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27 pages, 1777 KB  
Article
Managing Informational Uncertainty in Traceability Systems: A Structural Entropy-Based Model for Complex Production Systems
by Rommel Albuja, Juan Marcelo Ibujés-Villacís and Sang Guun Yoo
Adm. Sci. 2026, 16(8), 391; https://doi.org/10.3390/admsci16080391 - 14 Aug 2026
Viewed by 256
Abstract
The digital transformation of shrimp aquaculture in Ecuador has accelerated the adoption of traceability technologies to improve transparency, regulatory compliance, and supply chain coordination. However, persistent structural limitations—such as technological fragmentation, low interoperability, and inconsistent data quality—continue to constrain their effectiveness. This study [...] Read more.
The digital transformation of shrimp aquaculture in Ecuador has accelerated the adoption of traceability technologies to improve transparency, regulatory compliance, and supply chain coordination. However, persistent structural limitations—such as technological fragmentation, low interoperability, and inconsistent data quality—continue to constrain their effectiveness. This study develops an approach to managing informational uncertainty in traceability systems, grounded in information theory and operationalized through the Technological Management Model for Shrimp Production (TMMT-SP). Methodologically, the research follows an abductive systemic modeling approach, integrating a systematic literature review, structural analysis of the production system, and ontological modeling to identify and classify interdomain gaps. The findings show that informational uncertainty emerges as a structural property of the system, resulting from misalignments across informational, technological, and governance dimensions. These misalignments limit the coherence, reliability, and integration of traceability processes. In response, the study proposes a structural entropy-based framework (understood as an operational representation of systemic informational dispersion) to diagnose, prioritize, and address these gaps, shifting the focus from isolated technological adoption toward systemic coherence. This approach provides a conceptual and methodological basis for designing technology management strategies to reduce uncertainty in complex production systems. Full article
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19 pages, 21310 KB  
Article
Prediction of Potential Habitats for Pholidota chinensis in China Based on the MaxEnt Model
by Zihui Ye, Shimin Yang, Dongdong Wang, Jinchu Luo, Xu Li and Hongfeng Chen
Forests 2026, 17(8), 940; https://doi.org/10.3390/f17080940 - 9 Aug 2026
Viewed by 252
Abstract
Pholidota chinensis is a valuable medicinal epiphytic orchid in China. While its ethnomedicinal importance is recognized, the environmental constraints governing its distribution and its response to future climate change remain insufficiently understood. This study employed the Maximum Entropy (MaxEnt) model to identify dominant [...] Read more.
Pholidota chinensis is a valuable medicinal epiphytic orchid in China. While its ethnomedicinal importance is recognized, the environmental constraints governing its distribution and its response to future climate change remain insufficiently understood. This study employed the Maximum Entropy (MaxEnt) model to identify dominant environmental drivers and project current (1970–2000) and future (2041–2060, 2061–2080) potential climatically suitable habitats under SSP245 and SSP370 scenarios. Using 184 filtered occurrence records and 11 screened environmental variables, the model achieved high discrimination performance (mean AUC = 0.9614 ± 0.0092). Annual precipitation and precipitation of the driest quarter were identified as principal predictors, reflecting a coupled water-temperature niche. Future projections suggested an overall expansion of climatically suitable areas, particularly under SSP245, and a northwestward shift in suitability centroids. However, these projections represent potential climatic suitability rather than confirmed future distribution, as establishment depends on dispersal capacity, host availability, and microhabitat conditions. These findings provide a scientific basis for conservation prioritization and climate-adaptive cultivation planning. Full article
(This article belongs to the Section Forest Ecology and Management)
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23 pages, 608 KB  
Article
An Extended Lagrangian Zero-Truncated Poisson Distribution: Theory and Applications
by Amira F. Daghestani, Hassan S. Bakouch, Radhakumari Maya, Muraleedharan Pushpa Sarath Lal, C. Subramanian, Anhar S. Aloufi and Muhammed Rasheed Irshad
Symmetry 2026, 18(8), 1335; https://doi.org/10.3390/sym18081335 - 7 Aug 2026
Viewed by 245
Abstract
An extended Lagrangian zero-truncated Poisson (ELZTP) distribution is proposed as a new member of the Lagrangian distributions of the second kind. The model provides a flexible framework for capturing diverse dispersion patterns and tail behaviors. Key statistical properties are derived, including the probability [...] Read more.
