Entropy最新文献

{"title":"Dimensional Analysis over Finite Holographic Substrate.","authors":"Yosef Akhtman","doi":"10.3390/e28101122","DOIUrl":"https://doi.org/10.3390/e28101122","url":null,"abstract":"<p><p>The paper derives the fundamental physical units in a universe defined over a finite holographic substrate: a finite totality whose capacity bounds the state count of every embedded observer. The units are anchored at the substrate's four horizons: the Planck length, momentum, time and energy. The constants <i>c</i>, <i>ℏ</i>, <i>G</i>, kB follow uniquely from this quartet, over realisations stated with their falsifiers: <i>c</i> the ratio across the two Fourier pairs, <i>ℏ</i> the product within each conjugate pair, kB the mixed product, <i>G</i> the normalisation to the totality. The quartet admits one cancellation identity and no further independent relation; on an admissible substrate the constants are exact residues read as unit-face magnitudes. Beneath the quartet, dimensional analysis is a graded modular domain algebra on the framed shell, recovering the classical calculus exactly inside the sub-capacity window. The domain of <i>ℏ</i> is the unit flag; its torsion-free surrogate is the classical mass dimension, temperature inherits the acceleration domain, and the flag cancels in every count-valued comparison. Two predictions are staked: a resolution floor on single coherent registration and the exact constancy of the constants' dimensionless ratios. Every theorem of the paper is numerically verified and formalized in Lean 4.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mapping Information Flows in Urban Traffic Networks: A Transfer Entropy Approach.","authors":"Vera Pecorino, Giovanni Calabrò, Alessandro Pluchino, Giuseppe Inturri, Salvatore Cavalieri","doi":"10.3390/e28101127","DOIUrl":"https://doi.org/10.3390/e28101127","url":null,"abstract":"<p><p>This study applies Transfer Entropy (TE) to floating car data from the urban road network of Catania (Italy) to investigate directional dependencies in traffic flows and identify relevant patterns of information transfer. Unlike traditional correlation-based approaches, TE captures asymmetric directed information dependencies between road segments, enabling the identification of predictive relationships among congestion states across the network. We constructed TE-based influence networks using traffic speed data collected over 15 min intervals across 86 road segments over six weeks. The analysis examined information transfer using history lengths of 1, 2, and 3 observations, corresponding to 15, 30, and 45 min of past information, revealing distinct patterns between time windows. Key findings include the identification of recurring information-transfer relationships across multiple history lengths, and road segments with comparatively high outgoing or incoming information strength. Notably, the morning and evening time windows differ in network density, total strength and highest-ranked nodes, although some of these patterns depend on the discretisation and history length adopted, highlighting the dynamic nature of urban traffic systems. This approach shifts focus from traditional traffic prediction to network prioritisation, allowing the identification of candidate locations for enhanced traffic monitoring with minimal data requirements. The methodology provides practical insights for optimising sensor placement and informing further traffic-management analysis based on predictive influence patterns rather than congestion levels alone.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"FBS26: An Entropy-Based Metric for Assessing Architectural Maturity of UML Class Diagrams.","authors":"Wiktor Bohdan Daszczuk, Stanisław Jerzy Niepostyn","doi":"10.3390/e28101126","DOIUrl":"https://doi.org/10.3390/e28101126","url":null,"abstract":"<p><p>Entropy-based metrics can provide a quantitative representation of the information content of UML models, but their practical usefulness depends on a systematic and reproducible calibration of the parameters used to construct the underlying probability distribution. This paper presents FBS26, an extension of the FBS metric that introduces calibrated weights for UML element kinds while retaining the normalized Shannon entropy formulation. The proposed calibration procedure combines three criteria: avoiding false lack-of-information cases, reducing non-monotonic behavior of the metric, and achieving a pronounced decrease in the metric for balanced diagram series. The criteria are applied according to a predefined lexicographic priority. The approach is evaluated using a controlled series of UML class diagrams and 123 UML class diagrams from four industrial software projects, selected from a repository containing more than 2000 UML diagrams from 18 projects. Architectural maturity labels, assigned independently by an experienced software architect, serve as reference data for examining empirical thresholds for structural information. The results show that systematic weight calibration removes the undesirable behavior observed for the considered FBS16 configurations and provides a more stable basis for comparing UML class diagrams. The industrial analysis further indicates differences in the structural entropy ranges of commonly distinguished diagram categories. FBS26, therefore, provides a quantitative information-content measure that can support expert-based assessment of the architectural maturity of UML class diagrams.