Entropy

17 pages, 4827 KiB

Open AccessArticle

Compressed Adaptive-Sampling-Rate Image Sensing Based on Overcomplete Dictionary

by Jianming Wang, Dingpeng Li, Qingqing Yang and Yi Peng

Entropy 2025, 27(7), 709; https://doi.org/10.3390/e27070709 (registering DOI) - 30 Jun 2025

In this paper, a compressed adaptive image-sensing method based on an overcomplete ridgelet dictionary is proposed. Some low-complexity operations are designed to distinguish between smooth blocks and texture blocks in the compressed domain, and adaptive sampling is performed by assigning different sampling rates [...] Read more.

In this paper, a compressed adaptive image-sensing method based on an overcomplete ridgelet dictionary is proposed. Some low-complexity operations are designed to distinguish between smooth blocks and texture blocks in the compressed domain, and adaptive sampling is performed by assigning different sampling rates to different types of blocks. The efficient, sparse representation of images is achieved by using an overcomplete ridgelet dictionary; at the same time, a reasonable dictionary-partitioning method is designed, which effectively reduces the number of candidate dictionary atoms and greatly improves the speed of classification. Unlike existing methods, the proposed method does not rely on the original signal, and computation is simple, making it particularly suitable for scenarios where a device’s computing power is limited. At the same time, the proposed method can accurately identify smooth image blocks and more reasonably allocate sampling rates to obtain a reconstructed image with better quality. The experimental results show that our method’s image reconstruction quality is superior to that of existing ARCS methods and still maintains low computational complexity. Full article

(This article belongs to the Section Signal and Data Analysis)

7 pages, 156 KiB

Open AccessEditorial

Advancements in Information-Theoretic Methods for Data Analytics

by Kichun Lee

Entropy 2025, 27(7), 708; https://doi.org/10.3390/e27070708 (registering DOI) - 30 Jun 2025

Abstract

A defining feature of the current epoch is a historically unparalleled increase in information, data that originates from a wide spectrum of scientific disciplines, industrial processes, and societal interactions [...] Full article

(This article belongs to the Special Issue Information-Theoretic Methods in Data Analytics)

23 pages, 3224 KiB

Open AccessArticle

Inferring Cinematic Aesthetic Biases from the Statistics of Early Movies

by Daniel M. Grzywacz and Norberto M. Grzywacz

Entropy 2025, 27(7), 707; https://doi.org/10.3390/e27070707 (registering DOI) - 30 Jun 2025

Abstract

Cinematic aesthetic values have not been studied as thoroughly as those in music and the visual arts. Three hypotheses for these values are that they are like those of artistic paintings, that they emphasize the spatial coherence of the optical flow, and that [...] Read more.

Cinematic aesthetic values have not been studied as thoroughly as those in music and the visual arts. Three hypotheses for these values are that they are like those of artistic paintings, that they emphasize the spatial coherence of the optical flow, and that they are temporally smooth. Here, we test these hypotheses and investigate other candidate aesthetic values by comparing the statistics of narrative movies and those obtained spontaneously. We perform these tests by using narrative movies from the early stages of cinematic history because these films are simple. We statistically compare these films with spontaneous movies of scenes from daily life. These statistical comparisons do not support the first hypothesis for early movies. The comparisons show that symmetry, balance, and image complexity (normalized Shannon entropy) are not different in early and spontaneous movies. For similar reasons, our data do not support the spatial coherence of early-movie optical flows as having cinematic aesthetic functions. However, in support of the third hypothesis, the temporal smoothness of luminance, but not of motions, appears to have cinematic aesthetic value. The data also uncovered two other cinematic aesthetic value candidates in both statistical surprise and spatial and temporal complexities. We discuss these candidates, pointing out similarities to music and the importance of film editing. Full article

(This article belongs to the Section Multidisciplinary Applications)

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13 pages, 278 KiB

Open AccessArticle

Two-Level Regular Designs for Baseline Parameterization

by Shengli Zhao and Mengru Qin

Entropy 2025, 27(7), 706; https://doi.org/10.3390/e27070706 (registering DOI) - 30 Jun 2025

Abstract

This paper considers two-level regular fractional factorial designs for baseline parameterization. Some new results that reveal relationships between the K-values and word length pattern are developed. The new results help find two-level regular fractional factorial designs that are likely to be optimal [...] Read more.

