We present a novel technique for learning semantic representations, which extends the distributional hypothesis to multilingual data and joint-space embeddings. Our models leverage parallel data and learn to strongly align the embeddings of semantically equivalent sentences, while maintaining sufficient distance between those of dissimilar sentences. The models do not rely on word alignments or...

In this report, we use the complex-step derivative approximation technique to compute sensitivities for delay differential equations (DDEs) with non-smooth (discontinuous and even distributional) history functions. We compare the results with exact derivatives and with those computed using the classical sensitivity equations whenever possible. Our results demonstrate that the implementation of ...

Multivariate kernel density estimation provides information about structure in data. Feature significance is a technique for deciding whether features – such as local extrema – are statistically significant. This paper proposes a framework for feature significance in d-dimensional data which combines kernel density derivative estimators and hypothesis tests for modal regions. For the gradient a...

Penalized Spline Estimation in the Partially Linear Model by Ashley D. Holland Co-Chairs: Matias D. Cattaneo and Virginia R. Young Penalized spline estimators have received considerable attention in recent years because of their good finite-sample performance, especially when the dimension of the regressors is large. In this project, we employ penalized B-splines in the context of the partially...

Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations [2]. It can be interpreted as a “sparse” penalization of optimal balancing from the first up to the kth distributional derivative and leads to desirable results when applied to image denoising, i.e., L-fitting with TGV penalty. The present paper studi...

When analyzing point-referenced spatial data, interest will be in the first order or global behavior of associated surfaces. However, in order to better understand these surfaces, we may also be interested in second order or local behavior, e.g., in the rate of change of a spatial surface at a given location in a given direction. In a Bayesian parametric setting, such smoothness analysis has be...

The proof, established in a recent paper (A.J. Devaney, “Nonradiating surface sources”, J. Opt. Soc. Am. A, Vol. 21, 2216-2222, 2004), of existence of nonradiating surface sources formed by singlet plus doublet components whose generated fields vanish in either of the regions separated by a closed or infinite surface where the source resides is corroborated by means of an equivalent but slightl...

The aim of this paper is to analyze contractivity properties of Wasserstein-type metrics for one-dimensional scalar conservation laws with nonnegative, L∞ and compactly supported initial data and its implications on the long time asymptotics. The flux is assumed to be convex and without any growth condition at the zero state. We propose a time–parameterized family of functions as intermediate a...