Oscillations are everywhere, ranging from perfectly ordered periodic and quasiperiodic to completely disordered, irregular ones, often described by probabilistic laws. Turbulence, climate changes, neuron spiking, heart electrical activity / all of these are examples of processes where irregular oscillations are possible and play a prominent role.The irregularity of oscillations can have two different origins: deterministic and stochastic.In the former case, although the dynamics of the oscillating system is defined by deterministic laws, the oscillations themselves are very sensitive to the initial state of the system: even a very small change in this initial state can lead to a substantial difference in the behaviour. This kind of oscillations is usually called deterministic chaos. Another type of irregular oscillations occurs when the dynamics of the system is defined by random fluctuations existing within, or applied to, the system. Notably, in spite of their randomness, the noise-induced oscillations in some systems can look quite regular and resemble very much the deterministic ones. One of the brightest examples is a sensory neuron which demonstrates no oscillations unless the signal on its input exceeds a certain level, after which the neuron generates one electrical pulse whose shape and duration are defined deterministically and almost do not depend on the input. The usual signal coming from an environment is in fact a random signal, that being applied to the neuron can generate a sequence of pulses looking quite coherent. Amazingly, irregular oscillations of this kind are widely spread in nature and technology. Besides the neurons and neuron networks, such oscillations can arise in semiconductor nanostructures, chemical reactions, some engineering mechanisms like drill string and many others. It is obvious that our ability to control irregular oscillations for example by making them more predictable is hugely beneficial to industry, technology, medicine, etc. Control means that by imposing some, preferrably small, forcing or feedback on the system, one is able to change the amplitude, timescale or regularity of oscillations, or even to cease them altogether. In the last decade a good progress was made in the control of deterministic chaos. The advanced nonlinear control methods exploit the fact that deterministic trajectories with the desired timescales already exist in the system, but are unstable and thus invisible in experiment, and the control tools just stabilize them. However, the systems where oscillations occur only due to noise have no such trajectories and no deterministic timescales. All timescales or orbits can be introduced only in the statistical sense. The control of oscillations that are purely random has never (or rarely, depending on what one means by control) been addressed previously.The main aim of the current research is to develop a general effective method for the control of oscillations induced merely by external random fluctuations that would be feasible as applied to real-life problems. As a control tool delayed feedback will be considered, which looks the most promising from the viewpoint of simplicity and efficiency. The main objectives are: (i) To develop qualitative theories for the delayed feedback as applied to minimal models that describe a large class of nonlinear systems in which noise can induce oscillations. (ii) To establish if the method is applicable to more realistic models like neuron-like networks. (iii) To verify if the delayed feedback can work in a real experiment on control of heart rate and of its variability in experiments with healthy human volunteers. The work will be carried out in Loughborough University in collaboration with Technical University of Berlin and the Department of Cardiovascular Sciences of Leicester University.

The project brings together academics, performers, sound curators and archivists, and sound engineers and technicians to engage in discussion concerning the use and status of early recordings (1890-1945) as sources for the study of performance practice and performance history, establishing foundations for further collaborative research and knowledge exchange in the area. Researchers and performers have been using early recordings as primary sources for the study of performance and music history for the last thirty years, in topics ranging from the minutiae of performance practice in specific styles and instruments, to the radical transformations that early recording technologies introduced in listening practices and in discourses around music and performance. During this period, technological advances have made early recordings more widely accessible, with collections and archives around the world digitizing their holdings and making them available online for free or at negligible cost. However, most such research activity has been conducted in relative isolation, and opportunities for researchers to engage in discussion about their work with an audience of their peers are few and far between. This lack of connectedness has prevented the field from tackling ambitious, comparative research questions centring around systematic historical change, and detracted from its relevance and visibility both in the broader field of musicology and among non-academic performers and general concert audiences. The project proposes to tackle these issues through the following interconnected collaborative activities: -Five symposia (4 in different cities across the UK, 1 hosted by partner TU Berlin) will provide opportunities for experts (musicologists, performers, sound curators, archivists and engineers engaged in sound curation and digitizing initiatives - both based in and outside HEI) to engage in methodological discussion with the aim of both co-creating collaborative resources and identifying collaborative research and knowledge exchange opportunities in the field. -A concert series attached to the symposia will allow audiences across the UK to familiarize themselves with practice-led research conducted by network members, while allowing the latter to reflect, in conversation with other network members, on good practice, opportunities and challenges for knowledge exchange. -A series of video interviews with network members filmed at the symposia and concert series will make accessible an array of approaches to early recordings to other HEI and non-HEI experts, as well as to musicologists, performers and performance students beyond the immediate area of study. These videos will be accompanied by an open-access handbook for similar audiences, expanding on the issues raised in the interviews (to be published after the grant period). The project will also establish a permanent forum for those interested in early recordings as sources for the study of performance practice and history. This open international research network will organize regular conferences and meetings, fostering collaborative activities between its members. The forum's establishment will be supported by an 'early recording roadmap', drafted collaboratively by network-members, identifying urgent research questions and flagging up potential areas for knowledge exchange collaborations.

