On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization

There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. This norm is also useful in developing a stopping-rule theory for HSD-based interior-point methods such as SeDuMi. Under mild assumptions, we show that a standard stopping rule implicitly involves the sum of the sizes of the ε-optimal primal and dual solutions, as well as the size of the initial primal and dual infeasibility residuals. This theory suggests possible criteria for developing starting points for the homogeneous self-dual model that might improve the resulting solution time in practice

A Self-Organizing Multiple-View Representation of 3D Objects

We explore representation of 3D objects in which several distinct 2D views are stored for each object. We demonstrate the ability of a two-layer network of thresholded summation units to support such representations. Using unsupervised Hebbian relaxation, we trained the network to recognise ten objects from different viewpoints. The training process led to the emergence of compact representations of the specific input views. When tested on novel views of the same objects, the network exhibited a substantial generalisation capability. In simulated psychophysical experiments, the network's behavior was qualitatively similar to that of human subjects.

Programmable Self-Assembly: Constructing Global Shape using Biologically-inspire

In this thesis I present a language for instructing a sheet of identically-programmed, flexible, autonomous agents (``cells'') to assemble themselves into a predetermined global shape, using local interactions. The global shape is described as a folding construction on a continuous sheet, using a set of axioms from paper-folding (origami). I provide a means of automatically deriving the cell program, executed by all cells, from the global shape description. With this language, a wide variety of global shapes and patterns can be synthesized, using only local interactions between identically-programmed cells. Examples include flat layered shapes, all plane Euclidean constructions, and a variety of tessellation patterns. In contrast to approaches based on cellular automata or evolution, the cell program is directly derived from the global shape description and is composed from a small number of biologically-inspired primitives: gradients, neighborhood query, polarity inversion, cell-to-cell contact and flexible folding. The cell programs are robust, without relying on regular cell placement, global coordinates, or synchronous operation and can tolerate a small amount of random cell death. I show that an average cell neighborhood of 15 is sufficient to reliably self-assemble complex shapes and geometric patterns on randomly distributed cells. The language provides many insights into the relationship between local and global descriptions of behavior, such as the advantage of constructive languages, mechanisms for achieving global robustness, and mechanisms for achieving scale-independent shapes from a single cell program. The language suggests a mechanism by which many related shapes can be created by the same cell program, in the manner of D'Arcy Thompson's famous coordinate transformations. The thesis illuminates how complex morphology and pattern can emerge from local interactions, and how one can engineer robust self-assembly.

Self-Assembly of Stimuli-Responsive Water-Soluble [60]Fullerene End-Capped Ampholytic Block Copolymer

Well-defined, water-soluble, pH and temperature stimuli-responsive [60]fullerene (C₆₀) containing ampholytic block copolymer of poly((methacrylic acid)-block-(2-(dimethylamino)ethyl methacrylate))-block–C₆₀ (P(MAA-b-DMAEMA)-b-C₆₀) was synthesized by the atom transfer radical polymerization (ATRP) technique. The self-assembly behaviour of the C₆₀ containing polyampholyte in aqueous solution was characterized by dynamic light scattering (DLS), and transmission electron microscopy. This amphiphilic mono-C₆₀ end-capped block copolymer shows enhanced solubility in aqueous medium at room and elevated temperatures and at low and high pH but phase-separates at intermediate pH of between 5.4 and 8.8. The self assembly of the copolymer is different from that of P(MAA-b-DMAEMA). Examination of the association behavior using DLS revealed the co-existence of unimers and aggregates at low pH at all temperatures studied, with the association being driven by the balance of hydrophobic and electrostatic interactions. Unimers and aggregates of different microstructures are also observed at high pH and at temperatures below the lower critical solution temperature (LCST) of PDMAEMA. At high pH and at temperatures above the LCST of PDMAEMA, the formation of micelles and aggregates co-existing in solution is driven by the combination of hydrophobic, electrostatic, and charge-transfer interactions.