of defining redundant (or shared), unique and synergistic (or complementary) components of mutual information that a set of source variables provides about a target. This attention resulted in a number of measures proposed to capture these concepts, theoretical investigations into such measures, and applications to empirical data (in particular to datasets from neuroscience). In this Special Issue on “Information Decomposition of Target Effects from Multi-Source Interactions” at Entropy, we have gathered current work on such information decomposition approaches from many of the leading research groups in the field. We begin our editorial by providing the reader with a review of previous information decomposition research, including an overview of the variety of measures proposed, how they have been interpreted and applied to empirical investigations. We then introduce the articles included in the special issue one by one, providing a similar categorisation of these articles into: i. proposals of new measures; ii. theoretical investigations into properties and interpretations of such approaches, and iii. applications of these measures in empirical studies. We finish by providing an outlook on the future of the field.

]]>Entropy doi: 10.3390/e20040306

Authors: Chunhong Long Jin Yu

High fidelity gene transcription and replication require kinetic discrimination of nucleotide substrate species by RNA and DNA polymerases under chemical non-equilibrium conditions. It is known that sufficiently large free energy driving force is needed for each polymerization or elongation cycle to maintain far-from-equilibrium to achieve low error rates. Considering that each cycle consists of multiple kinetic steps with different transition rates, one expects that the kinetic modulations by polymerases are not evenly conducted at each step. We show that accelerations at different kinetic steps impact quite differently to the overall elongation characteristics. In particular, for forward transitions that discriminate cognate and non-cognate nucleotide species to serve as kinetic selection checkpoints, the transition cannot be accelerated too quickly nor retained too slowly to obtain low error rates, as balancing is needed between the nucleotide selectivity and the non-equilibrium driving. Such a balance is not the same as the speed-accuracy tradeoff in which high accuracy is always obtained at sacrifice of speed. For illustration purposes, we used three-state and five-state models of nucleotide addition in the polymerase elongation and show how the non-equilibrium steady state characteristics change upon variations on stepwise forward or backward kinetics. Notably, by using the multi-step elongation schemes and parameters from T7 RNA polymerase transcription elongation, we demonstrate that individual transitions serving as selection checkpoints need to proceed at moderate rates in order to sustain the necessary non-equilibrium drives as well as to allow nucleotide selections for an optimal error control. We also illustrate why rate-limiting conformational transitions of the enzyme likely play a significant role in the error reduction.

]]>Entropy doi: 10.3390/e20040305

Authors: Partha Maji Robert Mullins

Deep convolutional neural networks (ConvNets), which are at the heart of many new emerging applications, achieve remarkable performance in audio and visual recognition tasks. Unfortunately, achieving accuracy often implies significant computational costs, limiting deployability. In modern ConvNets it is typical for the convolution layers to consume the vast majority of computational resources during inference. This has made the acceleration of these layers an important research area in academia and industry. In this paper, we examine the effects of co-optimizing the internal structures of the convolutional layers and underlying implementation of fundamental convolution operation. We demonstrate that a combination of these methods can have a big impact on the overall speedup of a ConvNet, achieving a ten-fold increase over baseline. We also introduce a new class of fast one-dimensional (1D) convolutions for ConvNets using the Toom–Cook algorithm. We show that our proposed scheme is mathematically well-grounded, robust, and does not require any time-consuming retraining, while still achieving speedups solely from convolutional layers with no loss in baseline accuracy.

]]>Entropy doi: 10.3390/e20040304

Authors: Hongduo Cao Hui Ouyang Ying Li Xiaobin Li Ye Chen

For the first time, the power law characteristics of stock price jump intervals have been empirically found generally in stock markets. The classical jump-diffusion model is described as the jump-diffusion model with power law (JDMPL). An artificial stock market (ASM) is designed in which an agent&rsquo;s investment strategies, risk appetite, learning ability, adaptability, and dynamic changes are considered to create a dynamically changing environment. An analysis of these data packets from the ASM simulation indicates that, with the learning mechanism, the ASM reflects the kurtosis, fat-tailed distribution characteristics commonly observed in real markets. Data packets obtained from simulating the ASM for 5010 periods are incorporated into a regression analysis. Analysis results indicate that the JDMPL effectively characterizes the stock price jumps in the market. The results also support the hypothesis that the time interval of stock price jumps is consistent with the power law and indicate that the diversity and dynamic changes of agents&rsquo; investment strategies are the reasons for the discontinuity in the changes of stock prices.

]]>Entropy doi: 10.3390/e20040303

Authors: Tatsuaki Tsuruyama

Cell signal transduction is a non-equilibrium process characterized by the reaction cascade. This study aims to quantify and compare signal transduction cascades using a model of signal transduction. The signal duration was found to be linked to step-by-step transition probability, which was determined using information theory. By applying the fluctuation theorem for reversible signal steps, the transition probability was described using the average entropy production rate. Specifically, when the signal event number during the cascade was maximized, the average entropy production rate was found to be conserved during the entire cascade. This approach provides a quantitative means of analyzing signal transduction and identifies an effective cascade for a signaling network.

]]>Entropy doi: 10.3390/e20040302

Authors: Kailing Yao Yunpeng Luo Yang Yang Xin Liu Yuli Zhang Changhua Yao

This article investigates the traffic offloading problem in the heterogeneous network. The location of small cells is considered as an important factor in two aspects: the amount of resources they share for offloaded macrocell users and the performance enhancement they bring after offloading. A location-aware incentive mechanism is therefore designed to incentivize small cells to serve macrocell users. Instead of taking the amount of resources shared as the basis of the reward division, the performance promotion brought to the macro network is taken. Meanwhile, in order to ensure the superiority of small cell users, the significance of them weighs heavier than macrocell users instead of being treated equally. The offloading problem is formulated as a Stackelberg game where the macro cell base station is the leader and small cells are followers. The Stackelberg equilibrium of the game is proved to be existing and unique. It is also proved to be the optimum of the proposed problem. Simulation and numerical results verify the effectiveness of the proposed method.

]]>Entropy doi: 10.3390/e20040301

Authors: Takashi Arima Tommaso Ruggeri Masaru Sugiyama

After summarizing the present status of Rational Extended Thermodynamics (RET) of gases, which is an endeavor to generalize the Navier&ndash;Stokes and Fourier (NSF) theory of viscous heat-conducting fluids, we develop the molecular RET theory of rarefied polyatomic gases with 15 independent fields. The theory is justified, at mesoscopic level, by a generalized Boltzmann equation in which the distribution function depends on two internal variables that take into account the energy exchange among the different molecular modes of a gas, that is, translational, rotational, and vibrational modes. By adopting the generalized Bhatnagar, Gross and Krook (BGK)-type collision term, we derive explicitly the closed system of field equations with the use of the Maximum Entropy Principle (MEP). The NSF theory is derived from the RET theory as a limiting case of small relaxation times via the Maxwellian iteration. The relaxation times introduced in the theory are shown to be related to the shear and bulk viscosities and heat conductivity.

]]>Entropy doi: 10.3390/e20040300

Authors: J. A. Méndez-Bermúdez R. Aguilar-Sánchez

We perform a detailed numerical study of the localization properties of the eigenfunctions of one-dimensional (1D) tight-binding wires with on-site disorder characterized by long-tailed distributions: For large ϵ , P ( ϵ ) &sim; 1 / ϵ 1 + &alpha; with &alpha; &isin; ( 0 , 2 ] ; where ϵ are the on-site random energies. Our model serves as a generalization of 1D Lloyd&rsquo;s model, which corresponds to &alpha; = 1 . In particular, we demonstrate that the information length &beta; of the eigenfunctions follows the scaling law &beta; = &gamma; x / ( 1 + &gamma; x ) , with x = &xi; / L and &gamma; &equiv; &gamma; ( &alpha; ) . Here, &xi; is the eigenfunction localization length (that we extract from the scaling of Landauer&rsquo;s conductance) and L is the wire length. We also report that for &alpha; = 2 the properties of the 1D Anderson model are effectively reproduced.

]]>Entropy doi: 10.3390/e20040299

Authors: Alma Elena Piceno Martínez Ernesto Benítez Rodríguez Julio Abraham Mendoza Fierro Marcela Maribel Méndez Otero Luis Manuel Arévalo Aguilar

The Stern&ndash;Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C ( z , &theta; ) by redefining the Banaszek&ndash;W&oacute;dkiewicz correlation in terms of the Wigner operator, that is C ( z , &theta; ) = &lang; &Psi; | W ^ ( z , p z ) &sigma; ^ ( &theta; ) | &Psi; &rang; , where W ^ ( z , p z ) is the Wigner operator, &sigma; ^ ( &theta; ) is the Pauli spin operator in an arbitrary direction &theta; and | &Psi; &rang; is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser&ndash;Horne&ndash;Shimony&ndash;Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.

]]>Entropy doi: 10.3390/e20040298

Authors: Samuel A Cushman

Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal to the logarithm of the number of ways a lattice with a given dimensionality and number of classes can be arranged to produce the same total amount of edge between cells of different classes. However, that work seemed to also suggest that the feasibility of applying this method to real landscapes was limited due to intractably large numbers of possible arrangements of raster cells in large landscapes. Here I extend that work by showing that: (1) the proportion of arrangements rather than the number with a given amount of edge length provides a means to calculate unbiased relative configurational entropy, obviating the need to compute all possible configurations of a landscape lattice; (2) the edge lengths of randomized landscape mosaics are normally distributed, following the central limit theorem; and (3) given this normal distribution it is possible to fit parametric probability density functions to estimate the expected proportion of randomized configurations that have any given edge length, enabling the calculation of configurational entropy on any landscape regardless of size or number of classes. I evaluate the boundary limits (4) for this normal approximation for small landscapes with a small proportion of a minority class and show it holds under all realistic landscape conditions. I further (5) demonstrate that this relationship holds for a sample of real landscapes that vary in size, patch richness, and evenness of area in each cover type, and (6) I show that the mean and standard deviation of the normally distributed edge lengths can be predicted nearly perfectly as a function of the size, patch richness and diversity of a landscape. Finally, (7) I show that the configurational entropy of a landscape is highly related to the dimensionality of the landscape, the number of cover classes, the evenness of landscape composition across classes, and landscape heterogeneity. These advances provide a means for researchers to directly estimate the frequency distribution of all possible macrostates of any observed landscape, and then directly calculate the relative configurational entropy of the observed macrostate, and to understand the ecological meaning of different amounts of configurational entropy. These advances enable scientists to take configurational entropy from a concept to an applied tool to measure and compare the disorder of real landscapes with an objective and unbiased measure based on entropy and the second law.

