Graduate Student Publications

Theoretical Population Biology

Tung, H-R; Durrett, R

Chan, Durrett, and Lanchier introduced a multitype contact process with temporal heterogeneity involving two species competing for space on the d-dimensional integer lattice. Time is divided into two seasons. They proved that there is an open set of the parameters for which both species can coexist… read more about this publication »

Proceedings of the National Academy of Sciences of the United States of America

Boyle, L; Hletko, S; Huang, J; Lee, J; Pallod, G; Tung, H-R; Durrett, R

The main mathematical result in this paper is that change of variables in the ordinary differential equation (ODE) for the competition of two infections in a Susceptible-Infected-Removed (SIR) model shows that the fraction of cases due to the new variant satisfies the logistic differential equation… read more about this publication »

Journal of Mathematical Biology

Melikechi, O; Young, AL; Tang, T; Bowman, T; Dunson, D; Johndrow, J

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the model parameters based on noisy observations early in the… read more about this publication »

Bulletin of Mathematical Biology

Gong, Y; He, S; Kiselev, A

In this paper, we consider the dynamics of a 2D target-searching agent performing Brownian motion under the influence of fluid shear flow and chemical attraction. The analysis is motivated by numerous situations in biology where these effects are present, such as broadcast spawning of marine… read more about this publication »

Archive for Rational Mechanics and Analysis

Lu, J; Stubbs, KD; Watson, AB

Exponentially-localized Wannier functions (ELWFs) are an orthonormal basis of the Fermi projection of a material consisting of functions which decay exponentially fast away from their maxima. When the material is insulating and crystalline, conditions which guarantee existence of ELWFs in… read more about this publication »

Involve, a Journal of Mathematics

Chouliara, D; Gong, Y; He, S; Kiselev, A; Lim, J; Melikechi, O; Powers, K

The 2-dimensional motion of a particle subject to Brownian motion and ambient shear flow transportation is considered. Numerical experiments are carried out to explore the relation between the shear strength, box size, and the particle’s expected first hitting time of a given target. The simulation… read more about this publication »

Journal of Applied and Computational Topology

Arya, S; Boissonnat, J-D; Dutta, K; Lotz, M

AbstractGiven a set P of n points and a constant k, we are interested in computing the persistent homology of the Čech filtration of P for the k-distance, and investigate the effectiveness of dimensionality reduction for this problem, answering an open question of Sheehy (The persistent homology of… read more about this publication »

Journal of Personalized Medicine

Chen, HY; Malik, J; Wu, HT; Wang, CL

Background: The application of heart rate variability is problematic in patients with atrial fibrillation (AF). This study aims to explore the associations between all-cause mortality and the median hourly ambulatory heart rate range (ÃHRR24hr) compared with other parameters obtained from the… read more about this publication »

Siam Journal on Scientific Computing

Zhou, M; Han, J; Lu, J

We propose a novel numerical method for high dimensional Hamilton-Jacobi-Bellman (HJB) type elliptic partial differential equations (PDEs). The HJB PDEs, reformulated as optimal control problems, are tackled by the actor-critic framework inspired by reinforcement learning, based on neural network… read more about this publication »

Pure and Applied Mathematics Quarterly

Bray, H; Hamm, B; Hirsch, S; Wheeler, J; Zhang, Y

Flatly Foliated Relativity (FFR) is a new theory which conceptually lies between Special Relativity (SR) and General Relativity (GR), in which spacetime is foliated by flat Euclidean spaces. While GR is based on the idea that “matter curves spacetime”, FFR is based on the idea that “matter curves… read more about this publication »