Synchronization is optimal in non-diagonalizable networks

We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of non-diagonalizable networks. We then show that, unless some oscillator is connected to all the others, networks of maximum synchronizability are necessarily non-diagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths. The extension makes the formalism applicable to all possible network structures, while the maximization results provide insights into hierarchical structures observed in complex networks in which synchronization plays a significant role.Comment: 4 pages, 1 figure; minor revisio

Correlation filtering in financial time series

We apply a method to filter relevant information from the correlation coefficient matrix by extracting a network of relevant interactions. This method succeeds to generate networks with the same hierarchical structure of the Minimum Spanning Tree but containing a larger amount of links resulting in a richer network topology allowing loops and cliques. In Tumminello et al. \cite{TumminielloPNAS05}, we have shown that this method, applied to a financial portfolio of 100 stocks in the USA equity markets, is pretty efficient in filtering relevant information about the clustering of the system and its hierarchical structure both on the whole system and within each cluster. In particular, we have found that triangular loops and 4 element cliques have important and significant relations with the market structure and properties. Here we apply this filtering procedure to the analysis of correlation in two different kind of interest rate time series (16 Eurodollars and 34 US interest rates).Comment: 10 pages 7 figure

Link Clustering with Extended Link Similarity and EQ Evaluation Division.

Link Clustering (LC) is a relatively new method for detecting overlapping communities in networks. The basic principle of LC is to derive a transform matrix whose elements are composed of the link similarity of neighbor links based on the Jaccard distance calculation; then it applies hierarchical clustering to the transform matrix and uses a measure of partition density on the resulting dendrogram to determine the cut level for best community detection. However, the original link clustering method does not consider the link similarity of non-neighbor links, and the partition density tends to divide the communities into many small communities. In this paper, an Extended Link Clustering method (ELC) for overlapping community detection is proposed. The improved method employs a new link similarity, Extended Link Similarity (ELS), to produce a denser transform matrix, and uses the maximum value of EQ (an extended measure of quality of modularity) as a means to optimally cut the dendrogram for better partitioning of the original network space. Since ELS uses more link information, the resulting transform matrix provides a superior basis for clustering and analysis. Further, using the EQ value to find the best level for the hierarchical clustering dendrogram division, we obtain communities that are more sensible and reasonable than the ones obtained by the partition density evaluation. Experimentation on five real-world networks and artificially-generated networks shows that the ELC method achieves higher EQ and In-group Proportion (IGP) values. Additionally, communities are more realistic than those generated by either of the original LC method or the classical CPM method

An Adaptive Complex Network Model for Brain Functional Networks

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution

Analysis of the Structure and Dynamics of European Flight Networks

We analyze structure and dynamics of flight networks of 50 airlines active in the European airspace in 2017. Our analysis shows that the concentration of the degree of nodes of different flight networks of airlines is markedly heterogeneous among airlines reflecting heterogeneity of the airline business models. We obtain an unsupervised classification of airlines by performing a hierarchical clustering that uses a correlation coefficient computed between the average occurrence profiles of 4-motifs of airline networks as similarity measure. The hierarchical tree is highly informative with respect to properties of the different airlines (for example, the number of main hubs, airline participation to intercontinental flights, regional coverage, nature of commercial, cargo, leisure or rental airline). The 4-motif patterns are therefore distinctive of each airline and reflect information about the main determinants of different airlines. This information is different from what can be found looking at the overlap of directed links

Experimental study of a similarity metric for retrieving pieces from structured plan cases: its role in the originality of plan case solutions

This paper describes a quantitative similarity metric and its contribution to achieve original plan solutions. This similarity metric is used by an iterative process of piece retrieval from structured plan cases. Within our approach plan cases are tree-like networks of pieces (goals and actions). These case pieces are ill-related each other by links (explanations). These links may be classified as hierarchical or temporal, antecedent or consequent, and explicit or implicit. Besides links, each case piece has also information about its properties (the attributes-value pairs), its hierarchical and temporal position in the case (the address), and about its constraints in the relationship with others (the constraints). The similarity metric computes a similarity value between two case pieces taking into account similarities between these case piece’s information types. Each time a problem is proposed, different weights are given to some of those similarities, with the aim of solving it with an original solution. This similarity metric is used by the system INSPIRER (ImagiNation taking as Source Past and Imperfectly REalated Reasonings). We illustrate the role of the similarity metric in the creativity of solutions, focusing specially their originality, with the presentation of the experimental results obtained in the musical composition domain, which is considered by us as a planning domain

Learning Heterogeneous Network Embedding From Text and Links

Finding methods to represent multiple types of nodes in heterogeneous networks is both challenging and rewarding, as there is much less work in this area compared with that of homogeneous networks. In this paper, we propose a novel approach to learn node embedding for heterogeneous networks through a joint learning framework of both network links and text associated with nodes. A novel attention mechanism is also used to make good use of text extended through links to obtain much larger network context. Link embedding is first learned through a random-walk-based method to process multiple types of links. Text embedding is separately learned at both sentence level and document level to capture salient semantic information more comprehensively. Then, both types of embeddings are jointly fed into a hierarchical neural network model to learn node representation through mutual enhancement. The attention mechanism follows linked edges to obtain context of adjacent nodes to extend context for node representation. The evaluation on a link prediction task in a heterogeneous network data set shows that our method outperforms the current state-of-the-art method by 2.5%-5.0% in AUC values with p-value less than 10 -9 , indicating very significant improvement