Boundaries and Topological Algorithms

This thesis develops a model for the topological structure of situations. In this model, the topological structure of space is altered by the presence or absence of boundaries, such as those at the edges of objects. This allows the intuitive meaning of topological concepts such as region connectivity, function continuity, and preservation of topological structure to be modeled using the standard mathematical definitions. The thesis shows that these concepts are important in a wide range of artificial intelligence problems, including low-level vision, high-level vision, natural language semantics, and high-level reasoning.

Defects in Self Assembled Colloidal Crystals

Colloidal self assembly is an efficient method for making 3-D ordered nanostructures suitable for materials such as photonic crystals and macroscopic solids for catalysis and sensor applications. Colloidal crystals grown by convective methods exhibit defects on two different scales. Macro defects such as cracks and void bands originate from the dynamics of meniscus motion during colloidal crystal growth while micro defects like vacancies, dislocation and stacking faults are indigenous to the colloidal crystalline structure. This paper analyses the crystallography and energetics of the microscopic defects from the point of view of classical thermodynamics and discusses the strategy for the control of the macroscopic defects through optimization of the liquid-vapor interface.