The ability to probe the incredibly weak magnetism that results directly from nuclear spin is one of the wonders of physics, discovered in the middle of the last century. It relies on the fact that a nucleus will precess like a top in an applied magnetic field, at a rate that is species specific. In a MRI hospital magnet (typical field 1.5 T) the protons in the patient's body precess at around 60 MHz. This project relies on the use of Superconducting Quantum Interference Devices (SQUIDs), which operate as exquisitely sensitive flux to voltage transformers, to either measure still weaker signals from systems with low spin density or to perform spectroscopy and imaging in the Earth's magnetic field or lower. This work combines the technical challenge of building instruments, which open up a new domain for NMR, with new science. This new science ranges from fundamental low temperature physics to new applications for biological and medical diagnostics. Superfluidity is a state of matter that is characterised by the entire fluid being described by a macroscopic wavefunction. The lighter isotope of helium, helium-3, becomes superfluid when helium quasi-particles form pairs, at 0.94 mK for helium under its own vapour pressure. In 3He the pair diameter is around 70 nm at zero pressure. The aim of this project is to confine the superfluid in a cavity where the height is tuneable through the use of piezo-electric nanopositioning devices and comparable to the size of the pair. New phases and new physics are predicted to occur as the system is tuned into and through the two-dimensional limit. Predicted is an analogue of the quantum hall effect for transport of nuclear spin. But totally new, unexpected and exotic phenomena are likely to emerge as we enter uncharted territory. Nuclear magnetic resonance (NMR) experiments are sensitive to the phase of the superfluid and so provide the ideal probe with which to study the superfluid properties as a function of cavity height and temperature. The small size of these cavities, 10 -100 nm high, results in tiny signals so the high sensitivity of the SQUID, exploiting recent advances, is necessary for its detection. High resolution NMR spectroscopy and clinical magnetic resonance imaging, MRI, has revolutionised the study of chemical and biomolecular structure and the non-invasive diagnostic ability of the healthcare sector. One limiting factor to the use of these techniques is that the drive to improve performance has been focused on operation in ever higher magnetic fields. These high fields are obtained with sophisticated (expensive and large) superconducting magnets. This precludes the ability of these devices to be mobile, and results in a limited number of specialist facilities. This work aims to develop instruments for NMR and MRI that do not rely on a large superconducting magnet. The high, frequency independent, sensitivity of SQUIDs coupled with mechanisms to overcome the low intrinsic thermal polarisations in low fields means that operation in microtesla fields produced by simple magnets is possible. The long term aim is to couple SQUID based microtesla NMR/MRI instruments with cryogen free operation. More compact, cheaper, and mobile instruments, coupled to new imaging and spectroscopy techniques in the low field regime are expected to significantly extend the impact of the NMR method for analysis and a wide range of biodiagnostics. High spectral resolution, low field NMR spectroscopy offers the possibility of relating spin-lattice relaxation times, T1, to physical properties such as porosity. This could be exploited in the characterisation of bone porosity, used in the diagnosis of osteoporosis. The couplings between nuclei of different species result in a field independent frequency shift of the NMR signal that is sensitive to molecular conformations (the distance and angle between bonds) and has the potential to provide a sensitive detector of biomolecular interactions in vivo

The current state of Theoretical and Computational Chemistry is a paradox -- the fundamental equations governing physical reality in the chemical energy range (1-100 eV) are known completely, yet their exact solutions are in most cases far too complex to be computed: the best we can currently do, even with the largest modern supercomputers, is about the size of the benzene molecule. This basic computational problem is solved using physical approximations: calculating a given property to a given accuracy is often a much simpler task than obtaining the full molecular wavefunction. Computational Chemistry currently employs a large array of such approximations -- from the crudest (molecular dynamics) to medium accuracy (semi-empirics and density functional theory) to high accuracy (configuration interaction and high-order preturbation theory) to extreme precision (full configuration interaction). The primary parameter that makes an approximation computable is known as "scaling": polynomial (ideally linear) scaling makes an approximation computationally acceptable, whereas exponential scaling generally means that further theoretical work is required before meaningful calculations can be performed. This project will enable knowledge transfer between three sub-disciplines of Computational Chemistry -- time-domain electronic structure theory, spin dynamics and density matrix renormalization group (DMRG) -- that will bring some of the exponentially scaling computation stages down to polynomial scaling. Specifically, the latest DMRG algorithms will be adopted for dissipative spin dynamics (Cornell --> Oxford, Edinburgh), the state space restriction algorithms from spin dynamics will be adopted for time-domain electronic structure theory (Oxford, Edinburgh --> Stanford, Bristol) and the tensor factorization algorithms used in electronic structure theory will be applied to spin dynamics (Bristol, Cornell, Cardiff --> Edinburgh, Oxford). The six research groups (two US groups and four UK groups) involved in this project have extensive independent publication records on the subjects listed above, and view the possibility of joining forces on the computational scaling problem as a crucial opportunity in the ongoing effort towards improving the efficiency of Quantum Chemistry algorithms. Faster and more accurate simulation algorithms benefit all application areas of Quantum Chemistry -- computational drug design, biomolecular structure determination, MRI contrast agent design, metabolomics, magnetic resonance and optical spectroscopy, materials chemistry, etc. Our primary objective is to lift the (presently rather low) ceiling of what is possible to accurately compute using Quantum Chemistry techniques.

