arXiv subjects

Luciano da Fontoura Costa

Publications and source records attributed to Luciano da Fontoura Costa.

At least 55 records · Page 3Linked to original sources

arXiv2008

Trees = Networks ?!?

This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without loss of information. The extension of this methodology to more general networks, including unweighted structures, is also discussed and illustrated. It is shown that the identified duality between trees and graphs underlies several key concepts and issues of current interest in complex networks, including comprehensive characterization of trees and community detection. For instance, additional information about tree structures (e.g. phylogenetic trees) can be immediately obtained by taking into account several off-the-shelf network measurements -- such as the clustering coefficient, degree correlations and betweenness centrality. At the same time, the hierarchical structure of networks, including the respective communities, becomes clear when the network is represented in terms of the respective tree. Indeed, the network-tree mapping described in this work provides a simple and yet effective means of community detection.

physics.soc-ph↗

arXiv2008

Characterization of Subgraphs Relationships and Distribution in Complex Networks

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs (connected components) and their interrelationships and distribution through the network. Though such subgraphs can be completely general, our methodology focuses the cases in which the nodes of these subgraphs share some special feature, such as being critical for the proper operation of the network. Our methodology of subgraph characterization involves two main aspects: (i) a distance histogram containing the distances calculated between all subgraphs, and (ii) a merging algorithm, developed to progressively merge the subgraphs until the whole network is covered. The latter procedure complements the distance histogram by taking into account the nodes lying between subgraphs, as well as the relevance of these nodes to the overall interconnectivity. Experiments were carried out using four types of network models and four instances of real-world networks, in order to illustrate how subgraph characterization can help complementing complex network-based studies.

physics.comp-ph↗

arXiv2008

Connectivity and Dynamics of Neuronal Networks as Defined by the Shape of Individual Neurons

Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of neuron shape on the overall connectivity and dynamics of the emerging networks. The current work addresses this issue by considering simplified neuronal shapes consisting of circular regions (soma/axons) with spokes (dendrites). Networks are grown by placing these patterns randomly in the 2D plane and establishing connections whenever a piece of dendrite falls inside an axon. Several topological and dynamical properties of the resulting graph are measured, including the degree distribution, clustering coefficients, symmetry of connections, size of the largest connected component, as well as three hierarchical measurements of the local topology. By varying the number of processes of the individual basic patterns, we can quantify relationships between the individual neuronal shape and the topological and dynamical features of the networks. Integrate-and-fire dynamics on these networks is also investigated with respect to transient activation from a source node, indicating that long-range connections play an important role in the propagation of avalanches.

q-bio.NC↗

arXiv2008

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.

cs.DM↗

arXiv2008

The Web of Connections between Tourism Companies in Elba: Structure and Dynamics

Tourism destination networks are amongst the most complex dynamical systems, involving a myriad of human-made and natural resources. In this work we report a complex network-based systematic analysis of the Elba (Italy) tourism destination network, including the characterization of its structure in terms of a set of several traditional measurements, the investigation of its modularity, as well as its comprehensive study in terms of the recently reported superedges approach. In particular, structural (the number of paths of distinct lengths between pairs of nodes, as well as the number of reachable companies) and dynamical features (transition probabilities and the inward/outward activations and accessibilities) are measured and analyzed, leading to a series of important findings related to the interactions between tourism companies. Among the several reported results, it is shown that the type and size of the companies influence strongly their respective activations and accessibilities, while their geographical position does not seem to matter. It is also shown that the Elba tourism network is largely fragmented and heterogeneous, so that it could benefit from increased integration.

physics.soc-ph↗

arXiv2008

Entropy Moments Characterization of Statistical Distributions

This letter reports two moment extensions of the entropy of a distribution. By understanding the traditional entropy as the average of the original distribution up to a random variable transformation, the traditional moments equation become immediately applicable to entropy. We also suggest an alternative family of entropy moments. The discriminative potential of such entropy moment extensions is illustrated with respect to different types of distributions with otherwise undistinguishable traditional entropies.

cond-mat.stat-mech↗

arXiv2008

Outward Accessibility in Urban Street Networks: Characterization and Improvements

The dynamics of transportation through towns and cities is strongly affected by the topology of the connections and routes. The current work describes an approach combining complex networks and self-avoiding random walk dynamics in order to quantify in objective and accurate manner, along a range of spatial scales, the accessibility of places in towns and cities. The transition probabilities are estimated for several lengths of the walks and used to calculate the outward accessibility of each node. The potential of the methodology is illustrated with respect to the characterization and improvements of the accessibility of the town of Sao Carlos.

