VictorJuiz/thesis huggingface dataset:
Molecular dynamics simulations of membrane proteins in nanodiscs with investigation of protein-lipid interactions

Membrane proteins perform various important and wide-ranging functions. They exist within a lipid bilayer and their interactions with the components of this bilayer are of great scientific and pharmacological interest due to the ability of these components to regulate protein structure and function. Computational approaches such as multiscale molecular dynamics simulations are well suited to the study of these systems. As such, the research presented here uses an array of these approaches to examine and characterise the interactions between membrane proteins and lipids in two environments: nanodiscs and lipid bilayers.
There has been exponential growth in the use of nanodiscs for solubilisation of membrane proteins in a native-like environment, where the membrane protein is embedded in a patch of lipid bilayer constrained by helical proteins. However, the impact of constraining the nanodisc components in this manner is currently not well understood. In this research molecular dynamics simulations are used to investigate these effects; the results presented here describe the changes in lipid properties which occur as a consequence of constraining the nanodisc components and subsequent variations in protein lipid interactions.
One family of membrane proteins, the G-protein-coupled receptors, was selected for further study. A simulation approach was used to examine the binding of a membrane lipid, cholesterol, to potential allosteric modulatory sites on these proteins, including the previously identified TM345 site. Interactions with cholesterol at this site were found to be common to several members of this family despite limited sequence conservation.
The results presented here demonstrate the importance of understanding the environment in which membrane proteins exist and the impact of changes to this environment upon protein behaviour, properties and interactions.

Keywords: Cholesterol
Simulation
G-protein-coupled receptors
Molecular Dynamics
Protein-Lipid Interactions
Nanodiscs
Coarse Grained Simulations
Advisor: Sansom, M
Stansfeld, P
Solving product-mix markets and learning agents’ preferences

This thesis addresses computational questions arising in auctions with multiple goods available in multiple quantities, with a focus on establishing the tractability of auction mechanisms used in practice. It presents algorithms and hardness results for solving these auctions with the goal of maximising social welfare or revenue, and develops procedures to facilitate participating agents in expressing their preferences in the auction's bidding language.
The 'strong-substitutes product-mix auction' was originally designed for the Bank of England by Paul Klemperer and continues to be run at least monthly. It introduces a novel bidding language, which allows agents to submit sealed-bid strong-substitutes preferences over an arbitrary number of goods available in multiple discrete units. We study this language geometrically and computationally, and establish connections to related bidding languages in the literature.
In order to solve the strong-substitutes product-mix auction for social welfare, we develop the first efficient algorithms to find market-clearing prices and envy-free allocations of supply to participating bidders. The latter, in particular, requires solving a novel constrained matching problem. By contrast, we show that solving the auction for maximum revenue is APX-hard even in special cases, and present initial algorithms for this.
Agents participating in this auction may have trouble expressing their preferences in the auction's bidding language when faced with a large number of goods or non-trivial demand. Instead, they may be able to answer queries about their value of a given bundle or their demand at given prices. We propose algorithms that learn a bidder's preferences, assuming access to a demand or valuation oracle. In a special case currently implemented by the Bank of England, we present a linear-time algorithm. We also show super-polynomial lower bounds on the query complexity in the general case. Our algorithms constitute the first approach for bidders to express non-trivial preferences in these languages, lowering the barrier for participation in the strong-substitutes product-mix auction.
In the related 'arctic product-mix market', originally designed for the Icelandic government by Klemperer, buyers use a conceptually similar bidding language to express preferences across multiple divisible goods in conjunction with monetary budgets. In this setting we present a new coincidence of the solution concepts of competitive equilibrium and optimal revenue: market-clearing prices are unique, and these prices maximise not only social welfare but also revenue. We also provide an algorithm to identify these prices.

