Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

Search for W'→tb- in the lepton plus jets final state in proton-proton collisions at a centre-of-mass energy of s=8 TeV with the ATLAS detector

A search for new charged massive gauge bosons, called W′, is performed with the ATLAS detector at the LHC, in proton--proton collisions at a centre-of-mass energy of s√ = 8 TeV, using a dataset corresponding to an integrated luminosity of 20.3 fb−1. This analysis searches for W′ bosons in the W′→tb¯ decay channel in final states with electrons or muons, using a multivariate method based on boosted decision trees. The search covers masses between 0.5 and 3.0 TeV, for right-handed or left-handed W′ bosons. No significant deviation from the Standard Model expectation is observed and limits are set on the W′→tb¯ cross-section times branching ratio and on the W′-boson effective couplings as a function of the W′-boson mass using the CLs procedure. For a left-handed (right-handed) W′ boson, masses below 1.70 (1.92) TeV are excluded at 95% confidence level.

Search for the Standard Model Higgs boson produced in association with top quarks and decaying into bb in pp collisions at √s = 8 TeV with the ATLAS detector

A search for the Standard Model Higgs boson produced in association with a pair of top quarks, tt¯H, is presented. The analysis uses 20.3 fb−1 of pp collision data at s√ = 8 TeV, collected with the ATLAS detector at the Large Hadron Collider during 2012. The search is designed for the H to bb¯ decay mode and uses events containing one or two electrons or muons. In order to improve the sensitivity of the search, events are categorised according to their jet and b-tagged jet multiplicities. A neural network is used to discriminate between signal and background events, the latter being dominated by tt¯+jets production. In the single-lepton channel, variables calculated using a matrix element method are included as inputs to the neural network to improve discrimination of the irreducible tt¯+bb¯ background. No significant excess of events above the background expectation is found and an observed (expected) limit of 3.4 (2.2) times the Standard Model cross section is obtained at 95% confidence level. The ratio of the measured tt¯H signal cross section to the Standard Model expectation is found to be μ=1.5±1.1 assuming a Higgs boson mass of 125 GeV.