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

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.Comment: 3 pages, 1 figure, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.org

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 discussedComment: 3 pages, 1 figure, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.org

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

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.Comment: 8 pages, 10 figure

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

What are the Best Hierarchical Descriptors for Complex Networks?

This work reviews several hierarchical measurements of the topology of complex networks and then applies feature selection concepts and methods in order to quantify the relative importance of each measurement with respect to the discrimination between four representative theoretical network models, namely Erd\"{o}s-R\'enyi, Barab\'asi-Albert, Watts-Strogatz as well as a geographical type of network. The obtained results confirmed that the four models can be well-separated by using a combination of measurements. In addition, the relative contribution of each considered feature for the overall discrimination of the models was quantified in terms of the respective weights in the canonical projection into two dimensions, with the traditional clustering coefficient, hierarchical clustering coefficient and neighborhood clustering coefficient resulting particularly effective. Interestingly, the average shortest path length and hierarchical node degrees contributed little for the separation of the four network models.Comment: 9 pages, 4 figure

A Complex Network Approach to Topographical Connections

The neuronal networks in the mammals cortex are characterized by the coexistence of hierarchy, modularity, short and long range interactions, spatial correlations, and topographical connections. Particularly interesting, the latter type of organization implies special demands on the evolutionary and ontogenetic systems in order to achieve precise maps preserving spatial adjacencies, even at the expense of isometry. Although object of intensive biological research, the elucidation of the main anatomic-functional purposes of the ubiquitous topographical connections in the mammals brain remains an elusive issue. The present work reports on how recent results from complex network formalism can be used to quantify and model the effect of topographical connections between neuronal cells over a number of relevant network properties such as connectivity, adjacency, and information broadcasting. While the topographical mapping between two cortical modules are achieved by connecting nearest cells from each module, three kinds of network models are adopted for implementing intracortical connections (ICC), including random, preferential-attachment, and short-range networks. It is shown that, though spatially uniform and simple, topographical connections between modules can lead to major changes in the network properties, fostering more effective intercommunication between the involved neuronal cells and modules. The possible implications of such effects on cortical operation are discussed.Comment: 5 pages, 5 figure

Transient dynamics for sequence processing neural networks: effect of degree distributions

We derive a analytic evolution equation for overlap parameters including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely retrieved critical loading ratio $\alpha_c = N ^{-1/2}$ is obtained, where $N$ is the network size. In the presence of random networks, our theoretical predictions agree quantitatively with the numerical experiments for delta, binomial, and power-law degree distributions.Comment: 11 pages, 6 figure