Quantitative uniqueness for elliptic equations with singular lower order terms

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then describe two methods of propagation of smallness from sets of positive measure.Comment: 23 pages, v2 small changes are done and some mistakes are correcte

Star and Planet Formation with ALMA: an Overview

Submillimeter observations with ALMA will be the essential next step in our understanding of how stars and planets form. Key projects range from detailed imaging of the collapse of pre-stellar cores and measuring the accretion rate of matter onto deeply embedded protostars, to unravelling the chemistry and dynamics of high-mass star-forming clusters and high-spatial resolution studies of protoplanetary disks down to the 1 AU scale.Comment: Invited review, 8 pages, 5 figures; to appear in the proceedings of "Science with ALMA: a New Era for Astrophysics". Astrophysics & Space Science, in pres

Exploring gravitational theories beyond Horndeski

We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in arXiv:1404.6495. As they generalize Horndeski theories, or "generalized" galileons, we call them G$^3$. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformations that depend on the scalar field gradient, which also allow to map subfamilies of G$^3$ into Horndeski theories.Comment: 33 pages, added comments and corrected typos as in JCAP versio

Automatic lane detection in chromatography images

This paper proposes a method for automating the detection of lanes in Thin-Layer Chromatography images. Our approach includes a preprocessing step to detect the image region of interest, followed by background estimation and removal. This image is then projected onto the horizontal direction to integrate the information into a one-dimensional profile. A smoothing filter is applied to this profile and the outcome is the input of the lane detection process, which is performed in three phases. The first one aims at obtaining an initial set of candidate lanes that are further validated or removed in the second phase. The last phase is a refinement step that allows the inclusion of lanes that are not clearly distinguishable in the profile and that were not included in the initial set. The method was evaluated in 66 chromatography images and achieved values of recall, precision and F ß -measure of 97.0%, 99.4% and 98.2%, respectively

Operator product expansion of higher rank Wilson loops from D-branes and matrix models

In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N=4 super Yang-Mills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and D-branes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding perfect agreement in both the symmetric and the antisymmetric case.Comment: 28 pages, latex; v2: minor misprints corrected, references adde

Strain-facilitated process for the lift-off of a Si layer of less than 20 nm thickness

We report a process for the lift-off of an ultrathin Si layer. By plasma hydrogenation of a molecular-beam-epitaxy-grown heterostructure of SiSb-doped-SiSi, ultrashallow cracking is controlled to occur at the depth of the Sb-doped layer. Prior to hydrogenation, an oxygen plasma treatment is used to induce the formation of a thin oxide layer on the surface of the heterostructure. Chemical etching of the surface oxide layer after hydrogenation further thins the thickness of the separated Si layer to be only 15 nm. Mechanisms of hydrogen trapping and strain-facilitated cracking are discussed

Spin in relativistic quantum theory

We discuss the role of spin in Poincar\'e invariant formulations of quantum mechanics.Comment: 54 page

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York