Symmetric quadratic tetration interpolation using forward and backward operation combination

The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.

The Nonlinear Relationship Between Total Bilirubin and Coronary Heart Disease: A Dose-Response Meta-Analysis

Background: Evidence suggests that the total bilirubin has a protective effect on coronary heart disease (CHD), but the dose-response relationship remains controversial, and there is no meta-analysis to assess the relationship.Methods: As of October 1, 2021, relevant literature was selected from four databases (PubMed, Web of Science, Cochrane Library, and Embase) by using a retrieval strategy. The dose-response curve between the total bilirubin and CHD was fitted by a restricted cubic spline. Stata 12.0 was used for statistical analysis.Results: A total of 170,209 (6,342 cases) participants from 7 prospective studies were analyzed in our meta-analysis. We calculated the pooled relative risks (RRs) and 95% CIs for the association between serum bilirubin level and risk of CHD using random-effects models. Compared with the first quantile, the bilirubin level in the third quantile had a protective effect on the risk of CHD (RR, 0.90; 95% CI, 0.82–0.99). The restricted cubic spline functions depicted a U-type curve relationship between bilirubin (3.42–49 μmol/L) and CHD (Plinear < 0.001). When the bilirubin level was in the range of 3.42–13μmol/L, the protective effect of bilirubin on CHD was enhanced with increasing bilirubin levels. When the bilirubin level exceeded 13μmol/L, the protective effect of bilirubin weakened, and a dangerous effect gradually appeared with further increases in bilirubin levels.Conclusions: Compared with a low bilirubin level, a high bilirubin level has a protective effect on the risk of CHD, and there was a U-shaped dose-response relationship between them.

Effect of maternal height on the risk of caesarean section in singleton births: evidence from a large-scale survey in India

ObjectiveThis study examines the association of maternal height with caesarean section (CS) in India. It is hypothesised that maternal height has no significant effect on the risk of undergoing caesarean section.DesignA cross-sectional study based on a nationally representative large-scale survey data (National Family Health Survey-4), conducted in 2015–2016.Setting and participantsAnalysis is based on 125 936 women age 15–49 years, having singleton live births. Logistic regression has been performed to determine the contribution of maternal height to the ORs of CS birth, adjusting for other exposures. Restricted cubic spline was used as a smooth function to model the non-linear relationship between height and CS. Height data were decomposed using the restricted cubic spline with five knots located at the 5th, 27.5th, 50th, 72.5th and 95th, percentiles.Primary and secondary outcome measuresThe main outcome variable of interest in the study is CS. Maternal height is the key explanatory variable. Other explanatory variables are age, parity, sex of child, birth weight, wealth index, place of residence, place of child delivery and household health insurance status.ResultsThe results reveal that the odds of undergoing CS significantly decrease with increase in maternal heights. Mothers with a height of 120 cm (adjusted OR (AOR): 5.08; 95% CI 3.83 to 6.74) were five times more likely, while mothers with height of 180 cm were 23% less likely (AOR: 0.77; 95% CI 0.62 to 0.95) to undergo CS as compared with mothers with height of 150 cm.ConclusionsShorter maternal height is linked to a higher risk of CS. Our findings could be used to argue for policies that target stunting in infant girls and avoid unnecessary CS, as there is potential effect on growth during adolescence and early adulthood, with the goal to increase their adult heights, thereby lowering their risk of CS and adverse delivery outcomes.

Construction of an Effective Preconditioner for the Even-odd Splitting of Cubic Spline Wavelets

In this study, the method for decomposing splines of degree m and smoothness C^m-1 into a series of wavelets with zero moments is investigated. The system of linear algebraic equations connecting the coefficients of the spline expansion on the initial scale with the spline coefficients and wavelet coefficients on the embedded scale is obtained. The originality consists in the application of some preconditioner that reduces the system to a simpler band system of equations. Examples of applying the method to the cases of first-degree spline wavelets with two first zero moments and cubic spline wavelets with six first zero moments are presented. For the cubic case after splitting the system into even and odd rows, the resulting matrix acquires a seven-diagonals form with strict diagonal dominance, which makes it possible to apply an effective sweep method to its solution

Vitamin D Deficiency is Associated With Elevated Blood Concentrations of Ethylene Oxide

