VictorJuiz/thesis huggingface dataset:
On global existence for variants of Teichmueller harmonic map flow
Keywords: 58E20
53C43
53C44
53A10

We resolve questions of existence and singularity formation for the Teichmueller harmonic map flow, a geometric flow introduced by Rupflin and Topping that deforms surfaces immersed in a Riemannian manifold into minimal surfaces.
We obtain global solutions of Teichmueller harmonic map flow in new settings from cylinders into nonpositively curved targets, and prove their asymptotic convergence to solutions of the Douglas–Plateau problem of finding minimal surfaces spanning given boundary curves in a Riemannian manifold. Due to the nonlinear nature of the formulation with non-local projection operators and unusual boundary conditions, even short-time existence presents a challenge, requiring consideration of a time discretisation scheme and partial differential inequalities.
In the second part of the thesis, we present joint work with Rupflin establishing a mechanism by which solutions to Teichmueller harmonic map flow will degenerate in finite time into maps from surfaces of simpler topological type. We give sufficient criteria for degeneration for the flow both from closed surfaces and from cylinders in terms of the rate at which images of thin collars in the domain stretch out. Moreover, for the rescaled variant of the flow by Huxol, we show that such a rate is both necessary and sufficient for a degeneration. Furthermore, for both types of the flow from cylinders we construct settings in which the metric on the cylinder degenerates in finite time, settling an open question on whether such a finite-time degeneration is possible.
‘A most peculiar form of disease’: The creation of anorexia nervosa in late nineteenth-century Britain
Keywords: Women's Life-Writing
Anorexia Nervosa
Illness Narratives
Eating Disorders
Women's periodicals, British

Anorexia nervosa appeared as a newly named disorder in the 1870s in Britain, leading historians and other scholars to pinpoint this as the origin point of a medicalised understanding of female food refusal. An abiding interest in locating the historical roots of this contemporary disorder has led scholars to emphasise the ways in which anorexia nervosa is therefore an historical and not merely a ‘modern’ disorder. It has also resulted in a body of scholarship that emphasises continuity over discontinuity in anorexia nervosa’s medicalised history. This has meant that scholars have neglected to ask why after its introduction into the medical lexicon, anorexia nervosa failed to become established as a credible, universally recognised and endorsed, and utile diagnostic category.
This thesis is therefore concerned with two intertwined curiosities about anorexia nervosa’s appearance in this period. It on the one hand explores the conditions within the medical profession that facilitated anorexia nervosa’s identification and influenced the form in which it was articulated. It then pivots away from its emergence to show that this new disorder failed to make inroads into either the medical community or into late Victorian society and culture more broadly. The thesis argues that following its identification, anorexia nervosa failed to achieve supremacy within the medical profession and further failed to either reflect or influence women’s social reality or align neatly with the anxieties encoded within cultural discourses about young women’s health. As a result, and complicating the notion of a binary between continuity or discontinuity, it concludes that although the creation of anorexia nervosa as a new and distinct clinical syndrome in the late nineteenth century does indeed represent the origin point of a medicalised understanding of female food refusal, anorexia nervosa’s early history can be most aptly characterised as a ‘false start’ for what would become, much later, an enduring, troubling and highly visible psychiatric disorder.
Magmatism and volcanism on Io
Keywords: Two-phase flow
Geophysics
Fluid dynamics
Volcanism
Magmatism
Volcano
Planetary
Io
Geodynamics

Global volcanism has implications for planetary evolution far beyond the surface features that we observe. Magmatic and volcanic processes control the structural, thermal and compositional evolutions of the bodies where they operates. Jupiter’s moon Io, the most volcanically active body in the Solar System, is an extreme ‘end-member’ that allows us to investigate the effects of planetary magmatism and volcanism in relative isolation of other processes. Previous research has generally investigated melting and magmatism within Io’s partially-molten mantle separately from the volcanic systems in its lithosphere. In this thesis I present a suite of models that move beyond previous works by coupling mantle melting and magmatism to lithospheric evolution and volcanism. With this approach I show that magmatic intrusions within Io’s lithosphere are a fundamental part of the global heat balance, delivering significant mass and energy to the lithosphere and controlling its thickness. As well as transporting heat, magmatism and volcanism also transport chemical species. With the inclusion of a simple chemical system, I show how magmatism and volcanism control Io’s compositional evolution, leading to a layered mantle structure and the generation of ultra-high-temperature magmas in the deep mantle that can explain Io’s highest temperature eruptions. Finally, the structural implications of magmatism and volcanism can be related to underlying tidal heating; I show how tidal heating distributions can be inferred from improved observations of long-wavelength lithospheric thicknesses and topography.
Litigation funding: its place in the civil justice system
Keywords: Civil justice system
Access to justice
Litigation funding

