Probabilistic modelling permeates all branches of engineering and science, either in a fundamental way, addressing randomness and uncertainty in physical and economic phenomena, or as a device for the design of stochastic algorithms for data analysis, systems design and optimisation. Probability also provides the theoretical framework which underpins the analysis and design of algorithms in Data Science and Artificial Intelligence. The "CDT in Mathematics of Random Systems" is a new partnership in excellence between the Oxford Mathematical Institute, the Oxford Dept of Statistics, the Dept of Mathematics at Imperial College and multiple industry partners from the healthcare, technology and financial services sectors, whose goal is to establish an internationally leading PhD training centre for probability and its applications in physics, finance, biology and Data Science, providing a national beacon for research and training in stochastic modelling and its applications, reinforcing the UK's position as an international leader in this area and meeting the needs of industry for experts with strong analytical, computing and modelling skills. We bring together two of the worlds' best and foremost research groups in the area of probabilistic modelling, stochastic analysis and their applications -Imperial College and Oxford- to deliver a consolidated training programme in probability, stochastic analysis, stochastic simulation and computational methods and their applications in physics, biology, finance, healthcare and Data Science. Doctoral research of students will focus on the mathematical modelling of complex physical, economic and biological systems where randomness plays a key role, covering mathematical foundations as well as specific applications in collaboration with industry partners. Joint projects with industrial partners across several sectors -technology, finance, healthcare- will be used to sharpen research questions, leverage EPSRC funding and transfer research results to industry. Our vision is to educate the next generation of PhDs with unparalleled, cross-disciplinary expertise, strong analytical and computing skills as well as in-depth understanding of applications, to meet the increasing demand for such experts within the Technology sector, the Financial Service sector, the Healthcare sector, Government and other Service sectors, in partnership with industry partners from these sectors who have committed to co-funding this initiative. ALIGNMENT with EPSRC PRIORITIES This proposal reaches across various areas of pure and applied mathematics and Data Science and addresses the EPSRC Priority areas of (15. Mathematical and Computational Modelling), (22. Pure Mathematics and its Interfaces) ; however, the domain it covers is cross-disciplinary and broader than any of these priority areas taken in isolation. Probabilistic methods and algorithms form the theoretical foundation for the burgeoning area of Data Science and AI, another EPSRC Priority area which we plan to address, in particular through industry partnerships with AI/technology/data science firms. IMPACT By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to - sharpening the UK's research lead in this area and training a new generation of mathematical scientists who can tackle scientific challenges in the modelling of complex, simulation and control of complex random systems in science and industry, and explore the exciting new avenues in mathematical research many of which have been pioneered by researchers in our two partner institutions; - train the next generation of experts able to deploy sophisticated data driven models and algorithms in the technology, finance and healthcare sectors

A few grams of any material contain a bewildering number of individual particles. Interactions between these particles give rise to a vast array of emergent phenomena which cannot be understood from looking at any of the particles in isolation. An important example of this is superconductivity, which enables materials to conduct electricity without resistance. Novel emergent states also occur out of equilibrium, due to the presence of large external forces or the occurrence of extreme events. Examples include turbulence in fluids and plasmas, the spreading of epidemics and diseases, and shocks in the stock market. The above examples illustrate the breadth of this nationally and internationally recognised "Grand Challenge" in Emergence and Physics Far From Equilibrium. Addressing this Grand Challenge requires a coordinated approach, spanning different areas of physics and related disciplines. The Network will facilitate cross-cutting workshops and advanced working groups to enable UK researchers to plan and carry out targeted research programmes. Pump-prime initiatives and interaction with industry will stimulate collaborative research, ensuring UK competitiveness in this far-reaching field.

