Related papers: Conformal Coordinates for Molecular Geometry: from…
Ground-state 3D geometries of molecules are essential for many molecular analysis tasks. Modern quantum mechanical methods can compute accurate 3D geometries but are computationally prohibitive. Currently, an efficient alternative to…
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…
Molecular shape and geometry dictate key biophysical recognition processes, yet many graph neural networks disregard 3D information for molecular property prediction. Here, we propose a new contrastive-learning procedure for graph neural…
Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
We describe a new generation of algorithms capable of mapping the structure and conformations of macromolecules and their complexes from large ensembles of heterogeneous snapshots, and demonstrate the feasibility of determining both…
We present a new variant of the geometry reconstruction approach for the formulation of atomistic/continuum coupling methods (a/c methods). For multi-body nearest-neighbour interactions on the 2D triangular lattice, we show that patch test…
Protein structures can be encoded into binary sequences, these are used to define a Hamming distance in conformational space: the distance between two different molecular conformations is the number of different bits in their sequences.…
This article describes an entirely algebraic construction for developing conformal geometries, which provide models for, among others, the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown…
Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…
Inferring geometrically consistent dense 3D scenes across a tuple of temporally consecutive images remains challenging for self-supervised monocular depth prediction pipelines. This paper explores how the increasingly popular transformer…
Object 6D pose estimation, a crucial task for robotics and augmented reality applications, becomes particularly challenging when dealing with novel objects whose 3D models are not readily available. To reduce dependency on 3D models, recent…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical…
A set of rules is defined to systematically number the groups and the atoms of organic molecules and, particularly, of polypeptides in a modular manner. Supported by this numeration, a set of internal coordinates is defined. These…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
We present the graph-based molecule software Molassembler for building organic and inorganic molecules. Molassembler provides algorithms for the construction of molecules built from any set of elements from the periodic table. In…
Three-dimensional (3D) mappings are fundamental in various scientific and engineering applications, including computer-aided engineering (CAE), computer graphics, and medical imaging. They are typically represented and stored as…
In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…