Search Research Symposium Abstracts

Weisfeiler-Lehman meets Gromov-Wasserstein*

The Weisfeiler-Lehman (WL) test is a classical procedure for graph isomorphism testing. The WL test has also been widely used both for designing graph kernels and for analyzing graph neural networks. In this talk, I will describe the so-called Weisfeiler-Lehman (WL) distance we recently introduced, which is a new notion of distance between labeled measure [Read More...]

Presenter: Yusu Wang, University of California, San Diego
Authors: S. Chen, S. Lim, F. Memoli, Z. Wan and Y. Wang
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 9:50 am

Nerve Theorems for Threshold-Linear Networks

Combinatorial threshold-linear networks (CTLNs) are a mathematically tractable subfamily of threshold-linear networks whose dynamics are determined by the structure of a directed graph. Threshold-linear networks have been widely used to model neural networks with associative memory. ln spite of their simplicity, CTLNs exhibit the full range of nonlinear [Read More...]

Presenter: Nicole Sanderson, Penn State
Authors: Daniela Egas Santander, Stefania Ebli, Alice Patania, Nicole Sanderson, Felicia Burtscher, Katherine Morrison, and Carina Curto
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 10:15 am

Persistent cup-length

In topological data analysis, one uses persistent homology and its dual notion persistent cohomology to study the evolution of (co)homology across a filtration. Compared with homology, cohomology is enriched with a graded ring structure given by the cup product operation. In this talk, we utilize the cup product operation to define a new invariant for the [Read More...]

Presenter: Ling Zhou, The Ohio State University (Columbus, OH, US)
Authors: Marco Contessoto, Facundo Mémoli, Anastasios Stefanou and Ling Zhou
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 10:40 am

Topology of graphs and hypergraphs for computer network data

Computer networks operate as complex interconnected systems. Many types of data collected by network sensors can be modeled using a graph or hypergraph. For example, network traffic (commonly called NetFlow) can be modeled as a directed graph, while associations between users and the processes they run can be modeled as a hypergraph. In recent work my team [Read More...]

Presenter: Emilie Purvine, Pacific Northwest National Laboratory
Authors: Emilie Purvine
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 11:05 am

A medial axis-based compactness measure vs. the eye test for detecting gerrymandering*

We, like many other researchers, are interested in providing a mathematical basis for determining the likelihood of whether a congressional or legislative district has been gerrymandered. A judicial precedent exists that one cannot define an exact notion of a district's degree of “compactness” but you “know it when you see it.” Our paper explores the [Read More...]

Presenter: Ellen Gasparovic, Union College
Authors: Jason D'Amico, Ellen Gasparovic, Greg Malen, and Mushan Zhong
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 11:30 am

An Efficient Algorithm for the Computation of Reeb Spaces from Roadmaps

The Reeb graph is a tool from Morse theory that has recently found use in applied topology due to its ability to track the changes in connectivity of level sets of a function. The roadmap, a construction that arises in semi-algebraic geometry, is a one-dimensional set that encodes information about the connected components of a set. In this talk, I will [Read More...]

Presenter: Sarah Percival, Michigan State University
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 3:20 pm

Applications of persistent homology to spatial dynamics in cell biology

Actin filaments are polymers that interact with motor proteins inside cells and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of interacting proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Datasets that describe the interaction of [Read More...]

Presenter: Maria-Veronica Ciocanel, Duke University
Authors: Maria-Veronica Ciocanel, Scott McKinley
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 3:45 pm

Topological Data Analysis of Pollination Resource Complexes

Interactions between plants and pollinators are critical for species survival. Plants provide resources which are consumed by pollinators. Similarly, pollinators provide resources to plants in the form of pollination services. Sets of consumers sharing a common resource generate a combinatorial simplicial complex describing a community. A plant or pollinator [Read More...]

Presenter: Melinda Kleczynski, University of Delaware
Authors: Melinda Kleczynski, Chad Giusti
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 4:10 pm

Using Topological Data Analysis to distinguish cosmological models of our Universe*

Topological Data Analysis (TDA) is a beneficial technique for analyzing spatially complex web-like data such as the large-scale structure (LSS) of the Universe. The accepted cosmological model presumes cold dark matter but discriminating LSS under varying cosmological assumptions is of interest. Cosmologists develop large-scale simulations that allow for [Read More...]

Presenter: Jessi Cisewski-Kehe, University of Wisconsin-Madison
Authors: Jessi Cisewski-Kehe, Brittany T. Fasy, Wojciech Hellwing, Mark R. Lovell, Pawel Drozda, and Mike Wu
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 4:35 pm