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
Chip-Based Electronic System for Quantum Key Distribution
Entropy 2024, 26(5), 382; https://doi.org/10.3390/e26050382 (registering DOI) - 29 Apr 2024
Abstract
Quantum Key Distribution (QKD) has garnered significant attention due to its unconditional security based on the fundamental principles of quantum mechanics. While QKD has been demonstrated by various groups and commercial QKD products are available, the development of a fully chip-based QKD system,
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Quantum Key Distribution (QKD) has garnered significant attention due to its unconditional security based on the fundamental principles of quantum mechanics. While QKD has been demonstrated by various groups and commercial QKD products are available, the development of a fully chip-based QKD system, aimed at reducing costs, size, and power consumption, remains a significant technological challenge. Most researchers focus on the optical aspects, leaving the integration of the electronic components largely unexplored. In this paper, we present the design of a fully integrated electrical control chip for QKD applications. The chip, fabricated using 28 nm CMOS technology, comprises five main modules: an ARM processor for digital signal processing, delay cells for timing synchronization, ADC for sampling analog signals from monitors, OPAMP for signal amplification, and DAC for generating the required voltage for phase or intensity modulators. According to the simulations, the minimum delay is 11ps, the open-loop gain of the operational amplifier is 86.2 dB, the sampling rate of the ADC reaches 50 MHz, and the DAC achieves a high rate of 100 MHz. To the best of our knowledge, this marks the first design and evaluation of a fully integrated driver chip for QKD, holding the potential to significantly enhance QKD system performance. Thus, we believe our work could inspire future investigations toward the development of more efficient and reliable QKD systems.
Full article
(This article belongs to the Special Issue Progress in Quantum Key Distribution)
Open AccessArticle
In Search of Dispersed Memories: Generative Diffusion Models Are Associative Memory Networks
by
Luca Ambrogioni
Entropy 2024, 26(5), 381; https://doi.org/10.3390/e26050381 (registering DOI) - 29 Apr 2024
Abstract
Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological memory. Generative diffusion models are a type of generative machine learning
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Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological memory. Generative diffusion models are a type of generative machine learning techniques that have shown great performance in many tasks. Similar to associative memory systems, these networks define a dynamical system that converges to a set of target states. In this work, we show that generative diffusion models can be interpreted as energy-based models and that, when trained on discrete patterns, their energy function is (asymptotically) identical to that of modern Hopfield networks. This equivalence allows us to interpret the supervised training of diffusion models as a synaptic learning process that encodes the associative dynamics of a modern Hopfield network in the weight structure of a deep neural network. Leveraging this connection, we formulate a generalized framework for understanding the formation of long-term memory, where creative generation and memory recall can be seen as parts of a unified continuum.
Full article
(This article belongs to the Special Issue Deep Generative Modeling: Theory and Applications)
Open AccessArticle
Application of Recurrence Plot Analysis to Examine Dynamics of Biological Molecules on the Example of Aggregation of Seed Mucilage Components
by
Piotr Sionkowski, Natalia Kruszewska, Agnieszka Kreitschitz, Stanislav N. Gorb and Krzysztof Domino
Entropy 2024, 26(5), 380; https://doi.org/10.3390/e26050380 (registering DOI) - 29 Apr 2024
Abstract
The goal of the research is to describe the aggregation process inside the mucilage produced by plant seeds using molecular dynamics (MD) combined with time series algorithmic analysis based on the recurrence plots. The studied biological molecules model is seed mucilage composed of
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The goal of the research is to describe the aggregation process inside the mucilage produced by plant seeds using molecular dynamics (MD) combined with time series algorithmic analysis based on the recurrence plots. The studied biological molecules model is seed mucilage composed of three main polysaccharides, i.e. pectins, hemicellulose, and cellulose. The modeling of biological molecules is based on the assumption that a classical–quantum passage underlies the aggregation process in the mucilage, resulting from non-covalent interactions, as they affect the macroscopic properties of the system. The applied recurrence plot approach is an important tool for time series analysis and data mining dedicated to analyzing time series data originating from complex, chaotic systems. In the current research, we demonstrated that advanced algorithmic analysis of seed mucilage data can reveal some features of the dynamics of the system, namely temperature-dependent regions with different dynamics of increments of a number of hydrogen bonds and regions of stable oscillation of increments of a number of hydrophobic–polar interactions. Henceforth, we pave the path for automatic data-mining methods for the analysis of biological molecules with the intermediate step of the application of recurrence plot analysis, as the generalization of recurrence plot applications to other (biological molecules) datasets is straightforward.
