Entropy, Volume 17, Issue 8 (August 2015) – 42 articles , Pages 5145-5937

We provide an entropy analysis for light storage and light retrieval. In this analysis, entropy extraction and reduction in a typical light storage experiment are identified. The spatiotemporal behavior of entropy is presented for D1 transition in cold sodium atoms. The governing equations are the reduced Maxwell field equations and the Liouville–von Neumann equation for the density matrix of the dressed atom. Full article

The article discusses two mutually-incompatible hypotheses about the stochastic mechanism of the generation of texts in natural language, which could be related to entropy. The first hypothesis, the finite energy hypothesis, assumes that texts are generated by a process with exponentially-decaying probabilities. This hypothesis implies a logarithmic upper bound for maximal repetition, as a function of the text length. The second hypothesis, the strong Hilberg conjecture, assumes that the topological entropy grows as a power law. This hypothesis leads to a hyperlogarithmic lower bound for maximal repetition. By a study of 35 written texts in German, English and French, it is found that the hyperlogarithmic growth of maximal repetition holds for natural language. In this way, the finite energy hypothesis is rejected, and the strong Hilberg conjecture is partly corroborated. Full article

We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalized complex geometry, we examine a simplified version of the Unruh effect: the thermalising effect of gravitational fields on the Schroedinger wavefunction. Full article

In modern industrial processes, it is easier and less expensive to configure alarms by software settings rather than by wiring, which causes the rapid growth of the number of alarms. Moreover, because there exist complex interactions, in particular the causal relationship among different parts in the process, a fault may propagate along propagation pathways once an abnormal situation occurs, which brings great difficulty to operators to identify its root cause immediately and to take proper actions correctly. Therefore, causality detection becomes a very important problem in the context of multivariate alarm analysis and design. Transfer entropy has become an effective and widely-used method to detect causality between different continuous process variables in both linear and nonlinear situations in recent years. However, such conventional methods to detect causality based on transfer entropy are computationally costly. Alternatively, using binary alarm series can be more computational-friendly and more direct because alarm data analysis is straightforward for alarm management in practice. The methodology and implementation issues are discussed in this paper. Illustrated by several case studies, including both numerical cases and simulated industrial cases, the proposed method is demonstrated to be suitable for industrial situations contaminated by noise. Full article

In the last few years, complex networks have become an increasingly relevant research topic due to the large number of fields of application. Particularly, complex networks are especially significant in the area of modern online social networks (OSNs). OSNs are actually a challenge for complex network analysis, as they present some characteristics that hinder topology processing. Concretely, social networks’ volume is exceedingly big, as they have a high number of nodes and links. One of the most popular and influential OSNs is Twitter. In this paper, we present a model to describe the growth of scale-free networks. This model is applied to Twitter after checking that it can be considered a “scale-free” complex network fulfilling the small world property. Checking this property involves the calculation of the shortest path between any two nodes of the network. Given the difficulty of this computation for large networks, a new heuristic method is also proposed to find the upper bounds of the path lengths instead of computing the exact length. Full article

The aeroderivate gas turbines are widely used for power generation in the oil and gas industry. In offshore marine platforms, the aeroderivative gas turbines provide the energy required to drive mechanically compressors, pumps and electric generators. Therefore, the study of the performance of aeroderivate gas turbines based on a parametric analysis is relevant to carry out a diagnostic of the engine, which can lead to operational as well as predictive and/or corrective maintenance actions. This work presents a methodology based on the exergetic analysis to estimate the irrevesibilities and exergetic efficiencies of the main components of a two-shaft aeroderivate gas turbine. The studied engine is the Solar Turbine Mars 100, which is rated to provide 11.86 MW. In this engine, the air is compressed in an axial compressor achieving a pressure ratio of 17.7 relative to ambient conditions and a high pressure turbine inlet temperature of 1220 °C. Even if the thermal efficiency associated to the pressure ratio of 17.7 is 1% lower than the maximum thermal efficiency, the irreversibilities related to this pressure ratio decrease approximately 1 GW with respect to irreversibilities of the optimal pressure ratio for the thermal efficiency. In addition, this paper contributes to develop a mathematical model to estimate the high turbine inlet temperature as well as the pressure ratio of the low and high pressure turbines. Full article

