Identifying network structure similarity using spectral graph theory

Beyond nothingness in the formation and functional relevance of voids in polymer films

Voids-the nothingness-broadly exist within nanomaterials and impact properties ranging from catalysis to mechanical response. However, understanding nanovoids is challenging due to lack of imaging methods with the needed penetration depth and spatial resolution. Here, we integrate electron tomography, morphometry, graph theory and coarse-grained molecular dynamics simulation to study the formation of interconnected nanovoids in polymer films and their impacts on permeance and nanomechanical behaviour. Using polyamide membranes for molecular separation as a representative system, three-dimensional electron tomography at nanometre resolution reveals nanovoid formation from coalescence of oligomers, supported by coarse-grained molecular dynamics simulations. Void analysis provides otherwise inaccessible inputs for accurate fittings of methanol permeance for polyamide membranes. Three-dimensional structural graphs accounting for the tortuous nanovoids within, measure higher apparent moduli with polyamide membranes of higher graph rigidity. Our study elucidates the significance of nanovoids beyond the nothingness, impacting the synthesis‒morphology‒function relationships of complex nanomaterials.

Metrics for network comparison using egonet feature distributions

Identifying networks with similar characteristics in a given ensemble, or detecting pattern discontinuities in a temporal sequence of networks, are two examples of tasks that require an effective metric capable of quantifying network (dis)similarity. Here we propose a method based on a global portrait of graph properties built by processing local nodes features. More precisely, a set of dissimilarity measures is defined by elaborating the distributions, over the network, of a few egonet features, namely the degree, the clustering coefficient, and the egonet persistence. The method, which does not require the alignment of the two networks being compared, exploits the statistics of the three features to define one- or multi-dimensional distribution functions, which are then compared to define a distance between the networks. The effectiveness of the method is evaluated using a standard classification test, i.e., recognizing the graphs originating from the same synthetic model. Overall, the proposed distances have performances comparable to the best state-of-the-art techniques (graphlet-based methods) with similar computational requirements. Given its simplicity and flexibility, the method is proposed as a viable approach for network comparison tasks.

A dynamical graph-based feature extraction approach to enhance mental task classification in brain-computer interfaces

Graph theoretic approaches in analyzing spatiotemporal dynamics of brain activities are under-studied but could be very promising directions in developing effective brain-computer interfaces (BCIs). Many existing BCI systems use electroencephalogram (EEG) signals to record and decode human neural activities noninvasively. Often, however, the features extracted from the EEG signals ignore the topological information hidden in the EEG temporal dynamics. Moreover, existing graph theoretic approaches are mostly used to reveal the topological patterns of brain functional networks based on synchronization between signals from distinctive spatial regions, instead of interdependence between states at different timestamps. In this study, we present a robust fold-wise hyperparameter optimization framework utilizing a series of conventional graph-based measurements combined with spectral graph features and investigate its discriminative performance on classification of a designed mental task in 6 participants with amyotrophic lateral sclerosis (ALS). Across all of our participants, we reached an average accuracy of 71.1%±4.5% for mental task classification by combining the global graph-based measurements and the spectral graph features, higher than the conventional non-graph based feature performance (67.1%±7.5%). Compared to using either one of the graphic features (66.3%±6.5% for the eigenvalues and 65.9%±5.2% for the global graph features), our feature combination strategy shows considerable improvement in both accuracy and robustness performance. Our results indicate the feasibility and advantage of the presented fold-wise optimization framework utilizing graph-based features in BCI systems targeted at end-users.

The Cryptocurrency Market in Transition before and after COVID-19: An Opportunity for Investors?

We analyze the correlation between different assets in the cryptocurrency market throughout different phases, specifically bearish and bullish periods. Taking advantage of a fine-grained dataset comprising 34 historical cryptocurrency price time series collected tick-by-tick on the HitBTC exchange, we observe the changes in interactions among these cryptocurrencies from two aspects: time and level of granularity. Moreover, the investment decisions of investors during turbulent times caused by the COVID-19 pandemic are assessed by looking at the cryptocurrency community structure using various community detection algorithms. We found that finer-grain time series describes clearer the correlations between cryptocurrencies. Notably, a noise and trend removal scheme is applied to the original correlations thanks to the theory of random matrices and the concept of Market Component, which has never been considered in existing studies in quantitative finance. To this end, we recognized that investment decisions of cryptocurrency traders vary between bearish and bullish markets. The results of our work can help scholars, especially investors, better understand the operation of the cryptocurrency market, thereby building up an appropriate investment strategy suitable to the prevailing certain economic situation.