This paper considers two-level regular fractional factorial designs for baseline parameterization. Some new results that reveal relationships between the K-values and word length pattern are developed. The new results help find two-level regular fractional factorial designs that are likely to be optimal under the K-aberration criterion. Illustrative examples are included to demonstrate this point. Full article

(This article belongs to the Special Issue Number Theoretic Methods in Statistics: Theory and Applications)

17 pages, 2680 KiB

Open AccessArticle

Application of Shannon Entropy to Reaction–Diffusion Problems Using the Stochastic Finite Difference Method

by Marcin Kamiński and Rafał Leszek Ossowski

Entropy 2025, 27(7), 705; https://doi.org/10.3390/e27070705 (registering DOI) - 30 Jun 2025

Abstract

In this study, we introduce Shannon entropy as a key metric for assessing concentration variability in diffusion processes. Shannon entropy quantifies the uncertainty or disorder in the spatial distribution of diffusing particles, providing a novel perspective on diffusion dynamics. This proposed approach enables [...] Read more.

In this study, we introduce Shannon entropy as a key metric for assessing concentration variability in diffusion processes. Shannon entropy quantifies the uncertainty or disorder in the spatial distribution of diffusing particles, providing a novel perspective on diffusion dynamics. This proposed approach enables a more comprehensive characterization of mixing efficiency, equilibrium states, and transient diffusion behavior. Numerical simulations performed using the finite difference method in the MAPLE 2025 symbolic computing environment illustrate how entropy evolution correlates with diffusion kinetics. The computational model used in this study is based on a previously developed framework from our earlier research, ensuring consistency and validation of the results. The findings suggest that Shannon entropy can serve as a robust descriptor of diffusion-driven mixing, with potential applications in engineering, environmental science, and biophysics. Full article

(This article belongs to the Special Issue Uncertainty Quantification and Entropy Analysis)

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36 pages, 4216 KiB

Open AccessArticle

Research on the Tail Risk Spillover Effect of Cryptocurrencies and Energy Market Based on Complex Network

by Xiao-Li Gong and Xue-Ting Wang

Entropy 2025, 27(7), 704; https://doi.org/10.3390/e27070704 (registering DOI) - 30 Jun 2025

Abstract

As the relationship between cryptocurrency mining activities and electricity consumption becomes increasingly close, the risk spillover effect is steadily drawing a lot of attention to the energy and cryptocurrency markets. For the purpose of studying the risk contagion between the cryptocurrency and energy [...] Read more.

As the relationship between cryptocurrency mining activities and electricity consumption becomes increasingly close, the risk spillover effect is steadily drawing a lot of attention to the energy and cryptocurrency markets. For the purpose of studying the risk contagion between the cryptocurrency and energy market, this paper constructs a risk contagion network between cryptocurrency and China’s energy market using complex network methods. The tail risk spillover effects under various time and frequency domains were captured by the spillover index, which was assessed by the leptokurtic quantile vector autoregression (QVAR) model. Considering the spatial heterogeneity of energy companies, the spatial Durbin model was used to explore the impact mechanism of risk spillovers. The research showed that the framework of this paper more accurately reflects the tail risk spillover effect between China’s energy market and cryptocurrency market under various shock scales, with the extreme state experiencing a much higher spillover effect than the normal state. Furthermore, this study found that the tail risk contagion between cryptocurrency and China’s energy market exhibits notable dynamic variation and cyclical features, and the long-term risk spillover effect is primarily responsible for the total spillover. At the same time, the study found that the company with the most significant spillover effect does not necessarily have the largest company size, and other factors, such as geographical location and business composition, need to be considered. Moreover, there are spatial spillover effects among listed energy companies, and the connectedness between cryptocurrency and the energy market network generates an obvious impact on risk spillover effects. The research conclusions have an important role in preventing cross-contagion of risks between cryptocurrency and the energy market. Full article

