2017 CMP Academic Project Proposals

The objective is to find a full analytical solution with mathematical techniques originated from Quantum Mechanics. The level of noise will be calculated for different Mach numbers, nozzle geometries and flow configurations. The analytical solution will overcome the approximate asymptotic methods used in the literature and industry.

- Fluid dynamics and/or acoustics
- Hyperbolic Partial Differential Equations
- Perturbation methods

Over recent years we have been actively developing new data processing methodologies that enable the reconstruction of NMR data that is incompletely sampled in the time domain. Generally these methods are termed 'non uniform sampling’ (NUS) and typically these methods require non-Fourier Transform reconstruction techniques to convert irregularly sampled time domain data into the frequency domain. We have been working on the development and implementation of methodologies known as 'compressed sensing’ (CS), based on l_p-norm minimisation, where typically p=1. CS arose in the literature of information theory [1], [2] and has been applied widely for example in MRI [3] and NMR [4], [5] as well as other areas such as image compression, astronomy, tomography etc. [6]. The area is revolutionising the NMR field allowing us to obtain information which was previously inaccessible, and increasing the range of challenging biomolecules and scenarios which NMR can study. The main benefits of the combination of NUS recording and CS data reconstruction are increases in signal-to-noise and spectral resolution, both typically limiting factors in NMR spectroscopy.

Our current interests are the following:
1)Algorithm development
CS is an actively developing area within applied maths. New algorithms are regularly released with improvements in speed and reconstruction accuracy. We are interested in implementing some of these new algorithms for NMR data processing and assessing any improvements over the existing algorithms. This would require a literature search to identify new algorithms and then coding the algorithm within our existing software package for application to NMR data reconstruction.

2)Reducing the sampling requirements with prior information
Prior information is often available in NMR studies from existing experiments. Repeat measurements frequently look at spectral changes (difference experiments) to track biological processes. This prior information should allow a substantial reduction in sampling requirements. This would involve working with, for example, protein dynamics data and developing the existing algorithm to use available prior information.

3)Investigating the optimum sampling requirements
A currently under-explored area of this field is determining the optimum sampling schedule to use for data acquisition. While some general principles are understood [7], the requirements are likely to vary dependent on the properties of different experiments [8]. A good/bad sampling schedule can have a significant impact on reconstruction quality. Consequently a significant part of this research will involve developing metrics to assess the quality of different schedules and identifying optimum schedules for different experiments.

4)Develop GPU (graphical processing unit) approaches
Reconstruction times for CS processing of NMR data benefit significantly from parallelisation. GPUs are a currently under-exploited resource in this area. Adapting the existing code to use GPUs would provide further significant speed-ups in processing time, further expanding the range of experiments that can be studied.

References:
[1]E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.,” IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489–509, Feb. 2006.
[2]D. L. Donoho, “Compressed sensing.,” IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289–1306, Apr. 2006.
[3]M. Lustig, D. L. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging.,” Magn. Reson. Med., vol. 58, no. 6, pp. 1182–1195, Dec. 2007.
[4]D. J. Holland, M. J. Bostock, L. F. Gladden, and D. Nietlispach, “Fast multidimensional NMR spectroscopy using compressed sensing,” Angew. Chemie Int. Ed., vol. 50, no. 29, pp. 6548–6551, Jun. 2011.
[5]K. Kazimierczuk and V. Y. Orekhov, “Accelerated NMR spectroscopy by using compressed sensing,” Angew. Chemie Int. Ed., vol. 50, no. 24, pp. 5556–5559, Apr. 2011.
[6]D. J. Holland and L. F. Gladden, “Less is More: How Compressed Sensing is Transforming Metrology in Chemistry,” Angew. Chemie Int. Ed., vol. 53, pp. 13330–13340, 2014.
[7]S. G. Hyberts, H. Arthanari, and G. Wagner,

The project is focused on using a combined approach of cell biology, molecular genetics, and mathematical modelling to visualize and quantify hormone levels that contribute to plant cellular growth. The plant hormone gibberellin (GA) is a powerful growth regulator that controls key developmental transitions such as germination, flowering and fruiting. The Jones group is using a novel FRET biosensor for GA (GPS1) to reveal GA patterns and dynamics in living plants. As a first step, GA will be visualized (using GPS1 biosensor) in growing cells using confocal microscopy, and a spatiotemporal map of GA levels and cellular growth rates will be developed. To test hypotheses about the dynamic relationship between GA levels and cell growth, GA levels will be manipulated using mutant plants defective in GA biosynthesis and treatments with exogenous GA. The quantitative data generated from these experiments will be used to feedback on ongoing 3D finite element model of growing cells, and the key predictions of the models will be tested through the experimental approaches. We anticipate an iterative combination of modelling and experimental work leading to a holistic understanding of how spatiotemporal patterns of GA growth hormone quantitatively and mechanistically relate to cellular growth.

