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The overarching theme of this thesis is the study of Stein's method on manifolds. We detail an adaptation of the density method on intervals in R to the unit circle S¹ and give examples of bounds between circular probability distributions. We also use a recently proposed framework to bound the Wasserstein distance between a number of probability measures on Riemannian manifolds with both positive and negative curvature. Particularly, a finite parameter bound on the Wasserstein metric is given between the Riemannian-Gaussian distribution and heat kernel on H³, which gives a finite sample bound of the Varadhan asymptotic relation in this instance. We then develop a new framework to extend Stein's method to probability measures on manifolds with a boundary. This is done by the addition of a local time term in the diffusion. We find that many results carry over, with appropriate modifications, from the boundary-less case.

Evolutionary population synthesis models have been instrumental to our understanding of galaxy formation and evolution. For the successful application of these models, they must be underpinned by a comprehensive catalogue of theoretical or empirical stellar spectra. In the latter case, spectra must be described by certain atmospheric parameters: effective temperature (T eff), surface gravity (log g) and chemical abundance ([Fe/H] and [α/Fe]). Thus, to accurately model the spectrophotometric properties of distant galaxies, we must first study the stars around us. In this thesis we utilise the MaNGA Stellar Library (MaStar), an SDSS-IV survey of 80,592 spectra representing 27,945 unique stars, to create the basis for the next-generation of stellar population models for extragalactic astronomy. We have developed a stellar parameter pipeline that fits theoretical spectra from a combination of model atmosphere libraries to each MaStar observation using the penalised pixel-fitting method (pPXF). We match the MaStar observations to Gaia photometry and use this to set reliable, flat priors for Teff and log g. The stellar atmospheric parameters and their uncertainties are then estimated with a Bayesian approach in combination with the Markov Chain Monte Carlo (MCMC) algorithm. Initially, we calculated stellar parameters using solar-scaled [α/Fe] models, which was then expanded to include [α/Fe] as a fourth parameter. Our method is corroborated by its application to well known stars, such as the Sun and Vega, by comparing our results to several other literature sources of stellar parameters and by the parallel development and testing of stellar population models on star clusters. By applying quality flags based on MCMC convergence and the χ2 of the model fit, we recover the following parameter distributions for 52,276 spectra: 2913 ≤ Teff ≤ 26096 K, −0.5 ≤ log g ≤ 5.4, −2.5 ≤ [Fe/H] ≤ 0.7. For a sample of 17,214 spectra, we estimate [α/Fe] in the range of −0.25 < [α/Fe] < 0.48. We further leverage the vastness of MaStar by identifying carbon- and oxygen-rich, thermally-pulsing asymptotic giant branch (TP-AGB) stars for their inclusion in stellar population models. This research is done using the SDSS photometric bands (u, g, r, i, z) due to time efficiency and as a proof of application to future large photometric surveys, such as the Legacy Survey of Space and Time (LSST). We apply an unsupervised machine learning technique called t-distributed stochastic neighbour embedding to test its ability in TP-AGB identification. This method is able to isolate such stars and correlates well with the atmospheric parameters. We then define a novel colour selection of (g − r) > 2 and (g − i) < 1.55(g − r) −0.07, based solely on SDSS photometry. This is compared to literature colour cuts and a supervised learning, support vector machine (SVM) which we have trained. We find the SVM method most efficient, recovering an average F1-score, the chosen performance metric, of 0.82 over 200 test cases. Through such methods we are able to identify 69 carbon-type and 118 oxygen-type spectra in MaStar. Lastly, we determine the spectral types of MaStar TP-AGB stars using empirical templates and a discrete version of our stellar parameter fitting routine. The application of MaStar spectra has marked a new era in galaxy modelling, allowing for the study of complex stellar populations over a wide wavelength domain. The latest MaStar-based stellar population models, using the atmospheric parameters presented here, have already been applied to the SDSS MaNGA data analysis pipeline and can be used for future surveys by probing the optical and near-infrared window.

