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41 pages, 14242 KB  
Article
Assessing Community and Protected Area Exposure to Wildfires in Navarra, Spain
by Fermín Alcasena, Alan Ager, Julia Loján, Isabel Pinto, Ignacio García, Pere Gelabert, Mikel Repáraz and Cristóbal Molina
Forests 2026, 17(6), 699; https://doi.org/10.3390/f17060699 (registering DOI) - 15 Jun 2026
Abstract
The unprecedented 2022 wildfire season in Navarra, northern Spain, marked a turning point in regional wildfire management, when seven simultaneous large fires during a June heatwave burned more than 17,000 ha in just a few days, overwhelming suppression capacity and highlighting the limits [...] Read more.
The unprecedented 2022 wildfire season in Navarra, northern Spain, marked a turning point in regional wildfire management, when seven simultaneous large fires during a June heatwave burned more than 17,000 ha in just a few days, overwhelming suppression capacity and highlighting the limits of a strategy based primarily on ignition prevention and fire suppression. In this study, we implemented a stochastic wildfire modeling system based on the Minimum Travel Time algorithm, historical ignition patterns, spatial fuel data, and spatiotemporal weather variability to assess community and protected area exposure to wildfire. We simulated more than 50,000 fire season replicates under extreme fire weather conditions, estimating annual burn probability across fire intensity classes at 50 m spatial resolution. We then intersected modeled fire perimeters with building footprints representing residential and industrial structures, as well as protected areas, to assess the spatial distribution of exposure across the region. Results showed strong concentration of community exposure, with three fourths of residential and industrial exposure concentrated in just over one third of the total municipal area. Across Navarra, mean annual modeled exposure summed to 120 residential buildings and 16 industrial structures. Across the protected area network, mean annual burned area summed to 90 ha year−1, including 68 ha year−1 at flame lengths greater than 2.5 m, while burned forest area was 16 ha year−1. Protected areas in southern Navarra and forested protected areas in central and northern Navarra showed the highest modeled exposure, identifying priority landscapes where prevention, restoration, and evaluation of managed fire options could support more resilient ecosystems. This study provides a scientific basis for improving wildfire risk governance and strengthening the resilience of communities and protected areas under increasing wildfire pressure in the region. Full article
(This article belongs to the Special Issue Forest Fire Detection, Prevention and Management)
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35 pages, 2698 KB  
Article
A Discrete Analog of the Pham–Burr XII Distribution: Properties and Estimation with Medical and Environmental Applications
by Heba N. Salem, Neama T. AL-Sayed, Hebatalla H. Mohammad, Gannat R. AL-Dayian and Abeer A. EL-Helbawy
Mathematics 2026, 14(12), 2145; https://doi.org/10.3390/math14122145 (registering DOI) - 15 Jun 2026
Abstract
This article is concerned with proposing a discrete version of a competing risks model, namely, the Pham–Burr XII distribution, via the general approach of discretization. The proposed model’s probability mass function displays decreasing, unimodal and decreasing–unimodal patterns, while its hazard rate and alternative [...] Read more.
