3,075 research outputs found
Multiplexity versus correlation: the role of local constraints in real multiplexes
Several real-world systems can be represented as multi-layer complex
networks, i.e. in terms of a superposition of various graphs, each related to a
different mode of connection between nodes. Hence, the definition of proper
mathematical quantities aiming at capturing the level of complexity of those
systems is required. Various attempts have been made to measure the empirical
dependencies between the layers of a multiplex, for both binary and weighted
networks. In the simplest case, such dependencies are measured via
correlation-based metrics: we show that this is equivalent to the use of
completely homogeneous benchmarks specifying only global constraints, such as
the total number of links in each layer. However, these approaches do not take
into account the heterogeneity in the degree and strength distributions, which
are instead a fundamental feature of real-world multiplexes. In this work, we
compare the observed dependencies between layers with the expected values
obtained from reference models that appropriately control for the observed
heterogeneity in the degree and strength distributions. This leads to novel
multiplexity measures that we test on different datasets, i.e. the
International Trade Network (ITN) and the European Airport Network (EAN). Our
findings confirm that the use of homogeneous benchmarks can lead to misleading
results, and furthermore highlight the important role played by the
distribution of hubs across layers.Comment: 32 pages, 6 figure
Ground truth? Concept-based communities versus the external classification of physics manuscripts
Community detection techniques are widely used to infer hidden structures
within interconnected systems. Despite demonstrating high accuracy on
benchmarks, they reproduce the external classification for many real-world
systems with a significant level of discrepancy. A widely accepted reason
behind such outcome is the unavoidable loss of non-topological information
(such as node attributes) encountered when the original complex system is
represented as a network. In this article we emphasize that the observed
discrepancies may also be caused by a different reason: the external
classification itself. For this end we use scientific publication data which i)
exhibit a well defined modular structure and ii) hold an expert-made
classification of research articles. Having represented the articles and the
extracted scientific concepts both as a bipartite network and as its unipartite
projection, we applied modularity optimization to uncover the inner thematic
structure. The resulting clusters are shown to partly reflect the author-made
classification, although some significant discrepancies are observed. A
detailed analysis of these discrepancies shows that they carry essential
information about the system, mainly related to the use of similar techniques
and methods across different (sub)disciplines, that is otherwise omitted when
only the external classification is considered.Comment: 15 pages, 2 figure
Multiplexity and multireciprocity in directed multiplexes
Real-world multi-layer networks feature nontrivial dependencies among links
of different layers. Here we argue that, if links are directed, dependencies
are twofold. Besides the ordinary tendency of links of different layers to
align as the result of `multiplexity', there is also a tendency to anti-align
as the result of what we call `multireciprocity', i.e. the fact that links in
one layer can be reciprocated by \emph{opposite} links in a different layer.
Multireciprocity generalizes the scalar definition of single-layer reciprocity
to that of a square matrix involving all pairs of layers. We introduce
multiplexity and multireciprocity matrices for both binary and weighted
multiplexes and validate their statistical significance against maximum-entropy
null models that filter out the effects of node heterogeneity. We then perform
a detailed empirical analysis of the World Trade Multiplex (WTM), representing
the import-export relationships between world countries in different
commodities. We show that the WTM exhibits strong multiplexity and
multireciprocity, an effect which is however largely encoded into the degree or
strength sequences of individual layers. The residual effects are still
significant and allow to classify pairs of commodities according to their
tendency to be traded together in the same direction and/or in opposite ones.