Full article
(This article belongs to the Section Statistical Physics)
Open AccessArticle
Virtual Photon-Mediated Quantum State Transfer and Remote Entanglement between Spin Qubits in Quantum Dots Using Superadiabatic Pulses
by
Yue Wang, Ting Wang and Xing-Yu Zhu
Entropy 2024, 26(5), 379; https://doi.org/10.3390/e26050379 (registering DOI) - 29 Apr 2024
Abstract
Spin qubits in semiconductor quantum dots are an attractive candidate for scalable quantum information processing. Reliable quantum state transfer and entanglement between spatially separated spin qubits is a highly desirable but challenging goal. Here, we propose a fast and high-fidelity quantum state transfer
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Spin qubits in semiconductor quantum dots are an attractive candidate for scalable quantum information processing. Reliable quantum state transfer and entanglement between spatially separated spin qubits is a highly desirable but challenging goal. Here, we propose a fast and high-fidelity quantum state transfer scheme for two spin qubits mediated by virtual microwave photons. Our general strategy involves using a superadiabatic pulse to eliminate non-adiabatic transitions, without the need for increased control complexity. We show that arbitrary quantum state transfer can be achieved with a fidelity of within a 60 ns short time under realistic parameter conditions. We also demonstrate the robustness of this scheme to experimental imperfections and environmental noises. Furthermore, this scheme can be directly applied to the generation of a remote Bell entangled state with a fidelity as high as . These results pave the way for fault-tolerant quantum computation on spin quantum network architecture platforms.
Full article
(This article belongs to the Section Quantum Information)
Open AccessArticle
Systemic Importance and Risk Characteristics of Banks Based on a Multi-Layer Financial Network Analysis
by
Qianqian Gao, Hong Fan and Chengyang Yu
Entropy 2024, 26(5), 378; https://doi.org/10.3390/e26050378 (registering DOI) - 29 Apr 2024
Abstract
Domestic and international risk shocks have greatly increased the demand for systemic risk management in China. This paper estimates China’s multi-layer financial network based on multiple financial relationships among banks, assets, and firms, using China’s banking system data in 2021. An improved PageRank
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Domestic and international risk shocks have greatly increased the demand for systemic risk management in China. This paper estimates China’s multi-layer financial network based on multiple financial relationships among banks, assets, and firms, using China’s banking system data in 2021. An improved PageRank algorithm is proposed to identify systemically important banks and other economic sectors, and a stress test is conducted. This study finds that China’s multi-layer financial network is sparse, and the distribution of transactions across financial markets is uneven. Regulatory authorities should support economic recovery and adjust the money supply, while banks should differentiate competition and manage risks better. Based on the PageRank index, this paper assesses the systemic importance of large commercial banks from the perspective of network structure, emphasizing the role of banks’ transaction behavior and market participation. Different industries and asset classes are also assessed, suggesting that increased attention should be paid to industry risks and regulatory oversight of bank investments. Finally, stress tests confirm that the improved PageRank algorithm is applicable within the multi-layer financial network, reinforcing the need for prudential supervision of the banking system and revealing that the degree of transaction concentration will affect the systemic importance of financial institutions.
