140 research outputs found
Bursts of vertex activation and epidemics in evolving networks
The dynamic nature of contact patterns creates diverse temporal structures. In particular, empirical studies have shown that contact patterns follow heterogeneous inter-event time intervals, meaning that periods of high activity are followed by long periods of inactivity. To investigate the impact of these heterogeneities in the spread of infection from a theoretical perspective, we propose a stochastic model to generate temporal networks where vertices make instantaneous contacts following heterogeneous inter-event intervals, and may leave and enter the system. We study how these properties affect the prevalence of an infection and estimate , the number of secondary infections of an infectious individual in a completely susceptible population, by modeling simulated infections (SI and SIR) that co-evolve with the network structure. We find that heterogeneous contact patterns cause earlier and larger epidemics in the SIR model in comparison to homogeneous scenarios for a vast range of parameter values, while smaller epidemics may happen in some combinations of parameters. In the case of SI and heterogeneous patterns, the epidemics develop faster in the earlier stages followed by a slowdown in the asymptotic limit. For increasing vertex turnover rates, heterogeneous patterns generally cause higher prevalence in comparison to homogeneous scenarios with the same average inter-event interval. We find that is generally higher for heterogeneous patterns, except for sufficiently large infection duration and transmission probability
Principal Patterns on Graphs: Discovering Coherent Structures in Datasets
Graphs are now ubiquitous in almost every field of research. Recently, new
research areas devoted to the analysis of graphs and data associated to their
vertices have emerged. Focusing on dynamical processes, we propose a fast,
robust and scalable framework for retrieving and analyzing recurring patterns
of activity on graphs. Our method relies on a novel type of multilayer graph
that encodes the spreading or propagation of events between successive time
steps. We demonstrate the versatility of our method by applying it on three
different real-world examples. Firstly, we study how rumor spreads on a social
network. Secondly, we reveal congestion patterns of pedestrians in a train
station. Finally, we show how patterns of audio playlists can be used in a
recommender system. In each example, relevant information previously hidden in
the data is extracted in a very efficient manner, emphasizing the scalability
of our method. With a parallel implementation scaling linearly with the size of
the dataset, our framework easily handles millions of nodes on a single
commodity server
Epidemic Threshold in Continuous-Time Evolving Networks
Current understanding of the critical outbreak condition on temporal networks
relies on approximations (time scale separation, discretization) that may bias
the results. We propose a theoretical framework to compute the epidemic
threshold in continuous time through the infection propagator approach. We
introduce the {\em weak commutation} condition allowing the interpretation of
annealed networks, activity-driven networks, and time scale separation into one
formalism. Our work provides a coherent connection between discrete and
continuous time representations applicable to realistic scenarios.Comment: 13 pages, 2 figure
Temporal Networks
A great variety of systems in nature, society and technology -- from the web
of sexual contacts to the Internet, from the nervous system to power grids --
can be modeled as graphs of vertices coupled by edges. The network structure,
describing how the graph is wired, helps us understand, predict and optimize
the behavior of dynamical systems. In many cases, however, the edges are not
continuously active. As an example, in networks of communication via email,
text messages, or phone calls, edges represent sequences of instantaneous or
practically instantaneous contacts. In some cases, edges are active for
non-negligible periods of time: e.g., the proximity patterns of inpatients at
hospitals can be represented by a graph where an edge between two individuals
is on throughout the time they are at the same ward. Like network topology, the
temporal structure of edge activations can affect dynamics of systems
interacting through the network, from disease contagion on the network of
patients to information diffusion over an e-mail network. In this review, we
present the emergent field of temporal networks, and discuss methods for
analyzing topological and temporal structure and models for elucidating their
relation to the behavior of dynamical systems. In the light of traditional
network theory, one can see this framework as moving the information of when
things happen from the dynamical system on the network, to the network itself.
Since fundamental properties, such as the transitivity of edges, do not
necessarily hold in temporal networks, many of these methods need to be quite
different from those for static networks
Analytical computation of the epidemic threshold on temporal networks
The time variation of contacts in a networked system may fundamentally alter
the properties of spreading processes and affect the condition for large-scale
propagation, as encoded in the epidemic threshold. Despite the great interest
in the problem for the physics, applied mathematics, computer science and
epidemiology communities, a full theoretical understanding is still missing and
currently limited to the cases where the time-scale separation holds between
spreading and network dynamics or to specific temporal network models. We
consider a Markov chain description of the Susceptible-Infectious-Susceptible
process on an arbitrary temporal network. By adopting a multilayer perspective,
we develop a general analytical derivation of the epidemic threshold in terms
of the spectral radius of a matrix that encodes both network structure and
disease dynamics. The accuracy of the approach is confirmed on a set of
temporal models and empirical networks and against numerical results. In
addition, we explore how the threshold changes when varying the overall time of
observation of the temporal network, so as to provide insights on the optimal
time window for data collection of empirical temporal networked systems. Our
framework is both of fundamental and practical interest, as it offers novel
understanding of the interplay between temporal networks and spreading
dynamics.Comment: 22 pages, 6 figure
Bursting activity spreading through asymmetric interactions
People communicate with those who have the same background or share a common
interest by using a social networking service (SNS). News or messages propagate
through inhomogeneous connections in an SNS by sharing or facilitating
additional comments. Such human activity is known to lead to endogenous
bursting in the rate of message occurrences. We analyze a multi-dimensional
self-exciting process to reveal dependence of the bursting activity on the
topology of connections and the distribution of interaction strength on the
connections. We determine the critical conditions for the cases where
interaction strength is regulated at either the point of input or output for
each person. In the input regulation condition, the network may exhibit
bursting with infinitesimal interaction strength, if the dispersion of the
degrees diverges as in the scale-free networks. In contrast, in the output
regulation condition, the critical value of interaction strength, represented
by the average number of events added by a single event, is a constant
, independent of the degree dispersion. Thus, the
stability in human activity crucially depends on not only the topology of
connections but also the manner in which interactions are distributed among the
connections.Comment: 8 pages, 8 figure
Burstiness in activity-driven networks and the epidemic threshold
We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible model on activity-driven networks with burstiness. By using an activity-based mean-field approach, we derive a closed analytical form for the epidemic threshold for arbitrary activity and inter-event time distributions. We show that, as expected, burstiness lowers the epidemic threshold while its effect on prevalence is twofold. In low-infective systems burstiness raises the average infection probability, while it weakens epidemic spreading for high infectivity. Our results can help clarify the conflicting effects of burstiness reported in the literature. We also discuss the scaling properties at the transition, showing that they are not affected by burstiness.INFN BIOPHYS project, Spanish Ministry of Science as well as the Agencia Espanola de Investigacion (AEI) for financial support under grant FIS2017-84256-P (FEDER funds)
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