4,790 research outputs found
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
Towards real-world complexity: an introduction to multiplex networks
Many real-world complex systems are best modeled by multiplex networks of
interacting network layers. The multiplex network study is one of the newest
and hottest themes in the statistical physics of complex networks. Pioneering
studies have proven that the multiplexity has broad impact on the system's
structure and function. In this Colloquium paper, we present an organized
review of the growing body of current literature on multiplex networks by
categorizing existing studies broadly according to the type of layer coupling
in the problem. Major recent advances in the field are surveyed and some
outstanding open challenges and future perspectives will be proposed.Comment: 20 pages, 10 figure
Separating intrinsic interactions from extrinsic correlations in a network of sensory neurons
Correlations in sensory neural networks have both extrinsic and intrinsic
origins. Extrinsic or stimulus correlations arise from shared inputs to the
network, and thus depend strongly on the stimulus ensemble. Intrinsic or noise
correlations reflect biophysical mechanisms of interactions between neurons,
which are expected to be robust to changes of the stimulus ensemble. Despite
the importance of this distinction for understanding how sensory networks
encode information collectively, no method exists to reliably separate
intrinsic interactions from extrinsic correlations in neural activity data,
limiting our ability to build predictive models of the network response. In
this paper we introduce a general strategy to infer {population models of
interacting neurons that collectively encode stimulus information}. The key to
disentangling intrinsic from extrinsic correlations is to infer the {couplings
between neurons} separately from the encoding model, and to combine the two
using corrections calculated in a mean-field approximation. We demonstrate the
effectiveness of this approach on retinal recordings. The same coupling network
is inferred from responses to radically different stimulus ensembles, showing
that these couplings indeed reflect stimulus-independent interactions between
neurons. The inferred model predicts accurately the collective response of
retinal ganglion cell populations as a function of the stimulus
Coupling and robustness of intra-cortical vascular territories
Vascular domains have been described as being coupled to neuronal functional units enabling dynamic blood supply to the cerebral cyto-architecture. Recent experiments have shown that penetrating arterioles of the grey matter are the building blocks for such units. Nevertheless, vascular territories are still poorly known, as the collection and analysis of large three-dimensional micro-vascular networks are difficult. By using an exhaustive reconstruction of the micro-vascular network in an 18 mm 3 volume of marmoset cerebral cortex, we numerically computed the blood flow in each blood vessel. We thus defined arterial and venular territories and examined their overlap. A large part of the intracortical vascular network was found to be supplied by several arteries and drained by several venules. We quantified this multiple potential to compensate for deficiencies by introducing a new robustness parameter. Robustness proved to be positively correlated with cortical depth and a systematic investigation of coupling maps indicated local patterns of overlap between neighbouring arteries and neighbouring venules. However, arterio-venular coupling did not have a spatial pattern of overlap but showed locally preferential functional coupling, especially of one artery with two venules, supporting the notion of vascular units. We concluded that intra-cortical perfusion in the primate was characterised by both very narrow functional beds and a large capacity for compensatory redistribution, far beyond the nearest neighbour collaterals
Optimal noise-canceling networks
Natural and artificial networks, from the cerebral cortex to large-scale
power grids, face the challenge of converting noisy inputs into robust signals.
The input fluctuations often exhibit complex yet statistically reproducible
correlations that reflect underlying internal or environmental processes such
as synaptic noise or atmospheric turbulence. This raises the practically and
biophysically relevant of question whether and how noise-filtering can be
hard-wired directly into a network's architecture. By considering generic phase
oscillator arrays under cost constraints, we explore here analytically and
numerically the design, efficiency and topology of noise-canceling networks.
Specifically, we find that when the input fluctuations become more correlated
in space or time, optimal network architectures become sparser and more
hierarchically organized, resembling the vasculature in plants or animals. More
broadly, our results provide concrete guiding principles for designing more
robust and efficient power grids and sensor networks.Comment: 6 pages, 3 figures, supplementary materia
Global Robustness vs. Local Vulnerabilities in Complex Synchronous Networks
In complex network-coupled dynamical systems, two questions of central
importance are how to identify the most vulnerable components and how to devise
a network making the overall system more robust to external perturbations. To
address these two questions, we investigate the response of complex networks of
coupled oscillators to local perturbations. We quantify the magnitude of the
resulting excursion away from the unperturbed synchronous state through
quadratic performance measures in the angle or frequency deviations. We find
that the most fragile oscillators in a given network are identified by
centralities constructed from network resistance distances. Further defining
the global robustness of the system from the average response over ensembles of
homogeneously distributed perturbations, we find that it is given by a family
of topological indices known as generalized Kirchhoff indices. Both resistance
centralities and Kirchhoff indices are obtained from a spectral decomposition
of the stability matrix of the unperturbed dynamics and can be expressed in
terms of resistance distances. We investigate the properties of these
topological indices in small-world and regular networks. In the case of
oscillators with homogeneous inertia and damping coefficients, we find that
inertia only has small effects on robustness of coupled oscillators. Numerical
results illustrate the validity of the theory.Comment: 11 pages, 9 figure
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