Journal Description
Entropy
Entropy
is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI. The International Society for the Study of Information (IS4SI) and Spanish Society of Biomedical Engineering (SEIB) are affiliated with Entropy and their members receive a discount on the article processing charge.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), Inspec, PubMed, PMC, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Physics, Multidisciplinary) / CiteScore - Q1 (Mathematical Physics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 20.8 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Entropy.
- Companion journals for Entropy include: Foundations, Thermo and MAKE.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.6 (2022)
Latest Articles
Code Similarity Prediction Model for Industrial Management Features Based on Graph Neural Networks
Entropy 2024, 26(6), 505; https://doi.org/10.3390/e26060505 (registering DOI) - 9 Jun 2024
Abstract
The code of industrial management software typically features few system API calls and a high number of customized variables and structures. This makes the similarity of such codes difficult to compute using text features or traditional neural network methods. In this paper, we
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The code of industrial management software typically features few system API calls and a high number of customized variables and structures. This makes the similarity of such codes difficult to compute using text features or traditional neural network methods. In this paper, we propose an FSPS-GNN model, which is based on graph neural networks (GNNs), to address this problem. The model categorizes code features into two types, outer graph and inner graph, and conducts training and prediction with four stages—feature embedding, feature enhancement, feature fusion, and similarity prediction. Moreover, differently structured GNNs were used in the embedding and enhancement stages, respectively, to increase the interaction of code features. Experiments with code from three open-source projects demonstrate that the model achieves an average precision of 87.57% and an F0.5 Score of 89.12%. Compared to existing similarity-computation models based on GNNs, this model exhibits a Mean Squared Error (MSE) that is approximately 0.0041 to 0.0266 lower and an F0.5 Score that is 3.3259% to 6.4392% higher. It broadens the application scope of GNNs and offers additional insights for the study of code-similarity issues.
Full article
(This article belongs to the Special Issue Entropy-Centric Intelligent Computation with Graph: In Pursuit of Advanced Computational Theories, Methods, and Applications)
Open AccessArticle
Derivation of Bose’s Entropy Spectral Density from the Multiplicity of Energy Eigenvalues
by
Arnaldo Spalvieri
Entropy 2024, 26(6), 504; https://doi.org/10.3390/e26060504 (registering DOI) - 9 Jun 2024
Abstract
The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon’s energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to
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The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon’s energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three-dimensional continuous version of the three discrete quantum numbers, which leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose’s entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency.
Full article
(This article belongs to the Section Thermodynamics)
Open AccessArticle
Refinements and Extensions of Ziv’s Model of Perfect Secrecy for Individual Sequences
by
Neri Merhav
Entropy 2024, 26(6), 503; https://doi.org/10.3390/e26060503 (registering DOI) - 9 Jun 2024
Abstract
We refine and extend Ziv’s model and results regarding perfectly secure encryption of individual sequences. According to this model, the encrypter and the legitimate decrypter share a common secret key that is not shared with the unauthorized eavesdropper. The eavesdropper is aware of
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We refine and extend Ziv’s model and results regarding perfectly secure encryption of individual sequences. According to this model, the encrypter and the legitimate decrypter share a common secret key that is not shared with the unauthorized eavesdropper. The eavesdropper is aware of the encryption scheme and has some prior knowledge concerning the individual plaintext source sequence. This prior knowledge, combined with the cryptogram, is harnessed by the eavesdropper, who implements a finite-state machine as a mechanism for accepting or rejecting attempted guesses of the plaintext source. The encryption is considered perfectly secure if the cryptogram does not provide any new information to the eavesdropper that may enhance their knowledge concerning the plaintext beyond their prior knowledge. Ziv has shown that the key rate needed for perfect secrecy is essentially lower bounded by the finite-state compressibility of the plaintext sequence, a bound that is clearly asymptotically attained through Lempel–Ziv compression followed by one-time pad encryption. In this work, we consider some more general classes of finite-state eavesdroppers and derive the respective lower bounds on the key rates needed for perfect secrecy. These bounds are tighter and more refined than Ziv’s bound, and they are attained using encryption schemes that are based on different universal lossless compression schemes. We also extend our findings to the case where side information is available to the eavesdropper and the legitimate decrypter but may or may not be available to the encrypter.
