Cooperative driver pathways discovery by multiplex network embedding.

Cooperative driver pathways discovery helps researchers to study the pathogenesis of cancer. However, most discovery methods mainly focus on genomics data, and neglect the known pathway information and other related multi-omics data; thus they cannot faithfully decipher the carcinogenic process. We propose CDPMiner (Cooperative Driver Pathways Miner) to discover cooperative driver pathways by multiplex network embedding, which can jointly model relational and attribute information of multi-type molecules. CDPMiner first uses the pathway topology to quantify the weight of genes in different pathways, and optimizes the relations between genes and pathways. Then it constructs an attributed multiplex network consisting of micro RNAs, long noncoding RNAs, genes and pathways, embeds the network through deep joint matrix factorization to mine more essential information for pathway-level analysis and reconstructs the pathway interaction network. Finally, CDPMiner leverages the reconstructed network and mutation data to define the driver weight between pathways to discover cooperative driver pathways. Experimental results on Breast invasive carcinoma and Stomach adenocarcinoma datasets show that CDPMiner can effectively fuse multi-omics data to discover more driver pathways, which indeed cooperatively trigger cancers and are valuable for carcinogenesis analysis. Ablation study justifies CDPMiner for a more comprehensive analysis of cancer by fusing multi-omics data.

A network embedding framework based on integrating multiplex network for drug combination prediction.

Drug combination is a sensible strategy for disease treatment because it improves the treatment efficacy and reduces concomitant side effects. Due to the large number of possible combinations among candidate compounds, exhaustive screening is prohibitive. Currently, a large number of studies have focused on predicting potential drug combinations. However, these methods are not entirely satisfactory in terms of performance and scalability. In this paper, we proposed a Network Embedding frameWork in MultIplex Network (NEWMIN) to predict synthetic drug combinations. Based on a multiplex drug similarity network, we offered alternative methods to integrate useful information from different aspects and to decide the quantitative importance of each network. For drug combination prediction, we found seven novel drug combinations that have been validated by external sources among the top-ranked predictions of our model. To verify the feasibility of NEWMIN, we compared NEWMIN with other five methods, for which it showed better performance than other methods in terms of the area under the precision-recall curve and receiver operating characteristic curve.

The impact of the self-recognition ability and physical quality on coupled negative information-behavior-epidemic dynamics in multiplex networks.

In recent years, as the COVID-19 global pandemic evolves, many unprecedented new patterns of epidemic transmission continue to emerge. Reducing the impact of negative information diffusion, calling for individuals to adopt immunization behaviors, and decreasing the infection risk are of great importance to maintain public health and safety. In this paper, we construct a coupled negative information-behavior-epidemic dynamics model by considering the influence of the individual's self-recognition ability and physical quality in multiplex networks. We introduce the Heaviside step function to explore the effect of decision-adoption process on the transmission for each layer, and assume the heterogeneity of the self-recognition ability and physical quality obey the Gaussian distribution. Then, we use the microscopic Markov chain approach (MMCA) to describe the dynamic process and derive the epidemic threshold. Our findings suggest that increasing the clarification strength of mass media and enhancing individuals' self-recognition ability can facilitate the control of the epidemic. And, increasing physical quality can delay the epidemic outbreak and leads to suppress the scale of epidemic transmission. Moreover, the heterogeneity of the individuals in the information diffusion layer leads to a two-stage phase transition, while it leads to a continuous phase transition in the epidemic layer. Our results can provide favorable references for managers in controlling negative information, urging immunization behaviors and suppressing epidemics.

Coupled Information-Epidemic Spreading Dynamics with Selective Mass Media.

As a pandemic emerges, information on epidemic prevention disseminates among the populace, and the propagation of that information interacts with the proliferation of the disease. Mass media serve a pivotal function in facilitating the dissemination of epidemic-related information. Investigating coupled information-epidemic dynamics, while accounting for the promotional effect of mass media in information dissemination, is of significant practical relevance. Nonetheless, in the extant research, scholars predominantly employ an assumption that mass media broadcast to all individuals equally within the network: this assumption overlooks the practical constraint imposed by the substantial social resources required to accomplish such comprehensive promotion. In response, this study introduces a coupled information-epidemic spreading model with mass media that can selectively target and disseminate information to a specific proportion of high-degree nodes. We employed a microscopic Markov chain methodology to scrutinize our model, and we examined the influence of the various model parameters on the dynamic process. The findings of this study reveal that mass media broadcasts directed towards high-degree nodes within the information spreading layer can substantially reduce the infection density of the epidemic, and raise the spreading threshold of the epidemic. Additionally, as the mass media broadcast proportion increases, the suppression effect on the disease becomes stronger. Moreover, with a constant broadcast proportion, the suppression effect of mass media promotion on epidemic spreading within the model is more pronounced in a multiplex network with a negative interlayer degree correlation, compared to scenarios with positive or absent interlayer degree correlation.

