April 22, 2025, 1:00-2:00pm
Speaker: Shiva Mirzaeian (Georgia State University)
Title: A telescopic independent component analysis on functional magnetic resonance imaging data set
Abstract: Brain function can be modeled as dynamic interactions between functional sources at different spatial scales, and each spatial scale can contain its functional sources with unique information, thus using a single scale may provide an incomplete view of brain function. This paper introduces a novel approach, termed “telescopic independent component analysis (TICA),” designed to construct spatial functional hierarchies and estimate functional sources across multiple spatial scales using fMRI data. The method employs a recursive independent component analysis (ICA) strategy, leveraging information from a larger network to guide the extraction of information about smaller networks. We apply our model to the default mode network (DMN), visual network (VN), and right frontoparietal network (RFPN). We investigate further on the DMN by evaluating the difference between healthy people and individuals with schizophrenia. We show that the TICA approach can detect the spatial hierarchy of the DMN, VN, and RFPN. In addition, the TICA revealed DMN-associated group differences between cohorts that may not be captured if we focus on a single-scale ICA. In sum, our proposed approach represents a promising new tool for studying functional sources.
April 8, 2025, 1:00-2:00pm
Speaker: Dr. Mohit Dalwadi (University of Oxford)
Title: Microswimmer motility and natural robustness in pattern formation: the emergence and explanation of non-standard multiscale phenomena
Abstract: In this talk I use applied mathematics to understand emergent multiscale phenomena arising in two fundamental problems in fluids and biology.
In the first part, I discuss an overarching question in developmental biology: how is it that cells are able to decode spatio-temporally varying signals into functionally robust patterns in the presence of confounding effects caused by unpredictable or heterogeneous environments? This is linked to the general idea first explored by Alan Turing in the 1950s. I present a general theory of pattern formation in the presence of spatio-temporal input variations, and use multiscale mathematics to show how biological systems can generate non-standard dynamic robustness for 'free' over physiologically relevant timescales. This work also has applications in pattern formation more generally.
In the second part, I investigate how the rapid motion of 3D microswimmers affects their emergent trajectories in shear flow. This is an active version of the classic fluid mechanics result of Jeffery's orbits for inert spheroids, first explored by George Jeffery in the 1920s. I show that the rapid short-scale motion exhibited by many microswimmers can have a significant effect on longer-scale trajectories, despite the common neglect of this motion in some mathematical models, and how to systematically incorporate this effect into modified versions of Jeffery's original equations.
March 25, 2025, 1:00-2:00pm
Speaker: Hamed Karami (Georgia State University)
Title: Stable Parameter Estimation and Forecasting Strategies for the Cholera Model: Insights from the 1991–1997 Cholera Epidemic in Peru
Abstract: Environmental transmission plays a pivotal role in cholera dynamics, influencing the accuracy and stability of epidemiological models. This study focuses on stable parameter estimation by exploring three distinct strategies for determining the environmental transmission rate while concurrently estimating other key parameters, such as the reporting rate. Regularization techniques are employed to enhance stability and mitigate parameter uncertainty. Focusing on the 1991–1997 cholera outbreak in Peru, we apply these approaches to calibrate the model and assess parameter robustness. Additionally, we extend these methodologies to forecast cholera cases during this outbreak, incorporating uncertainty quantification to evaluate prediction reliability. Given the strong correlation between cholera incidence and temperature, we account for seasonal variations to improve forecast accuracy. While forecasting seasonal diseases like cholera poses challenges, particularly in short-term horizons, leveraging multiple datasets enhances prediction stability. The results provide several forecasts and an in-depth analysis of cholera trends, offering insights into model performance and practical implications for epidemic preparedness.
March 11, 2025, 1:00-2:00pm
Speaker: Marrium Shamshad (Georgia State University)
Title: Functional network reconstruction and aperiodic spectral neural activity for SOZ identification
Abstract: Seizure onset zone (SOZ) localization in epilepsy poses a fundamental challenge due to the dynamic nature of brain networks and the lack of precise biomarkers. We present two independent approaches that uncover distinct SOZ characteristics, offering novel insights into its identification. The first approach reconstructs functional network dynamics by analyzing the rate of change in node degree, or the temporal derivative, which captures rapid connectivity shifts overlooked by static network measures. This method pinpoints unstable regions and identifies critical SOZ nodes in most successful surgical cases, providing a transparent and computationally efficient alternative to machine learning-based models. The second approach quantifies aperiodic spectral activity, isolating deviations in power spectral density slope as a marker of excitation-inhibition imbalance. SOZ regions exhibit significantly steeper slopes in high-frequency bands, indicating pathological network excitability. By revealing critical network disruptions, these approaches redefine seizure localization and establish a stronger foundation for understanding pathological brain dynamics.
February 18, 2025, 1:00-2:00pm
Speaker: Amy Maria Sims (Georgia State University)
Title: Simplified and branching models for cell proliferation in a tissue-engineering scaffold
Abstract: While the effects of external factors like fluid mechanical forces and scaffold geometry on tissue growth have been extensively studied, the influence of cell behavior – particularly nutrient consumption and depletion within the scaffold – has received less attention. Incorporating such factors into mathematical models allows for a more comprehensive understanding of tissue-engineering processes. Our models use well-established governing equations like Darcy’s law and advection-diffusion-reaction equations to track the complex behavior of multiple parameters such as porosity/pore radii, shear stress, nutrient concentration, and nutrient flow pressure. Cells within the scaffold are fed nutrients to induce proliferation, and we assume a constant inlet flux of these suspended nutrients as the fluid flows through the scaffold. Our continuum model, recently published in BMAB, assumes homogeneity for any cross-section of the medium, allowing the reduction from three to two dimensions; and the crux of this earlier work offers a candidate for ideal pore shape for channels within the scaffold to achieve maximum tissue growth. Specifically, an investigation of scaffolds with specific two-dimensional initial porosity profiles determines that those which are uniformly graded in porosity throughout their depth promote more tissue growth. Our more recent project builds from the continuum model by featuring more complex geometry toward the goal of more precise results, albeit with greater computational cost. Namely, we utilize a branching structure wherein pores bifurcate at each layer junction, allowing for investigation of the input parameters at a pore level. By assuming homogeneity along two axes, the biological scaffold’s geometry is effectively reduced to one dimension. Varying the width of pores and the thickness of layers in each bifurcating set of branching channels facilitates predictions of candidates for ideal scaffold geometries according to priorities of time, cost, or total volume. Both models utilize simplifying methods such as nondimensionalization to reduce the number of parameters and asymptotic analysis based on the small aspect ratio of the scaffold; and the branching model also incorporates averaging along a cross-section of the pore. Because experiment is costly and time-consuming, our focus is to develop integrous models that unveil scaffold geometries that cultivate the highest volume of engineered tissue in the smallest amount of time, while respecting that the tissue mimic native tissue as closely as possible to curtail the possibility of transplant rejection.