A rapidly ageing population and the associated burden of age-related disease are two of the major societal and financial challenges facing developed and developing countries. Understanding the molecular processes that underpin ageing is a fundamental biological question and a critical step in designing interventions that could increase healthy life expectancy (healthspan). It is particularly important to understand the processes that contribute to ageing of neurons, as ageing is a major risk factor for many neurodegenerative diseases. The proposed project will advance our basic understanding of the cell biology of neuronal ageing by shedding light on the molecular mechanisms by which the communication between the ER and the mitochondria affects neuronal functionality over time. Communication between the two organelles regulates a number of processes, for instance calcium and phospholipids exchange, essential for proper cellular functions. The project will take advantage of a new platform that we developed to monitor ER-mitochondria interactions in Drosophila melanogaster as part of a long-term project aimed at studying the cell biology of neuronal ageing. Studying the cell biology of neurons in adult animals requires intravital or ex vivo imaging approaches, which in vertebrate model organisms are technically challenging and time-consuming. Moreover, such studies require a significant number of animals and often use surgical procedures. Our imaging system affords non-invasive, detailed imaging of intracellular dynamic processes in ageing neurons of ageing fruit flies. This system exploits the accessibility to microscopic observation of sensory neurons in the adult wing of Drosophila. The relatively short lifespan of fruit flies makes longitudinal studies feasible and the sophisticated genetic tools available in this organism greatly facilitate functional studies. Our methodology represents a significant advance for the field, allowing imaging of live neurons in an intact adult nervous system to be coupled to powerful genetic tools. With this system, we have been able to make significant progress towards understanding how specific neuronal functions decline during ageing. In our past work, we have discovered a remarkable age-dependent decline in the axonal transport of mitochondria in adult neurons of Drosophila. Reduced transport contributes to the broader decline of neuronal homeostasis that occurs during ageing while upregulation of this process appears to be beneficial in older neurons. Although these findings provide a strong association between mitochondrial motility and neuronal function, it is still unknown how modulation of transport mechanistically affects neuronal ageing phenotypes. An exciting possibility is that the interactions between the mitochondria and the ER would directly regulate mitochondrial transport and functions thus significantly impacting on neuronal ageing. By transferring our technology into the laboratory of Dr Tito Cali at the University of Padova (Italy), this work will reduce the number of mice and zebrafish used to study ER-mitochondria communications and further expand the utility of our Drosophila model to maximise its 3Rs potential.

This proposal is in the area of nonlinear partial differential equations (PDEs). More precisely I am interesting in proving rigorous convergence for solutions of a randomly perturbed nonlinear PDE to the solution of an effective deterministic nonlinear PDE. I look at different problems (both first-order and second-order) for nonlinear PDEs, associated to suitable Hoermander vector fields. The geometry of Hoermander vector fields (Carnot-Caratheodory spaces) is degenerate in the sense that some directions for the motion are forbidden (non admissible). A family of vector fields is said to satisfy the Hoermander condition (with step=k) if the vectors of the family together with all their commutators up to some order k-1 generate at any point the whole tangent space. If the Hoermander condition is satisfied, then one can always go everywhere by following only paths in the directions of the vector fields (admissible paths). The natural scaling for PDE problems associated to these underlying geometries is anisotropic. For example, thinking of homogenisation of a standard uniformly elliptic/parabolic PDE, one usually takes the limit as epsilon (i.e. a small parameter) tends to zero of an equation depending for example on (x/epsilon,y/epsilon,z/epsilon), where (x,y,z) is a point in the 3-dimensional Euclidean space. This means that the equation is isotropically rescaled. On the other end, when considering a degenerate PDE related to Hoermander vector fields, the rescaling needs to adapt to the new geometric underlying structure, e.g. a point (x,y,z) may scale as (x/epsilon,y/epsilon, z/epsilon^2). The challenge in the study of these limit theorems is to find approaches which do not rely on the commutativity of the Euclidean structure or on the identification between manifold (points) and tangent space (velocities). Further complications come from the limited use of geodesic arguments due to the highly irregular nature of such curves. Thus the proposed project requires an intricate combination of ideas and techniques from analysis, probability and geometry.

