AHRC : Alberto Martin : AH/L503939/1 My work is fundamentally music-theoretically/analytically driven, and McGill University's Schulich School of Music has one of the leading Music Theory departments in North America and, indeed, the world, which will provide a unique and stimulating intellectual environment that I will take full advantage of during the proposed placement. Although my current supervisory team in the UK possesses deep knowledge on both music-analytical techniques and cultural-historical aspects, my supervisors do not have specific expertise in theories of "formal functions" developed by William Caplin (a Professor of Music Theory at McGill University). "Caplinian" formal-function theory considers the "syntactical" roles played by various parts/sections of particular musical work in relation to the whole, and the capacity of different compositional techniques to express musical temporality, all resulting in well-defined archetypical formal constructions. During this research placement, I will study the applicability of Caplin's theories of formal functions to the music of the 19th-century Spanish composer Isaac Albéniz, and thus also their potential conceptual expansion beyond their original 18th-century "classical" framework. In particular, I will focus on Albéniz's use of one of Caplin's formal types: the sentence. This work will form one of the chapters of my PhD dissertation; my larger dissertation research project seeks to elucidate the importance of 18th-century tonal and formal syntax in the music of Albéniz. I will import the knowledge acquired during this placement to the UK through, for example, the organization of workshops and lectures at the University of Southampton and in collaboration with the UK's Society for Music Analysis. While traditional music-analytical scholarship has been centered on the "Germanic canon", my investigation will contribute to diversifying our discipline by enlarging the repertoire traditionally dealt with by music theory and analysis. My project will reveal the importance of pan-European influences in Albéniz's music, revising and nuancing his traditional nationalist image. Indeed, I believe it is the right time to vindicate figures like Albéniz, a non-nationalist Catalan who fostered ties between all Spanish people by using the richness of different Spanish cultural manifestations within a European tradition to create some of the most well-loved compositions in the history of Western Music.

When we open our eyes, we see, without effort. Our visual experience begins with the mechanics of focussing the image on the back of eye; but to make sense of the image-to perceive-our brains must identify the various parts of the image, and understand their relations. Just like a silicon-based computer, the brain performs millions of computations quickly and effectively, more efficiently than we can ever sense. But what are the computations that are needed to recognise, say, your mother; to segment an object from its background; or even appreciate that one part of an image belongs with another? The starting point for this analysis is the distribution of light levels across the retinal image, which we can think of as a set of pixels. Interesting parts of the image (e.g. object boundaries) occur at regions of change: where neighbouring pixels have very different values. These regions are identified by neurons in primary visual cortex (V1) by computing differences between adjacent pixel values to build a neural image of local contrasts: the 'contrast-image'. These contrast-defined local image features are then combined across retinal space at later stages of the visual hierarchy to represent elongated contours (e.g. the branches of a tree) and textured surfaces (e.g. a ploughed field) in what is sometimes known as a 'feature-map'.One major goal in vision science is to construct accurate computer models of the visual system so that computers can be made to process images in the same way as human brains. But there has been a major obstacle. Experiments confirm that feature integration (summing) is involved in constructing the 'feature-map', but also imply that contrast is not summed beyond the neighbourhood of each local contrast processor in V1. But how can local feature representations be summed without also summing the underlying contrast codes?We achieved the breakthrough on this by designing novel images containing patches of contrast distributed over retinal space (Meese & Summers, 2007). These allowed us to measure the contrast integration process while controlling the confounding effects of neural noise and retinal-inhomogeneity that have plagued previous studies. By analysing the relation between visual performance (an observer's probability of detecting the target stimulus) and stimulus contrast, we showed that contrast is summed over substantial regions of the retina after all, but that under normal viewing conditions its effects go unnoticed because of a counterbalancing effect of blanket suppression from a system of contrast gain control. In other words, we have shown that contrast summation is organised very differently from the way first proposed. These results have dispelled orthodoxy and now prompt a thorough re-evaluation of our understanding of contrast and feature integration in human vision.In the current proposed project we will use our new type of stimulus and modelling framework to investigate the computational rules that control the point-by-point integration of information in the 'contrast image'. In particular, our working hypothesis proposes that the visual system does this by maximising the 'signal to noise ratio'. But what directs and limits the signal integration? And how does this relate to the grouping rules of Gestalt psychology and other results on contour integration and contrast perception? Through careful stimulus manipulations, our 19+ experiments will address these issues, mainly using normal healthy observers, but we will also study the disrupted amblyopic visual system as a way of further probing the system's organization. Overall, this work will illuminate the links between pixel-based contrast responses, and later region-based symbolic feature analyses. Only with these links in place can we begin to appreciate how the brain transforms the retinal image to the subjective experience of seeing.

