Spline Functions Research Articles

An efficient fourth-order convergent scheme based on half-step spline function for two-point mixed boundary value problems

The present work aims to introduce a novel numerical method for solving second-order two-point mixed boundary value problems. Mixed boundary value problems occur in various scientific fields, including quantum mechanics, fluid dynamics, and chemical reactor theory. The proposed method provides a highly accurate, fourth-order convergent numerical solution, achieved by implementing a compact finite difference method based on non-polynomial spline in tension approximations. Notably, the discretisation involves the use of half-step grid points, eliminating the need to modify the method at singularities while dealing with singular boundary value problems. The article also includes a comprehensive convergence analysis that demonstrates the theoretical order of convergence of the method. Additionally, the results obtained from solving six diverse mixed boundary value problems, including Burger's equation and Bratu-type equation, are compared to showcase the superiority and effectiveness of the proposed method.

Carotid-Femoral pulse wave velocity progression in hypertensive patients is associated with subsequent cardiovascular outcomes

Abstract Background Arterial stiffness (Pulse Wave Velocity - PWV) is associated with CV events and mortality. However, little is known on the relationship of its progression (ΔPWV) over time with CV outcomes. Purpose The aim of our study was to evaluate the relationship between PWV progression and all-cause mortality and CV events in hypertensive subjects. Methods We enrolled 402 consecutive hypertensive outpatients. At baseline anamnestic, clinical, BP, laboratory data and PWV were assessed. We performed a PWV follow-up examination at a median time of 3.7±0.5 years. Patients were subsequently followed for a median time of 10.1 (IQR 9.5 -10.5) years recording all-cause mortality and CV events. Results At baseline the mean age was 53.2±13.0 years, SBP and DBP were 141.8±17.5 and 86.8±10.5 mmHg and PWV was 8.5±1.9 m/s. Despite an improvement in BP control (- 9.2±19.5 and -8.0±12.3 for SBP and DBP respectively), at follow-up the population showed a PWV increase (ΔPWV +0.6±1.9 m/s). Progressors (ΔPWV ≥ 0.5 m/s, 204 patients, 50.7%) had a significantly lower survival probability and higher cumulative incidence of composite events, while no differences were seen for CV events (unadjusted analysis). At cox multivariable analysis neither ΔPWV ≥ 0.5 m/s (progressors) nor ΔPWV (as a spline function) were associated with CV events and with all-cause mortality. However, the association with survival probability and cumulative incidence of CV events, as a composite outcome, was significant (HR = 2.32, 95% CI: 1.33 – 4.04, p=0.003). Conclusions In conclusion, our study shows that PWV progression of at least 0.5 m/s is frequent in hypertensive patients and that it is associated with a significantly higher risk of developing CV events or dying (composite outcome).

Association between average glucose concentration or glucose variability and acute kidney injury among CAD patients with prediabetes

Abstract Background Prediabetes, impacting approximately 10% of adults, lacks comprehensive attention, and there is limited data on effective glycemic control strategies. Meta-analysis suggests that intensive glycemic control is linked to a lower incidence of major adverse cardiovascular events, mainly driven by decreased reinfarction and reduced microvascular complications in coronary artery disease (CAD) patients. However, despite these associations, existing evidence does not conclusively establish the efficacy of intensive glycemic control in enhancing cardio-renal outcomes. Purpose In the present study, we aimed to validate the utility of intensive glycaemic control on acute kidney injury (AKI) prevention using a prospective, pragmatic clinical data of patients with CAD. Methods This study utilized data from the Prospective Registry of the Current Status of Care for Patients with Coronary Artery Disease database, a nationwide and pragmatic registry project initiated on January 17th, 2022. Data, including demographics, medical history, and lab results, were collected from electronic medical records. The time-weighted average glucose (TWAG) and glucose variability (CV) for each patient to assess glycaemic control, and outcomes including AKI were assessed. Statistical analysis involved logistic models and sensitivity analyses. SAS 9.4 and R software were used, with p<0.05 considered significant. Results Between January 2022 and June 2023, 2,454 CAD patients with prediabetes were included for final analysis. Among them, the average age was 62.6 ± 10.3 years, of whom 27.1% were females. In univariate model, the incidence of AKI was 1.51 (1.36,1.68) times higher in patients with an increasing TWAG per mmol/L. After the stepwise adjusting of covariates, the OR was 1.50 (1.35,1.67). CV of glucose also had positive association with AKI. An increasing of 0.1 unit of CV increased the risk of about 44%. When adjusting the TWAG and CV of glucose at the same time, both still had positive association with AKI. A restricted cubic splines plot showed an increasing trend of the ORs for AKI as both TWAG and CV of glucose increased. Subgroups analyses also showed stable positive association between TWAG, CV and AKI. Conclusions Our study reveals an association between TWAG or CV and AKI in individuals with both CAD and prediabetes. These findings underscore the importance of continuous glucose monitoring and the implementation of intensive glycaemic control for CAD patients coexistence of prediabetes.Restricted cubic splines function

