VictorJuiz/thesis huggingface dataset:
Nonstandard inner products and preconditioned iterative methods

By considering Krylov subspace methods in nonstandard inner products, we develop in this thesis new methods for solving large sparse linear systems and examine the effectiveness of existing preconditioners. We focus on saddle point systems and systems with a nonsymmetric, diagonalizable coefficient matrix.
For symmetric saddle point systems, we present a preconditioner that renders the preconditioned saddle point matrix nonsymmetric but self-adjoint with respect to an inner product and for which scaling is not required to apply a short-term recurrence method. The robustness and effectiveness of this preconditioner, when applied to a number of test problems, is demonstrated. We additionally utilize combination preconditioning (Stoll and Wathen. SIAM J. Matrix Anal. Appl. 2008; 30:582-608) to develop three new combination preconditioners. One of these is formed from two preconditioners for which only a MINRES-type method can be applied, and yet a conjugate-gradient type method can be applied to the combination preconditioned system. Numerical experiments show that application of these preconditioners can result in faster convergence.
When the coefficient matrix is diagonalizable, but potentially nonsymmetric, we present conditions under which the pseudospectra of a preconditioner and coefficient matrix are identical and characterize the pseudospectra when this condition is not exactly fulfilled. We show that when the preconditioner and coefficient matrix are self-adjoint with respect to nearby symmetric bilinear forms the convergence of a particular minimum residual method is bounded by a term that depends on the spectrum of the preconditioned coefficient matrix and a constant that is small when the symmetric bilinear forms are close. An iteration-dependent bound for GMRES in the Euclidean inner product is presented that shows precisely why a standard bound can be pessimistic. We observe that for certain problems known, effective preconditioners are either self-adjoint with respect to the same symmetric bilinear form as the coefficient matrix or one that is nearby.

Keywords: preconditioning
nonstandard inner products
linear systems
Krylov subspace methods
Advisor: Wathen, A
Hot gas and magnetic fields in clusters of galaxies

Many clusters of galaxies contain large quantities of hot diffuse gas. I have studied the properties of waves in this gas using Lagrangian perturbations. The gas is far more thermally stable than is commonly thought. For bremsstrahlung cooling, all modes that remain oscillatory are damped. Galaxy motions, especially the oscillations of a central cD galaxy, are an important way of generating large amplitude waves in cluster gas. This is especially pertinent in view of the growing realization that cD galaxies are not at rest with respect to the cluster.
I also present evidence that weak magnetic fields tangled on scales of ~ 10 kpc are common in cluster gas. Electrons responsible for the flow of heat in the gas must travel along the field lines, leading to a global reduction in heat flux. The superposition of many different field lines implies that the cluster gas is a multiphase medium. Such a picture has been suggested independently by the claimed observation of mass drop-out from cooling flows. I also show some results from a more advanced study using real magnetic fields rather than random walk models.

Advisor: Binney, J
The evaluation and expansion of methodologies relating to the reporting and analyses of intermediate test results: improving the clinical utility of diagnostic research

Background and objectives:
It has been argued that the binary framework frequently adopted to analyse test accuracy does not represent the clinical reality of diagnostic practice, and the recognition of an intermediate category of test result could make the utility of diagnostic tests more transparent. The objective of this thesis is to explore the value of moving away from the binary framework when evaluating and interpreting quantitative diagnostic tests.
Methods:
This thesis starts with an overview of the key arguments against dichotomising quantitative test results and a summary of some of the alternative methods proposed. Four distinct studies are then reported: 1) a systematic review of the methods currently used to evaluate the accuracy of quantitative cancer biomarkers, 2) a survey of GPs exploring preferences for threshold guidance 3) an evaluation of existing methods for identifying an intermediate range of test values, and 4) an assessment of the feasibility of applying these methods to the results of a meta-analysis.
Results:
The binary framework remains the most common method for evaluating the accuracy of quantitative tests, despite the survey of GPs indicating that a single threshold interpretation is less helpful than identifying rule-in and rule-out thresholds. Existing methods for identifying an intermediate range of values require some adaptation to incorporate the cost trade-offs relating to different outcomes but, given complete reporting at the primary research, could be applied to the results of a meta-analysis.
Conclusion:
The 2 x 2 diagnostic framework frequently fails to capture many of the realities and complexities of clinical research questions. Standardised methods that facilitate complete reporting of test accuracy in primary diagnostic accuracy studies are required to allow for greater flexibility when producing threshold recommendations further down the evidence pathway.

