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Entropy, Volume 18, Issue 1 (January 2016)

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Open AccessEditorial Acknowledgement to Reviewers of Entropy in 2015
Entropy 2016, 18(1), 37; https://doi.org/10.3390/e18010037
Received: 21 January 2016 / Accepted: 21 January 2016 / Published: 21 January 2016
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Abstract
The editors of Entropy would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...] Full article
Open AccessArticle The Entropy of Laughter: Discriminative Power of Laughter’s Entropy in the Diagnosis of Depression
Entropy 2016, 18(1), 36; https://doi.org/10.3390/e18010036
Received: 29 October 2015 / Revised: 22 December 2015 / Accepted: 18 January 2016 / Published: 21 January 2016
Cited by 1 | PDF Full-text (482 KB) | HTML Full-text | XML Full-text
Abstract
Laughter is increasingly present in biomedical literature, both in analytical neurological aspects and in applied therapeutic fields. The present paper, bridging between the analytical and the applied, explores the potential of a relevant variable of laughter’s acoustic signature—entropy—in the detection of a widespread
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Laughter is increasingly present in biomedical literature, both in analytical neurological aspects and in applied therapeutic fields. The present paper, bridging between the analytical and the applied, explores the potential of a relevant variable of laughter’s acoustic signature—entropy—in the detection of a widespread mental disorder, depression, as well as in gauging the severity of its diagnostic. In laughter, the Shannon–Wiener entropy of the distribution of sound frequencies, which is one of the key features distinguishing its acoustic signal from the utterances of spoken language, has not been a specific focus of research yet, although the studies of human language and of animal communication have pointed out that entropy is a very important factor regarding the vocal/acoustic expression of emotions. As the experimental survey of laughter in depression herein undertaken shows, it was possible to discriminate between patients and controls with an 82.1% accuracy just by using laughter’s entropy and by applying the decision tree procedure. These experimental results, discussed in the light of the current research on laughter, point to the relevance of entropy in the spontaneous bona fide extroversion of mental states toward other individuals, as the signal of laughter seems to imply. This is in line with recent theoretical approaches that rely on the optimization of a neuro-informational free energy (and associated entropy) as the main “stuff” of brain processing. Full article
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Open AccessArticle Average Contrastive Divergence for Training Restricted Boltzmann Machines
Entropy 2016, 18(1), 35; https://doi.org/10.3390/e18010035
Received: 22 September 2015 / Revised: 11 January 2016 / Accepted: 15 January 2016 / Published: 21 January 2016
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Abstract
This paper studies contrastive divergence (CD) learning algorithm and proposes a new algorithm for training restricted Boltzmann machines (RBMs). We derive that CD is a biased estimator of the log-likelihood gradient method and make an analysis of the bias. Meanwhile, we propose a
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This paper studies contrastive divergence (CD) learning algorithm and proposes a new algorithm for training restricted Boltzmann machines (RBMs). We derive that CD is a biased estimator of the log-likelihood gradient method and make an analysis of the bias. Meanwhile, we propose a new learning algorithm called average contrastive divergence (ACD) for training RBMs. It is an improved CD algorithm, and it is different from the traditional CD algorithm. Finally, we obtain some experimental results. The results show that the new algorithm is a better approximation of the log-likelihood gradient method and outperforms the traditional CD algorithm. Full article
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Open AccessArticle Schroedinger vs. Navier–Stokes
Entropy 2016, 18(1), 34; https://doi.org/10.3390/e18010034
Received: 17 November 2015 / Accepted: 13 January 2016 / Published: 19 January 2016
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Abstract
Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow.
