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Search Results (736)

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14 pages, 387 KB  
Article
Effects of Catastrophic Coverage Expansion on Out-of-Pocket Spending for Non-Covered Services and Financial Equity: Evidence from South Korea’s National Health Insurance
by Minjeong Kim, Donggyo Shin, Hyunwoung Shin and Jangho Yoon
Healthcare 2026, 14(3), 302; https://doi.org/10.3390/healthcare14030302 - 26 Jan 2026
Abstract
Background: Patients with catastrophic health conditions have continuously faced substantial out-of-pocket (OOP) costs for non-covered services despite universal health coverage in South Korea. In 2013, the National Health Insurance Service (NHIS) expanded coverage for four major catastrophic conditions—cancers, cardiovascular diseases, cerebrovascular diseases, and [...] Read more.
Background: Patients with catastrophic health conditions have continuously faced substantial out-of-pocket (OOP) costs for non-covered services despite universal health coverage in South Korea. In 2013, the National Health Insurance Service (NHIS) expanded coverage for four major catastrophic conditions—cancers, cardiovascular diseases, cerebrovascular diseases, and rare illnesses—aiming to strengthen financial protection for patients with catastrophic conditions. However, concerns remain that providers may respond by inducing more use of non-covered services, potentially offsetting reductions in patients’ financial burden. Methods: We evaluated the impact of the 2013 catastrophic coverage expansion on patients’ OOP spending for non-covered services using a quasi-experimental difference-in-differences design. Using nationally representative longitudinal healthcare expenditure data, the Korean Health Panel Survey (KHPS), from 2011 to 2016, we compared patients with the four targeted conditions to a control group with clinically comparable conditions. A two-part model was applied to separately estimate changes in the probability of incurring any non-covered OOP spending and changes in spending levels conditional on positive expenditures. We further examined whether effects differed by supplemental private health insurance (PHI) status. Results: We found that 7.3-, 5.2-, and 7.7-percentage-point decreases in annual probability of incurring any non-covered OOP spending for total, inpatient, and outpatient services, respectively, after policy implementation. Among patients with positive spending, OOP spending for total and inpatient non-covered services decreased by approximately 164 USD and 254 USD per year, while outpatient spending showed no statistically significant change. No statistically significant differential effects were also observed by PHI status. Conclusion: The catastrophic coverage expansion reduced patients’ exposure to and burden of non-covered OOP spending, indicating improved financial protection without evidence of compensatory increases in non-covered service use. These findings suggest that targeted benefit expansions for high-cost conditions can enhance financial equity within universal health systems. Full article
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25 pages, 4936 KB  
Article
Drone-Enabled Non-Invasive Ultrasound Method for Rodent Deterrence
by Marija Ratković, Vasilije Kovačević, Matija Marijan, Maksim Kostadinov, Tatjana Miljković and Miloš Bjelić
Drones 2026, 10(2), 84; https://doi.org/10.3390/drones10020084 - 25 Jan 2026
Abstract
Unmanned aerial vehicles open new possibilities for developing technologies that support more sustainable and efficient agriculture. This paper presents a non-invasive method for repelling rodents from crop fields using ultrasound. The proposed system is implemented as a spherical-cap ultrasound loudspeaker array consisting of [...] Read more.
