3 citations · 3 across the 6 of their papers we have counts for
4 papers · 1 filter
Weighted nonlocal operators and their applications in semi-supervised learning
Qiang Du, James M. Scott
Motivated by problems in machine learning, we study a class of variational problems characterized by nonlocal operators. These operators are characterized by power-type weights, wh…
Ginzburg--Landau Functionals in the Large-Graph Limit
Edith Zhang, James Scott, Qiang Du +1
Ginzburg--Landau (GL) functionals on graphs, which are relaxations of graph-cut functionals on graphs, have yielded a variety of insights in image segmentation and graph clustering…
Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems
Qiang Du, James M. Scott, Xiaochuan Tian
We present a study on asymptotically compatible Galerkin discretizations for a class of parametrized nonlinear variational problems. The abstract analytical framework is based on v…
Ohta-Kawasaki energy for amphiphiles: asymptotics and phase-field simulations
Qiang Du, James M. Scott, Zirui Xu
We study the minimizers of a degenerate case of the Ohta-Kawasaki energy, defined as the sum of the perimeter and a Coulombic nonlocal term. We start by investigating radially symm…