An extended Lagrangian zero-truncated Poisson (ELZTP) distribution is proposed as a new member of the Lagrangian distributions of the second kind. The model provides a flexible framework for capturing diverse dispersion patterns and tail behaviors. Key statistical properties are derived, including the probability mass function, moments, entropy, and the hazard rate function. Parameters are estimated using the maximum likelihood method, and the finite-sample behavior of the estimators is investigated through a simulation study. The effectiveness of the model is demonstrated using a real-life air-pollution dataset, highlighting the adaptability of the ELZTP distribution to environmental count data applications. Full article
(This article belongs to the Section B: Mathematics)
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22 pages, 18542 KB  
Article
Minimum Intervention Assessment in Historic Building Conservation: An Entropy-Weighted Intervention Intensity Index and Machine Learning Analysis at Caishen Temple, Xinzhou
by Tianxi Lu, Guihua Zu, Siti Sarah Binti Herman and Yang Wang
Buildings 2026, 16(15), 3113; https://doi.org/10.3390/buildings16153113 - 5 Aug 2026
Viewed by 221
Abstract
Conservation interventions in historic buildings require quantitative assessment to balance preservation needs and minimal intervention principles. This study presents a quantitative framework for minimum intervention assessment of heritage conservation, based on 133 documented interventions at Caishen Temple in Xinzhou across four periods: 1992, [...] Read more.
Conservation interventions in historic buildings require quantitative assessment to balance preservation needs and minimal intervention principles. This study presents a quantitative framework for minimum intervention assessment of heritage conservation, based on 133 documented interventions at Caishen Temple in Xinzhou across four periods: 1992, 2006, 2016, and 2017. Four dimensions were defined: Extent of Intervention (EI), Reversibility (RE), Information Loss (IL), and Necessity (NE). Expert scoring on a five-point Likert scale yielded high inter-rater reliability (ICC: 0.79–0.88). The entropy weight method was then used to derive data-driven weights from the expert-scoring matrix, IL=0.3149, EI=0.3025, NE=0.2572, RE=0.1253, and the Intervention Intensity Index (III) was calculated for each intervention. A random forest model was further developed as an exploratory cross-check, with 19 problematic interventions labelled as y=1 and 114 normal interventions as y=0. Target labels were defined through a dual-source procedure combining SSIM- and HSV-based image-similarity assessment for interventions with paired pre- and post-restoration photographs and explicit textual evidence from conservation records for interventions without paired photographs. Feature importance and SHAP analyses indicated that reversibility and necessity had the greatest discriminative importance for distinguishing problematic from normal interventions in this dataset, whereas the entropy-based ranking assigned higher weights to information loss and extent of intervention. This descriptive contrast, based on only four dimensions, highlights the distinction between data dispersion and discriminative capacity. Spatiotemporal analysis indicated that roof and rafter components exhibited the highest intervention intensity, while 1992 interventions contained the largest proportion of problematic practices. This study combines entropy-derived weighting with a machine-learning-based exploratory cross-check, providing a transparent, case-based framework for evidence-based conservation decision-making at historic heritage sites. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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23 pages, 9887 KB  
Article
Beyond Entropy: Organization as the Preservation of Structural Identity
by Ricardo J. Silva
Entropy 2026, 28(8), 876; https://doi.org/10.3390/e28080876 - 4 Aug 2026
Viewed by 318
Abstract
This work introduces a framework in which organization is defined as the degree to which identity-defining relationships among system states are preserved under transformation or perturbation. Existing descriptors such as energy, entropy, mutual information, and divergence measures characterize magnitude, statistical dispersion, dependency, and [...] Read more.