Non-linear relationship between relative fat mass and diabetes risk in Japanese adults: a retrospective cohort study

Background: Relative fat mass (RFM) represents a newly developed sex-specific anthropometric formula to estimate total body fat percentage. Nonetheless, research examining the correlation between RFM and the risk of diabetes remains scarce. This research assessed the link between RFM and DM risk within the Japanese demographic. Methods: From 2004 to 2015, 15,462 Japanese individuals without diabetes underwent physical evaluations at Murakami Memorial Hospital. The relationship between RFM and the onset of diabetes was analyzed separately using Cox proportional-hazards regression models. This study employed Cox proportional hazards regression incorporating cubic spline functions and smooth curve fitting to detect non-linear associations between RFM and new cases of diabetes, categorized by sex. Sensitivity analyses were performed to confirm the robustness of the link between RFM and incident diabetes. Results: After controlling for confounding factors, a significant positive correlation between RFM and diabetes risk was found in women (HR: 1.13, 95%CI: 1.04–1.24, P = 0.0061), while the association in men was not statistically significant (HR: 1.05, 95%CI: 0.98–1.13, P = 0.1511). Additionally, a non-linear relationship between RFM and the incidence of diabetes was detected in both genders. The RFM threshold was identified at 39.23 for women and 23.08 for men. For women, HR was 1.11 (95%CI: 1.01–1.21) below the threshold and 1.39 (95%CI: 1.17–1.65) above it. In men, an RFM above 23.08 was positively related to diabetes risk (HR: 1.16, 95%CI: 1.06–1.28, P = 0.0012), whereas an RFM below this point did not show a significant association (HR: 0.98, 95%CI: 0.91–1.06, P = 0.5899). Conclusion: Our findings suggest a non-linear relationship and threshold effect between RFM and the risk of diabetes. These findings imply that maintaining RFM at lower levels may be beneficial in mitigating the onset of DM.

A novel iterative algorithm for nonlinear inelastic dynamic analysis of truss structures; MCB-Spline+Sp time integration method

The focus of this work is on the development of a novel algorithm for the nonlinear dynamic analysis of structures. In the sake of a general and easy-to-implement solution method, the tangential stiffness matrix is calculated by combining the Cauchy-Riemann equations derived from the differentiation of complex functions and using the nodal displacement perturbation vector. An implicit direct time integration method based on a cubic B-Spline is integrated with the incremental-iterative method using a quadrature rule based on the interpolation of spline functions, which is referred to as the MCB-Spline+Sp time integration method. A step-by-step algorithm for developing a computer code to implement this method is provided. The effectiveness of the proposed approach is evaluated through several nonlinear time history analyses, which demonstrate its accuracy and efficiency by observing less computational efforts and fast convergence rate. Moreover, a comparison is made between the developed method and well-established techniques such as the Newmark and Standard-Bathe time integration methods in combination with the iterative Newton-Raphson method.