Keywords: diagnosis; inconclusive; accuracy
Advisor: Perera, R
Stevens, R
Challenging the boundaries of criminal justice and social policy: responses to priority offenders

This thesis examines the interaction of criminal justice policy and social policy within the Prolific and Priority Offenders Scheme (PPOS), a government initiative which aims to reduce offending by persistent offenders. The research on which this thesis is based takes an interpretative approach to social inquiry and employs a qualitative methodology. It examines the operation of four PPO Schemes in the Thames Valley through semi-structured interviews with 22 practitioners and 16 offenders, and participant observation of over 45 multi-agency meetings. The interaction between crime and social policy is explored through examination of three aspects of the PPOS: the coercion of offenders within the Schemes; the working practices and roles of the police and probation officers seconded to the Schemes; and the way in which information and intelligence is used and generated within the Schemes. The central argument of this thesis is that the widely-accepted idea that social policy is being ‘criminalised’ provides an inadequate account of the relationship between criminal justice and social policy in the PPOS. Rather, this Scheme evidences a merger of criminal justice and social welfare agendas, which includes elements of the ‘socialisation’ of crime policy in addition to elements of ‘criminalisation’ of social policy. Whilst the ultimate aim of the PPOS is to reduce crime, and whilst social welfare services such as health, housing and benefits are provided in pursuance of this aim, the ways in which these services are provided accords with the ethos and values of social policy. The idea of a merger of criminal justice and social policy has relevance beyond the PPOS, providing a framework for analysis of other contemporary criminal justice policies, and contributing to broader debates in criminology which have for so long been dominated by the ‘criminalisation’ thesis.

Keywords: persistent offenders
criminal justice policy
criminalisation of social policy
rehabilitation
drugs and crime
prolific offenders
information sharing
multi-agency working
policing
intelligence
probation
Advisor: Hoyle, C
Ashworth, A
Justice, governance and climate change: designing fair and effective climate institutions

Multilateral efforts are yet to produce meaningful action on climate change. Part of the problem with these approaches is a perceived lack of fairness among state actors. Whilst academic discussion has traditionally focused on the issue of distributive fairness, very little has been said about procedural fairness in this respect. To this end, this thesis analyses principles of procedural justice in order to develop practical policy measures for institutional design. It does so in four steps. First, it argues that procedural justice is important for reaching a mutually acceptable agreement when there is reasonable disagreement about the substantive ends that collective action should achieve. Second, it develops several principles of procedural justice that should govern the decision-making processes of climate institutions. This includes principles that govern who should participate in decisions, how these decisions should take place, and how transparent they should be. Third, it considers the relative value that procedural justice should be given against other important ends. In doing so, it proposes that procedural justice is a fundamental feature of fair and effective climate institutions. Finally, it considers what this means for climate institutions in practice by determining a set of pragmatic policy prescriptions that can guide the design of climate governance institutions.

Keywords: Climate Change
Procedural Justice
Governance
Democracy
Advisor: Caney, S
Does emotion processing ability mediate the relationship between psychopathy and group psychotherapy engagement?

Therapeutic engagement in psychopathy is an important area of study due to reports of poor engagement leading to poor treatment outcome for this group. One factor that may influence effective engagement is the ability to process emotional information, which has been shown to be impaired in psychopathy.
The study investigated the association between engagement in group therapy and level of psychopathy and assessed whether this relationship is mediated by emotion processing ability. It was hypothesised that higher levels of psychopathy would be associated with lower levels of therapy engagement; however, this relationship would be mediated by four emotion processing indicators believed to be important for good treatment outcome. Specifically, awareness and arousal of emotion, emotion regulation ability, interpretation bias and ability to transform emotion would: i. jointly mediate the relationship between psychopathy and therapy engagement ii. each uniquely mediate the relationship between psychopathy and therapy engagement.
Participants, violent offenders with varying levels of psychopathy, were interviewed in a cross-sectional design. Emotion processing ability was assessed using five computerised tasks each selected to best capture one of the cognitive mechanisms of emotion processing outlined above. Psychopathy was measured using the Psychopathy Check List-Revised. Therapy engagement was assessed by group therapists three months after interview using the Group Emotional Engagement Questionnaire (GEEQ). The GEEQ is a new measure designed, developed and tested as part of this study to measure its dependent variable accurately.
Psychometric evaluation of the GEEQ demonstrated high levels of reliability (internal, inter-rater) with between good and adequate validity (convergent, discriminant) and good predictive validity. Mediation analysis revealed high Factor 1 psychopathy (the affective component) was associated with poorer therapy engagement (lower GEEQ scores). Interpretation of emotion and transforming emotion acted as suppressors on this relationship. This may suggest that those with many Factor 1 traits used positive interpretation bias as a defence against experiencing distress (schema overcompensation). This response was resistant to change and gave high Factor 1 participants the appearance of being better engaged in therapy than they were. Reaction time data suggested this phenomenon occurred as an automatic response rather than a conscious effort to impression manage.

