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Heterologous alkene biosynthesis interfaced with biocompatible metathesis
No full textLong-chain alkenes, such as 10-eicosene, represent unnatural chemicals which are key intermediates in the synthesis of industrial lubricants. Current production methods rely on crude oil presenting a key challenge for their sustainable manufacture. Engineered biosynthetic pathways can enable the utilisation of renewable feedstocks to access small molecules, including aliphatic terminal alkenes. Ruthenium-catalysed metathesis of the generated olefins would provide access to the corresponding long-chain target alkene (Scheme 1).
Scheme 1:
Chain-selective aliphatic primary alkene biosynthesis, interfaced with ruthenium-catalysed alkene cross-metathesis, to access unnatural alkenes from glycerol.
Engineered alkene biosynthesis has been limited by a trade-off between control over alkene chain-length and reduced pathway performance. In this work, a proficient chain-selective alkene biosynthetic pathway was developed before intersection with a biocompatible metathesis catalyst. Production of 1-undecene from dodecanoic acid using whole-cell biocatalysis was initially investigated, using engineered Escherichia coli. Coexpression of an unusual redox relay, identified in the host proteome, enabled the production of 2.11 mM (325.0 mg/L) 1-undecene, representing a seven-fold titre improvement compared with the highest reported using this method. The identified decarboxylase was introduced to a chain-selective (>85%) dodecanoic acid biosynthetic pathway, enabling the production of 1-undecene from glycerol. Pathway productivity was enhanced through combinatorial plasmid optimisation, before complementary methods were developed to address two major bottlenecks. The optimised system enabled a biosynthetic titre of 1.65 mM (254.1 mg/L) 1-undecene from glycerol, representing nearly a five-fold titre improvement on the highest reported chain-selective alkene biosynthesis. Alkene metathesis catalysts were screened under biological conditions, identifying the Zhan 1B to be highly active. Toxicity investigation indicated that the Zhan 1B was biocompatible with E. coli, enabling the intersection of this chemical catalyst with the engineered 1-undecene pathway, to produce 0.23 mM (64 mg/L) 10-eicosene from glycerol. This represents the first example of biogenic 10-eicosene production, in addition to the first example of interfacing biocompatible alkene cross-metathesis with an engineered biosynthetic pathway from glycerol. Our approach demonstrates the opportunity to combine complex metabolic engineering, with the synthetic utility of alkene metathesis, to access industrially relevant unnatural chemicals from a renewable feedstock
Synthesis of B-N analogues of polymers of intrinsic microporosity (PIMs) and cages and investigation of their properties
No full textThis thesis investigates the synthesis and characterisation of novel boronnitrogen
(BN) containing analogues of Polymers of Intrinsic Microporosity (PIMs)
and related macrostructures, with an emphasis on addressing the synthetic
challenges and exploring their potential for porosity-driven applications used in
adsorption and filtration technology.
B←N dative bonds impart unique properties, including enhanced thermal
stability and tuneable electronic characteristics, which make them attractive for
developing advanced PIM materials.
The initial aim was to synthesise tetramethoxy- and tetrabromofunctionalised
B-N spirobifluorene (BN-SBF) monomers as building blocks for
microporous polymers. However, unexpected reactivity and stability issues
limited the synthesis to dimethoxy- and dibromo-BN-SBF compounds. Despite
these challenges, this led to the development of novel linear polymers
incorporating B-N units, including examples that represent the first solutionprocessable
B←N-containing polymers with microporosity. These materials
exhibited promising solubility and stability, demonstrating their potential for
practical applications.
The study further expanded to include the synthesis of macrocyclic and cagelike
structures incorporating tetrahedral boron centres as linking units. Three
novel macrostructures were successfully synthesised: a drum-shaped compound
and two square-shaped molecules, all featuring B←N units. Characterisation
revealed stable architectures with processability, and the drum-shaped
compound exhibited modest gas adsorption capabilities, offering insights into the
relationship between molecular architecture and porosity.
