In order to effectively approach high dimensional pattern recognition problems, one seeks to understand and exploit any inherent low dimensional structure. Recently, a number of manifold learning algorithms have been motivated by a geometric point of view that models high dimensional data as lying near a low dimensional submanifold of the original space. Our paper has two main goals: (i) to inv...

We introduce a two-dimensional frustrated Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. Classically the two sublattices decouple, and "order from disorder" drives them into a coplanar state. Applying Friedan's geometric approach to nonlinear sigma models, we obtain the scaling of the spin stiffnesses governed by the Ricci flow of a four-dimensional metric ten...

The fluid-structure energy exchange process for normal speech has been studied extensively, but it is not well understood for pathological conditions. Polyps and nodules, which are geometric abnormalities that form on the medial surface of the vocal folds, can disrupt vocal fold dynamics and thus can have devastating consequences on a patient's ability to communicate. Our laboratory has reporte...

Just asC principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady class. I consider an alternative, related, geometric realisation of three dimensional cohomology called a bundle gerbe. Every bundle gerbe gives rise to a gerbe and...

Simplified models have been used to simulate and study the flow-induced vibrations of the human vocal folds. While it is clear that the models' responses are sensitive to geometry, it is not clear how and to what extent specific geometric features influence model motion. In this study geometric features that played significant roles in governing the motion of a two-layer (body-cover), two-dimen...

We present a probabilistic structured prediction method for learning input-output dependencies where correlations between outputs are modeled as low-dimensional manifolds constrained by both geometric, distance preserving output relations, and predictive power of inputs. Technically this reduces to learning a probabilistic, input conditional model, over latent (manifold) and output variables us...

In this paper an approach is presented to digitize a drawing, to build up geometric and topologic models, to recognise construction parts and to interpret dimension lines and inscriptions. All recognized parts are transformed into a three-dimensional geometric model which provides all necessary geometric information for a product model. The recognition process of construction parts is based on ...

In this paper we present an experimental prototype called GEGROSS (GEsture & Geometric ReconstructiOn based Sketch System). This application allows using freehand sketches to create 3D parametric models onto a Tablet-PC. The modelling process consists of two stages. First, the user introduces the geometry of the 2D section using continuous sketches composed by line segments, circles and arcs, a...