The practice of third parties funding litigation for commercial purposes was, for centuries, impermissible, owing to the operation of the doctrines of maintenance and champerty. But it is now permissible in England and Australia, and accepted as part of the legal landscape. The change in the court’s attitude was largely driven by a pragmatic desire to improve access to justice for the impecunious.
The question motivating this thesis is: where does litigation funding fit in the modern civil justice system?
This thesis has three objectives. The first is to assess critically the various criticisms that are made of litigation funding (such as concern about the prospect of third-party control of litigation, or the commodification of legal claims). These criticisms – which are the vestiges of the doctrines of maintenance and champerty – can be seen as reflecting a particular concept of the proper role and values of the civil justice system. But recent decades have seen enormous changes in the civil justice system and the legal profession – including the acceptance (or imposition) of managerial culture, and market rhetoric. When one considers the values and priorities of the modern civil justice system, it can be seen that commercial third-party litigation funding is a consistent part of the broader picture.
Secondly, the thesis presents a more nuanced account of how litigation funding promotes ‘access to justice’: namely, that it removes or mitigates a variety of disincentives to ligation (which deter all rational litigants, and not just the impecunious).
Finally, the thesis identifies market failures which might exist or emerge in the litigation funding market, identifies some difficulties in the current state of regulation in England and Australia, and make some broad suggestions for regulatory options. The task of regulation ought to be informed by the conclusions reached in the first parts of the thesis.
Regulation of intestinal T cell homeostasis by autophagy
Keywords: Treg
Gata3
cellular degradation systems
Foxp3
GWAS
regulatory T cells
autophagy
Atg16l1
Seurat
WAT
single-cell RNA sequencing
FACS
proteasome
T cell metabolism
BAT
Th2 cells

Mice in which the autophagy protein ATG16L1 was selectively ablated in T cells develop spontaneous intestinal inflammation, characterized by loss of Foxp3+ Treg cells and a selective expansion of Gata3+ Th2 cells. This phenotype was most pronounced in the colonic lamina propria. Thus, a lack of autophagy simultaneously reduces anti-inflammatory Treg cells and increases pro-inflammatory Th2 effector cells in the intestine. This discrepancy could be partly attributed to an altered metabolic programme employed by Atg16l1-deficient Treg cells, with increased glycolysis and impaired fatty acid metabolism. In contrast, the metabolic profile of in vitro polarized Th2 cells seemed to be independent of autophagy.
The aims of this thesis are to investigate the mechanistic consequences of altered autophagy in different T cell subsets and also to explore the link between the dominant type 2 immune responses and the observed intestinal pathology.
Finite covers of graphs and cube complexes
Keywords: covering maps
Leighton's Theorem
quasi-isometric rigidity
cube complexes

In this thesis we study finite covers of graphs, cube complexes and related spaces, and explore applications to rigidity of groups.
Leighton's Theorem states that two finite graphs with a common universal cover must have a common finite cover. We prove three generalisations of this. The first restricts how balls of a given size in the universal cover can map down to the two finite graphs when factoring through the common finite cover. The second generalises to covers of graphs of spaces that restrict to isomorphisms between vertex spaces. And thirdly, if the two finite graphs admit regular coverings by the same quasitree, then we arrange for the common finite cover to also be covered by this quasitree. In addition, we provide counter-examples to show that the assumptions in these generalisations cannot be relaxed.
Central to Haglund and Wise's theory of special cube complexes is the construction of the canonical completion and retraction, which enables one to build finite covers of special cube complexes in a highly controlled manner. We give a new approach to this construction with the idea of imitator covers. This idea provides greater insight into the construction and leads to powerful generalisations. It enables us to prove various results about finite covers of special cube complexes - most of which generalise existing theorems of Haglund and Wise to the non-hyperbolic setting. In particular, we prove a convex version of omnipotence for virtually special cubulated groups. Continuing the theme of special cube complexes, we give a novel account of Agol's proof that hyperbolic cubulated groups are virtually special; we retain the underlying ideas and constructions of Agol, but substantially change or add to many parts of the argument to give a more transparent and detailed account.
Finally, we apply Leighton-type arguments similar to those in the aforementioned results to obtain a quasi-isometric rigidity theorem. To be more precise, let G be a group that is one-ended, hyperbolic relative to virtually abelian subgroups, and has JSJ decomposition over two-ended subgroups containing only virtually free vertex groups that aren't quadratically hanging; we prove that any group quasi-isometric to G is abstractly commensurable to G. In particular, this theorem applies to certain "generic" HNN extensions of a free group over cyclic subgroups.
Uncertain execution in order-driven markets
Keywords: optimal execution
fill ratios
marketable limit orders
market microstructure
latency
uncertain execution
algorithmic trading