The influence of a transport process on the epidemic threshold.

By generating transient encounters between individuals beyond their immediate social environment, transport can have a profound impact on the spreading of an epidemic. In this work, we consider epidemic dynamics in the presence of the transport process that gives rise to a multiplex network model. In addition to a static layer, the (multiplex) epidemic network consists of a second dynamic layer in which any two individuals are connected for the time they occupy the same site during a random walk they perform on a separate transport network. We develop a mean-field description of the stochastic network model and study the influence the transport process has on the epidemic threshold. We show that any transport process generally lowers the epidemic threshold because of the additional connections it generates. In contrast, considering also random walks of fractional order that in some sense are a more realistic model of human mobility, we find that these non-local transport dynamics raise the epidemic threshold in comparison to a classical local random walk. We also test our model on a realistic transport network (the Munich U-Bahn network), and carefully compare mean-field solutions with stochastic trajectories in a range of scenarios.

Coevolving spreading dynamics of negative information and epidemic on multiplex networks.

The widespread dissemination of negative information on vaccine may arise people's concern on the safety of vaccine and increase their hesitancy in vaccination, which can seriously impede the progress of epidemic control. Existing works on information-epidemic coupled dynamics focus on the suppression effects of information on epidemic. Here we propose a negative information and epidemic coupled propagation model on two-layer multiplex networks to study the effects of negative information of vaccination on epidemic spreading, where the negative information propagates on the virtual communication layer and the disease spreads on the physical contact layer. In our model, an individual getting an adverse event after vaccination will spread negative information and an individual affected by the negative information will reduce his/her willingness to get vaccinated and spread the negative information. By using the microscopic Markov chain method, we analytically predict the epidemic threshold and final infection density, which agree well with simulation results. We find that the spread of negative information leads to a lower epidemic outbreak threshold and a higher final infection density. However, the individuals' vaccination activities, but not the negative information spreading, has a leading impact on epidemic spreading. Only when the individuals obviously reduce their vaccination willingness due to negative information, the negative information can impact the epidemic spreading significantly.

The effect of information-driven resource allocation on the propagation of epidemic with incubation period.

In the pandemic of COVID-19, there are exposed individuals who are infected but lack distinct clinical symptoms. In addition, the diffusion of related information drives aware individuals to spontaneously seek resources for protection. The special spreading characteristic and coevolution of different processes may induce unexpected spreading phenomena. Thus we construct a three-layered network framework to explore how information-driven resource allocation affects SEIS (susceptible-exposed-infected-susceptible) epidemic spreading. The analyses utilizing microscopic Markov chain approach reveal that the epidemic threshold depends on the topology structure of epidemic network and the processes of information diffusion and resource allocation. Conducting extensive Monte Carlo simulations, we find some crucial phenomena in the coevolution of information diffusion, resource allocation and epidemic spreading. Firstly, when E-state (exposed state, without symptoms) individuals are infectious, long incubation period results in more E-state individuals than I-state (infected state, with obvious symptoms) individuals. Besides, when E-state individuals have strong or weak infectious capacity, increasing incubation period has an opposite effect on epidemic propagation. Secondly, the short incubation period induces the first-order phase transition. But enhancing the efficacy of resources would convert the phase transition to a second-order type. Finally, comparing the coevolution in networks with different topologies, we find setting the epidemic layer as scale-free network can inhibit the spreading of the epidemic.

Multi-dimensional data integration algorithm based on random walk with restart.

BACKGROUND: The accumulation of various multi-omics data and computational approaches for data integration can accelerate the development of precision medicine. However, the algorithm development for multi-omics data integration remains a pressing challenge. RESULTS: Here, we propose a multi-omics data integration algorithm based on random walk with restart (RWR) on multiplex network. We call the resulting methodology Random Walk with Restart for multi-dimensional data Fusion (RWRF). RWRF uses similarity network of samples as the basis for integration. It constructs the similarity network for each data type and then connects corresponding samples of multiple similarity networks to create a multiplex sample network. By applying RWR on the multiplex network, RWRF uses stationary probability distribution to fuse similarity networks. We applied RWRF to The Cancer Genome Atlas (TCGA) data to identify subtypes in different cancer data sets. Three types of data (mRNA expression, DNA methylation, and microRNA expression data) are integrated and network clustering is conducted. Experiment results show that RWRF performs better than single data type analysis and previous integrative methods. CONCLUSIONS: RWRF provides powerful support to users to decipher the cancer molecular subtypes, thus may benefit precision treatment of specific patients in clinical practice.

