Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (2,897)

Search Parameters:
Keywords = state entropy

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
24 pages, 10388 KB  
Article
Adaptive Content and Style Fusion for Text-to-Image Generations
by Yi-Fang Lee, Chun-Chieh Lee, Chi-Hung Chuang, Chih-Lung Lin and Kuo-Chin Fan
Electronics 2026, 15(13), 2800; https://doi.org/10.3390/electronics15132800 (registering DOI) - 25 Jun 2026
Abstract
Text-to-image generation aims to produce images that match the semantic content of a text prompt. In style transfer tasks, the model must further integrate reference styles while preserving prompt semantics. However, balancing semantic consistency and style fidelity remains challenging. Existing methods commonly rely [...] Read more.
Text-to-image generation aims to produce images that match the semantic content of a text prompt. In style transfer tasks, the model must further integrate reference styles while preserving prompt semantics. However, balancing semantic consistency and style fidelity remains challenging. Existing methods commonly rely on fixed feature weights and lack adaptive control, which often leads to style over-injection and content distortion. To address these issues, we propose a novel framework that performs dynamic regulation at both the feature and temporal levels. At the feature level, we propose an Entropy-Aware Adaptive Fusion (EAAF) module. It incorporates a bidirectional distribution transformation mechanism to enhance the statistical correlation between content and style features. The module further uses information entropy as a dynamic control signal to adaptively adjust the strength of style injection, thereby achieving a balance between semantic consistency and style fidelity. At the temporal level, we design a Progressive Feature Reweighting (PFR) strategy. By applying stage-wise weighting to content and style features at different diffusion steps, this strategy effectively improves structural stability and color consistency. In addition, our framework is modular and can be integrated into existing diffusion-based style transfer models without additional fine-tuning or retraining. Experimental results demonstrate that applying our approach to current state-of-the-art models, such as StyleStudio and CSGO, significantly enhances their performance, particularly in maintaining strong prompt alignment while achieving high-fidelity style transfer. Full article
(This article belongs to the Special Issue Recent Advances in Object Detection and Computer Vision)
Show Figures

Figure 1

21 pages, 21830 KB  
Article
Influence of Process Control Agents, Mill Type, and Elemental Substitution on the Mechanosynthesis of Selected High-Entropy Alloys
by Teresa García-Mendoza, Alfredo Martinez-Garcia, Carlos Gamaliel Garay-Reyes, Roberto Martinez-Sanchez, Jose Manuel Juárez-Barrientos, Magdaleno Caballero-Caballero, Alejandro Javier Cortés-López, Fernando Chiñas Castillo and Erick Adrian Juarez-Arellano
Alloys 2026, 5(3), 15; https://doi.org/10.3390/alloys5030015 (registering DOI) - 24 Jun 2026
Viewed by 57
Abstract
High-entropy alloys (HEAs) are a transformative class of materials with remarkable structural and functional properties. Solid-state processing techniques, such as high-energy ball milling, are being increasingly used for their production. In these processes, the use of a process control agent (PCA) seems to [...] Read more.
High-entropy alloys (HEAs) are a transformative class of materials with remarkable structural and functional properties. Solid-state processing techniques, such as high-energy ball milling, are being increasingly used for their production. In these processes, the use of a process control agent (PCA) seems to be essential to prevent excessive cold welding and agglomeration; however, the influence of different PCAs on alloy formation remains insufficiently understood. This study systematically examined the effects of the PCA type, milling configuration, and elemental substitution on HEAs mechanosynthesis. A non-equiatomic alloy, Al10Cr12Fe35Mn23Ni20 (selected for its known single-phase Face Center Cubic (FCC) behavior), was used to explore the PCA and mill-type effects. The alloy was synthesized in a planetary mill (Fritsch Pulverisette 7) and a vibratory mill (SPEX 8000M) using diverse PCAs, including liquid (methanol, ethanol, isopropyl, and n-heptane) and solid (stearic acid and sodium chloride) agents. In addition, lightweight equiatomic alloys MgAlTiNi(Co,Cr,Fe) were used to explore the influence of different PCAs and the effect of elemental substitution under similar PCA conditions as those used with the equiatomic alloy. The products were characterized using X-ray diffraction, scanning electron microscopy, thermogravimetric analysis, and differential thermal analysis techniques. The results highlighted that the PCA selection, milling configuration, and alloy chemistry influenced the phase evolution, particle size distribution, and thermal behavior. The results provide insights into the mechanosynthesis of selected high-entropy alloys produced under different PCA and milling conditions. Full article
Show Figures

