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Entropy, Volume 22, Issue 12 (December 2020) – 110 articles

Cover Story (view full-size image): Partial information decomposition (PID) and information deltas are two frameworks, each based in information theory, which seek to detect and characterize non-pairwise relationships between variables. This paper unites these frameworks, equating their key expressions. This allows for results in one framework to give insights toward open questions in the other. Furthermore, PID solutions can be mapped onto the space of Delta measures, with its well-characterized geometry. There is no universally accepted solution for PID computation, and this mapping distinguishes at a glance how putative solutions decompose information. We demonstrate this by computing and mapping the solutions of both Bertschinger et al. and Finn et al. for all three-variable, three-letter discrete functions. View this paper
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Article
Measuring the Coupling Direction between Neural Oscillations with Weighted Symbolic Transfer Entropy
Entropy 2020, 22(12), 1442; https://doi.org/10.3390/e22121442 - 21 Dec 2020
Cited by 1 | Viewed by 770
Abstract
Neural oscillations reflect rhythmic fluctuations in the synchronization of neuronal populations and play a significant role in neural processing. To further understand the dynamic interactions between different regions in the brain, it is necessary to estimate the coupling direction between neural oscillations. Here, [...] Read more.
Neural oscillations reflect rhythmic fluctuations in the synchronization of neuronal populations and play a significant role in neural processing. To further understand the dynamic interactions between different regions in the brain, it is necessary to estimate the coupling direction between neural oscillations. Here, we developed a novel method, termed weighted symbolic transfer entropy (WSTE), that combines symbolic transfer entropy (STE) and weighted probability distribution to measure the directionality between two neuronal populations. The traditional STE ignores the degree of difference between the amplitude values of a time series. In our proposed WSTE method, this information is picked up by utilizing a weighted probability distribution. The simulation analysis shows that the WSTE method can effectively estimate the coupling direction between two neural oscillations. In comparison with STE, the new method is more sensitive to the coupling strength and is more robust against noise. When applied to epileptic electrocorticography data, a significant coupling direction from the anterior nucleus of thalamus (ANT) to the seizure onset zone (SOZ) was detected during seizures. Considering the superiorities of the WSTE method, it is greatly advantageous to measure the coupling direction between neural oscillations and consequently characterize the information flow between different brain regions. Full article
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Article
Analysis on the Development of Digital Economy in Guangdong Province Based on Improved Entropy Method and Multivariate Statistical Analysis
Entropy 2020, 22(12), 1441; https://doi.org/10.3390/e22121441 - 20 Dec 2020
Cited by 1 | Viewed by 964
Abstract
The lack of adequate indicators in the research of digital economy may lead to the shortage of data support on decision making for governments. To solve this problem, first we establish a digital economy indicator evaluation system by dividing the digital economy into [...] Read more.
The lack of adequate indicators in the research of digital economy may lead to the shortage of data support on decision making for governments. To solve this problem, first we establish a digital economy indicator evaluation system by dividing the digital economy into four types: “basic type”, “technology type”, “integration type” and “service type” and select 5 indicators for each type. On this basis, the weight of each indicator is calculated to find the deficiencies in the development of some digital economic fields by the improved entropy method. By drawing on the empowerment idea of Analytic Hierarchy Process, the improved entropy method firstly compares the difference coefficient of indicators in pairs and maps the comparison results to the scales 1–9. Then, the judgment matrix is constructed based on the information entropy, which can solve as much as possible the problem that the difference among the weight of each indicator is too large in traditional entropy method. The results indicate that: the development of digital economy in Guangdong Province was relatively balanced from 2015 to 2018 and will be better in the future while the development of rural e-commerce in Guangdong Province is relatively backward, and there is an obvious digital gap between urban and rural areas. Next we extract two new variables respectively to replace the 20 indicators we select through principal component analysis and factor analysis methods in multivariate statistical analysis, which can retain the original information to the greatest extent and provide convenience for further research in the future. Finally, we and provide constructive comments of digital economy in Guangdong Province from 2015 to 2018. Full article
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Article
Technological Research of a Clean Energy Router Based on Advanced Adiabatic Compressed Air Energy Storage System
Entropy 2020, 22(12), 1440; https://doi.org/10.3390/e22121440 - 20 Dec 2020
Cited by 1 | Viewed by 862
Abstract
As a fundamental infrastructure of energy supply for future society, energy Internet (EI) can achieve clean energy generation, conversion, storage and consumption in a more economic and safer way. This paper demonstrates the technology principle of advanced adiabatic compressed air energy storage system [...] Read more.
