Graduate Students Seminar

Speaker 1: Paul Luongo

Title

Introducing doeLab: A Pythonic Approach to the Design and Analysis of Experiments

Abstract

Design of experiments (DOE) emphasizes that valid statistical inference depends fundamentally on how data are generated, not merely how they are analyzed. However, in the Python ecosystem, support for DOE remains fragmented: Experimental designs are often constructed informally, and model fitting is performed independently using general-purpose tools. This separation can obscure experimental structure and increase the risk of fitting statistically inappropriate models.

This talk introduces a pre-alpha version of doeLab, an aspiring Python-based DOE framework that seeks to treat the experimental design as a first-class object to the maximum extent practicable. Rather than inferring structure from a completed dataset, doeLab encodes treatments, blocks, and experimental roles explicitly, using these specifications to guide both run sheet generation and subsequent analysis. This design-first approach aims to improve reproducibility and ensure alignment between experimental structure and statistical modeling in Python using an approach analogous to that of R or SAS.

Using the randomized complete block design (RCBD) as a motivating example, this brief talk contrasts existing workflows in R and SAS with current practices in Python and demonstrates how doeLab seeks to unify a currently fragmented approach. Current limitations and open challenges are discussed, including the extent to which a fully declarative representation of experimental designs is feasible in practice.

Speaker 2: Emoke Galambos

Title

The Discrete Maximum Principle for Parabolic PDEs on a Rectangular Mesh

Abstract

The discrete maximum principle (DMP) guarantees that the numerical solutions of PDEs remain within physically meaningful bounds. This ensures that the computed values are constrained by the initial and boundary data, eliminating anomalies like negative chemical concentrations or mass densities.

In this talk, I would like to introduce the sufficient conditions, under which the Galerkin finite element method (using bilinear basis functions on a rectangular mesh), together with the Theta method successfully preserve these fundamental qualitative properties for parabolic systems.