Calcarine as a bridge between brain function and structure in irritable bowel syndrome: A multiplex network analysis.

BACKGROUND AND AIM: Jointly analyzing structural and functional brain networks enables a better understanding of pathological underpinnings of irritable bowel syndrome (IBS). Multiplex network analysis provides a novel framework to study complex networks consisting of different types of connectivity patterns in multimodal data. METHODS: In the present work, we integrated functional and structural networks to a multiplex network. Then, the multiplex metrics and the inner-layer/inter-layer hub nodes were investigated through 34 patients with IBS and 33 healthy controls. RESULTS: Significantly differential multiplex degree in both left and right parts of calcarine was found, and meanwhile, IBS patients lost inner-layer hub properties in these regions. In addition, the left fusiform was no longer practicing as an inner-layer hub node, while the right median cingulate acted as a new inner-layer hub node in the IBS patients. Besides, the right calcarine, which lost its inner-layer hub identity, became a new inter-layer hub node, and the multiplex degree of the left hippocampus, which lost its inter-layer hub identity in IBS patients, was significantly positively correlated with the IBS Symptom Severity Score scores. CONCLUSIONS: Inner-layer hub nodes of multiplex networks were preferentially vulnerable, and some inner-layer hub nodes would convert into inter-layer hub nodes in IBS patients. Besides, the inter-layer hub nodes might be influenced by IBS severity and therefore converted to general nodes.

Special issue on statistical analysis of networks: Preface by the guest editors.

The special issue on Statistical Analysis of Networks aspires to convey the breadth and depth of statistical learning with networks, ranging from networks that are observed to networks that are unobserved and learned from data. It includes ten select papers with methodological and theoretical advances, and demonstrates the usefulness of the network paradigm by applications to current problems.

An approach to incorporating inferred connectivity of adult movement into marine protected area design with limited data.

Marine protected areas (MPAs) are important conservation tools that can support the resilience of marine ecosystems. Many countries, including Canada, have committed to protecting at least 10% of their marine areas under the Convention on Biological Diversity's Aichi Target 11, which includes connectivity as a key aspect. Connectivity, the movement of individuals among habitats, can enhance population stability and resilience within and among MPAs. However, little is known about regional spatial patterns of marine ecological connectivity, particularly adult movement. We developed a method to assess and design MPA networks that maximize inferred connectivity within habitat types for adult movement when ecological data are limited. We used the Northern Shelf Bioregion in British Columbia, Canada, to explore two different approaches: (1) evaluating sites important for inferred regional connectivity (termed hotspots) and (2) assessing MPA network configurations based on their overlap with connectivity hotspots and interconnectedness between MPAs. To assess inferred connectivity via adult movement, we used two different threshold distances (15 and 50 km) to capture moderate home ranges, which are most appropriate to consider in MPA design. We applied graph theory to assess inferred connectivity within 16 habitat and depth categories (proxies for distinct ecological communities), and used novel multiplex network methodologies to perform an aggregated assessment of inferred connectivity. We evaluated inferred regional connectivity hotspots based on betweenness and eigenvector centrality metrics, finding that the existing MPA network overlapped a moderate proportion of these regional hotspots and identified key areas to be considered as candidate MPAs. Network density among existing MPAs was low within the individual habitat networks, as well as the multiplex. This work informs an ongoing MPA planning process, and approaches for incorporating connectivity into MPA design when data are limited, with lessons for other contexts.

Effects of asymptomatic infection on the dynamical interplay between behavior and disease transmission in multiplex networks.

