Ziv Scully

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The parallel chip-firing game is an automaton on graphs in which vertices “fire” chips to their neighbors. This simple model contains much emergent complexity and has many connections to different areas of mathematics. In this work, we study firing sequences, which describe each vertex’s interaction with its neighbors in this game. First, we introduce the(More)
We consider optimal job scheduling where each job consists of multiple tasks, each of unknown duration, with precedence constraints between tasks. A job is not considered complete until all of its tasks are complete. Traditional heuristics, such as favoring the job of shortest expected remaining processing time, are suboptimal in this setting. Furthermore,(More)
The parallel chip-firing game is an automaton on graphs in which vertices “fire” chips to their neighbors when they have enough chips to do so. In this work we first characterize positions that repeat every 2 turns. Using this we determine the eventual periods of games on trees given only the total number of chips. We introduce the concepts of motorized(More)
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant algorithms for numerical matrices are often not the fastest for symbolic matrices with many variables. We compare the(More)
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