]]>Entropy doi: 10.3390/e20040297

Authors: Conor Finn Joseph Lizier

What are the distinct ways in which a set of predictor variables can provide information about a target variable? When does a variable provide unique information, when do variables share redundant information, and when do variables combine synergistically to provide complementary information? The redundancy lattice from the partial information decomposition of Williams and Beer provided a promising glimpse at the answer to these questions. However, this structure was constructed using a much criticised measure of redundant information, and despite sustained research, no completely satisfactory replacement measure has been proposed. In this paper, we take a different approach, applying the axiomatic derivation of the redundancy lattice to a single realisation from a set of discrete variables. To overcome the difficulty associated with signed pointwise mutual information, we apply this decomposition separately to the unsigned entropic components of pointwise mutual information which we refer to as the specificity and ambiguity. This yields a separate redundancy lattice for each component. Then based upon an operational interpretation of redundancy, we define measures of redundant specificity and ambiguity enabling us to evaluate the partial information atoms in each lattice. These atoms can be recombined to yield the sought-after multivariate information decomposition. We apply this framework to canonical examples from the literature and discuss the results and the various properties of the decomposition. In particular, the pointwise decomposition using specificity and ambiguity satisfies a chain rule over target variables, which provides new insights into the so-called two-bit-copy example.

]]>Entropy doi: 10.3390/e20040296

Authors: Taymaz Rahkar Farshi Recep Demirci Mohammad-Reza Feizi-Derakhshi

In image clustering, it is desired that pixels assigned in the same class must be the same or similar. In other words, the homogeneity of a cluster must be high. In gray scale image segmentation, the specified goal is achieved by increasing the number of thresholds. However, the determination of multiple thresholds is a typical issue. Moreover, the conventional thresholding algorithms could not be used in color image segmentation. In this study, a new color image clustering algorithm with multilevel thresholding has been presented and, it has been shown how to use the multilevel thresholding techniques for color image clustering. Thus, initially, threshold selection techniques such as the Otsu and Kapur methods were employed for each color channel separately. The objective functions of both approaches have been integrated with the forest optimization algorithm (FOA) and particle swarm optimization (PSO) algorithm. In the next stage, thresholds determined by optimization algorithms were used to divide color space into small cubes or prisms. Each sub-cube or prism created in the color space was evaluated as a cluster. As the volume of prisms affects the homogeneity of the clusters created, multiple thresholds were employed to reduce the sizes of the sub-cubes. The performance of the proposed method was tested with different images. It was observed that the results obtained were more efficient than conventional methods.

]]>Entropy doi: 10.3390/e20040295

Authors: Chunlei Fan Zhigang Xie Qun Ding

In this paper, a three-dimensional chaotic system with a hidden attractor is introduced. The complex dynamic behaviors of the system are analyzed with a Poincar&eacute; cross section, and the equilibria and initial value sensitivity are analyzed by the method of numerical simulation. Further, we designed a new algorithm based on complementary ensemble empirical mode decomposition (CEEMD) and permutation entropy (PE) that can effectively enhance digital chaotic sequence complexity. In addition, an image encryption experiment was performed with post-processing of the chaotic binary sequences by the new algorithm. The experimental results show good performance of the chaotic binary sequence.

]]>Entropy doi: 10.3390/e20040294

Authors: Nathan Argaman

One of the basic assumptions underlying Bell&rsquo;s theorem is the causal arrow of time, having to do with temporal order rather than spatial separation. Nonetheless, the physical assumptions regarding causality are seldom studied in this context, and often even go unmentioned, in stark contrast with the many different possible locality conditions which have been studied and elaborated upon. In the present work, some retrocausal toy-models which reproduce the predictions of quantum mechanics for Bell-type correlations are reviewed. It is pointed out that a certain toy-model which is ostensibly superdeterministic&mdash;based on denying the free-variable status of some of quantum mechanics&rsquo; input parameters&mdash;actually contains within it a complete retrocausal toy-model. Occam&rsquo;s razor thus indicates that the superdeterministic point of view is superfluous. A challenge is to generalize the retrocausal toy-models to a full theory&mdash;a reformulation of quantum mechanics&mdash;in which the standard causal arrow of time would be replaced by a more lenient one: an arrow of time applicable only to macroscopically-available information. In discussing such a reformulation, one finds that many of the perplexing features of quantum mechanics could arise naturally, especially in the context of stochastic theories.

]]>Entropy doi: 10.3390/e20040293

Authors: Jaesung Lee

The long-wave approximation of a falling film down an inclined plane with constant temperature is used to investigate the volumetric averaged entropy production. The velocity and temperature fields are numerically computed by the evolution equation at the deformable free interface. The dynamics of a falling film have an important role in the entropy production. When the layer shows an unstable evolution, the entropy production by fluid friction is much larger than that of the film with a stable flat interface. As the heat transfers actively from the free surface to the ambient air, the temperature gradient inside flowing films becomes large and the entropy generation by heat transfer increases. The contribution of fluid friction on the volumetric averaged entropy production is larger than that of heat transfer at moderate and high viscous dissipation parameters.

]]>Entropy doi: 10.3390/e20040292

Authors: Mohammed Daoud Maurice R. Kibler

A relation is established in the present paper between Dicke states in a d-dimensional space and vectors in the representation space of a generalized Weyl&ndash;Heisenberg algebra of finite dimension d. This provides a natural way to deal with the separable and entangled states of a system of N = d &minus; 1 symmetric qubit states. Using the decomposition property of Dicke states, it is shown that the separable states coincide with the Perelomov coherent states associated with the generalized Weyl&ndash;Heisenberg algebra considered in this paper. In the so-called Majorana scheme, the qudit (d-level) states are represented by N points on the Bloch sphere; roughly speaking, it can be said that a qudit (in a d-dimensional space) is describable by a N-qubit vector (in a N-dimensional space). In such a scheme, the permanent of the matrix describing the overlap between the N qubits makes it possible to measure the entanglement between the N qubits forming the qudit. This is confirmed by a Fubini&ndash;Study metric analysis. A new parameter, proportional to the permanent and called perma-concurrence, is introduced for characterizing the entanglement of a symmetric qudit arising from N qubits. For d = 3 ( &hArr; N = 2 ), this parameter constitutes an alternative to the concurrence for two qubits. Other examples are given for d = 4 and 5. A connection between Majorana stars and zeros of a Bargmmann function for qudits closes this article.

]]>Entropy doi: 10.3390/e20040291

Authors: Tao Shang Ke Li Jianwei Liu

With the practical implementation of continuous-variable quantum cryptographic protocols, security problems resulting from measurement-device loopholes are being given increasing attention. At present, research on measurement-device independency analysis is limited in quantum key distribution protocols, while there exist different security problems for different protocols. Considering the importance of quantum digital signature in quantum cryptography, in this paper, we attempt to analyze the measurement-device independency of continuous-variable quantum digital signature, especially continuous-variable quantum homomorphic signature. Firstly, we calculate the upper bound of the error rate of a protocol. If it is negligible on condition that all measurement devices are untrusted, the protocol is deemed to be measurement-device-independent. Then, we simplify the calculation by using the characteristics of continuous variables and prove the measurement-device independency of the protocol according to the calculation result. In addition, the proposed analysis method can be extended to other quantum cryptographic protocols besides continuous-variable quantum homomorphic signature.

]]>Entropy doi: 10.3390/e20040290

Authors: Sadaqat Rehman Shanshan Tu Obaid Rehman Yongfeng Huang Chathura Magurawalage Chin-Chen Chang

The convolution neural network (CNN) has achieved state-of-the-art performance in many computer vision applications e.g., classification, recognition, detection, etc. However, the global optimization of CNN training is still a problem. Fast classification and training play a key role in the development of the CNN. We hypothesize that the smoother and optimized the training of a CNN goes, the more efficient the end result becomes. Therefore, in this paper, we implement a modified resilient backpropagation (MRPROP) algorithm to improve the convergence and efficiency of CNN training. Particularly, a tolerant band is introduced to avoid network overtraining, which is incorporated with the global best concept for weight updating criteria to allow the training algorithm of the CNN to optimize its weights more swiftly and precisely. For comparison, we present and analyze four different training algorithms for CNN along with MRPROP, i.e., resilient backpropagation (RPROP), Levenberg–Marquardt (LM), conjugate gradient (CG), and gradient descent with momentum (GDM). Experimental results showcase the merit of the proposed approach on a public face and skin dataset.

]]>Entropy doi: 10.3390/e20040289

Authors: Luai Al-Labadi Zeynep Baskurt Michael Evans

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a prior, checking the prior for bias, checking for prior-data conflict and estimation and hypothesis assessment inferences based on a measure of evidence. A long-standing anomalous example is resolved by this approach to inference and an application is made to a practical problem of considerable importance, which, among other novel aspects of the analysis, involves the development of a relevant elicitation algorithm.

]]>Entropy doi: 10.3390/e20040288

Authors: Deniz Gençağa

Statistical relationships among the variables of a complex system reveal a lot about its physical behavior[...]

]]>Entropy doi: 10.3390/e20040287

Authors: Jean-Marc Girault Anne Humeau-Heurtier

Several entropy measures are now widely used to analyze real-world time series. Among them, we can cite approximate entropy, sample entropy and fuzzy entropy (FuzzyEn), the latter one being probably the most efficient among the three. However, FuzzyEn precision depends on the number of samples in the data under study. The longer the signal, the better it is. Nevertheless, long signals are often difficult to obtain in real applications. This is why we herein propose a new FuzzyEn that presents better precision than the standard FuzzyEn. This is performed by increasing the number of samples used in the computation of the entropy measure, without changing the length of the time series. Thus, for the comparisons of the patterns, the mean value is no longer a constraint. Moreover, translated patterns are not the only ones considered: reflected, inversed, and glide-reflected patterns are also taken into account. The new measure (so-called centered and averaged FuzzyEn) is applied to synthetic and biomedical signals. The results show that the centered and averaged FuzzyEn leads to more precise results than the standard FuzzyEn: the relative percentile range is reduced compared to the standard sample entropy and fuzzy entropy measures. The centered and averaged FuzzyEn could now be used in other applications to compare its performances to those of other already-existing entropy measures.

]]>Entropy doi: 10.3390/e20040286

Authors: Taiguang Gao Qing Wang Min Huang Xingwei Wang Yu Zhang

Upstream and downstream of supply chain enterprises often form a tactic vertical alliance to enhance their operational efficiency and maintain their competitive edges in the market. Hence, it is critical for an alliance to collaborate over their internal resources and resolve the profit conflicts among members, so that the functionality required by stakeholders can be fulfilled. As an effective solution, automated negotiation for the vertical allied enterprises team and stakeholder will sufficiently make use of emerging team advantages and significantly reduce the profit conflicts in teams with grouping decisions rather than unilateral decisions by some leader. In this paper, an automated negotiation model is designed to describe both the collaborative game process among the team members and the competitive negotiation process between the allied team and the stakeholder. Considering the co-competitiveness of the vertical allied team, the designed model helps the team members making decision for their own sake, and the team counter-offers for the ongoing negotiation are generated with non-cooperative game process, where the profit derived from negotiation result is distributed with Shapley value method according to contribution or importance contributed by each team member. Finally, a case study is given to testify the effectiveness of the designed model.