The student will gain experience in: 1. plant culture methods; 2. cutting-edge confocal microscopy techniques (FRET) to collect 3D time-lapse images of GA levels and cellular growth in growing cells; 3.advanced 4D image processing; 4. develop metrics describing the quantitative relationship between GA levels and cell growth; 5. participate in the ongoing development of a 3D finite element computational model aimed at integrating GA hormone levels, physical properties of cell wall, and cellular growth. The student will work closely with a postdoc (Ankit Walia) to collect and analyze data.

This project is self contained.

[1] Sato et al. Nature 469, 415–418 (20 January 2011) doi:10.1038/nature09637
[2] Graner, F., Glazier, J.A.: Simulation of biological cell sorting using a two dimensional extended Potts model. Phys. Rev. Lett. 69, 2013–2016 (1992)

This project will look at different methods to normalise this data and see how they are affected by missing data. Possible parts of the project depending on ones background and interest might include
- simulating idealised datasets for normalisation (require general coding)
- normalising real datasets using different methods (requires R experience)
- developing a novel normalisation method (more mathematical)

The project is self contained.

[1] A step-by-step workflow for low level analysis of single cell RNA-seq data with bioconductor, Lun AT, McCarthy, DJ, Marioni JC, F1000Res. 2016 Aug 31;5 2122.

References
[1] Studer V, Bobin J, Chahid M, Mousavi HS, Candes E, Dahan M. Compressive fluorescence microscopy for biological and hyperspectral imaging. P Natl Acad Sci USA 2012;109:E1679-E1687
[2] Zhao R, Wang Q, Shen Y, Li J. Multidimensional dictionary learning algorithm for compressive sensing-based hyperspectral imaging. Journal of Electronic Imaging 2016;25:063013-063013

The goal of this project is to implement a tensor network scheme using TensorFlow, Google's open source library for computations using data flow graphs. This is an efficient way to represent the tensor network algorithm, and allows performance to be maximized using GPUs.

See https://arxiv.org/abs/1609.01552 for an introduction to the physics of the problem.

The dynamics of negative feedback is well understood, but things get more complicated as the signalling from CLV3 to WUS goes through several receptors. The receptors all perform signal processing on their own and at least one of them exhibit adaptation, meaning that it effectively filters out the average CLV3 input and only responds to recent changes. How do the other receptors work, and how is the signalling from the three integrated to a single output?

There is published data on what happens when you mutate these receptors, both one by one and in pairs. There is also data for how WUS is affected by changes in CLV3 concentration. With this, and with computational modelling, we aim to infer the relationship between these receptors, and what signal processing they must perform.

This project have some clear goals, and a well defined place to start. But the project is easily extensible, and while we have ideas of where one could go next you would be in charge of your own research. The project is also adaptable from a more analytical to a mainly computational approach.

The need for a quantitative understanding of cancer evolution is keenly highlighted by blood malignancies such as Acute Myeloid Leukemia (AML). At diagnosis, most AML patients harbour mutations in a ~3 - 10 out of a possible ~100 or so AML-associated genes. The currently accepted theory is that these mutations are acquired sequentially: clones with more mutations are fitter than those with fewer and selectively outcompete them. However, given the low mutation rates and lack of genomic instabilities in these cancers, exactly how it is possible to accumulate this many mutations in slowly cycling stem cell populations has been difficult to explain. Further complicating the issue, recent deep sequencing studies suggest that even in “healthy” people, there is a large degree of clonal evolution: subclones harboring different sets of somatic mutations compete with one another over the course of your life.

The goal of this research project will be to model how mutations arise and expand in tissues in order to understand what genomic signatures might be indicative of early cancer. Specifically we will: (i) Develop a stochastic “null” model of mutation dynamics in healthy (non-cancerous) tissues, maintained by a hierarchy of cell types. (ii) Modify the above model to include “driver” mutations that disrupt the homeostatic balance of the tissue, to model early cancer onset.

Methods used will be a combination of branching processes, nonlinear dynamics and stochastic simulations.

This project is to develop image analysis software running on a Raspberry Pi to analyse microscope images of faecal samples, identify the eggs present, then measure dimensions of the eggs and other simple parameters that could then be used to categorise the eggs. Efficient image analysis algorithms are required to ensure that the results are delivered to the user without significant delay.
To enable this project, ioLight will provide a microscope (containing the Raspberry Pi) and give assistance in learning how to use the microscope and get access to the images on the Raspberry Pi. MatLab, running on the Raspberry Pi could be used to develop the image analysis software.

This project will be jointly supervised by
Joana Grah jg704@cam.ac.uk
Jasmina Lazic Jasmina.Lazic@mathworks.co.uk
Stefanie Reichelt Stefanie.Reichelt@cruk.cam.ac.uk
Carola-Bibiane Schönlieb cbs31@cam.ac.uk
Richard Williams richard.williams@iolight.co.uk

This proposal would be to consider evaluations of both the original data sets and new data-sets using a number of modern methodologies for training and testing Internet traffic. This would permit us to evaluate such methods in new environments, e.g., the data-center, and to consider the actual value of new methodologies when compared with long-standing mechanisms for constructing Bayesian priors.