(This article belongs to the Special Issue Complexity of Social Networks)

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20 pages, 547 KiB

Open AccessArticle

Fine-Grained Semantics-Enhanced Graph Neural Network Model for Person-Job Fit

by Xia Xue, Jingwen Wang, Bo Ma, Jing Ren, Wujie Zhang, Shuling Gao, Miao Tian, Yue Chang, Chunhong Wang and Hongyu Wang

Entropy 2025, 27(7), 703; https://doi.org/10.3390/e27070703 (registering DOI) - 30 Jun 2025

Abstract

Online recruitment platforms are transforming talent acquisition paradigms, where a precise person-job fit plays a pivotal role in intelligent recruitment systems. However, current methodologies predominantly rely on coarse-grained semantic analysis, failing to address the textual structural dependencies and noise inherent in resumes and [...] Read more.

Online recruitment platforms are transforming talent acquisition paradigms, where a precise person-job fit plays a pivotal role in intelligent recruitment systems. However, current methodologies predominantly rely on coarse-grained semantic analysis, failing to address the textual structural dependencies and noise inherent in resumes and job descriptions. To bridge this gap, the novel fine-grained semantics-enhanced graph neural network for person-job fit (FSEGNN-PJF) framework is proposed. First, graph topologies are constructed by modeling word co-occurrence relationships through pointwise mutual information and sliding windows, followed by graph attention networks to learn graph structural semantics. Second, to mitigate textual noise and focus on critical features, a differential transformer and self-attention mechanism are introduced to semantically encode resumes and job requirements. Then, a novel fine-grained semantic matching strategy is designed, using the enhanced feature fusion strategy to fuse the semantic features of resumes and job positions. Extensive experiments on real-world recruitment datasets demonstrate the effectiveness and robustness of FSEGNN-PJF. Full article

(This article belongs to the Section Multidisciplinary Applications)

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19 pages, 765 KiB

Open AccessReview

Including Quantum Effects in Molecular Simulations Using the Feynman–Kleinert Linearized Path Integral Method

by Jens Aage Poulsen and Gunnar Nyman

Entropy 2025, 27(7), 702; https://doi.org/10.3390/e27070702 (registering DOI) - 30 Jun 2025

Abstract

During the last few decades, several approximate, but useful, methods for including dynamical quantum effects in molecular simulations have been developed. These methods can be applied to systems with hundreds of degrees of freedom and with arbitrary potentials. Among these methods, we find [...] Read more.

During the last few decades, several approximate, but useful, methods for including dynamical quantum effects in molecular simulations have been developed. These methods can be applied to systems with hundreds of degrees of freedom and with arbitrary potentials. Among these methods, we find the Feynman–Kleinert linearized path integral model, including its planetary versions, which are the focus of this review. The aim is to calculate quantum correlation functions for complex systems. Many important properties, e.g., transport coefficients, may thus be obtained. We summarize important applications of the method, and compare them to alternative ones, such as centroid molecular dynamics and ring polymer molecular dynamics. We finally discuss possible future improvements of the FK-LPI method. Full article

(This article belongs to the Section Statistical Physics)

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28 pages, 2850 KiB

Open AccessArticle

Quantification and Evolution of Online Public Opinion Heat Considering Interactive Behavior and Emotional Conflict

by Zhengyi Sun, Deyao Wang and Zhaohui Li

Entropy 2025, 27(7), 701; https://doi.org/10.3390/e27070701 (registering DOI) - 29 Jun 2025

Abstract

With the rapid development of the Internet, the speed and scope of sudden public events disseminating in cyberspace have grown significantly. Current methods of quantifying public opinion heat often neglect emotion-driven factors and user interaction behaviors, making it difficult to accurately capture fluctuations [...] Read more.

