Tag: Mathematics

Burn Notice: Using Changepoint Detection Algorithms to Improve Wildfire Tracking

Presenter: Sabrina Reis – Mathematics and Computer Science

Faculty Mentor(s): Weng-Keen Wong

Session: (In-Person) Oral Panel—Fuel, Fire, Grass and Compost

The ability to detect anomalous data is a critical component of any useful statistical analysis, but the process for identifying anomalies can prove time-consuming and arduous. To address these challenges, researchers often delegate data processing to an algorithm, which analyzes data with more speed, efficiency, and accuracy than manual calculations, enabling earlier detection of anomalies. The property of early detection is especially critical when monitoring spatio-temporal events such as wildfires. The critical impact of these events necessitate data sources that provide current and complete information. This need is often met by networks of sensors–for instance, air quality sensors–that collect real-time, localized data. When processed with an anomaly detection algorithm, the comprehensive data collected by sensor networks can reveal aberrations indicative of a spatio- temporal event. To explore how anomaly detection algorithms can facilitate early detection of events of interest using sensor data, we gathered historical data from open-source Purple Air sensors to build case studies of past wildfires. We then applied various types of changepoint detection algorithms to the data in hopes of identifying changes in the distribution of data that indicated a wildfire had broken out. The toolkit of detection methods produced by the project offer a cost-effective and portable way of enhancing our ability to monitor the formation and spread of wildfires.

Creating an Educational Graphic Novel about Psychedelics

Presenter: Audra McNamee – Mathematics and Computer Science

Faculty Mentor(s): Luca Mazzucato

Session: (In-Person) Poster Presentation

Scientific communication through the use of comics is an emerging trend across scientific disciplines. Comics are a promising medium for outreach because they appeal to non-scientifically trained audiences, hold the reader’s attention, and the storytelling approach lends itself to explaining complex scientific information. Psychedelics are a promising subject for a scientific comic: psychedelics have recently been designated by the FDA as breakthrough treatment for PTSD, depression, and addiction. While the press on psychedelics is unceasing, most publications about psychedelics are focused on venture capital, psychedelic retreats, and clinical trials. Missing is an explanation of the neuroscience of psychedelics, and reflection on how the history of psychedelics intersect with racial justice and cultural appropriation of indigenous traditions and practices. We are creating a comic addressing these gaps in the science and history of psychedelics by explaining scientific material accurately and accessibly.

The comic is structured around the conversation between two friends, one of whom is very pro-psychedelics, the other being staunchly anti-psychedelics. Having the comic take the form of a dialogue will offer space for argument and nuance: putting psychedelics into historical context, explaining and disproving common myths about psychedelics, explaining how social justice and psychedelics interact, and providing an introductory understanding of the science of psychedelics.

Welcome to Computer Science: Designing a Comic Tour of Computers and Computing

Presenter: Audra McNamee – Mathematics and Computer Science

Faculty Mentor(s): Kathleen Freeman

Session: (In-Person) Oral Panel—Comics, Classics and Analysis

While the number of high-quality educational comics is growing, there are no modern long-form comics discussing computer science at an undergraduate level. The computer science comics that do exist, along with being for a younger audience, are generally focused on teaching the reader programming concepts without exploring other aspects of computer science. For this thesis I scripted and drew the 54-page comic Welcome to Computer Science, which introduces the reader to computer science concepts including computer architecture, programming languages, and the internet. As a narrative comic written for an undergraduate audience, it can draw in readers who otherwise might not choose to engage with the material. As a breadth-first introduction, the comic provides the reader with a foundational understanding of computers and computer science; this work may provide even more experienced students with a better understanding of how their computer science classes relate to the rest of the field.

Simulating Dead-End State Distributions for Microbial Metabolism

Presenter: Nathan Malamud − Mathematics and Computer Science

Faculty Mentor(s): Stilianos Louca

Session: (In-Person) Poster Presentation

In this project, I simulate the influence of microbial metabolism on ocean geochemistry using the Cariaco Basin, Venezuela as a model system. In my investigation, I used bifurcation diagrams to visualize the distribution of possible dead-end states: geochemical configurations at which all metabolic reactions become energetically unfavorable and microbial metabolism slows to a halt. In a radically novel approach, I used an Ornstein-Uhlenbeck process to stochastically model kinetic rates.

