On the adaptive elastic-net with a diverging number of parameters

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J. Amer. Statist. Assoc. 96 (2001) 1348--1360] and [Ann. Statist. 32 (2004) 928--961] which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem, which should be properly handled by the ideal method. Many existing variable selection methods fail to achieve both goals simultaneously. In this paper, we propose the adaptive elastic-net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage. Under weak regularity conditions, we establish the oracle property of the adaptive elastic-net. We show by simulations that the adaptive elastic-net deals with the collinearity problem better than the other oracle-like methods, thus enjoying much improved finite sample performance.Comment: Published in at http://dx.doi.org/10.1214/08-AOS625 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Note on a Rapid Grid Search Method for Solving Dynamic Programming Problems in Economics

We introduce a rapid grid search method in solving the dynamic programming problems in economics. Compared to mainstream grid search methods, by using local information of the Bellman equation, this method can significantly increase the efficiency in solving dynamic programming problems by reducing the grid points searched in the control space.Dynamic Programming, Grid Search, Control Space

Open Spin Chains from Determinant Like Operators in ABJM Theory

We study the mixing problem of the determinant like operators in ABJM theory to two loop order in the scalar sector. The gravity duals of these operators are open strings attached to the maximal giant graviton, which is a D4-brane wrapping a $\mathbb{CP}^2$ inside $\mathbb{CP}^3$ in our case. The anomalous dimension matrix of these operators can be regarded as an open spin chain Hamiltonian. We provide strong evidence of its integrability based on coordinate Bethe ansatz method and boundary Yang-Baxter equation.Comment: 11 pages, no figures; v2, typos corrected, references added, 11 pages, no figures; v3 typos fixed, 11 pages, no figure

An intelligent approach to design three-dimensional aircraft sheet metal part model for manufacture

Aircraft sheet metal part manufacturing is a knowledge-intensive process, and the manufacturability and manufacturing information are required to be considered in three-dimensional (3D) model by knowledge reuse. This paper presents a 3D model structure of the aircraft sheet metal part and an intelligent approach to design the model for manufacture combining intelligent manufacturability analysis with manufacturing information definition. Processability of part, formability of material and cost of fabrication are proposed to analyse the manufacturability of the part. Knowledge base for manufacturability analysis is established, and knowledge is reused to evaluate the part’s manufacturability intelligently to meet the constraints of manufacturing conditions. Non-geometric information is defined in the 3D model to meet the needs of digital manufacturing and inspection using model-based technology. An example is given to describe the process of design for manufacture, which shows that the approach can realize the concurrent design and digital manufacturing of aircraft sheet metal