Aiming at the combined power quality +disturbance recognition, an automated recognition method based on wavelet packet entropy (WPE) and modified incomplete S-transform (MIST) is proposed in this paper. By combining wavelet packet Tsallis singular entropy, energy entropy and MIST, a 13-dimension vector of different power quality (PQ) disturbances including single disturbances and combined disturbances is extracted. Then, a ruled decision tree is designed to recognize the combined disturbances. The proposed method is tested and evaluated using a large number of simulated PQ disturbances and some real-life signals, which include voltage sag, swell, interruption, oscillation transient, impulsive transient, harmonics, voltage fluctuation and their combinations. In addition, the comparison of the proposed recognition approach with some existing techniques is made. The experimental results show that the proposed method can effectively recognize the single and combined PQ disturbances. Full article

For general metric theories of gravity, we compare the approach that describes/derives the field equations of gravity as a thermodynamic identity with the one which looks at them from entropy bounds. The comparison is made through the consideration of the matter entropy flux across (Rindler) horizons, studied by making use of the notion of a limiting thermodynamic scale l* of matter, previously introduced in the context of entropy bounds. In doing this: (i) a bound for the entropy of any lump of matter with a given energy-momentum tensor Tab is considered, in terms of a quantity, which is independent of the theory of gravity that we use; this quantity is the variation of the Clausius entropy of a suitable horizon when the element of matter crosses it; (ii) by making use of the equations of motion of the theory, the same quantity is then expressed as the variation of Wald’s entropy of that horizon (and this leads to a generalized form of the generalized covariant entropy bound, applicable to general diffeomorphism-invariant theories of gravity); and (iii) a notion of l* for horizons, as well as an expression for it, is given. Full article

Daily wind patterns and their relational associations with other metocean (oceanographic and meteorological) variables were algorithmically computed and extracted from a year-long wind and weather dataset, which was collected hourly from an ocean buoy located in the Penghu archipelago of Taiwan. The computational algorithm is called data cloud geometry (DCG). This DCG algorithm is a clustering-based nonparametric learning approach that was constructed and developed implicitly based on various entropy concepts. Regarding the bivariate aspect of wind speed and wind direction, the resulting multiscale clustering hierarchy revealed well-known wind characteristics of year-round pattern cycles pertaining to the particular geographic location of the buoy. A wind pattern due to a set of extreme weather days was also identified. Moreover, in terms of the relational aspect of wind and other weather variables, causal patterns were revealed through applying the DCG algorithm alternatively on the row and column axes of a data matrix by iteratively adapting distance measures to computed DCG tree structures. This adaptation technically constructed and integrated a multiscale, two-sample testing into the distance measure. These computed wind patterns and pattern-based causal relationships are useful for both general sailing and competition planning. Full article

In this paper, a fractional order economic system is studied. An active control technique is applied to control chaos in this system. The stabilization of equilibria is obtained by both theoretical analysis and the simulation result. The numerical simulations, via the improved Adams–Bashforth algorithm, show the effectiveness of the proposed controller. Full article

We consider the problem of learning a Bayesian network structure given n examples and the prior probability based on maximizing the posterior probability. We propose an algorithm that runs in O(n log n) time and that addresses continuous variables and discrete variables without assuming any class of distribution. We prove that the decision is strongly consistent, i.e., correct with probability one as n ! 1. To date, consistency has only been obtained for discrete variables for this class of problem, and many authors have attempted to prove consistency when continuous variables are present. Furthermore, we prove that the “log n” term that appears in the penalty term of the description length can be replaced by 2(1+ε) log log n to obtain strong consistency, where ε > 0 is arbitrary, which implies that the Hannan–Quinn proposition holds. Full article

A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems. Though the deformed exponential families are defined by deformed exponential functions, these functions do not satisfy the law of exponents in general. The deformed algebras have been introduced based on the deformed exponential functions. In this paper, after summarizing such deformed algebraic structures, it is clarified how deformed algebras work on deformed exponential families. In fact, deformed algebras cause generalization of expectations. The three kinds of expectations for random variables are introduced in this paper, and it is discussed why these generalized expectations are natural from the viewpoint of information geometry. In addition, deformed algebras cause generalization of independences. Whereas it is difficult to check the well-definedness of deformed independence in general, the κ-independence is always well-defined on κ-exponential families. This is one of advantages of κ-exponential families in complex systems. Consequently, we can well generalize the maximum likelihood method for the κ-exponential family from the viewpoint of information geometry. Full article

