Tony Samuel
One of the most classical examples of a dynamical system stem from β-transformations. Namely, self-maps on [0,1] of the form x→{βx}, where β is a real number with |β|>1 and where {βx} denotes the fractional part of βx. They are the simplest family of expanding interval maps and yet give rise to a variety of intricate dynamical behaviours. When β is not an integer, these transformations lead to a beautiful representation of real numbers, i.e. non-integer base expansions, which have their origins in the works of Alexander Gelfond [1], William Parry [4] and Alfréd Rényi [5]. These β-expansions possess very different properties to their integer counterparts (e.g. binary or decimal) and continued fraction expansions. By exploiting these discrepancies Yutaka Jitsumatsu et al. [3,4] have developed a new random number generator which was verified by the National Institute of Standards and Technology (NIST) statistical test suite. This is precisely where this project will kick off, namely to explore the results of Yutaka Jitsumatsu et al. and to tackle some of the open questions posed in [3,4].
[1] A. O. Gelfond, A common property of number systems, Izv. Akad. Nauk SSSR. Ser. Mat. 23, 809–814 (1959).
[2] K. Itaya and Y. Jitsumatsu, Random Number Generation Using Outputs from Multiple Beta Encoders, IEICE Proceedings Series 48, A4L-C-6 (2016).
[3] Y. Jitsumatsu and K. Matsumura, A β-ary to binary conversion for random number generation using a β-encoder, Nonlinear Theory and Its Applications, IEICE 7(1), 38–55 (2016).
[4] W. Parry, On the β-expansions of real numbers, Acta Math. Acad. Sci. Hungar. 11, 401–416 (1960).
[5] A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar. 8, 477–493 (1957).
Oscar Rodriguez de Rivera Ortega
Citizen science, or public participation in scientific research, presents a significant opportunity for enhancing data availability. However, this type of information is deeply intertwined with human knowledge and behaviour, which introduce several complexities into the modelling framework. These complexities manifest in various ways, including uncertainty, sampling bias, and variations in sampling effort.
The focus of this PhD project will be on analysing and developing various statistical methods to assess the advantages and drawbacks of incorporating citizen science data into predictive models. Throughout the research, the student will work with a diverse array of datasets. These will include earth observation data, structured sampling data, and citizen science data. By integrating these different sources of information, the student aims to explore how different approaches can be leveraged in statistical ecology and to understand how they influence prediction uncertainty.
Citizen science data, while valuable, comes with inherent challenges due to its reliance on non-expert participants. The variability in the accuracy and consistency of data collected by the general public can lead to significant uncertainties in the resulting models. Additionally, sampling bias can occur because citizen scientists may preferentially sample certain areas or species, leading to an unrepresentative dataset. Variations in sampling effort, where the intensity and frequency of data collection differ across locations and times, further complicate the analysis.
The PhD student will delve into these issues by applying and comparing different statistical techniques. This comparative analysis will help to identify which methods are most effective at mitigating the drawbacks of citizen science data while maximising its benefits. The goal is to develop robust statistical frameworks that can accurately incorporate this type of data into ecological models, thereby improving their predictive power and reliability.
By combining earth observation data with structured sampling and citizen science data, the student will have the opportunity to cross-validate findings and enhance the robustness of the models. Earth observation data, typically gathered through remote sensing technologies, offers a consistent and comprehensive overview of ecological variables across large spatial scales. Structured sampling, on the other hand, involves systematic and methodical data collection by trained professionals, providing high-quality and reliable data. When these structured approaches are supplemented with the widespread and often extensive data from citizen science, the potential for a more nuanced and comprehensive understanding of ecological patterns and processes increases.
Throughout the course of this research, the student will not only gain expertise in advanced statistical techniques but also contribute valuable insights into the field of statistical ecology. By addressing the challenges posed by citizen science data and developing effective strategies to incorporate it into predictive models, this research will help to advance the integration of diverse data sources in ecological studies. The aim is to enhance the accuracy and reliability of ecological predictions, which can inform better conservation and management decisions.
