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Entropy, Volume 24, Issue 1 (January 2022) – 138 articles

Cover Story (view full-size image): Line-entropy is a nonlinear metric from recurrence quantification analysis used to gauge the level of system complexity. For periodic systems (simple), long recurrent diagonal lines span from border to border and are truncated to unique lengths. Entropy values are high (high complexity). Restriction (masking) of the triangular recurrence area to a tilted box (red/pink) and long lines are truncated at the border to identical lengths. Entropy values are low (low complexity). However, for real-world systems, noise disallows long lines from forming and brings the two entropy values closer together. Thus, entropy values computed from Dow-Jones scores (green) track fairly closely for triangular areas (blue) versus boxed areas (red). View this paper
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17 pages, 16249 KiB  
Article
Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions
by Kornelia M. Batko, Izabella Ślęzak-Prochazka, Andrzej Ślęzak, Wioletta M. Bajdur and Radomir Ščurek
Entropy 2022, 24(1), 138; https://doi.org/10.3390/e24010138 - 17 Jan 2022
Cited by 1 | Viewed by 1857
Abstract
Based on Kedem–Katchalsky formalism, the model equation of the membrane potential (Δψs) generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes [...] Read more.
Based on Kedem–Katchalsky formalism, the model equation of the membrane potential (Δψs) generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations (Ci/Ce) at the membrane/concentration boundary layers. We present the calculation procedure (Ci/Ce) based on novel equations derived in the paper containing the transport parameters of the membrane (Lp, σ, and ω), solutions (ρ, ν), concentration boundary layer thicknesses (δl, δh), concentration Raileigh number (RC), concentration polarization factor (ζs), volume flux (Jv), mechanical pressure difference (ΔP), and ratio of known solution concentrations (Ch/Cl). From the resulting equation, Δψs was calculated for various combinations of the solution concentration ratio (Ch/Cl), the Rayleigh concentration number (RC), the concentration polarization coefficient (ζs), and the hydrostatic pressure difference (ΔP). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m−3 (Cl) was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m−3 (Ch). It is shown that (Δψs) depends on the value of one of the factors (i.e., ΔP, Ch/Cl, RC and ζs) at a fixed value of the other three. Full article
(This article belongs to the Section Thermodynamics)
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20 pages, 324 KiB  
Article
A Classical Formulation of Quantum Theory?
by William F. Braasch, Jr. and William K. Wootters
Entropy 2022, 24(1), 137; https://doi.org/10.3390/e24010137 - 17 Jan 2022
Cited by 2 | Viewed by 2027
Abstract
We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model [...] Read more.
We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model introduced by Spekkens. We obtain quantum theory only by combining a collection of restricted classical pictures. Our main challenge in this paper is to find a simple way of characterizing the allowed sets of classical pictures. We present one promising approach to this problem and show how it works out for the case of a single qubit. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
10 pages, 1703 KiB  
Article
Quantum Switchboard with Coupled-Cavity Array
by Wai-Keong Mok and Leong-Chuan Kwek
Entropy 2022, 24(1), 136; https://doi.org/10.3390/e24010136 - 17 Jan 2022
Viewed by 1408
Abstract
The ability to control the flow of quantum information is deterministically useful for scaling up quantum computation. In this paper, we demonstrate a controllable quantum switchboard which directs the teleportation protocol to one of two targets, fully dependent on the sender’s choice. Importantly, [...] Read more.
The ability to control the flow of quantum information is deterministically useful for scaling up quantum computation. In this paper, we demonstrate a controllable quantum switchboard which directs the teleportation protocol to one of two targets, fully dependent on the sender’s choice. Importantly, the quantum switchboard also acts as a optimal quantum cloning machine, which allows the receivers to recover the unknown quantum state with a maximal fidelity of 56. This protects the system from the complete loss of quantum information in the event that the teleportation protocol fails. We also provide an experimentally feasible physical implementation of the proposal using a coupled-cavity array. The proposed switchboard can be utilized for the efficient routing of quantum information in a large quantum network. Full article
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28 pages, 498 KiB  
Article
An Information Theoretic Interpretation to Deep Neural Networks
by Xiangxiang Xu, Shao-Lun Huang, Lizhong Zheng and Gregory W. Wornell
Entropy 2022, 24(1), 135; https://doi.org/10.3390/e24010135 - 17 Jan 2022
Cited by 9 | Viewed by 3346
Abstract
With the unprecedented performance achieved by deep learning, it is commonly believed that deep neural networks (DNNs) attempt to extract informative features for learning tasks. To formalize this intuition, we apply the local information geometric analysis and establish an information-theoretic framework for feature [...] Read more.