As a fundamental infrastructure of energy supply for future society, energy Internet (EI) can achieve clean energy generation, conversion, storage and consumption in a more economic and safer way. This paper demonstrates the technology principle of advanced adiabatic compressed air energy storage system (AA-CAES), as well as analysis of the technical characteristics of AA-CAES. Furthermore, we propose an overall architectural scheme of a clean energy router (CER) based on AA-CAES. The storage and mutual conversion mechanism of wind and solar power, heating, and other clean energy were designed to provide a key technological solution for the coordination and comprehensive utilization of various clean energies for the EI. Therefore, the design of the CER scheme and its efficiency were analyzed based on a thermodynamic simulation model of AA-CAES. Meanwhile, we explored the energy conversion mechanism of the CER and improved its overall efficiency. The CER based on AA-CAES proposed in this paper can provide a reference for efficient comprehensive energy utilization (CEU) (93.6%) in regions with abundant wind and solar energy sources. Full article
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Article
Bivariate Entropy Analysis of Electrocardiographic RR–QT Time Series
Entropy 2020, 22(12), 1439; https://doi.org/10.3390/e22121439 - 20 Dec 2020
Cited by 1 | Viewed by 826
Abstract
QT interval variability (QTV) and heart rate variability (HRV) are both accepted biomarkers for cardiovascular events. QTV characterizes the variations in ventricular depolarization and repolarization. It is a predominant element of HRV. However, QTV is also believed to accept direct inputs from upstream [...] Read more.
QT interval variability (QTV) and heart rate variability (HRV) are both accepted biomarkers for cardiovascular events. QTV characterizes the variations in ventricular depolarization and repolarization. It is a predominant element of HRV. However, QTV is also believed to accept direct inputs from upstream control system. How QTV varies along with HRV is yet to be elucidated. We studied the dynamic relationship of QTV and HRV during different physiological conditions from resting, to cycling, and to recovering. We applied several entropy-based measures to examine their bivariate relationships, including cross sample entropy (XSampEn), cross fuzzy entropy (XFuzzyEn), cross conditional entropy (XCE), and joint distribution entropy (JDistEn). Results showed no statistically significant differences in XSampEn, XFuzzyEn, and XCE across different physiological states. Interestingly, JDistEn demonstrated significant decreases during cycling as compared with that during the resting state. Besides, JDistEn also showed a progressively recovering trend from cycling to the first 3 min during recovering, and further to the second 3 min during recovering. It appeared to be fully recovered to its level in the resting state during the second 3 min during the recovering phase. The results suggest that there is certain nonlinear temporal relationship between QTV and HRV, and that the JDistEn could help unravel this nuanced property. Full article
(This article belongs to the Special Issue Entropy in Data Analysis)
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Editorial
Data Science: Measuring Uncertainties
Entropy 2020, 22(12), 1438; https://doi.org/10.3390/e22121438 - 20 Dec 2020
Viewed by 678
Abstract
With the increase in data processing and storage capacity, a large amount of data is available [...] Full article
(This article belongs to the Special Issue Data Science: Measuring Uncertainties)
Article
Emerging Complexity in Distributed Intelligent Systems
Entropy 2020, 22(12), 1437; https://doi.org/10.3390/e22121437 - 19 Dec 2020
Cited by 1 | Viewed by 1065
Abstract
Distributed intelligent systems (DIS) appear where natural intelligence agents (humans) and artificial intelligence agents (algorithms) interact, exchanging data and decisions and learning how to evolve toward a better quality of solutions. The networked dynamics of distributed natural and artificial intelligence agents leads to [...] Read more.
Distributed intelligent systems (DIS) appear where natural intelligence agents (humans) and artificial intelligence agents (algorithms) interact, exchanging data and decisions and learning how to evolve toward a better quality of solutions. The networked dynamics of distributed natural and artificial intelligence agents leads to emerging complexity different from the ones observed before. In this study, we review and systematize different approaches in the distributed intelligence field, including the quantum domain. A definition and mathematical model of DIS (as a new class of systems) and its components, including a general model of DIS dynamics, are introduced. In particular, the suggested new model of DIS contains both natural (humans) and artificial (computer programs, chatbots, etc.) intelligence agents, which take into account their interactions and communications. We present the case study of domain-oriented DIS based on different agents’ classes and show that DIS dynamics shows complexity effects observed in other well-studied complex systems. We examine our model by means of the platform of personal self-adaptive educational assistants (avatars), especially designed in our University. Avatars interact with each other and with their owners. Our experiment allows finding an answer to the vital question: How quickly will DIS adapt to owners’ preferences so that they are satisfied? We introduce and examine in detail learning time as a function of network topology. We have shown that DIS has an intrinsic source of complexity that needs to be addressed while developing predictable and trustworthy systems of natural and artificial intelligence agents. Remarkably, our research and findings promoted the improvement of the educational process at our university in the presence of COVID-19 pandemic conditions. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness II)
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Article
Impact of Feature Choice on Machine Learning Classification of Fractional Anomalous Diffusion
Entropy 2020, 22(12), 1436; https://doi.org/10.3390/e22121436 - 19 Dec 2020
Cited by 5 | Viewed by 1164
Abstract
The growing interest in machine learning methods has raised the need for a careful study of their application to the experimental single-particle tracking data. In this paper, we present the differences in the classification of the fractional anomalous diffusion trajectories that arise from [...] Read more.
