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Keywords = fractional difference maps

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13 pages, 2048 KB  
Article
Dual Energy CT-Derived Liver Extracellular Volume Fraction for Assessing Liver Functional Reserve in Patients with Liver Cirrhosis
by Seok Jin Hong, Ji Eun Kim, Jae Min Cho, Ho Cheol Choi, Mi Jung Park, Hye Young Choi, Hwa Seon Shin, Jung Ho Won, Wonjeong Yang and Hyun Ok Kim
Medicina 2025, 61(9), 1561; https://doi.org/10.3390/medicina61091561 - 30 Aug 2025
Viewed by 168
Abstract
Background and Objectives: The extracellular volume fraction (fECV) of the liver, as measured by contrast-enhanced computed tomography (CT), has been shown to correlate closely with the histological stages of hepatic fibrosis. This study aimed to investigate the diagnostic performance of a liver [...] Read more.
Background and Objectives: The extracellular volume fraction (fECV) of the liver, as measured by contrast-enhanced computed tomography (CT), has been shown to correlate closely with the histological stages of hepatic fibrosis. This study aimed to investigate the diagnostic performance of a liver extracellular volume fraction derived from dual-energy CT (DECT) for evaluating liver functional reserve based on the Child–Pugh class in cirrhotic patients, compared with other noninvasive markers. Materials and Methods: This retrospective study included 258 patients with liver cirrhosis who underwent contrast-enhanced DECT. The fECV was measured using iodine maps derived from equilibrium phase images obtained 3 min after contrast injection at 100/140 Sn kVp. Statistical analyses included Welch’s ANOVA with post hoc tests, Spearman’s correlation, and ROC analysis. The area under the curve (AUC) was compared among fECV and other noninvasive markers (aspartate transaminase to platelet ratio index [APRI], Fibrosis-4 [FIB-4], and model for end-stage liver disease [MELD]) using DeLong’s test. Intra- and interobserver reliability of fECV was assessed with the intraclass correlation coefficient (ICC). The area under the receiver operating characteristic curve (AUC) for differentiating Child–Pugh classes was compared among the fECV and other noninvasive markers (aspartate transaminase to platelet ratio index [APRI], Fibrosis-4 [FIB-4], and model for end-stage liver disease [MELD]). Results: The fECV increased significantly with advancing Child–Pugh classes (p < 0.001), showing a moderate correlation with Child–Pugh class (r = 0.53). The mean differences in fECV among the Child–Pugh classes were 8.88 between A and B (95% confidence interval [CI], 5.85–11.92; p < 0.001) and 7.42 between B and C (95% CI, 1.92–12.91: p < 0.001). The AUC for differentiating Child–Pugh classes A and B demonstrated no significant differences among the fECV (0.84), APRI (0.83, p > 0.99) and FIB-4 (0.83, p > 0.99), except for MELD, which had a significantly higher AUC (0.94, p = 0.047). For differentiating Child-Pugh classes B and C, the fECV demonstrated a significantly higher AUC (0.78), compared with FIB-4 (0.50, p = 0.038) and APRI (0.49, p = 0.037), whereas no significant difference was observed between fECV and MELD (0.92, p = 0.12). The intra- and interobserver reliabilities of the fECV measurements were excellent (ICC, 0.93; 95% CI, 0.91–0.95 and 0.91; 95% CI, 0.88–0.92, respectively). Conclusions: DECT derived fECV is a useful noninvasive marker for assessing liver functional reserve based on the Child–Pugh classification. Full article
(This article belongs to the Section Gastroenterology & Hepatology)
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13 pages, 1445 KB  
Article
Evaluating Simplified IVIM Diffusion Imaging for Breast Cancer Diagnosis and Pathological Correlation
by Abdullah Hussain Abujamea, Salma Abdulrahman Salem, Hend Samir Ibrahim, Manal Ahmed ElRefaei, Areej Saud Aloufi, Abdulmajeed Alotabibi, Salman Mohammed Albeshan and Fatma Eliraqi
Diagnostics 2025, 15(16), 2033; https://doi.org/10.3390/diagnostics15162033 - 14 Aug 2025
Viewed by 470
Abstract
Background/Objectives: This study aimed to evaluate the diagnostic performance of simplified intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) parameters in distinguishing malignant from benign breast lesions, and to explore their association with clinicopathological features. Methods: This retrospective study included 108 women who underwent [...] Read more.
