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Entropy, Volume 20, Issue 6 (June 2018)

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Cover Story (view full-size image) As far back as 1957, Andrew M. Gleason suggested that, in perfect measurements, quantum [...] Read more.
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Open AccessArticle Inferring the Population Mean with Second-Order Information in Online Social Networks
Entropy 2018, 20(6), 480; https://doi.org/10.3390/e20060480
Received: 12 May 2018 / Revised: 16 June 2018 / Accepted: 17 June 2018 / Published: 20 June 2018
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Abstract
With the increasing use of online social networking platforms, online surveys are widely used in many fields, e.g., public health, business and sociology, to collect samples and to infer the population characteristics through self-reported data of respondents. Although the online surveys can protect
[...] Read more.
With the increasing use of online social networking platforms, online surveys are widely used in many fields, e.g., public health, business and sociology, to collect samples and to infer the population characteristics through self-reported data of respondents. Although the online surveys can protect the privacy of respondents, self-reporting is challenged by a low response rate and unreliable answers when the survey contains sensitive questions, such as drug use, sexual behaviors, abortion or criminal activity. To overcome this limitation, this paper develops an approach that collects the second-order information of the respondents, i.e., asking them about the characteristics of their friends, instead of asking the respondents’ own characteristics directly. Then, we generate the inference about the population variable with the Hansen-Hurwitz estimator for the two classic sampling strategies (simple random sampling or random walk-based sampling). The method is evaluated by simulations on both artificial and real-world networks. Results show that the method is able to generate population estimates with high accuracy without knowing the respondents’ own characteristics, and the biases of estimates under various settings are relatively small and are within acceptable limits. The new method offers an alternative way for implementing surveys online and is expected to be able to collect more reliable data with improved population inference on sensitive variables. Full article
(This article belongs to the Special Issue Research Frontier in Chaos Theory and Complex Networks)
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Open AccessEditorial Phenomenological Thermodynamics of Irreversible Processes
Entropy 2018, 20(6), 479; https://doi.org/10.3390/e20060479
Received: 14 June 2018 / Accepted: 14 June 2018 / Published: 20 June 2018
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(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)
Open AccessArticle GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality
Entropy 2018, 20(6), 478; https://doi.org/10.3390/e20060478
Received: 21 March 2018 / Revised: 6 June 2018 / Accepted: 6 June 2018 / Published: 20 June 2018
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Abstract
We review an argument that bipartite “PR-box” correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger–Horne–Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask
[...] Read more.
We review an argument that bipartite “PR-box” correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger–Horne–Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask whether the argument extends to GHZ correlations. If it does—i.e., if it shows that GHZ correlations violate relativistic causality in the classical limit—then the argument must be incorrect (since GHZ correlations do respect relativistic causality in the classical limit.) However, we find that the argument does not extend to GHZ correlations. We also show that both PR-box correlations and GHZ correlations can be retrocausal, but the retrocausality of PR-box correlations leads to self-contradictory causal loops, while the retrocausality of GHZ correlations does not. Full article
(This article belongs to the Special Issue Quantum Nonlocality)
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Open AccessArticle The Complexity Measures Associated with the Fluctuations of the Entropy in Natural Time before the Deadly México M8.2 Earthquake on 7 September 2017
Entropy 2018, 20(6), 477; https://doi.org/10.3390/e20060477
Received: 22 May 2018 / Revised: 12 June 2018 / Accepted: 16 June 2018 / Published: 20 June 2018
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Abstract
We analyse seismicity during the 6-year period 2012–2017 in the new time domain termed natural time in the Chiapas region where the M8.2 earthquake occurred, Mexico’s largest earthquake in more than a century, in order to study the complexity measures associated with fluctuations
[...] Read more.
