Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Glocalization as a generic entrepreneurial strategy

Nobody would deny that we today live in a globalized world. Our digitalized living daily revises our worldwide mindmaps. Thanks to free trade and travel our material and social worlds have become global as well. This radical sociocultural change has since the last decade been preached all over the world with public institutions and business-interest organizations as megaphones. Since those carrying the globalization message mainly represent nations or super-nations such as the EU, the viewpoints of lower-level actors such as regions, localities, firms and individual citizens have seldom been considered. Paternalistically (super-)national bodies have instructured its subjects, not the least the many small firms that populate the (private) economy, what action to take. The basic message is: submit to the global forces – local is not beautiful any longer.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

Generic drugs in Spain: price competition vs. moral hazard

This paper examines competition between generic and brand-name drugs in the regulated Spanish pharmaceutical market. A nested logit demand model is specified for the three most consumed therapeutic subgroups in Spain: statins (anticholesterol), selective serotonin reuptake inhibitors (antidepressants) and proton pump inhibitors (antiulcers). The model is estimated with instrumental variables from a panel of monthly prescription data from 1999 to 2005. The dataset distinguishes between three different levels of patients’ copayments within the prescriptions and the results show that the greater the level of insurance that the patient has (and therefore the lower the patient’s copayment), the lower the proportion of generic prescriptions made by physicians. It seems that the low level of copayment has delayed the penetration of generics into the Spanish market. Additionally, the estimation of the demand model suggests that the substitution rules and promotional efforts associated with the reference pricing system have increased generic market share, and that being among the first generic entrants has an additional positive effect.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

An investigation on the pay-off to generic competences for core employees in Catalan manufacturing firms

The aim of this paper is to measure the returns to human capital. We use a unique data set consisting of matched employer-employee information. Data on individuals' human capital include a set of 26 competences that capture the utilization of workers' skills in a very detailed way. Thus, we can expand the concept of human capital and discuss the type of skills that are more productive in the workplace and, hence, generate a higher payoff for the workers. The rich information on firm's and workplace characteristics allows us to introduce a broad range of controls and to improve previous research in this field. This paper gives evidence that the returns to generic competences differ depending on the position of the worker in the firm. Only numeracy skills are reward independent of the occupational status of the worker. The level of technology used by the firm in the production process does not directly increase workers’ pay, but it influences the pay-off to some of the competences. JEL Classification: J24, J31

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

Local Distance-Based Generalized Linear Models using the dbstats package for R

This paper introduces local distance-based generalized linear models. These models extend (weighted) distance-based linear models firstly with the generalized linear model concept, then by localizing. Distances between individuals are the only predictor information needed to fit these models. Therefore they are applicable to mixed (qualitative and quantitative) explanatory variables or when the regressor is of functional type. Models can be fitted and analysed with the R package dbstats, which implements several distancebased prediction methods.

Convex linear combination processes for compositions

Aitchison and Bacon-Shone (1999) considered convex linear combinations ofcompositions. In other words, they investigated compositions of compositions, wherethe mixing composition follows a logistic Normal distribution (or a perturbationprocess) and the compositions being mixed follow a logistic Normal distribution. Inthis paper, I investigate the extension to situations where the mixing compositionvaries with a number of dimensions. Examples would be where the mixingproportions vary with time or distance or a combination of the two. Practicalsituations include a river where the mixing proportions vary along the river, or acrossa lake and possibly with a time trend. This is illustrated with a dataset similar to thatused in the Aitchison and Bacon-Shone paper, which looked at how pollution in aloch depended on the pollution in the three rivers that feed the loch. Here, I explicitlymodel the variation in the linear combination across the loch, assuming that the meanof the logistic Normal distribution depends on the river flows and relative distancefrom the source origins

Studies about the atomic capabilities concept for linear control systems in physical multi-agent environments

This paper shows the impact of the atomic capabilities concept to include control-oriented knowledge of linear control systems in the decisions making structure of physical agents. These agents operate in a real environment managing physical objects (e.g. their physical bodies) in coordinated tasks. This approach is presented using an introspective reasoning approach and control theory based on the specific tasks of passing a ball and executing the offside manoeuvre between physical agents in the robotic soccer testbed. Experimental results and conclusions are presented, emphasising the advantages of our approach that improve the multi-agent performance in cooperative systems