When we learnt classical thermodynamics from undergraduate physics/chemistry, we often assumed a large number of particles ~10^23, equilibrium, and quasi-static process. In this very restrictive limit, thermodynamic quantities such as heat dissipation Q, can be computed using the textbook formula Q= T\Delta S, where S is the configurational entropy. However, in real lives, most physical processes are neither quasi-static nor equilibrium. Furthermore, in many biological systems, the number of degrees of freedom is also much less than 10^23, and in this regime, thermal fluctuations become important. Thus, thermodynamic quantities such as heat, work and entropy need to be redefined properly (Stochastic Thermodynamics). The first aim of this research is to extend the theory of stochastic thermodynamics to include birth and death process, e.g., cellular division and apoptosis in living tissues and growing bacterial colonies. One important application of stochastic thermodynamics is the prospects of biological machines, which are powered by the swimming motility in some bacteria, or even cellular division and apoptosis in our bodies. For instance, it has been well known experimentally and theoretically that if we place an asymmetric cog inside a bath full of swimming bacteria, the cog can somehow rotate persistently in one direction. The bacteria themselves, in the absence of the cog, swim in a completely random direction; and yet the interaction between the bacteria and the asymmetric cog can break time reversal symmetry to create a macroscopic unidirectional current. Although this phenomenon has been well established in motile active matter (such as swimming bacteria), very little is known about non-motile growing active matter (such as cell division and apoptosis in living tissues and bacterial colonies). In this research, I will explore cellular division and apoptosis as a new route to the development of biological machines. This is important because unlike cell motility, cell division and apoptosis are universal properties of living matter. My design principles for such machines will pave the way for future possible applications in healthcare technologies and tissue engineering, such controlling the growth of tissue using non-uniform scaffolding. Finally, I will investigate the thermodynamic properties of these machines. In particular, I will quantify the informatic entropy production of the birth and death process inside biological tissues and bacterial colonies, i.e., particles dividing into two and disappearing elsewhere. To achieve this, I will extend the current theory of stochastic thermodynamics to include birth and death process and stochastic processes that are much faster than quasi-static (i.e., quenching). This information will be crucial in understanding how time reversal symmetry breaking at small scales (i.e., cell cycle) can be translated into large scales (i.e., collective motion in tissues and bacterial colonies). Apart from obvious applications to active/living matter, my research will also help to transform the science of thermodynamics, such as understanding the energy flow in a quenching process and/or processes close to a critical point, where thermal fluctuations are important.

Stochastic partial differential equations (SPDE) describe the behaviour of spatially extended systems under the influence of noise. They arise naturally in various fields of applications as diverse as data mining, mathematical finance, and population dynamics and genetics. The present proposal aims to study a class of stochastic partial differential equations from statistical mechanics. Many particle models exhibit a behaviour called phase transition, where the behaviour of the system changes drastically when one changes a given system parameter beyond a critical point. It is a very exciting question to understand the behaviour of such a system near a critical point. In such a regime one expects the dynamics to be governed by a non-linear SPDE. Analytically the understanding of these equations is very challenging, because of the interaction between the rough noise term and the non-linear evolution. But this is also what gives rise to interesting phenomena. In this proposal, we aim to deepen the understanding of these equations. On the one hand we will study the behaviour under the influence of a small noise term. Then we will establish that two different kinds of particle models can indeed be described by such an SPDE.

