Rainbow universe

The formalism of rainbow gravity is studied in a cosmological setting. We consider the very early universe which is radiation dominated. A novel treatment in our paper is to look for an ``averaged'' cosmological metric probed by radiation particles themselves. Taking their cosmological evolution into account, we derive the modified Friedmann-Robertson-Walker(FRW) equations which is a generalization of the solution presented by Magueijo and Smolin. Based on this phenomenological cosmological model we argue that the spacetime curvature has an upper bound such that the cosmological singularity is absent. These modified $FRW$ equations can be treated as effective equations in the semi-classical framework of quantum gravity and its analogy with the one recently proposed in loop quantum cosmology is also discussed.Comment: 5 page

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

Topology and singularities in cosmological spacetimes obeying the null energy condition

We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. In addition to (a refinement of) the Penrose singularity theorem, the proof makes use of some recent advances in the topology of 3-manifolds and of certain fundamental existence results for minimal surfaces.Comment: 8 pages; v2: minor changes, version to appear in CM

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

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

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'

High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity

Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these issues in the context of high-dimensional sparse linear regression, and propose novel estimators for the cases of noisy, missing and/or dependent data. Many standard approaches to noisy or missing data, such as those using the EM algorithm, lead to optimization problems that are inherently nonconvex, and it is difficult to establish theoretical guarantees on practical algorithms. While our approach also involves optimizing nonconvex programs, we are able to both analyze the statistical error associated with any global optimum, and more surprisingly, to prove that a simple algorithm based on projected gradient descent will converge in polynomial time to a small neighborhood of the set of all global minimizers. On the statistical side, we provide nonasymptotic bounds that hold with high probability for the cases of noisy, missing and/or dependent data. On the computational side, we prove that under the same types of conditions required for statistical consistency, the projected gradient descent algorithm is guaranteed to converge at a geometric rate to a near-global minimizer. We illustrate these theoretical predictions with simulations, showing close agreement with the predicted scalings.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1018 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org