59,466 research outputs found
A statistical network analysis of the HIV/AIDS epidemics in Cuba
The Cuban contact-tracing detection system set up in 1986 allowed the
reconstruction and analysis of the sexual network underlying the epidemic
(5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168
edges), shedding light onto the spread of HIV and the role of contact-tracing.
Clustering based on modularity optimization provides a better visualization and
understanding of the network, in combination with the study of covariates. The
graph has a globally low but heterogeneous density, with clusters of high
intraconnectivity but low interconnectivity. Though descriptive, our results
pave the way for incorporating structure when studying stochastic SIR epidemics
spreading on social networks
Reconciling long-term cultural diversity and short-term collective social behavior
An outstanding open problem is whether collective social phenomena occurring
over short timescales can systematically reduce cultural heterogeneity in the
long run, and whether offline and online human interactions contribute
differently to the process. Theoretical models suggest that short-term
collective behavior and long-term cultural diversity are mutually excluding,
since they require very different levels of social influence. The latter
jointly depends on two factors: the topology of the underlying social network
and the overlap between individuals in multidimensional cultural space.
However, while the empirical properties of social networks are well understood,
little is known about the large-scale organization of real societies in
cultural space, so that random input specifications are necessarily used in
models. Here we use a large dataset to perform a high-dimensional analysis of
the scientific beliefs of thousands of Europeans. We find that inter-opinion
correlations determine a nontrivial ultrametric hierarchy of individuals in
cultural space, a result unaccessible to one-dimensional analyses and in
striking contrast with random assumptions. When empirical data are used as
inputs in models, we find that ultrametricity has strong and counterintuitive
effects, especially in the extreme case of long-range online-like interactions
bypassing social ties. On short time-scales, it strongly facilitates a
symmetry-breaking phase transition triggering coordinated social behavior. On
long time-scales, it severely suppresses cultural convergence by restricting it
within disjoint groups. We therefore find that, remarkably, the empirical
distribution of individuals in cultural space appears to optimize the
coexistence of short-term collective behavior and long-term cultural diversity,
which can be realized simultaneously for the same moderate level of mutual
influence
Immune networks: multi-tasking capabilities at medium load
Associative network models featuring multi-tasking properties have been
introduced recently and studied in the low load regime, where the number of
simultaneously retrievable patterns scales with the number of nodes as
. In addition to their relevance in artificial intelligence,
these models are increasingly important in immunology, where stored patterns
represent strategies to fight pathogens and nodes represent lymphocyte clones.
They allow us to understand the crucial ability of the immune system to respond
simultaneously to multiple distinct antigen invasions. Here we develop further
the statistical mechanical analysis of such systems, by studying the medium
load regime, with . We derive three main
results. First, we reveal the nontrivial architecture of these networks: they
exhibit a high degree of modularity and clustering, which is linked to their
retrieval abilities. Second, by solving the model we demonstrate for
the existence of large regions in the phase diagram where the network can
retrieve all stored patterns simultaneously. Finally, in the high load regime
we find that the system behaves as a spin glass, suggesting that
finite-connectivity frameworks are required to achieve effective retrieval.Comment: 26 pages, 10 figure
Community Structure in Industrial SAT Instances
Modern SAT solvers have experienced a remarkable progress on solving
industrial instances. Most of the techniques have been developed after an
intensive experimental process. It is believed that these techniques exploit
the underlying structure of industrial instances. However, there are few works
trying to exactly characterize the main features of this structure.
The research community on complex networks has developed techniques of
analysis and algorithms to study real-world graphs that can be used by the SAT
community. Recently, there have been some attempts to analyze the structure of
industrial SAT instances in terms of complex networks, with the aim of
explaining the success of SAT solving techniques, and possibly improving them.
In this paper, inspired by the results on complex networks, we study the
community structure, or modularity, of industrial SAT instances. In a graph
with clear community structure, or high modularity, we can find a partition of
its nodes into communities such that most edges connect variables of the same
community. In our analysis, we represent SAT instances as graphs, and we show
that most application benchmarks are characterized by a high modularity. On the
contrary, random SAT instances are closer to the classical Erd\"os-R\'enyi
random graph model, where no structure can be observed. We also analyze how
this structure evolves by the effects of the execution of a CDCL SAT solver. In
particular, we use the community structure to detect that new clauses learned
by the solver during the search contribute to destroy the original structure of
the formula. This is, learned clauses tend to contain variables of distinct
communities
Delay Performance and Mixing Times in Random-Access Networks
We explore the achievable delay performance in wireless random-access
networks. While relatively simple and inherently distributed in nature,
suitably designed queue-based random-access schemes provide the striking
capability to match the optimal throughput performance of centralized
scheduling mechanisms in a wide range of scenarios. The specific type of
activation rules for which throughput optimality has been established, may
however yield excessive queues and delays.
Motivated by that issue, we examine whether the poor delay performance is
inherent to the basic operation of these schemes, or caused by the specific
kind of activation rules. We derive delay lower bounds for queue-based
activation rules, which offer fundamental insight in the cause of the excessive
delays. For fixed activation rates we obtain lower bounds indicating that
delays and mixing times can grow dramatically with the load in certain
topologies as well
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