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Predictive machine learning models generally excel on in-distribution data, but their performance degrades on out-of-distribution (OOD) inputs. Reliable deployment therefore requires robust OOD detection, yet this is particularly…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
Physicochemical characterization of materials is central to the field of science and engineering and is essential to design new/engineered materials with specific properties. Assays available for small-molecules, e.g., XRD, NMR, LC-MS,…
A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…
In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), or on a distance matrix denoting original space distances, is mapped to (projected onto) one point in a low dimensional space…
Distribution matching distillation (DMD) facilitates few-step image generation by aligning a distilled student with a reference multi-step teacher. In practice, however, optimizing DMD can reduce sample diversity in few-step synthesis, and…
The \textit{biharmonic distance} (BD) is a fundamental metric that measures the distance of two nodes in a graph. It has found applications in network coherence, machine learning, and computational graphics, among others. In spite of BD's…
The local arrangement of atoms is one of the most important predictors of mechanical and functional properties of materials. However, algorithms for identifying the geometrical arrangements of atoms in complex materials systems are lacking.…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
A new interpoint distance-based measure is proposed to identify the optimal number of clusters present in a data set. Designed in nonparametric approach, it is independent of the distribution of given data. Interpoint distances between the…
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
We study infinite Euclidean distance discriminants of algebraic varieties, defined as the loci of data points whose fibers under the second projection from the Euclidean distance correspondence are positive-dimensional. In particular, these…
Change point detection (CPD) and anomaly detection (AD) are essential techniques in various fields to identify abrupt changes or abnormal data instances. However, existing methods are often constrained to univariate data, face scalability…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
Lidar datasets now commonly reach Billions of points and are very dense. Using these point cloud becomes challenging, as the high number of points is intractable for most applications and for visualisation.In this work we propose a new…
Dynamical density functional theory (DDFT) is a powerful variational framework to study the nonequilibrium properties of colloids by only considering a time-dependent one-body number density. Despite the large number of recent successes,…
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…