Search Results (13,036)

We develop a quantitative Hardy scale for mixed quadratic energies combining the classical Dirichlet form and a fractional Dirichlet form, ${\mathcal{E}}_{\lambda ,s}\left(u\right)={\int }_{{\mathbb{R}}^n}{|\nabla u\left(x\right)|}^2\mathrm{d}x+\lambda {\int }_{{\mathbb{R}}^n}{\left|{(-\Delta )}^{s/2}u\left(x\right)\right|}^2\mathrm{d}x,0<s<1,\lambda >0.$ Here, the word scale denotes a parameterized family with a fixed interpolation variable, explicit constants, and the scaling exponent forced by the coexistence of the orders 2 and $2s$. For $n\ge 3$, we prove weighted $L^2$ inequalities indexed by $\gamma \in [s,1]$, which control ${\left|x\right|}^{-2\gamma }$ by ${\mathcal{E}}_{\lambda ,s}$ with the factor ${\lambda }^{-\theta }$, where $\theta =(1-\gamma )/(1-s)$. In dimension $n=2$, the local endpoint is replaced by the logarithmic Hardy weight and gives a mixed log–power family governed by the same parameter. The novelty lies in organizing the endpoint Hardy estimates into a $\lambda$-adapted form suitable for mixed-order operators, with explicit constants, scaling-level optimality of the $\lambda$ exponent, a planar endpoint formulation, and directly usable singular-potential thresholds. The operator consequences are stated at the level of form boundedness, coercivity, spectral lower bounds on bounded domains, semigroup generation, and variational well-posedness; they are presented as consequences of the Hardy scale rather than as a separate spectral theory. Full article

The Hilfer fractional derivative effectively captures non-locality, historical dependence, and memory effects, making it valuable for modeling real-world systems, and exponential growth can describe explosive growth phenomena in real-world problems. This paper focuses on the existence of mild solutions for infinite-delay differential equations involving Hilfer fractional derivatives, fractional Laplacian operator ${(-\Delta )}^{\delta }$, and exponentially growing functions in Orlicz spaces. First, by utilizing standard $L^p$-$L^q$ estimates for strongly continuous semigroups generated by fractional Laplacian operator, the existence of global solutions in the Orlicz space $exp{L}^p\left({\mathbb{R}}^d\right)$ and the time-weighted $L^z\left({\mathbb{R}}^d\right)$ space is established. Then, by leveraging Hölder’s interpolation inequality, the existence of local solutions in $L^1\left({\mathbb{R}}^d\right)\cap L^{\infty }\left({\mathbb{R}}^d\right)$ is established. Full article

Background: Hormone therapy (HT) is an effective treatment for relieving menopausal symptoms; however, its association with health-related quality of life (HRQoL) in Asian populations remains insufficiently characterized. Objective: The aim of this study was to examine the association between HT use and HRQoL dimensions in postmenopausal Korean women using nationally representative data from 2005, 2007, 2008, and 2009. Methods: In this cross-sectional study, we analyzed data from the Korea National Health and Nutrition Examination Survey (KNHANES) conducted in 2005, 2007, 2008, and 2009. Postmenopausal women aged 40–65 years were included (n = 2460). HRQoL was assessed using the EuroQol 5-Dimension 3-Level (EQ-5D-3L) instrument. Survey-weighted logistic regression models were used to estimate odds ratios (ORs) and 95% confidence intervals (CIs) to determine the association between HT use and each EQ-5D dimension, adjusting for age. Results: Of the 2460 participants, 464 (18.9%) were HT users. HT use was significantly more common among women with higher education levels (p < 0.001) and higher household income (p < 0.001). The weighted mean EQ-5D index was significantly higher among HT users (0.911, 95% CI: 0.902–0.921) than non-users (0.894, 95% CI: 0.889–0.900; p < 0.05). In age-stratified analyses, significant differences were observed between women aged <55 years (p < 0.05) and those aged ≥60 years (p < 0.05). The EQ-5D index was positively associated with HT duration in women aged <55 and ≥60 years (p for trend < 0.05). In age-adjusted, dimension-specific analyses, HT use was associated with lower odds of reporting problems across all five EQ-5D dimensions (all p < 0.001), with the strongest association observed for usual activities (OR = 0.719, 95% CI: 0.715–0.722). Conclusions: In this nationally representative sample of postmenopausal Korean women, HT use was associated with more favorable HRQoL outcomes, particularly in the usual activities domain, with patterns varying by age and BMI subgroups. These findings support individualized menopausal counseling that incorporates quality-of-life considerations into clinical decision-making. Full article