The U.K. population is projected to reach 80 million by 2050 and it is anticipated that the overwhelming majority will continue to live in cities. Besides becoming more densely populated, future cities will be surrounded with expanding urban areas. Interactions within cities; across urban areas and with surrounding cities, towns and 'rural' areas with the rest of the UK will place new and different demands on infrastructure, whether housing, energy, transport, freight distribution and disposal of waste. Decisions that are made now will have profound implications for the resultant pressures on transport, living space, energy use, and ecosystem services (the benefits humans receive from ecosystems). These decisions will play out at two fundamentally different spatial scales. First, and by far the better understood, are those decisions that concern individual households and their neighbourhoods. These include issues of how their members move around, what kinds of housing they occupy, how their energy demands and waste production are reduced, and how their negative influences on the wider environment generally will be limited. Second, broad scale strategic decisions regarding regional planning will determine where in the U.K. population growth is primarily accommodated. This will determine, and be shaped by, the kinds of transport and energy infrastructure required, and the environmental impacts. Obviously these two sets of decisions are not independent. The demands for and impacts of broad scale development (whether this be the creation of new urban areas or the intensification of existing ones) - and thus how this is best achieved to deliver sustainability- will be influenced not by the typical demands and impacts exhibited now by households, but by the way in which these have been changed in response to the modification to the associated infrastructure. This makes for a challenging problem in predicting and evaluating the possible consequences of different potential scenarios of regional development. The proposed study SElf Conserving URban Environments (SECURE) will address this grand challenge of integration across scales (the global aim) by developing a range of future regional urbanization scenarios, and exploring their consequences for selected high profile issues of resource demand and provision (transport, dwellings, energy, and ecosystem services) alongside sustainable waste utilisations. In doing so, it will build on findings of research outputs of several previous SUE projects and harness its relationship in the context of policy and economic growth. The study includes specific research objectives under five broad cross-cutting themes - Urbanisation, Ecosystems Services, Building and Energy, Stakeholder Engagement and Policy Integration across themes. SECURE is designed to assemble novel deliverables to bring about step change in current knowledge and practice. The North East Region will be used as a test bed and evaluation of transitional scenarios leading up to 2050 will quantify the benefits of integration across the scales through conservation across the themes. SECURE will deliver policy formulation and planning decisions for 2030 and 2050 with a focus on creating Sustainable Urban Environment.The contributors to this project are researchers of international standings who have collaborated extensively on several EPSRC funded projects, including the SUE research since its inception. The SECURE team builds on their current collaboration on the SUE2 4M project. The Project consortium is led by Newcastle - Prof Margaret Bell as PI and Dr Anil Namdeo as co-ordinator alongside Dr Jenny Brake with academic partners: Prof David Graham (Environmental Engineering), Prof David Manning (Geosciences); from Loughborough: Prof Kevin Lomas, Prof Jonathan Wright and Dr Steven Firth (Civil and Building Engineering); from Sheffield: Prof Kevin Gaston and Dr Jonathan Leake (Animal and Plant Sciences).

The financial services industry is at the forefront of the digital economy, and is crucial to the UK's, and especially London's, continuing social and economic prosperity. State-of-the-art Financial IT, Computational Finance and Financial Engineering (collectively Financial Computing) research is crucial to our international competitiveness in investment banking, investment funds or retail banking. Academically this DTC focuses on financial computing, as distinct from quantitative finance, already well resourced. Banks and funds view PhD students in science and engineering as an increasingly important and largely untapped talent pool; although one regrettably with little knowledge of finance. The Financial Services Skills Council notes that employers are placing increasing importance on high-level analytical skills, as well as their acute shortage, especially in the newly emerging areas that drive sector growth. This centre completely embraces the spirit of the Digital Economy programme. The proposed DTC is inherently multidisciplinary involving UCL Computer Science, one of the largest leading departments in its field in the UK, with LSE Finance and the London Business School; the two leading academic finance centres in the UK. Key to developing the financial services industry in the Digital Economy is the creation of a new cohort of researchers who have a strong research capability in IT and computation, but also understand finance and the needs of the wholesale financial services industry leading to early adoption of new financial information technology research.The research groups and centres that will participate in this DTC include worldclass groups