Mike O'Sullivan
The high latitudes comprise of Arctic and Boreal ecosystems. They currently experience the fastest warming, largest variability (extremes), especially in the winter due to cryosphere – albedo feedbacks. As such they are the canary in the coal mine for climate change and climate-carbon cycle feedbacks, given their enormous carbon stocks above-ground in the boreal forests and below-ground in Arctic tundra permafrost soils. IPCC predicts large future changes in snow cover and permafrost, and it is unclear the magnitude impact on the main greenhouse gases (GHGs), CO2, CH4 and N2O. There is a contemporary carbon sink in the growing season, yet future projections in response to climate change are uncertain. Massive stores of organic carbon are stored in permafrost which will likely become unstable under warming, triggering multiple climate feedbacks. There is also large uncertainty around the magnitude of the C sink in boreal forests; atmospheric inversions suggest a larger sink than process-based models. It has been proposed by this team that this may be link to the representation of forest age in process-based models. We therefore urgently need to focus on disturbance and mortality processes in high-latitudes (e.g. fire, permafrost thaw, wind stress) and both in above- and below-ground carbon stocks.
This PhD would form part of Schmidt future’s, Virtual Earth System Research Institute (VESRI). VESRI aims to use big data and AI techniques to improve Earth System Modelling. Under VESRI, the UEXE are funded through the CALIPSO - Carbon Loss In Plants, Soils and Oceans – project, where we have secured 50% funding for a studentship. The goal of CALIPSO is to make a step change in the representation of carbon loss processes in ESMs for three critical knowledge gaps in the global carbon cycle: tree biomass, soil carbon and marine biota.
James Salter ([email protected])
The overarching aims of this PhD project are to improve emulation and calibration of computer models where the model outputs are high-dimensional, with a focus on methodological development but with motivating applications from environmental models.
For computer models to be informative for studying complex real-world systems and making predictions and aiding decisions in the real-world, models must be properly calibrated, and uncertainties in the model understood. Even with increasing computing power, it is not always possible to run large ensembles of high-resolution models that can completely explore the often-large input parameter space, with emulators required to predict the model output at unseen versions of the inputs, allowing us to better explore the model and aid tuning/calibration of such models. For large output fields (spatial, spatio-temporal, multiple atmospheric levels), emulation approaches are often based around dimension reduction, with SVD a popular choice (Higdon et al 2008, Salter et al 2019). However, this may struggle with extrapolation; when important real-world patterns are not frequently seen in the model; or when there is large variability in the range of model outputs, leading to trade-offs in the basis vectors that can result in non-stationary behaviour in the projected coefficients.
This project will explore and develop alternative methods for emulating high dimensional output fields, with an emphasis on developing methods that can be used efficiently in calibration problems, and for studying model discrepancies (differences between the real world and model-world). Potential directions include: machine learning-based approaches to dimension reduction (convolutional neural networks, variational autoencoders), if the uncertainty in predictions can be properly characterised; and using models of the same system at different resolutions and learning patterns from the faster, lower resolution models and using these to aid emulation of input-dependent patterns at higher resolutions.
In this project, there will be the opportunity to apply methods to real environmental modelling problems, including relating to land surface modelling and atmospheric dispersion/volcanic ash modelling.
Piotr Slowinski
Hand and eye coordination is a basic skill crucial to perform countless daily activities. Hand-eye coordination is shaped by perception and action dynamics, the way we are reacting to external stimuli (e.g., spotting notification and reaching for a mobile phone). The perception and action dynamics depends on sensory-motor and neural latencies, i.e., time it takes to notice stimulus (perception), time to process it and decide on appropriate action (processing) and time it takes to complete the movement (action).
Deficits in perception and action dynamics are frequently observed in neurological and mental disorders. Similarly, it is commonly observed that outcomes of the neuropsychological tests of people experiencing mental health issues differ from the outcomes of typical population. However, understanding of how perception and action dynamics affects outcomes of neuropsychological tests is lacking.