]]>Entropy doi: 10.3390/e20040285

Authors: John Harte

In the maximum entropy theory of ecology (METE), the form of a function describing the distribution of abundances over species and metabolic rates over individuals in an ecosystem is inferred using the maximum entropy inference procedure. Favretti shows that an alternative maximum entropy model exists that assumes the same prior knowledge and makes predictions that differ from METE’s. He shows that both cannot be correct and asserts that his is the correct one because it can be derived from a classic microstate-counting calculation. I clarify here exactly what the core entities and definitions are for METE, and discuss the relevance of two critical issues raised by Favretti: the existence of a counting procedure for microstates and the choices of definition of the core elements of a theory. I emphasize that a theorist controls how the core entities of his or her theory are defined, and that nature is the final arbiter of the validity of a theory.

]]>Entropy doi: 10.3390/e20040284

Authors: Hans Havlicek Karl Svozil

A new way of orthogonalizing ensembles of vectors by “lifting” them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.

]]>Entropy doi: 10.3390/e20040283

Authors: Shuangxin Wang Xin Zhao Meng Li Hong Wang

The performance evaluation of wind power forecasting under commercially operating circumstances is critical to a wide range of decision-making situations, yet difficult because of its stochastic nature. This paper firstly introduces a novel TRSWA-BP neural network, of which learning process is based on an efficiency tabu, real-coded, small-world optimization algorithm (TRSWA). In order to deal with the strong volatility and stochastic behavior of the wind power sequence, three forecasting models of the TRSWA-BP are presented, which are combined with EMD (empirical mode decomposition), PSR (phase space reconstruction), and EMD-based PSR. The error sequences of the above methods are then proved to have non-Gaussian properties, and a novel criterion of normalized Renyi’s quadratic entropy (NRQE) is proposed, which can evaluate their dynamic predicted accuracy. Finally, illustrative predictions of the next 1, 4, 6, and 24 h time-scales are examined by historical wind power data, under different evaluations. From the results, we can observe that not only do the proposed models effectively revise the error due to the fluctuation and multi-fractal property of wind power, but also that the NRQE can reserve its feasible assessment upon the stochastic predicted error.

]]>Entropy doi: 10.3390/e20040282

Authors: Shuting Cai Linqing Huang Xuesong Chen Xiaoming Xiong

Recently, a variety of chaos-based image encryption algorithms adopting the traditional permutation-diffusion structure have been suggested. Most of these algorithms cannot resist the powerful chosen-plaintext attack and chosen-ciphertext attack efficiently for less sensitivity to plain-image. This paper presents a symmetric color image encryption system based on plaintext-related random access bit-permutation mechanism (PRRABPM). In the proposed scheme, a new random access bit-permutation mechanism is used to shuffle 3D bit matrix transformed from an original color image, making the RGB components of the color image interact with each other. Furthermore, the key streams used in random access bit-permutation mechanism operation are extremely dependent on plain image in an ingenious way. Therefore, the encryption system is sensitive to tiny differences in key and original images, which means that it can efficiently resist chosen-plaintext attack and chosen-ciphertext attack. In the diffusion stage, the previous encrypted pixel is used to encrypt the current pixel. The simulation results show that even though the permutation-diffusion operation in our encryption scheme is performed only one time, the proposed algorithm has favorable security performance. Considering real-time applications, the encryption speed can be further improved.

]]>Entropy doi: 10.3390/e20040281

Authors: Masengo Ilunga

This study focuses preliminarily on the intra-tertiary catchment (TC) assessment of cross MAR pseudo-elasticity of entropy, which determines the impact of changes in MAR for a quaternary catchment (QC) on the entropy of another (other) QC(s). The TCs of the Upper Vaal catchment were used preliminarily for this assessment and surface water resources (WR) of South Africa of 1990 (WR90), of 2005 (WR2005) and of 2012 (WR2012) data sets were used. The TCs are grouped into three secondary catchments, i.e., downstream of Vaal Dam, upstrream of Vaal dam and Wilge. It is revealed that, there are linkages in terms of mean annual runoff (MAR) between QCs; which could be complements (negative cross elasticity) or substitutes (positive cross elasticity). It is shown that cross MAR pseudo-elasticity can be translated into correlation strength between QC pairs; i.e., high cross elasticity (low catchment resilience) and low cross elasticity (high catchment resilience). Implicitly, catchment resilience is shown to be associated with the risk of vulnerability (or sustainability level) of water resources, in terms of MAR, which is generally low (or high). Besides, for each TC, the dominance (of complements or substitutes) and the global highest cross MAR elasticity are determined. The overall average cross MAR elasticity of QCs for each TC was shown to be in the zone of tolerable entropy, hence the zone of functioning resilience. This could assure that water resources remained fairly sustainable in TCs that form the secondary catchments of the Upper Vaal. Cross MAR pseudo-elasticity concept could be further extended to an intra-secondary catchment assessment.

]]>Entropy doi: 10.3390/e20040280

Authors: Andrei Khrennikov Irina Basieva

The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser&ndash;Horne&ndash;Shimony&ndash;Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein&ndash;Podolsky&ndash;Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR&ndash;Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound Q CHSH = 2 2 to the classical bound C CHSH = 2 , i.e., F CHSH = Q CHSH C CHSH = 2 is less than the fraction of the quantum bound for the OB inequality Q OB = 3 2 to the classical bound C OB = 1 , i.e., F OB = Q OB C OB = 3 2 . Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high.

]]>Entropy doi: 10.3390/e20040279

Authors: Vitali Podgursky Andrei Bogatov Maxim Yashin Sergey Sobolev Iosif S. Gershman

The study deals with tribological properties of diamond films that were tested under reciprocal sliding conditions against Si3N4 balls. Adhesive and abrasive wear are explained in terms of nonequilibrium thermodynamic model of friction and wear. Surface roughness alteration and film deformation induce instabilities in the tribological system, therefore self-organization can occur. Instabilities can lead to an increase of the real contact area between the ball and film, resulting in the seizure between the sliding counterparts (degenerative case of self-organization). However, the material cannot withstand the stress and collapses due to high friction forces, thus this regime of sliding corresponds to the adhesive wear. In contrast, a decrease of the real contact area leads to the decrease of the coefficient of friction (constructive self-organization). However, it results in a contact pressure increase on the top of asperities within the contact zone, followed by material collapse, i.e., abrasive wear. Mentioned wear mechanisms should be distinguished from the self-lubricating properties of diamond due to the formation of a carbonaceous layer.

]]>Entropy doi: 10.3390/e20040278

Authors: Ehtibar N. Dzhafarov Janne V. Kujala

The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: Has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the Einsten-Podolsky-Rosen-Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of contexts (closed-open arrangements of the slits) upon the marginal distributions of the random variables involved. The analysis presented is entirely within the framework of abstract classical probability theory (with contextually labeled random variables). The only physical constraint used in the analysis is that a particle cannot pass through a closed slit. The noncontextuality of the double-slit system does not generalize to systems describing experiments with more than two slits: in an abstract triple-slit system, almost any set of observable detection probabilities is compatible with both a contextual scenario and a noncontextual scenario of the particle passing though various combinations of open and closed slits (although the issue of physical realizability of these scenarios remains open).

]]>Entropy doi: 10.3390/e20040277

Authors: Tao Mei

We employ the spinor analysis method to evaluate exact expressions of spin-spin correlation functions of the two-dimensional rectangular Ising model on a finite lattice, special process enables us to actually carry out the calculation process. We first present some exact expressions of correlation functions of the model with periodic-periodic boundary conditions on a finite lattice. The corresponding forms in the thermodynamic limit are presented, which show the short-range order. Then, we present the exact expression of the correlation function of the two farthest pair of spins in a column of the model with periodic-free boundary conditions on a finite lattice. Again, the corresponding form in the thermodynamic limit is discussed, from which the long-range order clearly emerges as the temperature decreases.

]]>Entropy doi: 10.3390/e20040275

Authors: Jiaxiang Wang Jinshan Li Jun Wang Fan Bu Hongchao Kou Chao Li Pingxiang Zhang Eric Beaugnon

Strong static magnetic field (SSMF) is a unique way to regulate the microstructure and improve the properties of materials. FeCoNi(AlSi)0.2 alloy is a novel class of soft magnetic materials (SMMs) designed based on high-entropy alloy (HEA) concepts. In this study, a strong static magnetic field is introduced to tune the microstructure, mechanical, electrical and magnetic properties of FeCoNi(AlSi)0.2 high-entropy alloy. Results indicate that, with the increasing magnetic field intensity, the Vickers hardness and the saturation magnetization (Ms) increase firstly, and then decrease and reach the maximum at 5T, while the yield strength, the residual magnetization (Mr) and the coercivity (Hc) take the opposite trend. The resistivity values (ρ) are found to be enhanced by the increasing magnetic field intensity. The main reasons for the magnetic field on the above effects are interpreted by microstructure evolution (phase species and volume fraction), atomic-level structure and defects (vacancy and dislocation density).

]]>Entropy doi: 10.3390/e20040276

Authors: Xuxi Zhang Siqi Wang

In this paper, we study the admissible consensus for descriptor multi-agent systems (MASs) with exogenous disturbances that are generated by some linear systems. The topology among agents is represented by a directed graph. For solving the admissible consensus problem, the exogenous disturbance observer and distributed control protocol are proposed. With the help of the graph theory and the generalized Riccati equation, some conditions for admissible consensus of descriptor MASs with exogenous disturbances are obtained. Finally, we provide a numerical simulation to effectively illustrate the results we have reached before.

]]>Entropy doi: 10.3390/e20040274

Authors: Margarida Sousa Alexandra Carvalho

Dynamic Bayesian networks (DBN) are powerful probabilistic representations that model stochastic processes. They consist of a prior network, representing the distribution over the initial variables, and a set of transition networks, representing the transition distribution between variables over time. It was shown that learning complex transition networks, considering both intra- and inter-slice connections, is NP-hard. Therefore, the community has searched for the largest subclass of DBNs for which there is an efficient learning algorithm. We introduce a new polynomial-time algorithm for learning optimal DBNs consistent with a breadth-first search (BFS) order, named bcDBN. The proposed algorithm considers the set of networks such that each transition network has a bounded in-degree, allowing for p edges from past time slices (inter-slice connections) and k edges from the current time slice (intra-slice connections) consistent with the BFS order induced by the optimal tree-augmented network (tDBN). This approach increases exponentially, in the number of variables, the search space of the state-of-the-art tDBN algorithm. Concerning worst-case time complexity, given a Markov lag m, a set of n random variables ranging over r values, and a set of observations of N individuals over T time steps, the bcDBN algorithm is linear in N, T and m; polynomial in n and r; and exponential in p and k. We assess the bcDBN algorithm on simulated data against tDBN, revealing that it performs well throughout different experiments.

]]>Entropy doi: 10.3390/e20040273

Authors: Huiqin Wei Long Chen Li Guo

Ensemble clustering combines different basic partitions of a dataset into a more stable and robust one. Thus, cluster ensemble plays a significant role in applications like image segmentation. However, existing ensemble methods have a few demerits, including the lack of diversity of basic partitions and the low accuracy caused by data noise. In this paper, to get over these difficulties, we propose an efficient fuzzy cluster ensemble method based on Kullback–Leibler divergence or simply, the KL divergence. The data are first classified with distinct fuzzy clustering methods. Then, the soft clustering results are aggregated by a fuzzy KL divergence-based objective function. Moreover, for image segmentation problems, we utilize the local spatial information in the cluster ensemble algorithm to suppress the effect of noise. Experiment results reveal that the proposed methods outperform many other methods in synthetic and real image-segmentation problems.

