2026 Faculty and Student Summer Talks
The talks will take place every Monday and Thursday from June 1 to August * at 10:30 AM in Cullimore Hall Room 611.
Date | Day | Speaker, Title, and Abstract | |||
June 1 | M | Ye Su The use of Virtual Control Groups in preclinical studies This work focuses on the use of Virtual Control Groups (VCGs) in preclinical studies. Unlike concurrent control groups, VCGs rely on historical data and therefore face substantial challenges due to study heterogeneity, batch effects, covariate shift, and violations of exchangeability assumptions. The proposed research aims to study and compare existing Bayesian historical borrowing frameworks, including power priors, MAP priors, robust MAP priors, adaptive MAP priors, and EXNEX models. Simulated data will be used to reproduce and evaluate these methods under varying degrees of heterogeneity and prior-data conflict. The long-term goal is to develop a statistical framework that enables dynamic and robust borrowing of historical information for virtual control group construction in preclinical studies, while accounting for partial exchangeability and excessive between-study heterogeneity. | |||
June 4 | R | Name Title/Abstract forthcoming | |||
June 8 | M | Ellison O’Grady Data-driven modeling of closed-loop respiratory control In a clinical setting, breathing pathologies are diagnosed and studied via pulmonary function tests (PFTs), with the most ubiquitous of those being spirometry. We examine an existing model of respiration that incorporates essential lung biomechanics, oxygen chemosensation, and metabolism in a closed-loop control circuit. We aim to use spirometry and other clinical data to improve and extend this closed-loop model. In this talk, we will identify the essential characteristics of a spirogram and what these represent in the lungs; then, we will proceed to spirograms produced from clinical data to observe the typical curve; finally, we will discuss the work to bridge the gaps between the expected spirogram and the simulated one, and the benefits of establishing this data-driven link to clinical PFTs. | |||
June 11 | R | Philip Zaleski Convergence of Stochastic Gradient Descent as a Markov Chain Stochastic gradient descent (SGD) is an immensely popular algorithm for minimizing functions that arise in machine learning and data science. The iterates of constant step-size SGD form a Markov chain on a general state space. In this talk we obtain convergence theorems for the SGD Markov chain under no convexity assumptions on the objective function. The results of this thesis are split into two parts. Firstly, under a separability assumption on the objective function and a large (order one) step-size bound, an explicit decomposition of the state space into pairwise disjoint absorbing sets and a uniformly transient set is provided. The SGD Markov chain is shown to converge at a geometric rate to a convex combination of the invariant measures, each of which is supported on an absorbing set. The theory is highlighted by one-dimensional examples that demonstrate the failure of the diffusion approximation to characterize the long-time dynamics of SGD. Secondly, assuming that the objective function has only non-degenerate critical points and that the step-size is sufficiently small, an explicit decomposition of the state space into pairwise disjoint topologically recurrent sets and a weakly transient set is provided. On each topologically recurrent set, the SGD Markov chain admits a spectral gap with respect to a Wasserstein-one type metric. The SGD Markov chain is then shown to converge at a geometric rate to an invariant measure in the usual Wasserstein-one metric. The proofs in this setting make use of the weak Harris framework. *** Joseph Canavatchel A boundary integral method to solve quasi-periodic boundary value problems for Laplace's equation We propose a novel boundary integral method to solve quasi-periodic boundary value problems for Laplace's equation. The problem is inspired by a long term goal of developing a boundary integral method to study two-phase fluid flows. Two significant challenges in the development of this method are (i) the presence of a horizontal spatial domain in which the solution is neither decaying nor periodic and (ii) preserving the quasi-periodicity of the solution. Our approach is based on lifting the problem from 2D to a higher spatial dimension (here 3D), in which it is doubly or horizontally periodic. This lifting preserves the quasi-periodicity of the original 2D formulation. Perhaps the greatest difficulty of the lifted 3D problem is computing an integral over the Green's function; it is in fact an integral over all horizontally periodic images of the surface. In a 2D periodic setting, it is possible to sum over all the periodic images in closed form. By contrast we have no such closed form available in our 3D setting. An efficient method for computing this sum, by Ewald summation is described. | |||
