The regularity of harmonic maps into spheres and applications to Bernstein problems

We show the regularity of, and derive a-priori estimates for (weakly) harmonic maps from a Riemannian manifold into a Euclidean sphere under the assumption that the image avoids some neighborhood of a half-equator. The proofs combine constructions of strictly convex functions and the regularity theory of quasi-linear elliptic systems. We apply these results to the spherical and Euclidean Bernstein problems for minimal hypersurfaces, obtaining new conditions under which compact minimal hypersurfaces in spheres or complete minimal hypersurfaces in Euclidean spaces are trivial

Is the Dark Disc contribution to Dark Matter Signals important ?

Recent N-body simulations indicate that a thick disc of dark matter, co-rotating with the stellar disc, forms in a galactic halo after a merger at a redshift $z<2$. The existence of such a dark disc component in the Milky Way could affect dramatically dark matter signals in direct and indirect detection. In this letter, we discuss the possible signal enhancement in connection with the characteristics of the local velocity distributions. We argue that the enhancement is rather mild, but some subtle effects may arise. In particular, the annual modulation observed by DAMA becomes less constrained by other direct detection experiments

Electronic charge reconstruction of doped Mott insulators in multilayered nanostructures

Dynamical mean-field theory is employed to calculate the electronic charge reconstruction of multilayered inhomogeneous devices composed of semi-infinite metallic lead layers sandwiching barrier planes of a strongly correlated material (that can be tuned through the metal-insulator Mott transition). The main focus is on barriers that are doped Mott insulators, and how the electronic charge reconstruction can create well-defined Mott insulating regions in a device whose thickness is governed by intrinsic materials properties, and hence may be able to be reproducibly made.Comment: 9 pages, 8 figure

Neurological consequences of traumatic brain injuries in sports.

Traumatic brain injury (TBI) is common in boxing and other contact sports. The long term irreversible and progressive aftermath of TBI in boxers depicted as punch drunk syndrome was described almost a century ago and is now widely referred as chronic traumatic encephalopathy (CTE). The short term sequelae of acute brain injury including subdural haematoma and catastrophic brain injury may lead to death, whereas mild TBI, or concussion, causes functional disturbance and axonal injury rather than gross structural brain damage. Following concussion, symptoms such as dizziness, nausea, reduced attention, amnesia and headache tend to develop acutely but usually resolve within a week or two. Severe concussion can also lead to loss of consciousness. Despite the transient nature of the clinical symptoms, functional neuroimaging, electrophysiological, neuropsychological and neurochemical assessments indicate that the disturbance of concussion takes over a month to return to baseline and neuropathological evaluation shows that concussion-induced axonopathy may persist for years. The developing brains in children and adolescents are more susceptible to concussion than adult brain. The mechanism by which acute TBI may lead to the neurodegenerative process of CTE associated with tau hyperphosphorylation and the development of neurofibrillary tangles (NFTs) remains speculative. Focal tau-positive NFTs and neurites in close proximity to focal axonal injury and foci of microhaemorrhage and the predilection of CTE-tau pathology for perivascular and subcortical regions suggest that acute TBI-related axonal injury, loss of microvascular integrity, breach of the blood brain barrier, resulting inflammatory cascade and microglia and astrocyte activation are likely to be the basis of the mechanistic link of TBI and CTE. This article provides an overview of the acute and long-term neurological consequences of TBI in sports. Clinical, neuropathological and the possible pathophysiological mechanisms are discussed. This article is part of a Special Issue entitled 'Traumatic Brain Injury'

Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses

We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an open question about the significance of the inverse covariance matrix of a non-Gaussian distribution. The proof exploits a combination of ideas from the geometry of exponential families, junction tree theory and convex analysis. These population-level results have various consequences for graph selection methods, both known and novel, including a novel method for structure estimation for missing or corrupted observations. We provide nonasymptotic guarantees for such methods and illustrate the sharpness of these predictions via simulations.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1162 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Interference effects in second-harmonic generation within an optical cavity

An experiment is described that investigates certain interference effects for second-harmonic generation within a resonant cavity. By employing a noncollinear geometry, the phases of two fundamental beams from a frequency-stabilized dye laser can be controlled unrestricted by the boundary conditions imposed in an optical cavity containing a KDP crystal and resonant at the second harmonic. The fundamental beams are either traveling or standing waves and generate either one or two coherent sources of ultraviolet radiation within the cavity. The experiment demonstrates explicitly the dependence of second-harmonic phase on the fundamental phases and the dependence of coupling efficiency on the overlap of the harmonic polarization wave with the cavity-mode function. The measurements agree well with a simple theory

The geometry of Grassmannian manifolds and Bernstein type theorems for higher codimension

We identify a region \Bbb{W}_{\f{1}{3}} in a Grassmann manifold \grs{n}{m}, not covered by a usual matrix coordinate chart, with the following important property. For a complete $n-$submanifold in \ir{n+m} \, (n\ge 3, m\ge2) with parallel mean curvature whose image under the Gauss map is contained in a compact subset K\subset\Bbb{W}_{\f{1}{3}}\subset\grs{n}{m}, we can construct strongly subharmonic functions and derive a priori estimates for the harmonic Gauss map. While we do not know yet how close our region is to being optimal in this respect, it is substantially larger than what could be achieved previously with other methods. Consequently, this enables us to obtain substantially stronger Bernstein type theorems in higher codimension than previously known.Comment: 36 page