Full article
(This article belongs to the Collection Feature Papers in Information Theory)
Open AccessArticle
Modelling Heterogeneous Anomalous Dynamics of Radiation-Induced Double-Strand Breaks in DNA during Non-Homologous End-Joining Pathway
by
Nickolay Korabel, John W. Warmenhoven, Nicholas T. Henthorn, Samuel Ingram, Sergei Fedotov, Charlotte J. Heaven, Karen J. Kirkby, Michael J. Taylor and Michael J. Merchant
Entropy 2024, 26(6), 502; https://doi.org/10.3390/e26060502 (registering DOI) - 8 Jun 2024
Abstract
The process of end-joining during nonhomologous repair of DNA double-strand breaks (DSBs) after radiation damage is considered. Experimental evidence has revealed that the dynamics of DSB ends exhibit subdiffusive motion rather than simple diffusion with rare directional movement. Traditional models often overlook the
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The process of end-joining during nonhomologous repair of DNA double-strand breaks (DSBs) after radiation damage is considered. Experimental evidence has revealed that the dynamics of DSB ends exhibit subdiffusive motion rather than simple diffusion with rare directional movement. Traditional models often overlook the rare long-range directed motion. To address this limitation, we present a heterogeneous anomalous diffusion model consisting of subdiffusive fractional Brownian motion interchanged with short periods of long-range movement. Our model sheds light on the underlying mechanisms of heterogeneous diffusion in DSB repair and could be used to quantify the DSB dynamics on a time scale inaccessible to single particle tracking analysis. The model predicts that the long-range movement of DSB ends is responsible for the misrepair of DSBs in the form of dicentric chromosome lesions.
Full article
(This article belongs to the Special Issue Random Walks and Stochastic Processes in Complex Systems: From Physics to Socio-Economic Phenomena)
Open AccessArticle
Simultaneous Optimization and Integration of Multiple Process Heat Cascade and Site Utility Selection for the Design of a New Generation of Sugarcane Biorefinery
by
Victor Fernandes Garcia and Adriano Viana Ensinas
Entropy 2024, 26(6), 501; https://doi.org/10.3390/e26060501 (registering DOI) - 8 Jun 2024
Abstract
Biorefinery plays a crucial role in the decarbonization of the current economic model, but its high investments and costs make its products less competitive. Identifying the best technological route to maximize operational synergies is crucial for its viability. This study presents a new
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Biorefinery plays a crucial role in the decarbonization of the current economic model, but its high investments and costs make its products less competitive. Identifying the best technological route to maximize operational synergies is crucial for its viability. This study presents a new superstructure model based on mixed integer linear programming to identify an ideal biorefinery configuration. The proposed formulation considers the selection and process scale adjustment, utility selection, and heat integration by heat cascade integration from different processes. The formulation is tested by a study where the impact of new technologies on energy efficiency and the total annualized cost of a sugarcane biorefinery is evaluated. As a result, the energy efficiency of biorefinery increased from 50.25% to 74.5% with methanol production through bagasse gasification, mainly due to its high heat availability that can be transferred to the distillery, which made it possible to shift the bagasse flow from the cogeneration to gasification process. Additionally, the production of DME yields outcomes comparable to methanol production. However, CO2 hydrogenation negatively impacts profitability and energy efficiency due to the significant consumption and electricity cost. Nonetheless, it is advantageous for surface power density as it increases biofuel production without expanding the biomass area.
