Among different aspects of social networks, dynamics have been proposed to simulate how opinions can be transmitted. In this study, we propose a model that simulates the communication in an online social network, in which the posts are created from external information. We considered the nodes and edges of a network as users and their friendship, respectively. A real number is associated with each user representing its opinion. The dynamics starts with a user that has contact with a random opinion, and, according to a given probability function, this individual can post this opinion. This step is henceforth called post transmission. In the next step, called post distribution, another probability function is employed to select the user's friends that could see the post. Post transmission and distribution represent the user and the social network algorithm, respectively. If an individual has contact with a post, its opinion can be attracted or repulsed. Furthermore, individuals that are repulsed can change their friendship through a rewiring. These steps are executed various times until the dynamics converge. Several impressive results were obtained, which include the formation of scenarios of polarization and consensus of opinions. In the case of echo chambers, the possibility of rewiring probability is found to be decisive. However, for particular network topologies, with a well-defined community structure, this effect can also happen. All in all, the results indicate that the post distribution strategy is crucial to mitigate or promote polarization.

As synchronized activity is associated with basic brain functions and pathological states, spike train synchrony has become an important measure to analyze experimental neuronal data. Many measures of spike train synchrony have been proposed, but there is no gold standard allowing for comparison of results from different experiments. This work aims to provide guidance on which synchrony measure is best suited to quantify the effect of epileptiform-inducing substances (e.g., bicuculline, BIC) in in vitro neuronal spike train data. Spike train data from recordings are likely to suffer from erroneous spike detection, such as missed spikes (false negative) or noise (false positive). Therefore, different timescale-dependent (cross-correlation, mutual information, spike time tiling coefficient) and timescale-independent (Spike-contrast, phase synchronization (PS), A-SPIKE-synchronization, A-ISI-distance, ARI-SPIKE-distance) synchrony measures were compared in terms of their robustness to erroneous spike trains. For this purpose, erroneous spike trains were generated by randomly adding (false positive) or deleting (false negative) spikes (in silico manipulated data) from experimental data. In addition, experimental data were analyzed using different spike detection threshold factors in order to confirm the robustness of the synchrony measures. All experimental data were recorded from cortical neuronal networks on microelectrode array chips, which show epileptiform activity induced by the substance BIC. As a result of the in silico manipulated data, Spike-contrast was the only measure that was robust to false-negative as well as false-positive spikes. Analyzing the experimental data set revealed that all measures were able to capture the effect of BIC in a statistically significant way, with Spike-contrast showing the highest statistical significance even at low spike detection thresholds. In summary, we suggest using Spike-contrast to complement established synchrony measures because it is timescale independent and robust to erroneous spike trains.

Several natural and artificial structures, such as human skin and mammals cortices, exhibit a compound organization, with basic elements being distributed along a surface. The problem of quantifying the geometrical uniformity of this type of biological and physical compound structures is addressed in this work. This required the solution of several problems, including the detection, along the surface, of the borders of the compound system, defining the adjacency between the elements in the 3D space, and obtaining a reference of uniformity for calculating the polygonality. Specific approaches were devised and applied to address each of these difficulties, including connectivity criteria ensuring the adjacency to remain within the considered surface as well as the extension of the polygonality, originally suggested for 2D structures, to 3D compound systems. The potential of the so-obtained method is illustrated with respect to compound eyes of fungus gnats (small, forest dwelling flies), and interesting results are reported and discussed, including the fact that the uniformity tends to increase toward the center of the system, and the absence of correlation with two measurements traditionally used for characterizing this type of eyes.

The most beautiful recognizable feature of the toco toucan is its large and colorful bill. Despite its importance, such as in feeding and acting as a thermal regulator, few systematic approaches have been proposed for characterizing its structural organization. A framework for identifying and characterizing the trabecular bone tissue located inside the bill is reported in this work. An image processing pipeline for segmenting the trabecular bones is proposed, followed by the derivation of a 3D coordinate system defined by the shape of the bill. These coordinates are then used for further characterization of the mass distribution inside the bill.

The effect of different interconnecting topologies on the performance of SOM networks is investigated. Three different databases (digits, musical symbols and letters dataset) are considered, and small world, correlated models, and the deactivation network topologies were taken into account. We show that the topology has a definite influence on the performance of the network at short and middle learning time scales. The addition of long-range connections in the deactivation model tended to reduce accuracy. In addition, we examined the effect of degree-degree correlations, or assortativity, on SOM neural networks. It has been shown that high assortativity values tend to decrease the classification error.

