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ABSTRACT: This work reports a quantitative analysis to predicting the efficiency of
distributed computing running in three models of complex networks:
Barab\'asi-Albert, Erd\H{o}s-R\'enyi and Watts-Strogatz. A master/slave
computing model is simulated. A node is selected as master and distributes
tasks among the other nodes (the clients). Topological measurements associated
with the master node (e.g. its degree or betwenness centrality) are extracted
and considered as predictors of the total execution time. It is found that the
closeness centrality provides the best alternative. The effect of network size
was also investigated.
07/2012;
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ABSTRACT: We report a morphology-based approach for the automatic identification of outlier neurons, as well as its application to the NeuroMorpho.org database, with more than 5,000 neurons. Each neuron in a given analysis is represented by a feature vector composed of 20 measurements, which are then projected into a two-dimensional space by applying principal component analysis. Bivariate kernel density estimation is then used to obtain the probability distribution for the group of cells, so that the cells with highest probabilities are understood as archetypes while those with the smallest probabilities are classified as outliers. The potential of the methodology is illustrated in several cases involving uniform cell types as well as cell types for specific animal species. The results provide insights regarding the distribution of cells, yielding single and multi-variate clusters, and they suggest that outlier cells tend to be more planar and tortuous. The proposed methodology can be used in several situations involving one or more categories of cells, as well as for detection of new categories and possible artifacts.
Neuroinformatics 05/2012; 10(4):379-89. · 2.97 Impact Factor
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ABSTRACT: The study of complex networks has drawn much attention over the last years,
mainly by virtue of its potential to characterize the most diverse systems
through unified mathematical and computational tools. Not long ago the emphasis
on this field mostly focused on the effects of the structural properties on the
global behavior of a dynamical process taking place in the system. Recently,
some studies started to unveil the richness of interactions that occur between
groups of nodes when we look at the small scale of interactions occurring in
the network. Such findings call for a new systematic methodology to quantify,
at node level, how a dynamics is being influenced (or differentiated) by the
structure of the underlying system. Here we present a first step towards this
direction, in which we define a new measurement that, based on dynamical
characteristics obtained for a large set of initial conditions, compares the
dynamical behavior of the nodes present in the system. Through this measurement
we find the high capacity of networks, generated by the geographic and
Barab\'asi-Albert models, to exhibit groups of nodes with distinct dynamics
compared to the rest of the network. We also present a practical application of
the methodology by using the neuronal network of the nematode
\emph{Caenorhabditis elegans}, where we show that the interneurons of the
ventral cord presents a very large dynamical differentiation when compared to
the rest of the network.
05/2012;
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ABSTRACT: The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports results regarding the properties of accessibility, including its relationship with the average minimal time to visit all nodes reachable after h steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the exploration time), conjecture that the maximum accessibility implies the minimal exploration time, and confirm the relationship between the accessibility values and the number of nodes visited after a basic time unit. The latter relationship is investigated with respect to three types of dynamics: traditional random walks, self-avoiding random walks, and preferential random walks.
Physical Review E 03/2012; 85(3 Pt 2):036105. · 2.26 Impact Factor
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ABSTRACT: As the available public cerebral gene expression image data increasingly grows, the demand for automated methods to analyze such large amount of data also increases. An important study that can be carried out on these data is related to the spatial relationship between gene expressions. Similar spatial density distribution of expression between genes may indicate they are functionally correlated, thus the identification of these similarities is useful in suggesting directions of investigation to discover gene interactions and their correlated functions. In this paper, we describe the use of a high-throughput methodology based on Voronoi diagrams to automatically analyze and search for possible local spatial density relationships between gene expression images. We tested this method using mouse brain section images from the Allen Mouse Brain Atlas public database. This methodology provided measurements able to characterize the similarity of the density distribution between gene expressions and allowed the visualization of the results through networks and Principal Component Analysis (PCA). These visualizations are useful to analyze the similarity level between gene expression patterns, as well as to compare connection patterns between region networks. Some genes were found to have the same type of function and to be near each other in the PCA visualizations. These results suggest cerebral density correlations between gene expressions that could be further explored.
Journal of neuroscience methods 09/2011; 203(1):212-9. · 2.30 Impact Factor
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ABSTRACT: Over the last years, a great deal of attention has been focused on complex
networked systems, characterized by intricate structure and dynamics. The
latter has been often represented in terms of overall statistics (e.g. average
and standard deviations) of the time signals. While such approaches have led to
many insights, they have failed to take into account that signals at different
parts of the system can undergo distinct evolutions, which cannot be properly
represented in terms of average values. A novel framework for identifying the
principal aspects of the dynamics and how it is influenced by the network
structure is proposed in this work. The potential of this approach is
illustrated with respect to three important models (Integrate-and-Fire, SIS and
Kuramoto), allowing the identification of highly structured dynamics, in the
sense that different groups of nodes not only presented specific dynamics but
also felt the structure of the network in different ways.
