Related papers: Geometrical Eigen-subspace Framework Based Molecul…

Molecular representation is a critical element in our understanding of the physical world and the foundation for modern molecular machine learning. Previous molecular machine learning models have employed strings, fingerprints, global…

Image representations (artificial or biological) are often compared in terms of their global geometric structure; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a…

The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…

Affine transformations have been recently used for stereo vision. They can be exploited in various computer vision application, e.g., when estimating surface normals, homographies, fundamental and essential matrices. Even full 3D…

Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…

The success of intelligent robotic missions relies on integrating various research tasks, each demanding distinct representations. Designing task-specific representations for each task is costly and impractical. Unified representations…

Graph embedding is a central problem in social network analysis and many other applications, aiming to learn the vector representation for each node. While most existing approaches need to specify the neighborhood and the dependence form to…

X-ray as well as electron diffraction are powerful tools for structure determination of molecules. Studies on randomly oriented molecules in the gas-phase address cases in which molecular crystals cannot be generated or the interaction-free…

We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that…

Improving the detailed understanding of the underlying properties and functions of biomolecules has recently attracted growing interest, enabled by the possibility of real-space imaging of single, intact macromolecules using Scanning…

The high-throughput screening of periodic inorganic solids using machine learning methods requires atomic positions to encode structural and compositional details into appropriate material descriptors. These atomic positions are not…

Structure-informed protein representation learning is essential for effective protein function annotation and \textit{de novo} design. However, the presence of inherent noise in both crystal and AlphaFold-predicted structures poses…

Self-supervised learning by predicting transformations has demonstrated outstanding performances in both unsupervised and (semi-)supervised tasks. Among the state-of-the-art methods is the AutoEncoding Transformations (AET) by decoding…

Real-world objects and environments are predominantly composed of edge features, including straight lines and curves. Such edges are crucial elements for various applications, such as CAD modeling, surface meshing, lane mapping, etc.…

We explore the sensitivity of several core-level spectroscopic methods to the underlying atomistic structure by using the water molecule as our test system. We first define a metric that measures the magnitude of spectral change as a…

This paper presents a new distance geometry algorithm for calculating atomic coordinates from estimates of the interatomic distances, which maintains the positions of the atoms in a known rigid substructure. Given an $M \times 3$ matrix of…

The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the…

Unsupervised homogeneous network embedding (NE) represents every vertex of networks into a low-dimensional vector and meanwhile preserves the network information. Adjacency matrices retain most of the network information, and directly…

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…

Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one of most challenging tasks in biological science. In the present work, persistent homology is,…