A (k;K) circuit is one which can be decomposed into nonintersecting blocks of gates where each block has no more than K external inputs, such that the graph formed by letting each block be a node and inserting edges between blocks if they share a signal line, is a partial k-tree. (k;K) circuits are special in that they have been shown to be testable in time polynomial in the number of gates in ...

The absorption and plasma disappearance of vitamin K were investigated by uniformly labelling phylloquinone in kale with carbon-13, and by feeding the kale to study subjects. Seven healthy volunteers ingested a single 400 g serving of kale with 30 g vegetable oil. The kale provided 156 nmol of phylloquinone. Serial plasma samples were collected and analysed for the appearance of 13C-phylloquino...

k-means++ is a seeding technique for the k-means method with an expected approximation ratio of O(log k), where k denotes the number of clusters. Examples are known on which the expected approximation ratio of k-means++ is Ω(log k), showing that the upper bound is asymptotically tight. However, it remained open whether k-means++ yields an O(1)-approximation with probability 1/poly(k) or even wi...