The growing interest in machine learning methods has raised the need for a careful study of their application to the experimental single-particle tracking data. In this paper, we present the differences in the classification of the fractional anomalous diffusion trajectories that arise from the selection of the features used in random forest and gradient boosting algorithms. Comparing two recently used sets of human-engineered attributes with a new one, which was tailor-made for the problem, we show the importance of a thoughtful choice of the features and parameters. We also analyse the influence of alterations of synthetic training data set on the classification results. The trained classifiers are tested on real trajectories of G proteins and their receptors on a plasma membrane. Full article
(This article belongs to the Special Issue Recent Advances in Single-Particle Tracking: Experiment and Analysis)
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Article
A Comprehensive Framework for Uncovering Non-Linearity and Chaos in Financial Markets: Empirical Evidence for Four Major Stock Market Indices
Entropy 2020, 22(12), 1435; https://doi.org/10.3390/e22121435 - 18 Dec 2020
Cited by 3 | Viewed by 898
Abstract
The presence of chaos in the financial markets has been the subject of a great number of studies, but the results have been contradictory and inconclusive. This research tests for the existence of nonlinear patterns and chaotic nature in four major stock market [...] Read more.
The presence of chaos in the financial markets has been the subject of a great number of studies, but the results have been contradictory and inconclusive. This research tests for the existence of nonlinear patterns and chaotic nature in four major stock market indices: namely Dow Jones Industrial Average, Ibex 35, Nasdaq-100 and Nikkei 225. To this end, a comprehensive framework has been adopted encompassing a wide range of techniques and the most suitable methods for the analysis of noisy time series. By using daily closing values from January 1992 to July 2013, this study employs twelve techniques and tools of which five are specific to detecting chaos. The findings show no clear evidence of chaos, suggesting that the behavior of financial markets is nonlinear and stochastic. Full article
(This article belongs to the Special Issue Complexity in Economic and Social Systems)
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Article
Set-Wise Differential Interaction between Copy Number Alterations and Gene Expressions of Lower-Grade Glioma Reveals Prognosis-Associated Pathways
Entropy 2020, 22(12), 1434; https://doi.org/10.3390/e22121434 - 18 Dec 2020
Viewed by 664
Abstract
The integrative analysis of copy number alteration (CNA) and gene expression (GE) is an essential part of cancer research considering the impact of CNAs on cancer progression and prognosis. In this research, an integrative analysis was performed with generalized differentially coexpressed gene sets [...] Read more.
The integrative analysis of copy number alteration (CNA) and gene expression (GE) is an essential part of cancer research considering the impact of CNAs on cancer progression and prognosis. In this research, an integrative analysis was performed with generalized differentially coexpressed gene sets (gdCoxS), which is a modification of dCoxS. In gdCoxS, set-wise interaction is measured using the correlation of sample-wise distances with Renyi’s relative entropy, which requires an estimation of sample density based on omics profiles. To capture correlations between the variables, multivariate density estimation with covariance was applied. In the simulation study, the power of gdCoxS outperformed dCoxS that did not use the correlations in the density estimation explicitly. In the analysis of the lower-grade glioma of the cancer genome atlas program (TCGA-LGG) data, the gdCoxS identified 577 pathway CNAs and GEs pairs that showed significant changes of interaction between the survival and non-survival group, while other benchmark methods detected lower numbers of such pathways. The biological implications of the significant pathways were well consistent with previous reports of the TCGA-LGG. Taken together, the gdCoxS is a useful method for an integrative analysis of CNAs and GEs. Full article
(This article belongs to the Special Issue Statistical Inference from High Dimensional Data)
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Article
The Meta-Dynamic Nature of Consciousness
Entropy 2020, 22(12), 1433; https://doi.org/10.3390/e22121433 - 18 Dec 2020
Cited by 1 | Viewed by 821
Abstract
How, if at all, consciousness can be part of the physical universe remains a baffling problem. This article outlines a new, developing philosophical theory of how it could do so, and offers a preliminary mathematical formulation of a physical grounding for key aspects [...] Read more.