With the rapid development of the Internet, the speed and scope of sudden public events disseminating in cyberspace have grown significantly. Current methods of quantifying public opinion heat often neglect emotion-driven factors and user interaction behaviors, making it difficult to accurately capture fluctuations during dissemination. To address these issues, first, this study addressed the complexity of interaction behaviors by introducing an approach that employs the information gain ratio as a weighting indicator to measure the “interaction heat” contributed by different interaction attributes during event evolution. Second, this study built on SnowNLP and expanded textual features to conduct in-depth sentiment mining of large-scale opinion texts, defining the variance of netizens’ emotional tendencies as an indicator of emotional fluctuations, thereby capturing “emotional heat”. We then integrated interactive behavior and emotional conflict assessment to achieve comprehensive heat index to quantification and dynamic evolution analysis of online public opinion heat. Subsequently, we used Hodrick–Prescott filter to separate long-term trends and short-term fluctuations, extract six key quantitative features (number of peaks, time of first peak, maximum amplitude, decay time, peak emotional conflict, and overall duration), and applied K-means clustering algorithm (K-means) to classify events into three propagation patterns, which are extreme burst, normal burst, and long-tail. Finally, this study conducted ablation experiments on critical external intervention nodes to quantify the distinct contribution of each intervention to the propagation trend by observing changes in the model’s goodness-of-fit (

R^{2}

) after removing different interventions. Through an empirical analysis of six representative public opinion events from 2024, this study verified the effectiveness of the proposed framework and uncovered critical characteristics of opinion dissemination, including explosiveness versus persistence, multi-round dissemination with recurring emotional fluctuations, and the interplay of multiple driving factors. Full article

(This article belongs to the Special Issue Statistical Physics Approaches for Modeling Human Social Systems)

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19 pages, 994 KiB

Open AccessArticle

(Finite-Time) Thermodynamics, Hyperbolicity, Lorentz Invariance: Study of an Example

by Bernard Guy

Entropy 2025, 27(7), 700; https://doi.org/10.3390/e27070700 (registering DOI) - 29 Jun 2025

Abstract

Our study lies at the intersection of three fields: finite-time thermodynamics, relativity theory, and the theory of hyperbolic conservation laws. Each of these fields has its own requirements and richness, and in order to link them together as effectively as possible, we have [...] Read more.

Our study lies at the intersection of three fields: finite-time thermodynamics, relativity theory, and the theory of hyperbolic conservation laws. Each of these fields has its own requirements and richness, and in order to link them together as effectively as possible, we have simplified each one, reducing it to its fundamental principles. The example chosen concerns the propagation of chemical changes in a very large reactor, as found in geology. We ask ourselves two sets of questions: (1) How do the finiteness of propagation speeds modeled by hyperbolic problems (diffusion is neglected) and the finiteness of the time allocated to transformations interact? (2) How do the finiteness of time and that of resources interact? The similarity in the behavior of the pairs of variables (x, t and resources, resource flows) in Lorentz relativistic transformations allows us to put them on the same level and propose complementary-type relationships between the two classes of finiteness. If times are finite, so are resources, which can be neither zero nor infinite. In hyperbolic problems, a condition is necessary to select solutions with a physical sense among the multiplicity of weak solutions: this is given by the entropy production, which is Lorentz invariant (and not entropy alone). Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

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22 pages, 397 KiB

Open AccessArticle

Echo Chambers and Homophily in the Diffusion of Risk Information on Social Media: The Case of Genetically Modified Organisms (GMOs)

by Xiaoxiao Cheng and Jianbin Jin

Entropy 2025, 27(7), 699; https://doi.org/10.3390/e27070699 (registering DOI) - 29 Jun 2025

Abstract

This study investigates the mechanisms underlying the diffusion of risk information about genetically modified organisms (GMOs) on the Chinese social media platform Weibo. Drawing upon social contagion theory, we examine how endogenous and exogenous mechanisms shape users’ information-sharing behaviors. An analysis of 388,722 [...] Read more.

