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Piet Van Mieghem

Publications and source records attributed to Piet Van Mieghem.

At least 37 records · Page 2Linked to original sources
arXiv2020

Network-based Prediction of COVID-19 Epidemic Spreading in Italy

Initially emerged in the Chinese city Wuhan and subsequently spread almost worldwide causing a pandemic, the SARS-CoV-2 virus follows reasonably well the SIR (Susceptible-Infectious-Recovered) epidemic model on contact networks in the Chinese case. In this paper, we investigate the prediction accuracy of the SIR model on networks also for Italy. Specifically, the Italian regions are a metapopulation represented by network nodes and the network links are the interactions between those regions. Then, we modify the network-based SIR model in order to take into account the different lockdown measures adopted by the Italian Government in the various phases of the spreading of the COVID-19. Our results indicate that the network-based model better predicts the daily cumulative infected individuals when time-varying lockdown protocols are incorporated in the classical SIR model.

physics.soc-ph↗
arXiv2020

Mobile smartphone tracing can detect almost all SARS-CoV-2 infections

Currently, many countries are considering the introduction of tracing software on mobile smartphones with the main purpose to inform and alarm the mobile app user. Here, we demonstrate that, in addition to alarming and informing, mobile tracing can detect nearly all users that are infected by SARS-CoV-2. Our algorithm BETIS (Bayesian Estimation for Tracing Infection States) makes use of self-reports of the user's health status. Then, BETIS guarantees that almost all SARS-CoV-2 infections of the group of users can be detected. Furthermore, BETIS estimates the virus prevalence in the whole population, consisting of users and non-users. BETIS is based on a hidden Markov epidemic model and recursive Bayesian filtering. The potential that mobile tracing apps, in addition to medical testing and quarantining, can eradicate COVID-19 may persuade citizens to trade-off privacy against public health.

cs.SI↗
arXiv2020

Predicting Dynamics on Networks Hardly Depends on the Topology

Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an unknown network, based on past observations of the dynamics. For a general class of governing equations, we propose a prediction algorithm which infers the network as an intermediate step. Inferring the network is impossible in practice, due to a dramatically ill-conditioned linear system. Surprisingly, a highly accurate prediction of the dynamics is possible nonetheless: Even though the inferred network has no topological similarity with the true network, both networks result in practically the same future dynamics.

physics.soc-ph↗
arXiv2020

Network-Based Prediction of the 2019-nCoV Epidemic Outbreak in the Chinese Province Hubei

At the moment of writing (12 February, 2020), the future evolution of the 2019-nCoV virus is unclear. Predictions of the further course of the epidemic are decisive to deploy targeted disease control measures. We consider a network-based model to describe the 2019-nCoV epidemic in the Hubei province. The network is composed of the cities in Hubei and their interactions (e.g., traffic flow). However, the precise interactions between cities is unknown and must be inferred from observing the epidemic. We propose a network-based method to predict the future prevalence of the 2019-nCoV virus in every city. Our results indicate that network-based modelling is beneficial for an accurate forecast of the epidemic outbreak.

physics.soc-ph↗
arXiv2019

Constructing Laplacian matrices with Soules vectors: inverse eigenvalue problem and applications

The symmetric nonnegative inverse eigenvalue problem (SNIEP) asks which sets of numbers (counting multiplicities) can be the eigenvalues of a symmetric matrix with nonnegative entries. While examples of such matrices are abundant in linear algebra and various applications, this question is still open for matrices of dimension $N\geq 5$. One of the approaches to solve the SNIEP was proposed by George W. Soules, relying on a specific type of eigenvectors (Soules vectors) to derive sufficient conditions for this problem. Elsner et al. later showed a canonical way to construct all Soules vectors, based on binary rooted trees. While Soules vectors are typically treated as a totally ordered set of vectors, we propose in this article to consider a relaxed alternative: a partially ordered set of Soules vectors. We show that this perspective enables a more complete characterization of the sufficient conditions for the SNIEP. In particular, we show that the set of eigenvalues that satisfy these sufficient conditions is a convex cone, with symmetries corresponding to the automorphisms of the binary rooted tree from which the Soules vectors were constructed. As a second application, we show how Soules vectors can be used to construct graph Laplacian matrices with a given spectrum and describe a number of interesting connections with the concepts of hierarchical random graphs, equitable partitions and effective resistance.

physics.soc-ph↗
arXiv2019

Local electrodynamics of a disordered conductor model system measured with a microwave impedance microscope

