VictorJuiz/thesis huggingface dataset:
The bounded H^{infinity} calculus for sectorial, strip-type and half-plane operators

The main study of this thesis is the holomorphic functional calculi for three classes of unbounded operators: sectorial, strip-type and half-plane. The functional calculus for sectorial operators was introduced by McIntosh as an extension of the Riesz-Dunford model for bounded operators. More recently Haase has developed an abstract framework which incorporates analogous constructions for strip-type and half-plane operators. These operators are of interest since they arise naturally as generators of C0-(semi)groups.
The theory of bounded H∞-calculus for sectorial operators is well established and it has been found to have many applications in operator theory and parabolic evolution equations. We survey these known results, first on Hilbert space and then on general Banach space.
Our main goal is to fill the gaps in the parallel theory for strip-type operators. Whilst some of this can be deduced by taking exponentials and applying known results for sectorial operators, in general this is insu_cient to obtain our desired results and so we pursue an independent approach. Starting on Hilbert space, we broaden known characterisations of the bounded H∞-calculus for strip-type operators by introducing a notion of absolute calculus which is an analogue to the established notion for the sectorial case. Moving to general Banach space, we build on the work of Vörös, broadening his characterisation for strip-type operators in terms of weak integral estimates by introducing a new, but equivalent, notion of the bounded H∞-calculus, which we call the m-bounded calculus.
We also demonstrate that these characterisations fail for half-plane operators and instead present a weaker form of the bounded H-calculus which is more natural for these operators. This allows us to obtain new and simple proofs of well known generation theorems due to Gomilko and Shi-Feng, with extensions to polynomially bounded semigroups. The connection between the bounded H-calculus of semigroup generators and polynomial boundedness of their associated Cayley Transforms is also explored.
Finally we present a series of results on sums of operators, in connection with maximal regularity. We also establish stability results for the bounded H∞-calculus for strip-type operators by showing it is preserved under suitable bounded perturbations, which at time requires further assumptions on the underlying Banach space. This relies heavily on intermediate characterisations of the bounded H∞-calculus due to Kalton and Weis.

Keywords: Bounded calculus
Semigroups
Unbounded operators
Advisor: Batty, C
The poetics of colour in Stefan George, Rainer Maria Rilke, Wassily Kandinsky and Else Lasker-Schüler

This thesis looks at the poetics of colour in Stefan George, Rainer Maria Rilke, Wassily Kandinsky and Else Lasker-Schüler. It argues that focusing on colour words allows us to think more carefully about the sort of making that poetry, around the turn of the twentieth century, was seen to be, its purpose and effects. In doing so it thinks also about this making—about the ways that words can be seen as the material of poetry, the ways poems relate to objects, and are objects, the ways poets negotiate semantic space and communicability.
While other accounts argue for the specificity of a particular period, author, or hue, I argue for the specificity of the medium, a conclusion which seems necessary when considering how these particular poets thought about and through colour. While the poets’ projects differ, colour can be used in each case like a prism, to separate out their attitudes and commitments towards their medium and its place in the world.
The combination of these four poets, which is, to the best of my knowledge, unique, also allows new connections to be seen, whether, facing inward, in terms of colour itself, or outward towards the commitments regarding the poem that an approach via colour exposes. The four poets share an interest in the involvement, and in some cases, aesthetic education, of readers, and in how and what we can learn through reading, and particularly reading colour. What we learn has less to do with colours and how they are experienced than to do with the constructed world of the poem and its mechanisms, and of the role we have to play in animating this world.

Keywords: poetics
colour
aestheticism
expressionism
Advisor: Louth, C
Dependency and development in central and eastern Europe's new capitalist systems

This thesis tackles the puzzling developments in higher education (HE) in 10 countries of Central and Eastern Europe (CEE) since 1989. Enrolments increased up to six-fold in the next twenty years. One would expect this story to be matched by an equivalently extraordinary economic growth trend. However, it is not. Despite broadly similar economic and higher education policies, these countries have diverged from one another and most importantly from the rest of the EU to which they now belong. What are the factors that best explain these developments? Under what conditions do some countries upgrade economically while others do not?
I argue that dependency on foreign capital has been the key factor influencing HE. The CEE countries have become highly reliant on multinational companies (MNCs), given the economic growth strategy of their governments to attract foreign capital. Therefore, skills have developed as a response to the demand from MNCs. The less sophisticated the skills required by MNCs, the less developed these economies have remained. Therefore, some CEE countries have come to operate at a low-skills equilibrium, while others have managed to upgrade as a result of strategic government intervention.
The thesis combines case-study research with cross-national analyses over four empirical chapters preceded by the introduction and followed by the conclusion. The first chapter develops the argument in a case study of Romanian HE. The second chapter moves on to analyse the relationship of HE financing and MNCs in 10 countries by using firm-level data. The third and fourth chapters aim to explain differences between and within countries in the relationships between the sophistication of these economies and their HE development. The resarch links government partisanship to HE development. This work thus contributes to explaining processes of skill formation, which are becoming of increasingly broad interest to political economists and area studies scholars alike.

