Combinatorial Characterizations of Admissible Coxeter Sequences and Their Applications (2009)
Macauley, Matthew, Mortveit, Henning S.
We study the equivalence relation on the set of acyclic orientations of an undirected graph generated by source-to-sink conversions. These arise from admissible sequences in Coxeter theory and quiver...
Update Sequence Stability in Graph Dynamical Systems (2009)
Macauley, Matthew, Mortveit, Henning S.
In this article, we study finite dynamical systems defined over graphs, where the functions are applied asynchronously. Our goal is to quantify and understand stability of the dynamics with respect...
Dynamics Groups of Asynchronous Cellular Automata (2008)
Macauley, Matthew, McCammond, Jon, Mortveit, Henning S.
A sequential dynamical system, or SDS, consists of an undirected graph Y, a vertex-indexed list of update rules F_Y, and a word w over the vertex set that contains each vertex at least once and...
Cycle Equivalence of Graph Dynamical Systems (2008)
Macauley, Matthew, Mortveit, Henning S.
Graph dynamical systems (GDSs) can be used to describe a wide range of distributed, nonlinear phenomena. In this paper we characterize cycle equivalence of a class of finite GDSs called sequential...
On Enumeration of Conjugacy Classes of Coxeter Elements (2007)
Macauley, Matthew, Mortveit, Henning S.
In this paper we study the equivalence relation on the set of acyclic orientations of a graph Y that arises through source-to-sink conversions. This source-to-sink conversion encodes, e.g....
Equivalences on Acyclic Orientations (2007)
Macauley, Matthew, Mortveit, Henning S.
The cyclic and dihedral groups can be made to act on the set Acyc(Y) of acyclic orientations of an undirected graph Y, and this gives rise to the equivalence relations ~kappa and ~delta,...
Order Independence in Asynchronous Cellular Automata (2007)
Macauley, Matthew, McCammond, Jon, Mortveit, Henning S.
A sequential dynamical system, or SDS, consists of an undirected graph Y, a vertex-indexed list of local functions F_Y, and a word w over the vertex set, containing each vertex at least once, that...
Farid Merchant, Henning S. Mortveit, Chris L. Barrett, Reinhard Laubenbacher, Farid Merchant
Every year three million deaths are attributed to malaria, of which one-third are of children. Malaria is a vector-borne disease, where a mosquito acts as the vector that transmits the disease. In...