This work introduces a framework in which organization is defined as the degree to which identity-defining relationships among system states are preserved under transformation or perturbation. Existing descriptors such as energy, entropy, mutual information, and divergence measures characterize magnitude, statistical dispersion, dependency, and deviation, yet do not explicitly address the persistence of recognizable structure. To address this limitation, the concepts of organizational classes, reference organizational models, organizational deviation, and recognition boundaries are introduced within a generalized state-space representation. The proposed framework treats recognizable structures as members of organizational classes whose identities are determined by defining constraints and relationships rather than by specific physical realizations. A probabilistic implementation is developed in which organizational classes are represented by reference models and organizational preservation is estimated through measures of organizational deviation. Recognition is incorporated through observer-dependent recognition boundaries that determine whether a realization remains identifiable as a member of a given class. The framework is illustrated through geometric, perceptual, and communication-based examples, including structural degradation in a maximum-entropy background, observer-dependent recognition, channel-limited observability, and a quantitative Gaussian organizational model. These examples demonstrate that entropy and organization are complementary descriptors that may evolve independently: organizational identity may degrade while occupancy statistics remain largely unchanged. The results suggest that communication and sensing systems may be interpreted not only as processes that transport energy or information, but also as systems that preserve, transform, or degrade organizational structure. By providing a descriptor for structural identity alongside entropy and information, the proposed framework offers a foundation for studying how organized structures emerge, persist, transform, and degrade across a wide range of physical, informational, and complex systems. Full article
(This article belongs to the Special Issue Recent Progress in Uncertainty Measures)
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36 pages, 3372 KB  
Article
TDBF-Net: A Method for EEG Emotion Recognition Combining Adaptive Channel Selection and Topology-Aware Convolution
by Gaihua Wang, Wenjiao Ji, Yawei Fan, Xingya Yan, Yu Liu and Weitong Sun
Electronics 2026, 15(15), 3276; https://doi.org/10.3390/electronics15153276 - 24 Jul 2026
Viewed by 260
Abstract
Redundant channels, sparse electrode topology, and insufficient cross-layer feature fusion limit electroencephalography (EEG)-based emotion recognition. This study proposes the Topology-Aware Dual-Bridge Fusion Network (TDBF-Net), a compact framework that integrates adaptive channel selection, topology-aware sparse convolution, and bidirectional bridge fusion. First, sample entropy, dispersion [...] Read more.
Redundant channels, sparse electrode topology, and insufficient cross-layer feature fusion limit electroencephalography (EEG)-based emotion recognition. This study proposes the Topology-Aware Dual-Bridge Fusion Network (TDBF-Net), a compact framework that integrates adaptive channel selection, topology-aware sparse convolution, and bidirectional bridge fusion. First, sample entropy, dispersion entropy, and fuzzy entropy are fused to estimate channel importance, while particle swarm optimization (PSO) learns the entropy weights and an elbow-based criterion determines the retained channel subset. Second, differential entropy (DE) features from the θ, α, β, and γ bands are mapped to an 8×9 sparse topological tensor according to electrode locations. A fixed spatial validity mask is applied before and after convolution to suppress invalid responses from zero-padded regions and preserve real electrode topology. Third, a dual-bridge fusion module recalibrates shallow and deep features in both directions through channel attention and gated fusion, and a bidirectional long short-term memory network (BiLSTM) further captures short-term temporal dependencies. Subject-dependent experiments on the SJTU Emotion EEG Dataset (SEED) and the Database for Emotion Analysis using Physiological Signals (DEAP) show that TDBF-Net achieves 97.62% ± 1.59% accuracy on SEED and 98.46% ± 0.94% and 98.14% ± 0.77% on DEAP valence and arousal, respectively. Paired DEAP ablations support topology and bridge contributions for valence, whereas the corresponding arousal differences are not significant. Selector controls, robustness tests, computational profiling, and held-out visualizations further characterize the method’s compression, cost, and interpretability. The evidence supports TDBF-Net as an effective subject-dependent framework while leaving subject-independent and cross-dataset generalization for future validation. Full article
(This article belongs to the Section Bioelectronics)
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26 pages, 1053 KB  
Article
Short-Window Micro-Behavioral Triage for High-Throughput Firewall Telemetry: Limits, Features, and Operational Feasibility
by Kadir Kesgin, Vedat Tümen and Erdal Akın
Sensors 2026, 26(14), 4600; https://doi.org/10.3390/s26144600 - 20 Jul 2026
Viewed by 441
Abstract
High-throughput firewall telemetry increasingly demands real-time interpretation from short, dense observation windows rather than long historical baselines. We operationalize behavioral slicing, a privacy-preserving approach that extracts interpretable micro-behavioral signals—timing irregularities, destination dispersion (entropy), and intensity cues—from sub-minute traffic segments. This study does [...] Read more.