Complex networks have been found to provide a good representation of the structure of knowledge, as understood in terms of discoverable concepts and their relationships. In this context, the discovery process can be modeled as agents walking in a knowledge space. Recent studies proposed more realistic dynamics, including the possibility of agents being influenced by others with higher visibility or by their own memory. However, rather than dealing with these two concepts separately, as previously approached, in this study we propose a multi-agent random walk model for knowledge acquisition that incorporates both concepts. More specifically, we employed the true self avoiding walk alongside a new dynamics based on jumps, in which agents are attracted by the influence of others. That was achieved by using a L\'evy flight influenced by a field of attraction emanating from the agents. In order to evaluate our approach, we use a set of network models and two real networks, one generated from Wikipedia and another from the Web of Science. The results were analyzed globally and by regions. In the global analysis, we found that most of the dynamics parameters do not significantly affect the discovery dynamics. The local analysis revealed a substantial difference of performance depending on the network regions where the dynamics are occurring. In particular, the dynamics at the core of networks tend to be more effective. The choice of the dynamics parameters also had no significant impact to the acquisition performance for the considered knowledge networks, even at the local scale.

The shape of a neuron can reveal many interesting properties about its function. Therefore, organizing neuronal cells into appropriate classes according to their respective shape is a fundamental endeavor in neuroscience. Available online datasets allow new data-oriented approaches to solve such neuroscience problems. Here we analyze the feasibility of classifying neurons according not to their respective wholes, but to its constituent parts. Such a study may reveal interesting insights, including whether parts of the neuronal dendritic arborization preserve proper information about the morphology of the whole neuron. Experimental results using open datasets are reported, thus corroborating our approach.

Much work has been done in the field of texture analysis and classification. While promising classification methods have been proposed, most of them rely on classical image analysis approaches. This paper presents a texture classification method based on diffusion in directed networks. First, an image is modeled as a directed network by mapping each pixel as a node and connecting two nodes up to a maximum distance r. To reveal texture properties, links between two nodes are removed based on the pixel intensity difference. Once such a network is obtained, the activity of each node is estimated by random walks and combined into a histogram to describe the image. The main contribution of this paper is the use of directed networks, which tends to provide better performance than in undirected cases. Also, we have shown that the activity induced on these networks can be effectively used as texture descriptor. Experimental results show that the proposed method is favorably compared to traditional texture methods on widely used texture datasets. The proposed method is also found to be promising for plant species classification using samples of leaf texture.

Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify the symmetries around nodes, which we call connectivity patterns. We develop two topological transformations that allow a concise characterization of the different types of symmetry appearing on networks and apply these concepts to six network models, namely the Erd\H{o}s-R\'enyi, Barab\'asi-Albert, random geometric graph, Waxman, Voronoi and rewired Voronoi. Real-world networks, namely the scientific areas of Wikipedia, the world-wide airport network and the street networks of Oldenburg and San Joaquin, are also analyzed in terms of the proposed symmetry measurements. Several interesting results emerge from this analysis, including the high symmetry exhibited by the Erd\H{o}s-R\'enyi model. Additionally, we found that the proposed measurements present low correlation with other traditional metrics, such as node degree and betweenness centrality. Principal component analysis is used to combine all the results, revealing that the concepts presented here have substantial potential to also characterize networks at a global scale.

Positional information in developing embryos is specified by spatial gradients of transcriptional regulators. One of the classic systems for studying this is the activation of the hunchback (hb) gene in early fruit fly (Drosophila) segmentation by the maternally-derived gradient of the Bicoid (Bcd) protein. Gene regulation is subject to intrinsic noise which can produce variable expression. This variability must be constrained in the highly reproducible and coordinated events of development. We identify means by which noise is controlled during gene expression by characterizing the dependence of hb mRNA and protein output noise on hb promoter structure and transcriptional dynamics. We use a stochastic model of the hb promoter in which the number and strength of Bcd and Hb (self-regulatory) binding sites can be varied. Model parameters are fit to data from WT embryos, the self-regulation mutant hb(14F), and lacZ reporter constructs using different portions of the hb promoter. We have corroborated model noise predictions experimentally. The results indicate that WT (self-regulatory) Hb output noise is predominantly dependent on the transcription and translation dynamics of its own expression, rather than on Bcd fluctuations. The constructs and mutant, which lack self-regulation, indicate that the multiple Bcd binding sites in the hb promoter (and their strengths) also play a role in buffering noise. The model is robust to the variation in Bcd binding site number across a number of fly species. This study identifies particular ways in which promoter structure and regulatory dynamics reduce hb output noise. Insofar as many of these are common features of genes (e.g. multiple regulatory sites, cooperativity, self-feedback), the current results contribute to the general understanding of the reproducibility and determinacy of spatial patterning in early development.

MOTIVATION: The necessity to characterize the spatial uniformity (or lack of it) of symbols in biological sequences, given its implications for identification of the properties of the structures associated with the sequences. METHODS: A one-dimensional version of a recently introduced percolation-based approach is presented, which allows the accurate quantification of symbol distributions even in the presence of co-existing densities. An enhanced version of this methodology, which uses an agglomerative process to organize hierarchically the sequence into subsequences, is also proposed and illustrated. 3. RESULTS: The potential of the proposed methodology is illustrated with respect to synthetic and real data (1881 zebrafish and 1200 Xenopus proteins) and compared to two alternative multiscale methodologies, with encouraging results including the possibility to identify particularly remarkable amino acid arrangements in proteins. 4. CONTACT: [email protected].

