2022 CMP Academic Projects

The aim of this project is to develop a model to help us understand better how key parameters affect the balance between mutation helping the host, and mutation helping the virus. In particular, the aim is to understand to what extent both outcomes may occur in the same population if there is variability in the parameters within the population, and to estimate how often such outcomes occur. In the project, you will develop a simplified model capturing the key aspects of the mutation process, and implement and refine that model in one (or possibly more than one) infection scenario. To understand the parameter space developed, you will need to implement basic code to describe possible outcomes. This will be sufficiently straightforward that you can learn as you go if you have not done this before, but you should have basic familiarity with at least one programming language.

Funding for this project is not guaranteed, and if interested in this project you are encouraged to make contact as soon as possible, as many funding opportunities require a named student in the application and earlier contact will allow us to apply before deadlines for more funders. You will not be required to respond to any project offer before the common deadline for the placements.

A background to the way the mutational arms race proceeds in HIV as an example (although we may work on a problem with a simpler setup) is given in the following references:

1.  Armitage et al. "APOBEC3G-Induced Hypermutation of Human Immunodeficiency Virus Type-1 Is Typically a Discrete  "All or Nothing" Phenomenon" (https://doi.org/10.1371/journal.pgen.1002550) 
2. Sadler et al. "APOBEC3G Contributes to HIV-1 Variation through Sublethal Mutagenesis" (https://doi.org/10.1128/JVI.00056-10) [You do not need to understand the detail of the experiments performed in this paper, but should understand that it gives evidence that the real-world situation may be less clear-cut than suggested in reference (1).] A introduction to a completely different way this problem can be manifested is found in the following reference, which explains how molnupiravir, now licensed as a COVID-19 treatment, works: 
3. Kabinger et al. "Mechanism of molnupiravir-induced SARS-CoV-2 mutagenesis" (https://doi.org/10.1038/s41594-021-00651-0)

1. https://www.nature.com/articles/s41588-021-00862-7
2. https://doi.org/10.1093/gbe/evab087
3. https://doi.org/10.1101/2021.03.15.435416

This project would be especially suitable for somebody who wanted to explore moving into bioinformatics, or applying mathematical knowledge to microbiology. It will be advertised to both mathematicians and biologists, and the focus for a mathematician will be on learning the skills in handling biological data and in virology required to undertake an analysis and start interpreting the results. In this project you will apply to a set of virus genomes one of our mathematical techniques for searching for regions of interest.

You will need to:

• develop sufficient understanding of the mathematics of the analysis pipeline to understand the implications of the mathematics for interpretation of results;
• download and curate a set of virus sequences ready for analysis;
• adapt code (written in Mathematica) in order to apply it to your dataset;
• visualise the output (develop graphical methods of representing the results of your analysis);
• be able to discuss your findings in a cross-disciplinary fashion with colleagues in mathematics in virology to come to a shared interpretation of the results (in terms of regions of interest you have identified in the viral genome).

There are a few options for viruses it would be possible to work with on this project, which can be discussed prior to application. The project is likely to focus on a virus capable of causing human disease for which drug treatment is sought. The background work underpinning this project stretches all the way from open problems in probability theory, through the mathematics of signal processing and bioinformatics, to wet lab molecular biology and clinical applications. It is a requirement of the funding stream we propose to seek for this project that the project be strongly microbiological in nature and the project background be in microbiology in such a way that students undertaking it will be exposed to core microbiology thinking. Funding for this project will be sought via application to an external body (and so cannot be guaranteed).

The deadline for the external body's funding applications necessitates an earlier deadline of *13th February 2022* for expressions of interest, although earlier expressions of interest will make funding application more straightforward.

These references are listed in priority order for background reading (the first two are key), but if you have time, the progression of ideas is slightly easier to follow if they are read chronologically. There is no need to have read the references prior to sending an enquiry about the project: they are included in case you would like more information. The references describe the mathematical underpinning of the techniques used, and demonstrate some previous applications of those techniques.

