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Entropy (ISSN 1099-4300; CODEN: ENTRFG) is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI. The International Society for Information Studies (IS4SI) is affiliated with Entropy and their members receive a discount on the article processing charge.
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Impact Factor: 2.305 (2017) ; 5-Year Impact Factor: 2.303 (2017)
Latest Articles
Alternation of Defects and Phase Turbulence Induces Extreme Events in an eXtended Microcavity Laser
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Entropy 2018, 20(10), 789; https://doi.org/10.3390/e20100789 (registering DOI) - 15 October 2018
Abstract
Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable
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Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable absorber media. This system is known to give rise experimentally and theoretically to extreme events characterized by rare and high amplitude optical pulses following the onset of spatiotemporal chaos. Based on a theoretical model, we reveal a dynamical behavior characterized by the chaotic alternation of phase and amplitude turbulence. The highest amplitude pulses, i.e., the extreme events, are observed in the phase turbulence zones. This chaotic alternation behavior between different turbulent regimes is at contrast to what is usually observed in a generic amplitude equation model such as the Ginzburg–Landau model. Hence, these regimes provide some insight into the poorly known properties of the complex spatiotemporal dynamics exhibited by secondary instabilities of an Andronov–Hopf bifurcation.
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A Fast Feature Selection Algorithm by Accelerating Computation of Fuzzy Rough Set-Based Information Entropy
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Entropy 2018, 20(10), 788; https://doi.org/10.3390/e20100788 - 13 October 2018
Abstract
The information entropy developed by Shannon is an effective measure of uncertainty in data, and the rough set theory is a useful tool of computer applications to deal with vagueness and uncertainty data circumstances. At present, the information entropy has been extensively applied
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The information entropy developed by Shannon is an effective measure of uncertainty in data, and the rough set theory is a useful tool of computer applications to deal with vagueness and uncertainty data circumstances. At present, the information entropy has been extensively applied in the rough set theory, and different information entropy models have also been proposed in rough sets. In this paper, based on the existing feature selection method by using a fuzzy rough set-based information entropy, a corresponding fast algorithm is provided to achieve efficient implementation, in which the fuzzy rough set-based information entropy taking as the evaluation measure for selecting features is computed by an improved mechanism with lower complexity. The essence of the acceleration algorithm is to use iterative reduced instances to compute the lambda-conditional entropy. Numerical experiments are further conducted to show the performance of the proposed fast algorithm, and the results demonstrate that the algorithm acquires the same feature subset to its original counterpart, but with significantly less time.
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A QUBO Formulation of the Stereo Matching Problem for D-Wave Quantum Annealers
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Entropy 2018, 20(10), 786; https://doi.org/10.3390/e20100786 - 12 October 2018
Abstract
In this paper, we propose a methodology to solve the stereo matching problem through quantum annealing optimization. Our proposal takes advantage of the existing Min-Cut/Max-Flow network formulation of computer vision problems. Based on this network formulation, we construct a quadratic pseudo-Boolean function and
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In this paper, we propose a methodology to solve the stereo matching problem through quantum annealing optimization. Our proposal takes advantage of the existing Min-Cut/Max-Flow network formulation of computer vision problems. Based on this network formulation, we construct a quadratic pseudo-Boolean function and then optimize it through the use of the D-Wave quantum annealing technology. Experimental validation using two kinds of stereo pair of images, random dot stereograms and gray-scale, shows that our methodology is effective.
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Colombian Export Capabilities: Building the Firms-Products Network
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Entropy 2018, 20(10), 785; https://doi.org/10.3390/e20100785 - 12 October 2018
Abstract
In this paper, we analyse the bipartite Colombian firms-products network, throughout a period of five years, from 2010 to 2014. Our analysis depicts a strongly modular system, with several groups of firms specializing in the export of specific categories of products. These clusters
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In this paper, we analyse the bipartite Colombian firms-products network, throughout a period of five years, from 2010 to 2014. Our analysis depicts a strongly modular system, with several groups of firms specializing in the export of specific categories of products. These clusters have been detected by running the bipartite variant of the traditional modularity maximization, revealing a bi-modular structure. Interestingly, this finding is refined by applying a recently proposed algorithm for projecting bipartite networks on the layer of interest and, then, running the Louvain algorithm on the resulting monopartite representations. Important structural differences emerge upon comparing the Colombian firms-products network with the World Trade Web, in particular, the bipartite representation of the latter is not characterized by a similar block-structure, as the modularity maximization fails in revealing (bipartite) nodes clusters. This points out that economic systems behave differently at different scales: while countries tend to diversify their production—potentially exporting a large number of different products—firms specialize in exporting (substantially very limited) baskets of basically homogeneous products.
