Validation of network communicability metrics for the analysis of brain structural networks.

Computational network analysis provides new methods to analyze the brain's structural organization based on diffusion imaging tractography data. Networks are characterized by global and local metrics that have recently given promising insights into diagnosis and the further understanding of psychiatric and neurologic disorders. Most of these metrics are based on the idea that information in a network flows along the shortest paths. In contrast to this notion, communicability is a broader measure of connectivity which assumes that information could flow along all possible paths between two nodes. In our work, the features of network metrics related to communicability were explored for the first time in the healthy structural brain network. In addition, the sensitivity of such metrics was analysed using simulated lesions to specific nodes and network connections. Results showed advantages of communicability over conventional metrics in detecting densely connected nodes as well as subsets of nodes vulnerable to lesions. In addition, communicability centrality was shown to be widely affected by the lesions and the changes were negatively correlated with the distance from lesion site. In summary, our analysis suggests that communicability metrics that may provide an insight into the integrative properties of the structural brain network and that these metrics may be useful for the analysis of brain networks in the presence of lesions. Nevertheless, the interpretation of communicability is not straightforward; hence these metrics should be used as a supplement to the more standard connectivity network metrics.

Transition to parenthood: The role of social interaction and endogenous networks

Empirical studies indicate that the transition to parenthood is influenced by an individual's peer group. To study the mechanisms creating interdepen- dencies across individuals' transition to parenthood and its timing we apply an agent-based simulation model. We build a one-sex model and provide agents with three different characteristics regarding age, intended education and parity. Agents endogenously form their network based on social closeness. Network members then may influence the agents' transition to higher parity levels. Our numerical simulations indicate that accounting for social inter- actions can explain the shift of first-birth probabilities in Austria over the period 1984 to 2004. Moreover, we apply our model to forecast age-specific fertility rates up to 2016.

Modelling non-industrial private forest landowners' strategic decision making by using logistic regression and neural networks: case of predicting the choice of forest taxation basis

Summary

Comparison between artificial neural networks and maximum likelihood classification in digital soil mapping

Soil surveys are the main source of spatial information on soils and have a range of different applications, mainly in agriculture. The continuity of this activity has however been severely compromised, mainly due to a lack of governmental funding. The purpose of this study was to evaluate the feasibility of two different classifiers (artificial neural networks and a maximum likelihood algorithm) in the prediction of soil classes in the northwest of the state of Rio de Janeiro. Terrain attributes such as elevation, slope, aspect, plan curvature and compound topographic index (CTI) and indices of clay minerals, iron oxide and Normalized Difference Vegetation Index (NDVI), derived from Landsat 7 ETM+ sensor imagery, were used as discriminating variables. The two classifiers were trained and validated for each soil class using 300 and 150 samples respectively, representing the characteristics of these classes in terms of the discriminating variables. According to the statistical tests, the accuracy of the classifier based on artificial neural networks (ANNs) was greater than of the classic Maximum Likelihood Classifier (MLC). Comparing the results with 126 points of reference showed that the resulting ANN map (73.81 %) was superior to the MLC map (57.94 %). The main errors when using the two classifiers were caused by: a) the geological heterogeneity of the area coupled with problems related to the geological map; b) the depth of lithic contact and/or rock exposure, and c) problems with the environmental correlation model used due to the polygenetic nature of the soils. This study confirms that the use of terrain attributes together with remote sensing data by an ANN approach can be a tool to facilitate soil mapping in Brazil, primarily due to the availability of low-cost remote sensing data and the ease by which terrain attributes can be obtained.

Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.

Artificial neural networks applied for soil class prediction in mountainous landscape of the Serra do Mar¹

Soil information is needed for managing the agricultural environment. The aim of this study was to apply artificial neural networks (ANNs) for the prediction of soil classes using orbital remote sensing products, terrain attributes derived from a digital elevation model and local geology information as data sources. This approach to digital soil mapping was evaluated in an area with a high degree of lithologic diversity in the Serra do Mar. The neural network simulator used in this study was JavaNNS and the backpropagation learning algorithm. For soil class prediction, different combinations of the selected discriminant variables were tested: elevation, declivity, aspect, curvature, curvature plan, curvature profile, topographic index, solar radiation, LS topographic factor, local geology information, and clay mineral indices, iron oxides and the normalized difference vegetation index (NDVI) derived from an image of a Landsat-7 Enhanced Thematic Mapper Plus (ETM+) sensor. With the tested sets, best results were obtained when all discriminant variables were associated with geological information (overall accuracy 93.2 - 95.6 %, Kappa index 0.924 - 0.951, for set 13). Excluding the variable profile curvature (set 12), overall accuracy ranged from 93.9 to 95.4 % and the Kappa index from 0.932 to 0.948. The maps based on the neural network classifier were consistent and similar to conventional soil maps drawn for the study area, although with more spatial details. The results show the potential of ANNs for soil class prediction in mountainous areas with lithological diversity.

Absence of epidemic threshold in scale free networks with degree correlations

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide for the susceptible-infected-susceptible model an exact result showing that a scale-free degree distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or disassortative mixing. Degree correlations result therefore irrelevant for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbors degree, enforced by the degree detailed balance condition.

Synchronization reveals topological scales in complex networks

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Percolation and epidemic thresholds in clustered networks

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks, thus extending this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.

Clustering in complex networks. I. General formalism

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two¿and not just one¿vertices. The formalism is completed with the definition of a three-vertex correlation function, which is the fundamental quantity describing the properties of clustered networks. The formalism suggests different metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of this formalism and the metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the weak and the strong transitivity classes. In the first class, edge multiplicity is small, with triangles being disjoint. In the second class, edge multiplicity is high and so triangles share many edges. As we shall see in the following paper, the class a network belongs to has strong implications in its percolation properties.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edgesthat is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

Clustering in complex networks. II. Percolation properties

The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows us to find the critical threshold and the size of the giant component. Numerical simulations confirm the accuracy of our results. In more general terms, we show that weak clustering hinders the onset of the giant component whereas strong clustering favors its appearance. This is a direct consequence of the differences in the k-core structure of the networks, which are found to be totally different depending on the level of clustering. An empirical analysis of a real social network confirms our predictions.