Related papers: Conformal Coordinates for Molecular Geometry: from…

A comprehensive framework for detection and characterization of overlapping intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled…

Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…

Existing works based on molecular knowledge neglect the 3D geometric structure of molecules and fail to learn the high-dimensional information of medications, leading to structural confusion. Additionally, it does not extract key…

In this paper we develop a geometrical model of functional architecture for the processing of spatio-temporal visual stimuli. The model arises from the properties of the receptive field linear dynamics of orientation and speed-selective…

We present a new method for assessing the intrinsic 3D shape of prestellar cores from molecular column densities. We have employed hydrodynamic simulations of contracting, isothermal cores considering three intrinsic geometries: spherical,…

The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present…

Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to…

We present MoGe, a powerful model for recovering 3D geometry from monocular open-domain images. Given a single image, our model directly predicts a 3D point map of the captured scene with an affine-invariant representation, which is…

Accurate camera models are essential for photogrammetry applications such as 3D mapping and object localization, particularly for long distances. Various stereo-camera based 3D localization methods are available but are limited to few…

After the recent ground-breaking advances in protein structure prediction, one of the remaining challenges in protein machine learning is to reliably predict distributions of structural states. Parametric models of fluctuations are…

As a crucial task of autonomous driving, 3D object detection has made great progress in recent years. However, monocular 3D object detection remains a challenging problem due to the unsatisfactory performance in depth estimation. Most…

This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…

The Molecular Distance Geometry Problem (MDGP) is essential in structural biology, as it seeks to determine three-dimensional protein structures from partial interatomic distances. Its discretizable subclass (DMDGP) admits an exact…

Deep learning for molecular science has so far mainly focused on 2D molecular graphs. Recently, however, there has been work to extend it to 3D molecular geometry, due to its scientific significance and critical importance in real-world…

Cohomology and cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical…

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…

We propose a novel method of finding the classical limit of the matrix geometry. We define coherent states for a general matrix geometry described by a large-N sequence of D Hermitian matrices X_\mu (\mu =1,2, ..., D) and construct a…

When modeling physical properties of molecules with machine learning, it is desirable to incorporate $SO(3)$-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness…

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…