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Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…
The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest…
Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained…
Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability. Several centrality measures have been proposed recently to evaluate the performance of nodes based on their…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
Graph neural networks (GNNs) have been applied to a large variety of applications in materials science and chemistry. Here, we recapitulate the graph construction for crystalline (periodic) materials and investigate its impact on the GNNs…
Graphs are often used to organize data because of their simple topological structure, and therefore play a key role in machine learning. And it turns out that the low-dimensional embedded representation obtained by graph representation…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…
Geometric scattering has recently gained recognition in graph representation learning, and recent work has shown that integrating scattering features in graph convolution networks (GCNs) can alleviate the typical oversmoothing of features…
Learning correspondences aims to find correct correspondences (inliers) from the initial correspondence set with an uneven correspondence distribution and a low inlier rate, which can be regarded as graph data. Recent advances usually use…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
We introduce the \emph{graphical reconfigurable circuits (GRC)} model as an abstraction for distributed graph algorithms whose communication scheme is based on local mechanisms that collectively construct long-range reconfigurable channels…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…
Graph Neural Networks (GNNs) offer a compact and computationally efficient way to learn embeddings and classifications on graph data. GNN models are frequently large, making distributed minibatch training necessary. The primary contribution…
Graph Neural Networks (GNNs) have demonstrated remarkable effectiveness in recommendation systems. However, conventional graph-based recommenders, such as LightGCN, require maintaining embeddings of size $d$ for each node, resulting in a…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…
This work introduces a systematic algorithm for generating directed networks with prescribed symmetries by constructing expansions from a given quotient network. The method enables researchers to synthesize realistic network models with…
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…
We introduce a technique that is capable to filter out information from complex systems, by mapping them to networks, and extracting a subgraph with the strongest links. This idea is based on the Minimum Spanning Tree, and it can be applied…
In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…