Academic CMP project proposals from summer 2023
- Sainsbury Laboratory, Cambridge University (SLCU) - How does cell division impact plant cell mechanical properties
Keywords: plants, mechanics, modelling, cell division - Sainsbury Laboratory, Cambridge University (SLCU) - Microtubule alignment during plant cell elongation
Keywords: Plants; Mathematical biology; computational; cytoskeleton; organisation - MRC Cognition & Brain Sciences Unit, University of Cambridge - Nonlinear optimization and/or development of bayesian inference approaches for modelling efficiency of signal processing and delivery in users of cochlear implants
Keywords: auditory neuroscience, neuroprosthetics, cochlear implants, non-linear optimization, Bayesian inference - Department of Computer Science and Technology (Computer Lab) - Infinity-Categories in Type Theory
Keywords: omega-categories, type theory, proof assistants - Department of Computer Science and Technology (Computer Lab) - Formalisation of material in number theory/additive combinatorics using Isabelle/HOL
Keywords: number theory, additive combinatorics, proof assistants, interactive theorem proving, Isabelle/HOL - Department of Computer Science and Technology (Computer Lab) - Sheaf Cohomology Without Dependent Types
Keywords: formalisation, type theory, Isabelle/HOL, cohomology, sheaves - Department of Computer Science and Technology (Computer Lab) - Lehmer's Conjecture in Isabelle/HOL
Keywords: Lehmer's conjecture, number theory, Isabelle/HOL, proof assistants, verification - Cambridge Judge Business School - Epidemic forecasting with growth curve models and leading indicators
Keywords: Kalman filter, negative binomial distribution, stochastic trend, Gompertz curve, leading indicators - Department of Chemistry, Nitschke Group - Design of molecular polyhedra based on non-planar, 'twisted' building-blocks.
Keywords: Chemistry, Topology, Polyhedra, Mathematica - Department of Computer Science and Technology (Computer Lab) - Puiseux series in Isabelle/HOL
Keywords: formalisation, Isabelle/HOL, computer algebra, real closed field, Puiseux series - Department of Geography and Sainsbury Laboratory Cambridge University - Modelling tree growth responses to climate change
Keywords: tree growth climate carbon photosynthesis - BioModels, European Bioinformatics Institute (EMBL-EBI) - Disseminating FAIR Machine Learning Models via BioModels
Keywords: BioModels, Machine Learning, FAIR, reproducibility - Molecular Networks Team, European Bioinformatics Institute (EMBL-EBI) - Path4Drug: Data Science Workflow for Identification of Tissue-Specific Biological Pathways Modulated by Toxic Drugs
Keywords: chemoinformatics, drug discovery, database, clustering, network analysis - Goldman group at EMBL-EBI - Research in the Goldman group: nanopore sequencing and pandemic-scale phylogenetics
Keywords: Sequencing, algorithmics, phylogenetics, mathematical modeling, information theory. - MRC-LMB and PDN, University of Cambridge - Super-resolution microscopy applications
Keywords: Single molecule localisation microscopy, point clouds, biological applications - Department of Engineering / Civil Engineering - Seismic response of foundations for offshore wind turbines
Keywords: offshore wind turbine, foundation design, seismic loading, renewable energy, hyperplasticity
How does cell division impact plant cell mechanical properties
Project Title | How does cell division impact plant cell mechanical properties |
Keywords | plants, mechanics, modelling, cell division |
Project listed | 5 January 2023 |
Project status | Filled |
Contact Name | Sarah Robinson |
Contact Email | sarah.robinson@slcu.cam.ac.uk |
Company/Lab/Department | Sainsbury Laboratory, Cambridge University (SLCU) |
Address | 47 Bateman Street, Cambridge, CB2 1LR |
Period of the Project | 8 weeks full time. |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | My lab is interested in how cell division alters tissue growth in plants from a mechanical point of view. Plant cells have cell walls which surround them, this makes them rigid and prevents them from moving. The cells divide to add new cell walls in carefully controlled ways but the consequence of this on the growing tissue is not well understood. We have experimental and modelling tools to induce cell division and measure the changes in mechanical properties. We are interested in how changing the placement of the new cell wall impacts the properties of the tissue around it and how the pattern of stress might be altered. |
Brief Description of the Project | Our goal is to understand what determines and what are the consequences of the plant cell division plane. Plant cells are rigidly connected to each other so where they decide to divide helps to determine their overall growth and tissue shape. To investigate this phenomenon, we apply experimental and modelling approaches. Join us for a project and you can help develop tools to understand this vital process. There is flexibility in what you choose to do but we apply a mix of image analysis, mechanical modelling and network theory. For this project, you will have access to actual data and experience working directly with experimentalists in an interdisciplinary environment. The main focus currently is to understand the consequence of junction distance on the stress patterns in the tissues. A successful student will be able to model different cell division rules and determine their likely impact on the tissue. |
Work Environment | The student will be supervised by a post-doc with a maths background. They may work from home if they want to, but I prefer on site. |
References | |
Prerequisite Skills | |
Other Skills Used in the Project | Image processing; Mathematical Analysis; Geometry/Topology; Simulation; Predictive Modelling |
Programming Languages | C++ |
Microtubule alignment during plant cell elongation
Project Title | Microtubule alignment during plant cell elongation |
Keywords | Plants; Mathematical biology; computational; cytoskeleton; organisation |
Project listed | 5 January 2023 |
Project status | Filled |
Contact Name | Tamsin A. Spelman |
Contact Email | tas46@cam.ac.uk |
Company/Lab/Department | Sainsbury Laboratory, Cambridge University (SLCU) |
Address | 47 Bateman Street, Cambridge, CB2 1LR |
Period of the Project | 8 weeks between late June and September, but we are flexible if an alternative is preferred |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | Microtubules (MTs) are long, thin active fibres found within all living cells and essential for many cell functions. MT arrangement within growing cells contributes to asymmetric growth generating the myriad of different cell shapes necessary for the organism to survive. The aim of this project is to understand if and how MTs change their alignment as the cell grows and its aspect ratio changes using microtubule modelling software previously developed in the group. |