To address this knowledge gap, the project seeks to develop and analyse mathematical models of perception and action dynamics. The models will allow to investigate both sources and effects of (1) slower and more variable reaction times observed in people at risk of or experiencing mental illness (represented in the models as a temporal delay), and (2) variability in sensory processing or inaccuracies in motor execution (represented in the models as a different sources of noise). The models will use a system of non-homogeneous (driven by external signal) delay differential equations (with scalar, distributed or state dependent delays). The equations will describe eyes and hand movement driven by an input signal (e.g., object observed on the screen). The models will include neurologically motivated coupling between hands and eyes. Model analysis will combine dynamical systems theory, computational non-linear dynamics approaches and simulations.
Mathematical modelling will allow to understand complex interactions between parts of the nervous system (eyes, brain, motor neurons, muscles) involved in on eye-hand coordination and perception and action dynamics more generally. The causal/ mechanistic relations encoded in the model parameters (eye-brain-hand coupling, sources of noise, sources of sensory-motor latencies) will allow to precisely define and compare behavioural mechanisms (cognitive/ compensatory strategies) employed by people to complete neuropsychological tests. Crucially, the models will be validated in behavioural experiments using digital versions of neuropsychological tests.
Project outcomes will directly help in development of devices and technologies fostering better mental health (faster and personalised diagnosis), individually adaptive, minimally intrusive monitoring technologies (cheap, non-invasive, portable data collection set-up, suitable for clinic and home) and new methods of recognising abnormal data patterns (based on individual cognitive strategies and objective, model-driven metrics).
In a longer term, understanding relation between perception and action dynamics and cognitive function might revolutionise the way we define symptoms used to diagnose mental health problems e.g., by facilitating development mathematical nosology and neurosymptomatics.
Tanja Schindler
(currently: )
We consider an ergodic system (X, μ, T) and an observable f:X→ℝ. It is one of the most classical problems in ergodic theory to study the long term behaviour of f,...,f∘︎T^n; in particular of the Birkhoff sum f+...+f∘︎T^n. Such systems are often better suited as models than iid random variables as short term dependencies can be taken into account.
Besides the easiest case - to study limit theorems for μ a probability measure and f an integrable (often even very nicely behaved, e.g. Hölder continuous) observable - in the last 10 to 20 years a number of limit theorems have been proven for the following settings:
a) μ is probability measure and f is a non-integrable observable - in this setting often clustering, i.e. the successive occurrence of large events, made those dynamical systems behave qualitatively different from iid random variables with the same distribution function.
b) μ is an infinite measure space and f is either integrable or at least bounded - this setting has e.g. been used to model anomalous diffusion.
In this project the general aim is to combine the above two settings, namely we assume that μ is an infinite measure and additionally f is non-integrable - even non-integrable over a finite measure set. In this setting, both the infinite measure as well as the non-integrable observable influence the qualitative behaviour and it is the aim of the project to study under which conditions each of the two has the leading influence on the system.
The main limit theorems to be proven for such settings are stable laws, extreme value laws, and almost sure limit theorems - possibly two sided and possibly under truncation.
Moreover, a suitable notion of mixing is supposed to be developed. While there are notions like ψ- or α-mixing in the case of random variables over a finite measure space and Krickeberg-mixing for dynamical systems with a infinite invariant measure, so far there is no notion of mixing that helps describing the systems in our setting.
Some of the results are expected to be obtained mostly by a applying a combination of the methods from settings a) and b), e.g. in the case of stable laws or two-sided almost sure limit theorems. These parts of the project can be considered as a lower risk and in an optimal case give already early publishable results.
Depending on the student's progress and interest there are different possibilities in which the project can continue: For instance, there are a number of number theoretic examples which exhibit this behaviour, e.g. different non-standard continued fraction expansions which could give nice applications. On the other hand, there are also a number of zero-entropy dynamical systems (like suspension flows or adding machines) and together with a non-integrable observable they fall into the above described setting - however for them even in setting a) and b) a lot less is known.
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University of exeter, different course options.
Tuition fees, entry requirements, similar courses at different universities, key information data source : idp connect, qualification type.
