We establish that Hitchin’s connection exist for any rigid holomorphic family of Kähler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove that Hitchin’s connection induces a unique formal connection on smooth functions on the symplectic manifold. Parallel transport of this formal connection pro...

This Demo presents a framework for the live synchronization of an RDF view defined on top of relational database. In the proposed framework, rules are responsible for computing and publishing the changeset required for the RDB-RDF view to stay synchronized with the relational database. The computed changesets are then used for the incremental maintenance of the RDB_RDF views as well as applicat...

We develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure. Taking the viewpoint of affine connection control systems, we derive reduced formulations of the Levi-Civita and the nonholonomic affine connections, along with the symmetric product, in the presence of symmetries and nonholonomic constraint...

By replacing syntactical unification with rigid E-unification, equality handling can be added to rigid variable calculi for first-order logic, including free variable tableau (Fitting, 1996), the mating method (Andrews, 1981), the connection method (Bibel, 1982), and model elimination (Loveland, 1969); for an overview of these calculi, see Chapters I.1.1 and I.1.2. Rigid E-unification and its s...

By replacing syntactical unification with rigid E-unification, equality handling can be added to rigid variable calculi for first-order logic, including free variable tableau (Fitting, 1996), the mating method (Andrews, 1981), the connection method (Bibel, 1982), and model elimination (Loveland, 1969); for an overview of these calculi, see Chapters I.1.1 and I.1.2. Rigid E-unification and its s...

On a Riemannian manifold, a solution of the Killing equation is an infinitesimal isometry. Since the Killing equation is overdetermined, infinitesimal isometries do not exist in general. The complete prolongation of the Killing equation is a PDE on the bundle of 1-jets of vector fields. Restricted to a curve, it becomes an ODE that generalizes the Jacobi equation. A solution of this ODE is call...

This paper describes a novel technique for synthesizing a dynamic scene from two images without the use of a 3D model. A scene containing rigid or non-rigid objects, in which each object can move in any orientation or direction, is considered. It is shown that such a scene can be converted into several equivalent static scenes, where each scene only includes one rigid object. Our method can gen...

RDF has gained great interest in both academia and industry as an important language to describe graph data. Several approaches have been proposed for storing and querying RDF data efficiently; each works best under certain circumstances, e.g. certain types of data and/or queries. However, there was lack of a thorough understanding of exactly what these circumstances are, as different data-sets...

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ , or are weakly rigid. As a consequence we obtain tha...