The odds ratio measure is used in health and social surveys where the odds of a certain event is to be compared between two populations. It is defined using logistic regression, and requires that data from surveys are accompanied by their weights. A
nonparametric estimation method that incorporates survey weights and auxiliary information may improve the precision of the odds ratio estimator. It consists in $B$-spline calibration which can handle the nonlinear structure of the parameter. The variance is estimated through linearization. Implementation is possible through standard survey softwares. The gain in precision depends on the data as shown on two examples.
In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame $cF$ for $hilcongC^d$ we compute those dual frames $cG$ of $cF$ that are optimal perturbations of the canonical dual frame for $cF$ under certain
restrictions on the norms of the elements of $cG$. On the other hand, for a fixed finite frame $cF={f_j}_{jinIn}$ for $hil$ we compute those invertible operators $V$ such that $V^*V$ is a perturbation of the identity and such that the frame $Vcdot cF={V,f_j}_{jinIn}$ - which is equivalent to $cF$ - is optimal among such perturbations of $cF$. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskiis inequality in terms of log-majorization and a characterization of the case of equality.
In this paper we consider two problems in frame theory. On the one hand, given a set of vectors $mathcal F$ we describe the spectral and geometrical structure of optimal completions of $mathcal F$ by a finite family of vectors with prescribed norms,
where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Bendetto-Fickus frame potential. On the other hand, given a fixed frame $mathcal F$ we describe explicitly the spectral and geometrical structure of optimal frames $mathcal G$ that are in duality with $mathcal F$ and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.
The relationship between star formation and super-massive black hole growth is central to our understanding of galaxy formation and evolution. Hyper-Luminous Infrared Galaxies (HLIRGs) are unique laboratories to investigate the connection between sta
rburst (SB) and Active Galactic Nuclei (AGN), since they exhibit extreme star formation rates, and most of them show evidence of harbouring powerful AGN. Our previous X-ray study of a sample of 14 HLIRGs shows that the X-ray emission of most HLIRGs is dominated by AGN activity. To improve our estimate of the relative contribution of the AGN and SB emission to its total bolometric output, we have built broad band spectral energy distributions (SEDs) for these HLIRGs, and we have fitted empirical AGN and SB templates to these SEDs. In broad terms, most sources are well fitted using this method, and we found AGN and SB contributions similar to those obtained by previous studies of HLIRGs. We have classified the HLIRGs SEDs in two groups, named class A and class B. Class A HLIRGs show a flat SED from the optical to the infrared energy range. Three out of seven class A sources can be modelled with a pure luminosity-dependent QSO template, while the rest of them require a type 1 AGN template and a SB template. The SB component is dominant in three out of four class A objects. Class B HLIRGs show SEDs with a prominent and broad IR bump. These sources can not trivially be modelled with a combination of pure AGN and pure SB, they require templates of composite objects, suggesting that >50% of their emission comes from stellar formation processes. We propose that our sample is actually composed by three different populations: very luminous QSO, young galaxies going through their maximal star formation period and the high luminosity tail of ULIRG population distribution.
We have theoretically and experimentally address the possible tandem electro-optical modulator configurations that can be employed to implement Frequency Coded Quantum Key Distribution systems (FC-QKD). A closed and general formulation of the end to
end field propagation in a dispersion compensated FC-QKD optical fiber system under the low modulation index regime is presented which accounts for all the possible tandem combinations. The properties and the parameter selection of the modulators to achieve each one are summarized. We also address which protocol (B92, BB84 or either) is feasible to be implemented with each configuration. The results confirm those reported for the configurations previously reported in the literature and, at the same time, show the existence of four novel tandem modulator configurations that can also be employed. We have also provided experimental evidence of the successful operation of the novel configurations that confirm the behavior predicted by the theoretical results.
