Emerging areas in Mathematical Biology: Celebrating research from the Mathematical Biosciences Institute

Jae Kyoung Kim

Korea Advanced Institute of Science & Technology

"Advancing Static and Time-series data: Random Matrix Theory, Causal Inference and Mathematical Modeling"

In this talk, I will discuss methods for extracting meaningful information from static and time-series data. For static data, Principal Component Analysis (PCA) is widely used to detect signals in noisy datasets. However, determining the appropriate number of signals often relies on subjective judgment. I will introduce an approach based on random matrix theory to objectively select the optimal number of signals. For time-series data, causal inference techniques such as Granger causality are commonly employed. Unfortunately, these methods often yield high false-positive rates. I will present a novel mathematical model-based approach to causal inference.

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Janet Best

The Ohio State University

"Energy Allocation and Sleep Homeostasis"

The upregulation of diverse functions, including memory consolidation and restorative processes, suggests sleep is a time for specialized energy use. While sleep was long considered an energy conservation strategy, the modest calculated savings led to skepticism that energy conservation is the function of sleep, particularly given sleep’s inherent costs in vulnerability. This talk will present a mathematical model based in an evolutionary perspective on the function and timing of sleep.

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Punit Gandhi

Virginia Commonwealth University

"Using transformation information to characterize symmetry transitions"

Transformation information (TI) provides a versatile, entropy-based method for identifying approximate symmetries by quantifying deviations from exact symmetry with respect to a parametrized family of transformations. We define notions of approximate symmetry and maximal asymmetry in terms of critical points in TI as a function of a transformation parameter. This framework allows us to characterize transitions in symmetry by tracking qualitative changes with respect to these critical points. We apply TI to mathematical models inspired by developmental biology and actual biological images. Our analysis of the qualitative changes in symmetry properties indicates a potential pathway toward a general mathematical framework for characterizing symmetry transitions akin to bifurcation theory for dynamical systems.

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Anastasios Matzavinos

Pontifical Catholic University of Chile

"Chemotaxis and Stochastic Gradient Ascent: Fractional Brownian Motion in Optimization and Biological Models"

Chemotaxis, the directed movement of cells and microorganisms in response to chemical signals, is a fundamental biological process. Modern modeling approaches often combine Brownian motion with gradient-driven motility, drawing parallels to stochastic gradient ascent algorithms used in optimization. At its core, chemotaxis can be viewed as a natural optimization process that steers cells toward regions of higher chemoattractant concentration. However, recent experimental findings challenge this classical view. In the absence of chemotactic cues, many cell types exhibit motility patterns that resemble fractional Brownian motion, with correlated increments that differ fundamentally from those of Brownian motion. This shift in perspective has important implications for how we understand and model cell migration. In this talk, we present computational evidence showing that cells with positively correlated movement patterns explore their environment more effectively and are better equipped to handle fluctuations in the chemotactic landscape. We also discuss the broader relevance of these findings in contexts such as tumor-induced angiogenesis and developmental processes. This work was supported in part by ANID FONDECYT Regular grant No. 1221220.

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