ALTRUISM, EGOISM AND GROUP COHESION IN A LOCAL INTERACTION MODEL

In this paper we have introduced and parameterized the concept of ?group cohesion? in a model of local interaction with a population divided into groups. This allows us to control the level of ?isolation? of these groups: We thus analyze if the degree of group cohesion is relevant to achieve an efficient behaviour and which level would be the best one for this purpose. We are interested in situations where there is a trade off between efficiency and individual incentives. This trade off is stronger when the efficient strategy or norm is strictly dominated, as in the Prisoner?s Dilemma or in some cases of Altruism. In our model we have considered that agents could choose to be Altruist of Egoist, in fact, they behave as in Eshel, Samuelson and Shaked (1998) model.Group Cohesion, Cooperation, Local Interaction, Altruism, Group selection.

Some generalizations of the notion of Lie algebra

We introduce the notion of left (and right) quasi-Loday algebroids and a "universal space" for them, called a left (right) omni-Loday algebroid, in such a way that Lie algebroids, omni-Lie algebras and omni-Loday algebroids are particular substructures.Comment: Second version. 14 pages. Included some comments about previous works related to Leibniz algebras, and updated bibliography. A new example adde

Singular random matrix decompositions: distributions.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution

Singular random matrix decompositions: Jacobians.

For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L'U, L'DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky's, L'DL and symmetric non-negative definite square root, of the cross-product matrix S = Y'Y

On Lie Algebroids and Poisson Algebras

We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe Poisson algebras by using the notions of algebroid and Lie connections

SINGULAR RANDOM MATRIX DECOMPOSITIONS: DISTRIBUTIONS.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution.