A generalized simplicial model and its application.

Higher-order structures, consisting of more than two individuals, provide a new perspective to reveal the missed non-trivial characteristics under pairwise networks. Prior works have researched various higher-order networks, but research for evaluating the effects of higher-order structures on network functions is still scarce. In this paper, we propose a framework to quantify the effects of higher-order structures (e.g., 2-simplex) and vital functions of complex networks by comparing the original network with its simplicial model. We provide a simplicial model that can regulate the quantity of 2-simplices and simultaneously fix the degree sequence. Although the algorithm is proposed to control the quantity of 2-simplices, results indicate it can also indirectly control simplexes more than 2-order. Experiments on spreading dynamics, pinning control, network robustness, and community detection have shown that regulating the quantity of 2-simplices changes network performance significantly. In conclusion, the proposed framework is a general and effective tool for linking higher-order structures with network functions. It can be regarded as a reference object in other applications and can deepen our understanding of the correlation between micro-level network structures and global network functions.

Network Higher-Order Structure Dismantling.

Diverse higher-order structures, foundational for supporting a network's "meta-functions", play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been consistently overlooked. In this paper, we introduce the concept of dismantling higher-order structures, with the objective of disrupting not only network connectivity but also eradicating all higher-order structures in each branch, thereby ensuring thorough functional paralysis. Given the diversity and unknown specifics of higher-order structures, identifying and targeting them individually is not practical or even feasible. Fortunately, their close association with k-cores arises from their internal high connectivity. Thus, we transform higher-order structure measurement into measurements on k-cores with corresponding orders. Furthermore, we propose the Belief Propagation-guided Higher-order Dismantling (BPHD) algorithm, minimizing dismantling costs while achieving maximal disruption to connectivity and higher-order structures, ultimately converting the network into a forest. BPHD exhibits the explosive vulnerability of network higher-order structures, counterintuitively showcasing decreasing dismantling costs with increasing structural complexity. Our findings offer a novel approach for dismantling malignant networks, emphasizing the substantial challenges inherent in safeguarding against such malicious attacks.

Transcriptomics of Leaf Development in the Endangered Dioecious Magnolia kwangsiensis: Molecular Basis Underpinning Specialized Metabolism Genes.

Magnolia kwangsiensis, a dioecious tree native to China, is recognized not only for its status as an at-risk species but also for its potential in therapeutic applications courtesy of its bioactive compounds. However, the genetic underpinnings of its leaf development and compound biosynthesis are not well documented. Our study aims to bridge this knowledge gap through comparative transcriptomics, analyzing gene expression through different leaf maturation stages. We studied the transcriptome of M. kwangsiensis leaves by applying RNA sequencing at juvenile, tender, and mature phases. We identified differentially expressed genes (DEGs) to explore transcriptional changes accompanying the developmental trajectory. Our analysis delineates the transcriptional landscape of over 20,000 genes with over 6000 DEGs highlighting significant transcriptional shifts throughout leaf maturation. Mature leaves demonstrated upregulation in pathways related to photosynthesis, cell wall formation, and polysaccharide production, affirming their structural integrity and specialized metabolic functions. Our GO and KEGG enrichment analyses underpin these findings. Furthermore, we unveiled coordinated gene activity correlating development with synthesizing therapeutically relevant polysaccharides. We identified four novel glycosyltransferases potentially pivotal in this synergistic mechanism. Our study uncovers the complementary evolutionary forces that concurrently sculpt structural and chemical defenses. These genetic mechanisms calibrate leaf tissue resilience and biochemical efficacy.

Integrative analysis of microbiota and metabolomics in chromium-exposed silkworm (Bombyx mori) midguts based on 16S rDNA sequencing and LC/MS metabolomics.