Dusty star-forming galaxies (DSFGs) are highly luminous (LFIR ≳ 10¹² L⊙), very distant (z ≳2.5) and ≳ 10x rarer then 'normal', NIR-selected (BzK), star-forming galaxies. Capable of producing a Mstars ≳ 10¹¹-M⊙ galaxy after a tburst ~ 100-Myr burst of late-stage, merger-induced star formation, DSFGs naturally provide extreme laboratories with which to study the formation and evolution of massive structures within the Universe. Thus far, however, theoretical models have struggled to reconcile the observed abundance and redshift distribution of these massive, dust-enshrouded galaxies that occupy the high-end tail of the galaxy stellar mass function. Therefore, it is of paramount importance, from an observational point of view, to both increase the number of known distant (z ≳ 4) DSFGs and to thoroughly explore their extreme environments in order to provide further constraints on such models. Thus, in Chapter 2 of this thesis, I report on efforts to substantially increase the number of distant DSFGs using the uniquely wide H-ATLAS imaging survey. I analysed a sample of 109, so-called 'ultra-red galaxies' selected via their red Herschel-SPIRE flux densities (σ500 > 3.5 and S500 < 100mJy) and flux-density ratios (S500/S250 > 1.5 and S500/S350 > 0.85). Ground-Based continuum imaging at ~ 850 μm with the JCMT and APEX telescopes allowed me to locate the dust peaks of these S500 ≳ 30-mJy ultra-red galaxies and derive a median photometric redshift of zphot = 3.66 (3.30-4.27, IQR) for them (assuming that they can satisfactorily be represented by a Tdust ~ 30-K template SED). Using 25 spectroscopically confirmed DSFGs with SPIRE flux densities matching this ultra-red criteria, I determined that these FIR photometric redshift estimates have a minimum intrinsic scatter of σ = 0.14(1 + zspec) and systematically under-estimate the spectroscopic redshifts below zspec ≲ 5. With over a third of these ultra-red galaxies lying above z > 4, I derived a space density of at least p ≈ 6 x 10⁻⁷Mpc⁻³ for this sample (assuming a tburst = 100-Myr burst of star formation), which is only a factor of 7x less numerous than that of the most massive (Mstars ≳ 10¹¹M⊙), compact, quiescent galaxies selected in the NIR at z ~ 3. Finally, although the space density of z > 4 ultra-red galaxies aligns very well with that of massive (MBH ≳ 10⁸M⊙) AGN at z > 6, none have yet to be uncovered within this sample to date. In the following chapter, I present wide images obtained with LABOCA of a sub-sample of 22, representative ultra-red galaxies to see if these galaxies are signposting over-dense regions in the early Universe, as might be expected if they were to evolve into the most massive, compact, quiescent galaxies at z ~ 0. This LABOCA ultra-red galaxy survey covers an area of ≈ 0.8 deg² down to an average r.m.s. of 3.9mJy beam⁻¹, with the five deepest images going ≈ 2x deeper still. I catalogue 86 galaxies detected above > 3.5σ870 surrounding these 22 ultra-red galaxies, which implies a δ ≈ 100 ± 30% over-density of S870 > 8.5-mJy (LFIR ≈ (7-30) x 10¹² L⊙) DSFGs when compared against LESS. Thus, I am 99.93% confident that these ultra-red galaxies are pinpointing over-dense regions in the Universe, and ≈ 95% confident that these regions are over-dense by a factor of at least ≥ 1.5x. Using the same template SEDs as in the previous chapter, I derived a consistent median photometric redshift of z = 3.2 ± 0.2 with an IQR of z = 2.8-3.6 for these ultra-red galaxies. I constrained the surrounding galaxies likely responsible for this over-density to within |∆z| ≤ 0.65 of their respective ultra-red galaxies. However, on average, I was only able to associate one surrounding galaxy to within |∆z| ≤ 0.5 of its respective ultra-red galaxy. These 'associated' galaxies are radially distributed within (physical) distances of 1.6 ± 0.5Mpc from their ultra-red galaxies, have median SFRs of vI≈ (1.0±0.2)x10³M⊙ yr⁻¹ (assuming a Salpeter stellar IMF) and median gas reservoirs of Mgas ~ 1.7 x 10¹¹M⊙. These candidate proto-clusters have average total SFRs of at least Ψ ≈ (2.3 ± 0.5) x 10³M⊙ yr⁻¹ and a space density of ~ 9 x 10⁻⁷Mpc⁻³, consistent with the idea that their constituents may occupy the centres of rich galaxy clusters seen today. Finally, in Chapter 4 of this thesis, I extracted Herschel-SPIRE photometry at the 850-μm positions of DSFGs detected within in the S2CLS and S2COSMOS imaging surveys. I then analysed the multi-wavelength environmental properties around a robust sample of 64 ultra-red galaxies selected via their 'ultra-red probability'. Similar to the findings in Chapter 3, I found that these ultra-red galaxies are preferentially located in over-dense regions extending over scales of ~ 5' (or ~ 2Mpc at z ~ 3). Furthermore, I found that these candidate, high-redshift proto-clusters have FIR total dust masses and total SFRs of Mdust ~ 10⁹M⊙ and Ψ ~ 10³M⊙ yr⁻¹, respectively. Ground-Based, optical/NIR imaging around a subset of 42 ultra-red galaxies shows a factor of ~ 5x increase in both the stellar mass and the (MB -MI )-colour of associated LBGs as the radial distance decreases from . 500 kpc - consistent with the emergence of a galaxy red sequence at z ~ 3. Furthermore, these data show a 1-σ increase in the fraction of 'green-valley' galaxies within scales of ~ 5' compared to the field - supporting the concept that red-sequence galaxies are appearing at a faster rate around ultra-red galaxies compared to the field. There is a sizeable contribution of Mstars ~ 10¹²M⊙ from these high-redshift LBGs within the environments of ultra-red galaxies. On average, I was able to associate ≈ 28 LBGs to a given ultra-red galaxy (~ 30x the number of associated DSFGs). Although these systems have average optical/NIR/FIR properties that are consistent with their evolution into present-day galaxy clusters with DM halos of mass Mhalo ~ 10¹⁴-10¹⁵M⊙, I am still likely missing a sizeable contribution from unassociated LBGs and DSFGs due to the large photometric redshift uncertainties for the ultra-red galaxies. Therefore, the results presented in this thesis should be regarded as firm lower limits on these environmental properties around ultra-red galaxies, which can now only be improved upon when spectroscopic data increases the accuracy of the photometric redshift estimates presented here.