This article is concerned with proposing a discrete version of a competing risks model, namely, the Pham–Burr XII distribution, via the general approach of discretization. The proposed model’s probability mass function displays decreasing, unimodal and decreasing–unimodal patterns, while its hazard rate and alternative hazard rate functions exhibit different and important shapes, which are decreasing, bathtub (Vtub), modified bathtub and unimodal shapes. Through these shapes, the flexibility and diversity in shapes of the characteristic functions of the discrete Pham–Burr XII distribution can be demonstrated. Therefore, the discrete Pham–Burr XII distribution can provide a better fit for several types of discrete data and count data. The main characteristic functions of the discrete Pham–Burr XII distribution are derived, and its properties are studied. Moreover, the parameters and the main characteristic functions of the discrete Pham–Burr XII distribution are estimated via the maximum likelihood method. Also, the asymptotic confidence intervals and percentile bootstrap confidence intervals are considered. Moreover, point and interval estimation of some entropy measures is discussed. Furthermore, a simulation study is achieved to assess the performance of the delivered maximum likelihood estimates. Finally, the applicability of the discrete Pham–Burr XII distribution is examined though different applications. Full article
20 pages, 19123 KB  
Article
Spatial Exceedance Probability Mapping of Monthly Rainfall Using Gridded Precipitation Products in an Orographically Complex Monsoon Basin, Western Thailand
by Manatchanok Pannak, Ketvara Sittichok, Chaiyapong Thepprasit and Chuphan Chompuchan
Hydrology 2026, 13(6), 155; https://doi.org/10.3390/hydrology13060155 (registering DOI) - 15 Jun 2026
Abstract
In many orographically complex monsoon basins, rain gauge networks are sparse and lack the long-term continuous records required for reliable precipitation probability analysis. Traditional regional frequency analysis assumes spatially uniform precipitation across the analysis zone, which is inadequate for basins with steep rainfall [...] Read more.
In many orographically complex monsoon basins, rain gauge networks are sparse and lack the long-term continuous records required for reliable precipitation probability analysis. Traditional regional frequency analysis assumes spatially uniform precipitation across the analysis zone, which is inadequate for basins with steep rainfall gradients and strong seasonal variability. Gridded precipitation products (GPPs) provide spatially continuous, long-term records that enable grid-cell-level probability distribution fitting. However, GPPs may exhibit local biases and errors, and statistical evaluation against gauge observations is necessary before application. This study was conducted in the Phetchaburi–Prachuap Khiri Khan River Basin, western Thailand, a region with steep orographic and coastal rainfall gradients. Four GPPs, namely CHIRPS, CHELSA, WorldClim, and PERSIANN-CCS-CDR, were evaluated against gauge observations. The best-performing product, after monthly bias correction, was then used to generate spatially continuous monthly exceedance probability maps using grid-cell gamma distribution fitting. CHELSA showed the best overall performance across all evaluation metrics (correlation coefficient (r) = 0.908, percent bias (PBIAS) = 7.0%, root mean square error (RMSE) = 48.3 mm), passing the Kolmogorov–Smirnov (KS) goodness-of-fit test at all 96 station-months. CHIRPS and WorldClim showed satisfactory overall performance but exhibited localized biases in complex terrain, whereas PERSIANN-CCS-CDR substantially overestimated wet-season rainfall, limiting its suitability for this basin. Spatial precipitation patterns varied markedly between monsoon regimes, shifting from a dominant west-to-east orographic gradient during the southwest monsoon to a less differentiated advective pattern during the northeast monsoon. Furthermore, analysis at the 75% exceedance probability level showed that mean-based effective rainfall overestimated reliable water supply in high-variance months, leading to underestimation of supplemental irrigation demand. The generated maps provide spatially explicit dependable rainfall estimates across the basin, supporting probabilistic agricultural water management at multiple planning scales in orographically complex monsoon basins. Full article
(This article belongs to the Section Statistical Hydrology)
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20 pages, 4012 KB  
Article
Systematic Undercoverage in Bootstrap Confidence Intervals for Xi Correlation Coefficient: A Simulation Study
by Figen Ceritoğlu
Mathematics 2026, 14(12), 2136; https://doi.org/10.3390/math14122136 (registering DOI) - 15 Jun 2026
Abstract
This study uses a comprehensive simulation to investigate the performance of bootstrap confidence intervals for the Pearson correlation coefficient and Xi correlation coefficient (XICOR). Different distributional settings (normal, lognormal, uniform, and t(3)), sample sizes ( [...] Read more.
