VictorJuiz/thesis huggingface dataset:
Topics in analytic number theory

In this thesis we prove several different results about the number of primes represented by linear functions.
The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(phi(q)log{x}) for some value C depending on log{x}/log{q}. Different authors have provided different estimates for C in different ranges for log{x}/log{q}, all of which give C>2 when log{x}/log{q} is bounded. We show in Chapter 2 that one can take C=2 provided that log{x}/log{q}> 8 and q is sufficiently large. Moreover, we also produce a lower bound of size x/(q^{1/2}phi(q)) when log{x}/log{q}>8 and is bounded. Both of these bounds are essentially best-possible without any improvement on the Siegel zero problem.
Let k>1 and Pi(n) be the product of k linear functions of the form a_in+b_i for some integers a_i, b_i. Suppose that Pi(n) has no fixed prime divisors. Weighted sieves have shown that for infinitely many integers n, the number of prime factors of Pi(n) is at most r_k, for some integer r_k depending only on k. In Chapter 3 and Chapter 4 we introduce two new weighted sieves to improve the possible values of r_k when k>2. In Chapter 5 we demonstrate a limitation of the current weighted sieves which prevents us proving a bound better than r_k=(1+o(1))klog{k} for large k.
Zhang has shown that there are infinitely many intervals of bounded length containing two primes, but the problem of bounded length intervals containing three primes appears out of reach. In Chapter 6 we show that there are infinitely many intervals of bounded length containing two primes and a number with at most 31 prime factors. Moreover, if numbers with up to 4 prime factors have `level of distribution' 0.99, there are infinitely many integers n such that the interval [n,n+90] contains 2 primes and an almost-prime with at most 4 prime factors.

Keywords: sieve methods
number theory
prime numbers
Advisor: Heath-Brown, D
Ultracold quantum gases in time-averaged adiabatic potentials

This thesis describes the experimental realisation and characterisation of three non-trivial trapping geometries for ultracold atoms. The double-well, ring and to some degree shell trap are examples of a highly versatile class of traps called time-averaged adiabatic potentials (TAAPs). In this experiment the TAAPs arise from the combination of three independent magnetic fields; a static quadrupole field dressed by a uniform radio-frequency field is time-averaged by a bias field oscillating at in the kHz regime. The result is a very smooth potential, within which ultracold atoms can be evaporatively cooled to quantum degeneracy, and subsequently manipulated into new geometries without destroying the quantum coherence.
The vertically offset double-well potential provided the first example of ultracold atoms confined in a TAAP. The same potential is used to demonstrate efficient evaporative cooling across the Bose-Einstein condensate (BEC) phase transition using only the Landau-Zener loss mechanism. Switching off the time-averaging fields loads atoms from the double-well TAAP into the rf-dressed shell trap. A characterisation of this potential measured low heating rates and lifetimes of up to 58s. With efforts ongoing to increase the trap anisotropy, this potential shows promise for research into the static and rapidly rotating 2D systems. In the presence of a single time-averaging field, the shell geometry is transformed into a ring-shaped trap with an adjustable radius. The ring trap can be controllably tilted and progress towards multiply connected condensates is being made. A rotation scheme to spin up atoms in the ring trap has been demonstrated, presenting the opportunity to investigate the dynamics of superflow in degenerate quantum gases.

Keywords: adiabatic
ultracold
time-averaged
Advisor: Foot, C
Micromechanics of stress corrosion cracking in 304 stainless steel and Ni Alloy 600