Keywords: bidding languages
computational complexity
learning demand
auction
mechanism design
Advisor: Goldberg, PW
Synthesis and reactivity of main-group complexes with heteroatomic double bonds

The synthesis and reactivity of compounds containing heteroatomic double bonds are described in this thesis. An overview of multiple bonds between heavier p-block elements is presented in Chapter 1, including the general synthetic routes for the formation of homoatomic and heteroatomic main group multiple bonds. The formation of group 15–element double bonds from azides and phosphaketenes is also outlined.
Chapter 2 describes the synthesis of phosphagallenes through the decarbonylation of phosphaketenes. Attempts at forming analogous iminogallenes are also described herein.
Chapter 3 explores the reactivity of a phosphanyl phosphagallene towards small molecules such as H2, CO2 and E–H substrates. Two different reaction pathways were found for the activation of amines, both of which were investigated by Density Functional Theory calculations.
Chapter 4 expands on the synthesis of group 15–element double bonds by demonstrating the synthesis of Ge=P and Sn=P double bonds. Additionally, the reactivity of a phosphanyl phosphagermene with CO2, amines and silanes is described.
Finally, Chapter 5 discusses the aim of using compounds with multiple bonds between the heavier main group elements in order to catalyse the hydroamination of substrates. Two different catalyst designs containing transition metals are targeted: a transition metal- phosphinidene complex and a transition metal substituted phosphagallene. The attempted synthesis of these compounds is described.

Keywords: tin
Small molecule activation
multiple bond
germanium
double bond
Frustrated Lewis Pair
phosphinidene
phosphorus
gallium
main group
Advisor: Goicoechea, J
CP violation measurements using fully reconstructed B± -> D* h± decays, h ∈ (K, π)

Measurements of CP observables using fully reconstructed B± -> D* h± decays are made, h ∈ (K, π), where the D*0 meson is reconstructed in the D0π0 and D0γ final states. The analysis is conducted using proton-proton collision data collected by the LHCb experiment, corresponding to a total integrated luminosity of 8.7 fb−1: 3 fb−1 taken at centre-of-mass energies of 7 TeV and 8 TeV (Run 1); and 5.7 fb−1 at 13 TeV (Run 2). This work presents the first reconstruction of these decays at a hadron collider, and the first time D*0 mesons have been fully reconstructed for a CP violation analysis at a hadron collider. The 2-body D meson final states K−π+, K−K+, π−π+, and π−K+ are considered, facilitating the measurement of 16 CP observables in order to further constrain the CKM angle γ and the hadronic parameters (rBD* K, deltaBD* K, rBD* π, deltaBD* π). The first observation of the suppressed B± -> (D* -> [π∓ K±]D γ) K± decay channel is also presented, colloquially known as the D0γ ADS mode.

Keywords: Frequentist statistical analysis
High energy physics
Hadronic physics
CP violation
Particle physics
Neutral particle reconstruction
Advisor: John, M
Three problems in additive combinatorics

The problems considered in this thesis involve several fundamental objects in additive combinatorics. In this project, we mainly focus on the structure of subsets of integers. As integers are the most fundamental objects in number theory, one of our main interests in this project is to understand additive combinatorial problems related to sets which arise naturally in number theory, such as prime numbers and smooth numbers.
In Chapter 1, we study the size of subsets of smooth numbers which are free of geometric progressions. By taking a Freiman isomorphism, we shall use additive results to study the multiplicative structure in smooth numbers. Our result is proved in Section 1.2 and Section 1.3. For completeness, we illustrate a typical counterexample in Section 1.4, namely the set of k-free smooth numbers.
In the second problem, we focus on difference sets which do not contain shifted primes. Let ℙ denote the set of the prime numbers. Suppose A ⊆ [N] is nonempty and it satisfies (A-A) ∩ (ℙ - 1) = ∅. We are primarily interested in estimating the cardinality of the set A In Chapter 2, we prove a new upper bound on the cardinality of A. In Chapter 3, we investigate sets A such that nA - nA avoids ℙ - 1. We first prove an upper bound on |A| which depends on n, then we generalise an example of Ruzsa.
In the third problem, we are interested in the quantitative aspect of partition regularity of the equation x+y = z when x,y,z are restricted to shifted primes ℙ - 1. In Chapter 4, we provide an exposition of the work of Li and Pan, which is the first result concerning partition regularity over shifted primes. We focus on the analytical ingredients of their transference principle and the quantitative bound that follows from it. In Chapter 5, we improve the bound produced by the method of Li and Pan using a different approach. The main ingredient of the proof is an iteration lemma from Chapter 2.

