Crickets, Cross-Veins, Crumpling, Crystals, and Computers

Abstract

The world around us appears unimaginably complex: creases on sheets of paper, the patterns on animals, not to mention the assembly of life itself. In this thesis, I use computational tools to shed light on the organizing principles of a selection of systems that appear disordered at first glance. The topics are diverse, as are the tools I used to investigate them. Yet, in all cases, the ultimate aim has been the same: to uncover simple rules/patterns about seemingly complex systems using an evolving computational toolbox. The first chapter looks at how nuclei arrange themselves in the dance of life. In collaboration with the Extavour Lab (Harvard Department of Organismic and Evolutionary Biology (OEB)), we tracked live imaged 3-D datasets of nuclei from the cricket \emph{Gryllus bimaculatus}. We found that nearly every quantifiable aspect of the motion of nuclei can be explained by the local density that the nuclei experience. From this experimental data, we developed a computational model that we used to bolster our findings and make concrete predictions about embryonic development. Some of these predictions we were able to experimentally validate through experimental modification of developing embryos. In the second chapter, my collaborators and I characterize the geometric patterns formed by the veins in insect wings. Dividing up the wing into a series of polygonal shapes, we ask geometric questions about the open spaces formed by the veins. Looking at odonate wings (dragonflies and damselflies), we propose a simple developmental that is able to recapitulate the complex patterns observed. Then, we extend the mathematical toolkit introduced in the first manuscript to a broader selection of insect wings. In the third chapter, I use machine learning to ask if we can uncover geometric order in a classically disordered system: crumpled sheets. We find that by augmenting experimental datasets of crumpled mylar with simulated examples from a sister system---rigid flat folding---we are able to achieve non-trivial predictions on the geometric arrangement of ridges and valleys in the experimental data. In the fourth chapter, I use a variational autoencoder (VAE) to encode and decode 3-D crystal structures. This project is a first step in a larger goal of using modern deep learning methods as a way to search the unimaginably large space of potential structures for possibly (environmentally) useful molecules. The approaches presented in this chapter could easily be extended to many other types of 3-D structure, a topic that is still largely unexplored in the field of generative models. In the fifth chapter, I discuss a few other projects that I worked on in the course of my PhD. In the first project, I discuss a collaboration where we develop a novel machine learning architecture with a physically informed inductive bias. We assume the world is composed of sparsely interacting mechanisms that infrequently interact. We create a neural network architecture based on this idea and show that it achieves impressive prediction results on physical systems and also generalizes better than current methods. In the latter part of the chapter, I discuss two new computational methods relating to Graph Neural Networks that my collaborators and I developed. These disparate topics can all be characterized by using data-driven methods and developing data-driven techniques to cast a simplifying light on seemingly complex systems.