This work advances the field of microporous materials by introducing B←N
bond incorporation through straightforward synthetic procedures and exploring
their implications for material properties. The findings highlight both the potential
and the challenges of leveraging B-N chemistry in designing advanced materials
for applications in gas storage, separation, and catalysis
Extra-terrestrial fullerenes as a food source for microorganisms on the early Earth
Get PDFThe search for extra-terrestrial life is an ever-evolving field of research that seeks to identify and understand life elsewhere in the universe. In order to narrow down this expansive search it is necessary to establish a set of parameters pertaining to habitability. It is therefore of significant interest for astrobiologists to study the conditions extra-terrestrial life may need to arise. Earth is the only planet currently known to host life and therefore provides an excellent model system as a case study for astrobiologists seeking to search for and understand life on distant planets. Very little is currently known about primitive terrestrial microorganisms, particularly with regard to their energetic processes and metabolism. It is well established that the origin of terrestrial life occurred simultaneously with the Late Heavy Bombardment, during which time a massive amount of organic-rich meteoritic material was accreted. This likely resulted in the accumulation of a large reservoir of extra-terrestrial carbon on the early Earth around the time primitive microorganisms were evolving more advanced metabolic processes. While it was previously assumed early life must have been purely autotrophic, the presence of potentially biologically accessible organics in the early Earth environment introduces the possibility that primitive microbes may have evolved to exploit these resources and develop early heterotrophic mechanisms much earlier than is currently postulated.
Fullerenes are found in abundance in carbonaceous chondrites and were therefore almost certainly present in relatively high amounts on the early Earth. Very little is known about the effect of fullerenes and their naturally occurring water-soluble derivatives, fullerols, on microorganisms, particularly in anoxic environments, and therefore very limited conclusions can be drawn for their potential effects on primitive microbes. Furthermore, the effects of the extreme early Earth environmental conditions, such as short-wave UV exposure, on the chemical properties of fullerenes and their derivatives are yet to be characterised; yet investigating this is critical in understanding how fullerenes may have fulfilled an important ecological niche.
In this thesis, I will explore the effect of fullerenes C60 and C70 and their fullerol derivatives on microorganisms and their potential as carbon sources for heterotrophic metabolism. An anaerobic community was studied as an analogue of a primitive microbial system, with an isolate derived from this community used for further, more comprehensive analyses of biological fullerene interactions. Furthermore, the effect of fullerenes and fullerols on select aerobic environmental isolates and model species E. coli was examined. With these microbiology studies, I show that fullerene response is highly species-specific and closely linked to the growth environment. It is demonstrated that fullerene C60, while inaccessible in its native form, can be converted to a highly accessible carbon source for anaerobic microorganisms when exposed to the high UV and anoxic conditions found on early Earth. To further understand the biodegradation pathways involved in C60 utilisation and the mechanism of toxicity to aerobic species, a comprehensive metabolomics study was carried out in which I present a novel set of results describing the innate biological effect of fullerenes on both an aerobic and anaerobic microorganism. The results presented in this thesis in their entirety give a clearer picture of how fullerenes on the early Earth and other habitable planets could provide primitive microbes with a previously undescribed source of carbon and energy
Investigating Wnt3-mediated symmetry breaking and cell fate in engineered gastruloids
No full textEstablishment of the anteroposterior (AP) axis in developing mouse embryos is informed by cues from extraembryonic tissues (Arnold & Robertson, 2009; Rivera-Pérez & Magnuson, 2005). In contrast, aggregates of embryonic stem cells (ESCs) termed gastruloids are able to display symmetry breaking and develop an AP axis in the absence of extraembryonic tissues or localised exogenous positional signalling (Baillie-Johnson, van den Brink, Balayo, Turner, & Arias, 2015; Beccari et al., 2018; Turner et al., 2017; Van Den Brink et al., 2014). The exact mechanisms behind these processes remain unclear but depend on feedback in Wnt signalling (Turner et al., 2017), as well as heterogeneity in Wnt activity, which has been shown to precede symmetry breaking (McNamara, Solley, Adamson, Chan, & Toettcher, 2023).
