Optimisation -- the problem of identifying a satisficing solution among a vast set of candidates -- is not only a fundamental problem in Artificial Intelligence and Computer Science, but essential to the competitiveness of UK businesses. Real-world optimisation problems are often tackled using evolutionary algorithms, which are optimisation techniques inspired by Darwin's principles of natural selection. Optimisation with classical evolutionary algorithms has a fundamental problem. These algorithms depend on a user-provided fitness function to rank candidate solutions. However, for real world problems, the quality of candidate solutions often depend on complex adversarial effects such as competitors which are difficult for the user to foresee, and thus rarely reflected in the fitness function. Solutions obtained by an evolutionary algorithm using an idealised fitness function, will therefore not necessarily perform well when deployed in a complex and adversarial real-world setting. So-called co-evolutionary algorithms can potentially solve this problem. They simulate a competition between two populations, the "prey" which attempt to discover good solutions, and the "predators" which attempt to find flaws in these. This idea greatly circumvents the need for the user to provide a fitness function which foresees all ways solutions can fail. However, due to limited understanding of their working principles, co-evolutionary algorithms are plagued by a number of pathological behaviours, including loss of gradient, relative over-generalisation, and mediocre objective stasis. The causes and potential remedies for these pathological behaviours are poorly understood, currently limiting the usefulness of these algorithms. The project has been designed to bring a break-through in the theoretical understanding of co-evolutionary algorithms. We will develop the first mathematically rigorous theory which can predict when a co-evolutionary algorithm reaches a solution efficiently, and when pathological behaviour occurs. This theory has the potential to make co-evolutionary algorithms a reliable optimisation method for complex real-world problems.

The properties of light are already exploited in communications, the Internet of Things, big data, manufacturing, biomedical applications, sensing and imaging, and are behind many of the inventions that we take for granted today. Nevertheless, there is still a plethora of emerging applications with the potential to effect positive transformations to our future societies and economies. UK researchers develop cutting-edge technologies that will make these applications a reality. The characteristics of these technologies already surpass the operating wavelength range and electronic bandwidth of our existing measurement equipment (as well as other facilities in the UK), which currently forms a stumbling block to demonstrating capability, and eventually generating impact. Several important developments, relating for example, to integrated photonic technologies capable of operating at extremely high speeds or the invention of new types of optical fibres and amplifiers that are capable of breaking the traditional constraints of conventional silica glass technology, necessitate the use of ever more sophisticated equipment to evaluate the full extent of their capabilities. This project aims at establishing an open experimental facility for the UK research community that will enable its users to experiment over a wide range of wavelengths, and generate, detect and analyse signals at unprecedented speeds. The new facility will enable the characterisation of signals in time and will offer a detailed analysis of their frequency components. Coherent detection will be possible, thereby offering information on both the amplitude and phase characteristics of the signals. This unique capability will enable its users to devise and execute a range of novel experiments. For example, it will be possible to experiment using signals, such as those that will be adopted in the communication networks of the future. It will make it possible to reveal the characteristics of novel devices and components to an extent that has previously not been possible. It will also be possible to analyse the response of experimental systems in unprecedented detail. The facility will benefit from being situated at the University of Southampton, which has established strong experimental capabilities in areas, such as photonics, communications and the life sciences. Research at the extended cleanroom complex of Southampton's Zepler Institute, a unique facility in UK academia, will benefit from the availability of this facility, which will enable fabrication and advanced applications research to be intimately connected. Furthermore, this new facility will be attached to EPSRC's National Dark Fibre Facility - this is the UK National Research Facility for fibre network research, offering access and control over the optical layer of a dedicated communications network for research-only purposes. The two together will create an experimental environment for communications research that is unique internationally.

Our understanding of the Earth's core, its formation and the geodynamo on geological timescales is derived from palaeomagnetic studies. Similarly, palaeomagnetic data plays a key role in the fields of palaeogeography, palaeoclimatology, tectonics, volcanology and many other geological areas. These studies rely on the ability of a rock's constituent magnetic minerals to record a meaningful and decipherable magnetic remanence. To reliably interpret palaeomagnetic data we need to understand the mechanisms that induce magnetic remanence and can subsequently alter it. Whilst some mechanisms, e.g., thermoremanent magnetisation (TRM) acquisition, are well understood, there is a broad class of remanence acquiring or altering mechanisms termed chemical (or crystallisation) remanent magnetisation (CRM) or chemical alteration, that are poorly understand yet are frequent in nature and so commonly contribute to palaeomagnetic observations. CRM refers to any process that physically or chemically alters the magnetic minerals of a rock. It can take many forms, for example: (1) it can be a remanence induced and retained in magnetic grains as they grow at ambient temperature, i.e. a growth CRM, or (2) it can be the resultant change in a mineral's magnetic remanence as it chemically alters through oxidation or reduction, where the new phase can be either magnetically stronger or weaker. The problem is further complicated in that it is often difficult to distinguish between say a TRM and CRM, yet the origin and interpretation of the two remanence signals is completely different. For example, if the ancient geomagnetic field intensity (palaeointensity) is a growth CRM yet wrongly assumed to be a TRM in origin, this will lead to an over-estimate of the ancient geomagnetic field strength. Theoretical treatment of CRM and chemical alteration has been limited due to the broadness and complexity of the problem, and the difficulty in quantifying these processes experimentally. Theoretical models only exist for the smallest magnetic grains, termed single domain (SD) as their magnetisation is uniform. Larger grains have complex domain patterns and are termed multidomain (MD); small MD grains just above the SD threshold size tend display some SD characteristics and are termed pseudo-SD (PSD). Such PSD grains tend to dominate the signal of rocks, yet no rigorous theoretical understanding exists for PSD CRM. The aim of this proposal is to apply state-of-the-art experimental and numerical techniques to the understanding and quantification of the CRM and chemical alteration processes in SD and PSD samples. We will employ the latest advanced transmission electron microscopy (TEM) techniques including electron holography that allows us to image magnetisation on atomic scales in real-time as the minerals alter under controlled oxidising/reducing atmospheres. To link the TEM images to the bulk magnetic properties we will use our recently developed multiphase micromagnetic models, allowing us to relate nanometre sized chemical changes to the magnetic mineralogy to the measured bulk magnetic properties. We will quantify how different types of chemical alteration affect both palaeo-directional and palaeointensity information. In particular we will examine experimentally and numerically: (1) grain growth/dissolution and (2) low-temperature oxidation, e.g., the oxidation of titanomagnetite to titanomaghemite at temperatures < 150 C.