Background/Objectives: This study aimed to evaluate the diagnostic performance of simplified intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) parameters in distinguishing malignant from benign breast lesions, and to explore their association with clinicopathological features. Methods: This retrospective study included 108 women who underwent breast MRI with multi-b-value DWI (0, 20, 200, 500, 800 s/mm2). Of those 108 women, 73 had pathologically confirmed malignant lesions. IVIM maps (ADC_map, D, D*, and perfusion fraction f) were generated using IB-Diffusion™ software version 21.12. Lesions were manually segmented by radiologists, and clinicopathological data including receptor status, Ki-67 index, cancer type, histologic grade, and molecular subtype were extracted from medical records. Nonparametric tests and ROC analysis were used to assess group differences and diagnostic performance. Additionally, a binary logistic regression model combining D, D*, and f was developed to evaluate their joint diagnostic utility, with ROC analysis applied to the model’s predicted probabilities. Results: Malignant lesions demonstrated significantly lower diffusion parameters compared to benign lesions, including ADC_map (p = 0.004), D (p = 0.009), and D* (p = 0.016), indicating restricted diffusion in cancerous tissue. In contrast, the perfusion fraction (f) did not show a significant difference (p = 0.202). ROC analysis revealed moderate diagnostic accuracy for ADC_map (AUC = 0.671), D (AUC = 0.657), and D* (AUC = 0.644), while f showed poor discrimination (AUC = 0.576, p = 0.186). A combined logistic regression model using D, D*, and f significantly improved diagnostic performance, achieving an AUC of 0.725 (p < 0.001), with 67.1% sensitivity and 74.3% specificity. ADC_map achieved the highest sensitivity (100%) but had low specificity (11.4%). Among clinicopathological features, only histologic grade was significantly associated with IVIM metrics, with higher-grade tumors showing lower ADC_map and D* values (p = 0.042 and p = 0.046, respectively). No significant associations were found between IVIM parameters and ER, PR, HER2 status, Ki-67 index, cancer type, or molecular subtype. Conclusions: Simplified IVIM DWI offers moderate accuracy in distinguishing malignant from benign breast lesions, with diffusion-related parameters (ADC_map, D, D*) showing the strongest diagnostic value. Incorporating D, D*, and f into a combined model enhanced diagnostic performance compared to individual IVIM metrics, supporting the potential of multivariate IVIM analysis in breast lesion characterization. Tumor grade was the only clinicopathological feature consistently associated with diffusion metrics, suggesting that IVIM may reflect underlying tumor differentiation but has limited utility for molecular subtype classification. Full article
(This article belongs to the Section Medical Imaging and Theranostics)
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17 pages, 4182 KB  
Article
Revealing Unproductive Areas in the Caatinga Biome: A Remote Sensing Approach to Monitoring Land Degradation in Drylands
by Diêgo P. Costa, Rodrigo N. Vasconcelos, Soltan Galano Duverger, Stefanie M. Herrmann, Washington J. S. Franca Rocha, Nerivaldo Afonso Santos, Deorgia T. M. Souza, André T. Cunha Lima and Carlos A. D. Lentini
Earth 2025, 6(3), 96; https://doi.org/10.3390/earth6030096 - 11 Aug 2025
Viewed by 546
Abstract
Land degradation in drylands represents a critical environmental challenge, with persistent bare soil serving as a key indicator of ecosystem vulnerability, including in the Caatinga biome. This study maps and analyzes the spatial and temporal dynamics of persistent bare soils over three decades [...] Read more.
