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 $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.

HouSI: Heuristic for delimitation of housing submarkets and price homogeneous areas

This paper seeks to address the problem of the empirical identification of housing market segmentation,once we assume that submarkets exist. The typical difficulty in identifying housing submarkets when dealing with many locations is the vast number of potential solutions and, in such cases, the use of the Chow test for hedonic functions is not a practical solution. Here, we solve this problem by undertaking an identification process with a heuristic for spatially constrained clustering, the"Housing Submarket Identifier" (HouSI). The solution is applied to the housing market in the city of Barcelona (Spain), where we estimate a hedonic model for fifty thousand dwellings aggregated into ten groups. In order to determine the utility of the procedure we seek to verify whether the final solution provided by the heuristic is comparable with the division of the city into ten administrative districts.

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Social capital and government in the production of public goods

As a response to the rapidly growing empirical literature on social capital and the evidence of its correlation with government performance, we build a theoretical framework to study the interactions between social capital and government's action. This paper presents a model of homogeneous agents in an overlapping generations framework incorporating social capital as the values transmitted from parent to child. The government's role is to provide public goods. First, government expenditure is exogenously given. Then, it will be chosen at the preferred level of the representative agent. For both setups the equilibrium outcomes are characterized and the resulting dynamics studied. Briefly we include an analysis of the effect of productivity growth on the evolution of social capital. The results obtained caution caution against both the crowding out effect of the welfare state and the impact of sustained economic growth on social capital.

Regional decomposition of CO2 emissions in the world: a cluster analysis

The purpose of this paper is to study the possible differences among countries as CO2 emitters and to examine the underlying causes of these differences. The starting point of the analysis is the Kaya identity, which allows us to break down per capita emissions in four components: an index of carbon intensity, transformation efficiency, energy intensity and social wealth. Through a cluster analysis we have identified five groups of countries with different behavior according to these four factors. One significant finding is that these groups are stable for the period analyzed. This suggests that a study based on these components can characterize quite accurately the polluting behavior of individual countries, that is to say, the classification found in the analysis could be used in other studies which look to study the behavior of countries in terms of CO2 emissions in homogeneous groups. In this sense, it supposes an advance over the traditional regional or rich-poor countries classifications .

Modelo de un grupo de robots colaboradores cazadores

El nombre d'aplicacions dels microrobots en biomedicina creix a mesura que el seu desenvolupament avança. Entre elles hi ha les consistents a examinar cèl·lules amb microrobots cooperants. En aquest treball es presenta un prototip a escala d'aquest problema, convenientment simplificat: dos robots tracten d'agafar una pilota que representa la cèl·lula que s'examina. Com a resultat, s'ha obtingut un algorisme deliberatiu per a la resolució d'aquest problema amb robots homogenis.

Free Mobility and Taste-Homogeneity of Jurisdiction Structures

We consider a population of agents distributed on the unit interval. Agents form jurisdictions in order to provide a public facility and share its costs equally. This creates an incentive to form large entities. Individuals also incur a transportation cost depending on their location and that of the facility which makes small jurisdictions advantageous. We consider a fairly general class of distributions of agents and generalize previous versions of this model by allowing for non-linear transportation costs. We show that, in general, jurisdictions are not necessarily homogeneous. However, they are if facilities are always intraterritory and transportation costs are superadditive. Superadditivity can be weakened to strictly increasing and strictly concave when agents are uniformly distributed. Keywords: Consecutiveness, stratification, local public goods, coalition formation, country formation. JEL Classification: C71 (Cooperative Games), D71 (Social Choice; Clubs; Committees; Associations), H73 (Interjurisdictional Differentials and Their Effects).

Series enlazadas de algunos agregados económicos nacionales y regionales, 1955-2007 Versión 2.1

I construct "homogeneous" series of GVA at current and constant prices, employment and population for the Spain and its regions covering the period 1955-2007. The series are obtained by linking the Regional Accounts of the National Statistical Institute with the series constructed by Julio Alcaide and his team for the BBVA Foundation. The "switching point" at which this last source stops being used as a reference to construct the linked series is determined using a procedure that allows me to estimate which of the two competing series would produce an estimator with the lowest MSE when it is used as dependent variable in a regression on an arbitrary independent variable. To the extent that it is possible, the difference between the two series found at the point of linkage is distributed between the initial levels of the older series and its subsequent growth using external estimates of the relevant variables at the beginning of the sample period.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

The Division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.

Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.

Series enlazadas de empleo asalariado y rentas del trabajo regionales (RegDat versión 2.2)

I construct "homogeneous" series of salaried employment, employee compensation and total labor income for Spain and its regions covering the period 1955-2008. I also estimate labor's share in regional and national GVA and construct an indicator of the average cost of labor including both employees and non-salaried workers.

Desarrollo de una colección de Líneas Casi Isogénicas (NIL) para el estudio de caracteres de interés agronómico en especies del género Fragaria

Fragaria vesca posee varias características que la hacen interesante como especie modelo en la familia Rosaceae. Además, su naturaleza diploide permite sortear la complejidad genética de la fresa cultivada. Considerando que los genomas de las especies diploides y octoploides de Fragaria mantienen una relación de sintenia y colinearidad, estamos desarrollando una colección de Líneas Casi Isogénicas (NIL) en Fragaria diploide, usando Fragaria bucharica, una variedad asiática, como donante de introgresiones y Fragaria vesca var. Reine des Vallées, una variedad francesa comúnmente cultivada en España para usos industriales, como parental recurrente. Para obtener introgresiones de F. bucharica en un fondo genético homogéneo de F. vesca, se desarrolló un retrocruzamiento y se obtuvo una población BC1 que fue analizada para la presencia de alelos de F. bucharica a lo largo de los 7 grupos de ligamiento (LG) del mapa de referencia de Fragaria. Los individuos con bajo número de introgresiones de gran tamaño, que en conjunto abarcaron todo el genoma de F. bucharica, fueron seleccionados y retrocruzados con el parental recurrente. La descendencia fue analizada para los loci segregantes y los individuos BC2 con 1 ó 2 introgresiones fueron seleccionados como líneas donadoras de introgresiones de las NIL. Hasta el momento se han descrito tres fenotipos dominantes diferentes bajo condiciones de invernadero en varias NIL heterozigóticas: Las plantas con introgresiones en LG2 presentan estolones. Las plantas con introgresiones en LG1 y LG3 presentan floración temprana. Las plantas con introgresiones en LG6 presentan floración estacional. Actualmente se está trabajando en la selección y caracterización de introgresiones de pequeño tamaño mediante la autofecundación de las líneas seleccionadas. La caracterización fenotípica de los recombinantes seleccionados permitirá localizar y estimar los patrones de herencia de los genes implicados en los caracteres descritos, además de la identificación de nuevos caracteres recesivos que aparecerán en homozigosis.