Related papers: Graph theory and tunable slow dynamics in quantum …

The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…

We investigate the behavior of the recently proposed quantum Google algorithm, or quantum PageRank, in large complex networks. Applying the quantum algorithm to a part of the real World Wide Web, we find that the algorithm is able to…

Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset…

Spatiotemporal graph neural networks (STGNNs) have shown promising results in many domains, from forecasting to epidemiology. However, understanding the dynamics learned by these models and explaining their behaviour is significantly more…

Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis. To this…

This paper introduces graphemes for constructing and analyzing stochastic processes that describe the evolution of large dynamic graphs. Unlike graphons, which capture the static properties of dense graphs via exchangeability or subgraph…

This paper addresses the problem of traffic prediction in distributed backend systems and proposes a graph neural network based modeling approach to overcome the limitations of traditional models in capturing complex dependencies and…

We present an innovative framework for traffic dynamics analysis using High-Order Evolving Graphs, designed to improve spatio-temporal representations in autonomous driving contexts. Our approach constructs temporal bidirectional bipartite…

We investigate the low energy continuum limit theory for electrons in a graphene sheet under strain. We use the quantum field theory in curved spaces to analyze the effect of the system deformations into an effective gauge field. We study…

In the past, the dichotomy between homophily and heterophily has inspired research contributions toward a better understanding of Deep Graph Networks' inductive bias. In particular, it was believed that homophily strongly correlates with…

The proposed approach yields a numerical method that provably executes in linear time with respect to the number of nodes and edges in a graph. The graph, constructed from the power system model, requires only knowledge of the dependencies…

Random circuit models often describe local dynamics using generic two-qubit gates, which have proven successful in capturing entanglement growth and operator spreading in many contexts. This approach naturally leads to the expectation that…

Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…

We consider the problem of controlling a partially-observed dynamic process on a graph by a limited number of interventions. This problem naturally arises in contexts such as scheduling virus tests to curb an epidemic; targeted marketing in…

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials,…

The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation,…

We present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of…

We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…

This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…