[1] “A new method for detecting signal regions in ordered sequences of real numbers, and application to viral genomic data'  Julia R. Gog, Andrew M.L. Lever, Jordan P. Skittrall. PLoS ONE, 2018 13(4):e0195763. (https://doi.org/10.1371/journal.pone.0195763)
[2] “A scale-free analysis of the HIV-1 genome demonstrates multiple conserved regions of structural and functional importance.' Jordan P. Skittrall, Carin K. Ingemarsdotter, Julia R. Gog, Andrew M.L. Lever. PLoS Comput Biol, 2019 15(9):e1007345. (https://doi.org/10.1371/journal.pcbi.1007345)
[3] “Codon conservation in the influenza A virus genome defines RNA packaging signals.' Julia R. Gog, Emmanuel Dos Santos Afonso, Rosa M. Dalton, India Leclerq, Laurence Tiley, Debra Elton, Johann C. von Kirchbach, Nadia Naffakh, Nicolas Escriou, Paul Digard. Nucleic Acids Res, 2007 (35) 1897-1907. (https://doi.org/10.1093/nar/gkm087)
[4] “Genomic analysis of codon, sequence and structural conservation with selective biochemical-structure mapping reveals highly conserved and dynamic structures in rotavirus RNAs with potential cis-acting functions.' Wilson Li, Emily Manktelow, Johann C. von Kirchbach, Julia R. Gog, Ulrich Desselberger, Andrew M. Lever. Nucleic Acids Res, 2010 (38) 7718-7735. (https://doi.org/10.1093/nar/gkq663)

Deep learning brought substantial improvements to speech recognition, enhancement or separation systems by estimating a time-frequency mask (by a masking network) in a deterministic transformed domain for time-domain sound signals (i.e. Fourier domain). The masked representation is then transformed back to a time-domain signal (i.e. Inverse Fourier transform) to yield the enhanced sound. In recent years, new artificial neural network architectures (Recurrent Neural Networks, Attention mechanisms) along with the introduction of end-to-end learning systems provided a significant boost of performance [1]. These new techniques work in an Encoder-Mask-Decoder fashion where the mask is no longer estimated from a fixed transformed domain but from learned representations available at the encoder stage. At the decoder stage, the masked representations are then transformed back to a time-domain signal ("decoded") to obtain the enhanced sound signals. This project will explore the impact of such learned representations over deterministic transforms (auditory inspired, discrete Fourier transforms, ....) in the context of noise and reverberation compensation for hearing impaired people that use hearing aids or cochlear implants.

The student will investigate the following research questions (but not limited to):
1. How does learning the encoder, decoder or both affect speech enhancement performance compared to applying deterministic auditory inspired transforms?
2. Are there any properties of learned or fixed transforms that allow complexity or dimensionality reduction with similar performance?

The outcomes of the study will be systematically evaluated using objective measures and pilot listening tests and results will contribute to an ongoing research project. The student will use common high-level (Python) deep learning frameworks for speech separation/enhancement including filterbank design tools for comparing the encoder-decoder models and deterministic transforms [2].

• Abbott, B.W., Bishop, K., Zarnetske, J.P., Minaudo, C., Chapin, F.S., Krause, S., Hannah, D.M., Conner, L., Ellison, D., Godsey, S.E., Plont, S., Marçais, J., Kolbe, T., Huebner, A., Frei, R.J., Hampton, T., Gu, S., Buhman, M., Sara Sayedi, S., Ursache, O., Chapin, M., Henderson, K.D., Pinay, G., 2019. Human domination of the global water cycle absent from depictions and perceptions. Nat. Geosci. 12, 533-540. https://doi.org/10.1038/s41561-019-0374-y
• Bonan, G.B., Williams, M., Fisher, R.A., Oleson, K.W., 2014. Modeling stomatal conductance in the earth system: linking leaf water-use efficiency and water transport along the soil-plant-atmosphere continuum. Geosci. Model Dev. 7, 2193-“2222. https://doi.org/10.5194/gmd-7-2193-2014
• Dewar, R.C., 2002. The Ball-Berry-Leuning and Tardieu-Davies stomatal models: synthesis and extension within a spatially aggregated picture of guard cell function. Plant. Cell Environ. 25, 1383-1398. https://doi.org/10.1046/j.1365-3040.2002.00909.x
• Eller, C.B., Rowland, L., Mencuccini, M., Rosas, T., Williams, K., Harper, A., Medlyn, B.E., Wagner, Y., Klein, T., Teodoro, G.S., Oliveira, R.S., Matos, I.S., Rosado, B.H.P., Fuchs, K., Wohlfahrt, G., Montagnani, L., Meir, P., Sitch, S., Cox, P.M., 2020. Stomatal optimization based on xylem hydraulics (SOX) improves land surface model simulation of vegetation responses to climate. New Phytol. 226, 1622-1637. https://doi.org/10.1111/nph.16419
• Greve, P., Roderick, M.L., Ukkola, A.M., Wada, Y., 2019. The aridity Index under global warming. Environ. Res. Lett. 14, 124006. https://doi.org/10.1088/1748-9326/ab5046
• Kennedy, D., Swenson, S., Oleson, K.W., Lawrence, D.M., Fisher, R., Lola da Costa, A.C., Gentine, P., 2019. Implementing Plant Hydraulics in the Community Land Model, Version 5. J. Adv. Model. Earth Syst. 11, 485-513. https://doi.org/10.1029/2018MS001500
• Pokhrel, Y., Felfelani, F., Satoh, Y., Boulange, J., Burek, P., Gädeke, A., Gerten, D., Gosling, S.N., Grillakis, M., Gudmundsson, L., Hanasaki, N., Kim, H., Koutroulis, A., Liu, J., Papadimitriou, L., Schewe, J., Müller Schmied, H., Stacke, T., Telteu, C.-E., Thiery, W., Veldkamp, T., Zhao, F., Wada, Y., 2021. Global terrestrial water storage and drought severity under climate change. Nat. Clim. Chang. https://doi.org/10.1038/s41558-020-00972-w
• Samaniego, L., Thober, S., Kumar, R., Wanders, N., Rakovec, O., Pan, M., Zink, M., Sheffield, J., Wood, E.F., Marx, A., 2018. Anthropogenic warming exacerbates European soil moisture droughts. Nat. Clim. Chang. 8, 421-426. https://doi.org/10.1038/s41558-018-0138-5
• Stocker, B.D., Zscheischler, J., Keenan, T.F., Prentice, I.C., Seneviratne, S.I., Peñuelas, J., 2019. Drought impacts on terrestrial primary production underestimated by satellite monitoring. Nat. Geosci. 12, 264-270. https://doi.org/10.1038/s41561-019-0318-6
• Trugman, A.T., Medvigy, D., Mankin, J.S., Anderegg, W.R.L., 2018. Soil Moisture Stress as a Major Driver of Carbon Cycle Uncertainty. Geophys. Res. Lett. 45, 6495-6503. https://doi.org/10.1029/2018GL078131

