# TriCAMS Abstracts

# Poster Abstracts

## 1 Andrew Atanasiu

### Modeling S. cerevisiae chromatin domains and highlighting nucleus heterogeneity

## 2 Ayesh Awad

### Mathematical Model of Covid-19 Immune Response

The COVID-19 virus has significantly impacted our society. Despite the development of vaccines, our understanding of the disease and its interaction with the human immune system remains limited. With the emergence of new SARS-CoV-2 strains, current treatment methods may become ineffective. Jenner et al. made notable advancements in mathematically modeling of the immune response to SARS-CoV-2. Building on this work, we have enhanced the model by incorporating three additional critical factors: NK cells, IFN-γ, and TNF-α to investigate the mechanisms responsible for severity of the disease.

## 3 Amartya Banerjee

### Trajectory Inference in Wasserstein Space

Capturing data from dynamic processes through cross-sectional measurements is seen in fields from computer graphics to robot path planning and cell trajectory inference. This inherently involves the challenge of understanding and reconstructing the continuous trajectory of these processes from discrete data points, for which interpolation and approximation plays a crucial role. In this work, we propose a method to compute measure-valued B-splines in the Wasserstein space through consecutive averaging. Our method can carry out approximation with high precision and at a chosen level of refinement, including the ability to accurately infer trajectories in scenarios where particles undergo splitting (division) over time. We rigorously evaluate our method using simulated cell data characterized by bifurcations and merges, comparing its performance against both state-of-the-art trajectory inference techniques and other interpolation methods. The results of our work not only underscore the effectiveness of our method in addressing the complexities of inferring trajectories in dynamic processes but also highlight its proficiency in performing spline interpolation that respects the inherent geometric properties of the data.

## 4 Akash Bhowmik

### High-Throughput Quantitation for Measuring Cell Contractility in μTUG Devices

“Background: Phase contrast imaging is a critical tool for visualizing live samples, particularly in measuring forces generated by contractile tissues. Traditionally, image registration and calculation of micropillar deformation are performed manually, creating a significant bottleneck in the processing pipeline. Automating this process with an algorithm could enhance the efficiency and applicability of phase contrast imaging.

Aims: The objective is to use a well-established cell/hydrogel seeding protocol to integrate a cell-laden hydrogel into a printed annulus. This aims to identify the optimal geometry and material that support the formation and contraction of a collagen type I hydrogel embedded with smooth muscle cells (SMCs).

Methods: The study will adhere to an established method for microTUGs, utilizing flexible materials for printing the annulus. Engineering parameters such as geometry, material stiffness, and hydrogel adhesion will be explored. Practical considerations may necessitate refinements in geometry to effectively introduce the cell/hydrogel slurry.

Results: Pending the results from supplementary aims, the goal is to achieve the formation of a contracted ring, with the ability to measure deformation within the annulus considered a bonus. The primary outcome is the successful formation and contraction of the hydrogel, regardless of annulus deformation.

Conclusions: This exploration aims to advance the methodology for tissue engineering applications, particularly in creating contractile tissue constructs. By identifying the optimal geometry and material for the hydrogel and annulus, the study seeks to improve the efficiency of measuring contractile forces in engineered tissues.”

## 5 Austin Blitstein

### Anomalous interference drives oscillatory dynamics in wave-dressed active particles

A recent surge of discoveries has sparked significant interest in driven-dissipative systems where a particle self-propels due to a resonant interaction with its self-generated wave field. These wave-dressed active particles frequently undergo rapid changes in velocity due to a variety of factors, including boundaries altering their direction of motion, media inhomogeneities distorting their wave field, and direct interactions with their own wave field. We deduce the emergence of a non-local wave-mediated force caused by an anomalous type of wave interference in the vicinity of jerking points, places where the particle’s velocity changes most rapidly. In contrast to the typical case of constructive interference at points of stationary phase, waves excited by the particle at jerking points avoid cancellation through rapid changes in frequency. Through an asymptotic analysis, we approximate the wave force at jerking points, allowing us to rationalize in-line speed oscillations, non-specular reflections off potential walls, and wave-like statistics in certain potential wells. The results we derive are generic, and thus applicable to a relatively large class of wave-dressed active particles.