Figure 1

26 pages, 29473 KB  
Article
Cross-Modal Degradation Rivalry for Self-Supervised Structural Fatigue Health Monitoring
by Tianbao Nie, Yu Yang and Xiang Li
Mathematics 2026, 14(13), 2245; https://doi.org/10.3390/math14132245 (registering DOI) - 23 Jun 2026
Viewed by 69
Abstract
Fatigue health monitoring of engineering structures requires continuous degradation assessment, yet ground-truth health labels are unavailable during run-to-failure tests. Existing self-supervised approaches rely on monotonic degradation assumptions that are violated by the structured non-monotonic behaviour of acoustic emission signals during fatigue. A self-supervised [...] Read more.
Fatigue health monitoring of engineering structures requires continuous degradation assessment, yet ground-truth health labels are unavailable during run-to-failure tests. Existing self-supervised approaches rely on monotonic degradation assumptions that are violated by the structured non-monotonic behaviour of acoustic emission signals during fatigue. A self-supervised framework called Cross-Modal Degradation Rivalry (CMDR) is proposed, which introduces the Modal Rivalry Index (MRI) as a directional measure of cross-modal predictability between heterogeneous sensor modalities. CMDR comprises a label-free representation-learning stage trained via the Cross-Modal Prediction Asymmetry (CMPA) pretext task, followed by a lightweight supervised stage that maps MRI features to scalar health indicators (HIs) using normalised lifecycle labels. The MRI is conceptually related, under the stated assumptions only loosely met in practice, to the Transfer Entropy difference between sensor latent channels. Experiments on a structural fatigue dataset with seven specimens under two loading conditions demonstrate that CMDR achieves competitive trendability and prognosability, as well as the lowest remaining useful life (RUL) error in three of four scenarios. RUL evaluations are additionally repeated under a fully online estimator that uses only training specimens. A strictly inductive ablation that re-pre-trains the self-supervised stage within each leave-one-specimen-out fold confirms a bounded transductive-vs-inductive gap, and CMDR remains the best against three further self-supervised baselines on the within-condition and mixed-condition scenarios. Ablation studies confirm the necessity of directional asymmetry, bottleneck architecture, and momentum-updated target encoders. Full article
11 pages, 588 KB  
Article
Behavioral Complexity in Alzheimer’s Disease: A Diversity-Based Analysis of Neuropsychiatric Symptoms
by YoungSoon Yang and Yong Tae Kwak
Brain Sci. 2026, 16(7), 659; https://doi.org/10.3390/brainsci16070659 (registering DOI) - 23 Jun 2026
Viewed by 124
Abstract
Background and Objectives: To quantify behavioral complexity in probable Alzheimer’s disease (AD), compare complexity phenotypes, and determine whether behavioral complexity provides clinically meaningful information beyond total neuropsychiatric burden. We also explored whether global amyloid extent and lobar amyloid topography added explanatory value. [...] Read more.
Background and Objectives: To quantify behavioral complexity in probable Alzheimer’s disease (AD), compare complexity phenotypes, and determine whether behavioral complexity provides clinically meaningful information beyond total neuropsychiatric burden. We also explored whether global amyloid extent and lobar amyloid topography added explanatory value. Methods: In this cross-sectional retrospective study, we analyzed 245 psychotropic drug-naïve patients with probable AD, positive 18F-FC119S amyloid positron emission tomography (PET), and complete neuropsychiatric, cognitive, functional, and regional PET data. Behavioral complexity was derived from 12 Korean Neuropsychiatric Inventory domains using symptom count, normalized Shannon entropy of the frequency × severity profile, and a composite index. Patients were classified into tertiles. Multivariable regression and burden-stratified analyses examined associations with cognition, dementia severity, function, and amyloid measures. Results: Higher behavioral complexity was associated with lower Korean Mini-Mental State Examination (K-MMSE) scores and higher Clinical Dementia Rating (CDR) and Global Deterioration Scale (GDS) stages. In multivariable analysis, higher CDR, higher GDS, and lower Barthel Index independently predicted greater complexity, whereas amyloid extent did not. After adjustment for total neuropsychiatric burden, higher CDR remained independently associated with the composite complexity index and normalized entropy, while amyloid extent remained non-significant. Complexity-related clinical differences were most evident in the lowest burden stratum and attenuated at higher burden levels. Regional amyloid analyses yielded only selective signals. Conclusions: Behavioral complexity is a clinically meaningful neuropsychiatric phenotype in AD. Although strongly related to total neuropsychiatric burden, it is not fully reducible to it, with its clearest independent association seen for global dementia severity, particularly at lower overall burden. Full article
(This article belongs to the Section Behavioral Neuroscience)
Show Figures