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Uncertainty-Robust Decision Framework Based on Fractional Einstein Aggregation for Prioritizing Renewable Power Generation Technologies with Unknown Weights.","authors":"Majed Albaity, Muhammad Rahim","doi":"10.3390/e28101129","DOIUrl":"https://doi.org/10.3390/e28101129","url":null,"abstract":"<p><p>Renewable power generation plays a central role in the transition toward sustainable, low-carbon energy systems. However, selecting an appropriate technology remains challenging because technical, economic, environmental, and operational criteria may conflict, while expert judgments may involve uncertainty and diversity. To address these challenges, this study proposes a fractional fuzzy multi-criteria group decision-making framework for evaluating and ranking renewable power generation technologies under uncertain expert assessments. A new family of aggregation operators is developed by incorporating fractional fuzzy information into the Einstein operational framework, providing a mechanism for representing and aggregating uncertain assessments. An entropy-based weighting mechanism is further employed to determine criterion weights from the available decision information. The proposed components are integrated into a unified decision procedure that combines expert weighting, fractional fuzzy aggregation, criterion weighting, and distance-based TOPSIS assessment within a common computational framework. The numerical case study considers technical, economic, environmental, and operational criteria for renewable power generation technology selection. A sensitivity analysis examines the influence of the fractional parameters on the resulting rankings, while a comparative analysis with existing decision-making approaches is conducted to examine the consistency of the obtained results. The findings demonstrate the application of the proposed framework under the specified assessment conditions and illustrate the role of fractional fuzzy information and Einstein-based aggregation in the decision process. The study provides an integrated approach for incorporating uncertain expert information into renewable energy technology selection.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ZK-AdapterMark: Privacy-Preserving Provenance Evidence for LoRA Adapters.","authors":"Yicheng Yu, Wangyu Wu, Renwen Ma","doi":"10.3390/e28101128","DOIUrl":"https://doi.org/10.3390/e28101128","url":null,"abstract":"<p><p>Low-rank adaptation (LoRA) fine-tunes a large model with a low-rank update over frozen weights. The update travels as a separate adapter file that is easy to copy, alter, and re-upload; so, a hub may have to decide whether a disputed file derives from a registered adapter. Since an altered copy no longer matches the original byte for byte, the usual tool is a fingerprint, secret measurements of the weights that survive moderate edits. Verifying a fingerprint currently requires disclosing either the measurements, which a copier can then evade, or the possibly confidential weights. ZK-AdapterMark is, to our knowledge, the first to verify a LoRA fingerprint in zero knowledge: a hub confirms that a disputed file passes a registered fingerprint without learning the secret or the weights. The proof is practical because our fingerprint is expressed over the two low-rank factors, making the complete proof circuit up to 44 times smaller than rebuilding the update. The acceptance threshold fixes a relative-entropy bound on the probability of accepting an unrelated adapter, which gives it an information-theoretic footing. Across ten model families, the fingerprint survives moderate quantization, noise, and rank reduction, and no pair among 904 independently trained adapters is accepted.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"OneBoot GRU: Validation-Locked Polynomial Calibration for Level-Invariant Encrypted Inference.","authors":"Xinxia Song, Zhigang Chen, Liqun Chen","doi":"10.3390/e28101118","DOIUrl":"https://doi.org/10.3390/e28101118","url":null,"abstract":"<p><p>Encrypted recurrent inference must preserve both ciphertext depth and the numerical behavior of a feedback model. We develop OneBoot GRU, which couples the validation-locked selection of degree-three Sigmoid and degree-seven Tanh domains with a CKKS GRU cell that refreshes one hidden-state ciphertext after each step. On TwoPatterns, the locked polynomial model completed finite official-test trajectories with 92.431% macro accuracy, versus 98.114% for exact