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Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising…
A common problem in numerous research areas, particularly in clinical trials, is to test whether the effect of an explanatory variable on an outcome variable is equivalent across different groups. In practice, these tests are frequently…
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…
The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied…
We propose a bootstrap-based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls…
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…
This paper describes a method for performing inference on models chosen by cross-validation. When the test error being minimized in cross-validation is a residual sum of squares it can be written as a quadratic form. This allows us to apply…
The block Kaczmarz method is an iterative scheme for solving overdetermined least-squares problems. At each step, the algorithm projects the current iterate onto the solution space of a subset of the constraints. This paper describes a…
We propose a new inference framework called localized conformal prediction. It generalizes the framework of conformal prediction by offering a single-test-sample adaptive construction that emphasizes a local region around this test sample,…
This paper is concerned with the nonconforming finite element discretization of geometric partial differential equations. In specific, we construct a surface Crouzeix-Raviart element on the linear approximated surface, analogous to a flat…
Stochastic approximation algorithms are iterative procedures which are used to approximate a target value in an environment where the target is unknown and direct observations are corrupted by noise. These algorithms are useful, for…
This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof…
We propose a new method for preconditioning Kaczmarz method by sketching. Kaczmarz method is a stochastic method for solving overdetermined linear systems based on a sampling of matrix rows. The standard approach to speed up convergence of…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
A method is presented for the fast evaluation of the transient acoustic field generated outside a spherical surface using surface data on the sphere. The method employs Lebedev quadratures, which are optimal integration on the sphere, and…