With the unprecedented performance achieved by deep learning, it is commonly believed that deep neural networks (DNNs) attempt to extract informative features for learning tasks. To formalize this intuition, we apply the local information geometric analysis and establish an information-theoretic framework for feature selection, which demonstrates the information-theoretic optimality of DNN features. Moreover, we conduct a quantitative analysis to characterize the impact of network structure on the feature extraction process of DNNs. Our investigation naturally leads to a performance metric for evaluating the effectiveness of extracted features, called the H-score, which illustrates the connection between the practical training process of DNNs and the information-theoretic framework. Finally, we validate our theoretical results by experimental designs on synthesized data and the ImageNet dataset. Full article
(This article belongs to the Special Issue Information Theory and Machine Learning)
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12 pages, 1728 KiB  
Article
Instance Segmentation of Multiple Myeloma Cells Using Deep-Wise Data Augmentation and Mask R-CNN
by May Phu Paing, Adna Sento, Toan Huy Bui and Chuchart Pintavirooj
Entropy 2022, 24(1), 134; https://doi.org/10.3390/e24010134 - 17 Jan 2022
Cited by 5 | Viewed by 2660
Abstract
Multiple myeloma is a condition of cancer in the bone marrow that can lead to dysfunction of the body and fatal expression in the patient. Manual microscopic analysis of abnormal plasma cells, also known as multiple myeloma cells, is one of the most [...] Read more.
Multiple myeloma is a condition of cancer in the bone marrow that can lead to dysfunction of the body and fatal expression in the patient. Manual microscopic analysis of abnormal plasma cells, also known as multiple myeloma cells, is one of the most commonly used diagnostic methods for multiple myeloma. However, as it is a manual process, it consumes too much effort and time. Besides, it has a higher chance of human errors. This paper presents a computer-aided detection and segmentation of myeloma cells from microscopic images of the bone marrow aspiration. Two major contributions are presented in this paper. First, different Mask R-CNN models using different images, including original microscopic images, contrast-enhanced images and stained cell images, are developed to perform instance segmentation of multiple myeloma cells. As a second contribution, a deep-wise augmentation, a deep learning-based data augmentation method, is applied to increase the performance of Mask R-CNN models. Based on the experimental findings, the Mask R-CNN model using contrast-enhanced images combined with the proposed deep-wise data augmentation provides a superior performance compared to other models. It achieves a mean precision of 0.9973, mean recall of 0.8631, and mean intersection over union (IOU) of 0.9062. Full article
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17 pages, 790 KiB  
Article
Learn Quasi-Stationary Distributions of Finite State Markov Chain
by Zhiqiang Cai, Ling Lin and Xiang Zhou
Entropy 2022, 24(1), 133; https://doi.org/10.3390/e24010133 - 17 Jan 2022
Cited by 1 | Viewed by 1917
Abstract
We propose a reinforcement learning (RL) approach to compute the expression of quasi-stationary distribution. Based on the fixed-point formulation of quasi-stationary distribution, we minimize the KL-divergence of two Markovian path distributions induced by candidate distribution and true target distribution. To solve this challenging [...] Read more.
We propose a reinforcement learning (RL) approach to compute the expression of quasi-stationary distribution. Based on the fixed-point formulation of quasi-stationary distribution, we minimize the KL-divergence of two Markovian path distributions induced by candidate distribution and true target distribution. To solve this challenging minimization problem by gradient descent, we apply a reinforcement learning technique by introducing the reward and value functions. We derive the corresponding policy gradient theorem and design an actor-critic algorithm to learn the optimal solution and the value function. The numerical examples of finite state Markov chain are tested to demonstrate the new method. Full article
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15 pages, 1641 KiB  
Article
Understanding Dilated Mathematical Relationship between Image Features and the Convolutional Neural Network’s Learnt Parameters
by Eyad Alsaghir, Xiyu Shi, Varuna De Silva and Ahmet Kondoz
Entropy 2022, 24(1), 132; https://doi.org/10.3390/e24010132 - 16 Jan 2022
Cited by 1 | Viewed by 1740
Abstract
Deep learning, in general, was built on input data transformation and presentation, model training with parameter tuning, and recognition of new observations using the trained model. However, this came with a high computation cost due to the extensive input database and the length [...] Read more.