Full article
(This article belongs to the Special Issue Thermodynamic Optimization of Industrial Energy Systems)
Open AccessArticle
Intermediate Judgments and Trust in Artificial Intelligence-Supported Decision-Making
by
Scott Humr and Mustafa Canan
Entropy 2024, 26(6), 500; https://doi.org/10.3390/e26060500 (registering DOI) - 8 Jun 2024
Abstract
Human decision-making is increasingly supported by artificial intelligence (AI) systems. From medical imaging analysis to self-driving vehicles, AI systems are becoming organically embedded in a host of different technologies. However, incorporating such advice into decision-making entails a human rationalization of AI outputs for
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Human decision-making is increasingly supported by artificial intelligence (AI) systems. From medical imaging analysis to self-driving vehicles, AI systems are becoming organically embedded in a host of different technologies. However, incorporating such advice into decision-making entails a human rationalization of AI outputs for supporting beneficial outcomes. Recent research suggests intermediate judgments in the first stage of a decision process can interfere with decisions in subsequent stages. For this reason, we extend this research to AI-supported decision-making to investigate how intermediate judgments on AI-provided advice may influence subsequent decisions. In an online experiment (N = 192), we found a consistent bolstering effect in trust for those who made intermediate judgments and over those who did not. Furthermore, violations of total probability were observed at all timing intervals throughout the study. We further analyzed the results by demonstrating how quantum probability theory can model these types of behaviors in human–AI decision-making and ameliorate the understanding of the interaction dynamics at the confluence of human factors and information features.
Full article
(This article belongs to the Section Quantum Information)
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Open AccessReview
On Casimir and Helmholtz Fluctuation-Induced Forces in Micro- and Nano-Systems: Survey of Some Basic Results
by
Daniel Dantchev
Entropy 2024, 26(6), 499; https://doi.org/10.3390/e26060499 - 7 Jun 2024
Abstract
Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces.
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Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force.
Full article
(This article belongs to the Collection Foundations of Statistical Mechanics)
Open AccessArticle
A Semiparametric Bayesian Approach to Heterogeneous Spatial Autoregressive Models
by
Ting Liu, Dengke Xu and Shiqi Ke
Entropy 2024, 26(6), 498; https://doi.org/10.3390/e26060498 - 7 Jun 2024
Abstract
Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed
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Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis–Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method.
Full article
(This article belongs to the Special Issue Markov Chain Monte Carlo for Bayesian Inference)
Open AccessArticle
Finite-Time Dynamics of an Entanglement Engine: Current, Fluctuations and Kinetic Uncertainty Relations
by
Jeanne Bourgeois, Gianmichele Blasi, Shishir Khandelwal and Géraldine Haack
Entropy 2024, 26(6), 497; https://doi.org/10.3390/e26060497 - 7 Jun 2024
Abstract
Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach,
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Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there is more than one possible definition for KURs at finite times. Although the two definitions agree in the steady-state regime, they lead to different parameter ranges for violating KUR at finite times.
Full article
(This article belongs to the Special Issue Advances in Quantum Thermodynamics)
Open AccessArticle
Purported Self-Organized Criticality of the Cardiovascular Function: Methodological Considerations for Zipf’s Law Analysis
by
Jacques-Olivier Fortrat
Entropy 2024, 26(6), 496; https://doi.org/10.3390/e26060496 - 7 Jun 2024
Abstract
Self-organized criticality is a universal theory for dynamical systems that has recently been applied to the cardiovascular system. Precise methodological approaches are essential for understanding the dynamics of cardiovascular self-organized criticality. This study examines how the duration and quality of data recording affect
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Self-organized criticality is a universal theory for dynamical systems that has recently been applied to the cardiovascular system. Precise methodological approaches are essential for understanding the dynamics of cardiovascular self-organized criticality. This study examines how the duration and quality of data recording affect the analysis of cardiovascular self-organized criticality, with a focus on the beat-by-beat heart rate variability time series obtained from seven healthy subjects in a standing position. Drawing a Zipf diagram, we evaluated the distribution of cardiovascular events of bradycardia and tachycardia. We identified tipping points for the distribution of both bradycardia and tachycardia events. By varying the recording durations (1, 2, 5, 10, 20, 30, and 40 min) and sampling frequencies (500, 250, and 100 Hz), we investigated their influence on the observed distributions. While shorter recordings can effectively capture cardiovascular events, they may underestimate the variables describing their distribution. Additionally, the tipping point of the Zipf distribution differs between bradycardia and tachycardia events. Comparisons of the distribution of bradycardia and tachycardia events should be conducted using long data recordings. Utilizing devices with lower sampling frequencies may compromise data fidelity. These insights contribute to refining experimental protocols and advancing our understanding of the complex dynamics underlying cardiovascular regulation.
