Graphs are popular as a structure for modelling systems of connections in the real world, and graph theory has taken a major role in the wider field of algorithmics and computational complexity. Many of the algorithmic problems we might wish to solve on graphs (e.g. extracting useful information, or identifying optimal modifications) are intractable in general, but there has been significant progress in recent decades in our understanding of how mathematical structure in graphs can be exploited to design efficient algorithms. However, many real-world datasets are not sufficiently highly structured for this approach to be effective. In this project we aim to address this issue by exploiting the fact that many real-world systems exhibit qualitatively different types of connections, driven by fundamentally different processes. For example, online friendships are not geographically constrained, and you may have online friends that you have never met in person. In contrast, the set of friends you see regularly in person is subject to geographical factors, and may revolve around common activities or meeting places. These two types of links are different in the processes that produce them, in the structure of the graph they form, and in their role in answering different questions. We call a system like this, with multiple different types of links, a multilayer system, and we can model it with a multilayer graph in which entities represented by nodes are linked by several different classes of links, or 'edges'. Such multilayer systems arise in a huge range of different real-world applications, and the crucial observation for our work is that the structure of each individual layer is typically much easier to understand and to describe mathematically than that of the entire system. Our strategy is therefore to develop methods that allow us to use our understanding of the structure of the individual layers to answer questions about the entire system within an acceptable amount of time. Our theoretical results will produce dichotomy meta-theorems which allow us to identify precisely, for a wide range of problems involving systems of this kind, the structural properties of individual layers that will allow us to solve the problems efficiently. Central to the development of these new algorithmic results will be a better understanding of the structure of real-world multilayer systems, so we will also develop new ways to model and simulate multilayer graphs. Our work will include a variety of case studies on real-world data, including human contact information from online social networks, medical statistics, and ecological and epidemiological disease transmission data.

There is increasing evidence that intense commercial fishing pressure is not only depleting fish stocks but also causing evolutionary changes to fish populations. In particular, a wide body of research suggests size-selective harvesting is altering growth rates, body size, and fecundity in wild fish populations. More recent work also suggests that there are a range of traits besides body size which could also affect the vulnerability of fish to fishing gears - and therefore the fisheries-induced evolution. For example, within a given species, variation in physiological traits related to energy demand and swimming ability are especially likely to influence vulnerability to capture through a variety of mechanisms. Critically, many of the same traits that may make individuals vulnerable to capture by fishing could also be linked to a fish's sensitivity to climate change. For fishes, factors such as aerobic capacity, swimming performance, metabolic rate and feeding levels are all affected by ambient temperature. Therefore, as fish are exposed to varying environmental conditions while moving throughout a habitat, the individuals that are most susceptible to capture may change depending on the prevailing temperature. Novel modelling approaches that incorporate behaviour and respiratory constraints are well suited to generate predictions for how populations may respond to the synergistic effects of fishing and climate change. However, such models urgently need information on how physiological phenotypes affect vulnerability of individual fish to capture in a natural setting. We propose to use current technology for tracking the movements of wild fish to examine: (1) whether individual variability in thermal physiology affects habitat use and vulnerability to capture; and (2) if selection on phenotypes by fishing make fish populations less able to cope with changing climates. Indeed, fishing may be causing evolutionary changes to the intrinsic physiological traits of fish that have so far gone unnoticed but which could be crucial for influencing species' geographic distributions, resilience, and capacity to respond to environmental degradation. This multi-disciplinary project will address this critical gap in knowledge by generating data on trait-based capture vulnerability and habitat use in a natural environment and then feeding this data directly into a modelling framework for understanding the interactive effects of fishing and climate change on populations over various timescales.

Diseases which affect the nervous system such as Alzheimer's, Parkinson's, depression and schizophrenia account for the single largest cost to the healthcare system of the UK and are often associated with long-term disability, and distress for patients and their families. A common clinical feature of many of these and other disorders is a cognitive (often learning/memory) deficit. However learning and memory is a very complex biological process that is only partly understood. Of particular interest to us are the changes that occur after learning (i.e. during memory establishment) in the synapses - the critical structures that join two neurons together and mediate information flow and processing in all brains. In this study we aim to identify the biochemical changes (at the protein level) that are associated with forming memories. In particular, we aim to test the involvement of several candidate molecules that have been implicated but whose importance has not yet been proven. This work will also allow us to try and bridge the gap between what we see at the biochemical level in terms of molecules and their abundance with the actual behaviour of the brain (and subsequently of the animal). The observed biochemical changes will be used to refine and extend computational models of neuronal synapses. These computational models will provide a unique method to visualise these complex biochemical networks which involve more than 1000 proteins. Mathematical methods will then be applied that allow us to predict which molecules are more likely to be involved in the memory and a selection of the best candidates will be tested in the laboratory. These new insights will help us understand how memory is formed in the brain. Unravelling these core biological processes is vital to our understanding of animal behaviour in the first instance. In the longer term our research will have relevance to human cognition ultimately aiding the search for new drug therapies for cognitive illness.