Advisor: Soskice, D
The handling, analysis and reporting of missing data in patient reported outcome measures for randomised controlled trials

Missing data is a potential source of bias in the results of randomised controlled trials (RCTs), which can have a negative impact on guidance derived from them, and ultimately patient care.
This thesis aims to improve the understanding, handling, analysis and reporting of missing data in patient reported outcome measures (PROMs) for RCTs.
A review of the literature provided evidence of discrepancies between recommended methodology and current practice in the handling and reporting of missing data. Particularly, missed opportunities to minimise missing data, the use of inappropriate analytical methods and lack of sensitivity analyses were noted.
Missing data patterns were examined and found to vary between PROMs as well as across RCTs. Separate analyses illustrated difficulties in predicting missing data, resulting in uncertainty about assumed underlying missing data mechanisms.
Simulation work was used to assess the comparative performance of statistical approaches for handling missing available in standard statistical software. Multiple imputation (MI) at either the item, subscale or composite score level was considered for missing PROMs data at a single follow-up time point. The choice of an MI approach depended on a multitude of factors, with MI at the item level being more beneficial than its alternatives for high proportions of item missingness. The approaches performed similarly for high proportions of unit-nonresponse; however, convergence issues were observed for MI at the item level. Maximum likelihood (ML), MI and inverse probability weighting (IPW) were evaluated for handling missing longitudinal PROMs data. MI was less biased than ML when additional post-randomisation data were available, while IPW introduced more bias compared to both ML and MI.
A case study was used to explore approaches to sensitivity analyses to assess the impact of missing data. It was found that trial results could be susceptible to varying assumptions about missing data, and the importance of interpreting the results in this context was reiterated.
This thesis provides researchers with guidance for the handling and reporting of missing PROMs data in order to decrease bias arising from missing data in RCTs.

Keywords: Randomised controlled trials
Multiple imputation
Missing data
Advisor: Rivero-Arias, O
Gray, A
Jenkinson, C
Questioning the patient, questioning Hippocrates: Rufus of Ephesus and the limits of medical authority

Rufus of Ephesus's Quaestiones Medicinales is an under-studied work by one of the most respected doctors of Greco-Roman antiquity. This thesis presents a new translation – the first in English of the complete work – and a reassessment of the treatise. I propose that, far from being a simple handbook teaching doctors how to take a patient history, as has hitherto been assumed, QM is an ardent plea for doctors to recognise the limits of their own knowledge and the indispensability of questioning the patient. I argue that QM articulates the idea that the aim of medicine cannot be achieved through medical knowledge alone, and that, in constructing the patient as an essential partner in diagnosis and decisions about treatment, Rufus implies a sharing of authority between doctor and patient that is noticeably different from the emphasis that other authors, particularly the determinedly hierarchical Galen, place on securing patients’ obedience, a subject on which Rufus is noticeably silent. I argue that Rufus is unusual in the clarity and candour with which he perceives and acknowledges the limits of medical knowledge, in his conceptualisation of questioning as a discursive rather than a formulaic activity, in his explicit insistence that it must be addressed directly to the patient, in his psychological concept of habits, and in his recommendation of questioning as a strategy for resolving the tension between universal theory and individual experience. I look at modern cross-cultural research into the factors that drive patient compliance, and note that chief among them is patients feeling they are partners in the treatment process. This raises the question whether and to what extent the features that drive compliance are diachronically as well as cross-culturally consistent, and whether Rufus's shared authority model is more likely to have produced successful treatment outcomes than the autocratic paradigm promoted by Galen, and subsequently absorbed into Western medical tradition, that seems to have met with so much resistance.

Keywords: medical authority
patients in the ancient world
Rufus of Ephesus
Hippocratic questioning
clinical encounter
patient's perspective
Aelius Aristides illness
patient compliance
Advisor: Pelling, C
King, H
Design and utilisation of a poised fragment library against epigenetic proteins