]]>Entropy doi: 10.3390/e20040272

Authors: Dagmar Markechová Batool Mosapour Abolfazl Ebrahimzadeh

In the presented article, we define the R-norm entropy and the conditional R-norm entropy of partitions of a given fuzzy probability space and study the properties of the suggested entropy measures. In addition, we introduce the concept of R-norm divergence of fuzzy P-measures and we derive fundamental properties of this quantity. Specifically, it is shown that the Shannon entropy and the conditional Shannon entropy of fuzzy partitions can be derived from the R-norm entropy and conditional R-norm entropy of fuzzy partitions, respectively, as the limiting cases for R going to 1; the Kullback–Leibler divergence of fuzzy P-measures may be inferred from the R-norm divergence of fuzzy P-measures as the limiting case for R going to 1. We also provide numerical examples that illustrate the results.

]]>Entropy doi: 10.3390/e20040271

Authors: Abdullah Makkeh Dirk Theis Raul Vicente

Makkeh, Theis, and Vicente found that Cone Programming model is the most robust to compute the Bertschinger et al. partial information decomposition (BROJA PID) measure. We developed a production-quality robust software that computes the BROJA PID measure based on the Cone Programming model. In this paper, we prove the important property of strong duality for the Cone Program and prove an equivalence between the Cone Program and the original Convex problem. Then, we describe in detail our software, explain how to use it, and perform some experiments comparing it to other estimators. Finally, we show that the software can be extended to compute some quantities of a trivaraite PID measure.

]]>Entropy doi: 10.3390/e20040270

Authors: Fabio Bagarello Francesco Gargano

We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.

]]>Entropy doi: 10.3390/e20040269

Authors: Christian Chapman Hans Mittelmann Adam Margetts Daniel Bliss

Bounds are developed on the maximum communications rate between a transmitter and a fusion node aided by a cluster of distributed receivers with limited resources for cooperation, all in the presence of an additive Gaussian interferer. The receivers cannot communicate with one another and can only convey processed versions of their observations to the fusion center through a Local Array Network (LAN) with limited total throughput. The effectiveness of each bound’s approach for mitigating a strong interferer is assessed over a wide range of channels. It is seen that, if resources are shared effectively, even a simple quantize-and-forward strategy can mitigate an interferer 20 dB stronger than the signal in a diverse range of spatially Ricean channels. Monte-Carlo experiments for the bounds reveal that, while achievable rates are stable when varying the receiver’s observed scattered-path to line-of-sight signal power, the receivers must adapt how they share resources in response to this change. The bounds analyzed are proven to be achievable and are seen to be tight with capacity when LAN resources are either ample or limited.

]]>Entropy doi: 10.3390/e20040268

Authors: Massimo Stella Manlio De Domenico

We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated for a variety of synthetic network models. By coupling distance entropy information with closeness centrality, we introduce a network cartography which allows one to reduce the degeneracy of ranking based on closeness alone. We apply this methodology to the empirical multiplex lexical network encoding the linguistic relationships known to English speaking toddlers. We show that the distance entropy cartography better predicts how children learn words compared to closeness centrality. Our results highlight the importance of distance entropy for gaining insights from distance patterns in complex networks.

]]>Entropy doi: 10.3390/e20040267

Authors: Chenguang Shi Fei Wang Sana Salous Jianjiang Zhou Zhentao Hu

This paper presents a novel Nash bargaining solution (NBS)-based cooperative game-theoretic framework for power control in a distributed multiple-radar architecture underlying a wireless communication system. Our primary objective is to minimize the total power consumption of the distributed multiple-radar system (DMRS) with the protection of wireless communication user’s transmission, while guaranteeing each radar’s target detection requirement. A unified cooperative game-theoretic framework is proposed for the optimization problem, where interference power constraints (IPCs) are imposed to protect the communication user’s transmission, and a minimum signal-to-interference-plus-noise ratio (SINR) requirement is employed to provide reliable target detection for each radar. The existence, uniqueness and fairness of the NBS to this cooperative game are proven. An iterative Nash bargaining power control algorithm with low computational complexity and fast convergence is developed and is shown to converge to a Pareto-optimal equilibrium for the cooperative game model. Numerical simulations and analyses are further presented to highlight the advantages and testify to the efficiency of our proposed cooperative game algorithm. It is demonstrated that the distributed algorithm is effective for power control and could protect the communication system with limited implementation overhead.

]]>Entropy doi: 10.3390/e20040266

Authors: Yangyang Wang Xiaofei Qi Jinchuan Hou

A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B ) &lt; 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 ) -mode Gaussian states and an estimate of N for ( n + m ) -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.

]]>Entropy doi: 10.3390/e20040265

Authors: Matheus Martinez Garcia Rafael Une Silvio de Oliveira Junior Carlos Keutenedjian Mady

This article focuses on studying the effects of muscle and fat percentages on the exergy behavior of the human body under several environmental conditions. The main objective is to relate the thermal comfort indicators with exergy rates, resulting in a Second Law perspective to evaluate thermal environment. A phenomenological model is proposed of the human body with four layers: core, muscle, fat and skin. The choice of a simplified model is justified by the facility to variate the amount of mass in each tissue without knowing how it spreads around the body. After validated, the model was subjected to a set of environmental conditions and body compositions. The results obtained indicate that the area normalization (Watts per square meter) may be used as a safe generalization for the exergy transfer to environment. Moreover, the destroyed exergy itself is sufficient to evaluate the thermal sensation when the model is submitted to environmental temperatures lower than that considered for the thermal neutrality condition (and, in this text, the thermal comfort) . Nevertheless, for environments with temperatures higher than the calculated for the thermal neutrality, the combination of destroyed exergy and the rate of exergy transferred to the environment should be used to properly evaluate thermal comfort.

]]>Entropy doi: 10.3390/e20040264

Authors: Zahra Karevan Johan Suykens

Entropy measures have been a major interest of researchers to measure the information content of a dynamical system. One of the well-known methodologies is sample entropy, which is a model-free approach and can be deployed to measure the information transfer in time series. Sample entropy is based on the conditional entropy where a major concern is the number of past delays in the conditional term. In this study, we deploy a lag-specific conditional entropy to identify the informative past values. Moreover, considering the seasonality structure of data, we propose a clustering-based sample entropy to exploit the temporal information. Clustering-based sample entropy is based on the sample entropy definition while considering the clustering information of the training data and the membership of the test point to the clusters. In this study, we utilize the proposed method for transductive feature selection in black-box weather forecasting and conduct the experiments on minimum and maximum temperature prediction in Brussels for 1–6 days ahead. The results reveal that considering the local structure of the data can improve the feature selection performance. In addition, despite the large reduction in the number of features, the performance is competitive with the case of using all features.

]]>Entropy doi: 10.3390/e20040263

Authors: Qing Li Wei Hu Erfei Peng Steven Liang

High-speed remote transmission and large-capacity data storage are difficult issues in signals acquisition of rotating machines condition monitoring. To address these concerns, a novel multichannel signals reconstruction approach based on tunable Q-factor wavelet transform-morphological component analysis (TQWT-MCA) and sparse Bayesian iteration algorithm combined with step-impulse dictionary is proposed under the frame of compressed sensing (CS). To begin with, to prevent the periodical impulses loss and effectively separate periodical impulses from the external noise and additive interference components, the TQWT-MCA method is introduced to divide the raw vibration signal into low-resonance component (LRC, i.e., periodical impulses) and high-resonance component (HRC), thus, the periodical impulses are preserved effectively. Then, according to the amplitude range of generated LRC, the step-impulse dictionary atom is designed to match the physical structure of periodical impulses. Furthermore, the periodical impulses and HRC are reconstructed by the sparse Bayesian iteration combined with step-impulse dictionary, respectively, finally, the final reconstructed raw signals are obtained by adding the LRC and HRC, meanwhile, the fidelity of the final reconstructed signals is tested by the envelop spectrum and error analysis, respectively. In this work, the proposed algorithm is applied to simulated signal and engineering multichannel signals of a gearbox with multiple faults. Experimental results demonstrate that the proposed approach significantly improves the reconstructive accuracy compared with the state-of-the-art methods such as non-convex Lq (q = 0.5) regularization, spatiotemporal sparse Bayesian learning (SSBL) and L1-norm, etc. Additionally, the processing time, i.e., speed of storage and transmission has increased dramatically, more importantly, the fault characteristics of the gearbox with multiple faults are detected and saved, i.e., the bearing outer race fault frequency at 170.7 Hz and its harmonics at 341.3 Hz, ball fault frequency at 7.344 Hz and its harmonics at 15.0 Hz, and the gear fault frequency at 23.36 Hz and its harmonics at 47.42 Hz are identified in the envelope spectrum.

]]>Entropy doi: 10.3390/e20040262

Authors: Hea-Jung Kim Mihyang Bae Daehwa Jin

In a regression analysis, a sample-selection bias arises when a dependent variable is partially observed as a result of the sample selection. This study introduces a Maximum Entropy (MaxEnt) process regression model that assumes a MaxEnt prior distribution for its nonparametric regression function and finds that the MaxEnt process regression model includes the well-known Gaussian process regression (GPR) model as a special case. Then, this special MaxEnt process regression model, i.e., the GPR model, is generalized to obtain a robust sample-selection Gaussian process regression (RSGPR) model that deals with non-normal data in the sample selection. Various properties of the RSGPR model are established, including the stochastic representation, distributional hierarchy, and magnitude of the sample-selection bias. These properties are used in the paper to develop a hierarchical Bayesian methodology to estimate the model. This involves a simple and computationally feasible Markov chain Monte Carlo algorithm that avoids analytical or numerical derivatives of the log-likelihood function of the model. The performance of the RSGPR model in terms of the sample-selection bias correction, robustness to non-normality, and prediction, is demonstrated through results in simulations that attest to its good finite-sample performance.

]]>Entropy doi: 10.3390/e20040261

Authors: Tong Qiao Wei Shan Ganjun Yu Chen Liu

Measuring centrality has recently attracted increasing attention, with algorithms ranging from those that simply calculate the number of immediate neighbors and the shortest paths to those that are complicated iterative refinement processes and objective dynamical approaches. Indeed, vital nodes identification allows us to understand the roles that different nodes play in the structure of a network. However, quantifying centrality in complex networks with various topological structures is not an easy task. In this paper, we introduce a novel definition of entropy-based centrality, which can be applicable to weighted directed networks. By design, the total power of a node is divided into two parts, including its local power and its indirect power. The local power can be obtained by integrating the structural entropy, which reveals the communication activity and popularity of each node, and the interaction frequency entropy, which indicates its accessibility. In addition, the process of influence propagation can be captured by the two-hop subnetworks, resulting in the indirect power. In order to evaluate the performance of the entropy-based centrality, we use four weighted real-world networks with various instance sizes, degree distributions, and densities. Correspondingly, these networks are adolescent health, Bible, United States (US) airports, and Hep-th, respectively. Extensive analytical results demonstrate that the entropy-based centrality outperforms degree centrality, betweenness centrality, closeness centrality, and the Eigenvector centrality.