Full article
(This article belongs to the Special Issue Complexity in Financial Networks)
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Open AccessArticle
Modeling Tree-like Heterophily on Symmetric Matrix Manifolds
by
Yang Wu, Liang Hu and Juncheng Hu
Entropy 2024, 26(5), 377; https://doi.org/10.3390/e26050377 (registering DOI) - 29 Apr 2024
Abstract
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Tree-like structures, characterized by hierarchical relationships and power-law distributions, are prevalent in a multitude of real-world networks, ranging from social networks to citation networks and protein–protein interaction networks. Recently, there has been significant interest in utilizing hyperbolic space to model these structures, owing
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Tree-like structures, characterized by hierarchical relationships and power-law distributions, are prevalent in a multitude of real-world networks, ranging from social networks to citation networks and protein–protein interaction networks. Recently, there has been significant interest in utilizing hyperbolic space to model these structures, owing to its capability to represent them with diminished distortions compared to flat Euclidean space. However, real-world networks often display a blend of flat, tree-like, and circular substructures, resulting in heterophily. To address this diversity of substructures, this study aims to investigate the reconstruction of graph neural networks on the symmetric manifold, which offers a comprehensive geometric space for more effective modeling of tree-like heterophily. To achieve this objective, we propose a graph convolutional neural network operating on the symmetric positive-definite matrix manifold, leveraging Riemannian metrics to facilitate the scheme of information propagation. Extensive experiments conducted on semi-supervised node classification tasks validate the superiority of the proposed approach, demonstrating that it outperforms comparative models based on Euclidean and hyperbolic geometries.
Full article
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Open AccessArticle
Fast Fusion Clustering via Double Random Projection
by
Hongni Wang, Na Li, Yanqiu Zhou, Jingxin Yan, Bei Jiang, Linglong Kong and Xiaodong Yan
Entropy 2024, 26(5), 376; https://doi.org/10.3390/e26050376 (registering DOI) - 28 Apr 2024
Abstract
In unsupervised learning, clustering is a common starting point for data processing. The convex or concave fusion clustering method is a novel approach that is more stable and accurate than traditional methods such as k-means and hierarchical clustering. However, the optimization algorithm
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In unsupervised learning, clustering is a common starting point for data processing. The convex or concave fusion clustering method is a novel approach that is more stable and accurate than traditional methods such as k-means and hierarchical clustering. However, the optimization algorithm used with this method can be slowed down significantly by the complexity of the fusion penalty, which increases the computational burden. This paper introduces a random projection ADMM algorithm based on the Bernoulli distribution and develops a double random projection ADMM method for high-dimensional fusion clustering. These new approaches significantly outperform the classical ADMM algorithm due to their ability to significantly increase computational speed by reducing complexity and improving clustering accuracy by using multiple random projections under a new evaluation criterion. We also demonstrate the convergence of our new algorithm and test its performance on both simulated and real data examples.
Full article
(This article belongs to the Special Issue Big Data Analytics and Information Science for Business and Biomedical Applications: Third Edition)
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Open AccessArticle
Likelihood Ratio Test and the Evidential Approach for 2 × 2 Tables
by
Peter M. B. Cahusac
Entropy 2024, 26(5), 375; https://doi.org/10.3390/e26050375 (registering DOI) - 28 Apr 2024
Abstract
Categorical data analysis of 2 × 2 contingency tables is extremely common, not least because they provide risk difference, risk ratio, odds ratio, and log odds statistics in medical research. A test analysis is most often used, although some researchers use
[...] Read more.
Categorical data analysis of 2 × 2 contingency tables is extremely common, not least because they provide risk difference, risk ratio, odds ratio, and log odds statistics in medical research. A test analysis is most often used, although some researchers use likelihood ratio test (LRT) analysis. Does it matter which test is used? A review of the literature, examination of the theoretical foundations, and analyses of simulations and empirical data are used by this paper to argue that only the LRT should be used when we are interested in testing whether the binomial proportions are equal. This so-called test of independence is by far the most popular, meaning the test is widely misused. By contrast, the test should be reserved for where the data appear to match too closely a particular hypothesis (e.g., the null hypothesis), where the variance is of interest, and is less than expected. Low variance can be of interest in various scenarios, particularly in investigations of data integrity. Finally, it is argued that the evidential approach provides a consistent and coherent method that avoids the difficulties posed by significance testing. The approach facilitates the calculation of appropriate log likelihood ratios to suit our research aims, whether this is to test the proportions or to test the variance. The conclusions from this paper apply to larger contingency tables, including multi-way tables.