The current thesis takes a step forward into understanding the intergranular stress corrosion cracking (IGSCC) by applying a relatively new micro-mechanical technique to look at the crack growth rate of individual grain boundaries in 304 stainless steel (SS) and to measure fracture toughness for different grain boundaries in Ni Alloy 600. In addition, a model is tested and proposed that could predict crack initiation in 304 SS. Pentagonal cross-section cantilevers 5 μm wide by 25 μm long were milled at individual grain boundaries in both 304 SS and Ni Alloy 600. The cantilevers milled in 304 SS were tested in-situ in a customised stage, using the nanoindenter. Crack growth rate was measured for two different cantilevers to be approximately 40 μm/s (K = 1.1 MPa(m)^(1/2)) and 120 μm/s (K = 1.7 MPa(m)^(1/2)). Cantilevers were milled in Ni Alloy 600 for three different samples: samples that were exposed to simulated pressurized water reactors (PWR) environment for 4500 h, for 1500 h and un-oxidised samples. The fracture toughness calculated for the fractured cantilevers in samples that were exposed for 4500 h was measured to be between 0.73 and 1.82 MPa(m)^(1/2). No intergranular fracture occurred in the samples that were exposed for 1500 h and in the un-oxidised samples. The grain boundary misorientation was measured for the tested cantilevers but no direct correlation was observed between the misorientation angle and the fracture toughness.
A Schmid-modified grain boundary stress (SMGBS) model previously used to study the intergranular behaviour of irradiated 316L steel in supercritical water was applied to predict crack initiation in 304 stainless steel. The model was successfully applied and accurately predicted crack initiation. To extend the model, sensitisation was also included. In addition, different areas of the specimen, including the initiation site were analysed using High resolution electron backscatter diffraction (HR-EBSD) technique to measure the geometrically necessary dislocations (GNDs) density. It was observed that the boundary average GNDs is lower for the intact boundaries and higher for the cracked grain boundaries.

Keywords: IGSCC
micro mechanical testing
Advisor: Roberts, S
Marrow, J
Leicester's literary patronage

During the Duke of Alençon's second courtship of Queen Elizabeth the Earl of Leicester emerged as the leading opponent of the marriage. At the same time he began to patronize a circle of writers which included Gabriel Harvey, Edmund Spenser and Philip Sidney, who helped to create the 'golden 1 literature of the English Renaissance. In this thesis I investigate their relations with Leicester and by a detailed examination of their main works, such as the Spenser-Harvey Letters, the Old Arcadia, theShepheardes Calender and theFaerie Queene, and their development, show how they reflect the Earl's intellectual and political concerns. I argue that Alençon was a notable patron and that his growing knowledge of his rival's academic interests encouraged Leicester to maintain his own literary faction. One of his aims was to show the French that English culture was not provincial and he demon- strated this in the entertainment The Four Foster Children of Desire for which he was largely responsible.
Having outlined the background of the crisis of the courtship I evoke Leicester's life and circumstances during this period, particularly his relationship with the Queen and patronage at Oxford. I then describe the distinctive interests of his circle in law, history, politics and poetry and go on to establish that Alençon took part in the French academic movement and that his courtiers included distinguished poets and thinkers. The second half of the thesis is a series of detailed studies of Harvey, Spenser and Sidney in relation to Leicester, and their writings during the Alençon court- ship. Finally I examine the court entertainments of this period and argue for the Four Foster Children as a turning-point in Elizabethan literature.
My conclusion is that Leicester was a more loyal and discriminating patron than he is usually said to have been and that he played a significant part in introducing the 'golden' age of Elizabethan literature.
B cell and antibody responses to influenza a virus in human

Neutralising antibodies and antigen-specific B cells are important for protection against influenza A virus. However, the antigenic evolution of influenza A viruses has made a continuing challenge to the design of vaccine and the public health. The ability to generate cross-reactive response against influenza remains unclear in human. It is important to explore the antibody and B cell repertoire at single cell level.
The pandemic H1N1 and seasonal influenza vaccine induced robust antibody response in adults. However, pre- or co-vaccination with the seasonal vaccine led to a significantly reduced antibody response to pandemic H1N1 virus. Whether this interference has impact on subsequent infection rates remains undetermined. There observed substantial cross-reactive antibody response upon vaccination, as measured by HI, MN and B cell ELISpot assays. The antibody recognizing conserved proteins could be the main component of cross-reactivity against influenza A strains and subtypes. A significant expansion of influenza-specific MBC was observed after infection. Crossreactive response was also noted in the MBC response. Importantly, a robust early-phase ASC response was detected in the peripheral blood upon influenza vaccination or infection. The size of ASC response significantly correlated with serum HI, MN and anti-HA IgG titre three weeks after vaccination. The sequence analysis revealed that early-phase ASC accumulated high level of somatic mutations on Ig variable region and affinity maturation, as well as anti-influenza mAb, which suggested their origin from pre-existing MBC. Eight anti-influenza mAb were made from early-phase ASC, including one high-titre virus-neutralising HA1-specific, two other HA1-specific, one cross-reactive HA2-specific, and four cross-reactive NP-specific antibodies, indicating of the broad diversity of ASC repertoire.
In conclusion, this study demonstrated the properties of antibody and B cell responses to influenza A virus at serological, cellular and sequence level. The virus-neutralising and cross-reactive mAb derived from ASC could have therapeutic potential and their analysis might direct the vaccine design in the near future.

