Following the work of Duistermaat-Singer [DS] on isomorphisms of algebras of global pseudodifferential operators, we classify isomorphisms of algebras of microlocally defined semiclassical pseudodifferential operators. Specifically, we show that any such isomorphism is given by conjugation by A = BF , where B is a microlocally elliptic semiclassical pseudodifferential operator, and F is a micro...

We have developed Metis, a question-answering system that finds an answer by matching a question graph with the knowledge graphs. The question graph is obtained as a result of semantic analysis of a question sentence, the knowledge graphs are similarly analyzed from knowledge sentences retrieved from a database using keywords extracted from the question sentence. In retrieving such knowledge se...

A spanning subgraph S= (V ,E′) of a connected graph G= (V ,E) is an (x+ c)-spanner if for any pair of vertices u and v, dS(u, v) dG(u, v) + c where dG and dS are the usual distance functions in G and S, respectively. The parameter c is called the delay of the spanner. We study edge-disjoint spanners in graphs, focusing on graphs formed as Cartesian products. Our approach is to construct sets of...

A spanning subgraph S=(V; E′) of a connected simple graph G=(V; E) is an (x+c)-spanner if for any pair of vertices u and v; dS(u; v)6dG(u; v)+c where dG and dS are the usual distance functions in graphs G and S, respectively. The parameter c is called the delay of the spanner. We investigate the number of edge-disjoint spanners of a given delay that can exist in complete bipartite graphs. We de...

Primitive equivalence of graphs and matrices was used by Enomoto, Fujii and Watatani [EFW] to classify Cuntz-Krieger algebras of 3×3 irreducible matrices. It was shown by Drinen and the author [DS] that a graph and its primitive transfer have isomorphic groupoids and therefore isomorphic C-algebras. Franks [Fra, Corollary 2.2] used a similar operation to find a canonical form for the flow equiv...