Select Large Variable selection via generalized SELO-penalized linear regression models SHI Yue-yong, CAO Yong-xiu, YU Ji-chang, JIAO Yu-ling Applied Mathematics-A Journal of Chinese Universities. 2018, (2)   DOI: https://doi.org/10.1007/s11766-018-3496-x 摘要( 7 )     PDF(0KB)( 2 ) The seamless-$L_0$ (SELO) penalty is a smooth function on $[0,\wq)$ that very  closely resembles the $L_0$ penalty, which has been  demonstrated theoretically and practically to be effective in nonconvex penalization for  variable selection. In this paper, we first generalize SELO to a class of penalties  retaining good features of SELO, and then  propose variable selection and estimation in  linear models  using the proposed  eneralized SELO (GSELO)  penalized least squares (PLS) approach. We show that the GSELO-PLS procedure possesses the oracle property  and consistently selects the true model under some regularity conditions in the presence of a diverging number of variables.  The entire path of GSELO-PLS estimates can  be efficiently computed through a smoothing quasi-Newton (SQN) method. A modified BIC coupled with a continuation  strategy is developed to select the optimal tuning parameter. Simulation studies and analysis of a clinical data are carried out to evaluate the finite sample performance of the proposed method. In addition, numerical experiments involving simulation studies and analysis of a microarray data are also conducted for GSELO-PLS in the high-dimensional settings.
 Select Double sampling derivatives and truncation error estimates Rashad M. Asharabi, Aisha M. Al-Hayzea Applied Mathematics-A Journal of Chinese Universities. 2018, (2)   DOI: https://doi.org/10.1007/s11766-018-3444-9 摘要( 2 )     PDF(0KB)( 0 ) This paper investigates  double sampling series derivatives for bivariate functions defined on $\mathbb{R}^{2}$ that are in the Bernstein space. For this sampling series, we  estimate some of the  pointwise and uniform bounds when the function satisfies some decay conditions.   The truncated series of this  formula allow us to approximate any order of partial derivatives for function   from  Bernstein  space   using only a finite number of samples from the function itself. This sampling  formula will be useful  in the approximation theory and its applications, especially after having the truncation  error    well-established.  Examples with tables and figures are given at the end of the paper  to illustrate the advantages of this formula.
 Select A note on Pythagorean hodograph quartic spiral ZHENG Zhi-hao , WANG Guo-zhao Applied Mathematics-A Journal of Chinese Universities. 2018, (2)   DOI: https://doi.org/10.1007/s11766-018-3465-4 摘要( 3 )     PDF(0KB)( 0 ) By using the geometric constraints on the control polygon of a Pythagorean hodograph (PH) quartic curve,  we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. Based on the results, we discuss the construction of spiral PH quartic curves between two given points and formulate the transition curve of a $G^2$ contact between two circles with one circle inside another circle. In particular, we deduce an attainable range of the distance between the centers of the two circles and summarize the algorithm for implementation. Compared with the construction of a PH quintic curve, the complexity of the solution of the equation for obtaining the transition curves is reduced.