How, if at all, consciousness can be part of the physical universe remains a baffling problem. This article outlines a new, developing philosophical theory of how it could do so, and offers a preliminary mathematical formulation of a physical grounding for key aspects of the theory. Because the philosophical side has radical elements, so does the physical-theory side. The philosophical side is radical, first, in proposing that the productivity or dynamism in the universe that many believe to be responsible for its systematic regularities is actually itself a physical constituent of the universe, along with more familiar entities. Indeed, it proposes that instances of dynamism can themselves take part in physical interactions with other entities, this interaction then being “meta-dynamism” (a type of meta-causation). Secondly, the theory is radical, and unique, in arguing that consciousness is necessarily partly constituted of meta-dynamic auto-sensitivity, in other words it must react via meta-dynamism to its own dynamism, and also in conjecturing that some specific form of this sensitivity is sufficient for and indeed constitutive of consciousness. The article proposes a way for physical laws to be modified to accommodate meta-dynamism, via the radical step of including elements that explicitly refer to dynamism itself. Additionally, laws become, explicitly, temporally non-local in referring directly to quantity values holding at times prior to a given instant of application of the law. The approach therefore implicitly brings in considerations about what information determines states. Because of the temporal non-locality, and also because of the deep connections between dynamism and time-flow, the approach also implicitly connects to the topic of entropy insofar as this is related to time. Full article
(This article belongs to the Special Issue Models of Consciousness)
Article
Generalised Geometric Brownian Motion: Theory and Applications to Option Pricing
Entropy 2020, 22(12), 1432; https://doi.org/10.3390/e22121432 - 18 Dec 2020
Cited by 5 | Viewed by 1522
Abstract
Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics, due to irregularities found when [...] Read more.
Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics, due to irregularities found when comparing its properties with empirical distributions. As a solution, we investigate a generalisation of GBM where the introduction of a memory kernel critically determines the behaviour of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and then obtain the corresponding probability density functions using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) in order to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness. Full article
(This article belongs to the Special Issue New Trends in Random Walks)
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Article
A Continuous-Time Random Walk Extension of the Gillis Model
Entropy 2020, 22(12), 1431; https://doi.org/10.3390/e22121431 - 18 Dec 2020
Viewed by 859
Abstract
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional non-homogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic [...] Read more.
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional non-homogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-local and transport properties in the presence of heavy-tailed waiting-time distributions lacking the first moment: we provide here exact results concerning hitting times, first-time events, survival probabilities, occupation times, the moments spectrum and the statistics of records. Specifically, normal diffusion gives way to subdiffusion and we are witnessing the breaking of ergodicity. Furthermore we also test our theoretical predictions with numerical simulations. Full article
(This article belongs to the Special Issue New Trends in Random Walks)
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Perspective
Prospects of Observing Ionic Coulomb Blockade in Artificial Ion Confinements
Entropy 2020, 22(12), 1430; https://doi.org/10.3390/e22121430 - 18 Dec 2020
Cited by 2 | Viewed by 1069
Abstract
Nanofluidics encompasses a wide range of advanced approaches to study charge and mass transport at the nanoscale. Modern technologies allow us to develop and improve artificial nanofluidic platforms that confine ions in a way similar to single-ion channels in living cells. Therefore, nanofluidic [...] Read more.
Nanofluidics encompasses a wide range of advanced approaches to study charge and mass transport at the nanoscale. Modern technologies allow us to develop and improve artificial nanofluidic platforms that confine ions in a way similar to single-ion channels in living cells. Therefore, nanofluidic platforms show great potential to act as a test field for theoretical models. This review aims to highlight ionic Coulomb blockade (ICB)—an effect that is proposed to be the key player of ion channel selectivity, which is based upon electrostatic exclusion limiting ion transport. Thus, in this perspective, we focus on the most promising approaches that have been reported on the subject. We consider ion confinements of various dimensionalities and highlight the most recent advancements in the field. Furthermore, we concentrate on the most critical obstacles associated with these studies and suggest possible solutions to advance the field further. Full article
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Article
Examining the Causal Structures of Deep Neural Networks Using Information Theory
Entropy 2020, 22(12), 1429; https://doi.org/10.3390/e22121429 - 18 Dec 2020
Cited by 1 | Viewed by 1634
Abstract
Deep Neural Networks (DNNs) are often examined at the level of their response to input, such as analyzing the mutual information between nodes and data sets. Yet DNNs can also be examined at the level of causation, exploring “what does what” within the [...] Read more.
