相关论文: Graphon-based sensitivity analysis of SIS epidemic…

This paper investigates how the structure of the underlying graph influences the behavior of stochastic partial differential equations (SPDEs) on finite tree graphs, where each edge is driven by space-time white noise. We first introduce a…

A recent paper, ``A Graphon-Signal Analysis of Graph Neural Networks'', by Levie, analyzed message passing graph neural networks (MPNNs) by embedding the input space of MPNNs, i.e., attributed graphs (graph-signals), to a space of…

This report is based on the work in (1). We first review definitions and notation developped there and provide derivations for the exact mathematical description of an SIS epidemic on a hypergraph. We then generalise the work in (1) to a…

Graph neural networks have been widely utilized to solve graph-related tasks because of their strong learning power in utilizing the local information of neighbors. However, recent studies on graph adversarial attacks have proven that…

Stochastic models for collections of interacting populations have crucial roles in scientific fields such as epidemiology and ecology, yet the standard approach to extending an ordinary differential equation model to a Markov chain does not…

There are many methods to estimate the quasi-stationary infected fraction of the SIS process on (random) graphs. A challenge is to adequately incorporate correlations, which is especially important in sparse graphs. Methods typically are…

We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models…

We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree $\kappa $. Using very simple rules for forming such preferred degree networks, we find…

In network epidemic models, controlling the spread of a disease often requires targeted interventions such as vaccinating high-risk individuals based on network structure. However, typical approaches assume complete knowledge of the…

We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining the overall grid behavior and performance. Specifically, we show that…

Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…

We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering a graph Laplacian that is approximately diagonalizable by a…

In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the…

Graph states are an important class of entangled states that serve as a key resource for distributed information processing and communication in quantum networks. In this work, we propose a protocol that utilizes a Bell sampling subroutine…

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to parameter changes of coupled dynamical systems on complex…

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…

In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (Susceptible-Infected-Susceptible) epidemic model recently proposed in [A. Gray et al., SIAM. J. Appl. Math., 71 (2011), 876-902]. We…

We consider the problem of learning the weighted edges of a graph by observing the noisy times of infection for multiple epidemic cascades on this graph. Past work has considered this problem when the cascade information, i.e., infection…

Rigidity theory enables us to specify the conditions of unique localizability in the cooperative localization problem of wireless sensor networks. This paper presents a combinatorial rigidity approach to measure (i) generic rigidity and…

We study the spread of an SIRS-type epidemic with vaccination on network. Starting from an exact Markov description of the model, we investigate the mean epidemic lifetime by providing a sufficient condition for fast extinction that depends…