We study the electrodynamic impedance of percolating conductors with a pre-defined network topology using a scanning microwave impedance microscope (sMIM) at GHz frequencies. For a given percolation number we observe strong spatial variations across a sample which correlate with the connected regions (clusters) in the network when the resistivity is low such as in Aluminum. For the more resistive material NbTiN the impedance becomes dominated by the local structure of the percolating network (connectivity). The results can qualitatively be understood and reproduced with a network current spreading model based on the pseudo-inverse Laplacian of the underlying network graph.

cond-mat.mtrl-sci↗
arXiv2019

Pulse strategy for suppressing spreading on networks

In networked spreading models, each node can infect its neighbors and cure spontaneously. The curing is assumed to occur uniformly over time. A pulse immunization/curing strategy is more efficient and broadly applied to suppressing spreading processes. We model the epidemic process by the basic Susceptible-Infected (SI) process with a pulse curing and incorporate the underlying contact network. The mean-field epidemic threshold of the pulse SI model is shown to be $\frac{1}{λ_1}\ln\frac{1}{1-p}$, where $λ_1$ and $p$ are the largest eigenvalue of the adjacency matrix and the fraction of nodes covered by each curing, respectively. Compared to the extensively studied uniform curing process, we show that the pulse curing strategy saves about $36.8$\%, i.e. $p\approx 0.632$, of the number of curing operations invariant to the network structure. Our results may help related policy makers to estimate the cost of controlling spreading processes.

physics.soc-ph↗
arXiv2019

The Viral State Dynamics of the Discrete-Time NIMFA Epidemic Model

The majority of research on epidemics relies on models which are formulated in continuous-time. However, real-world epidemic data is gathered and processed in a digital manner, which is more accurately described by discrete-time epidemic models. We analyse the discrete-time NIMFA epidemic model on directed networks with heterogeneous spreading parameters. In particular, we show that the viral state is increasing and does not overshoot the steady-state, the steady-state is globally exponentially stable, and we provide linear systems that bound the viral state evolution. Thus, the discrete-time NIMFA model succeeds to capture the qualitative behaviour of a viral spread and provides a powerful means to study real-world epidemics.

math.OC↗
arXiv2019

The Simplex Geometry of Graphs

Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a unique way. Here, we discuss a novel approach to study graphs: the simplex geometry (a simplex is a generalized triangle). This perspective, proposed by Miroslav Fiedler, introduces techniques from (simplex) geometry into the field of graph theory and conversely, via an exact correspondence. We introduce this graph-simplex correspondence, identify a number of basic connections between graph characteristics and simplex properties, and suggest some applications as example.

cs.DM↗
arXiv2018

Network localization is unalterable by infections in bursts

To shed light on the disease localization phenomenon, we study a bursty susceptible-infected-susceptible (SIS) model and analyze the model under the mean-field approximation. In the bursty SIS model, the infected nodes infect all their neighbors periodically, and the near-threshold steady-state prevalence is non-constant and maximized by a factor equal to the largest eigenvalue $λ_1$ of the adjacency matrix of the network. We show that the maximum near-threshold prevalence of the bursty SIS process on a localized network tends to zero even if $λ_1$ diverges in the thermodynamic limit, which indicates that the burst of infection cannot turn a localized spreading into a delocalized spreading. Our result is evaluated both on synthetic and real networks.

physics.soc-ph↗
arXiv2018

Network Reconstruction and Prediction of Epidemic Outbreaks for NIMFA Processes

Predicting the viral dynamics of an epidemic process requires the knowledge of the underlying contact network. However, the network is not known for most applications and has to be inferred from observing the viral state evolution instead. We propose a polynomial-time network reconstruction algorithm for the discrete-time NIMFA model based on a basis pursuit formulation. Given only few initial viral state observations, the network reconstruction method allows for an accurate prediction of the further viral state evolution of every node provided that the network is sufficiently sparse.