Background: Serum 25-hydroxyvitamin D [25(OH)D] interpretation requires clear distinction between epidemiological thresholds, routine-data distributions, and clinical decision limits. This study evaluated vitamin D status and clinically pre-filtered routine laboratory data-derived 25(OH)D distributional benchmarks among adults from Şanlıurfa, southeastern Türkiye, according to sex, age, and season. Methods: This retrospective single-center routine laboratory database study included adults aged 18–65 years tested between 1 January and 31 December 2025, at the Medical Biochemistry Laboratory of Şanlıurfa Mehmet Akif İnan Training and Research Hospital. After eligibility screening, duplicate removal, analytical screening, and predefined clinical pre-filtering, 48,826 participant-level records were analyzed. Serum 25(OH)D was measured using the Elecsys Vitamin D total III electrochemiluminescence immunoassay on a cobas e 801 analyzer/module. The primary distributional estimate was the nonparametric 2.5th–97.5th percentile range. Results: Median age was 38 [28–49] years, and 35,043 records were from female participants (71.8%). Median serum 25(OH)D was 12.74 [8.28–19.00] ng/mL. Vitamin D deficiency, severe deficiency, insufficiency, and sufficiency were observed in 38,072 (78.0%), 17,163 (35.2%), 8235 (16.9%), and 2519 (5.2%) records, respectively. Lower 25(OH)D concentrations and higher deficiency prevalence were observed among females, younger adults, and winter/spring samples, with small-to-modest effect magnitudes. The clinically pre-filtered routine-data 2.5th–97.5th percentile range was 3.46–35.50 ng/mL. Conclusions: Low 25(OH)D status was widespread among routinely tested adults in Şanlıurfa. The derived range should be interpreted only as a local routine-data distributional benchmark for the tested population, not as a healthy-volunteer reference interval, clinical sufficiency threshold, treatment threshold, or clinical decision limit. Full article

Adjuvant XELOX (capecitabine plus oxaliplatin) and TS-1 (S-1) monotherapy are both guideline-recommended following D2 gastrectomy for gastric cancer, yet head-to-head real-world data exclusively in stage III disease remain scarce. Using Taiwan’s National Health Insurance Research Database linked to the Taiwan Cancer Registry–Long Form, we identified stage III gastric cancer patients who underwent D2 gastrectomy (2010–2019) and received adjuvant XELOX or TS-1 for ≥3 months. Propensity score matching balanced chemotherapy and non-chemotherapy cohorts (1706/group). Overall survival (OS) was the primary endpoint; disease progression was defined as initiation of FOLFOX salvage chemotherapy (used as a pragmatic proxy for disease recurrence). A second propensity score matching was performed directly between XELOX (n = 533) and TS-1 (n = 893) groups, yielding 490 matched pairs with well-balanced baseline characteristics. Multivariable Cox regression was adjusted for sex, age, comorbidities, and Charlson Comorbidity Index. TS-1 was associated with significantly better OS (adjusted HR 0.73, 95% CI 0.61–0.86; p < 0.001) and lower progression (adjusted HR 0.38, 95% CI 0.23–0.62; p < 0.001) versus XELOX; the corresponding 3-year OS was approximately 65.4% for TS-1 versus 56.8% for XELOX, and extrapolated 5-year OS approximately 50.2% versus 41.7%, respectively (note: these 5-year estimates are Kaplan–Meier projections beyond the mean follow-up of ~2.6 years and carry substantial uncertainty; they should be interpreted with caution). Benefits were confined to stage IIIA (OS HR 0.64, 95% CI 0.45–0.89; p = 0.009; interaction p = 0.006; progression HR 0.29, 95% CI 0.11–0.76; p = 0.011), with comparable outcomes in IIIB and IIIC. Adjuvant TS-1 monotherapy was associated with superior OS and lower disease progression versus XELOX in stage III gastric cancer, particularly in stage IIIA; these findings are hypothesis-generating and warrant confirmation in prospective randomized trials, whereas in stage IIIB/IIIC outcomes were comparable between the two regimens. Full article

