Related papers: Algebraic 3D Graphic Statics: reciprocal construct…

The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to…

We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…

We extend the duality between acyclic orientations and totally cyclic orientations on planar graphs to dualities on graphs on orientable surfaces by introducing boundary acyclic orientations and totally bi-walkable orientations. In…

Discovery of atomistic systems with desirable properties is a major challenge in chemistry and material science. Here we introduce a novel, autoregressive, convolutional deep neural network architecture that generates molecular equilibrium…

We consider the problem of finding a continuous and non-rigid matching between a 2D contour and a 3D mesh. While such problems can be solved to global optimality by finding a shortest path in the product graph between both shapes, existing…

Combinations of advanced X-ray sources and zero-noise detector of enormous dynamic range have significantly increased the opportunity of mapping the reciprocal space of crystal lattices. It is particularly important in the design of new…

3D Gaussian Splatting (3DGS) has shown remarkable success in synthesizing novel views given multiple views of a static scene. Yet, 3DGS faces challenges when applied to dynamic scenes because 3D Gaussian parameters need to be updated per…

Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…

In this paper, we propose a novel graph convolutional network architecture, Graph Stacked Hourglass Networks, for 2D-to-3D human pose estimation tasks. The proposed architecture consists of repeated encoder-decoder, in which…

Volumetric design is the first and critical step for professional building design, where architects not only depict the rough 3D geometry of the building but also specify the programs to form a 2D layout on each floor. Though 2D layout…

3D Gaussian Splatting (3DGS) has emerged as a key rendering pipeline for digital asset creation due to its balance between efficiency and visual quality. To address the issues of unstable pose estimation and scene representation distortion…

Tolerancing of assembly mechanisms is a major interest in the product life cycle. One can distinguish several models with growing complexity, from 1-dimensional (1D) to 3-dimensional (3D) (including form deviations), and two main…

The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…

With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…

In the past several decades, many attempts have been made to model synthetic realistic geometric data. The goal of such models is to generate plausible 3D geometries and textures. Perhaps the best known of its kind is the linear 3D…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…

Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…

Recently, deep learning based methods have demonstrated promising results on the graph matching problem, by relying on the descriptive capability of deep features extracted on graph nodes. However, one main limitation with existing deep…

The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…