A Discussion on the Application of the Smoothing Function of the Plus Function

2017 ◽  
pp. 229-233
Author(s):  
Shu-ting Shao ◽  
Shou-qiang Du
Keyword(s):  
Smoothing Function

scholarly journals Intra-urban differentials of congenital and acquired syphilis and syphilis in pregnant women in an urban area in northeastern Brazil

2021 ◽  
Author(s):  
Talita Araujo de Souza ◽  
Karen Kaline Teixeira ◽  
Reginaldo Lopes Santana ◽  
Cinthia Barros Penha ◽  
Arthur de Almeida Medeiros ◽  
...  
Keyword(s):  
Relative Risk ◽  
Pregnant Women ◽  
Congenital Syphilis ◽  
Kernel Density ◽  
Poisson Model ◽  
Northeastern Brazil ◽  
Smoothing Function ◽  
Density Estimator ◽  
Epidemic Disease ◽  
Peripheral Areas

Abstract Background Currently syphilis is considered an epidemic disease worldwide. The objective of this study was to identify intra-urban differentials in the occurrence of congenital and acquired syphilis and syphilis in pregnant women in the city of Natal, in northeast Brazil. Methods Cases of syphilis recorded by the municipal surveillance system from 1 January 2011 to 30 December 2018 were analysed. Spatial statistical analyses were performed using the kernel density estimator of the quadratic smoothing function (weighted). SaTScan software was applied for the calculation of risk based on a discrete Poisson model. Results There were 2163 cases of acquired syphilis, 738 cases of syphilis in pregnant women and 1279 cases of congenital syphilis. Kernel density maps showed that the occurrence of cases is more prevalent in peripheral areas and in areas with more precarious urban infrastructure. In 2011–2014 and 2015–2018, seven statistically significant clusters of acquired syphilis were identified. From 2011 to 2014, the most likely cluster had a relative risk of 3.54 (log likelihood ratio [LLR] 38 895; p<0.001) and from 2015 to 2018 the relative risk was 0.54 (LLR 69 955; p<0.001). Conclusions In the municipality of Natal, there was a clustered pattern of spatial distribution of syphilis, with some areas presenting greater risk for the occurrence of new cases.

Intensity modulated radiation therapy (IMRT) in the radiotherapy treatment of colo-rectal cancer: the influence of profile smoothing on the efficiency of delivery

2002 ◽  
Vol 2 (4) ◽  
pp. 189-198 ◽  
Author(s):  
W. Laub ◽  
D. Yan ◽  
J. Robertson ◽  
A. Martinez
Keyword(s):  
Rectal Cancer ◽  
Radiation Therapy ◽  
Small Bowel ◽  
Intensity Modulated Radiation Therapy ◽  
Smoothing Function ◽  
Treatment Technique ◽  
Intensity Modulated ◽  
Treatment Implementation ◽  
Close Proximity ◽  
Radiotherapy Treatment

Small bowel toxicity due to radiotherapy treatment of rectal cancer is common. The potential use of intensity modulated radiation therapy (IMRT) to reduce the volume of small bowel irradiated during radiation therapy (RT) for cancer has previously been reported. However, IMRT treatment implementation is relatively difficult for these patients. The PTV is large and has a concave shape, with the small bowel in very close proximity. Therefore, the intensity profile calculated by an inverse planning engine could be highly modulated and complicated to deliver.In this study, two methods were used to optimise IMRT plans for rectal cancer patients. Scatter contribution when backprojecting dose values to fluence values and a smoothing function were only implemented in the optimisation searching of one method. A common arrangement of five beams, each separated by equal gantry angle, was adopted. With both methods used, the dose coverage of the PTV was satisfactory. Small bowel irradiated to a dose of 95 % was reduced by about 70% as compared to a 3D conformal 3-field treatment technique. However, incorporation of scatter contribution and a smoothing function in the iteration of optimisation searching greatly reduced the degree of modulation in the two-dimensional intensity profiles. Instead of 120–160 step-and-shoot MLC segments only 30–60 segments were necessary to deliver the five intensity profiles. The number of monitor units per fraction was reduced accordingly to about one half. Therefore, by controlling the smoothness of the intensity profiles during optimisation, the produced IMRT plans could be delivered more efficiently. Moreover, the possibility to account for overlap of organs was found to be very valuable to avoid hot spots in these regions and to get the full DVHs of all organs at the same time.

scholarly journals A new smoothing function to introduce long-range electrostatic effects in QM/MM calculations

2015 ◽  
Vol 143 (4) ◽  
pp. 044103 ◽  
Author(s):  
Dong Fang ◽  
Robert E. Duke ◽  
G. Andrés Cisneros
Keyword(s):  
Long Range ◽  
Smoothing Function ◽  
Electrostatic Effects

U-Shaped Association Between the Triglycerides-Glucose index and the Risk of Incident Diabetes in Apparently Healthy Population: A Population-based Cohort Study