]]>Entropy doi: 10.3390/e20040260

Authors: Shuting Wan Xiong Zhang Longjiang Dou

The fast spectrum kurtosis (FSK) algorithm can adaptively identify and select the resonant frequency band and extract the fault feature via the envelope demodulation method. However, the FSK method has some limitations due to its susceptibility to noise and random knocks. To overcome this shortage, a new method is proposed in this paper. Firstly, we use the binary wavelet packet transform (BWPT) instead of the finite impulse response (FIR) filter bank as the frequency band segmentation method. Following this, the Shannon entropy of each frequency band is calculated. The appropriate center frequency and bandwidth are chosen for filtering by using the inverse of the Shannon entropy as the index. Finally, the envelope spectrum of the filtered signal is analyzed and the faulty feature information is obtained from the envelope spectrum. Through simulation and experimental verification, we found that Shannon entropy is—to some extent—better than kurtosis as a frequency-selective index, and that the Shannon entropy of the binary wavelet packet transform method is more accurate for fault feature extraction.

]]>Entropy doi: 10.3390/e20040259

Authors: Devendra Kumar Fairouz Tchier Jagdev Singh Dumitru Baleanu

In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.

]]>Entropy doi: 10.3390/e20040258

Authors: Xiaoqiang Hua Yongqiang Cheng Hongqiang Wang Yuliang Qin

This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices estimated by the secondary data set. A new class of total Bregman divergence is presented on the Riemanian manifold of Hermitian positive-definite (HPD) matrix, which is the foundation of information geometry. On the basis of this divergence, total Bregman divergence medians are derived instead of the sample covariance matrix (SCM) of the secondary data. Unlike the SCM, resorting to the knowledge of statistical characteristics of the sample data, the geometric structure of matrix space is considered in our proposed estimators, and then the performance can be improved in a heterogeneous clutter. At the analysis stage, numerical results are given to validate the detection performance of an adaptive normalized matched filter with our estimator compared with existing alternatives.

]]>Entropy doi: 10.3390/e20040257

Authors: Alexander Kartun-Giles Dmitri Krioukov James Gleeson Yamir Moreno Ginestra Bianconi

A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model that does not depend on the order in which nodes are sampled. Despite a large variety of non-equilibrium (growing) and equilibrium (static) sparse complex network models that are widely used in network science, how to reconcile sparseness (constant average degree) with the desired statistical properties of projectivity and exchangeability is currently an outstanding scientific problem. Here we propose a network process with hidden variables which is projective and can generate sparse power-law networks. Despite the model not being exchangeable, it can be closely related to exchangeable uncorrelated networks as indicated by its information theory characterization and its network entropy. The use of the proposed network process as a null model is here tested on real data, indicating that the model offers a promising avenue for statistical network modelling.

]]>Entropy doi: 10.3390/e20040256

Authors: Xiaoqiang Hua Haiyan Fan Yongqiang Cheng Hongqiang Wang Yuliang Qin

This paper proposes a radar target detection algorithm based on information geometry. In particular, the correlation of sample data is modeled as a Hermitian positive-definite (HPD) matrix. Moreover, a class of total Jensen–Bregman divergences, including the total Jensen square loss, the total Jensen log-determinant divergence, and the total Jensen von Neumann divergence, are proposed to be used as the distance-like function on the space of HPD matrices. On basis of these divergences, definitions of their corresponding median matrices are given. Finally, a decision rule of target detection is made by comparing the total Jensen-Bregman divergence between the median of reference cells and the matrix of cell under test with a given threshold. The performance analysis on both simulated and real radar data confirm the superiority of the proposed detection method over its conventional counterparts and existing ones.

]]>Entropy doi: 10.3390/e20040255

Authors: Huichen Jiang Liyan Han

We collected data pertaining to Chinese listed commercial banks from 2008 to 2016 and found that the competition between banks is becoming increasingly fierce. Commercial banks have actively carried out diversification strategies for greater returns, and the financial reports show that profits are increasingly coming from the non-interest income benefits of diversification strategies. However, diversification comes with risk. We built a panel threshold model and investigated the effect of income diversification on a bank’s profitability and risk. Diversification was first measured by the Herfindahl–Hirschman index (HHI), and the results show that there is a nonlinear relationship between diversification and profitability or risk does exist. We introduced an interesting index based on the entropy to test the robustness of our model and found that a threshold effect exists in both our models, which is statistically significant. We believe the combination of the entropy index (ENTI) and the HHI enables more efficient study of the relationship between diversification and profitability or risk more efficiently. Bankers and their customers have increasingly been interested in income diversification, and they value risk as well. We suggest that banks of different sizes should adopt the corresponding diversification strategy to achieve sustainable development.

]]>Entropy doi: 10.3390/e20040254

Authors: Shui-Hua Wang Hong Cheng Preetha Phillips Yu-Dong Zhang

Aim: Currently, identifying multiple sclerosis (MS) by human experts may come across the problem of “normal-appearing white matter”, which causes a low sensitivity. Methods: In this study, we presented a computer vision based approached to identify MS in an automatic way. This proposed method first extracted the fractional Fourier entropy map from a specified brain image. Afterwards, it sent the features to a multilayer perceptron trained by a proposed improved parameter-free Jaya algorithm. We used cost-sensitivity learning to handle the imbalanced data problem. Results: The 10 × 10-fold cross validation showed our method yielded a sensitivity of 97.40 ± 0.60%, a specificity of 97.39 ± 0.65%, and an accuracy of 97.39 ± 0.59%. Conclusions: We validated by experiments that the proposed improved Jaya performs better than plain Jaya algorithm and other latest bioinspired algorithms in terms of classification performance and training speed. In addition, our method is superior to four state-of-the-art MS identification approaches.

]]>Entropy doi: 10.3390/e20040253

Authors: Cass T. Miller William G. Gray Christopher E. Kees

The thermodynamically constrained averaging theory (TCAT) is a comprehensive theory used to formulate hierarchies of multiphase, multiscale models that are closed based upon the second law of thermodynamics. The rate of entropy production is posed in terms of the product of fluxes and forces of dissipative processes. The attractive features of TCAT include consistency across disparate length scales; thermodynamic consistency across scales; the inclusion of interfaces and common curves as well as phases; the development of kinematic equations to provide closure relations for geometric extent measures; and a structured approach to model building. The elements of the TCAT approach are shown; the ways in which each of these attractive features emerge from the TCAT approach are illustrated; and a review of the hierarchies of models that have been formulated is provided. Because the TCAT approach is mathematically involved, we illustrate how this approach can be applied by leveraging existing components of the theory that can be applied to a wide range of applications. This can result in a substantial reduction in formulation effort compared to a complete derivation while yielding identical results. Lastly, we note the previous neglect of the deviation kinetic energy, which is not important in slow porous media flows, formulate the required equations to extend the theory, and comment on applications for which the new components would be especially useful. This work should serve to make TCAT more accessible for applications, thereby enabling higher fidelity models for applications such as turbulent multiphase flows.

]]>Entropy doi: 10.3390/e20040252

Authors: Zhiqing Hu Zhuo Li Kai Tang Zi Wen Yongfu Zhu

A formula has been established, which is based on the size-dependence of a metal&rsquo;s melting point, to elucidate the atomic diffusion coefficient of nanostructured materials by considering the role of grain-boundary energy. When grain size is decreased, a decrease in the atomic diffusion activation energy and an increase in the corresponding diffusion coefficient can be observed. Interestingly, variations in the atomic diffusion activation energy of nanostructured materials are small relative to nanoparticles, depending on the size of the grain boundary energy. Our theoretical prediction is in accord with the computer simulation and experimental results of the metals described.

]]>Entropy doi: 10.3390/e20040251

Authors: Xiaoran Lin Shangbo Zhou Hongbin Tang Ying Qi Xianzhong Xie

Visual information processing is one of the fields of cognitive informatics. In this paper, a two-layer fractional-order chaotic network, which can simulate the mechanism of visual selection and shifting, is established. Unlike other object selection models, the proposed model introduces control units to select object. The first chaotic network layer of the model is used to implement image segmentation. A control layer is added as the second layer, consisting of a central neuron, which controls object selection and shifting. To implement visual selection and shifting, a strategy is proposed that can achieve different subnets corresponding to the objects in the first layer synchronizing with the central neuron at different time. The central unit acting as the central nervous system synchronizes with different subnets (hybrid systems), implementing the mechanism of visual selection and shifting in the human system. The proposed model corresponds better with the human visual system than the typical model of visual information encoding and transmission and provides new possibilities for further analysis of the mechanisms of the human cognitive system. The reasonability of the proposed model is verified by experiments using artificial and natural images.

]]>Entropy doi: 10.3390/e20040250

Authors: Dick Bedeaux Signe Kjelstrup

We derive in a new way that the intensive properties of a fluid-fluid Gibbs interface are independent of the location of the dividing surface. When the system is out of global equilibrium, this finding is not trivial: In a one-component fluid, it can be used to obtain the interface temperature from the surface tension. In other words, the surface equation of state can serve as a thermometer for the liquid-vapor interface in a one-component fluid. In a multi-component fluid, one needs the surface tension and the relative adsorptions to obtain the interface temperature and chemical potentials. A consistent set of thermodynamic properties of multi-component surfaces are presented. They can be used to construct fluid-fluid boundary conditions during transport. These boundary conditions have a bearing on all thermodynamic modeling on transport related to phase transitions.

]]>Entropy doi: 10.3390/e20040247

Authors: J. M. Isidro P. Fernández de Córdoba

We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the literature. This reflects the fact that the internal energy of the ideal gas depends exclusively on its temperature. We also present a Poisson algebra of thermodynamic operators for a quantum-like description of the classical ideal gas. The central element of this Poisson algebra is proportional to Boltzmann’s constant. A Hilbert space of states is identified and a system of wave equations governing the wavefunction is found. Expectation values for the operators representing pressure, volume and temperature are found to satisfy the classical equations of state.

]]>Entropy doi: 10.3390/e20040249

Authors: Krzysztof Gajowniczek Arkadiusz Orłowski Tomasz Ząbkowski

Artificial neural networks are currently one of the most commonly used classifiers and over the recent years they have been successfully used in many practical applications, including banking and finance, health and medicine, engineering and manufacturing. A large number of error functions have been proposed in the literature to achieve a better predictive power. However, only a few works employ Tsallis statistics, although the method itself has been successfully applied in other machine learning techniques. This paper undertakes the effort to examine the q -generalized function based on Tsallis statistics as an alternative error measure in neural networks. In order to validate different performance aspects of the proposed function and to enable identification of its strengths and weaknesses the extensive simulation was prepared based on the artificial benchmarking dataset. The results indicate that Tsallis entropy error function can be successfully introduced in the neural networks yielding satisfactory results and handling with class imbalance, noise in data or use of non-informative predictors.