We analyse seismicity during the 6-year period 2012–2017 in the new time domain termed natural time in the Chiapas region where the M8.2 earthquake occurred, Mexico’s largest earthquake in more than a century, in order to study the complexity measures associated with fluctuations of entropy as well as with entropy change under time reversal. We find that almost three months before the M8.2 earthquake, i.e., on 14 June 2017, the complexity measure associated with the fluctuations of entropy change under time reversal shows an abrupt increase, which, however, does not hold for the complexity measure associated with the fluctuations of entropy in forward time. On the same date, the entropy change under time reversal has been previously found to exhibit a minimum [Physica A 506, 625–634 (2018)]; we thus find here that this minimum is also accompanied by increased fluctuations of the entropy change under time reversal. In addition, we find a simultaneous increase of the Tsallis entropic index q. Full article
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Open AccessArticle Approach to Evaluating Accounting Informatization Based on Entropy in Intuitionistic Fuzzy Environment
Entropy 2018, 20(6), 476; https://doi.org/10.3390/e20060476
Received: 14 May 2018 / Revised: 4 June 2018 / Accepted: 12 June 2018 / Published: 20 June 2018
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Abstract
Accounting informatization is an important part of enterprise informatization. It affects the accounting and finance operational efficiency. With the comprehensive evaluation of accounting informatization from multiple aspects, we can find the strengths and weaknesses of corporate accounting informatization, which then can be improved
[...] Read more.
Accounting informatization is an important part of enterprise informatization. It affects the accounting and finance operational efficiency. With the comprehensive evaluation of accounting informatization from multiple aspects, we can find the strengths and weaknesses of corporate accounting informatization, which then can be improved precisely. In this paper, an evaluation approach of accounting informatization is proposed. Firstly, the evaluation index system is constructed from the aspects of strategic position, infrastructure construction, implementation of accounting informatization, informatization guarantee, and application efficiency. Considering the complexity and ambiguity of the index, experts are required to give linguistic ratings which are then converted into intuitionistic fuzzy number. Then, an entropy and cross entropy method based on intuitionistic fuzzy sets is proposed to derive the weights of experts so as to reduce the error caused by personal bias. By combining the weights of the index and weighted ratings, the evaluation results are obtained. Finally, a case of accounting information evaluation is given to illustrate the feasibility of the proposed approach. Full article
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Open AccessArticle Approaching Retinal Ganglion Cell Modeling and FPGA Implementation for Robotics
Entropy 2018, 20(6), 475; https://doi.org/10.3390/e20060475
Received: 21 March 2018 / Revised: 1 June 2018 / Accepted: 15 June 2018 / Published: 19 June 2018
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Abstract
Taking inspiration from biology to solve engineering problems using the organizing principles of biological neural computation is the aim of the field of neuromorphic engineering. This field has demonstrated success in sensor based applications (vision and audition) as well as in cognition and
[...] Read more.
Taking inspiration from biology to solve engineering problems using the organizing principles of biological neural computation is the aim of the field of neuromorphic engineering. This field has demonstrated success in sensor based applications (vision and audition) as well as in cognition and actuators. This paper is focused on mimicking the approaching detection functionality of the retina that is computed by one type of Retinal Ganglion Cell (RGC) and its application to robotics. These RGCs transmit action potentials when an expanding object is detected. In this work we compare the software and hardware logic FPGA implementations of this approaching function and the hardware latency when applied to robots, as an attention/reaction mechanism. The visual input for these cells comes from an asynchronous event-driven Dynamic Vision Sensor, which leads to an end-to-end event based processing system. The software model has been developed in Java, and computed with an average processing time per event of 370 ns on a NUC embedded computer. The output firing rate for an approaching object depends on the cell parameters that represent the needed number of input events to reach the firing threshold. For the hardware implementation, on a Spartan 6 FPGA, the processing time is reduced to 160 ns/event with the clock running at 50 MHz. The entropy has been calculated to demonstrate that the system is not totally deterministic in response to approaching objects because of several bioinspired characteristics. It has been measured that a Summit XL mobile robot can react to an approaching object in 90 ms, which can be used as an attentional mechanism. This is faster than similar event-based approaches in robotics and equivalent to human reaction latencies to visual stimulus. Full article
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Open AccessArticle On Ontological Alternatives to Bohmian Mechanics
Entropy 2018, 20(6), 474; https://doi.org/10.3390/e20060474
Received: 20 April 2018 / Revised: 6 June 2018 / Accepted: 13 June 2018 / Published: 19 June 2018
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Abstract
The article describes an interpretation of the mathematical formalism of standard quantum mechanics in terms of relations. In particular, the wave function ψ(x) is interpreted as a complex-valued relation between an entity (often called “particle”) and a second entity x
[...] Read more.
