Infinite dimensional Lie algebras in 4D conformal quantum field theory

The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V_m(x,y), where the m span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite dimensional Lie algebra: a central extension of sp(infty,R) corresponding to the field R of reals, of u(infty,infty) associated to the field C of complex numbers, and of so*(4 infty) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N), and U(N,H)=Sp(2N), respectively.Comment: 16 pages, with minor improvements as to appear in J. Phys.

Global existence results for nonlinear Schrodinger equations with quadratic potentials

We prove that no finite time blow up can occur for nonlinear Schroedinger equations with quadratic potentials, provided that the potential has a sufficiently strong repulsive component. This is not obvious in general, since the energy associated to the linear equation is not positive. The proof relies essentially on two arguments: global in time Strichartz estimates, and a refined analysis of the linear equation, which makes it possible to use continuity arguments and to control the nonlinear effects.Comment: Some typos fixed, Proposition 1.1 extended. Final version to appear in DCD

Learning the optimal buffer-stock consumption rule of Carroll

This article questions the rather pessimistic conclusions of Allen et Carroll (2001) about the ability of consumer to learn the optimal buffer-stock based consumption rule. To this aim, we develop an agent based model where alternative learning schemes can be compared in terms of the consumption behaviour that they yield. We show that neither purely adaptive learning, nor social learning based on imitation can ensure satisfactory consumption behaviours. By contrast, if the agents can form adaptive expectations, based on an evolving individual mental model, their behaviour becomes much more interesting in terms of its regularity, and its ability to improve performance (which is as a clear manifestation of learning). Our results indicate that assumptions on bounded rationality, and on adaptive expectations are perfectly compatible with sound and realistic economic behaviour, which, in some cases, can even converge to the optimal solution. This framework may therefore be used to develop macroeconomic models with adaptive dynamics.Consumption decisions; Learning; Expectations; Adaptive behaviour, Computational economics

An analysis of income polarization in rural and urban China

The purpose of this article is to contribute to the analysis of Chinese income inequality by focusing more specifically on income polarization, which captures both alienation (i.e. heterogeneity between income groups) and identification (i.e. homogeneity within groups). The empirical investigations conducted as part of this research are based on the China Health and Nutrition Survey data from 1989 to 2006 and indicate that Chinese household income is strongly polarized. After a period of stagnation between 1989 and 1997, the degree of polarization increased significantly between 1997 and 2006, indicating the constitution of identified groups in middle and upper income ranges. Although the level of income polarization is higher in rural areas, the increase in polarization is far more conspicuous in urban areas, suggesting that the risk of social tensions is more pregnant in Chinese cities. The analysis of the sources of income polarization in rural areas shows that the increase in polarization is closely linked to non agricultural opportunities. In urban areas, the emergence of identified groups in middle and upper income classes can be explained both by the sharp decline in subsidies and by the liberalization of the urban labor market and state enterprises.inequality, polarization, kernel density, China

Clustering of categorical variables around latent variables

In the framework of clustering, the usual aim is to cluster observations and not variables. However the issue of variable clustering clearly appears for dimension reduction, selection of variables or in some case studies (sensory analysis, biochemistry, marketing, etc.). Clustering of variables is then studied as a way to arrange variables into homogeneous clusters, thereby organizing data into meaningful structures. Once the variables are clustered into groups such that variables are similar to the other variables belonging to their cluster, the selection of a subset of variables is possible. Several specific methods have been developed for the clustering of numerical variables. However concerning categorical variables, much less methods have been proposed. In this paper we extend the criterion used by Vigneau and Qannari (2003) in their Clustering around Latent Variables approach for numerical variables to the case of categorical data. The homogeneity criterion of a cluster of categorical variables is defined as the sum of the correlation ratio between the categorical variables and a latent variable, which is in this case a numerical variable. We show that the latent variable maximizing the homogeneity of a cluster can be obtained with Multiple Correspondence Analysis. Different algorithms for the clustering of categorical variables are proposed: iterative relocation algorithm, ascendant and divisive hierarchical clustering. The proposed methodology is illustrated by a real data application to satisfaction of pleasure craft operators.clustering of categorical variables, correlation ratio, iterative relocation algorithm, hierarchical clustering