Brief Description of the Project | We have previously shown computationally and experimentally that MTs preferentially align along the long axis of the cell (specifically in plant protoplast cells) [1]. In this project you will consider questions such as: How quickly does MT alignment change with cell elongation? If a transverse MT alignment is sufficiently strong before cell elongation can a transverse MT alignment be maintained? What happens if biases are introduced in the MT dynamics? We have C++ implemented open-source software [2] for simulating microtubules within different cell shapes which has been developed over multiple years [1,3]. This project will involve running (and if there is interest also developing) this microtubule modelling software and analysing the results for which we normally use Python, but you can use your preferred software. We are very flexible with the outcomes from this project so the project can be taken in a direction that interests you. |
Work Environment | You will be part of the Jonsson group currently consisting of 10 group members and led by Professor Henrik Jonsson, the director of the Sainsbury Laboratory. You are welcome to all group activities such as our group meetings (held weekly but normally with a couple of weeks break sometime during the summer) and wider lab activities such as twice weekly coffee gatherings and other activities organised by the lab social societies. We will meet at least weekly but more regularly to begin with, and I will be available for further conversations as needed. We will have more irregular meetings with Henrik. |
References | [1] P. Durand-Smet et. al. (2020) Cytoskeleton organization in isolated plant cells under geometry control. Proc. Natl. Acad. Sci. 202003184 [2] https://gitlab.com/slcu/teamHJ/tubulaton [3] V. Mirabet et. al (2018) The self-organization of plant microtubules inside the cell volume yields cortical localization, stable alignment, and sensitivity to external cues. PLoS Comp Biol. |
Prerequisite Skills | |
Other Skills Used in the Project | Mathematical Analysis; Simulation |
Programming Languages | Python; MATLAB; C++; No Preference; Data analysis can be done in your choice of programming language. We mostly use Python but also Matlab. The microtubule modelling software is coded in C++ but you should only need to run that code not edit/develop it unless you wish to. |
Nonlinear optimization and/or development of bayesian inference approaches for modelling efficiency of signal processing and delivery in users of cochlear implants
Project Title | Nonlinear optimization and/or development of bayesian inference approaches for modelling efficiency of signal processing and delivery in users of cochlear implants |
Keywords | auditory neuroscience, neuroprosthetics, cochlear implants, non-linear optimization, Bayesian inference |
Project listed | 5 January 2023 |
Project status | Filled |
Contact Name | Charlotte Garcia |
Contact Email | charlotte.garcia@mrc-cbu.cam.ac.uk |
Company/Lab/Department | MRC Cognition & Brain Sciences Unit, University of Cambridge |
Address | 15 Chaucer Road, Cambridge, CB27EF |
Period of the Project | any 8-week period from late June to September |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | There are a few kinds of hearing technologies that help people with hearing loss to hear. These include hearing aids that acoustically amplify sound entering someone’s ear. While hearing aids are normally prescribed and programmed by a healthcare professional, many over-the-counter hearing aids have recently become available as well, and even Air Pods contain hearing-assistive programs. However, these types of devices do not help those with more severe hearing loss. A more complex hearing device involves bypassing the outermost parts of the auditory system and are more like bionic ears: these are cochlear implants. A cochlear implant is neural prosthetic that provide people with a profound hearing impairment with auditory perception by directly electrically stimulating the auditory nerve. It requires a surgical operation wherein a small string of electrodes is inserted into the patient’s inner ear. These electrodes are then controlled using a speech processor with a microphone that sits behind the patient’s ear. Most recipients can perceive speech well with their implant, and some enjoy music. They are arguably the most successful auditory prosthetic in existence today, with close to 1 million users globally. However, many struggle to understand speech with their implants, especially in challenging listening conditions with background noise. This may be due to the fact that individual cochlear implant users lose their hearing for different reasons, and the cochlear implant software and settings are not optimized for their unique pattern of hearing loss. We have developed a diagnostic tool called the Panoramic ECAP method that is designed to provide patient-specific indicators of the interaction between a patient’s implant and their auditory system. It involves applying a non-linear optimization algorithm to electrophysiological measurements of neural activity in the cochlea. These measurements are called ‘Electrically Evoked Compound Action Potentials’ or ‘ECAPs’ for short. It is our hope that this tool can be used in a clinical setting to personalize and optimize cochlear implant software and enable patients to hear as well as possible with their device. |
Brief Description of the Project | The Panoramic ECAP (PECAP) method provides two estimates that describe the interaction between a cochlear implant patient’s inner ear (a.k.a. cochlea [1]) and their implant: the health of the auditory nerves and the spread of electrical current. The two PECAP estimates are quantified for each electrode of the cochlear implant. Areas of poor neural health or wide current spread reduce the efficiency of delivering auditory information from the neuroprosthetic device to the brain. The PECAP method estimates the neural health and the current spread at each electrode separately, using a nonlinear optimization algorithm based on sequential quadratic programming whose structure is based on a theoretical framework [2]. We have conducted experiments to validate that these estimates are accurate and indeed separate from each other. While the estimates appear to detect independent manipulations to neural health and current spread respectively, we have evidence that they are not necessarily separating the two estimates as well as desirable. This project will include investigating a number of adjustments to the structure of the PECAP algorithm using data collected during previous experiments to: (1) Determine if the changes to the model separate the two estimates more accurately than the current state: a. For instance, the current spread estimate currently uses symmetrical Gaussian curves to estimate the spread of electrical current, but there is some evidence that current does not spread symmetrically due to cochlear geometry: the entrance to the cochlea has a wider diameter than the other end (the centre of the snail shell). One adjustment could be to allow these current spread curves to be asymmetric to allow for this phenomenon. b. Another, more complex adjustment may involve