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Evaluating the (dis)similarity of crystalline, disordered and molecular compounds is a critical step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural…
While dealing with matching shapes to their parts, we often apply a tool known as functional maps. The idea is to translate the shape matching problem into "convenient" spaces by which matching is performed algebraically by solving a least…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. A straightforward approach to this problem consists of…
Single particle diffraction imaging experiments at free-electron lasers (FEL) have a great potential for structure determination of reproducible biological specimens that can not be crystallized. One of the challenges in processing the data…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider…
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree…
A convex partition of a point set P in the plane is a planar partition of the convex hull of P with empty convex polygons or internal faces whose extreme points belong to P. In a convex partition, the union of the internal faces give the…
The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…
This paper addresses the challenge of classifying polarimetric SAR images by leveraging the peculiar characteristics of the polarimetric covariance matrix (PCM). To this end, a general framework to solve a multiple hypothesis test is…
Determining the structure of a protein has been a decades-long open question. A protein's three-dimensional structure often poses nontrivial computation costs, when classical simulation algorithms are utilized. Advances in the transformer…
We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a…
To extend rational materials design and discovery into the space of metastable polymorphs, rapid and reliable assessment of their lifetimes is essential. Motivated by the early work of Buerger (1951), here we investigate the routes to…
We demonstrate a new algorithm for finding protein conformations that minimize a non-bonded energy function. The new algorithm, called the difference map, seeks to find an atomic configuration that is simultaneously in two constraint…
Let P be a d-dimensional n-point set. A Tverberg-partition of P is a partition of P into r sets P_1, ..., P_r such that the convex hulls conv(P_1), ..., conv(P_r) have non-empty intersection. A point in the intersection of the conv(P_i)'s…
We consider the problem of representing the fraction $5/P$ as a sum of three distinct unit fractions $1/A+1/B+1/C$ with $A<B<C$ and $A,B,C\in\mathbb{N}$. The case of primes $P\equiv 1 \pmod{5}$ is analyzed, where two constructive types of…
We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…
We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…
Structure prediction has become a key task of the modern atomistic sciences, and depends on the rapid and reliable computation of the energy landscape. First principles density functional based calculations are highly reliable, faithfully…