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.

Exponential growth of the semiconductor industry, historically driven by transistor scaling, is now facing fundamental challenges. In this talk, I will discuss an emerging class of devices that, by merging electronic with ionics, offer the potential to control the materials’ electronic properties in-situ and have led to promising memory and circuit concepts. These devices exhibit history-dependent, resistive switching behavior and are termed memristors (memory + resistor) or resistive memory (RRAM) devices. I will discuss our efforts on the development and optimization of memristor devices and integrated systems, including techniques of controlling the dynamic ionic migration processes and associated modeling efforts. Functional high-density crossbar arrays have been integrated directly on top of CMOS circuits using a back-end-of-line (BEOL) process, enabling hybrid non-volatile memory and reconfigurable circuit applications.

Dirichlet problems for the second order elliptic partial differential equations have been studied for many years and obtained many existence results in 1980s. But there has been little research on Neumann problem in the past thirty years. In this talk, we will especially introduce Neumann problem for mean curvature equations and give the existence Theorem of classical solutions of mean curvature equations. The key point is to prove the boundary gradient estimate. (This is a joint work with Prof. Xinan Ma.

We discuss some results and problems concerning the construction of quantum channels with desired properties. No quantum mechanics background is required. Basic linear algebra knowledge is assumed.