Keywords: Influenza A virus
B cell
Monoclonal antibody
Advisor: McMichael, A
Xu, X
Holonomy of Cartan collections

This thesis looks into the holonomy algebras of Tractor/Cartan connections for both projective and conformal structures. Using a splitting formula and a cone construction in the Einstein case, it classifies all reductive, non-irreducible holonomy groups for conformal structures (thus fully solving the question in the definite signature case). The thesis then analyses the geometric consequences of of holonomy reduction for the projective Tractor connection. A general, Ricci-flat, cone construction pertains in the projective case, and this thesis fully classifies the irreducibly acting holonomy algebras by analysing which holonomy families admit a torsion-free Ricci-flat affine connection, and constructing cones with these properties.

Advisor: Hitchin, N
Molecular dynamics simulations of the equilibrium dynamics of non-ideal plasmas

Molecular dynamics (MD) simulations are used to compute the equilibrium dynamics of a single component fluid with Yukawa interaction potential v(r) = (Ze)^2 exp(−r/λs )/4π eps_0 r. This system, which is known as the Yukawa one-component plasma (YOCP), represents a simplified description of a non-ideal plasma consisting of ions, charge Ze, and electrons.
For finite screening lengths λs, the MD results are used to investigate the domain of validity of the hydrodynamic description, i.e., the description given by the Navier-Stokes equations. The way in which this domain depends on the thermodynamic conditions of the YOCP, as well as the strength and range of the interactions, is determined. Remarkably, it is found that the domain of validity is completely determined by the range of the interactions (i.e., λs); this alone determines the maximum wave number k_max at which the hydrodynamic description is applicable.
The dynamics of the YOCP at wavevectors beyond k_max are then investigated; these are shown to be in striking agreement with a simple and well known generalisation of the Navier-Stokes equations.
In the extreme case of the Coulomb interaction potential (λs = ∞), the very existence of a hydrodynamic description is a known but unsolved problem [Baus & Hansen, 1980]. For this important special case, known as the one-component plasma (OCP), it is shown that the ordinary hydrodynamic description is never valid.
Since the OCP is the prototypical system representing a non-ideal plasma, a number of different approaches for modelling its dynamics have been formulated previously. By computing the relevant quantities with MD, the applicability of a number of models proposed in the literature is examined for the first time.

Keywords: strongly coupled plasma
one-component plasma
Advisor: Gregori, G
Decision-making in the context of pain

Clinical and behavioural evidence has shown that the threat value of pain biases decisions about whether a stimulus is perceived as painful or not, and if yes, how intense is the sensation. This thesis aims to investigate the neural mechanisms underlying the effect of perceived threat on perceptual decisions about pain. The first study investigates the neural mechanisms underlying the effect of threat on the decision about the quality of the sensation, i.e., whether it is perceived as painful or not. The perception of pain (relative to no pain) was associated with activation in the anterior insula as well as an increased connectivity between this region and the mid-cingulate cortex (MCC). Activity in the MCC was correlated with the threat-related bias to perceived pain. In the second study, probabilistic tractography was performed with diffusion tensor imaging to investigate the structural connectivity between subdivisions of the insula and other pain-related regions. Additional analyses revealed that the structural connectivity between the anterior insula and the MCC, and between the posterior insula and somatosensory cortices, is positively correlated with the threat-related bias toward pain. In the third study, a multivariate pattern analysis (MVPA) was performed to investigate whether pain can be decoded from functional neuroimaging data acquired during the anticipation and during the receipt of pain. The results show that pain can be predicted by the pattern of neural activity in the right anterior insula during anticipation and stimulation. The fourth study investigated the effect of uncertainty about the stimulation intensity as a form of threat on the perceived intensity of pain. Uncertainty was found to be associated with an increased activation in the anterior insula. Overall, these findings suggest that a neural network consisting of the anterior insula and the MCC plays a key role in decisions about the quality and the quantity of nociceptive sensation. Results from the MVPA analysis support the notion that perceptual decisions are encoded by a distributed network of brain regions. The variability in anatomical connections between these regions may account for the individual differences in the susceptibility to a threat-mediated bias toward pain.