09/2011;
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ABSTRACT: Thanks to recent advances in molecular biology, allied to an ever increasing amount of experimental data, the functional state of thousands of genes can now be extracted simultaneously by using methods such as cDNA microarrays and RNA-Seq. Particularly important related investigations are the modeling and identification of gene regulatory networks from expression data sets. Such a knowledge is fundamental for many applications, such as disease treatment, therapeutic intervention strategies and drugs design, as well as for planning high-throughput new experiments. Methods have been developed for gene networks modeling and identification from expression profiles. However, an important open problem regards how to validate such approaches and its results. This work presents an objective approach for validation of gene network modeling and identification which comprises the following three main aspects: (1) Artificial Gene Networks (AGNs) model generation through theoretical models of complex networks, which is used to simulate temporal expression data; (2) a computational method for gene network identification from the simulated data, which is founded on a feature selection approach where a target gene is fixed and the expression profile is observed for all other genes in order to identify a relevant subset of predictors; and (3) validation of the identified AGN-based network through comparison with the original network. The proposed framework allows several types of AGNs to be generated and used in order to simulate temporal expression data. The results of the network identification method can then be compared to the original network in order to estimate its properties and accuracy. Some of the most important theoretical models of complex networks have been assessed: the uniformly-random Erdös-Rényi (ER), the small-world Watts-Strogatz (WS), the scale-free Barabási-Albert (BA), and geographical networks (GG). The experimental results indicate that the inference method was sensitive to average degree variation, decreasing its network recovery rate with the increase of . The signal size was important for the inference method to get better accuracy in the network identification rate, presenting very good results with small expression profiles. However, the adopted inference method was not sensible to recognize distinct structures of interaction among genes, presenting a similar behavior when applied to different network topologies. In summary, the proposed framework, though simple, was adequate for the validation of the inferred networks by identifying some properties of the evaluated method, which can be extended to other inference methods.
Journal of computational biology: a journal of computational molecular cell biology 05/2011; 18(10):1353-67. · 1.69 Impact Factor
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ABSTRACT: The measurement called accessibility has been proposed as a means to quantify
the efficiency of the communication between nodes in complex networks. This
article reports important results regarding the properties of the
accessibility, including its relationship with the average minimal time to
visit all nodes reachable after $h$ steps along a random walk starting from a
source, as well as the number of nodes that are visited after a finite period
of time. We characterize the relationship between accessibility and the average
number of walks required in order to visit all reachable nodes (the exploration
time), conjecture that the maximum accessibility implies the minimal
exploration time, and confirm the relationship between the accessibility values
and the number of nodes visited after a basic time unit. The latter
relationship is investigated with respect to three types of dynamics, namely:
traditional random walks, self-avoiding random walks, and preferential random
walks.
01/2011;
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ABSTRACT: We discuss potential caveats when estimating topologies of 3D brain networks from surface recordings. It is virtually impossible to record activity from all single neurons in the brain and one has to rely on techniques that measure average activity at sparsely located (non-invasive) recording sites. Effects of this spatial sampling in relation to structural network measures like centrality and assortativity were analyzed using multivariate classifiers. A simplified model of 3D brain connectivity incorporating both short- and long-range connections served for testing. To mimic M/EEG recordings we sampled this model via non-overlapping regions and weighted nodes and connections according to their proximity to the recording sites. We used various complex network models for reference and tried to classify sampled versions of the "brain-like" network as one of these archetypes. It was found that sampled networks may substantially deviate in topology from the respective original networks for small sample sizes. For experimental studies this may imply that surface recordings can yield network structures that might not agree with its generating 3D network.
NeuroImage 11/2010; 53(2):439-49. · 5.89 Impact Factor
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ABSTRACT: Since its recent introduction, the small-world effect has been identified in
several important real-world systems. Frequently, it is a consequence of the
existence of a few long-range connections, which dominate the original regular
structure of the systems and implies each node to become accessible from other
nodes after a small number of steps, typically of order $\ell \propto \log N$.
However, this effect has been observed in pure-topological networks, where the
nodes have no spatial coordinates. In this paper, we present an alalogue of
small-world effect observed in real-world transportation networks, where the
nodes are embeded in a hree-dimensional space. Using the multidimensional
scaling method, we demonstrate how the addition of a few long-range connections
can suubstantially reduce the travel time in transportation systems. Also, we
investigated the importance of long-range connections when the systems are
under an attack process. Our findings are illustrated for two real-world
systems, namely the London urban network (streets and underground) and the US
highways network enhanced by some of the main US airlines routes.