High-throughput firewall telemetry increasingly demands real-time interpretation from short, dense observation windows rather than long historical baselines. We operationalize behavioral slicing, a privacy-preserving approach that extracts interpretable micro-behavioral signals—timing irregularities, destination dispersion (entropy), and intensity cues—from sub-minute traffic segments. This study does not claim confirmed intrusion detection. Instead, it evaluates whether short-window firewall telemetry can support privacy-preserving candidate triage under high-throughput conditions and quantifies the limits, feature stability, detector complementarity, and real-time feasibility of such a pipeline. Our case study uses a real operational firewall telemetry slice that was irreversibly anonymized prior to analysis. Using unsupervised outlier detection with explainable summaries, the slice-level pipeline produces investigation-oriented anomaly candidates for triage, without making longitudinal routine or habit claims. Synthetic anomaly injection is used only for relative validation, while behavioral findings are derived from the real telemetry slice. Scenario-level ablations show strong separation for scanning and exfiltration but weak performance for low-variance C2 beaconing, indicating that behavioral slicing should be treated as a triage pre-filter rather than a universal detector. In the context of IoT and edge-network monitoring, firewall telemetry can be treated as a high-rate network sensing stream that reflects device-level communication behavior under operational constraints. Overall, results support behavioral slicing as an operationally feasible pre-filtering and triage method under extreme network load, with clear trade-offs and limits. Full article
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22 pages, 18814 KB  
Article
Effect of High-Pressure Torsion on the Hydrogen Storage Properties of Ti-V-Cr-Mn Medium-Entropy Alloy
by Paula C. Cintrón-Núñez, Karina Suárez-Alcántara, Ignacio A. Figueroa-Vargas, Juan R. Tena-García, Joaquín E. González-Hernández, Jorge M. Cubero-Sesin, Yoshikazu Todaka, Daniel Bahena-Uribe, Armando Salinas-Rodríguez and José G. Cabañas-Moreno
Metals 2026, 16(7), 807; https://doi.org/10.3390/met16070807 - 20 Jul 2026
Viewed by 443
Abstract
Hydrogen storage represents a key technological challenge to the widespread use of hydrogen as a fuel and energy carrier. For this purpose, the hydrogen storage properties of medium-entropy and high-entropy alloys are under extensive investigation, including the study of the effects of compositional [...] Read more.
Hydrogen storage represents a key technological challenge to the widespread use of hydrogen as a fuel and energy carrier. For this purpose, the hydrogen storage properties of medium-entropy and high-entropy alloys are under extensive investigation, including the study of the effects of compositional variations, nanostructuring, and catalyst additions. The present work characterizes the hydrogen storage behavior of a medium-entropy, near equiatomic Ti-V-Cr-Mn alloy, both in the as-cast condition and after nanostructuring by severe plastic deformation. The alloy consists of a matrix of BCC solid solution and a dispersed C14 Laves phase. Processing by high-pressure torsion results in the refinement of the crystallite size of the BCC phase down to about 30 nm. The absorption capacity of the alloy at 45 °C and 2.5 MPa is 1.6 wt%. Regardless of its initial condition, the first hydrogenation of the Ti-V-Cr-Mn alloy at room temperature and 2.5 MPa occurs without any pre-activation treatment. On the other hand, hydrogen is partially released at room temperature, while full dehydrogenation requires a temperature of 300 °C. Severe plastic deformation considerably reduces the susceptibility of the alloy to become deactivated for hydrogen absorption. These results highlight the potential of plastic straining to tailor the hydrogen storage properties of metallic BCC alloys. Full article
(This article belongs to the Special Issue Hydrogen Storage Alloys: State of the Art)
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14 pages, 18797 KB  
Article
Ultrasonic Atomization of a Refractory High-Entropy Alloy TiZrNbHfTa for Additive Manufacturing
by Brendon S. Dodge, Suyash Niraula, Naiyer Shokri, Justin D. Gillham and Thomas A. Berfield
Powders 2026, 5(3), 25; https://doi.org/10.3390/powders5030025 - 16 Jul 2026
Viewed by 879
Abstract
Growing attention in additive manufacturing (AM) of high-entropy alloys has intensified the demand for techniques in creating high-quality powder for AM. This study characterizes the effectiveness of a multifunctional vacuum arc melting (VAM) and ultrasonic-plasma atomization (UPA) system for creating TiZrNbHfTa powder. The [...] Read more.