Multiplex network theory is widely introduced to deepen the understanding of the dynamical interplay between self-protective behavior and epidemic spreading. Most of the existing studies assumed that all infected individuals can transmit disease- related information or can be perceived by their neighbors. However, owing to lack of distinct symptoms for patients in the initial stage of infection, the disease information cannot be transmitted in the population, which may lead to the wrong perception of infection risk and inappropriate behavior response. In this work, we divide infected individuals into Exposed-state (without obvious clinical symptoms) individuals and Infected-state (with evident clinical symptoms) individuals, both of whom can spread disease, but only Infected-state individuals can diffuse disease information. Then, in this work we establish UAU-SEIS (Unaware-Aware-Unaware-Susceptible-Exposed-Infected-Susceptible) model in multiplex networks and analyze the effect of asymptomatic infection and the isolation of Infected-state individuals on the density of infection and the epidemic threshold. Furthermore, we extend the UAU-SEIS model by taking the individual heterogeneity into consideration. Combined Markov chain approach and Monte-Carlo Simulations, we find that asymptomatic infection has an effect on the density of infected individuals and the epidemic threshold, and the extent of the effect is influenced by whether Infected-state individuals are isolated or treated. In addition, results show that the individual heterogeneity can lower the density of infected individuals, but cannot enhance the epidemic threshold.

Selective impairment of hippocampus and posterior hub areas in Alzheimer's disease: an MEG-based multiplex network study.

Although frequency-specific network analyses have shown that functional brain networks are altered in patients with Alzheimer's disease, the relationships between these frequency-specific network alterations remain largely unknown. Multiplex network analysis is a novel network approach to study complex systems consisting of subsystems with different types of connectivity patterns. In this study, we used magnetoencephalography to integrate five frequency-band specific brain networks in a multiplex framework. Previous structural and functional brain network studies have consistently shown that hub brain areas are selectively disrupted in Alzheimer's disease. Accordingly, we hypothesized that hub regions in the multiplex brain networks are selectively targeted in patients with Alzheimer's disease in comparison to healthy control subjects. Eyes-closed resting-state magnetoencephalography recordings from 27 patients with Alzheimer's disease (60.6 ± 5.4 years, 12 females) and 26 controls (61.8 ± 5.5 years, 14 females) were projected onto atlas-based regions of interest using beamforming. Subsequently, source-space time series for both 78 cortical and 12 subcortical regions were reconstructed in five frequency bands (delta, theta, alpha 1, alpha 2 and beta band). Multiplex brain networks were constructed by integrating frequency-specific magnetoencephalography networks. Functional connections between all pairs of regions of interests were quantified using a phase-based coupling metric, the phase lag index. Several multiplex hub and heterogeneity metrics were computed to capture both overall importance of each brain area and heterogeneity of the connectivity patterns across frequency-specific layers. Different nodal centrality metrics showed consistently that several hub regions, particularly left hippocampus, posterior parts of the default mode network and occipital regions, were vulnerable in patients with Alzheimer's disease compared to control subjects. Of note, these detected vulnerable hubs in Alzheimer's disease were absent in each individual frequency-specific network, thus showing the value of integrating the networks. The connectivity patterns of these vulnerable hub regions in the patients were heterogeneously distributed across layers. Perturbed cognitive function and abnormal cerebrospinal fluid amyloid-ß42 levels correlated positively with the vulnerability of the hub regions in patients with Alzheimer's disease. Our analysis therefore demonstrates that the magnetoencephalography-based multiplex brain networks contain important information that cannot be revealed by frequency-specific brain networks. Furthermore, this indicates that functional networks obtained in different frequency bands do not act as independent entities. Overall, our multiplex network study provides an effective framework to integrate the frequency-specific networks with different frequency patterns and reveal neuropathological mechanism of hub disruption in Alzheimer's disease.

The impact of indirect structure on functional connectivity in schizophrenia using a multiplex brain network.

It is known that abnormal functional connectivity (FC) in schizophrenia (SZ) is closely related to structural connectivity (SC). We speculate that indirect SC also have an impact on FC in SZ patients. Conventional single-layer network has limitations for studying the relationship between indirect SC and FC. Thus, this study constructed a multiplex network based on structural connectivity and functional connectivity (SC-FC). The SC-FC bandwidth and SC-FC cost are used to analyze the impact of indirect SC on FC. Moreover, this paper proposed mediation ability, mediation cost, mediated strength and mediated cost to quantify the effects of mediator nodes and mediated nodes on indirect SC. The results show that SZ patients exhibit lower SC-FC bandwidth and SC-FC cost compared to healthy controls (HC), which could be caused by the limbic and subcortical network (LSN), default mode network (DMN) and visual network (VN). The mediator and mediated nodes in indirect SC of SZ patients also showed diminished effects. These findings suggest that functional communication ability and cost in SZ patients are influenced by indirect SC. This study provides new perspectives for understanding the relationship between indirect SC and FC, and provides strong evidence for interpreting the physiological mechanisms of SZ patients.