MPhil - Master of Philosophy
Computer Science
Our main areas of Computer Science research include Artificial Intelligence, Computer Vision, Cyber Security, Data and Network Science, Evolutionary Computing and Optimisation, High Performance Computing and Networking, and Machine Learning.
Research overview
Our main areas of Computer Science research are:
Artificial intelligence research areas focus on social network understanding, remote sensing, human-computer interaction, cognitive science and on the philosophical foundations of artificial intelligence and computer science.
Computer vision research activities include visual attention, autonomous control, collaboration and decision strategies for cooperative robots, deep multi-modal embedding, graph neural networks etc.
Cyber security research mainly focuses on formal methods, security/safety engineering, and software engineering with the aim to build secure, reliable, resilient software and hardware systems.
Data and network science research the phenomena, intrinsic properties and real-world applications of complex networks (such as complex networks and human dynamics), which are often inspired by nature and occur in many real-world contexts including social, biological and neural networks.
Evolutionary computing and optimisation research focuses on developing evolutionary algorithms, genetic programming, hyperheuristics, swarm intelligence and multi- and many- objective versions of these for problems such as hydroinformatics, bioinformatics, optimisation under uncertainty and interactive evolution.
High performance computing and networking investigates the advanced computational and networking challenges associated with the future Internet, 5G mobile networks, cloud and edge computing, unmanned vehicles, and high performance computing.
Machine learning research at Exeter spans the range of data, applications and methodologies from kernel methods to deep neural architectures and reinforcement learning applied to both continuous and discrete, graph-based data.
For this course (per year)
For all research degrees you will normally be required to have obtained or expect to obtain a first degree equivalent to at least a UK 2:1 Honours degree. You will need at least a 2:1 or its equivalent in order to be considered by any of the main funding bodies. For some programmes we also consider evidence of relevant personal, professional and educational experience.
London school of hygiene & tropical medicine, university of london, msc entertainment management & analytics, norwich university of the arts, msc advanced computer science, northumbria university, newcastle, msc artificial intelligence.
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The University of Exeter and Tsinghua University have launched a jointly-awarded PhD degree programme in climate and environmental sciences which supports six students to be co-supervised between Tsinghua's Department of Earth System Science and Colleges at Exeter that conduct research on earth systems and environmental sciences. Read more.
Choosing to study Computer Science at Exeter means you'll learn from teaching that draws directly from our particular research strengths in AI, machine learning, data science, statistical modelling, high performance computing and networks, and cyber-security. We have designed these programmes to support you in lifelong learning, so you can ...
Computer Science at the University of Exeter provides a collaborative and inclusive environment in which students and researchers can advance their knowledge of this dynamic subject and establish foundations for future careers. Our research-led, business-linked programmes explore the breadth of Computer Science and its applications, enabling ...
The programme structure is designed to provide the core concepts in computer science in term 1, such as algorithms and architectures, data systems, programming and security. In term 2 this foundation of knowledge will be extended to the practical domains with the introduction of ethical and governance frameworks as well as professional ...
About. This Computer Science MPhil/PhD programme from The University of Exeter will be given an up-to-date or specialised computer for daily research work. Visit the Visit programme website for more information. The University of Exeter. Exeter , England , United Kingdom. Top 1% worldwide. Studyportals University Meta Ranking. 4.1 Read 71 reviews.
PhD Computer Science. UNIVERSITY OF EXETER. Compare Different course options ... Our main areas of Computer Science research include Artificial Intelligence, Computer Vision, Cyber Security, Data and Network Science, Evolutionary Computing and Optimisation, High Performance Computing and Networking, and Machine Learning. ... based at Exeter ...
A jointly awarded Engineering Doctorate (EngD) from the Universities of Edinburgh, Exeter, Strathclyde and Swansea, offering ten places per year funded by the UK Engineering and Physical Sciences Research Council (EPSRC). Read more. Funded PhD Programme (European/UK Students Only)EngD ProgrammeNERC Centre for Doctoral Training. More Details.
FindAPhD. Search Funded PhD Projects, Programmes & Scholarships in Computer Science at University of Exeter.