Graphical abstract

25 pages, 11051 KB  
Article
Spectral, Information-Theoretic and Thermodynamic Properties of a Fractal Position-Dependent Mass Schrödinger System
by Q. R. D. S. Moreira, L. F. Ximenes, A. R. P. Moreira, D. M. Neves, J. B. R. Silva and J. C. Nascimento
Nanomaterials 2026, 16(13), 787; https://doi.org/10.3390/nano16130787 (registering DOI) - 23 Jun 2026
Viewed by 123
Abstract
In this work, we investigate the spectral, information-theoretic, and thermodynamic properties of a fractal Schrödinger system with position-dependent mass subject to an effective semiconductor-like confinement. We employ a fractal momentum operator and a Von Roos Hamiltonian with BenDaniel–Duke ordering to obtain exact analytical [...] Read more.
In this work, we investigate the spectral, information-theoretic, and thermodynamic properties of a fractal Schrödinger system with position-dependent mass subject to an effective semiconductor-like confinement. We employ a fractal momentum operator and a Von Roos Hamiltonian with BenDaniel–Duke ordering to obtain exact analytical solutions for the energy spectrum and wave functions. The interplay between the fractal parameter α, the effective lattice scale l0, and the harmonic confinement strength ω is explored. We perform a comprehensive analysis of the Shannon entropy, Fisher information, and Fisher–Shannon complexity in both coordinate and momentum spaces. Our results demonstrate that these parameters directly control the localization–delocalization transition and the informational architecture of the quantum states, while satisfying the entropic and Fisher uncertainty relations. Furthermore, we derive the exact partition function and the corresponding thermodynamic properties (free energy, internal energy, entropy, and specific heat) of the system. The analytical framework presented offers valuable insights into the spectral, information-theoretic, and thermodynamic behavior of quantum systems in fractal semiconductor-like environments. Full article
(This article belongs to the Section Theory and Simulation of Nanostructures)
Show Figures

Figure 1

20 pages, 2552 KB  
Article
An Integrated AHP–EWM–SPA Approach for Evaluating Safety Management in Highway Tunnel Construction
by Shuangxing Qi, Hualin Zhang, Xuhui Zhou, Bo Wu and Shixiang Xu
Eng 2026, 7(6), 303; https://doi.org/10.3390/eng7060303 (registering DOI) - 22 Jun 2026
Viewed by 126
Abstract
Safety management evaluation in highway tunnel construction involves significant complexity due to multi-level, multi-indicator, and uncertain characteristics. To address these challenges, this study proposes an integrated evaluation approach combining the Analytic Hierarchy Process (AHP), Entropy Weight Method (EWM), and Set Pair Analysis (SPA). [...] Read more.
Safety management evaluation in highway tunnel construction involves significant complexity due to multi-level, multi-indicator, and uncertain characteristics. To address these challenges, this study proposes an integrated evaluation approach combining the Analytic Hierarchy Process (AHP), Entropy Weight Method (EWM), and Set Pair Analysis (SPA). An evaluation index system is established from the perspective of system defensive capability, encompassing four dimensions—organizational, personnel, material, and information management—with 19 indicators. SPA is employed to quantify the relationships among indicators through identity, discrepancy, and opposition, while a hybrid weighting scheme combines subjective judgments and objective data. A confidence-based identification criterion is further introduced to improve the robustness of classification. The proposed model is applied to a highway tunnel project, and the results show good agreement with observed field conditions. The analysis indicates that the method effectively captures intermediate states and uncertainty in safety management systems while reducing bias associated with single weighting strategies and maximum membership-based decisions. The proposed framework provides a practical and reliable approach for safety management evaluation and supports risk-informed decision-making in tunnel construction. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
Show Figures