So-called 'latency' refers to the various small but significant time delays that occur in the course of the communications between a trader and a market. Such delays happen between the time an exchange streams market data to a trader, the time at which the trader processes the information and decides to trade, and the time at which the exchange receives and processes the order from the trader. Latency is a challenge faced by all traders and is of great importance in modern financial markets. In the present work, we develop mathematical models to solve a variety of problems faced by liquidity takers regarding uncertainty in executions.
Firstly, we devise a model for computing the price that traders are willing to pay to reduce their latency. This latency-optimal strategy balances the tradeoff, over a period of time, between the costs of walking the limit order book and the percentage of orders filled. This work may lead to social benefits, since it offers a way to stop the arms race to being faster in the marketplace.
Secondly, we develop a latency-optimal trading strategy that improves the marksmanship of liquidity takers. We make use of the techniques of variational analysis to obtain the optimal price limit of each marketable limit order (MLO) that the trader sends. The price limit of each MLO is characterized as the solution to a new class of forward-backward stochastic differential equations (FBSDEs) driven by random measures. We prove the existence and uniqueness of the FBSDE solution and solve the FBSDE numerically to illustrate the performance of the strategies.
Finally, we show how traders can optimally liquidate a position over a trading window when there is latency in the marketplace. We frame our model as an impulse control problem with stochastic delay -- this work contributes to the stochastic control literature by allowing one to have random delays before the impulses take place. We show that impatient liquidity takers submit MLOs that may walk the book (capped by the limit price) to increase the probability of filling the trades. Patient traders who are fast do not use their speed to hit the quotes they observe, nor to finish the execution programme early: they use speed to complete the execution with as many speculative MLOs as possible. We use foreign exchange data to implement the random-latency-optimal strategy and to compare it with various benchmarks. We find that for patient traders, the random-latency optimal strategy outperforms the bechmarks that do not account for latency by a quantity that is greater than the transaction costs paid by liquidity takers. Around news announcements, the value of the outperformance significantly increases. The superiority of the latency-optimal strategies is due to both the speculative MLOs that are filled and the price protection of the MLOs.
Higher-order constrained Horn clauses for higher-order program verification
Keywords: resolution
higher-order model checking
higher-order recursion schemes
Horn clauses
higher-order program verification
Hoare logic
program verification
coinduction
higher-order constrained Horn clauses
higher-order logic

Higher-order constrained Horn clauses (HoCHC) are a fragment of higher-order logic modulo theories recently introduced by Cathcart Burn et al. (2018). This thesis explores the adequacy of HoCHC as a unifying framework for the algorithmic verification of higher-order programs, through links with existing approaches to program verification as well as a sound and refutationally complete solution method for HoCHC.
We establish a continuous interpretation for HoCHC in which the semantic domains are restricted to Scott-continuous functions. We show that the continuous HoCHC decision problem is equivalent to the original problem. This continuous interpretation serves as a foundation for a sound and refutation-complete resolution proof system - based on SLD-resolution - for solving unsatisfiable instances of the HoCHC problem over a semi-decidable background theory.
To address the relation between HoCHC and higher-order model checking, we introduce a coinductive version of HoCHC that is characterised by a greatest fixpoint construction. We define an encoding of higher-order recursion schemes into a HoCHC logic program, which can be used to reduce the open higher-order recursion scheme equivalence problem - and thus the lambdaY-calculus Böhm tree equivalence problem - to semi-decidability of coinductive HoCHC over Maher's complete and decidable background theory of trees (Maher, 1988; Djelloul et al., 2008).
Finally, we develop an axiomatic basis for relations as higher-order program invariants in the form of a Hoare logic. Our approach to Hoare logic for higher-order programs distinguishes itself from the literature through the combination of a higher-order assertion logic and a relatively complete proof system.
Reputational concerns in online platform competition
Keywords: competition
platforms
reputation