Land degradation in drylands represents a critical environmental challenge, with persistent bare soil serving as a key indicator of ecosystem vulnerability, including in the Caatinga biome. This study maps and analyzes the spatial and temporal dynamics of persistent bare soils over three decades using multi-temporal remote sensing data. We applied Spectral Mixture Analysis (SMA), temporal metrics, and machine learning classifiers within Google Earth Engine to process long-term Landsat datasets and to derive the Normalized Difference Fraction Index Adjusted (NDFIa). The results indicate a widespread increase in bare soil, with over 63% of mapped hexagons showing expansion, particularly in the São Francisco Basin. Peaks in soil exposure coincided with severe drought events, highlighting the link between climate variability and land degradation. Moreover, abandoned agricultural lands and pasturelands emerged as the dominant contributors to persistent bare soils. These findings reinforce the need for targeted policies to mitigate land degradation and to promote sustainable land management in semi-arid ecosystems. This research provides a robust framework for long-term environmental monitoring in drylands by integrating satellite data with advanced analytical techniques. These advancements support more effective land management and conservation strategies in semi-arid ecosystems. Full article
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15 pages, 2487 KB  
Article
Feasibility of Sodium and Amide Proton Transfer-Weighted Magnetic Resonance Imaging Methods in Mild Steatotic Liver Disease
by Diana M. Lindquist, Mary Kate Manhard, Joel Levoy and Jonathan R. Dillman
Tomography 2025, 11(8), 89; https://doi.org/10.3390/tomography11080089 - 6 Aug 2025
Viewed by 293
Abstract
Background/Objectives: Fat and inflammation confound current magnetic resonance imaging (MRI) methods for assessing fibrosis in liver disease. Sodium or amide proton transfer-weighted MRI methods may be more specific for assessing liver fibrosis. The purpose of this study was to determine the feasibility [...] Read more.
Background/Objectives: Fat and inflammation confound current magnetic resonance imaging (MRI) methods for assessing fibrosis in liver disease. Sodium or amide proton transfer-weighted MRI methods may be more specific for assessing liver fibrosis. The purpose of this study was to determine the feasibility of sodium and amide proton transfer-weighted MRI in individuals with liver disease and to determine if either method correlated with clinical markers of fibrosis. Methods: T1 and T2 relaxation maps, proton density fat fraction maps, liver shear stiffness maps, amide proton transfer-weighted (APTw) images, and sodium images were acquired at 3T. Image data were extracted from regions of interest placed in the liver. ANOVA tests were run with disease status, age, and body mass index as independent factors; significance was set to p < 0.05. Post-hoc t-tests were run when the ANOVA showed significance. Results: A total of 36 participants were enrolled, 34 of whom were included in the final APTw analysis and 24 in the sodium analysis. Estimated liver tissue sodium concentration differentiated participants with liver disease from those without, whereas amide proton transfer-weighted MRI did not. Estimated liver tissue sodium concentration negatively correlated with the Fibrosis-4 score, but amide proton transfer-weighted MRI did not correlate with any clinical marker of disease. Conclusions: Amide proton-weighted imaging was not different between groups. Estimated liver tissue sodium concentrations did differ between groups but did not provide additional information over conventional methods. Full article
(This article belongs to the Section Abdominal Imaging)
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14 pages, 1252 KB  
Article
Non-Invasive Prediction of Atrial Fibrosis Using a Regression Tree Model of Mean Left Atrial Voltage
by Javier Ibero, Ignacio García-Bolao, Gabriel Ballesteros, Pablo Ramos, Ramón Albarrán-Rincón, Leire Moriones, Jean Bragard and Inés Díaz-Dorronsoro
Biomedicines 2025, 13(8), 1917; https://doi.org/10.3390/biomedicines13081917 - 6 Aug 2025
Viewed by 350
Abstract
Background: Atrial fibrosis is a key contributor to atrial cardiomyopathy and can be assessed invasively using mean left atrial voltage (MLAV) from electroanatomical mapping. However, the invasive nature of this procedure limits its clinical applicability. Machine learning (ML), particularly regression tree-based models, [...] Read more.
