Let A ∈ Cn be an exceptional extremal copositive n × n matrix with positive diagonal. A zero u of A is a non-zero nonnegative vector such that uTAu = 0. The support of a zero u is the index set of the positive elements of u. A zero u is minimal if there is no other zero v such that supp v ⊂ suppu strictly. Let G be the graph on n vertices which has an edge (i, j) if and only if A has a zero wit...

BACKGROUND AND PURPOSE To our knowledge, no published functional map of the human lower brainstem exists. Our purpose was to use 1.5-T functional MR imaging (fMRI) to visualize the location of cranial nerve (CN) nuclei and other pontine, bulbar, and cervical spinal cord nuclei by using specific sensory stimulation or motor performance. METHODS We localized nuclei by using cross-correlation an...

C strategies assemble different products from at least one common component and one other product-specific component. The distinguishing feature of commonality, i.e., the presence of dedicated components to be assembled with a common component, is shown to be mathematically inconsequential in the sense that the unified commonality problem for two products can be reduced to an equivalent substit...

We consider a Hermitian matrix valued function A(x) ∈ C, smoothly depending on parameters x ∈ Ω ⊂ R, where Ω is an open bounded region of R. We develop an algorithm to locate parameter values where the eigenvalues of A coalesce. We give theoretical justification and implementation details. Finally, we illustrate the technique on several problems. Notation. With A ∈ Cn×n we indicate an n×n compl...

Unsupervised discovery of commonalities in images has recently attracted much interest due to the need to find correspondences in large amounts of visual data. A natural extension, and a relatively unexplored problem, is how to discover common semantic temporal patterns in videos. That is, given two or more videos, find the subsequences that contain similar visual content in an unsupervised man...

This paper studies liquidity and volatility commonality in the Canadian stock market. We show that five various liquidity measures display strong evidence of commonality at both market-wide and industry specific levels. Our findings extend the results of previous studies in liquidity commonality, and show that even after controlling for individual determinants of liquidity such as price, volume...

Local structure in the colossal thermal expansion material Ag3[Co(CN)6] is studied here using a combination of neutron total scattering and reverse Monte Carlo (RMC) analysis. We show that the large thermal variations in cell dimensions occur with minimal distortion of the [Co(CN)6] coordination polyhedra, but involve significant flexing of the Co–CN–Ag–NC– Co linkages. We find real-space evide...

Let {a1, a2, . . . , an} be an alphabet of n symbols and let Cn be the language of circular shifts of the word a1a2 · · · an; so Cn = {a1a2 · · · an−1an, a2a3 · · · ana1, . . . , ana1 · · · an−2an−1}. We discuss a few families of context-free grammars Gn (n ≥ 1) in Chomsky normal form such that Gn generates Cn. The grammars in these families are investigated with respect to their descriptional ...