VictorJuiz/thesis huggingface dataset:
Parabolic equations and diffusion processes with divergence-free vector fields

The study of this thesis is motivated by the stochastic Lagrangian representations of solutions to the Navier-Stokes equations. The stochastic Lagrangian formulation to the Navier-Stokes equations is described by stochastic differential equations, which essentially represent the diffusions under divergence-free velocity fields. The associated stochastic differential equations are closely related to a class of parabolic equations and these two types of equations are the central objects of this thesis. The difficulty of the problem mainly comes from the low regularity of the velocity field. The key point is that we use the divergence-free condition to relax the regularity assumptions.
The thesis is divided into two parts. The first part is the Aronson-type estimate which is an a priori estimate on the fundamental solutions (transition probability) independent of the smoothness of the coefficients. In the critical case, we obtain the Aronson estimate in its classical form, while in supercritical cases we obtain a weaker Aronson-type estimate. In the second part, we use approximation arguments to apply the Aronson estimate to the construction of solutions to the parabolic equations and the stochastic differential equations, and further regularity theory of the solutions is obtained for the critical case. Under the supercritical conditions, we will focus on the uniqueness of solutions to the parabolic equations and their relation to the construction of the diffusion processes.

Advisor: Qian, Z
Chen, G
Essays in empirical labor economics and alternative finance

This thesis consists of three independent chapters. The first two chapters are motivated by an empirical fact: most countries in Latin America experienced sharp changes in the wage structure since the mid-1990s, characterised by a substantial reduction of earnings inequality. At the same time that inequality was falling, the economies in the region experienced a rapid transformation of the age, education, and gender composition of their workforces. To what extent are these two phenomena interconnected? Did the wage structure changed as a consequence of the recomposition of labor supply? To answer these questions I propose two stylized models of the labor market, and estimate their main parameters using household survey data ranging more than two decades from Argentina, Brazil, Chile and Mexico. I provide evidence that supply side trends are the major driver of the observed patterns in relative earnings. While relative demands favoured high-skilled workers during the 1990s, they shifted in favour of low-skilled workers during the 2000s.
In the third chapter the subject matter changes altogether. Here I will focus on the workings of newly developed financial technologies used by entrepreneurs to raise capital for their businesses. In particular, the rapidly growing equity crowdfunding market is analysed. The chapter is motivated by the concerns of analysts and regulators that crowdfunding markets are vulnerable to investment herding, so that prior investors' decisions induce future investors to make similar choices. We develop a stylised model to answer the following question: how should herding be characterised in an equity crowdfunding setting where much of the inter-temporal information about a project is based on the amounts previously invested? The model generates predictions that we test using a unique investment-level dataset from one of the leading UK equity crowdfunding platforms. We provide evidence of a considerable level of immediate inter-temporal herding on an equity crowdfunding platform that, nevertheless, quickly dissipates.

Advisor: Bell, B
Quintana-Domeque, C
Mathematical modelling of elastoplasticity at high stress

This thesis is concerned with the mathematical modelling of elastic-plastic deformation in regimes of stress far exceeding the yield stress. Such scenarios are typically encountered in violent impact testing, where millimetre-thick samples of metal are subjected to pressures on the order of the bulk modulus of the material.
We begin with an overview of violent impact testing, with particular attention paid to a specific class of experiments known as isentropic compression experiments (ICEs), which will provide motivation for the mathematical modelling and analysis in subsequent chapters. In chapter 2, by appealing to sound notions from rational mechanics and thermodynamics, we construct a mathematical model which aims to encapsulate the essential phenomena involved in violent elastic-plastic deformation. This is followed in chapter 3 with a numerical analysis of the mathematical model in uniaxial strain, which is the geometry relevant ICEs. In chapters 4 and 5, we corroborate the observations made in chapter 3 via a systematic mathematical analysis. In particular, our focus will be on the elastic and plastic waves that can propagate through finite metal samples during isentropic compression. Finally, in chapter 6, we explore the applicability of our model to other geometries, specifically the radially axisymmetric expansion of a circular cavity embedded in an infinite elastic-plastic medium. We conclude with a summary of our findings and suggest some avenues for future investigation.

