610 research outputs found
Complex Networks: New Concepts and Tools for Real-Time Imaging and Vision
This article discusses how concepts and methods of complex networks can be
applied to real-time imaging and computer vision. After a brief introduction of
complex networks basic concepts, their use as means to represent and
characterize images, as well as for modeling visual saliency, are briefly
described. The possibility to apply complex networks in order to model and
simulate the performance of parallel and distributed computing systems for
performance of visual methods is also proposed.Comment: 3 page
Exploring Complex Networks through Random Walks
Most real complex networks -- such as protein interactions, social contacts,
the internet -- are only partially known and available to us. While the process
of exploring such networks in many cases resembles a random walk, it becomes a
key issue to investigate and characterize how effectively the nodes and edges
of such networks can be covered by different strategies. At the same time, it
is critically important to infer how well can topological measurements such as
the average node degree and average clustering coefficient be estimated during
such network explorations. The present article addresses these problems by
considering random and Barab\'asi-Albert (BA) network models with varying
connectivity explored by three types of random walks: traditional, preferential
to untracked edges, and preferential to unvisited nodes. A series of relevant
results are obtained, including the fact that random and BA models with the
same size and average node degree allow similar node and edge coverage
efficiency, the identification of linear scaling with the size of the network
of the random walk step at which a given percentage of the nodes/edges is
covered, and the critical result that the estimation of the averaged node
degree and clustering coefficient by random walks on BA networks often leads to
heavily biased results. Many are the theoretical and practical implications of
such results.Comment: 5 pages, 5 figure
The Path-Star Transformation and its Effects on Complex Networks
A good deal of the connectivity of complex networks can be characterized in
terms of their constituent paths and hubs. For instance, the Barab\'asi-Albert
model is known to incorporate a significative number of hubs and relatively
short paths. On the other hand, the Watts-Strogatz model is underlain by a long
path and almost complete absence of hubs. The present work investigates how the
topology of complex networks changes when a path is transformed into a star
(or, for long paths, a hub). Such a transformation keeps the number of nodes
and does not increase the number of edges in the network, but has potential for
greatly changing the network topology. Several interesting results are reported
with respect to Erdos-R\'enyi, Barab\'asi-Albert and Watts-Strogats models,
including the unexpected finding that the diameter and average shortest path
length of the former type of networks are little affected by the path-star
transformation. In addition to providing insight about the organization of
complex networks, such transformations are also potentially useful for
improving specific aspects of the network connectivity, e.g. average shortest
path length as required for expedite communication between nodes.Comment: 8 pages, 2 figures, 1 table. A working manuscript, comments welcome
Trajectory Networks and Their Topological Changes Induced by Geographical Infiltration
In this article we investigate the topological changes undergone by
trajectory networks as a consequence of progressive geographical infiltration.
Trajectory networks, a type of knitted network, are obtained by establishing
paths between geographically distributed nodes while following an associated
vector field. For instance, the nodes could correspond to neurons along the
cortical surface and the vector field could correspond to the gradient of
neurotrophic factors, or the nodes could represent towns while the vector
fields would be given by economical and/or geographical gradients. Therefore
trajectory networks are natural models of a large number of geographical
structures. The geographical infiltrations correspond to the addition of new
local connections between nearby existing nodes. As such, these infiltrations
could be related to several real-world processes such as contaminations,
diseases, attacks, parasites, etc. The way in which progressive geographical
infiltrations affect trajectory networks is investigated in terms of the
degree, clustering coefficient, size of the largest component and the lengths
of the existing chains measured along the infiltrations. It is shown that the
maximum infiltration distance plays a critical role in the intensity of the
induced topological changes. For large enough values of this parameter, the
chains intrinsic to the trajectory networks undergo a collapse which is shown
not to be related to the percolation of the network also implied by the
infiltrations.Comment: 10 pages, 8 figures. A working manuscript: suggestions and
collaborations welcome
On the Separability of Attractors in Grandmother Dynamic Systems with Structured Connectivity
The combination of complex networks and dynamic systems research is poised to
yield some of the most interesting theoretic and applied scientific results
along the forthcoming decades. The present work addresses a particularly
important related aspect, namely the quantification of how well separated can
the attractors be in dynamic systems underlined by four types of complex
networks (Erd\H{o}s-R\'enyi, Barab\'asi-Albert, Watts-Strogatz and as well as a
geographic model). Attention is focused on grandmother dynamic systems, where
each state variable (associated to each node) is used to represent a specific
prototype pattern (attractor). By assuming that the attractors spread their
influence among its neighboring nodes through a diffusive process, it is
possible to overlook the specific details of specific dynamics and focus
attention on the separability among such attractors. This property is defined
in terms of two separation indices (one individual to each prototype and the
other considering also the immediate neighborhood) reflecting the balance and
proximity to attractors revealed by the activation of the network after a
diffusive process. The separation index considering also the neighborhood was
found to be much more informative, while the best separability was observed for
the Watts-Strogatz and the geographic models. The effects of the involved
parameters on the separability were investigated by correlation and path
analyses. The obtained results suggest the special importance of some
measurements in underlying the relationship between topology and dynamics.Comment: 23 pages, 12 figures, 3 table
Knitted Complex Networks
To a considerable extent, the continuing importance and popularity of complex
networks as models of real-world structures has been motivated by scale free
degree distributions as well as the respectively implied hubs. Being related to
sequential connections of edges in networks, paths represent another important,
dual pattern of connectivity (or motif) in complex networks (e.g., paths are
related to important concepts such as betweeness centrality). The present work
proposes a new supercategory of complex networks which are organized and/or
constructed in terms of paths. Two specific network classes are proposed and
characterized: (i) PA networks, obtained by star-path transforming
Barabasi-Albert networks; and (ii) PN networks, built by performing progressive
paths involving all nodes without repetition. Such new networks are important
not only from their potential to provide theoretical insights, but also as
putative models of real-world structures. The connectivity structure of these
two models is investigated comparatively to four traditional complex networks
models (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz and a geographical model).
