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The theoretical and computational aspects of interval methodology based on Chebyshev polynomials for modeling multibody dynamic systems in the presence of parametric uncertainties are proposed, where the uncertain parameters are modeled by uncertain-but-bounded interval variables which only need the bounds of uncertain parameters, not necessarily knowing the probabilistic distribution. The Chebyshev inclusion function which employs the truncated Chevbyshev series expansion to approximate the original function is proposed. Based on Chebyshev inclusion function, the algorithm for solving the nonlinear equations with interval parameters is proposed. Combining the HHT-I3 method, this algorithm is used to calculate the multibody systems dynamic response which is governed by differential algebraic equations (DAEs). A numerical example that is a slider-crank with uncertain parameters is presented, which shows that the novel methodology can control the overestimation effectively and is computationally faster than the scanning method.
BackgroundBirth weight has been reported to be associated with the risk of incident cardiovascular disease (CVD); however, the relationship remains inconclusive. Here, we aimed to prospectively assess the associations between birth weight and CVD risk using the data from UK Biobank, a large-scale, prospective cohort study.MethodsWe included 270,297 participants who were free of CVD at baseline and reported their birth weight for analyses. The primary outcome was incident CVD. Hazard ratios (HRs) and 95% confidence intervals (CIs) for outcomes were calculated using Cox proportional hazards models adjusted for potential confounding variables.ResultsDuring a median follow-up of 8.07 years (IQR: 7.4–8.7 years), 10,719 incident CVD events were recorded. The HRs for low birth weight vs. normal birth weight (2.5–4.0 kg) were 1.23 (95% CI: 1.09–1.38) for risk of incident CVD, 1.52 (95% CI: 1.18–1.95) for stroke, 1.33 (95% CI: 1.07–1.64) for myocardial infarction, and 1.15 (95% CI: 1.01–1.32) for CHD. For the ones with low birth weight, the risk of CVD is reduced by 11% for every kilogram of birth weight gain. The association of low birth weight with CVD was stronger among those younger than 55 years (p = 0.001). No association between high birth weight and risk of cardiovascular outcomes was found.ConclusionLow birth weight was associated with an increased risk of cardiovascular events. These findings highlight the longstanding consequence of low birth weight on cardiovascular system.
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