We review in this paper some recent yet fundamental results on evaluating queries over probabilistic databases. While one can see this problem as a special instance of general purpose probabilistic inference, we describe in this paper two key database specific techniques that significantly reduce the complexity of query evaluation on probabilistic databases. The first is the separation of the q...

where ∧ denotes exterior product. The above expression is the exterior product of M two-forms of rank two, which produces a volume form D2,2(v1, . . . , v4M ) in the 2M -dimensional linear space. If we fix a basis e1, . . . , e2M in the linear space, then each of the vectors vi can be expressed as a sequence of 2M numbers, and D2,2(v1, . . . , v4M ) is also a number (the coefficient at e1∧. . ....

Phases of the 600 km. deep earthquake of April 16, 1957, which have not been reflected at the earth's surface show very sharp beginnings arriving within the limits of error of a few seconds at the cMculated times. However, phases which have been reflected at the surface, for example PP, pP', pPP, have more or less emergent beginnings which arrive between a few seconds and as much as 30 seconds ...

Extensive studies of high-energy deuteron photodisintegration over the past two decades have probed the limits of meson-baryon descriptions of nuclei and reactions. At high energies, photodisintegration cross sections have been shown to follow the constituent counting rules, which suggests that quarks are the relevant degrees of freedom. In an attempt to more clearly identify the underlying dyn...