VictorJuiz/thesis huggingface dataset:
Stability for nonlinear diffusive PDEs
Keywords: Stability estimates
Cross-diffusion systems

This thesis focuses on well-posedness and stability estimates (i.e. continuous dependence with respect to the nonlinearities) for a family of cross-diffusion systems that includes several models used to describe cell diffusion in Mathematical Biology for one or more species. We discuss rigorous quantitative results for a class of (possibly degenerate) parabolic PDEs, including scalar equations as well as systems. The approach is typical of Analysis of PDEs, hence the concepts of weak solutions in Sobolev spaces, a priori estimates and well-posedness are crucial. Considering scalar, nonlinear diffusion, we extend the existing solvability, uniqueness, boundedness and stability results. Regarding non-degenerate models for multiple species, we work in the framework of systems with an entropy structure and a limited set of other assumptions that allow us to prove stability estimates, improving some of the existing results. Finally, we have been working on the multi-species, degenerate case, providing a continuous dependence estimate under suitable (but rather restrictive) assumptions. Two different types of numerical simulations are presented in order to complement the abstract results.
Analysis of stochastic PDEs arising from large portfolios of stochastic volatility models
Keywords: fast mean-reversion
large portfolio limit
partial Malliavin calculus
Malliavin calculus
stochastic volatility
probabilistic solution
SPDE
empirical measure
ornstein-uhlenbeck
Sobolev estimate
empirical limit
weighted Sobolev space
mean-reverting
particle approximation
conditional expectation
boundary condition
CIR process
fast mean-reverting asymptotics
Regular density
half-space

The aim of this thesis is to study a large market model of defaultable assets in which the asset price processes are modelled as stochastic volatility models with volatility mean-reversion and default upon hitting a lower boundary. We assume that both the asset prices and their volatilities are correlated through systemic Brownian motions. In the first part of the thesis, we are interested in the loss process that arises in this setting and we prove the existence of a large portfolio limit for the empirical measure process of this system. This limit evolves as a measure valued process and we show that it will have a density given in terms of a solution to a stochastic partial differential equation of filtering type in the two-dimensional half-space, with a Dirichlet boundary condition. Next, we employ Malliavin calculus to establish the existence of a regular density for the volatility component of the SPDE, and an approximation by models of piecewise constant volatilities combined with a kernel smoothing technique to obtain existence and regularity for the full two-dimensional filtering problem. We are able to establish good regularity properties and uniqueness for solutions, except in the CIR case where uniqueness remains an open problem. In the second part of the thesis, we study the convergence of the total mass of a solution to this stochastic initial-boundary value problem when the mean-reversion coefficients of the volatilities are multiples of a parameter which tends to infinity. When the coefficients of the noises of the volatilities are multiples of the square root of the same parameter, the convergence is extremely weak. On the other hand, when the noise coefficients are independent of this exploding parameter, the volatilities converge to their means and we can have much better approximations. Such approximations can be used to improve the accuracy of certain risk-management methods in markets where fast volatility mean-reversion is observed.
Signal processing for next generation coriolis flow metering
Keywords: Two-phase Flow
Coriolis Flow Meter,
Signal Processing
Batching

This thesis aims to develop new signal processing techniques for Coriolis flowmeters. Two/multi-phase flow metering is a long established problem in many applications (e.g. the oil & gas, chemical, biotech, pharmaceutical industries) and no perfect solution is available.
In the light of this challenge, recent developments in the Coriolis flowmeters are explored and issues for applying Coriolis flowmeter in two-phase flow conditions are identified. Benchmarks for both empty-to-full batch and continuous two-phase flow reflecting real-world applications are developed for evaluating signal processing techniques. Then current Coriolis flowmeter signal processing techniques are reviewed and tested using the benchmark examples.
A new family of signal processing techniques based on complex signal processing are developed: these include Complex Bandpass Filter (CBF), Complex Notch Filter (CNF) and a combination of CBF with CNF (CBF-CNF). The new techniques are compared with the current methods via the benchmarks and exhibit good performance.
CBF and CBF-CNF are implemented in a prototype transmitter to test alongside with an ‘Oxbox’ transmitter which is a laboratory version of the Foxboro CFT-50/1 (a commercial transmitter developed by the Oxford research group). Signal generator tests are carried out first in order to validate the proper operation of each new technique. Next, single-phase flow tests are carried out to demonstrate that the new algorithms running on the prototype transmitter measure accurately and, joined to a flow tube, can perform as a basic Coriolis flowmeter. Finally, two-phase (water/air) flow tests are carried out with the new algorithms. The performance is compared with that of the Oxbox. From the results, the new CBF and CBF-CNF algorithms perform comparably with the Oxbox at low Gas Void Fraction (GVF), while at high GVF they reduce frequency and phase difference standard deviation by as much as 10 times.
Finally, a new non-linear state space model with Extended Kalman Filter (EKF) is developed as a further promising signal processing technique for Coriolis flowmeter. The new model shows good performance compared with both existing and complex signal processing based techniques but some challenges need to be solved before EKF can be implemented in a prototype transmitter.
Writing against theodicy: evil, secular ethics, and Victorian realism
Keywords: Problem of Evil
Narrative
Secularity
Ethical criticsim
Realism
Theodicy
Victorian literature
Ethics