Fruit classification is quite difficult because of the various categories and similar shapes and features of fruit. In this work, we proposed two novel machine-learning based classification methods. The developed system consists of wavelet entropy (WE), principal component analysis (PCA), feedforward neural network (FNN) trained by fitness-scaled chaotic artificial bee colony (FSCABC) and biogeography-based optimization (BBO), respectively. The K-fold stratified cross validation (SCV) was utilized for statistical analysis. The classification performance for 1653 fruit images from 18 categories showed that the proposed “WE + PCA + FSCABC-FNN” and “WE + PCA + BBO-FNN” methods achieve the same accuracy of 89.5%, higher than state-of-the-art approaches: “(CH + MP + US) + PCA + GA-FNN ” of 84.8%, “(CH + MP + US) + PCA + PSO-FNN” of 87.9%, “(CH + MP + US) + PCA + ABC-FNN” of 85.4%, “(CH + MP + US) + PCA + kSVM” of 88.2%, and “(CH + MP + US) + PCA + FSCABC-FNN” of 89.1%. Besides, our methods used only 12 features, less than the number of features used by other methods. Therefore, the proposed methods are effective for fruit classification. Full article

This paper grounds the critique of the reduction of regions in a country , not only in its geographical and social context but also in its entropic space. The various recent plans leading to the reduction of the number of regions in metropolitan France are discussed, based on the mere distribution in the number of municipalities in the plans and analyzed according to various distribution laws. Each case, except the present distribution with 22 regions, on the mainland, does not seem to fit presently used theoretical models. In addition, the number of inhabitants is examined in each plan. The same conclusion holds. Therefore, a theoretical argument based on entropy considerations is proposed, thereby pointing to whether more order or less disorder is the key question—discounting political considerations. Full article

In this paper, we investigate the basic properties of binary classification with a pseudo model based on the Itakura–Saito distance and reveal that the Itakura–Saito distance is a unique appropriate measure for estimation with the pseudo model in the framework of general Bregman divergence. Furthermore, we propose a novelmulti-task learning algorithm based on the pseudo model in the framework of the ensemble learning method. We focus on a specific setting of the multi-task learning for binary classification problems. The set of features is assumed to be common among all tasks, which are our targets of performance improvement. We consider a situation where the shared structures among the dataset are represented by divergence between underlying distributions associated with multiple tasks. We discuss statistical properties of the proposed method and investigate the validity of the proposed method with numerical experiments. Full article

We consider a geometric entropy as a measure of complexity for Gaussian networks, namely networks having Gaussian random variables sitting on vertices and their correlations as weighted links. We then show how the network dynamics described by the well-known Ornstein–Uhlenbeck process reflects into such a measure. We unveil a crossing of the entropy time behaviors between switching on and off links. Moreover, depending on the number of links switched on or off, the entropy time behavior can be non-monotonic. Full article

Signature schemes, proposed in 1976 by Diffie and Hellman, have become ubiquitous across modern communications. They allow for the exchange of messages from one sender to multiple recipients, with the guarantees that messages cannot be forged or tampered with and that messages also can be forwarded from one recipient to another without compromising their validity. Signatures are different from, but no less important than encryption, which ensures the privacy of a message. Commonly used signature protocols—signatures based on the Rivest–Adleman–Shamir (RSA) algorithm, the digital signature algorithm (DSA), and the elliptic curve digital signature algorithm (ECDSA)—are only computationally secure, similar to public key encryption methods. In fact, since these rely on the difficulty of finding discrete logarithms or factoring large primes, it is known that they will become completely insecure with the emergence of quantum computers. We may therefore see a shift towards signature protocols that will remain secure even in a post-quantum world. Ideally, such schemes would provide unconditional or information-theoretic security. In this paper, we aim to provide an accessible and comprehensive review of existing unconditionally securesecure signature schemes for signing classical messages, with a focus on unconditionally secure quantum signature schemes. Full article