## 6 Han Cao

## 7 Souradip Chattopadhyay

### Odd viscosity in falling film instabilities

For a thin liquid flowing down an inclined plane, breaking time-reversal symmetry leads to a viscosity tensor that consists of even (symmetric) and odd (antisymmetric) components. The antisymmetric part introduces an odd viscosity term, which is essential for stabilizing interfacial instabilities in the low to moderate Reynolds number regime.

## 8 Michael Facci

### A Robust Immersed Interface Method for Viscous Incompressible Fluids

The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work using the IIM for fluid dynamic applications has focused on smooth interfaces, but boundaries with sharp features such as corners and edges can appear in practical analyses, particularly of engineered structures. We introduce a discontinuous Galerkin (DG) interface representation that captures sharp features exactly. We also investigate smooth geometries which encapsulate high pressure flows, and introduce a geometry smoothing technique from computer graphics, Phong shading. Phong shaded interfacial normal vectors allow for simulations involving cardiological pressure loaded vessels to see in an increase in accuracy of three to four orders of magnitude. Lastly, we address near contact between two interface within one Cartesian grid cell by introducing a modified interpolation operator which involves jump conditions evaluated on both boundaries. We show that the newly modified interpolation operator converges in the limit as the distance between the two interfaces vanishes, whereas prior interpolation operators diverge in the limit.

## 9 Jake Grdadolnik

### A New Bonding Model for Platelet Aggregation

Hemostasis is the healthy clotting response to a blood vessel injury, with a major component of clotting being platelet aggregation mainly facilitated through platelet 𝛼IIbβ3 integrins. When clotting disorders affect 𝛼IIbβ3, resulting in excessive bleeding, treatments exist to restore hemostasis, however the mechanism of restoring aggregation without 𝛼IIbβ3 remains speculative. We simulate individual platelets using the molecular dynamics software, LAMMPS, and track the platelet-platelet and platelet-wall bonds that form during aggregation. We model the bonds as links formed between platelet receptors (GPVI and GP1b), and platelet integrins (𝛼2β1 and 𝛼IIbβ3), with plasma-borne molecules (von Willebrand factor and fibrinogen) and wall adherent collagen. Our bonding model is a novel approach to simulate platelet aggregation in LAMMPS because it incorporates these detailed biophysical processes. Currently, the strength of the bonds depend on the local shear rate of a prescribed background flow and the platelet activation state which is tracked on individual platelets using ordinary differential equations. Simulations based on these models show stable aggregation for healthy platelets under flow. Future work is to improve our modeling framework by parameterizing with experimental measurements and study the mechanisms of hemostasis restoration in platelet integrin disorders.

## 10 Aidan Guenthner

## 11 Riley Harper

### K-Means Time Clustering of Respiratory Mortality Trends

We analyzed mortality trends related to influenza, pneumonia, and COVID-19 across the United States. By applying K-Means Time Clustering, a variant of traditional K-Means Clustering tailored for time series data, we grouped states based on their mortality trends from 2019 to 2023. The primary data included total deaths from pneumonia, influenza, and COVID-19 across all 50 states. Dynamic Time Warping (DTW) was used as a distance measure to capture similarities between the temporal data of state-level death trends. Additionally, we incorporated flight cancellation data to create an interactive Streamlit-hosted data visualization. Our analysis revealed distinct regional clusters of mortality trends. States within the Southeast, Southwest, and West regions experienced similar mortality trends, with peaks that aligned with the Delta variant, while the Midwest and Northeast states exhibited similar mortality trends, with peaks that aligned with the nationwide mandatory lockdown. All regions also shared overlapping peaks due to major pandemic waves and seasonal respiratory illness patterns. The findings illustrate which regions of the United States exhibited similar responses to handling the pandemic, as reflected in their mortality trends. These regional patterns provide insight into the effectiveness and variation in pandemic responses across the country. With the ongoing impacts of these respiratory illnesses, understanding regional variations in death rates can provide insights for future public health interventions.