cs.CY↗

arXiv2008

Transient and Equilibrium Synchronization in Complex Neuronal Networks

Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is estimated computationally so as to obtain the activation at each node along each instant of time. In the transient case, the dynamics is implemented so as to conserve the total activation entering the system. In our equilibrium investigations, the internally stored activation is limited to the value of the respective threshold. The synchronization of the activation of the network is then quantified in terms of its normalized entropy. The equilibrium investigations involve the application of a number of complementary characterization methods, including spectra and Principal Component Analysis, as well as of an equivalent model capable of reproducing both the transient and equilibrium dynamics. The potential of such concepts and measurements is explored with respect to several theoretical models, as well as for the neuronal network of \emph{C. elegans}. A series of interesting results are obtained and discussed, including the fact that all models led to a transient period of synchronization, whose specific features depend on the topological structures of the networks. The investigations of the equilibrium dynamics revealed a series of remarkable insights, including the relationship between spiking oscillations and the hierarchical structure of the networks and the identification of twin correlation patterns between node degree and total activation, implying that hubs of connectivity are also hubs of integrate-and-fire activation.

q-bio.NC↗

arXiv2008

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.

physics.soc-ph↗

arXiv2008

Avalanches of Activation and Spikes in Neuronal Complex Networks

As shown recently (arXiv:0801.3056), several types of neuronal complex networks involving non-linear integration-and-fire dynamics exhibit an abrupt activation along their transient regime. Interestingly, such an avalanche of activation has also been found to depend strongly on the topology of the networks: while the Erdős-Rény, Barabási-Albert, path-regular and path-transformed BA models exhibit well-defined avalanches; Watts-Strogatz and geographical structures present instead a gradual dispersion of activation amongst their nodes. The current work investigates such phenomena by considering a mean-field equivalent model of a network which is strongly founded on the concepts of concentric neighborhoods and degrees. It is shown that the hierarchical number of nodes and hierarchical degrees define the intensity and timing of the avalanches. This approach also allowed the identification of the beginning activation times during the transient dynamics, which is particularly important for community identification (arXiv:0801.4269, arXiv:0801.4684). The main concepts and results in this work are illustrated with respect to theoretical and real-world (\emph{C. elegans}) networks. Several results are reported, including the identification of secondary avalanches, the validation of the equivalent model, the identification of the possible universality of the avalanches for most networks (depending only on the network size), as well as the identification of the fact that different avalanches can be obtained by locating the activation source at different neurons of the \emph{C. elegans} network.

physics.soc-ph↗

arXiv2008

Communities in Neuronal Complex Networks Revealed by Activation Patterns

Recently, it has been shown that the communities in neuronal networks of the integrate-and-fire type can be identified by considering patterns containing the beginning times for each cell to receive the first non-zero activation. The received activity was integrated in order to facilitate the spiking of each neuron and to constrain the activation inside the communities, but no time decay of such activation was considered. The present article shows that, by taking into account exponential decays of the stored activation, it is possible to identify the communities also in terms of the patterns of activation along the initial steps of the transient dynamics. The potential of this method is illustrated with respect to complex neuronal networks involving four communities, each of a different type (Erdős-Rény, Barabási-Albert, Watts-Strogatz as well as a simple geographical model). Though the consideration of activation decay has been found to enhance the communities separation, too intense decays tend to yield less discrimination.

q-bio.NC↗

arXiv2008

Detecting Neuronal Communities from Beginning of Activation Patterns

The detection of neuronal communities is addressed with basis on two important concepts from neuroscience: facilitation of neuronal firing and nearly simultaneous beginning of activation of sets of neurons. More specifically, integrate-and-fire complex neuronal networks are activated at each of their nodes, and the dissemination of activation is monitored. As the activation received by each neuron accumulates, its firing gets facilitated. The time it takes for each neuron, other than the source, to receive the first non-zero input (beginning activation time) and the time for it to produce the first spike (beginning spiking time) are identified through simulations. It is shown, with respect to two synthetic and a real-world (\emph{C. elegans}) neuronal complex networks, that the patterns of beginning activation times (and to a lesser extent also of the spiking times) tend to cluster into groups corresponding to communities of neurons in the original complex neuronal network. Such an effect is identified to be a direct consequence of the almost simultaneous activation between the nodes inside the same community in which the source of activation is placed, as well as of the respective trapping of activation implied by the integration of activiation prior to firing. Interestingly, the accumulation of activity and thresholds inside each neuron were found to be essential for constraining the initial activations within each respective community during the transient activation (no clear clusters were observed when using overall activation or spiking rates). In addition to its intrinsic value for neuroscience and structure-dynamics studies, these results confirm the importance of the consideration of transient dynamics in complex systems investigations.

