Adapting Stochastic Block Models to Power-Law Degree Distributions

An agent-based model of the spread of behavioural risk-factors for cardiovascular disease in city-scale populations

Cardiovascular disease (CVD) is the leading cause of mortality globally, and is the second main cause of mortality in the UK. Four key modifiable behaviours are known to increase CVD risk, namely: tobacco use, unhealthy diet, physical inactivity and harmful use of alcohol. Behaviours that increase the risk of CVD can spread through social networks because individuals consciously and unconsciously mimic the behaviour of others they relate to and admire. Exploiting these social influences may lead to effective and efficient public health interventions to prevent CVD. This project aimed to construct and validate an agent-based model (ABM) of how the four major behavioural risk-factors for CVD spread through social networks in a population, and examine whether the model could be used to identify targets for public health intervention and to test intervention strategies. Previous ABMs have typically focused on a single risk factor or considered very small populations. We created a city-scale ABM to model the behavioural risk-factors of individuals, their social networks (spousal, household, friendship and workplace), the spread of behaviours through these social networks, and the subsequent impact on the development of CVD. We compared the model output (predicted CVD events over a ten year period) to observed data, demonstrating that the model output is realistic. The model output is stable up to at least a population size of 1.2M agents (the maximum tested). We found that there is scope for the modelled interventions targeting the spread of these behaviours to change the number of CVD events experienced by the agents over ten years. Specifically, we modelled the impact of workplace interventions to show that the ABM could be useful for identifying targets for public health intervention. The model itself is Open Source and is available for use or extension by other researchers.

Probabilistic activity driven model of temporal simplicial networks and its application on higher-order dynamics

Network modeling characterizes the underlying principles of structural properties and is of vital significance for simulating dynamical processes in real world. However, bridging structure and dynamics is always challenging due to the multiple complexities in real systems. Here, through introducing the individual's activity rate and the possibility of group interaction, we propose a probabilistic activity-driven (PAD) model that could generate temporal higher-order networks with both power-law and high-clustering characteristics, which successfully links the two most critical structural features and a basic dynamical pattern in extensive complex systems. Surprisingly, the power-law exponents and the clustering coefficients of the aggregated PAD network could be tuned in a wide range by altering a set of model parameters. We further provide an approximation algorithm to select the proper parameters that can generate networks with given structural properties, the effectiveness of which is verified by fitting various real-world networks. Finally, we construct the co-evolution framework of the PAD model and higher-order contagion dynamics and derive the critical conditions for phase transition and bistable phenomenon using theoretical and numerical methods. Results show that tendency of participating in higher-order interactions can promote the emergence of bistability but delay the outbreak under heterogeneous activity rates. Our model provides a basic tool to reproduce complex structural properties and to study the widespread higher-order dynamics, which has great potential for applications across fields.

The role of connectivity on COVID-19 preventive approaches

Preventive and modeling approaches to address the COVID-19 pandemic have been primarily based on the age or occupation, and often disregard the importance of heterogeneity in population contact structure and individual connectivity. To address this gap, we developed models based on Erdős-Rényi and a power law degree distribution that first incorporate the role of heterogeneity and connectivity and then can be expanded to make assumptions about demographic characteristics. Results demonstrate that variations in the number of connections of individuals within a population modify the impact of public health interventions such as lockdown or vaccination approaches. We conclude that the most effective strategy will vary depending on the underlying contact structure of individuals within a population and on timing of the interventions.

Vicinal Vertex Allocation for Matrix Factorization in Networks

In this article, we present a novel matrix-factorization-based model, labeled here as Vicinal vertex allocated matrix factorization (VVAMo), for uncovering clusters in network data. Different from the past related efforts of network clustering, which consider the edge structure, vertex features, or both in their design, the proposed model includes the additional detail on vertex inclinations with respect to topology and features into the learning. In particular, by taking the latent preferences between vicinal vertices into consideration, VVAMo is then able to uncover network clusters composed of proximal vertices that share analogous inclinations, and correspondingly high structural and feature correlations. To ensure such clusters are effectively uncovered, we propose a unified likelihood function for VVAMo and derive an alternating algorithm for optimizing the proposed function. Subsequently, we provide the theoretical analysis of VVAMo, including the convergence proof and computational complexity analysis. To investigate the effectiveness of the proposed model, a comprehensive empirical study of VVAMo is conducted using extensive commonly used realistic network datasets. The results obtained show that VVAMo attained superior performances over existing classical and state-of-the-art approaches.