The gut microbiota, a complex ecosystem integral to host wellbeing, is modulated by environmental triggers, including exposure to heavy metals such as chromium. This study aims to comprehensively explore chromium-induced gut microbiota and metabolomic shifts in the quintessential lepidopteran model organism, the silkworm (Bombyx mori). The research deployed 16S rDNA sequence analysis and LC/MS metabolomics in its experimental design, encompassing a control group alongside low (12 g/kg) and high (24 g/kg) feeding chromium dosing regimens. Considerable heterogeneity in microbial diversity resulted between groups. Weissella emerged as potentially resilient to chromium stress, while elevated Propionibacterium was noted in the high chromium treatment group. Differential analysis tools LEfSe and random forest estimation identified key species like like Cupriavidus and unspecified Myxococcales, offering potential avenues for bioremediation. An examination of gut functionality revealed alterations in the KEGG pathways correlated with biosynthesis and degradation, suggesting an adaptive metabolic response to chromium-mediated stress. Further results indicated consequential fallout in the context of metabolomic alterations. These included an uptick in histidine and dihydropyrimidine levels under moderate-dose exposure and a surge of gentisic acid with high-dose chromium exposure. These are critical players in diverse biological processes ranging from energy metabolism and stress response to immune regulation and antioxidative mechanisms. Correlative analyses between bacterial abundance and metabolites mapped noteworthy relationships between marker bacterial species, such as Weissella and Pelomonas, and specific metabolites, emphasizing their roles in enzyme regulation, synaptic processes, and lipid metabolism. Probiotic bacteria showed robust correlations with metabolites implicated in stress response, lipid metabolism, and antioxidant processes. Our study reaffirms the intricate ties between gut microbiota and metabolite profiles and decodes some systemic adaptations under heavy-metal stress. It provides valuable insights into ecological and toxicological aspects of chromium exposure that can potentially influence silkworm resilience.

Hyper-Null Models and Their Applications.

Null models are crucial tools for investigating network topological structures. However, research on null models for higher-order networks is still relatively scarce. In this study, we introduce an innovative method to construct null models for hypergraphs, namely the hyperedge swapping-based method. By preserving certain network properties while altering others, we generate six hyper-null models with various orders and analyze their interrelationships. To validate our approach, we first employ hypergraph entropy to assess the randomness of these null models across four datasets. Furthermore, we examine the differences in important statistical properties between the various null models and the original networks. Lastly, we investigate the impact of hypergraph randomness on network dynamics using the proposed hyper-null models, focusing on dismantling and epidemic contagion. The findings show that our proposed hyper-null models are applicable to various scenarios. By introducing a comprehensive framework for generating and analyzing hyper-null models, this research opens up avenues for further exploration of the intricacies of network structures and their real-world implications.

Higher-order link prediction via local information.

Link prediction has been widely studied as an important research direction. Higher-order link prediction has gained, in particular, significant attention since higher-order networks provide a more accurate description of real-world complex systems. However, higher-order networks contain more complex information than traditional pairwise networks, making the prediction of higher-order links a formidable challenging task. Recently, researchers have discovered that local features have advantages over long-range features in higher-order link prediction. Therefore, it is necessary to develop more efficient and concise higher-order link prediction algorithms based on local features. In this paper, we proposed two similarity metrics via local information, simplicial decomposition weight and closed ratio weight, to predict possible future higher-order interactions (simplices) in simplicial networks. These two algorithms capture local higher-order information at two aspects: simplex decomposition and cliques' state (closed or open). We tested their performance in eight empirical simplicial networks, and the results show that our proposed metrics outperform other benchmarks in predicting third-order and fourth-order interactions (simplices) in most cases. In addition, we explore the robustness of the proposed algorithms, and the results suggest that the performance of these novel algorithms is advanced under different sizes of training sets.

Predicting the Popularity of Information on Social Platforms without Underlying Network Structure.