Keywords: Equation of state
Plasticity
Asymptotic analysis
Elasticity
Advisor: Howell, P
Ockendon, J
The role of attention in working memory

Attention is usually defined as the ability to select a limited amount of information from the abundance that we are continuously faced with, and short-term memory is often described as a temporary storage for this selected information. However, this description does not do justice to the complexities of the interplay between attention and short-term memory. This thesis explores how attention acts in and on short-term memory. It describes how attentionally selected information flows into short-term memory, and finds that encoding of several items can occur in parallel. It also demonstrates that encoding can occur in a serial fashion too, with behaviourally relevant items being selected and encoded first, and other items second. This thesis not only investigates the initial allocation of these resources during encoding, but also the re-allocation of short-term memory resources during eye movements. Specifically, it fails to replicate the finding that resources are re-allocated to saccade targets, but it does find that the location of items is stored at a higher precision than items’ other features are. Finally, this thesis describes how cancellation tasks (multi-target visual search tasks in which participants have to find and cross out targets among distractors) can be used to measure spatial attention and short-term memory in healthy adults and patient groups. Data is presented to show that cancellation performance can potentially be improved in subtle ways in stroke patients with hemispatial neglect syndrome, using the noradrenergic agonist guanfacine. In sum, attention acts as a gateway to and (re-)allocator of shortterm memory resources, and is an important target for pharmacological interventions in sensitive groups.

Advisor: Husain, M
Stokes, M
Apocryphal Joyce: fuga per canonem

This dissertation explores the idea of an 'apocryphal Joyce' by tracing the evolving apocryphal conflicts — crises of truth, doubt, authority and authorship — in his work. Building on the original meaning of 'apocryphal' as hidden writing (apocrypha scripta), this dissertation follows what it calls Joyce’s fuga per canonem: his flight through the canon. This phrase, from his notes for Ulysses, is especially apt for Joyce given his early connection of the writer as craftsman and apostate with Daedalus, the mythic figure whose wings symbolized for Joyce the liberated intellect of the artist.
With the frame of the canon and the canonical versus 'hidden writing' and the apocryphal this dissertation traces Joyce's various styles of interrogating canonical, authoritative discourse through transgressive or illicit forms of writing. Specifically, this dissertation shows how these various 'apocryphal modes' of Joyce converge as a growing movement of flight. This 'taking flight' shows Joyce’s evolution from his depictions of spiritual and psychological unrest in his early work into his creation of a poetics of unrest, his prodigious invasion and evasion of canonical categories in the transgressive somatic imagery of Ulysses. Finally, this dissertation offers new insights into the humor of Finnegans Wake by exploring the heretofore overlooked comedy of Joyce's many references to canonical and apocryphal scripture in his depiction of the authors of the four canonical Gospels, 'Mamalujo,' and the controversy of the apocrypha scripta they seek, the spurious 'hen's letter.' Ultimately we see that the apogee of Joyce's flight is his embrace of the artist's intellectual liberation, creativity and insight in the apocryphal positions of the outlaw, the marginalized, the exiled and the disenfranchised. The radical experiences and alternative systems of value of these vantages become, as we will see, Joyce's most fundamental creative mode.

Advisor: Johnson, J
The response of Johann Wolfgang von Goethe to the French Revolution

This thesis seeks to explain the reasons behind Johann Wolfgang von Goethe’s critical response to the French Revolution, and to identify his broader political views. It casts Goethe as a reform-minded conservative, who strove to advance civilisation and law-abiding liberty, and deplored tyranny, whether of the few or of the many. He deemed the Revolution politically and socially destructive, as it countered Enlightenment values of reason, tolerance, independent thought, and self-cultivation. While acknowledging the faults of the traditional ruling elite of the monarchy and aristocracy, Goethe also recognised the inherently flawed nature of human beings. This led him to support modest changes to redress specific grievances, rather than to overturn an entire political system in the utopian hope of realising a vice-ridden ‘brotherhood of Man’. The fictional works indicate an author who favoured clearly definable freedoms over an abstract ‘universal’ freedom, who believed that Bürger should develop their intellect and find an occupation best suited to their personal attributes, and that the most temperate and politically astute among them should influence government by co-operating with aristocrats. Goethe also portrays the fall of the ancien régime as largely self-inflicted, presenting many selfish and gullible courtiers, and incompetent kings. He appears to lament its demise, however, and not wish for a repeat in Germany, as the insurgent Bürger-dominated and/or republican regimes seem even more reckless. The advocates of 'liberté, égalité, fraternité' generally come across as perilously naïve or fraudulent, often using altruistic rhetoric to conceal egocentric and vindictive aims. The best cure for a flagging regime is (sometimes considerable) reform, not revolution. Political power should be treated with humility and self-restraint, and the relationship between rulers and subjects should be as intimate as possible. Above all, no part of the social hierarchy should suffer oppression from another, and people should be free to express various opinions, and criticise their government. For Goethe, the Revolution thwarted such principles.