physics.soc-ph↗
arXiv2018

Structural transition in interdependent networks with regular interconnections

Networks are often made up of several layers that exhibit diverse degrees of interdependencies. A multilayer interdependent network consists of a set of graphs $G$ that are interconnected through a weighted interconnection matrix $ B $, where the weight of each inter-graph link is a non-negative real number $ p $. Various dynamical processes, such as synchronization, cascading failures in power grids, and diffusion processes, are described by the Laplacian matrix $ Q $ characterizing the whole system. For the case in which the multilayer graph is a multiplex, where the number of nodes in each layer is the same and the interconnection matrix $ B=pI $, being $ I $ the identity matrix, it has been shown that there exists a structural transition at some critical coupling, $ p^* $. This transition is such that dynamical processes are separated into two regimes: if $ p > p^* $, the network acts as a whole; whereas when $ p<p^* $, the network operates as if the graphs encoding the layers were isolated. In this paper, we extend and generalize the structural transition threshold $ p^* $ to a regular interconnection matrix $ B $ (constant row and column sum). Specifically, we provide upper and lower bounds for the transition threshold $ p^* $ in interdependent networks with a regular interconnection matrix $ B $ and derive the exact transition threshold for special scenarios using the formalism of quotient graphs. Additionally, we discuss the physical meaning of the transition threshold $ p^* $ in terms of the minimum cut and show, through a counter-example, that the structural transition does not always exist. Our results are one step forward on the characterization of more realistic multilayer networks and might be relevant for systems that deviate from the topological constrains imposed by multiplex networks.

physics.soc-ph↗
arXiv2018

Maximum-Likelihood Network Reconstruction for SIS Processes is NP-Hard

The knowledge of the network topology is imperative to precisely describing the viral dynamics of an SIS epidemic process. In scenarios for which the network topology is unknown, one resorts to reconstructing the network from observing the viral state trace. This work focusses on the impact of the viral state observations on the computational complexity of the resulting network reconstruction problem. We propose a novel method of constructing a specific class of viral state traces from which the inference of the presence or absence of links is either easy or difficult. In particular, we use this construction to prove that the maximum-likelihood SIS network reconstruction is NP-hard. The NP-hardness holds for any adjacency matrix of a graph which is connected.

cs.CC↗
arXiv2017

Optimal curing policy for epidemic spreading over a community network with heterogeneous population

The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.

math.OC↗
arXiv2017

Designing virus-resistant, high-performance networks: a game-formation approach

Designing an optimal network topology while balancing multiple, possibly conflicting objectives like cost, performance, and resiliency to viruses is a challenging endeavor, let alone in the case of decentralized network formation. We therefore propose a game-formation technique where each player aims to minimize its cost in installing links, the probability of being infected by a virus and the sum of hopcounts on its shortest paths to all other nodes. In this article, we (1) determine the Nash Equilibria and the Price of Anarchy for our novel network formation game, (2) demonstrate that the Price of Anarchy (PoA) is usually low, which suggests that (near-)optimal topologies can be formed in a decentralized way, and (3) give suggestions for practitioners for those cases where the PoA is high and some centralized control/incentives are advisable.

cs.GT↗
arXiv2017

Universal mean-field framework for SIS epidemics on networks, based on graph partitioning and the isoperimetric inequality

We propose a new approximation framework that unifies and generalizes a number of existing mean-field approximation methods for the SIS epidemic model on complex networks. We derive the framework, which we call the Universal Mean-Field Framework (UMFF), as a set of approximations of the exact Markovian SIS equations. Our main novelty is that we describe the mean-field approximations from the perspective of the isoperimetric problem, an insight which results in bounds on the UMFF approximation error. These new bounds provide insight in the accuracy of existing mean-field methods, such as the widely-used N-Intertwined Mean-Field Approximation (NIMFA) and Heterogeneous Mean-Field method (HMF). Additionally, the geometric perspective of the isoperimetric problem enables the UMFF approximation accuracy to be related to the regularity notions of Szemerédi's regularity lemma, which yields a prediction about the behavior of the SIS process on large graphs.

physics.soc-ph↗
arXiv2016

Universality of the SIS prevalence in networks

Epidemic models are increasingly used in real-world networks to understand diffusion phenomena (such as the spread of diseases, emotions, innovations, failures) or the transport of information (such as news, memes in social on-line networks). A new analysis of the prevalence, the expected number of infected nodes in a network, is presented and physically interpreted. The analysis method is based on spectral decomposition and leads to a universal, analytic curve, that can bound the time-varying prevalence in any finite time interval. Moreover, that universal curve also applies to various types of Susceptible-Infected-Susceptible (SIS) (and Susceptible-Infected-Removed (SIR)) infection processes, with both homogenous and heterogeneous infection characteristics (curing and infection rates), in temporal and even disconnected graphs and in SIS processes with and without self-infections. The accuracy of the universal curve is comparable to that of well-established mean-field approximations.

physics.soc-ph↗