Background: Atrial fibrosis is a key contributor to atrial cardiomyopathy and can be assessed invasively using mean left atrial voltage (MLAV) from electroanatomical mapping. However, the invasive nature of this procedure limits its clinical applicability. Machine learning (ML), particularly regression tree-based models, may offer a non-invasive approach for predicting MLAV using clinical and echocardiographic data, improving non-invasive atrial fibrosis characterisation beyond current dichotomous classifications. Methods: We prospectively included and followed 113 patients with paroxysmal or persistent atrial fibrillation (AF) undergoing pulmonary vein isolation (PVI) with ultra-high-density voltage mapping (uHDvM), from whom MLAV was estimated. Standardised two-dimensional transthoracic echocardiography was performed before ablation, and clinical and echocardiographic variables were analysed. A regression tree model was constructed using the Classification and Regression Trees—CART-algorithm to identify key predictors of MLAV. Results: The regression tree model exhibited moderate predictive accuracy (R2 = 0.63; 95% CI: 0.55–0.71; root mean squared error = 0.90; 95% CI: 0.82–0.98), with indexed minimum LA volume and passive emptying fraction emerging as the most influential variables. No significant differences in AF recurrence-free survival were found among MLAV tertiles or model-based generated groups (log-rank p = 0.319 and p = 0.126, respectively). Conclusions: We present a novel ML-based regression tree model for non-invasive prediction of MLAV, identifying minimum LA volume and passive emptying fraction as the most significant predictors. This model offers an accessible, non-invasive tool for refining atrial cardiomyopathy characterisation by reflecting the fibrotic substrate as a continuum, a crucial advancement over existing dichotomous approaches to guide tailored therapeutic strategies. Full article
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32 pages, 15216 KB  
Article
Leveraging Soil Geography for Land Use Planning: Assessing and Mapping Soil Ecosystem Services Indicators in Emilia-Romagna, NE Italy
by Fabrizio Ungaro, Paola Tarocco and Costanza Calzolari
Geographies 2025, 5(3), 39; https://doi.org/10.3390/geographies5030039 - 1 Aug 2025
Viewed by 484
Abstract
An indicator-based approach was implemented to assess the contributions of soils in supplying ecosystem services, providing a scalable tool for modeling the spatial heterogeneity of soil functions at regional and local scales. The method consisted of (i) the definition of soil-based ecosystem services [...] Read more.
An indicator-based approach was implemented to assess the contributions of soils in supplying ecosystem services, providing a scalable tool for modeling the spatial heterogeneity of soil functions at regional and local scales. The method consisted of (i) the definition of soil-based ecosystem services (SESs), using available point data and thematic maps; (ii) the definition of appropriate SES indicators; (iii) the assessment and mapping of potential SESs provision for the Emilia-Romagna region (22.510 km2) in NE Italy. Depending on data availability and on the role played by terrain features and soil geography and its complexity, maps of basic soil characteristics (textural fractions, organic C content, and pH) covering the entire regional territory were produced at a 1 ha resolution using digital soil mapping techniques and geostatistical simulations to explicitly consider spatial variability. Soil physical properties such as bulk density, porosity, and hydraulic conductivity at saturation were derived using pedotransfer functions calibrated using local data and integrated with supplementary information such as land capability and remote sensing indices to derive the inputs for SES assessment. Eight SESs were mapped at 1:50,000 reference scale: buffering capacity, carbon sequestration, erosion control, food provision, biomass provision, water regulation, water storage, and habitat for soil biodiversity. The results are discussed and compared for the different pedolandscapes, identifying clear spatial patterns of soil functions and potential SES supply. Full article
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21 pages, 23129 KB  
Article
Validation of Global Moderate-Resolution FAPAR Products over Boreal Forests in North America Using Harmonized Landsat and Sentinel-2 Data
by Yinghui Zhang, Hongliang Fang, Zhongwen Hu, Yao Wang, Sijia Li and Guofeng Wu
Remote Sens. 2025, 17(15), 2658; https://doi.org/10.3390/rs17152658 - 1 Aug 2025
Viewed by 302
Abstract
The fraction of absorbed photosynthetically active radiation (FAPAR) stands as a pivotal parameter within the Earth system, quantifying the energy exchange between vegetation and solar radiation. Accordingly, there is an urgent need for comprehensive validation studies to accurately quantify uncertainties and improve the [...] Read more.
