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This is a list of industrial and governmental project proposals from Summer 2016.

End to End MATHS diagnostic review in equipment health monitoring process.

Contact Name Geoff Walker
Contact Email Geoff.walker@artesis.co.uk
Company Name Artesis LLP
Address St John’s Innovation Centre, Cowley Road, Cambridge, CB4 0WS
Period of the Project Mid June - Mid August 2016 (Flexible to be earlier or later if preferred)
Brief Description of Project Artesis LLP identifies and diagnoses problems in industrial equipment, by analysing the distortions on the waveform of the 3-phase AC current drawn by the motor. We already use a whole series of mathematical techniques, some of which are standard techniques like Fast Fourier Transforms, and others that are rather more bespoke, involving System Identification algorithms. Some of these have been in use for over 20 years, others have been developed much more recently. Artesis as a company is predominantly staffed by engineers rather than mathematicians, and whilst the mathematical approaches we use work from a pragmatic point of view, we believe they may not be the optimum or "best practice" techniques from a mathematical point of view, taking into account the massive increase in computing power available to us now compared to 20 years ago, and also the general development in mathematical techniques during the same time. The project will require the Mathematician to carry out an end-to-end review of our processing, understanding the techniques used and how they interact with one another to create usable outputs. Having understood the current situation, the Mathematician is asked to consider what a "best practice" alternative might be to each of the current stages in our process, and evaluate the benefits of changing to the new technique. This should also take into account the overall process rather than just replicating the existing steps one-by-one, so for example an alternative approach might use a completely different set of steps to get from the initial measured parameters to the desired final outputs. The assessment is also to consider how any existing gaps in our process might be filled (we are aware of a couple, which we think are a really interesting challenge - we can describe these at the briefing meeting on Jan 20th) For the areas where benefits are identified, the task will then be to assess what would be required to adopt the new technique, and to develop outline improvement definitions and plans. If time is available, we would hope the Mathematician will then be able to develop one or more of these improvement areas, to create a fully working system.
Skills Required Mathematician! Familiarity with Signal processing techniques - FFT, Windowing, Anti-Aliasing, etc. Familiarity with Linear Regression and its different System structures (AR, ARMAX, etc) and Prediction Error Methods. Comfortable with wave equations. Structured, logical approach. Ability to write about mathematical concepts in plain English, in a way non-Mathematicians can understand. Familiarity with Matlab/Scilab.
Skills Desired Some familiarity with System Identification approaches, possibly including subspace identification methods such as MOESP, N4SID and CVA; Some familiarity, or at least comfort and willingness to learn about, rotating machinery and the behaviour of oil film bearings and rolling element bearings; Possibly, some familiarity with electric motors and electrical theory.

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Structured exploration of clinical trial datasets

Contact Name Paul Metcalfe
Contact Email paul.metcalfe@astrazeneca.com
Company Name AstraZeneca
Address da Vinci Building Melbourn Science Park Melbourn
Period of the Project 8 - 10 weeks
Brief Description of Project When clinical trial results are analysed a rigorous and formal statistical analysis plan is used, in part to avoid an unscientific data dredging exercise. Structured exploration is a middle ground between both rigorous analysis and data dredging. We want to gain the flexibility to explore data in such a way as to improve our understanding of our medicines and improve patient outcomes, but we want to avoid the false results that an uncontrolled approach would generate. The aim of this project is to explore clinical trial data using structured machine learning methods to see how they work in practice.
Skills Required Strong R and computational skills, with an interest in data mining and machine learning.
Skills Desired  

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Modeling Client Behaviour Using Machine Learning Techniques

Contact Name David West
Contact Email david.west@lbbwuk.com
Company Name LBBW
Address 7th Floor 201 Bishopsgate London EC2M 3UN
Period of the Project 8-12 Weeks
Brief Description of Project Developing predictive models for client behavior in Financial Markets is a difficult task. You will be working over multiple asset classes and with high value data sets. A specific problem will be assigned to you and you will have flexibility to decide on your approach. Original ideas are welcome.
Skills Required R Statistical Package. Machine Learning, Feature Extraction. Excellent Communication.
Skills Desired Python with Matplotlib. Interest in Financial Markets.

