6,100 research outputs found
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
Discrimination of Supersymmetric Grand Unified Models in Gaugino Mediation
We consider supersymmetric grand unified theory (GUT) with the gaugino
mediated supersymmetry breaking and investigate a possibility to discriminate
different GUT models in terms of predicted sparticle mass spectra. Taking two
example GUT models, the minimal SU(5) and simple SO(10) models, and imposing a
variety of theoretical and experimental constraints, we calculate sparticle
masses. Fixing parameters of each model so as to result in the same mass of
neutralino as the lightest supersymmetric particle (LSP), giving the observed
dark matter relic density, we find sizable mass differences in the left-handed
slepton and right-handed down-type squark sectors in two models, which can be a
probe to discriminate the GUT models realized at the GUT scale far beyond the
reach of collider experiments.Comment: 14 pages, 4 figures, version to be published in PR
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