The fraction of absorbed photosynthetically active radiation (FAPAR) stands as a pivotal parameter within the Earth system, quantifying the energy exchange between vegetation and solar radiation. Accordingly, there is an urgent need for comprehensive validation studies to accurately quantify uncertainties and improve the reliability of FAPAR-based applications. This study validated five global FAPAR products, MOD15A2H, MYD15A2H, VNP15A2H, GEOV2, and GEOV3, over four boreal forest sites in North America. Qualitative quality flags (QQFs) and quantitative quality indicators (QQIs) of each product were analyzed. Time series high-resolution reference FAPAR maps were developed using the Harmonized Landsat and Sentinel-2 dataset. The reference FAPAR maps revealed a strong agreement with the in situ FAPAR from AmeriFlux (correlation coefficient (R) = 0.91; root mean square error (RMSE) = 0.06). The results revealed that global FAPAR products show similar uncertainties (RMSE: 0.16 ± 0.04) and moderate agreement with the reference FAPAR (R = 0.75 ± 0.10). On average, 34.47 ± 6.91% of the FAPAR data met the goal requirements of the Global Climate Observing System (GCOS), while 54.41 ± 6.89% met the threshold requirements of the GCOS. Deciduous forests perform better than evergreen forests, and the products tend to underestimate the reference data, especially for the beginning and end of growing seasons in evergreen forests. There are no obvious quality differences at different QQFs, and the relative QQI can be used to filter high-quality values. To enhance the regional applicability of global FAPAR products, further algorithm improvements and expanded validation efforts are essential. Full article
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18 pages, 4218 KB  
Article
Impact of Snow on Vegetation Green-Up on the Mongolian Plateau
by Xiang Zhang, Chula Sa, Fanhao Meng, Min Luo, Xulei Wang, Xin Tian and Endon Garmaev
Plants 2025, 14(15), 2310; https://doi.org/10.3390/plants14152310 - 26 Jul 2025
Viewed by 318
Abstract
Snow serves as a crucial water source for vegetation growth on the Mongolian Plateau, and its temporal and spatial variations exert profound influences on terrestrial vegetation phenology. In recent years, global climate change has led to significant changes in snow and vegetation start [...] Read more.
Snow serves as a crucial water source for vegetation growth on the Mongolian Plateau, and its temporal and spatial variations exert profound influences on terrestrial vegetation phenology. In recent years, global climate change has led to significant changes in snow and vegetation start of growing season (SOS). Therefore, it is necessary to study the mechanism of snow cover on vegetation growth and changes on the Mongolian Plateau. The study found that the spatial snow cover fraction (SCF) of the Mongolian Plateau ranged from 50% to 60%, and the snow melt date (SMD) ranged from day of the year (DOY) 88 to 220, mainly concentrated on the northwest Mongolian Plateau mountainous areas. Using different SOS methods to calculate the vegetation SOS distribution map. Vegetation SOS occurs earlier in the eastern part compared to the western part of the Mongolian Plateau. In this study, we assessed spatiotemporal distribution characteristics of snow on the Mongolian Plateau over the period from 2001 to 2023. The results showed that the SOS of the Mongolian Plateau was mainly concentrated on DOY 71-186. The Cox survival analysis model system established SCF and SMD on vegetation SOS. The SCF standard coefficient is 0.06, and the SMD standard coefficient is 0.02. The SOSNDVI coefficient is −0.15, and the SOSNDGI coefficient is −0.096. The results showed that the vegetation SOS process exhibited differential response characteristics to snow driving factors. These research results also highlight the important role of snow in vegetation phenology and emphasize the importance of incorporating the unique effects of vegetation SOS on the Mongolian Plateau. Full article
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20 pages, 11438 KB  
Article
Investigating Chaotic Techniques and Wave Profiles with Parametric Effects in a Fourth-Order Nonlinear Fractional Dynamical Equation
by Jan Muhammad, Ali H. Tedjani, Ejaz Hussain and Usman Younas
Fractal Fract. 2025, 9(8), 487; https://doi.org/10.3390/fractalfract9080487 - 24 Jul 2025
Viewed by 461
Abstract
In this article, we investigate the fractional soliton solutions as well as the chaotic analysis of the fourth-order nonlinear Ablowitz–Kaup–Newell–Segur wave equation. This model is considered an intriguing high-order nonlinear partial differential equation that integrates additional spatial and dispersive effects to extend the [...] Read more.
