Small-world Structure in Children’s Featured Semantic Networks

Background: Knowing the development pattern of children’s language is applicable in developmental psychology. Network models of language are helpful for the identification of these patterns. Objectives: We examined the small-world properties of featured semantic networks of developing children. Materials & Methods: In this longitudinal study, the featured semantic networks of children aged 18-30 months were obtained using R software version 3.5.2 and the igraph software package. The data of 2000 English (British)-speaking children, half boy and half girls, were gathered from existing databases of MCDI (between 2000 and 2007) and McRae feature norms. The growth pattern of these networks was illustrated by graph measures. Comparing these measures with those of the reference random networks, the small-world structure can be examined. Results: To have a comparison between path length and clustering coefficient of featured semantic networks with those of random networks, we computed the Q quotient. The results showed that the values of the Q quotient at 18, 22, 26, and 30 months of age were all more than 1, which confirms the small-world characteristic of the networks. Conclusion: Featured semantic networks of children exhibited a small-world structure, in which there was a local structure in the form of clusters of words. For global access, some words act as bridges connecting semantically distant clusters. These networks possess small-world property from the early months of age. The small-world structure cannot be seen in the less dense networks built with a higher cut-off threshold.

Three-State Majority-Vote Model on Small-World Networks

In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1−q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing the dissensus among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We employ Monte Carlo simulations to investigate the second-order phase transition of the system, and obtain the critical noise qc, as well as the standard critical exponents β/ν, γ/ν, and 1/ν for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

Inferring long-distance connectivity shaped by air-mass movement for improved experimental design in aerobiology

The collection and analysis of air samples for the study of microbial airborne communities or the detection of airborne pathogens is one of the few insights that we can grasp of a continuously moving flux of microorganisms from their sources to their sinks through the atmosphere. For large-scale studies, a comprehensive sampling of the atmosphere is beyond the scopes of any reasonable experimental setting, making the choice of the sampling locations and dates a key factor for the representativeness of the collected data. In this work we present a new method for revealing the main patterns of air-mass connectivity over a large geographical area using the formalism of spatio-temporal networks, that are particularly suitable for representing complex patterns of connection. We use the coastline of the Mediterranean basin as an example. We reveal a temporal pattern of connectivity over the study area with regions that act as strong sources or strong receptors according to the season of the year. The comparison of the two seasonal networks has also allowed us to propose a new methodology for comparing spatial weighted networks that is inspired from the small-world property of non-spatial networks.

Models And Mining Of On-Line Social Networks

Power law degree distribution, the small world property, and bad spectral expansion are three of the most important properties of On-line Social Networks (OSNs). We sampled YouTube and Wikipedia to investigate OSNs. Our simulation and computational results support the conclusion that OSNs follow a power law degree distribution, have the small world property, and bad spectral expansion. We calculated the diameters and spectral gaps of OSNs samples, and compared these to graphs generated by the GEO-P model. Our simulation results support the Logarithmic Dimension Hypothesis, which conjectures that the dimension of OSNs is m = [log N]. We introduced six GEO-P type models. We ran simulations of these GEO-P-type models, and compared the simulated graphs with real OSN data. Our simulation results suggest that, except for the GEO-P (GnpDeg) model, all our models generate graphs with power law degree distributions, the small world property, and bad spectral expansion.

Models And Mining Of On-Line Social Networks

Power law degree distribution, the small world property, and bad spectral expansion are three of the most important properties of On-line Social Networks (OSNs). We sampled YouTube and Wikipedia to investigate OSNs. Our simulation and computational results support the conclusion that OSNs follow a power law degree distribution, have the small world property, and bad spectral expansion. We calculated the diameters and spectral gaps of OSNs samples, and compared these to graphs generated by the GEO-P model. Our simulation results support the Logarithmic Dimension Hypothesis, which conjectures that the dimension of OSNs is m = [log N]. We introduced six GEO-P type models. We ran simulations of these GEO-P-type models, and compared the simulated graphs with real OSN data. Our simulation results suggest that, except for the GEO-P (GnpDeg) model, all our models generate graphs with power law degree distributions, the small world property, and bad spectral expansion.

