A general formula for the Magnus expansion in terms of iterated integrals of right-nested commutators

We present a general expression for any term of the Magnus series as an iterated integral of a linear combination of independent right-nested commutators with given coefficients. The relation with the Malvenuto--Reutenauer Hopf algebra of permutations is also discussed.Comment: 16 page

Economic Regions Based on the Agglomeration Economics: an Evaluation for the Spanish Case.

What is region? From an economic point of view, a region is a unit in which capital and labour move freely and goods and services are totally open to trade with other regions without any frontiers or limitations. The openness of the regions and their interaction with other regions are their main characteristics. From a statistical point of view internal homogeneity and also heterogeneity between the regions are both desirable properties of a set of regions. The objective of this chapter is revise the concept of region and propose a division of the territory which satisfy the statistical and economical region concept requirements in the way of propose a classification that has economic theoretical meaning but, at the same time, satisfy the internal homogeneity and heterogeneity among classes. Using micro data from the latest Census available, the Spanish territory can be divided into functional regions that emphasize the importance of location and agglomeration economies (a classification with theoretical economic meaning). A set of contrast and indexes is applied to prove that, when studying labor economic issues, such classification based on economic criteria results on more convenient regions than the administrative ones commonly used.

MAPS OF CONTINUOUS SPATIAL DEPENDENCE

Heterogeneity is one of the distinguishing features in spatial econometric models. It is a frequent problem in applied work and can be very damaging for statistical inference. In this paper, we focus on the problems implied by the existence of instabilities in the mechanism of spatial dependence in a spatial lag model, assuming that the other terms of the specification remain stable. We begin the discussion with the role played by the algorithms of local estimation in detecting the instabilities. Problems appear when one must decide what to do once the existence of heterogeneity has been confirmed. The logical reaction is trying to parameterize this lack of stability. However, the solution is not obvious. Assuming that a set of indicators related to the problem has been identified, we propose a simple technique to deal with the unknown functional form. In the final part of the paper, we present some Monte Carlo evidence and an application to evaluate the instability in the mechanisms of spatial dependence in the convergence process of the European Regions.DEPENDENCE, LOCAL ESTIMATION, MONTE-CARLO, SPATIAL INSTABILITY

The use of computers for graduate education in Project Management. Improving the integration to the industry.

This paper presents an initiative for monitoring the competence acquisition by a team of students with different backgrounds facing the experience of being working by projects and in a project. These students are graduated bachelor engineering are inexperienced in the project management field and they play this course on a time-shared manner along with other activities. The goal of this experience is to increase the competence levels acquired by using an structured web based portfolio tool helping to reinforce how relevant different project management approaches can result for final products and how important it becomes to maintain the integration along the project. Monitoring is carried out by means of have a look on how the work is being done and measuring different technical parameters per participant. The use of this information could make possible to bring additional information to the students involved in terms of their individual competencies and the identification of new opportunities of personal improvement. These capabilities are strongly requested by companies in their daily work as well as they can be very convenient too for students when they try to organize their PhD work