Related papers: Ellipsis and Quantification: a substitutional appr…
We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause…
Most, if not all forms of ellipsis (e.g., so does Mary) are similar to reading comprehension questions (what does Mary do), in that in order to resolve them, we need to identify an appropriate text span in the preceding discourse. Following…
We present a hybrid text understanding methodology for the resolution of textual ellipsis. It integrates conceptual criteria (based on the well-formedness and conceptual strength of role chains in a terminological knowledge base) and…
A hybrid methodology for the resolution of text-level ellipsis is presented in this paper. It incorporates conceptual proximity criteria applied to ontologically well-engineered domain knowledge bases and an approach to centering based on…
We represent in this note the solutions of the electronic Schr\"odinger equation as traces of higher-dimensional functions. This allows to decouple the electron-electron interaction potential but comes at the price of a degenerate elliptic…
This paper compares classical copying and quantum entanglement in natural language by considering the case of verb phrase (VP) ellipsis. VP ellipsis is a non-linear linguistic phenomenon that requires the reuse of resources, making it the…
We investigate the quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients. Quantitative unique continuation described by the vanishing order is a quantitative form of strong unique…
We consider elliptic differential operators on either the entire Euclidean space $\mathbb{R}^d$ or on subsets consisting of a cube $\Lambda_L$ of integer length $L$. For eigenfunctions of the operator, and more general solutions of elliptic…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
This paper presents a theoretical research based approach to ellipsis resolution in machine translation. The formula of discourse is applied in order to resolve ellipses. The validity of the discourse formula is analyzed by applying it to…
Summability has been a central object of study in difference algebra over the past half-century. It serves as a cornerstone of algebraic methods to study linear recurrences over various fields of coefficients and with respect to various…
In this paper, we discuss the question whether phrasal comparatives should be given a direct interpretation, or require an analysis as elliptic constructions, and answer it with Yes and No. The most adequate analysis of wide reading…
In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
In this paper we develop numerical analysis for finite element discretization of semilinear elliptic equations with potentially non-Lipschitz nonlinearites. The nonlinearity is essecially assumed to be continuous and monotonically…
A new variational approach to solve the problem of estimating the (possibly discontinuous) coefficient functions $p$, $q$ and $f$ in elliptic equations of the form $-\nabla \cdot (p(x)\nabla u) + \lambda q(x) u = f$, $x \in \Omega \subset…
We provide a general account of parallelism in discourse, and apply it to the special case of resolving possible readings for instances of VP ellipsis. We show how several problematic examples are accounted for in a natural and…
We obtain comparison theorems for non-negative solutions of quasilinear elliptic inequalities
The paper concerns singular solutions of nonlinear elliptic equations.
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…