We present the results of the fully automated CAFASP3 experiment, which was carried out in parallel with CASP5, using the same set of prediction targets. CAFASP participation is restricted to fully automatic structure prediction servers. The servers' performance is evaluated by using previously announced, objective, reproducible and fully automated evaluation methods. More than 60 servers parti...

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite...

for a given graph $g=(v,e)$, let $mathscr l(g)={l(v) : vin v}$ be a prescribed list assignment. $g$ is $mathscr l$-$l(2,1)$-colorable if there exists a vertex labeling $f$ of $g$ such that $f(v)in l(v)$ for all $v in v$; $|f(u)-f(v)|geq 2$ if $d_g(u,v) = 1$; and $|f(u)-f(v)|geq 1$ if $d_g(u,v)=2$. if $g$ is $mathscr l$-$l(2,1)$-colorable for every list assignment $mathscr l$ with $|l(v)|geq k$ ...

Given a family of Abelian varieties over a positive-dimensional base, we prove that for a sufficiently general curve in the base, every rational section of the family over the curve is contained in a unique rational section over the entire base. 1. Main results sec-intro The starting point for this article is the following theorem. Theorem 1.1. [GHMS05, Theorem 6.2] Let B be a smooth, quasi-pro...

Let X/K be an absolutely simple abelian variety over a number field; we study whether the reductions Xp tend to be simple, too. We show that if End(X) is a definite quaternion algebra, then the reduction Xp is geometrically isogenous to the self-product of an absolutely simple abelian variety for p in a set of positive density, while if X is of Mumford type, then Xp is simple for almost all p. ...

Focusing on two determinant aspects of retail competition, prices and catchment area, this paper aims to specifically investigate the importance of the relative price density function. We answer such questions as whether it pays for a store to offer more low-priced items in a given category than its close competitors and whether a retailer should have a consistent assortment in terms of price t...