For centuries people have used magnetic compasses to guide them on their way and explore new territories. This has led scientists to embark on their own journeys of discovery about Earth's magnetism, and to the discovery of electromagnetism that is at the heart of modern technology - phones, TVs, computers, etc. Now, in the age of GPS, you might think that compasses are obsolete, but guidance by the Earth's magnetic field is still vital to explore for oil and minerals below ground (where GPS can't reach) and as a safety backup for planes etc. And ironically, GPS is affected by natural hazards caused by the Earth's magnetic field. So the scientific study of Earth's magnetism continues to be important in many ways, so much so that in 2012 the European Space Agency will launch a mission called Swarm in which three satellites will orbit the Earth to survey its magnetic field in unprecedented detail. These measurements will be used to improve mathematical models of the geomagnetic field that provide a standard reference for various applications. One target area is a better understanding and description of the relatively rapid and complex magnetic fluctuations caused by electrical currents flowing in the upper atmosphere and in Space, ultimately driven by disturbances happening on the Sun that wax and wane with an 11-year solar cycle. This so-called external magnetic field also induces currents to flow in oceans and under the Earth's surface which in turn creates additional magnetic fluctuations. Together, the external and induced magnetic field (EIMF) limits the accuracy of geomagnetic field models such that they aren't useful for surveys and navigation at places and times when the EIMF fluctuations are large, such as in the polar regions and during so-called magnetic storms that may happen once a month and last several days. The EIMF also creates a natural hazard for large-scale electrically conducting systems such as power outages in electricity grids, corrosion in oil pipelines, and even phantom railway signals. In this project we will study the EIMF using a solar cycle's worth of measurements made at over 300 different locations around the world, recently collected together for the first time by an international project called SuperMAG. Our idea is to borrow mathematical techniques usually used by meteorologists for studying the weather and climate to identify the natural cycles and patterns of the EIMF. In conjunction with the Swarm mission, the resulting new descriptions and understanding of the EIMF "weather" and "climate" should help to improve the next generation of computer models of Earth's magnetic field. It can also be used to as a basis to assess and predict the risk of power outages in UK's National Grid caused by extreme EIMF fluctuations.

Earthquakes occur when blocks of the Earth's crust slide past east other along fractures called tectonic faults. Motion between crustal blocks is a result of tectonic processes such as formation of new oceanic crust at mid-ocean ridges, sinking of old crust into the interior of the Earth at subduction zones and collision between continental plates. Friction and normal stresses across faults cause them to be inactive, or 'locked' most of the time. Motion between crustal fragments is accommodated by elastic bending of rocks either side of the locked fault. When the stress parallel to the fault becomes sufficient to overcome friction and normal stresses, the fault slips rapidly. Seismic waves are a result of this sudden release of elastic energy. They radiate through the crust and spread around the Earth in a matter of minutes. The magnitude of an earthquake is related to the length of the fault rupture, and the amount of elastic bending since the previous earthquake. Today the Indian plate is moving north relative to Eurasia, accompanied by widespread seismicity. The Himalayan mountains are an expression of the convergence between these two continental plates since 50 million years ago. Along its eastern margin the Indian plate is sliding sideways past Indochina. More than half the annual motion across this sideways, or 'transform', plate boundary is focussed on the 1500 km-long Sagaing Fault in Myanmar. Since 1918 there have been 6 major earthquakes (magnitude 7.0 to 7.9) along the Sagaing Fault. They were unequally distributed along the length of the fault, and a 260 km-long section remains un-ruptured. It is likely that this section is locked and may fail in a single large earthquake in the near future. The capital city of Myanmar, Nay Pyi Taw, straddles the Sagaing Fault in the centre of the un-ruptured section. On 11/11/12, a magnitude 6.8 earthquake ruptured the Sagaing Fault at Shwebo, near Mandalay. The earthquake focus was at a shallow depth of about 10 km. Sixteen people were killed and fifty-two injured by the earthquake. Hundreds of houses, schools and religious buildings were damaged along a 150 km section of the Sagaing Fault. Aftershocks still continue. The ultimate aim of this project is to mathematically model the state of stress along the Sagaing Fault. Stress modelling highlights where the fault is relaxed, and where stress is elevated. Earthquakes nucleate in areas of elevated stress. Data about previous earthquake ruptures is required to model the stress pattern along the fault. The 11th November Shwebo earthquake is the first large earthquake since Myanmar became accessible to foreign researchers, and offers an unprecedented opportunity to collect such data directly from the field. During an earthquake like the Shwebo event, the sides of the fault will slide about 0.2-1 m past each other. This displacement will cause a surface rupture, with sideways and vertical displacements. Systematic mapping of the surface rupture quantifies the amount and direction of slip along the fault, and shows whether the fault at depth is a single fracture or more segmented. Mapping the terminations of the fault rupture gives important information about how rupture is arrested. For example, ruptures often terminate across large gaps in the main fault where there is subsidence. This research will use surface rupture data collected within 3 months of the Shwebo earthquake to understand how rupture propagates along the Sagaing Fault, and to find where future earthquakes are likely, with particular attention to the fault immediately south of Mandalay, where a long section has conspicuously little historical seismicity. The research will be a collaboration between experts in structural geology, seismology and seismic hazard assessment in Europe and Myanmar. The results will be widely communicated so they may be used to inform development policy in Myanmar and other seismically active areas.