Unmanned aerial vehicles open new possibilities for developing technologies that support more sustainable and efficient agriculture. This paper presents a non-invasive method for repelling rodents from crop fields using ultrasound. The proposed system is implemented as a spherical-cap ultrasound loudspeaker array consisting of eight transducers, mounted on a drone that overflies the field while emitting sound in the 20–70 kHz range. The hardware design includes both the loudspeaker array and a custom printed circuit board hosting power amplifiers and a signal generator tailored to drive multiple ultrasonic transducers. In parallel, a genetic algorithm is used to compute flight paths that maximize coverage and increase the probability of driving rodents away from the protected area. As part of the validation phase, artificial intelligence models for rodent detection using a thermal camera are developed to provide quantitative feedback on system performance. The complete prototype is evaluated through a series of experiments conducted both in controlled laboratory conditions and in the field. Field trials highlight which parts of the concept are already effective and identify open challenges that need to be addressed in future work to move from a research prototype toward a deployable product. Full article
(This article belongs to the Special Issue Advances of UAV in Precision Agriculture—2nd Edition)
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28 pages, 564 KB  
Article
CONFIDE: CONformal Free Inference for Distribution-Free Estimation in Causal Competing Risks
by Quang-Vinh Dang, Ngoc-Son-An Nguyen and Thi-Bich-Diem Vo
Mathematics 2026, 14(2), 383; https://doi.org/10.3390/math14020383 - 22 Jan 2026
Viewed by 19
Abstract
Accurate prediction of individual treatment effects in survival analysis is often complicated by the presence of competing risks and the inherent unobservability of counterfactual outcomes. While machine learning models offer improved discriminative power, they typically lack rigorous guarantees for uncertainty quantification, which are [...] Read more.
Accurate prediction of individual treatment effects in survival analysis is often complicated by the presence of competing risks and the inherent unobservability of counterfactual outcomes. While machine learning models offer improved discriminative power, they typically lack rigorous guarantees for uncertainty quantification, which are essential for safety-critical clinical decision-making. In this paper, we introduce CONFIDE (CONFormal Inference for Distribution-free Estimation), a novel framework that bridges causal inference and conformal prediction to construct valid prediction sets for cause-specific cumulative incidence functions. Unlike traditional confidence intervals for population-level parameters, CONFIDE provides individual-level prediction sets for time-to-event outcomes, which are more clinically actionable for personalized treatment decisions by directly quantifying uncertainty in future patient outcomes rather than uncertainty in population averages. By integrating semi-parametric hazard estimation with targeted bias correction strategies, CONFIDE generates calibrated prediction sets that cover the true potential outcome with a user-specified probability, irrespective of the underlying data distribution. We empirically validate our approach on four diverse medical datasets, demonstrating that CONFIDE achieves competitive discrimination (C-index up to 0.83) while providing robust finite-sample marginal coverage guarantees (e.g., 85.7% coverage on the Bone Marrow Transplant dataset). We note two key limitations: (1) coverage may degrade under heavy censoring (>40%) unless inverse probability of censoring weighted (IPCW) conformal quantiles are used, as demonstrated in our sensitivity analysis; (2) while the method guarantees marginal coverage averaged over the covariate distribution, conditional coverage for specific covariate values is theoretically impossible without structural assumptions, though practical approximations via locally-adaptive calibration can improve conditional performance. Our framework effectively enables trustworthy personalized risk assessment in complex survival settings. Full article
(This article belongs to the Special Issue Statistical Models and Their Applications)
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14 pages, 1167 KB  
Article
Nationwide Survival Impact of Bevacizumab Under National Reimbursement for Advanced Cervical Cancer in South Korea
by Junhwan Kim, Jieun Jang, Krishnansu S. Tewari, Kyung Su Kim, Hyun-Cheol Kang and Sokbom Kang
Cancers 2026, 18(2), 346; https://doi.org/10.3390/cancers18020346 - 22 Jan 2026
Viewed by 40
Abstract
Background: The aim of this study was to evaluate the effectiveness of bevacizumab in advanced cervical cancer (CC) patients using nationwide data after its inclusion in South Korea’s National Health Insurance (NHI), considering various clinicopathologic factors. Methods: This retrospective study analyzed 3869 advanced [...] Read more.
Background: The aim of this study was to evaluate the effectiveness of bevacizumab in advanced cervical cancer (CC) patients using nationwide data after its inclusion in South Korea’s National Health Insurance (NHI), considering various clinicopathologic factors. Methods: This retrospective study analyzed 3869 advanced CC patients from South Korea’s cancer registry (2012–2019), alongside claims and death records (2012–2021). Among these 2792 patients diagnosed after bevacizumab’s NHI inclusion (August 2015), survival outcomes were compared between those receiving bevacizumab with platinum-based chemotherapy (n = 1787, 64.0%) versus chemotherapy alone (n = 1005, 36.0%). Overall survival (OS) was assessed using Cox proportional hazard regression with inverse probability of treatment weighting. Results: Following NHI coverage of bevacizumab, median OS increased from 1.5 to 2.5 years, and the 5-year OS rate increased from 25.6% to 41.4% (weighted hazard ratio [wHR], 0.63; 95% confidence interval [CI], 0.60–0.67). Among patients receiving bevacizumab, median OS was 2.6 years compared to 2.2 years for those not receiving bevacizumab, with 5-year OS rates of 42.0% and 40.2%, respectively (wHR, 0.84; 95% CI, 0.78–0.90). Subgroup analyses revealed that bevacizumab was associated with significantly better OS in patients with prior concurrent chemoradiation therapy (CCRT) history (wHR, 0.67; 95% CI, 0.61–0.75), regardless of histologic subtype (squamous cell carcinoma [SCC]: wHR, 0.69 [95% CI, 0.61–0.78] vs. non-SCC: wHR, 0.66 [95% CI, 0.55–0.79]). Conclusions: The national investment in the implementation of bevacizumab was associated with favorable survival outcomes in advanced CC patients. Particularly, bevacizumab showed pronounced survival benefit for patients with prior CCRT history, regardless of histologic subtype. Full article
(This article belongs to the Section Clinical Research of Cancer)
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16 pages, 26561 KB  
Article
Optimal Policies in an Insurance Stackelberg Game: Demand Response and Premium Setting
by Cuixia Chen, Bing Liu, Fumei He and Darhan Bahtbek
Mathematics 2026, 14(2), 370; https://doi.org/10.3390/math14020370 - 22 Jan 2026
Viewed by 16
Abstract
This paper examines a stochastic Stackelberg differential game between an insurer and a pool of homogeneous policyholders. Policyholders dynamically optimize insurance coverage and risky asset allocations to minimize the probability of wealth shortfall, while the insurer, acting as the leader, sets the premium [...] Read more.
This paper examines a stochastic Stackelberg differential game between an insurer and a pool of homogeneous policyholders. Policyholders dynamically optimize insurance coverage and risky asset allocations to minimize the probability of wealth shortfall, while the insurer, acting as the leader, sets the premium loading to maximize the expected exponential utility of terminal surplus. Employing dynamic programming techniques, we derive closed-form equilibrium strategies for both parties. The analysis reveals that a strong positive correlation between insurance claims and financial market returns incentivizes full coverage with modest premiums, whereas a strong negative correlation may induce market collapse as insurers exit underwriting to exploit natural hedging opportunities. Furthermore, larger policyholder pools generate diversification benefits that reduce equilibrium premiums and stimulate insurance demand. Full article
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34 pages, 7175 KB  
Article
Hybrid Unsupervised–Supervised Learning Framework for Rainfall Prediction Using Satellite Signal Strength Attenuation
by Popphon Laon, Tanawit Sahavisit, Supavee Pourbunthidkul, Sarut Puangragsa, Pattharin Wichittrakarn, Pattarapong Phasukkit and Nongluck Houngkamhang
Sensors 2026, 26(2), 648; https://doi.org/10.3390/s26020648 - 18 Jan 2026
Viewed by 227
Abstract
Satellite communication systems experience significant signal degradation during rain events, a phenomenon that can be leveraged for meteorological applications. This study introduces a novel hybrid machine learning framework combining unsupervised clustering with cluster-specific supervised deep learning models to transform satellite signal attenuation into [...] Read more.