Advisor: Burns, T
Yiend, J
Underpowered: electricity policy and the state in India, 1991-2014

How has the Indian state changed with economic liberalization? While many scholars have explored the altered party politics and class basis of the liberalization-era state, few have studied its transforming internal organizational forms and functioning. This thesis aims to provide an empirically grounded answer to this question. To do this it uses the lens of electricity: the sector lies at the heart of contemporary capital accumulation, state power, and distributive politics, and has witnessed almost a quarter-century of institutional reforms since 1991.
In the sector, new or reworked organizational forms—such as imported regulatory agencies, corporatized state-owned enterprises, and public-private partnerships—have been grafted onto the older statist system in a process of institutional layering. Favouring state-business collaboration and prioritizing rapid economic growth, this mode of state operation is distinct both from a liberal, market-oriented state and from India’s older state-led mode. It combines state intervention and selective adoption of parts of the Washington Consensus template to produce a reinvented mode of power governance that I term state capitalism 2.0.
India’s new state-market hybrid is not a functional alternative to the older models, however. The layered process through which it has emerged means that it is distinctively dysfunctional. Organizations have emerged in an ad hoc fashion, each shaped and reshaped by multiple collective interests, while existing organizations are rarely destroyed. The resulting layered amalgam institutionalizes contradictory state strategies, co-optation by competing interest groups, and a dualistic system of services and subsidies. Consequently the sector’s performance remains poor.
As a result, developments in the Indian power sector suggest that the state's 'pro-business' transition has been painful and incomplete. At least in this sector, the Indian state remains simultaneously more indispensable, more ambivalently pro-business, and more chaotic than much theory might suggest.

Keywords: India
economic reform
policy
energy
electricity
government
Advisor: Harriss-White, B
Nonlinear oscillations and chaos in chemical cardiorespiratory control

We report progress made on an analytic investigation of low-frequency cardiorespiratory variability in humans. The work is based on an existing physiological model of chemically-mediated blood-gas control via the central and peripheral chemoreceptors, that of Grodins, Buell & Bart (1967). Scaling and simplification of the Grodins model yields a rich variety of dynamical subsets; the thesis focusses on the dynamics obtained under the normoxic assumption (i.e., when oxygen is decoupled from the system). In general, the method of asymptotic reduction yields submodels that validate or invalidate numerous (and more heuristic) extant efforts in the literature. Some of the physiologically-relevant behaviour obtained here has therefore been reported before, but a large number of features are reported for the first time. A particular novelty is the explicit demonstration of cardiorespiratory coupling via chemosensory control. The physiology and literature reviewed in Chapters 1 and 2 set the stage for the investigation. Chapter 3 scales and simplifies the Grodins model; Chapters 4, 5, 6 consider carbon dioxide dynamics at the central chemoreceptor. Chapter 7 begins analysis of the dynamics mediated by the peripheral receptor. Essentially all of the dynamical behaviour is due to the effect of time delays occurring within the conservation relations (which are ordinary differential equations). The pathophysiology highlighted by the analysis is considerable, and includes central nervous system disorders, heart failure, metabolic diseases, lung disorders, vascular pathologies, physiological changes during sleep, and ascent to high altitude. Chapter 8 concludes the thesis with a summary of achievements and directions for further work.
Groups acting on graphs

In the first part of this thesis we investigate the automorphism groups of regular trees. In the second part we look at the action of the automorphism group of a locally finite graph on the ends of the graph. The two part are not directly related but trees play a fundamental role in both parts.
Let Tn be the regular tree of valency n. Put G := Aut(Tn) and let G0 be the subgroup of G that is generated by the stabilisers of points. The main results of the first part are :
Theorem 4.1 Suppose 3 ≤ n < N0 and α ϵ Tn. Then Gα (the stabiliser of α in G) contains 22N0 subgroups of index less than 22N0.
Theorem 4.2 Suppose 3 ≤ n < N0 and H ≤ G with G : H |< 2N0. Then H = G or H = G0 or H fixes a point or H stabilises an edge.
Theorem 4.3 Let n = N0 and H ≤ G with | G : H |< 2N0. Then H = G or H = G0 or there is a finite subtree ϕ of Tn such that G(ϕ) ≤ H ≤ G{ϕ}.
These are proved by finding a concrete description of the stabilisers of points in G, using wreath products, and also by making use of methods and results of Dixon, Neumann and Thomas [Bull. Lond. Math. Soc. 18, 580-586]. It is also shown how one is able to get short proofs of three earlier results about the automorphism groups of regular trees by using the methods used to prove these theorems.
In their book Groups acting on graphs, Warren Dicks and M. J. Dunwoody [Cambridge University Press, 1989] developed a powerful technique to construct trees from graphs. An end of a graph is an equivalence class of half-lines in the graph, with two half-lines, L1 and L2, being equivalent if and only if we can find the third half-line that contains infinitely many vertices of both L1 and L2.
In the second part we point out how one can, by using this technique, reduce questions about ends of graphs to questions about trees. This allows us both to prove several new results and also to give simple proofs of some known results concerning fixed points of group actions on the ends of a locally finite graph (see Chapter 10). An example of a new result is the classification of locally finite graphs with infinitely many ends, whose automorphism group acts transitively on the set of ends (Theorem 11.1).

