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This is a list of project proposals from Summer 2015.

Optimal Project Funding Decisions under Uncertainty

Contact Name Nektarios Oraiopoulos
Contact CRSid no245@cam.ac.uk
Lab/Department Judge Business School
Address Trumpington Street, Cambridge
Period of the Project Summer 2015 (exact dates to be agreed)
Brief Description of Project Within the highly uncertain and complex environment that most organizations operate, resource allocation decision can be particularly challenging. In particularly, organizations are prone to the two fundamental types of decision errors: failing to support an initiative that would have been successful (Type I error), or pursuing projects that are bound to fail (Type II error). The problem is further complicated by the fact that such decisions are often made by committees of decision makers who tend to have diverse preferences regarding the potential of the project. In this study, we aim to understand how the properties of the distribution (e.g., variance) of preferences of the decision makers affect the project termination time, along with the likelihood of Type I and Type II errors.
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Skills Required Dynamic Programming, Matlab (preferably)) or Mathematica
Skills Desired An interest in financial/business contexts.
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Weather Prediction with the Met Office

Company/Lab The Met Office
FitzRoy Road, Exeter
Devon EX1 3PB
Contact Name Sharon Jewell and Robert Scovell
Contact Email Address Sharon.jewell@metoffice.gov.uk,Robert.scovell@metoffice.gov.uk
Brief Description of Project Two projects are available:
1) Optimal merging of rain gauge and weather radar rainfall data using Kriging. (contact Jewell)
2) Understanding the correlation of irregularly spaced radar observations to improve the creation of regularly spaced 3d gridded data. (contact Scovell)
Skills Required Experience in programming; specifically the ability to code in either Python or FORTRAN (Project 1) or Python or C++ (Project 2)
Skills Desired Experience using Linux operating systems.
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Vegetation responses to climate and CO2 changes

Contact Name Andrew Friend
Contact CRSid adf10@cam.ac.uk
Lab/Department Geography
Address Department of Geography
University of Cambridge
Downing Place CB2 3EN
Cambridge
Period of the Project mid-June to mid-August (flexible)
Brief Description of Project Plant growth models have tended to be driven by photosynthesis routines treating fairly detailed plant biochemistry. These approaches have been incorporated into regional and global scale models of the global carbon cycle. They have predicted a substantial historical and future effect of CO2 fertilization, with major impacts on the forecasted growth rate of atmospheric CO2. However, the subject of CO2 fertilization of plant growth is highly controversial. Our group has a number of novel ideas concerning how to model plant growth that takes as its starting point the internal control of growing regions ('meristems'), such that the plant controls photosynthesis rather than the other way round. A range of mathematical approaches have been attempted so far, but none has been stable or proved rigorous to date. We would like a mathematician to assess what we have done, the ideas behind our theories, and potentially suggest/write a new approach. This would be done in close collaboration with members of my research group, and may result in a completely new approach to modelling plant growth, and new insights into the potential future response of the global biosphere to environmental change.
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Skills Required Programming
Skills Desired Appreciation for the functioning of biological systems. Fortran 90.
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eQTL-GWAS colocalisation to identify causal genes for type 1 diabetes

Contact Name Chris Wallace
Contact CRSid chris.wallace@cimr.cam.ac.uk
Lab/Department JDRF/Wellcome Trust Diabetes and Inflammation Laboratory
Address  
Period of the Project 8-10 weeks ending early to mid-September
Brief Description of Project See here
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Skills Required You should have excellent computational skills including basic shell or other scripting language, understand how to distribute jobs across a cluster of computers, and a willingness to learn R, given example scripts.
Skills Desired Previous experience with R
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Decoding Life

Contact Name Philip Wigge
Contact CRSid lp15
Lab/Department Sainsbury Laboratory
Address

47 Bateman Street
CB2 1LR

Period of the Project 8 weeks
Brief Description of Project

Regulatory logic of transcription

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Skills Required Mathematical and computer coding skills. A curious mind.
Skills Desired See above
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Formalisation of Mathematics using Isabelle

