相关论文: Graph kinematics of discrete physical objects: bey…

Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…

The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…

We highlight a topological aspect of the graph limit theory. Graphons are limit objects for convergent sequences of dense graphs. We introduce the representation of a graphon on a unique metric space and we relate the dimension of this…

Learning data-efficient object dynamics models for robotic manipulation remains challenging, especially for deformable objects. A popular approach is to model objects as sets of 3D particles and learn their motion using graph neural…

The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links…

Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale…

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning…

Graph representations of solid state materials that encode only interatomic distance lack geometrical resolution, resulting in degenerate representations that may map distinct structures to equivalent graphs. Here we propose a hypergraph…

A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…

The understanding of the structural and thermal properties of membranes, low-dimensional flexible systems in a space of higher dimension, is pursued in many fields from string theory to chemistry and biology. The case of a two-dimensional…

We introduce various notions of quantum symmetry in a directed or undirected multigraph with no isolated vertex and explore relations among them. If the multigraph is single edged (that is, a simple graph where loops are allowed), all our…

The past decade has seen a flourishing of advances in harmonic analysis of graphs. They lie at the crossroads of graph theory and such analytical tools as graph Laplacians, Markov processes and associated boundaries, analysis of path-space,…

These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…

Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…

Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…

We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing "strips" along their natural boundaries according to a given graph structure. The most familiar example is the one dimensional complex…

This work analyzes monolayer graphene in external electromagnetic fields, which is described by the Dirac equation with minimal coupling. Supersymmetric quantum mechanics allows building new Dirac equations with modified magnetic fields.…

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of…

Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…