New methods for the asymmetric synthesis of α-alkylated ketones and 1,3-amino alcohols

A large number of optically active drugs and natural products contain α-functionalised ketones or simple derivatives thereof. Furthermore, chiral α-alkylated ketones are useful synthons and have found widespread use in total synthesis. The asymmetric alkylation of ketones represents one of the most powerful and longstanding procedures in organic chemistry. Surprisingly, however, only one effective methodology is available, and this involves the use of chiral auxiliaries. This is discussed in Chapter 1, which also provides a background of other key topics discussed throughout the thesis. Expanding on the existing methodology of chiral auxiliaries, Chapter 2 details the synthesis of a novel chiral auxiliary containing a pyrrolidine ring and its use in the asymmetric preparation of α-alkylated ketones with good enantioselectivity. The synthesis of racemic α-alkylated ketones as reference standards for GC chromatography is also reported in this chapter. Chapter 3 details a new approach to chiral α-alkylated ketones using an intermolecular chirality transfer methodology. This approach employs the use of simple non-chiral dimethylhydrazones and their asymmetric alkylation using the chiral diamine ligands, (+)- and (-)-sparteine. The methodology described represents the first example of an asymmetric alkylation of non-chiral azaenolates. Enantiomeric ratios up to 83 : 17 are observed. Chapter 4 introduces the first aldol-Tishchenko reaction of an imine derivative for the preparation of 1,3-aminoalcohol precursors. 1,3-Aminoalcohols can be synthesised via indirect routes involving various permutations of stepwise construction with asymmetric induction. Our approach offers an alternative highly diastereomeric route to the synthesis of this important moiety utilising N-tert-butanesulfinyl imines in an aldol-Tishchenko-type reaction. Chapter 5 details the experimental procedures for all of the above work. Chapter 6 discusses the results of a separate research project undertaken during this PhD. 2-alkyl-quinolin-4-ones and their N-substituted derivatives have several important biological functions such as the role of Pseudomonas quinolone signal (PQS) in quorum sensing. Herein, we report the synthesis of its biological precursor, 2-heptyl-4-hydroxy-quinoline (HHQ) and possible isosteres of PQS; the C-3 Cl, Br and I analogues. N-Methylation of the iodide was also feasible and the usefulness of this compound showcased in Pd-catalysed cross-coupling reactions, thus allowing access to a diverse set of biologically important molecules.

The development of new methods for high resolution radio astronomy imaging

Very Long Baseline Interferometry (VLBI) polarisation observations of the relativistic jets from Active Galactic Nuclei (AGN) allow the magnetic field environment around the jet to be probed. In particular, multi-wavelength observations of AGN jets allow the creation of Faraday rotation measure maps which can be used to gain an insight into the magnetic field component of the jet along the line of sight. Recent polarisation and Faraday rotation measure maps of many AGN show possible evidence for the presence of helical magnetic fields. The detection of such evidence is highly dependent both on the resolution of the images and the quality of the error analysis and statistics used in the detection. This thesis focuses on the development of new methods for high resolution radio astronomy imaging in both of these areas. An implementation of the Maximum Entropy Method (MEM) suitable for multi-wavelength VLBI polarisation observations is presented and the advantage in resolution it possesses over the CLEAN algorithm is discussed and demonstrated using Monte Carlo simulations. This new polarisation MEM code has been applied to multi-wavelength imaging of the Active Galactic Nuclei 0716+714, Mrk 501 and 1633+382, in each case providing improved polarisation imaging compared to the case of deconvolution using the standard CLEAN algorithm. The first MEM-based fractional polarisation and Faraday-rotation VLBI images are presented, using these sources as examples. Recent detections of gradients in Faraday rotation measure are presented, including an observation of a reversal in the direction of a gradient further along a jet. Simulated observations confirming the observability of such a phenomenon are conducted, and possible explanations for a reversal in the direction of the Faraday rotation measure gradient are discussed. These results were originally published in Mahmud et al. (2013). Finally, a new error model for the CLEAN algorithm is developed which takes into account correlation between neighbouring pixels. Comparison of error maps calculated using this new model and Monte Carlo maps show striking similarities when the sources considered are well resolved, indicating that the method is correctly reproducing at least some component of the overall uncertainty in the images. The calculation of many useful quantities using this model is demonstrated and the advantages it poses over traditional single pixel calculations is illustrated. The limitations of the model as revealed by Monte Carlo simulations are also discussed; unfortunately, the error model does not work well when applied to compact regions of emission.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Towards a new model of criminal justice system in the era of globalised criminality: the biggest challenges for criminal process legislation

The main objective of this thesis is the critical analysis of the evolution of the criminal justice systems throughout the past decade, with special attention to the fight against transnational terrorism. It is evident – for any observer - that such threats and the associated risk that terrorism entails, has changed significantly throughout the past decade. This perception has generated answers – many times radical ones – by States, as they have committed themselves to warrant the safety of their populations and to ease a growing sentiment of social panic. This thesis seeks to analyse the characteristics of this new threat and the responses that States have developed in the fight against terrorism since 9/11, which have questioned some of the essential principles and values in place in their own legal systems. In such sense, freedom and security are placed into perspective throughout the analysis of the specific antiterrorist legal reforms of five different States: Israel, Portugal, Spain, the United Kingdom and the United States of America. On the other hand, in light of those antiterrorist reforms, it will be questioned if it is possible to speak of the emergence of a new system of criminal justice (and of a process of a convergence between common law and civil law systems), built upon a control and preventive security framework, significantly different from traditional models. Finally, this research project has the fundamental objective to contribute to a better understanding on the economic, social and civilization costs of those legal reforms regarding human rights, the rule of law and democracy in modern States.