We have 20 Computer Science (exeter) PhD Projects, Programmes & Scholarships. Show more Show all . More Details . Optical metasurfaces for multifunctional infrared spectroscopy and hyperspectral imaging. University of Exeter Department of Physics and Astronomy. About the project. Infrared (IR) spectroscopy reveals nearly all chemical/biological ...
Overview. Prof. Jia Hu is an Associate Professor in Computer Science at the University of Exeter. He received his PhD in Computer Science from the University of Bradford, UK, in 2010, and M.Eng. and B.Eng degrees in Electronic Engineering from Huazhong University of Science and Technology, Wuhan, China, in 2006 and 2004, respectively.
The University of Exeter and Tsinghua University have launched a jointly-awarded PhD degree programme in climate and environmental sciences which supports six students to be co-supervised between Tsinghua's Department of Earth System Science and Colleges at Exeter that conduct research on earth systems and environmental sciences. Read more.
This programme is research-led. More than 94% of our Computer Science research outputs are internationally excellent. Students have the opportunity to carry out work on the University's High Performance Computing environment which represents a £3m investment by the University, designed to serve the advanced computing requirements.
The University of Exeter and Tsinghua University have launched a jointly-awarded PhD degree programme in climate and environmental sciences which supports six students to be co-supervised between Tsinghua's Department of Earth System Science and Colleges at Exeter that conduct research on earth systems and environmental sciences. Read more.
We have 5 University of Exeter Computer Science PhD Projects, Programmes & Scholarships. University of Exeter. A Russell Group university with world-class research and high student satisfaction. Find out more. Show more Show all . More Details . AI for the Environment: Collaborative Exeter-Turing PhD Studentship.
The University of British Columbia. Activities between the University of British Columbia and Exeter include a joint research symposium focused on Community, Culture, Creativity, and Wellbeing held at Exeter in May 2018 and a faculty-led, co-funded initiatives in Sport, Exercise and Health Sciences, Climate Change and Digital Humanities.
The University of Exeter and Tsinghua University have launched a jointly-awarded PhD degree programme in climate and environmental sciences which supports six students to be co-supervised between Tsinghua's Department of Earth System Science and Colleges at Exeter that conduct research on earth systems and environmental sciences. Read more.
PhD in Computer Science at the prestigious University of Exeter is a prestigious degree that offers in-depth learning in Computer Science. Being a renowned university, University of Exeter receives enough funds to ensure the best education facilities for its students across all programs. This doctorate program offered full-time primarily focuses on the practical implementation of fresh ideas ...
Professor Neil Vaughan is Associate Professor of Data Science and AI at University of Exeter. He recently completed Royal Academy of Engineering Research Fellowship. ... Professor Neil Vaughan is available to supervise more PhD or post-doc research projects. Current PhD funding opportunities: EPSRC DTP, MRC, China Scholarship Council (CSC) and ...
The University of Exeter and Tsinghua University have launched a jointly-awarded PhD degree programme in climate and environmental sciences which supports six students to be co-supervised between Tsinghua's Department of Earth System Science and Colleges at Exeter that conduct research on earth systems and environmental sciences. Read more.
As an Exeter Computer Science and IT graduate you may find yourself working with business IT systems, the web, mobile communications, games technology, or in the management and development of the safety-critical systems that control planes, trains and power stations.
In the PhD in Computer Science program at Columbia Engineering, you'll find a vibrant, collaborative community of research with broad interests including natural language processing, security and privacy, graphics and user interfaces, computational biology, computer vision, robotics, machine learning, and artificial intelligence. ...
Course Summary. Overview. Our main areas of Computer Science research include Artificial Intelligence, Computer Vision, Cyber Security, Data and Network Science, Evolutionary Computing and Optimisation, High Performance Computing and Networking, and Machine Learning. The. as well as a list of our current postgraduate researchers.
The University of Exeter and Tsinghua University have launched a jointly-awarded PhD degree programme in climate and environmental sciences which supports six students to be co-supervised between Tsinghua's Department of Earth System Science and Colleges at Exeter that conduct research on earth systems and environmental sciences. Read more.