Relative Entropy of Distance Distribution Based Similarity Measure of Nodes in Weighted Graph Data

Many similarity measure algorithms of nodes in weighted graph data have been proposed by employing the degree of nodes in recent years. Despite these algorithms obtaining great results, there may be still some limitations. For instance, the strength of nodes is ignored. Aiming at this issue, the relative entropy of the distance distribution based similarity measure of nodes is proposed in this paper. At first, the structural weights of nodes are given by integrating their degree and strength. Next, the distance between any two nodes is calculated with the help of their structural weights and the Euclidean distance formula to further obtain the distance distribution of each node. After that, the probability distribution of nodes is constructed by normalizing their distance distributions. Thus, the relative entropy can be applied to measure the difference between the probability distributions of the top d important nodes and all nodes in graph data. Finally, the similarity of two nodes can be measured in terms of this above-mentioned difference calculated by relative entropy. Experimental results demonstrate that the algorithm proposed by considering the strength of node in the relative entropy has great advantages in the most similar node mining and link prediction.

Subsampling Sparse Graphons Under Minimal Assumptions

We study the properties of two subsampling procedures for networks, (vertex subsampling and p-subsampling), under the sparse graphon model. The consistency of network subsampling is demonstrated under the minimal assumptions of weak convergence of corresponding network statistics and an (expected) subsample size growing to infinity slower than the number of vertices in the network. Furthermore, under appropriate sparsity conditions, we derive limiting distributions for the nonzero eigenvalues of an adjacency matrix under the sparse graphon model. Our weak convergence result implies the consistency of our subsampling procedures for eigenvalues under appropriate conditions.

Do social identity and cognitive diversity correlate in environmental stakeholders? A novel approach to measuring cognitive distance within and between groups

Groups with higher cognitive diversity, i.e. variations in how people think and solve problems, are thought to contribute to improved performance in complex problem-solving. However, embracing or even engineering adequate cognitive diversity is not straightforward and may even jeopardize social inclusion. In response, those that want to promote cognitive diversity might make a simplified assumption that there exists a link between identity diversity, i.e. range of social characteristics, and variations in how people perceive and solve problems. If this assumption holds true, incorporating diverse identities may concurrently achieve cognitive diversity to the extent essential for complex problem-solving, while social inclusion is explicitly acknowledged. However, currently there is a lack of empirical evidence to support this hypothesis in the context of complex social-ecological systems-a system wherein human and environmental dimensions are interdependent, where common-pool resources are used or managed by multiple types of stakeholders. Using a fisheries example, we examine the relationship between resource stakeholders' identities and their cognitive diversity. We used cognitive mapping techniques in conjunction with network analysis to measure cognitive distances within and between stakeholders of various social types (i.e., identities). Our results empirically show that groups with higher identity diversity also demonstrate more cognitive diversity, evidenced by disparate characteristics of their cognitive maps that represent their understanding of fishery dynamics. These findings have important implications for sustainable management of common-pool resources, where the inclusion of diverse stakeholders is routine, while our study shows it may also achieve higher cognitive coverage that can potentially lead to more complete, accurate, and innovative understanding of complex resource dynamics.

Structural and spectral properties of generative models for synthetic multilayer air transportation networks

To understand airline transportation networks (ATN) systems we can effectively represent them as multilayer networks, where layers capture different airline companies, the nodes correspond to the airports and the edges to the routes between the airports. We focus our study on the importance of leveraging synthetic generative multilayer models to support the analysis of meaningful patterns in these routes, capturing an ATN’s evolution with an emphasis on measuring its resilience to random or targeted attacks and considering deliberate locations of airports. By resorting to the European ATN and the United States ATN as exemplary references, in this work, we provide a systematic analysis of major existing synthetic generation models for ATNs, specifically ANGEL, STARGEN and BINBALL. Besides a thorough study of the topological aspects of the ATNs created by the three models, our major contribution lays on an unprecedented investigation of their spectral characteristics based on Random Matrix Theory and on their resilience analysis based on both site and bond percolation approaches. Results have shown that ANGEL outperforms STARGEN and BINBALL to better capture the complexity of real-world ATNs by featuring the unique properties of building a multiplex ATN layer by layer and of replicating layers with point-to-point structures alongside hub-spoke formations.

