eaction-diffusion epidemic models are proposed in order to understand how spatial heterogeneity influences the transmission dynamics of infectious diseases. In this talk, I will first present our recent numerical studies of the seasonal influenza epidemics in Puerto Rico based on a diffusive susceptible-infected-recovered model. Our simulations demonstrate that even simple diffusive epidemic models have potential applications in real-world situations. Then I will present our theoretical investigations of a reaction-diffusion vector-host epidemic model.

By the super version of the Wedderburn Theorem, a finite dimensional complex simple (associative) superalgebras is isomorphic to either a (full) matrix superalgebra or a queer matrix superalgebra. This gives rise to two series Lie superalgebras: the general linear Lie superalgebra and the queer Lie superalgebra. In this talk, I am going to introduce the queer q-Schur superalgebras associated with the latter and discuss their fundamental structure. The Schur-Weyl-Sergeev duality involving the quantum queer supergroup and Hecke-Clifford superalgebra will also discussed.

Vector-borne infectious diseases may involve horizontal transmission between hosts in addition to transmission from infected vectors to susceptible hosts. In this talk, we develop a vector-borne disease model with general nonlinear incidence rates and continuous age structures in both infectious hosts and vectors. We first study the existence and local stability of steady states, which is completely determined by the basic reproduction number. With the assistance of the existence of a global attractor and the uniform persistence, a threshold dynamics is established by employing the Fluctuation Lemma and the approach of Lyapunov functionals.

In this talk, we discuss the Diederich-Fornæss index in several complex variables. A domain Ω in C^n is said to be pseudoconvex if -log(-δ(z)) is plurisubharmonic in Ω, where δ is a signed distance function of Ω. The Diederich-Fornæss index has been introduced since 1977 as an index to refine the notion of pseudoconvexity. After a brief review of pseudoconvexity, we discuss this index from the point of view of geometric analysis. We will find an equivalent index associated to the boundary of domains and with it, we are able to obtain accurate values of the Diederich-Fornæss index for many types of domains.

This report considers methods for the solution of the time dependent Stokes Darcy problem that can be implemented by use of existing surface water and ground water codes. Porous media problems for groundwater flows overwhelmingly use mixed discretizations due to their superior conservation properties and the conservation for problems on large domains with relatively coarse meshes.

The Navier-Stokes equation coupled with the Darcy equation through interface conditions has attracted scientists’ attention due to its wide range of applications and significant difficulty in the nonlinearity and interface conditions. This presentation discusses a multi-physics domain decomposition method for decoupling the coupled Navier-Stokes-Darcy system with the Beavers-Joseph interface condition. The wellposedness of this system is first showed by using a branch of singular solutions and the existing theoretical results on the Beavers-Joseph interface condition.

In this talk, I will discuss quantile regression with group-specific parameters when the group membership is unknown. Identifying groups with homogeneous parameters can be viewed as a model-based clustering problem. I will first introduce a concave fusion penalization method that can perform simultaneous parameter estimation and group identification. The method relies on penalizing the differences of parameters between pairs of units and thus could be computationally costly for large samples. Next I will introduce an iterative two-step algorithm using a similar idea of k-means clustering to identify groups and estimate group-specific parameters for panel data. In practice the signal differentiating groups may vary across quantiles though the group membership may be common.

In this talk, I will discuss quantile regression with group-specific parameters when the group membership is unknown. Identifying groups with homogeneous parameters can be viewed as a model-based clustering problem. I will first introduce a concave fusion penalization method that can perform simultaneous parameter estimation and group identification. The method relies on penalizing the differences of parameters between pairs of units and thus could be computationally costly for large samples. Next I will introduce an iterative two-step algorithm using a similar idea of k-means clustering to identify groups and estimate group-specific parameters for panel data.