05/2010;
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ABSTRACT: The continuing neuroscience advances, catalysed by multidisciplinary collaborations between the biological, computational, physical and chemical areas, have implied in increasingly more complex approaches to understand and model the mammals nervous systems. One particularly important related issue regards the investigation of the relationship between morphology and function of neuronal cells, which requires the application of effective means for their classification, for instance by using multivariated, pattern recognition and clustering methods. The current work aims at such a study while considering a large number of neuronal cells obtained from the NeuroMorpho database, which is currently the most comprehensive such a repository. Our approach applies an unsupervised clustering technique, known as Superparamagnetic Clustering, over a set of morphological measurements regarding four major neuronal categories. In particular, we target two important problems: (i) we investigate the coherence between the obtained clusters and the original categories; and (ii) we verify for eventual subclusters inside each of these categories. We report a good agreement between the obtained clusters and the original categories, as well as the identification of a relatively complex structure of subclusters in the case of the pyramidal neuronal cells. Comment: 15 pages, 3 tables, 7 figures
03/2010;
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ABSTRACT: Radial glia in the developing optic tectum express the key guidance molecules responsible for topographic targeting of retinal axons. However, the extent to which the radial glia are themselves influenced by retinal inputs and visual experience remains unknown. Using multiphoton live imaging of radial glia in the optic tectum of intact Xenopus laevis tadpoles in conjunction with manipulations of neural activity and sensory stimuli, radial glia were observed to exhibit spontaneous calcium transients that were modulated by visual stimulation. Structurally, radial glia extended and retracted many filopodial processes within the tectal neuropil over minutes. These processes interacted with retinotectal synapses and their motility was modulated by nitric oxide (NO) signaling downstream of neuronal NMDA receptor (NMDAR) activation and visual stimulation. These findings provide the first in vivo demonstration that radial glia actively respond both structurally and functionally to neural activity, via NMDAR-dependent NO release during the period of retinal axon ingrowth.
Journal of Neuroscience 11/2009; 29(45):14066-76. · 7.11 Impact Factor
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ABSTRACT: One of the most fascinating aspects of plant morphology is the regular geometric arrangement of leaves and flowers, called phyllotaxy. The shoot apical meristem (SAM) determines these patterns, which vary depending on species and developmental stage. Auxin acts as an instructive signal in leaf initiation, and its transport has been implicated in phyllotaxy regulation in Arabidopsis (Arabidopsis thaliana). Altered phyllotactic patterns are observed in a maize (Zea mays) mutant, aberrant phyllotaxy1 (abph1, also known as abphyl1), and ABPH1 encodes a cytokinin-inducible type A response regulator, suggesting that cytokinin signals are also involved in the mechanism by which phyllotactic patterns are established. Therefore, we investigated the interaction between auxin and cytokinin signaling in phyllotaxy. Treatment of maize shoots with a polar auxin transport inhibitor, 1-naphthylphthalamic acid, strongly reduced ABPH1 expression, suggesting that auxin or its polar transport is required for ABPH1 expression. Immunolocalization of the PINFORMED1 (PIN1) polar auxin transporter revealed that PIN1 expression marks leaf primordia in maize, similarly to Arabidopsis. Interestingly, maize PIN1 expression at the incipient leaf primordium was greatly reduced in abph1 mutants. Consistently, auxin levels were reduced in abph1, and the maize PIN1 homolog was induced not only by auxin but also by cytokinin treatments. Our results indicate distinct roles for ABPH1 as a negative regulator of SAM size and a positive regulator of PIN1 expression. These studies highlight a complex interaction between auxin and cytokinin signaling in the specification of phyllotactic patterns and suggest an alternative model for the generation of altered phyllotactic patterns in abph1 mutants. We propose that reduced auxin levels and PIN1 expression in abph1 mutant SAMs delay leaf initiation, contributing to the enlarged SAM and altered phyllotaxy of these mutants.
Plant physiology 04/2009; 150(1):205-16. · 6.53 Impact Factor
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ABSTRACT: One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded on the recently introduced concept of node diversity. It is shown that this feature does not exhibit any relevant correlation with several well-established complex networks measurements. A methodology for the identification of the borders of complex networks is described and illustrated with respect to theoretical (geographical and knitted networks) as well as real-world networks (urban and word association networks), yielding interesting results and insights in both cases.
03/2009;
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ABSTRACT: Along the internal carotid artery (ICA), atherosclerotic plaques are often located in its cavernous sinus (parasellar) segments (pICA). Studies indicate that the incidence of pre-atherosclerotic lesions is linked with the complexity of the pICA; however, the pICA shape was never objectively characterized. Our study aims at providing objective mathematical characterizations of the pICA shape.