Vaccine Hesitancy in Taiwan: Temporal, Multilayer Network Study of Echo Chambers Shaped by Influential Users.

BACKGROUND: Vaccine hesitancy is a growing global health threat that is increasingly studied through the monitoring and analysis of social media platforms. One understudied area is the impact of echo chambers and influential users on disseminating vaccine information in social networks. Assessing the temporal development of echo chambers and the influence of key users on their growth provides valuable insights into effective communication strategies to prevent increases in vaccine hesitancy. This also aligns with the World Health Organization's (WHO) infodemiology research agenda, which aims to propose new methods for social listening. OBJECTIVE: Using data from a Taiwanese forum, this study aims to examine how engagement patterns of influential users, both within and across different COVID-19 stances, contribute to the formation of echo chambers over time. METHODS: Data for this study come from a Taiwanese forum called PTT. All vaccine-related posts on the "Gossiping" subforum were scraped from January 2021 to December 2022 using the keyword "vaccine." A multilayer network model was constructed to assess the existence of echo chambers. Each layer represents either provaccination, vaccine hesitant, or antivaccination posts based on specific criteria. Layer-level metrics, such as average diversity and Spearman rank correlations, were used to measure chambering. To understand the behavior of influential users-or key nodes-in the network, the activity of high-diversity and hardliner nodes was analyzed. RESULTS: Overall, the provaccination and antivaccination layers are strongly polarized. This trend is temporal and becomes more apparent after November 2021. Diverse nodes primarily participate in discussions related to provaccination topics, both receiving comments and contributing to them. Interactions with the antivaccination layer are comparatively minimal, likely due to its smaller size, suggesting that the forum is a "healthy community." Overall, diverse nodes exhibit cross-cutting engagement. By contrast, hardliners in the vaccine hesitant and antivaccination layers are more active in commenting within their own communities. This trend is temporal, showing an increase during the Omicron outbreak. Hardliner activity potentially reinforces their stances over time. Thus, there are opposing forces of chambering and cross-cutting. CONCLUSIONS: Efforts should be made to moderate hardliner and influential nodes in the antivaccination layer and to support provaccination users engaged in cross-cutting exchanges. There are several limitations to this study. One is the bias of the platform used, and another is the lack of a comprehensive definition of "influence." To address these issues, comparative studies across different platforms can be conducted, and various metrics of influence should be explored. Additionally, examining the impact of influential users on network structure and chambering through network simulations and regression analysis provides more robust insights. The study also lacks an explanation for the reasons behind chambering trends. Conducting content analysis can help to understand the nature of engagement and inform interventions to address echo chambers. These approaches align with and further the WHO infodemic research agenda.

Effect of decay behavior of information on disease dissemination in multiplex network.

The diseases dissemination always brings serious problems in the economy and livelihood issues. It is necessary to study the law of disease dissemination from multiple dimensions. Information quality about disease prevention has a great impact on the dissemination of disease, that is because only the real information can inhibit the dissemination of disease. In fact, the dissemination of information involves the decay of the amount of real information and the information quality becomes poor gradually, which will affect the individual's attitude and behavior towards disease. In order to study the influence of the decay behavior of information on disease dissemination, in the paper, an interaction model between information and disease dissemination is established to describe the effect of the decay behavior of information on the coupled dynamics of process in multiplex network. According to the mean-field theory, the threshold condition of disease dissemination is derived. Finally, through theoretical analysis and numerical simulation, some results can be obtained. The results show that decay behavior is a factor that greatly affects the disease dissemination and can change the final size of disease dissemination. The larger the decay constant, the smaller final size of disease dissemination. In the process of information dissemination, emphasizing key information can reduce the impact of decay behavior.

The impact of disclosure of risk information on risk propagation in the industrial symbiosis network.

