Related papers: Embedding with a Rigid Substructure
The accurate approximation of critical strains for lattice instability is a key criterion for predictive computational modeling of materials. In this paper, we present a comparison of the lattice stability for atomistic chains modeled by…
The Erd\H{o}s distance problem concerns the least number of distinct distances that can be determined by $N$ points in the plane. The integer lattice with $N$ points is known as \textit{near-optimal}, as it spans $\Theta(N/\sqrt{\log(N)})$…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
Aberration-corrected scanning electron microscopy (AC-STEM) can provide valuable information on the atomic structure of nanoclusters, an essential input for gaining an understanding of their physical and chemical properties. A systematic…
In this work, we employ differential evolution algorithm to identify the optimal configurations of small atomic ensembles supporting quantum states with maximal radiative lifetime. We demonstrate that atoms mostly tend to assemble in…
Let $X$ be a set of $n$ points of norm at most $1$ in the Euclidean space $R^k$, and suppose $\varepsilon>0$. An $\varepsilon$-distance sketch for $X$ is a data structure that, given any two points of $X$ enables one to recover the square…
We introduce a new method, rooted in estimation theory, to detect individual atoms in site-resolved images of microtrap arrays, such as optical lattices or optical tweezers arrays. Using labelled test images, we demonstrate drastic…
In this paper numerical methods of computing distances between two Radon measures on R are discussed. Efficient algorithms for Wasserstein-type metrics are provided. In particular, we propose a novel algorithm to compute the flat metric…
We present a general framework for analyzing the complexity of subdivision-based algorithms whose tests are based on the sizes of regions and their distance to certain sets (often varieties) intrinsic to the problem under study. We call…
In this paper, we give the first algorithm that outputs a faithful reconstruction of a submanifold of Euclidean space without maintaining or even constructing complicated data structures such as Voronoi diagrams or Delaunay complexes. Our…
Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…
We investigate a geometric computational framework, called the "scaling-rotation framework", on ${\rm Sym}^+(p)$, the set of $p \times p$ symmetric positive-definite (SPD) matrices. The purpose of our study is to lay geometric foundations…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint…
We present a polynomial-time $\frac{3}{2}$-approximation algorithm for the problem of finding a maximum-cardinality stable matching in a many-to-many matching model with ties and laminar constraints on both sides. We formulate our problem…
Shortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the…
We investigate the retrieval of spatially resolved atomic displacements via the phases of the direct(real)-space image reconstructed from the strained crystal's coherent x-ray diffraction pattern. We demonstrate that limiting the spatial…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…
The fundamental inverse problem in distance geometry is the one of finding positions from inter-point distances. The Discretizable Molecular Distance Geometry Problem (DMDGP) is a subclass of the Distance Geometry Problem (DGP) whose search…