Unveiling the Genetic Architecture of Semen Traits in Thai Native Roosters: A Comprehensive Analysis Using Random Regression and Spline Function Models.

Improving reproductive traits, particularly semen quality and quantity, is crucial for optimizing poultry production and addressing the current limitations in native chicken reproduction. The aim of this study was to develop a genetic model to estimate genetic parameters guiding the selection of individual Thai native roosters. Using data collected from 3475 records of 242 Thai native grandparent roosters aged 1-4 years, we evaluated semen traits (mass movement, semen volume, and sperm concentration) over 54 weeks. A random regression test-day model incorporating five covariance functions, including a linear spline function with four, five, six, and eight knots (SP4, SP5, SP6, and SP8) and second-order Legendre polynomial function (LG2), was used to estimate genetic parameters. The results showed that the SP8 model consistently outperformed the other models across all traits, with the lowest mean square error, highest coefficient of determination, and superior predictive ability. Heritability estimates for mass movement, semen volume, and sperm concentration ranged from 0.10 to 0.25, 0.22 to 0.25, and 0.11 to 0.24, respectively, indicating moderate genetic influence on these traits. Genetic correlations between semen volume and sperm concentration were highest in the SP8 model, highlighting a strong genetic association between these traits. The SP8 model also revealed a high genetic correlation between mass movement and semen volume, supporting the potential for selecting mass movement as a predictor of semen volume. In conclusion, this study highlights the effectiveness of random regression models with linear spline functions to evaluate the genetic parameters of semen traits in native Thai roosters. The SP8 model is a robust tool for breeders to enhance the reproductive performance of native Thai chickens, contributing to sustainable poultry production systems.

Association between myocardial layer-specific strain and high 10-year risk of atherosclerotic cardiovascular disease in hypertension-findings from the China-PAR project study.

Myocardial layer-specific strain is a sensitive tool for detecting myocardial dysfunction. The objective of this study was to assess changes in the left ventricle (LV) function using myocardial layer-specific strain and its association with 10-year atherosclerotic cardiovascular disease risk (10Y-ASCVDR) in individuals with hypertension (HP). The parameters of LV structure, including layer-specific global longitudinal strain (GLSww, GLSendo, GLSmid, GLSepi) and layer-specific global circumferential strain (GCSww, GCSendo, GCSmid, GCSepi), were analyzed by two-dimensional speckle-tracking echocardiography in 239 hypertensive patients and 124 control subjects. In addition, participants were divided into low-risk (LR) and high-risk (HR) subgroups according to 10Y-ASCVDR scores . The correlation between myocardial layer-specific strain and 10Y-ASCVDR was further analyzed by the restricted cubic spline (RCS) function. The values of GLSww, GLSepi, GLSmid, and GLSendo were significantly lower in HP patients with HR than in HP patients with LR and controls (p < 0.05). However, no significant differences in layer-specific GCS were observed between the groups (p > 0.05). RCS analysis revealed that 10Y-ASCVDR exhibited a significant J-shaped relationship with layer-specific GLS and GCS. After adjusting for confounding factors, GLSww (β = 0.156, p = 0.042), GLSmid (β = 0.161, p = 0.032), GCSendo (β = 0.163, p = 0.024), and GCSmid (β = -0.175, p = 0.030) were identified as independent influencing factors for high 10Y-ASCVDR. In hypertensive patients, myocardial layer-specific strain, especially GLS, sensitively detected LV dysfunction and showed a significant J-shaped relationship with 10Y-ASCVDR. GCSmid may have a compensatory effect on myocardial impairment. LV myocardial layer-specific strain may help to understand the early compensatory mechanisms of the myocardium in hypertension.