Figure 1

18 pages, 712 KB  
Hypothesis
Correlation Entropy and Power-Law Kinetics
by Joseph B. Bernstein
Entropy 2026, 28(6), 712; https://doi.org/10.3390/e28060712 (registering DOI) - 21 Jun 2026
Viewed by 198
Abstract
Power-law kinetics are observed across a wide range of physical, chemical, biological, and engineering systems, yet the thermodynamic origin of the power-law exponent remains incompletely understood. This work proposes a thermodynamic hypothesis in which power-law behavior emerges naturally from correlation-dependent contributions to the [...] Read more.
Power-law kinetics are observed across a wide range of physical, chemical, biological, and engineering systems, yet the thermodynamic origin of the power-law exponent remains incompletely understood. This work proposes a thermodynamic hypothesis in which power-law behavior emerges naturally from correlation-dependent contributions to the Gibbs free energy. Rather than modifying the classical Boltzmann definition of entropy, a phenomenological Correlation Constant, χ, is introduced to quantify how accumulated microstate evolution influences the accessibility of future states. The resulting correlation entropy contribution produces a free-energy term that modifies the probability of subsequent transitions and leads naturally to power-law kinetic behavior. Positive values of χ correspond to cooperative evolution in which prior evolution promotes future evolution, while negative values correspond to self-limiting behavior in which prior evolution suppresses subsequent evolution. The conventional Arrhenius-Eyring description is recovered as the special case χ = 0. The resulting framework provides a thermodynamic interpretation of the power-law exponent, establishes a connection between entropy, free energy, and kinetic evolution, and offers a unified description applicable to degradation, relaxation, diffusion, fatigue, trapping, and other evolving processes. The present work is intended as a thermodynamic hypothesis motivating further experimental and theoretical investigation of correlation-dependent kinetics. Full article
(This article belongs to the Collection Foundations of Statistical Mechanics)
Show Figures

Figure 1

31 pages, 368 KB  
Article
State-Dependent Dynamics of Overconfidence in Frontier Equity Markets: A Transfer Entropy Approach from Bangladesh
by Muhammad Enamul Haque and Mahmood Osman Imam
J. Risk Financial Manag. 2026, 19(6), 449; https://doi.org/10.3390/jrfm19060449 (registering DOI) - 21 Jun 2026
Viewed by 187
Abstract
The study investigates the state-dependent dynamics of overconfidence in the Bangladesh equity market by exploring the relationship between market returns and trading volume within a nonlinear information-theoretic framework. Building up on the traditional return–volume literature, the study differentiates between total market returns and [...] Read more.
The study investigates the state-dependent dynamics of overconfidence in the Bangladesh equity market by exploring the relationship between market returns and trading volume within a nonlinear information-theoretic framework. Building up on the traditional return–volume literature, the study differentiates between total market returns and unexpected returns, with the latter representing unexpected information shocks obtained using the Market Index Model. Transfer Entropy with bootstrap inference estimates the directional and asymmetric information flows across five different market states, namely: bullish, bearish, crisis, extended crisis, and COVID-19. The evidence suggests that the overconfidence biases in aggregate market returns are small and intermittent and are reflected in poor and unstable information flow between market returns and trading volume. In comparison, unexpected market returns have a directionally significant impact on trading behavior, which supports the behavior of state-dependent overconfidence. The findings also reveal that overconfidence is higher in normal and bullish market situations but drops significantly in crisis-based situations. The asymmetric analysis indicates increased trading responses to negative returns shocks, as it is more evident that investors are more sensitive to losses and recovery expectations. The research adds to behavioral finance literature on frontier markets through an unexpected return decomposition with nonlinear causality model. The results have serious implications on market surveillance, assessment of investor behavior and design of regulatory policies. Full article
(This article belongs to the Section Financial Markets)
27 pages, 16838 KB  
Review
High-Entropy Alloys: A Review of Emerging Sensing Materials for Next-Generation Flexible Electronics
by Huatan Chen, Zhongyi Yu, Yang Huang, Bofeng Li, Fangting Feng, Yuming Jiang, Yuting Duan, Gaofeng Zheng and Zungui Shao
Materials 2026, 19(12), 2655; https://doi.org/10.3390/ma19122655 (registering DOI) - 20 Jun 2026
Viewed by 245
Abstract
High-entropy alloys (HEAs), composed of five or more principal elements in near-equimolar ratios, have emerged as a groundbreaking class of materials for next-generation flexible electronics. This review systematically examines the unique potential of HEAs as sensing materials, moving beyond their traditional role as [...] Read more.
High-entropy alloys (HEAs), composed of five or more principal elements in near-equimolar ratios, have emerged as a groundbreaking class of materials for next-generation flexible electronics. This review systematically examines the unique potential of HEAs as sensing materials, moving beyond their traditional role as structural components. We first elucidate the fundamental mechanisms—core effects including lattice distortion, sluggish diffusion, and the cocktail effect—that endow HEAs with an exceptional synergy of high strength, good ductility, tunable electrical resistivity, and superior electrocatalytic activity. Subsequently, we critically analyze the state-of-the-art strategies for processing HEA-based micro/nano structures, including mechanical alloying, wet-chemical synthesis, and non-equilibrium deposition techniques, with an emphasis on their compatibility with flexible substrates. The core of the review categorizes and discusses the latest advances in HEA-based flexible sensors for strain/stress, gas, and electrochemical (e.g., glucose, biomarkers, heavy metals) detection, highlighting the structure–property–performance relationships. Representative studies have demonstrated that HEA flexible strain sensors achieve a temperature coefficient of resistance as low as 45.59 ppm/K with no signal drift over 6000 stretching cycles; room-temperature hydrogen sensors reach a detection limit down to 31 ppb with a response time of 19 s; and non-enzymatic glucose sensors deliver a sensitivity up to 3043 μA·mM−1·cm−2. Finally, we summarize the key challenges—such as manufacturing scalability, long-term stability under dynamic deformation, and cost-effectiveness—and provide a forward-looking perspective on promising research directions, including high-throughput compositional screening, multi-functional sensor arrays, and the integration of machine learning for rational material design. Full article
(This article belongs to the Section Metals and Alloys)
Show Figures