investigating alternatives to the sequential quadratic programming optimization algorithm such as Bayesian inference. (2) Determine if it is possible to use less neural data without degrading the model estimates a. We have developed a fast method for obtaining ECAP (neural) data from cochlear implant patients in a time period that is more realistic to implement in the clinic [3]. However, reducing this time further would greatly improve clinical viability of the tool. b. Existing datasets can be used to determine what neural data can be removed without affecting the model estimates. For instance, recording conditions that generally result in no neural response can be removed. It would be necessary to determine a procedure that would work for newly collected data in real-time, not just those specific to an individual patient. The algorithm itself is programmed in MATLAB, and you will be expected to either modify the existing code or re-program the algorithm and associated adjustments in Python, if preferred. You will be expected to conduct statistical tests to determine if the adjustments to the algorithm have improved the separation of the two estimates, and how much input data can be removed without degrading the PECAP estimates, as well as generate and present visualization of the changes and their dis/advantages. A previous CMP student – Taren Rughooputh – conducted a similar project in our laboratory under the supervision of Tobias Goehring and Bob Carlyon in 2018. His work contributed to a publication on the topic, for which he is on the author list [2]. |
Work Environment | For this project, you will be working within a lab. You will have your own individual project stream that will be primarily supervised by Charlotte Garcia (a post-doc), but there are a number of other post-docs in the lab as well who you will be able to talk to as well. You will also have weekly meetings with our lab (lead by our PI, Bob Carlyon) at the MRC Cognition and Brain Sciences Unit (1), which is part of the larger Cambridge Hearing Group (2). (1) MRC Cognition & Brain Sciences Unit Website: https://www.mrc-cbu.cam.ac.uk/ (2) Cambridge Hearing Group Website: https://www.hearing-research.group.cam.ac.uk/ |
References | [1] Background Coursework from Duke University describing the peripheral auditory system: https://gb.coursera.org/lecture/medical-neuroscience/peripheral-auditory.... I recommend watching the first 3 videos of week 7 for a review of the human auditory system [2] The publication describing the ‘PECAP’ algorithm that this project is based on: Garcia, C., Goehring, T., Cosentino, S. et al. The Panoramic ECAP Method: Estimating Patient-Specific Patterns of Current Spread and Neural Health in Cochlear Implant Users. JARO 22, 567–589 (2021). https://doi.org/10.1007/s10162-021-00795-2 [3] The publication describing the efficient data-collection technique ‘SpeedCAP’: Garcia, C., Deeks, J. M., Goehring, T., Borsetto, D., Bance, M., Carlyon, R. P. SpeedCAP: An Efficient Method for Estimating Neural Activation Patterns Using Electrically Evoked Compound Action-Potentials in Cochlear Implant Users. Ear and Hearing (2022). https://doi.org/10.1097/AUD.0000000000001305 |
Prerequisite Skills | Statistics; Numerical Analysis; Data Visualization; basic programming skills in MATLAB or python are required |
Other Skills Used in the Project | Statistics; Simulation; Predictive Modelling |
Programming Languages | Python; MATLAB |
Infinity-Categories in Type Theory
Project Title | Infinity-Categories in Type Theory |
Keywords | omega-categories, type theory, proof assistants |
Project listed | 5 January 2023 |
Project status | Open |
Contact Name | Anthony Bordg |
Contact Email | apdb3@cam.ac.uk |
Company/Lab/Department | Department of Computer Science and Technology (Computer Lab) |
Address | William Gates Building, 15 JJ Thomson Avenue, Cambridge CB3 0FD |
Period of the Project | 8 weeks |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | |
Brief Description of the Project | Recently, strict omega-categories have been formalised in the interactive theorem prover Isabelle/HOL as well as many prerequisites for their generalisation: weak omega-categories. In this project, we propose to complete the formalisation of weak omega categories -- a model for infinity-categories -- following Leinster's textbook "Higher Operads, Higher Categories". |
Work Environment | The student will be part of the ERC-funded ALEXANDRIA project led by Prof. Larry Paulson. |
References | The paper "Encoding Dependently-Typed Constructions into Simple Type Theory" contains a formalisation of strict omega-categories in Isabelle/HOL (article accepted for CPP 2023, preprint available through the personal webpage of Anthony Bordg). See also Tom Leinster's book "Higher Operads, Higher Categories". |
Prerequisite Skills | Algebra/Number Theory; some familiarity with (functional) programming |
Other Skills Used in the Project | not required but helpful: previous experience with a proof assistant (Agda, Coq, Isabelle/HOL, Lean ...) |
Programming Languages | No Preference |
Formalisation of material in number theory/additive combinatorics using Isabelle/HOL
Project Title | Formalisation of material in number theory/additive combinatorics using Isabelle/HOL |
Keywords | number theory, additive combinatorics, proof assistants, interactive theorem proving, Isabelle/HOL |
Project listed | 5 January 2023 |
Project status | Filled |
Contact Name | Angeliki Koutsoukou-Argyraki |
Contact Email | ak2110@cam.ac.uk |
Company/Lab/Department | Department of Computer Science and Technology (Computer Lab) |
Address | 15 JJ Thomson Avenue CB30FD Cambridge |
Period of the Project | 8 weeks (full time): 19 Jun. - 11 Aug. |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | |
Brief Description of the Project | The student(s) will participate in a project involving the formalisation of material in number theory/additive combinatorics using the proof assistant (interactive theorem prover) Isabelle/HOL. We will be aiming at completing formalisation work to be submitted to the Archive of Formal Proofs. |
Work Environment | ALEXANDRIA group, please see https://www.cl.cam.ac.uk/~lp15/Grants/Alexandria/. Partly remote work is also possible. Flexible working hours. |
References | Seminar series: http://www.talks.cam.ac.uk/show/index/164015 Recent related work: * https://www.researchgate.net/publication/364144547_A_Formalisation_of_th... (paper accepted to the conference CPP 2023 in collaboration with CMP 2022 student) * https://www.isa-afp.org/entries/Balog_Szemeredi_Gowers.html (AFP entry in collaboration with CMP 2022 student) * https://www.isa-afp.org/entries/Kneser_Cauchy_Davenport.html (AFP entry in collaboration with CMP 2022 student) * 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 |
Prerequisite Skills | Mathematical Analysis; Algebra/Number Theory |
Other Skills Used in the Project | Previous experience in Isabelle/HOL or other proof assistants is desirable but not necessary. Please see https://www.cl.cam.ac.uk/research/hvg/Isabelle/index.html |
