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Alexandria Volkening

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math.DS nlin.AO physics.soc-ph Populations and Evolution Quantitative Methods physics.ed-ph Social and Information Networks Tissues and Organs

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preprint2026arXiv

Multi-objective Bayesian inference in an agent-based model of zebrafish patterns via topological data analysis

Spatial patterns arising from the collective behavior of individual agents are present across biological systems. While agent-based models offer a natural framework for uncovering unknown agent (e.g., cell) interactions, these stochastic models face significant challenges. For spatial patterns, agent-based modeling often involves manual tuning to attain qualitative consistency with multiple experiments. This process limits predictive power and raises questions about parameter identifiability and model uniqueness. Combining topological techniques and Bayesian computation, we present a multi-objective methodology for parameter inference in detailed models. We illustrate our approach by inferring parameters in an agent-based model of zebrafish patterns, achieving practical identifiability in several case studies. By introducing extended prior distributions, we then reframe parameter inference as rule inference, allowing us to search across over 80 candidate agent-based rules to identify an alternative, simpler model consistent with our data.

preprint2022arXiv

How do classroom-turnover times depend on lecture-hall size?

Academic spaces in colleges and universities span classrooms for 10 students to lecture halls that hold over 600 people. During the break between consecutive classes, students from the first class must leave and the new class must find their desks, regardless of whether the room holds 10 or 600 people. Here we address the question of how the size of large lecture halls affects classroom-turnover times, focusing on non-emergency settings. By adapting the established social-force model, we treat students as individuals who interact and move through classrooms to reach their destinations. We find that social interactions and the separation time between consecutive classes strongly influence how long it takes entering students to reach their desks, and that these effects are more pronounced in larger lecture halls. While the median time that individual students must travel increases with decreased separation time, we find that shorter separation times lead to shorter classroom-turnover times overall. This suggests that the effects of scheduling gaps and lecture-hall size on classroom dynamics depends on the perspective - individual student or whole class - that one chooses to take.

preprint2021arXiv

What's math got to do with patterns in fish?

When you think of fish, what comes to mind? Maybe you think of pet goldfish, movie characters like Dory or Nemo, or trout in a local river. One of the things that all of these fish have in common is patterns in their skin. Nemo sports black and white stripes in his orange skin, and trout have spots. Even goldfish have a pattern -- it's just plain gold (and kinda boring). Why do some fish have stripes, others have spots, and others have plain patterns? It turns out that this is a tricky question, so scientists need tools from several subjects to answer it. In this paper, we use biology, math, and computer coding to help figure out how fish get different skin patterns.

preprint2020arXiv

Forecasting elections using compartmental models of infection

Forecasting elections -- a challenging, high-stakes problem -- is the subject of much uncertainty, subjectivity, and media scrutiny. To shed light on this process, we develop a method for forecasting elections from the perspective of dynamical systems. Our model borrows ideas from epidemiology, and we use polling data from United States elections to determine its parameters. Surprisingly, our general model performs as well as popular forecasters for the 2012 and 2016 U.S. races for president, senators, and governors. Although contagion and voting dynamics differ, our work suggests a valuable approach to elucidate how elections are related across states. It also illustrates the effect of accounting for uncertainty in different ways, provides an example of data-driven forecasting using dynamical systems, and suggests avenues for future research on political elections. We conclude with our forecasts for the senatorial and gubernatorial races on 6~November 2018, which we posted on 5 November 2018.

preprint2019arXiv

Topological data analysis of zebrafish patterns

Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists within pattern-forming systems on both microscopic and macroscopic scales. Quantifying variability and measuring pattern features can inform the underlying agent interactions and allow for predictive analyses. Nevertheless, current methods for analyzing patterns that arise from collective behavior only capture macroscopic features, or rely on either manual inspection or smoothing algorithms that lose the underlying agent-based nature of the data. Here we introduce methods based on topological data analysis and interpretable machine learning for quantifying both agent-level features and global pattern attributes on a large scale. Because the zebrafish is a model organism for skin pattern formation, we focus specifically on analyzing its skin patterns as a means of illustrating our approach. Using a recent agent-based model, we simulate thousands of wild-type and mutant zebrafish patterns and apply our methodology to better understand pattern variability in zebrafish. Our methodology is able to quantify the differential impact of stochasticity in cell interactions on wild-type and mutant patterns, and we use our methods to predict stripe and spot statistics as a function of varying cellular communication. Our work provides a new approach to automatically quantifying biological patterns and analyzing agent-based dynamics so that we can now answer critical questions in pattern formation at a much larger scale.

preprint2014arXiv

Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model

Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and microenvironmental factors have been correlated with the emergence of drug resistance. With the goal of better understanding drug resistance and its connection with the tumor microenvironment, we have developed a hybrid discrete-continuous mathematical model. In this model, cancer cells described through a particle-spring approach respond to dynamically changing oxygen and DNA damaging drug concentrations described through partial differential equations. We thoroughly explored the behavior of our self-calibrated model under the following common conditions: a fixed layout of the vasculature, an identical initial configuration of cancer cells, the same mechanism of drug action, and one mechanism of cellular response to the drug. We considered one set of simulations in which drug resistance existed prior to the start of treatment, and another set in which drug resistance is acquired in response to treatment. This allows us to compare how both kinds of resistance influence the spatial and temporal dynamics of the developing tumor, and its clonal diversity. We show that both pre-existing and acquired resistance can give rise to three biologically distinct parameter regimes: successful tumor eradication, reduced effectiveness of drug during the course of treatment (resistance), and complete treatment failure.