Practically this work will start by identifying suitable ML algorithm candidate(s) and make baseline comparison with the datasets of the 2005/6/7 work. This will enable a direct comparison of the value of these new algorithms, and in particular to explore the opportunity for continuous refinement of the prior.

References:
[1] Internet Traffic Classification Using Bayesian Analysis Techniques
Moore AW, Zuev D
ACM SIGMETRICS 2005
http://www.cl.cam.ac.uk/~awm22/publications/moore2005internet.pdf

[2] Bayesian Neural Networks for Internet Traffic Classification
Auld T, Moore AW, Gull SF
IEEE Trans on NN
http://www.cl.cam.ac.uk/~awm22/publications/auld2006bayesian.pdf

[3] Probabilistic Graphical Models for Semi-Supervised Traffic Classification
Rotsos C, VanGael J, Moore AW, Ghahramani Z.
http://www.cl.cam.ac.uk/~awm22/publications/rotsos2010probabilistic.pdf

Modelling to date has relied on the independence of queues for (simplistic) modeling; yet the integration of the tandem nature is important to have the models encapsulate properties within modern data-center networks. Additionally, treating a collection of (tandem) queues as a reduced number of queues enables practical simulation and reproduction of queueing impact within large scale queue structures - such as DC networks - using current simulation tools.

As data centres grow in scale and complexity, common simulation tools can no longer support classical queueing modeling used in legacy models. This proposal would be to consider the collapse of multiple queues models into a complex single queue, representing a single end-host view of the queueing of packets within the network and the delay introduced by queuing for each packet.

Beyond the theoretical modelling, this work will aim to validate the conclusions using real packet traces measurements. This will enable a direct comparison of the theoretical modelling of the queueing in the network, using both legacy simulators and the new models, with the actual packet behavior.

Bipartite graphs are widely used across a range of disciplines. In economics, trade networks can depict edges between countries and the products they export. In the social sciences, affiliation networks, such as those depicting edges between users and the movies they have watched, are common. In ecology, bipartite graphs have been very widely adopted. For example, communities of plants and their pollinators can be represented as bipartite graphs, with plants and pollinators as two sets of vertices, and edges representing their interactions. Other types of ecological interaction can be represented the same way, such as those between plants and the birds that disperse their seeds, or between hosts and their parasites.

Alongside my collaborators, I have been working to extend the concept of motifs to undirected bipartite graphs, and develop code (in R, MATLAB and Python) so that these methods can be widely adopted.

We have already developed methods to count the frequency of all possible undirected bipartite motifs containing 2, 3, 4 and 5 vertices in any bipartite graph. The next stage is to develop methods for counting the number of times each vertex occurs in each topologically unique position within each motif. Once this is completed, we want to extend our methods to counting motifs containing 6 vertices.

The student would likely be focussed on (i) developing methods to count the frequency of motifs containing 6 vertices in bipartite graphs and, (ii) developing methods to count the number of times each vertex occurs in each topologically unique position within each of these 6-vertex motifs. Ideally, these methods would then be written into code (preferably in R or MATLAB).

The student would then be free to pursue questions of interest. As an ecologist, I’m particularly interested in ecological networks (especially those characterising mutualistic interactions between species, such as plant and pollinators). I’m especially interested in recurrent and statistically significant motifs, and what they can tell us about (i) the evolutionary processes involved in network assembly, and (ii) the robustness of graphs to simulated perturbations. Examining robustness can involve simple topological models, or more complex approaches, such as modelling population dynamics on networks using generalised Lotka-Volterra equations. Motifs can also help answer questions such as whether the ways in which species are embedded in networks is a fundamental property of the species involved, or a function of context. Such approaches could help advance our understanding of ecological communities, and eventually inform conservation to ensure their protection in the future.

If the student is keen to focus on other types of bipartite graph, this also possible: the project could follow the interests of the student once the core methods have been developed.

Francis Knights (Fellow and DoS in Music, Fitzwilliam College)

Currently, we are exploring three approaches and we are looking for interested students to become involved with work on each of these:

1. Probabilistic and statistical models
Probabilistic and statistical tools such as principal component analysis, clustering analysis and stochastic processes (Markov chains and generalizations) are being applied to characterize pieces of music from a stylistic perspective.

2. Graph theoretical methods
Studying stylistic similarities leads in a natural way to the study of connectivity and other topological properties such as modularity, community structure, and motif detection in graphs associated to the studied musical works.

3. Hierarchical signal processing and wavelet
Signal processing tools can be applied to study similarities of the information content of musical fragments. New insights are needed to understand the different levels of musical structure.

Probability, Statistics, clustering
Graph theory
Hierarchical signal processing and wavelet

Telephone: 01223 437144