We propose a new phase of the successful Mathematics for Real-World Systems (MathSys) Centre for Doctoral Training that will address the call priority area "Mathematical and Computational Modelling". Advanced quantitative skills and applied mathematical modelling are critical to address the contemporary challenges arising from biomedicine and health sectors, modern industry and the digital economy. The UK Commission for Employment and Skills as well as Tech City UK have identified that a skills shortage in this domain is one of the key challenges facing the UK technology sector: there is a severe lack of trained researchers with the technical skills and, importantly, the ability to translate these skills into effective solutions in collaboration with end-users. Our proposal addresses this need with a cross-disciplinary, cohort-based training programme that will equip the next generation of researchers with cutting-edge methodological toolkits and the experience of external end-user engagement to address a broad variety of real-world problems in fields ranging from mathematical biology to the high-tech sector. Our MSc training (and continued PhD development) will deliver a core of mathematical techniques relevant to all applied modelling, but will also focus on two cross-cutting methodological themes which we consider key to complex multi-scale systems prediction: modelling across spatial and temporal scales; and hybrid modelling integrating complex data and mechanistic models. These themes pervade many areas of active research and will shape mathematical and computational modelling for the coming decades. A core element of the CDT will be productive and impactful engagement with end-users throughout the teaching and research phases. This has been a distinguishing feature of the MathSys CDT and is further expanded in our new proposal. MSc Research Study Groups provide an ideal opportunity for MSc students to experience working in a collaborative environment and for our end-users to become actively involved. All PhD projects are expected to be co-supervised by an external partner, bringing knowledge, data and experience to the modelling of real-world problems; students will normally be expected to spend 2-4 weeks (or longer) with these end-users to better understand the case-specific challenges and motivate their research. The potential renewal of the MathSys CDT has provided us with the opportunity to expand our portfolio of external partners focusing on research challenges in four application areas: Quantitative biomedical research, (A2) Mathematical epidemiology, (A3) Socio-technical systems and (A4) Advanced modelling and optimization of industrial processes. We will retain the one-year MSc followed by three-year PhD format that has been successfully refined through staff experience and student feedback over more than a decade of previous Warwick doctoral training centres. However, both the training and research components of the programme will be thoroughly updated to reflect the evolving technical landscape of applied research and the changing priorities of end-users. At the same time, we have retained the flexibility that allows co-creation of activities with our end-users and allows us to respond to changes in the national and international research environments on an ongoing yearly basis. Students will share a dedicated space, with a lecture theatre and common area based in one of the UK's leading mathematical departments. The space is physically connected to the new Mathematical Sciences building, at the interface of Mathematics, Statistics and Computer Science, and provides a unique location for our interdisciplinary activities.

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Understanding how people's social and economics lives relate to their health is essential to improving the nation's health, society in general and the economy. Researchers in biomedical, social and economic sciences use robust, high quality data from world-leading studies to help develop this understanding. This research helps reveal hidden facts about the complex social and biological processes at work behind our everyday lives. This proposal seeks to support this ambition to better understand people's lives and their health. It is based on Understanding Society - a rich social and economic study, which interviews the same families every year and has recently included a health interview where nurses took a number of 'biomarkers' or objective health measurements. These objective measures such as blood pressure, lung function and blood samples, have subsequently been analysed for indicators of heart disease, diabetes and anaemia, liver and kidney function and frailty. The project is led by a multi-disciplinary research team with international partners and has two broad aims: * to contribute new scientific knowledge about the two-way relationship between people's social, economic, environmental circumstances and health; * to build understandings of the value of and capacity for using biomarkers, genetic social and economic data together in collaborative projects. The proposal will include a suite of exemplar research projects, which will not only address important research questions but demonstrate the value of inter-disciplinary [data and] research in these fields. It will investigate and use the best statistical techniques, and share learning with colleagues about these approaches. In addition, we will also: *undertake a set of 'outreach' initiatives in specific social science disciplines - such as geography, economics and sociology - to investigate and disseminate the value of employing biomarkers to address social research questions relevant to them. *establish a fellowship scheme for new researchers to propose projects at the interface of social and health sciences, which will be carried out with joint mentorship by social and biomedical scientists. * hold a range of workshops and training events, and produce supporting resources, such as special datasets, to build understanding and capacity of the use of biomarkers in social science research. * develop international collaborations to draw expertise from across the world into the project, and hold an annual master class and conference with contributions from them; * involve policy makers in the oversight of the project, as well as set aside some funds for them to undertake analyses of the data relevant to their policy responsibilities. Policy relevant findings will be shared widely through briefings and a policy event. This research will help to identify when and how health problems emerge in ways that enable policy makers to target policies more effectively. It will also help us understand how poor health affects people's ability to live their lives, which again may enable policy makers to identify appropriate times and situations when these negative consequences can be prevented or reduced. Such research directly contributes to the ESRC's strategic priority to influence behaviours and inform interventions. It will also improve the capacity of the research community to engage in this kind of research leading to future developments in this field.

