23 papers · ranked by Valyu relevance
Erik D. Demaine, Sándor P. Fekete, Phillip Keldenich, Dominik Krupke + 1 more
Computational Geometry is the study of algorithms for solving problems on geometric data. Geometric problem arise in numerous applications from fields that include Robotics (motion planning and visibility problems), Operations Research (geometric location and search, route planning), Integrated Circuit Design (IC…
Sharmila Devi, Anju Sangwan, Anupma Sangwan, Mazin Abed Mohammed + 5 more
'Krishna Kumar' 'Jan Nedoma' 'Radek Martinek' 'Petr Zmij' 'Jie Tang'] Wireless Sensor Networks (WSNs) enhance the ability to sense and control the physical environment in various applications. The functionality of WSNs depends on various aspects like the localization of nodes, the strategies of node deployment, and a…
Oswaldo Cadenas, Graham M. Megson, Krishna Garikipati
This paper presents a method to reduce a set of n 2D points to a smaller set of s 2D points with the property that the convex hull on the smaller set is the same as the convex hull of the original bigger set. The paper shows, experimentally, that such reduction accelerates computations; the time it takes to reduce from…
Hagai Har-Gil, Yoav Jacobson, Alvar Prönneke, Jochen F. Staiger + 3 more
The analysis of neuronal structure and its relation to function has become a fundamental pillar in neuroscience since its earliest days, with the underlying premise that morphological properties can modulate neuronal computations. It is often the case that the rich three-dimensional structure of neurons is quantified…
Keenan Crane, Marco Livesu, Enrico Puppo, Yipeng Qin
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and computer vision. Relative to Euclidean distance computation, these tasks are…
Wenjuan Gong, Bin Zhang, Chaoqi Wang, Hanbing Yue + 5 more
'Linjie Xing' 'Yu Qiao' 'Weishan Zhang' 'Faming Gong'] Geometric features, such as the topological and manifold properties, are utilized to extract geometric properties. Geometric methods that exploit the applications of geometrics, e.g., geometric features, are widely used in computer graphics and computer vision…
Gang Mei
Several key techniques in 3D geological modeling including planar mesh generation, spatial interpolation, and surface intersection are summarized in this paper. Note that these techniques are generic and widely used in various applications but play a key role in 3D geological modeling. There are two essential…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Authors not listed
Equivariant graph neural networks have shown remarkable success in molecular property prediction, but their performance on novel molecular geometries remains limited without extensive training data. We present a computationally efficient approach to cross-geometry pretraining for molecular systems that improves…
Lorenzo Diazzi, Daniele Panozzo, Amir Vaxman, Marco Attene
We build on the underlying theory of the well-known tetgen software, but use a floating-point implementation based on indirect geometric predicates to implicitly represent Steiner points: this new approach dramatically simplifies the implementation, removing the need for ad-hoc tolerances in geometric operations. Our…
Angan Mukherjee, ByungUk Park, Adam Malmstrom, Jessi Cisewski-Kehe + 2 more
Protein-protein interactions (PPIs) govern a wide range of cellular functions. The ability to predict PPI interfaces from protein molecular surfaces is important for understanding protein function and enabling therapeutic discovery. While recent advances in structure-based learning, particularly molecular-surface…
Peiran Jiang, Jose Lugo-Martinez
Protein pockets are essential for many proteins to carry out their functions. Locating and measuring protein pockets as well as studying the anatomy of pockets helps us further understand protein function. Most research studies focus on learning either local or global information from protein structures. However, there…
Jie Li, Paul Mach, Patrice Koehl
The molecular basis of life rests on the activity of biological macromolecules, mostly nucleic acids and proteins. A perhaps surprising finding that crystallized over the last handful of decades is that geometric reasoning plays a major role in our attempt to understand these activities. In this paper, we address this…
Eunjin Oh, Hee-Kap Ahn
Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple…
Jorge López, Salvador Botello, Rafael Herrera, Mauricio Carrillo-Tripp
The computational study of biomolecules has been undermined by the lack of models that accurately represent the structure of big complexes at the atomic level. In this work, we report the development of an algorithm to generate a volumetric mesh of a biomolecule, of any size and shape, based on its atomic structure.…
Andreas Buchgraitz Jensen, Jonas Elm
Atmospheric molecular clusters are important for the formation of new aerosol particles in the air. However, current experimental techniques are not able to yield direct insight into the cluster geometries. This implies that to date there is limited information about how accurately the applied computational methods…
Daniel T. Chang
The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule including its reactivity and biological activity. To facilitate the incorporation of…
Arian R. Jamasb, Pietro Lió, Tom L. Blundell
Graphein is a python library for constructing graph and surface-mesh representations of protein structures for computational analysis. The library interfaces with popular geometric deep learning libraries: DGL, PyTorch Geometric and PyTorch3D. Geometric deep learning is emerging as a popular methodology in…
Carlo Vittorio Cannistraci, Alessandro Muscoloni
We introduce in network geometry a measure of geometrical congruence (GC) to evaluate the extent a network topology follows an underlying geometry. This requires finding all topological shortest-paths for each nonadjacent node pair in the network: a nontrivial computational task. Hence, we propose an optimized…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Oliver Lee, Malte Gather, Eli Zysman-Colman
We describe a new tool for the efficient management of computational chemistry. Digichem is a program that automates and simplifies nearly the entire computational pipeline, including large-scale batch submission of calculations, analysis and results parsing, the generation of 3D density plots and 2D graphs of…
Eric Elmoznino, Michael F. Bonner
Geometric descriptions of deep neural networks (DNNs) have the potential to uncover core principles of computational models in neuroscience, while abstracting over the details of model architectures and training paradigms. Here we examined the geometry of DNN models of visual cortex by quantifying the latent…
Kazuma Tateiri
In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point s on a polyhedral surface and a positive real number r, to build a data structure that enables, for any point…