Fast alternating fitting methods for trigonometric curves for large data sets

This paper discusses and develops new methods for fitting trigonometric curves, such as circles, ellipses, and dumbbells, to data points in the plane. Available methods for fitting circles or ellipses are very sensitive to outliers in the data, and are time consuming when the number of data points is large. The present paper focuses on curve fitting methods that are attractive to use when the number of data points is large. We propose a direct method for fitting circles, and two iterative methods for fitting ellipses and dumbbell curves based on trigonometric polynomials. These methods efficiently minimize the sum of the squared geometric distances between the given data points and the fitted curves. In particular, we are interested in detecting the general shape of an object such as a galaxy or a nebula. Certain nebulae, for instance, the one shown in the experiment section, have a dumbbell shape. Methods for fitting dumbbell curves have not been discussed in the literature. The methods developed are not very sensitive to errors in the data points. The use of random subsampling of the data points to speed up the computations also is discussed. The techniques developed in this paper can be applied to fitting other kinds of curves as well

Large-scale regression with non-convex loss and penalty

We describe a computational method for parameter estimation in linear regression, that is capable of simultaneously producing sparse estimates and dealing with outliers and heavy-tailed error distributions. The method used is based on the image restoration method proposed in Huang et al. (2017) [13]. It can be applied to problems of arbitrary size. The choice of certain parameters is discussed. Results obtained for simulated and real data are presented

VAMOS: a Pathfinder for the HAWC Gamma-Ray Observatory

VAMOS was a prototype detector built in 2011 at an altitude of 4100m a.s.l. in the state of Puebla, Mexico. The aim of VAMOS was to finalize the design, construction techniques and data acquisition system of the HAWC observatory. HAWC is an air-shower array currently under construction at the same site of VAMOS with the purpose to study the TeV sky. The VAMOS setup included six water Cherenkov detectors and two different data acquisition systems. It was in operation between October 2011 and May 2012 with an average live time of 30%. Besides the scientific verification purposes, the eight months of data were used to obtain the results presented in this paper: the detector response to the Forbush decrease of March 2012, and the analysis of possible emission, at energies above 30 GeV, for long gamma-ray bursts GRB111016B and GRB120328B.Comment: Accepted for pubblication in Astroparticle Physics Journal (20 pages, 10 figures). Corresponding authors: A.Marinelli and D.Zaboro

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum