Dallas, and the USPTO. We are grateful to Daniel McCurdy, Christopher Reohr, and Shashank Tiwari of RPX Corporation for graciously providing data used in this study. We also thank Mike Lloyd and Doris Spielthenner of Ambercite for generously providing data. The authors gratefully acknowledge funding from the National Science Foundation (grants CCF-1216095… (More)
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 prove that any parallel chip-firing game on a graph G with at least 4|E(G)| − |V (G)| chips stabilizes, i.e. such a game has eventual period of length 1. Furthermore, we obtain a polynomial bound on the number of rounds before stabilization. This result is a counterpoint to previous results which showed that the eventual periods of parallel chip-firing… (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)
In this expository article, we introduce the topological ideas and context central to the Poincaré Conjecture. Our account is intended for a general audience, providing intuitive definitions and spatial intuition whenever possible. We define surfaces and their natural generalizations, manifolds. We then discuss the classification of surfaces as it relates… (More)