Keywords: Analytic number theory
Additive combinatorics
Shifted primes
Advisor: Sanders, T
Word problems on string diagrams

String diagrams are graphical representations of morphisms in various sorts of categories. The mathematical results which establish their soundness and completeness provide an elegant bridge between algebra and topology, equating a certain class of topological deformations to the equational theory of an algebraic structure. Beyond this conceptual appeal they also are practical tools to reason in the corresponding categories, making it easy to build intuition about the combinatorics of morphisms and efficiently communicate proofs to peers. Finally, they provide data structures to encode morphisms and manipulate them with computer programs such as proof assistants. Our contributions to the field explore three main directions.
First, we define a new class of string diagrams that we call sheet diagrams and prove their soundness and completeness for morphisms in free bimonoidal categories. This makes it possible to use string diagrams in situations involving two monoidal structures, one distributing over the other.
Second, the bulk of our work consists in studying how string diagram isotopy can be checked computationally. This is done by providing algorithms or hardness results for a particular class of decision problems, called word problems. Those word problems consist in determining whether two given diagrams can be related via a sequence of isotopy moves, whose nature depends on the algebraic structure at hand. We provide algorithms for the word problems for monoidal categories (or equivalently 2-categories or bicategories) and double categories. We also provide a hardness result for the word problem for braided monoidal categories, showing that this word problem is at least as hard as the unknotting problem, for which no polynomial-time solution is known to date.
Finally, we give a taste of how those techniques can be applied to real-world systems. We show how bimonoidal categories model the data transformation workflows offered by OpenRefine, an open source data wrangler focused on tabular data. This model has guided a refactoring of the architecture of the tool and suggests user interfaces to manipulate those workflows.

Keywords: bimonoidal category
string diagram
isotopy
word problem
monoidal category
openrefine
sheet diagram
Advisor: Vicary, J
Coecke, B
Staton, S
A gift of time: the contemporary artist-in-residency programme 


Contemporary artist residency programmes around the globe have proliferated since the early 1990s. Promoted through new online platforms such as Res Artis and TransArtists, they are now firmly embedded within artistic networking and discursive practices. Whereas residency programmes were originally valued for their role in enabling mobility and cultural exchange, this thesis addresses a countervailing tendency that identifies residencies as retreats, whose primary role is to shelter artists from external pressures and demands. Residency programmes frequently claim to provide artists with a ‘gift of time’, or even more commonly, to provide ‘time and space.’ This thesis identifies the concept of providing temporal-spatial withdrawal as a ‘problem-idea’ that courses through and also shapes residency programmes and discourses: in practice, the emphasis on withdrawal can occlude the real pressures and demands that residencies place on artists, the complexity of their entanglements within the wider art world and its institutions, and the extent to which artistic practices and residency practices are intertwined. The thesis is structured through an analysis of some of the main types of artist residencies, since these are also related to the key concepts that shape contemporary residency thinking. The first part examines residency programmes within museums, which are frequently used to reinscribe the concept of the museum as a patron and supporter of living artists. The second part focuses on retreat-type residencies, programmes that actively promote the ‘gift of time’ idea by offering to ‘shelter’ artists in rural and remote places. The final part addresses discourses on artistic labour, together with case studies of experimental residency models, in order to consider the different ways that residencies ameliorate, contribute to, and make visible, contemporary conditions for artistic working. One of the aims of the thesis is to challenge the tendency of residency programmes to disavow their own institutional character. This requires that we acknowledge the extensive infrastructure of contemporary residency programmes and the ways in which they actively shape contemporary artistic production.