In this article, we investigate the fractional soliton solutions as well as the chaotic analysis of the fourth-order nonlinear Ablowitz–Kaup–Newell–Segur wave equation. This model is considered an intriguing high-order nonlinear partial differential equation that integrates additional spatial and dispersive effects to extend the concepts to more intricate wave dynamics, relevant in engineering and science for understanding complex phenomena. To examine the solitary wave solutions of the proposed model, we employ sophisticated analytical techniques, including the generalized projective Riccati equation method, the new improved generalized exponential rational function method, and the modified F-expansion method, along with mathematical simulations, to obtain a deeper insight into wave propagation. To explore desirable soliton solutions, the nonlinear partial differential equation is converted into its respective ordinary differential equations by wave transforms utilizing β-fractional derivatives. Further, the solutions in the forms of bright, dark, singular, combined, and complex solitons are secured. Various physical parameter values and arrangements are employed to investigate the soliton solutions of the system. Variations in parameter values result in specific behaviors of the solutions, which we illustrate via various types of visualizations. Additionally, a key aspect of this research involves analyzing the chaotic behavior of the governing model. A perturbed version of the system is derived and then analyzed using chaos detection techniques such as power spectrum analysis, Poincaré return maps, and basin attractor visualization. The study of nonlinear dynamics reveals the system’s sensitivity to initial conditions and its dependence on time-decay effects. This indicates that the system exhibits chaotic behavior under perturbations, where even minor variations in the starting conditions can lead to drastically different outcomes as time progresses. Such behavior underscores the complexity and unpredictability inherent in the system, highlighting the importance of understanding its chaotic dynamics. This study evaluates the effectiveness of currently employed methodologies and elucidates the specific behaviors of the system’s nonlinear dynamics, thus providing new insights into the field of high-dimensional nonlinear scientific wave phenomena. The results demonstrate the effectiveness and versatility of the approach used to address complex nonlinear partial differential equations. Full article
(This article belongs to the Section Mathematical Physics)
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23 pages, 406 KB  
Article
Periodically Kicked Rotator with Power-Law Memory: Exact Solution and Discrete Maps
by Vasily E. Tarasov
Fractal Fract. 2025, 9(7), 472; https://doi.org/10.3390/fractalfract9070472 - 21 Jul 2025
Viewed by 657
Abstract
This article discusses the transformation of a continuous-time model of the fractional system into a discrete-time model of the fractional system. For the continuous-time model, the exact solution of the nonlinear equation with fractional derivatives (FDs) that has the form of the damped [...] Read more.
This article discusses the transformation of a continuous-time model of the fractional system into a discrete-time model of the fractional system. For the continuous-time model, the exact solution of the nonlinear equation with fractional derivatives (FDs) that has the form of the damped rotator type with power non-locality in time is obtained.This equation with two FDs and periodic kicks is solved in the general case for the arbitrary orders of FDs without any approximations. A three-stage method for solving a nonlinear equation with two FDs and deriving discrete maps with memory (DMMs) is proposed. The exact solutions of the nonlinear equation with two FDs are obtained for arbitrary values of the orders of these derivatives. In this article, the orders of two FDs are not related to each other, unlike in previous works. The exact solution of nonlinear equation with two FDs of different orders and periodic kicks are proposed. Using this exact solution, we derive DMMs that describe a kicked damped rotator with power-law non-localities in time. For the discrete-time model, these damped DMMs are described by the exact solution of nonlinear equations with FDs at discrete time points as the functions of all past discrete moments of time. An example of the application, the exact solution and DMMs are proposed for the economic growth model with two-parameter power-law memory and price kicks. It should be emphasized that the manuscript proposes exact analytical solutions to nonlinear equations with FDs, which are derived without any approximations. Therefore, it does not require any numerical proofs, justifications, or numerical validation. The proposed method gives exact analytical solutions, where approximations are not used at all. Full article
17 pages, 6578 KB  
Article
Influence of Friction-Stir-Processing Parameters on the Microstructure and Local Mechanical Properties of an Aluminium-6% Magnesium-H18 Alloy
by Samir Mourad Chentouf, Philippe Grandmont, Mohammad Saadati, Nora Amimer and Mohammad Jahazi
Metals 2025, 15(7), 709; https://doi.org/10.3390/met15070709 - 26 Jun 2025
Viewed by 951
Abstract
One major challenge of friction stir processing (FSP) is its sensitivity to parameters like advancing and rotational speeds. This study examined the effect of tool travel speed on the microstructural evolution and mechanical properties of a new-generation Al-6Mg alloy. Optical and electron microscopy, [...] Read more.