Full article
(This article belongs to the Special Issue Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications)
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Open AccessArticle
Novel Entropy for Enhanced Thermal Imaging and Uncertainty Quantification
by
Hrach Ayunts, Artyom Grigoryan and Sos Agaian
Entropy 2024, 26(5), 374; https://doi.org/10.3390/e26050374 (registering DOI) - 28 Apr 2024
Abstract
This paper addresses the critical need for precise thermal modeling in electronics, where temperature significantly impacts system reliability. We emphasize the necessity of accurate temperature measurement and uncertainty quantification in thermal imaging, a vital tool across multiple industries. Current mathematical models and uncertainty
[...] Read more.
This paper addresses the critical need for precise thermal modeling in electronics, where temperature significantly impacts system reliability. We emphasize the necessity of accurate temperature measurement and uncertainty quantification in thermal imaging, a vital tool across multiple industries. Current mathematical models and uncertainty measures, such as Rényi and Shannon entropies, are inadequate for the detailed informational content required in thermal images. Our work introduces a novel entropy that effectively captures the informational content of thermal images by combining local and global data, surpassing existing metrics. Validated by rigorous experimentation, this method enhances thermal images’ reliability and information preservation. We also present two enhancement frameworks that integrate an optimized genetic algorithm and image fusion techniques, improving image quality by reducing artifacts and enhancing contrast. These advancements offer significant contributions to thermal imaging and uncertainty quantification, with broad applications in various sectors.
Full article
(This article belongs to the Special Issue Thermal Science and Engineering Applications)
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Open AccessArticle
Optimal Quaternary Hermitian LCD Codes
by
Liangdong Lu, Ruihu Li and Yuezhen Ren
Entropy 2024, 26(5), 373; https://doi.org/10.3390/e26050373 (registering DOI) - 28 Apr 2024
Abstract
Linear complementary dual (LCD) codes, which are a class of linear codes introduced by Massey, have been extensively studied in the literature recently. It has been shown that LCD codes play a role in measures to counter passive and active side-channel analyses on
[...] Read more.
Linear complementary dual (LCD) codes, which are a class of linear codes introduced by Massey, have been extensively studied in the literature recently. It has been shown that LCD codes play a role in measures to counter passive and active side-channel analyses on embedded cryptosystems. In this paper, tables are presented of good quaternary Hermitian LCD codes and they are used in the construction of puncturing, shortening and combination codes. The results of this, including three tables of the best-known quaternary Hermitian LCD codes of any length with corresponding dimension k, are presented. In addition, many of these quaternary Hermitian LCD codes given in this paper are optimal and saturate the lower or upper bound of Grassl’s code table, and some of them are nearly optimal.
Full article
(This article belongs to the Special Issue Discrete Math in Coding Theory)
Open AccessArticle
Phase Space Spin-Entropy
by
Davi Geiger
Entropy 2024, 26(5), 372; https://doi.org/10.3390/e26050372 (registering DOI) - 28 Apr 2024
Abstract
Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a
[...] Read more.
Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a quantum state are position and spin. We focus on the spin degree of freedom and elucidate the spin-entropy. Then, we present some of its properties and show how entanglement increases spin-entropy. A dynamic model for the time evolution of spin-entropy concludes the paper.
Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
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Open AccessArticle
A Personalized Collaborative Filtering Recommendation System Based on Bi-Graph Embedding and Causal Reasoning
by
Xiaoli Huang, Junjie Wang and Junying Cui
Entropy 2024, 26(5), 371; https://doi.org/10.3390/e26050371 (registering DOI) - 28 Apr 2024
Abstract
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The integration of graph embedding technology and collaborative filtering algorithms has shown promise in enhancing the performance of recommendation systems. However, existing integrated recommendation algorithms often suffer from feature bias and lack effectiveness in personalized user recommendation. For instance, users’ historical interactions with
[...] Read more.
