4,191 research outputs found
Smeared phase transitions in percolation on real complex networks
Percolation on complex networks is used both as a model for dynamics on
networks, such as network robustness or epidemic spreading, and as a benchmark
for our models of networks, where our ability to predict percolation measures
our ability to describe the networks themselves. In many applications,
correctly identifying the phase transition of percolation on real-world
networks is of critical importance. Unfortunately, this phase transition is
obfuscated by the finite size of real systems, making it hard to distinguish
finite size effects from the inaccuracy of a given approach that fails to
capture important structural features. Here, we borrow the perspective of
smeared phase transitions and argue that many observed discrepancies are due to
the complex structure of real networks rather than to finite size effects only.
In fact, several real networks often used as benchmarks feature a smeared phase
transition where inhomogeneities in the topological distribution of the order
parameter do not vanish in the thermodynamic limit. We find that these smeared
transitions are sometimes better described as sequential phase transitions
within correlated subsystems. Our results shed light not only on the nature of
the percolation transition in complex systems, but also provide two important
insights on the numerical and analytical tools we use to study them. First, we
propose a measure of local susceptibility to better detect both clean and
smeared phase transitions by looking at the topological variability of the
order parameter. Second, we highlight a shortcoming in state-of-the-art
analytical approaches such as message passing, which can detect smeared
transitions but not characterize their nature.Comment: 10 pages, 8 figure
Entrograms and coarse graining of dynamics on complex networks
Using an information theoretic point of view, we investigate how a dynamics
acting on a network can be coarse grained through the use of graph partitions.
Specifically, we are interested in how aggregating the state space of a Markov
process according to a partition impacts on the thus obtained lower-dimensional
dynamics. We highlight that for a dynamics on a particular graph there may be
multiple coarse grained descriptions that capture different, incomparable
features of the original process. For instance, a coarse graining induced by
one partition may be commensurate with a time-scale separation in the dynamics,
while another coarse graining may correspond to a different lower-dimensional
dynamics that preserves the Markov property of the original process. Taking
inspiration from the literature of Computational Mechanics, we find that a
convenient tool to summarise and visualise such dynamical properties of a
coarse grained model (partition) is the entrogram. The entrogram gathers
certain information-theoretic measures, which quantify how information flows
across time steps. These information theoretic quantities include the entropy
rate, as well as a measure for the memory contained in the process, i.e., how
well the dynamics can be approximated by a first order Markov process. We use
the entrogram to investigate how specific macro-scale connection patterns in
the state-space transition graph of the original dynamics result in desirable
properties of coarse grained descriptions. We thereby provide a fresh
perspective on the interplay between structure and dynamics in networks, and
the process of partitioning from an information theoretic perspective. We focus
on networks that may be approximated by both a core-periphery or a clustered
organization, and highlight that each of these coarse grained descriptions can
capture different aspects of a Markov process acting on the network.Comment: 17 pages, 6 figue
Predicting Scientific Success Based on Coauthorship Networks
We address the question to what extent the success of scientific articles is
due to social influence. Analyzing a data set of over 100000 publications from
the field of Computer Science, we study how centrality in the coauthorship
network differs between authors who have highly cited papers and those who do
not. We further show that a machine learning classifier, based only on
coauthorship network centrality measures at time of publication, is able to
predict with high precision whether an article will be highly cited five years
after publication. By this we provide quantitative insight into the social
dimension of scientific publishing - challenging the perception of citations as
an objective, socially unbiased measure of scientific success.Comment: 21 pages, 2 figures, incl. Supplementary Materia
Network-based brain computer interfaces: principles and applications
Brain-computer interfaces (BCIs) make possible to interact with the external
environment by decoding the mental intention of individuals. BCIs can therefore
be used to address basic neuroscience questions but also to unlock a variety of
applications from exoskeleton control to neurofeedback (NFB) rehabilitation. In
general, BCI usability critically depends on the ability to comprehensively
characterize brain functioning and correctly identify the user s mental state.
To this end, much of the efforts have focused on improving the classification
algorithms taking into account localized brain activities as input features.
Despite considerable improvement BCI performance is still unstable and, as a
matter of fact, current features represent oversimplified descriptors of brain
functioning. In the last decade, growing evidence has shown that the brain
works as a networked system composed of multiple specialized and spatially
distributed areas that dynamically integrate information. While more complex,
looking at how remote brain regions functionally interact represents a grounded
alternative to better describe brain functioning. Thanks to recent advances in
network science, i.e. a modern field that draws on graph theory, statistical
mechanics, data mining and inferential modelling, scientists have now powerful
means to characterize complex brain networks derived from neuroimaging data.
Notably, summary features can be extracted from these networks to
quantitatively measure specific organizational properties across a variety of
topological scales. In this topical review, we aim to provide the
state-of-the-art supporting the development of a network theoretic approach as
a promising tool for understanding BCIs and improve usability
A sampling-guided unsupervised learning method to capture percolation in complex networks
The use of machine learning techniques in classical and quantum systems has
led to novel techniques to classify ordered and disordered phases, as well as
uncover transition points in critical phenomena. Efforts to extend these
methods to dynamical processes in complex networks is a field of active
research. Network-percolation, a measure of resilience and robustness to
structural failures, as well as a proxy for spreading processes, has numerous
applications in social, technological, and infrastructural systems. A
particular challenge is to identify the existence of a percolation cluster in a
network in the face of noisy data. Here, we consider bond-percolation, and
introduce a sampling approach that leverages the core-periphery structure of
such networks at a microscopic scale, using onion decomposition, a refined
version of the core. By selecting subsets of nodes in a particular layer of
the onion spectrum that follow similar trajectories in the percolation process,
percolating phases can be distinguished from non-percolating ones through an
unsupervised clustering method. Accuracy in the initial step is essential for
extracting samples with information-rich content, that are subsequently used to
predict the critical transition point through the confusion scheme, a recently
introduced learning method. The method circumvents the difficulty of missing
data or noisy measurements, as it allows for sampling nodes from both the core
and periphery, as well as intermediate layers. We validate the effectiveness of
our sampling strategy on a spectrum of synthetic network topologies, as well as
on two real-word case studies: the integration time of the US domestic airport
network, and the identification of the epidemic cluster of COVID-19 outbreaks
in three major US states. The method proposed here allows for identifying phase
transitions in empirical time-varying networks.Comment: 16 pages, 6 figure
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