Deep Neural Networks (DNNs) are often examined at the level of their response to input, such as analyzing the mutual information between nodes and data sets. Yet DNNs can also be examined at the level of causation, exploring “what does what” within the layers of the network itself. Historically, analyzing the causal structure of DNNs has received less attention than understanding their responses to input. Yet definitionally, generalizability must be a function of a DNN’s causal structure as it reflects how the DNN responds to unseen or even not-yet-defined future inputs. Here, we introduce a suite of metrics based on information theory to quantify and track changes in the causal structure of DNNs during training. Specifically, we introduce the effective information (EI) of a feedforward DNN, which is the mutual information between layer input and output following a maximum-entropy perturbation. The EI can be used to assess the degree of causal influence nodes and edges have over their downstream targets in each layer. We show that the EI can be further decomposed in order to examine the sensitivity of a layer (measured by how well edges transmit perturbations) and the degeneracy of a layer (measured by how edge overlap interferes with transmission), along with estimates of the amount of integrated information of a layer. Together, these properties define where each layer lies in the “causal plane”, which can be used to visualize how layer connectivity becomes more sensitive or degenerate over time, and how integration changes during training, revealing how the layer-by-layer causal structure differentiates. These results may help in understanding the generalization capabilities of DNNs and provide foundational tools for making DNNs both more generalizable and more explainable. Full article
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Editorial
Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors II
Entropy 2020, 22(12), 1428; https://doi.org/10.3390/e22121428 - 18 Dec 2020
Viewed by 631
Abstract
According to the pioneering work of Leonov and Kuznetsov [...] Full article
Article
Side Information Generation Scheme Based on Coefficient Matrix Improvement Model in Transform Domain Distributed Video Coding
Entropy 2020, 22(12), 1427; https://doi.org/10.3390/e22121427 - 17 Dec 2020
Cited by 2 | Viewed by 767
Abstract
In order to effectively improve the quality of side information in distributed video coding, we propose a side information generation scheme based on a coefficient matrix improvement model. The discrete cosine transform coefficient bands of the Wyner–Ziv frame at the encoder side are [...] Read more.
In order to effectively improve the quality of side information in distributed video coding, we propose a side information generation scheme based on a coefficient matrix improvement model. The discrete cosine transform coefficient bands of the Wyner–Ziv frame at the encoder side are divided into entropy coding coefficient bands and distributed video coding coefficient bands, and then the coefficients of entropy coding coefficient bands are sampled, which are divided into sampled coefficients and unsampled coefficients. For sampled coefficients, an adaptive arithmetic encoder is used for lossless compression. For unsampled coefficients and the coefficients of distributed video coding coefficient bands, the low density parity check accumulate encoder is used to calculate the parity bits, which are stored in the buffer and transmitted in small amount upon decoder request. At the decoder side, the optical flow method is used to generate the initial side information, and the initial side information is improved according to the sampled coefficients by using the coefficient matrix improvement model. The experimental results demonstrate that the proposed side information generation scheme based on the coefficient matrix improvement model can effectively improve the quality of side information, and the quality of the generated side information is improved by about 0.2–0.4 dB, thereby improving the overall performance of the distributed video coding system. Full article
(This article belongs to the Special Issue Distributed Signal Processing for Coding and Information Theory)
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Article
Novel Multi-AP Coordinated Transmission Scheme for 7th Generation WLAN 802.11be
Entropy 2020, 22(12), 1426; https://doi.org/10.3390/e22121426 - 17 Dec 2020
Cited by 1 | Viewed by 881
Abstract
The demand for high-data-rate and time-sensitive applications, such as 4k/8k video streaming and real-time augmented reality (AR), virtual reality (VR), and gaming, has increased significantly. Addressing the inefficiency of distributed channel access and the fairness problem between uplink and downlink flows is crucial [...] Read more.
The demand for high-data-rate and time-sensitive applications, such as 4k/8k video streaming and real-time augmented reality (AR), virtual reality (VR), and gaming, has increased significantly. Addressing the inefficiency of distributed channel access and the fairness problem between uplink and downlink flows is crucial for the development of wireless local area network (WLAN) technologies. In this study, we propose a novel transmission scheme for IEEE 802.11be networks that addresses the fairness problem and improves the system throughput. Utilizing the concept of multi-AP coordinated OFDMA introduced in the 7th-generation WLAN IEEE 802.11be, the proposed transmission scheme allows an AP to share a granted transmission opportunity (TXOP) with nearby APs. A mathematically analysis of the throughput performance of the proposed schemes was performed using a Markov chain model. The simulation results verify that the scheme effectively improves the downlink fairness and the system throughput. Combined with the advanced multiuser (MU) features of IEEE 802.11ax, such as TUA, MU cascading sequence, and MU EDCA, the proposed scheme not only enhances downlink AP transmission, but also guarantees improved control over the medium. The scheme is carefully designed to be fully compatible with conventional IEEE 802.11 protocols, and is thus potentially universal. Full article
(This article belongs to the Special Issue Information Theory and 5G/6G Mobile Communications)
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Article
Portfolio Tail Risk: A Multivariate Extreme Value Theory Approach
Entropy 2020, 22(12), 1425; https://doi.org/10.3390/e22121425 - 17 Dec 2020
Cited by 1 | Viewed by 814
Abstract
This paper develops a method for assessing portfolio tail risk based on extreme value theory. The technique applies separate estimations of univariate series and allows for closed-form expressions for Value at Risk and Expected Shortfall. Its forecasting ability is tested on a portfolio [...] Read more.
