We investigate, theoretically and empirically, the effectiveness of kernel K-means++ samples as landmarks in the Nyström method for low-rank approximation of kernel matrices. Previous empirical studies (Zhang et al., 2008; Kumar et al., 2012) observe that the landmarks obtained using (kernel) K-means clustering define a good lowrank approximation of kernel matrices. However, the existing work d...

We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and give a complete description in the Hermitian case. We also consider associated projection compression problems.

Secoisolariciresinol diglucoside is the main flax (Linum usitatissimum) lignan that is converted to the mammalian lignans enterodiol (ED) and enterolactone (EL) by gastrointestinal microbiota. The objectives of the present study were to investigate the role of ruminal microbiota and the effects of flax oil on in vivo metabolism of flax lignans and concentration of EL in biological fluids. Four ...

The objective of this study was to determine the effects of supplementing dried distillers grains soybean hulls, or combinations of the two to growing beef steers consuming bahiagrass hay. Angus steers were randomly allotted to one of four supplement treatments. Treatments included: 1) dried distillers grains; 2) dried distillers grains/soybean hulls; 3) soybean hulls/distillers grains; 4) soyb...

We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determin...

In this paper it is shown that if T ∈ L(H) satisfies (i) T is a pure hyponormal operator; (ii) [T ∗, T ] is of rank-two; and (iii) ker [T ∗, T ] is invariant for T , then T is either a subnormal operator or the Putinar’s matricial model of rank two. More precisely, if T |ker [T∗,T ] has the rank-one self-commutator then T is subnormal and if instead T |ker [T∗,T ] has the ranktwo self-commutato...