A quantitative approach to weighted Carleson Condition

Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea in the 80's for the operator $$\mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0$$ are obtained. As a consequence, some sufficient conditions for the boundedness of $\mathcal{M}$ in the two weight setting in the spirit of the results obtained by C. P\'erez and E. Rela and very recently by M.T. Lacey and S. Spencer for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained

Quantitative Precipitation Nowcasting: A Lagrangian Pixel-Based Approach

Short-term high-resolution precipitation forecasting has important implications for navigation, flood forecasting, and other hydrological and meteorological concerns. This article introduces a pixel-based algorithm for Short-term Quantitative Precipitation Forecasting (SQPF) using radar-based rainfall data. The proposed algorithm called Pixel- Based Nowcasting (PBN) tracks severe storms with a hierarchical mesh-tracking algorithm to capture storm advection in space and time at high resolution from radar imagers. The extracted advection field is then extended to nowcast the rainfall field in the next 3. hr based on a pixel-based Lagrangian dynamic model. The proposed algorithm is compared with two other nowcasting algorithms (WCN: Watershed-Clustering Nowcasting and PER: PERsistency) for ten thunderstorm events over the conterminous United States. Object-based verification metric and traditional statistics have been used to evaluate the performance of the proposed algorithm. It is shown that the proposed algorithm is superior over comparison algorithms and is effective in tracking and predicting severe storm events for the next few hours. © 2012 Elsevier B.V

Resolving the Quantitative-Qualitative Dilemma: A Critical Realist Approach

The philosophical issues underpinning the quantitative–qualitative divide in educational research are examined. Three types of argument which support a resolution are considered: pragmatism, false duality and warranty through triangulation. In addition a number of proposed strategies—alignment, sequencing, translation and triangulation—are critically assessed. The article concludes by suggesting that many of these ways of reconciling quantitative and qualitative methods and approaches are still deficient in relation to the development of an overarching and correct view of ontological and epistemological matters, and that critical realism offers a more coherent solution, where the reconciliation occurs at the ontological level

A Quantitative Clustering Approach to Ultrametricity in Spin Glasses

We discuss the problem of ultrametricity in mean field spin glasses by means of a hierarchical clustering algorithm. We complement the clustering approach with quantitative testing: we discuss both in some detail. We show that the elimination of the (in this context accidental) spin flip symmetry plays a crucial role in the analysis, since the symmetry hides the real nature of the data. We are able to use in the analysis disorder averaged quantities. We are able to exhibit a number of features of the low $T$ phase of the mean field theory, and to claim that the full hierarchical structure can be observed without ambiguities only on very large lattice volumes, not currently accessible by numerical simulations.Comment: 15 pages with color figure

A Latent Variable Approach to Multivariate Quantitative Trait Loci

A novel approach based on latent variable modelling is presented for the analysis of multivariate quantitative and qualitative trait loci. The approach is general in the sense that it enables the joint analysis of many kinds of quantitative and qualitative traits (including count data and censored traits) in a single modelling framework. In the framework, the observations are modelled as functions of latent variables, which are then affected by quantitative trait loci. Separating the analysis in this way means that measurement errors in the phenotypic observations can be included easily in the model, providing robust inferences. The performance of the method is illustrated using two real multivariate datasets, from barley and Scots pine