2D culture systems have been used to study heterogeneity and local propagation of Wnt activity and local community effect in other contexts (Martyn, Brivanlou, & Siggia, 2019; Nemashkalo, Ruzo, Heemskerk, & Warmflash, 2017; Yoney, Bai, Brivanlou, & Siggia, 2022). However, it is challenging to study the effects on symmetry breaking and AP axis determination in the absence of 3D architexture and patterning.
Chimeric gastruloids (Wehmeyer et al., 2022) generated by co-aggregating ES cell lines with distinct genetic backgrounds offer the opportunity to probe the effects of engineered heterogeneity in Wnt activity in a 3D environment. In combination with cell neighbour- labelling technologies (Malaguti, Lebek, Blin, & Lowell, 2024; Malaguti et al., 2021; Morsut et al., 2016), I attempt to investigate non-cell-autonomous effects of Wnt heterogeneity.
Here I present my work combining these two technologies to test the hypothesis that Wnt3 locally amplifies its own expression to influence the position, identity and local coherence of mesoderm fated cells during symmetry breaking in gastruloids.
I describe the design and engineering of novel tools for expressing tagged but functional Wnt3 in gastruloids, either in a uniform or chimeric manner. Building upon the resulting experimental background, I explore the use of cell contact-labelling technology in a 3D setting to ask how Wnt3 influences multicellular organisation of cell fate decisions.
I demonstrate that synthetic-Notch based cell contact labelling can successfully distinguish between neighbours and non-neighbours of Wnt3-overexpressing experimental or control cells in early gastruloids and discuss the limitations of this approach at later stages. My work probing the characteristics and limitations of this system have broader implications as it showcases areas that challenge synthetic neighbour-labelling technologies in their current form.
In addition, I describe the development of a set of image analysis pipelines for quantitative analysis of gastruloid morphology, cell fate decisions, local coherence of identity and the clustering and positioning of cells of shared identity within homogenous and chimeric gastruloids. In future, these could be adapted for comprehensive high-throughput analysis of self-organisation and morphogenesis in gastruloids or other 3D embryoid models.
Using these tools, I found that gastruloids are able to break symmetry, elongate and generate both mesodermal and neural cell types in the absence of exogenous Wnt activation when an internally tagged version of Wnt3 is constitutively expressed in all cells of the gastruloid. This observation is consistent with the idea that heterogeneity in Wnt expression may not be the only factor driving symmetry breaking. Moreover, consistently forming gastruloids in the absence of global exogenous Wnt activation opens up opportunities for manipulating Wnt activity in a mosaic manner in chimeric gastruloids.
Finally, by generating chimeric gastruloids from labelled and reporter cell lines, I have obtained preliminary evidence that in the absence of global Wnt activation Wnt3 over- expressing cells within chimeric gastruloids may be biased towards contribution to the elongating tip, that Wnt3 may upregulate Wnt3 expression in neighbours in some contexts, and that internal overexpression of Wnt3 may affect the proportion neural and mesodermal descendants.
Alongside these results, I discuss a number of technical challenges in obtaining and interpreting data from these complex experimental systems, and I offer suggestions for improving these systems in future work. The main barriers to interpretation of the collected data stem from variability within population-level gene expression analysis of sorted sub- populations, and from difficulties in single-cell resolution imaging and image analysis. Most of these obstacles could be overcome through single-cell RNA sequencing approaches in future studies.
In summary, I have established a novel set of tools and approaches to aid investigations into the role of Wnt signalling in mediating local cell identity to generate coherent patterning in gastruloids. These methods could be of use for future studies of the prerequisites and disruptors of self-organisation within 3D organoid systems
High-speed quantum key distribution in the presence of detector dead time
No full textQuantum technology, particularly quantum key distribution (QKD), has garnered increasing research interest in recent years. Despite significant advancements, the key generation rate of current QKD systems remains constrained by practical limitations, including imperfections in quantum sources, the performance of quantum detectors, and the characteristics of the quantum channel. This thesis primarily investigates the bandwidth limitations of quantum detectors caused by the dead time effect under high-speed conditions, while also addressing imperfections in quantum sources and channels through the study of the decoy-state method and the dispersive characteristics of underwater channels.
