DMS Graduate Student Seminar
Sep 25, 2024 03:00 PM
010 ACLC
Speaker: Dr. Huan He (Auburn University)
Title: Real-World Evidence Generative Modeling: A Deep Generative Model for Clinical Evidence Generation
Abstract: Current GPTs and NLPs have not yet focused on generating causal evidence from Real-World Data (RWD). Here, we develop the very first generative pretrained transformer (GPT) model designed specifically for RWD with negative control outcome (NCO) powered debiasing capability. Our model is a generalist for Real World Evidence (RWE) generation by first pretraining on large datasets and then fine-tuning on small but relevant cohorts.
DMS Graduate Student Seminar
Sep 18, 2024 03:00 PM
010 ACLC
Speaker: Professor Emeritus Frank Uhlig (auburn University)
Title: Introduce interactive teaching for Math 2026 Linear Algebra classes at AU, their history, and experiences.
Examples: find the invariants of REFs, based on My Lesson Plans, LP 3- 4.
DMS Graduate Student Seminar
Sep 11, 2024 03:00 PM
010 ACLC
Speaker: Dr. Zach Walsh (Auburn University)
Title: Delta-modular matroids
Abstract: Delta-modular matrices are integer matrices that arise in the theory of integer programming. Matroids are discrete structures that encode the combinatorics of linear independence. We show how matroids were used to find an upper bound on the maximum number of columns of a rank-r Delta-modular matrix. We assume no knowledge of matroid theory.
This is joint work with Joseph Paat, Ingo Stallknecht, and Luze Xu.
DMS Graduate Student Seminar
Sep 04, 2024 03:00 PM
010 ACLC
Speaker: Ridvan Ozdemir (Auburn University)
Title: Mathematical Theories for Topological Phases and Edge Modes in Mechanical Systems
Abstract: We examine the topological phases of the spring-mass lattices when the spatial inversion symmetry of the system is broken and prove the existence of edge modes when two lattices with different topological phases are glued together. In particular, for the one-dimensional lattice consisting of an infinite array of masses connected by springs, we show that the Zak phase of the lattice is quantized, only taking the value 0 or π. We also prove the existence of an edge mode when two semi-infinite lattices with distinct Zak phases are connected. We characterize the valley Chern numbers for the two-dimensional honeycomb lattice when the masses on the lattice vertices are uneven. The existence of edge modes is proved for a joint honeycomb lattice formed by gluing two semi-infinite lattices with opposite valley Chern numbers together.
DMS Graduate Student Seminar
Aug 28, 2024 03:00 PM
010 ACLC
Speaker: Sean Grate
Title: How-To: Making a Website
Abstract: A website provides an interactive medium to showcase your work, experience, and interests. I will review some ways to quickly make a website and discuss what content you should (and should not) feature on your website.
DMS Graduate Student Seminar
Apr 17, 2024 03:00 PM
161 ACLC
Speaker: Dr. Jessica McDonald
Title: What is Discrete Mathematics (Combinatorics)?
Abstract: This talk aims to give an idea of what research in discrete mathematics (combinatorics) is all about. I will attempt to define the field and its many sub-fields, and we will discuss some example problems. I will also talk about our discrete group at Auburn – what the research interests of the faculty in our group are, and what graduate courses we offer.
DMS Graduate Student Seminar
Apr 03, 2024 03:00 PM
161 ACLC
Speaker: Profesor Hal Schenck (Auburn)
Title: Combinatorics and Commutative Algebra
Abstract: This talk will give an overview of the spectacular success of algebraic methods in studying problems in discrete geometry and combinatorics. First, we'll discuss the face vector (number of vertices, edges, etc.) of a convex polytope and recall Euler's famous formula for polytopes of dimension 3. Then, we'll discuss graded rings, focusing on polynomial rings and quotients. Associated with a simplicial polytope P (every face is "like" a triangle) is a graded ring called the Stanley-Reisner ring, which "remembers" everything about P and gives a beautiful algebra/combinatorics dictionary. I will sketch Stanley's solution to a famous conjecture using this machinery and touch on connections between P and objects from algebraic geometry (toric varieties). No prior knowledge of the terms above will be assumed or needed for the talk.
DMS Graduate Student Seminar
Feb 28, 2024 03:00 PM
161ACLC
Speaker: Professor Nedret Billor
Title: A Journey from Program Overview to Capstone Projects and Beyond
Abstract: In this seminar, we'll explore our statistics and data science programs, from foundational learning to capstone applications, and their role in advancing Ph.D. research. We will also discuss the diverse research areas within our statistics and data science programs. Further, we will delve into the advantages that a background in data science brings to traditional statistics and mathematics education, particularly through the lens of a PhD student who has been navigating both fields simultaneously.
DMS Graduate Student Seminar
Jan 24, 2024 03:00 PM
161 ACLC
Speaker: Professor Junshan Lin
Title: Overview of Computational Mathematics: Algorithms, Theory, and Applications
This semester, we will only have four talks at the designated time.
DMS Graduate Student Seminar
Nov 29, 2023 03:00 PM
108 ACLC
Speaker: Rui Shi, Auburn University
Title: Outlier Detection with Cluster Catch Digraphs (CCDs)
Abstract: Outlier detection is one of the most popular research topics and also a challenging task. Many outlier detection approaches based on different techniques have been developed. We propose approaches that are based on Cluster Catch Digraphs (CCDs).
CCDs are a family of clustering algorithms. The CCD algorithms are graph-based, density-based, and distribution-based approaches. They construct a certain number of hyperspheres to capture latent cluster structures. There are two main versions of CCDs: KS-CCDs and RK-CCDs. The latter ones are especially appealing as they do not require parameter input.
We develop two outlier detection algorithms that first utilize RK-CCDs to build hyperspheres for each cluster structure. Then, by constructing a Mutual Catch Graph (MCG) from the KS-CCD, outliers can be identified among those points that are not in any of the hyperspheres. We called these two approaches the Mutual catch graph with Cluster Catch Digraph (M-CCD) algorithm and the Fast Mutual catch graph with Cluster Catch Digraph (Fast M-CCD) algorithm. However, due to some shortcomings of RK-CCDs, they perform poorly with high dimensionality. To resolve this issue, we propose a new version of CCDs with the Nearest Neighbor Distance (NND) and refer to it as NN-CCD. Subsequently, we proposed another outlier detection algorithm based on NN-CCDs, which has much better performance with high dimensionality; we call this approach the Mutual catch graph with Nearest Neighbor Cluster Catch Digraph (M-NNCCD) algorithm. We also propose ways to adapt the above algorithm to the cases when the shapes of clusters are arbitrary; we call those approaches the Mutual catch graph with Flexible Cluster Catch Digraph (M-FCCD) algorithm and the Mutual catch graph with Flexible Nearest Neighbor Cluster Catch Digraph (M-FNNCCD) algorithm. Additionally, we offer an approach to calculate the outlying-ness scores for all the CCD-based algorithms.
Keywords: Outlier detection, Graph-based clustering, Cluster catch digraphs, \(k\)-nearest neighborhood, Mutual catch graphs, Nearest neighbor distance, Outlying-ness score.
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