Automatic Feature Selection via Weighted Kernels and Regularization

Selecting important features in nonlinear kernel spaces is a difficult challenge in both classification and regression problems. This article proposes to achieve feature selection by optimizing a simple criterion: a feature-regularized loss function. Features within the kernel are weighted, and a lasso penalty is placed on these weights to encourage sparsity. This feature-regularized loss function is minimized by estimating the weights in conjunction with the coefficients of the original classification or regression problem, thereby automatically procuring a subset of important features. The algorithm, KerNel Iterative Feature Extraction (KNIFE), is applicable to a wide variety of kernels and high-dimensional kernel problems. In addition, a modification of KNIFE gives a computationally attractive method for graphically depicting nonlinear relationships between features by estimating their feature weights over a range of regularization parameters. The utility of KNIFE in selecting features through simulations and examples for both kernel regression and support vector machines is demonstrated. Feature path realizations also give graphical representations of important features and the nonlinear relationships among variables. Supplementary materials with computer code and an appendix on convergence analysis are available online.     

Longitudinal dispersion of solutes in porous media solely by advection

The purpose of this work is to predict the transport of non-sorbing solutes through water flow in the subsurface. We derive what we consider to be the first reliable calculations of the entire distribution of arrival times, W(t), for non-sorbing solutes in advective flow in strongly disordered porous media. Solutes treated can be contaminant plumes from any source or radioactive tracers, both experimentally and naturally generated. Our approach is microscopic and based on effects of disorder. It generates longitudinal dispersion (in the direction of flow) in the absence of diffusion. Effects on dispersion from a single capillary tube velocity distribution, known to produce long-tailed arrival time distributions, are also neglected. On the other hand, our calculations are based on effects generated from real porous media, such as wide pore-size distributions and complex connectivity. In particular, the calculation of the distribution of arrival times is based on a distribution of conserved fluxes and the known tortuosity of the associated geometrical paths. The results are found to be predictive when compared with simulations of two-dimensional flow on percolation structures, and appear to have relevance for experiments as well.     

PATHS AND CYCLES EMBEDDING ON FAULTY ENHANCED HYPERCUBE NETWORKS

Let Qn,k(n≥3,1≤k≤n-1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges,fv and fe be the numbers of faulty vertices and faulty edges,respectively.In this paper,we give three main results.First,a fault-free path P [u,v] of length at least 2n-2fv-1(respectively,2n-2fv-2) can be embedded on Qn,k with fv+fe≤n-1 when d Qn,k(u,v) is odd(respectively,d Qn,k(u,v) is even).Secondly,an Qn,k is(n-2) edgefault-free hyper Hamiltonian-laceable when n(≥3) and k have the same parity.Lastly,a fault-free cycle of length at least 2n-2fv can be embedded on Qn,k with fe≤n-1 and fv+fe≤2n-4.     

一种基于光栅的滚转角测量新方法

提出了一种利用一维平面透射光栅作为敏感器件的滚转角测量新方法。利用聚焦透镜及光电位置探测器组成接收测量单元, 避免了直线度误差带来的影响; 利用光栅的±1级衍射光束构成双光路差动测量, 基本避免了俯仰、偏摆角的串扰, 实现了误差分离, 同时增强了抗干扰能力。通过详细的理论分析, 论证了方案的可行性, 并在此基础上通过实验得到了定标曲线, 其线性相关度为1, 滚转角测量的角度分辨率可以达到0.6″。测量方法简单灵活, 仅需更换不同线数的光栅便可满足不同测量精度的要求。     

Rapid Growth Paths in Multivalued Dynamical Systems Generated by Homogeneous Convex Stochastic Operators

The paper examines dynamical systems generated by convex homogeneous multivalued operators in spaces of random vectors. The primary goal is to investigate the growth rates of random trajectories of these dynamical systems. Existence and characterization theorems for rapid trajectories, growing faster in a certain sense than others, are obtained.     

Elliptic enumeration of nonintersecting lattice paths

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Turaev's summation. This appears to be the first combinatorial proof of the latter, and at the same time of some important degenerate cases including Jackson's and Dougall's summation. By considering nonintersecting lattice paths we are led to a multivariate extension of the summation which turns out to be a special case of an identity originally conjectured by Warnaar, later proved by Rosengren. We conclude with discussing some future perspectives.     

On weights of induced paths and cycles in claw‐free and K1,r‐free graphs

Let G be a K_1,r ‐free graph (r ≥ 3) on n vertices. We prove that, for any induced path or induced cycle on k vertices in G (k ≥ 2r − 1 or k ≥ 2r, respectively), the degree sum of its vertices is at most (2r − 2)(n − α) where α is the independence number of G. As a corollary we obtain an upper bound on the length of a longest induced path and a longest induced cycle in a K_1,r ‐free graph. Stronger bounds are given in the special case of claw‐free graphs (i.e., r = 3). Sharpness examples are also presented. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 131–143, 2001     

Rank and biclique partitions of the complement of paths

The problem was posed of determining the biclique partition number of the complement of a Hamiltonian path (Monson, Rees, and Pullman, Bull. Inst. Combinatorics and Appl. 14 (1995), 17–86). We define the complement of a path P, denoted P , as the complement of P in K_m,n where P is a subgraph of K_m,n for some m and n. We give an exact formula for the biclique partition number of the complement of a path. In particular, we solve the problem posed in [9]. We also summarize our more general results on biclique partitions of the complement of forests. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 111–122, 1998