Frequency-based brain networks: From a multiplex framework to a full multilayer description

We explore how to study dynamical interactions between brain regions using functional multilayer networks whose layers represent the different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as a multilayer network in which all brain regions can interact with each other at different frequency bands, instead of as a multiplex network, in which interactions between different frequency bands are only allowed within each brain region and not between them. We study the second smallest eigenvalue of the combinatorial supra-Laplacian matrix of the multilayer network in detail, and we thereby show that the heterogeneity of interlayer edges and, especially, the fraction of missing edges crucially modify the spectral properties of the multilayer network. We illustrate our results with both synthetic network models and real data sets obtained from resting state magnetoencephalography. Our work demonstrates an important issue in the construction of frequency-based multilayer brain networks.Comment: 13 pages, 8 figure

Missing data in multiplex networks: a preliminary study

A basic problem in the analysis of social networks is missing data. When a network model does not accurately capture all the actors or relationships in the social system under study, measures computed on the network and ultimately the final outcomes of the analysis can be severely distorted. For this reason, researchers in social network analysis have characterised the impact of different types of missing data on existing network measures. Recently a lot of attention has been devoted to the study of multiple-network systems, e.g., multiplex networks. In these systems missing data has an even more significant impact on the outcomes of the analyses. However, to the best of our knowledge, no study has focused on this problem yet. This work is a first step in the direction of understanding the impact of missing data in multiple networks. We first discuss the main reasons for missingness in these systems, then we explore the relation between various types of missing information and their effect on network properties. We provide initial experimental evidence based on both real and synthetic data.Comment: 7 page

Predicting real-time roadside CO and NO2 concentrations using neural networks

The main aim of this paper is to develop a model based on neural network (NN) theory to estimate real-time roadside CO and $hbox{NO}_{2}$ concentrations using traffic and meteorological condition data. The location of the study site is at a road intersection in Melton Mowbray, which is a town in Leicestershire, U.K. Several NNs, which can be classified into three types, namely, the multilayer perceptron, the radial basis function, and the modular network, were developed to model the nonlinear relationships that exist in the pollutant concentrations. Their performances are analyzed and compared. The transferability of the developed models is studied using data collected from a road intersection in another city. It was concluded that all NNs provide reliable estimates of pollutant concentrations using limited information and noisy data

Predicting real-time roadside CO and NO2 concentrations using neural networks

The main aim of this paper is to develop a model based on neural network (NN) theory to estimate real-time roadside CO and $hbox{NO}_{2}$ concentrations using traffic and meteorological condition data. The location of the study site is at a road intersection in Melton Mowbray, which is a town in Leicestershire, U.K. Several NNs, which can be classified into three types, namely, the multilayer perceptron, the radial basis function, and the modular network, were developed to model the nonlinear relationships that exist in the pollutant concentrations. Their performances are analyzed and compared. The transferability of the developed models is studied using data collected from a road intersection in another city. It was concluded that all NNs provide reliable estimates of pollutant concentrations using limited information and noisy data

Technological Innovation Performance Analysis Using Multilayer Networks: Evidence from the Printer Industry

Department of Management EngineeringThe importance of collaboration and technology boundary spanning has been emphasized in other inquiries into technological innovation. Therefore, this research project first tried to investigate the effect of collaboration on technology boundary spanning. Then, we investigated the effect of collaboration and technology boundary spanning on technological innovation within a firm by using a multilayer network to analyze patent data. The aim of this paper is to provide new insight into the process of analyzing patent data using multilayer networks. This empirical study is based on a sample of 408 firms within the printer industry from 1996 to 2005. Starting with a theoretical discussion of R&D collaboration, technology boundary spanning and innovation performance, the importance of a firm???s collaboration and technology boundary spanning in its technology innovation performance was empirically analyzed using patent data. We followed changes in collaboration networks, technology class networks and the connection between them and tried to find the meaning of those changes in firms??? technology innovation performances. We used degree centrality within the collaboration network and the ratio of collaborated patents to the total number of patents in order to measure a firm???s collaboration and formulated technology boundary spanning represented by exploitation and exploration by using edges of the multilayer network. As dependent variables, we used the number of patents and the average number of citations received over three, five, and 10 years to measure the firm???s quantitative and qualitative innovation performance respectively. The results of the analysis can be summarized as follows: a firm???s collaboration has positive effects on both exploitation and exploration. Firms with more collaborations show higher quantitative innovation performances while firms with more collaborations exhibit lower qualitative innovation performance. Exploitation has a positive impact on a firm???s quantitative innovation performance while exploration has negative effects on a firm???s quantitative innovation performance. The relationship between a firm???s exploration activities and a firm???s qualitative innovation performance manifests as an inverted U-shape. On the other hand, a firm???s exploitation activities have a U-shape relationship with the firm???s qualitative innovation performance. The implication of this study is that multilayer networks can be used to analyze patent data. This study used multilayer networks to formulate the exploitation and exploration only. However, in further research it can be utilized to find the hub firms that fuse technologies.clos

Multilayer weighted social network model

Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out to be overlapping. This implies that the society has a multilayered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of interlayer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multilayer WSN model, where the indirect interlayer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved.Comment: 9 pages, 9 figure

Hidden geometric correlations in real multiplex networks

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the individual layers. We find that these correlations are strong in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate: (i) the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers; (ii) accurate trans-layer link prediction, where connections in one layer can be predicted by observing the hidden geometric space of another layer; and (iii) efficient targeted navigation in the multilayer system using only local knowledge, which outperforms navigation in the single layers only if the geometric correlations are sufficiently strong. Our findings uncover fundamental organizing principles behind real multiplexes and can have important applications in diverse domains.Comment: Supplementary Materials available at http://www.nature.com/nphys/journal/v12/n11/extref/nphys3812-s1.pd