Bivariate Left Fractional Polynomial Monotone Approximation

2016 ◽  
pp. 1-13
Author(s):  
George A. Anastassiou
Keyword(s):  
Monotone Approximation ◽  
Fractional Polynomial

scholarly journals Univariate right fractional polynomial high order monotone approximation

2016 ◽  
Vol 49 (1) ◽  
pp. 1-10
Author(s):  
George A. Anastassiou
Keyword(s):  
High Order ◽  
Monotone Approximation ◽  
Fractional Polynomial

AbstractLet

scholarly journals The Impact of Time Interval between Hepatic Resection and Liver Transplantation on Clinical Outcome in Patients with Hepatocellular Carcinoma

Cancers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 2398
Author(s):  
Matteo Serenari ◽  
Enrico Prosperi ◽  
Marc-Antoine Allard ◽  
Michele Paterno ◽  
Nicolas Golse ◽  
...  
Keyword(s):  
Hepatocellular Carcinoma ◽  
Liver Transplantation ◽  
Hepatic Resection ◽  
Primary Outcome ◽  
Polynomial Regression ◽  
Secondary Outcome ◽  
Time Interval ◽  
Comprehensive Complication Index ◽  
Fractional Polynomial ◽  
The Impact

Hepatic resection (HR) for hepatocellular carcinoma (HCC) may require secondary liver transplantation (SLT). However, a previous HR is supposed to worsen post-SLT outcomes. Data of patients treated by SLT between 2000 and 2018 at two tertiary referral centers were analyzed. The primary outcome of the study was to analyze the impact of HR on post-LT complications. A Comprehensive Complication Index ≥ 29.6 was chosen as cutoff. The secondary outcome was HCC-related death by means of competing-risk regression analysis. In the study period, 140 patients were included. Patients were transplanted in a median of 23 months after HR (IQR 14–41). Among all the features analyzed regarding the prior HR, only time interval between HR and SLT (time HR-SLT) was an independent predictor of severe complications after LT (OR = 0.98, p < 0.001). According to fractional polynomial regression, the probability of severe complications increased up to 15 months after HR (43%), then slowly decreased over time (OR = 0.88, p < 0.001). There was no significant association between HCC-related death and time HR-SLT at the multivariable competing risks regression model (SHR, 1.06; 95% CI: 0.69–1.62, p = 0.796). This study showed that time HR-SLT was key in predicting complications after LT, without affecting HCC-related death.

scholarly journals An improved medical admissions risk system using multivariable fractional polynomial logistic regression modelling

QJM ◽  
2009 ◽  
Vol 103 (1) ◽  
pp. 23-32 ◽  
Author(s):  
B. Silke ◽  
J. Kellett ◽  
T. Rooney ◽  
K. Bennett ◽  
D. O’Riordan
Keyword(s):  
Logistic Regression ◽  
Regression Modelling ◽  
Fractional Polynomial ◽  
Logistic Regression Modelling

Blood Pressure, Hypertension and The Risk of Aortic Dissection Incidence and Mortality: results from the Japan-Specific Health Checkups Study, the UK Biobank Study and a Meta-analysis of Cohort Studies

Circulation ◽  
2021 ◽  
Author(s):  
Makoto Hibino ◽  
Yoichiro Otaki ◽  
Elsa Kobeissi ◽  
Han Pan ◽  
Hiromi Hibino ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Aortic Dissection ◽  
Dose Response ◽  
Meta Analysis ◽  
Response Relationship ◽  
Uk Biobank ◽  
Dose Response Relationship ◽  
Fractional Polynomial ◽  
The Uk ◽  
Specific Health