Growing attention in additive manufacturing (AM) of high-entropy alloys has intensified the demand for techniques in creating high-quality powder for AM. This study characterizes the effectiveness of a multifunctional vacuum arc melting (VAM) and ultrasonic-plasma atomization (UPA) system for creating TiZrNbHfTa powder. The focus is to evaluate the morphology, microstructural homogeneity, and phase composition of ultrasonically atomized powder to assess process capability for preparing powder feedstock for AM. Atomized powder was sieved into three size ranges, 15–63 µm, 63–125 µm, and 125–250 µm for characterization by scanning electron microscopy (SEM), electron dispersive spectroscopy (EDS), X-ray diffraction (XRD), and micro-computed tomography (micro-CT). SEM, EDS, and XRD results show that the powder is highly homogenous with an elemental distribution independent of powder size range and a microstructure comprising a BCC solid solution and minor monoclinic Ti oxide. Micro-CT scans indicate low porosity (0.24%, 0.08%, 0.24%) and high sphericity (0.93, 0.90, 0.93) for the 15–63 µm, 63–125 µm, and 125–250 µm distributions, respectively. Overall, the key innovation of this study is the successful application of ultrasonic atomization to produce high-quality TiZrNbHfTa refractory high-entropy alloy powder for additive manufacturing, a technique that has a limited scope of research. Specifically, this work demonstrates that ultrasonic atomization can produce highly homogeneous powder with high sphericity, low porosity, and a particle size distribution suitable for laser powder bed fusion and powder directed energy deposition, establishing ultrasonic atomization as a viable route for producing refractory high-entropy alloy powder for AM. Full article
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27 pages, 25455 KB  
Article
Optimization of Preparation Process and Performance of Crumb Rubber/SBS-Composite-Modified Bitumen
by Renzhe Lei, Jianzhong Huang, Zhao Wang, Haojie Ji, Zunqing Liu and Jian Sun
Materials 2026, 19(14), 3041; https://doi.org/10.3390/ma19143041 - 14 Jul 2026
Viewed by 321
Abstract
To enhance the comprehensive performance of crumb rubber (CR)/SBS-composite-modified bitumen, an orthogonal experimental design was first adopted to analyze the effects of process parameters—including the addition sequence, shearing duration, shearing temperature and shearing speed—on the conventional properties of bitumen. Furthermore, based on the [...] Read more.
To enhance the comprehensive performance of crumb rubber (CR)/SBS-composite-modified bitumen, an orthogonal experimental design was first adopted to analyze the effects of process parameters—including the addition sequence, shearing duration, shearing temperature and shearing speed—on the conventional properties of bitumen. Furthermore, based on the Box–Behnken response surface methodology, quadratic regression predictive models for the dosages of SBS, waste crumb rubber and aromatic oil were constructed, and the entropy-weighted TOPSIS method was introduced to comprehensively evaluate and multi-objectively optimize the proportioning schemes. The results indicate that a reasonable preparation process can significantly promote the uniform dispersion of modifiers, distinct non-linear interactions exist among the dosages of each modifier, and the optimal proportion balancing both high- and low-temperature performance was obtained through optimization. The constructed models exhibit good predictive accuracy, and the optimized CR/SBS-composite-modified bitumen showed excellent conventional properties and storage stability, which can provide a theoretical reference for the recycling of waste tires and the engineering application of composite-modified bitumen. Full article
(This article belongs to the Section Construction and Building Materials)
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27 pages, 14418 KB  
Article
From Energy Balance to Information Structure: An Entropy-Based Analysis of PV–Building Energy Flows
by Arkadiusz Małek
Energies 2026, 19(14), 3323; https://doi.org/10.3390/en19143323 - 14 Jul 2026
Viewed by 356
Abstract
Photovoltaic (PV)–building systems are commonly assessed using aggregated energy indicators that obscure the structural diversity of energy flows. This study introduces an entropy-based approach for quantifying the operational structure of energy flows in a real PV–building system from an information-theoretic perspective. High-resolution 15-min [...] Read more.
