25 research outputs found
Interaction driven real-space condensation
We study real-space condensation in a broad class of stochastic mass
transport models. We show that the steady state of such models has a
pair-factorised form which generalizes the standard factorized steady states.
The condensation in this class of models is driven by interactions which give
rise to a spatially extended condensate that differs fundamentally from the
previously studied examples. We present numerical results as well as a
theoretical analysis of the condensation transition and show that the criterion
for condensation is related to the binding-unbinding transition of
solid-on-solid interfaces.Comment: 4 page
The spectral dimension of simplicial complexes: a renormalization group theory
(30 pages, 5 figures)(30 pages, 5 figures
Studying the Emerging Global Brain: Analyzing and Visualizing the Impact of Co-Authorship Teams
This paper introduces a suite of approaches and measures to study the impact
of co-authorship teams based on the number of publications and their citations
on a local and global scale. In particular, we present a novel weighted graph
representation that encodes coupled author-paper networks as a weighted
co-authorship graph. This weighted graph representation is applied to a dataset
that captures the emergence of a new field of science and comprises 614 papers
published by 1,036 unique authors between 1974 and 2004. In order to
characterize the properties and evolution of this field we first use four
different measures of centrality to identify the impact of authors. A global
statistical analysis is performed to characterize the distribution of paper
production and paper citations and its correlation with the co-authorship team
size. The size of co-authorship clusters over time is examined. Finally, a
novel local, author-centered measure based on entropy is applied to determine
the global evolution of the field and the identification of the contribution of
a single author's impact across all of its co-authorship relations. A
visualization of the growth of the weighted co-author network and the results
obtained from the statistical analysis indicate a drift towards a more
cooperative, global collaboration process as the main drive in the production
of scientific knowledge.Comment: 13 pages, 9 figure
Random Walks on deterministic Scale-Free networks: Exact results
We study the random walk problem on a class of deterministic Scale-Free
networks displaying a degree sequence for hubs scaling as a power law with an
exponent . We find exact results concerning different
first-passage phenomena and, in particular, we calculate the probability of
first return to the main hub. These results allow to derive the exact analytic
expression for the mean time to first reach the main hub, whose leading
behavior is given by , where denotes the size of
the structure, and the mean is over a set of starting points distributed
uniformly over all the other sites of the graph. Interestingly, the process
turns out to be particularly efficient. We also discuss the thermodynamic limit
of the structure and some local topological properties.Comment: 7 pages, 3 figures; accepted for publication in Phys. Rev.
Dynamical Patterns of Cattle Trade Movements
Despite their importance for the spread of zoonotic diseases, our
understanding of the dynamical aspects characterizing the movements of farmed
animal populations remains limited as these systems are traditionally studied
as static objects and through simplified approximations. By leveraging on the
network science approach, here we are able for the first time to fully analyze
the longitudinal dataset of Italian cattle movements that reports the mobility
of individual animals among farms on a daily basis. The complexity and
inter-relations between topology, function and dynamical nature of the system
are characterized at different spatial and time resolutions, in order to
uncover patterns and vulnerabilities fundamental for the definition of targeted
prevention and control measures for zoonotic diseases. Results show how the
stationarity of statistical distributions coexists with a strong and
non-trivial evolutionary dynamics at the node and link levels, on all
timescales. Traditional static views of the displacement network hide important
patterns of structural changes affecting nodes' centrality and farms' spreading
potential, thus limiting the efficiency of interventions based on partial
longitudinal information. By fully taking into account the longitudinal
dimension, we propose a novel definition of dynamical motifs that is able to
uncover the presence of a temporal arrow describing the evolution of the system
and the causality patterns of its displacements, shedding light on mechanisms
that may play a crucial role in the definition of preventive actions
Dynamical Patterns of Cattle Trade Movements
Despite their importance for the spread of zoonotic diseases, our
understanding of the dynamical aspects characterizing the movements of farmed
animal populations remains limited as these systems are traditionally studied
as static objects and through simplified approximations. By leveraging on the
network science approach, here we are able for the first time to fully analyze
the longitudinal dataset of Italian cattle movements that reports the mobility