The ability to predict the size of information cascades in online social networks is crucial for various applications, including decision-making and viral marketing. However, traditional methods either rely on complicated time-varying features that are challenging to extract from multilingual and cross-platform content, or on network structures and properties that are often difficult to obtain. To address these issues, we conducted empirical research using data from two well-known social networking platforms, WeChat and Weibo. Our findings suggest that the information-cascading process is best described as an activate-decay dynamic process. Building on these insights, we developed an activate-decay (AD)-based algorithm that can accurately predict the long-term popularity of online content based solely on its early repost amount. We tested our algorithm using data from WeChat and Weibo, demonstrating that we could fit the evolution trend of content propagation and predict the longer-term dynamics of message forwarding from earlier data. We also discovered a close correlation between the peak forwarding amount of information and the total amount of dissemination. Finding the peak of the amount of information dissemination can significantly improve the prediction accuracy of our model. Our method also outperformed existing baseline methods for predicting the popularity of information.

Toward Detecting Previously Undiscovered Interaction Types in Networked Systems.

Studying networked systems in a variety of domains, including biology, social science, and Internet of Things, has recently received a surge of attention. For a networked system, there are usually multiple types of interactions between its components, and such interaction-type information is crucial since it always associated with important features. However, some interaction types that actually exist in the network may not be observed in the metadata collected in practice. This article proposes an approach aiming to detect previously undiscovered interaction types (PUITs) in networked systems. The first step in our proposed PUIT detection approach is to answer the following fundamental question: is it possible to effectively detect PUITs without utilizing metadata other than the existing incomplete interaction-type information and the connection information of the system? Here, we first propose a temporal network model which can be used to mimic any real network and then discover that some special networks which fit the model shall a common topological property. Supported by this discovery, we finally develop a PUIT detection method for networks which fit the proposed model. Both analytical and numerical results show this detection method is more effective than the baseline method, demonstrating that effectively detecting PUITs in networks is achievable. More studies on PUIT detection are of significance and in great need since this approach should be as essential as the previously undiscovered node-type detection which has gained great success in the field of biology.

The simple regularities in the dynamics of online news impact.

Online news can quickly reach and affect millions of people, yet we do not know yet whether there exist potential dynamical regularities that govern their impact on the public. We use data from two major news outlets, BBC and New York Times, where the number of user comments can be used as a proxy of news impact. We find that the impact dynamics of online news articles does not exhibit popularity patterns found in many other social and information systems. In particular, we find that a simple exponential distribution yields a better fit to the empirical news impact distributions than a power-law distribution. This observation is explained by the lack or limited influence of the otherwise omnipresent rich-get-richer mechanism in the analyzed data. The temporal dynamics of the news impact exhibits a universal exponential decay which allows us to collapse individual news trajectories into an elementary single curve. We also show how daily variations of user activity directly influence the dynamics of the article impact. Our findings challenge the universal applicability of popularity dynamics patterns found in other social contexts. Supplementary Information: The online version contains supplementary material available at 10.1007/s42001-021-00140-w.

History-dependent percolation on multiplex networks.

The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, study of the connections between different percolation transitions is still lacking. Here we propose a unified framework to study the origins of the discontinuous transitions of the percolation process on interacting networks. The model evolves in generations with the result of the present percolation depending on the previous state, and thus is history-dependent. Both theoretical analysis and Monte Carlo simulations reveal that the nature of the transition remains the same at finite generations but exhibits an abrupt change for the infinite generation. We use brain functional correlation and morphological similarity data to show that our model also provides a general method to explore the network structure and can contribute to many practical applications, such as detecting the abnormal structures of human brain networks.

Deep Collaborative Filtering for Prediction of Disease Genes.