This thesis contributes to the ongoing work of rethinking the relationship between secularization and literature by exploring the ways in which three mutually influential authors – James Anthony Froude, Arthur Hugh Clough, and George Eliot – struggled with theodicy. The term theodicy describes a response to the problem of evil in which God’s justice is maintained despite the apparent existence of evil. Because theodicy discourse tends to present suffering as reconcilable with divine goodness, it is frequently considered unethical. Avoiding theodicy is therefore desirable, particularly for those invested in secular ethics. That realism fosters secularity has often been claimed – by Martha Nussbaum, George Levine, Bruce Robbins, for example – and this thesis asks whether, as has also been suggested, realist literature urges readers away from theodicy. Previous studies of theodicy in literature have focused on religious authors; this study takes the opposite approach, looking at authors commonly associated with secularization to highlight the difficulties of staying true to a secular project and the pull towards religious patterns of signification which even realist literature exhorts. Before turning to Victorian writers, the thesis sets up a historical and philosophical context of theodicy discourse from Leibniz and Pope to Voltaire, Goethe, and Coleridge, differentiating between three types of evil (moral, metaphysical, physical) and two types of theodicy (Augustinian, Irenaean). The Victorian authors on which the thesis focuses were chosen because of their role in narratives of secularization and because they are each preoccupied with a different kind of evil, thus their writing exemplifies different kinds of struggle with theodicy. The thesis concludes that while literature, particularly where it claims to represent reality, gravitates towards theodicy, authors and critics can yet foster resistance to those patterns. Rather than trusting formal realism to urge readers away from theodicy, those who want literature and its criticism to champion secular ethics would be well advised to pay renewed attention to those aspects of literature which pull towards religious significance, and the strategies used to resist them.
Searches for new physics involving massive invisible particles
Keywords: The ATLAS experiment
Particle physics
High energy physics

One of the most obvious problems with the Standard Model is the lack of any explanation for dark matter: a form of matter predicted from astrophysical observations but not compatible with any known subatomic particle. Many theories of new physics predict dark matter candidates which could be produced in 13 TeV collisions at the LHC. The primary experimental signature expected to accompany the production of a dark matter candidate is an imbalance in measurements of transverse momenta, referred to as ETmiss. This thesis first covers the ETmiss trigger, a system responsible for selecting events with large ETmiss for later use in analyses and a vital component in many analyses. This signature suffers from very large backgrounds from QCD events with little true ETmiss and the high thresholds that would be required to control pass rates pose a risk to the efficiencies of analyses. A technique is presented that is shown to be able to reduce the rate by a factor of almost 4 while retaining high efficiencies in analysis signal regions. This thesis then documents a search for new physics using 36.1 fb−1 of data collected by the ATLAS detector. The search targets final states with no leptons and very high jet multiplicities, ranging from ≥ 7 to ≥ 11 in the tightest signal regions, which are characteristic of long decay chains which can be predicted by certain new physics models, especially supersymmetry. By using this signature the analysis is able to use a looser selection on ETmiss, gaining sensitivity to areas of model spaces which may not be accessible to analyses reliant on the ETmiss trigger. No significant deviation from the Standard Model is observed and the analysis sets strong limits on the masses of supersymmetric particles, excluding gluino masses up to 1.8 TeV at the 95% confidence level.
Quantification of cerebral vascular hemodynamics using MRI
Keywords: MRI
Perfusion
Cerebral blood flow
Arterial spin labeling