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Entropy Inequalities for Lattices
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Entropy 2018, 20(10), 784; https://doi.org/10.3390/e20100784 - 12 October 2018
Abstract
We study entropy inequalities for variables that are related by functional dependencies. Although the powerset on four variables is the smallest Boolean lattice with non-Shannon inequalities, there exist lattices with many more variables where the Shannon inequalities are sufficient. We search for conditions
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We study entropy inequalities for variables that are related by functional dependencies. Although the powerset on four variables is the smallest Boolean lattice with non-Shannon inequalities, there exist lattices with many more variables where the Shannon inequalities are sufficient. We search for conditions that exclude the existence of non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group. In order to formulate and prove the results, one has to bridge lattice theory, group theory, the theory of functional dependences and the theory of conditional independence. It is demonstrated that the Shannon inequalities are sufficient for planar modular lattices. The proof applies a gluing technique that uses that if the Shannon inequalities are sufficient for the pieces, then they are also sufficient for the whole lattice. It is conjectured that the Shannon inequalities are sufficient if and only if the lattice does not contain a special lattice as a sub-semilattice.
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A New and Stable Estimation Method of Country Economic Fitness and Product Complexity
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Entropy 2018, 20(10), 783; https://doi.org/10.3390/e20100783 - 12 October 2018
Abstract
We present a new metric estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a
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We present a new metric estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a suitable rescaling of the relevant quantities, the non homogeneous terms are eventually set to zero so that this new metric is parameter free. This new map almost reproduces the results of the original homogeneous metrics already defined in literature and allows for an approximate analytic solution in case of actual binarized matrices based on the Revealed Comparative Advantage (RCA) indicator. This solution is connected with a new quantity describing the neighborhood of nodes in bipartite graphs, representing in this work the relations between countries and exported products. Moreover, we define the new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products. Eventually, we demonstrate analytically the local convergence of the algorithm involved.
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From Nash Equilibria to Chain Recurrent Sets: An Algorithmic Solution Concept for Game Theory
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Entropy 2018, 20(10), 782; https://doi.org/10.3390/e20100782 - 12 October 2018
Abstract
In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point
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In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point theorem, the most sophisticated result in his era’s topology—in fact, recent algorithmic work has established that Nash equilibria are computationally equivalent to fixed points. In this paper, we propose a new class of universal non-equilibrium solution concepts arising from an important theorem in the topology of dynamical systems that was unavailable to Nash. This approach starts with both a game and a learning dynamics, defined over mixed strategies. The Nash equilibria are fixpoints of the dynamics, but the system behavior is captured by an object far more general than the Nash equilibrium that is known in dynamical systems theory as chain recurrent set. Informally, once we focus on this solution concept—this notion of “the outcome of the game”—every game behaves like a potential game with the dynamics converging to these states. In other words, unlike Nash equilibria, this solution concept is algorithmic in the sense that it has a constructive proof of existence. We characterize this solution for simple benchmark games under replicator dynamics, arguably the best known evolutionary dynamics in game theory. For (weighted) potential games, the new concept coincides with the fixpoints/equilibria of the dynamics. However, in (variants of) zero-sum games with fully mixed (i.e., interior) Nash equilibria, it covers the whole state space, as the dynamics satisfy specific information theoretic constants of motion. We discuss numerous novel computational, as well as structural, combinatorial questions raised by this chain recurrence conception of games.
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Quantum-Inspired Evolutionary Approach for the Quadratic Assignment Problem
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Entropy 2018, 20(10), 781; https://doi.org/10.3390/e20100781 - 12 October 2018
Abstract
The paper focuses on the opportunity of the application of the quantum-inspired evolutionary algorithm for determining minimal costs of the assignment in the quadratic assignment problem. The idea behind the paper is to present how the algorithm has to be adapted to this
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The paper focuses on the opportunity of the application of the quantum-inspired evolutionary algorithm for determining minimal costs of the assignment in the quadratic assignment problem. The idea behind the paper is to present how the algorithm has to be adapted to this problem, including crossover and mutation operators and introducing quantum principles in particular procedures. The results have shown that the performance of our approach in terms of converging to the best solutions is satisfactory. Moreover, we have presented the results of the selected parameters of the approach on the quality of the obtained solutions.