The article describes an interpretation of the mathematical formalism of standard quantum mechanics in terms of relations. In particular, the wave function ψ(x) is interpreted as a complex-valued relation between an entity (often called “particle”) and a second entity x (often called “spatial point”). Such complex-valued relations can also be formulated for classical physical systems. Entanglement is interpreted as a relation between two entities (particles or properties of particles). Such relations define the concept of “being next to each other”, which implies that entangled entities are close to each other, even though they might appear to be far away with respect to a classical background space. However, when space is also considered to be a network of relations (of which the classical background space is a large-scale continuum limit), such nearest neighbor configurations are possible. The measurement problem is discussed from the perspective of this interpretation. It should be emphasized that this interpretation is not meant to be a serious attempt to describe the ontology of our world, but its purpose is to make it obvious that, besides Bohmian mechanics, presumably many other ontological interpretations of quantum theory exist. Full article
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)
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Open AccessArticle Revisiting Entanglement within the Bohmian Approach to Quantum Mechanics
Entropy 2018, 20(6), 473; https://doi.org/10.3390/e20060473
Received: 24 April 2018 / Revised: 2 June 2018 / Accepted: 12 June 2018 / Published: 18 June 2018
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Abstract
We revisit the concept of entanglement within the Bohmian approach to quantum mechanics. Inspired by Bohmian dynamics, we introduce two partial measures for the amount of entanglement corresponding to a pure state of a pair of quantum particles. One of these measures is
[...] Read more.
We revisit the concept of entanglement within the Bohmian approach to quantum mechanics. Inspired by Bohmian dynamics, we introduce two partial measures for the amount of entanglement corresponding to a pure state of a pair of quantum particles. One of these measures is associated with the statistical correlations exhibited by the joint probability density of the two Bohmian particles in configuration space. The other partial measure corresponds to the correlations associated with the phase of the joint wave function, and describes the non-separability of the Bohmian velocity field. The sum of these two components is equal to the total entanglement of the joint quantum state, as measured by the linear entropy of the single-particle reduced density matrix. Full article
(This article belongs to the Special Issue Quantum Foundations: 90 Years of Uncertainty)
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Open AccessArticle Quantum Statistical Manifolds
Entropy 2018, 20(6), 472; https://doi.org/10.3390/e20060472
Received: 26 May 2018 / Revised: 15 June 2018 / Accepted: 15 June 2018 / Published: 17 June 2018
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Abstract
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose, the emphasis is shifted from a manifold
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Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose, the emphasis is shifted from a manifold of strictly positive density matrices to a manifold of faithful quantum states on the C*-algebra of bounded linear operators. In addition, ideas from the parameter-free approach to information geometry are adopted. The underlying Hilbert space is assumed to be finite-dimensional. In this way, technicalities are avoided so that strong results are obtained, which one can hope to prove later on in a more general context. Two different atlases are introduced, one in which it is straightforward to show that the quantum states form a Banach manifold, the other which is compatible with the inner product of Bogoliubov and which yields affine coordinates for the exponential connection. Full article
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
Open AccessArticle Coupled Node Similarity Learning for Community Detection in Attributed Networks
Entropy 2018, 20(6), 471; https://doi.org/10.3390/e20060471
Received: 22 May 2018 / Revised: 12 June 2018 / Accepted: 14 June 2018 / Published: 17 June 2018
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Abstract
Attributed networks consist of not only a network structure but also node attributes. Most existing community detection algorithms only focus on network structures and ignore node attributes, which are also important. Although some algorithms using both node attributes and network structure information have
[...] Read more.