• 'A gentle introduction to graph neural networks' https://distill.pub/2021/gnn-intro/
• 'A practical tutorial on graph neural networks' https://arxiv.org/pdf/2010.05234.pdf

• https://www.isa-afp.org/entries/Roth_Arithmetic_Progressions.html
• https://www.isa-afp.org/entries/Szemeredi_Regularity.html
• Index of the Archive of Formal Proofs: https://www.isa-afp.org/topics.html
• Isabelle: https://www.cl.cam.ac.uk/research/hvg/Isabelle/index.html

In this project the student will work with Dr Handley and his team investigating the development and application of Bayesian machine learning techniques to modern and future cosmological and particle physics datasets.

The precise details of the project will be tailored to the student interest and skill set, but possible topics/projects include
1. Developing machine learning algorithms for nested sampling and applying these to cosmological data sets - https://arxiv.org/abs/1506.00171 - https://arxiv.org/abs/2007.08496
2. Model independent reconstruction of the primordial universe from cosmic microwave background data and cosmic dawn data - https://arxiv.org/abs/1908.00906
3. Developing and applying mathematical schemes for disentangling physical signatures in the primordial universe - https://arxiv.org/abs/1907.08524 - https://arxiv.org/abs/2009.05573
4. Combining particle physics and cosmological data as part of the GAMBIT team - https://gambit.hepforge.org/ - https://arxiv.org/abs/2009.03286 - https://arxiv.org/abs/2009.03287
5. Investigating quantum initial conditions for inflation - https://arxiv.org/abs/2112.07547 - https://arxiv.org/abs/1607.04148

Over the course of the project students can expect to learn some/all of:

• up-to-date cosmological research questions
• Science grade python
• High performance computing
• Bayesian inference
• Machine learning
• Computer algebra

Essential:

• Three years of undergraduate physics, mathematics or equivalent
• Basic to intermediate Python experience and good programming skills
• Strong mathematical skills

Desirable:

• Interest/Knowledge of general relativity/cosmology
• Experience using Mathematica/Maple/Computer algebra

Einstein's General Relativity (GR) remains the preferred effective theory of gravity as spacetime curvature, explaining the orbital precession of Mercury and solar bending of starlight while underpinning modern cosmology. However GR does not explain dark matter or dark energy, while an alleged `Hubble tension' indicates that our Universe is expanding 10% faster than it should be. And of course, GR continues to stubbornly resist attempts at (complete) quantum reformulation.

We recently attracted some attention by proposing an alternative theory of gravity as a blend of spacetime torsion and curvature: this appears to provide a cosmological constant and alleviate the Hubble tension. Our Lagrangian is wildly different from that of GR, with a quantum structure suggestive of renormalisability. We believe the theory adopts a torsion vacuum expectation value (VEV) at a primordial epoch, on the back of which the good classical phenomena emerge. However many quantum/classical aspects of this torsion VEV, and the violent early-Universe physics of its formation, remain shrouded in mystery...