This study uses a comprehensive simulation to investigate the performance of bootstrap confidence intervals for the Pearson correlation coefficient and Xi correlation coefficient (XICOR). Different distributional settings (normal, lognormal, uniform, and t(3)), sample sizes (n = 10, 30, 100, 1000), and Gaussian copula dependence levels (ρ0 = 0.1, 0.3, 0.5, 0.8) were considered. For each scenario, the true population Pearson and XICOR values were separately estimated via a large-sample Monte Carlo reference. The coverage probability (CP), mean confidence interval width (MCIW) and absolute bias detection (BD) were used to evaluate the percentile, bias-corrected and accelerated (BCa) bootstrap methods. The results showed that bootstrap confidence intervals based on the Pearson correlation coefficient generally achieve coverage probabilities close to the nominal level across most scenarios, with some degradation observed under heavy-tailed distributions at large sample sizes. By contrast, confidence intervals based on XICOR showed a significant and systematic undercoverage problem across most sample sizes, especially for n ≥ 30, which worsened as sample size increased. Although XICOR tends to produce narrower intervals, these intervals were associated with low coverage and increased variability, indicating a false precision. The BCa method did not meaningfully improve XICOR’s coverage performance. In conclusion, reducing bias alone is insufficient for reliable inference when dealing with non-smooth dependence measures. Classical bootstrap methods may be inappropriate for XICOR since they do not provide accurate quantification of uncertainty. Full article
(This article belongs to the Special Issue Stochastic Simulation: Theory and Applications)
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12 pages, 395 KB  
Article
Research on Logistics Distribution Center Location Problem Based on Genetic Variation Firefly Algorithm
by Lang Yang, Changan Ren, Zhangwei Yu and Mengya Ma
Algorithms 2026, 19(6), 481; https://doi.org/10.3390/a19060481 (registering DOI) - 15 Jun 2026
Abstract
The selection of locations for logistics distribution centers poses a significant challenge in logistics network planning. Traditional methods often demonstrate limited accuracy in solutions and a tendency to become trapped in local optima when addressing large-scale, multi-constraint location models. To address these shortcomings, [...] Read more.
The selection of locations for logistics distribution centers poses a significant challenge in logistics network planning. Traditional methods often demonstrate limited accuracy in solutions and a tendency to become trapped in local optima when addressing large-scale, multi-constraint location models. To address these shortcomings, this study introduces a firefly algorithm enhanced by genetic mutation strategies (GVFA) to optimize the location of distribution centers. Within the framework of the standard firefly algorithm, we incorporate an adaptive step-size decay mechanism and a mutation operator. The movement step size adjusts dynamically based on iteration counts, while a mutation probability of 5% is implemented to maintain population diversity, effectively reducing the risk of premature convergence. A specialized boundary-handling strategy ensures that the search process remains within the feasible solution space, guiding the population toward the global optimum. Experiments were conducted using latitude–longitude coordinates and logistics demand data from 159 Cainiao Post stations in Hengyang City, resulting in the construction of a location model aimed at minimizing total costs. The findings confirm the efficiency and stability of our method in optimizing distribution center locations, thereby providing a novel intelligent optimization approach for the siting of logistics distribution centers. Full article
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26 pages, 10582 KB  
Review
Calibration of Ensemble Forecasts for Extreme Rainfall Using Bayesian Model Averaging: A Comparative Review of Gaussian and Gamma Distributions
by Defi Yusti Faidah, Gumgum Darmawan, Bertho Tantular, Febrianggi Caesar Immanuel and Norizan Mohamed
Sustainability 2026, 18(12), 6121; https://doi.org/10.3390/su18126121 (registering DOI) - 15 Jun 2026
Abstract
Global climate change is causing an increase in extreme rainfall events, which impacts the risk of hydrometeorological disasters. To support disaster mitigation and early warning systems, accurate and reliable rainfall predictions are required. Although ensemble forecasting is widely used to model atmospheric uncertainty, [...] Read more.