MOTIVATION: The need is to visualize and quantify gene expression spatial patterns. Because of their generality for representation of interaction among several elements, complex networks are used to measure the spatial interactions and adjacencies defined by gene expression patterns. RESULTS: Enhanced visualization of spatial interactions between elements where genes are expressed is possible, allowing the identification of structures which would go unnoticed by using conventional imaging. The quantification of the expression intensity in terms of the node degree and clustering coefficient allows the identification of different types of interactions, yielding insights about cell signaling and differentiation, and providing the basis for comparison and discrimination of the patterns along the developmental stages. AVAILABILITY: Supplementary Material, including visualizations as well as the basic routines for translating gene expression images into complex networks and obtaining node degree and clustering coefficient measurements, are provided. CONTACT: [email protected]; [email protected].

MOTIVATION: The importance of a systematic methodology for the mathematical characterization of three-dimensional gene expression patterns in embryonic development. METHODS: By combining lacunarity and multiscale fractal dimension analyses with computer-based methods of three-dimensional reconstruction, it becomes possible to extract new information from in situ hybridization studies. Lacunarity and fractality are appropriate measures for the cloud-like gene activation signals in embryonic tissues. The newly introduced multiscale method provides a natural extension of the fractal dimension concept, being capable of characterizing the fractality of geometrical patterns in terms of spatial scale. This tool can be systematically applied to three-dimensional patterns of gene expression. RESULTS: Applications are illustrated using the three-dimensional expression patterns of the myogenic marker gene Myf5 in a series of differentiating somites of a mouse embryo.

Dynamic shapes represent an important issue in several scientific and technological contexts. The current article presents a model-based mathematic-computational approach for inferring the processes of neural evolution, including analytical mappings, convolution models and normal wavefront propagation, illustrated with respect to stationary and non-stationary evolutions along time and space.

The estimation of the number of people in an area under surveillance is very important for the problem of crowd monitoring. When an area reaches an occupation level greater than the projected one, people's safety can be in danger. This paper describes a new technique for crowd density estimation based on Minkowski fractal dimension. The fractal dimension has been widely used to characterize data texture in a large number of physical and biological sciences. The results of our experiments show that fractal dimension can also be used to characterize levels of people congestion in images of crowds. The proposed technique is compared with a statistical and a spectral technique, in a test study of nearly 300 images of a specific area of the Liverpool Street Railway Station, London, UK. Results obtained in this test study are presented.

This paper presents a technique for oriented texture classification which is based on the Hough transform and Kohonen's (1990) neural network model. In this technique, oriented texture features are extracted from the Hough space by means of two distinct strategies. While the first operates on a non-uniformly sampled Hough space, the second concentrates on the peaks produced in the Hough space. The described technique gives good results for the classification of oriented textures, a common phenomenon in nature underlying an important class of images. Experimental results are presented to demonstrate the performance of the new technique in comparison with an implemented technique based on Gabor filters.

This paper reports the development of a cost-effective framework for the implementation of a versatile computer vision system, namely the Cyvis-1. Presenting a strong biological motivation, the Cyvis-1 approach is characterized by the multi-stage integration paradigm, which is inherently suitable for parallelization and representation through the OOP/GUI concepts. A model for the parallelization of this system has been developed that incorporates multitasking, distributed processors, and message interchange through channels. The implementation of each of these parallel features in IBM-PC compatible machines running under Windows 95/NT has been described. An application example of RGB image edge and line detection has been presented and assessed in terms of execution time, efficiency of hardware utilization and speed-up.

This paper presents how morphologically more realistic artificial neural networks have been obtained by using vectorial-stochastic grammars and used as subsidies for modeling biological neural systems and developing novel artificial neural structures. The paper includes the description of the vectorial-stochastic grammars, a review of the primate striate cortex, a mathematical analysis of the principles underlying orientation encoding by centric domains, and the development and application of morphologically realistic neural centric models of orientation encoding.

We present a new approach to shape representation and analysis, which consists in treating the contour of a 2D shape as an 1D signal and analyzing it with the 1D continuous wavelet transform. Application is made to the detection of corners, natural scales and fractal behavior in 2D shapes.

This work presents a new approach to shape characterization and analysis based on multiscale bending energy. Shapes are represented by their outlines and their respective multiscale curvatures, i.e. the curvegram, are estimated by using a scheme based on Fourier descriptors. The shrinkage problem is circumvented through perimeter normalization, which is crucial for allowing the quantitative analysis of the curvegram. Local and global multiscale bending energies are calculated from the curvegram, and the latter (i.e. global energy) is used in order to define the natural scales of the shape under analysis. Several issues concerning multiscale curvature quantitative analysis are discussed. The results regarding the application of the proposed technique to neuromorphometry are presented and discussed.