Undergraduate Summer Research Project

The UCD School of Mathematics and Statistics, SFI’s Centre for Research Training in Foundations of Data Science, the Royal Society SFI University Research Fellowship scheme and the UCD College of Science are pleased to offer a number of undergraduate summer research placements in 2024. The list of potential projects is given below. A stipend of €3,000 will be paid per student. The programme is aimed specifically at penultimate-year undergraduate students, although students in other years may be admitted in exceptional circumstances. The programme is not restricted to UCD students.

Applicants should submit:

1. their application form online here (opens in a new window)shorturl.at/bryKP
2. a cover letter (max 1 page), and 
3. a CV (max 2 pages) as a single PDF file with filename <lastname_firstname.pdf> to be to be emailed to (opens in a new window)robert.osburn@ucd.ie Please see guidance on writing a CV suitable for this programme.

The deadline for applications is Monday, April 8, 2024 at 17:00. Where a mismatch occurs between the number of offers and the demand for projects, candidates will be ranked according to a weighted average of GPA and other factors (e.g. quality of CV, suitability of candidate to a particular project). Successful candidates will be notified in mid to late April. It is envisaged that the projects will last a minimum of 6 weeks, starting in early June. Details of start dates can be negotiated with individual supervisors.

An undergraduate research project is a great opportunity for students to develop their research skills. See previous year's reports and what some of our alumni have gone on to do! Also, see this recent (opens in a new window)article on their success.

Project Titles, Supervisors and Abstracts

Title: Instrumental variables for the effect of multiple treatments
Supervisors: (opens in a new window)Dr. Leonard Henckel

Questions of cause and effect are central to many areas of scientific research and public policy making. The gold standard to answer such questions is to perform a randomized controlled experiment but in many cases it is unethical, impractical or too resource consuming to do so. A popular alternative in such cases is to use instrumental variables (Angrist et al., 1996). These are auxiliary variables that under certain conditions can be used to infer causal effects from observational data, i.e., in the presence of unmeasured confounding. It is well understood that instrumental variable methods only work, if the instruments satisfy certain conditions and understanding these conditions is a major research area (e.g., Brito and Pearl, 2022; Pearl, 2009). Recently, Henckel et al. (2023) have provided a necessary and sufficient criterion for a conditional instrumental set to be valid in linear causal models. This result, however, only holds for single interventions, i.e., settings with a single treatment. In some cases, one may be interested in the causal effect of multiple treatments simultaneously (Pfister and Peters, 2022). In this project we will investigate whether it is possible to derive a necessary and sufficient validity criterion for the multiple treatment setting. As a starting point we will consider the sufficient criterion by Pfister and Peters (2022) and investigate what cases it does not cover.

References:

Angrist, J. D., Imbens, G. W., and Rubin, D. B. (1996). Identification of causal effects using instrumental variables. Journal of the American Statistical Association, 91 (434), 444-455.

Brito, C. and Pearl, J. (2002). Generalized instrumental variables. In Proceedings of the Eighteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-02), 85-93.

Henckel, L., Buttenschoen, M., and Maathuis, M. (2023). Graphical tools for selecting conditional instrumental sets. Biometrika, asad066

Pearl, J. (2009). Causality. Cambridge University Press, Cambridge, second edition.

Pfister, N. and Peters, J. (2022). Identifiability of spare causal effects using instrumental variables. In The Proceedings of the 38th Annual Conference on Uncertainty in Artificial Intelligence (UAI-22), 1613-1622.

Title: Black holes virtual reality experience
Supervisor: (opens in a new window)Dr. Christiana Pantelidou

Black holes, arising as solutions to Einstein’s equations of general relativity, are naturally complex objects. Yet, they are also wonderfully simple; a black hole can be fully characterised by just three numbers: its mass, spin and charge. They also don’t suck in everything around them; that is, unless you are very close to them, black holes act like any other celestial body. These are just some of the ideas that come up when discussing black holes with a broad audience.