Keywords: artist-in-residency programmes
institutional art history
contemporary artist-in-residency programmes
residency
AIR
contemporary art
artist residency
Advisor: Gardner, A
Dynamical network models for melt ponds on sea ice

We present a model for the formation and evolution of melt ponds on sea ice, written as a dynamical system on a network. These ponds have long been suggested as a contributing factor to the discrepancy between observed and predicted sea ice extent; ponds have a lower albedo than bare ice, so they contribute to the ice-albedo feedback. Of particular interest here is the geometry and topology of the ponds as they grow and connect. It has been observed that there is a change in the fractal dimension of the pond system. Further, it has been suggested that pond systems go through a percolation process with ponds connecting across a whole oe at a phase transition, and that a percolation threshold plays a key role in pond dynamics.
We present a physically based network model for systems of ponds, which can be used to examine both their individual and collective behaviour. Each pond initially occupies a distinct catchment basin, modelled as a node; a di erential equation represents the melting dynamics, and mass conservation governs the evolution of the pond volume and water level. Ponds can connect together through uxes of water between catchment basins, represented by edges. Ponds can also drain into the sea, through another form of edge.
We use the model to explore how the evolution of pond area and hence melting depends on model parameters, and  nd that it depends most sensitively on surface roughness and the timing of onset of drainage from the ponds. We qualitatively reproduce the observed transition in fractal dimension as the ponds grow, and the typical life-cycle of the pond system, with the areal coverage growing, then shrinking as the ponds drain to sea level, and then slowly increasing again. We examine the importance of percolation thresholds, and in some cases,  nd evidence of anomalous percolation. We also use model results to predict the extent of pond coverage in the future, warming Arctic.

Keywords: Dynamical systems on networks
networks
mathematical geoscience
complex systems
Sea ice
Advisor: Hewitt, I
Wells, A
Howison, S
Combinatorial aspects of scattering amplitudes: amplituhedra, T-duality, and cluster algebras

A paradigm shift has been occurring, according to which physical observables and their fundamental properties, symmetries and dualities emerge from underlying geometry and combinatorics. This has led to major new insights in both Physics and Mathematics. In the first part of this work, we discover a duality between two seemingly unrelated objects. On one side, the hypersimplex Delta_{k+1,n} – a polytope which has been studied in connection with the moment map, torus orbits in the Grassmannian, tropical geometry and cluster algebras. On the other side, the amplituhedron A_{n,k,2} – a subset of the Grassmannian (not a polytope!) which was introduced in the context of the physics of scattering amplitudes in planar N = 4 super Yang-Mills (SYM). We show these two objects are closely related by a combinatorial-geometric incarnation of T-duality from String Theory. Exploiting T-duality, we both draw striking connections between Delta_{k+1,n} and A_{n,k,2} and discover new properties of them. One of the main results is proving that positroid triangulations of the hypersimplex and of the amplituhedron are T-dual. Moreover, some of these triangulations can be obtained from BCFW recursions and the positive tropical Grassmannian Trop+Gr_{k+1,n} – both central in computations of scattering amplitudes. We then define the sought-after positive geometry of tree-level N = 4 SYM amplitudes in momentum space – the momentum amplituhedron. We conjecture that its positroid triangulations are T-dual to the ones of the m = 4 amplituhedron A_{n,k,4}, reflecting the physical Amplitudes/Wilson loops duality. In the last part, we pave the way for both connecting amplituhedra theory to cluster algebras and tropical geometry, and finding a geometric origin of cluster phenomena – increasingly emerging in scattering amplitudes. In particular, we show how cluster adjacency for Yangian invariants emerge purely from amplituhedra. We prove this for A_{n,k,2} in full generality and provide some results for the m = 4 amplituhedron. Finally, using the geometry of loop amplituhedra, we conjecture a new phenomenon for planar N = 4 SYM at loop level – LL-cluster adjacency – relating Leading Singularities and Landau Singularities, with checks and general proves at one loop.