Three-dimensional (3D) computer models, reconstructed from contrast enhanced computed tomography (CT) data of 30 randomly selected patients (60 pICAs) were analyzed with modern visualization software and new mathematical algorithms. As objective measures for the pICA shape complexity, we provide calculations of curvature energy, torsion energy, and total complexity of 3D skeletons of the pICA lumen. We further measured the posterior knee of the so-called "carotid siphon" with a virtual goniometer and performed correlations between the objective mathematical calculations and the subjective angle measurements.
Firstly, our study provides mathematical characterizations of the pICA shape, which can serve as objective reference data for analyzing connections between pICA shape complexity and vascular diseases. Secondly, we provide an objective method for creating such data. Thirdly, we evaluate the usefulness of subjective goniometric measurements of the angle of the posterior knee of the carotid siphon.
Surgical and Radiologic Anatomy 08/2008; 30(6):519-26. · 1.06 Impact Factor
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ABSTRACT: The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks have been comprehensively investigated along the last decade in terms of their topological measurements, relatively less attention has been focused on the characterization of the respective dynamics. Introduced recently, the diversity entropy of complex systems can provide valuable information about the respective possible unfolding of dynamics. In the case of self-avoiding random walks, the situation assumed here, the diversity measurement allows one to quantify in how many different places an agent may effectively arrive after a given number of steps from its initial activity. Because this measurement is highly affected by border effects frequently found as a consequence of network sampling, it becomes critical to devise means for sound estimation of the diversity without being affected by this type of artifacts. We describe such an algorithm and illustrate its potential with respect to the characterization of the self-avoiding random walk dynamics in two real-world networks, namely bone canals and air transportation.
06/2008;
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ABSTRACT: Inside the 'cavernous sinus' or 'parasellar region' the human internal carotid artery takes the shape of a siphon that is twisted and torqued in three dimensions and surrounded by a network of veins. The parasellar section of the internal carotid artery is of broad biological and medical interest, as its peculiar shape is associated with temperature regulation in the brain and correlated with the occurrence of vascular pathologies. The present study aims to provide anatomical descriptions and objective mathematical characterizations of the shape of the parasellar section of the internal carotid artery in human infants and its modifications during ontogeny. Three-dimensional (3D) computer models of the parasellar section of the internal carotid artery of infants were generated with a state-of-the-art 3D reconstruction method and analysed using both traditional morphometric methods and novel mathematical algorithms. We show that four constant, demarcated bends can be described along the infant parasellar section of the internal carotid artery, and we provide measurements of their angles. We further provide calculations of the curvature and torsion energy, and the total complexity of the 3D skeleton of the parasellar section of the internal carotid artery, and compare the complexity of this in infants and adults. Finally, we examine the relationship between shape parameters of the parasellar section of the internal carotid artery in infants, and the occurrence of intima cushions, and evaluate the reliability of subjective angle measurements for characterizing the complexity of the parasellar section of the internal carotid artery in infants. The results can serve as objective reference data for comparative studies and for medical imaging diagnostics. They also form the basis for a new hypothesis that explains the mechanisms responsible for the ontogenetic transformation in the shape of the parasellar section of the internal carotid artery.
Journal of Anatomy 06/2008; 212(5):636-44. · 2.37 Impact Factor
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ABSTRACT: The success of new scientific areas can be assessed by their potential for
contributing to new theoretical approaches and in applications to real-world
problems. Complex networks have fared extremely well in both of these aspects,
with their sound theoretical basis developed over the years and with a variety
of applications. In this survey, we analyze the applications of complex
networks to real-world problems and data, with emphasis in representation,
analysis and modeling, after an introduction to the main concepts and models. A
diversity of phenomena are surveyed, which may be classified into no less than
22 areas, providing a clear indication of the impact of the field of complex
networks.
12/2007;
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ABSTRACT: In this work we propose the use of a hirarchical extension of the polygonality index as a means to characterize and model geographical networks: each node is associated with the spatial position of the nodes, while the edges of the network are defined by progressive connectivity adjacencies. Through the analysis of such networks, while relating its topological and geometrical properties, it is possible to obtain important indications about the development dynamics of the networks under analysis. The potential of the methodology is illustrated with respect to synthetic geographical networks. Comment: 3 page, 3 figures. A wokring manuscript: suggestions welcomed
06/2007;
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ABSTRACT: The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real networks were fundamental to stimulate more realistic models and to understand some dynamical processes such as network growth. However, properties related to the network borders (nodes with degree equal to one), one of its most fragile parts, remain little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze complex networks by looking for border trees, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider a series of their measurements, including their number of vertices, number of leaves, and depth. We investigate the properties of border trees for several theoretical models as well as real-world networks. Comment: 5 pages, 1 figure, 2 tables. A working manuscript, comments and suggestions welcomed
06/2007;