Predictors of ischemic stroke in Chagas disease: Insights into mechanisms beyond cardiomyopathy severity

BackgroundChagas disease is a risk factor for ischemic stroke, which causes high mortality rates and significant disability. This study aims to determine the incidence and risk factors for ischemic strokes in a large cohort of Chagas cardiomyopathy patients, with a particular focus on the mechanisms involved in the pathophysiology of stroke in this condition. MethodsThe study enrolled 517 patients with Chagas cardiomyopathy who were referred to our institution from March 2000 to December 2021. All patients underwent systematic cardiological and neurological assessments. The primary outcome was the occurrence of ischemic stroke during the follow-up period, classified based on the SSS-TOAST and CCS criteria. Natural cubic splines functions were applied to examine the potential nonlinear association between continuous variables and stroke risk. ResultsThe mean age of the cohort was 52 ± 13 years, and 299 (58 %) were men. During a mean follow-up period of 4.8 years (interquartile range-IQR 1.1 to 7.1 years), a total of 72 patients (14.8 %) had an ischemic stroke, being fatal in 10. The overall incidence rate of ischemic stroke was 3.0/100 patient-years (95 % confidence interval 2.4 to 3.8). The stroke subtypes were cardioembolic (n = 41), undetermined (n = 11), and other subtypes (n = 20). The predictors of stroke were age, left atrial volume, left ventricular ejection fraction (LVEF), LV thrombus and prior stroke with thrombus. There was a nonlinear relationship between stroke risk, LVEF, and left atrial volume. A bimodal distribution of stroke occurrences was observed according to the severity of LV dysfunction, with a threshold for LVEF of 45 %. The final model for stroke risk prediction showed good discrimination, with a C statistic of 0.775. ConclusionsIn a contemporary cohort of Chagas disease patients with a broad spectrum of disease severity, stroke incidence remains high despite anticoagulation. Stroke risk shows a nonlinear association with ventricular dysfunction and left atrial size, highlighting a distinct bimodal pattern of stroke occurrence in Chagas disease.

The ketogenic diet has the potential to decrease all-cause mortality without a concomitant increase in cardiovascular-related mortality

The impact of the ketogenic diet (KD) on overall mortality and cardiovascular disease (CVD) mortality remains inconclusive.This study enrolled a total of 43,776 adults from the National Health and Nutrition Examination Survey (NHANES) conducted between 2001 and 2018 to investigate the potential association between dietary ketogenic ratio (DKR) and both all-cause mortality as well as cardiovascular disease(CVD) mortality.Three models were established, and Cox proportional hazards regression analysis was employed to examine the correlation. Furthermore, a restricted cubic spline function was utilized to assess the non-linear relationship. In addition, subgroup analysis and sensitivity analysis were performed.In the adjusted Cox proportional hazards regression model, a significant inverse association was observed between DKR and all-cause mortality (HR = 0.76, 95% CI = 0.63–0.9, P = 0.003). However, no significant association with cardiovascular mortality was found (HR = 1.13; CI = 0.79–1.6; P = 0.504). Additionally, a restricted cubic spline(RCS) analysis demonstrated a linear relationship between DKR and all-cause mortality risk. In the adult population of the United States, adherence to a KD exhibits potential in reducing all-cause mortality risk while not posing an increased threat of CVD-related fatalities.

Predicting Recurrence after Sublobar Resection in Patients with Lung Adenocarcinoma Using Preoperative Chest CT Scans.