The design of a modular moving trap Zeeman decelerator capable of decelerating gas pulses produced from a supersonic source is presented here. Unlike the conventional form of Zeeman decelerator, paramagnetic particles are confined in a 3D potential throughout the deceleration process. The decelerator field is produced by flattened helical coils and currents of up to 1000 A peak. As the coils are periodic in nature, each coil produces a number of deep, quadrupole traps along the molecular beam axis. The resultant periodic field is described as a travelling wave. The application of the appropriate time dependent current allows the traps to move through the four coil modules. In order to compensate for the weaker transverse confinement, a quadrupole guide, operating at 700 A DC, is required to prevent further losses during the deceleration process. The operation of the decelerator relies on the power electronics developed specifically for the quadrupole and the decelerator coils. Due to the electromagnetic interference generated through the switching of the large currents, much of the electronics used to control the power electronics had to be developed specifically. The quadrupole power electronics have been designed to produce fast switching edges. This is necessary to minimise the interaction of the particles within the fringe field regions while maximising the interaction time within the pure quadrupole field. Even at a modest voltage applied to the circuitry, the rise time in current to 700 A has been reduced by a half. The decelerator power electronics must be capable of producing an alternating waveform with an amplitude of at least 500 A for each of the coil phases. Furthermore, the frequency of the waveforms must be tunable within a range of 10 kHz to 0 Hz. Through a combination of pulse width modulation and knowledge of the electrical properties of the coil it is possible to synthesise an alternating current waveform from a 800 V DC supply using a suitable switching circuit. %The challenge of switching such high powers is the transient voltage spikes that can be produced, however, these can be avoided through careful consideration of the layout of the circuit. Decelerators such as this do not cool the sample but instead reduces the mean velocity of a subset of particles which remained trapped. This maintains the phase space density of trapped particles. Modelling the magnetic fields generated by the decelerator coils has been necessary in order to understand the phase space acceptance of the decelerator. The helical nature of the coils required the development of a specific algorithm in order to calculate the field generated by each wire element. The resultant potential can then be interpolated using a tricubic interpolator to extract the field gradients necessary for numerical simulations of the particle trajectories. Including the effects of the pulse width modulated on the trap facilitates the characterisation of the acceptance of the decelerator and the limitations of the current iteration of the design. The numerical simulations can also be compared to experimental results gathered for metastable argon. The 3D guiding, or velocity bunching, of the gas packet over a range of velocities has been demonstrated. The ability to 3D guide and decelerate were severely hampered by the failure of key electronic components, limiting three coils to 100 A peak, moreover, these traps were sub-optimally loaded. Deceleration from 350 to 347 m/s and 342 to 310 m/s has been observed. The design of a trap capable of simultaneously loading samples of decelerated CaH and Li while allowing the cooling of Li would potentially allow for the sympathetic cooling of a molecular species with an atomic refrigerant. This particular atom-molecule system would also facilitate the examination of controlled chemistry and collisions over a range of temperatures through state selection of the reactants. The loading of the trap has been optimised in 1D for CaH with a loading efficiency of 52.2 % while only 7.3 % of Li is loaded when each of the gas packets has a mean velocity of 11 m/s. This implies that the source of the Li must be at least 130 times brighter than that of the CaH.