This study investigates the mechanisms underlying the diffusion of risk information about genetically modified organisms (GMOs) on the Chinese social media platform Weibo. Drawing upon social contagion theory, we examine how endogenous and exogenous mechanisms shape users’ information-sharing behaviors. An analysis of 388,722 reposts from 2444 original GMO risk-related texts enabled the construction of a comprehensive sharing network, with computational text-mining techniques employed to detect users’ attitudes toward GMOs. To bridge the gap between descriptive and inferential network analysis, we employ a Shannon entropy-based approach to quantify the uncertainty and concentration of attitudinal differences and similarities among sharing and non-sharing dyads, providing an information-theoretic foundation for understanding positional and differential homophily. The entropy-based analysis reveals that information-sharing ties are characterized by lower entropy in attitude differences, indicating greater attitudinal alignment among sharing users, especially among GMO opponents. Building on these findings, the Exponential Random Graph Model (ERGM) further demonstrates that both endogenous network mechanisms (reciprocity, preferential attachment, and triadic closure) and positional homophily influence GMO risk information sharing and dissemination. A key finding is the presence of a differential homophily effect, where GMO opponents exhibit stronger homophilic tendencies than non-opponents. Despite the prevalence of homophily, this paper uncovers substantial cross-attitude interactions, challenging simplistic notions of echo chambers in GMO risk communication. By integrating entropy and ERGM analyses, this study advances a more nuanced, information-theoretic understanding of how digital platforms mediate public perceptions and debates surrounding controversial socio-scientific issues, offering valuable implications for developing effective risk communication strategies in increasingly polarized online spaces. Full article

(This article belongs to the Special Issue Complexity of Social Networks)

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11 pages, 670 KiB

Open AccessArticle

LLM-Enhanced Chinese Morph Resolution in E-Commerce Live Streaming Scenarios

by Xiaoye Ouyang, Liu Yuan, Xiaocheng Hu, Jiahao Zhu and Jipeng Qiang

Entropy 2025, 27(7), 698; https://doi.org/10.3390/e27070698 (registering DOI) - 29 Jun 2025

Abstract

E-commerce live streaming in China has become a major retail channel, yet hosts often employ subtle phonetic or semantic “morphs” to evade moderation and make unsubstantiated claims, posing risks to consumers. To address this, we study the Live Auditory Morph Resolution (LiveAMR) task, [...] Read more.

E-commerce live streaming in China has become a major retail channel, yet hosts often employ subtle phonetic or semantic “morphs” to evade moderation and make unsubstantiated claims, posing risks to consumers. To address this, we study the Live Auditory Morph Resolution (LiveAMR) task, which restores morphed speech transcriptions to their true forms. Building on prior text-based morph resolution, we propose an LLM-enhanced training framework that mines three types of explanation knowledge—predefined morph-type labels, LLM-generated reference corrections, and natural-language rationales constrained for clarity and comprehensiveness—from a frozen large language model. These annotations are concatenated with the original morphed sentence and used to fine-tune a lightweight T5 model under a standard cross-entropy objective. In experiments on two test sets (in-domain and out-of-domain), our method achieves substantial gains over baselines, improving

F_{0.5}

by up to 7 pp in-domain (to 0.943) and 5 pp out-of-domain (to 0.799) compared to a strong T5 baseline. These results demonstrate that structured LLM-derived signals can be mined without fine-tuning the LLM itself and injected into small models to yield efficient, accurate morph resolution. Full article

(This article belongs to the Special Issue Natural Language Processing and Data Mining)

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12 pages, 2038 KiB

Open AccessArticle

Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach

by Edward Bormashenko and Michael Nosonovsky

Entropy 2025, 27(7), 697; https://doi.org/10.3390/e27070697 (registering DOI) - 29 Jun 2025

Abstract

We introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature T. Synchronization is achieved by transmitting photons from one clock to another; the absorption of a photon [...] Read more.

We introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature T. Synchronization is achieved by transmitting photons from one clock to another; the absorption of a photon by a clock reduces the uncertainty in its timekeeping. The minimum energy required for this reduction in uncertainty is determined by the Landauer bound. We distinguish between the time-bearing and non-time-bearing degrees of freedom of the clocks. A reduction in uncertainty under synchronization in the time-bearing degrees of freedom necessarily leads to heat dissipation in the non-time-bearing ones. The minimum energy dissipation in these non-time-bearing degrees of freedom is likewise given by the Landauer limit. The same is true for mechanical synchronization of clocks. We also consider lattices of clocks and analyze synchronization using a Ramsey graph approach. Notably, clocks operating at the same temperature may be synchronized using photons of different frequencies. Each clock is categorized as either synchronized or non-synchronized, resulting in a bi-colored complete graph of clocks. By Ramsey’s theorem, such a graph inevitably contains a triad (or loop) of clocks that are either all synchronized or all non-synchronized. The extension of the Ramsey approach to infinite lattices of clocks is reported. Full article

(This article belongs to the Special Issue The Landauer Principle in Physics, Biophysics, Engineering and Computer Science: From Foundations of Thermodynamics to Computer Engineering)

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13 pages, 886 KiB

Open AccessArticle

Semi-Device-Independent Randomness Expansion Using n→1 Parity-Oblivious Quantum Random Access Codes

by Xunan Wang, Xu Chen, Mengke Xu, Wanglei Mi and Xiao Chen

Entropy 2025, 27(7), 696; https://doi.org/10.3390/e27070696 (registering DOI) - 28 Jun 2025

Abstract

Quantum mechanics enables the generation of genuine randomness through its intrinsic indeterminacy. In device-independent (DI) and semi-device-independent (SDI) frameworks, randomness generation protocols can further ensure that the output remains secure and unaffected by internal device imperfections, with certification grounded in violations of generalized [...] Read more.

Quantum mechanics enables the generation of genuine randomness through its intrinsic indeterminacy. In device-independent (DI) and semi-device-independent (SDI) frameworks, randomness generation protocols can further ensure that the output remains secure and unaffected by internal device imperfections, with certification grounded in violations of generalized Bell inequalities. In this work, we propose an SDI randomness expansion protocol using

n \to 1

parity-oblivious quantum random access code (PO-QRAC), where the presence of true quantum randomness is certified through the violation of a two-dimensional quantum witness. For various values of n, we derive the corresponding maximal expected success probabilities. Notably, for

n = 4

, the expected success probability obtained under our protocol exceeds the upper bound reported in prior work. Furthermore, we establish an analytic relationship between the certifiable min-entropy and the quantum witness value, and demonstrate that, for a fixed witness value, PO-QRAC–based protocols certify more randomness than those based on standard QRACs. Among all configurations satisfying the parity-obliviousness constraint, the protocol based on the

3 \to 1

PO-QRAC achieves optimal randomness expansion performance. Full article

(This article belongs to the Special Issue Quantum Probability and Randomness V)

28 pages, 2338 KiB

Open AccessArticle

A Hybrid Framework Integrating Traditional Models and Deep Learning for Multi-Scale Time Series Forecasting

by Zihan Liu, Zijia Zhang and Weizhe Zhang

Entropy 2025, 27(7), 695; https://doi.org/10.3390/e27070695 (registering DOI) - 28 Jun 2025

Abstract

Time series forecasting is critical for decision-making in numerous domains, yet achieving high accuracy across both short-term and long-term horizons remains challenging. In this paper, we propose a general hybrid forecasting framework that integrates a traditional statistical model (ARIMA) with modern deep learning [...] Read more.

Time series forecasting is critical for decision-making in numerous domains, yet achieving high accuracy across both short-term and long-term horizons remains challenging. In this paper, we propose a general hybrid forecasting framework that integrates a traditional statistical model (ARIMA) with modern deep learning models (such as LSTM and Transformer). The core of our approach is a novel multi-scale prediction mechanism that combines the strengths of both model types to better capture short-range patterns and long-range dependencies. We design a dual-stage forecasting process, where a classical time series component first models transparent linear trends and seasonal patterns, and a deep neural network then learns complex nonlinear residuals and long-term contexts. The two outputs are fused through an adaptive mechanism to produce the final prediction. We evaluate the proposed framework on eight public datasets (electricity, exchange rate, weather, traffic, illness, ETTh1/2, and ETTm1/2) covering diverse domains and scales. The experimental results show that our hybrid method consistently outperforms stand-alone models (ARIMA, LSTM, and Transformer) and recent, specialized forecasters (Informer and Autoformer) in both short-horizon and long-horizon forecasts. An ablation study further demonstrates the contribution of each module in the framework. The proposed approach not only achieves state-of-the-art accuracy across varied time series but also offers improved interpretability and robustness, suggesting a promising direction for combining statistical and deep learning techniques in time series forecasting. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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18 pages, 1001 KiB

