Related papers: Graphoids
Neural networks for structured data like graphs have been studied extensively in recent years. To date, the bulk of research activity has focused mainly on static graphs. However, most real-world networks are dynamic since their topology…
We construct a new order 1 invariant for knot diagrams. We use it to determine the minimal number of Reidemeister moves needed to pass between certain pairs of knot diagrams.
This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…
Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers.…
We investigate the property of a spatial graph of having a leveled embedding and characterize the abstract graphs with this property. We show that all leveled embeddings are free and we compare leveled and paneled (also known as flat)…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup, which we prove is an $E^*$-unitary inverse…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
The homology of Kontsevich's commutative graph complex parameterizes finite type invariants of odd dimensional manifolds. This {\it graph homology} is also the twisted homology of Outer Space modulo its boundary, so gives a nice point of…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics systems, learning molecular fingerprints, predicting protein interface, and classifying diseases demand a model…
In this brief note I try to give a simple example of where physical intuition about a collection of interacting qubits can lead to the construction of "natural" versions of what are, generically, quite abstract mathematical objects - in…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…
The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, firstly, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…