Background Sublobar resection for lung cancer is usually guided by cutoff values for consolidation size (maximal diameter of the solid tumor component) and consolidation-to-tumor ratio (CTR). The effects of these factors as continuous variables and the reason for established cutoffs are, to the knowledge of the authors, unexplored. Purpose To quantitatively assess the predictive value of CTR and consolidation size for cancer recurrence risk after sublobar resection in clinical stage IA lung adenocarcinoma. Materials and Methods This retrospective study reviewed sublobar resection for clinical stage IA lung adenocarcinoma performed between January 2010 and December 2019. A restricted cubic spline function verified linearity by estimating recurrence probabilities using CTR and consolidation size obtained on preoperative CT scans. Statistical analyses included a Cox proportional hazards model to identify risk factors for cancer recurrence and the Cochran-Armitage trend test for the association between CTR and consolidation size. Results Of 1032 enrolled patients (age, 63.9 years ± 9.9 [SD]; 464 male patients), 523 (50.7%) and 509 (49.3%) underwent wedge resection and segmentectomy, respectively. Among patients with a CTR between 1% and 50% (n = 201), 187 (93.0%) had a consolidation size of less than or equal to 10 mm (P < .001). There was a positive association between the risk of recurrence with CTR and consolidation size (r2 = 0.727; P < .001). The recurrence rate showed the greatest increase when CTR was greater than 50% or consolidation size was greater than 10 mm. Specifically, the recurrence rate increased from 2.1% (three of 146) at 26%-50% CTR to 8.3% (nine of 108) at 51%-75% CTR, and from 4.4% (eight of 183) for 6-10-mm consolidation size to 11.9% (23 of 194) for 11-15-mm consolidation size. The probability of recurrence exhibited linearity and increased with CTR and consolidation size. Conclusion Cancer recurrence risk after sublobar resection for stage IA adenocarcinoma consistently rises with CTR and consolidation size. Current guideline cutoffs for sublobar resection remain clinically relevant given observed recurrence rates. © RSNA, 2024 Supplemental material is available for this article.

Urinary phthalate metabolites associated with bone mineral density in adults: Data from the NHANES 2011–2018

Phthalates (PAEs) are common environmental endocrine disruptors and environmental bone poisons that can reduce bone mineral density (BMD). The purpose of this study is to investigate whether the concentration of PAE metabolites in urine is related to BMD in many parts of adult bones. We examined a series of cross-sectional data of male (n = 1835) and female (n = 1756) participants aged 18 to 59 years old in the National Health and Nutrition Examination Survey from 2011 to 2018 and measured urine PAE metabolites and dual-energy X-ray absorption to determine BMD (total body, lumbar spine, and pelvis). We used linear regression to test the correlation between a single phthalate biomarker and BMD. After adjusting all confounding variables, MEHP was positively correlated with BMD of total body, lumbar spine and pelvis, and BMD levels of the total body, lumbar spine and pelvis decreased with the increase of MECPP concentration. We used the restricted cubic spline function to test the nonlinear correlation between PAE biomarkers and BMD. The results show that urinary PAE metabolites have a nonlinear relationship with total body BMD, lumbar spine BMD, and pelvic BMD. With the increase in the PAE concentration, the BMD level first increased and then decreased, showing an inverted U-shaped trend (P < 0.05). Gender stratification also shows the same related trend. PAEs may be related to the BMD of adults. When the concentration of PAEs increases to a certain threshold, it will lead to a significant decrease in BMD.

Postnatal weight loss and neurodevelopmental outcomes at age 3 years in extremely preterm infants: a cohort study

BackgroundPrevious research has suggested a correlation between postnatal maximum weight loss (MWL) and both neonatal mortality and morbidities in extremely preterm infants. However, the relationship between MWL and neurodevelopmental outcomes remains underexplored.MethodsIn a single-center, retrospective cohort study at Okayama Medical Center, we evaluated data from extremely preterm infants admitted to the neonatal intensive care unit from 2010 to 2020. Infants who died within the first 10 days of life were excluded. MWL in the first 10 days was the main exposure, categorized into three groups: >15%, 5–15%, and < 5%. The primary outcome evaluated was the occurrence of death or neurodevelopmental impairment (NDI) at age 3 years, defined as developmental impairments (developmental quotient [DQ] < 85), cerebral palsy, hearing impairments, or visual impairments. Data analysis involved robust Poisson regression, adjusted for perinatal confounders, with a restricted cubic spline function to examine the dose-response relationship. We also conducted a sensitivity analysis using a DQ of < 70 to define developmental impairment.ResultsAmong 135 infants assessed for neurodevelopmental outcomes, 40 were in the > 15% MWL group, 71 in the 5–15% group, and 24 in the < 5% group. Median gestational ages and birth weights were 25.9 weeks and 821 g for > 15% MWL; 26.1 weeks and 818 g for 5–15% MWL; and 26.0 weeks and 734 g for < 5% MWL. Compared with the 5–15% MWL group, the < 5% group exhibited a higher risk of death or NDI at age 3 years (62.8% vs. 80.8%, risk ratio [RR] 1.36, 95% confidence interval [CI] 1.04–1.79) and NDI alone (59.2% vs. 79.2%, RR 1.43, 95% CI 1.06–1.94). Furthermore, higher risks of developmental impairment were also noted in the > 15% (RR 1.32, 95% CI 1.00–1.75) and < 5% (RR 1.46, 95% CI 1.08–1.98) groups. These associations were confirmed by spline analyses. In contrast, the associations between MWL and neurodevelopmental outcomes using a DQ of < 70 were not apparent.ConclusionsMWL within the first 10 days of life may be associated with increased risks of NDI and developmental impairments by age 3 years in extremely preterm infants.

