Related papers: Gradient-prolongation commutativity and graph theo…

There are a variety of existing conditions for a degree sequence to be graphic. When a degree sequence satisfies any of these conditions, there exists a graph that realizes the sequence. We formulate several novel sufficient graphicality…

The success of deep learning has revolutionized many fields of research including areas of computer vision, text and speech processing. Enormous research efforts have led to numerous methods that are capable of efficiently analyzing data,…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…

Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…

Distribution shifts between training and testing datasets significantly impair the model performance on graph learning. A commonly-taken causal view in graph invariant learning suggests that stable predictive features of graphs are causally…

Federated graph learning collaboratively learns a global graph neural network with distributed graphs, where the non-independent and identically distributed property is one of the major challenges. Most relative arts focus on traditional…

We consider the problem of identifying a conditional causal effect through covariate adjustment. We focus on the setting where the causal graph is known up to one of two types of graphs: a maximally oriented partially directed acyclic graph…

We prove a theorem that can be thought of as a common generalization of the Discrete Nodal Theorem and (one direction of) Cheeger's Inequality for graphs. special case of this result will assert that if the second and third eigenvalues of…

We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions while sharing many nonlinear properties…

Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…

A graph $G$ of order $2n$ is called degree-equipartite if for every $n$-element set $A\subseteq V(G)$, the degree sequences of the induced subgraphs $G[A]$ and $G[V(G)\setminus A]$ are the same. In this paper, we characterize all…

Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by…

We prove a new generalisation of Ramsey's theorem by showing that every $2$-edge-coloured graph with sufficiently large minimum degree contains a monochromatic induced subgraph whose minimum degree remains large. From this, we also derive…

This paper presents a contextualized graph attention network that combines edge features and multiple sub-graphs for improving relation extraction. A novel method is proposed to use multiple sub-graphs to learn rich node representations in…

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…

This paper considers the topological degree of $G$-shifts of finite type for the case where $G$ is a nonabelian monoid. Whenever the Cayley graph of $G$ has a finite representation and the relationships among the generators of $G$ are…

Coarse-grained (CG) molecular dynamics (MD) simulations can simulate large molecular complexes over extended timescales by reducing degrees of freedom. A critical step in CG modeling is the selection of the CG mapping algorithm, which…

We construct relative Gromov--Witten theory with expanded degenerations in the normal crossings setting and establish a degeneration formula for the resulting invariants. Given a simple normal crossings pair $(X,D)$, we show that there…

Suppose a finite, unweighted, combinatorial graph $G = (V,E)$ is the union of several (degree-)regular graphs which are then additionally connected with a few additional edges. $G$ will then have only a small number of vertices $v \in V$…