## 12 Kaitlyn Hohmeier

### Application of Gromov-Wasserstein Barycenters to Classification Problems

We will examine the Gromov Wasserstein barycenter, a generalization of the Wasserstein barycenter to metric measure spaces. The Gromov Wasserstein framework allows us to compare objects that carry different geometries in an intrinsic manner. We will use it to study barycenters of graphs, interpreting graphs as a metric spaces, and therefore ensuring that networks’ inherent structure is respected. The main result is the presentation of a proof-of-concept involving Gromov-Wasserstein barycenters of graphs in nearest centroid classification. Given a set of graph data that can be assigned to qualitative classes, we compute the Gromov-Wasserstein barycenter of each class, treat these barycenters as the centroids of each class, and then use the Gromov-Wasserstein distance to compute the distance between a test graph and the barycenter of each class. The test graph will then be assigned to the class whose barycenter it is closest to. This algorithm will be demonstrated on two data sets: brain data collected from the Center of Biomedical Research Excellence (COBRE) and a collection of randomly generated graphs from two distinct classes. While ultimately the classification results were poor for the COBRE data due to the nature of the graphs in the dataset, the algorithm performed well on the dataset of random graphs.

## 13 Aaron Jacobson

### Spatio-Temporal Analysis of Brain Functional Connectome

The goal of this research is the development of methods which make use of the functional connectivity of regions in the human brain for the early detection and prediction of neurodegenerative diseases such as Alzheimer’s disease. Functional connectivity has been widely investigated to understand brain disease in imaging-based neuroscience and clinical studies, and it appears to change in topology over time. Examination of changes in functional connectivity is proving to be a valuable tool for understanding human brains; notably, functional connections are progressively disrupted by the molecular mechanisms characteristic of neurodegenerative diseases such as Alzheimer’s disease. We are developing novel mathematical models and accompanying machine learning algorithms which make use of this fact to characterize the spatial and temporal dynamics of functional brain connectivity. Success in this research will lead to discoveries about the mechanisms that link brain function with cognition and behavior, and the tools developed may be used to improve the accuracy of Alzheimer’s diagnosis, especially in early stages of the disease.

## 14 Logan Keener

## 15 Aryan Kokkanti

### TopoLoop: A new tool for chromatin loop detection in live cells via single-particle tracking

“We report the development of an analytical method to identify topological features of chromatin domains through single particle tracking in live cells. Advances in studies of chromosome structure reveal chromosome loops as a driving organizational principle beyond the nucleosome. The ability to map the topology of chromatin trajectories in live cells would provide an important advance in identification of chromosome loops in single cells. Traditional time series analysis commonly represents a particle’s trajectory as a sequence of discrete points. While this approach effectively captures linear motion and overall displacement, it often falls short in detecting complex spatial patterns, such as loops. In contrast, topological data analysis (TDA) considers the entire particle trajectory as a continuous path embedded in a three- or four-dimensional space (x, y, z, time). TDA uses methods of persistent homology, including simplicial structures and connected components, to characterize the ‘shape’ of a data set. Further analysis via persistence amplitude can provide additional insight into the data.

We used polymer bead-spring models to assess the method’s accuracy. Positions of a single chromatin segment (bead) were plotted over time and under different permutations of conditions regarding chain persistence length, tethering, and a cross-linking spring strength (simulated condensin). A sliding window approach was utilized to measure the persistence amplitude over time and track temporally local trends of the chromatin segment. We can predict when a bead is in a chromatin loop if the amplitude at that time is above a threshold. We were able to accurately detect chromatin loops in tethered chains in simulations with high tethering weights. Through quantitative analyses of simulations over a range of parameter space we can assess the efficacy of loop identification and put limits on our ability to detect small and short-lived loops. We will report tracking results from integrate lacO-LacI-GFP arrays. Current results indicate that the application of TDA provides an important new tool for studying structural features of chromatin dynamics in live cells.”