To address the problem of high-frequency roll disturbances generated during dynamic balancing in non-coaxial two-wheeled robots, this paper proposes a Rotation-Optimized Inertial–Visual SLAM system (ROIV-SLAM) for robust state estimation. The proposed approach adopts a decoupled architecture for translation and rotation estimation. In the front-end, an Extended Kalman Filter (EKF) is employed to fuse LiDAR, an inertial measurement unit (IMU), and wheel odometry to obtain an initial translation estimate. Meanwhile, a physical manifold constraint is constructed using the gravity vector and surface normals extracted from RGB-D point clouds, supporting stable rotation estimation under high-frequency disturbances through Lie-group-based optimization. In the back-end, a factor graph is established, and loop closure robustness is enhanced through vision–LiDAR scan matching. Experimental results indicate that ROIV-SLAM achieves improved trajectory consistency with respect to the optimized reference trajectory and more robust mapping performance compared with the evaluated baseline approaches in the tested scenarios. The results further suggest that introducing task-specific physical dynamic constraints and a decoupled estimation mechanism helps suppress high-frequency motion noise inherent to balancing robots, thereby improving the robustness of state estimation in complex environments. Full article

Two-dimensional (2D) human pose estimation is one of the key research directions in Computer Vision (CV), which has wide application prospects in behavior recognition, such as gesture tracking, intelligent monitoring, and identity recognition. Therefore, it has recently attracted extensive attention from academia and industry. However, although a large amount of literature has been published, existing reviews often lack a unified theoretical perspective and fail to capture the latest paradigm shifts brought by foundation models. To this end, this paper reviews the applications of deep learning in the domain of 2D body pose estimation from 2010 to 2025 through a cascading approach. First, the mainstream body pose datasets and related evaluation metrics are introduced in a comprehensive and convincing way through mathematical formulas. Subsequently, an in-depth analysis of the performance of the algorithms in single-person and multi-person scenarios, and a comprehensive comparative analysis of the strengths and weaknesses of each algorithmic model, are conducted. A comprehensive comparative analysis encompassing both traditional architectures and the latest deep learning breakthroughs are provided, specifically highlighting Vision Foundation Models (VFMs), generative Diffusion processes, and State Space Models (SSMs). Finally, the current state of research in the field of 2D human pose estimation is summarized, and three main challenges, emerging solutions, and expected development trends are pointed out. This survey is an exhaustive compilation of existing research in 2D human pose estimation, providing a blueprint for researchers in the field and laying the foundation for future research work. Full article

Cancer risk may be influenced by genetic variation and altered expression of xenobiotic-metabolizing enzymes, yet their role in endometrial cancer remains incompletely understood. This study evaluated the association between four polymorphisms in xenobiotic metabolism-related genes CYP1A1 rs1799814, CYP2D6 rs3892097, NAT1 rs72554606, and NAT2 rs1799930 and the risk of endometrial cancer, and assessed CYP1A1 and CYP2D6 expression in tumor and control tissues. Genetic association analyses, including multivariate and histology-stratified models, were performed, and gene expression levels were compared between cancer and control tissues. Variants in NAT2, CYP1A1, and CYP2D6 were significantly associated with an increased risk of endometrial cancer, whereas NAT1 rs72554606 showed a protective effect, particularly in the dominant model. The strongest association was observed for NAT2 rs1799930 in additive and recessive models. Expression analysis revealed significantly higher CYP1A1 and CYP2D6 levels in tumor tissues than in control tissues. Stratified analyses showed generally consistent effects, especially for endometrioid carcinoma, although estimates for the serous subtype were limited by sample size. These findings suggest that polymorphisms and altered expression of xenobiotic-metabolizing genes may contribute to endometrial carcinogenesis. Further studies, including independent validation and analyses of gene–environment interactions, are needed. Full article

Water injection allocation is critical for maintaining pressure support in mature offshore waterflooding reservoirs, but its optimization is complicated by delayed injection–production responses, interwell interference, limited intervention windows, and incomplete field labels for injector–producer connectivity. This study proposes a connectivity-aware optimization framework that couples an attention-based connectivity identification network, a group-level long short-term memory (LSTM) production surrogate, and particle swarm optimization (PSO). The methodological novelty lies in using prescribed connectivity labels in a field-informed semi-synthetic benchmark to quantitatively test whether dynamic injection–production sequences and static well-pair attributes can be transformed into interpretable connectivity estimates for injection allocation decision support. The benchmark contains five injectors, ten producers, daily injection and production histories, static well-pair attributes, response lags, and normalized connectivity coefficients generated under practical injection rate, lag, water cut, and adjustment constraints. The attention model recovered the dominant injector–producer relationships with MAE = 0.0146, RMSE = 0.0240, R² = 0.9835, cosine similarity = 0.9962, and top-three overlap = 100%. The group-level LSTM achieved MAE = 4.524 m³/d, RMSE = 5.963 m³/d, MAPE = 1.255%, and R² = 0.964 on the chronological test set. Across 15 optimization cases, the PSO module generated feasible injection reallocations under single-well rate, total-injection balance, and +/−15% adjustment constraints. The results should be interpreted as controlled methodological validation rather than direct field deployment; further testing with anonymized field data is required. Full article

