Related papers: Conformal Coordinates for Molecular Geometry: from…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper…
Acquiring 3D geometry of real world objects has various applications in 3D digitization, such as navigation and content generation in virtual environments. Image remains one of the most popular media for such visual tasks due to its…
-Molecular simulations allow the study of properties and interactions of molecular systems. This article presents an improved version of the Adaptive Resolution Scheme that links two systems having atomistic (also called fine-grained) and…
Segment matching is an important intermediate task in computer vision that establishes correspondences between semantically or geometrically coherent regions across images. Unlike keypoint matching, which focuses on localized features,…
We introduce a method for modeling a configuration of objects in 2D or 3D images using a mathematical "skeletal linking structure" which will simultaneously capture the individual shape features of the objects and their positional…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…
Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…
In an earlier paper (Class. Quantum Grav. 19 (2002) p.259) the author wrote the homothetic equations for vacuum solutions in a first order formalism allowing for arbitrary alignment of the dyad. This paper generalises that method to…
Multimodal learning plays a pivotal role in advancing artificial intelligence systems by incorporating information from multiple modalities to build a more comprehensive representation. Despite its importance, current state-of-the-art…
A novel method, named Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed for high dimensional data classification, dimension reduction, and visualization. CAMEL utilizes a topology metric defined on the Riemannian…
Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…
The latest research of the proportionality of atomic weights of chemical elements made it possible to obtain 3 x 3 matrices for the calculation of information coefficients of proportionality Ip that can be used for 3D modeling of the…
We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the…
Spatial perception aims to estimate camera motion and scene structure from visual observations, a problem traditionally addressed through geometric modeling and physical consistency constraints. Recent learning-based methods have…
Recovering the metric 3D shape from a single image is particularly relevant for robotics and embodied intelligence applications, where accurate spatial understanding is crucial for navigation and interaction with environments. Usually, the…
Conformal tracking is an innovative and comprehensive pattern recognition technique using a cellular automaton-based track finding performed in a conformally-mapped space. It is particularly well-suited for light-weight silicon systems with…
High-throughput chromatin conformation capture (Hi-C) data provide insights into the 3D structure of chromosomes, with normalization being a crucial pre-processing step. A common technique for normalization is matrix balancing, which…
An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…
We investigate and provide optimal sets of reaction coordinates for mixed pairs of molecules displaying polar, uniaxial, or spherical symmetry in two and three dimensions. These coordinates are non-redundant, i.e., they implicitly involve…