We study a graph transformation (defined by Seidel) called switching which, given a graph G = ( V,E) and a subset W C Jf of its vertices, builds a new graph by exchanging the cocycle linking W to V\ W with its complement. Switching is an equivalence relation and the associated equivalence classes are called switching classes. A switching class is perfect if it contains only perfect graphs. We s...

BY DAVID H. KAYE O ne might expect to hear phrases like ‘‘Not statistical significance there!’’ and, ‘‘There is no way that anybody would tell you that these ten cases are statistically significant’’ hurled by a disgruntled professor at an underperforming statistics student. Yet, in January 2011, they came from the Supreme Court bench during the argument in Matrixx Initiatives Inc. v. Siracusano.

You don’t need to be a rocket scientist to observe one fact about Mars: it has a lot of rocks. While each is typically given a name based on protocols of scientific classification, many are known by informal, often humorous names like "Grandma" and "Space Ghost." And now on Mars, there’s a rock for fans of Civil War history—"Chamberlain," named of course for Joshua Lawrence Chamberlain, the her...

This study investigated fast mapping in late-talking (LT) toddlers and toddlers with normal language (NL) development matched on age, nonverbal cognition, and maternal education. The fast mapping task included novel object labels and familiar words. The LT group performed significantly worse than the NL group on novel word comprehension and production, as well as familiar word production. For b...

make us a robust and disease-free people, the prospect would be rosy indeed. A plethora of talk is, no doubt, a necessary evil, and it is only by saying the same thing very often and very loudly that we at last succeed in getting something done, whatever the desired direction. Next month the country will be asked, as it has been asked annually since 1912, for a whole week to talk and write abou...

We discuss the problem of the stability of the isotropy of the universe in the space of ever-expanding spatially homogeneous universes with a compact spatial topology. The anisotropic modes which prevent isotropy being asymptotically stable in Bianchi-type V IIh universes with non-compact topologies are excluded by topological compactness. Bianchi type V and type V IIh universes with compact to...

We introduce the concept of group state transfer on graphs, summarize its relationship to other concepts in theory quantum walks, set up a basic theory, and discuss examples. Let X be graph with adjacency matrix A consider walks vertex V(X) governed by continuous time-dependent unitary transition operator U(t)=exp(itA). For S,T⊆V(X), we say admits “group transfer” from S T at time τ if submatri...

We study a self-dual N = 1 super vertex operator algebra, denoted A, and prove that the full symmetry group is Conway’s largest sporadic simple group Co1. We verify a uniqueness result for A which is analogous to that conjectured to characterize the Moonshine vertex operator algebra V . The action of Co1 on A is sufficiently transparent that one can derive explicit expressions for the McKay-Tho...

We discuss the problem of the stability of the isotropy of the universe in the space of ever-expanding spatially homogeneous universes with a compact spatial topology. The anisotropic modes which prevent isotropy being asymptotically stable in Bianchi-type V IIh universes with non-compact topologies are excluded by topological compactness. Bianchi type V and type V IIh universes with compact to...