No / The key equations of BiCGStab are summarised to show its connections with Pade and vector-Pade approximation. These considerations lead naturally to stabilised vector-Pade approximation of a vector-valued function (VPAStab), and an algorithm for the acceleration of convergence of a linearly generated sequence of vectors. A generalisation of this algorithm for the acceleration of convergence of a nonlinearly generated system is proposed here, and comparative numerical results are given.

No / Background: Slowness of movement, known as bradykinesia, is the core clinical sign of Parkinson's and fundamental to its diagnosis. Clinicians commonly assess bradykinesia by making a visual judgement of the patient tapping finger and thumb together repetitively. However, inter-rater agreement of expert assessments has been shown to be only moderate, at best. Aim: We propose a low-cost, contactless system using smartphone videos to automatically determine the presence of bradykinesia. Methods: We collected 70 videos of finger-tap assessments in a clinical setting (40 Parkinson's hands, 30 control hands). Two clinical experts in Parkinson's, blinded to the diagnosis, evaluated the videos to give a grade of bradykinesia severity between 0 and 4 using the Unified Pakinson's Disease Rating Scale (UPDRS). We developed a computer vision approach that identifies regions related to hand motion and extracts clinically-relevant features. Dimensionality reduction was undertaken using principal component analysis before input to classification models (Naïve Bayes, Logistic Regression, Support Vector Machine) to predict no/slight bradykinesia (UPDRS = 0–1) or mild/moderate/severe bradykinesia (UPDRS = 2–4), and presence or absence of Parkinson's diagnosis. Results: A Support Vector Machine with radial basis function kernels predicted presence of mild/moderate/severe bradykinesia with an estimated test accuracy of 0.8. A Naïve Bayes model predicted the presence of Parkinson's disease with estimated test accuracy 0.67. Conclusion: The method described here presents an approach for predicting bradykinesia from videos of finger-tapping tests. The method is robust to lighting conditions and camera positioning. On a set of pilot data, accuracy of bradykinesia prediction is comparable to that recorded by blinded human experts.

In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function.” This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. I identify a freedom/constraint situation encountered by vectors when, employed in accordance with adopted quantum representational methodology, and representing angular momentum states in particular. Complex vectors, quite simply, provide more available adjustable variables than do real vectors. The additional variables relax the constraint situation allowing the theory’s representational program to carry through. This complex number issue, which lies at the deepest foundations of the theory, has implications for important issues located higher in the theory. For example, any unification of the classical and quantum accounts of the settled order of nature, will rest squarely on our ability to account for the introduction of the imaginary unit.

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The feasibility of using a vectorized banded direct solver for the compressible Euler and Navier-Stokes equations is examined for both single-grid and multi-grid strategies. A procedure is developed for comparing the computational effort required for the direct method with that of the vertical line Gauss-Seidel iteration scheme in order to provide a criteria for choosing between the two techniques. The direct method is shown to have a relatively wide range of application on a vector processor with large memory. Indeed, the primary limitation of the direct method at this time is machine memory. Results for both inviscid and viscous test problems over a range of Mach numbers and Reynolds numbers are examined for two dimensions. / Ph. D.

Quick Response codes are a widespread feature commonly used to conveyinformation to users who scan them. During Covid 19 these codes became evenmore widespread as restaurants had to adapt to using contactless visits to hinder thespread of the disease, but since quick response codes can also be leveraged formalicious purposes the number of phishing attempts also increased. In this thesis, weexplored the security implications of QR codes by investigating how they can beexploited and secured, as well as surveying how aware people are of these securityimplications. The result of the thesis shows that QR codes can be leveraged to send maliciousprograms directly through the QR code without having to download anything.Through the survey we learned that people are relatively unaware of phishingthrough QR codes, but also that some of the participants knew someone who hadbeen a victim of it.

Two-dimensional geometric textures are the geometric analogues of raster (pixel-based) textures and consist of planar distributions of discrete shapes with an inherent structure. These textures have many potential applications in art, computer graphics, and cartography. Synthesizing large textures by hand is generally a tedious task. In raster-based synthesis, many algorithms have been developed to limit the amount of manual effort required. These algorithms take in a small example as a reference and produce larger similar textures using a wide range of approaches. Recently, an increasing number of example-based geometric synthesis algorithms have been proposed. I refer to them in this dissertation as Geometric Texture Synthesis (GTS) algorithms. Analogous to their raster-based counterparts, GTS algorithms synthesize arrangements that ought to be judged by human viewers as “similar” to the example inputs. However, an absence of conventional evaluation procedures in current attempts demands an inquiry into the visual significance of synthesized results. In this dissertation, I present an investigation into GTS and report on my findings from three projects. I start by offering initial steps towards grounding texture synthesis techniques more firmly with our understanding of visual perception through two psychophysical studies. My observations throughout these studies result in important visual cues used by people when generating and/or comparing similarity of geometric arrangements as well a set of strategies adopted by participants when generating arrangements. Based on one of the generation strategies devised in these studies I develop a new geometric synthesis algorithm that uses a tile-based approach to generate arrangements. Textures synthesized by this algorithm are comparable to the state of the art in GTS and provide an additional reference in subsequent evaluations. To conduct effective evaluations of GTS, I start by collecting a set of representative examples, use them to acquire arrangements from multiple sources, and then gather them into a dataset that acts as a standard for the GTS research community. I then utilize this dataset in a second set of psychophysical studies that define an effective methodology for comparing current and future geometric synthesis algorithms.

Acetylcholinesterase (AChE) is an essential enzyme with an evolutionary conserved function: to terminate nerve signaling by rapid hydrolysis of the neurotransmitter acetylcholine. AChE is an important target for insecticides. Vector control by the use of insecticide-based interventions is today the main strategy for controlling mosquito-borne diseases that affect millions of people each year. However, the efficiency of many insecticides is challenged by resistant mosquito populations, lack of selectivity and off-target toxicity of currently used compounds. New selective and resistance-breaking insecticides are needed for an efficient vector control also in the future. In the work presented in this thesis, we have combined structural biology, biochemistry and medicinal chemistry to characterize mosquito AChEs and to develop selective and resistance-breaking inhibitors of this essential enzyme from two disease-transmitting mosquitoes.We have identified small but important structural and functional differences between AChE from mosquitoes and AChE from vertebrates. The significance of these differences was emphasized by a high throughput screening campaign, which made it evident that the evolutionary distant AChEs display significant differences in their molecular recognition. These findings were exploited in the design of new inhibitors. Rationally designed and developed thiourea- and phenoxyacetamide-based non-covalent inhibitors displayed high potency on both wild type and insecticide insensitive AChE from mosquitoes. The best inhibitors showed over 100-fold stronger inhibition of mosquito than human AChE, and proved insecticide potential as they killed both adult and larvae mosquitoes.We show that mosquito and human AChE have different molecular recognition and that non-covalent selective inhibition of AChE from mosquitoes is possible. We also demonstrate that inhibitors can combine selectivity with sub-micromolar potency for insecticide resistant AChE.

In this thesis, we introduce several tools, each coming from a different branch of mathematics, for analyzing real vector fields and their associated flows. Beginning with a discussion about generalized vector field decompositions, that mainly have been derived from the classical Helmholtz-Hodge-decomposition, we decompose a field into a kernel and a rest respectively to an arbitrary vector-valued linear differential operator that allows us to construct decompositions of either toroidal flows or flows obeying differential equations of second (or even fractional) order and a rest. The algorithm is based on the fast Fourier transform and guarantees a rapid processing and an implementation that can be directly derived from the spectral simplifications concerning differentiation used in mathematics. Moreover, we present two combinatorial methods to process 3D steady vector fields, which both use graph algorithms to extract features from the underlying vector field. Combinatorial approaches are known to be less sensitive to noise than extracting individual trajectories. Both of the methods are extensions of an existing 2D technique to 3D fields. We observed that the first technique can generate overly coarse results and therefore we present a second method that works using the same concepts but produces more detailed results. Finally, we discuss several possibilities for categorizing the invariant sets with respect to the flow. Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In the frame of this work, we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies. Gauss\' theorem, which relates the flow through a surface to the vector field inside the surface, is an important tool in flow visualization. We are exploiting the fact that the theorem can be further refined on polygonal cells and construct a process that encodes the particle movement through the boundary facets of these cells using transition matrices. By pure power iteration of transition matrices, various topological features, such as separation and invariant sets, can be extracted without having to rely on the classical techniques, e.g., interpolation, differentiation and numerical streamline integration.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfillment of the requirements for the degree of Master of Science. Pretoria 1991. / Remote sensing can be used to produce maps of land-cover, but to be of use to the GIS community these maps must first be vectorized in an intelligent manner. Existing algorithms suffer from the defects of being slow, memory intensive and producing vast quantities of very short vectors. Furthermore if these vectors are thinned via standard algorithms, errors are introduced. The process of vectorizing raster maps is subject to major ambiguities. Thus an infinite family of vector maps ccrresponds to each raster map. This dissertation presents an algorithm for converting raster maps in a rapid manner to accurate vector maps with a minimum of vectors. The algorithm converts raster maps to vector maps using local information only, (a two by two neighbourhood). the method is "exact" in the sense that rasterizing the resulting polygons would produce exactly the same raster map, pixel for pixel. The method is "near optimal" in that it produces, in a local sense, that "exacb" vector map having the least number of vectors. The program is built around a home-grown object oriented Programming System (OOPS) for the C programming language. The main features of the OOPS system, (called OopCdaisy), are virtual and static methods, polymorphism, generalized containers, container indices and thorough error checking, The following general purpose objects are implemented with a large number of sophistiated methods :- Stacks, LIFO lists, scannable containers with indices, trees and 2D objects like points, lines etc. / AC2017