Satellite communication systems experience significant signal degradation during rain events, a phenomenon that can be leveraged for meteorological applications. This study introduces a novel hybrid machine learning framework combining unsupervised clustering with cluster-specific supervised deep learning models to transform satellite signal attenuation into a predictive tool for rainfall prediction. Unlike conventional single-model approaches treating all atmospheric conditions uniformly, our methodology employs K-Means Clustering with the Elbow Method to identify four distinct atmospheric regimes based on Signal-to-Noise Ratio (SNR) patterns from a 12-m Ku-band satellite ground station at King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bangkok, Thailand, combined with absolute pressure and hourly rainfall measurements. The dataset comprises 98,483 observations collected with 30-s temporal resolutions, providing comprehensive coverage of diverse tropical atmospheric conditions. The experimental platform integrates three subsystems: a receiver chain featuring a Low-Noise Block (LNB) converter and Software-Defined Radio (SDR) platform for real-time data acquisition; a control system with two-axis motorized pointing incorporating dual-encoder feedback; and a preprocessing workflow implementing data cleaning, K-Means Clustering (k = 4), Synthetic Minority Over-Sampling Technique (SMOTE) for balanced representation, and standardization. Specialized Long Short-Term Memory (LSTM) networks trained for each identified cluster enable capture of regime-specific temporal dynamics. Experimental validation demonstrates substantial performance improvements, with cluster-specific LSTM models achieving R2 values exceeding 0.92 across all atmospheric regimes. Comparative analysis confirms LSTM superiority over RNN and GRU. Classification performance evaluation reveals exceptional detection capabilities with Probability of Detection ranging from 0.75 to 0.99 and False Alarm Ratios below 0.23. This work presents a scalable approach to weather radar systems for tropical regions with limited ground-based infrastructure, particularly during rapid meteorological transitions characteristic of tropical climates. Full article
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24 pages, 2148 KB  
Article
Distribution Network Electrical Equipment Defect Identification Based on Multi-Modal Image Voiceprint Data Fusion and Channel Interleaving
by An Chen, Junle Liu, Wenhao Zhang, Jiaxuan Lu, Jiamu Yang and Bin Liao
Processes 2026, 14(2), 326; https://doi.org/10.3390/pr14020326 - 16 Jan 2026
Viewed by 180
Abstract
With the explosive growth in the quantity of electrical equipment in distribution networks, traditional manual inspection struggles to achieve comprehensive coverage due to limited manpower and low efficiency. This has led to frequent equipment failures including partial discharge, insulation aging, and poor contact. [...] Read more.
With the explosive growth in the quantity of electrical equipment in distribution networks, traditional manual inspection struggles to achieve comprehensive coverage due to limited manpower and low efficiency. This has led to frequent equipment failures including partial discharge, insulation aging, and poor contact. These issues seriously compromise the safe and stable operation of distribution networks. Real-time monitoring and defect identification of their operation status are critical to ensuring the safety and stability of power systems. Currently, commonly used methods for defect identification in distribution network electrical equipment mainly rely on single-image or voiceprint data features. These methods lack consideration of the complementarity and interleaved nature between image and voiceprint features, resulting in reduced identification accuracy and reliability. To address the limitations of existing methods, this paper proposes distribution network electrical equipment defect identification based on multi-modal image voiceprint data fusion and channel interleaving. First, image and voiceprint feature models are constructed using two-dimensional principal component analysis (2DPCA) and the Mel scale, respectively. Multi-modal feature fusion is achieved using an improved transformer model that integrates intra-domain self-attention units and an inter-domain cross-attention mechanism. Second, an image and voiceprint multi-channel interleaving model is applied. It combines channel adaptability and confidence to dynamically adjust weights and generates defect identification results using a weighting approach based on output probability information content. Finally, simulation results show that, under the dataset size of 3300 samples, the proposed algorithm achieves a 8.96–33.27% improvement in defect recognition accuracy compared with baseline algorithms, and maintains an accuracy of over 86.5% even under 20% random noise interference by using improved transformer and multi-channel interleaving mechanism, verifying its advantages in accuracy and noise robustness. Full article
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32 pages, 4385 KB  
Article
Probabilistic Wind Speed Forecasting Under at Site and Regional Frameworks: A Comparative Evaluation of BART, GPR, and QRF
by Khaled Haddad and Ataur Rahman
Climate 2026, 14(1), 21; https://doi.org/10.3390/cli14010021 - 15 Jan 2026
Viewed by 145
Abstract
Reliable probabilistic wind speed forecasts are essential for integrating renewable energy into power grids and managing operational uncertainty. This study compares Quantile Regression Forests (QRF), Bayesian Additive Regression Trees (BART), and Gaussian Process Regression (GPR) under at-site and regional pooled frameworks using 21 [...] Read more.
