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The discovery of a new truth in the older fields of mathematics is a rare event. Here an investigator may hope at best to secure greater elegance in method or notation, or to extend known results by some process of generalization. It is our purpose to make a study of conic sections in the spirit of the above remark, using the symbolism developed by Josiah Williard Gibbs.

Several space vector modulation schemes have been analyzed for three-leg and four-leg voltage source inverters. The analysis is performed with respect to a) switching losses, b) total harmonic distortion, c) peak-to-peak ripple in the line current and d) the ease of digital implementation. The analysis is performed over the entire range of modulation index and for varying load power factors (leading and lagging) under both balanced and unbalanced load conditions. The analysis shows that the performance of four-leg inverters is similar to three-leg inverters for various space vector modulation schemes. The analysis also verifies the fact that a modulation scheme with good harmonic performance usually has high switching losses and vice-versa. The analysis is verified using simulation and experiments. A novel algorithm for the calculation of total harmonic distortion of PWM signals has been proposed. / Master of Science

Yes / Integrating a desired DNA sequence into the yeast genomes is a widely-used genetic manipulation in the budding yeast Saccharomyces cerevisiae. The conventional integration method is to use an integrative plasmid such as pRS or YIplac series as the target DNA carrier. The nature of this method risks multiple integrations of the target DNA and the potential loss of integrated DNA during cell proliferation. In this study, we developed a novel yeast integration strategy based on the widely used CRISPR-Cas9 system and created a set of plasmids for this purpose. In this system, a plasmid bearing Cas9 and gRNA expression cassettes will induce a double-strand break (DSB) inside a biosynthesis gene such as Met15 or Lys2. Repair of the DSB will be mediated by another plasmid bearing upstream and downstream sequences of the DSB and an integration sequence in between. As a result of this repair the sequence is integrated into genome by replacing the biosynthesis gene, the disruption of which leads to a new auxotrophic genotype. The newly-generated auxotroph can serve as a traceable marker for the integration. In this study, we demonstrated that a DNA fragment up to 6.3 kb can be efficiently integrated into the Met15 or Lys2 locus using this system. This novel integration strategy can be applied to various yeasts, including natural yeast isolated from wild environments or different yeast species such as Candida albicans. / This work was supported by the Wellcome Trust [202062 to B.H. and 207127 to A.M.] This work was also supported by a SURE studentship from the University of Sheffield [325537] awarded to P.W.D

BLAST reports can be complicated. Viewing them graphically helps to understand them better, especially when the reports are long. At present "Web BLAST" and the stand-alone "wwwBLAST" versions, distributed by the NCBI, include graph- ical viewers for BLAST results. An alternative approach is "BLAST Graphic Viewer" developed by GMOD as part of the BioPerl library. It provides a more aesthetically pleasing and informative graphical visualization to represent BLAST results. All the strategies mentioned above are based on the use of bitmap graph- ics and dependent on JavaScript code embedded in HTML. We present Vector Graphic BLAST (VEGRA) a Python object orientated library based on BioPy- thon to yield graphical visualization of results from BLAST utilizing vector graph- ics. Graphics produced by VEGRA are better than bitmaps for illustration, more exible because they can be resized and stretched, require less memory, and their interactivity is more e ective as it is independent of tertiary technologies due to its integration into the graphic. In addition, the library facilitates a de nition of any layout for the di erent components of the graphic, as well as adjustment of size and colour properties. This dissertation studies previous alternatives and improves them by making use of vector graphics and thus allowing more e ective presentation of results. VEGRA is not just an improvement for BLAST visualiza- tion but a model that illustrates how other visualization tools could make use of vector graphics. VEGRA currently works with BLAST, nevertheless the library has been written to be extended to other visualization problems. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2007.

Doctor of Philosophy / Department of Physics / Andrew G. Ivanov / A search is performed for heavy vector-like top quark partner (T) with electric charge +2/3 by using proton-proton collision events from Large Hadron Collider (LHC) at a centre- of-mass energy of 13 TeV. The data corresponds to an integrated luminosity of 35.9fb−1 collected by the Compact Muon Solenoid (CMS) experiment during 2016. The production of this new hypothetical particle is assumed to be in pairs and strong interaction is responsible for such production mechanism. T quarks can decay to various combinations of third generation quarks and standard model bosons: T → bW, tZ, or tH, and hence the final states consist of pair of opposite-sign leptons consistent with coming from a Z boson and jets. No significant excess has been observed and hence 95% CL upper limits are obtained on TT production cross section by assuming different branching ratios. T quark mass values below 1280 GeV are excluded in case of 100% branching fraction for T → tZ.

Using both single and vector processes, we fitted the Box-Jenkin’s ARIMA model and the Vector Autoregressive model following the Johansen approach, to forecast soy bean and green bean prices on the Chinese futures markets. The results are encouraging and provide empirical evidence that the vector processes perform better than the single series. The co-integration test indicated that the null hypothesis of no co-integration among the relevant variables could be rejected. This is one of the most important findings in this paper. The purposes for analyzing and modeling the series jointly are to understand the dynamic relationships over time among the series and improve the accuracy of forecasts for individuals series by utilizing the additional information available from the related series in the forecasts for each series.