This paper develops a method for assessing portfolio tail risk based on extreme value theory. The technique applies separate estimations of univariate series and allows for closed-form expressions for Value at Risk and Expected Shortfall. Its forecasting ability is tested on a portfolio of U.S. stocks. The in-sample goodness-of-fit tests indicate that the proposed approach is better suited for portfolio risk modeling under extreme market movements than comparable multivariate parametric methods. Backtesting across multiple quantiles demonstrates that the model cannot be rejected at any reasonable level of significance, even when periods of stress are included. Numerical simulations corroborate the empirical results. Full article
(This article belongs to the Special Issue Extreme Value Theory)
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Article
Foundations of the Quaternion Quantum Mechanics
Entropy 2020, 22(12), 1424; https://doi.org/10.3390/e22121424 - 17 Dec 2020
Cited by 2 | Viewed by 1364
Abstract
We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy [...] Read more.
We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity. Full article
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations)
Article
Multi-Modal Medical Image Fusion Based on FusionNet in YIQ Color Space
Entropy 2020, 22(12), 1423; https://doi.org/10.3390/e22121423 - 17 Dec 2020
Cited by 2 | Viewed by 695
Abstract
In order to obtain the physiological information and key features of source images to the maximum extent, improve the visual effect and clarity of the fused image, and reduce the computation, a multi-modal medical image fusion framework based on feature reuse is proposed. [...] Read more.
In order to obtain the physiological information and key features of source images to the maximum extent, improve the visual effect and clarity of the fused image, and reduce the computation, a multi-modal medical image fusion framework based on feature reuse is proposed. The framework consists of intuitive fuzzy processing (IFP), capture image details network (CIDN), fusion, and decoding. First, the membership function of the image is redefined to remove redundant features and obtain the image with complete features. Then, inspired by DenseNet, we proposed a new encoder to capture all the medical information features in the source image. In the fusion layer, we calculate the weight of each feature graph in the required fusion coefficient according to the trajectory of the feature graph. Finally, the filtered medical information is spliced and decoded to reproduce the required fusion image. In the encoding and image reconstruction networks, the mixed loss function of cross entropy and structural similarity is adopted to greatly reduce the information loss in image fusion. To assess performance, we conducted three sets of experiments on medical images of different grayscales and colors. Experimental results show that the proposed algorithm has advantages not only in detail and structure recognition but also in visual features and time complexity compared with other algorithms. Full article
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Article
Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution
Entropy 2020, 22(12), 1422; https://doi.org/10.3390/e22121422 - 16 Dec 2020
Viewed by 708
Abstract
Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not [...] Read more.
Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics and Quantum Information Theory)
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Article
Artificial Intelligence for Modeling Real Estate Price Using Call Detail Records and Hybrid Machine Learning Approach
Entropy 2020, 22(12), 1421; https://doi.org/10.3390/e22121421 - 16 Dec 2020
Cited by 6 | Viewed by 1211
Abstract
Advancement of accurate models for predicting real estate price is of utmost importance for urban development and several critical economic functions. Due to the significant uncertainties and dynamic variables, modeling real estate has been studied as complex systems. In this study, a novel [...] Read more.
Advancement of accurate models for predicting real estate price is of utmost importance for urban development and several critical economic functions. Due to the significant uncertainties and dynamic variables, modeling real estate has been studied as complex systems. In this study, a novel machine learning method is proposed to tackle real estate modeling complexity. Call detail records (CDR) provides excellent opportunities for in-depth investigation of the mobility characterization. This study explores the CDR potential for predicting the real estate price with the aid of artificial intelligence (AI). Several essential mobility entropy factors, including dweller entropy, dweller gyration, workers’ entropy, worker gyration, dwellers’ work distance, and workers’ home distance, are used as input variables. The prediction model is developed using the machine learning method of multi-layered perceptron (MLP) trained with the evolutionary algorithm of particle swarm optimization (PSO). Model performance is evaluated using mean square error (MSE), sustainability index (SI), and Willmott’s index (WI). The proposed model showed promising results revealing that the workers’ entropy and the dwellers’ work distances directly influence the real estate price. However, the dweller gyration, dweller entropy, workers’ gyration, and the workers’ home had a minimum effect on the price. Furthermore, it is shown that the flow of activities and entropy of mobility are often associated with the regions with lower real estate prices. Full article
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Article
Time Delay Complex Chen Chaotic System and Secure Communication Scheme for Wireless Body Area Networks
Entropy 2020, 22(12), 1420; https://doi.org/10.3390/e22121420 - 16 Dec 2020
Cited by 1 | Viewed by 603
Abstract
Although many chaotic systems with time delays have been studied in recent years, most studies have only focused on the theoretical level, without special applications. Therefore, we present a basic introduction of a time delay complex Chen chaotic system, including the influence of [...] Read more.