2020 ◽  
Author(s):  
Xiuping Xuan ◽  
Masahide Hamaguchi ◽  
Qiuli Cao ◽  
Okamura Takuro ◽  
Yoshitaka Hashimoto ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Piecewise Linear ◽  
Incident Diabetes ◽  
Smoothing Function ◽  
Healthy Population ◽  
Piecewise Linear Regression ◽  
Tyg Index ◽  
Apparently Healthy

Abstract Background Although the triglycerides-glucose (TyG) index was thought to be a practical predictor of incident diabetes, the association between them has not been well characterized. The study aimed to further examine the association between the TyG index and incident diabetes in Japanese adults. Methods The cases were extracted of the individual participating in the NAGALA (NAfld in the Gifu Area, Longitudinal Analysis) study at Murakami Memorial Hospital from 2004 to 2015, and 14297individuals apparently healthy at baseline were included in the study. Cox proportional hazards models were used to evaluate the associations between baseline TyG levels and incident of T2DM, and a two-piecewise linear regression model was use to examine the threshold effect of the baseline TyG on incident diabetes using a smoothing function. The threshold level (i.e., turning point) was determined using trial and error. A log likelihood ratio test was also conducted to compare the one-line linear regression model with a two-piecewise linear model. Results During a median follow-up period of 5.26 (women) and 5.88 (men) years, 47 women and 182 men developed Type 2 diabetes. The risk of diabetes was strongly associated with the baseline TyG index in the fully adjusted model in men but not in women, and no dose-dependent positive relationship between incident diabetes and TyG was observed across TyG tertiles. Intriguingly, two-piecewise linear regression analysis showed a U-shaped association between the TyG index and incident T2DM. The risk of incident diabetes decreased by around 90% in women with TyG < 7.27 (HR: 0.09; P = 0.0435) and 80% in men with TyG < 7.97 (HR 0.21, P = 0.002) with each increment of the TyG index after adjusting for confounders. In contrast, the risk of incident T2DM significantly elevated with the increase in TyG index in men with TyG > 7.97 (HR: 2.42, P < 0.001) and women with TyG > 7.29 (HR 2.76, P = 0.0166). Conclusions A U-shaped association was observed between the TyG index and incident T2DM among healthy individuals, with the TyG threshold of 7.97 in men and 7.27 in women. This information may be useful for reducing incident diabetes by maintaining the TyG index near these thresholds.

scholarly journals The primordial black hole formation criterion re-examined: Parametrisation, timing and the choice of window function

2019 ◽  
Vol 29 (02) ◽  
pp. 2030002 ◽  
Author(s):  
Sam Young
Keyword(s):  
Black Hole ◽  
Density Perturbation ◽  
Density Contrast ◽  
Smoothing Function ◽  
Primordial Black Hole ◽  
Curvature Perturbation ◽  
Order Of Magnitude ◽  
Horizon Limit ◽  
First Time ◽  
Peak Value

In this paper, the criterion used to determine whether a density perturbation will collapse to form a primordial black hole (PBH) is re-examined in respect of its use to determine the abundance of PBHs. There is particular focus on which parameter to use, the time at which the abundance should be calculated, and the use of different smoothing functions. It is concluded that, with the tools currently available, the smoothed density contrast should be used rather than the peak value, and should be calculated from the time-independent component of the density contrast in the super-horizon limit (long before perturbations enter the horizon) rather than at horizon crossing. For the first time, the effect of the choice of smoothing function upon the formation criterion is calculated, and, for a given abundance of PBHs, it is found that the uncertainty in the amplitude of the power spectrum due to this is [Formula: see text], an order of magnitude smaller than that suggested by previous calculations. The relation between the formation criterion stated in terms of the density contrast and the curvature perturbation [Formula: see text] is also discussed.

A Smoothing Function Approach to Joint Chance-Constrained Programs

2014 ◽  
Vol 163 (1) ◽  
pp. 181-199 ◽  
Author(s):  
Feng Shan ◽  
Liwei Zhang ◽  
Xiantao Xiao
Keyword(s):  
Function Approach ◽  
Smoothing Function

scholarly journals An Active Set Smoothing Method for Solving Unconstrained Minimax Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Zhengyong Zhou ◽  
Qi Yang
Keyword(s):  
Minimax Problems ◽  
Unconstrained Minimization ◽  
Smoothing Method ◽  
Smoothing Function ◽  
Active Set ◽  
Maximum Function ◽  
Minimization Method ◽  
Lipschitz Continuous ◽  
Locally Lipschitz ◽  
Smoothing Parameters

In this paper, an active set smoothing function based on the plus function is constructed for the maximum function. The active set strategy used in the smoothing function reduces the number of gradients and Hessians evaluations of the component functions in the optimization. Combing the active set smoothing function, a simple adjustment rule for the smoothing parameters, and an unconstrained minimization method, an active set smoothing method is proposed for solving unconstrained minimax problems. The active set smoothing function is continuously differentiable, and its gradient is locally Lipschitz continuous and strongly semismooth. Under the boundedness assumption on the level set of the objective function, the convergence of the proposed method is established. Numerical experiments show that the proposed method is feasible and efficient, particularly for the minimax problems with very many component functions.

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