Category: Statistics

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-52289-x. Online ahead of print.

ABSTRACT

This study compared two widely used biomechanical models-Plug-in Gait (PiG) and Conventional Gait Model 2.3 (CGM2.3)-during overground walking (WALK) and single-leg squats (SLS) in 24 healthy adults. Data was collected using a 20-camera Vicon system and force plates. Static trials were analyzed with medial knee and ankle markers to align joint axes across models. Kinematic and kinetic outputs were compared using root mean square differences (RMSD) and statistical parametric mapping (SPM) paired t-tests. During WALK, PiG produced greater internal rotation at the knee (RMSD 17.8°, p < 0.001) and hip (RMSD 5.0°, p < 0.001), and smaller sagittal-plane flexion angles (RMSD 2.6° knee, 2.3° hip) compared with CGM2.3. In single-leg squats, these discrepancies increased to 29.1° and 9.0°, respectively, with sagittal-plane differences of 4.4° at the knee and 5.1° at the hip. CGM2.3 yielded higher knee flexion moments (31% in WALK, 104% in SLS), while PiG produced higher frontal-plane knee moments (28% and 89%). The differences were most pronounced at deeper flexion angles. These results demonstrate that biomechanical outcomes differ systematically between models, emphasizing the impact of model selection on joint kinematics and kinetics in human movement analysis.

PMID:42129499 | DOI:10.1038/s41598-026-52289-x

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-52543-2. Online ahead of print.

ABSTRACT

In this study, we explore the (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation because of its significant role in modeling the nonlinear spin-wave propagation and magnetic excitations in ferromagnetic materials. The aim is to develop exact analytical solutions of the model through two different methods: a modified (addendum-type) Kudryashov method and a unified Riccati equation method. These methods provide a range of exact wave solutions, such as periodic, hyperbolic, trigonometric and rational structures, which exhibit a rich nonlinear behavior of the model. The solutions are discussed and depicted graphically in 2D and 3D forms, exhibiting stable, bounded, and finite propagation of waves without singularities. A key novelty of this study lies in the combined application of the two analytical methods to the HFSC model, which has not been extensively explored in previous literature. The outcome indicates the success and compatibility of these methods in describing the nonlinear behavior of spin-wave structures. The results could be applied for the study of nonlinear magnetic structures and may find applications in spintronics and modeling of ferromagnetic materials.

PMID:42129492 | DOI:10.1038/s41598-026-52543-2

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-52883-z. Online ahead of print.

ABSTRACT

High predictive accuracy is frequently misinterpreted as evidence of causal understanding or population-level signal. Models can exploit spurious correlations, confounding, or protocol-induced artefacts, while post-hoc explanations may faithfully describe model behaviour yet remain misleading about the underlying phenomenon. We propose a framework that separates three layers of evidence: (i) causal relations in the phenomenon, (ii) population-level statistical dependence, and (iii) finite-sample, protocol-dependent predictive effects. This separation clarifies why predictive success and feature attributions do not license mechanistic interpretations without additional assumptions. Under log-loss and Bayes-risk-consistent protocols, the population predictive value of adding a feature equals the conditional mutual information, providing a principled reference for “true signal”. Using controlled simulations, we illustrate that bootstrap resampling can induce persistent false positives by amplifying chance correlations, and that SHAP can assign high importance to confounded variables while remaining faithful to the fitted model. These results suggest that “feature importance” is best treated as protocol-bounded evidence, and that interpretation benefits from reporting the protocol, robustness checks, and the intended inferential scope.

PMID:42129446 | DOI:10.1038/s41598-026-52883-z

Commun Biol. 2026 May 13. doi: 10.1038/s42003-026-10231-x. Online ahead of print.

ABSTRACT

Body size is a fundamental driver of metabolism, yet it remains unclear whether colonial organisms such as corals conform to the universal ¾-power scaling law. As climate change accelerates metabolic demands, characterizing these scaling relationships is essential to identifying which species are most physiologically vulnerable to environmental shifts. Here, we test whether coral polyp morphological traits can predict aerobic metabolism across a diverse range of reef-building species. We examine relationships between respiration and polyp biovolume, surface area, and corallite width, finding isometric scaling with biovolume and slight positive allometry with surface area, with both exponents close to one. Using median corallite width, we further extrapolate our model to theoretically predict per-polyp respiration for 727 coral species from a publicly available trait database.

