Since its introduction into the NLP community, pointwise mutual information has proven to be a useful association measure in numerous natural language processing applications such as collocation extraction and word space models. In its original form, it is restricted to the analysis of two-way co-occurrences. NLP problems, however, need not be restricted to twoway co-occurrences; often, a parti...

Using finite element methods, we need to answer these questions: • What is the appropriate functional space V for the solution? • What is the appropriate weak or variational form of a differential equation? • What kind of basis functions or finite element spaces should we choose? • How accurate is the finite element solution? We briefly address these questions in this Chapter. Recalling that fi...

We consider infinite-dimensional convex minimization problems with pointwise inequality constraints. We do not impose a constraint qualification condition, so that first-order necessary conditions are not available. To handle such problems we propose a method which combines advantages both from well-known penalty and barrier methods. For solving the resulting subproblems we develop a Newton-typ...

In this paper we consider a parabolic optimal control problem with a pointwise (Dirac type) control in space, but variable in time, in two space dimensions. To approximate the problem we use the standard continuous piecewise linear approximation in space and the piecewise constant discontinuous Galerkin method in time. Despite low regularity of the state equation, we show almost optimal h2 + k ...

An algorithm for convex parametric QPs is studied. The algorithm explores the parameter space by stepping a sufficiently small distance over the facets of each critical region and thereby identifying the neighboring regions. Some conjectures concerning this algorithm and the structure of the solution of a parametric QP are presented.

We study a class of discounted infinite horizon stochastic games with strategic complementarities. Using monotone operators on the space of values and strategies, we prove existence of a Stationary Markov Nash equilibrium under different set of assumptions than Curtat (1996), Amir (2002, 2005) or Nowak (2007) via constructive methods. In addition, we provide monotone comparative statics results...

Let p be a prime number. In this article we present a theorem, suggested by Peter Scholze, which states that Gal(Qp/Qp) is the étale fundamental group of a certain object Z which is defined over an algebraically closed field. This object is the quotient of the “punctured perfectoid open disk” by an action of the group Qp . The proof of this fact combines two themes: the tilting equivalence for ...