116 research outputs found
Insights from exact social contagion dynamics on networks with higher-order structures
Recently there has been an increasing interest in studying dynamical
processes on networks exhibiting higher-order structures, such as simplicial
complexes, where the dynamics acts above and beyond dyadic interactions. Using
simulations or heuristically derived epidemic spreading models it was shown
that new phenomena can emerge, such as bi-stability/multistability. Here, we
show that such new emerging phenomena do not require complex contact patterns,
such as community structures, but naturally result from the higher-order
contagion mechanisms. We show this by deriving an exact higher-order SIS model
and its limiting mean-field equivalent for fully connected simplicial
complexes. Going beyond previous results, we also give the global bifurcation
picture for networks with 3- and 4-body interactions, with the latter allowing
for two non-trivial stable endemic steady states. Differently from previous
approaches, we are able to study systems featuring interactions of arbitrary
order. In addition, we characterise the contributions from higher-order
infections to the endemic equilibrium as perturbations of the pairwise
baseline, finding that these diminish as the pairwise rate of infection
increases. Our approach represents a first step towards a principled
understanding of higher-order contagion processes beyond triads and opens up
further directions for analytical investigations.Comment: 19 pages, 14 figure
Rapid convergence of time-averaged frequency in phase synchronized systems
Numerical and experimental evidence is presented to show that many phase
synchronized systems of non-identical chaotic oscillators, where the chaotic
state is reached through a period-doubling cascade, show rapid convergence of
the time-averaged frequency. The speed of convergence toward the natural
frequency scales as the inverse of the measurement period. The results also
suggest an explanation for why such chaotic oscillators can be phase
synchronized.Comment: 6 pages, 9 figure
Synchronization and oscillator death in oscillatory media with stirring
The effect of stirring in an inhomogeneous oscillatory medium is
investigated. We show that the stirring rate can control the macroscopic
behavior of the system producing collective oscillations (synchronization) or
complete quenching of the oscillations (oscillator death). We interpret the
homogenization rate due to mixing as a measure of global coupling and compare
the phase diagrams of stirred oscillatory media and of populations of globally
coupled oscillators.Comment: to appear in Phys. Rev. Let
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Network Events in a Large Commercial Network: What can we learn?
ISP and commercial networks are complex and thus difficult to characterise and manage. Network operators rely on a continuous flow of event log messages to identify and handle service outages. However, there is little published information about such events and how they are typically exploited. In this paper, we describe in as much detail as possible the event logs and network topology of a major commercial network. Through analysing the network topology, textual information of events and time of events, we highlight opportunities and challenges brought by such data. In particular, we suggest that the development of methods for inferring functional connectivity could unlock more of the informational value of event log messages and assist network management operators
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Functional topology inference from network events
In this paper we present a novel approach for inferring functional connectivity within a large-scale network from time series of emitted node events. We do so under the following constraints: (a) non-stationarity of the underlying connectivity, (b) sparsity of the time-series of events, and (c) absence of an explicit model describing how events propagate through the network. We develop an inference method whose output is an undirected weighted network, where the weight of an edge between two nodes denotes the probability of these nodes being functionally connected. Two nodes are assumed to be functionally connected if they show significantly more coincident or short-lagged events than randomly picked pairs of nodes with similar levels of activity. We develop a model of time-varying connectivity whose parameters are determined by maximising the model’s predictive power from one time window to the next. We assess the accuracy, efficiency and scalability of our method on a real dataset of network events spanning multiple months
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