Algebraic topology uses various techniques allowing to reduce problems about flexible geometric objects to questions about rigid algebraic structures. Cohomological methods are currently among the most effective techniques which are used in situations motivated by problems of mathematical analysis, algebraic geometry, engineering and mathematical physics. In this research we shall use topological tools (and in particular methods of cohomology theory) to analyse algorithms of making decisions in situations when the outcome is a choice made from a continuum of possibilities rather than from a discrete set of values. In many such situations an algorithms can be interpreted as a section of a fibration and the topological concept of Schwartz genus of a fibration is a natural reflection of complexity of the task. In this research we shall develop mathematical methods to study algorithms for motion planning in engineering, algorithms for coordination of computations in distributed computing and algorithms for aggregation of personal preferences and reaching consensus in negotiations and their relations to social choice theory. Although these problems may appear to be very different at the first glance, they involve quite similar underlying mathematics and can be analysed by analogous methods. We shall develop theory of parametrised topological complexity which will be applicable in a variety of real life situations. The fundamental novelty in our approach consists in the assumption that the configuration space is "large" and is known to us only partially and, besides, the motion planning algorithm will operate without prior knowledge of the positions of the obstacles. Mathematically this will be reflected in the assumption that the actual configuration space is one of a large family of spaces parametrised by a base of a fibration. We shall also study motion planning algorithms in situations when motion of the system is constrained by technical limitations. This theory will be applicable in the context of distributed computing and will help to design computational algorithms for multiple computers performing simultaneous computations and sharing common resources. We shall tackle the Rationality Conjecture which predicts behaviour of the sequential topological complexity in the case of a large number of intermediate destinations. Besides, we shall further develop theory of geodesic motion planning where one requires that motion planning algorithms produce geodesic paths of minimal lengths. In the classical theory of social choice the preferences are assumed to be given on discrete sets of alternatives. We shall study a topological approach aiming to devise methods allowing to quantify the necessary failure of aggregation methods of various kind, along the lines of topological complexity and its quantitative variants, and to produce some positive results in this direction.

Micro-organisms are found in virtually all environments. Typically, they form the base of the food chain (such as plankton in the sea) and play essential roles in their ecosystems. There is often a complex interplay between different micro-organisms, with some organisms requiring that others be present in order for them to exist. When there is an imbalance within a community, this can lead to severe effects, such as disease in the human gut, or the inability for plants to grow efficiently in soil. An understanding of the composition and interplay within the communities allows us to potentially manipulate them. Thus, there is intense research into micro-organism communities in many different fields, such as improving livestock yields, the recovery from bacterial infections using fecal transplants and the efficient production of biofuels. Many of these communities also contain important proteins that could be useful to the biotechnological and pharmaceutical industries, such as enzymes involved in the production of antibiotics. Metagenomics is the study of these different micro-organism communities, which is achieved by isolating the DNA from the organisms within an environmental sample (e.g. water, soil, animal stool), sequencing the DNA, followed by the computational analysis to decode which organisms are present and the functions they might be performing. This computation is complicated: (1) there is a huge amount of data; (2) The sequence data is a jumbled mix of fragments from different organisms; (3) Decoding the DNA is hard - typically >90% of organisms within a sample are not well characterised. This proposal brings together three major resources within the field of metagenomics data archiving and analysis. The European Nucleotide Archive (ENA) is a repository of DNA sequence data. Importantly, ENA also captures metagenomic contextual data, such as where and when the sample was taken, how the DNA was extracted and sequenced. The EBI metagenomics portal (EMG, UK) and MG-RAST (MGR, US) are two metagenomics sequence analysis platforms. Uniquely, they represent the only free to use services, whereby researchers can upload sequence data and have it analysed without restriction. Despite the widespread use of metagenomics, currently the community lacks standards to ensure that metagenomics sequence data and the derived functional and taxonomic information are deposited within a database of record. Consequently, the navigation between metagenomics datasets is very difficult for even experienced users. As they offer slightly different, yet complementary, analysis services, there is often the desire to have a metagenomics dataset analysed by both resources. But, the number of equivalent datasets between the two resources is unknown. Unless a user has prior knowledge about equivalent projects, they remain disconnected. Also, sequence data submitted to MGR may not necessarily be deposited in ENA. We propose to set up a computational framework, termed Metagenomics Exchange (ME), to enable metagenomics datasets and the results of their analysis to be linked. All sequences will become available to the research community via ENA and analysis results we be automatically exchanged between EMG and EMR. The ME will be implemented to enable other metagenomics analysis providers to join, and so that it can be used by researchers wishing to perform large scale analyses. We will also investigate ways that our own pipelines can be enhanced through the use of the ME, sharing software and processing tasks, for example. This will lead to computational savings, increasing the capacity for metagenomics analysis. We will also generate a knowledge transfer forum, enabling the exchange of ideas on a range of topics, from hardware solutions to algorithms. Finally, we will undertake a research program to investigate the optimal combination of pipeline analysis components, and whether a single, unified analysis pipeline could be engineered.