The findings of the project may debunk our theory or, if we are lucky, propel it further into the spotlight of community interest. The student may wish to target one of several new fronts we are opening in our research campaign:

1) *Quantum stability and the infrared* -- This is an urgent question; we don't really know if the torsion VEV is stable against quantum fluctuations, as is the case for the Minkowski vacuum of GR. The student will apply well established effective field theory and ghost condensate techniques to characterise the infrared environment of the VEV. Extensions to the ultraviolet are of course welcome depending on expertise, though expected to be more challenging. A stable vacuum is quite a big deal, while convincing instabilities would seem to rule our theory out: either way this avenue promises high returns.

2) *Cosmological perturbation theory* -- There is a very well established theory dictating how cosmic density perturbations evolve under gravity, which supports GR to amazing precision based on tiny anisotropies in the cosmic microwave background and the clustering of matter on the grandest scales. The student will extract and characterise the classical perturbation equations (and perhaps convenient gauges) around the torsion VEV, matching against GR where possible. This also targets aspects of the infrared environment, but uses classical methods so does not require prior knowledge of QFT. Apart from offering a neat standalone stability test the perturbation theory will facilitate, in the long run (2023), sophisticated Monte Carlo tests against cosmological survey data: to this end a successful student would also have a stake in these future research way points.

3) *Primordial symmetry breaking* -- We imagine that the Big Bang left our gravity theory in a torsionless conformal phase, bathed in the standard model plasma. So how and when does the torsion VEV form in relation to the condensation of the Higgs field? Could this process have driven inflation, the violent expansion thought to have occurred in the very early Universe? A decaying deviation from the torsion VEV just after inflation can alleviate the Hubble tension: what physics sets this initial condition? The student may wish to merely explore these questions using the background cosmology equations, and there is a viable research-grade project at this level. However depending on interest/experience in electroweak symmetry breaking or effective quantum theories of inflation, we may hope to propose a novel inflationary mechanism.

These topics are not exhaustive and are subject to shift as we study the theory throughout spring 2022.

• For the history of our new theory, skim chapters 2-4/refs therein: https://wevbarker.com/assets/papers/Barker_PhDThesis.pdf
• For an intro to spacetime torsion, skim the first three chapters: http://alpha.sinp.msu.ru/~panov/LibBooks/GRAV/Blagojevic_M.-Gravitation_and_gauge_symmetries(2002).pdf
• For ghost condensates and the infrared analysis: https://arxiv.org/abs/hep-th/0312099
• For more infrared techniques that will apply near the VEV: https://arxiv.org/abs/hep-th/9210046
• The excellent Les Houches notes on effective field theories: https://arxiv.org/abs/1804.05863
• For effective field theories of inflation: https://physics.mcmaster.ca/~cburgess/Notes/InflationEFTs.pdf
• For an intro to cosmological perturbations: https://arxiv.org/abs/hep-th/0306071

• https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0...
• https://www.nature.com/articles/nrd3078?report=reader 

This project will be based at the Department of Veterinary Medicine, and will involve genomic analysis of the canine transmissible venereal tumour (CTVT). CTVT is a transmissible cancer, which is a rare class of cancer that has developed the ability to infect new hosts, and behaves rather like a parasitic organism. CTVT is spread among dogs when they come in direct physical contact with tumour tissue infecting another individual, usually during mating. CTVT is by far the oldest clonally reproducing cancer known on Earth.

The project will build on recent work done in our lab to unravel the earliest events that befell the tumour in its progression towards becoming infectious and globally endemic. Using high coverage DNA sequencing information from several CTVT samples, as well as from the uninfected tissue of their hosts, we have previously estimated the evolutionary tree that relates these tumours. This work has identified a previously unseen mutational signature (‘signature A’) that was active during the early evolution of CTVT, but was later switched off. In this project we will take estimates of genomic copy number in our samples, and use these to find genomic regions that have been duplicated in CTVT’s development. From these duplications we can identify ‘frozen time points’: fragments of DNA sequence that were gained during the early evolution of the cancer. The relative ages of these fragments will be estimated by the degree to which they have accumulated new mutations. Combined with this timing information, by examining the fragments for the presence of signature A we will be able to determine whether signature A occurred continuously, or in bursts. Additionally, the earliest fragments will be highly representative of the genotype of the animal in which CTVT arose, illuminating perhaps the characteristics of the earliest domesticated dogs.