Cooperative game theory is a branch of game theory that offers a conceptually simple and intuitive mathematical framework to model collaborative settings involving multiple decision makers (players). Solutions of cooperative games offer different ways to share the profit or cost among the players in a way that ensures the fairness and stability of the collaboration, while considering the possibility that any subgroup of players has the option to form their own coalition. The focus of this project is on the most generic class of cooperative games - the integer maximisation games. These games arise in settings where the players in each coalition need to solve an integer maximisation problem to achieve the best interests of their coalition. This proposed research addresses a fundamental question of how to distribute payoff under a new paradigm with the presence of uncertainty and in the context of reasonably large games. Often, formulating a real-life application as a cooperative game, where relevant, is not a difficult task. The part that discourages the use of cooperative game theory is the difficulty in undertaking numerical computation of the solutions due to their combinatorial structures. This is particularly true in integer maximisation games where the set of inputs of the problem, i.e., the value that each coalition can create, involves solving an exponentially large number of integer linear programs. The first part of the proposed research provides efficient algorithms for payoff allocation in reasonably large integer maximisation games. In addition, an open-source software package for computing these solutions and showcase real-world applications is made available. This promises to extend the impact to wide groups of practitioners and academics who want to apply cooperative game theory to profit-/cost-sharing applications. The proposed project also aims to study cooperative games with uncertain payoffs. While uncertainty is a natural part of most decision-making problems, the issue has been largely ignored in the literature of cooperative game theory and there is currently no rigorous framework for handling these. We propose a new framework where fundamental concepts such as stability and fairness are redefined in the face of uncertainty.

Broad ThemesCrime and terrorism threaten States, businesses and individuals; they increasingly exploit technology, sometimes more effectively than the security forces that oppose them. Our proposed Security Science DTC aims to promote fundamental science and research but to do so in a training environment that will provide a broader understanding of these threats; the pace at which they evolve, and the extent to which holistic responses are increasingly required if we are to contain them or to recover more rapidly from attack. We aim to prepare a future generation of security scientists better able to face these rapidly emerging new threats in crime and security. To do so this DTC will catalyse a truly interdisciplinary research effort that brings together multiple domains in security science to focus on the physical and cyber security of the State (borders and critical infrastructures, broadly construed, including financial, transport, energy, health and communication), business and the individual. Need and impact on the research landscape Science and technology have been utilized to protect against the threats outlined above, yet it is now widely accepted that security must be integrated, with a much greater awareness of the environmental operating contexts. This need has been expressed by governments (through policy papers and the creation of new bodies with interorganisational mandates such as the Serious and Organised Crime Agency), industry (through their increasing engagement with academic institutions to develop a new generation of security technologies that take into account factors such as behavioral response and ethical sensitivity) and research councils (eg. through their new 'Global Uncertainties: Security for all in a changing world' programme which cuts across all research council remits). The EPSRC is in an ideal position to invest in a national DTC where a critical mass of researchers can foster innovation and encourage and nurture an integrated systems approach that recognizes the importance of environmental context, human factors, and public policy to security solutions. This vision is based on the observation that the benefits of introducing advanced technologies into the security arena are significantly enhanced by engagement with the broader social, political and economic contexts within which those technological solutions apply. It is clear that disciplines as far apart as psychology and electronic engineering should come together in new ways to combat security threats in a holistic manner. This enhanced sensitivity to interconnectedness and multidisciplinary will lead to more effective science and encourage synergies to develop, increase knowledge transfer and facilitate engagement with end-users. Security is a challenging domain that drives adventurous research in a wide range of disciplines represented in this proposal (e.g. cryptography, radiation physics, nanotechnology). A DTC that helps secure the future supply of researchers with strong links to and appreciation of problems in the security context will help support the long term vigour of these disciplines. The DTC will also provide the UK with a hub to spark synergistic collaboration with other centres working in these areas such as the US Centres for Excellence (eg. National Consortium for the Study of Terrorism and Responses to Terrorism (START), University of Maryland). We further believe that this DTC in integrated security science will act as a prototype for future similar activities around the world. Ultimately, research associated with this DTC will help to position the UK as the international leader in the development of a uniquely equipped generation of security scientists, delivering innovative research to meet one of society's greatest challenges.