This project funds collaborative work between Dr Itamar Francez and Prof Chris Kennedy, experts in the semantics of adjectives and possession at the University of Chicago, Dr Yuni Kim (Co-PI), a Huave (Isolate; Mexico) specialist at the University of Manchester, Dr Andrew Koontz-Garboden (PI), a formal semanticist and Ulwa (Misumalpan; Nicaragua) specialist at the University of Manchester, and a postdoctoral researcher in formal syntax and semantics. The project explores the linguistic phenomenon known as multifunctionality, which occurs in language any time that a single element (whether a word or a unit smaller than a word) is used in more than one distinct context, as with, for example, the suffix --ka that appears on nouns in Ulwa to indicate possession. It appears not only on the possessed noun in a noun phrase like Andrew balauh-ka `Andrew's table', but also on adjectives, as in pau-ka `red'. If this happened only in Ulwa, we might rightly think it an accident, but there are a number of other unrelated languages that show the same kind of use of possessive morphology on adjectives, Hausa (Chadic; Nigeria), Huave, Moseten (Mostenan; Bolivia), among them. \n\nWe aim to show through the detailed study of multifunctionality in possessive morphology, that phenomena of this kind have been underappreciated and have serious consequences for formal linguistic architecture. We accomplish this through breadth and depth studies. In order to better understand its extent and variation, we cull the linguistic literature for additional instances of multifunctional use of possessive marking across languages, building a publicly-accessible wiki to display them and access them for our own purposes (and for use by anyone interested in the public, academic or otherwise). In order to understand the multifunctionality in greater depth, we undertake detailed fieldwork on it in Ulwa, developing an analysis of possession in the context of Ulwa grammar that has the multifunctional use of the possessive marker as one of its explananda. We then explore the consequences of this analysis, both internal to Ulwa, and crosslinguistically. Internal to Ulwa, we carry out additional fieldwork on constructions in the language that are related to adjectives, specifically comparative constructions (e.g., Kim is taller than Sandy) and degree-based constructions (e.g., Kim is 6 feet tall), since our analysis of possession with adjectives involves a treatment of them in Ulwa whereby they have a fundamentally different meaning from their English counterparts, thereby raising questions about the analysis of constructions involving them. Beyond Ulwa, we undertake detailed fieldwork on Huave and Hausa to better understand the nature of the multifunctional use of possession in these languages and the extent to which it can or cannot be analyzed similarly to Ulwa.\n\nThe project will demonstrate, though this detailed case study, the consequences of taking multifunctionality seriously in formal linguistic analysis. Beyond this, it also has implications for the understanding of the nature of possession and crosslinguistic variation in the nature of the use of possessive marking. It will further contribute valuable data and analysis to developing efforts to understand the nature of variation in adjectival semantics crosslinguistically. Additionally, the data collected on Huave and Ulwa, both highly endangered languages, will contribute to the documentation of these languages at the same time that they shed light on the nature of language more broadly.\n\nResults of the project will be disseminated in the form of 6 conference presentations and 3 journal papers, outlined in the case for support

The origin and evolution of mammals is a key event in vertebrate evolutionary history, and a textbook example of an evolutionary transition. From around 230 million years ago, the fossil record documents an uncharacteristically well-preserved sequence of transitional fossils evolving key mammalian features such as deciduous and permanent teeth, a large brain, strong skull and the unique mammalian middle ear. Rather than a single middle ear bone, mammals have a more finely tuned middle ear comprising three small bones, or ossicles, the malleus, incus and the stapes. Along with a coiled cochlea, this structure enables high frequency sound detection. Combined evidence from the fossil record, embryology and development reveal a remarkable example of transformation in structure and function: bones forming the jaw joint of mammalian ancestors transform into the minute middle ear structures of mammals. We know that as the tooth-bearing bone, the dentary, increases in size, the jaw joint bones become smaller and loosely attached. Eventually the dentary contacts the squamosal part of the skull forming a true mammalian 'dentary-squamosal' (temperomandibular) hinge. We even know that at one point in mammalian evolution, animals