Ethylene oxide has been associated with increased oxidative stress and related disorders in recent studies, while vitamin D is a widely recognized antioxidant. Whether vitamin D deficiency is related to elevated blood concentrations of ethylene oxide is still unknown. We aimed to explore the relationship between vitamin D deficiency and blood concentrations of ethylene oxide in the general population. A total of 4125 adults who participated in the National Health and Nutrition Examination Survey (NHANES) 2013–2016 were analyzed. Participants were divided into 3 groups: vitamin D sufficiency (≥75.0 nmol/L), insufficiency (50–74.9 nmol/L), and deficiency (<50.0 nmol/L). Adjusted linear and restricted cubic spline regression models were performed to evaluate the associations between vitamin D levels and blood concentrations of ethylene oxide. Compared with participants with vitamin D sufficiency, the adjusted mean ethylene oxide level was approximately 0.08 and 0.23 log2-units higher in the presence of vitamin D insufficiency and vitamin D deficiency (P for trend <0.001). The adjusted percent difference with a 95% confidence interval in ethylene oxide per interquartile range increase in vitamin D was -1.13 (-1.68, -0.57). A restricted cubic spline model demonstrated that vitamin D levels are nonlinearly and inversely associated with blood concentrations of ethylene oxide (P for nonlinearity =0.021). Further research is warranted to understand how vitamin D may have a role in reducing blood concentrations of ethylene oxide.

Association Between Serum Calcium and the Prevalence of Hypertension Among US Adults

Background: Hypertension is a significant risk factor of cardiovascular diseases, posing a serious threat to global health. Calcium plays an important role in regulating body homeostasis. The association of calcium with hypertension remains uncertain in the general population.Methods and Results: Cross-sectional data from the 2007–2018 National Health and Nutrition Examination Survey (NHANES) were analyzed. Adjusted multivariable logistic regression analysis and restricted cubic spline were used to investigate the association of serum calcium with the prevalence of hypertension. A total of 26,778 participants were included. The increase in calcium levels showed a positive association with the prevalence of hypertension in all three models with ORs of 1.347 (1.249–1.454), 1.522 (1.401–1.654), and 1.438 (1.306–1.583). The further subgroup analysis demonstrated a robust trend across all categories by sex, age, race, BMI, and eGFR. The restricted cubic spline plot exhibited an S-curve relationship between calcium and hypertension.Conclusion: Our cross-sectional study demonstrated a positive association between higher serum calcium level and the prevalence of hypertension. Our findings highlighted serum calcium level in hypertensive patients.

Is Hemoglobin Concentration a Linear Predictor of Mortality in Older Adults From Chinese Longevity Regions?

Introduction: The association patterns of hemoglobin (HB) concentrations with mortality among the longevity older adults are unclear. We aimed to evaluate the relationship among older adults form Chinese longevity regions.Methods: We included 1,785 older adults aged ≥65 years (mean age, 86.7 years; 1,002 women, 783 men) from the community-based Chinese Longitudinal Healthy Longevity Survey. We estimated the hazard ratios (HRs) and 95% confidence intervals (CIs) for all-cause mortality using multivariable Cox proportional hazards models and Cox models with restricted cubic spline.Results: In total, 999 deaths occurred during a median follow-up of 5.4 years from 2011 to 2017. Restricted cubic spline analysis found no non-linear association between HB concentrations and all-cause mortality after a full adjustment for covariates among the older adults form longevity regions (p &gt; 0.05 for non-linearity). The risk for all-cause mortality was significantly higher in the groups with HB concentration of &lt;11.0 g/dL (HR: 1.37, 95% CI: 1.10–1.70) and 11.0–12.0 g/dL (HR: 1.25, 95% CI: 1.01–1.54); the risk of all-cause mortality was significantly lower in the groups with HB concentration ≥14.0 g/dL (HR: 0.76, 95% CI: 0.60–0.97) compared with the reference group (13.0–13.9 g/dL).Conclusions: Among older adults form Chinese longevity regions, HB concentrations were found to be inversely and linearly associated with all-cause mortality. Further prospective intervention trials are needed to confirm whether higher HB concentrations had a lower risk of mortality in these older adults.