糖心TV Complexity Science Events
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Complexity Forum- Thomas Fink
Title: Dynamics of network motifs; and, a note on the game of conkers
Abstract:
I will talk about the dynamics of small networks and, independently and briefly, explain the theory of the game of conkers.
We have studied the dynamics of network motifs by treating them as small Boolean networks and comprehensively evaluating all possible binary (Boolean) update rules. We introduce a formalism for classifying dynamical behaviour and show that some network motifs are fundamentally more versatile—capable of executing a variety of tasks—than others. While versatility roughly increases with motif complexity, we find evidence of a critical complexity, after which increasing the number of bonds confers no advantage.
Conkers is a popular game in which pairs of players take turns swiping each other's conker with their own until one nut is broken. All new conkers start with a score of 1. Each time a conker beats another conker, it adds to its score the score of the defeated. We have studied a simple model of competition in which each player has a fixed strength. Randomly selected pairs of players compete and the stronger one wins. We show that the best indicator of future success is not the number of wins but a player's wealth: the accumulated wealth of all defeated players. We calculate statistics of a conker with a given score and offer advice o