Global climate change is causing an increase in extreme rainfall events, which impacts the risk of hydrometeorological disasters. To support disaster mitigation and early warning systems, accurate and reliable rainfall predictions are required. Although ensemble forecasting is widely used to model atmospheric uncertainty, raw ensemble results often exhibit insufficient bias and dispersion. Therefore, post-processing techniques are needed to improve the quality of probabilistic predictions. The most commonly used calibration method is Bayesian Model Averaging (BMA). This study conducted a scoping review of peer-reviewed papers on ensemble forecast calibration using BMA, based on the PRISMA-ScR framework. Furthermore, this study presents a comprehensive bibliometric analysis involving co-authorship networks of productive authors and bibliometric maps with clustered terms. A total of 35 relevant articles were identified from 49 screened publications. The bibliometric analysis revealed that “ensemble forecasting” and “Gaussian distribution” are the most dominant terms in the research network, indicating that Gaussian-based approaches remain more widely used in ensemble forecast calibration studies. In contrast, studies explicitly applying Gamma-based approaches are still relatively limited despite their relevance for modeling asymmetric rainfall data. The results obtained in this study highlight the importance of developing and integrating more appropriate probability distributions, such as those within the Extreme Value Theory framework, into BMA models. These findings suggest that the selection of appropriate probabilistic distributions in BMA-based calibration frameworks plays an important role in improving forecast reliability and the representation of uncertainty in rainfall prediction. Furthermore, the development of more suitable probability distributions, including Extreme Value Theory (EVT)-based distributions, has strong potential to enhance probabilistic calibration performance for asymmetric rainfall data. This approach is expected to improve the accuracy and reliability of extreme rainfall predictions. The findings of this study provide an important contribution to the development of early warning systems for hydrometeorological disasters and support the achievement of Sustainable Development Goals (SDGs). Full article
(This article belongs to the Section Hazards and Sustainability)
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20 pages, 2078 KB  
Article
Structural Characteristics Analysis of Pinus taiwanensis Plantation in Climate Transition Zone
by Mengli Zhou, Jianbo Shen, Peilin Pang, Fang Guo and Dongfeng Yan
Plants 2026, 15(12), 1842; https://doi.org/10.3390/plants15121842 (registering DOI) - 14 Jun 2026
Abstract
Understanding the structural characteristics of Pinus taiwanensis plantations in climatically transitional regions is essential for developing science-based management strategies under global change. This study investigated 23 plots in Huangbai Mountain Forest Farm, Henan Province, China, classified into low-, medium-, and high-density stands ( [...] Read more.
Understanding the structural characteristics of Pinus taiwanensis plantations in climatically transitional regions is essential for developing science-based management strategies under global change. This study investigated 23 plots in Huangbai Mountain Forest Farm, Henan Province, China, classified into low-, medium-, and high-density stands (n = 9, 9, and 5, respectively). Diameter distributions were fitted using six probability functions, and four spatial structure parameters—mixing degree (Mc), size ratio (U), uniform angle index (W), and forest layer index (S)—were quantified. In addition, five comprehensive spatial structure indices—average superiority coefficient index (SPV), spatial structure comprehensive index (Q), stand spatial structure distance index (FSI), Comprehensive Distance Evaluation (CDEV), and Comprehensive Assessment of Proximity Vector (CAPV)—were constructed using a combined analytic hierarchy process and entropy weight method. Given the unbalanced sample sizes, non-parametric Kruskal–Wallis tests were employed for comparisons, and bootstrap resampling (1000 iterations) was performed to assess the reliability of mean estimates. The results showed that both the Gamma and Weibull distributions were equally suitable for describing diameter distribution under different stand densities, as their AIC differences were below 2 for all density classes. Correlation analysis indicated that the relative importance of spatial parameters followed the order S > U > Mc > W. Medium-density stands exhibited the most optimal spatial structure, whereas low-density stands showed the poorest performance. These findings suggest that both overly dense and sparse stands negatively affect spatial organization. Appropriate management practices, such as thinning or enrichment planting, are recommended to optimize stand structure and enhance ecological resilience. Full article
(This article belongs to the Special Issue AI-Driven Machine Vision Technologies in Plant Science)
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22 pages, 3318 KB  
Article
Research on Global Seismic Reliability Analysis of Steel Frames Based on Machine Learning
by Ziyang Wu, Dewei Kong, Mingming Jia and Xianbao Li
Buildings 2026, 16(12), 2379; https://doi.org/10.3390/buildings16122379 (registering DOI) - 14 Jun 2026
Abstract
Seismic reliability assessment of steel frame structures using nonlinear finite element analysis is often hindered by implicit limit state functions and high computational cost. To address these challenges, this study proposes a machine learning-based framework for global seismic reliability analysis. A nine-story steel [...] Read more.