PMID:42129431 | DOI:10.1038/s42003-026-10231-x

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-53171-6. Online ahead of print.

ABSTRACT

Cerebral small vessel disease (CSVD) poses major public health challenges, yet current MRI based diagnosis detects only established damage, and existing auxiliary methods, mostly based on conventional statistics, lack sufficient feature extraction capability and generalizability, thereby limiting early warning and precision management. Accordingly, we developed an intelligent auxiliary diagnostic system grounded in an interpretable ensemble learning framework, aiming to enable early detection and warning of CSVD. To support this development, a total of 597 sets of electronic medical record data from Quzhou Affiliated Hospital of Wenzhou Medical University were used as the study cohort. Firstly, a multidimensional feature evaluation and selection method was proposed, identifying 12 key predictive factors out of 23 relevant variables. Subsequently, the optimal algorithm was selected from Logistic Regression, Decision Tree, Random Forest, Support Vector Machine, Gradient Boosting Machine, XGBoost, and Multilayer Perceptron Classifier, based on Area Under the Curve (AUC) and Accuracy metrics, and a stacking ensemble learning strategy was then employed for model construction. The developed model demonstrated excellent discriminative performance, achieving an AUC of 0.881 while maintaining a low Brier score of 0.1271. By integrating the SHAP interpretability algorithm, the model provided intuitive visualizations of feature importance, thereby enhancing transparency and facilitating clinical adoption. Ultimately, this study achieved effective integration of early warning and auxiliary diagnostic functions for CSVD. These results indicate that the proposed system possesses high accuracy, interpretability, and deployability, underscoring its broad potential for early warning and personalized management of CSVD.

PMID:42129429 | DOI:10.1038/s41598-026-53171-6

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-49743-1. Online ahead of print.

ABSTRACT

Rumor spreading has become a critical social issue with the widespread use of social media platforms. This study develops a stochastic fractional delay differential equation (SFDDE) model to describe rumor propagation in a population divided into four compartments: susceptible [Formula: see text], spreaders [Formula: see text], counter-rumor spreaders [Formula: see text], and stiflers [Formula: see text]. The proposed model ensures nonnegativity and boundedness of solutions for nonnegative initial conditions. Rigorous analytical investigations establish the local and global stability of both the Rumor-Free Equilibrium (RFE) and the Rumor-Present Equilibrium (RPE), with the reproduction number identified as a key threshold parameter. Supported by classical stability theorems, the model’s positivity, boundedness, local and global dynamics, and sensitivity around the reproduction number are systematically examined. Furthermore, the Generalized Nonstandard Finite Difference (GL-NSFD) method is employed to obtain accurate and dynamically consistent numerical approximations, demonstrating the model’s reliability and efficiency through simulations and graphical validation.

PMID:42129419 | DOI:10.1038/s41598-026-49743-1

Sci Rep. 2026 May 13;16(1):15067. doi: 10.1038/s41598-026-50965-6.

ABSTRACT

Acute SARS-CoV-2 infection has been implicated in the development of endothelial dysfunction and metabolic alterations. These disturbances may contribute to the pathophysiology of post-COVID-19 syndrome (PCS), a multifaceted condition characterized by persistent symptoms, including neuropsychiatric symptoms. The diagnosis of PCS primarily relies on symptom-based criteria. Here, we aimed to identify biomarkers associated with PCS and disease severity. This prospective single-center cohort study investigated soluble blood biomarkers related to endothelial dysfunction and amino acid, fatty acid, carnitine, eicosanoid and resolvin metabolism in individuals post-acute SARS-CoV-2 infection with or without PCS compared with individuals without documented SARS-CoV-2 infection. Additionally, we explored the association between these biomarkers and PCS-related fatigue severity as assessed by the Multidimensional Fatigue Inventory (MFI). At a median of 37.4 weeks after SARS-CoV-2 infection, participants with prior infection showed higher levels of soluble thrombomodulin (TM) and L-lactate dehydrogenase (LDH) than those without previous infection. Alterations in arginine biosynthesis and taurine and hypotaurine metabolism indicate disruption of the NO-metabolism. These findings were made in participants without and with symptoms of PCS. In participants with PCS-related high fatigue severity, concentrations of the polyunsaturated fatty acid (PUFA) linoleic acid (LA), and the monounsaturated fatty acids (MUFAs) oleic acid (OA) and palmitoleic acid (PA) were higher than in participants with low fatigue severity. Alterations in markers of endothelial dysfunction and NO-metabolism are detectable at a median of 37.4 weeks after SARS-CoV-2 infection independent of PCS-related fatigue severity. Additionally, in individuals with high PCS-related fatigue severity, specific fatty acid alterations were observed.