Rotation in Multiple Correspondence Analysis: a planar rotation iterative procedure

Multiple Correspondence Analysis (MCA) is a well-known multivariate method for statistical description of categorical data (see for instance Greenacre and Blasius, 2006). Similarly to what is done in Principal Component Analysis (PCA) and Factor Analysis, the MCA solution can be rotated to increase the components simplicity. The idea behind a rotation is to find subsets of variables which coincide more clearly with the rotated components. This implies that maximizing components simplicity can help in factor interpretation and in variables clustering. In PCA, the probably most famous rotation criterion is the varimax one introduced by Kaiser (1958). Besides, Kiers (1991) proposed a rotation criterion in his method named PCAMIX developed for the analysis of both numerical and categorical data, and including PCA and MCA as special cases. In case of only categorical data, this criterion is a varimax-based one relying on the correlation ratio between the categorical variables and the MCA numerical components. The optimization of this criterion is then reached by the algorithm of De Leeuw and Pruzansky (1978). In this paper, we give the analytic expression of the optimal angle of planar rotation for this criterion. If more than two principal components are to be retained, similarly to what is done by Kaiser (1958) for PCA, this planar solution is computed in a practical algorithm applying successive pairwise planar rotations for optimizing the rotation criterion. A simulation study is used to illustrate the analytic expression of the angle for planar rotation. The proposed procedure is also applied on a real data set to show the possible benefits of using rotation in MCA.categorical data, multiple correspondence analysis, correlation ratio, rotation, varimax criterion

Sustainable coalitions in the commons

It is well known that the non-cooperation among agents harvesting a renewable resource is critical for its sustainable management. The present paper gives insights on the complex balance between coalitions structure, resource state or dynamics and agents’ heterogeneity to avoid bio-economic collapses. A model bringing together coalition games and a viability approach is proposed to focus on the compatibility between bio-economic constraints and an exploited common stock dynamics. It is examined to what extent cooperation promotes sustainability. Based on the Shapley value, a measure of the marginal contribution of the users to the sustainability of the resource is proposed. It suggests that the stability of the grand coalition occurs for large enough stocks. By contrast, for lower levels of resource, the most efficient user plays the role of a dictator.Renewable resource, dynamic game, coalition, maxmin strategy, shapley value, viability kernel

Elitism and Stochastic Dominance

Stochastic dominance has been typically used with a special emphasis on risk and in-equality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance ap-proach goes far beyond risk and inequality measurement provided suitable adaptations be made. We apply in the paper the stochastic dominance approach to the measurement of elitism which may be considered the opposite of egalitarianism. While the usual stochastic dominance quasi-orderings attach more value to more equal and more effi-cient distributions, our criteria ensure that, the more unequal and the more efficient the distribution, the higher it is ranked. Two instances are provided by (i) comparisons of scientific performance across institutions like universities or departments, and (ii) com-parisons of affluence as opposed to poverty between countries.Decumulative Distribution Functions, Stochastic Dominance, Regressive Transfers, Elitism, Scientific Performance, Affluence

Economic Growth, inequality and environment quality: An empirical analysis applied to developing and transition countries

This article aims at examining the relationship between social inequalities and pollution. On the one hand, it proposes a survey which shows that from a theoretical point of view, a decrease in inequality has an undetermined effect on environment. On the other hand, on the basis of these theoretical considerations, we propose an econometric analysis based on panel data for developing and transition countries during the period 1988-2003. More precisely, we examine the effect of income inequalities on the degree of local pollution (sulphur dioxide emissions and organic water pollution) by integrating Gini index in the formulation of environmental Kuznets curve. Then, two effects may be tested: (i) a direct effect of inequalities on pollution; (ii) an indirect effect by which the degree of inequality influence pollution by his negative impact on political freedoms.pollution; inequality; environmental Kuznets curve; panel data