Deep learning, in general, was built on input data transformation and presentation, model training with parameter tuning, and recognition of new observations using the trained model. However, this came with a high computation cost due to the extensive input database and the length of time required in training. Despite the model learning its parameters from the transformed input data, no direct research has been conducted to investigate the mathematical relationship between the transformed information (i.e., features, excitation) and the model’s learnt parameters (i.e., weights). This research aims to explore a mathematical relationship between the input excitations and the weights of a trained convolutional neural network. The objective is to investigate three aspects of this assumed feature-weight relationship: (1) the mathematical relationship between the training input images’ features and the model’s learnt parameters, (2) the mathematical relationship between the images’ features of a separate test dataset and a trained model’s learnt parameters, and (3) the mathematical relationship between the difference of training and testing images’ features and the model’s learnt parameters with a separate test dataset. The paper empirically demonstrated the existence of this mathematical relationship between the test image features and the model’s learnt weights by the ANOVA analysis. Full article
(This article belongs to the Topic Machine and Deep Learning)
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29 pages, 1643 KiB  
Article
Optimal Control of Uniformly Heated Granular Fluids in Linear Response
by Natalia Ruiz-Pino and Antonio Prados
Entropy 2022, 24(1), 131; https://doi.org/10.3390/e24010131 - 16 Jan 2022
Cited by 4 | Viewed by 1474
Abstract
We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of [...] Read more.
We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously—from a mathematical point of view—prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated. Full article
(This article belongs to the Section Non-equilibrium Phenomena)
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16 pages, 535 KiB  
Article
Multifractal Company Market: An Application to the Stock Market Indices
by Michał Chorowski and Ryszard Kutner
Entropy 2022, 24(1), 130; https://doi.org/10.3390/e24010130 - 16 Jan 2022
Cited by 2 | Viewed by 1503
Abstract
Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical [...] Read more.
Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical properties of the company market and (ii) analyzing a real company market defined by the S&P500 index. As the valuable reference case, we considered a four-group market model that skillfully reconstructs this index’s empirical data. We point out that a four-group company market organization is universal because it can perfectly describe the essential features of the spectrum of dimensions, regardless of the analyzed series of shares. The apparent differences from the empirical data appear only at the level of subtle effects. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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15 pages, 1956 KiB  
Article
Cooperative Spectrum Sensing Based on Multi-Features Combination Network in Cognitive Radio Network
by Mingdong Xu, Zhendong Yin, Yanlong Zhao and Zhilu Wu
Entropy 2022, 24(1), 129; https://doi.org/10.3390/e24010129 - 15 Jan 2022
Cited by 14 | Viewed by 2525
Abstract
Cognitive radio, as a key technology to improve the utilization of radio spectrum, acquired much attention. Moreover, spectrum sensing has an irreplaceable position in the field of cognitive radio and was widely studied. The convolutional neural networks (CNNs) and the gate recurrent unit [...] Read more.
Cognitive radio, as a key technology to improve the utilization of radio spectrum, acquired much attention. Moreover, spectrum sensing has an irreplaceable position in the field of cognitive radio and was widely studied. The convolutional neural networks (CNNs) and the gate recurrent unit (GRU) are complementary in their modelling capabilities. In this paper, we introduce a CNN-GRU network to obtain the local information for single-node spectrum sensing, in which CNN is used to extract spatial feature and GRU is used to extract the temporal feature. Then, the combination network receives the features extracted by the CNN-GRU network to achieve multifeatures combination and obtains the final cooperation result. The cooperative spectrum sensing scheme based on Multifeatures Combination Network enhances the sensing reliability by fusing the local information from different sensing nodes. To accommodate the detection of multiple types of signals, we generated 8 kinds of modulation types to train the model. Theoretical analysis and simulation results show that the cooperative spectrum sensing algorithm proposed in this paper improved detection performance with no prior knowledge about the information of primary user or channel state. Our proposed method achieved competitive performance under the condition of large dynamic signal-to-noise ratio. Full article
(This article belongs to the Special Issue Methods in Artificial Intelligence and Information Processing)
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11 pages, 4944 KiB  
Article
Forest Fire Detection via Feature Entropy Guided Neural Network
by Zhenwei Guan, Feng Min, Wei He, Wenhua Fang and Tao Lu
Entropy 2022, 24(1), 128; https://doi.org/10.3390/e24010128 - 15 Jan 2022
Cited by 10 | Viewed by 2001
Abstract
Forest fire detection from videos or images is vital to forest firefighting. Most deep learning based approaches rely on converging image loss, which ignores the content from different fire scenes. In fact, complex content of images always has higher entropy. From this perspective, [...] Read more.