Zenith tropospheric delay model in mainland China based on geographically convolutional neural network weighted regression and tensor spline function

Zenith tropospheric delay model in mainland China based on geographically convolutional neural network weighted regression and tensor spline function

Nonlinear relationship between triglyceride-glucose index and the risk of prediabetes and diabetes: a secondary retrospective cohort study.

The triglyceride-glucose (TyG) index, recognized for its cost-efficiency and simplicity, serves as an accessible indicator of insulin resistance. Yet, its correlation with the risk of prediabetes and diabetes (Pre-DM/DM) in the Chinese demographic remains uncertain. Consequently, our study explored the association between the TyG index and the development of Pre-DM/DM within the Chinese population. The retrospective cohort study was carried out utilizing data from a health screening initiative. The study included 179541 adults over 20 who underwent medical examinations at the Rich Healthcare Group over a period spanning from 2010 to 2016. The correlation between the TyG index and Pre-DM/DM risk was investigated using Cox regression analysis. Furthermore, Cox proportional hazards regression with cubic spline functions and smooth curve fitting was incorporated to explore their non-linear connection. The mean age of study participants was 41.18 ± 12.20 years old, and 95255 (53.05%) were male. During a median follow-up of 3.01 years, 21281 (11.85%) participants were diagnosed with Pre-DM/DM. After adjusting the potential confounding factors, the results showed that the TyG index was positively correlated with incident Pre-DM/DM (HR: 1.67, 95%CI: 1.62-1.71, P< 0.001). Additionally, a non-linear association was observed between the TyG index and the onset of Pre-DM/DM, with an inflection point identified at 8.73. Hazard ratios (HR) to the left and right of this inflection point were 1.95 (95%CI: 1.86-2.04) and 1.34 (95%CI: 1.27-1.42), respectively. Furthermore, sensitivity analyses confirmed the stability of these findings. The TyG index exhibited a non-linear positive relationship with the risk of Pre-DM/DM. These findings imply that maintaining the TyG index at a lower, specified threshold may be beneficial in mitigating the onset of Pre-DM/DM.

Nonlinear association between remnant cholesterol and reversion from impaired fasting glucose to normoglycemia: a multicenter cohort study

