13,206 research outputs found
Modularity and the spread of perturbations in complex dynamical systems
We propose a method to decompose dynamical systems based on the idea that
modules constrain the spread of perturbations. We find partitions of system
variables that maximize 'perturbation modularity', defined as the
autocovariance of coarse-grained perturbed trajectories. The measure
effectively separates the fast intramodular from the slow intermodular dynamics
of perturbation spreading (in this respect, it is a generalization of the
'Markov stability' method of network community detection). Our approach
captures variation of modular organization across different system states, time
scales, and in response to different kinds of perturbations: aspects of
modularity which are all relevant to real-world dynamical systems. It offers a
principled alternative to detecting communities in networks of statistical
dependencies between system variables (e.g., 'relevance networks' or
'functional networks'). Using coupled logistic maps, we demonstrate that the
method uncovers hierarchical modular organization planted in a system's
coupling matrix. Additionally, in homogeneously-coupled map lattices, it
identifies the presence of self-organized modularity that depends on the
initial state, dynamical parameters, and type of perturbations. Our approach
offers a powerful tool for exploring the modular organization of complex
dynamical systems
A Model Based Metaheuristic for Hybrid Hierarchical Community Structure in Social Networks
In recent years, the study of community detection
in social networks has received great attention. The hierarchical
structure of the network leads to the emergence of the convergence
to a locally optimal community structure. In this paper, we aim
to avoid this local optimum in the introduced hybrid hierarchical
method. To achieve this purpose, we present an objective function
where we incorporate the value of structural and semantic similarity
based modularity and a metaheuristic namely bees colonies algorithm
to optimize our objective function on both hierarchical level divisive
and agglomerative. In order to assess the efficiency and the accuracy
of the introduced hybrid bee colony model, we perform an extensive
experimental evaluation on both synthetic and real networks
Post-Processing Hierarchical Community Structures: Quality Improvements and Multi-scale View
Dense sub-graphs of sparse graphs (communities), which appear in most
real-world complex networks, play an important role in many contexts. Most
existing community detection algorithms produce a hierarchical structure of
community and seek a partition into communities that optimizes a given quality
function. We propose new methods to improve the results of any of these
algorithms. First we show how to optimize a general class of additive quality
functions (containing the modularity, the performance, and a new similarity
based quality function we propose) over a larger set of partitions than the
classical methods. Moreover, we define new multi-scale quality functions which
make it possible to detect the different scales at which meaningful community
structures appear, while classical approaches find only one partition.Comment: 12 Pages, 4 figure
Community Detection in Quantum Complex Networks
Determining community structure is a central topic in the study of complex
networks, be it technological, social, biological or chemical, in static or
interacting systems. In this paper, we extend the concept of community
detection from classical to quantum systems---a crucial missing component of a
theory of complex networks based on quantum mechanics. We demonstrate that
certain quantum mechanical effects cannot be captured using current classical
complex network tools and provide new methods that overcome these problems. Our
approaches are based on defining closeness measures between nodes, and then
maximizing modularity with hierarchical clustering. Our closeness functions are
based on quantum transport probability and state fidelity, two important
quantities in quantum information theory. To illustrate the effectiveness of
our approach in detecting community structure in quantum systems, we provide
several examples, including a naturally occurring light-harvesting complex,
LHCII. The prediction of our simplest algorithm, semiclassical in nature,
mostly agrees with a proposed partitioning for the LHCII found in quantum
chemistry literature, whereas our fully quantum treatment of the problem
uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl
Resolving Structure in Human Brain Organization: Identifying Mesoscale Organization in Weighted Network Representations
Human brain anatomy and function display a combination of modular and
hierarchical organization, suggesting the importance of both cohesive
structures and variable resolutions in the facilitation of healthy cognitive
processes. However, tools to simultaneously probe these features of brain
architecture require further development. We propose and apply a set of methods
to extract cohesive structures in network representations of brain connectivity
using multi-resolution techniques. We employ a combination of soft
thresholding, windowed thresholding, and resolution in community detection,
that enable us to identify and isolate structures associated with different
weights. One such mesoscale structure is bipartivity, which quantifies the
extent to which the brain is divided into two partitions with high connectivity
between partitions and low connectivity within partitions. A second,
complementary mesoscale structure is modularity, which quantifies the extent to
which the brain is divided into multiple communities with strong connectivity
within each community and weak connectivity between communities. Our methods
lead to multi-resolution curves of these network diagnostics over a range of
spatial, geometric, and structural scales. For statistical comparison, we
contrast our results with those obtained for several benchmark null models. Our
work demonstrates that multi-resolution diagnostic curves capture complex
organizational profiles in weighted graphs. We apply these methods to the
identification of resolution-specific characteristics of healthy weighted graph
architecture and altered connectivity profiles in psychiatric disease.Comment: Comments welcom
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