at: UCL, such as the Software Systems Engineering Group and the Centre for Computational Statistics and Machine Learning, at LSE such as Financial Markets Group, and at the London Business School, including the Management Science and Operations and Finance Subject Areas. The total value of active grants currently held by the participating groups and centres exceeds 20 Million Pounds, and the number of currently registered PhD students exceeds 130. Collaborators in Statistics, Economics, Mathematics and Physics supplement the potential Supervisor pool.A great strength of this DTC proposal is our industry partners, which include: Abbey, Barclays, Barclays Capital, BNP Paribas, Credit Suisse, Deutsche Bank, Goldman Sachs, HSBC, Lloyds TSB, Man Investments, Merrill Lynch, Morgan Stanley, Nomura, RBS and Thomson Reuters. Regarding training and supervision, each DTC PhD student will follow a personally tailored programme of postgraduate courses drawn from the partners covering financial IT, networks & communications, HCI, computational finance, financial engineering and business, supplemented by lectures from our industry partners: * A tailored educational programme comprising graduate-level courses from UCL, LSE and LBS. * An academic supervisor (from UCL, LSE or LBS) and an industrial advisor (a partner bank, fund or Reuters), and a programme of research covered by an MOU. * A research project in financial IT, computational finance or financial engineering. * Training in industry software, such as Reuters 3000 Xtra, through UCL's virtual training floor.* A substantial period of industrial placement as agreed between the academic and industrial supervisors.* A short period at a leading foreign academic centre

The EPSRC Centre for Doctoral Training in Statistics and Machine Learning (StatML) will address the EPSRC research priority of the 'physical and mathematical sciences powerhouse' through an innovative cohort-based training program. StatML harnesses the combined strengths of Imperial and Oxford, two world-leading institutions in statistics and machine learning, in collaboration with a broad spectrum of industry partners, to nurture the next generation of leaders in this field. Our students will be at the forefront of advancing the core methodologies of data science and AI, crucial for unlocking the value inherent in data to benefit industry and society. They will be equipped with advanced research, technical, and practical skills, enabling them to make tangible real-world impacts. Our students will be ethical and responsible innovators, championing reproducible research and open science. Collaborating with students, charities and equality experts, StatML will also pioneer a comprehensive strategy to promote inclusivity, attract individuals from diverse backgrounds and eliminate biases. This will help diversify the UK's future statistics and machine learning workforce, essential for ensuring data science is used for public good. Data science and AI are now part of our everyday lives, transforming all sectors of the economy. To future-proof the UK's prosperity and security, it is essential to develop new methodology, specifically tailored to meet the big societal challenges of the future. The techniques underpinning such methods are founded in statistics and machine learning. Through close collaboration with a broad range of industry partners, our cohort-based training will support the UK in producing a critical mass of world-leading researchers with expertise in developing cutting-edge, impactful statistical and machine learning methodology and theory. It is well documented in government and learned society reports that the UK economy has an urgent need for these people. The significant level of industry support for our proposal also highlights the necessity of filling this gap in the UK data science ecosystem. StatML will learn from and build upon our previous successful experiences in cohort training of doctoral students (our existing StatML CDT funded in 2018, as well as other CDTs at Imperial and Oxford). Our students will continue to produce impactful, internationally leading research in statistics and machine learning (as evidenced by our students' impressive publication record and our world-leading research environment, as rated by the REF 2021 evaluation), while complementing this with a bespoke cohort-based Advanced Training program in Statistics and Machine Learning (StatML-AT). StatML-AT has been developed from our experience and in partnership with industry. It will be responsive to emerging technologies and equip our students with the practical skills required to transform how data is used. It will be delivered by our outstanding academics from both institutions alongside with industry leaders to ensure that students receive training in cutting edge technologies, along with the latest ideas in ethics, responsible innovation, sustainability and entrepreneurship. This will be complemented by industrial and academic placements to allow the students to develop their own international network and produce high-impact research. Together, StatML and its partners will train 90+ students over 5 cohorts. More than half of these will be funded from external sources, including 25+ by industry, representing excellent value for money. Our diverse cohorts will benefit from a unique and responsive training program combining academic excellence, industry engagement, and interdisciplinary culture. This will make StatML a vibrant research environment inspiring the next methodological advancements to transform the use of data and AI across industry and society.