existed with two jaw hinges with a dual feeding and auditory function. A long-standing point of debate is how the bones of the ancestral jaw hinge were able to reduce in size, whilst at the same time still functioning as a viable jaw joint. Additionally puzzling, is that during this transition, the skull is supposed to be strengthening, as the jaw-closing musculature reorganises to become a more efficient force generating system. The jaw joint should become stronger, not weaker and degenerate. Perhaps most startling, is that this transition has happened more than once. Theoretical models proposed in the 1970s and 80s suggested that reorganization of the jaw musculature lead to reduced loading at the jaw joint in the ancestors of mammals, allowing the ancestral hinge to become smaller and detect sound whilst the new mammalian hinge took over. These predictions are central to how the mammalian jaw and ear evolved, yet they have never been tested. This is largely because we have not had the means, until recently, to go beyond theory. We are now able to bring new computational biomechanical techniques, that we as a team have pioneered, to address the question of how the definitive mammalian middle ear and jaw joint were able to evolve yet remain functionally viable. We have obtained CT scans of five key transitional taxa. Through detailed study of fossil specimens we will reconstruct the patterns of musculoskeletal evolution across the origin of mammals, particularly in light of new fossil discoveries and suggestions of reversal back to ancestral forms. Using 3D muscle reconstructions and multibody dynamics analysis, we will determine how the ancestral, dual jaw joint and true mammalian jaw joint function during feeding behaviour. We will test if there is a transfer of function from ancestral to modern mammals with the evolution of the dual jaw joint as predicted. For example, do the component parts of the dual joint bear load, and can they function without joint disarticulation; and how is load transferred from the ancestral to modern hinge during this transition. Using finite element models we will test how the bones of the jaw hinge withstand load and strains during feeding. We will test if skulls do become stronger across the transition, as predicted, and how this relates to predicted bite forces. Comparative anatomists, biomechanists, evolutionary and developmental biologists, palaeontologists and biomedical engineers will benefit from this work. Benefits to UK science include multidisciplinary training of a young scientist and overseas collaboration. The visual aspect of this work and the focus on mammals is likely to appeal to the general public, offering engagement opportunities and media interest.

This proposal contains two subprojects about the physics of light-matter systems, both sharing a common theme and methods, but also quite different in aims and specifics. I propose to theoretically investigate the physics of two classes of artificial quantum devices: random lasers and superconducting circuits. Random lasing in a disordered photonic medium is relatively new and only partially understood phenomenon, in which the mechanisms of scattering and gain determine the lasing spectrum and directionality, and the cavity boundaries play only a secondary role. There is a strong potential for applications of random lasers, since they are easy to manufacture, shape, and are relatively cheap. The second part of the project concerns the physics of superconducting circuits, which is described by a theoretical framework called Circuit Quantum Electrodynamics (circuit QED). This is an emerging field which aims to study the implementation of superconducting qubits and circuits to quantum information processing and quantum optics, with an emphasis on methods of control of the individual components of the system. The first quantum algorithms in a solid state device have been demonstrated in these systems, and the complexity of the circuits experienced a steady growth in scale in the recent years, which is expected to continue. This proposal aims to address some of the theoretical needs of both fields which are central to their development, by which we will also explore a frontier of many-body non-equilibrium quantum theory and develop computational methods for quantum control. Non-equilibrium physics of light-matter interaction stands at the basis of both systems and therefore we propose to employ similar theoretical methods to investigate the role of quantum fluctuations in the optical nonlinear response of the two systems. In circuit QED this effort will extend existing analytical theory of superconducting qubits, and complement the proposed development of exact simulations. For random lasers we will gain insight into the temporal and spatial fluctuations of the lasing modes, as well as to the role of photonic disorder in statistical studies of random spectra.