Full article
(This article belongs to the Special Issue Entropy and Nonlinear Signal Processing in Cardiovascular Applications)
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Open AccessArticle
Neural Activity in Quarks Language: Lattice Field Theory for a Network of Real Neurons
by
Giampiero Bardella, Simone Franchini, Liming Pan, Riccardo Balzan, Surabhi Ramawat, Emiliano Brunamonti, Pierpaolo Pani and Stefano Ferraina
Entropy 2024, 26(6), 495; https://doi.org/10.3390/e26060495 - 6 Jun 2024
Abstract
Brain–computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective
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Brain–computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro and meso scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neuron activity, and generalize the maximum entropy model for neural networks so that the time evolution of the system is also taken into account. This is obtained by bridging particle physics and neuroscience, paving the way for particle physics-inspired models of the neocortex.
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(This article belongs to the Special Issue Entropy and Information in Biological Systems)
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Open AccessArticle
The Information Length Concept Applied to Plasma Turbulence
by
Johan Anderson, Kenji Imadera, Sara Moradi and Tariq Rafiq
Entropy 2024, 26(6), 494; https://doi.org/10.3390/e26060494 - 5 Jun 2024
Abstract
A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position,
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A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position, which is studied in a novel manner using statistical methods. The simulation data exhibit transport processes with both medium and long correlation length along the radius. A typical example of a phenomenon with long correlation length is avalanches. In order to investigate the evolution of the turbulent state, two basic configurations are studied, one flux-driven and one gradient-driven with decaying turbulence. The information length concept in tandem with Boltzmann–Gibbs and Tsallis entropy is used in the investigation. It is found that the dynamical states in both flux-driven and gradient-driven cases are surprisingly similar, but the Tsallis entropy reveals differences between them. This indicates that the types of probability distribution function are nevertheless quite different since the higher moments are significantly different.
Full article
(This article belongs to the Special Issue Editorial Board Members' Collection Series: Nonequilibrium Dynamics and Statistical Theory in Plasmas Physics)
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Open AccessArticle
Classical Modeling of a Lossy Gaussian Bosonic Sampler
by
Mikhail V. Umanskii and Alexey N. Rubtsov
Entropy 2024, 26(6), 493; https://doi.org/10.3390/e26060493 - 5 Jun 2024
Abstract
Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for the approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion, and increasing the number of terms of the
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Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for the approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion, and increasing the number of terms of the expansion that are used in the calculation yields greater accuracy. The complexity of the algorithm is polynomial in the number of modes given the number of terms is fixed. We describe conditions for the input state squeezing parameter and loss level that provide the best efficiency for this algorithm (by efficient, we mean that the Taylor series converges quickly). In recent experiments that claim to have demonstrated quantum advantage, these conditions are satisfied; thus, this algorithm can be used to classically simulate these experiments.
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(This article belongs to the Topic Quantum Information and Quantum Computing, 2nd Volume)
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Open AccessArticle
Chaos-Assisted Dynamical Tunneling in Flat Band Superwires
by
Anton M. Graf, Ke Lin, MyeongSeo Kim, Joonas Keski-Rahkonen, Alvar Daza and Eric J. Heller
Entropy 2024, 26(6), 492; https://doi.org/10.3390/e26060492 - 5 Jun 2024
Abstract
Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static
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Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static or energetic confinement observed in traditional wave guides or one-dimensional electron wires. The quantum properties of superwires give rise to elastic dynamical tunneling, linking disjoint regions of the corresponding classical phase space, and enabling the emergence of several parallel channels. This paper provides the underlying theory and mechanisms that facilitate dynamical tunneling assisted by chaos in periodic lattices. Moreover, we show that the mechanism of dynamical tunneling can be effectively conceptualized through the lens of a paraxial approximation. Our results further reveal that superwires predominantly exist within flat bands, emerging from eigenstates that represent linear combinations of conventional degenerate Bloch states. Finally, we quantify tunneling rates across various lattice configurations and demonstrate that tunneling can be suppressed in a controlled fashion, illustrating potential implications in future nanodevices.