The integration of graph embedding technology and collaborative filtering algorithms has shown promise in enhancing the performance of recommendation systems. However, existing integrated recommendation algorithms often suffer from feature bias and lack effectiveness in personalized user recommendation. For instance, users’ historical interactions with a certain class of items may inaccurately lead to recommendations of all items within that class, resulting in feature bias. Moreover, accommodating changes in user interests over time poses a significant challenge. This study introduces a novel recommendation model, RCKFM, which addresses these shortcomings by leveraging the CoFM model, TransR graph embedding model, backdoor tuning of causal inference, KL divergence, and the factorization machine model. RCKFM focuses on improving graph embedding technology, adjusting feature bias in embedding models, and achieving personalized recommendations. Specifically, it employs the TransR graph embedding model to handle various relationship types effectively, mitigates feature bias using causal inference techniques, and predicts changes in user interests through KL divergence, thereby enhancing the accuracy of personalized recommendations. Experimental evaluations conducted on publicly available datasets, including “MovieLens-1M” and “Douban dataset” from Kaggle, demonstrate the superior performance of the RCKFM model. The results indicate a significant improvement of between 3.17% and 6.81% in key indicators such as precision, recall, normalized discount cumulative gain, and hit rate in the top-10 recommendation tasks. These findings underscore the efficacy and potential impact of the proposed RCKFM model in advancing recommendation systems.
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Open AccessArticle
Intrinsic Information-Theoretic Models
by
D. Bernal-Casas and J. M. Oller
Entropy 2024, 26(5), 370; https://doi.org/10.3390/e26050370 (registering DOI) - 28 Apr 2024
Abstract
With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate
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With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions ( , , as before, but with a constant not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution with a constant variance–covariance matrix not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger’s equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of , altogether leading to the concept of “intrinsic”. Similarly, as in our previous work with the estimator’s variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the “intrinsic” Cramér–Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of “intrinsic” information-theoretic models, which are essential for developing physics.
Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Reversibility and Time Arrow in Quantum Theory)
Open AccessArticle
A Comparative Analysis of Discrete Entropy Estimators for Large-Alphabet Problems
by
Assaf Pinchas, Irad Ben-Gal and Amichai Painsky
Entropy 2024, 26(5), 369; https://doi.org/10.3390/e26050369 (registering DOI) - 28 Apr 2024
Abstract
This paper presents a comparative study of entropy estimation in a large-alphabet regime. A variety of entropy estimators have been proposed over the years, where each estimator is designed for a different setup with its own strengths and caveats. As a consequence, no
[...] Read more.
This paper presents a comparative study of entropy estimation in a large-alphabet regime. A variety of entropy estimators have been proposed over the years, where each estimator is designed for a different setup with its own strengths and caveats. As a consequence, no estimator is known to be universally better than the others. This work addresses this gap by comparing twenty-one entropy estimators in the studied regime, starting with the simplest plug-in estimator and leading up to the most recent neural network-based and polynomial approximate estimators. Our findings show that the estimators’ performance highly depends on the underlying distribution. Specifically, we distinguish between three types of distributions, ranging from uniform to degenerate distributions. For each class of distribution, we recommend the most suitable estimator. Further, we propose a sample-dependent approach, which again considers three classes of distribution, and report the top-performing estimators in each class. This approach provides a data-dependent framework for choosing the desired estimator in practical setups.
Full article
(This article belongs to the Special Issue Information Theory for Data Science)
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Open AccessArticle
Learning in Deep Radial Basis Function Networks
by
Fabian Wurzberger and Friedhelm Schwenker
Entropy 2024, 26(5), 368; https://doi.org/10.3390/e26050368 (registering DOI) - 26 Apr 2024
Abstract
Learning in neural networks with locally-tuned neuron models such as radial Basis Function (RBF) networks is often seen as instable, in particular when multi-layered architectures are used. Furthermore, universal approximation theorems for single-layered RBF networks are very well established; therefore, deeper architectures are
[...] Read more.
Learning in neural networks with locally-tuned neuron models such as radial Basis Function (RBF) networks is often seen as instable, in particular when multi-layered architectures are used. Furthermore, universal approximation theorems for single-layered RBF networks are very well established; therefore, deeper architectures are theoretically not required. Consequently, RBFs are mostly used in a single-layered manner. However, deep neural networks have proven their effectiveness on many different tasks. In this paper, we show that deeper RBF architectures with multiple radial basis function layers can be designed together with efficient learning schemes. We introduce an initialization scheme for deep RBF networks based on k-means clustering and covariance estimation. We further show how to make use of convolutions to speed up the calculation of the Mahalanobis distance in a partially connected way, which is similar to the convolutional neural networks (CNNs). Finally, we evaluate our approach on image classification as well as speech emotion recognition tasks. Our results show that deep RBF networks perform very well, with comparable results to other deep neural network types, such as CNNs.