## 16 Ying Liang

### Neural Network-Assisted Methods For Inverse Random Source Problem

Inverse source scattering problems are essential in various fields, including antenna synthesis, medical imaging, and earthquake monitoring. In many applications, it is necessary to consider uncertainties in the model, and such problems are known as stochastic inverse problems. Traditional methods require a large number of realizations and information on medium coefficients to achieve accurate reconstruction for inverse random source problems. To address this issue, we propose a data-assisted approach that uses boundary measurement data to reconstruct the statistical properties of the random source with fewer realizations. We compare the performance of different data-driven algorithms under this framework to enhance the initial approximation obtained from integral equations. Our numerical experiments demonstrate that the data-assisted approach achieves better reconstruction with only 1/10 of the realizations required by traditional methods. Among the various Image-to-Image translation algorithms that we tested, the pix2pix method outperforms others in reconstructing well-separated inclusions with accurate positions. Our proposed approach results in stable reconstruction with respect to the observation data noise.

## 17 Frane Ljubetic

### Memory-enhanced diffusivity in stochastically forced walking droplets

The motion of particles subject to random perturbations is a ubiquitous problem in numerous fields, including biology, active matter, and electronics. Whether induced by ambient fluctuations or spatial heterogeneities, the stochastic forces in these settings often lead the particle to exhibit diffusive behavior in the long-time limit. Recent experiments demonstrating the localization of walking droplets in disordered media have called into question the role that path memory, which is characterized by the wave-decay time in the walker system, may play in the emergent diffusive dynamics. We demonstrate that walking droplets subject to stochastic forces have straighter trajectories and thus an enhanced diffusion coefficient relative to active particles without path memory. Through an analysis of the nonlocal wave forces produced during a rapid change in the direction of the droplet, we find restoring forces that drive the walkers back to its past direction of motion, thereby rationalizing their memory-enhanced diffusion. Our results readily extend to similar systems with wave-dressed active particles and introduce the possibility to fine tune diffusion through variable memory.

## 18 Sharon Lubkin

## 19 Shenghan Mei

### Minimizing a weakly convex function

We study the minimization of a weakly convex function that is the sum of two components: the first is convex, while the second is nonconvex. In particular, we focus on two types for the second function: one is weakly convex (WC) and the other is a difference-of-convex (DC) function. To solve both cases, we apply the alternating direction method of multipliers (ADMM), where the subproblems either have closed-form solutions or can be solved iteratively. To enhance computational efficiency while maintaining accuracy, we adopt an early stopping condition. We demonstrate the performance of the proposed algorithms on two examples: the three-hump Camel function and a regularized sparse recovery problem.

## 20 Lorenzo Micalizzi

### Active Flux Method for Accurate Multifluid Simulations

“Numerical simulation of hyperbolic PDEs is of fundamental importance in many different applications, for example, in the description of phenomena involving fluid flows.

The particular structure of these problems poses several challenges at the numerical level, like the occurrence of discontinuities in the analytical solutions, whose improper handling can cause simulation crashes and blow-ups.

These challenges are even harder when considering phenomena with more fluids of different nature interacting with each other.

The accurate numerical simulation of such phenomena is the main goal of this presentation.”

## 21 Rithvik Prakki

### Demonstrating the Continual Learning Capabilities and Practical Application of Discrete-Time Active Inference

Active inference provides a powerful mathematical framework for understanding how agents—biological or artificial—interact with their environments, enabling continual adaptation and decision-making. It combines the principles of Bayesian inference and free energy minimization to model the process of perception, action, and learning in uncertain and dynamic contexts. Unlike reinforcement learning, active inference integrates both exploration and exploitation seamlessly, driven by a unified objective to minimize expected free energy. We present a continual learning framework for agents operating in discrete time environments, using active inference as the foundation. We derive the core mathematical formulations of variational and expected free energy and apply these principles to the design of a self-learning research agent. This agent continually updates its beliefs and adapts its actions based on new data, without manual intervention. Through experiments in dynamically changing environments, we demonstrate the agent’s ability to relearn and refine its internal models efficiently, making it highly suitable for complex and volatile domains such as quantitative finance and healthcare. We conclude by discussing how the proposed framework generalizes to other systems and domains, positioning active inference as a robust and flexible approach for adaptive artificial intelligence.

