73,673 research outputs found
On the extraction of spectral densities from lattice correlators
Hadronic spectral densities are important quantities whose non-perturbative
knowledge allows for calculating phenomenologically relevant observables, such
as inclusive hadronic cross-sections and non-leptonic decay-rates. The
extraction of spectral densities from lattice correlators is a notoriously
difficult problem because lattice simulations are performed in Euclidean time
and lattice data are unavoidably affected by statistical and systematic
uncertainties. In this paper we present a new method for extracting hadronic
spectral densities from lattice correlators. The method allows for choosing a
smearing function at the beginning of the procedure and it provides results for
the spectral densities smeared with this function together with reliable
estimates of the associated uncertainties. The same smearing function can be
used in the analysis of correlators obtained on different volumes, such that
the infinite volume limit can be studied in a consistent way. While the method
is described by using the language of lattice simulations, in reality it is
completely general and can profitably be used to cope with inverse problems
arising in different fields of research.Comment: 15 pages, 14 figures. Updated to match published versio
Ordering Algorithms and Confidence Intervals in the Presence of Nuisance Parameters
We discuss some issues arising in the evaluation of confidence intervals in
the presence of nuisance parameters (systematic uncertainties) by means of
direct Neyman construction in multi-dimensional space. While this kind of
procedure provides rigorous coverage, it may be affected by large overcoverage,
and/or produce results with counterintuitive behavior with respect to the
uncertainty on the nuisance parameters, or other undesirable properties. We
describe a choice of ordering algorithm that provides results with good general
properties, the correct behavior for small uncertainties, and limited
overcoverage.Comment: 5 pages, 3 figures, to appear in proceedings of PhyStat2005, Oxford,
UK, Sept 2005, Imperial College Pres
Global sensitivity analysis for the boundary control of an open channel
The goal of this paper is to solve the global sensitivity analysis for a
particular control problem. More precisely, the boundary control problem of an
open-water channel is considered, where the boundary conditions are defined by
the position of a down stream overflow gate and an upper stream underflow gate.
The dynamics of the water depth and of the water velocity are described by the
Shallow Water equations, taking into account the bottom and friction slopes.
Since some physical parameters are unknown, a stabilizing boundary control is
first computed for their nominal values, and then a sensitivity anal-ysis is
performed to measure the impact of the uncertainty in the parameters on a given
to-be-controlled output. The unknown physical parameters are de-scribed by some
probability distribution functions. Numerical simulations are performed to
measure the first-order and total sensitivity indices
Anatomy of the Higgs fits: a first guide to statistical treatments of the theoretical uncertainties
The studies of the Higgs boson couplings based on the recent and upcoming LHC
data open up a new window on physics beyond the Standard Model. In this paper,
we propose a statistical guide to the consistent treatment of the theoretical
uncertainties entering the Higgs rate fits. Both the Bayesian and frequentist
approaches are systematically analysed in a unified formalism. We present
analytical expressions for the marginal likelihoods, useful to implement
simultaneously the experimental and theoretical uncertainties. We review the
various origins of the theoretical errors (QCD, EFT, PDF, production mode
contamination...). All these individual uncertainties are thoroughly combined
with the help of moment-based considerations. The theoretical correlations
among Higgs detection channels appear to affect the location and size of the
best-fit regions in the space of Higgs couplings. We discuss the recurrent
question of the shape of the prior distributions for the individual theoretical
errors and find that a nearly Gaussian prior arises from the error
combinations. We also develop the bias approach, which is an alternative to
marginalisation providing more conservative results. The statistical framework
to apply the bias principle is introduced and two realisations of the bias are
proposed. Finally, depending on the statistical treatment, the Standard Model
prediction for the Higgs signal strengths is found to lie within either the
or confidence level region obtained from the latest analyses of
the and TeV LHC datasets.Comment: 62 pages, 10 figure
Set-based design of mechanical systems with design robustness integrated
This paper presents a method for parameter design of mechanical products based on a set-based approach. Set-based concurrent engineering emphasises on designing in a multi-stakeholder environment with concurrent involvement of the stakeholders in the design process. It also encourages flexibility in design through communication in terms of ranges instead of fixed point values and subsequent alternative solutions resulting from intersection of these ranges. These alternative solutions can then be refined and selected according to the designers’ preferences and clients’ needs. This paper presents a model and tools for integrated flexible design that take into account the manufacturing variations as well as the design objectives for finding inherently robust solutions using QCSP transformation through interval analysis. In order to demonstrate the approach, an example of design of rigid flange coupling with a variable number of bolts and a choice of bolts from ISO M standard has been resolved and demonstrated
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