Open AccessArticle

Time-Resolved Information-Theoretic and Spectral Analysis of fNIRS Signals from Multi-Channel Prototypal Device

by Irene Franzone, Yuri Antonacci, Fabrizio Giuliano, Riccardo Pernice, Alessandro Busacca, Luca Faes and Giuseppe Costantino Giaconia

Entropy 2025, 27(7), 694; https://doi.org/10.3390/e27070694 (registering DOI) - 28 Jun 2025

Abstract

Functional near-infrared spectroscopy (fNIRS) is a non-invasive imaging technique that measures brain hemodynamic activity by detecting changes in oxyhemoglobin and deoxyhemoglobin concentrations using light in the near-infrared spectrum. This study aims to provide a comprehensive characterization of fNIRS signals acquired with a prototypal [...] Read more.

Functional near-infrared spectroscopy (fNIRS) is a non-invasive imaging technique that measures brain hemodynamic activity by detecting changes in oxyhemoglobin and deoxyhemoglobin concentrations using light in the near-infrared spectrum. This study aims to provide a comprehensive characterization of fNIRS signals acquired with a prototypal continuous-wave fNIRS device during a breath-holding task, to evaluate the impact of respiratory activity on scalp hemodynamics within the framework of Network Physiology. To this end, information-theoretic and spectral analysis methods were applied to characterize the dynamics of fNIRS signals. In the time domain, time-resolved information-theoretic measures, including entropy, conditional entropy and, information storage, were employed to assess the complexity and predictability of the fNIRS signals. These measures highlighted distinct informational dynamics across the breathing and apnea phases, with conditional entropy showing a significant modulation driven by respiratory activity. In the frequency domain, power spectral density was estimated using a parametric method, allowing the identification of distinct frequency bands related to vascular and respiratory components. The analysis revealed significant modulations in both the amplitude and frequency of oscillations during the task, particularly in the high-frequency band associated with respiratory activity. Our observations demonstrate that the proposed analysis provides novel insights into the characterization of fNIRS signals, enhancing the understanding of the impact of task-induced peripheral cardiovascular responses on NIRS hemodynamics. Full article

(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)

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50 pages, 1143 KiB

Open AccessArticle

Entropies of the Classical Dimer Model

by John C. Baker, Marilyn F. Bishop and Tom McMullen

Entropy 2025, 27(7), 693; https://doi.org/10.3390/e27070693 (registering DOI) - 28 Jun 2025

Abstract

Biological processes often involve the attachment and detachment of extended molecules to substrates. Here, the classical dimer model is used to investigate these geometric effects on the free energy, which governs both the equilibrium state and the reaction dynamics. We present a simplified [...] Read more.

Biological processes often involve the attachment and detachment of extended molecules to substrates. Here, the classical dimer model is used to investigate these geometric effects on the free energy, which governs both the equilibrium state and the reaction dynamics. We present a simplified version of Fisher’s derivation of the partition function of a two-dimensional dimer model at filling factor

ν = 1

, which takes into account the blocking of two adjacent sites by each dimer. Physical consequences of the dimer geometry on the entropy that are not reflected in simpler theories are identified. Specifically, for dimers adsorbing on the DNA double helix, the dimer geometry gives a persistently nonzero entropy and there is a significant charge inversion as the force binding the particles to the lattice increases relative to the thermal energy, which is not true of the simple lattice gas model for the dimers, in which all the sites are independent. Full article

(This article belongs to the Section Entropy and Biology)