Keywords: Goethe
conservatism
political philosophy
French Revolution
Advisor: Robertson, R
Coeliac disease: health-related quality of life and patients' experiences of health care services

Coeliac disease (CD) is a chronic gastrointestinal condition, the only treatment for which is a gluten-free diet (GFD). Following a GFD is restrictive, burdensome, and can impact health-related quality of life (HRQOL). People with CD can experience long delays to diagnosis and evidence suggests large variations in follow-up care, but the relationship between health care experiences and HRQOL is unknown.
The main aim of this research was to develop a patient-reported outcome measure and patient experience questionnaire, and use these to investigate the relationship between adults’ experiences of health care services and HRQOL in CD. The questionnaires, named the Coeliac Disease Assessment Questionnaire (CDAQ) and the Coeliac Disease Patient Experience Questionnaire (CD-PEQ), were developed following qualitative interviews with adults with CD, and refined with input from experts, and cognitive interviews. The CDAQ was also subject to a translatability assessment to assess its linguistic and cultural translatability, and a cross-sectional survey to assist with item reduction and scale generation. Members of Coeliac UK (n=267) completed the CDAQ and CD-PEQ, together with the SF-36v2 and demographic questions as part of a postal survey.
Psychological health, vitality, general health, and dietary burden were found to have the greatest impact on HRQOL, with physical health and social isolation the least affected. HRQOL was found to have a strong correlation with patients’ experiences of health care services. Aspects most strongly related were: the provision of information; communication with HCPs; difficulty obtaining prescriptions; and GPs' knowledge.
This research has identified aspects of health care services that are strongly related to HRQOL in CD. Health care providers are recommended to focus service improvement efforts on these areas. A reliable and valid disease-specific patient-reported outcome measure and patient experience questionnaire have been developed as part of this study. The CDAQ is suitable for use in research studies, including clinical trials, to assess HRQOL in CD.

Keywords: Patient-reported outcome measure
Patient experience
Quality of life
Coeliac disease
Advisor: Peters, M
Jenkinson, C
Comprehensive mapping of the 3D epigenome by high-content super-resolution image analysis

A full understanding of the relationship between the density and packing arrangements of chromatin in interphase mammalian nuclei and epigenetic function at the nanometer size scale remains an elusive goal in the field of chromatin biology. Over the last years great technical leaps have been made through sequencing-based methods to address this question. Advancements have also allowed research to bypass long-held optical limits to resolve chromatin at a scale where its 3D topology can start to be analysed.
The work in this thesis represents attempts at high-throughput data mining of 3D SIM datasets, encoding rich nanometer-scale spatial information from immunofluorescence detection of histone modifications and key epigenetic markers relative to a chromatin landscape. To do so, an automated and high-throughput image analysis workflow (ChaiN , for ChaiN analysis of the in situ Nucleome) was developed.
Novel metrics for the quantitation and correlation of chromatin and the 3D epigenome reveal a chromatin network of filaments at the size scale proposed from sequencing approaches, and with segregated regions of genomic activities as a function of chromatin accessibility (its density and depth). Furthermore, ChaiN has allowed characterisation of the local and global rearrangements of chromatin when subjected to replication pressures or exogenous perturbation showing for the first time how individual genomic markers are affected at different locations throughout the chromatin network.
The model hypothesised from these results tries to reconcile previous data obtained from Hi-C population ensemble studies and in silico modelling, to single cell observations at super-resolution.

Advisor: Schermelleh, L
Klose, R
Pinto, D
Kinship and strategies for family survival on Bodmin Moor during the long nineteenth century (1793 - 1911)

This thesis has used family reconstitution techniques in order to analyse kinship patterns for the Bodmin Moor parishes of St Neot and Bolventor in Cornwall. A kinship database of more than 13,000 individuals was created and kinship links between households in 1793, 1851 and 1911 were then measured. The results revealed the persistence of dense kinship networks that were very different from those found in English studies, and similar to those found in Wales and Brittany.
Twelve factors were identified that contributed to the creation and persistence of high kinship densities. However, the principal underlying reason was the remarkably consistent spatial pattern of Cornish rural society. St Neot and Bolventor, with their structures of hamlets and small, isolated farm settlements, matched the pattern found across most of Cornwall. It was a structure that enabled people to find both marriage partners and employment in close proximity to their places of birth.
Kinship densities were reinforced by remnants of ancient Cornish manorial systems that survived until the end of the eighteenth century, and then by the ultra-local structures of Methodism in the following century. The latter grew at the same time as the rapid expansion in copper mining. Surprisingly, migrating miners from mid and west Cornwall were also found to have dense local kinship networks. Enclosure also reinforced kinship patterns because of the security of tenure offered to occupiers of the newly created moorland farms, and also because the spatial pattern of settlements repeated the structure of lowland communities enclosed in the medieval period.
The collapse in mining and the greater general mobility of the population did result in a weakening of kinship densities towards the end of the nineteenth century. Despite this, first-order kinship links at the beginning of the twentieth century remained higher than for any comparable study of modern or early modern agricultural or mining communities in England, yet remarkably similar to those in Wales. This shared Welsh and Cornish kinship culture provides fresh evidence, along with other factors such as religious experience and a Brittonic language heritage, to support a Celtic narrative for Cornwall that is perhaps more comprehensive and enduring than has sometimes been supposed.