Programming Languages | Isabelle/HOL. Please see https://www.cl.cam.ac.uk/research/hvg/Isabelle/index.html |
Sheaf Cohomology Without Dependent Types
Project Title | Sheaf Cohomology Without Dependent Types |
Keywords | formalisation, type theory, Isabelle/HOL, cohomology, sheaves |
Project listed | 5 January 2023 |
Project status | Open |
Contact Name | Anthony Bordg |
Contact Email | apdb3@cam.ac.uk |
Company/Lab/Department | Department of Computer Science and Technology (Computer Lab) |
Address | William Gates Building, 15 JJ Thomson Avenue, Cambridge CB3 0FD |
Period of the Project | 8 weeks |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | |
Brief Description of the Project | Would you like to take up a formalisation challenge? As part of the formalisation of Grothendieck's schemes with the proof assistant Isabelle/HOL in 2021, sheaves (of rings) were formalised without dependent types using Isabelle's module system called "locales". In this project, we propose to formalise sheaf cohomology in Isabelle/HOL. |
Work Environment | The student will be part of the ALEXANDRIA team led by Prof. Lawrence Paulson. |
References | - Anthony Bordg, Lawrence Paulson & Wenda Li (2022) "Simple Type Theory is not too Simple: Grothendieck’s Schemes Without Dependent Types", Experimental Mathematics, 31:2, 364-382 (https://www.tandfonline.com/doi/full/10.1080/10586458.2022.2062073) |
Prerequisite Skills | Geometry/Topology; Algebra/Number Theory |
Other Skills Used in the Project | experience with a proof assistant (Agda, Coq, Lean, Isabelle/HOL ...) would be helpful (but is not required) |
Programming Languages | No Preference |
Lehmer's Conjecture in Isabelle/HOL
Project Title | Lehmer's Conjecture in Isabelle/HOL |
Keywords | Lehmer's conjecture, number theory, Isabelle/HOL, proof assistants, verification |
Project listed | 5 January 2023 |
Project status | Open |
Contact Name | Anthony Bordg |
Contact Email | apdb3@cam.ac.uk |
Company/Lab/Department | Department of Computer Science and Technology (Computer Lab) |
Address | 15 JJ Thomson Avenue, Cambridge, CB3 0FD |
Period of the Project | 8 weeks |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | |
Brief Description of the Project | In the last few years, a large amount of analytic number theory has been formalised in the proof assistant Isabelle/HOL, in particular the whole textbook "Introduction to Analytic Number Theory" of Apostol and more recently a large part of his graduate textbook "Modular Functions and Dirichlet Series in Number Theory". Building on these previous successes, we propose in this internship to take the next step and to formalise the statement of the so-called Lehmer's conjecture and to prove formally some results related to this open conjecture in number theory. |
Work Environment | The student will be part of the ALEXANDRIA project led by Prof. Lawrence Paulson. |
References | See the article in Wikipedia on Lehmer's conjecture: https://en.wikipedia.org/wiki/Lehmer%27s_conjecture |
Prerequisite Skills | Mathematical Analysis; Algebra/Number Theory |
Other Skills Used in the Project | While not mandatory, previous experience with a proof assistant (Agda, Coq, Isabelle, Lean ...) will be helpful. |
Programming Languages |
Epidemic forecasting with growth curve models and leading indicators
Project Title | Epidemic forecasting with growth curve models and leading indicators |
Keywords | Kalman filter, negative binomial distribution, stochastic trend, Gompertz curve, leading indicators |
Project listed | 5 January 2023 |
Project status | Filled |
Contact Name | Paul Kattuman |
Contact Email | p.kattuman@jbs.cam.ac.uk |
Company/Lab/Department | Cambridge Judge Business School |
Address | Trumpington Street |
Period of the Project | 8 weeks: July, August 2023 |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | As the pandemic threatened to overwhelm the health system, the need for quick and robust decisions on operational questions led the NHS in the East of England region to form a Joint Evidence and Intelligence Cell with academic partners. The remit was to forecast epidemic and related trajectories. This led to the development of a new dynamic growth curve model for forecasting epidemic like processes. A significant innovation in this approach is that the model is dynamic and capable of adapting estimates and forecasts rapidly to recent changes in the epidemic trajectory. In particular, the new model is designed to detect upcoming turning points in the epidemic, and to make accurate predictions of them. The success of this modelling approach in providing accurate short-term forecasts led to its adoption as the method of choice in many jurisdictions. The summer project will build on this program of work with methodological refinement, and potential applications of the approach in non-epidemic contexts. |
Brief Description of the Project | Technical aspects of the dynamic growth curve model are documented in Harvey and Kattuman (2020). Some refinements are reported in Harvey, Kattuman, Thamotheram (2021) and Harvey and Kattuman (2021). There are two useful methodological extensions of the model. One is the use of leading indicators to improve forecasts, particularly for daily and high frequency data, employing dynamic lag structures between the leading and lagging series. A second methodological refinement is to extend the model to situations where numbers are relatively small, for example, when a disease is endemic. In terms of applications there are a numbers of non-epidemiological contexts where the model promises to be very useful. These include: innovation diffusion (for example., adoption of energy efficient technologies); diffusion of new technology knowledge (relating to anti-cancer drugs, for example); diffusion of fake news and disinformation (around COVID-19 related policy announcements). Applications listed above will lead to interesting research outputs with publication potential and well as practical usefulness. A manageable program of work will be designed depending on interests and skills of the student selected. |
Work Environment | Part of a team: Three others involved are: Prof: Andrew Harvey, Prof: Stefan Scholtes, and Dr. Michael Ashby |
References | Harvey. A., Kattuman, P. (2020). ‘Time series models based on growth curves with applications to forecasting coronavirus’, Harvard Data Science Review, Special issue 1— COVID-19. https://doi:10.1162/99608f92.828f40de Harvey, A., Kattuman, P. and Thamotheram, C. (2021). ‘Tracking the mutant: Forecasting and nowcasting COVID-19 in the UK in 2021’, National Institute Economic Review, 256, pp. 110–26. https://doi.org/10.1017/nie.2021.12 Harvey, A. and Kattuman. P. (2021). ‘Farewell to R: time-series models for tracking and forecasting epidemics’, Journal of the Royal Society Interface, 18, 210179. https://doi.org/10.1098/rsif.2021.0179 |
Prerequisite Skills | Statistics; Probability/Markov Chains |
Other Skills Used in the Project | Predictive Modelling |
Programming Languages | R |
Design of molecular polyhedra based on non-planar, 'twisted' building-blocks.