One major challenge of friction stir processing (FSP) is its sensitivity to parameters like advancing and rotational speeds. This study examined the effect of tool travel speed on the microstructural evolution and mechanical properties of a new-generation Al-6Mg alloy. Optical and electron microscopy, EBSD, and shear-punch testing (SPT) were used. Two travel speeds, 50 and 120 mm/min, revealed significant differences in microstructure and properties at ambient temperature. EBSD provided misorientation maps and boundary fraction data. Microstructure analysis showed continuous dynamic recrystallization in the nugget zone, with finer grains observed at the higher speed. Microhardness was greater on both sides at 120 mm/min. The TMAZ showed elongated grains at 120 mm/min, while recrystallized grains were more prominent at 50 mm/min. In the HAZ, partial recrystallization occurred at 120 mm/min, whereas extensive recrystallization was observed at 50 mm/min. The SPT results indicated variations in stiffness between advancing and retreating sides, especially 2 mm from the nugget center. At 10 and 20 mm from the center, higher stiffness and strength were recorded at 120 mm/min. This study established correlations between joint stiffness, grain misorientation, and travel speed. Full article
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27 pages, 3680 KB  
Article
Fuzzy Convexity Under cr-Order with Control Operator and Fractional Inequalities
by Qi Liu, Muhammad Zakria Javed, Muhammad Uzair Awan, Loredana Ciurdariu and Badr S. Alkahtani
Fractal Fract. 2025, 9(6), 391; https://doi.org/10.3390/fractalfract9060391 - 18 Jun 2025
Viewed by 318
Abstract
This study is organized to introduce the concept of center–radius (cr)-ordered fuzzy number-valued convex mappings. Based on this class of mappings, we have initiated the idea of fuzzy number-valued extended cr- convex mappings incorporating control mapping [...] Read more.
This study is organized to introduce the concept of center–radius (cr)-ordered fuzzy number-valued convex mappings. Based on this class of mappings, we have initiated the idea of fuzzy number-valued extended cr- convex mappings incorporating control mapping . Furthermore, several potential new classes of convexity will be provided to discuss its generic nature. Also, some essential properties, criteria, and detailed characterizations through Jensen’s and Hermite–Hadamard-like inequalities are provided, incorporating Riemann–Liouville fractional operators, which are defined by ρ-level mappings. To validate the proposed fractional bounds through simulations, we consider both triangular and trapezoidal fuzzy numbers. Our results are based on totally ordered fuzzy-valued mappings, which are new and generic. The under-consideration class also includes a blend of new classes of convexity, which are controlled by non-negative mapping . In previous studies, the researchers have focused on different partially ordered relations. Full article
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications, 3rd Edition)
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33 pages, 3330 KB  
Review
Collateral Damage from Offensive Cyber Operations—A Systematic Literature Review
by Emil Larsson
J. Cybersecur. Priv. 2025, 5(2), 35; https://doi.org/10.3390/jcp5020035 - 16 Jun 2025
Viewed by 1095
Abstract
As offensive cyber operations have become more commonplace, cyber collateral damage (CCD) to society and to civilian infrastructure has expanded in impact and severity. Several research contexts, frameworks, and methods apply to these collateral effects, especially as they pertain to reducing them. To [...] Read more.