Figure 1

22 pages, 475 KB  
Article
Labor Mobility and the Coupling Coordination of Economic and Ecological Welfare in Northeast China’s State-Owned Forest Regions
by Qiuhua Song and Hongliang Lu
Sustainability 2026, 18(12), 6317; https://doi.org/10.3390/su18126317 (registering DOI) - 19 Jun 2026
Viewed by 373
Abstract
Under the concurrent advancement of ecological civilization and resource-dependent region transformation, key state-owned forest areas in northeast China have shifted from timber supply to ecosystem protection. However, while the Natural Forest Protection Program has restored forest resources and increased coverage, it has also [...] Read more.
Under the concurrent advancement of ecological civilization and resource-dependent region transformation, key state-owned forest areas in northeast China have shifted from timber supply to ecosystem protection. However, while the Natural Forest Protection Program has restored forest resources and increased coverage, it has also led to the contraction of traditional industries, reduced employment, population outflow, and a structural tension between weak economic growth and enhanced ecological functions. This study aims to investigate how labor mobility affects the coordinated development of economic and ecological welfare in these regions. To achieve this, we construct economic and ecological welfare indices using entropy weighting and calculate their coupling coordination degree based on panel data from the China Forestry Statistical Yearbook (2000–2017) and the China Forestry and Grassland Statistical Yearbook (2018–2025). Our key scientific contributions are as follows: (1) we reveal a nonlinear and significantly negative impact of labor mobility on coupling coordination; (2) we identify industrial structure as a partial mediating channel; and (3) we uncover significant regional and developmental stage heterogeneity. Methodologically, we employ fixed-effects, mediation, threshold, and spatial panel models to ensure robustness. The findings provide novel insights into labor–environment trade-offs in forest-dependent regions and offer policy implications for optimizing labor allocation, strengthening ecological compensation and industrial synergy, and improving regional governance to achieve coordinated economic–ecological development. Full article
(This article belongs to the Section Environmental Sustainability and Applications)
Show Figures