BackgroundRemnant cholesterol (RC), a potent atherogenic lipid, has been shown to be strongly correlated with insulin resistance and the pathogenesis of diabetes mellitus. However, the relationship between RC and normoglycemia reversal in individuals with impaired fasting glucose (IFG) is crucial and remains unclear. This investigation, which aimed to clarify this association, is important for understanding and potentially improving the management of diabetes.MethodThis study, which included 15,019 IFG participants from 11 Chinese cities between 2010 and 2016, was conducted with a rigorous research process. Cox regression analysis revealed intriguing findings regarding the relationship between RC and normoglycemia reversal in individuals with IFG. Potential nonlinear associations were further explored via smooth curve-fitting techniques and 4-knot restricted cubic spline functions, ensuring a comprehensive analysis. To examine the validity of the results, an array of subgroup and sensitivity analyses were conducted, further bolstering the robustness of the findings.ResultsBy the end of the 2.89-year median follow-up period, 6,483 of the 15,019 IFG participants (43.17%) had reverted to normoglycemia. The findings, which reveal that increased RC levels are inversely associated with the likelihood of normoglycemia reversal, are novel and significant. According to the fully adjusted Cox proportional hazards model analysis, an increase of one standard deviation in RC was associated with a 20% decrease in the likelihood of normoglycemia reversal among IFG participants (HR: 0.80, 95% CI: 0.77–0.82). A nonlinear association between RC and normoglycemia reversal was observed, with an inflection point at 41.37 mg/dL. This suggests that the growth rate of the likelihood of reversion decreased and stabilized after the inflection point was reached. Moreover, significant interactions were observed between the age groups, providing a more nuanced understanding of this complex relationship.ConclusionAmong Chinese adults with IFG, RC exhibited a negative nonlinear relationship with the probability of normoglycemia reversal. When RC levels reached or exceeded 41.38 mg/dL, the probability of achieving normoglycemia progressively diminished and subsequently stabilized. Maintaining RC levels below 41.38 mg/dL can significantly improve the probability of normoglycemia reversal among individuals with IFG, especially those aged 60 years or older.

Patient Factors Associated with 10-Year Survival After Arthroplasty for Hip Fracture: A Population-Based Study in Ontario, Canada.

The aim of this study was to describe long-term (10-year) patient survival after arthroplasty for hip fracture and to determine what patient factors are associated with that outcome. We performed a retrospective cohort analysis of patients ≥60 years old who underwent either hemiarthroplasty or total hip arthroplasty for femoral neck fracture between 2002 and 2009. We used routinely collected, validated health-care databases linked through ICES (formerly known as the Institute for Clinical Evaluative Sciences). We estimated the association between baseline variables and survival 10 years post-fracture using Poisson regression. Restricted cubic spline functions modeled the probability of 10-year survival by age and tested whether there was an inflection point after which the probability of 10-year survival decreased more rapidly. We estimated 10-year survival probabilities for different patient groups. There were 19,659 patients in the final cohort. Eighteen percent (3,564) of the patients were alive at 10 years postoperatively. Factors associated with a higher likelihood of 10-year survival included younger age, female sex (risk ratio [RR] = 1.56, 95% confidence interval [CI] = 1.46 to 1.68), lower American Society of Anesthesiologists (ASA) class (ASA I or II versus IV or V: RR = 1.96, 95% CI = 1.76 to 2.19), independent living status (RR = 2.68, 95% CI = 2.23 to 3.22), and fewer specific comorbidities. A threshold age of 73 years was the inflection point after which the probability of 10-year survival decreased more rapidly in females. Estimated 10-year survival probabilities ranged from 79.0% (95% CI = 75.5% to 82.5%) to 0.8% (95% CI = 0.6% to 1.0%). Approximately 1 in 6 patients live at least 10 years following a hip fracture. This study identifies baseline characteristics that predict survival greater than 10 years, including an age of <75 years, an ASA class of I or II, and independent living status prior to the hip fracture. Results can inform discussions around treatment choices, anticipated outcomes, and the natural history of hip fractures. Prognostic Level III. See Instructions for Authors for a complete description of levels of evidence.

Individual participant data meta-analysis to examine linear or non-linear treatment-covariate interactions at multiple time-points for a continuous outcome.

