Ray helicity: a geometric invariant for multi-dimensional resonant wave conversion

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning it must be invariant under two groups of transformations: congruence transformations (which shuffle components of the multi-component wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray

Visual attention in autism families: ‘unaffected’ sibs share atypical frontal activation

Background: In addition to their more clinically evident abnormalities of social cognition, people with autism spectrum conditions (ASC) manifest perturbations of attention and sensory perception which may offer insights into the underlying neural abnormalities. Similar autistic traits in ASC relatives without a diagnosis suggest a continuity between clinically affected and unaffected family members

On the size of p-adic Whittaker functions

In this paper we tackle a question raised by N. Templier and A. Saha concerning the size of Whittaker new vectors appearing in infinite dimensional representations of GL(2) over non-archimedean fields. We derive precise bounds for such functions in all possible situations. Our main tool is the p-adic method of stationary phase.Comment: 41 pages, v4: Minor corrections, including suggestions by the anonymous Referee. Accepted for publication by the Transactions of the American Mathematical Societ

Permutations of Massive Vacua

We discuss the permutation group G of massive vacua of four-dimensional gauge theories with N=1 supersymmetry that arises upon tracing loops in the space of couplings. We concentrate on superconformal N=4 and N=2 theories with N=1 supersymmetry preserving mass deformations. The permutation group G of massive vacua is the Galois group of characteristic polynomials for the vacuum expectation values of chiral observables. We provide various techniques to effectively compute characteristic polynomials in given theories, and we deduce the existence of varying symmetry breaking patterns of the duality group depending on the gauge algebra and matter content of the theory. Our examples give rise to interesting field extensions of spaces of modular forms.Comment: 44 pages, 1 figur