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Topos approach to quantum information theory
Wed, Apr. 27 5pm (MATH 350)
Grad Student Seminar
A directed graph (or digraph) is a graph whose edges are ordered pairs of vertices. On a graph or digraph, a color change rule is a process by which a set of filled vertices can cause other vertices to become filled. The throttling number minimizes the sum of the size of the initial filled set and the amount of time it takes to fill every vertex. In this thesis, the positive semidefinite (PSD) color change rule is adapted to digraphs, and throttling for the PSD color change rule is studied specifically. The behavior of the PSD throttling number when the order (or direction) of an edge is changed is analyzed, and bounds for the PSD throttling number of a digraph are discussed. These bounds are later shown to be tight for trees. We then look further into what happens if the direction of every edge is changed simultaneously (the resulting digraph is called the reversal). We demonstrate that a PSD throttling process on a digraph can also be reversed to obtain a PSD throttling process on the digraph's reversal. Finally, we use this fact to study the behavior of the sum of the throttling number of a digraph and the throttling number of its reversal.
Positive Semidefinite Throttling on Directed Graphs