June 15 | M | Matthew Illingsworth On Correlating Topology and Performance of Membrane Filter Pore Networks Membrane filtration is an important and ubiquitous process in industrial applications, and there is a growing body of mathematical models that capture this complex process. We model the internal structure of membrane filters as a network of pores whose radii are drawn from a log-normal distribution, with fouling modeled as an adsorption process; i.e. the gradual accretion of fouling particles on the inner walls of the pores. Simulation-based approaches are used to measure membrane filter performance, using metrics such as total throughput and accumulated foulant concentration. In the present work, we investigate the correlation between the performance of these networks and their topological properties, in order to discover optimal pore topologies for membrane filter design. We use persistent homology as our principal tool for quantifying topological features, where the radii of a network’s pores are represented by a collection of two-dimensional points known as a persistence diagram. The data encoded in these persistence diagrams are then statistically correlated with the performance metrics, particularly with total throughput. Favorably strong correlation between total throughput and filter topology will be presented. We will also discuss the temporal evolution and spatial distribution of filter topology, and their strong agreement with empirical findings. *** Elizabeth Tootchen A Minimal Model for the Dynamics of REM Sleep with Atonia Atonia, muscle paralysis due to the inhibition of motoneurons in the spinal cord, normally occurs during REM sleep. A role of atonia is to prevent one from acting out dreams during REM sleep, which could cause inadvertent harm to the individual or those around them. REM active neurons, which are part of the sleep-wake circuitry, project via two pathways to the spinal cord motoneurons which control atonia. Damage to the subcoeruleus nucleus (SubC) or ventral medial medulla (VMM), which are key elements of these pathways, may result in an individual experiencing REM sleep without atonia. We construct a firing rate model that combines the sleep-wake cycle and atonia pathways to discern the roles of SubC and VMM on network dynamics. We will also begin to develop a Hodgkin-Huxley based biophysical formalism to provide insight into the internal dynamics within each of the populations in the wake-sleep network. The model will allow for the study of individual populations and subpopulations in wake and NREM sleep-promoting regions. Analysis of this network will reveal how the populations in these two regions are relevant to changes in wake/sleep states and REM bouting, and how they support the current understanding of the flip flop mechanism. | |||
June 18 | R | Nastaran Rezaei Instability of Two-layer Flows Multilayer flows, particularly those involving polymeric fluids, are of significant importance due to their broad range of applications, including lubrication, drug delivery, and material design. The viscoelastic materials exhibit both elastic and viscous behavior. However, predicting the hydrodynamic stability of these flows is a complicated task due to the presence of elastic stresses. This study investigates the stability of the two-layer Poiseuille flow and the role of viscoelasticity on the interface dynamical phenomenology. The objective of this research is to study the instabilities that arise in two-layer viscoelastic flows to address effects concerning fluid inertia, viscoelastic relaxation time, thickness ratio, viscosity and density ratio, and the growth of perturbations. One of the computational fluid dynamics methods to track the movement at the interface is the Volume of Fluid (VOF) method. In this work, VOF and Chebyshev Spectral Collocation (CSC) methods are used to model the problem. It is observed that the presence of viscoelasticity affects the growth rate in comparison to the Newtonian fluid by shifting the critical value of the Reynolds number and wavenumber. This study also focuses on the analysis of energy behavior and flow stability in fluid systems. The distribution, transfer, and dissipation of energy are examined to understand their influence on flow characteristics. Flow stability is evaluated by observing the response of the system to disturbances and the conditions leading to instability. The results offer valuable guidance for enhancing efficiency and forecasting performance. *** Michael Storm Spectral Stability of Pulse Solutions of the Swift-Hohenberg Equation with Computer Assisted Proofs