Search results for "Descriptive set theory"
showing 10 items of 94 documents
Cosmological Vector Perturbations and CMB Anomalies
2010
Recently, it has been proved that large scale vector modes could explain most of the CMB anomalies in the first temperature multipoles. Some divergenceless (vortical) velocity fields–which are superimpositions of vector modes–can explain both the alignment of the second and third multipoles and the planar character of the octopole. In this paper we comment: (a) some papers trying to account for the mentioned anomalies, (b) our explanation based on vector modes, and (c) some current ideas about the possible origin of these modes.
The loop-tree duality at work
2014
We review the recent developments of the loop-tree duality method, focussing our discussion on analysing the singular behaviour of the loop integrand of the dual representation of one-loop integrals and scattering amplitudes. We show that within the loop-tree duality method there is a partial cancellation of singularities at the integrand level among the different components of the corresponding dual representation. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
Target localization in the three-dimensional space by wavelength multiplexing.
2002
A method to localize a target in the three-dimensional space is presented. Each different position of the target on the depth axis produces, when captured with a CCD camera, an image of a different size on its sensor plane. The size of this image depends only on the distance between the target and the camera. The use of a white light optical correlator that gives us a different response depending on the scale of the input image permits us to know the depth position of the particular target. The obtained results demonstrate the utility of the newly proposed method.
Unified atmospheric neutrino passing fractions for large-scale neutrino telescopes
2018
The atmospheric neutrino passing fraction, or self-veto, is defined as the probability for an atmospheric neutrino not to be accompanied by a detectable muon from the same cosmic-ray air shower. Building upon previous work, we propose a redefinition of the passing fractions by unifying the treatment for muon and electron neutrinos. Several approximations have also been removed. This enables performing detailed estimations of the uncertainties in the passing fractions from several inputs: muon losses, cosmic-ray spectrum, hadronic-interaction models and atmosphere-density profiles. We also study the passing fractions under variations of the detector configuration: depth, surrounding medium a…
Minimal Absent Words in Rooted and Unrooted Trees
2019
We extend the theory of minimal absent words to (rooted and unrooted) trees, having edges labeled by letters from an alphabet \(\varSigma \) of cardinality \(\sigma \). We show that the set \(\text {MAW}(T)\) of minimal absent words of a rooted (resp. unrooted) tree T with n nodes has cardinality \(O(n\sigma )\) (resp. \(O(n^{2}\sigma )\)), and we show that these bounds are realized. Then, we exhibit algorithms to compute all minimal absent words in a rooted (resp. unrooted) tree in output-sensitive time \(O(n+|\text {MAW}(T)|)\) (resp. \(O(n^{2}+|\text {MAW}(T)|)\) assuming an integer alphabet of size polynomial in n.
In between the inequalities of Sobolev and Hardy
2015
We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions.
QCD matching conditions at thresholds
1993
The use of MS-like renormalization schemes in QCD requires an implementation of nontrivial matching conditions across thresholds, a fact often overlooked in the literature. We shortly review the use of these matching conditions in QCD and check explicitly that the prediction for $\alpha_s(M_Z)$, obtained by running the strong coupling constant from the $M_\tau$ scale, does not substantially depend on the exact value of the matching point chosen in crossing the $b$-quark threshold when the appropriate matching conditions are taken into account.
Consistent measurements of alpha(s) from precise oriented event shape distributions
2000
An updated analysis using about 1.5 million events recorded at $\sqrt{s} = M_Z$ with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in ${\cal O} (\alpha_s^2)$ including the event orientation. A combined fit of $\alpha_s$ and of the renormalization scale $x_{\mu}$ in $\cal O(\alpha_s^2$) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is $\alpha_s(M_Z^2) = 0.1174 \pm 0.0026$. The final result, derived from the jet cone energ…
Successive Reduction of Arms in Multi-Armed Bandits
2011
The relevance of the multi-armed bandit problem has risen in the past few years with the need for online optimization techniques in Internet systems, such as online advertisement and news article recommendation. At the same time, these applications reveal that state-of-the-art solution schemes do not scale well with the number of bandit arms. In this paper, we present two types of Successive Reduction (SR) strategies - 1) Successive Reduction Hoeffding (SRH) and 2) Successive Reduction Order Statistics (SRO). Both use an Order Statistics based Thompson Sampling method for arm selection, and then successively eliminate bandit arms from consideration based on a confidence threshold. While SRH…
Extraction of Endmembers from Spectral Mixtures
1999
Abstract Linear spectral mixture modeling (LSMM) divides each ground resolution element into its constituent materials using endmembers which represent the spectral characteristics of the cover types. However, it is difficult to identify and estimate the spectral signature of pure components or endmembers which form the scene, since they vary with the scale and purpose of the study. We propose three different methods to estimate the spectra of pure components from a set of unknown mixture spectra. Two of the methods consist in different optimization procedures based on objective functions defined from the coordinate axes of the dominant factors. The third one consists in the design of a neu…