Photovoltaic (PV)–building systems are commonly assessed using aggregated energy indicators that obscure the structural diversity of energy flows. This study introduces an entropy-based approach for quantifying the operational structure of energy flows in a real PV–building system from an information-theoretic perspective. High-resolution 15-min measurement data covering a full month were used to derive cumulative energy contributions associated with local self-consumption, surplus export to the grid, and electricity import from the grid. These flows were reformulated as a probability distribution and analyzed using Shannon entropy. The results reveal a high normalized entropy of monthly energy flows, indicating substantial dispersion among operating states despite the dominance of local self-consumption. Entropy decomposition shows that all flow components contribute meaningfully to system uncertainty, including surplus export, which exhibits a disproportionate informational impact relative to its energy share. The findings demonstrate that entropy captures structural properties of PV–building operation not accessible through conventional energy balance metrics. The proposed framework provides a compact, scale-independent descriptor of operational complexity and offers a new quantitative perspective for assessing predictability and structural heterogeneity in PV–building energy systems. Full article
(This article belongs to the Special Issue Solar Energy Conversion and Storage Technologies)
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30 pages, 42623 KB  
Article
Effect of Non-Periodic Leading-Edge Wear on Aerodynamic Performance and Stall-Precursor Coherence in Centrifugal Compressor
by Hong Xie, Zhibiao Cai, Bo Yang and Chunrong Wang
Aerospace 2026, 13(7), 630; https://doi.org/10.3390/aerospace13070630 - 11 Jul 2026
Viewed by 309
Abstract
Non-periodic leading-edge wear near the impeller tip is investigated with respect to the aerodynamic performance, steady flow organization, and near-stall unsteady evolution of a centrifugal compressor. A full-annulus three-dimensional impeller–vaned-diffuser model is established for a baseline configuration (O-M) and a non-periodically worn configuration [...] Read more.
Non-periodic leading-edge wear near the impeller tip is investigated with respect to the aerodynamic performance, steady flow organization, and near-stall unsteady evolution of a centrifugal compressor. A full-annulus three-dimensional impeller–vaned-diffuser model is established for a baseline configuration (O-M) and a non-periodically worn configuration (W-M). The two configurations are compared in terms of performance characteristics, near-tip pressure coefficient, static pressure, entropy, relative Mach number, three-dimensional vortical structures, and pressure fluctuation signals. The W-M generally produces a lower total pressure ratio than the O-M, with a maximum reduction of approximately 0.7%. Nevertheless, the isentropic efficiency is slightly improved over the main operating range, with a peak increase of about 0.6%, and the near-stall flow rate shifts toward a lower value. Pressure coefficient distributions at 95% span show that leading-edge wear weakens both the pressure-side pressure peak and the suction-side suction peak of the worn blades, redistributing the near-tip loading from a highly leading-edge-concentrated form to a broader chordwise distribution. The steady flow fields indicate that wear does not eliminate local low-pressure or high-entropy regions; rather, it reorganizes their circumferential arrangement, converting originally synchronized low-pressure zones, high-entropy bands, and high-speed shear layers into a non-uniform pattern with alternating strong and weak passages. Near-stall unsteady results further reveal that pressure cells, high-entropy zones, and large-scale vortical structures in the O-M exhibit clear cross-passage propagation, whereas the corresponding disturbances in the W-M remain predominantly localized, dispersed, and asynchronous. These results demonstrate that, for the wear location and blade-to-blade distribution considered here, non-periodic leading-edge wear affects stability primarily by weakening the circumferentially coherent amplification of disturbances, rather than by simply reducing all local loss sources. Full article
(This article belongs to the Section Aeronautics)
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20 pages, 2126 KB  
Article
Recovering 4f Electronic Shell Signatures from Collective Spectral Manifolds of Lanthanide Ions: A New Perspective for Rare-Earth Photonics
by Helena Cristina Vasconcelos and Maria Meirelles
Photonics 2026, 13(7), 658; https://doi.org/10.3390/photonics13070658 - 9 Jul 2026
Viewed by 413
Abstract
The electronic spectra of trivalent lanthanide ions constitute one of the most extensively characterised manifestations of partially filled 4f shells. Conventional rare-earth spectroscopy provides a detailed microscopic description based on assigned multiplets, angular-momentum structure, crystal-field effects and transition probabilities. Here, we examine [...] Read more.