Project Title | Design of molecular polyhedra based on non-planar, 'twisted' building-blocks. |
Keywords | Chemistry, Topology, Polyhedra, Mathematica |
Project listed | 10 January 2023 |
Project status | Filled |
Contact Name | Paula Teeuwen |
Contact Email | pcpt3@cam.ac.uk |
Company/Lab/Department | Department of Chemistry, Nitschke Group |
Address | Lensfield Road |
Period of the Project | 8 weeks (3, 4 or 5 days per week, flexible) |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information |
In the research group of Professor Nitschke, we are working with large molecules in the shapes of polyhedra [1]. Examples of such molecular polyhedra that our group has seen in the lab are tetrahedrons, cubes, octahedrons, cuboctahedrons, icosidodecahedrons etc. These types of molecular polyhedra, or also called metal organic cages, can encapsulate other smaller molecules inside their cavity. Various applications for such systems have been envisioned, for example biomedical, catalysis, molecular sensing, gas adsorption and separation [2–4]. These molecular polyhedra are assembled by mixing two types of building-blocks in solution. The vertices of these polyhedra are metal atoms that can coordinate to other molecular building-blocks (linkers) that span the faces [5]. The shape of the linker can influence what type of polyhedron is formed. One example is where a rectangular linker is twisted along one of the axes, leading to a non-planar face. In the lab, we observed that a new type of interesting, non-convex topology with tetrahedral symmetry could be formed from these ‘twisted’ linkers [6]. We would like to investigate whether other types of topologies based on flexible, non-planar faces can be made on a molecular scale. |
Brief Description of the Project |
The aim of this project is to construct a set of new polyhedra based on ‘twisted’ rectangular faces. Specifically, we would like to understand how the dimensions (e.g. length, width and degree of twisting) can lead to different topologies. We hypothesize that a topological series can be made for these types of cages with increasing size, similar to what has been seen for other molecular polyhedra [7,8]. The majority of the work will likely be done using Mathematica or another program for constructing and investigating topologies. Overall, the project is open-ended and the next steps are determined by what we learn along the way. Based on the results, we would like to design a new set of molecular building-blocks that correspond to the variables drawn from the constructed polyhedra. Follow-up experiments done after this project will elucidate whether these building-blocks will indeed assemble into the predicted polyhedral structures in the lab. |
Work Environment |
The student will work closely together with a chemistry PhD candidate (Paula Teeuwen), who is part of a lab in the chemistry department. A discussion at the beginning of the project will take into account the students working habits and preferences. The student may work remotely, however they are welcome to take up a place in our office and be surrounded by our group-members. A hybrid option is also possible. Core lab-hours are from 9.00-17.00, however flexible working hours can be discussed at the start of the project as the student will not be doing any lab-work. The student is expected to join our weekly group-meetings on Wednesday mornings. Regular meetings with the PhD student will make sure the student becomes familiar with the chemical background and can ask any relevant questions. In these meetings the progress is also monitored and new plans are made for the student to work on. The student is encouraged to also talk to the other group-members (postdocs, PhD students etc.) about the project. During scheduled meetings with the group-leader (professor Jonathan Nitschke) the student can present any interesting results together with the PhD candidate. |
References | 1. Lee, S.; Jeong, H.; Nam, D.; Soo Lah, M.; Choe, W. The Rise of Metal–Organic Polyhedra. Chemical Society Reviews 2021, 50, 528–555, doi:10.1039/D0CS00443J. 2. Vardhan, H.; Yusubov, M.; Verpoort, F. Self-Assembled Metal–Organic Polyhedra: An Overview of Various Applications. Coordination Chemistry Reviews 2016, 306, 171–194, doi:10.1016/j.ccr.2015.05.016. 3. Zhang, D.; Ronson, T.K.; Zou, Y.-Q.; Nitschke, J.R. Metal–Organic Cages for Molecular Separations. Nat Rev Chem 2021, 5, 168–182, doi:10.1038/s41570-020-00246-1. 4. Sholl, D.S.; Lively, R.P. Seven Chemical Separations to Change the World. Nature 2016, 532, 435–437, doi:10.1038/532435a. 5. Davies, J.A.; Tarzia, A.; Ronson, T.K.; Auras, F.; Jelfs, K.E.; Nitschke, J.R. Design Rules for the Assembly of Rectangular Subcomponents into Pseudo-Cubic Coordination Cages. (Not published yet, ask if interested.) 6. Davies, J.A.; Ronson, T.K.; Nitschke, J.R. Twisted Rectangular Subunits Self-Assemble into a Ferritin-like Capsule. Chem 2022, 8, 1099–1106, doi:10.1016/j.chempr.2022.01.003. 7. Fujita, D.; Ueda, Y.; Sato, S.; Mizuno, N.; Kumasaka, T.; Fujita, M. Self-Assembly of Tetravalent Goldberg Polyhedra from 144 Small Components. Nature 2016, 540, 563–566, doi:10.1038/nature20771. 8. Liu, Y.; Lee, T.-U.; Rezaee Javan, A.; Xie, Y.M. Extending Goldberg’s Method to Parametrize and Control the Geometry of Goldberg Polyhedra. Royal Society Open Science 9, 220675, doi:10.1098/rsos.220675. 9. Euler’s Polyhedron Formula Available online: https://plus.maths.org/content/eulers-polyhedron-formula. |
Prerequisite Skills | Geometry/Topology |
Other Skills Used in the Project | |
Programming Languages | Python; MATLAB; Mathematica |
Puiseux series in Isabelle/HOL
Project Title | Puiseux series in Isabelle/HOL |
Keywords | formalisation, Isabelle/HOL, computer algebra, real closed field, Puiseux series |
Project listed | 18 January 2023 |
Project status | Filled |
Contact Name | Wenda Li |
Contact Email | wl302@cam.ac.uk |
Company/Lab/Department | Department of Computer Science and Technology (Computer Lab) |
Address | Department of Computer Science and Technology, University of Cambridge, William Gates Building, 15 JJ Thomson Avenue, Cambridge, CB3 0FD |
Period of the Project | 8 weeks, ends before August 31 |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | Modern proof assistants allow users to interact with computers to mechanise mathematical theorems and their proofs. Here, all derivation steps will be mechanically checked, so that ambiguities and errors in normal hand-written proofs can be eliminated. Recent progress in proof assistants includes Grothendieck's Schemes in the Isabelle proof assistant [1] and some recent results from Peter Scholze being mechanised in the Lean proof assistant [2]. This project will involve doing mechanised proofs within the Isabelle proof assistant. |
