The narrative cloze is an evaluation metric commonly used for work on automatic script induction. While prior work in this area has focused on count-based methods from distributional semantics, such as pointwise mutual information, we argue that the narrative cloze can be productively reframed as a language modeling task. By training a discriminative language model for this task, we attain impr...

Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of particular interest. Existence of minimal weak upper gradients in this general setting is proven and corresponding representation formulae are given. Furthermore, t...

In this paper we provide an answer to a question found in [3], namely when given a quasi-metric ρ, if one examines all quasi-metrics which are pointwise equivalent to ρ, does there exist one which is most like an ultrametric (or, equivalently, exhibits an optimal amount of Hölder regularity)? The answer, in general, is negative, which we demonstrate by constructing a suitable Rolewicz–Orlicz sp...

In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction metric, which can be found by solving a pointwise linear matrix inequality. Extensions to approximate optimal control are straightforward. The conditions we give a...

As a consequence of Kirchberg’s work, Connes Embedding Conjecture is equivalent to the property that every homomorphism of the group F∞ ×F∞ into the unitary group U(l) with the strong topology is pointwise approximated by homomorphisms with a precompact range. In this form, the property (which we call Kirchberg’s property) makes sense for an arbitrary topological group. We establish the validit...

A smooth, compact 4–manifold with a Riemannian metric and b2+ ≥ 1 has a non-trivial, closed, self-dual 2–form. If the metric is generic, then the zero set of this form is a disjoint union of circles. On the complement of this zero set, the symplectic form and the metric define an almost complex structure; and the latter can be used to define pseudo-holomorphic submanifolds and subvarieties. The...

In terms of synthetic differential geometry, we give a variational characterization of the connection (parallelism) associated to a pseudo-Riemannian metric on a manifold.

There is a general method, applicable in many situations, whereby a pseudo–Riemannian metric, invariant under the action of some Lie group, can be deformed to obtain a new metric whose geodesics can be expressed in terms of the geodesics of the old metric and the action of the Lie group. This method applied to Euclidean space and the unit sphere produces new examples of complete Riemannian metr...

We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal, Whitney sum E⊕C where E is a given Courant algebroid and C is a flat, pseudo-Euclidean vector bundle. Then, we establish the general expression of the bracket of a transitive Courant algebroid, that is, a Courant algebroid with a surjective anchor, and describ...

In this paper we prove mean curvature comparisons and volume on a smooth metric measure space when the integral radial Bakry-Émery Ricci tensor potential function or its gradient are bounded. As applications, diameter estimates eigenvalue spaces. These results not only give supplement of author’s previous under bounds, but also generalizations Wei-Wylie’s pointwise results.