7,102 research outputs found
Antagonistic Structural Patterns in Complex Networks
Identifying and explaining the structure of complex networks at different
scales has become an important problem across disciplines. At the mesoscale,
modular architecture has attracted most of the attention. At the macroscale,
other arrangements --e.g. nestedness or core-periphery-- have been studied in
parallel, but to a much lesser extent. However, empirical evidence increasingly
suggests that characterizing a network with a unique pattern typology may be
too simplistic, since a system can integrate properties from distinct
organizations at different scales. Here, we explore the relationship between
some of those organizational patterns: two at the mesoscale (modularity and
in-block nestedness); and one at the macroscale (nestedness). We analytically
show that nestedness can be used to provide approximate bounds for modularity,
with exact results in an idealized scenario. Specifically, we show that
nestedness and modularity are antagonistic. Furthermore, we evince that
in-block nestedness provides a parsimonious transition between nested and
modular networks, taking properties of both. Far from a mere theoretical
exercise, understanding the boundaries that discriminate each architecture is
fundamental, to the extent modularity and nestedness are known to place heavy
constraints on the stability of several dynamical processes, specially in
ecology.Comment: 7 pages, 4 figures and 1 supplemental information fil
Food web topology and nested keystone species complexes
Important species may be in critically central network positions in ecological interaction networks. Beyond quantifying
which one is the most central species in a food web, a multi-node approach can identify the key sets of the most central
n species as well. However, for sets of different size n, these structural keystone species complexes may differ in their
composition. If larger sets contain smaller sets, higher nestedness may be a proxy for predictive ecology and efficient
management of ecosystems. On the contrary, lower nestedness makes the identification of keystones more complicated.
Our question here is how the topology of a network can influence nestedness as an architectural constraint. Here, we
study the role of keystone species complexes in 27 real food webs and quantify their nestedness. After quantifying their
topology properties, we determine their keystones species complexes, calculate their nestedness and statistically analyze
the relationship between topological indices and nestedness. A better understanding of the cores of ecosystems is crucial
for efficient conservation efforts and to know which networks will have more nested keystone species complexes would
be a great help for prioritizing species that could preserve the ecosystem’s structural integrity
The Dynamics of Nestedness Predicts the Evolution of Industrial Ecosystems
In economic systems, the mix of products that countries make or export has
been shown to be a strong leading indicator of economic growth. Hence, methods
to characterize and predict the structure of the network connecting countries
to the products that they export are relevant for understanding the dynamics of
economic development. Here we study the presence and absence of industries at
the global and national levels and show that these networks are significantly
nested. This means that the less filled rows and columns of these networks'
adjacency matrices tend to be subsets of the fuller rows and columns. Moreover,
we show that nestedness remains relatively stable as the matrices become more
filled over time and that this occurs because of a bias for industries that
deviate from the networks' nestedness to disappear, and a bias for the missing
industries that reduce nestedness to appear. This makes the appearance and
disappearance of individual industries in each location predictable. We
interpret the high level of nestedness observed in these networks in the
context of the neutral model of development introduced by Hidalgo and Hausmann
(2009). We show that, for the observed fills, the model can reproduce the high
level of nestedness observed in these networks only when we assume a high level
of heterogeneity in the distribution of capabilities available in countries and
required by products. In the context of the neutral model, this implies that
the high level of nestedness observed in these economic networks emerges as a
combination of both, the complementarity of inputs and heterogeneity in the
number of capabilities available in countries and required by products. The
stability of nestedness in industrial ecosystems, and the predictability
implied by it, demonstrates the importance of the study of network properties
in the evolution of economic networks.Comment: 26 page
Understanding Zipf's law of word frequencies through sample-space collapse in sentence formation
The formation of sentences is a highly structured and history-dependent
process. The probability of using a specific word in a sentence strongly
depends on the 'history' of word-usage earlier in that sentence. We study a
simple history-dependent model of text generation assuming that the
sample-space of word usage reduces along sentence formation, on average. We
first show that the model explains the approximate Zipf law found in word
frequencies as a direct consequence of sample-space reduction. We then
empirically quantify the amount of sample-space reduction in the sentences of
ten famous English books, by analysis of corresponding word-transition tables
that capture which words can follow any given word in a text. We find a highly
nested structure in these transition tables and show that this `nestedness' is
tightly related to the power law exponents of the observed word frequency
distributions. With the proposed model it is possible to understand that the
nestedness of a text can be the origin of the actual scaling exponent, and that
deviations from the exact Zipf law can be understood by variations of the
degree of nestedness on a book-by-book basis. On a theoretical level we are
able to show that in case of weak nesting, Zipf's law breaks down in a fast
transition. Unlike previous attempts to understand Zipf's law in language the
sample-space reducing model is not based on assumptions of multiplicative,
preferential, or self-organised critical mechanisms behind language formation,
but simply used the empirically quantifiable parameter 'nestedness' to
understand the statistics of word frequencies.Comment: 7 pages, 4 figures. Accepted for publication in the Journal of the
Royal Society Interfac
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