]]>Entropy doi: 10.3390/e20040248

Authors: Pan Zhao Jian Pan Benda Zhou Jixia Wang Yu Song

To describe the movement of asset prices accurately, we employ the non-extensive statistical mechanics and the semi-Markov process to establish an asset price model. The model can depict the peak and fat tail characteristics of returns and the regime-switching phenomenon of macroeconomic system. Moreover, we use the risk-minimizing method to study the hedging problem of contingent claims and obtain the explicit solutions of the optimal hedging strategies.

]]>Entropy doi: 10.3390/e20040246

Authors: Xiguang Xu Hua Qu Jihong Zhao Feiyu Yan Weihua Wang

Spectrum sensing is the most important task in cognitive radio (CR). In this paper, a new robust distributed spectrum sensing approach, called diffusion maximum correntropy criterion (DMCC)-based robust spectrum sensing, is proposed for CR in the presence of non-Gaussian noise or impulsive noise. The proposed distributed scheme, which does not need any central processing unit, is characterized by an adaptive diffusion model. The maximum correntropy criterion, which is insensitive to impulsive interference, is introduced to deal with the effect of non-Gaussian noise. Simulation results show that the DMCC-based spectrum sensing algorithm has an excellent robust property with respect to non-Gaussian noise. It is also observed that the new method displays a considerably better detection performance than its predecessor (i.e., diffusion least mean square (DLMS)) in impulsive noise. Moreover, the mean and variance convergence analysis of the proposed algorithm are also carried out.

]]>Entropy doi: 10.3390/e20040245

Authors: Zixuan Zhu Yuhai Zhao

Recently, Multi-Graph Learning was proposed as the extension of Multi-Instance Learning and has achieved some successes. However, to the best of our knowledge, currently, there is no study working on Multi-Graph Multi-Label Learning, where each object is represented as a bag containing a number of graphs and each bag is marked with multiple class labels. It is an interesting problem existing in many applications, such as image classification, medicinal analysis and so on. In this paper, we propose an innovate algorithm to address the problem. Firstly, it uses more precise structures, multiple Graphs, instead of Instances to represent an image so that the classification accuracy could be improved. Then, it uses multiple labels as the output to eliminate the semantic ambiguity of the image. Furthermore, it calculates the entropy to mine the informative subgraphs instead of just mining the frequent subgraphs, which enables selecting the more accurate features for the classification. Lastly, since the current algorithms cannot directly deal with graph-structures, we degenerate the Multi-Graph Multi-Label Learning into the Multi-Instance Multi-Label Learning in order to solve it by MIML-ELM (Improving Multi-Instance Multi-Label Learning by Extreme Learning Machine). The performance study shows that our algorithm outperforms the competitors in terms of both effectiveness and efficiency.

]]>Entropy doi: 10.3390/e20040244

Authors: Elaheh Sadat Karim Faez Mohsen Saffari Pour

In this paper, a new method is proposed for motion vector steganalysis using the entropy value and its combination with the features of the optimized motion vector. In this method, the entropy of blocks is calculated to determine their texture and the precision of their motion vectors. Then, by using a fuzzy cluster, the blocks are clustered into the blocks with high and low texture, while the membership function of each block to a high texture class indicates the texture of that block. These membership functions are used to weight the effective features that are extracted by reconstructing the motion estimation equations. Characteristics of the results indicate that the use of entropy and the irregularity of each block increases the precision of the final video classification into cover and stego classes.

]]>Entropy doi: 10.3390/e20040243

Authors: Sheng Shen Honghui Yang Meiping Sheng

The accuracy of underwater acoustic targets recognition via limited ship radiated noise can be improved by a deep neural network trained with a large number of unlabeled samples. However, redundant features learned by deep neural network have negative effects on recognition accuracy and efficiency. A compressed deep competitive network is proposed to learn and extract features from ship radiated noise. The core idea of the algorithm includes: (1) Competitive learning: By integrating competitive learning into the restricted Boltzmann machine learning algorithm, the hidden units could share the weights in each predefined group; (2) Network pruning: The pruning based on mutual information is deployed to remove the redundant parameters and further compress the network. Experiments based on real ship radiated noise show that the network can increase recognition accuracy with fewer informative features. The compressed deep competitive network can achieve a classification accuracy of 89.1 % , which is 5.3 % higher than deep competitive network and 13.1 % higher than the state-of-the-art signal processing feature extraction methods.

]]>Entropy doi: 10.3390/e20040242

Authors: Mehrdad Karimzadehkhouei Mostafa Shojaeian Abdolali Sadaghiani Kürşat Şendur M. Mengüç Ali Koşar

During the last decade, second law analysis via entropy generation has become important in terms of entropy generation minimization (EGM), thermal engineering system design, irreversibility, and energy saving. In this study, heat transfer and entropy generation characteristics of flows of multi-walled carbon nanotube-based nanofluids were investigated in horizontal minitubes with outer and inner diameters of ~1067 and ~889 µm, respectively. Carbon nanotubes (CNTs) with outer diameter of 10–20 nm and length of 1–2 µm were used for nanofluid preparation, and water was considered as the base fluid. The entropy generation based on the experimental data, a significant parameter in thermal design system, was examined for CNTs/water nanofluids. The change in the entropy generation was only seen at low mass fractions (0.25 wt.% and 0.5 wt.%). Moreover, to have more insight on the entropy generation of nanofluids based on the experimental data, a further analysis was performed on Al2O3 and TiO2 nanoparticles/water nanofluids from the experimental database of the previous study of the authors. The corresponding results disclosed a remarkable increase in the entropy generation rate when Al2O3 and TiO2 nanoparticles were added to the base fluid.

]]>Entropy doi: 10.3390/e20040241

Authors: Yuanyuan Wu Tao Hong Zhengming Tang Chun Zhang

The aim of this work is to present a model of a reaction tube with cross structures in order to improve ethyl acetate production and microwave heating uniformity. A commercial finite element software, COMSOL Multiphysics 4.3a (Newton, MA, USA), is used to build the proposed model for a BJ-22 rectangular waveguide system. Maxwell’s equations, the heat conduction equation, reaction kinetics equation and Navier-Stokes equation are combined to describe the continuous flow process. The electric field intensity, the temperature, the concentration of water, the coefficient of variation (COV) and the mean temperature at different initial velocities are compared to obtain the best flow rate. Four different initial velocities are employed to discuss the effect of flow velocity on the heating uniformity and heating efficiency. The point temperatures are measured by optical fibers to verify the simulated results. The results show the electric field intensity distributions at different initial velocities have little difference, which means the initial velocity will have the decisive influence on the heating process. At lower velocity, the COV will be smaller, which means better heating uniformity. Meanwhile, the distance between each cross structure has great influence on the heating uniformity and heating efficiency, while the angle has little. The proposed model can be applied to large-scale production of microwave-assisted ethyl acetate production.

]]>Entropy doi: 10.3390/e20040240

Authors: Jim Kay Robin Ince

The Partial Information Decomposition, introduced by Williams P. L. et al. (2010), provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method ( I dep ) has recently been proposed by James R. G. et al. (2017) for computing a two-predictor partial information decomposition over discrete spaces. A lattice of maximum entropy probability models is constructed based on marginal dependency constraints, and the unique information that a particular predictor has about the target is defined as the minimum increase in joint predictor-target mutual information when that particular predictor-target marginal dependency is constrained. Here, we apply the I dep approach to Gaussian systems, for which the marginally constrained maximum entropy models are Gaussian graphical models. Closed form solutions for the I dep PID are derived for both univariate and multivariate Gaussian systems. Numerical and graphical illustrations are provided, together with practical and theoretical comparisons of the I dep PID with the minimum mutual information partial information decomposition ( I mmi ), which was discussed by Barrett A. B. (2015). The results obtained using I dep appear to be more intuitive than those given with other methods, such as I mmi , in which the redundant and unique information components are constrained to depend only on the predictor-target marginal distributions. In particular, it is proved that the I mmi method generally produces larger estimates of redundancy and synergy than does the I dep method. In discussion of the practical examples, the PIDs are complemented by the use of tests of deviance for the comparison of Gaussian graphical models.

]]>Entropy doi: 10.3390/e20040239

Authors: Zhiwei Ye Juan Yang Mingwei Wang Xinlu Zong Lingyu Yan Wei Liu

Image segmentation is a significant step in image analysis and computer vision. Many entropy based approaches have been presented in this topic; among them, Tsallis entropy is one of the best performing methods. However, 1D Tsallis entropy does not consider make use of the spatial correlation information within the neighborhood results might be ruined by noise. Therefore, 2D Tsallis entropy is proposed to solve the problem, and results are compared with 1D Fisher, 1D maximum entropy, 1D cross entropy, 1D Tsallis entropy, fuzzy entropy, 2D Fisher, 2D maximum entropy and 2D cross entropy. On the other hand, due to the existence of huge computational costs, meta-heuristics algorithms like genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization algorithm (ACO) and differential evolution algorithm (DE) are used to accelerate the 2D Tsallis entropy thresholding method. In this paper, considering 2D Tsallis entropy as a constrained optimization problem, the optimal thresholds are acquired by maximizing the objective function using a modified chaotic Bat algorithm (MCBA). The proposed algorithm has been tested on some actual and infrared images. The results are compared with that of PSO, GA, ACO and DE and demonstrate that the proposed method outperforms other approaches involved in the paper, which is a feasible and effective option for image segmentation.

]]>Entropy doi: 10.3390/e20040238

Authors: Kan Wang Xu-Tao Yu Xiao-Fei Cai Zai-Chen Zhang

Quantum teleportation has significant meaning in quantum information. In particular, entangled states can also be used for perfectly teleporting the quantum state with some probability. This is more practical and efficient in practice. In this paper, we propose schemes to use non-symmetric quantum channel combinations for probabilistic teleportation of an arbitrary two-qubit quantum state from sender to receiver. The non-symmetric quantum channel is composed of a two-qubit partially entangled state and a three-qubit partially entangled state, where partially entangled Greenberger–Horne–Zeilinger (GHZ) state and W state are considered, respectively. All schemes are presented in detail and the unitary operations required are given in concise formulas. Methods are provided for reducing classical communication cost and combining operations to simplify the manipulation. Moreover, our schemes are flexible and applicable in different situations.

]]>Entropy doi: 10.3390/e20040237

Authors: Austin Hulse Benjamin Schumacher Michael Westmoreland

We present an axiomatic framework for thermodynamics that incorporates information as a fundamental concept. The axioms describe both ordinary thermodynamic processes and those in which information is acquired, used and erased, as in the operation of Maxwell’s demon. This system, similar to previous axiomatic systems for thermodynamics, supports the construction of conserved quantities and an entropy function governing state changes. Here, however, the entropy exhibits both information and thermodynamic aspects. Although our axioms are not based upon probabilistic concepts, a natural and highly useful concept of probability emerges from the entropy function itself. Our abstract system has many models, including both classical and quantum examples.