As offensive cyber operations have become more commonplace, cyber collateral damage (CCD) to society and to civilian infrastructure has expanded in impact and severity. Several research contexts, frameworks, and methods apply to these collateral effects, especially as they pertain to reducing them. To investigate and map this area of research, five leading scientific databases (Scopus, IEEE Xplore, Springer Link, ScienceDirect, and ProQuest) were searched for papers on CCD. From 716 search results, 74 relevant papers were selected. Using surface categories as well as thematic analysis, these were grouped into the main emergent categories of legal, ethical, targeting-oriented, and econometric papers, with each category showing a recent research trend. The papers were qualitatively assessed for importance and coverage and compared bibliographically to identify key papers and authors. Within the identified areas of research, significant gaps remain. While CCD is becoming increasingly well understood from a legal and operational perspective, this accounts only for a fraction of the civilian harm caused by offensive cyber operations. This study identifies potential pathways for the synthesis of the current research areas (targeting, taxonomy, econometrics) with broader definitions of collateral damage to include civilian harm. These include updating national cyber doctrines to require collateral damage estimates, as well as exploiting emerging open datasets to understand which cyber capabilities cause the greatest collateral effects. Finally, we observe that the research definitions and taxonomy of CCD differ widely and have been subjected to limited scrutiny and challenge to date. Full article
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15 pages, 1884 KB  
Article
A Procedure to Estimate Global Natural Recharge in Karst Aquifers
by Eugenio Sanz Pérez, Juan Carlos Mosquera-Feijóo, Joaquín Sanz de Ojeda and Ignacio Menéndez-Pidal
Water 2025, 17(12), 1779; https://doi.org/10.3390/w17121779 - 13 Jun 2025
Viewed by 650
Abstract
Natural recharge in karst aquifers is a key component of global water resources, yet its estimation remains challenging due to the complexity of karst hydrogeological processes. The recharge assessment deserves special consideration, especially in the current global climate and sustainability challenges. This study [...] Read more.
Natural recharge in karst aquifers is a key component of global water resources, yet its estimation remains challenging due to the complexity of karst hydrogeological processes. The recharge assessment deserves special consideration, especially in the current global climate and sustainability challenges. This study poses a methodology to appraise natural recharge rates in karst aquifers worldwide, drawing on climatic and geological data. In this regard, this study applies a methodology previously developed by two of the authors, in which natural recharge over large areas is considered a fixed fraction of precipitation, which varies according to different lithologies of similar hydrogeological behavior (hydro-lithological units). Given that carbonate rocks are known to have the highest recharge rate relative to precipitation (34.3%), the method builds on existing karst and average precipitation maps to calculate worldwide recharge in karst aquifers. Recharge is appraised at 4,381,063.7 hm3/yr, which represents 34.5% of the global groundwater resources, a percentage that indicates the importance of karst in this regard. Based on maps of recharge values worldwide, this study highlights the importance of carbonate aquifers when compared with assessments of the world’s groundwater resources made by international institutions or other types of aquifers. The method is contrasted with other ways of assessing groundwater resources used in diverse regions of Europe. The impact of different climate change scenarios on the natural recharge of these karst aquifers has also been analyzed. Thus, under a climate change scenario in 2050, it is estimated that natural recharge will be reduced by about 10%. Full article
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32 pages, 3058 KB  
Article
Mapping the Spatial Distribution of Noxious Weed Species with Time-Series Data in Degraded Grasslands in the Three-River Headwaters Region, China
by Xianglin Huang, Ru An and Huilin Wang
Sustainability 2025, 17(12), 5424; https://doi.org/10.3390/su17125424 - 12 Jun 2025
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Abstract
Noxious weeds (NWs) are increasingly recognized as a significant threat to the native alpine grassland ecosystems of the Qinghai–Tibetan Plateau (QTP). However, large-scale quantification of their continuous fractional cover remains challenging. This study proposes a pixel-level estimation framework utilizing time-series Sentinel-2 imagery. A [...] Read more.
Noxious weeds (NWs) are increasingly recognized as a significant threat to the native alpine grassland ecosystems of the Qinghai–Tibetan Plateau (QTP). However, large-scale quantification of their continuous fractional cover remains challenging. This study proposes a pixel-level estimation framework utilizing time-series Sentinel-2 imagery. A Dynamic Mask Non-Stationary Transformer (DMNST) model was developed and trained using multi-temporal multispectral data to map the spatial distribution of NWs in the Three-River Headwaters Region. The model was calibrated and validated using field data collected from 170 plots (1530 quadrats). The results demonstrated that both the dynamic masking module and the non-stationary normalization significantly enhanced the prediction accuracy and robustness, particularly when applied jointly. The model performance varied across different combinations of spectral bands and temporal inputs, with the optimal configurations achieving a test R2 of 0.770, MSE of 0.009, and RMSE of 0.096. These findings underscore the critical role of the input configuration and architectural enhancements in accurately modeling the fractional cover of NWs. This study confirms the applicability of Sentinel-2 time-series imagery for modeling the continuous fractional cover of NWs and provides a scalable tool for invasive species monitoring and ecological risk assessment in alpine ecosystems. Full article
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