We also find that the multireciprocity of the WTM is significantly lower than
the usual reciprocity measured on the aggregate network. Moreover, layers with
low (high) internal reciprocity are embedded within sets of layers with
comparably low (high) mutual multireciprocity. This suggests that, in the WTM,
reciprocity is inherent to groups of related commodities rather than to
individual commodities. We discuss the implications for international trade
research focusing on product taxonomies, the product space, and
fitness/complexity metrics.Comment: 20 pages, 8 figure
Reconstruction of multiplex networks with correlated layers
The characterization of various properties of real-world systems requires the knowledge of the underlying network of connections among the system's components. Unfortunately, in many situations the complete topology of this network is empirically inaccessible, and one has to resort to probabilistic techniques to infer it from limited information. While network reconstruction methods have reached some degree of maturity in the case of single-layer networks (where nodes can be connected only by one type of links), the problem is practically unexplored in the case of multiplex networks, where several interdependent layers, each with a different type of links, coexist. Even the most advanced network reconstruction techniques, if applied to each layer separately, fail in replicating the observed inter-layer dependencies making up the whole coupled multiplex. Here we develop a methodology to reconstruct a class of correlated multiplexes which includes the World Trade Multiplex as a specific example we study in detail. Our method starts from any reconstruction model that successfully reproduces some desired marginal properties, including node strengths and/or node degrees, of each layer separately. It then introduces the minimal dependency structure required to replicate an additional set of higher-order properties that quantify the portion of each node's degree and each node's strength that is shared and/or reciprocated across pairs of layers. These properties are found to provide empirically robust measures of inter-layer coupling. Our method allows joint multi-layer connection probabilities to be reliably reconstructed from marginal ones, effectively bridging the gap between single-layer properties and truly multiplex information
Irreducible network backbones: unbiased graph filtering via maximum entropy
Networks provide an informative, yet non-redundant description of complex systems only if links represent truly dyadic relationships that cannot be directly traced back to node-specific properties such as size, importance, or coordinates in some embedding space. In any real-world network, some links may be reducible, and others irreducible, to such local properties. This dichotomy persists despite the steady increase in data availability and resolution, which actually determines an even stronger need for filtering techniques aimed at discerning essential links from non-essential ones. Here we introduce a rigorous method that, for any desired level of statistical significance, outputs the network backbone that is irreducible to the local properties of nodes, i.e. their degrees and strengths. Unlike previous approaches, our method employs an exact maximum-entropy formulation guaranteeing that the filtered network encodes only the links that cannot be inferred from local information. Extensive empirical analysis confirms that this approach uncovers essential backbones that are otherwise hidden amidst many redundant relationships and inaccessible to other methods. For instance, we retrieve the hub-and-spoke skeleton of the US airport network and many specialised patterns of international trade. Being irreducible to local transportation and economic constraints of supply and demand, these backbones single out genuinely higher-order wiring principles
Local phase transitions in a model of multiplex networks with heterogeneous degrees and inter-layer coupling
Multilayer networks represent multiple types of connections between the same
set of nodes. Clearly, a multilayer description of a system adds value only if
the multiplex does not merely consist of independent layers, i.e. if the
inter-layer overlap is nontrivial. On real-world multiplexes, it is expected
that the observed overlap may partly result from spurious correlations arising
from the heterogeneity of nodes and partly from true interdependencies.
However, no rigorous way to disentangle these two effects has been developed.
In this paper we introduce an unbiased maximum-entropy model of multiplexes
with controllable node degrees and controllable overlap. The model can be
mapped to a generalized Ising model where the combination of node heterogeneity
and inter-layer coupling leads to the possibility of local phase transitions.
In particular, we find that an increased heterogeneity in the network results
in different critical points for different pairs of nodes, which in turn leads
to local phase transitions that may ultimately increase the overlap. The model
allows us to quantify how the overlap can be increased by either increasing the
heterogeneity of the network (spurious correlation) or the strength of the
inter-layer coupling (true correlation), thereby disentangling the two effects.
As an application, we show that the empirical overlap in the International
Trade Multiplex is not merely a spurious result of the correlation between node
degrees across different layers, but requires a non-zero inter-layer coupling
in its modeling
Stochastically timed predicate-based communication primitives for autonomic computing
Predicate-based communication allows components of a system to send messages and requests to ensembles of components that are determined at execution time through the
evaluation of a predicate, in a multicast fashion. Predicate-based communication can greatly simplify the programming of autonomous and adaptive systems. We present a
stochastically timed extension of the Software Component Ensemble Language (SCEL) that was introduced in previous work. Such an extension raises a number of non-trivial
design and formal semantics issues with different options as possible solutions at different levels of abstraction. We discuss four of these options. We provide formal semantics and an illustration of the use of the language modeling a variant of a bike sharing system, together with some preliminary analysis of the system performance
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