The quantum detector's dead time effect, which happens after each photon detection, limiting the maximum quantum bit transmission rate and consequently the key generation rate of QKD systems. Qubit transmission at the sub-dead-time regime (i.e., faster than the reciprocal of dead time) can introduce different security loopholes. In this thesis, we propose the use of a detector array instead of a single detector to measure the quantum state of individual photons in discrete variable QKD systems, showing that it can significantly alleviate the limitations induced by detectors' dead time. A dead-time compensated BB84 scheme is introduced, allowing qubit transmission at the sub-dead-time regime. Consequently, novel analytical expressions can be derived for the sifted bit rate (SBR) and secret key rate (SKR) of the proposed QKD system, showing excellent match with the Monte Carlo simulation results. A remarkable gain is observed for the BB84 system employing detector arrays, showing a potential M-fold improvement of SBR at high qubit transmission rates, where M is the size of the array.
In practice, weak coherent sources are commonly used as substitutes for perfect single-photon sources. However, these sources can sometimes emit more than one photon per pulse, enabling Eve to perform photon number splitting (PNS) attacks. The decoy-state method has been proposed to overcome this issue. Moreover, the key generation rate of QKD systems is also constrained by the practical limitations of detectors. In this thesis, we propose using four linked single-photon detectors (SPDs) in a high-speed decoy-state QKD system, considering the dead time effect of the SPDs. We introduce a Markov chain model to describe the impact of dead time on the operation of the proposed decoy-state BB84 system. This allows us to derive accurate analytical expressions for the sifted bit rate (SBR) and secret key rate (SKR) of the proposed QKD system, which show excellent agreement with Monte Carlo simulation results. We compare our more accurate model with the coarse model used in prior works, demonstrating that our model better captures system performance under different channel and noise conditions. Finally, we optimize the intensity of the signal source, determining the optimal signal intensity under various conditions, and compare the SKR with and without the optimal intensity.
In practical scenarios, underwater channels, such as those in coastal and harbor waters, exhibit dispersive characteristics. At higher qubit transmission rates, this dispersion causes photons from previous pulses to arrive within the same time window as current pulses, leading to inter-symbol interference (ISI). To evaluate this issue, this thesis subdivides the clock period into smaller chips to analyze the impact of ISI on the performance of QKD systems. A chip-scale Markov chain model is built to characterize the influence of detector dead time on qubit transmission in the sub-dead-time regime. Analytical expressions for SBR, QBER, and SKR are derived, and the effects of ISI are observed under various channel conditions
Managing minds: the power of corporate culture within the British banking and insurance sector in the First World War
Get PDFThis thesis analyses the ways in which the corporate culture of major banking and
insurance institutions influenced how their employees reacted practically and
emotionally to the First World War. Little researched until now, this level of influence
on young middle-class men and women, operating as it did below the level of
Government and press propaganda, is found to have played a significant role in British
support for the war effort.
The historiography on First World War Britain examining the factors which informed
the British citizen’s response to the war has largely concentrated on the
contemporaneous propaganda emanating from the Government and the press. For
the historian it is thus often difficult to quantify the effectiveness of such
communications. However, by narrowing the field of study to that of the financial
sector, it becomes possible in this thesis to detect the strong correlation between
corporate culture, management rhetoric and staff reactions throughout the war. In
particular, the thesis argues that these institutions created both the ‘corporate soldier’,
a man keen to enlist but who never lost touch with his pre-war persona, and the
‘corporate home front’, a supportive ‘family’ of managers and employees who willingly
worked together to support the war effort and their colleagues in uniform. A fresh
bridge is thus built between the concept of corporate culture, a field of study more
familiar to students of business management, and the work of historians of the First
World War. The thesis also highlights the importance of staff magazines as a powerful
yet under-researched source of cultural and social history.