Seismic reliability assessment of steel frame structures using nonlinear finite element analysis is often hindered by implicit limit state functions and high computational cost. To address these challenges, this study proposes a machine learning-based framework for global seismic reliability analysis. A nine-story steel frame model is established and validated through modal and pushover analysis. Global sensitivity analysis using the Sobol’ method is performed to identify key parameters governing the maximum inter-story drift ratio. Three machine learning models—PSO-SVR, PSO-XGBoost, and PSO-BPNN—are trained with the selected features and integrated into Monte Carlo simulation (MCS) for reliability calculation. The results show that the PSO-BPNN model achieves the highest accuracy with the maximum error of 1.0259% relative to direct MCS, outperforming the conventional MLE-based approach, which yields errors up to 11.9383% due to the non-standard distribution of the structural response. The impact of training sample size on model performance is also examined, with 1000 samples identified as a practical threshold for acceptable prediction accuracy. Existing code design methods require modifications based on the total probability approach for global reliability analysis. This study offers an efficient and precise methodology for seismic reliability design of steel frame structures, particularly when structural responses deviate from standard parametric distributions. Full article
(This article belongs to the Special Issue Resilience Analysis and Intelligent Simulation in Civil Engineering)
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16 pages, 15712 KB  
Article
Synthesis and In Silico Study of Pectolinarigenin–Metronidazole Hybrid Molecule as Anti-Helicobacter pylori
by Zeyneb Benramdane, Matteo Michelotti, Thamere Cheriet, Andrea Defant and Ines Mancini
Molecules 2026, 31(12), 2089; https://doi.org/10.3390/molecules31122089 (registering DOI) - 14 Jun 2026
Abstract
Metronidazole is an antibiotic used to treat Helicobacter pylori, a bacterium responsible for chronic infections in humans that cause gastric inflammation, ulcers, and cancer. However, its long-term administration is limited by toxicity and increased resistance. In the search for more effective agents [...] Read more.
Metronidazole is an antibiotic used to treat Helicobacter pylori, a bacterium responsible for chronic infections in humans that cause gastric inflammation, ulcers, and cancer. However, its long-term administration is limited by toxicity and increased resistance. In the search for more effective agents against H. pylori infection, molecular hybridization has now been applied to the synthesis of the new compound 3. Its structure connects the metronidazole moiety to pectolinarigenin, the latter obtained by acid hydrolysis of glycosylated flavonoids isolated from the plant Linaria reflexa Desf. The NOE effect supported the C-7 functionalization of 3, as evidenced by the energy-minimized DFT-calculated structure. The new molecule enriches the chemical space of known metronidazole–flavonoid analogs, among which the genistein derivative 2 was reported as the most active in inhibiting bacterial strains. The computational analysis of 2 and 3 compared with metronidazole as the reference has provided favorable data for both Absorption, Distribution, Metabolism, and Excretion (ADME) predictions and the probability of anti-H. pylori activity, besides rising docking evaluation on three specific targets and dynamics simulation as inhibitors of the flavodoxin enzyme. The results are promising for further in-depth biological investigation. Full article
(This article belongs to the Special Issue Molecular Modeling: Advancements and Applications, 4th Edition)
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24 pages, 15552 KB  
Article
Occurrence, Distribution and Population Genetics of Invasive Leafhoppers Arboridia kakogawana, Tautoneura polymitusa and Erasmoneura vulnerata (Hemiptera, Cicadellidae, Typhlocybinae) in the Viticultural Regions of Serbia
by Milana Mitrović, Tatjana Cvrković, Miljana Jakovljević, Slavica Marinković, Oliver Krstić, Ivo Toševski and Jelena Jović
Diversity 2026, 18(6), 364; https://doi.org/10.3390/d18060364 (registering DOI) - 14 Jun 2026
Abstract
Invasive leafhopper species Arboridia kakogawana, Tautoneura polymitusa and Erasmoneura vulnerata were investigated for distribution, routes of introduction and population genetics in the viticultural regions of Serbia. Surveillance traps were set up in vineyards and natural habitats across 26 administrative districts between 2017 [...] Read more.
