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Luciano da Fontoura Costa

Publications and source records attributed to Luciano da Fontoura Costa.

108 records · Page 6Linked to original sources
arXiv2004

The complex channel networks of bone structure

Bone structure in mammals involves a complex network of channels (Havers and Volkmann channels) required to nourish the bone marrow cells. This work describes how three-dimensional reconstructions of such systems can be obtained and represented in terms of complex networks. Three important findings are reported: (i) the fact that the channel branching density resembles a power law implies the existence of distribution hubs; (ii) the conditional node degree density indicates a clear tendency of connection between nodes with degrees 2 and 4; and (iii) the application of the recently introduced concept of hierarchical clustering coefficient allows the identification of typical scales of channel redistribution. A series of important biological insights is drawn and discussed

q-bio.TO↗
arXiv2004

Statistical Mechanics Characterization of Neuronal Mosaics

The spatial distribution of neuronal cells is an important requirement for achieving proper neuronal function in several parts of the nervous system of most animals. For instance, specific distribution of photoreceptors and related neuronal cells, particularly the ganglion cells, in mammal's retina is required in order to properly sample the projected scene. This work presents how two concepts from the areas of statistical mechanics and complex systems, namely the \emph{lacunarity} and the \emph{multiscale entropy} (i.e. the entropy calculated over progressively diffused representations of the cell mosaic), have allowed effective characterization of the spatial distribution of retinal cells.

q-bio.NC↗
arXiv2004

Growth-Driven Percolations: The Dynamics of Community Formation in Neuronal Systems

The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the simulation of neuronal development and the formation of neuronal communities. Starting from images of real neurons, geometrical measurements are obtained and used to construct probabilistic models which can be subsequently sampled in order to produce morphologically realistic neuronal cells. Such cells are progressively grown while monitoring their connections along time, which are analysed in terms of percolation concepts. However, unlike traditional percolation, the critical point is verified along the growth stages, not the density of cells, which remains constant throughout the neuronal growth dynamics. It is shown, through simulations, that growing beta cells tend to reach percolation sooner than the alpha counterparts with the same diameter. Also, the percolation becomes more abrupt for higher densities of cells, being markedly sharper for the beta cells.

q-bio.NC↗
arXiv2004

Strength distribution in gradient networks

This article describes a gradient complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown analytically and experimentally that the strength (i.e. the weighted node degree) density of such a network model can be well approximated by a power law with $γ\approx 0.35$. Possible implications for neuronal networks topology and dynamics are also discussed.

cond-mat.dis-nn↗
arXiv2004

Expanded Complex Networks and their Percolations

Given a complex network, its \emph{L-}paths correspond to sequences of $L+1$ distinct nodes connected through $L$ distinct edges. The \emph{L-}conditional expansion of a complex network can be obtained by connecting all its pairs of nodes which are linked through at least one \emph{L-}path, and the respective conditional \emph{L-}expansion of the original network is defined as the intersection between the original network and its \emph{L-}expansion. Such expansions are verified to act as filters enhancing the network connectivity, consequently contributing to the identification of communities in small-world models. It is shown in this paper for L=2 and 3, in both analytical and experimental fashion, that an evolving complex network with fixed number of nodes undergoes successive phase transitions -- the so-called \emph{L-}percolations, giving rise to Eulerian giant clusters. It is also shown that the critical values of such percolations are a function of the network size, and that the networks percolates for L=3 before L=2.

cond-mat.stat-mech↗
arXiv2004

The Heart of Protein-Protein Interaction Networks

Recent developments in complex networks have paved the way to a series of important biological insights, such as the fact that many of the essential proteins of S. cerevisae corresponds to the so-called hubs of the respective protein-protein interaction networks. Despite the special importance of hubs, other types of nodes such as those corresponding to the network border, as well as the innermost nodes, also deserve special attention. This work reports on how the application of the concept of distance transform to networks showed that a great deal of the innermost nodes correspond to essential proteins, with interesting biological implications.

q-bio.MN↗
arXiv2004

Hub-Based Community Finding

This article presents a hub-based approach to community finding in complex networks. After identifying the network nodes with highest degree (the so-called hubs), the network is flooded with wavefronts of labels emanating from the hubs, accounting for the identification of the involved communities. The simplicity and potential of this method, which is presented for direct/undirected and weighted/unweighted networks, is illustrated with respect to the Zachary karate club data, image segmentation, and concept association. Attention is also given to the identification of the boundaries between communities.

cond-mat.stat-mech↗
arXiv2004

Actively-induced percolation: An effective approach to multiple-object systems characterization

The present work proposes the concept of induced percolation over multiple-object systems, so that features such as the number of merged clusters can be used as a relevant measurement. The suggested approach involves the expansion of the objects while monitoring the evolving clusters. The potential of the proposed methodology for characterizing the spatial interaction and distribution between several objects is illustrated with respect to synthetic and real data.

cond-mat.dis-nn↗
arXiv2004

Complex Networks, Simple Vision

This paper proposes and illustrates a general framework to integrate the areas of vision research and complex networks. Each image pixel is associated to a network node and the Euclidean distance between the visual properties (e.g. gray-level intensity, color or texture) at each possible pair of pixels is assigned as the respective edge weight. In addition to investigating the therefore obtained weight and adjacency matrices in terms of node degree densities, it is shown that the combination of the concepts of network hub and \emph{2-}expansion of the adjacency matrix provides an effective means to separate the image elements, a challenging task in computer vision known as segmentation.