Full article
Open AccessFeature PaperArticle
Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement
by
Andrea Crisanti, Luca Salasnich, Alessandro Sarracino and Marco Zannetti
Entropy 2024, 26(5), 367; https://doi.org/10.3390/e26050367 (registering DOI) - 26 Apr 2024
Abstract
We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose–Einstein
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We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose–Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled optical microcavity under genuine grand canonical conditions, we apply our formalism to a system of non-interacting Bose particles confined in a two-dimensional harmonic trap. We discuss in detail the mathematical origin of the inequivalence of ensembles observed in the condensed phase, giving place to the so-called grand canonical catastrophe of density fluctuations. We also provide explicit analytical expressions for the internal energy and specific heat and compare them with available experimental data. For these quantities, we show the equivalence of ensembles in the thermodynamic limit.
Full article
(This article belongs to the Special Issue Matter-Aggregating Systems at a Classical vs. Quantum Interface)
Open AccessPerspective
Quo Vadis Particula Physica?
by
Xavier Calmet
Entropy 2024, 26(5), 366; https://doi.org/10.3390/e26050366 - 26 Apr 2024
Abstract
In this brief paper, I give a very personal account on the state of particle physics on the occasion of Paul Frampton’s 80th birthday.
Full article
(This article belongs to the Special Issue Particle Theory and Theoretical Cosmology—Dedicated to Professor Paul Howard Frampton on the Occasion of His 80th Birthday)
Open AccessArticle
Impact of Normalization on Entropy-Based Weights in Hellwig’s Method: A Case Study on Evaluating Sustainable Development in the Education Area
by
Ewa Roszkowska and Tomasz Wachowicz
Entropy 2024, 26(5), 365; https://doi.org/10.3390/e26050365 - 26 Apr 2024
Abstract
Determining criteria weights plays a crucial role in multi-criteria decision analyses. Entropy is a significant measure in information science, and several multi-criteria decision-making methods utilize the entropy weight method (EWM). In the literature, two approaches for determining the entropy weight method can be
[...] Read more.
Determining criteria weights plays a crucial role in multi-criteria decision analyses. Entropy is a significant measure in information science, and several multi-criteria decision-making methods utilize the entropy weight method (EWM). In the literature, two approaches for determining the entropy weight method can be found. One involves normalization before calculating the entropy values, while the second does not. This paper investigates the normalization effect for entropy-based weights and Hellwig’s method. To compare the influence of various normalization methods in both the EWM and Hellwig’s method, a study evaluating the sustainable development of EU countries in the education area in the year 2021 was analyzed. The study used data from Eurostat related to European countries’ realization of the SDG 4 goal. It is observed that vector normalization and sum normalization did not change the entropy-based weights. In the case study, the max–min normalization influenced EWM weights. At the same time, these weights had only a very weak impact on the final rankings of countries with respect to achieving the SDG 4 goal, as determined by Hellwig’s method. The results are compared with the outcome obtained by Hellwig’s method with equal weights. The simulation study was conducted by modifying Eurostat data to investigate how the different normalization relationships discovered among the criteria affect entropy-based weights and Hellwig’s method results.
Full article
(This article belongs to the Section Multidisciplinary Applications)
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Open AccessArticle
Minimizing Entropy and Complexity in Creative Production from Emergent Pragmatics to Action Semantics
by
Stephen Fox
Entropy 2024, 26(5), 364; https://doi.org/10.3390/e26050364 - 26 Apr 2024
Abstract
New insights into intractable industrial challenges can be revealed by framing them in terms of natural science. One intractable industrial challenge is that creative production can be much more financially expensive and time consuming than standardized production. Creative products include a wide range
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New insights into intractable industrial challenges can be revealed by framing them in terms of natural science. One intractable industrial challenge is that creative production can be much more financially expensive and time consuming than standardized production. Creative products include a wide range of goods that have one or more original characteristics. The scaling up of creative production is hindered by high financial production costs and long production durations. In this paper, creative production is framed in terms of interactions between entropy and complexity during progressions from emergent pragmatics to action semantics. An analysis of interactions between entropy and complexity is provided that relates established practice in creative production to organizational survival in changing environments. The analysis in this paper is related to assembly theory, which is a recent theoretical development in natural science that addresses how open-ended generation of complex physical objects can emerge from selection in biology. Parallels between assembly practice in industrial production and assembly theory in natural science are explained through constructs that are common to both, such as assembly index. Overall, analyses reported in the paper reveal that interactions between entropy and complexity underlie intractable challenges in creative production, from the production of individual products to the survival of companies.