Cerebral perfusion is a promising biomarker for the early diagnosis of dementia. Additionally, the change in perfusion in response to vasoactive stimuli, cerebrovascular reactivity (CVR), may also prone to be a valuable dementia biomarker. Arterial spin labeling (ASL) MRI is a non-invasive technique to quantify perfusion and in turn CVR. However, the precise estimation of perfusion using ASL MRI is not only limited by partial volume effects, due to the relatively low resolution of the ASL data, but also affected by confounding factors including arterial transit time (ATT) and blood flow velocity. This thesis investigates the sensitivity of partial volume correction (PVEc) methods for gray matter (GM) perfusion estimation and the impact of confounding factors on CVR measurements.
Linear regression (LR) and spatially regularized PVEc methods were examined using simulated ASL data by comparing the estimation accuracy and the ability to preserve spatial variations in perfusion images. Results indicated that the LR approach was less sensitive to uncertainties in data while the spatially regularized method was superior in preserving spatial details.
The impact of PVEc on the repeatability of GM perfusion was investigated using data from a healthy cohort. The repeatability improved after PVEc using both LR and spatially regularized methods, implying that PVEc is beneficial to increase the reliability of GM perfusion measurements.
CVR quantification was investigated using the standard implementation of ASL (single-PLD PCASL) and a novel ASL technique (Turbo QUASAR ASL). CVR, ATT, and blood flow velocity were estimated before and after acetazolamide administration in healthy volunteers. Regional differences of CVR were found between the two ASL methods. Both PCASL and Turbo QUASAR ASL are limited by the change in blood flow velocity for the use in CVR estimation, while PCASL is also hindered by ATT. Accounting for flow velocity enhanced the CVR estimation for both techniques.
Total synthesis of rubriflordilactone B and pseudo-rubriflordilactone B
Keywords: Total Synthesis

Rubriflordilactones B is a highly oxygenated nortriterpenoid natural product first isolated from Schisandra rubriflora in the year 2006. This natural product is of considerable interest due to its highly oxygenated polycyclic structure and significant anti-HIV activity. However, since the spectral data of the synthetically made natural product doesn’t match the isolated natural product, there is an ambiguity regarding the exact structure of the molecule. This thesis attempts to resolves the uncertainty around the structural motifs by synthesising both rubriflordilactone B and pseudo-rubriflordilactone B; the proposed compound responsible for the spectra in the isolation report.
A highly convergent strategy for the synthesis of the natural product rubriflordilactone B and pseudo-rubriflordilactone B is described hereafter. A common AB ring aldehyde is involved in the late stage coupling with the diynes containing the FG rings of the rubriflordilactone B as well as pseudo-rubriflordilactone B. The coupling is followed by a rhodium-catalysed [2+2+2] cyclotrimerisation reaction to form the ABCDEFG core of the natural product skeleton which is only a step away from the completion.
Scalable two-phase flow solvers
Keywords: Preconditioning
Two-phase flow
Finite elements
Navier-Stokes
Saddle point problems
Iterative methods
Schur complement

Two-phase flows arise in many areas of application such as in the study of coastal and hydraulic processes. Often the fluids involved can be modelled by incompressible phases which have disparate physical properties such as density and viscosity.
We utilise a two-phase flow model of immiscible Newtonian fluids. A key part of this model is a set of variable coefficient Navier–Stokes equations. This thesis focuses on the numerical solution of the linear systems which arise after linearisation of these equations. Solving these systems often dominates the computation time when running simulations.
One of the challenges in solving the model is that the density and viscosity coefficients are discontinuous and can have large jumps between the two phases. In this work we consider preconditioned iterative Krylov methods to solve the large and sparse linear systems and pay particular attention to incorporating the highly varying coefficients into the block preconditioners that we propose. We will see that such considerations can be essential in order to obtain good performance.
An important issue is the scalability of the solution methodology. Here, we will study how the convergence of the iterative solver depends on a grid parameter which controls the refinement of the computational mesh. We will see that the novel preconditioners we propose can lead to convergence which is effectively independent of the grid parameter. We also investigate dependence on other model parameters such as the Reynolds number as well as the density and viscosity ratios between the two fluids.
Another topic we examine is the use of a multipreconditioned iterative method allowing more than one preconditioner to be used simultaneously. Our results using this approach show some promising features.
Finally, we consider an implementation within a more realistic model used in practice for simulating complex air–water flows. In particular, we will provide results for a problem modelling the breaking of a dam.
Modeling and signal processing for flash memory
Keywords: Flash memory
Index Modulation
Error Correcting Codes
Inter-cell Interference
Signal Processing

This thesis examines the effects of noise and interference on the performance of NAND flash memory.
Chapter 3 studies the probabilistic input/output relation between the data stored and the read threshold voltage of a cell and generalizes it to a group of cells. It is then concluded that adjacent cells are correlated due to common aggressors. This motivates the study of adequate signal processing techniques to optimize the reliability performance.
Chapter 4 proposes two techniques that can reduce the error rate in light of the result of the previous chapter. The first is based on dividing a group of cells into sub-groups and detecting each sub-group independently. The second approximates the flash system model by a hidden Markov model, then uses the sum-product algorithm to detect the inputs. The soft outputs of the proposed detectors are passed on to the ECC soft decoder. It is shown that the second approach provides significant improvements. Then, it is shown that quantization negatively affects the performance of the sum-product algorithm more in comparison with the first approach. To partially mitigate this effect, an iterative detection/decoding strategy is proposed and shown to improve the performance.
Chapter 5 proposes a novel data representation scheme that provides a trade-off between reliability and the amount of data stored per cell, and partially mitigates the effects of device degradation. The scheme divides the stored data into two streams stored in the indices and levels of the non-erased cells, respectively, allowing the first to be detected without any knowledge about the channel. The simulation results show an improvement in the error rate while partially mitigating the need to track the channel parameters and the read references as the device degrade.
Respiratory quality indices for automated monitoring of respiration from sensor data
Keywords: Signal quality
Electrocardiography (ECG)
Photoplethysmography (PPG)
Signal fusion
Respiratory Quality Index (RQI)
Respiratory rate (RR)

