The similarity language model is a statistical model that makes efficient use of long distance information when possible and falls back to standard ngram language model when not. To estimate the probability distribution of a given target context, each training example of the ngram model is retrieved and its similarity to the target context is estimated. In this work, this is done by performing ...

At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...