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Maxwell interface problems are of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in 3D computation as they can circumvent generating complex 3D interface-fitted meshes. However, many…
A new effective solution to the problem of Hermite $G^1$ interpolation with a clothoid curve is here proposed, that is a clothoid that interpolates two given points in a plane with assigned unit tangent vectors. The interpolation problem is…
Let $M$ be an open Riemann surface and $A$ be the punctured cone in $\mathbb{C}^n\setminus\{0\}$ on a smooth projective variety $Y$ in $\mathbb{P}^{n-1}$. Recently, Runge approximation theorems with interpolation for holomorphic immersions…
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…
We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating…
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients,…
In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often…
Let X be a complex algebraic manifold of dimension n+1 embedded in a sufficiently higher dimensional complex projective space, and Y a generic hyperplane section of X. We describe the mixed Hodge structure on H^p(X-Y,C) and the Hodge…
Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to evaluate the integral accurately at points on or near the…
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…
Knowledge graph embeddings (KGEs) compactly encode multi-relational knowledge graphs (KGs). Existing KGE models rely on geometric operations to model relational patterns. Euclidean (circular) rotation is useful for modeling patterns such as…
In recent years, geotagged social media has become popular as a novel source for geographic knowledge discovery. Ground-level images and videos provide a different perspective than overhead imagery and can be applied to a range of…
We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are…
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the Hausdorff distance and have not been studied yet in the literature. Parametric polynomial curves of low…
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…
A new, simple method to approach enumerative questions about rational curves on rational surfaces is described. Applications include a short proof of Kontsevich's formula for plane curves and a the solution of the analogous problem for the…
We present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
Skin effect that all eigenmodes within a frequency range become edge states is dictated by the topological properties of complex eigenvalues unique in non-Hermitian systems. The prevailing attempts to realize such a fascinating effect are…