Reliable probabilistic wind speed forecasts are essential for integrating renewable energy into power grids and managing operational uncertainty. This study compares Quantile Regression Forests (QRF), Bayesian Additive Regression Trees (BART), and Gaussian Process Regression (GPR) under at-site and regional pooled frameworks using 21 years (2000–2020) of daily wind data from eleven stations in New South Wales and Queensland, Australia. Models are evaluated via strict year-based holdout validation across seven metrics: RMSE, MAE, R2, bias, correlation, coverage, and Continuous Ranked Probability Score (CRPS). Regional QRF achieves exceptional point forecast stability with minimal RMSE increase but suffers persistent under-coverage, rendering probabilistic bounds unreliable. BART attains near-nominal coverage at individual sites but experiences catastrophic calibration collapse under regional pooling, driven by fixed noise priors inadequate for spatially heterogeneous data. In contrast, GPR maintains robust probabilistic skill regionally despite larger point forecast RMSE penalties, achieving the lowest overall CRPS and near-nominal coverage through kernel-based variance inflation. Variable importance analysis identifies surface pressure and minimum temperature as dominant predictors (60–80%), with spatial covariates critical for regional differentiation. Operationally, regional QRF is prioritised for point accuracy, regional GPR for calibrated probabilistic forecasts in risk-sensitive applications, and at-site BART when local data suffice. These findings show that Bayesian machine learning methods can effectively navigate the trade-off between local specificity and regional pooling, a challenge common to wind forecasting in diverse terrain globally. The methodology and insights are transferable to other heterogeneous regions, providing guidance for probabilistic wind forecasting and renewable energy grid integration. Full article
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26 pages, 8620 KB  
Article
Two-Step Localization Method for Electromagnetic Follow-Up of LIGO-Virgo-KAGRA Gravitational-Wave Triggers
by Daniel Skorohod and Ofek Birnholtz
Universe 2026, 12(1), 21; https://doi.org/10.3390/universe12010021 - 14 Jan 2026
Viewed by 215
Abstract
Rapid detection and follow-up of electromagnetic (EM) counterparts to gravitational wave (GW) signals from binary neutron star (BNS) mergers are essential for constraining source properties and probing the physics of relativistic transients. Observational strategies for these early EM searches are therefore critical, yet [...] Read more.
Rapid detection and follow-up of electromagnetic (EM) counterparts to gravitational wave (GW) signals from binary neutron star (BNS) mergers are essential for constraining source properties and probing the physics of relativistic transients. Observational strategies for these early EM searches are therefore critical, yet current practice remains suboptimal, motivating improved, coordination-aware approaches. We propose and evaluate the Two-Step Localization strategy, a coordinated observational protocol in which one wide-field auxiliary telescope and one narrow-field main telescope monitor the evolving GW sky localization in real time. The auxiliary telescope, by virtue of its large field of view, has a higher probability of detecting early EM emission. Upon registering a candidate signal, it triggers the main telescope to slew to the inferred location for prompt, high-resolution follow-up. We assess the performance of Two-Step Localization using large-scale simulations that incorporate dynamic sky-map updates, realistic telescope parameters, and signal-to-noise ratio (SNR)-weighted localization contours. For context, we compare Two-Step Localization to two benchmark strategies lacking coordination. Our results demonstrate that Two-Step Localization significantly reduces the median detection latency, highlighting the effectiveness of targeted cooperation in the early-time discovery of EM counterparts. Our results point to the most impactful next step: next-generation faster telescopes that deliver drastically higher slew rates and shorter scan times, reducing the number of required tiles; a deeper, truly wide-field auxiliary improves coverage more than simply adding more telescopes. Full article
(This article belongs to the Section Compact Objects)
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31 pages, 13946 KB  
Article
The XLindley Survival Model Under Generalized Progressively Censored Data: Theory, Inference, and Applications
by Ahmed Elshahhat and Refah Alotaibi
Axioms 2026, 15(1), 56; https://doi.org/10.3390/axioms15010056 - 13 Jan 2026
Viewed by 97
Abstract
This paper introduces a novel extension of the classical Lindley distribution, termed the X-Lindley model, obtained by a specific mixture of exponential and Lindley distributions, thereby substantially enriching the distributional flexibility. To enhance its inferential scope, a comprehensive reliability analysis is developed under [...] Read more.