Natural hazard events claim thousands of lives every year, and financial losses amount to billions of dollars. The risk of losing wealth through natural hazard events is now increasing at a rate that exceeds the rate of wealth creation. Therefore natural hazards risk managers have the potential, through well-informed actions, to significantly reduce social impacts and to conserve economic assets. By extension, environmental science, through informing the risk manager's actions, can leverage research investment in the low millions into recurring social and economic benefits measured in billions. However, to be truly effective in this role, environmental science must explicitly recognize the presence and implications of uncertainty in risk assessment. Uncertainty is ubiquitous in natural hazards, arising both from the inherent unpredictability of the hazard events themselves, and from the complex way in which these events interact with their environment, and with people. It is also very complicated, with structure in space and time (e.g. the clustering of storms), measurements that are sparse especially for large-magnitude events, and losses that are typically highly non-linear functions of hazard magnitude. The tendency among natural hazard scientists and risk managers (eg actuaries in insurance companies) is to assess the 'simple' uncertainty explicitly, and assign the rest to a large margin for error. The first objective of our project is to introduce statistical techniques that allow some of the uncertainty to be moved out of the margin for error and back into an explicit representation, which will substantially improve the transparency and defensibility of uncertainty and risk assessment. Obvious candidates for this are hazard models fitted on a catalogue of previous events (for which we can introduce uncertainty about model parameters, and about the model class), and limitations in the model of the 'footprint' of the hazard on the environment, and the losses that follow from a hazard event. The second objective is to develop methods that allow us to assess less quantifiable aspects of uncertainty, such as probabilities attached to future scenarios (eg greenhouse gas emissions scenarios, or population growth projections). The third objective is to improve the visualisation and communication of uncertainty and risk, in order to promote a shared ownership of choices between actions, and close the gap between the intention to act (eg, to build a levee, or relocate a group of people living in a high-risk zone) and the completion of the act. In natural hazards this gap can be large, because the cost of the act is high, many people may be affected, and the act may take several years to complete. Ultimately, everyone benefits from better risk management for natural hazards, although the nature of the benefits will depend on location. In the UK, for example, the primary hazard is flooding, and this is an area of particular uncertainty, as rainfall and coastal storm surges are likely to be affected by changes in the climate. A second hazard is drought, leading to heat stress and water shortages. Our project has explicit strands on inland flooding, wind-storms, and droughts. Other parts of the world are more affected by volcanoes or by earthquakes, and our project has strands on volcanic ash, debris flows as found in volcanic eruptions (ie lahars; avalanches are similar), and earthquakes. In the future, new hazards might emerge, such as the effect of space weather on communications. A key part of our project is to develop generic methods that work across hazards, both current and emerging.

The continuous demand for device miniaturization poses technological and economic barriers that cannot be answered by current fabrication techniques. This proposal is aimed at the development of a simple technique for the fabrication of crossbar electrode arrays for non-volatile memory devices based on a modulated block copolymer/nanoparticle (BCP/NP) assembly approach, where the ability to control the interfacial interactions between the NPs and the BCP domains under an electric field is crucial for obtaining the desired structure. Through a tight collaboration between experimental chemists, theoreticians, and an electrical engineer we intend to unravel the fundamental behavior ofBCP/NP assembly under the influence of a directing electric field, and then to utilize the structures formed for the creation of an ultrahigh-density, multi-component memory device.

The water sector in the UK has, by many measures, been very successful. In England and Wales, drinking water standards stands at over 99.9%, water pipe leakage is down by a third, sewer flooding reduced by more three quarters in the last 10 years and bathing water standards are at record high levels. This success has been achieved using a 19th century design approach based on the idea of plentiful resources, unrestrained demand and a stable climate. However, a perfect storm of climate change, increasing population, urbanisation, demographic shifts and tighter regulation is brewing! Each one of these challenges is a threat to the water sector and, taken in isolation, existing approaches may be able to cope. Taken together and compounded by the speed, size and uncertainty of change, the system is heading for failure unless something radical is done. The current way of working looks increasingly out of date and out of step with emerging thinking and best practice in some leading nations. This fellowship aims to meet these emerging challenges and global uncertainties head on by developing a new approach to water management in UK cities. The starting point is a new vision that is: Safe & SuRe. In a sense, our existing water systems are all about safety goals: public health, flood management and environmental protection. These are important and still need to be respected, but they are NOT sufficient to rise to the coming challenges. In the new world of rapid and uncertain change, water systems in cities must also be Sustainable and Resilient. Only a 'Safe & SuRe' system can be moulded, adapted and changed to face the emerging threats and resulting impacts. In this fellowship. my vision will be developed, tested and championed into practice over a period of 5 years. It will draw from multi-disciplinary collaboration with leading academics inside and outside the field. A comprehensive, quantitative evaluation framework will be developed to test in detail what options or strategies can contribute towards a Safe & SuRe water future, focussing on the challenges of water scarcity, urban flooding and river pollution. Recommendations and best practice guidance will be developed in conjunction with key stakeholders.