]]>Entropy doi: 10.3390/e20040236

Authors: Xiaohong Li Ru Cao Jianye Hao

Networks will continue to become increasingly heterogeneous as we move toward 5G. Meanwhile, the intelligent programming of the core network makes the available radio resource be more changeable rather than static. In such a dynamic and heterogeneous network environment, how to help terminal users select optimal networks to access is challenging. Prior implementations of network selection are usually applicable for the environment with static radio resources, while they cannot handle the unpredictable dynamics in 5G network environments. To this end, this paper considers both the fluctuation of radio resources and the variation of user demand. We model the access network selection scenario as a multiagent coordination problem, in which a bunch of rationally terminal users compete to maximize their benefits with incomplete information about the environment (no prior knowledge of network resource and other users’ choices). Then, an adaptive learning based strategy is proposed, which enables users to adaptively adjust their selections in response to the gradually or abruptly changing environment. The system is experimentally shown to converge to Nash equilibrium, which also turns out to be both Pareto optimal and socially optimal. Extensive simulation results show that our approach achieves significantly better performance compared with two learning and non-learning based approaches in terms of load balancing, user payoff and the overall bandwidth utilization efficiency. In addition, the system has a good robustness performance under the condition with non-compliant terminal users.

]]>Entropy doi: 10.3390/e20040235

Authors: Danuta Makowiec Dorota Wejer Beata Graff Zbigniew Struzik

Shannon entropy (ShE) is a recognised tool for the quantization of the temporal organization of time series. Transfer entropy (TE) provides insight into the dependence between coupled systems. Here, signals are analysed that were produced by the cardiovascular system when a healthy human underwent a provocation test using the head-up tilt (HUT) protocol. The information provided by ShE and TE is evaluated from two aspects: that of the algorithmic stability and that of the recognised physiology of the cardiovascular response to the HUT test. To address both of these aspects, two types of symbolization of three-element subsequent values of a signal are considered: one, well established in heart rate research, referring to the variability in a signal, and a novel one, revealing primarily the dynamical trends. The interpretation of ShE shows a strong dependence on the method that was used in signal pre-processing. In particular, results obtained from normalized signals turn out to be less conclusive than results obtained from non-normalized signals. Systematic investigations based on surrogate data tests are employed to discriminate between genuine properties—in particular inter-system coupling—and random, incidental fluctuations. These properties appear to determine the occurrence of a high percentage of zero values of TE, which strongly limits the reliability of the couplings measured. Nevertheless, supported by statistical corroboration, we identify distinct timings when: (i) evoking cardiac impact on the vascular system, and (ii) evoking vascular impact on the cardiac system, within both the principal sub-systems of the baroreflex loop.

]]>Entropy doi: 10.3390/e20040234

Authors: Jürgen Schlitter

The second law of thermodynamics states the increase of entropy, Δ S &gt; 0 , for real processes from state A to state B at constant energy from chemistry over biological life and engines to cosmic events. The connection of entropy to information, phase-space, and heat is helpful but does not immediately convince observers of the validity and basis of the second law. This gave grounds for finding a rigorous, but more easily acceptable reformulation. Here, we show using statistical mechanics that this principle is equivalent to a force law ⟨ ⟨ f ⟩ ⟩ &gt; 0 in systems where mass centers and forces can be identified. The sign of this net force--the average mean force along a path from A to B--determines the direction of the process. The force law applies to a wide range of processes from machines to chemical reactions. The explanation of irreversibility by a driving force appears more plausible than the traditional formulation as it emphasizes the cause instead of the effect of motions.

]]>Entropy doi: 10.3390/e20040233

Authors: Barry Ganapol Domiziano Mostacci Vincenzo Molinari

The slowing down equation for elastic scattering of neutrons in an infinite homogeneous medium is solved analytically by decomposing the neutron energy spectrum into collision intervals. Since scattering physically smooths energy distributions by redistributing neutron energy uniformly, it is informative to observe how mathematics accommodates the scattering process, which increases entropy through disorder.

]]>Entropy doi: 10.3390/e20040232

Authors: Tomasz Banaszkiewicz Maciej Chorowski

Adsorption technology is currently one of the most popular methods of air separation. At relatively low energy expenditure, this allows oxygen to be obtained with sufficient purity for oxyfuel, metallurgy or medical applications. The adsorption process is dependent on several factors such as pressure, temperature, the concentration of adsorbed element in the gas phase, or the surface area of the phase boundary. The paper shows the calculation of the minimum energy needed for oxygen separation taking into account the advantages and disadvantages of the adsorption methods. The article shows how many times the energy consumption of a real oxygen-separation plant is higher than the theoretical energy consumption, and indicates which components of the adsoption installation can be further improved. The paper is supported by research conducted on an oxygen-separation installation at a semi-technical scale.

]]>Entropy doi: 10.3390/e20040231

Authors: Osvaldo Civitarese Manuel Gadella

In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy states. After introducing a generalized basis of states which includes resonances, and working with amplitudes instead of probabilities, we found an expression for the entropy which exhibits real and imaginary components. We discuss the meaning of the imaginary part of the entropy on the basis of the similarities existing between thermal and time evolutions.

]]>Entropy doi: 10.3390/e20040230

Authors: Jizhao Liu Jun Ma Jing Lian Pengbin Chang Yide Ma

Chaotic systems with hyperbolic sine nonlinearity have attracted the attention of researchers in the last two years. This paper introduces a new approach for generating a class of simple chaotic systems with hyperbolic sine. With nth-order ordinary differential equations (ODEs), any desirable order of chaotic systems with hyperbolic sine nonlinearity can be easily constructed. Fourth-order, fifth-order, and tenth-order chaotic systems are taken as examples to verify the theory. To achieve simplicity of the electrical circuit, two back-to-back diodes represent hyperbolic sine nonlinearity without any multiplier or subcircuits. Thus, these systems can achieve both physical simplicity and analytic complexity at the same time.

]]>Entropy doi: 10.3390/e20040229

Authors: Glauber De Bona Fabio Cozman

There are several formalisms that enhance Bayesian networks by including relations amongst individuals as modeling primitives. For instance, Probabilistic Relational Models (PRMs) use diagrams and relational databases to represent repetitive Bayesian networks, while Relational Bayesian Networks (RBNs) employ first-order probability formulas with the same purpose. We examine the coherence checking problem for those formalisms; that is, the problem of guaranteeing that any grounding of a well-formed set of sentences does produce a valid Bayesian network. This is a novel version of de Finetti’s problem of coherence checking for probabilistic assessments. We show how to reduce the coherence checking problem in relational Bayesian networks to a validity problem in first-order logic augmented with a transitive closure operator and how to combine this logic-based approach with faster, but incomplete algorithms.

]]>Entropy doi: 10.3390/e20040228

Authors: Sean Devine

This paper, using Algorithmic Information Theory (AIT), argues that once energy resources are considered, an economy, like an ecology, requires continuous energy to be sustained in a homeostatic state away from the decayed state of its (local) thermodynamic equilibrium. AIT identifies how economic actions and natural laws create an ordered economy through what is seen as computations on a real world Universal Turing Machine (UTM) that can be simulated to within a constant on a laboratory UTM. The shortest, appropriately coded, programme to do this defines the system’s information or algorithmic entropy. The computational behaviour of many generations of primitive economic agents can create a more ordered and advanced economy, able to be specified by a relatively short algorithm. The approach allows information flows to be tracked in real-world computational processes where instructions carried in stored energy create order while ejecting disorder. Selection processes implement the Maximum Power Principle while the economy trends towards Maximum Entropy Production, as tools amplify human labour and interconnections create energy efficiency. The approach provides insights into how an advanced economy is a more ordered economy, and tools to investigate the concerns of the Bioeconomists over long term economic survival.

]]>Entropy doi: 10.3390/e20040227

Authors: Alexander Wilce

This paper fails to derive quantum mechanics from a few simple postulates. However, it gets very close, and does so without much exertion. More precisely, I obtain a representation of finite-dimensional probabilistic systems in terms of Euclidean Jordan algebras, in a strikingly easy way, from simple assumptions. This provides a framework within which real, complex and quaternionic QM can play happily together and allows some (but not too much) room for more exotic alternatives. (This is a leisurely summary, based on recent lectures, of material from the papers arXiv:1206:2897 and arXiv:1507.06278, the latter joint work with Howard Barnum and Matthew Graydon. Some further ideas are also explored, developing the connection between conjugate systems and the possibility of forming stable measurement records and making connections between this approach and the categorical approach to quantum theory.)

]]>Entropy doi: 10.3390/e20040226

Authors: Bernardo Spagnolo Angelo Carollo Davide Valenti

The stabilizing effect of quantum fluctuations on the escape process and the relaxation dynamics from a quantum metastable state are investigated. Specifically, the quantum dynamics of a multilevel bistable system coupled to a bosonic Ohmic thermal bath in strong dissipation regime is analyzed. The study is performed by a non-perturbative method based on the real-time path integral approach of the Feynman-Vernon influence functional. We consider a strongly asymmetric double well potential with and without a monochromatic external driving, and with an out-of-equilibrium initial condition. In the absence of driving we observe a nonmonotonic behavior of the escape time from the metastable region, as a function both of the system-bath coupling coefficient and the temperature. This indicates a stabilizing effect of the quantum fluctuations. In the presence of driving our findings indicate that, as the coupling coefficient γ increases, the escape time, initially controlled by the external driving, shows resonant peaks and dips, becoming frequency-independent for higher γ values. Moreover, the escape time from the metastable state displays a nonmonotonic behavior as a function of the temperature, the frequency of the driving, and the thermal-bath coupling, which indicates the presence of a quantum noise enhanced stability phenomenon. Finally, we investigate the role of different spectral densities, both in sub-Ohmic and super-Ohmic dissipation regime and for different cutoff frequencies, on the relaxation dynamics from the quantum metastable state. The results obtained indicate that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the spectral properties of the thermal bath influence non-trivially the short time behavior and the time scales of the relaxation dynamics from the metastable state.

]]>Entropy doi: 10.3390/e20040225

Authors: Jesús Puente Fernández Luis García Villalba Tai-Hoon Kim

Nowadays, different protocols coexist in Internet that provides services to users. Unfortunately, control decisions and distributed management make it hard to control networks. These problems result in an inefficient and unpredictable network behaviour. Software Defined Networks (SDN) is a new concept of network architecture. It intends to be more flexible and to simplify the management in networks with respect to traditional architectures. Each of these aspects are possible because of the separation of control plane (controller) and data plane (switches) in network devices. OpenFlow is the most common protocol for SDN networks that provides the communication between control and data planes. Moreover, the advantage of decoupling control and data planes enables a quick evolution of protocols and also its deployment without replacing data plane switches. In this survey, we review the SDN technology and the OpenFlow protocol and their related works. Specifically, we describe some technologies as Wireless Sensor Networks and Wireless Cellular Networks and how SDN can be included within them in order to solve their challenges. We classify different solutions for each technology attending to the problem that is being fixed.

