SAMBa aims to create a generation of interdisciplinary mathematicians at the interface of stochastics, numerical analysis, applied mathematics, data science and statistics, preparing them to work as research leaders in academia and in industry in the expanding world of big models and big data. This research spectrum includes rapidly developing areas of mathematical sciences such as machine learning, uncertainty quantification, compressed sensing, Bayesian networks and stochastic modelling. The research and training engagement also encompasses modern industrially facing mathematics, with a key strength of our CDT being meaningful and long term relationships with industrial, government and other non-academic partners. A substantial proportion of our doctoral research will continue to be developed collaboratively through these partnerships. The urgency and awareness of the UK's need for deep quantitative analytical talent with expert modelling skills has intensified since SAMBa's inception in 2014. Industry, government bodies and non-academic organisations at the forefront of technological innovation all want to achieve competitive advantage through the analysis of data of all levels of complexity. This need is as much of an issue outside of academia as it is for research and training capacity within academia and is reflected in our doctoral training approach. The sense of urgency is evidenced in recent government policy (cf. Government Office for Science report "Computational Modelling, Technological Futures, 2018"), through the EPSRC CDT priority areas of Mathematical and Computational Modelling and Statistics for the 21st century as well as through our own experience of growing SAMBa since 2014. We have had extensive collaboration with partners from a wide range of UK industrial sectors (e.g. agri-science, healthcare, advanced materials) and government bodies (e.g. NHS, National Physical Laboratory, Environment Agency and Office for National Statistics) and our portfolio is set to expand. SAMBa's approach to doctoral training, developed in conjunction with our industrial partners, will create future leaders both in academia and industry and consists of: - A broad-based first year developing mathematical expertise across the full range of Statistical Applied Mathematics, tailored to each incoming student. - Deep experience in academic-industrial collaboration through Integrative Think Tanks: bespoke problem-formulation workshops developed by SAMBa. - Research training in a department which produces world-leading research in Statistical Applied Mathematics. - Multiple cohort-enhanced training activities that maximise each student's talents and includes mentoring through cross-cohort integration. - Substantial international opportunities such as academic placements, overseas workshops and participation in jointly delivered ITTs. - The opportunity for co-supervision of research from industrial and non-maths academic supervisors, including student placements in industry. This proposal will initially fund over 60 scholarships, with the aim to further increase this number through additional funding from industrial and international partners. Based on the CDT's current track record from its inception in 2014 (creating 25 scholarships to add to an initial investment of 50), our target is to deliver 90 PhD students over the next five years. With 12 new staff positions committed to SAMBa-core areas since 2015, students in the CDT cohort will benefit from almost 60 Bath Mathematical Sciences academics available for lead supervisory roles, as well as over 50 relevant co-supervisors in other departments.

The ever-increasing demand in traffic and diversity of services, along with the growing complexity and heterogeneity of the infrastructure supporting their provision is presenting an important challenge to current approaches to the management of communication networks. In particular, it becomes increasingly difficult for network management systems to keep a complete and tractable picture of the state of computing/network resources and running services, and their interdependencies, which in turn makes it difficult to achieve optimal performance. This proposal aims to transform the way ICT networks are being conceptualised for management, by developing a data-driven characterisation of emerging dependencies between ICT components inspired by recent neuroscientific paradigms used to study the brain and allowing to capture and act upon the functional impact of complex and changing interactions across layers and processes. By releasing network operators from human intervention and/or manual application of domain expertise, this research paves the way for the development of automated processes that can scale up to the size, heterogeneity and complexity of future ICT infrastructures.

Large-scale wireless networks are expected to become prevalent in various Internet-of-Things (IoT) applications involving environment sensing and monitoring, communications, and computing. It is a fundamental task of many networks to deduce the network topology, both during the establishment of the network and periodically as the network state evolves. The availability of network topology and performance information is crucial for the operation and management of large wireless systems comprising low-power devices that are required to provide low-latency, high-reliability services. For example, state-of-the-art smart meter networks require this information to carry out routing and resource scheduling tasks, and the estimation of the number of devices in a network is useful for finding out how many sensors are still active or for detecting failures of some subnetworks. Inferring topology information even possess great importance in matters of national security in which one may have to learn the structure of a target network passively from external observables, such as the spectral activity of devices, without having access to the network devices and protocols. Many network characteristics can be inferred by observing end-to-end data, which often takes the form of packet probes. The general field of study concentrating on such techniques is known as "network tomography". Over the past twenty years, this field has been developed to include the inference of link loss statistics (loss tomography), internal queuing delays (delay tomography), and structural characteristics (topology tomography). Much of the work to date has focused on the formulation of optimal and efficient estimation methods that are primarily geared toward computer networks that exhibit certain constraints on their topologies. Some more recent studies of network tomography have considered wireless systems. However, investigations have largely been limited by the lack of available statistical models that incorporate spatial and physical characteristics inherent to wireless networks. For example, spatial (wireless) networks exhibit distinctive features (e.g., transitivity, clustering), which have not been fully exploited in topology inference tasks. This project is concerned with developing improved active methods (topology discovery) and passive techniques (topology inference) of obtaining the topology of a wireless communications network or a portion thereof. The underlying hypothesis is that probabilistic knowledge of structural properties of wireless networks can be used as prior information to improve network inference tasks, particularly topology tomography, in practical systems. The project will begin with fundamental research into the correct modelling and statistical characterisation of wireless networks designed for particular applications, such as smart meter infrastructure and tactical systems. The results of this research will be exploited to develop new topology tomography algorithms that are optimised for use in the chosen applications. The technical contributions of the project will be accompanied and supported by a number of activities aimed at delivering impact through dissemination and technology transfer. The project is supported by three hands-on partners (Toshiba, Moogsoft, and HMGCC), each of which is at the leading edge of its respective field.