Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Room: Exhibit Hall
Caelyn Sobie - Arizona State University - West
Co-Author(s): Awildo Gutierrez, Hamilton College, Clinton, NY; Eli Leake, DePaul University, Chicago, IL
A chemical reaction network is a model consisting of sets of species, sets of complexes, and sets of reactions that model actual chemical systems. Such networks are represented using weighted, directed graphs where nodes are simulated (or real) chemical compounds and edges are reactions. This research analyzes operations on chemical reaction networks which include but are not limited to: adding new species, adding new dependent and independent reactions, and adding new complexes. Banaji investigated six operations on networks called enlargements that preserve multistationarity of steady states and orbits. We investigate the effect of these operations on deficiency. Deficiency is an important property to be studied because a low deficiency (either 1 or 0) means that we can understand more about the system. Along with being an important index for us to study the effect of enlarging a given network, deficiency plays an essential in the study of chemical reaction networks. The deficiency tells us how linearly independent the reaction vectors are, given a network. We have proved preliminary results in which applying operations (as defined by Banaji) to a system either preserves deficiency or the deficiency always changes by a predictable amount.
Funder Acknowledgement(s): This research was funded by MSRI, the Alfred P. Sloane Foundation, and the NSF.
Faculty Advisor: Dr. Anne Shiu, firstname.lastname@example.org
Role: I wrote pseudocode that calculated deficiency given any chemical reaction network. I also came up with and proved half of our conjectures.