Network science is a powerful framework for modelling interacting systems and connected data. The strength of network science comes from its generality in distilling connectivity into core elements --- nodes and edges --- that can combine to form indirect connections. Many social, natural and engineered systems can be represented as networks, such as international relationships, gene regulation, airport networks and the Internet. Modelling dynamical systems such as information or virus spreading on networks reveals the interplay between structure and dynamics. Despite much success, the node-and-edge paradigm of network science has fundamental modelling limitations. These limitations, combined with the availability of detailed network data, have led to the early development of several higher-order network models of richer interactions. This proposal centres on the mathematical development of multiway networks, which model interactions that cannot be decomposed into pairwise edges simply because the atomic interactions involve more than two nodes. For example, chemical reaction networks model interactions between several compounds, small teams of people work together on projects in schools and businesses, and brain activity is mediated by groups of neurones. The joint coordination of multiple entities is not captured by combining pairwise interactions, but can be analyzed with models for multiway networks, such as hypergraphs and simplicial complexes. As a starting point, we will consider the problem of defining dynamical processes on multiway networks. We will consider a variety of approaches, starting with simple, linear Markov random walks, and their dual consensus model, aiming to understand how certain hypergraph structures translate into spectral properties of associated operators. As a next step, we will consider non-linear and non-Markovian processes that cannot be encoded in a standard graph, in order to reveal in full the importance of non-binary interactions between the nodes. A similar exploration will be conducted for random walk dynamics on simplicial complexes, building on the diffusion based on Hodge Laplacian. The flows of probability generated by these dynamical models will then be used to construct efficient ranking and clustering algorithms that take advantage of the rich multiway network structure.

Tuberculosis (TB) remains one of the leading infectious causes of death. At present, the World Health Organization (WHO) recommends treating drug susceptible pulmonary TB (pTB) with a two-month course of Rifampicin, Isoniazid, Pyrazinamide and Ethambutol (RHZE), followed by a four-month course of Rifampicin and Isoniazid (RH). Some patients are unable to adhere to this protracted treatment and discontinue treatment prematurely. This often results in TB recurrence and development of drug resistance. TB requires protracted treatment because Mycobacterium tuberculosis (Mtb), the causative agents for TB, exists as a heterogenous population of bacilli, a fraction of which are tolerant to anti-TB agents. New TB treatment regimens that are more effective against drug-tolerant Mtb would therefore help improve outcomes of TB treatment. While more than 800,000 people are successfully cured of TB every year, all-cause mortality rates are 6 times higher in TB survivors than in the general population. This is in-part because up to half of pTB survivors sustain severe lung damage and develop post-tuberculosis lung disease (PTLD) . At present, there are no interventions for preventing or managing PTLD. PTLD is largely caused by host responses to Mtb. Anti-Mtb host responses also promote Mtb drug tolerance. Host-directed therapies could therefore help alleviate both PTLD and Mtb drug tolerance. More than a hundred host molecular pathways, and even more genes, have been implicated in the evolution of PTLD and Mtb drug tolerance. It remains unclear which of these genes, or combinations of genes, should be targeted to reduce Mtb drug tolerance and/or PTLD. While single-gene-knockout experiments can be performed relatively easily, it is difficult to simultaneously knockout multiple genes to identify the ideal combination of genes to target to reduce Mtb drug tolerance or PTLD, given the myriad possibilities. Further, as most of the genes and pathways have been identified from animal models and in-vitro experiments, their relevance in natural human Mtb infections remains unclear. We, therefore, propose to leverage 1) single-cell transcriptomics of lung airway cells from pTB patients, 2) functional assessment of lung injury, and 3) sputum microbiologic assessment to identify the host cell types and molecular pathways associated with Mtb drug tolerance and PTLD. We will then leverage computational biology and machine learning to perform in-silico knock-up and knock-down experiments to hasten identification of single or combination host-directed therapeutics for reversing host transcriptomic perturbations associated with Mtb drug tolerance and PTLD. Finally, we will test the predicted compounds in an ex-vivo Mtb-human alveolar macrophage infection model.

