Over the past decade, the constraint-based approach to metabolic modeling has become an important tool for understanding and controlling biology. Unfortunately, the application of this novel approach to systems biology in biotechnology has been limited by three significant technical issues: existing metabolic modeling methods cannot completely model the overflow metabolism, cannot model the metabolism of microbial communities, and cannot design strains optimized for productivity and titer. Three computational methods – the Flux Balance Analysis with Membrane Economics (FBAME) method, the Dynamic Multi-species Metabolic Modeling (DyMMM) framework, and the Dynamic Strain Scanning Optimization (DySScO) strategy – have been developed to resolve these issues respectively. First, the FBAME method, which adopts the membrane occupancy limitation hypothesis, was used to explain and predict the phenomenon of overflow metabolism, an important metabolic phenomenon in industrial fermentation, in Escherichia coli. Then, the DyMMM framework was used to investigate the community metabolism during uranium bioremediation, and demonstrated that the simultaneous addition of acetate and Fe(III) may be a theoretically viable uranium bioremediation strategy. Lastly, the DySScO strategy, which combines the DyMMM framework with existing strain design algorithms, was used to design commodity-chemical producing E. coli optimized for a balanced product yield, titer, and volumetric productivity. These novel computational methods allow for broader applications of constraint-based metabolic models in biotechnology settings.

Consideration of the environmental impact of aircraft has become critical in commercial aviation. The continued growth in air traffic has come with increasing concerns and demands to reduce aircraft emissions and this has imposed new constraints on the de- sign and development of future airplane concepts. In this work, an environmental design framework has been developed to design and optimize aircraft for specific environmental metrics. Multidisciplinary design optimization is used to optimize aircraft by simulta- neously considering airframe, engine and mission design. The environmental metrics considered include fuel burn, landing-takeoff NOx and fuel burn per distance flown. Additional concepts such as the design of large aircraft for short ranges are also presented. Multi-objective optimization is also used to illustrate the tradeoffs between the various environmental objective functions.

Many space vehicles have been launched with large flexible components such as booms and solar panels. These large space structures (LSSs) have the potential to make attitude control unstable due to their lightly damped vibration. These vibrations can be controlled using a collection of control moment gyros (CMGs). CMGs consist of a spinning wheel in gimbals and produce a torque when the orientation of the wheel is changed. This study investigates the optimal distribution of these CMGs on LSSs for vibration suppression. The investigation considers a beam and a plate structure with evenly placed CMGs. The optimization allocates the amount of stored angular momentum possessed by these CMGs according to a cost function dependent on how quickly vibration motions are damped and how much control effort is exerted. The optimization results are presented and their effect on the motions of the beam and plate are investigated.

This is an expository thesis. In this thesis we study out-orientations of hypergraphs, where every hyperarc has one tail vertex. We study hypergraphs that admit out-orientations covering supermodular-type connectivity requirements. For this, we follow a paper of Frank. We also study the Steiner rooted orientation problem. Given a hypergraph and a subset of vertices S ⊆ V, the goal is to give necessary and sufficient conditions for an orientation such that the connectivity between a root vertex and each vertex of S is at least k, for a positive integer k. We follow a paper by Kiraly and Lau, where they prove that every 2k-hyperedge connected hypergraph has such an orientation.

We develop algebraic methods to solve join-cut equations, which are partial differential equations that arise in the study of permutation factorizations. Using these techniques, we give a detailed study of the recently introduced monotone Hurwitz numbers, which count factorizations of a given permutation into a fixed number of transpositions, subject to some technical conditions known as transitivity and monotonicity. Part of the interest in monotone Hurwitz numbers comes from the fact that they have been identified as the coefficients in a certain asymptotic expansion related to the Harish-Chandra-Itzykson-Zuber integral, which comes from the theory of random matrices and has applications in mathematical physics. The connection between random matrices and permutation factorizations goes through representation theory, with symmetric functions in the Jucys-Murphy elements playing a key role. As the name implies, monotone Hurwitz numbers are related to the more classical Hurwitz numbers, which count permutation factorizations regardless of monotonicity, and for which there is a significant body of work. Our results for monotone Hurwitz numbers are inspired by similar results for Hurwitz numbers; we obtain a genus expansion for the related generating functions, which yields explicit formulas and a polynomiality result for monotone Hurwitz numbers. A significant difference between the two cases is that our methods are purely algebraic, whereas the theory of Hurwitz numbers relies on some fairly deep results in algebraic geometry. Despite our methods being algebraic, it seems that there should be a connection between monotone Hurwitz numbers and geometry, although this is currently missing. We give some evidence for this connection by identifying some of the coefficients in the monotone Hurwitz genus expansion with coefficients in the classical Hurwitz genus expansion known to be Hodge integrals over the moduli space of curves.