In this project we use rigorous numerical methods to determine the spectral stability of standing pulse solutions of the Swift-Hohenberg equation, a model often used for pattern formation. To determine spectral stability of a stationary solution, one must determine if the linearization about the pulse has positive eigenvalues, which in this scenario may be put into 1-1 correspondence with so-called conjugate points. We numerically count these conjugate points in several steps. First we find a standing pulse as a solution to a BVP on a finite domain with boundary conditions on the stable and unstable manifolds. The conjugate points may then be identified with the zeros of a 1d function, implicitly defined via solutions of the linearized equation about the pulse. Lastly, we find all conjugate points in a finite interval, and use the vector bundles of the manifolds to analyze the asymptotic behavior of the solutions to ensure there are no conjugate points outside of the finite interval. We use computer-assisted proofs to rigorously implement every step, with a posteriori error estimates. | |||
June 22 | M | Andrew White Calcium (Ca2+) ions signal key physiological processes in cells. Muscle contraction, gene expression, neurotransmitter release, and oocyte fertilization are a few examples of the physiological functions relying on Ca2+ signaling. The Ca2+ ion is an ideal signaler due to all cells containing low basal Ca2+ concentration since prolonged Ca2+ elevation is detrimental to cell physiology. A key participant in Ca2+ signaling and Ca2+ regulation is a family of protein molecules known as buffers.These proteins bind free Ca2+ ions and bring the intracellular Ca2+ concentration to resting levels. They are found in all types of cells including skeletal and smooth muscle tissue, endocrine cells, and neurons. However, different buffers have different binding properties and cell expression profiles, leading to different Ca2+-buffer dynamics across cells. A key property that influences spatiotemporal interactions between Ca2+ and buffer is the number of Ca2+ ions a buffer molecule can bind, especially if the kinetics of each binding site are different. This work systematically explores the impact of buffers with multiple binding sites on select physiological phenomena using mathematical modeling of the corresponding reaction-diffusion systems. The calcium-dependent biological processes that we analyze are neurotransmitter release caused by vesicle fusion, in particular dynamic changes in the release probability called short-term synaptic plasticity (STP/STSP), and the process called calcium-induced-calcium-release (CICR) which can induce a wave of increased Ca2+ concentration propagating within the cell. Such waves are known to trigger many important physiological functions such as muscle contraction. We explore in detail short-term synaptic plasticity effects and calcium wave propagation in the presence of buffers with multiple binding sites as a function of the buffer’s binding kinetics and diffusivity states. *** Bryan Currie Enumerating Rooted Binary Phylogenetic Forests and the Coalescent Model The (Network) Multi-Species Coalescent models evolution of genes among current and ancestral species. Compared with other standard mathematical models of evolution that are analyzed with algebraic geometry, it tends to produce polynomials of higher degree and with more terms, and so symbolic computation quickly becomes essential as the frontiers are pushed. Current methods for symbolic computation of probabilities focus on probabilities of unrooted gene trees, which are often the data of interest. This can have issues when considering more complex networks, and lacks the ability to focus on more minute network features. A more general way to track probabilities within the coalescent setting is with probabilities of rooted binary phylogenetic (leaf-labeled) forests, which are the intermediate stages of the coalescent process. Dealing with these systematically requires an easily-computable enumeration. This work presents such a particular enumeration that is computed recursively, inspired by a new direct proof of a long-known combinatorial result concerning rooted binary phylogenetic forests. | |||
