Posters
Nadia Benakli,
2-neighborhood degree list of a graph
Finding the important vertices in a graph is a key area of Social Network Analysis. There are several measures of "centrality." Some are local measures such as degree centrality while others are global measures designed for specialized applications. Last year a New York Times article titled “The follower factory” explained how celebrities, wanting to prove that they are influential, purchase for example Instagram followers from companies that create millions of fake accounts. So a celebrity may have many Instagram followers (i.e. high degree in the social network), but the followers are mostly vertices of low degree. Such fake followers will be flagged if instead of focusing on the degree of a vertex, we compute the degrees of the neighbors, and degrees of neighbors of neighbors, and so on. Building on prior work by Barrus and Donavan, we introduced the notion of k-neighborhood degree list and characterized when two labeled graphs of diameter 2 on the same vertex set have the same 2-neighborhood degree list. In the probabilistic sense, almost every graph has diameter 2, so our result applies to a large subclass of graphs. This is joint work with Ezra Halleck and Sandra Kingan.
Mariah Boudreau, UVM
Network Analysis and its Application to Epidemiology
This Honors Thesis project evaluates the mathematical concepts of graph theory that lead into understanding the network dynamics that describe the spread of disease. A proof for a specific disease spreading model was detailed in this investigation.
Jonathon B. Ferrell, Dillon McCarthy, University of Vermont, Department of Chemistry
DNA-BACon: Molecular Modeling Tools For Rational Design of DNA-Based Supramolecular Nanomaterials
DNA nanocages represent a new class of nano materials. As they rely on the well understand Watson-Crick base pairing for both assembly and modification, they demonstrate a remarkable amount of versatility and reliability. In order to further elucidate the qualities of this new material we sought out to study the dynamics of these nanocages. In order to generate all of the structures necessary to study the dynamics of these cages it was necessary to create a program, DNA-BACon, to generate the nanocages. We used traditional molecular dynamics and metadynamics to assess the dynamics. However, the cages are quite flexible so a second program, Tree-BACon was developed to derive the metastable states.
Joel Foisy, SUNY Potsdam
Title: Intrinsically linked and intrinsically knotted directed graphs
A graph is said to be intrinsically linked if it contains, in every spatial embedding, a non-split linked pair of cycles. Conway-Gordon and Sachs showed in the early 80s that $K_6$ is intrinsically linked. An analogous notion for directed graphs can be defined, where linked cycles are required to be consistently oriented. We show a proof (due to the author, Howards and Rich) that the double of $K_6$ is intrinsically linked. We also demonstrate a directed graph that is intrinsically knotted (joint work with Fleming).
Evangelos Nastas, Florida Atlantic University
On Graph Cutwidth ≤ 2
Jonathan W. Sands, UVM
L-functions for Graph Coverings and Annihilation of Graph Jacobians
Abstract: We consider an unramified Galois covering of a graph X by a graph Y, and denote the group of automorphisms of Y over X by G. For the graph Y, the Jacobian J(Y) is a group with a variety of other names whose order is the tree-number k(Y) of Y. In our situation, J(Y) becomes a module over the integral group ring Z[G]. Using L-functions, we define an element in this group ring and show that it annihilates the group J(Y). This is an analog of the classical Stickelberger theorem for cyclotomic fields.
Christino Tamon and Weichen Xie, Clarkson University
On the Complexity of Quantum Transducers
Quantum generalizations of Markov models in machine learning were introduced recently. We show that quantum transducers provide a natural and useful framework to study these Markov models and their corresponding computational problems. The complexity of these problems can be analyzed via this connection.