Brief Description of the Project | Puiseux series are a generalisation of formal power series that allow for negative and fractional exponents of the indeterminate. An interesting property with Puiseux series is that its field provides an example of a non-Archimedean real closed field [Sec 2.6, 3]. Namely, when the coefficients are from a real closed field R and the indeterminate is replaced with an infinitesimal ϵ, we can derive the resulting Puiseux series in ϵ: R<<ϵ>> is real closed. In this project, we want to formally verify this result in Isabelle/HOL using the existing theory of Formal Puiseux series [4] and an ongoing development of real closed field. |
Work Environment | The student will be part of the ALEXANDRIA project led by Prof. Lawrence Paulson. |
References | [1] Bordg, Anthony, Lawrence Paulson, and Wenda Li. "Simple Type Theory is not too Simple: Grothendieck's Schemes without Dependent Types." arXiv preprint arXiv:2104.09366(2021). [2] Castelvecchi, Davide. "Mathematicians welcome computer-assisted proof in 'grand unification' theory." Nature (2021). [3] Bochnak, J., Coste, M. and Roy, M. F. (2013). Real algebraic geometry (Vol. 36). Springer. [4] Manuel Eberl. "Formal Puiseux Series". Archive of Formal Proofs (2021). |
Prerequisite Skills | Mathematical Analysis; Algebra/Number Theory |
Other Skills Used in the Project | |
Programming Languages | None Required |
Modelling tree growth responses to climate change
Project Title | Modelling tree growth responses to climate change |
Keywords | tree growth climate carbon photosynthesis |
Project listed | 23 January 2023 |
Project status | Filled |
Contact Name | Professor Andrew D. Friend |
Contact Email | adf10@cam.ac.uk |
Company/Lab/Department | Department of Geography and Sainsbury Laboratory Cambridge University |
Address | Department of Geography, Downing Place, Cambridge CB2 3EN |
Period of the Project | 8 weeks in the summer, full time |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | Tree growth is typically considered as a direct function of photosynthesis, and there are many models that use this relationship. We have a joint experimental-modelling project to reassess this approach by focussing more on the process of growth itself. We are growing small trees in growth chambers and in the field, measuring them, and developing and testing model approaches to simulating their growth dynamics. The project is more fully described here: https://gtr.ukri.org/projects?ref=NE%2FW000199%2F1 |
Brief Description of the Project | We would like the student to help develop and test new approach to simulating the coupled dynamics of carbon in trees and tree growth. We are working with a number of ideas regarding internal metabolic feedback that require systematic evaluation and mathematical exploration and efficient coding. A successful outcome would be a series of analytical solutions to the coupled behaviour of the tree metabolic system. |
Work Environment | Part of a small team. PhD students and post-doc. Flexible hours, Can work remotely for some, but not all, of the time. |
References |
Friend, A.D., Eckes-Shephard, A.H. and Tupker, Q., 2022. Wood structure explained by complex spatial source-sink interactions. Nature Communications, v. 13, p.7824-. doi:10.1038/s41467-022-35451-7. |
Prerequisite Skills | Mathematical Analysis; Simulation; Predictive Modelling |
Other Skills Used in the Project | Data Visualization |
Programming Languages | Python; MATLAB; C++; Fortran |
Disseminating FAIR Machine Learning Models via BioModels
Project Title | Disseminating FAIR Machine Learning Models via BioModels |
Keywords | BioModels, Machine Learning, FAIR, reproducibility |
Project listed | 23 January 2023 |
Project status | Filled |
Contact Name | Rahuman Sheriff |
Contact Email | sheriff@ebi.ac.uk |
Company/Lab/Department | BioModels, European Bioinformatics Institute (EMBL-EBI) |
Address | Wellcome Genome Campus, Hinxton, Cambridge, CB10 1SD |
Period of the Project | At least 8 weeks or more, full time. Longer availability preferred |
Project Open to | Master's (Part III) students |
Background Information | Machine learning (ML) models are widely used as tools in life science and medical research. However, ML models are scattered across various resources including personal websites, git-hub, bitbucket, and supplementary material, making it difficult to find, access, and reuse them. We aim to extend the BioModels to support Findable, Accessible, Interoperable, and Reusable (FAIR) dissemination of ML models in biomedical sciences. BioModels is a world-leading repository of mechanistic models of biological processes, hosted by EMBL-EBI and accessed by about 51,000 unique users (IPs) every year. BioModels’s infrastructure was recently enhanced to support version-controlled dissemination and curation of a wide range of modelling frameworks and formats, providing capabilities to host and disseminate ML models. We aim to build a collection of useful biomedical ML models, that can easily be searched and accessed by researchers around the globe and reused. |
Brief Description of the Project | The summer project is ideal for a student aiming to move towards Machine Learning in the next step of their career. The applicant should have some experience in machine learning approaches including deep learning neural networks and other equivalent methods. During the internship, the intern will rebuild interesting ML models published in life science journals and submit them to the BioModels repository. There are potential possibilities for the intern to be a co-author on our high-impact manuscript. Our previous interns have co-authored manuscripts with us (e.g., PMID: 31701150, PMID: 33620773) and have secured PhD positions in top organizations including Harvard Medical School, Cambridge, Oxford, EMBL and ICR. |
Work Environment | Will work with the BioModels team at EBI. There are currently other interns working on this project. Software engineers in the team will also be available to support if needed. Flexible working is possible, but the candidate is roughly expected to be on the EMBL-EBI campus at Hinxton, twice a week and free campus buses are available. |
References | PMID: 31701150, PMID: 33620773 |
Prerequisite Skills | Statistics; Probability/Markov Chains; Predictive Modelling; some experience in ML modelling |
Other Skills Used in the Project | |
Programming Languages | No Preference |
Path4Drug: Data Science Workflow for Identification of Tissue-Specific Biological Pathways Modulated by Toxic Drugs
Project Title | Path4Drug: Data Science Workflow for Identification of Tissue-Specific Biological Pathways Modulated by Toxic Drugs |
Keywords | chemoinformatics, drug discovery, database, clustering, network analysis |
Project listed | 23 January 2023 |
Project status | Open |
Contact Name | Rahuman Sheriff |
Contact Email | sheriff@ebi.ac.uk |
Company/Lab/Department | Molecular Networks Team, European Bioinformatics Institute (EMBL-EBI) |
Address | Wellcome Genome Campus, Hinxton, Cambridge CB10 1SD |
Period of the Project | At least 8 weeks or more, full time. Longer availability preferred |