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From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time
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Entropy 2018, 20(10), 779; https://doi.org/10.3390/e20100779 - 11 October 2018
Abstract
For historic reasons, industrial knowledge of reproducibility and restrictions imposed by regulations, open-loop feeding control approaches dominate in industrial fed-batch cultivation processes. In this study, a generic gray box biomass modeling procedure uses relative entropy as a key to approach the posterior similarly
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For historic reasons, industrial knowledge of reproducibility and restrictions imposed by regulations, open-loop feeding control approaches dominate in industrial fed-batch cultivation processes. In this study, a generic gray box biomass modeling procedure uses relative entropy as a key to approach the posterior similarly to how prior distribution approaches the posterior distribution by the multivariate path of Lagrange multipliers, for which a description of a nuisance time is introduced. The ultimate purpose of this study was to develop a numerical semi-global convex optimization procedure that is dedicated to the calculation of feeding rate time profiles during the fed-batch cultivation processes. The proposed numerical semi-global convex optimization of relative entropy is neither restricted to the gray box model nor to the bioengineering application. From the bioengineering application perspective, the proposed bioprocess design technique has benefits for both the regular feed-forward control and the advanced adaptive control systems, in which the model for biomass growth prediction is compulsory. After identification of the gray box model parameters, the options and alternatives in controllable industrial biotechnological processes are described. The main aim of this work is to achieve high reproducibility, controllability, and desired process performance. Glucose concentration measurements, which were used for the development of the model, become unnecessary for the development of the desired microbial cultivation process.
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Unconventional Deformation Behaviours of Nanoscaled High-Entropy Alloys
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Entropy 2018, 20(10), 778; https://doi.org/10.3390/e20100778 - 11 October 2018
Abstract
The bulk high-entropy alloys (HEAs) exhibit similar deformation behaviours as traditional metals. These bulk behaviours are likely an averaging of the behaviours exhibited at the nanoscale. Herein, in situ atomic-scale observation of deformation behaviours in nanoscaled CoCrCuFeNi face-centred cubic (FCC) HEA was performed.
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The bulk high-entropy alloys (HEAs) exhibit similar deformation behaviours as traditional metals. These bulk behaviours are likely an averaging of the behaviours exhibited at the nanoscale. Herein, in situ atomic-scale observation of deformation behaviours in nanoscaled CoCrCuFeNi face-centred cubic (FCC) HEA was performed. The deformation behaviours of this nanoscaled FCC HEA (i.e., nanodisturbances and phase transformations) were distinct from those of nanoscaled traditional FCC metals and corresponding bulk HEA. First-principles calculations revealed an obvious fluctuation of the stacking fault energy and stability difference at the atomic scale in the HEA. The stability difference was highlighted only in the nanoscaled HEA and induced unconventional deformation behaviours. Our work suggests that the nanoscaled HEA may provide more chances to discover the long-expected essential distinction between the HEAs and traditional metals.
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Statistical Mechanics of On-Line Learning Under Concept Drift
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Entropy 2018, 20(10), 775; https://doi.org/10.3390/e20100775 - 10 October 2018
Abstract
We introduce a modeling framework for the investigation of on-line machine learning processes in non-stationary environments. We exemplify the approach in terms of two specific model situations: In the first, we consider the learning of a classification scheme from clustered data by means
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We introduce a modeling framework for the investigation of on-line machine learning processes in non-stationary environments. We exemplify the approach in terms of two specific model situations: In the first, we consider the learning of a classification scheme from clustered data by means of prototype-based Learning Vector Quantization (LVQ). In the second, we study the training of layered neural networks with sigmoidal activations for the purpose of regression. In both cases, the target, i.e., the classification or regression scheme, is considered to change continuously while the system is trained from a stream of labeled data. We extend and apply methods borrowed from statistical physics which have been used frequently for the exact description of training dynamics in stationary environments. Extensions of the approach allow for the computation of typical learning curves in the presence of concept drift in a variety of model situations. First results are presented and discussed for stochastic drift processes in classification and regression problems. They indicate that LVQ is capable of tracking a classification scheme under drift to a non-trivial extent. Furthermore, we show that concept drift can cause the persistence of sub-optimal plateau states in gradient based training of layered neural networks for regression.
