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Chlamydia Trachomatis and Neisseria Gonorrhoeae rank as the two most commonly reported sexually transmitted diseases (STDs) in the United States. Under limited budget, publicly funded clinics are not able to screen and treat the two diseases for all patients. They have to make a decision as to which group of population shall go through the procedure for screening and treating the two diseases. Therefore, we propose a cubic integer programming model on maximizing the number of units of cured diseases. At the same time, a two-step algorithm is established to solve the cubic integer program. We further develop a web-server, which immediately make recommendation on identifying population groups, screening assays and treatment regimens. Running on the empirical data provided by the Centers for Disease Control and Prevention, our program gives more accurate optimal results comparing to MS Excel solver within a very short time.

Rotor dynamic analysis, which requires extensive amount of data and rigorous analytical processing, has been eased by the advent of powerful and affordable digital computers. By incorporating the processor and a graphical interface post processor in a single set up, this program offers a consistent and efficient approach to rotor dynamic analysis. The graphic user interface presented in this program effectively addresses the inherent complexities of rotor dynamic analyses by linking the required computational algorithms together to constitute a comprehensive program by which input data and the results are exchanged, analyzed and graphically plotted with minimal effort by the user. Just by selecting an input file and appropriate options as required, the user can carry out a comprehensive rotor dynamic analysis (synchronous response, stability analysis, critical speed analysis with undamped map) of a particular design and view the results with several options to save the plots for further verification. This approach helps the user to modify the design of turbomachinery quickly, until an efficient design is reached, with minimal compromise in all aspects.

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This thesis involves systems for virtual presence in remote locations, a field referred to as telepresence. Recent image-based representations such as Google map's street view provide a familiar example. Several areas of research are open; such image-based representations are huge in size and the necessity to compress data efficiently for storage is inevitable. On the other hand, users are usually located in remote areas, and thus efficient transmission of the visual information is another issue of great importance. In this work, real-world images are used in preference to computer graphics representations, mainly due to the photorealism that they provide as well as to avoid the high computational cost required for simulating large-scale environments. The cubic format is selected for panoramas in this thesis. A major feature of the captured cubic-panoramic image datasets in this work is the assumption of static scenes, and major issues of the system are compression efficiency and random access for storage, as well as computational complexity for transmission upon remote users' requests. First, in order to enable smooth navigation across different view-points, a method for aligning cubic-panorama image datasets by using the geometry of the scene is proposed and tested. Feature detection and camera calibration are incorporated and unlike the existing method, which is limited to a pair of panoramas, our approach is applicable to datasets with a large number of panoramic images, with no need for extra numerical estimation. Second, the problem of cubic-panorama image dataset compression is addressed in a number of ways. Two state-of-the-art approaches, namely the standardized scheme of H.264 and a wavelet-based codec named Dirac, are used and compared for the application of virtual navigation in image based representations of real world environments. Different frame prediction structures and group of pictures lengths are investigated and compared for this new type of visual data. At this stage, based on the obtained results, an efficient prediction structure and bitstream syntax using features of the data as well as satisfying major requirements of the system are proposed. Third, we have proposed novel methods to address the important issue of disparity estimation. A client-server based scheme is assumed and a remote user is assumed to seek information at each navigation step. Considering the compression stage, a fast method that uses our previous work on the geometry of the scene as well as the proposed prediction structure together with the cubic format of panoramas is used to estimate disparity vectors efficiently. Considering the transmission stage, a new transcoding scheme is introduced and a number of different frame-format conversion scenarios are addressed towards the goal of free navigation. Different types of navigation scenarios including forward or backward navigation, as well as user pan, tilt, and zoom are addressed. In all the aforementioned cases, results are compared both visually through error images and videos as well as using the objective measures. Altogether free navigation within the captured panoramic image datasets will be facilitated using our work and it can be incorporated in state-of-the-art of emerging cubic-panorama image dataset compression/transmission schemes.