My rationale for doing this was to show how stoichiometry and energetics alone could potentially determine long-term biogeochemical states. By running N=9,336 simulations written in Python, I found that the dead-end state of an isolated system with aerobic sulfide-oxidizing microbes could be determined fairly consistently based on varying oxygen levels. At high oxygen concentrations (>100 micromolars), oxygen was utilized to the fullest metabolic extent (until the Gibbs free energy yield reached 0 kJ / mol) by the simulated microbes in order to convert all available sulfide to sulfate.

At lower oxygen levels, nitrate was utilized instead due to its biochemical role as an alternative electron acceptor. At higher oxygen levels, final nitrate concentrations were far less predictable, and significant variation in nitrate consumption can be seen in the associated bifurcation plot. This theoretical exercise may aid in the development of biogeochemical models of climate-influenced ocean processes.

Gender Representation in 1970s Science Fiction: Joanna Russ and Ursula Le Guin

Presenter: Makenna Greenwalt − Mathematics

Co-Presenter(s): Amelia Hartman-Warr

Faculty Mentor(s): Judith Raiskin

Session: (In-Person) Poster Presentation

Science fiction has long been a medium through which harmful gender stereotypes have thrived. Despite being forward-thinking in terms of science and technology, sci-fi novels and short stories often portray societies that are patriarchal and male-centric. Enter Ursula K. Le Guin and Joanna Russ, two women whose writing became highly popular and influential in the science fiction scene of the 1970s. Despite the societal norms of the time, Le Guin and Russ were able to use their science fiction to explore then-unconventional ideas of gender. Yet, despite taking revolutionary steps that transformed the world of science fiction, both Le Guin and Russ struggled to fight the sexist culture they were immersed in and find an understanding of gender within it.

Using Information Theory to Understand Neural Representation in the Auditory Cortex

Presenter: Hannah (Qiaochu) Cui — Mathematics

Faculty Mentor(s): James Murray, Christian Schmid

Session: (In-Person) Poster Presentation

Neurons in the brain face the challenge of representing sensory stimuli in a way that accurately encodes the features of these stimuli while minimizing the effects of noise. This thesis will use the concept of mutual information from information theory, which quantifies the amount of information one variable can tell us about another and vice versa, to better understand neural coding in the auditory cortex. Previous research has been done in maximizing mutual information to better understand neural behavior patterns in the visual cortex, with limited auditory findings. We will perform numerical optimization in Python to maximize information that a population of neurons contains about an auditory stimulus within the framework of information theory. This is done by first finding the optimal width and location of tuning curves that characterize neural response to one dimensional stimuli (sound frequency), then updating the optimization algorithm to fit two-dimensional stimuli (sound frequency and intensity). By testing the algorithm with a set of natural sound data, our computations show that in the latter case, optimal stimulus information is represented by multiple populations of neurons that respond in qualitatively different ways to auditory stimulus features, rather than by a homogeneous population with similar response properties. Our findings provide a method to better understand neural representation in the auditory cortex.

Verifying the Implementation of Secure Multi-Party Computation Systems

Presenter: Jonathan Eskeldson

Mentor: Kevin Butler

Poster: 14

Major: Computer Science/Mathematics 

As technology has advanced, applications have arisen which rely on sensitive data. In the past, users had to trust these application’s creators with private data. However, breaches of private data and abuses of power, such as
the Snowden NSA revelations, have eroded users’ trust. A recent development in cryptography, called multi-party computation (MPC), allows multiple parties to compute a function over sensitive inputs, in such a way that the
inputs themselves are not revealed, bypassing the issue of trust. This is usually done by performing Yao’s Garbled Circuit protocol. This was mostly theoretical work until a few years ago, when systems capable of performing these operations were created. While there is confidence in the theory driving such systems, little attention has been paid to their implementations, which are prone to error due to their large size and complexity. These errors could create discrepancies between what a system claims to do and what that system actually does, which could weaken its security. The purpose of this study is to rigorously evaluate the security of leading MPC implementations, and expose bugs that weaken the system’s security. This research will help inspire confidence in the implementation of these systems, making them suitable for use in areas where security is a high priority, including electronic elections and private auctions.