Contact Name Lawrence Paulson
Contact CRSid lp15
Lab/Department Computer Laboratory
Address 15 JJ Thomson Avenue
Cambridge CB3 0FD
Period of the Project 15/6/2015 - 15/8/2015
Brief Description of Project Isabelle/HOL is an interactive theorem prover for higher-order logic. A substantial amount of mathematics has already been formalised using Isabelle, such as measure and probability theory and fragments of number theory and complex analysis. But there is much, much more that could be formalised. The purpose of formalising mathematics within such a software system is twofold: (1) to highlight subtleties in traditional proofs, including degenerative and admitted cases (2) to develop a digital repository of mathematical knowledge (including proofs) that can be used as a foundation for modelling and verifying a variety of systems.
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Skills Required Knowledge of undergraduate-level logic
Skills Desired Prior experience with other proof assistants, such as Coq, would be helpful, though training can be given.
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Explaining quantum dynamics algorithms

Contact Name Dr Tim Hele
Contact CRSid tjhh2@cam.ac.uk
Lab/Department Chemistry
Address Department of Chemistry
University of Cambridge
Lensfield Road
Cambridge
CB2 1EW
Period of the Project 8 weeks (negotiable)
Brief Description of Project The computation of accurate quantum dynamics is a long-standing intractable problem, but there exist a number of ad hoc methods which appear to do surprisingly well. The successful applicant will examine the (sometimes minimal) justification for them, and if possible derive analytic expressions for their error from the exact quantum result. In doing so they could provide an explanation for the success (and occasional failure) of such methods, and inform the scientific community of when and why they will be valid.
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Skills Required Basic knowledge of quantum mechanics, and enthusiasm.
Skills Desired Time-dependent quantum mechanics, classical dynamics, partial differential equations.
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Analysis of Geometry for the Design of New Self-Assembled Structures

Contact Name Prof Jonathan Nitschke, Dr Tanya Ronson
Contact CRSid jrn34@cam.ac.uk, tr352@cam.ac.uk
Lab/Department Department of Chemistry
Address Lensfield Road
CB2 1EW
Period of the Project Summer - timing flexible
Brief Description of Project The Nitschke group has characterised through X-ray crystallography a substantial collection of polyhedral (and less regular) molecular cages, prepared through the self-assembly of simple organic molecules around transition metal ions. Based upon what we have observed so far, we can infer in broad terms whether a proposed structure is likely to be stable, but not quantify this stability.

This project would involve working with Dr Tanya Ronson, a senior postdoc and the group’s crystallography expert, to analyse our library of crystal structures in order to quantify the geometrical parameters characteristic of a stable structure. This process will likely involve abstraction of key features of the geometries of molecular building blocks and the metal ions that link them together and analysis of the degrees of freedom explored by the system during self-assembly. Statistical analysis would likely be undertaken upon geometry data extracted from X-ray crystal structures.

We would aim to generate a model able to predict how a given set of building blocks and metal ions are likely to self-assemble, if at all. A high-impact publication is likely to result

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Skills Required Computer modeling
Statistical analysis
Basic geometry
Skills Desired Some knowledge of / affinity for chemical crystallography and coordination chemistry
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Sensitivity of surface growth to nucleation events

Contact Name Austen Lamacraft
Contact CRSid al200@cam.ac.uk
Lab/Department Physics
Address Cavendish Laboratory, JJ Thomson Avenue.
Period of the Project 8 weeks
Brief Description of Project The past decade has seen a revolution in our understanding of a class of stochastic models describing the evolution in time of an interface between two phases. Because an extended interface consists of an infinite number of fluctuating degrees of freedom, their study fits into the class of problems known as dynamical critical phenomena, described by strongly coupled quantum field theories.

A universal description of these phenomena is provided by a stochastic partial differential equation called the KPZ equation (after its inventors: Kardar, Parisi, and Zhang). While the KPZ equation provides a overarching framework, a lot of progress has arisen from the analysis of specific models. The goal of this project is to use one such model, called Polynuclear Growth (PNG) to study the effect of changes in the random nucleation events that cause the interface to grow.