June 25 | R | Joseph D’Addessa Modeling Vibration Induced Droplet Spreading: Dynamic Response and Force Balance Comparisons This work investigates how applied vertical vibration affects the spreading of liquid drops and films. We compare two modeling approaches, a reduced thin film model and full Navier Stokes simulations, across three geometries: a filament, an axisymmetric drop, and a three dimensional drop. The filament geometry provides a useful setting for diagnosing model differences, while the axisymmetric drop more closely represents the experimental system. The thin film model captures the overall trend that stronger forcing leads to greater spreading, but it often overpredicts the magnitude of spreading compared with the full Navier Stokes model and experiments. High viscosity cases produce a weaker response and help clarify the role of inertia. The three dimensional simulations extend the comparison to a more realistic drop geometry and provide a first look at how the spreading behavior changes beyond the axisymmetric approximation. To interpret these differences more directly, force balance calculations are used to connect the spreading trends to the underlying pressure, viscous, surface tension, and contact line effects. Together, the results show that geometry, inertia, and model assumptions all play important roles in predicting spreading driven by vibration. | |||
June 29 | M | Patrick Grice The Inverse Elasto-Acoustic Problem A stable and numerically efficient boundary integral method formulation of the elasto-acoustic problem is presented, based on Fourier analysis. We demonstrate the method generalizes well to multiple scattering. After deriving the derivative of the elasto-acoustic problem with respect to shape perturbations, we describe techniques from geometric flow theory necessary for stable simulating of shape perturbations. The shape derivative is used to define a regularized Gauss-Newton algorithm for shape fitting of elasto-acoustic scatterers. *** Mikhail Nauth Topic #1 Accurate identification of severe X-class solar flares is critical for mitigating space weather disruptions to near-Earth infrastructure. While machine learning architectures are increasingly deployed to capture the non-linear magnetic properties of Active Regions, the optimal dimensionality of these feature spaces for rare-event detection remains underexplored. We address this by performing multiclass classification using features extracted at the flare onset (T = 0). Utilizing SDO/HMI data (2010–2016) and a Stratified Grouped 10-Fold Cross-Validation strategy to prevent spatial data leakage, model performance is evaluated on a classic 13-parameter SHARP dataset versus an expanded 25-parameter dataset. Topic #2 The epithelium is the body's primary line of defense against bacterial pathogens in the gut. Particles or bacteria may reach the epithelial lining when they overcome physical filtering mechanisms or through dysfunction of the mucosal barrier. In this study, we aim to understand the dynamics of particle penetration or successful particle filtering using a comprehensive model of particles in gut mucus. We implement a LSTM neural network to predict particle penetration under varying environmental/physical conditions. | |||
July 2 | R | Yun Li Conformal Prediction under Label Shift Machine learning models are increasingly used in high-stakes applications, making reliable uncertainty quantification essential. Conformal prediction provides prediction sets with finite-sample coverage guarantees, but these guarantees generally rely on the training and test data following the same distribution. This assumption is often violated in practice due to distribution shift. In this talk, we focus on the label shift setting, where class proportions change while the class-conditional feature distributions remain unchanged. The talk begins by reviewing conformal prediction methods that provide marginal coverage guarantees in the standard no-shift setting, followed by weighted conformal prediction for label shift. We then introduce Split Adaptive Mondrian (Split-AM), which extends label-conditional (Mondrian) conformal prediction by learning label-specific significance levels to reduce the expected prediction set size while preserving valid marginal coverage under label shift. Finally, we present the theoretical guarantees of the proposed method and discuss the practical setting in which the target label distribution is unknown. *** Jack Wang Statistical Analysis in Mass Spectrometry Microplastics and nanoplastics (MNPs) are pervasive environmental contaminants linked to cardiovascular, inflammatory, and neurological health risks, motivating initiatives to quantify MNPs in human tissue. Mass spectrometry (MS) offers a sensitive way to identify and quantify these chemical signals. However, MS intensity data are noisy, right-skewed, and collected from very small sample sizes, making reliable signal detection difficult. This project adapts DESeq2, a statistical framework originally built for RNA-sequencing, to mass spectrometry data. Both data types share the same core challenges: heterogeneity of variance and few replicates per condition. In DESeq2, Negative Binomial modeling and empirical Bayes shrinkage stabilize dispersion and fold-change estimates by borrowing statistical strength across signals. In this talk, we introduce the biological motivation, the mass spectrometry workflow, and the dispersion estimation and shrinkage pipeline which help identify reliable mass-to-charge signals for MNPs across experimental conditions. The preliminary results of our analysis provide a promising foundation for more complex experiment conditions. | |||
