Overlapping Optimized Schwarz Methods for Parabolic Equations in n-Dimensions

We introduce in this paper a new tool to prove the convergence of the Overlapping Optimized Schwarz Methods with multisubdomains. The technique is based on some estimates of the errors on the boundaries of the overlapping strips. Our guiding example is an n-Dimensional Linear Parabolic Equation

Model Selection with the Loss Rank Principle

A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polynomials. We suggest a novel principle - the Loss Rank Principle (LoRP) - for model selection in regression and classification. It is based on the loss rank, which counts how many other (fictitious) data would be fitted better. LoRP selects the model that has minimal loss rank. Unlike most penalized maximum likelihood variants (AIC, BIC, MDL), LoRP depends only on the regression functions and the loss function. It works without a stochastic noise model, and is directly applicable to any non-parametric regressor, like kNN.Comment: 31 LaTeX pages, 1 figur

Positively deflected anomaly mediation in the light of the Higgs boson discovery

Anomaly-mediated supersymmetry breaking (AMSB) is a well-known mechanism for flavor-blind transmission of supersymmetry breaking from the hidden sector to the visible sector. However, the pure AMSB scenario suffers from a serious drawback, namely, the tachyonic slepton problem, and needs to be extended. The so-called (positively) deflected AMSB is a simple extension to solve the problem and also provides us with the usual neutralino lightest superpartner as a good candidate for dark matter in the Universe. Motivated by the recent discovery of the Higgs boson at the Large Hadron Collider (LHC) experiments, we perform the parameter scan in the deflected AMSB scenario by taking into account a variety of phenomenological constraints such as the dark matter relic density and the observed Higgs boson mass around 125-126 GeV. We identify the allowed parameter region and list benchmark mass spectra. We find that in most of the allowed parameter regions, the dark matter neutralino is Higgsino-like and its elastic scattering cross section with nuclei is within the future reach of the direct dark matter search experiments, while (colored) sparticles are quite heavy and their discovery at the LHC is challenging.Comment: 16 pages, 5 figures, Version to be published in PR