We present a novel connection between binary search trees (BSTs) and points in the plane satisfying a simple property. Using this correspondence, we achieve the following results: 3. The first proposal for dynamic optimality not based on splay trees. A natural greedy but offline algorithm was presented by Lucas [1988], and independently by Munro [2000], and was conjectured to be an (additive) approximation of the best binary search tree. We show that there exists an equal-cost online algorithm, transforming the conjecture of Lucas and Munro into the conjecture that the greedy algorithm is dynamically optimal.
Predicting panic is of critical importance in many areas of human and animal behavior, notably in the context of economics. The recent financial crisis is a case in point. Panic may be due to a specific external threat or self-generated nervousness. Here we show that the recent economic crisis and earlier large single-day panics were preceded by extended periods of high levels of market mimicry—direct evidence of uncertainty and nervousness, and of the comparatively weak influence of external news. High levels of mimicry can be a quite general indicator of the potential for self-organized crises.
Predicting panic is of critical importance in many areas of human and animal behavior, notably in the context of economics. The recent financial crisis is a case in point. Panic may be due to a specific external threat, or self-generated nervousness. Here we show that the recent economic crisis and earlier large single-day panics were preceded by extended periods of high levels of market mimicry -direct evidence of uncertainty and nervousness, and of the comparatively weak influence of external news. High levels of mimicry can be a quite general indicator of the potential for selforganized crises.
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