The electronic spectra of trivalent lanthanide ions constitute one of the most extensively characterised manifestations of partially filled 4f shells. Conventional rare-earth spectroscopy provides a detailed microscopic description based on assigned multiplets, angular-momentum structure, crystal-field effects and transition probabilities. Here, we examine a complementary question: whether information associated with the underlying 4f electronic architecture remains detectable after the spectroscopic labels normally used to identify it are deliberately removed. Using the multiplet-centre energies of Ln3+ ions in LaF3, each ion was represented as an energy-only spectral manifold, Mn={Ei}, obtained after removing term identity, angular-momentum labels and transition assignments. The resulting manifolds were analysed through a controlled information-reduction sequence involving spectral occupancy and four complementary descriptors: spectral entropy S, compactness C, mean manifold energy μE and spectral dispersion σE. The results show that the reduced manifolds do not collapse into featureless collections of energies. Instead, they retain structured organisation across the lanthanide series, with distinctive behaviour associated with the shell-edge configurations Ce3+ (4f1) and Yb3+ (4f13), and with the half-filled-shell configuration Gd3+ (4f7). A blind reconstruction test provides the strongest internal validation: when Gd3+ is excluded from the reference evolution and subsequently reintroduced, it emerges as the dominant positive deviation of the mean manifold-energy coordinate. This demonstrates that the 4f7 signature is not encoded only in explicit term labels or selected multiplets but leaves a measurable fingerprint in the collective energy distribution. The comparison of normalised descriptor responses further indicates that electronic shell information is distributed across state occupation, compactness, energetic displacement and spectral spreading. These results suggest that lanthanide spectra can be analysed not only as collections of assigned transitions, but also as collective spectral manifolds whose global organisation preserves physically meaningful information about shell filling. This approach does not replace conventional rare-earth spectroscopy; rather, it provides a complementary framework for testing which aspects of electronic structure remain accessible after microscopic spectroscopic identity has been removed. Full article
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29 pages, 11440 KB  
Article
Ecological Vulnerability Assessment and Prediction in the Middle Reach of the West Liaohe River Basin
by Chunhui Xu, Cheng Han, Qixin Liu and Yinghui Ye
Land 2026, 15(7), 1221; https://doi.org/10.3390/land15071221 - 7 Jul 2026
Viewed by 246
Abstract
The middle reaches of the West Liaohe River Basin, a typical semi-arid to semi-humid transition and agro-pastoral ecotone in northern China, exhibit high ecological sensitivity, low resilience, and pronounced fragility. Despite growing concerns, existing studies in this region lack a comprehensive assessment paradigm [...] Read more.
The middle reaches of the West Liaohe River Basin, a typical semi-arid to semi-humid transition and agro-pastoral ecotone in northern China, exhibit high ecological sensitivity, low resilience, and pronounced fragility. Despite growing concerns, existing studies in this region lack a comprehensive assessment paradigm that effectively couples inherent ecological attributes with nonlinear predictive modeling. To fill this gap, we developed an integrative framework that innovatively combined the SRP conceptual model with a stacking ensemble learning technique. This coupling is methodologically novel because it moves beyond linear assumptions, enables the detection of complex nonlinear response surfaces, and establishes a seamless analytical chain from historical evaluation to future projection. By selecting 13 indicators, including topography, climate, soil, vegetation, and socio-economic factors, the weight was determined by the comprehensive application of the analytic hierarchy process and entropy weight method, and the ecological fragility of the middle reaches of the West Liaohe River Basin from 2000 to 2020 was evaluated at multiple scales. The spatial differentiation driving factors were analyzed using a geographic detector. Therefore, an Ensemble Learning Regression model was used to simulate and predict the ecological fragility pattern in 2030. The results show that from 2000 to 2020, the ecological fragility of the study area showed a decreasing trend overall, with the Ecological Vulnerability Synthetical Index (EVSI) decreasing from 3.48 to 2.68, and the spatial pattern gradually shifting from “high in the northwest, low