PMID:42129413 | DOI:10.1038/s41598-026-50965-6

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-52453-3. Online ahead of print.

ABSTRACT

Coal and gas outburst represents a highly destructive dynamic phenomenon inherent in deep coal mining operations. Currently, outburst prediction frameworks rely heavily on a uniform critical threshold system recommended by national regulations. However, within heterogeneous coal seams characterized by complex geological conditions, this universal approach frequently leads to “low-index outburst” incidents or excessive engineering redundancy, significantly undermining the intrinsic safety of mine operations. To address this core scientific bottleneck, the present study establishes a theoretical methodology for the quantitative determination of sensitive prediction indicators and proposes a hierarchical optimization framework for both regional and local critical thresholds. By integrating long-term historical statistics, laboratory kinetic tests of gas desorption, and in-situ multi-point tracking and verification, the critical thresholds undergo scientific calibration and site-specific alignment. Empirical research conducted on the No. 1 coal seam of the Miluo Coal Mine in Guizhou demonstrates that, at the regional prediction level, gas content and gas pressure exhibit equivalent sensitivity, with established critical values of 8.0 m³/t and 0.74 MPa, respectively. Furthermore, the sensitivity hierarchy for local prediction indicators was determined as [Formula: see text]. Significantly, the finalized local thresholds ([Formula: see text]= 0.47 mL/(g·min^0.5), [Formula: see text]= 184 Pa, and S= 6.0 kg/m) are more stringent than the recommendations set forth in the Detailed Rules for Prevention and Control of Coal and Gas Outburst. The proposed prediction system effectively standardizes disaster characterization in complex coal seams and provides strategic guidance for coal mining enterprises to establish precision-based, site-specific outburst prevention standards. Coal and gas outbursts constitute a highly destructive dynamic phenomenon inherent in deep coal mining operations. Current outburst prediction frameworks largely depend on a uniform critical threshold system mandated by national regulations. However, in heterogeneous coal seams characterized by complex geological conditions, this universal approach frequently leads to “low-index outburst” incidents or excessive engineering redundancy, significantly undermining the intrinsic safety of mining operations. To resolve this fundamental scientific bottleneck, the present study establishes a theoretical methodology for the quantitative determination of sensitive prediction indicators and proposes a hierarchical optimization framework for both regional and local critical thresholds. By integrating long-term historical statistics, laboratory kinetic tests of gas desorption, and in-situ multi-point tracking and verification, the critical thresholds undergo rigorous scientific calibration and site-specific alignment. Empirical research conducted on the No. 1 coal seam of the Miluo Coal Mine in Guizhou demonstrates that, at the regional prediction level, gas content (w) and gas pressure (p) exhibit equivalent sensitivity, with established critical values of 8.0 m³/t and 0.74 MPa, respectively. Furthermore, the sensitivity hierarchy for local prediction indicators was established as [Formula: see text]. Significantly, the finalized local thresholds ([Formula: see text]= 0.47 mL/(g·min^0.5), [Formula: see text]= 184 Pa, and S= 6.0 kg/m) are more stringent than the standards set forth in the Detailed Rules for Prevention and Control of Coal and Gas Outburst. The proposed prediction system effectively standardizes hazard characterization in complex coal seams and provides strategic guidance for coal mining enterprises to establish precision-based, site-specific outburst prevention standards.