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Analysis Techniques in Sustainment Research

Contact Name Michael Hartley
Contact Email mchartley@dstl.gov.uk
Company Name Defence Science and Technology Laboratory
Address Michael Hartley Dstl Defence Security and Analysis Division Room C036, West Court Portsdown West Portsdown Hill Road, Fareham Hampshire PO17 6AD
Period of the Project Flexible, ~8 weeks in the summer.
Brief Description of Project Sustainment Analysis: Analysis of sustainment for a deployed military force is undertaken to investigate if the force is able to provide the required amount of supplies at the right location at the right time, based on the deployed logistics capability (i.e. through the use of a deployed number of transport vehicles with specific capabilities). On top of the consideration of the laydown, emergent issues must be dealt with, such as knock on effects of changes to one part of the system. For example a small increase in a route length could cause the journey to exceed a threshold and require time for personnel to rest part way and thus cause a greater than expected demand on the transport capability. There are several ways that such problems can be approached, including system dynamics modelling, various methods of simulation, mixed integer linear programming and simplified spreadsheet calculations, to name a few. Currently sustainment analysis is undertaken by Dstl using spreadsheet calculations; however, this approach can be time consuming and there is a requirement for this assessment to be smarter (quicker and less labour intensive). Task: This task is to investigate potential technical approaches that could be utilised to investigate sustainment analysis for an operational deployment, to complement existing methods. It is essential that the approaches are not focused solely on Defence approaches currently used, as there are expected to be approaches used across different domains that focus on a similar problem space. As an example, systems dynamics methods are expected to be particularly suitable; they are often quick to run, present a more dynamic environment for analysis, potentially better suited to changing situations and allow easier identification of critical factors in a scenario. SD is also used across the world within different areas of research and analysis. The benefits and limitations of the methods investigated should be described and a recommendation for the optimal method (based on effectiveness, speed of data input and runtime and other useful factors) should be provided as a key part of the output from this investigation. Prototyping the best method within this sustainment context would be a particularly useful in illustrating its suitability (time permitting). Example output: A report identifying and evaluating potential technical approaches. A model prototype that can consider a Defence sustainment problem.
Skills Required Good analytical skills Research skills Computer modelling (programming)
Skills Desired Familiarity with a range of operational research techniques/methods Statistics skills Familiarity with supply chain principals

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Analysis of deployed Military Hospital Capability

Contact Name Karen Irvine
Contact Email kirvine@dstl.gov.uk
Company Name Defence Science and Technology Laboratory
Address Logistics And Medical Analysis Team Defence and Security Analysis Division Grenville West C-036 Dstl Portsdown West PO17 6AD
Period of the Project 8 weeks
Brief Description of Project When the UK military deploy on operations, the UK Government’s Ministry of Defence (MoD), have a duty of care, to provide medical treatment to sick and injured UK personnel and captured enemy combatants. In addition, where capacity and circumstances allow, treatment is also offered to indigenous civilians. In order to enable this duty of care, the UK MoD deploys its own medical treatment facilities, including first aid capabilities, battlefield ambulances and emergency evacuation assets, both locally and internationally. There is a trade off in deploying medical facilities that are too small to meet demand and deploying facilities with large amount of excess capacity that places additional medical staff at risk of attack, as well as increasing the logistic burden and mission cost. The task is to design a technique, tool or model that will allow the MoD to conduct analysis on the requirement for and capability of medical treatment facilities, given an expected number of patients and resources available (equipment, personnel and commodities). The design should account for: • Various types of patient (e.g. disease, accidents, varying severity of battle casualties) • Various types of patient treatment areas and resources (e.g. general ward, isolation ward, intensive treatment units, operating theatres) • Various types of staff (e.g. nurses, doctors, surgeons) • Resource availability (e.g. equipment, personnel) • Patient / casualty arrival rates.
Skills Required Modelling, Operational Research, Optimisation ,Queueing theory, Benefits analysis
Skills Desired Multi criteria decision analysis, Programming, Statistical analysis

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Identification of Radar Targets from 4-D Image Processing