This will involve numerical simulation of the model — which is easy as it has very simple rules — coupled with a theoretical analysis of the simulation data to extract the universal scaling functions describing the sensitivity to disorder.

Some useful background can be found in Section 1 of Viktor S Dotsenko 2011 Phys.-Usp. 54 259 http://iopscience.iop.org/1063-7869/54/3/R02/

You can play with Java simulations of the model (and others) at http://wt.iam.uni-bonn.de/ferrari/research/#animations

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Skills Required Computational modelling skills (e.g. in Python)
Skills Desired Some background in critical phenomena and statistical physics would be desirable.
Any Other Information Any questions, please email Amy Rimmer (ajr80)

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Improving Quantitative Optoacoustic Tomography for Tissue Oxygenation Mapping

Contact Name Dr Sarah Bohndiek
Contact CRSid seb53@cam.ac.uk
Lab/Department Physics
Address Biological and Soft Systems Sector
Cavendish Laboratory
JJ Thomson Ave
Cambridge
CB3 0HE
Period of the Project minimum 8 weeks
Brief Description of Project

Optoacoustic tomography is an emerging imaging modality using nanosecond laser pulses to precisely map the location of absorbing molecules in living subjects, and in particular, blood oxygenation. Excited molecules emit ultrasound waves allowing us to pinpoint their location using standard detection techniques with high precision. Image quantification relates the signal intensity to the actual concentration of the absorbing molecules in a given tissue.

As in other tomographic modalities, a 3D image is formed by combining data from 2D slices together. However, the limited focusing ability of the acoustic transducers means that some regions of the imaged slice receive signal contributions from pixels from nearby slices, distorting the intensity map in the final image and in turn affecting our ability to accurately quantify the concentrations of the absorbing molecules in the slice.

This project aims to evaluate for each pixel of the slice the amount of signal intensity coming from nearby slices and apply a global correction matrix to the image to compensate for this effect. The goal is to achieve a more accurate signal intensity map for image quantification. To realise this goal, it will be necessary to apply the Boltzmann equation to calculate the scattered light intensity in neighbouring planes, and use acoustic wave propagation to find which out-of-plane pixels are relevant for corrections and map them to the related slice pixels.

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Skills Required Prerequisites for this project are a working knowledge of MATLAB, systems of differential equations and numerical methods including finite volume differences.
Skills Desired  
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Constrained downsampling of molecular electrostatic potentials for molecular footprinting

Contact Name Prof. Chris Hunter
Contact CRSid ch664@cam.ac.uk
Lab/Department Chemistry
Address

Hunter Group
Department of Chemistry
Lensfield Road
Cambridge CB2 1EW

Period of the Project 8 weeks
Brief Description of Project

Molecular electrostatic potentials (MEP) are three dimensional maps which indicate the potential a proton would feel in the region around a molecule and can be calculated using quantum mechanical methods. From this continuum, specific regions that interact with other molecules, in a non-covalent manner, may be identified and abstracted as a set of, coarser, discrete interaction sites, termed surface site interaction points (SSIPs). In turn, useful macro scale properties, such as the molecule’s free energy of solvation may be inferred by the interactions between an ensemble of SSIPs[1].

The algorithm for determining the location of SSIPs can be considered a constrained optimisation. For a typical molecule, quantum chemistry calculations produce a MEP surface described by thousands of xyz coordinates each with an electrostatic potential. The number of SSIPs required is approximately 100-fold smaller, and we require a method to identify which sites we should pick from the MEP. The optimal set of SSIPs are the set of points from the MEP that maximize the sum of the electrostatic potentials.

The current algorithm we are using is very inefficient and produces a best guess rather than a defined solution. The result is that for certain molecular topologies, unphysical artifactual anisotropies manifest. We have already attempted ensure rotational invariance by sampling multiple molecular orientations when generating the starting MEP, but we would like to investigate the SSIP selection method from a formal mathematical point of view.

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Skills Required Experience with working in a unix/linux environment.
Skills Desired Familiarity with JAVA, python and git.
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