Keywords: Anxiety
Pain
Functional MRI
Neuroimaging
Decision-making
Advisor: Tracey, I
Wiech, K
Transition metal promoted oxidation and reduction reactions

Two areas of organotransition metal chemistry and their potential application to organic transformations are discussed.
The synthesis of cations of the type [Fe(η5-C5H5)(L)2(CO)]+, [Fe(η5-C5H4CH3)(L)2(CO)]+, [Fe(η5-C5(CH3)5)(L)2(CO)]+ (where (L)2=(CO)2, (PPh3)(CO), (PMe3)(CO), (PPh3)2,(diphos) and (PMe3)2) and [Mo(η5-C5H5)(L)3(CO)] (where (L)3=(PPh3)(CO)2, (diphos)(CO) and (triphos)), many of them novel, is described. Investigations into the site of nucleophilic attack on the cations using hydride as a probe and the effect of varying the overall charge distribution of the cation are discussed. Hydride attack on a carbonyl ligand leads to the formation of metal formyl moieties and their detection by low temperature 1H n.m.r. spectroscopy is described; furthermore, the fate of the metal formyls was found to be dependent upon the nature of the other ligands in the complex. A new criterion for establishing the stereoselectivity of nucleophilic attack on η5-C5H5 ligands is proposed. Hydride attack on an η5-C5H4CH3 ligand was discovered to be regioselective occurring at the carbon atom alpha to the methyl-bearing carbon. The direct oxidation of alkenes to epoxides by hydrogen peroxide was shown to be catalysed by some of the metal carbonyl cations.
The use of organotitanium reagents to convert vic-dibromides and epoxides to alkenes is discussed. (C5H5)2TiCl2 was shown to catalyse both a sodium amalgam debromination of disubstituted vic-dibromides and a zinc debromination of mono and disubstituted vic-dibromides. The latter reaction was developed into a synthetically useful procedure. Reduction of (C5H5)2TiCl2 by both sodium amalgam and zinc dust gave reagents which deoxygenated epoxides. Investigations into the regioselectivity and chemoselectivity of these reagents are discussed. During the synthesis of molecules containing both vic-dibromide and epoxide functionalities, a novel cyclisation was discovered which may have relevance to the biosynthesis of certain marine natural products.

Advisor: Davies, S
Observations of the Sunyaev-Zel'dovich effect using the Cosmic Background Imager 2

This thesis describes the analysis of pointed thermal Sunyaev-Zel'dovich (SZ) effect data from observations using the Cosmic Background Imager 2 (CBI2). CBI2 is an upgrade to the original Cosmic Background Imager, with antennas that have twice the effective collecting area, and hence provide greater sensitivity on longer baselines. Observations of the thermal SZ effect constrain the line-of-sight integrated gas pressure within clusters of galaxies and, when combined with X-ray data, provide an excellent tool for deriving the physical properties of these large structures. The CBI2 SZ data combine relatively low-resolution with a large field-of-view, and can therefore be used to constrain the gas properties of medium-redshift clusters out to the virial radius. By jointly fitting a suitable analytical model to SZ data and X-ray surface brightness data, it is possible to obtain constraints on the temperature and total mass of the cluster. For the analysis work presented in this thesis I choose to parametrise the gas based upon the known behaviour of the entropy, and the total mass by the Navarro, Frenk and White (NFW) prescription. This model is tested against Hydrodynamic/N-body simulations and is found to reproduce the radial behaviour of key cluster properties. The CBI2 observations presented in this work focus on the REFLEX-DXL clusters, an X-ray luminous sub-sample of the REFLEX survey at z ~ 0.3, which have previously published X-ray surface brightness data. The Bullet Cluster, a significant merger system, is a member of this sample and is presented here as a case study for use of the entropy-based model. The derived total mass and gas mass fraction of this cluster are found to be consistent with results from previous X-ray observations. The derived properties from the REFLEX-DXL sample are used to construct a preliminary set of SZ scaling relations out to the virial radius, and are found to be consistent with the self-similar model for massive clusters.

