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30 papers · 1 filter
A Probabilistic Approach to Knowledge Translation
Shangpu Jiang, Daniel Lowd, Dejing Dou
In this paper, we focus on a novel knowledge reuse scenario where the knowledge in the source schema needs to be translated to a semantically heterogeneous target schema. We refer…
Ontology Matching with Knowledge Rules
Shangpu Jiang, Daniel Lowd, Dejing Dou
Ontology matching is the process of automatically determining the semantic equivalences between the concepts of two ontologies. Most ontology matching algorithms are based on two t…
A bound for the order of the fundamental group of a complete noncompact Ricci shrinker
Bennett Chow, Peng Lu
For complete shrinking (gradient) Ricci solitons, we observe a quantification of Wylie's result that the fundamental group is finite.
Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay
Bennett Chow, Peng Lu
We discuss an elementary consequence of the works of (1) Brett Kotschwar and Lu Wang and (2) Ovidiu Munteanu and Jiaping Wang.
A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations
Micah Warren
Using an rotation of Yuan, we observe that the gradient graph of any semiconvex function is a Liouville manifold, that is, does not admit bounded harmonic functions. As a corollary…
Third law of thermodynamics and the shape of the phase diagram for systems with a first-order quantum phase transition
T. R. Kirkpatrick, D. Belitz
The Third Law of Thermodynamics constrains the phase diagram of{systems with a first-order quantum phase transition. For zero conjugate field, the coexistence curve has an infinite…