The diversity bonus in pooling local knowledge about complex problems

Recently, theoreticians have hypothesized that diverse groups, as opposed to groups that are homogeneous, may have relative merits [S. E. Page, The Diversity Bonus (2019)]-all of which lead to more success in solving complex problems. As such, understanding complex, intertwined environmental and social issues may benefit from the integration of diverse types of local expertise. However, efforts to support this hypothesis have been frequently made through laboratory-based or computational experiments, and it is unclear whether these discoveries generalize to real-world complexities. To bridge this divide, we combine an Internet-based knowledge elicitation technique with theoretical principles of collective intelligence to design an experiment with local stakeholders. Using a case of striped bass fisheries in Massachusetts, we pool the local knowledge of resource stakeholders represented by graphical cognitive maps to produce a causal model of complex social-ecological interdependencies associated with fisheries ecosystems. Blinded reviews from a scientific expert panel revealed that the models of diverse groups outranked those from homogeneous groups. Evaluation via stochastic network analysis also indicated that a diverse group more adequately modeled complex feedbacks and interdependencies than homogeneous groups. We then used our data to run Monte Carlo experiments wherein the distributions of stakeholder-driven cognitive maps were randomly reproduced and virtual groups were generated. Random experiments also predicted that knowledge diversity improves group success, which was measured by benchmarking group models against an ecosystem-based fishery management model. We also highlight that diversity must be moderated through a proper aggregation process, leading to more complex yet parsimonious models.

The influence of social relationships on substance use behaviors among pregnant women with opioid use disorder

OBJECTIVE

To describe the social network characteristics of pregnant women with opioid use disorder (OUD) and explore how changes in social relationships during pregnancy may influence substance use behaviors.

METHODS

Between 2017 and 2018, we conducted an exploratory pilot study among 50 pregnant women with OUD. Participants completed a detailed social network inventory to describe the behaviors (e.g. substance-using), social support characteristics (e.g. financial, emotional, informational) and roles (e.g. family member, friend) of network members. The primary outcome was a self-reported decrease in substance use during pregnancy. Pearson correlations were used to test for associations between covariates reflecting different aspects of participants' social networks and decreased substance use during pregnancy.

RESULTS

Most participants (84.0 %) decreased substance use during pregnancy and stated that pregnancy motivated them to engage in treatment (94.0 %). Participants had a median of 8 (IQR: 4-18) network members with differing proportions of those who did and did not use substances. Pregnancy prompted participants to significantly increase contact with (26.4 % vs. 5.0 %), have increased support from (35.7 % vs. 7.5 %), and a have a feeling of increased closeness with (26.1 % vs. 3.3 %) network members who did not use substances. However, decreased substance use during pregnancy was most strongly (negatively) associated with the proportion of network members who used substances and provided informational support (r=-0.25, p = 0.08) and a feeling of closeness (r=-0.26, p = 0.08).

CONCLUSIONS

Our findings indicate that pregnancy has a profound influence on women's substance use behaviors and that changes in social relationships due to pregnancy may influence substance use.

Spacing ratio characterization of the spectra of directed random networks

Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however, depends crucially on eigenvalue unfolding procedures, which in many situations represent a major hindrance due to constraints in the calculation, especially in the case of complex spectra. Here we study the spectra of directed networks using the recently introduced ratios between nearest and next-to-nearest eigenvalue spacing, thus circumventing the shortcomings imposed by spectral unfolding. Specifically, we characterize the eigenvalue statistics of directed Erdős-Rényi (ER) random networks by means of two adjacency matrix representations, namely, (1) weighted non-Hermitian random matrices and (2) a transformation on non-Hermitian adjacency matrices which produces weighted Hermitian matrices. For both representations, we find that the distribution of spacing ratios becomes universal for a fixed average degree, in accordance with undirected random networks. Furthermore, by calculating the average spacing ratio as a function of the average degree, we show that the spectral statistics of directed ER random networks undergoes a transition from Poisson to Ginibre statistics for model 1 and from Poisson to Gaussian unitary ensemble statistics for model 2. Eigenvector delocalization effects of directed networks are also discussed.

