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

Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy

Nonexistence of Generalized Apparent Horizons in Minkowski Space

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space

Description and Predictive Factors of individual outcomes in a refugee camp based mental health intervention (Beirut, Lebanon)

There is little evidence on the effectiveness of services for the care of people with mental disorders among refugee populations. Médecins sans Frontières (MSF) has established a mental health centre in a mixed urban-refugee population in Beirut to respond to the significant burden of mental health problems. Patients received comprehensive care through a multidisciplinary team. A cohort of people with common and severe mental disorders has been analysed between December 2008 and June 2011 to evaluate individual outcomes of treatment in terms of functionality

Multi-user detection for multi-carrier communication systems

Doctor of PhilosophyDepartment of Electrical and Computer EngineeringBalasubramaniam NatarajanWireless broadband communications is a rapidly growing industry. New enabling technologies such as multi-carrier code division multiple access (MC-CDMA) are shaping the future of wireless systems. However, research efforts in improving MC-CDMA receiver performance have received limited attention and there is a need for innovative receiver designs for next generation MC-CDMA. In this thesis, we propose novel multi-user detection (MUD) schemes to enhance the performance of both synchronous and asynchronous MC-CDMA. First, we adapt the ant colony optimization (ACO) approach to solve the optimal MUD problem in MC-CDMA systems. Our simulations indicate that the ACO based MUD converges to the optimal BER performance in relatively few iterations providing more that 95% savings in computational complexity. Second, we propose a new MUD structure specifically for asynchronous MC-CDMA. Previously proposed MUDs for asynchronous MC-CDMA perform the detection for one user (desired user) at a time, mandating multiple runs of the algorithm to detect all users' symbols. In this thesis, for the first time we present a MUD structure that detects all users' symbols simultaneously in one run by extending the receiver's integration window to capture the energy scattered in two consecutive symbol durations. We derive the optimal, decorrelator and minimum mean square error (MMSE) MUD for the extended window case. Our simulations demonstrate that the proposed MUD structures not only perform similar to a MUD that detects one user at a time, but its computational complexity is significantly lower. Finally, we extend the MUD ideas to multicarrier implementation of single carrier systems. Specifically, we employ the novel MUD structure as a multi-symbol detection scheme in CI-CDMA and illustrate the resulting performance gain via simulations

Solar Wind Sputtering of Lunar Soil Analogs: The Effect of Ionic Charge and Mass

In this contribution we report sput-tering measurements of anorthite, an analog material representative of the lunar highlands, by singly and multicharged ions representative of the solar wind. The ions investigated include protons, as well as singly and multicharged Ar ions (as proxies for the heavier solar wind constituents), in the charge state range +1 to +9, and had a fixed solar-wind-relevant impact velocity of approximately 310 km/s or 500 eV/ amu. The goal of the measurements was to determine the sputtering contribution of the heavy, multicharged minority solar wind constituents in comparison to that due to the dominant H+ fraction

Extending a perfect matching to a Hamiltonian cycle

Graph TheoryInternational audienceRuskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle. Fink verified this for every perfect matching M, remarkably even if M contains external edges. We prove that this property also holds for sparse spanning regular subgraphs of the cubes: for every d ≥7 and every k, where 7 ≤k ≤d, the d-dimensional hypercube contains a k-regular spanning subgraph such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle. We do not know if this result can be extended to k=4,5,6. It cannot be extended to k=3. Indeed, there are only three 3-regular graphs such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle, namely the complete graph on 4 vertices, the complete bipartite 3-regular graph on 6 vertices and the 3-cube on 8 vertices. Also, we do not know if there are graphs of girth at least 5 with this matching-extendability property