Project Open to | Master's (Part III) students |
Background Information |
The early prediction of drug adverse effects is of great interest to pharmaceutical industry, as toxicity is one of the leading reasons for drug attrition. Analysing publicly available big data to understand the cell signalling and regulatory pathways affected by a drug candidate can greatly benefit the study of drug toxicity. Novel computational approaches to predict the toxicity and adverse effects of drug candidates in the pre-clinical stage are critical to improving human safety during clinical trials. In a recent industrial-academic collaborative project carried out within the EU IMI Translational Quantitative Systems Toxicology (TransQST) consortium (ww.transqst.org), we developed a big data analytics tool that predicts pathways affected by drugs and used it to explore the toxic effect of drugs [1,2]. Our computational technique employs the propagation of drug-protein interactions to connect compounds to biological pathways. Target profiles for drugs were built by retrieving drug target proteins from public repositories such as ChEMBL, DrugBank, IUPHAR, PharmGKB, and TTD. Subsequent enrichment tests of the protein pool using Reactome database revealed potential pathways affected by the drugs. Furthermore, an optional tissue filter utilizing the Human Protein Atlas was applied to identify tissue-specific pathways. The analysis pipeline was implemented in an open-source KNIME workflow called Path4Drug to allow automated data retrieval and reconstruction for any given drug present in ChEMBL. The pipeline was applied to withdrawn drugs and cardio- and hepatotoxic drugs with black box warnings to identify biochemical pathways they affect and to find pathways that can be potentially connected to the toxic events. |
Brief Description of the Project |
In this internship, you will implement the workflow in python and apply the analysis on all approved drugs available in the market. You will also identify toxicity-specific pathway fingerprints through clustering analysis and apply a supervised machine-learning approach to predict the toxicity class of new drug candidates. This tool will be implemented in the Reactome database. There are also opportunities to co-author and publish the manuscript on this work. Our previous interns have co-authored manuscripts with us (e.g., PMID: 31701150, PMID: 33620773) and have secured PhD positions in top organizations including Harvard Medical School, Cambridge, Oxford, EMBL. A fixed monthly allowance is provided to help towards living costs if no other funding is available to the candidates. Support for a UK visa will be offered to the selected candidate if needed. |
Work Environment | Will work with the BioModels / Reactome team at EBI. There are currently other interns working on various projects. Software engineers / Curators in the team will also be available to support if needed. Flexible working is possible, but the candidate is roughly expected to be on the EMBL-EBI campus at Hinxton, twice a week and free campus buses are available. |
References | [1] Füzi B, Gurinova J, Hermjakob H, Ecker GF, Sheriff R. Path4Drug: Data Science Workflow for Identification of Tissue-Specific Biological Pathways Modulated by Toxic Drugs. Front Pharmacol. 2021 Oct 14;12:708296. doi: 10.3389/fphar.2021.708296. PMID: 34721010; PMCID: PMC8551608. [2] Füzi B, Malik-Sheriff RS, Manners EJ, Hermjakob H, Ecker GF. KNIME workflow for retrieving causal drug and protein interactions, building networks, and performing topological enrichment analysis demonstrated by a DILI case study. J Cheminform. 2022 Jun 13;14(1):37. doi: 10.1186/s13321-022-00615-6. PMID: 35692045; PMCID: PMC9188852. |
Prerequisite Skills | Statistics;Mathematical Analysis;Database Queries;Data Visualization |
Other Skills Used in the Project | |
Programming Languages | Python |
Research in the Goldman group: nanopore sequencing and pandemic-scale phylogenetics
Project Title | Research in the Goldman group: nanopore sequencing and pandemic-scale phylogenetics |
Keywords | Sequencing, algorithmics, phylogenetics, mathematical modelling, information theory. |
Project listed | 23 January 2023 |
Project status | Open |
Contact Name | Nicola De Maio |
Contact Email | demaio@ebi.ac.uk |
Company/Lab/Department | Goldman group at EMBL-EBI |
Address | Wellcome Genome Campus, Hinxton, Cambridgeshire, CB10 1SD, UK. |
Period of the Project | At least 8 weeks, full time. |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | There is a Computational Biology M.Phil. seminar on Wednesday 8 February, 2-3pm, by Nicola De Maio and Nick Goldman of the EMBL-European Bioinformatics Institute (EBI). They will describe some of their recent research at EBI, including projects in which internships will be available in Summer 2023. Details of the talk are given here: http://talks.cam.ac.uk/talk/index/192041. Anyone is welcome to attend - if you are not an M.Phil student then please register in advance with Samantha Noel via compbiomphil@maths.cam.ac.uk. |
Brief Description of the Project |
The Goldman group at EMBL-EBI can offer a number of projects to best fit the interests and skills of the students. One of our main areas of research is sequencing technologies, which can read DNA and amino acid sequences. Nanopore sequencing is one of the most promising of these technologies. A useful feature of nanopore sequencing is that it allows selective sequencing: we can reject a DNA molecule if deemed uninteresting after reading only a small portion of it. This allows users to save time and reagents and to gather more useful information from the sequencing process. We have recently developed BOSS-RUNS, a mathematical model and algorithmic framework based on information theory principles that can dynamically optimise the sequencing process using the information collected so far by the sequencing machine, see https://www.nature.com/articles/s41587-022-01580-z. We are currently expanding the applicability and features of this method, and possible projects in this context could involve conducting simulations of the sequencing process with the proposed method and quantitative analysis of the resulting assemblies. For this project some knowledge of python and UNIX is desirable. While nanopore sequencing is often applied to DNA, we are also collaborating with a project aimed at developing nanopore sequencing technologies for proteins, based on single molecule surface enhanced Raman spectroscopy. In brief, a protein translocating through the nanopore is optically excited. A subsequent transition to the ground state results in Raman emission of photons. These photons are characteristic of the amino acid in the nanopore. The aim of a possible project in this area would be to develop a neural network which takes those photons and decodes it back to the protein sequence. Initially, the neural network can be trained/tested/validated