]]>Entropy doi: 10.3390/e20040224

Authors: Tatsuaki Tsuruyama

A cell signaling system is in a non-equilibrium state, and it includes multistep biochemical signaling cascades (BSCs), which involve phosphorylation of signaling molecules, such as mitogen-activated protein kinase (MAPK) pathways. In this study, the author considered signal transduction description using information thermodynamic theory. The ideal BSCs can be considered one type of the Szilard engine, and the presumed feedback controller, Maxwell’s demon, can extract the work during signal transduction. In this model, the mutual entropy and chemical potential of the signal molecules can be redefined by the extracted chemical work in a mechanicochemical model, Szilard engine, of BSC. In conclusion, signal transduction is computable using the information thermodynamic method.

]]>Entropy doi: 10.3390/e20040223

Authors: Isis Lins Márcio Moura Enrique Droguett Thaís Corrêa

The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsallis’ non-extensive entropy, namely the q-Exponential and the q-Weibull distributions. The q-Exponential and Weibull distributions can model decreasing, constant or increasing failure intensity functions. However, the power law behavior of the q-Exponential probability density function for specific parameter values is an advantage over the Weibull distribution when adjusting data containing extreme values. The q-Weibull probability distribution, in turn, can also fit data with bathtub-shaped or unimodal failure intensities in addition to the behaviors already mentioned. Therefore, the q-Exponential-GRP is an alternative for the Weibull-GRP model and the q-Weibull-GRP generalizes both. The method of maximum likelihood is used for their parameters’ estimation by means of a particle swarm optimization algorithm, and Monte Carlo simulations are performed for the sake of validation. The proposed models and algorithms are applied to examples involving reliability-related data of complex systems and the obtained results suggest GRP plus q-distributions are promising techniques for the analyses of repairable systems.

]]>Entropy doi: 10.3390/e20040222

Authors: Maziar Heidari Kurt Kremer Raffaello Potestio Robinson Cortes-Huerto

The spatial block analysis (SBA) method has been introduced to efficiently extrapolate thermodynamic quantities from finite-size computer simulations of a large variety of physical systems. In the particular case of simple liquids and liquid mixtures, by subdividing the simulation box into blocks of increasing size and calculating volume-dependent fluctuations of the number of particles, it is possible to extrapolate the bulk isothermal compressibility and Kirkwood–Buff integrals in the thermodynamic limit. Only by explicitly including finite-size effects, ubiquitous in computer simulations, into the SBA method, the extrapolation to the thermodynamic limit can be achieved. In this review, we discuss two of these finite-size effects in the context of the SBA method due to (i) the statistical ensemble and (ii) the finite integration domains used in computer simulations. To illustrate the method, we consider prototypical liquids and liquid mixtures described by truncated and shifted Lennard–Jones (TSLJ) potentials. Furthermore, we show some of the most recent developments of the SBA method, in particular its use to calculate chemical potentials of liquids in a wide range of density/concentration conditions.

]]>Entropy doi: 10.3390/e20040221

Authors: Claire Gilpin David Darmon Zuzanna Siwy Craig Martens

Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER) and specific entropy rate (SER) computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.

]]>Entropy doi: 10.3390/e20040220

Authors: Ichiro Shigekawa

We investigate the exponential convergence of a Markovian semigroup in the Zygmund space under the assumption of logarithmic Sobolev inequality. We show that the convergence rate is greater than the logarithmic Sobolev constant. To do this, we use the notion of entropy. We also give an example of a Laguerre operator. We determine the spectrum in the Orlicz space and discuss the relation between the logarithmic Sobolev constant and the spectral gap.

]]>Entropy doi: 10.3390/e20040219

Authors: Xiaoqiang Hua Yongqiang Cheng Hongqiang Wang Yuliang Qin

This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD) matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.

]]>Entropy doi: 10.3390/e20040218

Authors: Akira Takada Reinhard Conradt Pascal Richet

A new model of non-equilibrium thermodynamic states has been investigated on the basis of the fact that all thermodynamic variables can be derived from partition functions. We have thus attempted to define partition functions for non-equilibrium conditions by introducing the concept of pseudo-temperature distributions. These pseudo-temperatures are configurational in origin and distinct from kinetic (phonon) temperatures because they refer to the particular fragments of the system with specific energies. This definition allows thermodynamic states to be described either for equilibrium or non-equilibrium conditions. In addition; a new formulation of an extended canonical partition function; internal energy and entropy are derived from this new temperature definition. With this new model; computational experiments are performed on simple non-interacting systems to investigate cooling and two distinct relaxational effects in terms of the time profiles of the partition function; internal energy and configurational entropy.

]]>Entropy doi: 10.3390/e20040217

Authors: Elena Loubenets

We present a general approach for quantifying tolerance of a nonlocal N-partite state to any local noise under different classes of quantum correlation scenarios with arbitrary numbers of settings and outcomes at each site. This allows us to derive new precise bounds in d and N on noise tolerances for: (i) an arbitrary nonlocal N-qudit state; (ii) the N-qudit Greenberger–Horne–Zeilinger (GHZ) state; (iii) the N-qubit W state and the N-qubit Dicke states, and to analyse asymptotics of these precise bounds for large N and d .

]]>Entropy doi: 10.3390/e20040216

Authors: Kivanc Cetin Ozgur Afsar Ugur Tirnakli

In this paper, using the Poincaré section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rössler system, which is one of the most popular three-dimensional continuous systems. As Poincaré section points of the flow show similar behavior to that of the logistic map, for the Rössler system we also investigate the relationships with respect to important properties of nonlinear dynamics, such as correlation length, fractal dimension, and the Lyapunov exponent in the vicinity of the chaos threshold.

]]>Entropy doi: 10.3390/e20040215

Authors: Dianfa Wu Ningling Wang Zhiping Yang Chengzhou Li Yongping Yang

In recent years, coal-fired power plants contribute the biggest part of power generation in China. Challenges of energy conservation and emission reduction of the coal-fired power plant encountering with a rapid growth due to the rising proportion of renewable energy generation in total power generation. Energy saving power generation dispatch (ESPGD) based on power units sorting technology is a promising approach to meet the challenge. Therefore, it is crucial to establish a reasonable and feasible multi-index comprehensive evaluation (MICE) framework for assessing the performance of coal-fired power units accessed by the power grid. In this paper, a hierarchical multiple criteria evaluation system was established. Except for the typical economic and environmental indices, the evaluation system considering operational flexibility and power quality indices either. A hybrid comprehensive evaluation model was proposed to assess the unit operational performance. The model is an integration of grey relational analysis (GRA) with analytic hierarchy process (AHP) and a novel entropy-based method (abbreviate as BECC) which integrates bootstrap method and correlation coefficient (CC) into entropy principle to get the objective weight of indices. Then a case study on seven typical 600 megawatts coal-fired power units was carried out to illustrate the proposed evaluation model, and a weight sensitivity analysis was developed in addition. The results of the case study shows that unit 4 has the power generating priority over the rest ones, and unit 2 ranks last, with the lowest grey relational degree. The weight sensitivity analysis shows that the environmental factor has the biggest sensitivity coefficient. And the validation analysis of the developed BECC weight method shows that it is feasible for the MICE model, and it is stable with an ignorable uncertainty caused by the stochastic factor in the bootstrapping process. The elaborate analysis of the result reveals that it is feasible to rank power units with the proposed evaluation model. Furthermore, it is beneficial to synthesize the updated multiple criteria in optimizing the power generating priority of coal-fired power units.

]]>Entropy doi: 10.3390/e20040214

Authors: Sadiq Abdulhussain Abd Ramli M. Saripan Basheera Mahmmod Syed Al-Haddad Wissam Jassim

The recent increase in the number of videos available in cyberspace is due to the availability of multimedia devices, highly developed communication technologies, and low-cost storage devices. These videos are simply stored in databases through text annotation. Content-based video browsing and retrieval are inefficient due to the method used to store videos in databases. Video databases are large in size and contain voluminous information, and these characteristics emphasize the need for automated video structure analyses. Shot boundary detection (SBD) is considered a substantial process of video browsing and retrieval. SBD aims to detect transition and their boundaries between consecutive shots; hence, shots with rich information are used in the content-based video indexing and retrieval. This paper presents a review of an extensive set for SBD approaches and their development. The advantages and disadvantages of each approach are comprehensively explored. The developed algorithms are discussed, and challenges and recommendations are presented.

]]>Entropy doi: 10.3390/e20040213

Authors: Cristina Gasch Inmaculada Remolar Miguel Chover Cristina Rebollo

Plants and trees are an essential part of outdoor scenes. They are represented by such a vast number of polygons that performing real-time visualization is still a problem in spite of the advantages of the hardware. Some methods have appeared to solve this drawback based on point- or image-based rendering. However, geometry representation is required in some interactive applications. This work presents a simplification method that deals with the geometry of the foliage, reducing the number of primitives that represent these objects and making their interactive visualization possible. It is based on an image-based simplification that establishes an order of leaf pruning and reduces the complexity of the canopies of trees and plants. The proposed simplification method is viewpoint-driven and uses the mutual information in order to choose the leaf to prune. Moreover, this simplification method avoids the pruned appearance of the tree that is usually produced when a foliage representation is formed by a reduced number of leaves. The error introduced every time a leaf is pruned is compensated for if the size of the nearest leaf is altered to preserve the leafy appearance of the foliage. Results demonstrate the good quality and time performance of the presented work.

]]>Entropy doi: 10.3390/e20040212

Authors: Bin Ju Haijiao Zhang Yongbin Liu Fang Liu Siliang Lu Zhijia Dai

A feature extraction method named improved multi-scale entropy (IMSE) is proposed for rolling bearing fault diagnosis. This method could overcome information leakage in calculating the similarity of machinery systems, which is based on Pythagorean Theorem and similarity criterion. Features extracted from bearings under different conditions using IMSE are identified by the support vector machine (SVM) classifier. Experimental results show that the proposed method can extract the status information of the bearing. Compared with the multi-scale entropy (MSE) and sample entropy (SE) methods, the identification accuracy of the features extracted by IMSE is improved as well.

]]>Entropy doi: 10.3390/e20030211

Authors: Yujie Gu Qianyu Zhang Liying Yu

Rough random theory, generally applied to statistics, decision-making, and so on, is an extension of rough set theory and probability theory, in which a rough random variable is described as a random variable taking “rough variable” values. In order to extend and enrich the research area of rough random theory, in this paper, the well-known probabilistic inequalities (Markov inequality, Chebyshev inequality, Holder’s inequality, Minkowski inequality and Jensen’s inequality) are proven for rough random variables, which gives a firm theoretical support to the further development of rough random theory. Besides, considering that the critical values always act as a vital tool in engineering, science and other application fields, some significant properties of the critical values of rough random variables involving the continuity and the monotonicity are investigated deeply to provide a novel analytical approach for dealing with the rough random optimization problems.

]]>Entropy doi: 10.3390/e20030210

Authors: Hamed Azami Javier Escudero

Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel–Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326.

]]>