3'-UTR Shortening Contributes to Subtype-Specific Cancer Growth by Breaking Stable ceRNA Crosstalk of Housekeeping Genes

Shortening of 3'UTRs (3'US) through alternative polyadenylation is a post-transcriptional mechanism that regulates the expression of hundreds of genes in human cancers. In breast cancer, different subtypes of tumor samples, such as estrogen receptor positive and negative (ER+ and ER-), are characterized by distinct molecular mechanisms, suggesting possible differences in the post-transcriptional regulation between the subtype tumors. In this study, based on the profound tumorigenic role of 3'US interacting with competing-endogenous RNA (ceRNA) network (3'US-ceRNA effect), we hypothesize that the 3'US-ceRNA effect drives subtype-specific tumor growth. However, we found that the subtypes are available in different sample sizes, biasing the ceRNA network size and disabling the fair comparison of the 3'US-ceRNA effect. Using normalized Laplacian matrix eigenvalue distribution, we addressed this bias and built tumor ceRNA networks comparable between the subtypes. Based on the comparison, we identified a novel role of housekeeping (HK) genes as stable and strong miRNA sponges (sponge HK genes) that synchronize the ceRNA networks of normal samples (adjacent to ER+ and ER- tumor samples). We further found that distinct 3'US events in the ER- tumor break the stable sponge effect of HK genes in a subtype-specific fashion, especially in association with the aggressive and metastatic phenotypes. Knockdown of NUDT21 further suggested the role of 3'US-ceRNA effect in repressing HK genes for tumor growth. In this study, we identified 3'US-ceRNA effect on the sponge HK genes for subtype-specific growth of ER- tumors.

Comparing methods for comparing networks

With the impressive growth of available data and the flexibility of network modelling, the problem of devising effective quantitative methods for the comparison of networks arises. Plenty of such methods have been designed to accomplish this task: most of them deal with undirected and unweighted networks only, but a few are capable of handling directed and/or weighted networks too, thus properly exploiting richer information. In this work, we contribute to the effort of comparing the different methods for comparing networks and providing a guide for the selection of an appropriate one. First, we review and classify a collection of network comparison methods, highlighting the criteria they are based on and their advantages and drawbacks. The set includes methods requiring known node-correspondence, such as DeltaCon and Cut Distance, as well as methods not requiring a priori known node-correspondence, such as alignment-based, graphlet-based, and spectral methods, and the recently proposed Portrait Divergence and NetLSD. We test the above methods on synthetic networks and we assess their usability and the meaningfulness of the results they provide. Finally, we apply the methods to two real-world datasets, the European Air Transportation Network and the FAO Trade Network, in order to discuss the results that can be drawn from this type of analysis.

Multifractality in random networks with power-law decaying bond strengths

In this paper we demonstrate numerically that random networks whose adjacency matrices A are represented by a diluted version of the power-law banded random matrix (PBRM) model have multifractal eigenfunctions. The PBRM model describes one-dimensional samples with random long-range bonds. The bond strengths of the model, which decay as a power-law, are tuned by the parameter μ as A_{mn}∝|m-n|^{-μ}; while the sparsity is driven by the average network connectivity α: for α=0 the vertices in the network are isolated and for α=1 the network is fully connected and the PBRM model is recovered. Though it is known that the PBRM model has multifractal eigenfunctions at the critical value μ=μ_{c}=1, we clearly show [from the scaling of the relative fluctuation of the participation number I_{2} as well as the scaling of the probability distribution functions P(lnI_{2})] the existence of the critical value μ_{c}≡μ_{c}(α) for α<1. Moreover, we characterize the multifractality of the eigenfunctions of our random network model by the use of the corresponding multifractal dimensions D_{q}, that we compute from the finite network-size scaling of the typical eigenfunction participation numbers exp〈lnI_{q}〉.

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

We study the localization properties of the eigenvectors, characterized by their information entropy, of tight-binding random networks with balanced losses and gain. The random network model, which is based on Erdős–Rényi (ER) graphs, is defined by three parameters: the network size N, the network connectivity α, and the losses-and-gain strength γ. Here, N and α are the standard parameters of ER graphs, while we introduce losses and gain by including complex self-loops on all vertices with the imaginary amplitude iγ with random balanced signs, thus breaking the Hermiticity of the corresponding adjacency matrices and inducing complex spectra. By the use of extensive numerical simulations, we define a scaling parameter ξ≡ξ(N,α,γ) that fixes the localization properties of the eigenvectors of our random network model; such that, when ξ<0.1 (10<ξ), the eigenvectors are localized (extended), while the localization-to-delocalization transition occurs for 0.1<ξ<10. Moreover, to extend the applicability of our findings, we demonstrate that for fixed ξ, the spectral properties (characterized by the position of the eigenvalues on the complex plane) of our network model are also universal; i.e., they do not depend on the specific values of the network parameters.