Optimisation of the coalescent hyperbolic embedding of complex networks

Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between the nodes. A remarkable network model generating random graphs along this line is the popularity-similarity optimisation (PSO) model, offering a scale-free degree distribution, high clustering and the small-world property at the same time. These results provide a strong motivation for the development of hyperbolic embedding algorithms, that tackle the problem of finding the optimal hyperbolic coordinates of the nodes based on the network structure. A very promising recent approach for hyperbolic embedding is provided by the noncentered minimum curvilinear embedding (ncMCE) method, belonging to the family of coalescent embedding algorithms. This approach offers a high-quality embedding at a low running time. In the present work we propose a further optimisation of the angular coordinates in this framework that seems to reduce the logarithmic loss and increase the greedy routing score of the embedding compared to the original version, thereby adding an extra improvement to the quality of the inferred hyperbolic coordinates.

Anhedonia Relates to the Altered Global and Local Grey Matter Network Properties in Schizophrenia

Anhedonia is one of the major negative symptoms in schizophrenia and defined as the loss of hedonic experience to various stimuli in real life. Although structural magnetic resonance imaging has provided a deeper understanding of anhedonia-related abnormalities in schizophrenia, network analysis of the grey matter focusing on this symptom is lacking. In this study, single-subject grey matter networks were constructed in 123 patients with schizophrenia and 160 healthy controls. The small-world property of the grey matter network and its correlations with the level of physical and social anhedonia were evaluated using graph theory analysis. In the global scale whole-brain analysis, the patients showed reduced small-world property of the grey matter network. The local-scale analysis further revealed reduced small-world property in the default mode network, salience/ventral attention network, and visual network. The regional-level analysis showed an altered relationship between the small-world properties and the social anhedonia scale scores in the cerebellar lobule in patients with schizophrenia. These results indicate that anhedonia in schizophrenia may be related to abnormalities in the grey matter network at both the global whole-brain scale and local–regional scale.

Regional radiomics similarity networks (R2SNs) in the human brain: reproducibility, small-world properties and a biological basis

Background: A structural covariance network (SCN) has been used successfully to structural magnetic resonance imaging (MRI) studies. However, most SCNs were constructed by a unitary marker that was insensitive for discriminating different disease phases. The aim of this study was to devise a novel regional radiomics similarity network (R2SN) that could provide more comprehensive information in morphological network analysis. Methods: R2SNs were constructed by computing the Pearson correlations between the radiomics features extracted from any pair of regions for each subject. We further assessed the small-world property of R2SNs using the graph theory method, and we evaluated the reproducibility in different datasets and the reliability of the R2SNs through test-retest analysis. The relationship between the R2SNs and interregional coexpression of enriched genes was also explored, as well as the relationship with general intelligence. Results: R2SNs could be replicated in different datasets, regardless of the use of different feature subsets. R2SNs showed high reliability in the test-retest analysis (intraclass correlation coefficient (ICC)>0.7). In addition, the small-word property (σ>2) and the high correlation between gene expression (R=0.24, P<0.001) and general intelligence were determined for R2SNs. Conclusion: R2SNs provides a novel, reliable, and biologically plausible method to understand human morphological covariance based on structural MRI.

Characterizing several properties of high-dimensional random Apollonian networks

In this article, we investigate several properties of high-dimensional random Apollonian networks, including two types of degree profiles, the small-world effect (clustering property), sparsity and three distance-based metrics. The characterizations of the degree profiles are based on several rigorous mathematical and probabilistic methods, such as a two-dimensional mathematical induction, analytic combinatorics and Pólya urns, etc. The small-world property is uncovered by a well-developed measure—local clustering coefficient and the sparsity is assessed by a proposed Gini index. Finally, we look into three distance-based properties; they are total depth, diameter and Wiener index.