activations, and 0.830% mean domain violations. On SyntheticControl, polynomial and exact macro accuracies were 89.067% and 90.133%. Direct state-error comparisons show that improved domain coverage does not always reduce recurrent error; in a separate exploratory domain extension, screening reduced qualification tail error by 74.1% and 94.6% on ECG200 and ItalyPowerDemand. A parameter profile audited against pinned 128-bit sparse-secret references completed four encrypted recurrent steps, prefix pooling, and the trained head with maximum logit error 2.91 × 10^-6 relative to the plaintext polynomial circuit. In three matched four-step runs, GRU median circuit latency was 226.343 s versus 336.981 s for an implemented polynomial LSTM. Twelve additional distinct 128-step inputs were completed under an intentionally insecure structural profile, with 12/12 prediction agreement against the plaintext polynomial reference. These experiments provide measured calibration, arithmetic-fidelity, and system-cost operating points within their stated parameter and sampling scopes.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Entanglement Crossovers Under Time-Dependent U(1) Symmetry Breaking in Monitored Quantum Circuits.","authors":"Terrence Lingzhu Zhao, Zhou Shangnan","doi":"10.3390/e28101120","DOIUrl":"https://doi.org/10.3390/e28101120","url":null,"abstract":"<p><p>Conservation laws reshape quantum information dynamics by restricting how scrambling can occur. In monitored circuits, this raises a natural dynamical question: when a symmetry constraint is gradually relaxed, how quickly do the entanglement dynamics forget the symmetric regime? We address this question in one-dimensional monitored random circuits by driving the two-qubit gate ensemble from exact U(1) conservation toward unconstrained Haar dynamics. The response is not instantaneous: the entanglement retains a finite-depth memory of the conserving dynamics and crosses over toward the unconstrained behavior over a rate-dependent time window. Operational 25%, 50%, and 75% crossover times all move to later circuit depths for slower drives. At p=0.4, the same rate ordering is also observed through L=32 in a finite-time matrix-product-state consistency check with a limited trajectory ensemble. By contrast, the weak fixed perturbations studied here, ϵ(t)=ϵ0≤0.1, remain close to the conserving reference over the same finite observation window. Within this finite-time window, the driven crossover is therefore not reproduced merely by waiting under the fixed perturbations tested. Purification dynamics from a maximally mixed state exhibit the same qualitative response. We therefore interpret the results as a finite-time dynamical crossover from symmetry-constrained dynamics toward less constrained scrambling, rather than as evidence for a universal crossover exponent or a microscopic noise law. The study provides a controlled setting for asking how long symmetry-dependent information-processing behavior persists as a conservation law is deliberately weakened.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Traffic-State-Dependent Cascading-Failure Dynamics in Urban Bus Networks: An Improved Coupled Map Lattice Framework.","authors":"Jie Zhang, Xiaojuan Xie, Shungen Xiao, Ziqi Wang","doi":"10.3390/e28101115","DOIUrl":"https://doi.org/10.3390/e28101115","url":null,"abstract":"<p><p>Urban bus networks are exposed to cascading disruptions whose propagation depends not only on network topology but also on temporally varying traffic states and passenger-flow distributions. Existing vulnerability analyses often rely on static topology or hypothetical flows, limiting their ability to characterize traffic-dependent failure dynamics. This study develops a data-driven vulnerability framework for urban bus networks by integrating a coupled road-bus network, user-equilibrium assignment and a weighted Coupled Map Lattice (CML) model. Smart-card data are used to estimate passenger origin-destination demand, while road traffic states at four representative periods are mapped onto bus links to characterize travel-speed-dependent capacity reductions. The resulting weighted networks are evaluated using degree, strength, conventional betweenness, and traffic-flow betweenness. The improved CML model jointly incorporates topological connectivity, passenger-flow characteristics, external perturbations, and flow redistribution to simulate cascading failures under targeted and random attacks. The Harbin trunk bus network is used as an empirical case study. Results show that cascading-failure patterns are strongly traffic-state dependent: under more congested conditions, failures reach their peak propagation rate earlier. Across the tested parameter settings, perturbation intensity and coupling strength influence the timing and extent of cascade propagation, with responses varying by attack strategy and traffic condition. These findings demonstrate that incorporating time-varying traffic states and actual passenger flows can reveal vulnerability patterns that static topology-based analyses may overlook, providing a basis for time-sensitive disruption management and resilience-oriented bus operations.