Abnormal respiratory rate (RR) is known to be one of the most clinically effective predictors of catastrophic decline. Despite this, RR is often the least monitored and most inaccurately measured vital sign. This is primarily because of the lack of a non-invasive, robust, automated method for estimating RR. It has previously been shown that the amplitude modulation (AM), frequency modulation (FM), and baseline wander (BW) of both the electrocardiogram (ECG) and photoplethysmogram (PPG) contain respiratory waveform information. However, these respiratory modulations are driven by the physiologic interrelationship between the cardiovascular and respiratory systems and may or may not be present based on a patient's characteristics and condition. Despite this, current methods for RR estimation from ECG and PPG do not account for this physiologic variability. The investigations in this thesis describe the development and evaluation of respiratory quality indices (RQIs), a novel method for evaluating the presence or absence of physiologically important respiratory information from the AM, FM, and BW extracted from the ECG and PPG. This work is conducted in three unique data sets, CapnoBase, MIMIC-III, and Dialysis III, all of which represent important, different patient populations. Five initial RQIs are described based on five signal processing techniques: fast Fourier transform (FFT), autocorrelation, cosine correlation, autoregression, and Hjorth parameters. Of these, the individual RQIs based on the FFT, autocorrelation, and autoregression are deemed to be good predictors of the presence of respiratory waveform data. The three individual RQIs are used to derive three fusion RQIs based on two supervised learning algorithms: linear regression and support vector regression (SVR) and one unsupervised learning algorithm: principal component analysis (PCA). Both the linear regression and PCA fusion RQIs are accurate and robust. The linear regression fusion RQI is used in the development of an RR estimation algorithm, termed RQIFusion, which achieves highly accurate and more complete RR estimates than existing methods. In the Dialysis III data set, implementation of RQIFusion improved RR estimation error by between 1.35 to 2.29 breaths per minute (brpm) to achieve RR estimation errors between 2.18 to 3.46 brpm, depending on the RR estimation algorithm employed. These results represent a marked improvement in RR estimation and indicate the importance of conducting respiratory quality analysis using RQIs on respiratory modulations extracted from ECG and PPG prior to RR estimation.
Cognitive and neural foundations of perceptual biases for the self and social groups
Keywords: Social neuroscience
Social cognition
In-group bias
Self bias
Social identity

The notion of the self as distinct from other people is fundamental to the study of human psychology. Closely tied to this sense of self is the profound importance of belonging to social groups. The cognitive prioritisation of self- and ingroup-related information, known as self-bias and ingroup-bias, occurs across a multitude of cognitive domains. Although adaptively beneficial, biases arising from social categorisation are the source of prejudiced attitudes, discriminatory behaviours and intergroup conflict.
Several studies have demonstrated enhanced response times and accuracy performance in perceptual matching for self and ingroup stimuli compared to others and outgroups. However, the cognitive and neural mechanisms underlying these effects are relatively unexplored. The present thesis examines five core outstanding research questions: 1. What is the relationship between perceptual prioritisation for the self and social ingroups? 2. How does social context modulate ingroup-bias? 3. How quickly does group affiliation affect early perceptual processing? 4. Do trait differences underlie the strength of perceptual prioritisation for the self and social groups? 5. What are the commonalities and distinctions in the neural regions that underpin biases for the self and social ingroups?
Broadly, the findings of this thesis suggest that: 1. There is an overlap in the representation of stimuli associated with the self and ingroups but the performance advantages are likely to be driven by partly distinct processes. 2. Perceptual biases for ingroups are robust across differing social contexts. 3. Social categorisation quickly enhances low-level perceptual processing even when this categorisation is novel and random. 4. There is no evidence to suggest that individual trait differences in group identification or self-concept underpin the perceptual biases. 5. Cognitive prioritisation for the self and ingroups are supported at least in part by distinct neural mechanisms. Together, these findings provide a novel perspective on the relations between self and ingroup representation in brain and behaviour.