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(This article belongs to the Special Issue Tunneling in Complex Systems)
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Open AccessFeature PaperArticle
Correlations of Cross-Entropy Loss in Machine Learning
by
Richard Connor, Alan Dearle, Ben Claydon and Lucia Vadicamo
Entropy 2024, 26(6), 491; https://doi.org/10.3390/e26060491 - 3 Jun 2024
Abstract
Cross-entropy loss is crucial in training many deep neural networks. In this context, we show a number of novel and strong correlations among various related divergence functions. In particular, we demonstrate that, in some circumstances, (a) cross-entropy is almost perfectly correlated with the
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Cross-entropy loss is crucial in training many deep neural networks. In this context, we show a number of novel and strong correlations among various related divergence functions. In particular, we demonstrate that, in some circumstances, (a) cross-entropy is almost perfectly correlated with the little-known triangular divergence, and (b) cross-entropy is strongly correlated with the Euclidean distance over the logits from which the softmax is derived. The consequences of these observations are as follows. First, triangular divergence may be used as a cheaper alternative to cross-entropy. Second, logits can be used as features in a Euclidean space which is strongly synergistic with the classification process. This justifies the use of Euclidean distance over logits as a measure of similarity, in cases where the network is trained using softmax and cross-entropy. We establish these correlations via empirical observation, supported by a mathematical explanation encompassing a number of strongly related divergence functions.
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(This article belongs to the Section Information Theory, Probability and Statistics)
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Open AccessFeature PaperArticle
Continuous-Time Quantum Walk in Glued Trees: Localized State-Mediated Almost Perfect Quantum-State Transfer
by
Vincent Pouthier, Lucie Pepe and Saad Yalouz
Entropy 2024, 26(6), 490; https://doi.org/10.3390/e26060490 - 2 Jun 2024
Abstract
In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our
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In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our attention on leafier structures where each parent node could give rise to a larger number of children. Through extensive numerical simulations, we uncover a significant dependence of the transfer on the underlying graph architecture, particularly influenced by the branching rate (M) relative to the root degree (N). Our study reveals that the behavior of the walker is isomorphic to that of a particle moving on a finite-size chain. This chain exhibits defects that originate in the specific nature of both the roots and the leaves. Therefore, the energy spectrum of the chain showcases rich features, which lead to diverse regimes for the quantum-state transfer. Notably, the formation of quasi-degenerate localized states due to significant disparities between M and N triggers a localization process on the roots. Through analytical development, we demonstrate that these states play a crucial role in facilitating almost perfect quantum beats between the roots, thereby enhancing the transfer efficiency. Our findings offer valuable insights into the mechanisms governing quantum-state transfer on trees, with potential applications for the transfer of quantum information.
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(This article belongs to the Special Issue Quantum Walks for Quantum Technologies)
Open AccessReview
Entropy and the Limits to Growth
by
Reiner Kümmel
Entropy 2024, 26(6), 489; https://doi.org/10.3390/e26060489 - 31 May 2024
Abstract
In its business-as-usual scenario, the 1972 Club-of-Rome report—The Limits to Growth—describes the collapse of the world economy around the year 2030, either because of the scarcity of natural resources or because of pollution. Mainstream economists, the high priests of secular societies, condemned it
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In its business-as-usual scenario, the 1972 Club-of-Rome report—The Limits to Growth—describes the collapse of the world economy around the year 2030, either because of the scarcity of natural resources or because of pollution. Mainstream economists, the high priests of secular societies, condemned it fiercely. Their gospel of perpetual economic growth, during which technological progress would solve all problems, promises a bright future for all mankind. On the other hand, engineers, natural scientists, and mathematicians realized that the breakdown scenario is due to the inclusion of the First and the Second Law of Thermodynamics in the Club-of-Rome’s world model. According to these laws, nothing happens in the world without energy conversion and entropy production. In 1865, Rudolph Clausius, the discoverer of entropy, published the laws as the constitution of the universe. Entropy is the physical measure of disorder. Without a proper understanding of energy and entropy in the economy, all efforts to achieve sustainability will fail.