As a next-generation automotive display technology, Augmented Reality Head-Up Display (AR-HUD) has demonstrated immense potential in reshaping driving safety and enhancing the human–computer interaction experience. To address the challenges of barrel distortion and perspective distortion inherent in HUD systems, we propose a joint-learning-based dual-path pre-correction method. This approach employs a shared encoder to extract image features, which are then decoupled into two parallel branches: a classification branch and a distortion flow prediction branch. Building upon this architecture, a model-fitting method is introduced to estimate the distortion model parameters in the parameter space using the predicted distortion types and flows, thereby reconstructing a refined distortion flow. Finally, image rectification is achieved through a resampling method. On the ARHDD dataset, the proposed method achieves a PSNR of 24.617 dB (barrel) and 25.062 dB (perspective), an SSIM of 0.845 and 0.873, and an NRMSE of 0.163 and 0.157, respectively. On the Places 365 dataset, it achieves a PSNR of 23.914 dB (barrel) and 21.870 dB (perspective), an SSIM of 0.812 and 0.748, and an NRMSE of 0.174 and 0.211, respectively. Both quantitative and qualitative comparative experiments against other state-of-the-art methods demonstrate that the proposed approach achieves superior correction performance for both types of distortion. Finally, the simulation verification of the HUD system proved that this correction method demonstrated excellent potential, but further verification is still needed in a real or semi-real environment. Full article

Reconstructing building models from urban SAR tomography (TomoSAR) point clouds is often constrained by limited resolution, low positioning accuracy in elevation, as well as data incompleteness and artifacts caused by microwave imaging mechanisms. These challenges seriously restrict the extraction of high-accuracy building models with structural details from TomoSAR point clouds. This paper proposes a refined urban building modeling method that effectively utilizes structural priors, including directionality, orthogonality, and potential symmetry. First, a piecewise fitting strategy integrated with density-based segmentation is employed to iteratively estimate the main directions of the buildings and capture finer geometric variations of complex façade footprints than simple-plane approximations. Second, a roof extraction algorithm combining an adaptive Doug-las–Peucker approach with symmetry evaluation and constraints is developed to regularize roof outlines and repair data defects. Crucially, to handle extreme cases where roof data are entirely missing, a novel building width estimation method based on building shadow analysis is proposed. Experiments conducted on the SARMV3D-1.0 and SARMV3D-3.0 point cloud datasets demonstrate that the proposed method significantly enhances reconstruction accuracy and geometric fidelity in urban regions compared to state-of-the-art approaches. Full article

Facial emotion recognition (FER) in real-world settings is limited by the semantic mismatch between discrete emotion categories and continuous Valence–Arousal–Dominance (V-A-D) dimensions and the lack of reliable uncertainty estimates under incomplete facial evidence. Existing uncertainty-aware FER studies mainly address annotation ambiguity or training-time reliability, leaving the behavior of predictive uncertainty under progressive input degradation insufficiently examined. This paper proposes BGDC (Bayesian Gaussian-mixture Distributional Consistency), a multi-task FER framework that integrates a GMM-based soft consistency module with a context-conditioned Bayesian regression head and explicitly models aleatoric and epistemic uncertainty. To evaluate predictive reliability, a controlled masking protocol is introduced to remove facial information under different spatial configurations. On FER2013-VAD, BGDC attains the highest classification accuracy of 0.6943 and the highest mean V-A-D CCC of 0.6079 among the compared configurations, and it yields a stronger epistemic uncertainty-error correspondence than MC Dropout in a single-model setting. Controlled masking further shows that the epistemic uncertainty of BGDC tracks task-relevant facial information loss rather than masking ratio alone: it rises with regression error when diagnostically important regions are removed, and it contracts when the masked region is largely task-irrelevant. Combining Bayesian uncertainty with the GMM-based distributional prior thus enables reliability-aware multi-task FER, in which controlled masking serves as a diagnostic intervention rather than as a benchmark of accuracy degradation alone. Full article