Pairing-based cryptography has been employed to obtain several advantageous cryptographic protocols. In particular, there exist several identity-based variants of common cryptographic schemes. The computation of a single pairing is a comparatively expensive operation, since it often requires many operations in the underlying elliptic curve. In this thesis, we explore the efficient computation of pairings. Computation of the Tate pairing is done in two steps. First, a Miller function is computed, followed by the final exponentiation. We discuss the state-of-the-art optimizations for Miller function computation under various conditions. We are able to shave off a fixed number of operations in the final exponentiation. We consider methods to effectively parallelize the computation of pairings in a multi-core setting and discover that the Weil pairing may provide some advantage under certain conditions. This work is extended to the 192-bit security level and some unlikely candidate curves for such a setting are discovered. Electronic Toll Pricing (ETP) aims to improve road tolling by collecting toll fares electronically and without the need to slow down vehicles. In most ETP schemes, drivers are charged periodically based on the locations, times, distances or durations travelled. Many ETP schemes are currently deployed and although these systems are efficient, they require a great deal of knowledge regarding driving habits in order to operate correctly. We present an ETP scheme where pairing-based BLS signatures play an important role. Finally, we discuss the security of pairings in the presence of an efficient algorithm to invert the pairing. We generalize previous results to the setting of asymmetric pairings as well as give a simplified proof in the symmetric setting.

This thesis concerns sufficient conditions for a matroid to admit one of two types of structural characterization: a representation over a finite field or a description as a frame matroid. We call a restriction N of a matroid M modular if, for every flat F of M, r_M(F) + r(N) = r_M(F ∩ E(N)) + r_M(F ∪ E(N)). A consequence of a theorem of Seymour is that any 3-connected matroid with a modular U_{2,3}-restriction is binary. We extend this fact to arbitrary finite fields, showing that if N is a modular rank-3 restriction of a vertically 4-connected matroid M, then any representation of N over a finite field extends to a representation of M. We also look at a more general notion of modularity that applies to minors of a matroid, and use it to present conditions for a matroid with a large projective geometry minor to be representable over a finite field. In particular, we show that a 3-connected, representable matroid with a sufficiently large projective geometry over a finite field GF(q) as a minor is either representable over GF(q) or has a U_{2,q^2+1}-minor. A second result of Seymour is that any vertically 4-connected matroid with a modular M(K_4)-restriction is graphic. Geelen, Gerards, and Whittle partially generalized this from M(K_4) to larger frame matroids, showing that any vertically 5-connected, representable matroid with a rank-4 Dowling geometry as a modular restriction is a frame matroid. As with projective geometries, we prove a version of this result for matroids with large Dowling geometries as minors, providing conditions which imply that they are frame matroids.

Tensors can be viewed as multilinear arrays or generalizations of the notion of matrices. Tensor decompositions have applications in various fields such as psychometrics, signal processing, numerical linear algebra and data mining. When the data are nonnegative, the nonnegative tensor factorization (NTF) better reflects the underlying structure. With NTF it is possible to extract information from a given dataset and construct lower-dimensional bases that capture the main features of the set and concisely describe the original data. Nonnegative tensor factorizations are commonly computed as the solution of a nonlinear bound-constrained optimization problem. Some inherent difficulties must be taken into consideration in order to achieve good solutions. Many existing methods for computing NTF optimize over each of the factors separately; the resulting algorithms are often slow to converge and difficult to control. We propose an all-at-once approach to computing NTF. Our method optimizes over all factors simultaneously and combines two regularization strategies to ensure that the factors in the decomposition remain bounded and equilibrated in norm. We present numerical experiments that illustrate the effectiveness of our approach. We also give an example of digital-inpainting, where our algorithm is employed to construct a basis that can be used to restore digital images.

Thesis (PhDMathematics)--University of South Australia, 2003.

Thesis (MEng)--University of South Australia, 2001