Tatyana Benko, Ben Young
Preprint of extended abstract available here. Full paper is in preparation.
We give a combinatorial proof of a result in rank 2 Donaldson-Thomas theory, which states that the generating function for certain plane partition-like objects, called double-box configurations, is equal to a product of MacMahon's generating function for (boxed) plane partitions. We first give the correspondence between double-box configurations and double-dimer configurations on the hexagon lattice with a particular tripartite node pairing. Using this correspondence, we can apply graphical condensation and double-dimer condensation in our proof.
You can see a presentation I gave earlier this year on this research at the Graduate Online Combinatorics Colloquium here.
Tatyana Benko, Rebecca Jones, Lucas Tate
Under review.
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific relationships between objects in a graph database is often required. Given a larger graph and a smaller graph, one may wish to identify instances of the smaller query graph in the larger target graph. This task is called subgraph identification or matching. Subgraph matching is helpful in areas such as bioinformatics, binary analysis, pattern recognition, computer vision, and natural language processing. In these applications, many of the datasets frequently contain noise and errors, thus exact subgraph matching algorithms do not apply. To address this issue, we introduce a new algorithm for inexact subgraph matching. Our algorithm utilizes node and edge attributes which are often present in real-world datasets to narrow down the search space. The algorithm is flexible in the type of subgraph matching it can perform and the types of datasets it can process by using a modifiable graph edit distance cost function for pairing nodes. We show its effectiveness on several datasets, including family trees and control-flow graphs.
Lucas Tate, Rebecca Jones, Doug Dennis, Tatyana Benko, Jody Askren
Proceedings of the Cyber Supply Chain Risk Management for Critical Systems (CySCRM 24), Richland, WA, United States (2024)
Bills of materials (BOMs) are quickly becoming an effective tool for managing supply chain risk. As more BOMs enter circulation, the ability to compare them will be crucial to understanding how products differ and in managing BOMs from different tools or sources. This paper will describe some of the challenges of comparing BOMs followed by a discussion of several comparison methods
Tatyana Benko, Martin Buck, Ilya Amburg, Stephen J. Young, Sinan G. Aksoy
Published in Transactions on Machine Learning Research (TMLR), Aparil 2025
In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via symmetrized matrix representations, potentially losing important information. We propose an alternative approach to hypergraph neural networks in which the hypergraph is represented as a non-reversible Markov chain. We use this Markov chain to construct a complex Hermitian Laplacian matrix - the magnetic Laplacian - which serves as the input to our proposed hypergraph neural network. We study HyperMagNet for the task of node classification, and demonstrate its effectiveness over graph-reduction based hypergraph neural networks.
Tatyana Benko, Iva Stavrov Allen (lead author)
This article commences a study of convergence of discretized point-object configurations, which we call Brill-Lindquist-Riemann sums, towards a charged dust continuum from the perspective of relativistic initial data. We are motivated by the interpretation of Brill-Lindquist-Riemann sums as collections of relatively isolated astrophysical bodies such as stars and galaxies in the universe, and the interpretation of the dust continuum as the universe itself. Our work begins by establishing the existence and the uniqueness of horizons/minimal surfaces of Brill-Lindquist metrics in the vicinity of the point-sources ("stars"). We then study the geometries of the regions exterior to said minimal surfaces, and discuss their Gromov-Hausdorff and intrinsic flat limit. An interesting and purely geometric byproduct of our work are examples in which the scalar curvature jumps upon taking Gromov-Hausdorff and /or intrinsic flat limits.