Matroids and Geometric Invariant Theory of torus actions on flag spaces

We apply a theorem of Gel'fand, Goresky, MacPherson, and Serganova about matroid polytopes to study semistability of partial flags relative to a T-linearized ample line bundle of a flag space F = SL(n)/P where T is a maximal torus in SL(n) and P is a parabolic subgroup containing T. We find that the semistable points are all detected by invariant sections of degree one regardless of the line bundle or linearization thereof, provided there exists at least one nonzero invariant section of degree one. In this case the degree one sections are sufficient to give a well defined map from the G.I.T. quotient F//T to projective space. Additionally, we show that the closure of any T-orbit in SL(n)/P is a projectively normal toric variety for any projective embedding of SL(n)/P.Comment: 14 page

ABSTRACT Title of Dissertation: INVESTIGATIONS INTO THE NEURAL BASIS OF STRUCTURED REPRESENTATIONS

The problem of how the brain encodes structural representations is investigated via the formulation of computational theories constrained from the bottom-up by neurobiological factors, and from the top-down by behavioral data. This approach is used to construct models of letter-position encoding in visual word recognition, and of hierarchical representations in sentence parsing. The problem of letter-position encoding entails the specification of how the retinotopic representation of letter order. Consideration of the architecture of the visual system, letter perceptibility studies, and form-priming experiments led to the SERIOL model, which is comprised of five layers: (1) a (retinotopic) edge layer, in which letter activations are determined by the acuity gradient; (2) a (retinotopic) feature layer, in which letter activations conform to a monotonically decreasing activation gradient, dubbed the locational gradient; (3) an abstract letter layer, in which letter order is encoded sequentially. (4) a bigram layer, in which contextual units encode letter pairs that fire in a particular order; (5) a word layer. Because the acuity and locational gradients are congruent to each other in one hemispher

ABSTRACT Title of Dissertation: WORD SENSE DISAMBIGUATION WITHIN A MULTILINGUAL FRAMEWORK

Word Sense Disambiguation (WSD) is the process of resolving the meaning of a word unambiguously in a given natural language context. Within the scope of this thesis, it is the process of marking text with explicit sense labels. What constitutes a sense is a subject of great debate. An appealing perspective, aims to define senses in terms of their multilingual correspondences, an idea explore

ABSTRACT Title of Dissertation: ZOOMABLE USER INTERFACES FOR THE AUTHORING AND DELIVERY OF SLIDE PRESENTATIONS

Millions of slide presentations are being authored and delivered with computer software every day. Yet much of the computer’s power for these tasks remains untapped. Existing interaction techniques leave presenters wrestling with limited size computer displays to get meaningful overviews of their work. Without these overviews, they have trouble finding patterns in their data and experimenting with alternate organizations. They also have difficulty communicating the structure of large or complex talks to the audience and keeping the audience oriented during unexpected transitions between ideas. A natural solution is Zoomable User Interfaces (ZUIs) since they offer the capability to view information at multiple levels of detail and smoothly transition between ideas. This work presents two ZUIs, Niagara and CounterPoint, for authoring and delivering slide presentations. Niagara is a ZUI workspace for authoring presentation content with techniques to improve authoring in the zoomable environment. Empirical evaluations of ZUI-based authoring tools revealed performance improvements and subjective preferences over folder-based interfaces for organization tasks. Users were 30 % faster with ZUIs tha