The exploratory nature of phase II trials makes it quite common to include heterogeneous patient subgroups with different prognoses in the same trial. Incorporating such patient heterogeneity or stratification into statistical calculation for sample size can improve efficiency and reduce sample sizes...

Abstract: In this lecture series, I shall discuss finiteness properties of groups. In the first lecture, I will discuss the basic definitions and theorems, including type F_n, type FP_n and their relations, and homological dimension, geometric dimension and their relations. In the second lecture, ...

Abstract: Potential theory is the study of subharmonic and plurisubharmonic functions. In the first half of the 19th century, with the rise of electrostatics, mathematicians such as Poisson and Gauss began investigating the Poisson equation. Over the next hundred years, the necessary tools for solv...

Abstract: We will first show how to develop a thermodynamically consistent phase field model for the binary incompressible (quasi-incompressible) fluid, which allows for the different properties (densities, viscosities and heat conductivities) of each fluid component. A sharp-interface limit analysi...