18 citations · 47 across the 10 of their papers we have counts for
12 papers
Analysis of a dislocation model for earthquakes
Jing Liu, Xin Yang Lu, Noel J Walkington
Approximation of problems in linear elasticity having small shear modulus in a thin region is considered. Problems of this type arise when modeling ground motion due to earthquakes…
Real order total variation with applications to the loss functions in learning schemes
Pan Liu, Xin Yang Lu, Kunlun He
Loss function are an essential part in modern data-driven approach, such as bi-level training scheme and machine learnings. In this paper we propose a loss function consisting of a…
Average-distance problem with curvature penalization for data parameterization: regularity of minimizers
Xinyang Lu, Dejan Slepcev
We propose a model for finding one-dimensional structure in a given measure. Our approach is based on minimizing an objective functional which combines the average-distance functio…
An Asymptotically Compatible Approach For Neumann-Type Boundary Condition On Nonlocal Problems
Huaiqian You, Xin Yang Lu, Nathaniel Trask +1
In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter characterizing the range of nonlocal interactions, and consider the treatment of…
Bounds on the Geometric Complexity of Optimal Centroidal Voronoi Tesselations in 3D
Rustum Choksi, Xin Yang Lu
Gersho's conjecture in 3D asserts the asymptotic periodicity and structure of the optimal centroidal Voronoi tessellation. This relatively simple crystallization problem remains to…
Real order (an)-isotropic total variation in image processing - Part I: analytical analysis and functional properties
Pan Liu, Xin Yang Lu
In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the -order (an)-isotropic total variatio…