In the course of this thesis, a number of key themes are addressed: war enthusiasm,
justifications for the war, volunteering, common sacrifice, employment of middle-class
women, alienation, post-war unrest, trade-unionism, and memorialisation. The
common thread which runs throughout is the powerful corporate culture which,
particularly through the pages of staff magazines, encouraged, guided, inspired and
at times cajoled employees of financial institutions throughout the war
Synthesis of phosphorus- and boron-containing aromatic and π-conjugated compounds
No full textIsosteric compounds are those species that contain the same number and arrangement of electrons, but different charges of the constituent nuclei. Boron- and nitrogen-containing aromatic and π-conjugated compounds are some of the most widely studied isosteres. The incorporation of these main group elements leads to unique chemical properties that could be harnessed in a range of applications, including nanographene materials for optoelectronic devices. In comparison, phosphorus- and boron-containing aromatic and π-conjugated compounds have lacked in their development.
The work described in this thesis demonstrates the synthesis, structural and reactivity studies of several different classes of phosphorus- and boron-containing aromatic and π-conjugated compounds. To begin, chapter 1 provides an overview of the current state of polycyclic aromatic hydrocarbons containing nitrogen, boron and phosphorus. It encompasses azaborines and phosphaborines, focusing on their fundamental differences.
Chapter 2 includes the development of 1,2-phosphaborete chemistry including their derivatization and reactivity with alkynes. The syntheses of several 1,3-phosphaborines with halide substituents are detailed and discussed in terms of regioselectivity. Furthermore, the first synthesis of an anionic 1,3-phosphaborine, namely 1,3-phosphaborabenzenyl potassium, is described and its structure is compared to other main group-containing aryl carbanions.
Chapter 3 details a new class of [3]dendralenes, namely the phosphabora-[3]dendralenes. Their synthesis is described in detail followed by an in-depth analysis of their structure and confirmation using density functional theory calculations and 1D NOESY NMR experiments. Their different dendralene core confirmations being close in energy explain their observed Diels-Alder reactivity with dimethylacetylene dicarboxylate to form new phosphorus- and boron-containing polycyclic compounds.
Chapter 4 focuses on the frustrated Lewis pair-type reactivity of 1,2-phosphaboretes. Firstly, an isonitrile insertion reaction is discussed, drawing a comparison between 1,2-phosphaboretes and vicinal phosphorus- and boron-containing frustrated Lewis pairs. A similar frustrated Lewis pair-type insertion is described between 1,2-phosphaboretes and dimethylacetylene dicarboxylate, giving rise to a new route towards 1,4-phosphaborines. To conclude, a comparison between the synthesized 1,2-, 1,3- and 1,4-phosphaborines throughout chapter 2 and 4 is drawn.
And finally, chapter 5, highlights the synthesis and structural study of divinyl(amino)boranes by density functional theory calculations to examine their ability to take part in Diels-Alder reactions. In-depth analysis of their frontier molecular orbital energies reveals their incompatibility with a range of dienophiles and explains their lack of reactivity.2028-09-0
Creative teaching in English classrooms: the case of Indonesia
No full textThis research addresses a critical yet underexplored aspect of creative teaching: the need to consider the dynamic interplay of social structures, cultures, and teacher agency. While previous studies on creative teaching have primarily concentrated on the outcomes of creativity—often highlighting task constraints that can enhance creative expression—they tend to overlook the fundamental structures, cultures, and teacher agency that significantly influence teachers’ creative practices. The current qualitative study investigates the creative teaching practices of four secondary school English teachers from three different schools in Java, Indonesia: a public school, a private vocational school, and a private school.
Guided by Critical Realist philosophy and employing Margaret Archer’s Morphogenetic approach, the study examines how these teaching practices are shaped by teacher agency, social interactions, and existing social structures and cultures. Data were collected over six months through interviews with the teachers, 24 classroom observations, informal conversations documented as researcher notes, analysis of learning materials, and interviews with two professors involved in teacher preparation programs. The data were analyzed using Fryer’s Critical Realist Thematic Analysis.
The study identifies several institutional mechanisms that encompass social structures and cultures contributing to creative teaching, including (1) school and classroom climate, (2) autonomy and flexibility, and (3) resources availability, all of which are integral to the structural and cultural framework. At the individual level, it highlights the concept of autonomous reflexivity among the teachers, enabling them to make independent decisions free from external influence. This suggests a need to reevaluate the traditional focus on individual responsibility for creativity in teaching. This research also found that school support is crucial in facilitating teachers' creative practices, revealing that significant structural constraints hinder the development of these practices.
