An enormous amount of individuals' data is collected every day. These data could potentially be very valuable for scientific and medical research or for targeting business. Unfortunately, privacy concerns restrict the way this huge amount of information can be used and released. Several techniques have been proposed with the aim of making the data anonymous. These techniques however lose their effectiveness when attackers can exploit additional knowledge. Differential privacy is a promising approach to the privacy-preserving release of data: it offers a strong guaranteed bound on the increase in harm that a user I incurs as a result of participating in a differentially private data analysis, even under worst-case assumptions. A standard way to ensure differential privacy is by adding some statistical noise to the result of a data analysis. Differentially private mechanisms have been proposed for a wide range of interesting problems like statistical analysis, combinatorial optimization, machine learning, distributed computations, etc. Moreover, several programming language verification tools have been proposed with the goal of assisting a programmer in checking whether a given program is differentially private or not. These tools have been proved successful in checking differentially private programs that uses standard mechanisms. They offer however only a limited support for reasoning about differential privacy when this is obtained using non-standard mechanisms. One limitation comes from the simplified probabilistic models that are built-in to those tools. In particular, these simplified models provide no support (or only very limited support) for reasoning about explicit conditional distributions and probabilistic inference. From the verification point of view, dealing with explicit conditional distributions is difficult because it requires finding a manageable representation, in the internal logic of the verification tool, of events and probability measures. Moreover, it requires a set of primitives to handle them efficiently. In this project we aim at overcoming these limitations by extending the scope of verification tools for differential privacy to support explicit reasoning about conditional distributions and probabilistic inference. Support for conditional distributions and probabilistic inference is crucial for reasoning about machine learning algorithms. Those are essential tools for achieving efficient and accurate data analysis for massive collection of data. So, the goal of the project is to provide a novel programming language technology useful for enhancing privacy-preserving data analysis based on machine learning.

Programming is intrinsically based on the use of limited resources, such as memory and processing power of computers. Various abstractions of resources play an important role throughout computer science, but they are conceptualised in very different, and apparently unrelated ways. In particular, there is a big gap between studies focussing on precise quantitative issues of what we can do and how efficiently we can do it with limited resources, and those which concern more conceptual aspects, which underpin modern high-level programming languages, and application-oriented programming. In this project, building on some recent breakthrough developments which relate these different aspects, we aim to develop a unified theory of resources which will apply to all these aspects, and allow a flow of ideas between them. This will provide new tools and methods for computer scientists, and lead both to new kinds of results, and more general versions of existing ones.

Complex fluid flows are ubiquitous in both the natural and man-made worlds. From the pulsatile flow of blood through our bodies, to the pumping of personal products such as shampoos or conditioners through complex piping networks as they are processed. For such complex fluids the underlying microstructure can give rise to flow instabilities which are often totally absent in "simple" Newtonian fluids such as water or air. For example, many wormlike micellar surfactant ("soap/detergent") systems are known to exhibit shear-banding where the homogenous solution splits into two (or more) bands of fluid: such flows are often unstable to even infinitesimally small perturbations. At higher pump speeds the flows can develop chaotic motion caused by the elastic normal-stresses developed in flow. Such "elastic turbulence" can also develop for other flowing complex fluids, such as polymer solutions and melts, and give rise to new phenomena. Often such instabilities are unwelcome, for example in rheometric devices when the aim is to measure material properties or in simple pumping operations when they can give rise to unacceptably large pressure drops and prevent pumping. In other cases they can give rise to enhanced mixing of heat and mass which would otherwise be difficult to achieve (e.g. microfluidics applications).

Quantum technologies promise a transformation of measurement, communication and computation by using ideas originating from quantum physics. The UK was the birthplace of many of the seminal ideas and techniques; the technologies are now ready to translate from the laboratory into industrial applications. Since international companies are already moving in this area, there is a critical need across the UK for highly-skilled researchers who will be the future leaders in quantum technology. Our proposal is driven by the need to train this new generation of leaders. They will need to be equipped to function in a complex research and engineering landscape where quantum physics meets cryptography, complexity and information theory, devices, materials, software and hardware engineering. We propose to train a cohort of leaders to meet these challenges within the highly interdisciplinary research environment provided by UCL, its commercial and governmental laboratory partners. In their first year the students will obtain a background in devices, information and computational sciences through three concentrated modules organized around current research issues. They will complete a team project and a longer individual research project, preparing them for their choice of main research doctoral topic at the end of the year. Cross-cohort training in communication skills, technology transfer, enterprise, teamwork and career planning will continue throughout the four years. Peer to peer learning will be continually facilitated not only by organized cross-cohort activities, but also by the day to day social interaction among the members of the cohort thanks to their co-location at UCL.

The function of striated muscles, so called because of their highly regular striation pattern when viewed in a microscope, is crucial for the movement of our body and heart muscles. These stripes are formed from the repetitive arrangements of molecular machines, called sarcomeres that generate force and movement. In the sarcomere, three systems of molecular filaments are working together: actin filaments, which are held together at the Z-disk, myosin filaments, held together at the M-band, and the giant protein filament titin, which links the actin and myosin filaments. Muscle responds rapidly to changes in use, with disuse leading to muscle loss (called atrophy) and exercise leading to muscle growth (called hypertrophy). These processes need to be constantly balanced, and are linked in a coordinated way to those controlling muscle repair by making new proteins for sarcomere repair and replacement of other unwanted or damaged components of the cell. Signals controlling muscle protein turnover are emerging to originate at the M-band and the Z-disk. These structures contain proteins that can sense mechanical stress and control the activity of the protein degradation machinery. Many of these proteins, however, remain enigmatic or haven't even been discovered, and often even their most fundamental functions have not been elucidated. Yet, when the integration of the M-band as a machinery combining structural, mechanical and communication functions is disrupted by genetic defects, severe muscle diseases are the result. This study will shed light on the compositions and regulation of the M-band, its role as a regulator of proteostasis, and why mutations in two of the giant proteins that are involved in its assembly, titin and obscurin, can lead to muscle disease. Inherited defects in the giant muscle protein titin, the largest in the human body, are increasingly identified as common causes of a broad range of muscle diseases. Many of these mutations cause defective proteins that the muscle cell would need to prevent from behaving abnormally by clumping together and interfering with normal function, which may be a major disease mechanism. We will study the impact of code-changing "missense" mutations in titin on the ability of the cell to cope with defective proteins, called protein quality control. The findings will help us to understand the basic mechanisms of how sarcomeres regulate sarcomere quality control, and how this fundamental mechanism is perturbed in severe inherited myopathies affecting mainly children.