Forest fire detection from videos or images is vital to forest firefighting. Most deep learning based approaches rely on converging image loss, which ignores the content from different fire scenes. In fact, complex content of images always has higher entropy. From this perspective, we propose a novel feature entropy guided neural network for forest fire detection, which is used to balance the content complexity of different training samples. Specifically, a larger weight is given to the feature of the sample with a high entropy source when calculating the classification loss. In addition, we also propose a color attention neural network, which mainly consists of several repeated multiple-blocks of color-attention modules (MCM). Each MCM module can extract the color feature information of fire adequately. The experimental results show that the performance of our proposed method outperforms the state-of-the-art methods. Full article
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13 pages, 1454 KiB  
Article
Security Analysis of Continuous-Variable Measurement-Device-Independent Quantum Key Distribution Systems in Complex Communication Environments
by Yi Zheng, Haobin Shi, Wei Pan, Quantao Wang and Jiahui Mao
Entropy 2022, 24(1), 127; https://doi.org/10.3390/e24010127 - 14 Jan 2022
Cited by 2 | Viewed by 1868
Abstract
Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here [...] Read more.
Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here we investigate the security of the system under the effects of the fluctuating channel transmittance, where the transmittance is regarded as a fixed value related to communication distance in theory. We first discuss the parameter estimation in fluctuating channel transmittance based on these establishing of channel models, which has an obvious deviation compared with the estimated parameters in the ideal case. Then, we show the evaluated results when the channel transmittance respectively obeys the two-point distribution and the uniform distribution. In particular, the two distributions can be easily realized under the manipulation of eavesdroppers. Finally, we analyze the secret key rate of the system when the channel transmittance obeys the above distributions. The simulation analysis indicates that a slight fluctuation of the channel transmittance may seriously reduce the performance of the system, especially in the extreme asymmetric case. Furthermore, the communication between Alice, Bob and Charlie may be immediately interrupted. Therefore, eavesdroppers can manipulate the channel transmittance to complete a denial-of-service attack in a practical CV-MDI QKD system. To resist this attack, the Gaussian post-selection method can be exploited to calibrate the parameter estimation to reduce the deterioration of performance of the system. Full article
(This article belongs to the Topic Quantum Information and Quantum Computing)
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20 pages, 709 KiB  
Article
Immunity in the ABM-DSGE Framework for Preventing and Controlling Epidemics—Validation of Results
by Jagoda Kaszowska-Mojsa, Przemysław Włodarczyk and Agata Szymańska
Entropy 2022, 24(1), 126; https://doi.org/10.3390/e24010126 - 14 Jan 2022
Cited by 1 | Viewed by 1975
Abstract
The COVID-19 pandemic has raised many questions on how to manage an epidemiological and economic crisis around the world. Since the beginning of the COVID-19 pandemic, scientists and policy makers have been asking how effective lockdowns are in preventing and controlling the spread [...] Read more.
The COVID-19 pandemic has raised many questions on how to manage an epidemiological and economic crisis around the world. Since the beginning of the COVID-19 pandemic, scientists and policy makers have been asking how effective lockdowns are in preventing and controlling the spread of the virus. In the absence of vaccines, the regulators lacked any plausible alternatives. Nevertheless, after the introduction of vaccinations, to what extent the conclusions of these analyses are still valid should be considered. In this paper, we present a study on the effect of vaccinations within the dynamic stochastic general equilibrium model with an agent-based epidemic component. Thus, we validated the results regarding the need to use lockdowns as an efficient tool for preventing and controlling epidemics that were obtained in November 2020. Full article
(This article belongs to the Special Issue Entropy in Real-World Datasets and Its Impact on Machine Learning)
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17 pages, 1555 KiB  
Article
Inferring a Property of a Large System from a Small Number of Samples
by Damián G. Hernández and Inés Samengo
Entropy 2022, 24(1), 125; https://doi.org/10.3390/e24010125 - 14 Jan 2022
Cited by 1 | Viewed by 1407
Abstract
Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, [...] Read more.
Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature. Full article
(This article belongs to the Special Issue Applications of Information Theory in Statistics)
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10 pages, 985 KiB  
Article
Prebiotic Aggregates (Tissues) Emerging from Reaction–Diffusion: Formation Time, Configuration Entropy and Optimal Spatial Dimension
by Juan Cesar Flores
Entropy 2022, 24(1), 124; https://doi.org/10.3390/e24010124 - 14 Jan 2022
Cited by 2 | Viewed by 1445
Abstract
For the formation of a proto-tissue, rather than a protocell, the use of reactant dynamics in a finite spatial region is considered. The framework is established on the basic concepts of replication, diversity, and heredity. Heredity, in the sense of the continuity of [...] Read more.
For the formation of a proto-tissue, rather than a protocell, the use of reactant dynamics in a finite spatial region is considered. The framework is established on the basic concepts of replication, diversity, and heredity. Heredity, in the sense of the continuity of information and alike traits, is characterized by the number of equivalent patterns conferring viability against selection processes. In the case of structural parameters and the diffusion coefficient of ribonucleic acid, the formation time ranges between a few years to some decades, depending on the spatial dimension (fractional or not). As long as equivalent patterns exist, the configuration entropy of proto-tissues can be defined and used as a practical tool. Consequently, the maximal diversity and weak fluctuations, for which proto-tissues can develop, occur at the spatial dimension 2.5. Full article
(This article belongs to the Section Entropy and Biology)
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18 pages, 540 KiB  
Article
Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators
by María Jaenada and Leandro Pardo
Entropy 2022, 24(1), 123; https://doi.org/10.3390/e24010123 - 13 Jan 2022
Cited by 6 | Viewed by 1999
Abstract
Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these [...] Read more.
Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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15 pages, 15147 KiB  
Article
FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects
by Svitlana Matsenko, Oleksiy Borysenko, Sandis Spolitis, Aleksejs Udalcovs, Lilita Gegere, Aleksandr Krotov, Oskars Ozolins and Vjaceslavs Bobrovs
Entropy 2022, 24(1), 122; https://doi.org/10.3390/e24010122 - 13 Jan 2022
Cited by 2 | Viewed by 1983
Abstract
Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements [...] Read more.
Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio. Full article
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14 pages, 8783 KiB  
Article
A Damping-Tunable Snap System: From Dissipative Hyperchaos to Conservative Chaos
by Patinya Ketthong and Banlue Srisuchinwong
Entropy 2022, 24(1), 121; https://doi.org/10.3390/e24010121 - 13 Jan 2022
Cited by 3 | Viewed by 1463
Abstract
A hyperjerk system described by a single fourth-order ordinary differential equation of the form x=f(x,x¨,x˙,x) has been referred to as a snap system. A damping-tunable snap system, capable [...] Read more.
A hyperjerk system described by a single fourth-order ordinary differential equation of the form x=f(x,x¨,x˙,x) has been referred to as a snap system. A damping-tunable snap system, capable of an adjustable attractor dimension (DL) ranging from dissipative hyperchaos (DL<4) to conservative chaos (DL=4), is presented for the first time, in particular not only in a snap system, but also in a four-dimensional (4D) system. Such an attractor dimension is adjustable by nonlinear damping of a relatively simple quadratic function of the form Ax2, easily tunable by a single parameter A. The proposed snap system is practically implemented and verified by the reconfigurable circuits of field programmable analog arrays (FPAAs). Full article
(This article belongs to the Section Complexity)
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15 pages, 446 KiB  
Article
Weighted Relative Group Entropies and Associated Fisher Metrics
by Iulia-Elena Hirica, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae and Vasile Preda
Entropy 2022, 24(1), 120; https://doi.org/10.3390/e24010120 - 13 Jan 2022
Cited by 6 | Viewed by 1598
Abstract
A large family of new α-weighted group entropy functionals is defined and associated Fisher-like metrics are considered. All these notions are well-suited semi-Riemannian tools for the geometrization of entropy-related statistical models, where they may act as sensitive controlling invariants. The main result [...] Read more.