PMID:42129399 | DOI:10.1038/s41598-026-52453-3

Sci Rep. 2026 May 13. doi: 10.1038/s41598-026-53061-x. Online ahead of print.

ABSTRACT

Accurate representation of CO over India remains challenging because of large uncertainties in emissions, atmospheric transport, and sparse in‑situ measurements. This study examines the impact of assimilating MOPITT total column CO retrievals into the Weather Research and Forecasting model coupled with Chemistry (WRF‑Chem) using the Gridpoint Statistical Interpolation (GSI) system for October-December 2019, a period strongly influenced by post‑monsoon crop‑residue burning and stagnant meteorology over northern India. Model performance is evaluated against independent TROPOMI CO columns and MOPITT vertical profiles. The control simulation (WRF‑CNTL) shows a persistent positive bias, overestimating TROPOMI CO by about 0.4-0.6 × 10¹⁸ molecules cm⁻² across the Indo‑Gangetic Plain. Assimilation (WRF‑DA) markedly reduces these biases and better captures observed spatial and temporal variability. Normalized mean bias decreases from 33.5% to 14.4%, while the index of agreement increases from 0.45 in the control to 0.72 in the data assimilation run. Comparisons with MOPITT profiles indicate that assimilation lowers near‑surface CO by 40-100 ppbv and reduces profile errors by 40-60% in the lower troposphere. These results show that MOPITT CO assimilation effectively constrains regional CO distributions and substantially enhances WRF‑Chem performance over India.

PMID:42129394 | DOI:10.1038/s41598-026-53061-x

Int J Impot Res. 2026 May 13. doi: 10.1038/s41443-026-01283-y. Online ahead of print.

ABSTRACT

Most studies on the impact of vitamin D on sex hormones focus on specific populations, such as older males, Asian males, or those with certain health conditions. Limited evidence exists on the relationship between vitamin D and sex hormones in American women. This cross-sectional analysis used National Health and Nutrition Examination Survey (NHANES) data to explore the association between serum vitamin D levels and sex hormones levels in women. Data from NHANES (2021-2023) were analyzed. Participants were categorized by serum vitamin D levels: Deficient (<50 nmol/L), Insufficient (50-74.99 nmol/L), and Adequate ( ≥ 75 nmol/L). One-way ANOVA and Chi-square tests were used for comparisons, and linear regression evaluated associations. Our analysis specifically focused on a subset of 3181 women aged 18 years and older (18-80 years). Women in the adequate vitamin D group had lower body mass index (BMI) (29.16 vs. 32.10 kg/m², p < 0.001), lower total testosterone (24.10 vs. 32.28 ng/dL, p < 0.001), progesterone (139.05 vs. 229.73 ng/dL, p < 0.001), estrone sulfate (687.10 vs. 1023.08 pg/mL, p < 0.001), and dehydroepiandrosterone sulfate (DHEAS) (66.41 vs. 100.56 µg/dL, p < 0.001) compared to the deficient vitamin D group. They also had higher sex hormone-binding globulin (SHBG) (70.37 vs. 58.55 nmol/L, p < 0.001), follicle-stimulating hormone (FSH) (50.30 vs. 23.99 mIU/mL, p < 0.001), and luteinizing hormone (LH) (26.39 vs. 16.64 mIU/mL, p < 0.001) compared to the deficient vitamin D group. Linear regression revealed that higher serum vitamin D was inversely associated with 17α-hydroxyprogesterone (Beta = -0.85, P = 0.023), androstenedione (Beta = -0.181, p < 0.001), anti-Müllerian hormone (Beta = -0.238, p < 0.001), DHEAS (Beta = -0.204, p < 0.001), total testosterone (Beta = -0.080, P = 0.042), while showing a positive association with follicle-stimulating hormone (Beta = 0.260, p < 0.001) and luteinizing hormone (Beta = 0.208, p < 0.001). Serum vitamin D levels were negatively associated with testosterone and estradiol in American women, particularly in older individuals.

PMID:42129376 | DOI:10.1038/s41443-026-01283-y