Afternoon Sessions: 2:00-3:15 pm

1. Phuong Hoang: phoang3@charlotte.edu (in-person)

Title: Optimal Graph Joining with Applications to Isomorphism Detection and Identification

2. Keara Walsh: kwalsh27@charlotte.edu (in-person)

Title: Modeling the Transition of Laser Damage Mechanisms in Retinal Cells

3. Cong Van: cvan1@charlotte.edu(in-person)

Title: The inverse initial data problem for anisotropic Navier-Stokes equations via Legendre time reduction method

1 Title: Optimal Graph Joining with Applications to Isomorphism Detection and Identification

Abstract: In this talk, we first introduce and develop a new constrained optimal transport problem for graphs, called the optimal graph joining (OGJ) problem. Extending the idea of probabilistic couplings to the setting of graphs, we first introduce the notion of a graph joining of two graphs G and H, which is a graph K on the product of the vertex sets of G and H that has G and H as marginals in an appropriate sense. Given two graphs and a vertex-based cost function, OGJ aims to find a graph joining that minimizes the expected cost. Then we establish theoretical results connecting the OGJ problem to the graph isomorphism problem. In particular, we provide a variety of sufficient conditions on graph families under which OGJ detects and identifies isomorphisms between graphs within the family. 

2. Title: Modeling the Transition of Laser Damage Mechanisms in Retinal Cells

Abstract: Photochemical damage is a significant concern for retinal pigmented epithelial (RPE) cells, as it can lead to long-term or permanent cellular effects even at low temperatures and energy levels. We investigated the modeling of the effect of long-pulse, short-wavelength laser exposure to retinal cells, particularly to determine the time duration at which the main damage mechanism transitioned from photothermal to photochemical. Using the rate process model proposed by Clark et al. in 2011, we developed a MATLAB simulation to calculate photothermal and photochemical damage thresholds for a 413nm wavelength laser. The Arrhenius damage integral was utilized to determine the photothermal damage threshold while a two process rate model – a positive rate that is temperature independent and a negative quenching rate – was used to determine the photochemical damage threshold.

By implementation of a numerical search algorithm and a binary search, the MATLAB simulation only required input of a time duration vector to compute both the photothermal and photochemical damage thresholds for each time. Additionally, we conducted a study of interpolated points to pinpoint the exact damage transition point. In this study, we also gained insight into the sensitivity of our parameters, the dependence on wavelength, and the limitations of the model.

3. Title: The inverse initial data problem for anisotropic Navier-Stokes equations via Legendre time reduction method

Abstract: We consider the inverse initial data problem for the compressible anisotropic Navier-Stokes equations, where the goal is to reconstruct the initial velocity field from lateral boundary observations. This problem arises in applications where direct measurements of internal fluid states are unavailable. We introduce a novel computational framework based on Legendre time reduction, which projects the velocity field onto an exponentially weighted Legendre basis in time. This transformation reduces the original time-dependent inverse problem to a coupled, time-independent elliptic system. The resulting reduced model is solved iteratively using a Picard iteration and a stabilized least-squares formulation under noisy boundary data. Numerical experiments in two dimensions confirm that the method accurately and robustly reconstructs initial velocity fields, even in the presence of significant measurement noise and complex anisotropic structures. This approach offers a flexible and computationally tractable alternative for inverse modeling in fluid dynamics with anisotropic media.