63 research outputs found
A Fast and Accurate Nonlinear Spectral Method for Image Recognition and Registration
This article addresses the problem of two- and higher dimensional pattern
matching, i.e. the identification of instances of a template within a larger
signal space, which is a form of registration. Unlike traditional correlation,
we aim at obtaining more selective matchings by considering more strict
comparisons of gray-level intensity. In order to achieve fast matching, a
nonlinear thresholded version of the fast Fourier transform is applied to a
gray-level decomposition of the original 2D image. The potential of the method
is substantiated with respect to real data involving the selective
identification of neuronal cell bodies in gray-level images.Comment: 4 pages, 3 figure
Seeking for Simplicity in Complex Networks
Complex networks can be understood as graphs whose connectivity deviates from
those of regular or near-regular graphs, which are understood as being
`simple'. While a great deal of the attention so far dedicated to complex
networks has been duly driven by the `complex' nature of these structures, in
this work we address the identification of simplicity, in the sense of
regularity, in complex networks. The basic idea is to seek for subgraphs
exhibiting small dispersion (e.g. standard deviation or entropy) of local
measurements such as the node degree and clustering coefficient. This approach
paves the way for the identification of subgraphs (patches) with nearly uniform
connectivity, therefore complementing the characterization of the complexity of
networks. We also performed analysis of cascade failures, revealing that the
removal of vertices in `simple' regions results in smaller damage to the
network structure than the removal of vertices in the heterogeneous regions. We
illustrate the potential of the proposed methodology with respect to four
theoretical models as well as protein-protein interaction networks of three
different species. Our results suggest that the simplicity of protein
interaction grows as the result of natural selection. This increase in
simplicity makes these networks more robust to cascade failures.Comment: 5 pages, 3 figures, 1 table. Submitted to Physical Review Letter
On the Efficiency of Data Representation on the Modeling and Characterization of Complex Networks
Specific choices about how to represent complex networks can have a
substantial effect on the execution time required for the respective
construction and analysis of those structures. In this work we report a
comparison of the effects of representing complex networks statically as
matrices or dynamically as spase structures. Three theoretical models of
complex networks are considered: two types of Erdos-Renyi as well as the
Barabasi-Albert model. We investigated the effect of the different
representations with respect to the construction and measurement of several
topological properties (i.e. degree, clustering coefficient, shortest path
length, and betweenness centrality). We found that different forms of
representation generally have a substantial effect on the execution time, with
the sparse representation frequently resulting in remarkably superior
performance
The Spread of Opinions and Proportional Voting
Election results are determined by numerous social factors that affect the
formation of opinion of the voters, including the network of interactions
between them and the dynamics of opinion influence. In this work we study the
result of proportional elections using an opinion dynamics model similar to
simple opinion spreading over a complex network. Erdos-Renyi, Barabasi-Albert,
regular lattices and randomly augmented lattices are considered as models of
the underlying social networks. The model reproduces the power law behavior of
number of candidates with a given number of votes found in real elections with
the correct slope, a cutoff for larger number of votes and a plateau for small
number of votes. It is found that the small world property of the underlying
network is fundamental for the emergence of the power law regime.Comment: 10 pages, 7 figure
Complex networks: the key to systems biology
Though introduced recently, complex networks research has grown steadily because of its potential to represent, characterize and model a wide range of intricate natural systems and phenomena. Because of the intrinsic complexity and systemic organization of life, complex networks provide a specially promising framework for systems biology investigation. The current article is an up-to-date review of the major developments related to the application of complex networks in biology, with special attention focused on the more recent literature. The main concepts and models of complex networks are presented and illustrated in an accessible fashion. Three main types of networks are covered: transcriptional regulatory networks, protein-protein interaction networks and metabolic networks. The key role of complex networks for systems biology is extensively illustrated by several of the papers reviewed.FAPESPCNP
A Complex Networks Approach for Data Clustering
Many methods have been developed for data clustering, such as k-means,
expectation maximization and algorithms based on graph theory. In this latter
case, graphs are generally constructed by taking into account the Euclidian
distance as a similarity measure, and partitioned using spectral methods.
However, these methods are not accurate when the clusters are not well
separated. In addition, it is not possible to automatically determine the
number of clusters. These limitations can be overcome by taking into account
network community identification algorithms. In this work, we propose a
methodology for data clustering based on complex networks theory. We compare
different metrics for quantifying the similarity between objects and take into
account three community finding techniques. This approach is applied to two
real-world databases and to two sets of artificially generated data. By
comparing our method with traditional clustering approaches, we verify that the
proximity measures given by the Chebyshev and Manhattan distances are the most
suitable metrics to quantify the similarity between objects. In addition, the
community identification method based on the greedy optimization provides the
smallest misclassification rates.Comment: 9 pages, 8 Figure
Communication Structure of Cortical Networks
Large-scale cortical networks exhibit characteristic topological properties that shape communication between brain regions and global cortical dynamics. Analysis of complex networks allows the description of connectedness, distance, clustering, and centrality that reveal different aspects of how the network's nodes communicate. Here, we focus on a novel analysis of complex walks in a series of mammalian cortical networks that model potential dynamics of information flow between individual brain regions. We introduce two new measures called absorption and driftness. Absorption is the average length of random walks between any two nodes, and takes into account all paths that may diffuse activity throughout the network. Driftness is the ratio between absorption and the corresponding shortest path length. For a given node of the network, we also define four related measurements, namely in- and out-absorption as well as in- and out-driftness, as the averages of the corresponding measures from all nodes to that node, and from that node to all nodes, respectively. We find that the cat thalamo-cortical system incorporates features of two classic network topologies, Erdös–Rényi graphs with respect to in-absorption and in-driftness, and configuration models with respect to out-absorption and out-driftness. Moreover, taken together these four measures separate the network nodes based on broad functional roles (visual, auditory, somatomotor, and frontolimbic)
Analyzing Trails in Complex Networks
Even more interesting than the intricate organization of complex networks are
the dynamical behavior of systems which such structures underly. Among the many
types of dynamics, one particularly interesting category involves the evolution
of trails left by moving agents progressing through random walks and dilating
processes in a complex network. The emergence of trails is present in many
dynamical process, such as pedestrian traffic, information flow and metabolic
pathways. Important problems related with trails include the reconstruction of
the trail and the identification of its source, when complete knowledge of the
trail is missing. In addition, the following of trails in multi-agent systems
represent a particularly interesting situation related to pedestrian dynamics
and swarming intelligence. The present work addresses these three issues while
taking into account permanent and transient marks left in the visited nodes.
Different topologies are considered for trail reconstruction and trail source
identification, including four complex networks models and four real networks,
namely the Internet, the US airlines network, an email network and the
scientific collaboration network of complex network researchers. Our results
show that the topology of the network influence in trail reconstruction, source
identification and agent dynamics.Comment: 10 pages, 16 figures. A working manuscript, comments and criticisms
welcome
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