Full article
(This article belongs to the Special Issue Entropy and Organization in Natural and Social Systems II)
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Open AccessArticle
An Entropic Analysis of Social Demonstrations
by
Daniel Rico and Yérali Gandica
Entropy 2024, 26(5), 363; https://doi.org/10.3390/e26050363 - 25 Apr 2024
Abstract
Social media has dramatically influenced how individuals and groups express their demands, concerns, and aspirations during social demonstrations. The study of X or Twitter hashtags during those events has revealed the presence of some temporal points characterised by high correlation among their participants.
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Social media has dramatically influenced how individuals and groups express their demands, concerns, and aspirations during social demonstrations. The study of X or Twitter hashtags during those events has revealed the presence of some temporal points characterised by high correlation among their participants. It has also been reported that the connectivity presents a modular-to-nested transition at the point of maximum correlation. The present study aims to determine whether it is possible to characterise this transition using entropic-based tools. Our results show that entropic analysis can effectively find the transition point to the nested structure, allowing researchers to know that the transition occurs without the need for a network representation. The entropic analysis also shows that the modular-to-nested transition is characterised not by the diversity in the number of hashtags users post but by how many hashtags they share.
Full article
(This article belongs to the Special Issue Complex Systems Approach to Social Dynamics)
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Topics
Topic in
Algorithms, Computation, Entropy, Fractal Fract, MCA
Analytical and Numerical Methods for Stochastic Biological Systems
Topic Editors: Mehmet Yavuz, Necati Ozdemir, Mouhcine Tilioua, Yassine SabbarDeadline: 10 May 2024
Topic in
Algorithms, Diagnostics, Entropy, Information, J. Imaging
Application of Machine Learning in Molecular Imaging
Topic Editors: Allegra Conti, Nicola Toschi, Marianna Inglese, Andrea Duggento, Matthew Grech-Sollars, Serena Monti, Giancarlo Sportelli, Pietro CarraDeadline: 31 May 2024
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Education Sciences, Entropy, JAL, Societies, Sustainability
Sustainability in Aging and Depopulation Societies
Topic Editors: Shiro Horiuchi, Gregor Wolbring, Takeshi MatsudaDeadline: 15 June 2024
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Buildings, Energies, Entropy, Resources, Sustainability
Advances in Solar Heating and Cooling
Topic Editors: Salvatore Vasta, Sotirios Karellas, Marina Bonomolo, Alessio Sapienza, Uli JakobDeadline: 30 June 2024
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28–31 May 2024
XXII Conference on Non-equilibrium Statistical Mechanics and Nonlinear Physics—MEDYFINOL 2024
Special Issues
Special Issue in
Entropy
The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies
Guest Editor: Edward BormashenkoDeadline: 30 April 2024
Special Issue in
Entropy
Information Theory for Interpretable Machine Learning
Guest Editors: Sotiris Kotsiantis, Marco PiangerelliDeadline: 15 May 2024
Special Issue in
Entropy
Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications
Guest Editors: Brian Dennis, Mark L. Taper, Jose Miguel PoncianoDeadline: 31 May 2024
Special Issue in
Entropy
Nonlinear Dynamics in Cardiovascular Signals
Guest Editor: Claudia LermaDeadline: 15 June 2024
Topical Collections
Topical Collection in
Entropy
Algorithmic Information Dynamics: A Computational Approach to Causality from Cells to Networks
Collection Editors: Hector Zenil, Felipe Abrahão
Topical Collection in
Entropy
Wavelets, Fractals and Information Theory
Collection Editor: Carlo Cattani
Topical Collection in
Entropy
Entropy in Image Analysis
Collection Editor: Amelia Carolina Sparavigna