The goal of this project is to study ways to improve the performance of large scale networks, like the Internet, in the presence of selfish entities. This can only be achieved with a better understanding of these environments and their operational points, called Nash equilibria. A Nash equilibrium is a state in which no player improve their utility by changing to another strategy. In this project we focus on the very fundamental class of congestion games and the related class of potential games. In a congestion game, we are given a set of resources and each player selects a subset of them (e.g. a path in a network). Each resource has a cost function that depends on the load induced by the players that use it. Each player aspires to minimise the sum of the resources' costs in its strategy given the strategies chosen by the other players. Such games are expressive enough to capture a number of otherwise unrelated applications - including routing and network design - yet structured enough to permit a useful theory. In this project, we will push the frontiers of this theory even further. Moreover, in collaboration with XEROX, we will investigate applications of this theory to demand management in transportation systems. Two of these applications are smart road toll and parking management systems. Congestion games have attracted lots of research, but many fundamental problems are still open. We have identified three important directions in which we want to extent the current state-of-the-art. These are: (1) evaluation of Nash equilibria (2) computational complexity of Nash equilibria (3) approximation of optimal solutions

The vision of this research is to formalise the geometric foundations of computational statistics and provide the tools and analytic results required to realise the ambition of developing the advanced statistical methodology that is essential to address emerging inference problems of major importance across the sciences and industry. As ever more demanding and ambitious applications of existing statistical inference methods are being considered, the capabilities of computational statistics tools are constantly being stretched, often beyond what is practically feasible. For example the potential to gain insights into the mechanisms of cellular function, elucidating ecological dynamics; improving neurological diagnostics, and uncovering the deep mysteries of the cosmos are only some of the ongoing scientific studies that are heavily reliant on statistical inference methods and are placing unparalleled demand on the current capabilities of available statistical methodology. This situation motivates continual innovation in the development of statistical methods for the quantification of uncertainty. The aim of this proposed research is to be more ambitious and go much further in establishing a novel paradigm that underpins the advancement of next generation computational statistical methods by formalising and developing advanced Monte Carlo methods. The geometric foundations of computational statistics will be formalised within this proposed research in a way that reaches beyond traditional interfaces between statistical and mathematical sciences.

The vision of this research is to formalise the geometric foundations of computational statistics and provide the tools and analytic results required to realise the ambition of developing the advanced statistical methodology that is essential to address emerging inference problems of major importance across the sciences and industry. As ever more demanding and ambitious applications of existing statistical inference methods are being considered, the capabilities of computational statistics tools are constantly being stretched, often beyond what is practically feasible. For example the potential to gain insights into the mechanisms of cellular function, elucidating ecological dynamics; improving neurological diagnostics, and uncovering the deep mysteries of the cosmos are only some of the ongoing scientific studies that are heavily reliant on statistical inference methods and are placing unparalleled demand on the current capabilities of available statistical methodology. This situation motivates continual innovation in the development of statistical methods for the quantification of uncertainty. The aim of this proposed research is to be more ambitious and go much further in establishing a novel paradigm that underpins the advancement of next generation computational statistical methods by formalising and developing advanced Monte Carlo methods. The geometric foundations of computational statistics will be formalised within this proposed research in a way that reaches beyond traditional interfaces between statistical and mathematical sciences.

The vision of this research is to formalise the geometric foundations of computational statistics and provide the tools and analytic results required to realise the ambition of developing the advanced statistical methodology that is essential to address emerging inference problems of major importance across the sciences and industry. As ever more demanding and ambitious applications of existing statistical inference methods are being considered, the capabilities of computational statistics tools are constantly being stretched, often beyond what is practically feasible. For example the potential to gain insights into the mechanisms of cellular function, elucidating ecological dynamics; improving neurological diagnostics, and uncovering the deep mysteries of the cosmos are only some of the ongoing scientific studies that are heavily reliant on statistical inference methods and are placing unparalleled demand on the current capabilities of available statistical methodology. This situation motivates continual innovation in the development of statistical methods for the quantification of uncertainty. The aim of this proposed research is to be more ambitious and go much further in establishing a novel paradigm that underpins the advancement of next generation computational statistical methods by formalising and developing advanced Monte Carlo methods. The geometric foundations of computational statistics will be formalised within this proposed research in a way that reaches beyond traditional interfaces between statistical and mathematical sciences.

It is estimated that there are six million surveillance cameras in the UK, with only 17% of them publicly operated. Increasingly, people are installing CCTV cameras in their homes for security or remote monitoring of elderly, infants or pets. Despite this increase, the use of the overwhelming majority of these cameras is limited to evidence gathering or live viewing. These sensors are currently incapable of providing smart monitoring - identifying an infant in danger or a dehydrated elderly. Similarly, CCTV in public places is mostly used for evidence gathering. Following years of research, methods capable of automatically recognising activities of interest, such as a person departing a service station without making a payment for refueling the car, or one tampering with a fuel dispenser, are now available, achieving acceptable levels of success and low false alarms. Though automatic after installation, the installation process not only requires putting the hardware in place but also involves an expert studying the footage and designing a model suitable for the monitored location. At each new location, e.g. each new service station, a new model is needed, requiring the effort and time of an expert. This is expensive, difficult to scale and at times implausible such as for home monitoring for example. This requirement to build location-specific models is currently limiting the adoption of automatic recognition of activities, despite the potential benefits. This project, LOCATE, proposes an algorithmic solution that is capable of using a pre-built model in a different location and adapting it by simply observing the new scene for a few days. The solution is inspired by the human ability to intelligently apply previously-acquired knowledge to solve new challenges. The researchers will work with senior scientists from two leading UK video analytics industrial partners; QinetiQ and Thales. Using these partners' expertise, the project will provide practical and valuable insight that can further boost the strong UK industry of video analytics. The United Kingdom is currently a global player in the video analytics market, and the leading country in the Europe, Middle East and Africa (EMEA) region. The method will be applicable to various domains, including for home monitoring and CCTV in public places. To evaluate the proposed approach for home monitoring, LOCATE will work alongside the EPSRC-funded project SPHERE, which aims to develop and deploy a sensor-based platform for residential healthcare in and around Bristol. The findings of LOCATE will be integrated within the SPHERE platform, towards automatic monitoring of activities of daily living in a new home, such as preparing a meal, eating or taking medication. The targeted plug-and-play approach will enable a non-expert user to setup a camera and automatically detect whether an elderly in the home had had their meal and medication, for example. A shop owner can similarly detect pickpocketing attempts in their store. The community can thus make better use of the already in place network of visual sensors.