Figure 1

16 pages, 327 KB  
Article
Toward a Tripartite Taxonomy of Entropy in Physics
by Antoine Druilhe
Entropy 2026, 28(6), 704; https://doi.org/10.3390/e28060704 - 18 Jun 2026
Viewed by 266
Abstract
The term “entropy” denotes several mathematically distinct quantities across modern physics, including thermodynamic, statistical, quantum-informational, and geometric notions that are often conflated in foundational discussions. We propose an operational distinction among three such quantities: a geometric capacity entropy Scapacity proportional to a [...] Read more.
The term “entropy” denotes several mathematically distinct quantities across modern physics, including thermodynamic, statistical, quantum-informational, and geometric notions that are often conflated in foundational discussions. We propose an operational distinction among three such quantities: a geometric capacity entropy Scapacity proportional to a region’s bounding area, a microscopic content entropy Scontent given by the fine-grained von Neumann entropy of the reduced state, and a thermodynamic entropy Sthermo corresponding to the observer-relative ignorance that remains after accessible information is accounted for. We argue that keeping these quantities distinct is not merely terminological: within this framework, the second law of thermodynamics can be formulated as a typical consequence of unitary dynamics combined with bounded observational access, rather than as an independent postulate. The distinction also clarifies which entropy enters established results such as the Bekenstein–Hawking entropy of black holes and the Clausius relation in Jacobson’s thermodynamic derivation of Einstein’s equations. The proposed framework is conceptual and does not modify established physical theories; it is intended as a useful clarification for informational approaches to physics. Full article
(This article belongs to the Section Quantum Information)
22 pages, 549 KB  
Article
Learning from Crowds Using a Focal Loss Function: Dealing with Imbalanced Annotations
by Julian Gil-Gonzalez, David Augusto Cárdenas-Peña, Alvaro Orozco-Gutiérrez, Enrique D. Guijarro-Estelles and Andres M. Álvarez-Meza
Technologies 2026, 14(6), 370; https://doi.org/10.3390/technologies14060370 - 17 Jun 2026
Viewed by 143
Abstract
Obtaining high-quality labeled data for supervised learning is costly, motivating the use of crowdsourcing, which distributes the annotation process across multiple workers with varying levels of expertise. A key challenge in crowdsourced data is annotation sparsity, as each worker labels only a limited [...] Read more.
Obtaining high-quality labeled data for supervised learning is costly, motivating the use of crowdsourcing, which distributes the annotation process across multiple workers with varying levels of expertise. A key challenge in crowdsourced data is annotation sparsity, as each worker labels only a limited subset of instances. This sparsity can amplify class imbalance, reduce supervision for minority classes, and bias standard cross-entropy-based models toward the majority classes. To address this problem, we propose a correlated chained Gaussian process framework trained on a focal-loss-based variational objective (CCGPFL). This probabilistic framework jointly models latent ground-truth and instance-dependent annotator reliability while accounting for correlations among annotators. In addition, the focal-weighted objective mitigates the imbalance induced by sparse annotations by assigning greater importance to harder examples during training. Experiments on synthetic, semi-synthetic, and fully real multi-annotator datasets show that CCGPFL achieves competitive and often superior performance relative to state-of-the-art learning-from-crowds baselines in terms of Overall Accuracy (OA) and Area Under the ROC Curve (AUC). Full article
Show Figures

Figure 1

20 pages, 6237 KB  
Article
Belief-Guided Homeostatic Estimation for Regime Adaptation in Multi-Layer Industrial Network Scheduling
by Wei Xu, Yi Wan and T. Zuo
Algorithms 2026, 19(6), 487; https://doi.org/10.3390/a19060487 - 17 Jun 2026
Viewed by 189
Abstract
Scheduling in multi-layer industrial networks must remain stable even when the feedback mechanism of the environment changes inside a single production episode. The system can switch between a step-continuous regime with dense process feedback and a task-driven regime with sparse milestone feedback, so [...] Read more.
Scheduling in multi-layer industrial networks must remain stable even when the feedback mechanism of the environment changes inside a single production episode. The system can switch between a step-continuous regime with dense process feedback and a task-driven regime with sparse milestone feedback, so that the same state requires different behaviour before and after the switch. A regime-oblivious policy may therefore optimise the wrong action preference after a switch. We formulate this setting as a mode-switched multi-industrial-chain Markov decision process (MS-MIC-MDP) and prove that a single fixed action preference is necessarily suboptimal in at least one regime. We then propose BHERA, a belief-guided homeostatic estimation framework for regime adaptation. BHERA builds cross-layer representations, performs structured variational inference of slow and fast latent beliefs, estimates the posterior probability of the task-driven regime, and uses that posterior to regulate sample weights, entropy strength, return-prediction emphasis, and latent information capacity. A homeostatic feedback rule on the Kullback–Leibler (KL) divergence keeps the latent representation informative without allowing uncontrolled information growth, and we analyse it as a two-timescale stochastic approximation with an associated convergence argument and a per-iteration complexity bound. Experiments in a multi-layer industrial scheduling simulator show that BHERA achieves higher return, lower cost, and higher utility than CReSCENT, HiTAC-MuSE, Informed Switching, and WToE across all tested perturbations, with paired statistical tests confirming significance. Expanded ablations and parameter-sensitivity studies confirm the importance of regime belief, regime-balanced weighting, bootstrap prediction, homeostatic capacity control, and the dual-timescale latent split. Full article
Show Figures

