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  • Articles  (3,172)
  • MDPI Publishing  (3,172)
  • Entropy  (3,172)
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  • Articles  (3,172)
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  • 1
    Publication Date: 2015-08-11
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
    Published by MDPI Publishing
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  • 2
    Publication Date: 2015-08-11
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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  • 3
    Publication Date: 2015-08-13
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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  • 4
    Publication Date: 2015-08-13
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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  • 5
    Publication Date: 2015-08-04
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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  • 6
    Publication Date: 2015-08-04
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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  • 7
    Publication Date: 2015-08-07
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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  • 8
    Publication Date: 2015-08-08
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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  • 9
    Publication Date: 2015-08-21
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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  • 10
    Publication Date: 2015-08-21
    Description: 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.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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