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fine-Tuning Shifts Form Before Competence: Treatment-Correlated Style Drift Confounds Surface-Form Evaluation of Adapter Specialization.","authors":"Othmane Benyoucef, Latifa Dekhici","doi":"10.3390/e28101116","DOIUrl":"https://doi.org/10.3390/e28101116","url":null,"abstract":"<p><p>Stacking task adapters on a frozen domain adapter is a common approach for modular specialization of large language models, usually justified by knowledge injection; whether the surface-form graders standard in this setting can measure such specialization validly has remained unexamined. Two challenges follow: isolating the domain layer's marginal contribution under identical task training, and determining whether measured differences reflect competence or output form. In this work, both are addressed with a matched-arm DoRA ablation on a frozen Qwen 3.5 9B hybrid: a 242 M-parameter domain expert is trained on a licensed 27.8 M-token corpus, and byte-identical task adapters are trained flat, stacked (DFE-stacking), and jointly across three tasks and five conditions, with the key extraction pair replicated at a second training seed; every grader is audited by per-item failure classification and a dual-rater blind human re-grade with consensus adjudication. The principal finding is that fine-tuning shifts output form before competence: stacking yields no seen-task benefit; an apparent generalization collapse on an unseen schema reduces to a single, highly seed-stable formatting coercion that the domain layer dampens and task-mixture training eliminates, and most automated keyword-grading failures prove to be correct paraphrases, leaving no genuine capability loss detected on any instrument. Because such style drift is induced by the training condition itself, surface-sensitive grader error becomes bias aligned with experimental arms rather than noise. Three additional experiments extend the findings: the coercion replicates on Llama 3.1 8B (60% vs. 19% untuned); a pre-registered 240-item formatting-perturbation battery across four further unseen schemas and eight conventions reveals fine-tuned conditions ranking lowest under strict grading yet highest under format-normalized grading; and a matched-compute wrong-domain control shows the domain layer's coercion dampening to be generic substrate regularization, while value integrity under the induced drift tracked the substrate's domain. The principal contribution lies in the identification and quantification of this confound: surface-form evaluation of adapter specialization is structurally confounded, and per-item audits of the type released herein are a necessary component of specialization studies.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"FusionEP: Adaptive Cross-Modal Deep Fusion Network for Essential Protein Identification via Multi-Omics Integration and Contrastive Learning.","authors":"Chuanyan Wu, Bentao Lin, Qingju Zhang, Jialin Zhang, Rui Gao, Zhi-Ping Liu","doi":"10.3390/e28101117","DOIUrl":"https://doi.org/10.3390/e28101117","url":null,"abstract":"<p><p>Identifying essential proteins lays a foundation for dissecting disease mechanisms and mining therapeutic targets. Existing algorithms mostly adopt unimodal inputs and struggle to capture multi-level biological interactions from genomics, subcellular localization and proteomics. We present FusionEP, which is an adaptive cross-modal deep fusion network built upon contrastive learning to predict essential proteins. FusionEP integrates gene expression profiles, subcellular localization features, and protein interaction map structures. For gene expression information, we design a six-layer Transformer with 12 attention heads and learnable positional encodings for feature extraction. For subcellular features, a multi-scale convolutional neural network (CNN) with four kernel sizes and a channel spatial attention mechanism is designed for feature extraction. A four-layer Graph Attention Network (GAT) with dynamic attention, residual connections, and target node readout functionality is designed to extract feature from protein-protein interaction (PPI) networks. FusionEP employs an adaptive fusion gate for dynamic feature aggregation and supervised contrastive learning for cross-modal alignment. Furthermore, prototype-based classification with focal loss optimization is used to address class imbalance. We evaluated the model's performance on the yeast biological dataset. The results showed that FusionEP achieved an AUC-ROC of 0.9523 ± 0.003 in five independent experiments. FusionEP provides an end-to-end solution for multimodal protein analysis. This work sets a new method for integrating heterogeneous biological data in precision medicine applications.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}