26,802 research outputs found
Increasing the lensing figure of merit through higher order convergence moments
The unprecedented quality, the increased data set, and the wide area of ongoing and near future weak lensing surveys allows one to move beyond the standard two points statistics, thus making it worthwhile to investigate higher order probes. As an interesting step toward this direction, we explore the use of higher order moments (HOM) of the convergence field as a way to increase the lensing figure of merit (FoM). To this end, we rely on simulated convergence to first show that HOM can be measured and calibrated so that it is indeed possible to predict them for a given cosmological model provided suitable nuisance parameters are introduced and then marginalized over. We then forecast the accuracy on cosmological parameters from the use of HOM alone and in combination with standard shear power spectra tomography. It turns out that HOM allow one to break some common degeneracies, thus significantly boosting the overall FoM. We also qualitatively discuss possible systematics and how they can be dealt with
A New General Method to Generate Random Modal Formulae for Testing Decision Procedures
The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none of the proposed test generators is very satisfactory. To cope with this fact, we present a new random generation method that provides benefits over previous methods for generating empirical tests. It fixes and much generalizes one of the best-known methods, the random CNF_[]m test, allowing for generating a much wider variety of problems, covering in principle the whole input space. Our new method produces much more suitable test sets for the current generation of modal decision procedures. We analyze the features of the new method by means of an extensive collection of empirical tests
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
We introduce and study a notion of Orlicz hypercontractive semigroups. We
analyze their relations with general -Sobolev inequalities, thus extending
Gross hypercontractivity theory. We provide criteria for these Sobolev type
inequalities and for related properties. In particular, we implement in the
context of probability measures the ideas of Maz'ja's capacity theory, and
present equivalent forms relating the capacity of sets to their measure. Orlicz
hypercontractivity efficiently describes the integrability improving properties
of the Heat semigroup associated to the Boltzmann measures , when . As an application
we derive accurate isoperimetric inequalities for their products. This
completes earlier works by Bobkov-Houdr\'e and Talagrand, and provides a scale
of dimension free isoperimetric inequalities as well as comparison theorems.Comment: 76 pages, 1 figur
Minkowski Functionals of Convergence Maps and the Lensing Figure of Merit
Minkowski functionals (MFs) quantify the topological properties of a given
field probing its departure from Gaussianity. We investigate their use on
lensing convergence maps in order to see whether they can provide further
insights on the underlying cosmology with respect to the standard second-order
statistics, i.e., cosmic shear tomography. To this end, we first present a
method to match theoretical predictions with measured MFs taking care of the
shape noise, imperfections in the map reconstruction, and inaccurate
description of the nonlinearities in the matter power spectrum and bispectrum.
We validate this method against simulated maps reconstructed from shear fields
generated by the MICE simulation. We then perform a Fisher matrix analysis to
forecast the accuracy on cosmological parameters from a joint MFs and shear
tomography analysis. It turns out that MFs are indeed helpful to break the
-- degeneracy thus generating a sort of chain
reaction leading to an overall increase of the Figure of Merit.Comment: 16 pages, 5 figures. Matches published version in PR
Quantitative isoperimetric inequalities for log-convex probability measures on the line
The purpose of this paper is to analyze the isoperimetric inequality for
symmetric log-convex probability measures on the line. Using geometric
arguments we first re-prove that extremal sets in the isoperimetric inequality
are intervals or complement of intervals (a result due to Bobkov and Houdr\'e).
Then we give a quantitative form of the isoperimetric inequality, leading to a
somehow anomalous behavior. Indeed, it could be that a set is very close to be
optimal, in the sense that the isoperimetric inequality is almost an equality,
but at the same time is very far (in the sense of the symmetric difference
between sets) to any extremal sets! From the results on sets we derive
quantitative functional inequalities of weak Cheeger type
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