Related papers: Implicitly and Differentiably Representing Protein…
Existing methods in neural scene reconstruction utilize the Signed Distance Function (SDF) to model the density function. However, in indoor scenes, the density computed from the SDF for a sampled point may not consistently reflect its real…
We are seeing a Cambrian explosion of 3D shape representations for use in machine learning. Some representations seek high expressive power in capturing high-resolution detail. Other approaches seek to represent shapes as compositions of…
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,…
In this paper, we study the problem of continuous 3D shape representations. The majority of existing successful methods are coordinate-based implicit neural representations. However, they are inefficient to render novel views or recover…
This work reports a new methodology aimed at describing characteristics of protein structural shapes, and suggests a framework in which to resolve or classify automatically such structures into known families. This new approach to protein…
Autonomous robots should operate in real-world dynamic environments and collaborate with humans in tight spaces. A key component for allowing robots to leave structured lab and manufacturing settings is their ability to evaluate online and…
The protein backbone is described as a smooth curved and twisted line in three-dimensional (3D) space and characterized by its curvature $\kappa(s)$ and torsion $\tau(s)$ both expressed as a function of arc length s. It is shown that the…
We report a 3D structure-based method of predicting protein-protein interaction partners. It involves screening for pairs of tetrahedra representing interacting amino acids at the interface of the protein-protein complex, with one…
This paper presents a novel geometric representation for CAD Boundary Representation (B-Rep) based on volumetric distance functions, dubbed B-Rep Distance Functions (BR-DF). BR-DF encodes the surface mesh geometry of a CAD model as signed…
Implicit neural rendering, which uses signed distance function (SDF) representation with geometric priors (such as depth or surface normal), has led to impressive progress in the surface reconstruction of large-scale scenes. However,…
Unsigned Distance Functions (UDFs) can be used to represent non-watertight surfaces in a deep learning framework. However, UDFs tend to be brittle and difficult to learn, in part because the surface is located exactly where the UDF is…
Current diffusion or flow-based generative models for 3D shapes divide to two: distilling pre-trained 2D image diffusion models, and training directly on 3D shapes. When training a diffusion or flow models on 3D shapes a crucial design…
AI-based in silico methods have improved protein structure prediction but often struggle with large protein complexes (PCs) involving multiple interacting proteins due to missing 3D spatial cues. Experimental techniques like Cryo-EM are…
Signed distance fields (SDFs) are a form of surface representation widely used in computer graphics, having applications in rendering, collision detection and modelling. In interactive media such as games, high-resolution SDFs are commonly…
This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types…
Protein function is executed at the molecular surface, where shape and chemistry act together to govern interaction. Yet most comparison methods treat these aspects separately, privileging either global fold or local descriptors and missing…
From a geometric perspective most nonlinear binary classification algorithms, including state of the art versions of Support Vector Machine (SVM) and Radial Basis Function Network (RBFN) classifiers, and are based on the idea of…
We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their…
Deep learning-based 3D medical image segmentation methods relies on large-scale labeled datasets, yet acquiring such data is difficult due to privacy constraints and the high cost of expert annotation. Formula-Driven Supervised Learning…
Protein representation learning is a challenging task that aims to capture the structure and function of proteins from their amino acid sequences. Previous methods largely ignored the fact that not all amino acids are equally important for…