We propose a novel approach framed in terms of information theory and entropy to tackle the issue of the propagation of conspiracy theories. We represent the initial report of an event (such as the 9/11 terroristic attack) as a series of strings of information, each string classified by a two-state variable E_i = ±1, i = 1, …, N. If the values of the E_i are set to −1 for all strings, a state of minimum entropy is achieved. Comments on the report, focusing repeatedly on several strings E_k, might alternate their meaning (from −1 to +1). The representation of the event is turned fuzzy with an increased entropy value. Beyond some threshold value of entropy, chosen by simplicity to its maximum value, meaning N/2 variables with E_i = 1, the chance is created that a conspiracy theory might be initiated/propagated. Therefore, the evolution of the associated entropy is a way to measure the degree of penetration of a conspiracy theory. Our general framework relies on online content made voluntarily available by crowds of people, in response to some news or blog articles published by official news agencies. We apply different aggregation levels (comment, person, discussion thread) and discuss the associated patterns of entropy change. Full article

Fluid machinery operating in the supersonic regime unveil avenues towards more compact technology. However, internal supersonic flows are associated with high aerodynamic and thermal penalties, which usually prevent their practical implementation. Indeed, both shock losses and the limited operational range represent particular challenges to aerodynamic designers that should be taken into account at the initial phase of the design process. This paper presents a design methodology for supersonic passages based on direct evaluations of the velocity field using the method of characteristics and computation of entropy generation across shock waves. This meshless function evaluation tool is then coupled to an optimization scheme, based on evolutionary algorithms that minimize the entropy generation across the supersonic passage. Finally, we assessed the results with 3D Reynolds Averaged Navier Stokes calculations. Full article

In this paper, the problem of robust control of nonlinear fractional-order systems in the presence of uncertainties and external disturbance is investigated. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed Lemmas, an adaptive fuzzy controller is designed. The proposed method can guarantee all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small region of the origin. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results. Full article

This paper introduces a new simple system with a butterfly chaotic attractor. This system has rich and complex dynamics. With some typical parameters, its Lyapunov dimension is greater than other known three dimensional chaotic systems. It exhibits chaotic behavior over a large range of parameters, and the divergence of flow of this system is not a constant. The dynamics of this new system are analyzed via Lyapunov exponent spectrum, bifurcation diagrams, phase portraits and the Poincaré map. The compound structures of this new system are also analyzed. By means of topological horseshoe theory and numerical computation, the Poincaré map defined for the system is proved to be semi-conjugate to 3-shift map, and thus the system has positive topological entropy. Full article

The minimum error entropy (MEE) criterion is an important learning criterion in information theoretical learning (ITL). However, the MEE solution cannot be obtained in closed form even for a simple linear regression problem, and one has to search it, usually, in an iterative manner. The fixed-point iteration is an efficient way to solve the MEE solution. In this work, we study a fixed-point MEE algorithm for linear regression, and our focus is mainly on the convergence issue. We provide a sufficient condition (although a little loose) that guarantees the convergence of the fixed-point MEE algorithm. An illustrative example is also presented. Full article

This paper outlines a thermodynamic theory of biological evolution. Beginning with a brief summary of the parallel histories of the modern evolutionary synthesis and thermodynamics, we use four physical laws and processes (the first and second laws of thermodynamics, diffusion and the maximum entropy production principle) to frame the theory. Given that open systems such as ecosystems will move towards maximizing dispersal of energy, we expect biological diversity to increase towards a level, D_max, representing maximum entropic production (S_max). Based on this theory, we develop a mathematical model to predict diversity over the last 500 million years. This model combines diversification, post-extinction recovery and likelihood of discovery of the fossil record. We compare the output of this model with that of the observed fossil record. The model predicts that life diffuses into available energetic space (ecospace) towards a dynamic equilibrium, driven by increasing entropy within the genetic material. This dynamic equilibrium is punctured by extinction events, which are followed by restoration of D_max through diffusion into available ecospace. Finally we compare and contrast our thermodynamic theory with the MES in relation to a number of important characteristics of evolution (progress, evolutionary tempo, form versus function, biosphere architecture, competition and fitness). Full article

A Carnot type engine with a changing phase during the heating and the cooling is modeled with its thermal contact with the heat source. In a first optimization, the optimal high temperature of the cycle is determined to maximize the power output. The temperature and the mass flow rate of the heat source are given. This does not take into account the converter internal fluid and its mass flow rate. It is an exogenous optimization of the converter. In a second optimization, the endogenous optimization, the isothermal heating corresponds only to the vaporization of the selected fluid. The maximization of the power output gives the optimal vaporization temperature of the cycled fluid. Using these two optima allows connecting the temperature of the heat source to the working fluid used. For a given temperature level, mass flow rate and composition of the waste heat to recover, an optimal fluid and its temperature of vaporization are deduced. The optimal conditions size also the internal mass flow rate and the compression ratio (pump size). The optimum corresponds to the maximum of the power output and must be combined with the environmental fluid impact and the technological constraints. Full article

