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We give a new proof that any candy-passing game on a graph G with at least 4|E(G)| − |V (G)| candies stabilizes. Unlike the prior literature on candy-passing games, we use methods from the general theory of chip-firing games which allow us to obtain a polynomial bound on the number of rounds before stabilization.
We determine the behavior of Tanton's candy-passing game for all distributions of at least 3n − 2 candies, where n is the number of students. Specifically, we show that the configuration of candy in such a game eventually becomes fixed. The candy-passing game, as introduced by Tanton , is played according to the following rules: • At the beginning of the… (More)
— We define reality mining as quantifying and modeling long-term human behavior and social interactions, by using mobile phones and wearable badges as sensors that capture real-world face-to-face interactions. In this paper, we describe two experiments that use this approach: (a) understanding the diffusion of social behaviors using mobile phones at an… (More)
We let G be an undirected graph and denote the vertex and edge sets of G by V (G) and E(G), respectively. The candy-passing game on G is defined by the following rules: • At the beginning of the game, c > 0 candies are distributed among |V (G)| students, each of whom is seated at some distinct vertex v ∈ V (G). • A whistle is sounded at a regular interval.… (More)
Members' names are listed in chronological order of election to each category. The financial statements summarize the finances of MIT for the fiscal years 2013 and 2014. In fiscal 2014, MIT continued to advance knowledge, push the boundaries of research discovery, and extend its educational impact while further enhancing the Institute's solid financial… (More)