To facilitate public engagement, the Relativity Group has developed a Virtual Reality (VR) experience to demonstrate Einstein's theory of general relativity near a black hole. It allows the user to experience how light is distorted because of a black hole, to experiment with the motion of a body orbiting around a spinning black hole, and to visualise the effect of gravitational waves.

The aim of this project is to advance the efforts of the Relativity Group in this direction. Depending on the background of the student, this might be achieved by creating a tutorial for the current functionalities of the VR set or by adding new functionalities to it, such as hyperbolic orbits or visualisations of an in-falling observer.

This project is funded by Dr Pantelidou’s Royal Society-SFI award.

Title: Asbestos site detection using random forests and Bayesian additive regression trees
Supervisor: (opens in a new window)Dr. Riccardo Rastelli

Malignant mesothelioma is a rare but fatal form of lung cancer which is strongly associated with exposition to some types of asbestos fibers. Asbestos is a generic name used to indicate a type of building materials that have been widely used in the last century, and that are still used in many countries today. Since the incidence of mesothelioma has been increasing worldwide, there have been repeated calls for the need to stop using asbestos, and to safely remove damaged asbestos-containing materials. However, the discovery of problematic asbestos sites remains a challenge, thus posing potential health risks in the areas surrounding the site. The goal of this project is to use modern machine learning techniques to discover and map asbestos sites using satellite data and geospatial information. The project has a strong statistical and programming focus, and will require some familiarity with a data science programming language such as R or Python.

Title: Positive cones on algebras with involution
Supervisor: (opens in a new window)Dr. Thomas Unger

The purpose of this project is to work out a number of explicit examples of (pre-)positive cones in the context of two recent papers on positive cones and gauges on central simple algebras with involution by Astier and Unger. The student should be familiar with quadratic and hermitian forms and central simple algebra with involution.

This project is partially funded by the College of Science.

References:

V. Astier and T. Unger: Positive cones and gauges on algebras with involution, International Mathematics Research Notices, Volume 2022, Issue 10 (2022), 7259-7303

V. Astier and T. Unger: Positive cones on algebras with involution, Adv. Math. 361 (2020), 106954, 1-48

Title: Droplet Impact: Modelling and Applications
Supervisor: (opens in a new window)Dr. Lennon O'Naraigh

Droplet impact is a well-studied problem in Fluid Mechanics with applications in spray cooling, crop spraying, and Forensic Science. In this project the student will use the OpenFOAM software model to simulate droplet impact on a solid surface. This is a powerful software tool which can discretize the Navier-Stokes equations in case of a complex geometry, and solve the resulting equations. Minimal coding effort is required, the main focus is on mesh generation and understanding how to build a simulation case using fundamental concepts in Fluid Mechanics and Computational Mathematics. And yet the results can be very striking - see for instance, work from a previous student here: (opens in a new window)https://www.youtube.com/watch?v=Gmvl9ta6-JU

The aim of the proposed project is to build on these previous results and simulate in detail a real droplet-impact simulation generated by Dr Ó Náraigh with a high-speed camera - see here: (opens in a new window)https://www.youtube.com/watch?v=Bf2enan5VfY

Depending on the time available, the student might be able to explore some of the applications of droplet impact in Forensic Science.

By undertaking this project, the student will develop sought-after skills in Computational Fluid Dynamics (CFD). One student who worked on a similar project not long ago used the project as a springboard into a Master's in CFD and from there, to a career as a CFD engineer.

References:

Attinger, D., Moore, C., Donaldson, A., Jafari, A. and Stone, H.A., 2013. Fluid dynamics topics in bloodstain pattern analysis: Comparative review and research opportunities. Forensic science international, 231(1-3), pp.375-396.

O'Naraigh, L. and Mairal, J., 2023. Analysis of the spreading radius in droplet impact: The two-dimensional case. Physics of Fluids, 35(10).

Roisman, I.V., Rioboo, R. and Tropea, C., 2002. Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458(2022), pp.1411-1430.

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