This paper examines online platforms' incentives to protect their users' privacy, when users value the latter and the platforms' incentives arise through purely reputational concerns. The main question addressed is whether the introduction of a competing platform will increase effort incentives, relative to the monopoly case. When revenue is linear in market share and users' utilities are given by the Hotelling specification, I find that effort is reduced in the duopoly equilibrium. This is because in a duopoly setting, the expected increase in market share achieved through a high reputation is reduced. When the rewards-to-reputation function is sufficiently concave, the value of an increase in market share becomes larger for lower market shares and competition can increase effort incentives. I show that this "concavity" effect arises as the effect of platform popularity, when users' preferences favor one platform relative to the other and as the effect of decreasing marginal value of data, when users' data is used to estimate population parameters. Allowing platforms to respond to their posterior reputations through additional choice variables increases the convexity of the rewards-to-reputation mapping, thus worsening the impact of competition on effort incentives. I demonstrate this intuition by analyzing two-sided platform competition.
The reception history of Esther a genderqueer/non-binary reading of the ancient texts and in modern scholarship
Keywords: gender
reception history
Old Testament
The Book of Esther
non-binary
genderqueer

The Book of Esther has been regarded by some critics as displaying unusual gender roles for a biblical text, particularly because there appear to be some gender role reversals or gender ambiguities occurring in the text. Modern reception of Esther can be broadly grouped into two categories: characters in the text are interpreted in a cisnormative manner, or some characters are interpreted as being subversive. Both groups of scholarship are problematic for non-binary/genderqueer readers in different ways, and this thesis aims to take a non-binary/genderqueer approach to Esther to assess if this text has the capacity to be read in a manner free from the gender binary.
It is the purpose of this thesis to work from the issues raised in contemporary reception and read the ancient versions of Esther that they often reference. The versions studied are the Hebrew Masoretic Text, the Septuagint, the Greek Alpha Text, Josephus’s Paraphrase of Esther in the ‘Judean Antiquities’ and Jerome’s Latin Vulgate. A reception-historical framework and a non-binary/genderqueer lens is used to assess characters’ capacity for non-binary/genderqueer reading in the ancient reception. I also discuss the similarities and differences between versions and their effect on how we can interpret characters’ behaviour.
Subsequently, this thesis highlights which characters in which texts can be read as non- binary/genderqueer and which cannot. Then, it is discussed which of the ancient receptions appear to have had the greatest impact on the binary interpretations that are prevalent today. It will be shown that the Masoretic Text has the greatest, consistent capacity for genderqueer/non-binary reading. Conversely, the Greek Additions do not allow for a genderqueer/non-binary interpretation. However, this material seems to have had the greatest impact on modern reception. I explore why this is by looking to the body of Esther scholarship and to cognitive bias theory.
Monitoring and managing plant diversity in field margins in Southern England
Keywords: survey methods
hedgerows
plant diversity
butterflies
field margins
agriculture

Biodiversity is severely threatened by human activity, with one of the greatest threats coming from agriculture. To reduce the impacts of agriculture on biodiversity, one conservation strategy is to exclude strips of land with herbaceous vegetation from production, termed field margins. Conserving field margins provides a valuable habitat for plant and animal species, and is therefore predicted to boost biodiversity. However, despite being a widely implemented conservation strategy, regular monitoring of plant diversity in field margins is lacking, and the ecological impacts of field margin management are not well understood. This thesis aims to further our understanding of ecologically effective ways to monitor and manage field margin plant diversity, based on three years of fieldwork across four farms in Oxfordshire, England.
Based on this fieldwork, four main findings are presented. Firstly, I found that over two years of surveying only a limited amount of variation in plant community composition can be explained by margin-level characteristics. This suggests that margin-level management can only have a limited impact. Secondly, I observed little spatial variation in plant communities between different farms in the same county. This suggests that management recommendations for plant diversity in field margins can be generalised across farms within a region. Thirdly, I observed higher butterfly species richness in field margins with higher plant species richness and intermediate vegetation height. This suggests that management of plant height and diversity will have a positive effect on butterfly diversity. Finally, I found that assessing plant diversity using either transect or quadrat survey methods resulted in biases in the plant species recorded. This suggests that plant surveys in field margins should use both transects and quadrats, to reduce bias in plant species lists. Together, these findings provide ecological evidence to improve conservation efforts for farmland biodiversity, through monitoring and management of field margins.