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Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck’s constant, while the volume density of entropy is proportional to Boltzmann’s constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier–Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation). Full article
(This article belongs to the Special Issue Quantum Thermodynamics)
Open AccessArticle Measure of Uncertainty in Process Models Using Stochastic Petri Nets and Shannon Entropy
Entropy 2016, 18(1), 33; https://doi.org/10.3390/e18010033
Received: 4 May 2015 / Revised: 6 January 2016 / Accepted: 10 January 2016 / Published: 19 January 2016
Cited by 7 | PDF Full-text (2857 KB) | HTML Full-text | XML Full-text
Abstract
When modelling and analysing business processes, the main emphasis is usually put on model validity and accuracy, i.e., the model meets the formal specification and also models the relevant system. In recent years, a series of metrics has begun to develop, which
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When modelling and analysing business processes, the main emphasis is usually put on model validity and accuracy, i.e., the model meets the formal specification and also models the relevant system. In recent years, a series of metrics has begun to develop, which allows the quantification of the specific properties of process models. These characteristics are, for instance, complexity, comprehensibility, cohesion, and uncertainty. This work is focused on defining a method that allows us to measure the uncertainty of a process model, which was modelled by using stochastic Petri nets (SPN). The principle of this method consists of mapping of all reachable marking of SPN into the continuous-time Markov chain and then calculating its stationary probabilities. The uncertainty is then measured as the entropy of the Markov chain (it is possible to calculate the uncertainty of the specific subset of places as well as of whole net). Alternatively, the uncertainty index is quantified as a percentage of the calculated entropy against maximum entropy (the resulting value is normalized to the interval <0,1>). The calculated entropy can also be used as a measure of the model complexity. Full article
(This article belongs to the Section Information Theory)
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Open AccessArticle Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent
Entropy 2016, 18(1), 32; https://doi.org/10.3390/e18010032
Received: 2 November 2015 / Revised: 6 January 2016 / Accepted: 11 January 2016 / Published: 19 January 2016
Cited by 4 | PDF Full-text (1039 KB) | HTML Full-text | XML Full-text
Abstract
The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs), are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on
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The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs), are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase space, and a reduced dynamic system is obtained from the dynamic system viewpoint. Then, a numerical method for computing the largest Lyapunov exponent of the low-dimensional dynamic system is presented. Further, the longest predictable time, which is related to chaotic behaviors in the system, is studied using the largest Lyapunov exponent, and the Wolf method is used to predict the evolution of the traffic in a local area network by both Dot and Interval predictions, and a reliable result is obtained by the presented method. As the conclusion, the results show that the largest Lyapunov exponent can be used to describe the sensitivity of the trajectory in the reconstructed phase space to the initial values. Moreover, Dot Prediction can effectively predict the flow burst. The numerical simulation also shows that the presented method is feasible and efficient for predicting the complex dynamic behaviors in LAN traffic, especially for congestion and attack in networks, which are the main two complex phenomena behaving as chaos in networks. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics)
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Open AccessArticle Perturbation of Fractional Multi-Agent Systems in Cloud Entropy Computing
Entropy 2016, 18(1), 31; https://doi.org/10.3390/e18010031
Received: 2 December 2015 / Revised: 30 December 2015 / Accepted: 6 January 2016 / Published: 19 January 2016
Cited by 3 | PDF Full-text (378 KB) | HTML Full-text | XML Full-text
Abstract
A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural
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A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural approaches, and algorithms. In this study, we introduce a new perturbed algorithm based on the fractional Poisson process. The discrete dynamics are suggested by using fractional entropy and fractional type Tsallis entropy. Moreover, we study the algorithm stability. Full article
(This article belongs to the Special Issue Computational Complexity)
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Open AccessArticle Distributed Consensus of Nonlinear Multi-Agent Systems on State-Controlled Switching Topologies