Saints were the heroes of medieval culture, the centre of lively cults which presented them as active intercessors and examples for their fellow Christians. We will explore how devotion to medieval saints was constructed through the combination of liturgical, musical and material elements, in an area that has received little scholarly attention despite its rich culture: early medieval Iberia. Our study of the development and transmission of Iberian saints' cults from the Visigothic period to the 14th century will integrate hagiography, liturgical texts, chant, and material culture for the first time. This will offer a new perspective on how saints were constructed by and experienced by the communities that venerated them. We will publish a series of peer-reviewed journal articles and a team-authored monograph, as well as inviting an international general public to gain a new appreciation of this unique heritage via an interactive, multilingual and multimedia exhibition. We know that saints were proudly defended elsewhere in Western Europe as local patrons and community figureheads, and that veneration of saints was gendered: women were commemorated for virginity; and men were celebrated for leadership. Iberian saints, however, have not been analysed for their socio-cultural significance and integrated into wider European paradigms. This is the result of inaccessible manuscript sources, and lack of scholarly familiarity with the distinctive Old Hispanic rite. 'Iberian saints' brings together an interdisciplinary team to address these gaps in the research agenda, and to produce the first holistic study of saints' cults in early medieval Iberia, straddling multiple disciplinary specialisms, and engaging with how the veneration of Iberian saints shifted over the centuries, in particular during and after the 11th-century imposition of the Roman liturgy across much of Iberia. Our work will open up new research avenues for scholars in multiple disciplines, modelling an interdisciplinary approach that can shed new light on historical moments about which only fragmentary evidence survives. By adding a significant body of Old Hispanic material to www.musicahispanica.eu and www.cantusindex.org, we will facilitate integration of Old Hispanic liturgical evidence into the wider European context. Further, this data sharing will make the Old Hispanic materials widely accessible, with the (intricate and unfamiliar) liturgical structure ready parsed. We will undertake innovative transcription work in our web-based Chant Editing and Analysis Program (neumes.org.uk). Old Hispanic notation is unpitched, which poses significant challenges to scholars engaging with the melodies. In Iberian Saints, we will continue to develop analytical tools and methods that break new ground in our understanding of medieval monophonic melodic languages, available to all through our software and exemplified in our publications. Beyond academic discourse, our interactive digital exhibition will significantly increase the cultural value of our research findings. The exhibition will reconnect locals who visit archives and museums in Lamego, Coimbra, Salamanca and Toledo with this almost-forgotten aspect of their cultural heritage, as well as reaching out to tourists, and being available online. It will raise consciousness of Old Hispanic liturgy and its manuscripts, while communicating our new findings to the general public. The exhibition will engage audiences in ways that go far beyond superficial appreciation of the beauty and antiquity of the materials: they will be taught to navigate the texts, melodies and liturgical context, performing basic forms of analysis through interactive games, and navigating the GIS maps of each saint's cult. For some, there will be devotional and spiritual benefits as well; they will re-examine their own religious practices in the light of the thousand-year old culture to which we are drawing their attention.

