Graduate Students Seminar

Speaker 1: Mesfin Haileyesus

Title

Privacy-Preserving Cox Proportional Hazards Modeling in a Federated Learning Framework

Abstract

Federated learning is a decentralized approach to data analysis that enables collaborative model development without sharing raw data, thereby ensuring data privacy and compliance with regulatory constraints.  In this presentation, we explore the adaptation of the standard Cox PH survival model fitting procedure within a federated learning framework.  Parameter estimation is performed using an iterative gradient descent algorithm, and standard errors are obtained through resampling techniques.  The performance of the proposed method is evaluated using both simulated data and a publicly available colon cancer dataset. Comparative results with the traditional centralized Cox PH model show that the federated approach provides comparable performance, supporting its suitability for privacy-preserving survival analysis.

Speaker 2: Madison Christ

Title

Stability Analysis for Systems of PDEs

Abstract

The goal of this talk is to give a perspective on the analysis of partial differential equations (PDEs) using functional analysis, a priori estimates, as well as tools from ordinary differential equations (ODEs) and calculus. We first discuss the case of finite-dimensional systems for which we have ways to test for stability using results from the theory of dynamical systems such as asymptotic stability and Lyapunov stability. However, in the infinite-dimensional setting these methods no longer apply. By looking at examples of the heat and damped wave equations in Hilbert spaces we will see that in showing uniform exponential decay of the energy of these systems we obtain uniform stability. This talk will present several estimates in order to achieve this result. We also discuss another type of stability called strong stability and the coupled systems in which this is present.