physics.soc-ph↗

arXiv2008

Synchronization of Non-Linear Random Walk Dynamics in Complex Network

This work addresses synchronization in transient, non-linear stochastic dynamics corresponding to accesses performed by self-avoiding walks originating at each node of a complex network. More specifically, the synchronizability of accesses incoming from other nodes has been considered and quantified in terms of the entropy of the mean periods of access, being closely associated to the efficiency of access delivery to each node. The concept of synchronous support of a node $i$ has also been suggested as corresponding to the nodes which contribute the most for the synchronization of the accesses to $i$. These concepts have been applied to the analysis of 6 networks of different types, leading to markedly smaller synchronizability being obtained for the Watts-Strogatz and a geographical models. The more uniform synchronizabilities were identified for the Watts-Strogatz and path-regular structures. Varying degrees of correlations were found between the synchronizability and the degree or outward accessibility of the nodes. The synchronous support of a node $i$ has been found to present diverse structure, including nodes which may be near to $i$, or nodes which are scattered through the network and far away from $i$.

physics.soc-ph↗

arXiv2008

Inward and Outward Node Accessibility in Complex Networks as Revealed by Non-Linear Dynamics

In this work, the outward and inward accessibilities of individual nodes are defined and their potential for application is illustrated with respect to the investigation of 6 different types of networks. The outward accessibility quantifies the potential of an individual node for accessing other nodes through random walks. The inward accessibility measures the potential of a given node of being accessed by other nodes. Both the inward and outward accessibilities are measured with respect to successive time steps along the walks, providing an interesting means for the characterization of the transient non-linear dynamics of accessibility. Self-avoiding walks are considered here because they are more purposive and necessarily finite (unlike traditional random walks). The results include the identification of the fact that the inward values tend to be much smaller than the outward values, the tendency of the inward accessibility to be highly correlated with the node degree while the outward values are mostly uncorrelated with that measurements, the distinct behavior of the accessibility in geographical networks, the dominance of hubs in scale free networks, as well as the enhanced uniformity of the accessibilities for the path-regular model. Also investigated was the possibility to predict the accessibility of a given node in terms of its respective degree. The concepts of inward and outward accessibility, as well as the several obtained results, have several implications and potential for applications to several real-time problems including disease spreading, WWW surfing, protein interaction, cortical networks and network attacks, among others.

physics.soc-ph↗

arXiv2008

On the Diversity of Non-Linear Transient Dynamics in Several Types of Complex Networks

Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient dynamics obtained in undirected and unweighted complex networks as a consequence of self-avoiding random walks. The diversity of walks starting at a specific node $i$ is quantified in terms of a signature composed by the entropies of the node visit probabilities along each of the initial steps. Six theoretical models of complex networks are considered: Erdős-Rényi, Barabási-Albert, Watts-Strogatz, a geographical model, as well as two recently introduced knitted networks formed by paths. The random walk diversity is explored at the level of network categories and of individual nodes. Because the diversity at successive steps of the walks tends to be correlated, principal component analysis is systematically applied in order to identify the more relevant linear combinations of the diversity entropies and to obtain optimal dimensionality reduction. Several interesting results are reported, including the facts that the transient diversity tends to increase with the average degree for all considered network models and that the Watts and Strogatz and geographical models tend to yield diversity entropies which increase more gradually with the number of steps, contrasting sharply with the steep increases verified for the other four considered models. The principal linear combination of the diversities identified by the principal component analysis method is shown to allow an interesting characterization of individual nodes as well as partitioning of networks into subgraphs of similar diversity.

physics.soc-ph↗

arXiv2007

Random and Longest Paths: Unnoticed Motifs of Complex Networks

Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article introduces the concept of random path applies it for the investigation of structural properties of complex networks and as the means to estimate the longest path. Random paths are obtained by selecting one of the network nodes at random and performing a random self-avoiding walk (here called path-walk) until its termination. It is shown that the distribution of random paths are markedly different for diverse complex network models (i.e. Erdos-Renyi, Barabasi-Albert, Watts-Strogatz, a geographical model, as well as two recently introduced path-based network types), with the BA structures yielding the shortest random walks, while the longest paths are produced by WS networks. Random paths are also explored as the means to estimate the longest paths (i.e. several random paths are obtained and the longest taken). The convergence to the longest path and its properties ire characterized with respect to several networks models. Several results are reported and discussed, including the markedly distinct lengths of the longest paths obtained for the different network models.

physics.soc-ph↗

arXiv2007

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.

physics.soc-ph↗

arXiv2007

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 Barabási-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-Rényi, Barabási-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.

physics.soc-ph↗