While the investigation into the mechanisms producing creative teaching practices benefits from Margaret Archer’s Morphogenetic Approach, it is only through a decolonial lens that I can fully appreciate the cultural nuances of the teachers’ creative practices, particularly through Dewantara’s "Tri Sakti Jiwa" (Three Excellent Souls), which includes cipta (thinking ability), rasa (feeling), and karsa (intention). This framework highlights the significance of teachers' motivation and intent, the need for contextual adaptation, and the focus on affective domains.
Furthermore, I challenge the notion that creativity is inherently opposed to compliance, demonstrating that respectful compliance can actually enhance teachers' creative teaching practices. This research enriches the literature on creative teaching by providing a fresh perspective on creative practices from underrepresented contexts and offers a decolonial viewpoint that broadens the scope of understanding creativity
Computational methods for nonlocal PDE-constrained optimisation: applications in ecology, image processing, and phase separation
Get PDFComplex systems of interacting quantities commonly arise when studying physical and ecological processes. The toolbox of a mathematical modeller provides many approximations to capture the intricate nature of such interactions. In particular, the field of differential equations (DEs) offers a rich set of modelling tools that, when complemented with the backbone of numerical linear algebra, can effectively capture and offer detailed insights and predictions about a system of interest. A DE system describes a number of interacting quantities related through terms involving one or several partial derivatives and possible nonlocalities. A nonlocal interaction is, in essence, an integro-differential quantity that relates a pointwise quantity with one or several clouds of points that are not necessarily close to the point of interest. As the name suggests, nonlocalities generalise local evaluations (e.g., partial derivatives or pointwise evaluations) to gain a domain-informed perspective of a function. As a result, combining local and nonlocal operators offers a powerful, general-purpose, modelling tool. Such a combination is regulated by a set of parameters that are either provided by observation or set using the knowledge of the modeller. However, measuring parameters for complex differential models is not a straightforward task. Nonlinearity, nonlocality, and (dis)continuous dependencies impede experimental model calibration, which also lacks theoretical guarantees for a given fit. Optimal control theory offers an effective framework for data-driven parameter identification problems governed by DEs. An optimal control problem aims to optimise a quantity (e.g., a model fit) defined on a suitable function space, which is governed by a set of parameters (or control variables) that determine the profile of a given response (or state variables) modelled by a differential system. By generalising concepts of classical optimisation theory to abstract function spaces, optimal control provides existence and optimality certificates that allow us to design effective numerical schemes targeted for model calibration.
This work presents three parameter identification problems: a disease spread model, an image restoration problem, and a phase separation model. These problems arise in different application settings but share one common aspect: they contain a nonlocal term either in their formulation or as a by-product of the optimality conditions for the calibration process. Nonlocalities add additional complexity, as existence results are limited and problem-specific, while their discretisation often leads to dense and ill-conditioned systems. These challenges inform our approach, guiding the different analytical and numerical methods we develop for each problem.
Our baseline for the parametric study of disease evolution is the classical Susceptible, Infected, Recovered, and Deceased (SIRD) model. The SIRD, a nonlinear system of ordinary differential equations, provides a comprehensive understanding of an outbreak under mild assumptions. The system is governed by three parameters: the contact rate, the recovery rate, and the mortality rate. Determining these parameters is critical to understanding the evolution of the disease and predicting scenarios that can guide disease prevention and control policies. We present an optimal control framework for parameter identification of the SIRD from observed data. We derive existence and uniqueness results alongside optimality conditions for the problem under a constant-in-time assumption for the controls. The conditions on the control yield a nonlocality in the optimality system. We present a numerical study of tailored iterative optimisation routines to obtain efficient numerical approximations. We demonstrate the effectiveness of the optimal control tools under extensive scenario tests. Moreover, we show how this approach can extend to more complex systems that allow spatial interactions.