Cancer is among the leading causes of death worldwide. Cancers generate their own network of blood vessels to provide nutrients and oxygen to grow and spread. Detecting these developments early and treating them increases the chances of survival. However, current imaging methods are unable to detect these microscopic structures deep within the body. Therefore there is a crucial need to develop new imaging techniques that can fill this requirement. Additionally, imaging techniques which can look at the full 3D region of disease are urgently needed to reliably assess these. The research in this proposal is designed to develop and demonstrate an ultrasound imaging technique known as ultrasound super-resolution (US-SR) in 2D and 3D in the clinic. US-SR is able to image extremely fine details of the blood vessel network, previously unseen with standard ultrasound imaging. This technique involves adding small amounts of microbubbles into the blood stream, which show up on the ultrasound images because the sound is more strongly reflected from the bubbles than other tissues. These bubbles circulate harmlessly within the vessels until they dissolve after a few minutes. By pinpointing the location of these travelling bubbles over time, we can build up an image which 'paints out' the vessel structures containing those microbubbles. The ability to see these small vessels using ultrasound, which is able to image at depth (>10 cm) in humans, has the potential to identify these important changes in the vascular network Currently, however, US-SR has only been demonstrated in a small number of patients, it requires long scan times (in the range of 10s of minutes depending on the target) and ultrasound use in hospitals is generally limited to 2D. Within this proposed fellowship, it is my aim to firstly, develop faster ways to acquire the data needed to create these images. Secondly, to demonstrate the use of 2D US-SR in a large number of patients. And lastly, to use these developments to move 3D US-SR into the clinic. Successful 3D clinical US-SR demonstration could propel this technique into clinical practice. Its use could provide safe, low-cost microscopic assessment of blood vessels associated with disease. This could be crucial to patients with a wide range of micro-vascular related diseases including cancer due to early diagnosis and treatment. Given that US is an affordable imaging technique compared to for example x-ray CT and MRI, this could also provide significant cost-savings for the NHS.

Modern autonomous systems such as mobile robots and autonomous vehicles rely heavily on feedback controllers for motion control, particularly for path-following and obstacle avoidance, where they are employed to follow a trajectory set by a higher-level motion planner in a hierarchical control scheme. Model Predictive Control (MPC) is a popular controller choice for obstacle avoidance, as it allows constraints to be specified to ensure that the mobile robot or autonomous vehicle does not collide with obstacles. The behaviour of MPC is well understood from years of theoretical development and industrial practice, providing strong safety assurances, but considerable time and expert knowledge is required to implement it, especially in safety-critical applications such as autonomous vehicles. In recent years, research on deep Reinforcement Learning (RL) has provided new methods to automatically find nonlinear feedback controllers for challenging control problems. But unlike MPC, existing RL methods typically have no guarantees of stability or of constraint satisfaction, and for safety-critical applications it is difficult to verify their behaviour. To combine the predictability and safety guarantees of MPC with the power and convenience of modern RL methods, this project will develop methods to automatically learn MPC controllers in actor-critic RL frameworks, considering motion control and obstacle avoidance problems for autonomous vehicles. This will be a direct application of recent mathematical results showing that convex optimisations, such as MPC, can be employed as a trainable layer in RL frameworks such as PyTorch, allowing them to be learned. The goal is to enable rapid design and prototyping of path-following type MPC without requiring expert-knowledge of the underlying MPC algorithm, therefore reducing development time and cost and improving safety and reliability of future mobile robots and autonomous vehicles. To ensure the new algorithms are practically applicable, an example application of motorcycle path-following and stability assistance will be used to guide their development. The problem of stabilising a two-wheeled vehicle in forward motion to follow a predefined path, for example via steering actuation, is challenging and has important applications in the emerging area of active safety systems for motorcycles and scooters. For long term impact and to encourage adoption of the new methods by autonomous systems researchers, the new methods developed will be included in an open-source software library published on Github.

Describe the research in simple terms in a way that could be publicised to a general audience. This will be made publicly available, and Applicants are responsible for ensuring that the content is suitable for publication. No more than, 4000 characters including spaces and returns. Seismic hazards endanger both human lives and critical infrastructure, underscoring the need for a more profound understanding of earthquake dynamics and precise risk assessment, especially in regions prone to infrequent, long-recurrence events. Globally, earthquakes predominantly cluster along tectonic plate boundaries, where heightened seismic risk is acknowledged despite the lack of precise information on location and timing of earthquakes. Conversely, intraplate regions, situated away from these boundaries, also experience significant earthquakes, presenting a distinct challenge due to their rarity. Notably, these seismically active intraplate regions often coincide with large urban centres, amplifying potential risks. Key features that distinguish interplate and intraplate earthquakes include (1) variations in the stress on the fault that drives slip; (2) earthquake magnitude-frequency distributions - the number of small earthquakes in a region relative to large earthquakes; and (3) source parameters that dictate the severity of an earthquake, including the stress drop, duration of the event, and precursory phases that occur immediately preceding earthquakes. Investigating these distinctions and the underlying reasons responsible for them, as well as documenting historical earthquake events, holds promise for both a more comprehensive understanding of earthquakes and a pathway to enhanced regional seismic hazard assessment. Our project is dedicated to exploring the fundamental physics of earthquake rupture and documenting historical earthquakes within the Indian subcontinent including the public and state response to these events. These endeavours are inextricably linked and involve distinguishing the characteristic features between interplate and intraplate regions through a combination of laboratory experiments, borehole stress measurements, and seismic monitoring, and developing better records of historical seismicity and the response to it. By scrutinizing stress conditions, rock properties, earthquake magnitudes, source characteristics, and infrequent historical events, we aim to elevate the precision of risk analysis in key regions within India. The knowledge gained from these activities will be brought together to craft an educational and outreach initiative aimed at both the general population (through schools) and local government through education on the scientific and historical nature of earthquake hazard and development of tools to improve decision making. The program will heighten public awareness regarding earthquake risks, promote straightforward life-saving measures, and develop better planning to prepare and deal with future seismic hazard.