I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order 2. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only go down when limits are taken. This implies a corresponding semicontinuity result for the absolutely continuous spectrum, which applies to a very large class ...

This paper presents a semi-supervised training method for linear-chain conditional random fields that makes use of labeled features rather than labeled instances. This is accomplished by using generalized expectation criteria to express a preference for parameter settings in which the model’s distribution on unlabeled data matches a target distribution. We induce target conditional probability ...

Conditional Random Fields (CRFs) have been widely used for information extraction from free texts as well as from semi-structured documents. Interesting entities in semi-structured domains are often consistently structured within a certain context or document. However, their actual compositions vary and are possibly inconsistent among different contexts. We present two collective information ex...