Although many chaotic systems with time delays have been studied in recent years, most studies have only focused on the theoretical level, without special applications. Therefore, we present a basic introduction of a time delay complex Chen chaotic system, including the influence of parameter changes and time delay factors on the time delay system. On the basis of complex modified projection synchronization (CMPS), we detail the design of a new controller and communication scheme and apply this communication scheme to a wireless body area network (WBAN), in order to encrypt and decrypt body data collected by sensors. Finally, we perform a numerical simulation, demonstrating the effectiveness of the proposed communication scheme. Full article
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Article
On Yaglom’s Law for the Interplanetary Proton Density and Temperature Fluctuations in Solar Wind Turbulence
Entropy 2020, 22(12), 1419; https://doi.org/10.3390/e22121419 - 15 Dec 2020
Viewed by 662
Abstract
In the past decades, there has been an increasing literature on the presence of an inertial energy cascade in interplanetary space plasma, being interpreted as the signature of Magnetohydrodynamic turbulence (MHD) for both fields and passive scalars. Here, we investigate the passive scalar [...] Read more.
In the past decades, there has been an increasing literature on the presence of an inertial energy cascade in interplanetary space plasma, being interpreted as the signature of Magnetohydrodynamic turbulence (MHD) for both fields and passive scalars. Here, we investigate the passive scalar nature of the solar wind proton density and temperature by looking for scaling features in the mixed-scalar third-order structure functions using measurements on-board the Ulysses spacecraft during two different periods, i.e., an equatorial slow solar wind and a high-latitude fast solar wind, respectively. We find a linear scaling of the mixed third-order structure function as predicted by Yaglom’s law for passive scalars in the case of slow solar wind, while the results for fast solar wind suggest that the mixed fourth-order structure function displays a linear scaling. A simple empirical explanation of the observed difference is proposed and discussed. Full article
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Article
An Extended FMEA Model Based on Cumulative Prospect Theory and Type-2 Intuitionistic Fuzzy VIKOR for the Railway Train Risk Prioritization
Entropy 2020, 22(12), 1418; https://doi.org/10.3390/e22121418 - 15 Dec 2020
Cited by 1 | Viewed by 780
Abstract
This paper aims toward the improvement of the limitations of traditional failure mode and effect analysis (FMEA) and examines the crucial failure modes and components for railway train operation. In order to overcome the drawbacks of current FMEA, this paper proposes a novel [...] Read more.
This paper aims toward the improvement of the limitations of traditional failure mode and effect analysis (FMEA) and examines the crucial failure modes and components for railway train operation. In order to overcome the drawbacks of current FMEA, this paper proposes a novel risk prioritization method based on cumulative prospect theory and type-2 intuitionistic fuzzy VIKOR approach. Type-2 intuitionistic VIKOR handles the combination of the risk factors with their entropy weight. Triangular fuzzy number intuitionistic fuzzy numbers (TFNIFNs) applied as type-2 intuitionistic fuzzy numbers (Type-2 IFNs) are adopted to depict the uncertainty in the risk analysis. Then, cumulative prospect theory is employed to deal with the FMEA team member’s risk sensitiveness and decision-making psychological behavior. Finally, a numerical example of the railway train bogie system is selected to illustrate the application and feasibility of the proposed extended FMEA model in this paper, and a comparison study is also performed to validate the practicability and effectiveness of the novel FMEA model. On this basis, this study can provide guidance for the risk prioritization of railway trains and indicate a direction for further research of risk management of rail traffic. Full article
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Review
A Survey of Information Entropy Metrics for Complex Networks
Entropy 2020, 22(12), 1417; https://doi.org/10.3390/e22121417 - 15 Dec 2020
Cited by 3 | Viewed by 1051
Abstract
Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they [...] Read more.
Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Article
Experimental and Numerical Investigation on Effects of the Steam Ingestion on the Aerodynamic Stability of an Axial Compressor
Entropy 2020, 22(12), 1416; https://doi.org/10.3390/e22121416 - 15 Dec 2020
Viewed by 597
Abstract
In order to investigate the influence of steam ingestion on the aerodynamic stability of a two-stage low-speed axial-flow compressor, multiphase flow numerical simulation and experiment were carried out. The total pressure ratio and stall margin of the compressor was decreased under steam ingestion. [...] Read more.