Attributed networks consist of not only a network structure but also node attributes. Most existing community detection algorithms only focus on network structures and ignore node attributes, which are also important. Although some algorithms using both node attributes and network structure information have been proposed in recent years, the complex hierarchical coupling relationships within and between attributes, nodes and network structure have not been considered. Such hierarchical couplings are driving factors in community formation. This paper introduces a novel coupled node similarity (CNS) to involve and learn attribute and structure couplings and compute the similarity within and between nodes with categorical attributes in a network. CNS learns and integrates the frequency-based intra-attribute coupled similarity within an attribute, the co-occurrence-based inter-attribute coupled similarity between attributes, and coupled attribute-to-structure similarity based on the homophily property. CNS is then used to generate the weights of edges and transfer a plain graph to a weighted graph. Clustering algorithms detect community structures that are topologically well-connected and semantically coherent on the weighted graphs. Extensive experiments verify the effectiveness of CNS-based community detection algorithms on several data sets by comparing with the state-of-the-art node similarity measures, whether they involve node attribute information and hierarchical interactions, and on various levels of network structure complexity. Full article
(This article belongs to the Special Issue Research Frontier in Chaos Theory and Complex Networks)
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Open AccessArticle Noise Enhanced Signal Detection of Variable Detectors under Certain Constraints
Entropy 2018, 20(6), 470; https://doi.org/10.3390/e20060470
Received: 17 April 2018 / Revised: 4 June 2018 / Accepted: 12 June 2018 / Published: 17 June 2018
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Abstract
In this paper, a noise enhanced binary hypothesis-testing problem was studied for a variable detector under certain constraints in which the detection probability can be increased and the false-alarm probability can be decreased simultaneously. According to the constraints, three alternative cases are proposed,
[...] Read more.
In this paper, a noise enhanced binary hypothesis-testing problem was studied for a variable detector under certain constraints in which the detection probability can be increased and the false-alarm probability can be decreased simultaneously. According to the constraints, three alternative cases are proposed, the first two cases concerned minimization of the false-alarm probability and maximization of the detection probability without deterioration of one by the other, respectively, and the third case was achieved by a randomization of two optimal noise enhanced solutions obtained in the first two limit cases. Furthermore, the noise enhanced solutions that satisfy the three cases were determined whether randomization between different detectors was allowed or not. In addition, the practicality of the third case was proven from the perspective of Bayes risk. Finally, numerous examples and conclusions are presented. Full article
(This article belongs to the Special Issue Foundations of Statistics)
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Open AccessArticle Impact of Multi-Causal Transport Mechanisms in an Electrolyte Supported Planar SOFC with (ZrO2)x−1(Y2O3)x Electrolyte
Entropy 2018, 20(6), 469; https://doi.org/10.3390/e20060469
Received: 12 May 2018 / Revised: 7 June 2018 / Accepted: 14 June 2018 / Published: 16 June 2018
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Abstract
The calculation of the entropy production rate within an operational high temperature solid oxide fuel cell (SOFC) is necessary to design and improve heating and cooling strategies. However, due to a lack of information, most of the studies are limited to empirical relations,
[...] Read more.
The calculation of the entropy production rate within an operational high temperature solid oxide fuel cell (SOFC) is necessary to design and improve heating and cooling strategies. However, due to a lack of information, most of the studies are limited to empirical relations, which are not in line with the more general approach given by non-equilibrium thermodynamics (NET). The SOFC 1D-model presented in this study is based on non-equilibrium thermodynamics and we parameterize it with experimental data and data from molecular dynamics (MD). The validation of the model shows that it can effectively describe the behavior of a SOFC at 1300 K. Moreover, we show that the highest entropy production is present in the electrolyte and the catalyst layers, and that the Peltier heat transfer is considerable for the calculation of the heat flux in the electrolyte and cannot be neglected. To our knowledge, this is the first validated model of a SOFC based on non-equilibrium thermodynamics and this study can be extended to analyze SOFCs with other solid oxide electrolytes, with perovskites electrolytes or even other electrochemical systems like solid oxide electrolysis cells (SOECs). Full article
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Open AccessArticle Analytic Solution for a Complex Network of Chaotic Oscillators
Entropy 2018, 20(6), 468; https://doi.org/10.3390/e20060468
Received: 17 May 2018 / Revised: 12 June 2018 / Accepted: 14 June 2018 / Published: 16 June 2018
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Abstract
Chaotic evolution is generally too irregular to be captured in an analytic solution. Nonetheless, some dynamical systems do have such solutions enabling more rigorous analysis than can be achieved with numerical solutions. Here, we introduce a method of coupling solvable chaotic oscillators that
[...] Read more.
