# Interns 2010

Below you can find details of interns from summer 2010, including a description of their research project. Click here to view the weekly blog written by 2010 interns. **Helen BlueLancaster University, MSci Mathematics (2008-2012) Supervisor: Richard Eglese**

** Optimisation on road networks**There are many problems that involve optimising an objective that is relevant to journey planning over a road network. The first part of the project will be to review some of the existing methods for finding shortest (or least cost) paths in a network. The second part of the project is to develop an effective algorithm for finding the least cost path between two points where the speed and cost of travelling along an arc depends on the time of day.

**View Helen's presentation and poster. Rhian DaviesLancaster University, BSc Mathematics (2008-2011) **

**Supervisor: Dennis Prangle**

** Investigation of Approximate Bayesian Computation**For many complex phenomena, fitting realistic statistical models is mathematically intractable by standard methods. A recent computational alternative is to repeatedly simulate the model to find good fits. This project investigates one such method (Approximate Bayesian Computation) on data from a Tuberculosis outbreak. The aim is to assess various implementations of this method through computer experiments, which will involve exposure to modern statistical methods and software.

**View Rhian's presentation**

**and poster.**

**Jamie Fairbrother**

University of Warwick, MMath Mathematics (with a year abroad: Europe) (2006-2010)

Supervisor: Idris Eckley

Wavelets are a recent and powerful mathematical tool which were developed in the 80s. They provide a novel way of decomposing the information within signals and images, providing information at various scales (you can think of these as viewing windows). Texture analysis is a particular application area in which wavelets have been successfully used in recent years. Broadly speaking the texture of an image is the visual character of a region whose structure is, in some sense, regular (e.g. the appearance of a woven material). This project will investigate the potential of wavelets and related methods to modelling structure within textured images.

University of Warwick, MMath Mathematics (with a year abroad: Europe) (2006-2010)

Supervisor: Idris Eckley

*Multi-scale methods for texture analysis*

Dave Grant

University of Manchester, MMath Mathematics (2006-2010) **Supervisors: Navid Izady and Dave Worthington**

** Time-Dependent Queueing Systems**In general, in the area of mathematical modelling, modellers often make simplifying assumptions in order to make a problem ‘solvable’. In doing so the modeller is hoping that the solutions produced by the simplified model will nevertheless be valid (in some sense) despite the simplifying assumptions. Important examples in the area of modelling queueing systems are, for example, call centres, accident and emergency departments, hospital emergency admission units, intensive care units. Our interest is in modelling aspects of such queueing systems that typically exhibit time of day (and possibly day of week) variations in their underlying arrival rates of ‘customers’ as well as the usual stochastic variation in arrival times and service times.

**View Dave's presentation and poster.**

**Rachael GriffithsLancaster University, MSci Mathematics with Statistics (with a year abroad: Australia National University) (2007- 2011)**

**Supervisor: Ben Taylor**

** Dynamic modelling for wind-prediction**Dynamic linear modelling is a technique for the analysis of time series data when the governing parameters of the model themselves evolve over time. In particular, it is easy to obtain predictions using these methods. This project concerns the short term modelling and prediction of wind speeds and hence power output at wind farms. The application is important in deciding whether a potential new site will deliver an acceptable amount of energy.

**View Rachael's presentation and poster.**

**Dominic Hickie**

Lancaster University, MPhys Physics with Particle Physics and Cosmology (2007-2011)

Lancaster University, MPhys Physics with Particle Physics and Cosmology (2007-2011)

**Supervisor: Chris Kirkbride**

** Pricing on-demand online services**Cloud computing is a relatively new concept for Internet based computing in which resources, software, information and applications are provided to user devices (PC, laptop, mobile) on-demand. This project will consider various models for the cloud environment in order to determine how resources can best be utilised to meet demands for service and how to price such services effectively.

**View Dominic's presentation and poster.**

**Samantha Hinsley**

**Lancaster University, BSc Mathematics (2008-2011)**

Supervisor: Jenny Wadsworth

Supervisor: Jenny Wadsworth

*Examining applicability of a new technique for threshold selection in extreme value modelling*

It is the extreme values that are important in many applications, such as flooding, stock market crashes, and wind storms. To estimate the frequency of extreme events a statistical model is fitted to the extreme values and extrapolated to the value of interest. This project is concerned with investigating appropriate probability models for “extreme values”, or more precisely the tails of a probability distribution. However there is a challenge in defining what makes a value “extreme”, i.e., from what point should we begin to model the tail? The project will look at examining the applicability of a new method for helping to define a suitable threshold. This project will involve mathematical computation and exposure to real-life problems using a variety of different data sets.**View Samantha's ****presentation**** and ****poster****. **