Revisiting the recombinant history of HIV-1 group M with dynamic network community detection

Recombination is a major mechanism through which HIV type 1 (HIV-1) maintains genetic diversity and interferes with viral eradication efforts. There is growing evidence demonstrating a recombinant origin of primate lentiviruses including HIV-1 group M (HIV-1/M). Inferring the extent of recombination across the entire HIV-1/M genome is of great importance as it provides deeper insights into the origin, dynamics, and evolution of the global pandemic. Here we propose an alternative method that can reconstruct the extent of genome-wide recombination in HIV-1, uncover reticulate patterns, and serve as a framework for HIV-1 classification. Our method provides an alternative approach for understanding the roles of virus recombination in the early evolutionary history of zoonosis for other emerging viruses.

The prevailing abundance of full-length HIV type 1 (HIV-1) genome sequences provides an opportunity to revisit the standard model of HIV-1 group M (HIV-1/M) diversity that clusters genomes into largely nonrecombinant subtypes, which is not consistent with recent evidence of deep recombinant histories for simian immunodeficiency virus (SIV) and other HIV-1 groups. Here we develop an unsupervised nonparametric clustering approach, which does not rely on predefined nonrecombinant genomes, by adapting a community detection method developed for dynamic social network analysis. We show that this method (dynamic stochastic block model [DSBM]) attains a significantly lower mean error rate in detecting recombinant breakpoints in simulated data (quasibinomial generalized linear model (GLM), P<8×10−8), compared to other reference-free recombination detection programs (genetic algorithm for recombination detection [GARD], recombination detection program 4 [RDP4], and RDP5). When this method was applied to a representative sample of n = 525 actual HIV-1 genomes, we determined k = 29 as the optimal number of DSBM clusters and used change-point detection to estimate that at least 95% of these genomes are recombinant. Further, we identified both known and undocumented recombination hotspots in the HIV-1 genome and evidence of intersubtype recombination in HIV-1 subtype reference genomes. We propose that clusters generated by DSBM can provide an informative framework for HIV-1 classification.

The role of connectivity on COVID-19 preventive approaches

Preventive and modelling approaches to address the COVID-19 pandemic have been primarily based on the age or occupation, and often disregard the importance of heterogeneity in population contact structure and individual connectivity. To address this gap, we developed models based on Erdős-Rényi and a power law degree distribution that first incorporate the role of heterogeneity and connectivity and then can be expanded to make assumptions about demographic characteristics. Results demonstrate that variations in the number of connections of individuals within a population modify the impact of public health interventions such as lockdown or vaccination approaches. We conclude that the most effective strategy will vary depending on the underlying contact structure of individuals within a population and on timing of the interventions.

Contextual Correlation Preserving Multiview Featured Graph Clustering

Graph clustering, which aims at discovering sets of related vertices in graph-structured data, plays a crucial role in various applications, such as social community detection and biological module discovery. With the huge increase in the volume of data in recent years, graph clustering is used in an increasing number of real-life scenarios. However, the classical and state-of-the-art methods, which consider only single-view features or a single vector concatenating features from different views and neglect the contextual correlation between pairwise features, are insufficient for the task, as features that characterize vertices in a graph are usually from multiple views and the contextual correlation between pairwise features may influence the cluster preference for vertices. To address this challenging problem, we introduce in this paper, a novel graph clustering model, dubbed contextual correlation preserving multiview featured graph clustering (CCPMVFGC) for discovering clusters in graphs with multiview vertex features. Unlike most of the aforementioned approaches, CCPMVFGC is capable of learning a shared latent space from multiview features as the cluster preference for each vertex and making use of this latent space to model the inter-relationship between pairwise vertices. CCPMVFGC uses an effective method to compute the degree of contextual correlation between pairwise vertex features and utilizes view-wise latent space representing the feature-cluster preference to model the computed correlation. Thus, the cluster preference learned by CCPMVFGC is jointly inferred by multiview features, view-wise correlations of pairwise features, and the graph topology. Accordingly, we propose a unified objective function for CCPMVFGC and develop an iterative strategy to solve the formulated optimization problem. We also provide the theoretical analysis of the proposed model, including convergence proof and computational complexity analysis. In our experiments, we extensively compare the proposed CCPMVFGC with both classical and state-of-the-art graph clustering methods on eight standard graph datasets (six multiview and two single-view datasets). The results show that CCPMVFGC achieves competitive performance on all eight datasets, which validates the effectiveness of the proposed model.