Entropy 2016, 18(1), 29; https://doi.org/10.3390/e18010029
Received: 6 November 2015 / Revised: 3 January 2016 / Accepted: 11 January 2016 / Published: 18 January 2016
Cited by 1 | PDF Full-text (426 KB) | HTML Full-text | XML Full-text
Abstract
This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching
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This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching law, we show that the multi-agent system with the neighbor-based protocol can achieve consensus if the switching topologies jointly contain a spanning tree. Moreover, an easily manageable algebraic criterion is deduced to unravel the underlying mechanisms in reaching consensus. Finally, a numerical example is exploited to illustrate the effectiveness of the developed theoretical results. Full article
(This article belongs to the Section Complexity)
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Open AccessArticle Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
Entropy 2016, 18(1), 19; https://doi.org/10.3390/e18010019
Received: 10 September 2015 / Revised: 27 November 2015 / Accepted: 25 December 2015 / Published: 18 January 2016
Cited by 10 | PDF Full-text (218 KB) | HTML Full-text | XML Full-text
Abstract
In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The
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In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems. Full article
(This article belongs to the Section Complexity)
Open AccessArticle Using Multidimensional ADTPE and SVM for Optical Modulation Real-Time Recognition
Entropy 2016, 18(1), 30; https://doi.org/10.3390/e18010030
Received: 26 November 2015 / Revised: 6 January 2016 / Accepted: 11 January 2016 / Published: 16 January 2016
Cited by 1 | PDF Full-text (2211 KB) | HTML Full-text | XML Full-text
Abstract
Based on the feature extraction of multidimensional asynchronous delay-tap plot entropy (ADTPE) and multiclass classification of support vector machine (SVM), we propose a method for recognition of multiple optical modulation formats and various data rates. We firstly present the algorithm of multidimensional ADTPE,
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Based on the feature extraction of multidimensional asynchronous delay-tap plot entropy (ADTPE) and multiclass classification of support vector machine (SVM), we propose a method for recognition of multiple optical modulation formats and various data rates. We firstly present the algorithm of multidimensional ADTPE, which is extracted from asynchronous delay sampling pairs of modulated optical signal. Then, a multiclass SVM is utilized for fast and accurate classification of several widely-used optical modulation formats. In addition, a simple real-time recognition scheme is designed to reduce the computation time. Compared to the existing method based on asynchronous delay-tap plot (ADTP), the theoretical analysis and simulation results show that our recognition method can effectively enhance the tolerance of transmission impairments, obtaining relatively high accuracy. Finally, it is further demonstrated that the proposed method can be integrated in an optical transport network (OTN) with flexible expansion. Through simply adding the corresponding sub-SVM module in the digital signal processer (DSP), arbitrary new modulation formats can be recognized with high recognition accuracy in a short response time. Full article
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Open AccessEditorial Entropy Generation Results of Convenience But without Purposeful Analysis and Due Comprehension—Guidelines for Authors
Entropy 2016, 18(1), 28; https://doi.org/10.3390/e18010028
Received: 11 January 2016 / Accepted: 12 January 2016 / Published: 15 January 2016
Cited by 1 | PDF Full-text (135 KB) | HTML Full-text | XML Full-text
Abstract
There is a growing trend in recently-submitted manuscripts and publications to present calculated results of entropy generation, also known as entropy production, as field quantities in a system or device control volume, based on prior calculation of velocity and temperature fields, frequently using
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There is a growing trend in recently-submitted manuscripts and publications to present calculated results of entropy generation, also known as entropy production, as field quantities in a system or device control volume, based on prior calculation of velocity and temperature fields, frequently using CFD numerical methods. [...] Full article
(This article belongs to the Special Issue Exploring the Second Law of Thermodynamics)
Open AccessArticle Interacting Brownian Swarms: Some Analytical Results
Entropy 2016, 18(1), 27; https://doi.org/10.3390/e18010027
Received: 18 November 2015 / Revised: 7 January 2016 / Accepted: 11 January 2016 / Published: 14 January 2016
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Abstract
We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables.