**Nicola Huxley**

Lancaster University, MSci Mathematics (with a year abroad: Australia National University) (2007- 2011)

Supervisor: Rebecca Killick

Lancaster University, MSci Mathematics (with a year abroad: Australia National University) (2007- 2011)

Supervisor: Rebecca Killick

** Detecting changes in mean**In recent work we collaborated with a company to identify whether there was a change in storminess in the Gulf of Mexico. This project arises out of this work. Detecting changes in properties, such as the mean, of a process are important in many other areas of research such as quality control. Although there are many algorithms designed to detect changes in mean, there has been little comparison of the performance of these algorithms. This project will provide an opportunity to research different algorithms, program them and then conduct simulation studies to test their performances under various circumstances.

**View Nicola's presentation and poster.**

**Robert MaidstoneLancaster University, BSc Mathematics (2008-2011)**

**Supervisor: Adam Letchford**

** The Change-Making Problem**The

*Change-Making Problem*is concerned with finding the minimum number of coins needed, in a given currency, to reach a certain amount. Suppose, for example, you are in Britain and you wish to give somebody 39

*p*. The minimum number of coins needed is five (20

*p*, 10

*p*, 5

*p*, 2

*p*, 2

*p*). If you were in the US and you wish to give somebody 39

*c*, the minimum number of coins is six (25

*c*, 10

*c*, 1

*c*, 1

*c*, 1

*c*,1

*c*). This topic may seem, at first sight, to belong to recreational mathematics but it is in fact a classical operational research (OR) problem with many applications.

**View Robert's presentation and poster.**

Tim Park

Lancaster University, MPhys Physics (with a year abroad: North America) (2006-2010)**Supervisors: Idris Eckley & Matt Nunes**

** Non-stationary time series analysis**Most signals (i.e. time series) observed in the real-world are non-stationary in their nature. This project will explore the behaviour of datasets related to financial data. We will investigate the structure of these signals using wavelets – a form of localised basis functions. The project will give an opportunity to learn about wavelets, their application to time series and provide experience of conducting advanced exploratory data analyses.

View Tim's presentation and poster.

Emma Ross

University of Edinburgh, MA Mathematics (2007-2011)

View Tim's presentation and poster.

Emma Ross

University of Edinburgh, MA Mathematics (2007-2011)

**Supervisors: Yifei Zhao and Stein W. Wallace**

**Facility layout, in its simplicity, is about where to place different machines on a production floor in situations where the use of conveyor belts is not possible because the different products do not all visit all the machines and, even if they did, not necessarily in the same order. So transportation of the products from machine to machine can be complicated if the machines are far apart. In fact, it can result in total chaos. The ultimate goal is to place machines close to each other if it is likely that products need to be transported between them. The problem we study is simply: how should the machines be placed on the production floor? To do this we shall solve numerically small cases of the problem so as to try to understand the emerging structures (designs).**

*Facility layout*

**View Emma's presentation and poster.**

**Ben SlomanUniversity of Oxford, BSc Mathematics (2009-2012) **

**Supervisor: Ye Liu and Jonathan Tawn**

** Selecting a portfolio in finance**In finance the aim is typically to make as much money as possible while incurring as little risk as possible. One way of reducing the risk is to hold a selection of investments (a portfolio). However as some investments are correlated then statistical methods are required to find the best way of balancing risk and expected return. In this project you will explore the basic assumption that returns of investments are multivariate normal using a range of financial data and investigate some extensions of this assumption which are more realistic and result in better decision making in optimising the portfolio choice. The project will involve a real problem with real data, the need for statistical modelling, simulation and optimisation.

**View Ben's presentation and poster.**

**Michael ThistlethwaiteUniversity of Birmingham, BSc Physics (2008-2011)**

**Supervisor: Stephan Onggo**

** Agent-based Physical Asset Maintenance Simulation Modelling**Physical assets such as houses, motorways/roads, water pipes and electrical networks need maintenance because the condition of a physical asset deteriorates with time and usage. The risk of an asset failure (e.g. flooding) or not being able to provide the required service quality (due to weak water pressure) increases as the assets condition decreases. The cost of a repair/replacement process, including the liability incurred due to an asset failure, can be very high. Therefore, a good maintenance strategy is needed. In this project, we will use one of the least explored OR modelling techniques for evaluating asset maintenance strategies, that is, an agent-based simulation model.

**View Michael's presentation and poster.**