A large family of new α-weighted group entropy functionals is defined and associated Fisher-like metrics are considered. All these notions are well-suited semi-Riemannian tools for the geometrization of entropy-related statistical models, where they may act as sensitive controlling invariants. The main result of the paper establishes a link between such a metric and a canonical one. A sufficient condition is found, in order that the two metrics be conformal (or homothetic). In particular, we recover a recent result, established for α=1 and for non-weighted relative group entropies. Our conformality condition is “universal”, in the sense that it does not depend on the group exponential. Full article
(This article belongs to the Special Issue Measures of Information II)
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14 pages, 3078 KiB  
Article
Fusion Domain-Adaptation CNN Driven by Images and Vibration Signals for Fault Diagnosis of Gearbox Cross-Working Conditions
by Gang Mao, Zhongzheng Zhang, Bin Qiao and Yongbo Li
Entropy 2022, 24(1), 119; https://doi.org/10.3390/e24010119 - 13 Jan 2022
Cited by 26 | Viewed by 2657
Abstract
The vibration signal of gearboxes contains abundant fault information, which can be used for condition monitoring. However, vibration signal is ineffective for some non-structural failures. In order to resolve this dilemma, infrared thermal images are introduced to combine with vibration signals via fusion [...] Read more.
The vibration signal of gearboxes contains abundant fault information, which can be used for condition monitoring. However, vibration signal is ineffective for some non-structural failures. In order to resolve this dilemma, infrared thermal images are introduced to combine with vibration signals via fusion domain-adaptation convolutional neural network (FDACNN), which can diagnose both structural and non-structural failures under various working conditions. First, the measured raw signals are converted into frequency and squared envelope spectrum to characterize the health states of the gearbox. Second, the sequences of the frequency and squared envelope spectrum are arranged into two-dimensional format, which are combined with infrared thermal images to form fusion data. Finally, the adversarial network is introduced to realize the state recognition of structural and non-structural faults in the unlabeled target domain. An experiment of gearbox test rigs was used for effectiveness validation by measuring both vibration and infrared thermal images. The results suggest that the proposed FDACNN method performs best in cross-domain fault diagnosis of gearboxes via multi-source heterogeneous data compared with the other four methods. Full article
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16 pages, 8083 KiB  
Article
MFAN: Multi-Level Features Attention Network for Fake Certificate Image Detection
by Yu Sun, Rongrong Ni and Yao Zhao
Entropy 2022, 24(1), 118; https://doi.org/10.3390/e24010118 - 13 Jan 2022
Cited by 6 | Viewed by 2637
Abstract
Up to now, most of the forensics methods have attached more attention to natural content images. To expand the application of image forensics technology, forgery detection for certificate images that can directly represent people’s rights and interests is investigated in this paper. Variable [...] Read more.
Up to now, most of the forensics methods have attached more attention to natural content images. To expand the application of image forensics technology, forgery detection for certificate images that can directly represent people’s rights and interests is investigated in this paper. Variable tampered region scales and diverse manipulation types are two typical characteristics in fake certificate images. To tackle this task, a novel method called Multi-level Feature Attention Network (MFAN) is proposed. MFAN is built following the encoder–decoder network structure. In order to extract features with rich scale information in the encoder, on the one hand, we employ Atrous Spatial Pyramid Pooling (ASPP) on the final layer of a pre-trained residual network to capture the contextual information at different scales; on the other hand, low-level features are concatenated to ensure the sensibility to small targets. Furthermore, the resulting multi-level features are recalibrated on channels for irrelevant information suppression and enhancing the tampered regions, guiding the MFAN to adapt to diverse manipulation traces. In the decoder module, the attentive feature maps are convoluted and unsampled to effectively generate the prediction mask. Experimental results indicate that the proposed method outperforms some state-of-the-art forensics methods. Full article
(This article belongs to the Topic Machine and Deep Learning)
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19 pages, 1139 KiB  
Article
Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise
by Xuyou Li, Yanda Guo and Qingwen Meng
Entropy 2022, 24(1), 117; https://doi.org/10.3390/e24010117 - 12 Jan 2022
Cited by 3 | Viewed by 1928
Abstract
The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been [...] Read more.
