Encoding databases satisfying a given set of dependencies

Consider a relation schema with a set of dependency constraints. A fundamental question is what is the minimum space where the possible instances of the schema can be "stored". We study the following model. Encode the instances by giving a function which maps the set of possible instances into the set of words of a given length over the binary alphabet in a decodable way. The problem is to find the minimum length needed. This minimum is called the information content of the database. We investigate several cases where the set of dependency constraints consist of relatively simple sets of functional or multivalued dependencies. We also consider the following natural extension. Is it possible to encode the instances such a way that small changes in the instance cause a small change in the code. © 2012 Springer-Verlag

The Lamé Class of Lorenz Curves.

In this paper, the class of Lamé Lorenz curves is studied. This family has the advantage of modeling inequality with a single parameter. The family has a double motivation: it can be obtain from an economic model and from simple transformations of classical Lorenz curves. The underlying cumulative distribution functions have a simple closed form, and correspond to the Singh-Maddala and Dagum distributions, which are well known in the economic literature. The Lorenz order is studied and several inequality and polarization measures are obtained, including Gini, Donaldson-Weymark-Kakwani, Pietra and Wolfson indices. Some extensions of the Lamé family are obtained. Fitting and estimation methods under two different data configuration are proposed. Empirical applications with real data are given. Finally, some relationships with other curves are included.The authors thank to Ministerio de Econom a y Competitividad, project ECO2010-15455, for partial support. The second author thanks to the Ministerio de Educaci on (FPU AP-2010-4907) for partial support. We are grateful for the constructive suggestions provided by the reviewers, which improved the paper

Dynamical systems theory sheds new light on compound climate extremes in Europe and Eastern North America

International audienceWe propose a novel approach to the study of compound extremes , grounded in dynamical systems theory. Specifically, we present the co-recurrence ratio (α), which elucidates the dependence structure between variables by quantifying their joint recurrences. This approach is applied to daily climate extremes, derived from the ERA-Interim reanalysis over the 1979-2018 period. The analysis focuses on concurrent (i.e. same-day) wet (total precipitation) and windy (10m wind gusts) extremes in Europe and concurrent cold (2m temperature) extremes in Eastern North America and wet extremes in Europe. Results for wet and windy extremes in Europe, which we use as a test-bed for our methodology, show that α peaks during boreal winter. High α values correspond to wet and windy extremes in northwestern Europe, and to large-scale conditions resembling the positive phase of the North Atlantic Oscillation (NAO). This confirms earlier findings which link the positive NAO to a heightened frequency of extra-tropical cyclones impacting northwestern Europe. For the Eastern North America-Europe case, α extremes once again reflect concurrent climate extremes-in this case cold extremes over North America and wet extremes over Europe. Our analysis provides detailed spatial information on regional hotspots for these compound ex-