Lydia Lunch, David Wojnarowicz and Vaginal Davis are artists who each produced music, film, literature, performance, visual art and installation whilst participating in the subcultural communities of post-punk. This thesis frames them as post-punk polymaths, artists whose subcultural participation provides a link between their multiple artistic outputs. I position these artists in relation to the historical context of post-punk, and document its influence on both specific examples of their work and their artistic strategies more broadly. My original contribution is of a sustained process of attention to the work of these three artists that negotiates their personal antagonisms towards criticism and resistance to historicisation, the methodological challenge exemplified by their practice, and the critical potential of embracing this difficulty. Through an account of New York's post-punk scene (the formative artistic environment of both Lunch and Wojnarowicz), I examine the way the material conditions of the subculture provoked an undifferentiated, multi-media practice. I explore Lunch's work through this subcultural context, and the interrelations of her diverse outputs and intentional blurring of art and life in her public persona. Through the work of David Wojnarowicz, I explore the potential pitfalls of overdetermination, or confined articulations of his practice within popular criticism and academia. My third case study moves away from New York to focus on the work of Los Angeles post-punk artist Vaginal Davis, examining the responsibility subculturally invested artists may have in maintaining their own marginality, through a framing of Davis's practice as self-sabotaging. My thesis therefore highlights the difficulty of rationalising these practices as objects of disciplinarily constituted analysis, the problematic nature of their omission or selective and incomplete engagement, and examines the potential of the term polymath to understand artists whose work fails to map on to the disciplinary remits of academic scholars, genre critics or popular historians.

It is widely believed that quantum physics is a fundamental theory describing the Universe. As such, one would expect to be able to see how classical physics that is observed in the macroscopic world emerges from quantum theory. This has so far largely eluded physicists, due to the inherent linear nature of quantum physics and the non-linear behaviour of classical physics. One of the principle differences between classical and quantum physics is the statistical, probabilistic nature of quantum theory. It is from this property that non-classical states can arise, such as entangled states. These states possess maximal correlations. However, they are not the only way in which correlations are created in quantum systems. This thesis aims to show how open quantum systems naturally contain correlations from their quantum nature. Moreover, even seemingly simple open quantum systems can behave far more complexly than expected upon the introduction of quantum feedback. Using this effect, the dynamics may become non-linear and as such behave non-trivially. Furthermore, it is shown how these effects may be exploited for a variety of tasks, including a computational application in hidden quantum Markov models and a quantum metrology scheme that does not require the use of exotic quantum states. This results in the design of systems that benefit from the use of quantum mechanics, but are not constrained by the use of experimentally difficulties such as entanglement.

In this thesis further developments on the thermal cascade reaction discovered in the Parsons group have been made. The substrate scope has been increased to include the ketone linked 1,6-diynes, which had failed to cyclise in previous studies. Furthermore, variations on the precursor molecule have led to the cyclisation of nitrogen and sulphur analogues to provide the respective annulated pyrrole and thiophene products. The synthesis of these compounds using the Parsons-Board-Waters cyclisation had not been explored during earlier studies within the group. The increased scope of the Parsons-Board-Waters cyclisation was applied to the total synthesis of the natural product (+)-aphidicolin. The development of model systems are described, with the importance of the ketone functionality being highlighted by the unsuccessful cyclisation of dioxolane protected precursors. Furthermore, the enantioselective synthesis of a key intermediate containing the required 1,3-diol functionality present in the natural product is reported. This will provide a route to future research on the application of the Parsons-Board-Waters cyclisation to (+)-aphidicolin.

