A Bayesian Framework for Modifications of Probabilistic Relational Data

The inherent uncertainty pervasive over the real world often forces business decisions to be made using uncertain data. The conventional relational model does not have the ability to handle uncertain data. In recent years, several approaches have been proposed in the literature for representing uncertain data by extending the relational model, primarily using probability theory. However, the aspect of database modification has been overlooked in these investigations. It is clear that any modification of existing probabilistic data, based on new information, amounts to the revision of one’s belief about real world objects. In this paper, we examine the aspect of belief revision and develop a generalized algorithm that can be used for modification of existing data in a probabilistic relational database

Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory

The dynamical evolution of the Hajicek $1$-form is derived in Einstein-Cartan (EC) theory. We find that like Einstein theory of gravity, the evolution equation is related to a projected part of the Einstein tensor $(\hat{G}_{ab})$ on a generic null surface $\mathcal{H}$, particularly $\hat{G}_{ab}l^a q^b_{~c}$, where $l^a$ and $q^a_{~c}$ are the outgoing null generators of $\mathcal{H}$ and the induced metric to a transverse spatial cross-section of $\mathcal{H}$ respectively. Under the {\it geodesic constraint} a possible fluid interpretation of this evolution equation is then proposed. We find that it has the structure which is reminiscent to the {\it Cosserat generalization} of the Navier-Stokes fluid provided we express the dynamical evolution equation of the Hajicek $1$-form in a set of coordinates adapted to $\mathcal{H}$ and in a local inertial frame. An analogous viewpoint can also be built under the motive that the usual material derivative for fluids should be replaced by the Lie derivative. Finally, the tidal force equation in EC theory on the null surface is also derived.Comment: Published in Phys. Rev.