Contact Name Tim Darlington
Contact Email timothy.darlington@metoffice.gov.uk
Company Name Met Office
Address Met Office, Fitzroy Rd, Exeter, Devon EX1 3PB
Period of the Project Summer 2016
Brief Description of Project The UK weather radar network is required to map rain, snow, hail etc. However, the radars detect everything in their field of view that is more than mm size - insects, aircraft, birds, ships, buildings, masts, trees, hills. Current target discrimination algorithms make use of a wide range of radar parameters and supporting data, rely on 3-D spatial information in the radar data. Subjective analysis of the image data suggests that useful extra information lies in the time dimension. Processing capacity is now available to develop 4-D target discrimination algorithms. The project is to identify suitable techniques.
Skills Required Experience of linux or Unix and computer programming
Skills Desired Linux and Python

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Observational Network Design

Contact Name Mike Molyneux
Contact Email mike.molyneux@metoffice.gov.uk
Company Name Met Office
Address Met Office, Fitzroy Rd, Exeter, Devon EX1 3PB
Period of the Project Summer 2016
Brief Description of Project Meteorological observations are required to initialise and verify weather forecasting models; monitor the climate and some other applications. A wide range of platforms, instruments and sensors are deployed in the UK and globally in order the meet the diverse requirements. No objective methods are available for optimising the design of the total network (e.g. number and distribution of sensors), so this currently relies heavily upon experience and scientific intuition. The project is to see whether by combining limited available quantitative information, with some (heroic) assumptions, network design can be placed on a firmer footing.

Human-in-the-loop Medical Operational Research

Contact Name Laura Brudenell
Contact Email lmbrudenell@dstl.gov.uk
Company Name Defence Science and Technology Laboratory
Address Dstl Portsdown West Grenville Building Room C036, iSat J Fareham, Hants PO17 6AD
Period of the Project Summer 2016
Brief Description of Project The use of modelling and simulation is a vital capability in the process of planning military operations. Aspects such as hospital bed usage, MEDical EVACuation (MEDEVAC) of casualties from their point of wounding to a medical treatment facility and the STRATegic EVACuation (STRATEVAC) of patients from a deployed hospital can be modelled and the outputs analysed in detail, in order to support military planning decisions. The modelling capabilities described above are reliant upon user input and are currently unable to account for the ‘Human-in-the-Loop’ (HITL) concept. The aim of this work would be to identify the points in a process or system where a human would be required to make a decision and to explore the decision logic within the model that should be applied as a result. A HITL simulation model should give the user the ability to simulate and test different medical laydowns and different resource and asset allocation decisions, in order to explore the effect this will have on the scenario. The main mathematical focus of this task would be to investigate and implement the methods for coding the HITL concept. Outputs to include: A report identifying and evaluating potential technical approaches A model prototype considering a Defence HITL medical problem (time permitting) Suggested Reading: Schumann et al. Modeling Human-in-the-Loop Security Analysis and Decision-Making Processes, IEEE Transactions on Software Engineering, Vol 40. No 2 February 2014
Skills Required The student should have good analytical skills and knowledge of computer modelling and coding methods.
Skills Desired Knowledge of Operational Research methods Understanding of logistics principles Understanding of the medical care pathway (military) Software engineering Systems engineering Problem structuring Identifying relationships and system interactions

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Bookmaker stake optimization in sports betting

Contact Name Paul Doust
Contact Email paul@pauldoust.com
Company Name A private gambling syndicate
Address 52 Duncan Terrace Islington London N1 8AG
Period of the Project Summer 2016
Brief Description of Project A lot of professional gamblers use schemes based on the Kelly Criterion to work out how much to bet. The Kelly Criterion was published by Kelly in 1956 in the Bell Systems Technical Journal, and little academic work appears to have been done in this area since then. In particular, bookmakers face situations that are more complex that the simplistic scenario that the Kelly Criterion is based on. The broad aim of the project will be to do a little bit of research in this area. The host for this project completed his PhD in theoretical high energy physics in DAMTP in 1987, had career as a trader and quantitative analyst in the financial markets, and now runs a successful sports gambling syndicate.
Skills Required A keen desire to apply maths and computer skills to real life situations Probability and statistics Computer skills, e.g. Monte Carlo simulation, Excel spreadsheets Because little work has been done in this area, it's *possible* that there may be analytic results to derive and theorems that can be proved, but that will take time. However, it is hoped that useful results can be obtained in a short project using computer simulations.
Skills Desired  