in the southeast” to “overall stability, local optimization.” The spatial agglomeration of ecological fragility gradually weakened, indicating that high-fragility areas tend to disperse and low-fragility areas expand in contiguous areas, and the ecosystem structure tends to develop towards equilibrium. The driving mechanism shows an evolution characteristic from “soil erosion dominated” to “biological abundance dominated,” with the impact of climate factors first increasing and then stabilizing, and the direct pressure from human activities continuously weakening. Under the assumption that historical trends continue, the ensemble learning model projects that by 2030, the ecological vulnerability pattern will be dominated by Mild and Moderate levels, with the area of extremely vulnerable regions significantly reduced to 0.36%. This study verified the applicability of the SRP model in transitional river basins, and the constructed “evaluation-driving mechanism-prediction” framework can provide a scientific basis for the ecological protection and adaptive management of the West Liaohe River Basin and provide a methodological reference for ecological fragility research in similar areas. However, limitations persist: the indicator system and weight assignment are subject to inherent subjectivity, and the 2030 scenario projection based on the Stacking ensemble learning model relies on the BAU (Business-As-Usual) assumption, which fails to account for abrupt climate extremes or major policy shifts. Future studies should incorporate multi-scenario constraints to reduce predictive uncertainty. Full article
(This article belongs to the Special Issue Dynamic Monitoring and Sustainable Management of Land Resources)
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42 pages, 12047 KB  
Article
Quantitative Assessment of Urban Sprawl Dynamics in Moradabad City Using Built-Up Expansion Index and Shannon’s Entropy (1994–2024)
by Mohammed Faiz, Rashid Aziz Faridi, Fahdah Falah Ben Hasher, Martin Boltižiar and Mohamed Zhran
Land 2026, 15(7), 1212; https://doi.org/10.3390/land15071212 - 6 Jul 2026
Viewed by 475
Abstract
Urban sprawl in emerging Indian cities has accelerated over the last three decades as a consequence of rapid population growth, industrial expansion, infrastructure development, and market-driven land conversion. Moradabad, a fast-growing urban center in Uttar Pradesh, has undergone substantial morphological transformation between 1994 [...] Read more.
Urban sprawl in emerging Indian cities has accelerated over the last three decades as a consequence of rapid population growth, industrial expansion, infrastructure development, and market-driven land conversion. Moradabad, a fast-growing urban center in Uttar Pradesh, has undergone substantial morphological transformation between 1994 and 2024. This study undertakes a comprehensive and quantitative examination of urban sprawl dynamics in Moradabad through the integration of ward-wise and zone-wise built-up expansion, gradient directional analysis, Shannon’s entropy, the Urban Expansion Intensity Index (UEII), and spatial pattern typologies such as edge, ribbon, infill, and leapfrog development. Multi-temporal urban land data for 1994, 2004, 2014, and 2024 were utilized to assess patterns and magnitudes of expansion. The results indicate a nearly 2.5-fold growth in the urban area, increasing from 9.02 km2 in 1994 to 23.86 km2 in 2024, with sustained outward expansion accompanied by increasing fragmentation and dispersion from the urban core to the periphery. Shannon’s entropy values increased from 0.60 in 1994 to 0.73 in 2024, reflecting a marked shift from compact to dispersed development. The UEII increased from 0.45 (1994–2004) to a peak of 1.13 (2004–2014), followed by a decline to 0.85 (2014–2024), indicating an initial acceleration in urban expansion and intensity, and a subsequent moderation, while urban growth remains relatively high and dispersed. Edge development increases constantly by 24.45% to 30.93% throughout the decades. Ribbon development was the most dominant typology, constituting 37.89% of total urban expansion from 1994 to 2004. Ribbon development decreased from 37.89% to 32.56% by 2024, while leapfrog development showed a similar fall from 35.24% to 31.61% during the same period; in contrast, infill growth remained comparatively limited. The findings indicate a strong spatial association between urban expansion patterns and the distribution of transportation corridors and industrial areas. However, the present analysis does not directly quantify the causal influence of these factors on urban growth, particularly in the SSW, SSE, ESE, and NE zones, in contrast to prior studies. Full article
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