Distributions for one-lepton SUSY Searches with the ATLAS Detector

Using ATLAS data corresponding to 70 +- 8 nb^-1 of integrated luminosity from the 7 TeV proton-proton collisions at the LHC, distributions of relevant supersymmetry-sensitive variables are shown for the final state containing jets, missing transverse momentum and one isolated electron or muon. With increased integrated luminosities, selections based on these distributions will be used in the search for supersymmetric particles: it is thus important to show that the Standard Model backgrounds to these searches are under good control.Comment: 3 pages, to appear in the Proceedings of the Hadron Collider Physics Symposium 2010, Toronto, Ontario, Canada, 23 - 27 Aug 2010, available on the CERN document server under the number ATL-PHYS-PROC-2010-07

The Dunkl oscillator in the plane II : representations of the symmetry algebra

The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the Schwinger-Dunkl algebra sd(2), are investigated. The algebra sd(2) has six generators, including two involutions and a central element, and can be seen as a deformation of the Lie algebra u(2). Two of the symmetry generators, J_3 and J_2, are respectively associated to the separation of variables in Cartesian and polar coordinates. Using the parabosonic creation/annihilation operators, two bases for the representations of sd(2), the Cartesian and circular bases, are constructed. In the Cartesian basis, the operator J_3 is diagonal and the operator J_2 acts in a tridiagonal fashion. In the circular basis, the operator J_2 is block upper-triangular with all blocks 2x2 and the operator J_3 acts in a tridiagonal fashion. The expansion coefficients between the two bases are given by the Krawtchouk polynomials. In the general case, the eigenvectors of J_2 in the circular basis are generated by the Heun polynomials and their components are expressed in terms of the para-Krawtchouk polynomials. In the fully isotropic case, the eigenvectors of J_2 are generated by little -1 Jacobi or ordinary Jacobi polynomials. The basis in which the operator J_2 is diagonal is then considered. In this basis, the defining relations of the Schwinger-Dunkl algebra imply that J_3 acts in a block tridiagonal fashion with all blocks 2x2. The matrix elements of J_3 in this basis are given explicitly.Comment: 33 page

Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra

The algebraic underpinning of the tridiagonalization procedure is investigated. The focus is put on the tridiagonalization of the hypergeometric operator and its associated quadratic Jacobi algebra. It is shown that under tridiagonalization, the quadratic Jacobi algebra becomes the quadratic Racah-Wilson algebra associated to the generic Racah/Wilson polynomials. A degenerate case leading to the Hahn algebra is also discussed.Comment: 14 pages; Section 3 revise

The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients

The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is superintegrable and its symmetry generators are obtained by the Schwinger construction using parabosonic creation/annihilation operators. The algebra generated by the constants of motion, which we term the Schwinger-Dunkl algebra, is an extension of the Lie algebra u(2) with involutions. The system admits separation of variables in both Cartesian and polar coordinates. The separated wavefunctions are respectively expressed in terms of generalized Hermite polynomials and products of Jacobi and Laguerre polynomials. Moreover, the so-called Jacobi-Dunkl polynomials appear as eigenfunctions of the symmetry operator responsible for the separation of variables in polar coordinates. The expansion coefficients between the Cartesian and polar bases (overlap coefficients) are given as linear combinations of dual -1 Hahn polynomials. The connection with the Clebsch-Gordan problem of the sl_{-1}(2) algebra is explained.Comment: 25 pages; Added references; Added appendix on anti-Hermicity of the Dunkl derivativ

Extracting constraints from direct detection searches of supersymmetric dark matter in the light of null results from the LHC in the squark sector

The comparison of the results of direct detection of Dark Matter, obtained with various target nuclei, requires model-dependent, or even arbitrary, assumptions. Indeed, to draw conclusions either the spin-dependent (SD) or the spin-independent (SI) interaction has to be neglected. In the light of the null results from supersymmetry searches at the LHC, the squark sector is pushed to high masses. We show that for a squark sector at the TeV scale, the framework used to extract contraints from direct detection searches can be redefined as the number of free parameters is reduced. Moreover, the correlation observed between SI and SD proton cross sections constitutes a key issue for the development of the next generation of Dark Matter detectors.Comment: Figure 3 has been updated. Conclusions unchange

A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence

A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality

Determining the squark mass at the LHC

We propose a new way to determine the squark mass based on the shape of di-jet invariant mass distribution of supersymmetry (SUSY) di-jet events at the Large Hadron Collider (LHC). Our algorithm, which is based on event kinematics, requires that the branching ratio $B(\tilde{q} \rightarrow q \tilde{z}_1)$ is substantial for at least some types of squarks, and that $m_{\tilde{z}_1}^2/m_{\tilde{q}}^2 \ll 1$. We select di-jet events with no isolated leptons, and impose cuts on the total jet transverse energy, $E_T^{tot}=E_T(j_1)+E_T(j_2)$, on $\alpha = E_T(j_2)/m_{jj}$, and on the azimuthal angle between the two jets to reduce SM backgrounds. The shape of the resulting di-jet mass distribution depends sensitively on the squark mass, especially if the integrated luminosity is sufficient to allow a hard enough cut on $E_T^{tot}$ and yet leave a large enough signal to obtain the $m_{jj}$ distribution. We simulate the signal and Standard Model (SM) backgrounds for 100 fb$^{-1}$ integrated luminosity at 14 TeV requiring $E_T^{tot}> 700$ GeV. We show that it should be possible to extract $m_{\tilde{q}}$ to within about 3% at 95% CL --- similar to the precision obtained using $m_{T2}$ --- from the di-jet mass distribution if $m_{\tilde{q}} \sim 650$ GeV, or to within $\sim 5$% if $m_{\tilde{q}}\sim 1$ TeV.Comment: 20 pages, 9 figures. Footnote added, updated reference

Une synthèse des modèles de représentation des connaissances à base de Graphes Conceptuels et OWL

Nous présentons et comparons deux approches de modélisation, formelles et concrètes, pour représenter et manipuler des connaissances d’un domaine. Le modèle des graphes conceptuels permet de modéliser des connaissances en terme de graphes, basés sur un support. Cette approche de modélisation est intensionnelle, est munie d’une sémantique en logique du premier ordre, et fait l’hypothèse d’un monde fermé pour ses raisonnements. Le langage OWL permet de décrire des ontologies et des faits sur le Web, suivant une approche de modélisation extensionnelle. Il possède une sémantique issue des logiques de descriptions, et fait l’hypothèse d’un monde ouvert pour ses raisonnements

Modelling stochastic bivariate mortality

Stochastic mortality, i.e. modelling death arrival via a jump process with stochastic intensity, is gaining increasing reputation as a way to represent mortality risk. This paper represents a first attempt to model the mortality risk of couples of individuals, according to the stochastic intensity approach. On the theoretical side, we extend to couples the Cox processes set up, i.e. the idea that mortality is driven by a jump process whose intensity is itself a stochastic process, proper of a particular generation within each gender. Dependence between the survival times of the members of a couple is captured by an Archimedean copula. On the calibration side, we fit the joint survival function by calibrating separately the (analytical) copula and the (analytical) margins. First, we select the best fit copula according to the methodology of Wang and Wells (2000) for censored data. Then, we provide a sample-based calibration for the intensity, using a time-homogeneous, non mean-reverting, affine process: this gives the analytical marginal survival functions. Coupling the best fit copula with the calibrated margins we obtain, on a sample generation, a joint survival function which incorporates the stochastic nature of mortality improvements and is far from representing independency.On the contrary, since the best fit copula turns out to be a Nelsen one, dependency is increasing with age and long-term dependence exists