July 6 | M | Justin Maruthanal Title/Abstract forthcoming *** Jung Park Title/Abstract forthcoming | |||
July 9 | R | Gabriel Masarwa Title/Abstract forthcoming *** Souaad Lazergui Analysis of Multiple Scattering Iterations for High Frequency Scattering Problems This talk analyzes the integral equation method for solving high-frequency scattering problems, involving the collection of smooth convex obstacles. The main objective is to develop rigorous asymptotic methods for the analysis of multiple scattering phenomena and singular behavior under both Dirichlet and Neumann boundary conditions. For single scattering scenarios, asymptotic approximations of the unknown surface densities are derived through the stationary phase method. This work extends the analysis to multiple scattering scenarios by treating the scattered field from each reflection on the illuminated side of a prior obstacle as an incident wave for the next obstacle. Furthermore, explicit convergence rate formulas are derived for periodic ray trajectories, demonstrating that the error introduced by the approximation remains controllable and quantifiable. This result established that the proposed method achieves high accuracy with fewer terms and simplified computations, thereby ensuring computational efficiency while maintaining high precision. The second part of this talk is devoted to the analysis of singular scattering phenomena, arising when the incident wave becomes tangent to the obstacle boundary. In this singular case, the classical geometrical optics approximation ceases to be valid because of the presence of glancing rays. To control this difficulty, we adopt the Taylor-Melrose framework and develop a detailed asymptotic analysis for the Neumann problem. The geometry in the neighborhood of the glancing point is reduced to a canonical normal form, which removes the degeneracy of the phase function. A micro local decomposition is used to analyze the Fourier integral operators associated with the incident and diffracted fields, providing a rigorous treatment of the singular behavior. The stationary phase method then yields asymptotic expansions of the surface densities on the entire obstacle boundary, leading to a complete asymptotic description of the scattered wave field. This analysis extends high-frequency asymptotic methods to a class of singular scattering phenomena that cannot be treated within the standard geometrical optics framework. Finally, the results obtained in this thesis contribute to the Analysis of high-frequency scattering by providing rigorous asymptotic descriptions of multiple reflections, periodic ray dynamics, and singular diffraction phenomena. They also establish analytical tools that may serve as a basis for the investigation of more general scattering configurations and more complex propagation models. | |||
July 13 | M | Esther Wang Title/Abstract forthcoming *** Tareq Aldirawi Title/Abstract forthcoming | |||
July 16 | R | Nan Zhou Numerical Continuation and Stability of Multi-Pair Vortex Leapfrogging Leapfrogging vortex motion is a classical example of coherent vortex dynamics. In the four-vortex point-vortex model, two vortex pairs pass through one another periodically in a moving frame, and the stability transition of this orbit is well understood. In this talk, I will describe ongoing work extending this problem to multi-pair vortex systems, with emphasis on the three-pair, six-vortex case. The main computational approach is numerical continuation of periodic orbits in a moving frame. Using AUTO, I compute branches of mirror-symmetric leapfrogging orbits and study how the period depends on amplitude and Hamiltonian. I then compute full-space Floquet multipliers to determine when these orbits lose stability. Preliminary results suggest that, unlike the classical two-pair case, the three-pair orbit loses stability through a complex-conjugate pair of multipliers leaving the unit circle, consistent with a Hamiltonian Hopf-type bifurcation. *** Hong Xiao Statistical Analysis on Linear Networks Many real-world spatial point patterns occur on linear networks, such as road systems, river networks, and transportation infrastructures, motivating the development of statistical methods specifically designed for network-based data. This project investigates three related research directions: (1) using Physics-Informed Neural Networks (PINNs) to estimate intensity functions on linear networks by solving the underlying heat equation, (2) developing improved bandwidth selection methods that account for local network connectivity and geometric constraints, and (3) proposing a novel marked bootstrap framework for estimating the variance of second-order statistics such as the K-function on linear networks. Preliminary results show that the PINN approach produces density estimates comparable to existing methods on simple simulated networks, although challenges remain for more complex networks. In addition, current progress on bandwidth selection and bootstrap methods is summarized through a review of the relevant literature, along with proposed directions for future research. | |||