cond-mat.stat-mech↗
arXiv2004

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.

cond-mat.stat-mech↗
arXiv2003

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.

cond-mat.stat-mech↗
arXiv2003

An Analytical Approach to Connectivity in Regular Neuronal Networks

This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional orthogonal lattice with parameter $Δ$, it is possible to obtain the exact number of connections and cycles of any length from the autoconvolution function as well as from the respective spectral density derived from the adjacency matrix. It is shown that neuronal shape plays an important role in defining the spatial distribution of synapses in neuronal networks. In addition, we observe that neuromorphic networks typically exhibit an interesting phenomenon where the pattern of connections is progressively shifted along the spatial domain for increasing connection lengths. This is a consequence of the fact that in neurons the axon reference point usually does not coincide with the cell centre of mass. Morphological measurements for characterization of the spatial distribution of connections, including the adjacency matrix spectral density and the lacunarity of the connections, are suggested and illustrated. We also show that Hopfield networks with connectivity defined by different neuronal morphologies, quantified by the proposed analytical approach, lead to distinct performace for associative recall, as measured by the overlap index. The potential of the proposed approach is illustrated with respect to digital images of real neuronal cells.

cond-mat.dis-nn↗
arXiv2003

What's in a name?

Among the several findings deriving from the application of complex network formalism to the investigation of natural phenomena, the fact that linguistic constructions follow power laws presents special interest for its potential implications for psychology and brain science. By corresponding to one of the most essentially human manifestations, such language-related properties suggest that similar dynamics may also be inherent to the brain areas related to language and associative memory, and perhaps even consciousness. The present work reports a preliminary experimental investigation aimed at characterizing and modeling the flow of sequentially induced associations between words from the English language in terms of complex networks. The data is produced through a psychophysical experiment where a word is presented to the subject, who is requested to associate another word. Complex network and graph theory formalism and measurements are applied in order to characterize the experimental data. Several interesting results are identified, including the characterization of attraction basins, association asymmetries, context biasing, as well as a possible power-law underlying word associations, which could be explained by the appearance of strange loops along the hierarchical structure underlying word categories.

cond-mat.dis-nn↗
arXiv2003

Voronoi and Fractal Complex Networks and Their Characterization

Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a natural means for relating such networks with metric spaces, but also a natural means for obtaining fractal complex networks. A series of comprehensive measurements closely related to spatial aspects of these networks is proposed, which includes the effective length, adjacency, as well as the fractal dimension of the network in terms of the spatial scales defined by successive shortest paths starting from a specific node. The potential of such features is illustrated with respect to the random, small-world, scale-free and fractal network models.

cond-mat↗
arXiv2003

Neuromorphometric characterization with shape functionals

This work presents a procedure to extract morphological information from neuronal cells based on the variation of shape functionals as the cell geometry undergoes a dilation through a wide interval of spatial scales. The targeted shapes are alpha and beta cat retinal ganglion cells, which are characterized by different ranges of dendritic field diameter. Image functionals are expected to act as descriptors of the shape, gathering relevant geometric and topological features of the complex cell form. We present a comparative study of classification performance of additive shape descriptors, namely, Minkowski functionals, and the nonadditive multiscale fractal. We found that the proposed measures perform efficiently the task of identifying the two main classes alpha and beta based solely on scale invariant information, while also providing intraclass morphological assessment.

cond-mat↗
arXiv2003

Associative Recall in Non-Randomly Diluted Neuronal Networks

The potential for associative recall of diluted neuronal networks is investigated with respect to several biologically relevant configurations, more specifically the position of the cells along the input space and the spatial distribution of their connections. First we put the asymmetric Hopfield model onto a scale-free Barabasi-Albert network. Then, a geometrical diluted architecture, which maps from L-bit input patterns into $N$-neurons networks, with R=N/L<1 (we adopt R=0.1, 0.2 and 0.3), is considered. The distribution of the connections between cells along the one-dimensional input space follows a normal distribution centered at each cell, in the sense that cells that are closer to each other have increased probability to interconnect. The models also explicitly consider the placement of the neuronal cells along the input space in such a way that denser regions of that space tend to become denser, therefore implementing a special case of the Barabasi-Albert connecting scheme. The obtained results indicate that, for the case of the considered stimuli and noise, the network performance increases with the spatial uniformity of cell distribution.

cond-mat.stat-mech↗
arXiv2003

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of $N$ pixels (bits) each. Application of the network to an initial blurred version of one of $P$ pre-assigned patterns should converge to the correct pattern. In the "standard" Hopfield model, the $N$ "neurons'' are connected to each other via $N^2$ bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with $N^2$. The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabasi-Albert scale-free network, in which each newly added neuron is connected to only $m$ other neurons, and at the end the number of neurons with $q$ neighbours decays as $1/q^3$. Although the quality of retrieval decreases for small $m$, we find good associative memory for $1 \ll m \ll N$. Hence, these networks gain a factor $N/m \gg 1$ in the computer memory and time.

cond-mat.stat-mech↗