A detailed study has been made of thermally activated glide between 373 K and 20 K for UHV annealed single crystals of two Nb based substitutional alloy systems containing 1-16 at.%Mo or 4 - 60 at.%Ta, in conjunction with a study of the deformation of UHV annealed single crystals of Nb between 4.2 K and 77 K. Whilst the addition of Ta had only a small effect on the properties of Nb as measured by activation volume and enthalpy and the temperature dependence of the flow stress, it produced a large increase in the low temperature yield stress and displaced the appearance of anomalous slip to lower temperatures, e.g. 77 K for the 10 at.%Ta alloy. Addition of Mo produced more rapid changes Whilst the 1 at.%Mo alloy behaved like the Nb-Ta alloys, the appearance of anomalous slip was depressed to 113 K. Further additions appeared to suppress anomalous slip completely and radically alter the behaviour of the alloys. The thermodynamic analysis suggested that the more concentrated Nb-Mo alloys show a change in the rate limiting step at low temperatures, cf. a peak in the activation volume - effective stress curve. No solution softening was observed in the alloys. Complex transients were found for all the alloys at and below 77 K after changes in strain rate. The yield and thermal stresses for Nb deforming by anomalous slip were independent of temperature between 77 K and 50 K, only regaining a temperature sensitivity below 50 K. The importance of this for models of anomalous slip was discussed. Complex overshoots were observed after changes in the strain rate. Those observed at and below 20 K have been explained by reference to the change in specimen temperature produced by heat generation during dislocation glide.

Axisymmetric magnetic strings with a fixed sense of rotation and nanometer sizes (chiral magnetic vortices or Skyrmions) have been predicted to exist in a large group of non-centrosymmetric crystals more than two decades ago. Recently these extraordinary magnetic states have been directly observed in thin layers of cubic helimagnet (Fe,Co)Si. In this thesis we apply our earlier theoretical findings and recent results to review main properties of chiral Skyrmions, to elucidate their physical nature, and to analyse these recent experimental results on magnetic-field-driven evolution of Skyrmions and helicoids in chiral helimagnets. Concentrating on the physical side of the problem rather than on mathematical details we give an elementary introduction into the properties of chiral Skyrmions in magnetism.

The work in this thesis can be divided into two different parts. In the first part, we suggest an approximate edge 3-coloring polynomial time algorithm for cubic graphs. For any cubic graph with n vertices, using this coloring algorithm, we get an edge 3-coloring with at most n/3 error vertices. In the second part, we study Jim Propp's Rotor-Router model on some non-bipartite graph. We find the difference between the number of chips at vertices after performing a walk on this graph using Propp model and the expected number of chips after a random walk. It is known that for line of integers and d-dimenional grid, this deviation is constant. However, it is also proved that for k-ary infinite trees, for some initial configuration the deviation is no longer a constant and say it is D. We present a similar study on some non-bipartite graph constructed from k-ary infinite trees and conclude that for this graph with the same initial configuration, the deviation is almost (k²)D.

Doctor of Philosophy (PhD) / For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models.

[Truncated abstract] This thesis is concerned with geometrically-defined curves that can be used for interpolation in Riemannian or, more generally, semi-Riemannian manifolds. As in much of the existing literature on such curves, emphasis is placed on manifolds which are important in computer graphics and engineering applications, namely the unit 3-sphere S3 and the closely related rotation group SO(3), as well as other Lie groups and spheres of arbitrary dimension. All geometrically-defined curves investigated in the thesis are either higher order variational curves, namely critical points of cost functionals depending on (covariant) derivatives of order greater than 1, or defined by geometrical algorithms, namely generalisations to manifolds of algorithms from the field of computer aided geometric design. Such curves are needed, especially in the aforementioned applications, since interpolation methods based on applying techniques of classical approximation theory in coordinate charts often produce unnatural interpolants. However, mathematical properties of higher order variational curves and curves defined by geometrical algorithms are in need of substantial further investigation: higher order variational curves are solutions of complicated nonlinear differential equations whose properties are not well-understood; it is usually unclear how to impose endpoint derivative conditions on, or smoothly piece together, curves defined by geometrical algorithms. This thesis addresses these difficulties for several classes of curves. ... The geometrical algorithms investigated in this thesis are generalisations of the de Casteljau and Cox-de Boor algorithms, which define, respectively, polynomial B'ezier and piecewise-polynomial B-spline curves by dividing, in certain ratios and for a finite number of iterations, piecewise-linear control polygons corresponding to finite sequences of control points. We show how the control points of curves produced by the generalised de Casteljau algorithm in an (almost) arbitrary connected finite-dimensional Riemannian manifold M should be chosen in order to impose desired endpoint velocities and (covariant) accelerations and, thereby, piece the curves together in a C2 fashion. A special case of the latter construction simplifies when M is a symmetric space. For the generalised Cox-de Boor algorithm, we analyse in detail the failure of a fundamental property of B-spline curves, namely C2 continuity at (certain) knots, to carry over to M.