Keywords: micro-history
reconstitution
Cornwall
Cornish
Advisor: Tiller, K
Prospects for enhancing malaria vaccine efficacy by combining pre-erythrocytic antigens

Malaria causes almost half a million deaths each year. Existing interventions will almost certainly not be enough to tackle this enormous public health problem on their own. An effective vaccine is urgently needed. The leading malaria vaccine, RTS,S, confers suboptimal protective efficacy, and in addition targets only Plasmodium falciparum and not the other major species of human malaria, P. vivax. This thesis investigates the potential of combining pre-erythrocytic malaria vaccines as a means of enhancing protective efficacy. A novel mathematical model was developed which expresses probability of protection as a function of vaccine-induced humoural and cellular responses. The model predicts that combining partially effective vaccines should result in more than additive improvements in protective efficacy. This was supported by an experiment combining Rv21, a P. vivax circumsporozoite virus-like particle, with viral vectored P. vivax TRAP, the two leading pre-erythrocytic malaria vaccine antigens; this combination raised protective efficacy from 50% and 0%, respectively, to 100% sterile protection. It was also found that antigenic interference, a reduction in anti-CSP titres when Rv21 and PvTRAP are combined, occurred only in the presence of Matrix M adjuvant, and not when using alum, AddaVax or no adjuvant. With a view to creating a single-component multi-antigen vaccine, which would be more cost-effective than a multi-component vaccine, experiments were carried out to establish the virus-like particle Qβ as a platform capable of eliciting protective immunity via the display of short peptides derived from the CSP repeat region of both P. vivax and P. falciparum. For the first time, a tetramer peptide derived from the CSP repeat region of P. vivax VK210, AGDR, was shown capable of eliciting protective immunity alone. Finally, five novel linear B-cell epitopes were discovered, one from P. falciparum CSP, three from P. vivax TRAP and one from TRSP, each capable of conferring partial protection on mice. These epitopes were identified using novel screening methods, using sera from whole-protein vaccinated mice or by exploiting conservation within invasion protein sequences. Two of the protective epitopes, (NANP)6 and (ADGN long) were combined and found to enhance protective efficacy as predicted by the mathematical model. Thus this thesis lays the groundwork for the development of a single-component multi-epitope malaria vaccine with enhanced protective efficacy.

Keywords: Malaria
Vaccine
Immunology
Advisor: Reyes-Sandoval, A
Supergravity duals to five-dimensional supersymmetric gauge theories

In this thesis we study gauge/gravity duals in the 5d/6d AdS/CFT correspondence. We start with field theories defined on squashed five-spheres with SU(3) × U(1) symmetry. These five-sphere backgrounds are continuously connected to the round sphere. We find a one-parameter family of 3/4 BPS deformations and a two-parameter family of (generically) 1/4 BPS deformations. The gravity duals are constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplift to massive type IIA supergravity. We holographically renormalize the Romans theory, and use our general result to compute the renormalized on-shell actions for the solutions. The results agree perfectly with the large N limit of the dual gauge theory partition function, which we compute using large N matrix model techniques. In addition we compute BPS Wilson loops in these backgrounds, both in supergravity and in the large N matrix model, again finding precise agreement. We conjecture a general formula for the partition function on any five-sphere background, which for fixed gauge theory depends only on a certain supersymmetric Killing vector. We then proceed to study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic duals to squashed Sasaki-Einstein backgrounds, again matching to a field theory computation, and (iv) find new analytic solutions to the squashed five-sphere background. We also analyse the classification of gravity duals with zero B-field.

Keywords: Dualities
AdS/CFT correspondence
Supergravity
Gauge Theories
Advisor: Sparks, J