The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises. Full article
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12 pages, 304 KiB  
Article
On the Depth of Decision Trees with Hypotheses
by Mikhail Moshkov
Entropy 2022, 24(1), 116; https://doi.org/10.3390/e24010116 - 12 Jan 2022
Cited by 3 | Viewed by 1645
Abstract
In this paper, based on the results of rough set theory, test theory, and exact learning, we investigate decision trees over infinite sets of binary attributes represented as infinite binary information systems. We define the notion of a problem over an information system [...] Read more.
In this paper, based on the results of rough set theory, test theory, and exact learning, we investigate decision trees over infinite sets of binary attributes represented as infinite binary information systems. We define the notion of a problem over an information system and study three functions of the Shannon type, which characterize the dependence in the worst case of the minimum depth of a decision tree solving a problem on the number of attributes in the problem description. The considered three functions correspond to (i) decision trees using attributes, (ii) decision trees using hypotheses (an analog of equivalence queries from exact learning), and (iii) decision trees using both attributes and hypotheses. The first function has two possible types of behavior: logarithmic and linear (this result follows from more general results published by the author earlier). The second and the third functions have three possible types of behavior: constant, logarithmic, and linear (these results were published by the author earlier without proofs that are given in the present paper). Based on the obtained results, we divided the set of all infinite binary information systems into four complexity classes. In each class, the type of behavior for each of the considered three functions does not change. Full article
(This article belongs to the Special Issue Rough Set Theory and Entropy in Information Science)
20 pages, 914 KiB  
Article
Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method
by Hiroaki Inoue, Koji Hukushima and Toshiaki Omori
Entropy 2022, 24(1), 115; https://doi.org/10.3390/e24010115 - 12 Jan 2022
Cited by 2 | Viewed by 2053
Abstract
Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at [...] Read more.
Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods. Full article
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17 pages, 610 KiB  
Review
Singing Voice Detection: A Survey
by Ramy Monir, Daniel Kostrzewa and Dariusz Mrozek
Entropy 2022, 24(1), 114; https://doi.org/10.3390/e24010114 - 12 Jan 2022
Cited by 10 | Viewed by 3482
Abstract
Singing voice detection or vocal detection is a classification task that determines whether there is a singing voice in a given audio segment. This process is a crucial preprocessing step that can be used to improve the performance of other tasks such as [...] Read more.
Singing voice detection or vocal detection is a classification task that determines whether there is a singing voice in a given audio segment. This process is a crucial preprocessing step that can be used to improve the performance of other tasks such as automatic lyrics alignment, singing melody transcription, singing voice separation, vocal melody extraction, and many more. This paper presents a survey on the techniques of singing voice detection with a deep focus on state-of-the-art algorithms such as convolutional LSTM and GRU-RNN. It illustrates a comparison between existing methods for singing voice detection, mainly based on the Jamendo and RWC datasets. Long-term recurrent convolutional networks have reached impressive results on public datasets. The main goal of the present paper is to investigate both classical and state-of-the-art approaches to singing voice detection. Full article
(This article belongs to the Special Issue Methods in Artificial Intelligence and Information Processing)
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16 pages, 379 KiB  
Article
Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence
by Ignacio Baena, Pedro Pérez-Fernández, Manuela Rodríguez-Gallardo and José Miguel Arias
Entropy 2022, 24(1), 113; https://doi.org/10.3390/e24010113 - 12 Jan 2022
Cited by 2 | Viewed by 1613
Abstract
A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from [...] Read more.
A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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17 pages, 3890 KiB  
Article
Visual Recognition of Traffic Signs in Natural Scenes Based on Improved RetinaNet
by Shangwang Liu, Tongbo Cai, Xiufang Tang, Yangyang Zhang and Changgeng Wang
Entropy 2022, 24(1), 112; https://doi.org/10.3390/e24010112 - 12 Jan 2022
Cited by 11 | Viewed by 2936
Abstract
Aiming at recognizing small proportion, blurred and complex traffic sign in natural scenes, a traffic sign detection method based on RetinaNet-NeXt is proposed. First, to ensure the quality of dataset, the data were cleaned and enhanced to denoise. Secondly, a novel backbone network [...] Read more.
