March 15^{th}, 2024 - Poster: Radial Basis Function Techniques for Neural Field Models

My poster presentation for APPM Recruitment 2024.

October 26^{th}, 2023 - Python in Scientific Computing: Why and How?

Python is one of the more popular scripting languages in scientific computing and data science, along with MATLAB, R, and Julia. An interesting difference is that Python was not designed with scientific computing in mind. Rather, it is a general purpose language designed to be simple and flexible. Strangely, I find that it is uncommon for scientists to take advantage of the features that make Python so successful, and instead to write procedural codes with an overreliance on the array data structure. In this talk I will focus on one feature in particular: generators (also called streams). Generators are built into Python syntax, and they are a natural way to represent mathematical sequences. I will explain what generators are, how they are baked into the Python syntax, how I use them, and why you should use them in your scientific Python codes.

We examine traveling wave solutions of a neural field model (integro-differential system) incorporating synaptic depression, allowing for biologically realistic traveling pulse solutions similar to those observed experimentally. We use these pulses as a biologically plausible model for visual motion processing, and develop an asymptotic wave response function characterizing how traveling pulse solutions respond to perturbative stimuli. For some spatially localized moving stimuli, traveling pulse solutions can accelerate to match the speed and location of the stimulus - a phenomenon known as entrainment. Generally speaking, traveling pulse solutions will entrain to spatially localized moving stimuli if the stimuli are sufficiently weak and sufficiently slow. We use our wave response function to identify this speed-magnitude threshold to first order. Finally, we apply our wave response function to a stimulus meant to evoke the apparent motion illusion - a phenomenon where a sequence of stationary stimuli are presented and motion is perceived.

August 29^{th}, 2023 - Math-bio Seminar

We examine traveling wave solutions of a neural field model (integro-differential system) incorporating synaptic depression, allowing for biologically realistic traveling pulse solutions similar to those observed experimentally. We use these pulses as a biologically plausible model for visual motion processing, and develop an asymptotic wave response function characterizing how traveling pulse solutions respond to perturbative stimuli. For some spatially localized moving stimuli, traveling pulse solutions can accelerate to match the speed and location of the stimulus - a phenomenon known as entrainment. Generally speaking, traveling pulse solutions will entrain to spatially localized moving stimuli if the stimuli are sufficiently weak and sufficiently slow. We use our wave response function to identify this speed-magnitude threshold to first order. Finally, we apply our wave response function to a stimulus meant to evoke the apparent motion illusion - a phenomenon where a sequence of stationary stimuli are presented and motion is perceived.

August 16^{th}, 2023 - Group Update

I show our asymptotic entrainment threshold agrees with simulations for the apparent motion stimulus.

June 7^{th}, 2023 - Group Update

I discuss the new formula for the wave response and the entrainment threshold.

May 16^{th}, 2023 - SIADS 2023 Poster

My poster for the SIAD dynamical systems conference in 2023.

April 4^{th}, 2023 - Comprehensive Exam Presentation

My presentation for my comprehenisve exam. Also, my thesis proposal.

March 10^{th}, 2023 - APPM Recruitment Poster

My poster (and suplemental material) for the APPM 2023 recruitment poster session.

April 26^{th}, 2022 - Group Update

I discuss my current work in incorporating adaptation into a neural field model. I recap my failed attempt at incorporating hyper-polarizing adaptation current, and discuss my current approach incorporating a synaptic depression variable.

March 10^{th}, 2022 - CSCI 5314 Paper Presentation

I present a 15 minute summary of Ge and Liu's 2021 paper Foraging behaviours lead to spatiotemporal self-similar dynamics in grazing ecosystems.

December 6^{th}, 2021 - APPM 5370 Presentation

**The wave response function in an adaptive neural field model**

A very trimmed down version of the Math-bio seminar talk.

November 8^{th}, 2021 - APPM Math-bio Seminar

**The wave response function in an adaptive neural field model**

Neural field models are integro-differential equations describing the propagation of neural activity through the brain. The simplest of neural field models describes a single spatial dimension and exhibits traveling-front solutions where activity propagates into inactive regions then remains active indefinitely. More realistic models incorporate adaptation, which allows active regions to eventually decay back to base line inactivity, resulting in traveling pulse solutions. In this talk we will examine one such model that incorporates a hyperpolarizing adaptation current, explore some of its properties. In particular we will examine the wave response function: the shift in position of traveling pulses due to small perturbations.

August 26^{th}, 2021 - APPM Graduate Student Seminar

**Functional Programming in Python**

Functional programming (FP) is a declarative programming paradigm, in which functions are said to be "first-class citizens", and function composition is used to create complex procedures while maintaining modularity and extensibility. Proponents of FP say that it reduces errors, simplifies debugging, and makes programming more mathematical. Python supports programming in the functional paradigm. In this inaugural presentation of the APPM Graduate Student Seminar we explore the potential of the functional paradigm in scientific computing with specific examples implemented in Python.

July 8^{th}, 2021 - Research Group

Update the research group on my current work, including the $\mathcal{O}(\varepsilon)$ approximation to the wave response function for the adaptive model.