## 22 Madhumita Roy

### Attractors for Suspension bridge model

“The purpose of this paper is to address long-term behavior of solutions to a plate model describing a suspension bridge with mixed boundary condition in presence of wind-effect and polynomial type weak damping. We prove the wellposed of the dynamical system by

the traditional theory of nonlinear semigroups and monotone operators. Existence of the global attractor is shown by constructing an Absorbing set and then showing quasi-stability property of the system.The dynamical system is not dissipative; to overcome this difficulty we develop methodology for the construction of the Absorbing set.”

## 23 Anshuman Sabath

### Recursive Gram Transformation and non-repeating Matrix sequences over a modulo-Ring

Given a matrix M over a modulo ring Z_N of integers, could we devise a recursive operation on the matrix that would give rise to different matrices of the same size? We use a recursive gram transformation and empirically investigate the probability of obtaining non-repeating sequences for different values of N, and different sizes of square matrix. Starting from matrices with entries sampled from random normal over the Z_N ring, we find that for larger size of matrices (s=31), non-repeating sequences were generated with high probability, and for lower size of matrices (s=3) repeating sequences were obtained with certainty, irrespective of the size of N. Theoretically, constraining the matrices over a modulo ring of integers should prevent eigenvalues explosion/vanishing and check convergence of the sequence of matrices. However, we believe that the dependence of convergence based on the size of the matrix invites a more closer investigation.

## 24 Ian Stevenson

### Collective dynamics of freely interacting walking droplets

“Millimetric fluid droplets may “”walk”” along the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own wave field. These walking droplets, or walkers, represent a classical realization of a pilot-wave system that exhibits wave-particle features previously thought to be exclusive to the quantum realm. Notably, the development of Hydrodynamic Quantum Analogs (HQAs) involving multiple walkers has been limited by the inability to prevent the droplet-droplet coalescence resulting from direct collisions between walkers. We demonstrate that increasing the ambient pressure enables the experimental investigation of freely interacting walkers by strengthening the lubrication forces between droplets, thus preventing coalescence. Moreover, our accompanying simulations of large collections of walkers reveal that wave-mediated interactions may lead to coherent collective dynamics, including the emergence of wave-like statistics in corrals. We characterize the influence of various system parameters, including corral size, memory, particle inertia, and vertical phase. Our collective system opens avenues for the study of wave-mediated active matter and exploring new hydrodynamic analogs of quantum systems, including collective dynamics in quantum condensates.”

## 25 Tianyu Wang

### Some challenges in non-Euclidean learning

In this talk, I will discuss some challenges in non-Euclidean learning: the challenge for global learning, the challenge for specifying local coordinate systems, and the challenge for analyzing iterative algorithms. We will explore potential solutions for these challenges and demonstrate their effectiveness through important examples.

## 26 Chuxiangbo Wang

### Linear independent component analysis in Wasserstein space

This work introduces and analyzes a set-up for linear independent component analysis (ICA) in Wasserstein space. This is motivated by applications in which an instance of data is naturally interpreted as a probability measure or point-cloud, such as gene expression data, and the need to meaningfully analyze this type of data. ICA is a well-developed method for identifying independent components in multivariate data, but mainly focuses on data in Euclidean space. We propose an extension to Wasserstein space by viewing the linear ICA problem in this space as a deviation of the “classical” Euclidean setting. We then show how spectral methods

based on the Wasserstein distance can be used to identify independent components in point-cloud data.

## 27 Aric Wheeler

### Nonlinear stability of two-dimensional periodic waves in parabolic systems with conservation laws

We show that assuming the background periodic wave is diffusively stable, a stronger form of spectral stability, then the wave is nonlinearly stable even in the presence of conservation laws. The key difference with the case without conservation law analyzed by Melinand-Rodrigues is that even for extremely nice perturbations the linearized semigroup decays at a slow rate and so phase modulations play a deeper role. This work is joint with L. Miguel Rodrigues.

