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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

Monsoon systems influence the water supply and livelihoods of over half of the world. Observations are too short to provide estimates of monsoon variability on the multi-year timescale relevant to the future or to identify the causes of change on this timescale. The credibility of future projections of monsoon behavior is limited by the large spread in the simulated magnitude of precipitation changes. Past climates provide an opportunity to overcome these problems. This project will use annually-resolved palaeoenvironmental records of climate variability over the past 6000 years from corals, molluscs, speleothems and tree rings, together with global climate-model simulations and high-resolution simulations of the Indian, African, East Asia and South American monsoons, to provide a better understanding of monsoon dynamics and interannual to multidecadal variability (IM). We will use the millennium before the pre-industrial era (850-1850 CE) as the reference climate and compare this with simulations of the mid- Holocene (MH, 6000 years ago) and transient simulations from 6000 year ago to ca 850 CE. We will provide a quantitative and comprehensive assessment of what aspects of monsoon variability are adequately represented by current models, using environmental modelling to simulate the observations. By linking modelling of past climates and future projections, we will assess the credibility of these projections and the likelihood of extreme events at decadal time scales. The project is organized around four themes: (1) the impact of external forcing and extratropical climates on intertropical convergence and the hydrological cycle in the tropics; (2) characterization of IM variability to determine the extent to which the stochastic component is modulated by external forcing or changes in mean climate; (3) the influence of local (vegetation, dust) and remote factors on the duration, intensity and pattern of the Indian, African and South American monsoons; and (4) the identification of palaeo-constraints that can be used to assess the reliability of future monsoon evolution.

The famous cereal 'green revolution' of the 1960s/1970s increased crop yields, averted famine and fed a growing world population. Green Revolution Varieties (GRVs) of rice and wheat were the genetic foundation of the green revolution. GRVs carry mutant growth regulatory genes that confer dwarfism, and this dwarfism increases yield because it reduces loss due to 'lodging' (flattening of plants by wind and rain), hence causing the yield increases of the green revolution. However, the mutant growth regulatory genes also cause GRVs to be less efficient in assimilating the nitrogen (N) supplied to them in the form of fertilizer. As a result, N that is not assimilated by GRVs is dissipated into the wider environment, where it causes severe damage to terrestrial and aquatic ecosystems, together with atmospheric greenhouse-gas pollution that precipitates climate change. Because today's high-yielding crop varieties still depend upon the mutant dwarfing genes for their high yields, it is necessary to find ways of developing new crop varieties that retain the benefits of GRV dwarfism but that are more efficient in their use of N fertilizers (have improved N use efficiency, NUE). Here we propose to exploit the rapid genetics and molecular biology of the genetic model Arabidopsis to make discoveries that will enable future enhancement of GRV NUE. The GRV dwarfing genes cause accumulation of a class of growth inhibitory proteins called DELLAs, and DELLAs also accumulate in the dwarf Arabidopsis GRV mutant model gai. Accumulated DELLAs inhibit the action of another class of regulatory proteins, the PIFs (or Phytochrome Interacting Factors). Our recent preliminary evidence from studies of Arabidopsis suggest that the inhibitory effect of DELLAs on PIFs may explain the reduced NUE of GRVs, and it is this novel and exciting finding that we exploit in this proposal. We will therefore first further test our working hypothesis that interactions between DELLAs and PIFs affect the assimilation of N: that the DELLAs accumulated in GRVs and gai oppose PIF function, thus reducing N assimilation. If this hypothesis is correct, modulation of the DELLA-PIF relationship may provide a novel route towards improving GRV NUE. We have the following objectives: A. Obtain an in-depth understanding of PIF-regulation of Arabidopsis and rice N assimilation - essentially performing genetic tests of the role of PIFs in regulation of N metabolism and assimilation in Arabidopsis and rice. B. Determine how the DELLA-PIF interaction regulates the abundance of mRNA encoding nitrate reductase (NR), a key enzyme in N assimilation - this an exploration of how the DELLA-PIF interaction controls the expression of the gene encoding that enzyme. C. Determine if the DELLA-PIF interaction also directly affects the abundance and/or specific enzymatic activity of the NR enzyme itself. D. Determine if NUE can be increased despite retaining yield-enhancing dwarfism. This is important because it could lead to the development of crops which retain the high yields of current GRVs, but at reduced environmental cost. First, we will determine if increasing PIF activity might confer such benefits. However, because increasing the activity of PIFs themselves in GRVs might have additional unwanted consequences, we will additionally explore other routes (downstream of PIFs) to improving GRV NUE whilst retaining yield-enhancing dwarfism. Inherent in our strategy is initial translation of findings from Arabidopsis model to crop (rice), exploiting our long-standing combined expertise in DELLA biology, model-crop translations, and whole genome sequence analysis. Our long-term aim (future proposals) is to use the fundamental understanding gained here in the development of rice and wheat GRVs having enhanced NUE, thus enhancing global food security and reducing agricultural environmental degradation.

