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In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…
A routine crystallography technique, crystal structure analysis, is rarely performed in computational condensed matter research. The lack of methods to identify and characterize crystal structures reliably in particle simulation data…
Diffusion distillation provides an effective approach for learning lightweight and few-steps diffusion models with efficient generation. However, evaluating their generalization remains challenging: theoretical metrics are often impractical…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a distance in chaotic unidimensional maps. Based on that…
LiDAR-based 3D sensors provide point clouds, a canonical 3D representation used in various scene understanding tasks. Modern LiDARs face key challenges in several real-world scenarios, such as long-distance or low-albedo objects, producing…
A fast, parallel algorithm for distant-dependent calculation and simulation of crystal properties is presented along with speedup results and methods of application. An illustrative example is used to compute the Lennard-Jones lattice…
We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…
Distance-based methods involve the computation of distance values between features and are a well-established paradigm in machine learning. In anomaly detection, anomalies are identified by their large distance from normal data points.…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…
We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate…
The two parameter Poisson-Dirichlet Process (PDP), a generalisation of the Dirichlet Process, is increasingly being used for probabilistic modelling in discrete areas such as language technology, bioinformatics, and image analysis. There is…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature…
In this paper, we propose a novel, effective and efficient probabilistic pruning criterion for probabilistic similarity queries on uncertain data. Our approach supports a general uncertainty model using continuous probabilistic density…
Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e. mixtures of infinitely many components with sizes drawn from a continuous…
After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…