# MIORPA

MIORPA (Mathematical Institute’s Online Research Projects with Africa) is a virtual mentorship platform that supports pre-PhD students who are based in sub-Saharan Africa. During the eight-week programme, which will run from late June 2024, you will undertake an online research project meeting regularly with a mentor 1:1 remotely, attend training skills and information sessions, and have the opportunity to develop your research skills. MIORPA builds on the success of Mfano Africa, which was started by Geoffrey Mboya in 2020.

The Mathematical Institute is offering online research projects in different areas of mathematics. Interested applicants should apply to work on a specific project and, if successful, will be paired with a mentor based on shared research interests. We may add more projects to the list of available research projects, up until one week before the deadline.

Interested applicants should

- be ordinarily based in a sub-Saharan African country
- have completed a mathematical sciences BA or BSc degree;
- not yet enrolled in a PhD programme;
- demonstrate high academic excellence and give evidence of striving to improve;
- be motivated for further study.

Read more about the different MIORPA projects:

Project Title | Project Description | Mentor | |
---|---|---|---|

1. | Modelling antibiotic resistance in bacteria subject to environmental noise | Antibiotic resistance is poised to become one of the greatest and most complex challenges that humanity will confront this century. A key driver of resistance—and, indeed, the formation of many common infections, cancers, and other ailments—is the heterogeneity ubiquitous to biological systems. It is this heterogeneity that affords bacteria robustness in the face of adversarial antibiotic treatment, and allows the long-term adaptation that may one day render many infections incurable. In this project, we will draw on tools from financial mathematics, stochastic differential equations, and computer simulation to answer three questions. | Alex Browning |

2. | Intraday Volatility Forecasting Using Deep Learning In Cryptocurrency Markets | Volatility forecasting in cryptocurrency markets using intraday volatility data and machine learning methods. More specifically, studying the performance of a select few methods proposed in the volatility forecasting literature and see how well these techniques work in that asset class. Some examples of techniques that you will be looking at are transformers and WaveNet. | Emmanuel Djanga |

3. | Bending a elastic-viscoplastic beam — linearised and/or numerical analysis
| Bending of long, slender beams is a commonly encountered mechanical phenomenon; think of drinking straws, corn stalks, and paper clips as examples. Small amounts of curvature can spring back elastically, but larger bending can create irreversible curvature of the beam. This irreversible curvature sometimes localises to a point, creating a hinge-like structure. This project will consider a viscoplastic model of irreversible bending and try to understand what sets the spacing of hinge points in the beam. A linearised stability analysis will be used in the first instance.
| Richard Katz & Peter Howell |

4. | Buri’s Experiment and the Effective Population Size | In 1956, Peter Buri studied a population of fruit flies in which some individuals had red eyes and some had white eyes. He kept the population size fixed at 16 individuals and plotted the variance of eye-colour over 19 generations. His experimental data fit theoretical predictions well—if he substituted an effective population size of 12 instead of the census population size of 16. This discrepancy is due to the idealisations inherent in mathematical modelling. Nowadays, ecologists use the effective population size as a measure for the genetic diversity of a population, which is vital if the population needs to adapt to changing environmental conditions. In this project, we study the mathematical models and statistics underlying Buri’s analysis (Wright–Fisher model, Kingman Coalescent) and related topics based on the student’s interests. | Adrian Martini |

5. | Rate-dependent pattern formation | Regular patterns from those on animal coats to the spacing of ripples in sand and wrinkles in skin all reflect an equilibrium between different forces. They are therefore normally considered as being a static phenomenon. However, examples are now emerging of patterns that are determined by dynamics: the effect of ‘rate’ is important. This project would consider this in a model system such as the Turing model for animal coat patterns, seeking to understand what features of patterns are determined by the rate of instability. | Dominic Vella |

6. | Mathematical modelling of schistosomiasis transmission dynamics | This research project focuses on the modelling of infectious disease dynamics, with a specific application to schistosomiasis, a water-borne parasitic disease. Schistosomiasis is transmitted through contact with water contaminated by the larvae of parasitic flatworms called schistosomes released through the urine or faeces of infected individuals. The parasites can penetrate the skin and infect the body, leading to schistosomiasis. The aim is to adapt existing compartmental models to better understand the transmission dynamics within populations considering mixing patterns and mobility. The project will begin with a concise review of existing compartmental models for schistosomiasis and other infectious diseases, providing a foundational understanding of the methodologies employed. Building upon this knowledge, the project will adapt and refine existing models, integrating relevant parameters gathered from literature and available data sources. The methods employed will predominantly revolve around systems of ordinary differential equations, encompassing deterministic and/or stochastic approaches. Students will gain valuable skills in literature review, infectious disease modelling, and coding with an in-depth look to applied mathematics for real-world global health problems. Desirable skills for prospective students include a keen interest in infectious disease transmission and some proficiency in programming languages such as Julia, Python, or R. | Melissa Iacovidou |

7. | On the algebraic structure of multiple zeta values and the Drinfeld associator | The special values of the zeta function and their algebraic structure has been a focus of mathematical research since Euler. While the algebraic structure of multiple zeta values is known, at least conjecturally, the same problem is open in general fort the case of single-valued multiple zeta values except for a bound on the dimension obtained via general consideration. I have a proposal to study this problem by making use of the f-alphabet decomposition of MZVs. Some preliminary results have already been obtained with this method and interesting relation to the representation theory of symmetric groups has been identified. So the plan is to further explore this relation to understand the algebraic structure of single-valued MZVs. A part of this process will likely also require working with computer algebra systems such as Mathematica to gather data. Hence, prior experience with computer algebra systems and representation theory of symmetry groups will be a huge asset though in principle these can be learned while working on the project. Another window into the multiple zeta values is provided by the Drinfeld associator, an object of central interest in mathematics and physics with connection to diverse areas such as knot theory, Lie theory, motivic Galois theory, Feynman integrals etc. Therefore, an explicit and concrete understanding of the associator will be of huge consequence in many areas. Based on some heuristic arguments, I have a proposal to get a Dynkin Lie type recursive formula for certain commutators that appear as coefficients of the zeta values in the expression for the Drinfeld associator. This phenomenon can be studied via certain matrix representations for the associator I have come across in my research. Further, use of predictive machine learning algorithms may be of huge benefit in this exploration. Hence, interest in or prior experience with such machine learning programs will likely be a great asset in this project though not strictly necessary since these can be learned during the project. | Deepak Kamlesh |