The Centre for Doctoral Training MAC-MIGS will provide advanced training in the formulation, analysis, and implementation of state-of-the-art mathematical and computational models. The vision for the training offered is that effective modern modelling must integrate data with laws framed in explicit, rigorous mathematical terms. The CDT will offer 76 PhD students an intensive 4-year training and research programme that equips them with the skills needed to tackle the challenges of data-intensive modelling. The new generation of successful modelling experts will be able to develop and analyse mathematical models, translate them into efficient computer codes that make best use of available data, interpret the results, and communicate throughout the process with users in industry, commerce and government. Mathematical and computational models are at the heart of 21st-century technology: they underpin science, medicine and, increasingly, social sciences, and impact many sectors of the economy including high-value manufacturing, healthcare, energy, physical infrastructure and national planning. When combined with the enormous computing power and volume of data now available, these models provide unmatched predictive tools which capture systematically the experimental and observational evidence available. Because they are based on sound deductive principles, they are also the only effective tool in many problems where data is either sparse or, as is often the case, acquired in conditions that differ from the relevant real-world scenarios. Developing and exploiting these models requires a broad range of skills - from abstract mathematics to computing and data science - combined with expertise in application areas. MAC-MIGS will equip its students with these skills through a broad programme that cuts across disciplinary boundaries to include mathematical analysis - pure, applied, numerical and stochastic - data-science and statistics techniques and the domain-specific advanced knowledge necessary for cutting-edge applications. MAC-MIGS students will join the broader Maxwell Institute Graduate School in its brand-new base located in central Edinburgh. They will benefit from (i) dedicated academic training in subjects that include mathematical analysis, computational mathematics, multi-scale modelling, model reduction, Bayesian inference, uncertainty quantification, inverse problems and data assimilation, and machine learning; (ii) extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships; (iii) outstanding early-career training, with a strong focus on entrepreneurship; and (iv) a dynamic and forward-looking community of mathematicians and scientists, sharing strong values of collaboration, respect, and social and scientific responsibility. The students will integrate a vibrant research environment, closely interacting with some 80 MAC-MIGS academics comprised of mathematicians from the universities of Edinburgh and Heriot-Watt as well as computer scientists, engineers, physicists and chemists providing their own disciplinary expertise. Students will benefit from MAC-MIGS's diverse network of more than 30 industrial and agency partners spanning a broad spectrum of application areas: energy, engineering design, finance, computer technology, healthcare and the environment. These partners will provide internships, development programmes and research projects, and help maximise the impact of our students' work. Our network of academic partners representing ten leading institutions in the US and Europe, will further provide opportunities for collaborations and research visits.

The interaction between nano-objects of different dimensionality, e.g. electrostatic Coulomb-coupling of a zero-dimensional quantum dot (QD) to a two-dimensional (2D) system is of fundamental interest and of great relevance for charge-based memories. This interaction between a single QD and a 2D system shall be studied here. Innovative use of the complementary expertise of the partners will combine, for the first time, Sb-based QDs with a split-gate structure, which will allow the precise control of the charge-state of a single QD. Sb-based QDs have strong hole confinement yielding a potential retention time of many years at room temperature, enabling the analysis of the influence of charged QDs on a 2D system up to 300 K. In the mid-long term perspective, the results could be important for future generations of memories: knowledge of the interaction of a 2D system with a single QD might allow us to reach the ultimate limits of charged-based memories (e.g. Flash).

In today's society, the massive deployment of smart devices, the popularity of online services and social networks, and the increasing global data traffic, makes the ability to process large data volumes absolutely crucial. Demand for Artificial Intelligence (AI) has therefore exploded, fuelled by an increasing number of industries (e.g. energy, finance, healthcare, defence) heavily relying on the efficient processing of large data sets. Nonetheless, the ever-growing data processing demand creates a pressing need to find new paradigms in AI going beyond current systems, capable of operating at very high speeds whilst retaining low energy consumption. The human brain is exceptional at performing very quickly, and efficiently, highly complex computing tasks such as recognising patterns, faces in images or a specific song from just a few sounds. As a result, computing approaches inspired by the powerful capabilities of networks of neurons in the brain are the subject of increasing research interest world-wide, and are in fact already used by current AI platforms to perform these (and other) complex functions. Whilst these brain-inspired artificial neural networks (ANNs) are supported to date by traditional micro-electronic technologies, photonic techniques for brain emulation have also recently started to emerge due to their unique and superior properties. These include very high speeds and reduced interference, among others. Remarkably, ubiquitous photonic devices such as vertical-cavity surface emitting lasers (VCSELs), the very same devices used in supermarket barcode scanners, computer mice and in mobile phones for auto-focus functionalities, can exhibit responses analogous to those of neurons but up to 1 billion times faster. VCSELs are also compact, inexpensive and allow practical routes for integration in chip modules with very low footprints (just a few mm2) making them ideal for the development of ultrafast photonic ANNs using ultrafast light signals instead of electric currents to operate. This permits exploring radically new research directions aiming at exploiting the full potential of light-enabled technologies for new paradigms in ultrafast AI. This Fellowship project will focus on this key challenge to develop transformative photonic ANNs using VCSELs as building blocks capable of performing complex computational tasks at ultrafast speeds, using data rates below 1 billionth of a second to operate. These will include the ultrafast prediction of complex data signals, of interest for example in meteorology forecasting, to very high speed data classification of interest in green-energy systems (e.g. analysis of wind patterns in off-shore wind-energy farms). The research milestones of this programme are: (1) the design and fabrication of photonic ANNs using coupled VCSELs as building blocks, emulating the operation of the human brain at ultrafast speeds; (2) the development of chip-scale modules of VCSEL based photonic ANNs; (3) the demonstration of complex data processing tasks with photonic ANNs at ultrafast speeds (at data rates below 1 billionth of a second); (4) the delivery of photonic systems for AI, tackling key functionalities across strategic UK economic sectors (e.g. energy, defence). In summary, by bringing together the hitherto disparate fields of brain-inspired computing and photonics, this programme proposes unique pioneering research in photonic ANNs for future ultrafast AI technologies.