World food demand is predicted to double by 2050. Meeting this demand is a major global challenge, and requires increased crop yields at minimal environmental cost. Present-day high-yielding 'green revolution crop varieties' (GRVs) are inefficient in their use of nitrogen (N) fertiliser, an inefficiency that is costly to the farmer and damaging to the environment. The world needs new crops that are both higher yielding and have increased N use efficiency (NUE). Our project fuses distinct UK/China expertise to improve rice NUE. It retains the outstanding features of current rice GRVs, and transforms them into Super-Rice varieties that are high yielding and have enhanced NUE. Using a pioneering approach combining the discovery of natural genetic variants with marker-assisted breeding and 'genome editing', we will create Super-Rice that will be high-yielding when grown with reduced N fertiliser inputs. First, WPs1-3 exploit a variety of genetic, genomic and bioinformatics techniques to discover individual genetic variants that increase the NUE of rice GRVs. WP1 discovers the molecular identities of variant genes increasing NUE in the field. WP2 focusses on variants of the developmental regulatory genes that play overarching roles in controlling the growth and metabolism of plants. There is important precedent for exploiting such regulatory variation, because the initial GRVs themselves were created by use of such variants. WP3 focusses on the discovery of variants increasing the activity of the transporters that enable rice to extract N from the soil. However, the variants discovered in WPs1-3 may come from wild or other strains of rice that are not themselves GRVs. WPs1-3 therefore importantly use the new technique of genome-editing to specifically determine if these new variants increase NUE in GRV genetic backgrounds. Genome-editing enables precise alteration of genome sequence, thus enabling us to edit specific GRV gene sequences (change them into the newly discovered variant form). The yield of these genome-edited GRVs will then be measured in low-N soils, thus telling us if the newly discovered variant can indeed increase the NUE of the GRV. Next, WP4 further exploits the ability of genome editing to simultaneously edit more than one genomic location. This enables the combined ('stacked') introduction of multiple variants into one GRV. It is possible that variant combinations will generate NUE increases that are at least additive (a simple sum of individual variant effects) and that may be synergistic (increases that are greater than the simple sum effects of individual variants). Thus, in WP4, we will combine ('stack') multiple selected variants into Super-Rice genotypes, and then determine the yields of these Super-Rice genotypes in low-N soils. Our genome-edited Super-Rice will not contain any 'foreign' transgenes, and may therefore more readily receive regulatory approval for agricultural use than will transgenic 'GM' varieties. However, because full adoption of Super-Rice requires general public acceptance, we will also pioneer the use of genome-edited Super-Rice to enhance the efficiency, focus and speed of conventional marker-assisted breeding of Super-Rice. Genome-edited Super-Rice will guide plant breeders in the development of (non-genome-edited) Super-Rice that will be bred using natural rice variants and that will be publicly acceptable because it is neither GM nor genome-edited. The promotion of bilateral UK-China rice research relationships is another major objective of our proposal. We build upon and sustain pre-existing partnerships (XF and NPH; XF and QQ), and derive added value from a new one (NPH and QQ). In summary, we propose a transnational UK-China partnership that will breed publicly acceptable enhanced-NUE Super-Rice that will enhance the sustainability of Chinese and world agriculture and help feed the world in the years leading up to 2050 and beyond.