Projects
Machine Learning for Air Quality Models
In this work, we derive a mathematical framework for machine learned replacements that conserves properties, say mass, atoms, or energy, to machine precision. This framework can be used to develop machine learned operator replacements in environmental models.
Image Guidance for Robot-Assisted Ankle Fracture Repair
This project concerns developing and validating an image guidance framework for
application to a robotic-assisted fibular reduction in ankle fracture surgery. The aim is to
produce and demonstrate proper functioning of software for automatic determination of
directions for fibular repositioning with the ultimate goal of application to a robotic reduction
procedure that can reduce the time and complexity of the procedure as well as provide the
benefits of reduced error in ideal final fibular position, improved syndesmosis restoration and
reduced incidence of post-traumatic osteoarthritis. The focus of this product will be developing
and testing the image guidance software, from the input of preoperative images through the
steps of automated segmentation and registration until the output of a final transformation that
can be used as instructions to a robot on how to reposition the fibula, but will not involve
developing or implementing the hardware of the robot itself.
Robust and Low Cost Drag Sphere Anemometer
We have developed a low cost device for measuring wind speed and direction by revisiting the concept
of a Drag Sphere Anemometer. In short, a spherical float is held in the air and wind drag acts upon the
sphere. The sphere is connected to an instrumented base via a rod. Force on the sphere is transmitted to the base, where it is translated into component vectors using load cells. This simple design has no moving parts and no exposed delicate components. A microcontroller reads the load cells, handles data collection, and is capable of interacting with other devices such as aerosol samplers via serial communication. We will present data comparing our prototype to established commercial wind sensors in outdoor environments
Sketchup Slicer Ruby plugin for converting 3D model to image stack
3D models are frequently used in Computer Vision applications to simulate real world objects. For example in medical applications, 3D models of bones, organs, and other anatomical features are commonly constructed and used to study drugs, diseases, and procedures [1,4,7]. Furthermore, 3D models can be combined with machine learning, such as being fed as input into deep neural networks, for purposes such as diagnosis or surgical guidance [2,5]. It is often necessarily or at least useful to have the 3D model stored in the form of a sequence of 2-dimensional slices, otherwise known as an image stack [3]. Image stacks are often usually the output format of medical imaging devices, such as with DICOM and TIFF formats. Neural networks and other machine learning algorithms also usually require fixed grid input such as images [6]. However, 3D modeling software packages generally offer few if any methods to directly export 3D models, such as an .stl file, to an image stack. This work presents a novel method for instantly converting a 3D model to an image stack directly in the form of a Ruby script written for use in Sketchup, a 3D CAD program originally developed by Google. Sketchup is written in Ruby and provides an API allowing for development of custom plugins which made this possible. The plugin was tested using an example of a 3D lung model.
A Game-theoretic Model of Blepharisma Population and Cannibalism Dynamics
This was my Extended Essay in Mathematics for the IB Diploma.
Blepharisma are single-celled organisms that have the ability to consume other members of their species. Those that engage in cannibalism become giants, creating a distinct polymorphism of two possible states- either regular dwarf or cannibalistic giant. The exact conditions in the environment that give rise to this cannibalistic behaviour, in blepharisma and other cannibalistic species, has been the subject of some speculation and study. However, it has been suggested that a game-theoretic approach may be appropriate for determining when individuals may choose to engage in cannibalism. In this paper, a game-theoretic model of the dynamics of cannibalism within Blepharisma populations is created by incorporating best response dynamics into a discrete time population model. The model is used to test the effects of both total resource availability and population density on the prevalence of cannibalism, finding that increasing either of these environmental factors increases cannibalistic behaviour. It also reveals that cannibalism can have implications on total population size. Furthermore, it is possible, under certain conditions, for the modelled population to arrive at an equilibrium in which the entire population is either purely cannibalistic or non-cannibalistic rather than a coexistence of both states, and these conditions are mathematically solved for.