I was recently invited to talk on a podcast hosted by The Noor Podcast. In this podcast, I spoke about what it was like doing a PhD in mathematics. I also talked about my life story leading up to my PhD, my PhD journey so far, and discussions revolving around my research in mathematical biology, among other topics. If you are interested in listening in, you can find the podcast on YouTube below or on Spotify....
In this blog, I will give a basic MATLAB tutorial on plotting and how to use BibTex in LaTeX. In addition, I show how to insert the MATLAB figure into Overleaf. This video was made from my recent teachings of a first-year advanced mathematics course where there was a need to show students how to make nice plots and referencing for their reports. I hope you enjoy the tutorial if you are interested....
Introduction In my master’s and PhD project, I explore the world of mathematical biology. More specifically, I aim to better understand the growth patterns and behaviour of yeast colonies commonly used for making bread and alcoholic beverages. I find this interdisciplinary collaboration extremely rewarding because it empowers me to make contributions to benefit winemakers, bioengineers, material scientists etc. My work is done under the wonderful supervision of A/Prof Benjamin Binder and Dr Edward Green, where we are developing new mathematical models to predict the spatial patterns in yeast colonies....
In many mathematical biology modelling, we eventually encounter the problem of coupling experimental data with simulation data. In many of these cases, we also care about uncertainty quantification of our model parameters in prediciton experimental results. Once approach for parameter inference is Bayesian inference. However, in many modelling senarios the likelihood is intractable meaning the likelihood is unavailable in closed form, or where evaluation of the likelihood is infeasible. Hence, we turn to approximating of the posterior distribution using a technique called approximate Bayesian computation (ABC)....
The goal of this blog is to implement my favorite cellular automata (CA) of all time; Conway’s game of life. This CA model has a special place in my heart because it inspired me to pursue my current masters topic. In fact, this was my first ever CA model I ever coded (on bus home from uni). The algorithm is a lattice model that has only four different rules, but can generate endless patterns given appropriate initial grid positioning....
The goal of this blog is to understand how Melnikov theory can be used to determine the wavespeed of travelling waves in a perturbed reaction-diffusion system. In particular the focus of this blog will be on the paper Wavespeed in reaction-diffusion systems, with application to chemotaxis and population pressure (Balasuriya and Gottwald 2010). We wish to investigate perturbing a standard form of a reaction-diffusion partial differential equation (PDE) which allows us to use tools from Melnikov method to find the wavespeed of the solution....
Method of lines is a numerical technique used to solve a large class of partial differential equations (PDEs). Method to lines uses finite differences methods by discretising all spatial variables of a PDE while time remains continuous. This results in a system of ordinary differential equations (ODEs) which can be solve numerically using solvers such as ode15s() in Matlab. One prime example of a PDE encountered by many undergraduate students is the diffusion equation....
Cellular automata (CA) is a interesting mathematical tool that is used to model many natural phenomena such as biological behaviors. One prime example of CA models is it’s use in mathematical biology to model cellular interactions and behaviors by studying cells on a molecular level. In a CA model an individual square may represent a cell or particle on a grid/lattice. These elements can only take up a discrete number of states such as on or off and in a biological sense this can be interpreted as alive or empty....