The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive

The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.

Wage inequality and economic growth in Mexican regions

Only a few studies have analysed the relationship between intraregional inequality and growth, although several studies have measured inequality at the regional level. The objective of this paper is to analyse the relationship between income (wage) inequality and economic growth in different regions of Mexico. We also try to identify factors that explain the variation of intra-regional inequality across Mexican regions and over time. Using macroeconomic databases and publicly available microdata, we apply techniques used in the fields of statistics and econometrics to obtain robust evidence on the relationship between growth and inequality. Our aim is to provide policy recommendations to support the design and implementation of growth-promoting measures thatavoid the exclusion of certain social groups. This paper provides reasons to use a spatial approach and an analysis of particular regions to avoid «one size fits all» policy recommendations.

Sticky income inequality in the Spanish transition (1973-1990)

This paper investigates the evolution of income inequality in Spain during its transition to democracy, suggesting a method for the correction of under-reporting of earnings and profits in the Household Budget Surveys’ data. The contribution is twofold: the methodological proposal, based on income expenditure discrepancy and scaling-up to National Accounts, improves on previous work, and can be convenient for similar historical sources in other countries. Secondly, its application results in an alternative history of the distribution of income in this case, changing the levels and also the observed trend. Previous literature asserted a substantial equalization, related to the democratization process, while after the adjustment inequality in disposable income is shown to have been quite persistent.

The International Distribution of Energy Intensities: some synthetic results

The paper examines the international distribution of energy intensities as a conventional proxy indicator of energy efficiency and sustainability in the consumption of resources, by employing some descriptive tools from the analysis of inequality and polarization. The analysis specifically focuses on the following points: firstly, inequalities are evaluated synthetically based on diverse summary measures and Lorenz curves; secondly, different factorial decompositions are undertaken that assist in investigating some explanatory factors (weighting factors, multiplicative factors and decomposition by groups); and thirdly, an analysis is made of the polarization of intensities when groups of countries are defined endogenously and exogenously. The results obtained have significant implications from both academic and political perspectives.

Eliminació d'artefactes en EGG mitjançant l'ús de la Multivariate Empirical Mode Decomposition

La tècnica de l’electroencefalograma (EEG) és una de les tècniques més utilitzades per estudiar el cervell. En aquesta tècnica s’enregistren els senyals elèctrics que es produeixen en el còrtex humà a través d’elèctrodes col•locats al cap. Aquesta tècnica, però, presenta algunes limitacions a l’hora de realitzar els enregistraments, la principal limitació es coneix com a artefactes, que són senyals indesitjats que es mesclen amb els senyals EEG. L’objectiu d’aquest treball de final de màster és presentar tres nous mètodes de neteja d’artefactes que poden ser aplicats en EEG. Aquests estan basats en l’aplicació de la Multivariate Empirical Mode Decomposition, que és una nova tècnica utilitzada per al processament de senyal. Els mètodes de neteja proposats s’apliquen a dades EEG simulades que contenen artefactes (pestanyeigs), i un cop s’han aplicat els procediments de neteja es comparen amb dades EEG que no tenen pestanyeigs, per comprovar quina millora presenten. Posteriorment, dos dels tres mètodes de neteja proposats s’apliquen sobre dades EEG reals. Les conclusions que s’han extret del treball són que dos dels nous procediments de neteja proposats es poden utilitzar per realitzar el preprocessament de dades reals per eliminar pestanyeigs.