A series of interesting results are described, including the corroboration of
the distinct nature of the two proposed models and the importance of
considering a comprehensive set of measurements and multivariated statistical
methods for the characterization of complex networks.Comment: 10 pages, 5 figures, 1 table. A working manuscript, comments and
suggestions welcome
Diffusion of Time-Varying Signals in Complex Networks: A Structure-Dynamics Investigation Focusing the Distance to the Source of Activation
The way in which different types of dynamics unfold in complex networks is
intrinsically related to the propagation of activation along nodes, which is
strongly affected by the network connectivity. In this work we investigate to
which extent a time-varying signal emanating from a specific node is modified
as it diffuses, at the equilibrium regime, along uniformly random
(Erd\H{o}s-R\'enyi) and scale-free (Barab\'asi-Albert) networks. The degree of
preservation is quantified in terms of the Pearson cross-correlation between
the original signal and the derivative of the signals appearing at each node
along time. Several interesting results are reported. First, the fact that
quite distinct signals are typically obtained at different nodes in the
considered networks implies mean-field approaches to be completely inadequate.
It has also been found that the peak and lag of the similarity time-signatures
obtained for each specific node are strongly related to the respective distance
between that node and the source node. Such a relationship tends to decrease
with the average degree of the networks. Also, in the case of the lag, a less
intense relationship is verified for scale-free networks. No relationship was
found between the dispersion of the similarity signature and the distance to
the source.Comment: 9 pages, 5 figure
Reinforcing the Resilience of Complex Networks
Given a connected network, it can be augmented by applying a growing strategy
(e.g. random or scale-free rules) over the previously existing structure.
Another approach for augmentation, recently introduced, involves incorporating
a direct edge between any two nodes which are found to be connected through at
least one self-avoiding path of length L. This work investigates the resilience
of random and scale-free models augmented by using the three schemes identified
above. Considering random and scale-free networks, their giant cluster are
identified and reinforced, then the resilience of the resulting networks with
respect to highest degree node attack is quantified through simulations. The
results, which indicate that substantial reinforcement of the resilience of
complex networks can be achieved by the expansions, also confirm the superior
robustness of the random expansion.Comment: 5 pages, 3 figures, 1 tabl
Activation Confinement Inside Complex Networks Communities
In this work it is described how to enhance and generalize the equivalent
model (arXiv:0802.0421) of integrate-and-fire dynamics in order to treat any
complex neuronal networks, especially those exibiting modular structure. It has
been shown that, though involving only a handful of equivalent neurons, the
modular equivalent model was capable of providing impressive predictions about
the non-linear integrate-and-fire dynamics in two hybrid modular networks. The
reported approach has also allowed the identification of the causes of
transient spiking confinement within the network communities, which correspond
to the fact that the little activation sent from the source community to the
others implies in long times for reaching the nearly-simultaneous activation of
the concentric levels at the other communities and respective avalanches.
Several other insights are reported in this work, including the smoothing of
the spiking functions, the consideration of intra-ring connections and its
effects, as well as the identification of how the weights in the equivalent
model change for different source nodes. This work has paved the way for a
number of promising developments, which are identified and discussed.
Preliminary results are also described which reveal waves induced by the
integrate-and-fire dynamics along the steady-state regime.Comment: 18 pages, 15 figures. A working manuscrip. Suggestions and comments
welcome
The Hierarchical Backbone of Complex Networks
Given any complex directed network, a set of acyclic subgraphs - the
hierarchical backbone of the network - can be extracted that will provide
valuable information about its hierarchical structure. The current paper
presents how the interpretation of the network weight matrix as a transition
matrix allows the hierarchical backbone to be identified and characterized in
terms of the concepts of hierarchical degree, which expresses the total number
of virtual edges established along successive transitions, and of hierarchical
successors, namely the number of nodes accessible from a specific node while
moving successive hierarchical levels. The potential of the proposed approach
is illustrated with respect to word associations and gene sequencing data.Comment: 4 pages, 5 figure
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