Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for the usual Dirac operator. The limiting cases are also investigated.Comment: 2007, 18 pages, submitted 02 June 200

The Dirac operator on untrapped surfaces

We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.Comment: 16 page

Integración continua y su aplicación a gvHIDRA utilizando Selenium y Hudson

Hijazi, YMT. (28-0). Integración continua y su aplicación a gvHIDRA utilizando Selenium y Hudson. http://hdl.handle.net/10251/14854.Archivo delegad

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

Spectral Bounds for Dirac Operators on Open Manifolds

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's estimate on surfaces.Comment: pdflatex, 14 pages, 3 figure

Instantons and Killing spinors

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.Comment: 40 pages, 2 figures v2: author email addresses and affiliations adde

World Health Organization Guidelines for Management of Acute Stress, PTSD, and Bereavement: Key Challenges on the Road Ahead

Wietse Tol and colleagues discuss some of the key challenges for implementation of new WHO guidelines for stress-related mental health disorders in low- and middle-income countries. Please see later in the article for the Editors' Summar

The Energy Application Domain Extension for CityGML: enhancing interoperability for urban energy simulations

The road towards achievement of the climate protection goals requires, among the rest, a thorough rethinking of the energy planning tools (and policies) at all levels, from local to global. Nevertheless, it is in the cities where the largest part of energy is produced and consumed, and therefore it makes sense to focus the attention particularly on the cities as they yield great potentials in terms of energy consumption reduction and efficiency increase. As a direct consequence, a comprehensive knowledge of the demand and supply of energy resources, including their spatial distribution within urban areas, is therefore of utmost importance. Precise, integrated knowledge about 3D urban space, i.e. all urban (above and underground) features, infrastructures, their functional and semantic characteristics, and their mutual dependencies and interrelations play a relevant role for advanced simulation and analyses. As a matter of fact, what in the last years has proven to be an emerging and effective approach is the adoption of standard-based, integrated semantic 3D virtual city models, which represent an information hub for most of the abovementioned needs. In particular, being based on open standards (e.g. on the CityGML standard by the Open Geospatial Consortium), virtual city models firstly reduce the effort in terms of data preparation and provision. Secondly, they offer clear data structures, ontologies and semantics to facilitate data exchange between different domains and applications. However, a standardised and omni-comprehensive urban data model covering also the energy domain is still missing at the time of writing (January 2018). Even CityGML falls partially short when it comes to the definition of specific entities and attributes for energy-related applications. Nevertheless, and starting from the current version of CityGML (i.e. 2.0), this article describes the conception and the definition of an Energy Application Domain Extension (ADE) for CityGML. The Energy ADE is meant to offer a unique and standard-based data model to fill, on one hand, the above-mentioned gap, and, on the other hand, to allow for both detailed single-building energy simulation (based on sophisticated models for building physics and occupant behaviour) and city-wide, bottom-up energy assessments, with particular focus on the buildings sector. The overall goal is to tackle the existing data interoperability issues when dealing with energy-related applications at urban scale. The article presents the rationale behind the Energy ADE, it describes its main characteristics, the relation to other standards, and provides some examples of current applications and case studies already adopting it