At the end of the spring term, we were welcomed by Imperial College London to their South Kensington campus for the inaugural ICLMS Research Project Presentation Day and Finale.
Students have been working on these projects since the start of October, alongside a mentor from academia or industry. The meetings with mentors helped students get their heads around the difficult scientific and mathematical concepts that they tackled in their research projects, but ultimately the emphasis of the programme was for students to focus on their own research and pursue their own ideas. Having opportunities like this – outside of the traditional structure of the classroom – is a part of one of our core ideals at ICLMS: providing opportunity for students to explore ideas beyond the standard curriculum. Throughout the Research Project, students have developed their independence, communication skills, self-confidence, and many other technical abilities that will allow them to thrive at ICLMS at beyond.
The Research Project Presentation Day was a culmination of six months of work from our students and their mentors, who included Professor Richard Craster, Dean of Imperial’s Faculty of Natural Scientists. About the day, Professor Craster said: "It was a highlight of my term attending and seeing all the enthusiastic students, proud parents and guardians and busy staff from the ICLMS. It is a real pleasure to see the school coming into shape and this event demonstrated the benefits of universities working in partnership with schools to deliver excellent educational experiences and training."
The projects consisted of a wide range of topics, which can be read about here:
On the Associativity of Floating-Point Arithmetic
Sarp, Atlas, Rishikesh
Mentors: Mr. Samuel Coward, Dr. Theo Drane
"(3 + 2) + (-1) = 4 and 3 + (2 + (-1)) = 4. This is called the associative property of addition and is an elementary property of simple arithmetic. Floating-point arithmetic is used to represent real numbers with fractional parts (like 12.625) within a computer. Without it, computers would not be able to operate on numbers with decimal points. However, the use of floating-point arithmetic in computers sometimes produces unprecedented errors that disobey the associative property of addition! So, it is possible that your computer thinks that (1.2 + 3.4) - 5.6 is not equal to 1.2 + (3.4 - 5.6). Our presentation delves into finding the probability that such an error occurs within a computer."
Galaxy Rotation Curves and Dark Matter
Dhylan, Arijeet, Benjamin, Mathias
Mentor: Mr. Jan Kozuszek
"Our project explores the idea of an invisible substance that creates a force. This substance does not interact with light, hence its name, dark matter. By looking at data from the galaxy Andromeda, we observe that the speeds of celestial bodies orbiting a galaxy do not match our predicted models. We explore the possible reasons for the discrepancy and discuss how the existence of dark matter could resolve this."
The Game of Sim
Muhammad, Will, Tetsu, Catherine
Mentor: Professor Richard Craster
"In this project, we look into the mathematics around the Game of Sim, a game as simple as Noughts and Crosses to play but with surprisingly complex mathematical theories surrounding it. Throughout our report, we explore how and why the game works and what the winning strategy involves. We also touch on similar games, and how the same concepts that form the fundamentals in the game of sim and its strategy apply to these variations."
Dyson Extractor Fan
Max, Raito, Amr
Mentor: Mr. Freddie Lock
"Our group had the task to redesign a product that is commonly used but has many flaws. We decided to design an extractor fan as we know that the quality of it can affect pollution and air quality. We wished to improve upon modern designs with the help of our mentor from Dyson Limited and use of knowledge of Dyson motors to make the best product possible."
Investigating the Genus of Topological Manifolds
Vivaan, Joey, Nathan, Ada
Mentor: Mr. Calvin Chen
"In our group project, we explore how to determine the number of holes of a surface. In two or three dimension we can just "count the number of holes". However, we show how this can be done using functions in morse theory and vector fields in the Poincare-Hopf theorem. These methods can then be extended into higher dimensions."
Vessel Mooring
Thomas, Kai
Mentor: Ms. Natalie Martinkova
"Our task was to explore the methods used by maritime civil engineers to calculate the forces involved with mooring a large ship. To do this we used methods from British standards and the world association for waterborne transport infrastructure (PIANC). We then used these methods to create an automated Excel spreadsheet and calculated the forces for an example vessel."
Period Doubling and Chaos in Nonlinear Maps
Alexander, Aneesh, Rohan, Yendo
Mentor: Dr. Phil Ramsden
"Suppose we wanted to model a population of rabbits. A nonlinear map (called the logistic map) can be used to model just this. The final population will vary with the reproductive rate of the rabbits. For some reproductive rates the final population of the rabbits is predictable, but for a reproductive rate of 3.57 and almost all larger rates the final population is unpredictable: it is chaotic. This does not only apply to rabbits; chaos pervades the real world, from the weather to turbulent fluid flow. How can we actually model and 'quantify' chaos and how does it emerge?"
Social Networks, Compartmental Models & COVID-19
Christian, Charikleia, Wajidullah, Thomas
Mentor: Ms. Emilie Olufsen
"Our research project was an exploration of how mathematics can be used to predict the spread of disease with a particular focus on the recent COVID-19 pandemic. We looked at one of the most popular methods of epidemiological modelling, the SIR model, and the ways in which many of its limitations can be mitigated. We used the programming language R to simulate varying degrees of lockdown success, and how this impacts the spread of COVID-19 through a population."
Dyson Motor-Powered Shoes
Shaheer, Otto, Nabeel
Mentor: Ms. Leigh Crozier
"In our group project we employed design engineering strategies, as used at Dyson, focusing on developing our novel idea of motor-powered shoes. Working closely with a Dyson engineer, we researched trends in children's shoes, conducted calculations to determine the specifics of our motors and used computer aided design (CAD) in order to visualise our design. Throughout our enquiry, we carefully considered many aspects of our product, combining statistical analysis and engineering considerations, leading to a final plan for our motor-powered shoes."
Pursuit Problems
Mohamed, Jacob, Bright, Domenico
Mentor: Dr James Munro
"Pursuit problems are dilemmas which involve two or more objects that obey simple rules within an environment. We have simulated and investigated different possible pursuit problems, ranging from studying only a few entities, to hundreds. Subsequently, we have drawn parallels to natural phenomena such as ant "death spirals" and flocking birds. Additionally, we have also investigated the practical applications of pursuit, such as in crowd safety and the military."
Global Dynamics of Connected Vehicle Systems
Samuel, Kai, Tejas, Ojas
Mentor: Mr Swapnil Kumar
"In our project we study the behaviour of connected vehicle systems by simulating a mathematical model of both human-driven and autonomous vehicles interacting, which we have developed in Python. This simulation is of a single lane circular road, where we investigate the effect of autonomous vehicles on the formation of traffic waves. We observe that even single autonomous vehicles in large traffic waves can entirely eliminate the traffic wave, and that increasing the number of autonomous vehicles on the road will lead to smoother traffic flow."
The Application of K-Means Clustering to a Diabetes Dataset
Kirby, Monica, Somiga, Alessandro
Mentor: Dr Marina Evangelou, Ms. Ella Orne
"Our project explores the use of K-means; a method of clustering groups from a given dataset. In our case we are using it to analyse a gene expression dataset of diabetic patients. Through the application of K-means algorithm we used distance measurements to calculate the closeness of individuals within groups. The research we conducted aimed to identity clusters of patients within the dataset. This would allow us to identity clusters, and so subtypes of the condition. This is a technique used to in the real world to help with the treatment of conditions by identifying groups and genetic similarities."