Invasive leafhopper species Arboridia kakogawana, Tautoneura polymitusa and Erasmoneura vulnerata were investigated for distribution, routes of introduction and population genetics in the viticultural regions of Serbia. Surveillance traps were set up in vineyards and natural habitats across 26 administrative districts between 2017 and 2025. The mitochondrial cytochrome oxidase subunit I (COX1) and a nuclear wingless gene (Wg) were used in phylogenetic analysis. Arboridia kakogawana showed a significant invasive potential with its populations sampled from 19 districts. A single COX1 haplotype detected was identical with specimens from Bulgaria and Georgia suggesting a shared origin and probable invasion route via the Black Sea region. Tautoneura polymitusa expressed limited invasiveness, predominantly with northern distribution and very low population density. One detected COX1 haplotype shared identity with samples from Hungary, indicating their joint origin. Erasmoneura vulnerata has the greatest invasive potential, detected in all inspected districts. Eighteen COX1 haplotypes clustered into a monophyletic group. Three lineages were separated but morphologically indistinguishable, with a 7.5 to 9.5% average divergence between the groups. Analysis of Wg sequences led to the discovery of only two haplotypes, confirming their common ancestry. Diversity of Serbian COX1 haplotypes entirely reflected genetic variability in the native range, indicating a complex scenario of E. vulnerata introduction from multiple sources with admixed genotypes, including co-introduction of uncovered cryptic lineages. Full article
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19 pages, 1698 KB  
Article
Pharmacokinetic/Pharmacodynamic Modelling of Cefquinome in Lactating Sheep and Lactating Goats After Intravenous, Subcutaneous and Long-Acting Administrations
by Carlos Mario Carceles-Rodríguez, Emilio Fernández-Varón, Cristina Bernal Alcaraz, Carlos Cárceles, Rocío Morón-Romero, Xando Díaz-Villamarín, Pilar Muñoz-Rascón and Juan Manuel Serrano-Rodríguez
Vet. Sci. 2026, 13(6), 580; https://doi.org/10.3390/vetsci13060580 (registering DOI) - 13 Jun 2026
Abstract
The pharmacokinetics (PK) and pharmacokinetic–pharmacodynamic (PK/PD) relationships of cefquinome in small ruminants remain incompletely characterized, particularly for long-acting (LA) formulations. This study evaluated cefquinome disposition after intravenous (IV), subcutaneous (SC) and LA subcutaneous (SC-LA) administration in lactating sheep and goats using nonlinear mixed-effects [...] Read more.
The pharmacokinetics (PK) and pharmacokinetic–pharmacodynamic (PK/PD) relationships of cefquinome in small ruminants remain incompletely characterized, particularly for long-acting (LA) formulations. This study evaluated cefquinome disposition after intravenous (IV), subcutaneous (SC) and LA subcutaneous (SC-LA) administration in lactating sheep and goats using nonlinear mixed-effects models (NLMEs) and Monte Carlo (MC) simulations. Cefquinome exhibited low volumes of distribution (0.21–0.31 L/kg), with goats showing higher clearance and shorter terminal half-lives than sheep. The SC-LA formulation reduced the absorption rate constant and increased both the mean absorption time and terminal half-life by 4–6-fold, resulting in sustained systemic exposure over 48 h. PK/PD analysis showed higher PK/PD cut-off values for the LA formulation, with values of 0.125 μg/mL for the fT > MIC index and 0.25 μg/mL for the fAUC/MIC index, respectively, whereas IV and SC regimens achieved lower thresholds. MC simulations indicated that only the LA formulation achieved ≥ 90% probability of target attainment (PTA) values at MICs equivalent to tentative epidemiological cut-off values (TECOFF) for respiratory pathogens. Notably, fAUC/MIC provided a more informative descriptor of efficacy for the LA formulation. These findings highlight the advantage of LA formulations and demonstrate improved performance compared with conventional dosing regimens in sheep and goats. Full article
(This article belongs to the Section Veterinary Physiology, Pharmacology, and Toxicology)
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27 pages, 443 KB  
Article
Origin of the Covariant Wigner Operator as a Quantum Amplitude in QCD
by Chueng-Ryong Ji and Daniel W. Piasecki
Symmetry 2026, 18(6), 1018; https://doi.org/10.3390/sym18061018 (registering DOI) - 12 Jun 2026
Viewed by 60
Abstract
The Wigner function plays a central role in QCD as a phase-space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent work based on the Koopman–von Neumann–Sudarshan (KvNS) Hilbert space [...] Read more.
The Wigner function plays a central role in QCD as a phase-space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent work based on the Koopman–von Neumann–Sudarshan (KvNS) Hilbert space formulation of classical mechanics suggests the Wigner function arises as a quantum probability amplitude projected onto classical phase space, rather than a quasiprobability density. In the classical limit, this amplitude reduces to the classical Koopman wavefunction. In this work, we extend this perspective to relativistic QCD by constructing a Koopman description of the quark Wigner operator. We show that the Wigner operator is naturally isomorphic to a phase-space spinor, providing a unified framework in which both classical and quantum dynamics are expressed. Within this formulation, the Wigner function retains its interpretation as an amplitude even in the relativistic regime. This viewpoint clarifies the origin of negativity and other nonclassical features, and provides a more transparent foundation for parton distribution functions in QCD. Remarkably, the relativistic Koopman framework reproduces the classical limit of QCD. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Quantum Chromodynamics (QCD))
13 pages, 400 KB  
Article
Reconsideration of Information-Theoretic Principles—Perspective from the Dual Probability Distribution
by Yoshikazu Ohtaki, Tomomi Nakamura, Hiroshi-H. Hasegawa and Tatsuaki Wada
Entropy 2026, 28(6), 681; https://doi.org/10.3390/e28060681 (registering DOI) - 12 Jun 2026
Viewed by 65
Abstract
We reconsider information-theoretic principles, such as the maximum entropy principle/minimum Massieu potential principle, from the perspective of the dual probability distribution. This is introduced through Sanov’s Lemma for the multinomial distribution. The dual correspondence becomes asymptotically manifest. The Massieu potential is rewritten as [...] Read more.
We reconsider information-theoretic principles, such as the maximum entropy principle/minimum Massieu potential principle, from the perspective of the dual probability distribution. This is introduced through Sanov’s Lemma for the multinomial distribution. The dual correspondence becomes asymptotically manifest. The Massieu potential is rewritten as the Kullback–Leibler divergence between the dual probability distribution and the dual reference distribution. Similarly, the dual potential is rewritten as the cumulant generating function with respect to the dual reference distribution. This perspective gives us new insight into information-theoretic principles. As the dual probability distribution naturally arises in data sampling, we anticipate that this new perspective will play a significant role in data analysis. Full article
26 pages, 7221 KB  
Article
Siting and Sizing of Electric Vehicle Charging Stations Considering Distribution Network Flexibility
by Jiazheng Chen and Xue Li
Energies 2026, 19(12), 2821; https://doi.org/10.3390/en19122821 (registering DOI) - 12 Jun 2026
Viewed by 121
Abstract
The location and capacity of electric vehicle charging stations (EVCSs) directly determine the capital invested and construction costs while also affecting the travelling convenience and economy of electric vehicle (EV) users. Furthermore, the siting and sizing of EVCSs has an impact on distribution [...] Read more.