Background: Hypertension or elevated blood pressure (BP) is an important risk factor for aortic dissection (AD); however, few prospective studies concerning this topic have been published. We investigated the association between hypertension/elevated BP and AD in two cohorts and conducted a meta-analysis of published prospective studies, including these two studies. Methods: We analyzed data from the Japan Specific Health Checkups (J-SHC) Study and UK Biobank, which prospectively followed 534,378 and 502,424 participants, respectively. Multivariable Cox regression was used to estimate hazard ratios (HRs) and 95% confidence intervals (95% CIs) for the association of hypertension/elevated BP with AD incidence in the UK Biobank and AD mortality in the J-SHC Study. In the meta-analysis, summary relative risks (RRs) were calculated using random effects models. A potential nonlinear dose-response relationship between BP and AD was tested using fractional polynomial models, and the best-fitting second-order fractional polynomial regression model was determined. Results: In the J-SHC Study and UK Biobank, there were 84 and 182 ADs during 4- and 9-year follow-up, and the adjusted HRs of AD were 3.57 (95% CI, 2.17-6.11) and 2.68 (95% CI: 1.78-4.04) in hypertensive individuals, 1.33 (95% CI: 1.05-1.68) and 1.27 (95% CI: 1.11-1.48) per 20-mmHg increase in systolic BP (SBP), and 1.67 (95% CI: 1.40-2.00) and 1.66 (95% CI: 1.46-1.89) per 10-mmHg increase in diastolic BP (DBP), respectively. In the meta-analysis, the summary RRs were 3.07 (95% CI 2.15-4.38, I2=76.7%, n=7 studies, 2,818 ADs, 4,563,501 participants) for hypertension and 1.39 (95% CI: 1.16-1.66, I2=47.7%, n=3) and 1.79 (95% CI: 1.51-2.12, I2=57.0%, n=3) per 20-mmHg increase in SBP and per 10-mmHg in DBP, respectively. The AD risk showed a strong, positive dose-response relationship with SBP and even more so with DBP. The risk of AD in the nonlinear dose-response analysis was significant at SBP >132 mmHg and DBP >75 mmHg. Conclusions: Hypertension and elevated SBP and DBP are associated with a high risk of AD. The risk of AD was positively dose-dependent, even within the normal BP range. These findings provide further evidence for the optimization of BP to prevent AD.

Some negative results for the interpolation monotone approximation of functions having a fractional derivative

2020 ◽  
pp. 122-127
Author(s):  
T. O. Petrova ◽  
I. P. Chulakov
Keyword(s):  
Fractional Derivative ◽  
Convex Function ◽  
Nondecreasing Function ◽  
Degree Of Approximation ◽  
Approximation Of Functions ◽  
Monotone Approximation ◽  
Convex Approximation ◽  
Negative Results ◽  
Positive Functions ◽  
Approximation Of A Function

We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function $f є W^r [0,1]$ by polynomials. The problem of positive approximation is to estimate the pointwise degree of approximation of a function $f є C^r [0,1] \cap \Delta^0$ where $\Delta^0$ is the set of positive functions on [0,1]. Estimates of the form (1) for positive approximation are known ([1],[2]). The problem of monotone approximation is that of estimating the degree of approximation of a monotone nondecreasing function by monotone nondecreasing polynomials. Estimates of the form (1) for monotone approximation were proved in [3],[4],[8]. In [3],[4] is consider $r є , r > 2$. In [8] is consider $r є , r > 2$. It was proved that for monotone approximation estimates of the form (1) are fails for $r є , r > 2$. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is consider in ([5],[6]). In [5] is consider $r є , r > 2$. In [6] is consider $r є , r > 2$. It was proved that for convex approximation estimates of the form (1) are fails for $r є , r > 2$. In this paper the question of approximation of function $f є W^r \cap \Delta^1, r є (3,4)$ by algebraic polynomial $p_n є \Pi_n \cap \Delta^1$ is consider. The main result of the work generalize the result of work [8] for $r є (3,4)$.

scholarly journals Solving Fractional Polynomial Problems by Polynomial Optimization Theory

2018 ◽  
Vol 25 (10) ◽  
pp. 1540-1544 ◽  
Author(s):  
Andrea Pizzo ◽  
Alessio Zappone ◽  
Luca Sanguinetti
Keyword(s):  
Polynomial Optimization ◽  
Optimization Theory ◽  
Fractional Polynomial
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