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Future of the cities: Monitoring and data analytics for urban environment using satellite and terrestrial data sources

Contact Name Elena Baron and Stephane Ctretein
Contact Email elena.barton@npl.co.uk
Company Name NPL Mathematics and Modelling
Address National Physical Laboratory Hampton Road Teddington Middlesex TW11 0LW
Period of the Project summer 2016
Brief Description of Project The project is concerned with data analysis and time series. The goal of the project is to find meaningful correlation between data sources of different natures (satellite data and ground sources data) for the purpose of studying the ground movements at a city scale. This study will make use of cutting edge technology for data collection and new methodologies for data analysis. The student will have to select the most appropriate and efficient methods for this study and apply it to a specific real life example, e.g. validation of subsidence hazard score algorithm against satellite data and insurance claims.
Skills Required Data analysis, Time series, Correlation analysis, Matlab programming.
Skills Desired Model selection, Model averaging, Aggregation, State space models, Kalman filtering.

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Mathematical Modelling in Drug Discovery

Contact Name Dr James Yates
Contact Email james.yates@astrazeneca.com
Company Name AstraZeneca
Address Li Ka Shing Centre (Cambridge Institute), Robinson Way, Cambridge CB2 0RE, U.K.
Period of the Project 8 weeks
Brief Description of Project Mathematical modelling is used in drug discovery to understand the relationship between dose, dosing frequency, resulting drug concentration in blood and other tissues and biological effect (including hopefully disease modification). In this placement the student will investigate mathematical models (desctibed by ODEs) that describe the cell cycle including cell cycle control due to DNA response and repair. The focus will be on deriving parsimonious models that describe the known biology but can be supported by experimental data.
Skills Required some background in ordinary differential equations and dynamic systems analysis
Skills Desired some statistics (including maximum likelihood estimation of parameters) Programming in matlab

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Application of Monte Carlo Estimators for the Fast, Efficient Calculation of Complex Option Greeks in the Presence of Stochastic Volatility

Contact Name Robert Doubble
Contact Email robert.doubble@bp.com
Company Name BP Oil International Ltd
Address BP Oil International 20 Canada Square London E14 5NJ
Period of the Project 3-4 months
Brief Description of Project The pricing of certain financial instruments offered by BP IST’s Global Structured Products team to external customers for the management of fuel price risk are sensitive to the dynamics of the implied volatility surface, for example compound options and TARN-like products. A robust valuation of these derivatives in the domain of energy and commodities therefore requires both a stochastic description of the price term structure, and the volatility dynamics, see for example [1]. Because of the complexity of the derivative payoffs Monte Carlo simulation is typically used to determine the option premium and Greeks. Finite difference estimators, whilst simple to implement, may not offer the right balance of speed, efficiency and un-biasedness required to support a material derivatives trading activity. The purpose of this project is to empirically determine, by means of numerical testing, the relative merits and demerits of finite difference, path-wise, likelihood ratio method and adjoint estimators for the option Greeks, for the stochastic volatility price process described in [1], and for a range of option pay-offs, including vanillas, Asians, calendar spread options, best-of and baskets. The interested reader is referred to [2] and [3], and references therein. [1] L.B.G Andersen (2008), Markov Models for Commodity Futures: Theory and Practice [2] M. Broadie and O. Kaya (2004), Exact Simulation of Option Greeks Under Stochastic Volatility and Jump Diffusion Models [3] M. Giles and P. Glasserman (2005) Smoking Adjoints: Fast Evaluation of Greeks in Monte Carlo Calculations
Skills Required Some experience of computer programming. Knowledge of Black Scholes option pricing and stochastic calculus
Skills Desired Familiarity with Python Knowledge of Monte Carlo simulation techniques applied to Mathematical Finance Some knowledge of the Heston Stochastic Volatility model

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