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(This article belongs to the Section Complexity)
Open AccessArticle
Quantum Key Distribution with Displaced Thermal States
by
Adam Walton, Anne Ghesquière and Benjamin T.H. Varcoe
Entropy 2024, 26(6), 488; https://doi.org/10.3390/e26060488 - 31 May 2024
Abstract
Secret key exchange relies on the creation of correlated signals, serving as the raw resource for secure communication. Thermal states exhibit Hanbury Brown and Twiss correlations, which offer a promising avenue for generating such signals. In this paper, we present an experimental implementation
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Secret key exchange relies on the creation of correlated signals, serving as the raw resource for secure communication. Thermal states exhibit Hanbury Brown and Twiss correlations, which offer a promising avenue for generating such signals. In this paper, we present an experimental implementation of a central broadcast thermal-state quantum key distribution (QKD) protocol in the microwave region. Our objective is to showcase a straightforward method of QKD utilizing readily available broadcasting equipment. Unlike conventional approaches to thermal-state QKD, we leverage displaced thermal states. These states enable us to share the output of a thermal source among Alice, Bob, and Eve via both waveguide channels and free space. Through measurement and conversion into bit strings, our protocol produces key-ready bit strings without the need for specialized equipment. By harnessing the inherent noise in thermal broadcasts, our setup facilitates the recovery of distinct bit strings by all parties involved.
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(This article belongs to the Special Issue Quantum Resource Theories: From Entanglement to Time Correlations and Measurement-Induced Noise)
Open AccessArticle
A Circular-Linear Probabilistic Model Based on Nonparametric Copula with Applications to Directional Wind Energy Assessment
by
Jie Liu and Zaizai Yan
Entropy 2024, 26(6), 487; https://doi.org/10.3390/e26060487 - 31 May 2024
Abstract
The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated
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The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated in Inner Mongolia, China. Optimal bandwidth algorithms and transformation techniques are used to determine the nonparametric copula method. Various parameter copula models and models without considering dependency relationships are introduced and compared with this approach. The results indicate a significant advantage of employing the nonparametric copula model for fitting joint probability distributions of both wind speed and wind direction, as well as conducting correlation analyses. By utilizing the proposed KDE-COP-CV model, it becomes possible to accurately and reliably analyze how wind power density fluctuates in relation to wind direction. This study reveals the researched region possesses abundant wind resources, with the highest wind power density being highly dependent on wind direction at maximum speeds. Wind resources in selected regions of Inner Mongolia are predominantly concentrated in the northwest and west directions. These findings can contribute to improving the accuracy of micro-siting for wind farms, as well as optimizing the design and capacity of wind turbine generators.
Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
Open AccessArticle
Unveiling Influence in Networks: A Novel Centrality Metric and Comparative Analysis through Graph-Based Models
by
Nada Bendahman and Dounia Lotfi
Entropy 2024, 26(6), 486; https://doi.org/10.3390/e26060486 - 31 May 2024
Abstract
Abstract: Identifying influential actors within social networks is pivotal for optimizing information flow and mitigating the spread of both rumors and viruses. Several methods have emerged to pinpoint these influential entities in networks, represented as graphs. In these graphs, nodes correspond to individuals
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Abstract: Identifying influential actors within social networks is pivotal for optimizing information flow and mitigating the spread of both rumors and viruses. Several methods have emerged to pinpoint these influential entities in networks, represented as graphs. In these graphs, nodes correspond to individuals and edges indicate their connections. This study focuses on centrality measures, prized for their straightforwardness and effectiveness. We divide structural centrality into two categories: local, considering a node’s immediate vicinity, and global, accounting for overarching path structures. Some techniques blend both centralities to highlight nodes influential at both micro and macro levels. Our paper presents a novel centrality measure, accentuating node degree and incorporating the network’s broader features, especially paths of different lengths. Through Spearman and Pearson correlations tested on seven standard datasets, our method proves its merit against traditional centrality measures. Additionally, we employ the susceptible–infected–recovered (SIR) model, portraying virus spread, to further validate our approach. The ultimate influential node is gauged by its capacity to infect the most nodes during the SIR model’s progression. Our results indicate a notable correlative efficacy across various real-world networks relative to other centrality metrics.
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(This article belongs to the Special Issue Advances in Complex Networks and Artificial Intelligence)
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