How magma is emplaced and interacts with its surrounding rock is of central interest in the Earth Sciences. The intrusion of magma into the Earth's crust plays a major role in the dynamics and the evolution of continental crust. In many cases magmas are funnelled upwards and erupt at volcanoes that dot the Earth's surface, particularly in areas where tectonic plates collide. The Andes are part of such a collision zone where large magma bodies (batholiths) form, due to chemical evolution of intruding deeper magma as well as partial melting of surrounding rocks. A common style of volcanic activity in the Andes is the catastrophic eruption of many hundreds to thousands of cubic kilometres of magma in the form of ignimbrites (volcanic rock containing ash and pumice) which often results in the collapse of the magma chamber roof upon eruption, leaving behind more or less ring-shaped surface depressions with diameters of many kilometres. The project is motivated by results obtained from space-borne satellites indicating ground deformation and significant uplift at in the central Andes at Uturuncu volcano, Bolivia, where magma may be accumulating for 270 thousand years. It is suspected that this inflation is caused by the growth of a large magma body at depth. If this interpretation is correct then these anomalies provide an outstanding opportunity to answer questions such as how large magma bodies are assembled in the crust to form plutons, how they evolve, how they relate to volcanism in general and how they manifest at the Earth's surface, potentially before eruption. We aim to find answers to these questions via a coordinated, integrated approach across various disciplines of the Earth Sciences. Central to this ambitious project lies the amalgamation of geodesy, geophysics, geology, petrology and mathematical modelling to document pluton growth in real time. The implications of the proposed work include assessing the role of plutons in continental dynamics and the potential for large volcanic eruptions. We requests funds for the UK component of a collaborative UK-US project, which also involves partners from Spain, Chile and Bolivia. We propose an integrated investigation of the Uturuncu uplift to test the hypothesis that pluton growth is occurring, to document the dynamics of growth, and to explore the links between plutonism, volcanism and tectonics. The core of the study will be a geophysical experiment over a 4-year period to study the ground deformation, mass changes and seismicity, and to image the sub-surface structure beneath the volcano. The geophysical experiment will be complemented by geological and petrological investigations as well as mathematical modelling to set the geophysical experiment in the context with igneous processes and the long-term magmatic evolution. A key outcome of the research will be a new generation of mathematical models to inform on how large magma chambers grow and which geodetic or geophysical signals we might expect to record at the Earth's surface. We will quantify the nature of the sources responsible for ground inflation by separating the contributions of shallow migration of (hot) water and gases, and deep magma replenishment and ponding, to geophysical signals. We are also interested to find out where these reservoirs are located, how many there are and how they relate to the depth of magma chambers that have led to eruptions in the volcano's past. For the latter, lava morphology studies and petrology will give insights onto the conditions in these magma chambers. We aim at developing advanced models of magma systems embedded in continental crust incorporating complexities such as variable mechanical properties of the crust, plastic deformation of deeper crust as well as the influence of crystallization of gas-saturated magma and shallow hydrothermal systems on ground deformation.