Advisor: Neumann, P
Correction of miscarriages of justice in New Zealand and England

This thesis sets out to provide a deep analysis of the mechanisms for review of convictions in New Zealand and England after initial appeal rights are exhausted, and to identify the key areas of similarity and difference between these systems, the reasons for these differences, and their implications.
The appeal systems in each jurisdiction are briefly examined, alongside the pressures and restrictions on their functioning. Particular attention is paid to the options for appeal out of time, and for revisiting appeal decisions if new material comes to light.
The main discussion is of the specialist procedures for review of suspect convictions in each jurisdiction: the Royal Prerogative of Mercy process carried out by the New Zealand Ministry of Justice and the work of the English Criminal Cases Review Commission. This discussion presents the results of empirical research carried out by the author utilising the files of each of these bodies. It investigates the legal context in which each body functions, and provides an account of how each body functions in practice, by examining the circumstances in which each body will contemplate referring a matter back to an appeal court and the means by which a determination is made as to whether to do so in an individual case. In addition it examines the various factors (legal and non-legal) which impact on their work.
Finally, the key features of the two systems are contrasted, with a discussion of the areas of similarity and difference, as well as the possible implications of these, in particular for reform of the New Zealand processes.

Keywords: Royal prerogative of mercy
New Zealand
CCRC
miscarriages of justice
wrongful convictions
criminal cases review commission
England
criminal procedure
criminal appeals
Advisor: Ashworth, A
Functional significance of human sensory ERPs: insights from modulation by preceding events

The electroencephalogram (EEG) reflects summated, slow post-synaptic potentials of cortical neurons. Sensory, motor or cognitive events (such as a fast-rising sensory stimulus, a brisk self-paced movement or a stimulus-triggered cognitive task) can elicit transient changes in the ongoing human EEG, called event-related potentials (ERPs). ERPs are widely used in clinical practice, and believed to reflect the activity of the sensory system activated by the stimulus (for example, laser-evoked potentials are used to substantiate the neuropathic nature of clinical pain conditions). When ERPs are elicited by pairs or trains of stimuli delivered at short inter-stimulus intervals (ISIs), the magnitude of the ERP elicited by the repeated stimuli is markedly reduced, a phenomenon known as response decrement. While the interval between two consecutive stimuli becomes longer, the reduced response is recovered. Thus, this phenomenon has been traditionally interpreted in terms of neural refractoriness of generators of ERPs ("neural refractoriness hypothesis"). This thesis, however, challenges this neural refractoriness hypothesis by describing the results of manipulating the preceding events of the eliciting stimulus. The first study examined the effect of variable and short ISIs on sensory ERPs, delivering trains of auditory and electrical stimuli with random ISIs ranging from 100 to 1000ms. In the second study, pairs of laser stimuli were presented in two comparable conditions. In the constant condition, the ISI was identical across trials in each block, while in the variable condition, the ISI was variable across trials. By directly comparing ERPs elicited by laser stimulation, this study aimed to explore whether lack of saliency in the eliciting stimulus could explain the response decrement during stimulus repetition. Finally, the third study tested the hypothesis that the reduced eliciting ERPs would recover if saliency were introduced by changing the modality of the preceding event. Thus, trains of three stimuli (S1-S2-S3) with 1s ISI were presented; S2 was either same or different in modality as S1 and S3 in each block. Results from these three experiments demonstrate that this "refractoriness hypothesis" does not hold, and suggest that the magnitude of ERPs is only partly related to the magnitude of the incoming sensory input, and instead largely reflects neural activities triggered by salient events in the sensory environment. These results are important for the correct interpretation of ERPs in both physiological and clinical studies.

Keywords: electroencephalogram (EEG)
functional significance
nociceptive system
sensory event-related potentials (ERPs)
Advisor: Iannetti, G