Fragment based drug discovery has become an important method in biomedical research. In particular, it has enabled academic researchers to develop drug-like compounds and chemical probes which can be used for target validation. Recent developments at Diamond Light Source have made X-ray crystallography a viable primary fragment screen. The hits identified by X-ray screening are in general too weak to be verified by orthogonal solution assays, yet such information is a common requirement in medicinal chemistry operations. Progressing weak hits to a potent lead series requires changes not only to the periphery, where conventional SAR operates, but also to the core of the compound. To overcome the problem, I introduce the concept of poised fragment screening. Poised fragments can be synthesised in one step from commercially available starting materials using robust, high yielding reactions. As a result, a library of analogues can be synthesised quickly and at relatively low cost.
In this thesis I report the design and purchase of a 776-compound, chemically diverse poised fragment library (DSPL) for screening using X-ray crystallography, which is in regular use at Diamond. To aid researchers performing follow-up campaigns of poised hits, I developed a computational tool, XPoise, which systematically builds virtual libraries of follow-up compounds using poised reactions.
Follow-up campaigns against four epigenetic proteins revealed the benefit of using poised chemistry over traditional methods such as SAR by catalogue. Weak hits were improved into lead compounds with modest potency alongside structural data. Finally, a lead series of PHIP(2) inhibitors was elaborated using bespoke organic synthesis and late stage biotransformation to build complex, chiral compounds in the search for a potent and selective chemical probe.

Advisor: Brennan, P
Von Delft, F
Probing and modulating brain circuits by deep brain stimulation

Backgrounds. The periaqueductal grey(PAG) plays an important role in the descending pain modulation systems, which has been known to inhibit incoming nociceptive signals at the level of the spinal dorsal horn. But pain mechanism involves the brain and the spinal cord to maintain homeostasis, so theoretically pain modulation mechanism should involve both direction: ascending and descending pathways to the brain and spinal cord dorsal horn. However, literature addressing this question is limited. The sensory thalamus is the most important brain area receiving sensory signals. Moreover, with the fact that evidence indicates the PAG and the thalamus have functional connections, therefore we wanted to test if there is a functional connection between the PAG and the sensory thalamus related to pain modulation.
Aims. To investigate the functional connectivity between the periaqueductal grey and the sensory nuclei of the thalamus in pain modulation
Methods. Three experiments have been conducted. The first experiment is to investigate the effect of PAG DBS on the sensory thalamus, and vice versa, in chronic neuropathic pain patients. The second experiment is to estimate the change of spectral coherence between the sensory thalamus and the PAG during various pain states, when chronic neuropathic pain patients were being peripheral stimulated by ice to evoke pain. The third experiment is to test whether the functional connectivity between the two areas would be affected by general anaesthetics propofol.
Results. PAG DBS inhibited the sensory thalamus with decreasing thalamic delta, theta, alpha and beta power, and sensory thalamus DBS excited the PAG with increasing PAG delta and theta power. The PAG and the sensory thalamus interact reciprocally at short latency, which may be related to pain modulation. The sensory thalamus and the periaqueductal grey also have high gamma coherence which would be inhibited by pain. This high-gamma coherence was increased during propofol induction period which is compatible with the hypothesis that propofol induces loss of consciousness via its GABAergic activity.
Conclusions. This thesis suggests that the sensory thalamus and the periaqueductal grey have a reciprocal connection. Functionally this connectivity might be related to pain modulation. Also this functional connectivity might represent the fact that the transmission and processing of pain signals is always monitored and modified by central pain modulation systems so that organisms can respond properly to the incoming signals.

Advisor: Aziz, T
Embodying trace: the theatre of Wajdi Mouawad

This thesis explores the profound influence of twentieth-century philosophy, and in particular the writings of phenomenologist Jan Patočka, on Wajdi Mouawad. While Mouawad's literary and dramatic sources have been widely discussed in recent scholarship, his philosophical sources have remained under-explored. Seeking to rectify this critical lacuna, the thesis addresses the key concepts Mouawad draws from the writings of Patočka including the central role of 'trace'. Through its investigation of Mouawad’s engagement with Patočka, this thesis delineates Mouawad’s philosophical and ethical aims.
The thesis first considers the multiplicity of self in Mouawad's work, and its relationship to Patočka's 'shakenness' and 'care for the soul'. Chapter 1 investigates how an internal confrontation provoked by trace leads to a search for meaning as ‘the soul discovers itself'. It analyses Mouawad's first play, Willy Protagoras enfermé dans les toilettes, and the more recent Seuls, to address the evolution of Mouawad's notion of self. Chapter 2 explores the significance of temporal awareness and time, as Patočka's three movements of human existence drive Mouawad's protagonists in their experience of shakenness. The plays discussed are Littoral, in which Mouawad first essayed non-linear time structures, and Incendies, which utilises a complex temporal oscillation. Chapter 3 turns to space as what arises through the individual’s relationship to the world, focusing on Forêts and Ciels, two of Mouawad's most spatially complex productions. Chapter 4 examines two of Mouawad's recent plays, Temps and Sœurs, in its investigation of the role of testimony in developing the solidarity that emerges through the encounter with the other. The thesis then concludes with a discussion of how, and to what extent, Mouawad tackles his ambitions, particularly in their relation to trace.

