The Schur-Horn theorem for operators and frames with prescribed norms and frame operator

Let $\mathcal H$ be a Hilbert space. Given a bounded positive definite operator $S$ on $\mathcal H$, and a bounded sequence $\mathbf{c} = \{c_k \}_{k \in \mathbb N}$ of non negative real numbers, the pair $(S, \mathbf{c})$ is frame admissible, if there exists a frame $\{f_k \}_{k \in \mathbb{N}}$ on $\mathcal H$ with frame operator $S$, such that $\|f_k \|^2 = c_k$, $k \in \mathbb {N}$. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use it to get necessary conditions (and to generalize known sufficient conditions) for a pair $(S, \mathbf{c})$, to be frame admissible.Comment: To appear in Illinois Journal of Mat

Nullspaces and frames

In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms.Comment: 16 page

Weak-Type Boundedness of the Hardy–Littlewood Maximal Operator on Weighted Lorentz Spaces

The main goal of this paper is to provide a characterization of the weak-type boundedness of the Hardy–Littlewood maximal operator, M, on weighted Lorentz spaces Λpᵤ(w), whenever p > 1. This solves a problem left open in (Carro et al., Mem Am Math Soc. 2007). Moreover, with this result, we complete the program of unifying the study of the boundedness of M on weighted Lebesgue spaces and classical Lorentz spaces, which was initiated in the aforementioned monograph.Facultad de Ciencias Exacta

Risk of Dengue Incidence in Children and Adolescents in Zulia, Venezuela, using a Negative Binomial Generalized Linear Mixed Model

Introduction: Dengue is the most important arboviral disease. Its incidence has increased 30-fold over the last 50 years, causing global concerns. Studies have showed children to be the most vulnerable. Methods: Observational study using dengue cases from Zulia state, Venezuela, modelling through a Negative Binomial Generalized Linear Mixed Model (GLMM) accounting for heterogeneity in the variance via a hierarchical Bayesian framework, was done. We assessed risk factors such as age and sex. The Bayesian framework enabled the estimation of Relative Risk (RR) and a Binomial regression was run using the WinBUGS software. Results: During 2002-2008, there were 49,330 cases of dengue in Zulia state, Venezuela. Most of them (18.71%) in 2007. The model revealed that children aged from 5 to 14 y-old had 1.59-higher risk (95%CI 1.41-1.79) compared with those aged from 0-4 y-old. Those aged 25-44 years old and ≥45, have significantly less RR than the baseline category, RR 0.5228 (95%CI 0.46-0.59) and 0.3069 (95%CI 0.27-0.34). Conclusions: The findings confirmed that groups most at risk were children aged 5 to 14 years. Modelling and predicting dengue epidemiology are still a need in multiple countries, especially those at risk of newer epidemics, as is the case of Zulia and Venezuela

The CHilean Automatic Supernova sEarch (CHASE)

The CHASE project started in 2007 with the aim of providing young southern supernovae (SNe) to the Carnegie Supernova Project (CSP) and Millennium Center for Supernova Studies (MCSS) follow-up programs. So far CHASE has discovered 33 SNe with an average of more than 2.5 SNe per month in 2008. In addition to the search we are carrying out a follow-up program targeting bright SNe. Our fully automated data reduction allows us to follow the evolution on the light curve in real time, triggering further observations if something potentially interesting is detectedComment: 4 pages, 2 figures, conference proceedin

Risk of Dengue Incidence in Children and Adolescents in Zulia, Venezuela, using a Negative Binomial Generalized Linear Mixed Model

Introduction: Dengue is the most important arboviral disease. Its incidence has increased 30-fold over the last 50 years, causing global concerns. Studies have showed children to be the most vulnerable. Methods: Observational study using dengue cases from Zulia state, Venezuela, modelling through a Negative Binomial Generalized Linear Mixed Model (GLMM) accounting for heterogeneity in the variance via a hierarchical Bayesian framework, was done. We assessed risk factors such as age and sex. The Bayesian framework enabled the estimation of Relative Risk (RR) and a Binomial regression was run using the WinBUGS software. Results: During 2002-2008, there were 49,330 cases of dengue in Zulia state, Venezuela. Most of them (18.71%) in 2007. The model revealed that children aged from 5 to 14 y-old had 1.59-higher risk (95%CI 1.41-1.79) compared with those aged from 0-4 y-old. Those aged 25-44 years old and ≥45, have significantly less RR than the baseline category, RR 0.5228 (95%CI 0.46-0.59) and 0.3069 (95%CI 0.27-0.34). Conclusions: The findings confirmed that groups most at risk were children aged 5 to 14 years. Modelling and predicting dengue epidemiology are still a need in multiple countries, especially those at risk of newer epidemics, as is the case of Zulia and Venezuela

The Distance to SN 1999em from the Expanding Photosphere Method

We present optical and IR spectroscopy of the first two months of evolution of the Type II SN 1999em. We combine these data with high-quality optical/IR photometry beginning only three days after shock breakout, in order to study the performance of the ``Expanding Photosphere Method'' (EPM) in the determination of distances. With this purpose we develop a technique to measure accurate photospheric velocities by cross-correlating observed and model spectra. The application of this technique to SN 1999em shows that we can reach an average uncertainty of 11% in velocity from an individual spectrum. Our analysis shows that EPM is quite robust to the effects of dust. In particular, the distances derived from the VI filters change by only 7% when the adopted visual extinction in the host galaxy is varied by 0.45 mag. The superb time sampling of the BVIZJHK light-curves of SN 1999em permits us to study the internal consistency of EPM and test the dilution factors computed from atmosphere models for Type II plateau supernovae. We find that, in the first week since explosion, the EPM distances are up to 50% lower than the average, possibly due the presence of circumstellar material. Over the following 65 days, on the other hand, our tests lend strong credence to the atmosphere models, and confirm previous claims that EPM can produce consistent distances without having to craft specific models to each supernova. This is particularly true for the VI filters which yield distances with an internal consistency of 4%. From the whole set of BVIZJHK photometry, we obtain an average distance of 7.5+/-0.5 Mpc, where the quoted uncertainty (7%) is a conservative estimate of the internal precision of the method obtained from the analysis of the first 70 days of the supernova evolution.Comment: 68 pages, 15 tables, 22 figures, to appear in Ap