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Atomistic simulations are a powerful tool for studying the dynamics of molecules, proteins, and materials on wide time and length scales. Their reliability and predictiveness, however, depend directly on the accuracy of the underlying…

Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…

One of the goals of current particle physics research is to obtain evidence for new physics, that is, physics beyond the Standard Model (BSM), at accelerators such as the Large Hadron Collider (LHC) at CERN. The searches for new physics are…

Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…

We establish sufficient conditions for perfect simulation of chains of infinite order on a countable alphabet. The new assumption, localized continuity, is formalized with the help of the notion of context trees, and includes the…

In this paper, we propose a robust end-to-end multi-modal pipeline for place recognition where the sensor systems can differ from the map building to the query. Our approach operates directly on images and LiDAR scans without requiring any…

Scene understanding is an important capability for robots acting in unstructured environments. While most SLAM approaches provide a geometrical representation of the scene, a semantic map is necessary for more complex interactions with the…

We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that…

The similarity of local atomic environments is an important concept in many machine-learning techniques which find applications in computational chemistry and material science. Here, we present and discuss a connection between the…

This paper is about the local geometry of a real surfaces. It introduces machinery for studying families of subsets which are determined by conditions which are similar to base conditions, but also involve positivity/non-negativity. The…

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

Super-symmetric tensors - a higher-order extension of scatter matrices - are becoming increasingly popular in machine learning and computer vision for modelling data statistics, co-occurrences, or even as visual descriptors. However, the…

We introduce a machine learning method in which energy solutions from the Schrodinger equation are predicted using symmetry adapted atomic orbitals features and a graph neural-network architecture. \textsc{OrbNet} is shown to outperform…

Many robotics applications require precise pose estimates despite operating in large and changing environments. This can be addressed by visual localization, using a pre-computed 3D model of the surroundings. The pose estimation then…

The rapid emergence of universal Machine Learning Interatomic Potentials (uMLIPs) has transformed materials modeling. However, a comprehensive understanding of their generalization behavior across configurational space remains an open…

Despite the fundamental progress in autonomous molecular and materials discovery, data scarcity throughout chemical compound space still severely hampers the use of modern ready-made machine learning models as they rely heavily on the…

Simulations at the atomic scale provide a direct and effective way to understand the mechanical properties of materials. In the regime of classical mechanics, simulations for the thermodynamic properties of metals and alloys can be done by…

Despite the extent of recent advances in Machine Learning (ML) and Neural Networks, providing formal guarantees on the behavior of these systems is still an open problem, and a crucial requirement for their adoption in regulated or…

Biological systems display impressive capabilities in effectively responding to environmental signals in real time. There is increasing evidence that organisms may indeed be employing near optimal Bayesian calculations in their…

Rational design of compounds with specific properties requires conceptual understanding and fast evaluation of molecular properties throughout chemical compound space (CCS) -- the huge set of all potentially stable molecules. Recent…