The multiphoton microscope is a powerful imaging tool that is widely used across the biological sciences. The strength of this system, compared with the conventional optical microscope, lies in its ability to image specimen structures at high resolution in three-dimensions rather than two-dimensions. Typically, this is achieved by refocusing the microscope and acquiring a series of two dimensional images at a number of different specimen depths. The resulting image stack can then be manipulated by computer algorithms in a number of different ways to reveal a wealth of information about the object structure. Recently, it has become of interest to collect these three dimensional image stacks at high speed in order to observe the dynamic behaviour of biological specimens. As a result, technological advances have been made to improve image acquisition speeds.The problem is that although a single in-focus image can be obtained very quickly the real bottleneck in three-dimensional data acquisition is the process of refocusing the microscope to successive image planes. For fundamental optical reasons, refocusing must be carried out by physically changing the distance between the objective lens and specimen, which is problematic for two reasons. First, this process is generally slow and second it can lead to undesirable specimen agitation.In order to alleviate these restrictions, I have recently developed a new system architecture that permits refocusing to be carried out at far superior speeds than current technology will allow. Furthermore, refocusing is carried out remotely from the specimen, which simulates a more natural environment in which to perform investigations. During this research project, I propose to implement this new technique on a two photon microscope to permit a number of unique imaging modalities. For instance, this system will be able to acquire images directly from a curved surface at high speed. Previously, such information could only be derived from a three dimensional image stack, which, due to the aforementioned limitations, would have lower temporal resolution. This is particularly of interest in applications where the dynamic behaviour of cell movements is limited to take place over a well defined surface that is not flat. Furthermore, I propose to apply this technique of refocusing to a microscope system that already exists at the Laboratory of Optics and Biosciences in Paris. This specialized system acquires three-dimensional data with a number of different imaging modes and has already been used to investigate the early stages of embryo development, where cell movements are mainly localized around the embryo surface. As a result of this new refocusing strategy, such biological problems will be investigated further and better insight gained.

Recently, there has been a paradigm shift from the isolated focus on the health impact of a single behaviour (i.e. PA, sedentary behaviour or sleep) to the combination of these 24/7 movement behaviours for maximum health benefits. However, current public health guidelines are largely based on inaccurate self-report data and are, therefore, rather general (e.g. "move more and sit less"). Technological advancements have led to wearable sensor techniques providing rich time-series data over longer periods. Consequently, novel analysis methods are required to provide detailed insight into the links between multi-dimensional 24/7 movement behaviour profiles and health; which subgroups need particular attention; and what behavioural profiles are most important to target in interventions. Developing such novel analysis methods, essential for creating the evidence base needed for optimal, tailored guidelines and feedback, requires a specific combination of knowledge and skills in epidemiology, data science, method development, and public health with a thorough understanding of what is needed to translate knowledge to guidelines and improve wearable technology feedback. In LABDA, we will therefore train 10 doctoral fellows to advance this interdisciplinary field and deliver a toolbox of advanced analysis methods for sensor-based behavioural data, together with a guide for other researchers and policy makers to decide which methods to use for which (research) question.