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On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases
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Entropy 2018, 20(10), 773; https://doi.org/10.3390/e20100773 - 9 October 2018
Abstract
We explore some important consequences of the quantum ideal Bose gas, the properties of which are described by a non-extensive entropy. We consider in particular two entropies that depend only on the probability. These entropies are defined in the framework of superstatistics, and
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We explore some important consequences of the quantum ideal Bose gas, the properties of which are described by a non-extensive entropy. We consider in particular two entropies that depend only on the probability. These entropies are defined in the framework of superstatistics, and in this context, such entropies arise when a system is exposed to non-equilibrium conditions, whose general effects can be described by a generalized Boltzmann factor and correspondingly by a generalized probability distribution defining a different statistics. We generalize the usual statistics to their quantum counterparts, and we will focus on the properties of the corresponding generalized quantum ideal Bose gas. The most important consequence of the generalized Bose gas is that the critical temperature predicted for the condensation changes in comparison with the usual quantum Bose gas. Conceptual differences arise when comparing our results with the ones previously reported regarding the q-generalized Bose–Einstein condensation. As the entropies analyzed here only depend on the probability, our results cannot be adjusted by any parameter. Even though these results are close to those of non-extensive statistical mechanics for
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Entropy Signature for Crack Networks in Old Paintings: Saturation Prospectus
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Entropy 2018, 20(10), 772; https://doi.org/10.3390/e20100772 - 8 October 2018
Abstract
In desiccated films, particularly with old paintings, molecular bonds may break to create intricate patterns of macroscopic cracks. The resulting directions of the cracks quantifiably enable an evaluation of the entropy and degree of disorder in the network. Experimental tests on prepared samples
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In desiccated films, particularly with old paintings, molecular bonds may break to create intricate patterns of macroscopic cracks. The resulting directions of the cracks quantifiably enable an evaluation of the entropy and degree of disorder in the network. Experimental tests on prepared samples and a two-interacting-variables model allow the evolution of entropy to be tracked. Calculations were performed, primarily using data from the painting Girl with a Pearl Earring by Vermeer, revealing that the left side of the girl’s face features a crack structure with higher entropy (or less order) than the right side. Other old paintings were considered. The extrapolation of experiments to these old paintings confirms that saturation still is not reached.
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21 September 2018
Meet Us at the 2018 IEEE Information Theory Workshop in Guangzhou, China, 25–29 November 2018
Meet Us at the 2018 IEEE Information Theory Workshop in Guangzhou, China, 25–29 November 2018
Conferences
Special Issues
Special Issue in
Entropy
Information-Processing and Embodied, Embedded, Enactive Cognition Part 2: Morphological Computing and Cognitive Agency
Guest Editors: Gordana Dodig-Crnkovic, Robert LoweDeadline: 15 October 2018
Special Issue in
Entropy
Biological Statistical Mechanics
Guest Editors: Alessandro Giuliani, Mariano Bizzarri Deadline: 28 October 2018
Special Issue in
Entropy
Advances in Quantum Metrology
Guest Editors: Jacob A. Dunningham, Simon A. HaineDeadline: 15 November 2018
Special Issue in
Entropy
Entropy and Information Inequalities
Guest Editors: James Melbourne, Varun JogDeadline: 30 November 2018
Topical Collections
Topical Collection in
Entropy
Wavelets, Fractals and Information Theory
Collection Editor: Carlo Cattani
Topical Collection in
Entropy
Advances in Applied Statistical Mechanics
Collection Editor: Antonio M. Scarfone
Topical Collection in
Entropy
Entropy-Based Applied Cryptography and Enhanced Security for Future IT Environments
Collection Editor: James ParkJobs in Research
Posted: 25 Sep 2018
Postdoc Position in Stochastic Thermodynamics, University of Houston, Department of Physics, Houston
Categorized in
Entropy
Posted: 11 Oct 2018
Categorized in
Entropy