using a nanopore simulator developed by a previous CMP student. Further hyperparameter optimisation, warm/cold start of the trained model can be done using new experimental data. Lastly, a long term research interest in our group is algorithms and mathematical models in molecular phylogenetics, that is, the reconstruction of evolutionary histories using DNA sequences. While advancements in sequencing technologies make DNA sequence data ever more affordable and ubiquitous, our algorithms and models to study this data are not efficient enough for analysing large datasets. This has been made painfully obvious during the COVID-19 pandemic: while millions of SARS-CoV-2 genomes have been sequences, traditional phylogenetic methods can only study a few thousands of them at the time. For this reason we have been developing new phylogenetic algorithms and mathematical models that allow the study of millions of closely related genomes, see https://doi.org/10.1101/2022.03.22.485312 . A possible project in this area could involve extending the functionalities and models of our methods, improving the algorithms, or running simulations and benchmark analyses. Useful skills for these projects are familiarity with Python, basic probability concepts, and algorithmic skills. |
Work Environment | The students will work closely with other members of the group (2 postdocs and 1 PhD student in the group, depending on the specific project chosen). Group members are expected to attend the campus on average about 3 days per week. |
References | https://www.nature.com/articles/s41587-022-01580-z https://doi.org/10.1101/2022.03.22.485312 |
Prerequisite Skills | Probability/Markov Chains; Programming (Python) |
Other Skills Used in the Project | Simulation; |
Programming Languages | Python; C++ |
Super-resolution microscopy applications
Project Title | Super-resolution microscopy applications |
Keywords | Single molecule localisation microscopy, point clouds, biological applications |
Project listed | 23 January 2023 |
Project status | Filled |
Contact Name | Jerome Boulanger, Leila Muresan |
Contact Email | Jerome Boulanger <jeromeb@mrc-lmb.cam.ac.uk> |
Company/Lab/Department | MRC-LMB and PDN, University of Cambridge |
Address | Cambridge Biomedical Campus, Francis Crick Ave, Trumpington, Cambridge CB2 0QH or Downing Site, CB2 3DY |
Period of the Project | 8 weeks, full time |
Project Open to | Master's (Part III) students |
Background Information |
The advent of single molecule localization microscopy enabled the improvement of the resolution by an order of magnitude beyond the diffraction limit. For the first time biological structures and processes could be observed via fluorescence microscopy at sub-diffraction scales. However, the reconstruction are not an images in a classical sense, but noisy point clouds. Dedicated approaches are necessary to extract the relevant biological information from the collected data, disentangling them from the characteristics and limitations of the technique. |
Brief Description of the Project | The project is an opportunity to discover single molecule localisation microscopy (SMLM) and its applications. We will revisit typical applications of this technique, and explore potential solutions based on e.g. protein clustering, molecule tracking and trajectory classification, surface approximation. The focus of the project will be adapted to the interest of the student. |
Work Environment | Two supervisors and at least one post-doc would support the student. |
References | |
Prerequisite Skills | Statistics; Image processing |
Other Skills Used in the Project | Statistics; Image processing; Simulation |
Programming Languages | Python; MATLAB; R |
Seismic response of foundations for offshore wind turbines
Project Title | Seismic response of foundations for offshore wind turbines |
Keywords | offshore wind turbine, foundation design, seismic loading, renewable energy, hyperplasticity |
Project listed | 1 February 2023 |
Project status | Filled |
Contact Name | Christelle Abadie |
Contact Email | cna24@cam.ac.uk |
Company/Lab/Department | Department of Engineering / Civil Engineering |
Address | 7a JJ Thomson Avenue, Cambridge, CB3 0FA |
Period of the Project | 8 weeks, starting late June/beginning of July |
Project Open to | Undergraduates; Master's (Part III) students |
Background Information | |
Brief Description of the Project |
This project aims at developing a rigorous mathematical model to capture the behaviour of soils when subjected to earthquake loads. This is essential to the assessment of wind turbine behaviour under earthquake loads, and to the imminent need for offshore wind deployment in East Asia and North America. The model will be developed within the hyperplasticity framework. The hyperplasticity framework is a rigorous mathematical framework that brings together thermodynamics and mechanics, enabling to formulate models for mechanical applications that obey the fundamental principles of thermodynamics. The framework is highly mathematical and would benefit from the rigorous grounding of a maths student. The project will also require implementation of the model, and therefore strong coding skills. The project will aim at (i) performing a thorough literature review on the methods that could be used to capture this specific behaviour, (ii) exploring formulations and implementing them, and (iii) implementing a model for offshore wind turbine monopile design under earthquake loads. The outcome of the project will enable advances in modelling of foundations for offshore wind turbines, both current ones and floating wind. This project is ideally suited to an applied mathematician interested in engineering who is comfortable with mathematical (convex) analysis, in particular differentiation and integration, as well as numerical implementation. Basic knowledge of mechanics and thermodynamics is also desirable. The selected students will learn aspects of civil engineering for foundation design for offshore wind turbines, and hyperplasticity. |
Work Environment | The student will work together with one primary supervisor (Dr. Christelle Abadie) but will benefit from the environment at the new civil engineering building (North West Cambridge), where the project will be based. The new civil engineering building is a recently built research facility, with exciting cutting edge laboratories. The project in itself will be desk-based, but the selected student is very welcome to explore and discover our laboratories and research. The building also has a common hub where to meet other researchers for a cup of coffee. Most researchers within the building work on aspects of civil engineering in the context of climate change. |
References | |
Prerequisite Skills | Mathematical physics; Mathematical Analysis |
Other Skills Used in the Project | Numerical Analysis; PDE's; Predictive Modelling; Mechanics, Thermodynamics |
Programming Languages | Python; MATLAB |