I aim to develop high level structures for reasoning about knowledge of agents in a multi-agent system where agents communicate and as a result update their information. All of us take part in such situations when communicating through the internet, surfing the web, bidding in auctions, or buying on financial markets. Reasoning about knowledge acquisition in these situations becomes more challenging when some agents are not honest and they cheat and lie in their actions and as a result other agents acquire wrong information. The current models of these situations are low level: they require specifying untidy details and hide the high level structure of information flow between the agents. This makes modeling a hard task and proving properties of the model an involved and complicated problem. The complexity of reasoning in these situations raises the question: ``Which structures are required to reason about knowledge acquisition?'', in other words, ``What are the foundational structures of knowledge acquisition?''. High level methods provide us with a minimal unifying structure that benefits from partiality of information: we do not need to specify all the details of the situations we are modeling. They also bring out the conceptual structure of information and update, hide the untidy details, and tidy up the proofs. My plan is to (1) Study the foundational structures that govern knowledge acquisition as a result of information flow between the agents and then develop a unifying framework to formally express these structures in a logical syntax with a comprehensive semantics. I aim to use known mathematical structures, such as algebra, coalegbra and topology, for the semantics. The syntactic theory will be a rule-based proof-theoretic calculus that helps us prove properties about knowledge acquisition in a programmatic algorithmic manner. (2) Apply this framework to reason about security properties of multi-agent protocols. Examples of these protocols are communication protocols between a client and a bank for online banking. We want to make sure that such a protocol is secure, that is, the client's information remains secret throughout the transaction. Because of the potentially unlimited computational abilities of the intruder, these protocols become very complex and verifying their security becomes a challenging task. It is exactly here that our high level setting becomes a necessity, that is, in formal analysis of these protocols and in proving their security properties. The semantic structures that I aim to use have also been used to model the logic of Quantum Mechanics. So my model will be flexible enough to accommodate quantum situations. These situations are important for security protocols because they benefit from additional non-local capabilities of Quantum Mechanics, which guarantee better safety properties. I aim to apply the knowledge acquisition framework to Quantum protocols and prove their sharing and secrecy properties. On the same track, similar semantic structures have been used for information retrieval from the web. I aim to exploit these models and study their relationship to my framework. (3) Write a computer program to implement the axiomatic semantic structure and produce a software package. This software will help us automatically verify properties of multi-agent protocols, such as the security protocols mentioned above.

The EPSRC Centre for Doctoral Training in Statistics and Machine Learning (StatML) will address the EPSRC research priority of the 'physical and mathematical sciences powerhouse' through an innovative cohort-based training program. StatML harnesses the combined strengths of Imperial and Oxford, two world-leading institutions in statistics and machine learning, in collaboration with a broad spectrum of industry partners, to nurture the next generation of leaders in this field. Our students will be at the forefront of advancing the core methodologies of data science and AI, crucial for unlocking the value inherent in data to benefit industry and society. They will be equipped with advanced research, technical, and practical skills, enabling them to make tangible real-world impacts. Our students will be ethical and responsible innovators, championing reproducible research and open science. Collaborating with students, charities and equality experts, StatML will also pioneer a comprehensive strategy to promote inclusivity, attract individuals from diverse backgrounds and eliminate biases. This will help diversify the UK's future statistics and machine learning workforce, essential for ensuring data science is used for public good. Data science and AI are now part of our everyday lives, transforming all sectors of the economy. To future-proof the UK's prosperity and security, it is essential to develop new methodology, specifically tailored to meet the big societal challenges of the future. The techniques underpinning such methods are founded in statistics and machine learning. Through close collaboration with a broad range of industry partners, our cohort-based training will support the UK in producing a critical mass of world-leading researchers with expertise in developing cutting-edge, impactful statistical and machine learning methodology and theory. It is well documented in government and learned society reports that the UK economy has an urgent need for these people. The significant level of industry support for our proposal also highlights the necessity of filling this gap in the UK data science ecosystem. StatML will learn from and build upon our previous successful experiences in cohort training of doctoral students (our existing StatML CDT funded in 2018, as well as other CDTs at Imperial and Oxford). Our students will continue to produce impactful, internationally leading research in statistics and machine learning (as evidenced by our students' impressive publication record and our world-leading research environment, as rated by the REF 2021 evaluation), while complementing this with a bespoke cohort-based Advanced Training program in Statistics and Machine Learning (StatML-AT). StatML-AT has been developed from our experience and in partnership with industry. It will be responsive to emerging technologies and equip our students with the practical skills required to transform how data is used. It will be delivered by our outstanding academics from both institutions alongside with industry leaders to ensure that students receive training in cutting edge technologies, along with the latest ideas in ethics, responsible innovation, sustainability and entrepreneurship. This will be complemented by industrial and academic placements to allow the students to develop their own international network and produce high-impact research. Together, StatML and its partners will train 90+ students over 5 cohorts. More than half of these will be funded from external sources, including 25+ by industry, representing excellent value for money. Our diverse cohorts will benefit from a unique and responsive training program combining academic excellence, industry engagement, and interdisciplinary culture. This will make StatML a vibrant research environment inspiring the next methodological advancements to transform the use of data and AI across industry and society.