Keywords: T-duality
scattering amplitudes
hypersimplex
tilings
positive geometries
cluster algebras
N=4 Super Yang-Mills Theory
tropical geometry
matroid and positroid theory
amplituhedron
positive grassmannian
triangulations
Advisor: Mason, L
Lukowski, T
Low density plasma waveguides for multi-GeV laser Wakefield accelerators

Particle accelerators are vital tools for discovery in the fields of medicine, engineering, life sciences and physics. These machines, however, are becoming increasingly large, technically challenging to construct, and uneconomical. Laser wakefield accelerators (LWFAs) provide immense accelerating fields, and offer the potential to reduce the size of particle accelerators by a factor of 1000, though several challenges are yet to be overcome. One such challenge is the development of a low density plasma waveguide capable of guiding high-intensity laser pulses of distances up to a metre to form the basis of a multi-GeV LWFA stage. It has been shown that Hydrodynamic Optical-Field-Ionsied (HOFI) plasma channels can support low-density LWFA stages operating at a high repetition rate (\frep≳\SI1kHz).
This thesis focuses on the development of low density, HOFI plasma channels through experiments and simulation. Optical guiding is demonstrated of laser pulses with a peak input intensity of \SI6E17W.cm−2 through \SI{100}{mm} long plasma channels with on-axis densities measured to be as low as \nedd=\SI1.0(3)e17cm−3. It is found that the attenuation lengths of HOFI plasma channels were limited by the channel depth and radial extent to \Latt≲\SI100mm.
To account for this, a new method for extending such plasma channels to the metre-scale is proposed. Through transverse interferometry measurements taken as the guided pulse arrives, it is shown that a neutral collar of gas which surrounds the initial HOFI channel is ionised by the guided pulse. The attenuation length increased instantaneously from \Latt=\SI15(8)mm to \Latt=\SI0.42(1)m. Particle-in-cell simulations demonstrate that the leading edge of a conditioning pulse injected into this structure ionises the neutral gas in its transverse wings, forming a deep plasma channel which guides the bulk of the pulse with low propagation losses.
Design of an experiment employing a metre-scale CHOFI plasma channel and of electron acceleration to the multi-GeV level is presented, including a novel gas cell design. Simulations demonstrating propagation and electron acceleration in CHOFI plasma channels for the first time are discussed. Two different injection mechanisms capable of injecting electrons without significantly increasing experimental complexity are considered --- ionisation injection, and density transition injection. It is shown that electron bunches with peak energies ΔW=\SI3.57GeV with a relative energy spread of just \SI2.5% can be generated.
It is clear that CHOFI plasma channels are likely to be very well suited to high repetition rate, multi-GeV LWFA stages.

Keywords: lwfa
laser-plasma
laser plasma accelerator
plasma channels
Advisor: Hooker, S
Walczak, R
Natural selection in spatially distributed populations

We introduce the spatial Lambda-Fleming-Viot model for natural selection within a population distributed on a spatial continua. We then analyse the behaviour of this model when one considers the appearance of a rare mutation. We investigate how the mechanism for reproduction will effect the resulting limiting behaviour. In particular, we not only show convergence to classical superBrownian motion but also, under suitable assumptions, to superBrownian motion with stable branching mechanism. We then look at the effect of a randomly fluctuating environment on the spatial Lambda-Fleming-Viot model. This is motivated by the changing effects of natural selection driven by the environment such as the El Niño effect. The final part of the thesis is devoted to an investigation of the genealogies within a population evolving under sweepstakes reproduction. This is related to the stable branching mechanism discussed earlier, but with a focus on the practical implications when sampling from a population one might expect to be modeled with a stable branching mechanism.

Advisor: Etheridge, A