In order to investigate the influence of steam ingestion on the aerodynamic stability of a two-stage low-speed axial-flow compressor, multiphase flow numerical simulation and experiment were carried out. The total pressure ratio and stall margin of the compressor was decreased under steam ingestion. When the compressor worked at 40% and 53% of the nominal speed, the stall margin decreased, respectively, by 1.5% and 6.3%. The ingested steam reduced the inlet Mach number and increased the thickness of the boundary layer on the suction surface of the blade. The low-speed region around the trailing edge of the blade was increased, and the flow separation region of the boundary layer on the suction surface of the blade was expanded; thus, the compressor was more likely to enter the stall state. The higher the rotational speed, the more significant the negative influence of steam ingestion on the compressor stall margin. The entropy and temperature of air were increased by steam. The heat transfer between steam and air was continuous in compressor passages. The entropy of the air in the later stage was higher than that in the first stage; consequently, the flow loss in the second stage was more serious. Under the combined action of steam ingestion and counter-rotating bulk swirl distortion, the compressor stability margin loss was more obvious. When the rotor speed was 40% and 53% of the nominal speed, the stall margin decreased by 6.3% and 12.64%, respectively. Full article
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Article
Statistical Features in High-Frequency Bands of Interictal iEEG Work Efficiently in Identifying the Seizure Onset Zone in Patients with Focal Epilepsy
Entropy 2020, 22(12), 1415; https://doi.org/10.3390/e22121415 - 15 Dec 2020
Viewed by 1448
Abstract
The design of a computer-aided system for identifying the seizure onset zone (SOZ) from interictal and ictal electroencephalograms (EEGs) is desired by epileptologists. This study aims to introduce the statistical features of high-frequency components (HFCs) in interictal intracranial electroencephalograms (iEEGs) to identify the [...] Read more.
The design of a computer-aided system for identifying the seizure onset zone (SOZ) from interictal and ictal electroencephalograms (EEGs) is desired by epileptologists. This study aims to introduce the statistical features of high-frequency components (HFCs) in interictal intracranial electroencephalograms (iEEGs) to identify the possible seizure onset zone (SOZ) channels. It is known that the activity of HFCs in interictal iEEGs, including ripple and fast ripple bands, is associated with epileptic seizures. This paper proposes to decompose multi-channel interictal iEEG signals into a number of subbands. For every 20 s segment, twelve features are computed from each subband. A mutual information (MI)-based method with grid search was applied to select the most prominent bands and features. A gradient-boosting decision tree-based algorithm called LightGBM was used to score each segment of the channels and these were averaged together to achieve a final score for each channel. The possible SOZ channels were localized based on the higher value channels. The experimental results with eleven epilepsy patients were tested to observe the efficiency of the proposed design compared to the state-of-the-art methods. Full article
(This article belongs to the Section Signal and Data Analysis)
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Article
Whole Time Series Data Streams Clustering: Dynamic Profiling of the Electricity Consumption
Entropy 2020, 22(12), 1414; https://doi.org/10.3390/e22121414 - 15 Dec 2020
Cited by 2 | Viewed by 804
Abstract
Data from smart grids are challenging to analyze due to their very large size, high dimensionality, skewness, sparsity, and number of seasonal fluctuations, including daily and weekly effects. With the data arriving in a sequential form the underlying distribution is subject to changes [...] Read more.
Data from smart grids are challenging to analyze due to their very large size, high dimensionality, skewness, sparsity, and number of seasonal fluctuations, including daily and weekly effects. With the data arriving in a sequential form the underlying distribution is subject to changes over the time intervals. Time series data streams have their own specifics in terms of the data processing and data analysis because, usually, it is not possible to process the whole data in memory as the large data volumes are generated fast so the processing and the analysis should be done incrementally using sliding windows. Despite the proposal of many clustering techniques applicable for grouping the observations of a single data stream, only a few of them are focused on splitting the whole data streams into the clusters. In this article we aim to explore individual characteristics of electricity usage and recommend the most suitable tariff to the customer so they can benefit from lower prices. This work investigates various algorithms (and their improvements) what allows us to formulate the clusters, in real time, based on smart meter data. Full article
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Article
Dichotomic Decision Optimization for the Design of HVDC Superconducting Links
Entropy 2020, 22(12), 1413; https://doi.org/10.3390/e22121413 - 15 Dec 2020
Cited by 1 | Viewed by 586
Abstract
Superconducting links are an innovative solution for bulk power transmission, distinguished by their compact dimensions, high efficiency and small environmental footprint. As with any new technology field, there is a large amount of design possibilities for such links, each of them having a [...] Read more.
Superconducting links are an innovative solution for bulk power transmission, distinguished by their compact dimensions, high efficiency and small environmental footprint. As with any new technology field, there is a large amount of design possibilities for such links, each of them having a profound impact on the system configuration. For instance, changing the material can imply a change in the working temperature from 20 to 70 K and has consequences on the maximum link length. This article presents the dichotomic decision possibilities for the optimized design of a high-power superconducting link, focusing on some of the key components of the cable system. The complex design optimization process is exemplified using the European project Best Paths, in which the first 3-gigawatt-class superconducting cable system was designed, optimized, manufactured, and successfully tested. Full article
(This article belongs to the Special Issue Thermodynamic Optimization of Complex Energy Systems)
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