From Bosonic Grand-Canonical Ensembles to Nonlinear Gibbs Measures

In a recent paper, in collaboration with Mathieu Lewin and Phan Th{\`a}nh Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This text summarizes these findings. It focuses on the simplest, but most physically relevant, case we could treat so far, namely that of the defocusing cubic NLS functional on a 1D interval. The measure obtained in the limit, which (almost) lives over H^{1/2} , has been previously shown to be invariant under the NLS flow by Bourgain.Comment: This is the text of a Laurent Schwartz X-EDP seminar I gave in November 2014. It summarizes some of the results of arXiv:1410.033

General covariance of the non-abelian DBI-action: Checks and Balances

We perform three tests on our proposal to implement diffeomorphism invariance in the non-abelian D0-brane DBI action as a basepoint independence constraint between matrix Riemann normal coordinate systems. First we show that T-duality along an isometry correctly interchanges the potential and kinetic terms in the action. Second, we show that the method to impose basepoint independence using an auxiliary dN^2-dimensional non-linear sigma model also works for metrics which are curved along the brane, provided a physical gauge choice is made at the end. Third, we show that without alteration this method is applicable to higher order in velocities. Testing specifically to order four, we elucidate the range of validity of the symmetrized trace approximation to the non-abelian DBI action.Comment: LaTeX, 22 page

Temporal Feature Selection with Symbolic Regression

Building and discovering useful features when constructing machine learning models is the central task for the machine learning practitioner. Good features are useful not only in increasing the predictive power of a model but also in illuminating the underlying drivers of a target variable. In this research we propose a novel feature learning technique in which Symbolic regression is endowed with a ``Range Terminal\u27\u27 that allows it to explore functions of the aggregate of variables over time. We test the Range Terminal on a synthetic data set and a real world data in which we predict seasonal greenness using satellite derived temperature and snow data over a portion of the Arctic. On the synthetic data set we find Symbolic regression with the Range Terminal outperforms standard Symbolic regression and Lasso regression. On the Arctic data set we find it outperforms standard Symbolic regression, fails to beat the Lasso regression, but finds useful features describing the interaction between Land Surface Temperature, Snow, and seasonal vegetative growth in the Arctic

Software as a service: Undo

This paper proposes a highly automated mechanism to build an undo facility into a new or existing system easily. Our proposal is based on the observation that for a large set of operators it is not necessary to store in-memory object states or executed system commands to undo an action; the storage of input data is instead enough. This strategy simplifies greatly the design of the undo process and encapsulates most of the functionalities required in a framework structure similar to the many object-oriented programming frameworks

Service Oriented Architecture for Undo Functionality

This paper proposes a highly automated mechanism to build an undo facility into a new or existing system easily encapsulated into a service. Our proposal is based on the observation that for a large set of operators it is not necessary to store in-memory object states or executed system commands to undo an action; the storage of input data is instead enough. The use of services strategy simplifies greatly the design of the undo process and encapsulates most of the functionalities required in a framework structure similar to the many object-oriented programming frameworks. We present a proof of concept illustrating the simplicity and reusability of the proposed framework under alignments of Software as a Service.Trabajo presentado en el VI International Conference on Research and Practical Issues of Enterprise Information Systems, realizado del 19 al 21 de septiembre en Bélgica