This paper introduces a novel extension of the classical Lindley distribution, termed the X-Lindley model, obtained by a specific mixture of exponential and Lindley distributions, thereby substantially enriching the distributional flexibility. To enhance its inferential scope, a comprehensive reliability analysis is developed under a generalized progressive hybrid censoring scheme, which unifies and extends several traditional censoring mechanisms and allows practitioners to accommodate stringent experimental and cost constraints commonly encountered in reliability and life-testing studies. Within this unified censoring framework, likelihood-based estimation procedures for the model parameters and key reliability characteristics are derived. Fisher information is obtained, enabling the establishment of asymptotic properties of the frequentist estimators, including consistency and normality. A Bayesian inferential paradigm using Markov chain Monte Carlo techniques is proposed by assigning a conjugate gamma prior to the model parameter under the squared error loss, yielding point estimates, highest posterior density credible intervals, and posterior reliability summaries with enhanced interpretability. Extensive Monte Carlo simulations, conducted under a broad range of censoring configurations and assessed using four precision-based performance criteria, demonstrate the stability and efficiency of the proposed estimators. The results reveal low bias, reduced mean squared error, and shorter interval lengths for the XLindley parameter estimates, while maintaining accurate coverage probabilities. The practical relevance of the proposed methodology is further illustrated through two real-life data applications from engineering and physical sciences, where the XLindley model provides a markedly improved fit and more realistic reliability assessment. By integrating an innovative lifetime model with a highly flexible censoring strategy and a dual frequentist–Bayesian inferential framework, this study offers a substantive contribution to modern survival theory. Full article
(This article belongs to the Special Issue Recent Applications of Statistical and Mathematical Models)
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46 pages, 1025 KB  
Article
Confidence Intervals for the Difference and Ratio Means of Zero-Inflated Two-Parameter Rayleigh Distribution
by Sasipong Kijsason, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2026, 18(1), 109; https://doi.org/10.3390/sym18010109 - 7 Jan 2026
Viewed by 135
Abstract
The analysis of road traffic accidents often reveals asymmetric patterns, providing insights that support the development of preventive measures, reduce fatalities, and improve road safety interventions. The Rayleigh distribution, a continuous distribution with inherent asymmetry, is well suited for modeling right-skewed data and [...] Read more.
The analysis of road traffic accidents often reveals asymmetric patterns, providing insights that support the development of preventive measures, reduce fatalities, and improve road safety interventions. The Rayleigh distribution, a continuous distribution with inherent asymmetry, is well suited for modeling right-skewed data and is widely used in scientific and engineering fields. It also shares structural characteristics with other skewed distributions, such as the Weibull and exponential distributions, and is particularly effective for analyzing right-skewed accident data. This study considers several approaches for constructing confidence intervals, including the percentile bootstrap, bootstrap with standard error, generalized confidence interval, method of variance estimates recovery, normal approximation, Bayesian Markov Chain Monte Carlo, and Bayesian highest posterior density methods. Their performance was evaluated through Monte Carlo simulation based on coverage probabilities and expected lengths. The results show that the HPD method achieved coverage probabilities at or above the nominal confidence level while providing the shortest expected lengths. Finally, all proposed confidence intervals were applied to fatalities recorded during the seven hazardous days of Thailand’s Songkran festival in 2024 and 2025. Full article
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25 pages, 908 KB  
Article
Statistical Estimation of Common Percentile in Birnbaum–Saunders Distributions: Insights from PM2.5 Data in Thailand
by Warisa Thangjai, Sa-Aat Niwitpong, Suparat Niwitpong and Rattana Prommai
Symmetry 2026, 18(1), 100; https://doi.org/10.3390/sym18010100 - 6 Jan 2026
Viewed by 158
Abstract
This study develops approaches for estimating the common percentile of Birnbaum–Saunders (BS) distributions and applies them to daily PM2.5 concentration data from six monitoring stations in Chiang Mai Province, Thailand. Percentiles provide a robust representation of typical pollutant exposure, being less sensitive [...] Read more.