A Computational Approach To Tangled String

Presenter(s): Nathaniel Schieber − Mathematics

Faculty Mentor(s): Robert Lipshitz

Oral Session 2S

Research Area: Knot Theory (Mathematics)

Funding: Mercer Family Foundation Scholarship, UO Department of Mathematics Juilfs Scholarship

Knot theory is exactly what it sounds like. It studies how pieces of string can be tied around themselves and around each other. From this tangible starting point, a wealth of abstract mathematics has arisen. My research in knot theory has had two main goals: to study a specific tangle and to classify tangles up to small complexity. Both have centered on encoding and manipulating the three dimensional geometry of knots within a computer program. The specific tangle I am studying is known as Krebes’s Tangle, named for the mathematician who first asked if it were possible to connect the ends of this specific tangle to the ends of a second tangle in order to form a single un-knotted circle of string. My method in approaching this question has been computational, writing code which generates random tangles, accomplishes the gluing process, and then computes a knot invariant known as the Alexander polynomial. In order to classify tangles, my code takes these randomly generated tangles and organizes them into equivalence classes based on what are known as quantum invariants. Both projects are still on–going.

Knot theory has found applications across mathematics as well as in data analysis and DNA research. However, the software for generating and manipulating generic knots directly has remained relatively limited. Along with working toward generalizing the Alexander polynomial, my work adds to the computational resources available to mathematicians studying knots. I hope it to prove of experimental benefit.

The Atomistic Reconstruction of Coarse-Grained Polymeric Systems via Machine Learning Techniques

Presenter(s): Jake Olsen—Chemistry and Mathematics

Faculty Mentor(s): Marina Guenza, Jake Searcy

Session 1: It’s a Science Thing

Polymeric systems, things like proteins, DNA, and synthetic plastics, are of great interest for their applications in material design and the biomedical industry . Therefore, having time-efficient and inexpensive approaches to investigate these systems on multiple scales, from the microscopic to the macroscopic level, is of great importance and necessity . Molecular dynamics (MD) simulations are one such tool for investigating these systems; however, MD simulations that simulate polymer systems in their atomistic (AT) representation are unable to reach the time scale necessary so that the system exhibits the correct chain characteristics . Thus, coarse-graining (CG) methods, a process by which the local degrees of freedom are averaged out, are applied to improve upon computational time . Unfortunately, the computational gain is coupled with the loss of statistical information from the CG process . Therefore, to regain the lost AT information the CG trajectories need to be transformed back to an AT representation . This process is known as backmapping . Utilizing state- of-the-art machine learning techniques coupled with AT data, we have developed a backmapping procedure for CG polymeric systems . The model, centered around a recurrent neural network (RNN), shows strong agreement with the AT data across many statistical quantities prompting further investigation and development of the model .

Simulation of Bacterial Motion in Sterically Complex Environments

Presenter(s): Matthew Kafker—Physics, Mathematics

Faculty Mentor(s): Tristan Ursell

Session: Prerecorded Poster Presentation

Many species of bacteria navigate complex and heterogeneous environments to search for metabolic resources and avoid toxins . Common among such complexities is steric structure—solid objects whose surface curvature alters bacterial trajectories upon impact . In previous experiments, we characterized scattering of bacteria from vertical pillars of different radii, which provides the basis for understanding how impact with a solid, curved object alters bacterial motion . However, it remains poorly understood how multiple interactions affect bacterial trajectories and whether distinct object curvatures or length-scales of separation between steric objects have qualitatively distinct effects on bacterial motion . We address this question using agent-based computer simulations of cells moving within 2D environments . Each environment presents simulated cells with steric objects (i .e . circular pillars) of radius 8 .3μm and a controlled separation between pillars of L μm, where L is a parameter of the simulation . Cells then diffuse through this environment, scattering with pillars they encounter . By measuring the mean squared displacement (MSD) of the ensemble of trajectories in time for different values of L, we are able to quantify precisely how the length-scales of separation between steric structures affect bacterial trajectories . These MSD measurements will also allow us to compare our results with future experimental work . Ultimately, we hope that our results may contribute to a more realistic model of the behavior of motile cells in natural environments such as soils or a mammalian gut .