15 pages, 5676 KiB

Open AccessArticle

Transverse Self-Propulsion Enhances the Aggregation of Active Dumbbells

by Pasquale Digregorio, Claudio Basilio Caporusso, Lucio Mauro Carenza, Giuseppe Gonnella, Daniela Moretti, Giuseppe Negro, Massimiliano Semeraro and Antonio Suma

Entropy 2025, 27(7), 692; https://doi.org/10.3390/e27070692 (registering DOI) - 27 Jun 2025

Abstract

We investigate a two-dimensional system of active Brownian dumbbells using molecular dynamics simulations. In this model, each dumbbell is driven by an active force oriented perpendicular to the axis connecting its two constituent beads. We characterize the resulting phase behavior and find that, [...] Read more.

We investigate a two-dimensional system of active Brownian dumbbells using molecular dynamics simulations. In this model, each dumbbell is driven by an active force oriented perpendicular to the axis connecting its two constituent beads. We characterize the resulting phase behavior and find that, across all values of activity, the system undergoes phase separation between dilute and dense phases. The dense phase exhibits hexatic order, and for large enough activity, we observe a marked increase in local polarization, with dumbbells predominantly oriented towards the interior of the clusters. Compared to the case of axially self-propelled dumbbells, we find that the binodal region is enlarged towards lower densities at all activities. This shift arises because dumbbells with transverse propulsion can more easily form stable cluster cores, serving as nucleation seeds, and show a highly suppressed escaping rate from the cluster boundary. Finally, we observe that clusters exhibit spontaneous rotation, with the modulus of the angular velocity scaling as

ω \sim r_{g}^{- 2}

, where

r_{g}

is the cluster’s radius of gyration. This contrasts with axially propelled dumbbells, where the scaling follows

ω \sim r_{g}^{- 1}

. We develop a simplified analytical model to rationalize this scaling behavior. Full article

(This article belongs to the Section Non-equilibrium Phenomena)

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13 pages, 706 KiB

Open AccessArticle

Jointly Optimizing Resource Allocation, User Scheduling, and Grouping in SBMA Networks: A PSO Approach

by Jianjian Wu, Chanzi Liu, Xindi Wang, Chi-Tsun Cheng and Qingfeng Zhou

Entropy 2025, 27(7), 691; https://doi.org/10.3390/e27070691 (registering DOI) - 27 Jun 2025

Abstract

Blind Interference Alignment (BIA) and Sparse Code Multiple Access (SCMA) offer the potential for massive connectivity but face limitations. Our recently proposed Sparsecode-and-BIA-based Multiple Access (SBMA) scheme synergizes their strengths, promising enhanced performance. SBMA leverages flexible user grouping (UG) strategies to effectively manage [...] Read more.

Blind Interference Alignment (BIA) and Sparse Code Multiple Access (SCMA) offer the potential for massive connectivity but face limitations. Our recently proposed Sparsecode-and-BIA-based Multiple Access (SBMA) scheme synergizes their strengths, promising enhanced performance. SBMA leverages flexible user grouping (UG) strategies to effectively manage its unique combination of sparse code constraints and interference alignment requirements, thereby facilitating the fulfillment of diverse Quality of Service (QoS) demands. However, realizing SBMA’s full potential requires efficient joint resource allocation (RA), user scheduling (US), and user grouping (UG). The inherent coupling of these factors within the SBMA framework complicates this task significantly, rendering RA/US solutions designed purely for SCMA or BIA insufficient. This paper addresses this critical open issue. We first formulate the joint RA, US, and UG problems specifically for SBMA systems as an integer optimization task, aiming to maximize the number of users meeting QoS requirements. To tackle this NP-hard problem, we propose an effective algorithm based on Particle Swarm Optimization (PSO), featuring a carefully designed update function tailored specifically for the joint US and UG decisions required in SBMA. Comprehensive simulations demonstrate show that the proposed algorithm significantly outperforms the random-based scheme. Under certain conditions, it serves approximately 280% more users who meet their QoS requirements in high-SNR scenarios. Full article

(This article belongs to the Special Issue Advances in Information and Coding Theory, the Third Edition)

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