The interdependent symbiotic relationship between enterprises may bring potential risks to the stability of the industrial symbiosis network (ISN). In order to reduce the damage caused by further risk propagation to the system, this paper establishes the multiplex network to study the impact of disclosure of risk information on risk propagation. In the multiplex network, we use a small-world network to simulate a social network and propose an evolutionary model with scale-free characteristics to simulate the symbiotic relationships between enterprises. Then we establish a risk propagation model by defining transition rules among various states. Through theoretical analysis using the Microscopic Markov Chain Approach (MMCA), we find that the proportion of disclosed enterprises, the network structure of the ISN, the recovery rate of enterprises, and the degree of symbiotic dependence affect the risk propagation threshold of the ISN. Numerical simulation results show that increasing the disclosure probability of risk information can reduce the scope of risk propagation. Moreover, once the disclosure probability of risk information reaches a certain value, the risk propagation threshold can be increased. Finally, relevant suggestions are put forward: (i) strengthening the information communication between symbiotic enterprises may reduce risks caused by information asymmetry. (ii) In addition to the authenticity and integrity of risk information, it is necessary to prevent risk information from being over-interpreted or exaggerated. (iii) Enterprises should strengthen the ability to recover from risks, appropriately reduce the degree of symbiotic dependence, and enhance risk awareness to reduce the possibility of risk occurrence.

Structural-functional connectivity bandwidth predicts processing speed in mild traumatic brain Injury: A multiplex network analysis.

An emerging body of work has revealed alterations in structural (SC) and functional (FC) brain connectivity following mild TBI (mTBI), with mixed findings. However, these studies seldom integrate complimentary neuroimaging modalities within a unified framework. Multilayer network analysis is an emerging technique to uncover how white matter organization enables functional communication. Using our novel graph metric (SC-FC Bandwidth), we quantified the information capacity of synchronous brain regions in 53 mild TBI patients (46 females; age mean = 40.2 years (y), σ = 16.7 (y), range: 18-79 (y). Diffusion MRI and resting state fMRI were administered at the acute and chronic post-injury intervals. Moreover, participants completed a cognitive task to measure processing speed (30 Seconds and Counting Task; 30-SACT). Processing speed was significantly increased at the chronic, relative to the acute post-injury intervals (p = <0.001). Nonlinear principal components of direct (t = -1.84, p = 0.06) and indirect SC-FC Bandwidth (t = 3.86, p = <0.001) predicted processing speed with a moderate effect size (R2 = 0.43, p < 0.001), while controlling for age. A subnetwork of interhemispheric edges with increased SC-FC Bandwidth was identified at the chronic, relative to the acute mTBI post-injury interval (pFDR = 0.05). Increased interhemispheric SC-FC Bandwidth of this network corresponded with improved processing speed at the chronic post-injury interval (partial r = 0.32, p = 0.02). Our findings revealed that mild TBI results in complex reorganization of brain connectivity optimized for maximum information flow, supporting improved cognitive performance as a compensatory mechanism. Moving forward, this measurement may complement clinical assessment as an objective marker of mTBI recovery.

Delving into gene-set multiplex networks facilitated by a k-nearest neighbor-based measure of similarity.

Gene sets are functional units for living cells. Previously, limited studies investigated the complex relations among gene sets, but documents about their altering patterns across biological conditions still need to be prepared. In this study, we adopted and modified a classical k-nearest neighbor-based association function to detect inter-gene-set similarities. Based on this method, we built multiplex networks of gene sets for the first time; these networks contain layers of gene sets corresponding to different populations of cells. The context-based multiplex networks can capture meaningful biological variation and have considerable differences from knowledge-based networks of gene sets built on Jaccard similarity, as demonstrated in this study. Furthermore, at the scale of individual gene sets, the structural coefficients of gene sets (multiplex PageRank centrality, clustering coefficient, and participation coefficient) disclose the diversity of gene sets from the perspective of structural properties and make it easier to identify unique gene sets. In gene set enrichment analysis (GSEA), each gene set is treated independently, and its contextual and relational attributes are ignored. The structural coefficients of gene sets can supplement GSEA with information about the overall picture of gene sets, promoting the constructive reorganization of the enriched terms and helping researchers better prioritize and select gene sets.

Boundary heat diffusion classifier for a semi-supervised learning in a multilayer network embedding.

The scarcity of high-quality annotations in many application scenarios has recently led to an increasing interest in devising learning techniques that combine unlabeled data with labeled data in a network. In this work, we focus on the label propagation problem in multilayer networks. Our approach is inspired by the heat diffusion model, which shows usefulness in machine learning problems such as classification and dimensionality reduction. We propose a novel boundary-based heat diffusion algorithm that guarantees a closed-form solution with an efficient implementation. We experimentally validated our method on synthetic networks and five real-world multilayer network datasets representing scientific coauthorship, spreading drug adoption among physicians, two bibliographic networks, and a movie network. The results demonstrate the benefits of the proposed algorithm, where our boundary-based heat diffusion dominates the performance of the state-of-the-art methods.