Bio-Inspired Search Heuristics (BISHs) are general purpose randomized search heuristics (RSHs). Well known BISHs are Evolutionary Algorithms, Ant Colony Optimisation and Artificial Immune Systems. They have been applied successfully to combinatorial optimization in many fields. However, their computational complexity is far from being understood in depth. In this project the mathematical methodology will be developed to reveal where the real power of BISHs is in comparison with the traditional problem-specific algorithms. The project impacts the field of BISHs in several ways. A feature that distinguishes BISHs from most other algorithms is their population of individuals that simultaneously explore the search space. The first objective is to explain the performance of realistic BISHs for well-known combinatorial optimization problems through runtime analyses, highlighting the relationships between the solution quality and the exploration capabilities of the population. The second objective is to theoretically explain how BISHs can take advantage of the parallelisation available inherently in new technologies to achieve the population diversity required to produce solutions of higher quality in shorter time. The third objective of this project is to create a mathematical basis to explain the working principles of Genetic Programming (GP) and allow the effective and efficient self-evolution of computer programs. The fourth objective is to devise a suitable computational complexity model for the problem classification of BISHs. The enlargement of the established computational complexity picture with BISH complexity classes will enable the understanding of the relationships between traditional problem-specific algorithms and BISHs. Through industrial collaborators, the final objective is the direct exploitation of the theoretical results in real-world applications related to the combinatorial optimization problems studied in this project.

All living organisms contain proteins - nanoscale molecular machines which have a myriad of functions. A large fraction of these proteins are "electron transfer" proteins which, as the name suggests, are capable of moving electrical charge from one place to another - either within the protein or between proteins. Such proteins are absolutely essential to the physics of life, controlling biological processes as varied as respiration, photosynthesis and the creation of organic molecules from basic elements (hydrogen, carbon, nitrogen, oxygen, etc.). Although they actually function at essentially the single molecule level, most of our understanding of electron transfer (ET) proteins comes from experiments performed on large assemblies of protein molecules, not individual molecules. This is perhaps not surprising since it is usually difficult to locate a single molecule, or to obtain a measurable signal from just one molecule. Many traditional measurements therefore look at the optical properties of an assembly of molecules in solution. Others measure the electrical properties of metal surfaces covered in a layer of molecules. The aim of our project is to develop a new way to measure individual ET protein molecules, and use these measurements to gain a better understanding of the ET process (directly relevant to theorists and a prerequisite for any biolectronic applications). To do this we first make two electrical contacts to the protein, and then incorporate it as part of an electrical circuit. By measuring how easy it is to pass current through the circuit, we can examine just how the protein functions to transfer electrons. We can also change other properties of the protein (such as a metal centre which is common in ET proteins) to examine their role in the ET process. The first problem is how to make a reliable electrical contact to a single molecule. Fortunately, the methods already developed in protein engineering allow this to be done: it is possible to modify the protein surface to introduce specific chemical groups which strongly attach the molecule to a metal surface. This is achieved by altering the genetic material encoding the protein, so that the required chemical groups can be placed at precisely known positions in the protein. Multiple identical copies of the modified protein are produced in this way. The second problem is how to examine just a single molecule. This has become possible over the past few years following the invention of the scanning tunnelling microscope or STM. This instrument allows an almost atomically-sharp metal tip to be brought close to a (sufficiently flat) metal surface; if the distance between tip and surface is small enough (around one nanometre - a millionth of a millimetre - or so) electrons in the tip can pass to the surface when a voltage is applied between them. The tip and surface don't have to touch, but the electrons pass because of the quantum mechanical "tunnelling" effect. By scanning the tip across the metal surface under computer control, it is possible to measure exactly how flat the surface is, and even form an image of individual metal atoms. If our protein molecules are sprinkled on the surface, it is possible to use the STM to see exactly where they have adhered, and to put the tip in contact with them. This completes our electrical circuit. Measuring electron transfer through proteins in this way has not previously been done, and lets us explore the protein with a high degree of control. But it is not interesting simply for its own sake - it means we can better understand just how ET proteins operate at the level of a single molecule. Also, development of bioelectronic components using ET proteins, which is a subject of rapidly growing interest, ultimately depends on our ability to study them at the single molecule level and with electrical contacts.