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We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact). Depending on the values of the control parameters, one of the following patterns emerges after collision: (i) Both swarms remain essentially flocked, or (ii) the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings. Full article
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Open AccessArticle Information and the Quantum World
Entropy 2016, 18(1), 26; https://doi.org/10.3390/e18010026
Received: 24 October 2015 / Revised: 14 December 2015 / Accepted: 8 January 2016 / Published: 13 January 2016
Cited by 1 | PDF Full-text (207 KB) | HTML Full-text | XML Full-text
Abstract
The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material
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The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics. Full article
(This article belongs to the Special Issue Information: Meanings and Interpretations)
Open AccessArticle Hot Spots and Persistence of Nitrate in Aquifers Across Scales
Entropy 2016, 18(1), 25; https://doi.org/10.3390/e18010025
Received: 29 May 2015 / Revised: 3 December 2015 / Accepted: 5 January 2016 / Published: 13 January 2016
Cited by 7 | PDF Full-text (1608 KB) | HTML Full-text | XML Full-text
Abstract
Nitrate-N (NO3 -- N) is one of the most pervasive contaminants in groundwater. Nitrate in groundwater exhibits long-term behavior due to complex interactions at multiple scales among various geophysical factors, such as sources of nitrate-N, characteristics of the vadose zone and
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Nitrate-N (NO3 -- N) is one of the most pervasive contaminants in groundwater. Nitrate in groundwater exhibits long-term behavior due to complex interactions at multiple scales among various geophysical factors, such as sources of nitrate-N, characteristics of the vadose zone and aquifer attributes. To minimize contamination of nitrate-N in groundwater, it is important to estimate hot spots (>10 mg/L of NO3 -- N), trends and persistence of nitrate-N in groundwater. To analyze the trends and persistence of nitrate-N in groundwater at multiple spatio-temporal scales, we developed and used an entropy-based method along with the Hurst exponent in two different hydrogeologic settings: the Trinity and Ogallala Aquifers in Texas at fine (2 km × 2 km), intermediate (10 km × 10 km) and coarse (100 km × 100 km) scales. Results show that nitrate-N exhibits long-term persistence at the intermediate and coarse scales. In the Trinity Aquifer, overall mean nitrate-N has declined with a slight increase in normalized marginal entropy (NME) over each decade from 1940 to 2008; however, the number of hot spots has increased over time. In the Ogallala Aquifer, overall mean nitrate-N has increased with slight moderation in NME since 1940; however, the number of hot spots has significantly decreased for the same period at all scales. Full article
(This article belongs to the Special Issue Applications of Information Theory in the Geosciences)
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Open AccessTechnical Note Entropy Analysis of Solar Two-Step Thermochemical Cycles for Water and Carbon Dioxide Splitting
Entropy 2016, 18(1), 24; https://doi.org/10.3390/e18010024
Received: 3 November 2015 / Revised: 16 December 2015 / Accepted: 7 January 2016 / Published: 11 January 2016
Cited by 5 | PDF Full-text (3383 KB) | HTML Full-text | XML Full-text
Abstract
The present study provides a thermodynamic analysis of solar thermochemical cycles for splitting of H2O or CO2. Such cycles, powered by concentrated solar energy, have the potential to produce fuels in a sustainable way. We extend a previous study
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The present study provides a thermodynamic analysis of solar thermochemical cycles for splitting of H2O or CO2. Such cycles, powered by concentrated solar energy, have the potential to produce fuels in a sustainable way. We extend a previous study on the thermodynamics of water splitting by also taking into account CO2 splitting and the influence of the solar absorption efficiency. Based on this purely thermodynamic approach, efficiency trends are discussed. The comprehensive and vivid representation in T-S diagrams provides researchers in this field with the required theoretical background to improve process development. Furthermore, results about the required entropy change in the used redox materials can be used as a guideline for material developers. The results show that CO2 splitting is advantageous at higher temperature levels, while water splitting is more feasible at lower temperature levels, as it benefits from a great entropy change during the splitting step. Full article
(This article belongs to the Special Issue Selected Papers from 13th Joint European Thermodynamics Conference)
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