Portae Inferi Non Praevalebunt

To believe that a latent and very discrete process continuously improves the quality of life all around is called \u201cto have a positive attitude\u201d. However, there is enough matter all-around for generating some stress and misunderstanding. We need air-conditioners and the more the climate is warming, the faster we will be in the hell. Worrisome data are available about biodiversity. Our earliest ancestor Sahelanthropus tchadensis was living about 7 million years ago. Compared to other species, we are relatively young. A site characterized by low biodiversity may be incompatible with a species (Homo sapiens) born in a very biodiverse space-time. Are we sure that system Earth will be sensible to our will and respond to our influence keeping us in its evolving germination forever? As every species in an expansion phase, humans are experiencing a collective, optimistic, unconscious prospect of immortality. On this point, why do not ask our peers for advice and consider a worldwide organized riposte for: a) Have less impacting actions on the climate, or at least try to stem those too impacting in progress; b) Better use the natural and human resources we own, avoiding excessive losses of time and money; c) Planning the continuity of the humankind, following common hopeful rules. Easier to say than to do, of course

Structure preserving stochastic Galerkin methods for Fokker-Planck equations with background interactions

This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution. The proposed methods are capable to preserve physical properties in the approximation of statistical moments of the problem like nonnegativity, entropy dissipation and asymptotic behaviour of the expected solution. The introduced methods are second order accurate in the transient regimes and high order for large times. We present applications of the developed schemes to the case of fixed and dynamic background distribution for models of collective behaviour

Discrete Choice with Social Interactions and Endogenous Memberships

This paper tackles the issue of self-selection in social interactions models. I develop a theory of sorting and behavior, when the latter is subject to social influences, extending the model developed by Brock and Durlauf (2001a, 2003) to allow for equilibrium group formation. Individuals choose a group, and a behavior subject to an endogenous social effect. The latter turns out to be a segregating force, and stable equilibria are stratified. The sorting process may induce, inefficiently, multiple behavioral equilibria. Such a theory serves as a means to solve identification and selection problems that may undermine the empirical detection of social effects on individual behavior. I exploit the theoretical model to build a nonlinear (in the social effect) selection correction term. Such a term allows identification, and solves the selection problem that arises when individuals can choose the group whose effect the researcher is trying to disentangle. The resulting econometric model, although relying on strict parametric assumptions, indicates a viable alternative when reliable instrumental variables are not available, or randomized experiments not possible.social interactions, neighborhood effects, sorting, self-selection, nested logit, identification of social effects