This study develops approaches for estimating the common percentile of Birnbaum–Saunders (BS) distributions and applies them to daily PM2.5 concentration data from six monitoring stations in Chiang Mai Province, Thailand. Percentiles provide a robust representation of typical pollutant exposure, being less sensitive to outliers and suitable for skewed environmental data. Estimating the same percentile across multiple monitoring sites offers a standardized metric for regional air quality assessment, enabling meaningful comparisons and informing evidence-based environmental policy. Four statistical approaches—Generalized Confidence Interval (GCI), bootstrap, Bayesian, and Highest Posterior Density (HPD)—were employed to construct confidence intervals (CIs) for the common percentile. Simulation studies evaluated the methods in terms of average length (AL) and coverage probability (CP), showing that the GCI approach offers the best balance between precision and reliability. Application to real PM2.5 data confirmed that the BS distribution appropriately models pollutant concentrations and that the common percentile provides a meaningful measure for environmental assessment. These findings highlight the GCI method as a robust tool for constructing CIs in environmental data analysis. Full article
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20 pages, 802 KB  
Article
CNL-Diff: A Nonlinear Data Transformation Framework for Epidemic Scale Prediction Based on Diffusion Models
by Boyu Ma and Yifei Du
Mathematics 2026, 14(2), 207; https://doi.org/10.3390/math14020207 - 6 Jan 2026
Viewed by 183
Abstract
In recent years, the complexity and suddenness of infectious disease transmission have posed significant limitations for traditional time-series forecasting methods when dealing with the nonlinearity, non-stationarity, and multi-peak distributions of epidemic scale variations. To address this challenge, this paper proposes a forecasting framework [...] Read more.
In recent years, the complexity and suddenness of infectious disease transmission have posed significant limitations for traditional time-series forecasting methods when dealing with the nonlinearity, non-stationarity, and multi-peak distributions of epidemic scale variations. To address this challenge, this paper proposes a forecasting framework based on diffusion models, called CNL-Diff, aimed at tackling the prediction challenges in complex dynamics, nonlinearity, and non-stationary distributions. Traditional epidemic forecasting models often rely on fixed linear assumptions, which limit their ability to accurately predict the incidence scale of infectious diseases. The CNL-Diff framework integrates a forward–backward consistent conditioning mechanism and nonlinear data transformations, enabling it to capture the intricate temporal and feature dependencies inherent in epidemic data. The results show that this method outperforms baseline models in metrics such as Mean Absolute Error (MAE), Continuous Ranked Probability Score (CRPS), and Prediction Interval Coverage Probability (PICP). This study demonstrates the potential of diffusion models in complex-distribution time-series modeling, providing a more reliable probabilistic forecasting tool for public health monitoring, epidemic early warning, and risk decision making. Full article
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12 pages, 439 KB  
Article
Trends in Survival and Mortality of “Early” Metastatic Breast Cancer in Northern Italy Following the Introduction of Targeted Therapies
by Francesco Marinelli, Maria Barbara Braghiroli, Isabella Bisceglia, Guglielmo Ferrari, Fortunato Morabito, Filippo Giovanardi, Carmine Pinto and Lucia Mangone
Cancers 2026, 18(1), 108; https://doi.org/10.3390/cancers18010108 - 29 Dec 2025
Viewed by 328
Abstract
Background/Objectives: In high-income settings, the incidence of metastatic breast cancer (MBC) at diagnosis has declined, reflecting the impact of effective screening and therapeutic advances. This study examined long-term trends in MBC incidence, mortality, and survival in a province of North Italy, an area [...] Read more.