Practical image-acquisition methods introduce artefacts, such as noise, that corrupt the digital output of a ground observation. In particular, the stochastic nature of noise makes its identification and removal a particular ill-posed problem. Variational models offer a theory-rich and mesh-independent solution approach for the image denoising problem. This perspective relies on the combination of a regularising term modulated by a fidelity term to produce a new image with flattened regions that resemble the observed image. Here, the choice of a regulariser determines which information is removed. Nonlocal image denoising offers a class of regularisers by taking into account the redundancy of information in an image. This class of methods has been particularly effective at recovering images featuring textures and highly-varying regions. Bilevel optimisation and optimal control theory can determine an appropriate fidelity weight. We focus on finding optimal fidelity weights for a quadratic nonlocal regularising term. Specifically, we present the unnormalised extended Gaussian ANOVA kernel as an extension of the classical nonlocal means kernel. Naïve discretisations of the nonlocal kernel can be carried out in O(N²) operations, where N is the number of pixels in the image. Nonetheless, computing the ANOVA kernel can be done via the nonequispaced fast Fourier transform (NFFT), yielding a reduced O(N) complexity. Thus, we obtain efficient evaluations of the nonlocal kernel, which is crucial when solving the Euler-Lagrange system for the denoising problem. The discretised system is characterised by a graph Laplacian, for which we present a spectral study. We propose a family of diagonal preconditioners and dense variants to accelerate matrix-free iterative methods, that perform impressively under a suitable change of basis. Extensive numerical tests are presented, highlighting the effectiveness of the dense preconditioners and the NFFT in significatively reducing computation times and hardware requirements for solving nonlocal problems.
Phase separation studies the evolutive formation of two or more distinct layers from a homogeneous mixture. Several PDE models have been proposed to capture this behaviour, effectively describing the dynamics of multi-component systems where different patterns spontaneously form and evolve. One of these models is the Cahn-Hilliard equation, a quasilinear PDE describing a separation and coarsening stage. Characterised by fourth-order derivative terms, the equation relies on high regularity assumptions for the solution. A less restrictive extension is the nonlocal Cahn-Hilliard equation, allowing for more flexibility in the involved nonlinear terms and less regularity for the solution. Determining the mobility term is a question that can be addressed using optimal control theory. When discretising the system, we first encounter the problem of adequately approximating the action of a singular kernel. We propose a pseudospectral-element method for obtaining detailed and accurate solutions of DEs in the presence of singular kernels. It is based on the MultiShape extension of the 2DChebClass library that allows us to isolate the singularity of the kernel on an arbitrarily small neighbourhood, effectively approximating the action of the singular kernel to machine precision. We present an extensive set of tests to showcase the robustness of our method and provide computationally cost-effective solutions to the nonlocal system
Some extensions of particle Metropolis-Hastings and their applications
Get PDFState-space models are fundamental tools for representing and analysing dynamic systems or phenomena, with applications spanning numerous scientific fields, such as signal processing, finance, and ecology. The fundamental idea of a state-space model (SSM) is to model observations as the result of a stochastic process, which is influenced by a hidden state process that changes over time based on some parameters. Particle filters are effective inference methods that approximate the posterior distributions of hidden states in these models over time by utilizing a collection of random samples, known as “particles”. A key challenge in working with state-space models is effective parameter estimation. This thesis delves into exploring novel enhancements to the Particle Metropolis-Hastings (PMH) algorithm, which is a particle-based Markov Chain Monte Carlo (MCMC) method that allows for parameter inference in state-space settings. In one chapter, we introduce a novel approach that leverages the Integrated Nested Laplace Approximation (INLA) to design efficient proposal distributions for particle filters. These enhanced filters are incorporated into the PMMH framework, leading to improved sampling efficiency and accuracy in parameter estimation. In addition, we extend the Hamiltonian Monte Carlo (HMC) method, a popular algorithm in Bayesian inference, to develop a particle MCMC version tailored for state-space models. These methodologies were tested on data to address questions in transport modelling, such as cycling behaviour, and in predicting primary school student populations. The resulting algorithms offer efficient tools for inference in state-space models
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