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In this article we give a geometrical description of the (in general non-selfadjoint) in/out Laplacian $\mathcal{L}^{+/-} = (d^{+/-})^* d$ and adjacency matrix on digraphs with arbitrary weights, where $(d^{+/-})^*$ is the adjoint of the…
The topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and has been widely observed for electromagnetic and acoustic…
Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…
This paper introduces a novel Laplacian matrix aiming to enable the construction of spectral convolutional networks and to extend the signal processing applications for directed graphs. Our proposal is inspired by a Haar-like transformation…
Non-reciprocity and asymmetric transmission in optical and plasmonic systems is a key element for engineering the one-way propagation structures for light manipulation. Here we investigate topological nanostructures covered with…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
This work introduces NetDiff, an expressive graph denoising diffusion probabilistic architecture that generates wireless ad hoc network link topologies. Such networks, with directional antennas, can achieve unmatched performance when the…
The increasing share of renewable energy sources on distribution grid level as well as the emerging active role of prosumers lead to both higher distribution grid utilization, and at the same time greater unpredictability of energy…
The celebrated Cheeger's Inequality establishes a bound on the edge expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and eigenvectors of the adjacency…
We develop a calibrated diffusion framework by synthesizing three established concepts: linear Laplacian smoothing, nonlinear graph p-Laplacian flows, and a learnable dissipation term derived from a strongly convex potential. This synthesis…
Interconnected networks of rigid struts are critical for application in lightweight, load-bearing structures. However, accurately modeling stress distribution in these strut lattices poses significant computational challenges due to its…
A support structure is required to successfully create structural parts in the powder bed fusion process for additive manufacturing. In this study, we present the topology optimization of a support structure that improves the heat…
In this paper, we present GGSD, a novel graph generative model based on 1) the spectral decomposition of the graph Laplacian matrix and 2) a diffusion process. Specifically, we propose to use a denoising model to sample eigenvectors and…
We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC)…
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…
Several statistical problems, such as multiple heterogeneous graph analysis, distributed PCA, integrative data analysis, and simultaneous dimension reduction of images, can involve a collection of $m$ matrices whose leading subspaces…
Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…
We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial…
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian…
We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of `relative compactness' for such graphs and study sufficient and necessary conditions for…