Chaotic evolution is generally too irregular to be captured in an analytic solution. Nonetheless, some dynamical systems do have such solutions enabling more rigorous analysis than can be achieved with numerical solutions. Here, we introduce a method of coupling solvable chaotic oscillators that maintains solvability. In fact, an analytic solution is given for an entire network of coupled oscillators. Importantly, a valid chaotic solution is shown even when the coupling topology is complex and the population of oscillators is heterogeneous. We provide a specific example of a solvable chaotic network with star topology and a hub that oscillates much faster than its leaves. We present analytic solutions as the coupling strength is varied showing states of varying degrees of global organization. The covariance of the network is derived explicity from the analytic solution characterizing the degree of synchronization across the network as the coupling strength varies. This example suggests that analytic solutions may constitute a new tool in the study of chaotic network dynamics generally. Full article
(This article belongs to the Special Issue Research Frontier in Chaos Theory and Complex Networks)
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Open AccessArticle Strong Secrecy on a Class of Degraded Broadcast Channels Using Polar Codes
Entropy 2018, 20(6), 467; https://doi.org/10.3390/e20060467
Received: 15 May 2018 / Revised: 8 June 2018 / Accepted: 12 June 2018 / Published: 15 June 2018
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Abstract
Asymptotic secrecy-capacity achieving polar coding schemes are proposed for the memoryless degraded broadcast channel under different reliability and secrecy requirements: layered decoding or layered secrecy. In these settings, the transmitter wishes to send multiple messages to a set of legitimate receivers keeping them
[...] Read more.
Asymptotic secrecy-capacity achieving polar coding schemes are proposed for the memoryless degraded broadcast channel under different reliability and secrecy requirements: layered decoding or layered secrecy. In these settings, the transmitter wishes to send multiple messages to a set of legitimate receivers keeping them masked from a set of eavesdroppers. The layered decoding structure requires receivers with better channel quality to reliably decode more messages, while the layered secrecy structure requires eavesdroppers with worse channel quality to be kept ignorant of more messages. Practical constructions for the proposed polar coding schemes are discussed and their performance evaluated by means of simulations. Full article
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Open AccessArticle The Gibbs Paradox and Particle Individuality
Entropy 2018, 20(6), 466; https://doi.org/10.3390/e20060466
Received: 3 April 2018 / Revised: 21 May 2018 / Accepted: 6 June 2018 / Published: 15 June 2018
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Abstract
A consensus seems to have developed that the Gibbs paradox in classical thermodynamics (the discontinuous drop in the entropy of mixing when the mixed gases become equal to each other) is unmysterious: in any actual situation, two gases can be separated or not,
[...] Read more.
A consensus seems to have developed that the Gibbs paradox in classical thermodynamics (the discontinuous drop in the entropy of mixing when the mixed gases become equal to each other) is unmysterious: in any actual situation, two gases can be separated or not, and the associated harmless discontinuity from “yes” to “no” is responsible for the discontinuity. By contrast, the Gibbs paradox in statistical physics continues to attract attention. Here, the problem is that standard calculations in statistical mechanics predict a non-vanishing value of the entropy of mixing even when two gases of the same kind are mixed, in conflict with thermodynamic predictions. This version of the Gibbs paradox is often seen as a sign that there is something fundamentally wrong with either the traditional expression S=klnW or with the way W is calculated. It is the aim of this article to review the situation from the orthodox (as opposed to information theoretic) standpoint. We demonstrate how the standard formalism is not only fully capable of dealing with the paradox, but also provides an intuitively clear picture of the relevant physical mechanisms. In particular, we pay attention to the explanatory relevance of the existence of particle trajectories in the classical context. We also discuss how the paradox survives the transition to quantum mechanics, in spite of the symmetrization postulates. Full article
(This article belongs to the Special Issue Gibbs Paradox 2018)
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