Events

Xinyue Zhao
University of Notre Dame
 

3:30 PM
154 Hurley Hall

A Free Boundary Tumor Growth Model with Time Delay

Being a leading cause of death, tumor is one of the most important health problems facing the whole world. While there is a lot of work on the tumor growth models, only a few of them included time delay; and nearly in all the literature, only the radially symmetric case was considered with a time delay. In this talk, I will present a non-radially symmetric tumor growth model with a time delay in cell proliferation. The time delay represents the time taken for cells to undergo replication (approximately 24 hours). The model is a coupled system of an elliptic equation, a parabolic equation and an ordinary differential equation. It incorporates the cell location under the presence of time delay, with the tumor boundary as a free boundary. The inclusion of a small time delay makes the system non-local, which produces technical difficulties for the PDE estimates. I will discuss the stability and bifurcation results we obtained concerning this model. Through stability analysis, the result indicates that tumor with large aggressiveness parameter would trigger instability, which is biologically reasonable.…

Giang Tran
University of Waterloo
 

3:30 PM
154 Hurley Hall

A Supervised Learning Problem and Compressed Sensing

Learning the underlying process from a finite set of input-output observations is an important but challenging task in various scientific disciplines. The learned model will then be helpful to study the mathematical fundamental of the learning process and to make future predictions. In general, this data-based learning problem is ill-posed due to the nonlinearity of the unknown function and the complicated properties of given data. One of the main directions is to investigate the sparsity-of-effect in the data-driven methods to select a suitable model. Along this direction, we study the problem of learning nonlinear functions from various types of data ranging from independent to weakly dependent data. We provide a reconstruction guarantee for the associated l1-optimization problem, given that the data is bounded and satisfies a suitable concentration inequality. When the amount of given data is limited, especially in high dimensional spaces, we propose a sampling strategy to guarantee a reconstruction. This is joint work with Rachel Ward (UT Austin), Hayden Schaeffer (CMU), and Lam Ho (Dalhousie University).…

Mikyoung Jun, Department of Statistics, Texas A & M University, will give a colloquium titled, "TBA " at 4:30 PM in 127 Hayes - Healy Center.

Full List of ACMS Colloquia…