Nematic liquid crystals are mesogenic materials that are popular working materials for optical displays. There has been an increased interest in bistable liquid crystal devices which support two optically distinct stable equilibria. These devices typically exploit a complex geometry or anchoring conditions, which often induces defects in the equilibria. There remains a great deal to be understood about the structure of the defects and how they stabilize multiple equilibria in modern devices. This thesis focuses on four problems: the first three explore the effect of confinement and defects on nematic equilibria in simple geometries, with the aim of exploring multistability in these geometries; the fourth problem concerns the fine structure of point defects, essential for future modelling of nematic equilibria in more complex geometries. Firstly, we study nematic liquid crystals confined to two-dimensional rectangular wells using the Oseen-Frank theory. Secondly, we study equilibria within a semi-infinite rectangular domain with weak tangential anchoring on the surfaces. Thirdly, we study nematic equilibria within two-dimensional annuli. We derive explicit expressions for the director fields and free energies of equilibria within these geometries and discuss the stability of the predicted states. These three problems are motivated by the experimental work on colloidal nematic liquid crystals, which we interpret in the context of our results. Finally, we study the fine structure and stability of the radial hedgehog defect in the Landau-de Gennes theory with a sixth order bulk potential, relevant to the observability of global biaxial phases in a model with higher order potential terms.

When an organism migrates from one area to another it comes into contact with many boundaries to its survival and fitness. The fruitfly Drosophila melanogaster has migrated from Africa, into Europe and colonised much of the rest of the world. The subject of this thesis is to better understand how Drosophila has adapted to survive the temperate climates in Europe. The variability of temperature and light from one season to the next makes adaptation of the circadian clock and life history strategy all the more important. Drosophila appear to have adjusted to the new conditions by exhibiting diapause in low temperatures when the nights are long and by altering several other characteristics of its circadian clock that may be related to diapause. One of these is a novel European single nucleotide polymorphism in the timeless gene that allows flies to maintain a more robust diapause than flies carrying the ancestral allele. This variant exists in all European populations and winter simulation experiments reveal that it maintains its diapause for longer than the ancestral variant. These experiments also supported the possibility that Drosophila diapause can be maintained for much longer periods than previous studies have indicated. Experiments with ancestral African D. melanogaster lines alongside several closely related species indicates that diapause may not be a recent adaptation, but an ancient response to stressful conditions that has adapted in Europe to be more sensitive to low temperatures and short photoperiods. I also discover that a splice variant of the period gene has a dramatic, further cementing the controversial relationship between clock genes and diapause. In addition I have performed a study of putative functional polymorphisms in this untranslated region around this splice site from European populations. Finally, a study of putative clock genes reported in Chapter 3 provides a cautionary tale as to the dangers of using RNAi.

cl+ is an important intracellular messenger with a role in a wide range of processes. Ca2 + is normally maintained at a very low concentration on the cytosol, but in order to generate a signal, its concentration may be increased by influx through channels in the plasma membrane, or by means of release from intracellular stores. Release of Ca2 + from intracellular stores may be initiated by ci+ itself, or by a Ca:!T-releasing second messenger such as inositol 1,4,5-trisphosphate. Another such Ca2+-releasing second messenger is the recently discovered nicotinic acid adenine dinucleotide phosphate (NAADP). The second messenger functions of NAADP have thus far been defined onlv in a limited munber of model tissues. This thesis aims to develop a versatile and sensitive method for measuring changes in NAADP levels in a \vide variety of cell and tissue types. This method is then used to address a munber of outstanding questions \\1th regard to the physiological functions ofNAADP. The sea urchin sperm model system is used to investigate possible steps in the transduction cascade and the synthesis pathway for NAADP. The first data regarding a possible function for NAADP within the speml is also presented. The possible fimction ofNAADP as a second messenger bas then been investigated in two mammalian tissue types. Changes in NAADP levels in response to extracellular agol1ists are measured in cardiac ventricular and neuronal tissues, providing important insight into exactly which receptor types use NAADP as a part of their intracellular transduction cascade. For example, stimulation of dopamine D2-like, but not DJ-like receptors produces an increase in NAADP. The development of two new chemical tools, NAADP-AM and Ned-14 is also detailed. These are the first cell-permeant compolUlds to he identified for NAADP. Ned-14 is an antagonist of the NAADP receptor with an IC50 of 2 J.!M. As such, it is hoped that their use will allow much more rapid and definitive elucidation of the pathways of NAADP-mediated Ca2+signalling than has previously been possible.