Background/Objectives: In high-income settings, the incidence of metastatic breast cancer (MBC) at diagnosis has declined, reflecting the impact of effective screening and therapeutic advances. This study examined long-term trends in MBC incidence, mortality, and survival in a province of North Italy, an area characterized by high screening participation and broad access to modern systemic treatments. Methods: All invasive breast cancer cases (n = 10,966) diagnosed between 2000 and 2022 were retrieved from the Reggio Emilia Cancer Registry (population: 532,000). Metastatic cases were defined “early” if distant metastases occurred within six months of diagnosis. Mortality trends were assessed using joinpoint regression to estimate annual percentage changes (APCs). One-, three-, and five-year survival probabilities were calculated, with follow-up through December 2024. Results: Overall, 511 cases (4.7%) were “early” metastatic breast cancers at diagnosis. This proportion declined from 6.4% in 2000–2003 to 3.8% in 2019–2022. One-year mortality decreased from 38.4% to 26.7% (APC = −6.6; 95% CI −13.1 to −0.5), and two-year mortality from 54.5% to 34.9% (APC = −7.3; 95% CI −12.3 to −1.4) after 2017. One- and three-year survival increased from 63% to 66% and from 39% to 42%, respectively, while five-year survival improved from 21% to 30%. Conclusions: Over more than two decades, the incidence of MBC at diagnosis and early mortality both declined, accompanied by improved survival. These trends temporally coincide with the widespread adoption of targeted therapies and sustained high screening coverage, suggesting a possible combined contribution of early detection and advances in precision medicine to the observed outcomes. Full article
(This article belongs to the Section Cancer Metastasis)
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27 pages, 4733 KB  
Article
MDD Detection Based on Time-Spatial Features from EEG Symmetrical Microstate–Brain Networks
by Yang Xi, Bingjie Shi, Ting Lu, Pengfei Tian and Lu Zhang
Symmetry 2026, 18(1), 59; https://doi.org/10.3390/sym18010059 - 29 Dec 2025
Viewed by 287
Abstract
Major depressive disorder (MDD), identified by the World Health Organization as the leading cause of disability worldwide, remains underdiagnosed due to the lack of objective diagnostic tools. Electroencephalogram (EEG) signals offer potential biomarkers, yet conventional analyses often overlook the brain’s nonlinear dynamics. In [...] Read more.
Major depressive disorder (MDD), identified by the World Health Organization as the leading cause of disability worldwide, remains underdiagnosed due to the lack of objective diagnostic tools. Electroencephalogram (EEG) signals offer potential biomarkers, yet conventional analyses often overlook the brain’s nonlinear dynamics. In this study, we analyzed resting-stage EEG data to identify four microstate types in MDD patients. Symmetrical microstate–brain networks were then constructed for each microstate by using time series of four types of microstates as dynamic windows. Then, we compared microstate features (duration, occurrence, coverage, transition probability) and brain network parameters (clustering coefficient, characteristic path length, local and global efficiency) between MDD patients and healthy controls to analyze the characteristics of the changes in the brain activities of the patients with MDD and the topological patterns of the functional connectivity. The comparative analysis showed that MDD patients showed more frequent microstate transitions and reduced network efficiency, suggesting elevated energy consumption and impaired neural integration, which may imply a cognitive shift in MDD patients toward internal focus and psychological withdrawal from external stimuli. By integrating microstate and brain network features, we captured the temporal and spatial characteristics of MDD-related brain activity and validated their diagnostic utility using our previously proposed multiscale spatiotemporal convolutional attention network (MSCAN). Our MSCAN achieved an accuracy of 98.64% for MDD detection, outperforming existing approaches. Our study can offer promising implications for the intelligent diagnosis of MDD and a deeper understanding of its neurophysiological underpinnings. Full article
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