Aiming at recognizing small proportion, blurred and complex traffic sign in natural scenes, a traffic sign detection method based on RetinaNet-NeXt is proposed. First, to ensure the quality of dataset, the data were cleaned and enhanced to denoise. Secondly, a novel backbone network ResNeXt was employed to improve the detection accuracy and effection of RetinaNet. Finally, transfer learning and group normalization were adopted to accelerate our network training. Experimental results show that the precision, recall and mAP of our method, compared with the original RetinaNet, are improved by 9.08%, 9.09% and 7.32%, respectively. Our method can be effectively applied to traffic sign detection. Full article
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17 pages, 496 KiB  
Article
A Verifiable Arbitrated Quantum Signature Scheme Based on Controlled Quantum Teleportation
by Dianjun Lu, Zhihui Li, Jing Yu and Zhaowei Han
Entropy 2022, 24(1), 111; https://doi.org/10.3390/e24010111 - 11 Jan 2022
Cited by 16 | Viewed by 1610
Abstract
In this paper, we present a verifiable arbitrated quantum signature scheme based on controlled quantum teleportation. The five-qubit entangled state functions as a quantum channel. The proposed scheme uses mutually unbiased bases particles as decoy particles and performs unitary operations on these decoy [...] Read more.
In this paper, we present a verifiable arbitrated quantum signature scheme based on controlled quantum teleportation. The five-qubit entangled state functions as a quantum channel. The proposed scheme uses mutually unbiased bases particles as decoy particles and performs unitary operations on these decoy particles, applying the functional values of symmetric bivariate polynomial. As such, eavesdropping detection and identity authentication can both be executed. The security analysis shows that our scheme can neither be disavowed by the signatory nor denied by the verifier, and it cannot be forged by any malicious attacker. Full article
(This article belongs to the Special Issue Practical Quantum Communication)
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21 pages, 368 KiB  
Article
Function Computation under Privacy, Secrecy, Distortion, and Communication Constraints
by Onur Günlü
Entropy 2022, 24(1), 110; https://doi.org/10.3390/e24010110 - 11 Jan 2022
Cited by 4 | Viewed by 1588 | Correction
Abstract
The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include (1) privacy leakage to an eavesdropper [...] Read more.
The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include (1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals’ observed sequences; (2) the information leakage to a fusion center with respect to the remote source is considered a new privacy leakage metric; (3) the function computed is allowed to be a distorted version of the target function, which allows the storage rate to be reduced compared to a reliable function computation scenario, in addition to reducing secrecy and privacy leakages; (4) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless and lossy single-function computation with two transmitting nodes, which recover previous results in the literature. For special cases, including invertible and partially invertible functions, and degraded measurement channels, simplified lossless and lossy rate regions are characterized, and one achievable region is evaluated as an example scenario. Full article
(This article belongs to the Special Issue Information-Theoretic Approach to Privacy and Security)
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21 pages, 425 KiB  
Article
Attaining Fairness in Communication for Omniscience
by Ni Ding, Parastoo Sadeghi, David Smith and Thierry Rakotoarivelo
Entropy 2022, 24(1), 109; https://doi.org/10.3390/e24010109 - 11 Jan 2022
Viewed by 1497
Abstract
This paper studies how to attain fairness in communication for omniscience that models the multi-terminal compress sensing problem and the coded cooperative data exchange problem where a set of users exchange their observations of a discrete multiple random source to attain omniscience—the state [...] Read more.
This paper studies how to attain fairness in communication for omniscience that models the multi-terminal compress sensing problem and the coded cooperative data exchange problem where a set of users exchange their observations of a discrete multiple random source to attain omniscience—the state that all users recover the entire source. The optimal rate region containing all source coding rate vectors that achieve omniscience with the minimum sum rate is shown to coincide with the core (the solution set) of a coalitional game. Two game-theoretic fairness solutions are studied: the Shapley value and the egalitarian solution. It is shown that the Shapley value assigns each user the source coding rate measured by their remaining information of the multiple source given the common randomness that is shared by all users, while the egalitarian solution simply distributes the rates as evenly as possible in the core. To avoid the exponentially growing complexity of obtaining the Shapley value, a polynomial-time approximation method is proposed which utilizes the fact that the Shapley value is the mean value over all extreme points in the core. In addition, a steepest descent algorithm is proposed that converges in polynomial time on the fractional egalitarian solution in the core, which can be implemented by network coding schemes. Finally, it is shown that the game can be decomposed into subgames so that both the Shapley value and the egalitarian solution can be obtained within each subgame in a distributed manner with reduced complexity. Full article
(This article belongs to the Special Issue Machine Learning for Communications)
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