Background/Objectives: Type 2 diabetes (T2D) remission can be defined as a return to a HbA1c < 6.5% (<48 mmol/mol) sustained without ongoing treatment for at least 3 months. Prevalence estimates and factors associated remain unknown for LMIC and resource-limited settings. Methods: We conducted a retrospective observational analysis of electronic medical records from 8463 adults who received multidisciplinary care at Mexico’s primary care specialized units (UNEMES-EC) between 2015 and 2019 and who were referred for inadequate metabolic control. Remission was defined per 2021 ADA criteria as HbA1c <6.5% sustained for ≥3 months without glucose-lowering medications. After estimating the prevalence of T2D remission, logistic regression models were used to evaluate its sociodemographic and clinical predictors, with particular attention to weight change and baseline adiposity interactions. Results: RT2D prevalence was 0.87% (95% CI: 0.68–1.10) over a median 393-day follow-up. Weight loss ≥10% (adjusted OR 2.75; 95% CI: 1.21-6.27) and systolic blood pressure (tertile 3 vs tertile 1: OR 2.49; 95% CI: 1.17–5.26) were positively associated with RT2D, while elevated baseline HbA1c (tertile 3 vs. tertile 1: OR 0.09; 95% CI: 0.02–0.33), triglyceride levels (tertile 3 vs. tertile 1: OR 0.49; 95% CI: 0.24–0.98) and intensive pharmacotherapy were inversely associated with RT2D. No associations with HDL and total cholesterol were found. Age, sex, educational attainment, and income demonstrated no independent associations with remission. Among lifestyle-treated patients achieving ≥5% weight loss, remission prevalence reached approximately 11%. No significant interaction between baseline BMI and weight change was detected (p = 0.60). Conclusions: This first large-scale Mexican study establishes RT2D as an achievable endpoint in patients with poor baseline metabolic control. The findings suggest that remission could be achieved with equity-focused, weight-centered interventions even in resource-constrained health systems and populations. Full article

Background: Intraductal carcinoma (IDC) and invasive cribriform (Cr) histologic patterns are important adverse morphologies in prostate cancer (PCa) and may influence pretreatment risk stratification. This study evaluated the feasibility of time-dependent diffusion magnetic resonance imaging (t_d-dMRI)-based microstructural mapping for preoperative characterization of these aggressive morphologies. Methods: This retrospective study included 95 men with pathologically confirmed PCa on radical prostatectomy specimens from March 2023 to March 2025. T_d-dMRI was performed using pulsed and oscillating gradient diffusion sequences. Microstructural parameters, including extracellular diffusivity (D_ex), cell diameter (d), intracellular volume fraction (f_in), cellularity, and diffusivities at 0, 17, and 33 Hz (ADC_0Hz, ADC_17Hz, and ADC_33Hz), were estimated using a two-compartment model. Conventional apparent diffusion coefficient (ADC_DWI) values were obtained from standard diffusion-weighted imaging. Parameters were compared between tumors with and without Cr/IDC patterns, and diagnostic performance was assessed using receiver operating characteristic analysis. Pairwise comparisons of AUCs were performed using the DeLong test. Results: Among 95 participants, 62 (65.3%) had Cr/IDC patterns. Compared with Cr/IDC-negative tumors, Cr/IDC-positive tumors showed higher f_in and cellularity (both p < 0.001) and lower ADC_DWI, ADC_0Hz, ADC_17Hz, and ADC_33Hz values (all p < 0.05). D_ex and d did not differ significantly between groups. Among t_d-dMRI-derived parameters, f_in showed the highest diagnostic performance (AUC = 0.757; 95% CI, 0.654–0.860). Conclusions: T_d-dMRI-based microstructural mapping demonstrates promise for characterizing the Cr/IDC morphologies in PCa. Full article

Accurate and non-destructive volume estimation of agricultural products is essential for precision agriculture, yet remains challenging when transitioning from controlled laboratory conditions to complex orchard environments. Although 2D image-based volume estimation methods provide a cost-effective and scalable solution, existing studies are fragmented and lack a unified perspective on their real-world applicability. This review presents a systematic synthesis of 2D image-based volume estimation methods, explicitly framed through the laboratory-to-orchard transition. We categorized existing volume estimation approaches according to the sensing modality into monocular RGB-based approaches and depth-assisted methods, and further reviewed them based on the image processing methods. A key finding is that high-precision geometric estimation can be achieved in laboratory environments, whereas deep learning and RGB-D fusion have driven a shift from conventional geometric modeling toward data-driven and hybrid learning frameworks in orchard settings. However, 2D image-based volume estimation remains fundamentally limited by scale ambiguity, severe occlusion, and sensitivity to illumination and background variability in real orchard environment. Overall, this review provides a unified perspective for understanding volume estimation methodology across environments and offers guidance for developing robust, scalable, and field-deployable volume estimation systems for real-world agricultural applications. Full article