## 28 Alexandra Whiteside

### A Mathematical Model of the Intrinsic Pathway of Coagulation

Blood coagulation is initiated via two major pathways, the extrinsic pathway mediated by tissue factor, and the intrinsic pathway mediated by negatively charged molecules or surfaces activating factor XII. Both pathways converge on a common cascade of reactions that result in the generation of thrombin, the key enzyme responsible for clot formation. Proper regulation of coagulation is crucial to prevent excessive bleeding, while improper activation can lead to thrombosis. Novel anticoagulants are needed to prevent thrombosis while minimizing bleeding risk safely. Several agents target activated factor XI, a critical enzyme involved in both extrinsic and intrinsic pathway-initiated coagulation. These agents have shown promising clinical efficacy in preventing thrombosis, although concerns about their safety and efficacy persist. New therapeutic agents targeting other components of the intrinsic pathway are being developed, but they have yet to be evaluated in clinical settings related to thrombotic diseases. To explore the potential of therapies targeting the intrinsic pathway, we developed a mechanistic mathematical model to simulate thrombin generation over time. The model incorporates key reactions within the intrinsic pathway, including interactions between enzymes, zymogens, cofactors, and negatively charged surfaces. Our simulations closely matched experimental thrombin generation data, particularly when coagulation was initiated with silica particles. We specifically focused on analyzing the dynamics involving the silica surface, which initiates the autoactivation of factor XII, and high-molecular-weight kininogen (HK), a cofactor for many intrinsic reactions including factor XIIa activation of factor XI, factor XIIa activation of PK, and PKa activation of factor XII. The cofactor activity of HK is thought to be surface-dependent, but the mechanisms of how it works are not fully understood. After considering various mechanisms of HK activity using our mathematical model, we hypothesize that we hypothesize that HK’s cofactor activity involves not only anchoring factor XI to the surface but also enhancing its binding affinity and catalytic efficiency in reactions with factor XIIa. These findings suggest that targeting HK may have therapeutic potential for developing safer anticoagulants.

## 29 Alexander Winn

### A multi-scale robust coding system in biology: the grid cells

The parametrization of spatial location within the brain has been studied extensively in several species; in rats and mice, researchers have observed dedicated neurons in the entorhinal cortex that use an implicit multiresolution parametrization. In particular, these grid neurons have the following special properties: 1) each neuron activates when the animal is located in a particular region of physical space, which is called the neuron’s receptive field; each neuron’s receptive field consists of circular regions that are arranged in a triangular lattice on the plane; 3) grid neurons can be grouped into modules where the receptive fields are translates of one another; 4) there are about 5-10 modules with geometrically increasing lattice spacing and a fixed orientation o””set between subsequent modules. We study mathematically the corresponding location-encoder design, in terms of its resolution, coverage, and robustness. The values of the parameters that optimize for these criteria are remarkably close to the empirically observed ones. This presents a biological example of a multi-scale, robust encoding system with rotation.

## 30 Haoke Zhang

### Nonconvex approaches for background modeling and video surveillance

In video surveillance, separating the background from the dynamic foreground is a critical task. Robust Principal Component Analysis (RPCA) is a widely used technique for this purpose, which is typically formulated as a convex optimization problem involving the minimization of a weighted combination of the nuclear norm of one matrix representing background and the L1 norm of another matrix representing the foreground. In this project, we explore a variety of nonconvex functions, such as transformed L1 and L_{1/2}, as alternative to the L1 norm, and solve the corresponding optimization problem by the alternating direction method of multipliers (ADMM). Experimental results are provided to demonstrate the effectiveness and efficiency of our proposed methods.

## 31 Jiaqi Zhang

### A Three-dimensional tumor growth model and its boundary instability

In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al 2023. Building upon the insights derived from the analytical reconstruction of key results in the aforementioned work in one dimension (1D) and two dimensions (2D), we extend our analysis to three dimensions (3D). Specifically, we focus on the determination of boundary instability using perturbation and asymptotic analysis along with spherical harmonics. Additionally, we have validated our analytical results in a two-dimensional framework by implementing the Alternating Directional Implicit (ADI) method, as detailed in Witelski and Bowen (2003). Our primary focus has been on ensuring that the numerical simulation of the propagation speed aligns accurately with the analytical findings. Furthermore, we have matched the simulated boundary stability with the analytical predictions derived from the evolution function, which will be defined in subsequent sections of our paper. These alignment is essential for accurately determining the stability or instability of tumor boundaries.