Related papers: Proof Tree Preserving Interpolation
Hierarchical vector field interpolation introduces a structured probabilistic framework for lexical representation, ensuring that word embeddings transition smoothly across a continuous manifold rather than being constrained to discrete…
We introduce an approach that aims to combine the usage of satisfiability modulo theories (SMT) solvers with the Combinatory Logic Synthesizer (CL)S framework. (CL)S is a tool for the automatic composition of software components from a…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
We show that there exist linear-time algorithms that compute the strong chromatic index and a maximum induced matching of tree-cographs when the decomposition tree is a part of the input. We also show that there exist efficient algorithms…
Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…
The method of constructing trigonometric Hermite splines, which interpolate the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered. The proposed method is based on the periodicity properties…
Multicopy search structures such as log-structured merge (LSM) trees are optimized for high insert/update/delete (collectively known as upsert) performance. In such data structures, an upsert on key $k$, which adds $(k,v)$ where $v$ can be…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
This paper will focus on the semantic representation of verbs in computer systems and its impact on lexical selection problems in machine translation (MT). Two groups of English and Chinese verbs are examined to show that lexical selection…
Cross-modal retrieval is generally performed by projecting and aligning the data from two different modalities onto a shared representation space. This shared space often also acts as a bridge for translating the modalities. We address the…
This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…
The theory of symmetric multivariate Lagrange interpolation is a beautiful but rather unknown tool that has many applications. Here we derive from it an Exchange Lemma that allows to explain in a simple and natural way the full description…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…
We present a sequent-style proof system for provability logic GL that admits so-called circular proofs. For these proofs, the graph underlying a proof is not a finite tree but is allowed to contain cycles. As an application, we establish…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial differential equations (PDEs) with large near-kernels, such as…