Current approaches to characterize the complexity of dynamical systems usually rely on state-space trajectories. In this article instead we focus on causal structure, treating discrete dynamical systems as directed causal graphs—systems of elements implementing local update functions. This allows us to characterize the system’s intrinsic cause-effect structure by applying the mathematical and conceptual tools developed within the framework of integrated information theory (IIT). In particular, we assess the number of irreducible mechanisms (concepts) and the total amount of integrated conceptual information Φ specified by a system. We analyze: (i) elementary cellular automata (ECA); and (ii) small, adaptive logic-gate networks (“animats”), similar to ECA in structure but evolving by interacting with an environment. We show that, in general, an integrated cause-effect structure with many concepts and high Φ is likely to have high dynamical complexity. Importantly, while a dynamical analysis describes what is “happening” in a system from the extrinsic perspective of an observer, the analysis of its cause-effect structure reveals what a system “is” from its own intrinsic perspective, exposing its dynamical and evolutionary potential under many different scenarios. Full article

A scoring rule is a device for evaluation of forecasts that are given in terms of the probability of an event. In this article we will restrict our attention to binary forecasts. We may think of a scoring rule as a penalty attached to a forecast after the event has been observed. Thus a relatively small penalty will accrue if a high probability forecast that an event will occur is followed by occurrence of the event. On the other hand, a relatively large penalty will accrue if this forecast is followed by non-occurrence of the event. Meteorologists have been foremost in developing scoring rules for the evaluation of probabilistic forecasts. Here we use a published meteorological data set to illustrate diagrammatically the Brier score and the divergence score, and their statistical decompositions, as examples of Bregman divergences. In writing this article, we have in mind environmental scientists and modellers for whom meteorological factors are important drivers of biological, physical and chemical processes of interest. In this context, we briefly draw attention to the potential for probabilistic forecasting of the within-season component of nitrous oxide emissions from agricultural soils. Full article

Cuprous oxide (Cu₂O) nanocubes were synthesized by reducing Cu(OH)₂ in the presence of sodium citrate at room temperature. The samples were characterized in detail by field-emission scanning electron microscopy, transmission electron microscopy, high-resolution transmission electron microscopy, X-ray powder diffraction, and N₂ absorption (BET specific surface area). The equations for acquiring reaction kinetic parameters and surface thermodynamic properties of Cu₂O nanocubes were deduced by establishment of the relations between thermodynamic functions of Cu₂O nanocubes and these of the bulk Cu₂O. Combined with thermochemical cycle, transition state theory, basic theory of chemical thermodynamics, and in situ microcalorimetry, reaction kinetic parameters, specific surface enthalpy, specific surface Gibbs free energy, and specific surface entropy of Cu₂O nanocubes were successfully determined. We also introduced a universal route for gaining reaction kinetic parameters and surface thermodynamic properties of nanomaterials. Full article

Automated planning is a well-established field of artificial intelligence (AI), with applications in route finding, robotics and operational research, among others. The task of developing a plan is often solved by finding a path in a graph representing the search domain; a robust plan consists of numerous paths that can be chosen if the execution of the best (optimal) one fails. While robust planning for a single entity is rather simple, development of a robust plan for multiple entities in a common environment can lead to combinatorial explosion. This paper proposes a novel hybrid approach, joining heuristic search and the wavefront algorithm to provide a plan featuring robustness in areas where it is needed, while maintaining a low level of computational complexity. Full article

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis. Full article

Entropy-based tools are commonly used to describe the dynamics of complex systems. In the last few decades, non-extensive statistics, based on Tsallis entropy, and multifractal techniques have shown to be useful to characterize long-range interaction and scaling behavior. In this paper, an approach based on generalized Tsallis dimensions is used for the formulation of mutual-information-related dependence coefficients in the multifractal domain. Different versions according to the normalizing factor, as well as to the inclusion of the non-extensivity correction term are considered and discussed. An application to the assessment of dimensional interaction in the structural dynamics of a seismic real series is carried out to illustrate the usefulness and comparative performance of the measures introduced. Full article