Related papers: Reduced Google matrix
Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be…
We describe a method to construct directed networks from multivariate time series which has several advantages over the widely accepted methods. This method is based on an information theoretic reduction of linear (auto-regressive) models.…
The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is…
The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable…
Graph convolutional networks (GCNs) have shown promising results in processing graph data by extracting structure-aware features. This gave rise to extensive work in geometric deep learning, focusing on designing network architectures that…
Numerous Graph Neural Networks (GNNs) have been developed to tackle the challenge of Knowledge Graph Embedding (KGE). However, many of these approaches overlook the crucial role of relation information and inadequately integrate it with…
Graph Neural Networks (GNNs) have led to state-of-the-art performance on a variety of machine learning tasks such as recommendation, node classification and link prediction. Graph neural network models generate node embeddings by merging…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
The task of data integration for multi-omics data has emerged as a powerful strategy to unravel the complex biological underpinnings of cancer. Recent advancements in graph neural networks (GNNs) offer an effective framework to model…
Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community. While being…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…
Many scientific problems seek to find the ground state in a rugged energy landscape, a task that becomes prohibitively difficult for large systems. Within a particular class of problems, however, the short-range correlations within energy…
Online social networks have emerged as useful tools to communicate or share information and news on a daily basis. One of the most popular networks is Twitter, where users connect to each other via directed follower relationships.…
This paper describes a new approach to the problem of the structural research of clusters based on the theory of geodetic and k-geodetic graphs. We firmly believe that this same approach can be used when solving problems of correlation…
Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
Gated networks are networks that contain gating connections, in which the outputs of at least two neurons are multiplied. Initially, gated networks were used to learn relationships between two input sources, such as pixels from two images.…
Social network analysis has long been an untiring topic of sociology. However, until the era of information technology, the availability of data, mainly collected by the traditional method of personal survey, was highly limited and…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…