39,209 research outputs found
Infinite Volume of Noncommutative Black Hole Wrapped by Finite Surface
The volume of a black hole under noncommutative spacetime background is found
to be infinite, in contradiction with the surface area of a black hole, or its
Bekenstein-Hawking (BH) entropy, which is well-known to be finite. Our result
rules out the possibility of interpreting the entropy of a black hole by
counting the number of modes wrapped inside its surface if the final
evaporation stage can be properly treated. It implies the statistical
interpretation for the BH entropy can be independent of the volume, provided
spacetime is noncommutative. The effect of radiation back reaction is found to
be small and doesn't influence the above conclusion
Expressive Completeness of Existential Rule Languages for Ontology-based Query Answering
Existential rules, also known as data dependencies in Databases, have been
recently rediscovered as a promising family of languages for Ontology-based
Query Answering. In this paper, we prove that disjunctive embedded dependencies
exactly capture the class of recursively enumerable ontologies in
Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness
result does not rely on any built-in linear order on the database. To establish
the expressive completeness, we introduce a novel semantic definition for OCQA
ontologies. We also show that neither the class of disjunctive tuple-generating
dependencies nor the class of embedded dependencies is expressively complete
for recursively enumerable OCQA ontologies.Comment: 10 pages; the full version of a paper to appear in IJCAI 2016.
Changes (regarding to v1): a new reference has been added, and some typos
have been correcte
Fast generation of 3D deformable moving surfaces
Dynamic surface modeling is an important subject of geometric modeling due to their extensive applications in engineering design, entertainment and medical visualization. Many deformable objects in the real world are dynamic objects as their shapes change over time. Traditional geometric modeling methods are mainly concerned with static problems, therefore unsuitable for the representation of dynamic objects. Apart from the definition of a dynamic modeling problem, another key issue is how to solve the problem. Because of the complexity of the representations, currently the finite element method or finite difference method is usually used. Their major shortcoming is the excessive computational cost, hence not ideal for applications requiring real-time performance. We propose a representation of dynamic surface modeling with a set of fourth order dynamic partial differential equations (PDEs). To solve these dynamic PDEs accurately and efficiently, we also develop an effective resolution method. This method is further extended to achieve local deformation and produce n-sided patches. It is demonstrated that this new method is almost as fast and accurate as the analytical closed form resolution method and much more efficient and accurate than the numerical methods
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