Keywords: radio interferometry
Sunyaev-Zel'dovich effect
clusters of galaxies
cosmic microwave background
cosmology
radio astronomy
Advisor: Jones, M
Land acquisition in British India c. 1894-1927

This study offers the first instalment of a general history of land acquisition in British India, c. 1894–1927. It advances eight principal theses: (i) that the first law of land acquisition was enacted in 1668, as part of a political settlement by the East India Company with the Portuguese landlords of Bombay island; (ii) that, to a remarkable degree, land acquisition law was shaped in the interest of the sterling railway companies; (iii) that the state habitually used land acquisition not so much to effect non- consensual transfers but to ‘launder’ titles free of encumbrances and other claims; (iv) that the primary beneficiaries of land acquisition were public bodies, the sterling railway companies, and elite private interests; (v) that the executive was hostile to legislative and judicial oversight of land acquisition, and successfully resisted or co-opted attempts to impose such oversight; (vi) that the courts were in any event content with the role they were assigned under the 1894 Act, and generally deferred to the executive in land acquisition cases; (vii) that the land-acquiring executive, although hostile to and unencumbered by meaningful legislative and judicial oversight, as a general rule displayed a legal fastidiousness; (viii) that, despite an appearance of impartiality, land acquisition bore the stain of imperialism. These theses are advanced in the course of explaining the failure of the forgotten Kelkar Bill (1927), an attempt by the Maharashtrian nationalist N. C. Kelkar (1872–1947) to enact far-reaching amendments to the Land Acquisition Act 1894. Kelkar’s fellow nationalists withheld their open support from the measure and thereby guaranteed its failure: a counterintuitive choice that, it is argued, exemplifies the tactical compromises of nationalism.

Keywords: India
History
Eminent domain
Advisor: Getzler, J
Miniature buildings in the Liao (907-1125) and the Northern Song (960-1127) periods

This thesis is concerned with the construction and uses of miniature buildings in the Liao (907-1125) and the Northern Song (960-1127) periods in China. These miniature buildings exploited the components of Chinese traditional architecture on a small or greatly reduced scale. To date no work has taken the position of this thesis to examine this corpus of miniature buildings that were used widely in tombs and temples as containers to provide coverings for coffins, and to hold images of deities, Buddhist relics and sutras, as seen in both archaeological discoveries and textual resources. The purpose of the thesis is to define this corpus and to consider its significance in the light of the functions that these tiny buildings fulfilled.
This thesis proposes that these miniature buildings contributed a unique and indispensable part in presenting the positions of their owners in society. Made as containers, miniature buildings particularly emphasize decoration, which enabled viewers to make a connection with life-size buildings, in the ways of which they were fitted into an existing architectural hierarchied system in the deeply rooted tradition of the Liao and the Northern Song. The thesis makes considerable use of the concepts of reception, for the reaction of viewers to these miniature buildings defined also their reactions to the contents. Several types of analogies were achieved between full-scale buildings and miniature representations, as well as between their contents, which allowed specific types of interpretation of the miniature buildings as taking the roles of actual buildings and fictional structures.
The thesis considers the use of miniature buildings as one of the ways in which complex ideas can be reinforced by material forms. A wider discussion on miniature models presents that the significance of miniaturization lies in the power of control that can be achieved by creating and using the miniature.

Keywords: models
Song
architecture
Liao
China
miniature
Advisor: Rawson, J