July 20 | M | Luc Brancheau McKean-Vlasov Equations for the Mean-Field Analysis of Large Systems of Neurons Classical high-dimensional particle models using McKean-Vlasov theory traditionally assume instantaneous interactions between independent agents. However, in biological contexts, this assumption is often violated due to complex, time-dependent interactions between neurons. This presentation reviews the foundational framework of stochastic differential equations (SDEs) and Itô integration required to model mean-field limits in large networks. To deal with noninstantaneous interactions, we introduce a system of stochastic differential equations to capture both the node and edge dynamics. Finally, we suggest an extension incorporating the dynamics astrocyte resource diffusion, offering a roadmap for more realistic neural field analysis. *** Ebru Degdelen Robustness of Persistent Homology when Noising and Denoising 3D Images Fluid flow through porous media is critical in many industrial and natural processes, such as oil recovery and groundwater filtration. Permeability is a widely-used measure of how easily fluid flows through a porous medium, so developing fast and accurate methods to estimate it is important. In this project we investigate whether machine learning (ML) models informed by geometric, topological, and network-based descriptors can accurately predict permeability. We generate synthetic 3D porous structures using PuMA software and compute their permeability using flow simulations, from which we extract structural descriptors and two-point correlation functions. We also reduce the 3D datasets to pore-scale network representations using PoreSpy, and we utilize computational tools from topological data analysis to calculate topological measures of the porous structures. The combined set of descriptors is used to train ML models for permeability prediction. Our results show that ML models trained on this combination of features are able to predict permeability with high accuracy. In particular, models that include topological information consistently perform better than those using geometric or network data alone. These findings suggest that topological features can serve as effective descriptors for fluid flow in porous media. *** Heba Yousef Rayleigh–Plesset Equation with Coupling We investigate modeling approaches for cluster formation in nanobubble clouds under acoustic forcing. The framework is based on extending the Rayleigh–Plesset equation to a system of interacting bubbles by incorporating acoustic coupling between bubbles. This leads to a system of coupled nonlinear ordinary differential equations, where each bubble’s dynamics is influenced by pressure contributions from its neighbors. Numerical simulations are used to explore how bubble size, spacing, and driving conditions affect the collective behavior of the system. The model provides a basis for studying how pairwise interactions contribute to the emergence of cluster-like dynamics in multi-bubble systems. | |||
July 23 | R | Elizabeth Epstein Title/Abstract forthcoming *** Christopher Agesen C. elegans Locomotion We aim to understand forward and backward undulatory locomotion in C. elegans. A proposed biological neural network for a single segment of the C. elegans body is extended to 6 repeating segments of 17 neurons. Bistable neurons with recovery are used to investigate the network for mechanism of forward and backward locomotion in the same network structure. Bifurcations in the network parameters are investigated. Future work involving a mechanical model and optimization are discussed. *** Amelia Zakroff Title/Abstract forthcoming *** Elif Onat Title/Abstract forthcoming | |||
July 27 | M | Tamanna Title/Abstract forthcoming *** Bikash Thakur Title/Abstract forthcoming *** Antonio Madrigal Title/Abstract forthcoming *** Michael Pallante Title/Abstract forthcoming | |||
July 30 | R | Weizhao Wang Title/Abstract forthcoming *** Hsin-I Hsieh Title/Abstract forthcoming *** Riya Goyal Title/Abstract forthcoming *** Shumiao Xu Title/Abstract forthcoming | |||
Updated: July 23, 2026