In this paper, we study the confounder detection problem in the linear model, where the target variable Y is predicted using its n potential causes Xn = (x1, ..., xn) T . Based on an assumption of rotation invariant generating process of the model, recent study shows that the spectral measure induced by the regression coefficient vector with respect to the covariance matrix of Xn is close to a ...

In the process of obtaining these results we make some observations, which may be of more general interest, concerning the problems of singularity and continuity of the spectral types of skew products. See §2 and §4. Our approach is based on the method of approximations as formulated by Katok and Stepin [4, 5] and later developed and modified by a number of authors [1, 3, 8, 9]. For the continu...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

In this paper, we discuss a generalization of Balakrishnan skew-normal distribution with two parameters that contains the skew-normal, the Balakrishnan skew-normal and the two-parameter generalized skew-normal distributions as special cases. Furthermore, we establish some useful properties and two extensions of this distribution. 

We design an arbitrary high order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from a skew-symmetric formulation of the continuous problem. We prove that this discretisation exactly p...