Supplementary material A. Symmetric tensors A.1. Background Let Rd1⇥···⇥dm be the set of d1⇥ · · ·⇥dm real m-order tensors. In this paper, we focus on cubical tensors, i.e., d1 = · · · = dm = d. We denote the set of m-order cubical tensors by Rd m . We denote the elements of M 2 Rdm by Mj1,...,jm , where j1, . . . , jm 2 [d]. Let = [ 1, . . . , m] be a permutation of {1, . . . ,m}. Given M 2 Rd...

In pointwise differential geometry, i.e., linear algebra, we prove two theorems about the curvature operator of isometrically immersed submanifolds. We restrict our attention to Euclidean immersions because here the results are most easily stated and the curvature operator can be simply expressed as the sum of wedges of second fundamental form matrices. First, we reprove and extend a 1970 resul...

In this paper the problem of comparing several treatments with a control in a one-way repeated measures design is considered. Multiple testing procedures based on rank transformation data are proposed for determining which treatments are more effective than the control. The results of a Monte Carlo level and power study are presented.

We consider conditions under which the SR1 iteration is locally convergent. We apply the result to a pointwise structured SR1 method that has been used in optimal control.

Rank aggregation, which combines multiple individual rank lists to obtain a better one, is a fundamental technique in various applications such as meta-search and recommendation systems. Most existing rank aggregation methods blindly combine multiple rank lists with possibly considerable noises, which often degrades their performances. In this paper, we propose a new model for robust rank aggre...

We study an estimator with a convex formulation for recovery of low-rank matrices from rank-one projections. Using initial estimates the factors target $d_1\times d_2$ matrix rank-$r$, admits practical subgradient method operating in space dimension $r(d_1+d_2)$. This property makes significantly more scalable than estimators based on lifting and semidefinite programming. Furthermore, we presen...