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We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…

For two decades, reproducing kernels and their associated discrepancies have facilitated elegant theoretical analyses in the setting of quasi Monte Carlo. These same tools are now receiving interest in statistics and related fields, as…

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape…

We propose a novel molecular fingerprint-based variational autoencoder applied for molecular generation on real-world drug molecules. We define more suitable and pharma-relevant baseline metrics and tests, focusing on the generation of…

In this paper, we propose a method to represent a fingerprint image by an ordered, fixed-length bit-string providing improved accuracy performance, faster matching time and compressibility. First, we devise a novel minutia-based local…

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…

Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…

Atomic environment fingerprints are widely used in computational materials science, from machine learning potentials to the quantification of similarities between atomic configurations. Many approaches to the construction of such…

In the majority of molecular optimization tasks, predictive machine learning (ML) models are limited due to the unavailability and cost of generating big experimental datasets on the specific task. To circumvent this limitation, ML models…

We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with a…

As computers get faster, researchers -- not hardware or algorithms -- become the bottleneck in scientific discovery. Computational study of colloidal self-assembly is one area that is keenly affected: even after computers generate massive…

Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine…

To learn about a physical system of interest, experimental results must be able to discriminate among models. We introduce a geometrical measure to quantify the distance between models for pseudoscalar-meson photoproduction in amplitude…

This paper proposes minimum distance inference for a structural parameter of interest, which is robust to the lack of identification of other structural nuisance parameters. Some choices of the weighting matrix lead to asymptotic…

Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…

We consider the chordal product determinant, a measure of the distance between two subspaces of the same dimension. In information theory, collections of elements in the complex Grassmannian are searched with the property that their…

The simulation of intrinsic contributions to molecular properties holds the potential to allow for chemistry to be directly inferred from changes to electronic structures at the atomic level. In the present study, we demonstrate how such…

We explore learning pixelwise correspondences between images of deformable objects in different configurations. Traditional correspondence matching approaches such as SIFT, SURF, and ORB can fail to provide sufficient contextual information…

Independence analysis is an indispensable step before regression analysis to find out essential factors that influence the objects. With many applications in machine Learning, medical Learning and a variety of disciplines, statistical…