Individual participant data (IPD) meta-analysis projects obtain, harmonise, and synthesise original data from multiple studies. Many IPD meta-analyses of randomised trials are initiated to identify treatment effect modifiers at the individual level, thus requiring statistical modelling of interactions between treatment effect and participant-level covariates. Using a two-stage approach, the interaction is estimated in each trial separately and combined in a meta-analysis. In practice, two complications often arise with continuous outcomes: examining non-linear relationships for continuous covariates and dealing with multiple time-points. We propose a two-stage multivariate IPD meta-analysis approach that summarises non-linear treatment-covariate interaction functions at multiple time-points for continuous outcomes. A set-up phase is required to identify a small set of time-points; relevant knot positions for a spline function, at identical locations in each trial; and a common reference group for each covariate. Crucially, the multivariate approach can include participants or trials with missing outcomes at some time-points. In the first stage, restricted cubic spline functions are fitted and their interaction with each discrete time-point is estimated in each trial separately. In the second stage, the parameter estimates defining these multiple interaction functions are jointly synthesised in a multivariate random-effects meta-analysis model accounting for within-trial and across-trial correlation. These meta-analysis estimates define the summary non-linear interactions at each time-point, which can be displayed graphically alongside confidence intervals. The approach is illustrated using an IPD meta-analysis examining effect modifiers for exercise interventions in osteoarthritis, which shows evidence of non-linear relationships and small gains in precision by analysing all time-points jointly.

Revolutionizing E-Commerce Logistics

The traditional approach to logistics path planning is hindered by lengthy procedures. In this study, we explore the multi-objective optimization of logistics management, considering the conventional path and time efficiency indices alongside shelf safety and stability as additional objective functions. Based on particle swarm optimization (PSO), we optimize objective functions for internal path planning, scheduling timeliness, and shelf safety and stability. We then determine optimal routes under varying order demands using PSO and ultimately optimize the final path using dynamic programming and spline function restrictions to meet actual demand. Empirical results indicate that the proposed solution method outperforms other calculation methods, such as genetic algorithm (GA) and simulated annealing (SA), demonstrating over 10% improvement in time and total distance consumption. Further practical application tests demonstrate that the model in this study has a beneficial impact on all five distinct types of orders through efficient deployment optimization.

SPLINE FUNCTION INTERPOLATION TECHNIQUES FOR GENERATING SMOOTH CURVE

The Present paper deals with a special type of interpolation problem, in which we have prescribed the values of the function at Ki and Ki+1 and the whole interval is divided into n equal sub-intervals of width.. We will derive a spline function of Degree 3 which will be able to interpolate this polynomial function, we name it three point spline (TPS). We have shown here how to change the next control point during further interpolation. We have also discussed the case, of whether this spline can be used for evaluating curvature.

MATHEMATICAL MODELS OF THE THERMAL PROTECTION COATING OF THE GAS GENERATOR OF THE HYDROGEN STORAGE AND SUPPLY SYSTEM

The article describes the properties of the thermal protection coating of the gas generator of the hydrogen storage and supply system by two transfer functions with Hurwitz polynomials of the third order. Obtaining such transfer functions is based on the solution of the non-stationary heat conduction equation, represented in operator form using the integral Laplace transform, and in which approximating spline functions in the form of second-order polynomials are used. The article gives the solution of the non-stationary thermal conductivity equation, which describes the thermal processes in the heat-protective coating of the gas generator of the hydrogen storage and supply system under the thermal effect of a fire. This solution comes in the operator form for the surface temperature of the heat-protective coating on the side of the gas generator wall. The peculiarity of this decision is the presence of hyperbolic functions of an irrational argument in its composition. The structural and dynamic scheme of the thermodynamic system ‘gas generator wall – heat-protective coating’ is presented, the feature of which is the presence of two entrances. The signal at the scheme’s first input reflects the thermal effect of the fire, and the signal at the second input reflects the thermal state of the gas generator cavity. An equivalent mathematical transition to the description of thermal processes in the heat-protective coating of the gas generator of the hydrogen storage and supply system was carried out. This transition happened due to the use of spline functions, which approximate the hyperbolic functions of the irrational argument and are polynomials of the second order. The article gives a verbal interpretation of the algorithm for determining the transfer functions of the heat-protective coating of the gas generator of the hydrogen storage and supply system and also an example of its implementation. Furthermore, it shows that for the given conditions of functioning of the gas generator heat-protective coating, the relative errors in approximation of hyperbolic functions by second-order polynomials do not exceed 1.7 %, and the average relative error when equivalent replacement of transfer functions does not exceed 3.8 %. Keywords: gas generator, hydrogen storage and supply system, thermal protection coating.