Related papers: E(3)-equivariant models cannot learn chirality: Fi…

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…

We use continuum theory to show that chirality is a key thermodynamic control parameter for the aggregation of biopolymers: chirality produces a stable disperse phase of hexagonal bundles under moderately poor solvent conditions, as has…

Chirality is a highly important topic in modern chemistry, given the dramatically different pharmacological effects that enantiomers can have on the body. Chirality of natural molecules can be controlled by reconfiguration of molecular…

Molecule generation, especially generating 3D molecular geometries from scratch (i.e., 3D \textit{de novo} generation), has become a fundamental task in drug designs. Existing diffusion-based 3D molecule generation methods could suffer from…

Advances in deep learning models have revolutionized the study of biomolecule systems and their mechanisms. Graph representation learning, in particular, is important for accurately capturing the geometric information of biomolecules at…

Geometrical chirality is a property of objects that describes three-dimensional mirror-symmetry violation and therefore it requires a non-vanishing spatial extent. In contrary, optical chirality describes only the local handedness of…

Topological defects, or singularities, play a key role in the statics and dynamics of complex systems. In magnetism, Bloch point singularities represent point defects that mediate the nucleation of textures such as skyrmions and hopfions.…

Chiral tetrahedral molecules can be dealt under the standard of quaternionic algebra. Specifically, non-commutativity of quaternions is a feature directly related to the chirality of molecules. It is shown that a quaternionic representation…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

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…

Molecular pretrained representations (MPR) has emerged as a powerful approach for addressing the challenge of limited supervised data in applications such as drug discovery and material design. While early MPR methods relied on 1D sequences…

It has been long recognized that the spatial polarization of the electronic clouds in molecules, and the spatial arrangements of atoms into chiral molecular structures, play crucial roles in physics, chemistry and biology. However, these…

Contemporary registration devices for 3D visual information, such as LIDARs and various depth cameras, capture data as 3D point clouds. In turn, such clouds are challenging to be processed due to their size and complexity. Existing methods…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

To overcome the restriction of identical distribution assumption, invariant representation learning for unsupervised domain adaptation (UDA) has made significant advances in computer vision and pattern recognition communities. In UDA…

This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our…

We unveil the key-role of dimensionality in describing chiroptical properties of molecules embedded inside an optical Fabry-P\'erot cavity. For a 2D-layer configuration, we show that the interplay between molecular chirality and spatial…

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…

Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of…

The article seeks to formulate a synergetic law that is posited to be of common physicochemical and biological nature: an evolving system, possessing free energy and elements with chiral asymmetry may change the type of symmetry inside one…