Graduate Students Seminar

Speaker 1: Bo Liu

Title

Bayesian Latent Growth Curve Model with Application to Item Response Data

Abstract

The discovery of the effectiveness of students' learning and instructors' teaching is a challenge in educational assessment. To study educational progress, we propose a flexible latent variable model to model individual differences in growth given longitudinal item response data. We developed a Bayesian growth curve model together with an MCMC algorithm to estimate the student ability and quantify the influence of test items and target covariates. A simulation study and analysis of real data are conducted to demonstrate the performance of the proposed method.

Speaker 2: Ahmet Kaan Aydin

Title

Several Robust Model Reductions for the Boundary Feedback Stabilization of Fully Magnetic Piezoelectric Smart Beams

Abstract

Piezoelectric materials exhibit electric responses to mechanical stress and mechanical responses to electric stress. The electrostatic and magnetizable PDE models, describing the longitudinal oscillations on the beam, with boundary feedback sensors/actuators are known to have exponentially stable solutions. Firstly, a thorough analysis of the maximal decay rate via the optimal choice of feedback sensor amplifiers is discussed. Next, model reductions by standard Finite Differences and Finite Elements are proposed. Indeed, numerical filtering is implemented for each case to eliminate the spurious high-frequency modes. Finally, we propose a recently developed Finite-difference-based model reduction that uniformly retains the exponential decay property of the PDE. This novel model reduction approach is promising for coupled PDE systems of the same sort.