PV
P.F.A. Van Mieghem
286 records found
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Two approximations for network reliability polynomials, only based upon the knowledge of the degree vector of the graph, are compared: the first-order approximation by Brown et al. and our stochastic approximation. Our method is an extension of the connectivity probability of Erd
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Continuous-time Markov processes are governed by the Chapman-Kolmogorov differential equation. We show that replacing the standard time derivative of the governing equation with a Caputo fractional derivative of order 0<α<1, leads to a fractional differential equation whose
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We study human mobility networks through timeseries of contacts between individuals. Our proposed Random Walkers Induced temporal Graph (RWIG) model generates temporal graph sequences based on independent random walkers that traverse an underlying graph in discrete time steps. Co
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We derive an expression for the exact probability Pr[i∼j] of a link between a node i with degree di and a node j with degree dj in a graph belonging to the class of Erdos-Rényi G(N,L) random graphs with N nodes and L links. The probability Pr[i∼j] is commonly approximated as didj
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We examine the Random Walkers Induced temporal Graph (RWIG) model, which generates temporal graphs based on the co-location principle of M independent walkers that traverse the underlying Markov graph with different transition probabilities. Given the assumption that each random
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Transition from time-variant to static networks
Timescale separation in N -intertwined mean-field approximation of susceptible-infectious-susceptible epidemics
We extend the N-intertwined mean-field approximation (NIMFA) for the susceptible-infectious-susceptible (SIS) epidemiological process to time-varying networks. Processes on time-varying networks are often analyzed under the assumption that the process and network evolution happen
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Finding the source of an epidemic is important, because correct source identification can help to stop a budding epidemic or prevent new ones. We investigate the backward equations of the N-intertwined mean-field approximation susceptible-infectious-susceptible (SIS) process. The
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Although eigenvectors belong to the core of linear algebra, relatively few closed-form expressions exist, which we bundle and discuss here. A particular goal is their interpretation for graph-related matrices, such as the adjacency matrix of an undirected, possibly weighted graph
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Federated learning is an effective method to train a machine learning model without requiring to aggregate the potentially sensitive data of agents in a central server. However, the limited communication bandwidth, the hardware of the agents and a potential application-specific l
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Epidemic forecasts are only as good as the accuracy of epidemic measurements. Is epidemic data, particularly COVID-19 epidemic data, clean, and devoid of noise? The complexity and variability inherent in data collection and reporting suggest otherwise. While we cannot evaluate th
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Except for the empty graph, we show that the orthogonal matrix X of the adjacency matrix A determines that adjacency matrix completely, but not always uniquely. The proof relies on interesting properties of the Hadamard product Ξ = X ◦ X. As a consequence of the theory, we show t
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Individualized epidemic spreading models predict epilepsy surgery outcomes
A pseudo-prospective study
Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but up to 50% of patients continue to have seizures one year after the resection. In order to aid presurgical planning and predict postsurgical outcome on a patient-by-patient basis, we developed a
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Although resource management schemes and algorithms for networks are well established, we present two novel ideas, based on graph theory, that solve inverse all shortest path problem. Given a symmetric and non-negative demand matrix, the inverse all shortest path problem (IASPP)
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Predicting future dynamics on networks is challenging, especially when the complete and accurate network topology is difficult to obtain in real-world scenarios. Moreover, the higher-order interactions among nodes, which have been found in a wide range of systems in recent years,
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We propose a linear clustering process on a network consisting of two opposite forces: attraction and repulsion between adjacent nodes. Each node is mapped to a position on a one-dimensional line. The attraction and repulsion forces move the nodal position on the line, depending
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Modelling temporal networks is an open problem that has attracted researchers from a diverse range of fields. Currently, the existing modelling solutions of time-evolving graphs do not allow us to provide an accurate graph sequence. In this paper, we examine the network dynamics
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Interpreting natural language is an increasingly important task in computer algorithms due to the growing availability of unstructured textual data. Natural Language Processing (NLP) applications rely on semantic networks for structured knowledge representation. The fundamental p
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For this study, we investigated efficient strategies for the recovery of individual links in power grids governed by the direct current (DC) power flow model, under random link failures. Our primary objective was to explore the efficacy of recovering failed links based solely on
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Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but only leads to seizure freedom for roughly two in three patients. To address this problem, we designed a patient-specific epilepsy surgery model combining large-scale magnetoencephalography (MEG)
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In this paper, we focus on the link density in random geometric graphs (RGGs) with a distance-based connection function. After deriving the link density in D dimensions, we focus on the two-dimensional (2D) and three-dimensional (3D) space and show that the link density is accura
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