Figure 1

22 pages, 2927 KB  
Article
Control Subarea Division for Coordinated Signal Control: A Colored Random Walk and Path Entropy Approach to Traffic-State Propagation
by Pengcheng Li, Bin Li, Lin Wang, Wei Zhang, Sixian Li and Jun Hua
Entropy 2026, 28(6), 692; https://doi.org/10.3390/e28060692 - 16 Jun 2026
Viewed by 198
Abstract
Control subarea division is essential for coordinated signal control, but methods based mainly on local correlation or static topology may not adequately capture traffic-state propagation under dynamic traffic loading. This study proposes a control subarea division method that explicitly models traffic-state propagation by [...] Read more.
Control subarea division is essential for coordinated signal control, but methods based mainly on local correlation or static topology may not adequately capture traffic-state propagation under dynamic traffic loading. This study proposes a control subarea division method that explicitly models traffic-state propagation by integrating state-guided colored random walk and path entropy analysis. Intersection correlation degree and traffic state are used to construct a state-guided colored random walk process, in which transition probabilities are updated according to network connectivity and traffic-state consistency. Path entropy characterizes propagation uncertainty, and control subareas are identified by minimizing the distribution discrepancy between node-level and subarea-level path responses. To compare partitioning schemes, five complementary metrics were adopted: variance reduction rate of spatial delay, delay reduction rate, congestion mitigation index, stop reduction rate, and queue reduction rate. A VISSIM microsimulation model with dynamic traffic loading was developed to compare the proposed method with the Whitson and Fast Newman methods. The proposed method achieved the best performance across all five metrics, with values of 41.47%, 23.77%, 25.96%, 23.59%, and 15.08%, respectively. These results indicate that the proposed method improves spatial balance and network efficiency while mitigating bottlenecks, reducing stops, and suppressing queue accumulation. Full article
(This article belongs to the Section Complexity)
Show Figures

Figure 1

32 pages, 456 KB  
Article
Analytical Entropy Approach for Measuring Blockchain Immutability and Tamper-Resilient Trust
by Lanlan Li, Charles Z. Liu and Sanjeeb Shrestha
Entropy 2026, 28(6), 690; https://doi.org/10.3390/e28060690 - 15 Jun 2026
Viewed by 144
Abstract
This work presents a comprehensive study of entropy-based metrics for evaluating blockchain systems, focusing on on-chain ledger immutability, off-chain data integrity, and computational dynamics within blockchain virtual machines (BVMs). We develop a unified framework that models blockchain states as probabilistic distributions, quantifying uncertainty [...] Read more.
This work presents a comprehensive study of entropy-based metrics for evaluating blockchain systems, focusing on on-chain ledger immutability, off-chain data integrity, and computational dynamics within blockchain virtual machines (BVMs). We develop a unified framework that models blockchain states as probabilistic distributions, quantifying uncertainty through Shannon entropy and examining its evolution under varying adversarial fractions. Extensive simulations demonstrate that on-chain entropy exhibits near-exponential decay, reflecting the cumulative reinforcement of honest consensus, while off-chain entropy remains static, highlighting the limitations of conventional data storage. Furthermore, the BVM is analyzed in terms of computation entropy, establishing its Turing completeness and demonstrating that smart-contract state evolution mirrors the information dynamics of arbitrary Turing machines. Our results provide quantitative evidence that entropy serves as both a theoretical and operational measure of immutability, tamper evidence, and protocol resilience. The proposed entropy framework offers practical tools for monitoring ledger integrity, detecting tampering, and assessing computational complexity, bridging the gap between information-theoretic principles and distributed ledger applications. This study advances both the theoretical understanding and practical evaluation of blockchain security, providing a principled methodology for analyzing distributed systems under adversarial conditions. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
Show Figures

Figure 1

Back to TopTop