The location and capacity of electric vehicle charging stations (EVCSs) directly determine the capital invested and construction costs while also affecting the travelling convenience and economy of electric vehicle (EV) users. Furthermore, the siting and sizing of EVCSs has an impact on distribution network flexibility. Therefore, a method for the siting and sizing of EVCSs that takes into account distribution network flexibility is proposed. Firstly, based on the definition of distribution network flexibility, the flexibility deficit is analyzed, and five flexibility assessment indicators are established. Secondly, the travel characteristics of EVs are simulated based on urban road topology and a trip probability matrix, and a model incorporating users’ bounded rationality is adopted to predict the temporal and spatial distribution of EV charging requirements. Furthermore, based on charging requirements and distribution network flexibility deficit, this paper establishes a model for the siting and sizing of EVCSs considering distribution network flexibility. Finally, case studies are conducted with a 29-node transportation network and a 33-node distribution network. The results show that the proposed method can formulate a more reasonable siting and sizing scheme for EVCSs, decrease the flexibility deficit of the distribution network, and reduce the annual comprehensive cost by 11.96%. Full article
(This article belongs to the Section F1: Electrical Power System)
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27 pages, 3120 KB  
Article
Causal Effects of Social Vulnerability and Multimorbidity on Tooth Loss in Chile: A National Survey Analysis
by Jaime Jamett, Marjorie Borgeat, Karina Cordero-Torres, Patricio Meléndez, Ximena Collao-Ferrada, María Guerra Zúñiga and Alejandro Veloz
Oral 2026, 6(3), 72; https://doi.org/10.3390/oral6030072 (registering DOI) - 12 Jun 2026
Viewed by 127
Abstract
Background/Objectives: Tooth loss reflects cumulative biological and social processes across the life course. However, population-level causal evidence on the influence of structural social vulnerability and multimorbidity on tooth-loss severity remains limited in middle-income contexts. This study evaluated the causal impacts of social vulnerability [...] Read more.
Background/Objectives: Tooth loss reflects cumulative biological and social processes across the life course. However, population-level causal evidence on the influence of structural social vulnerability and multimorbidity on tooth-loss severity remains limited in middle-income contexts. This study evaluated the causal impacts of social vulnerability and multimorbidity on tooth-loss severity in Chilean adults under explicit potential-outcomes assumptions. Methods: We analyzed nationally representative data from the Chilean National Health Survey 2016–2017 (N=5165 adults aged ≥20 years with oral examination; analytic sample n=4521). Outcomes comprised ordinal severity (y1: functioning dentition, moderate loss, severe loss, edentulism) and continuous tooth count (y2). Exposures included a Social Vulnerability Index (SVI, 0–1) and Multimorbidity Score (MS, 0–1). We estimated confounder-adjusted proportional-odds and survey-weighted linear regression models. Population-averaged causal contrasts were obtained via g-computation comparing 75th and 25th exposure percentiles, with 95% confidence intervals from probability-proportional-to-size bootstrap (1000 replications). Age-dependent edentulism trajectories were generated using discrete-time Markov projections. Results: In the weighted population, 72.6% retained functional dentition, whereas 5.5% were edentulous. Increasing SVI from 0.091 to 0.345 was associated with a 0.110-point severity increase and 1.95 fewer teeth. Increasing MS from 0.00 to 0.20 was associated with a 0.062-point severity increase and 1.20 fewer teeth. SVI showed larger population-averaged effects than multimorbidity. Conclusions: Within a potential-outcomes framework and under the stated identifying assumptions, structural social vulnerability and multimorbidity each exerted independent effects on tooth-loss severity, with socioeconomic disadvantage showing the stronger distributional gradient across the life course. Because the data are cross-sectional, this causal interpretation is conditional on those assumptions rather than established by the design. Full article
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