Keywords: Phenomenology
Mouawad
Patočka
Advisor: Garfitt, T
Imagined futures of the everyday: middle class households in south-east London

Discussions of hope and the imagined future have thus far focussed on grand ambitions at the expense of the more mundane, modest wants that are the preoccupation of everyday life. Studies of the home have demonstrated the role of material culture in embodying memory and household pasts but little has been said of household futures and their impact on household presents. This ethnographic study of the lives of three middle class households in south-east London addresses these gaps through an exploration of the role of imagined futures in orienting everyday life in the household. The ways in which householders work to make household life what they want it to be, and to secure the longer-term futures they imagine for their children, are explored through the frustrations, disappointments and anxieties that stem from the frequent failures of these efforts. Objects are demonstrated to be both the means through which householders attempt to make household life what they want it to be – their potentiality shaping and enabling imagined futures – and the means through which these imagined futures are reconfigured or derailed. The period of maternity leave, that all three of my women participants were in the midst of, is shown to be one in which the work of bringing the household's imagined futures, and children's imagined futures to fruition falls disproportionately to mothers, often at the expense of their own wants. Finally, a broader lens is used to explore how middle class householders' efforts to live the life they want contributes to and shapes the processes of gentrification credited with bringing dramatic change to south-east London.

Keywords: London
Home
Material Culture
Household
Middle class
Ethnography
Advisor: Daniels, I
Carbon burial in continental and marine settings: Lacustrine and marine records of major environmental change in deep time and their depositional and diagenetic consequences

The Early Jurassic Toarcian Oceanic Anoxic Event (T-OAE; &Tilde;183 Ma) is recognized as possibly the most extreme oceanographic and global climatic change event of the Phanerozoic. The T-OAE was marked by massive carbon release into the ocean–atmosphere system, widespread oceanic de-oxygenation, global organic-matter burial, and a strongly perturbed global carbon cycle. Although effects of the T-OAE are extensively studied in the marine realm, the environmental and climatic response on the continents is effectively unknown. In this thesis, I identify the first lacustrine record of the T-OAE, in the Da'anzhai Member of the Sichuan Basin (China), and demonstrate that a major lake system developed contemporaneously with the T-OAE, likely due to enhanced hydrological cycling under elevated atmospheric pCO2. Increased lacustrine organic productivity from elevated fluvial nutrient supply resulted in ˜460 Gt of organic carbon burial in the palaeo-Sichuan lake alone, representing a major, but hitherto overlooked, carbon sink and negative feedback in the T-OAE global carbon cycle, and likely other similar events. Algal dominated biomass, deposited under a stratified water column during lake level rise, marks the Da’anzhai Member as potential hydrocarbon source rock. Given the challenges associated with Mesozoic stratigraphic correlation, I further present the first integrated (marine) stratigraphic reference framework for the complete Toarcian Stage from the Llanbedr (Mochras Farm) Borehole (Cardigan Bay Basin, UK), which allows precise correlation between the T-OAE and coeval Karoo-volcanism. I also show that accelerated global weathering rates during the T-OAE resulted in widespread mass transport deposits at different palaeolatitudes and changes in ocean chemistry leading to pronounced marine siderite deposition. Periodic smaller-magnitude carbon cycle perturbations in the Hettangian and Sinemurian were possibly in phase with short (&Tilde;100kyr) and long (~405kyr) eccentricity astronomical forcing, with the formation of organic-rich laminated black shales in the Bristol Channel Basin, similar to Mediterranean sapropels in the Pleistocene.

Advisor: Jenkyns, H
Hesselbo, S
Topics in ergodic control and backward stochastic differential equations

The core of this thesis focuses on a number of different aspects of ergodic stochastic control in connection with backward stochastic differential equations (BSDEs for short). Chapter 1 serves as an introduction to the problem formulation in various contexts and states a number of results we will be using in the sequel. Chapter 2 deals with the so called weak formulation, where the control is represented as a change of measure. The optimal value and feedback control are obtained using a relatively recent object called ergodic BSDEs. In order to achieve this we establish the existence and uniqueness of solutions to these equations along the way.
Chapter 3 is concerned with non zero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of Ergodic BSDEs, and prove the existence of a Nash equilibrium under general conditions.
In Chapter 4 we show a novel duality between the existence of a solution to an infinite horizon adjoint BSDE and strong dissipativity of the forward process. Thus the link between ergodicity of the controlled process and the infinite horizon stochastic maximum principle is established. Finally, in Chapter 5 we provide conclusions, conjectures and directions for future research.

Advisor: Cohen, S