Epidemic models for pathogens transmitted from human to human are, naturally, concerned with the interaction between individuals that leads to transmission. This is clearly a major simplification; there are many processes at work, from the feedack loop of epidemics on behaviour and interventions, to resource constraints limiting the production of prophylaxis and availability of diagnostic tests, to the response of the immune system to the pathogen and pharmaceuticals. Epidemic models do not normally include an account of these highly influential processes. Instead, only the assumed effect of these processes is sometimes included. This strongly limits the scope of epidemic models. By contrast, in molecular biology, it is typical to consider a much larger class of possible interactions. There exist methods as well as mature software for expressing and simulating systems with many interactions. We have successfully shown that these techniques can be fruitfully applied directly to epidemics, including in a multi- scale setting incorporating immune response and, with suitable extensions, to detailed epidemic reconstruction in a complex community setting. We will build on this success in order to consolidate this capability within the infectious disease modelling community. We will improve accessibility of the tools that we used in our pioneering work, facilitating adoption of our epidemic modelling methods more widely. We will foster a community of practice by conducting a series of case studies to establish documented and standardisable approaches to bringing our advanced techniques to bear on pressing current and future questions relevant to reducing the public health burden of infectious disease.

Images are rich in data of significant economic and social value, and over the past decade, they have become fundamental sources of information in many disciplines (e.g., medicine, biology, agriculture, defence, earth sciences, and non-destructive testing). These disciplines now drive the development of sophisticated and specialised imaging devices. Such devices tightly combine two forms of innovation to deliver state-of-the-art performance: 1) sophisticated instrumentation and sensors that push technology and physics to the limits, and 2) highly advanced computational imaging (CI) methods that carefully analyse the generated raw data to produce sharp images with fine detail. This proposal focuses on CI methodology for quantum-enhanced imaging, a new imaging paradigm that seeks to exploit the quantum nature of light to go far beyond what is possible in classical optics in terms of spatial and temporal resolution and dynamic range. This transformative approach is poised to dramatically advance imaging technologies and generate great social and economic impact. To make sure that the UK is at the forefront of this strategic technological developments, the UK government created the Quantum Enhanced Imaging Hub (QUANTIC) in 2014 as part of the UK National Quantum Technology Programme, which was renewed this year. QUANTIC has developed impressive new sensors for extreme imaging conditions. However, these advances in sensor technology have not been matched by progress in CI methodology, gravely jeopardizing the impact of these promising technologies. The aim of this proposal is to develop CI methodology specifically designed for solving quantum-enhanced imaging problems in which very few photons are observed (i.e., low-photon and single-photon imaging problems). Our methods will be formulated in the Bayesian statistical framework, which is particularly appropriate for solving these challenging imaging problems because: 1) it enables the use of sophisticated statistical models to accurately describe the underlying physics, 2) it allows the automatic calibration of models, and 3) it provides tools to quantify the uncertainty in the solutions delivered. At present, the benefits and superior performance of Bayesian statistical CI methods is obtained at the expense of a prohibitively high computational cost. We plan to significantly accelerate Bayesian solutions for quantum-enhanced imaging problems by developing specialised computation methods that combine and extend ideas from different areas of applied mathematics, computational statistics, and artificial intelligence. We believe that the availability of fast Bayesian computation methods will unlock the potential of these promising quantum-enhanced imaging technologies and lead to their wide adoption in science and engineering, generating generate great social and economic benefit through an impact on medicine, biology, agriculture, defence, earth sciences, and non-destructive testing. In order to guarantee this impact, during the project, we will apply the proposed methods to three important quantum-enhanced imaging problems (low-photon multispectral single-pixel imaging, high-resolution PGET, and single-photon 3D LIDAR with array sensors). These applications will be investigated in collaboration with world-leading experts who will provide data and training, and help disseminate the research outputs. To maximise the impact of our work, we will also develop open-source software - with documentation and demonstrations - that we will share online and use in outreach activities aimed at informing the public about STEM research and inspiring young people to pursue STEM careers. This project will also help train the next generation of top-tier talent in AI and quantum technology.

Smart Shrinkage Solutions - Fostering Resilient Cities in Inner Peripheries of Europe is a project that offers the best practice and most feasible solutions to the problem of urban shrinkage - a continuous population decline affecting more than 1,500 cities all over Europe. By learning from the experience of the cities that once were on the edge of an abyss but have bounced back to life, by sharing the key ingredients of their success across Europe and beyond, this project enables as many shrinking cities as possible to adapt, transform, and thrive in the face of continuously and often dramatically changing circumstances.