of individual animals among farms on a daily basis. The complexity and
inter-relations between topology, function and dynamical nature of the system
are characterized at different spatial and time resolutions, in order to
uncover patterns and vulnerabilities fundamental for the definition of targeted
prevention and control measures for zoonotic diseases. Results show how the
stationarity of statistical distributions coexists with a strong and
non-trivial evolutionary dynamics at the node and link levels, on all
timescales. Traditional static views of the displacement network hide important
patterns of structural changes affecting nodes' centrality and farms' spreading
potential, thus limiting the efficiency of interventions based on partial
longitudinal information. By fully taking into account the longitudinal
dimension, we propose a novel definition of dynamical motifs that is able to
uncover the presence of a temporal arrow describing the evolution of the system
and the causality patterns of its displacements, shedding light on mechanisms
that may play a crucial role in the definition of preventive actions
An Empirical Study of the Mexican Banking System's Network and Its Implications for Systemic Risk
With the purpose of measuring and monitoring systemic risk, some topological properties of the interbank exposures and the payments system networks are studied. We propose non-topological measures which are useful to describe the individual behavior of banks in both networks. The evolution of such networks is also studied and some important conclusions from the systemic risks perspective are drawn. A unified measure of interconnectedness is also created. The main findings of this study are: the payments system network is strongly connected in contrast to the interbank exposures network; the type of exposures and payment size reveal different roles played by banks; behavior of banks in the exposures network changed considerably after Lehmans failure; interconnectedness of a bank, estimated by the unified measure, is not necessarily related with its assets size
Protein Networks Reveal Detection Bias and Species Consistency When Analysed by Information-Theoretic Methods
We apply our recently developed information-theoretic measures for the characterisation and comparison of proteinâprotein interaction networks. These measures are used to quantify topological network features via macroscopic statistical properties. Network differences are assessed based on these macroscopic properties as opposed to microscopic overlap, homology information or motif occurrences. We present the results of a largeâscale analysis of proteinâprotein interaction networks. Precise null models are used in our analyses, allowing for reliable interpretation of the results. By quantifying the methodological biases of the experimental data, we can define an information threshold above which networks may be deemed to comprise consistent macroscopic topological properties, despite their small microscopic overlaps. Based on this rationale, data from yeastâtwoâhybrid methods are sufficiently consistent to allow for intraâspecies comparisons (between different experiments) and interâspecies comparisons, while data from affinityâpurification massâspectrometry methods show large differences even within intraâspecies comparisons
Lectures on complex networks
This text is an introduction to the science of complex networks which fills the gap between popular science books and comprehensive reference volumes on complex networks. It discusses the main directions of modern research in this active field, as well as the history of network studies
The degree distribution of the generalized duplication model
AbstractWe study and generalize the duplication model of Pastor-Satorras et al. [Evolving protein interaction networks through gene duplication, J. Theor. Biol. 222 (2003) 199â210]. This model generates a graph by iteratively âduplicatingâ a randomly chosen node as follows: we start at t0 with a fixed graph G(t0) of size t0. At each step t>t0 a new node vt is added. The node vt selects an existing node u from V(G(t-1))={v1,âŚ,vt-1} uniformly at random (uar). The node vt then connects to each neighbor of the node u in G(t-1) independently with probability p. Additionally, vt connects uar to every node of V(G(t-1)) independently with probability r/t, and parallel edges are merged. Unlike other copy-based models, the degree of the node vt in this model is not fixed in advance; rather it depends strongly on the degree of the original node u it selected.Our main contributions are as follows: we show that (1) the duplication model of Pastor-Satorras et al. does not generate a truncated power-law degree distribution as stated in Pastor-Satorras et al. [Evolving protein interaction networks through gene duplication, J. Theor. Biol. 222 (2003) 199â210]. (2) The special case where r=0 does not give a power-law degree distribution as stated in Chung et al. [Duplication models for biological networks, J. Comput. Biol. 10 (2003) 677â687]. (3) We generalize the Pastor-Satorras et al. duplication process to ensure (if required) that the minimum degree of all vertices is positive. We prove that this generalized model has a power-law degree distribution