Related papers: Interpolating splines on graphs for data science a…

We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by Grone, and Grone and…

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…

We investigate the fine structure in the energy spectrum of bilayer graphene in the presence of various stacking defaults, such as a translational or rotational mismatch. This fine structure consists of four Dirac points that move away from…

In graphene moir\'e superlattices, electronic interactions between layers are mostly hidden as band structures get crowded because of folding, making their interpretation cumbersome. Here, the evolution of the electronic band structure as a…

We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in…

Graphs possess exotic features like variable size and absence of natural ordering of the nodes that make them difficult to analyze and compare. To circumvent this problem and learn on graphs, graph feature representation is required. A good…

Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively…

We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible…

The purpose of this paper is to establish that for any compact, connected C^{\infty} Riemannian manifold there exists a robust family of kernels of increasing smoothness that are well suited for interpolation. They generate Lagrange…

The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order…

Graphs are irregular structures which naturally account for data integrity, however, traditional approaches have been established outside Signal Processing, and largely focus on analyzing the underlying graphs rather than signals on graphs.…

Knowledge Graph Embedding (KGE) models are used to learn continuous representations of entities and relations. A key task in the literature is predicting missing links between entities. However, Knowledge Graphs are not just sets of links…

Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…

Due to the elimination property held by the lexicographic monomial order, the corresponding Groebner bases display strong structural properties from which meaningful informations can easily be extracted. We study these properties for…

We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…

Slater basis functions have desirable properties that can improve electronic structure simulations, but improved numerical integration methods are needed. This work builds upon the SlaterGPU library for evaluation of Hamiltonian matrix…

Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the…

Graphs are useful to interpret widely used image processing methods, e.g., bilateral filtering, or to develop new ones, e.g., kernel based techniques. However, simple graph constructions are often used, where edge weight and connectivity…