Accurate prioritization of potential disease genes is a fundamental challenge in biomedical research. Various algorithms have been developed to solve such problems. Inductive Matrix Completion (IMC) is one of the most reliable models for its well-established framework and its superior performance in predicting gene-disease associations. However, the IMC method does not hierarchically extract deep features, which might limit the quality of recovery. In this case, the architecture of deep learning, which obtains high-level representations and handles noises and outliers presented in large-scale biological datasets, is introduced into the side information of genes in our Deep Collaborative Filtering (DCF) model. Further, for lack of negative examples, we also exploit Positive-Unlabeled (PU) learning formulation to low-rank matrix completion. Our approach achieves substantially improved performance over other state-of-the-art methods on diseases from the Online Mendelian Inheritance in Man (OMIM) database. Our approach is 10 percent more efficient than standard IMC in detecting a true association, and significantly outperforms other alternatives in terms of the precision-recall metric at the top-k predictions. Moreover, we also validate the disease with no previously known gene associations and newly reported OMIM associations. The experimental results show that DCF is still satisfactory for ranking novel disease phenotypes as well as mining unexplored relationships. The source code and the data are available at https://github.com/xzenglab/DCF.

Relationship Between Body Mass Index and Recurrence/Anal Fistula Formation Following Initial Operation for Anorectal Abscess.

BACKGROUND The association between body mass index (BMI) and recurrence of anorectal abscess remains controversial. This study investigated the exact relationship between BMI and anorectal abscess recurrence or anal fistula formation following initial surgery. MATERIAL AND METHODS This was a retrospective registry-based study conducted at the First Affiliated Hospital of Guizhou University of Chinese Medicine. Patients treated for anorectal abscess from 01/2015 to 03/2016 were included. Clinical data and time to recurrence were recorded. The Cox regression model was used to estimate the association between BMI and recurrence. RESULTS A total of 790 patients were operated on during the study period. The average age of the participants was 38.3±11.6 years, and 83.2% were male. Median follow-up was 27 (range, 1-38) months. Compared with the low BMI (range, 15.7-22.8 kg/m²) patients, the high BMI (range, 26.0-40.6 kg/m²) patients showed higher risk of recurrence (HR=1.75, 95% CI: 1.15-2.67). In the non-adjusted model, high BMI was found to be positively correlated with recurrence (HR=1.62, 95% CI: 1.10-2.40, P=0.02), and a stronger association was found in the fully adjusted model (HR=1.75, 95% CI: 1.15-2.67, P=0.01). BMI was also used as a continuous variable for sensitivity analysis, and a similar trend was observed (P=0.01 for trend). CONCLUSIONS Elevated BMI is an independent risk factor of anorectal abscess recurrence and for increased risk of abscess recurrence or anal fistula formation.

Totally homogeneous networks.

In network science, the non-homogeneity of node degrees has been a concerning issue for study. Yet, with today's modern web technologies, the traditional social communication topologies have evolved from node-central structures into online cycle-based communities, urgently requiring new network theories and tools. Switching the focus from node degrees to network cycles could reveal many interesting properties from the perspective of totally homogenous networks or sub-networks in a complex network, especially basic simplexes (cliques) such as links and triangles. Clearly, compared with node degrees, it is much more challenging to deal with network cycles. For studying the latter, a new clique vector-space framework is introduced in this paper, where the vector space with a basis consisting of links has a dimension equal to the number of links, that with a basis consisting of triangles has the dimension equal to the number of triangles and so on. These two vector spaces are related through a boundary operator, for example mapping the boundary of a triangle in one space to the sum of three links in the other space. Under the new framework, some important concepts and methodologies from algebraic topology, such as characteristic number, homology group and Betti number, will play a part in network science leading to foreseeable new research directions. As immediate applications, the paper illustrates some important characteristics affecting the collective behaviors of complex networks, some new cycle-dependent importance indexes of nodes and implications for network synchronization and brain-network analysis.

Prediction of potential disease-associated microRNAs using structural perturbation method.

Motivation: The identification of disease-related microRNAs (miRNAs) is an essential but challenging task in bioinformatics research. Similarity-based link prediction methods are often used to predict potential associations between miRNAs and diseases. In these methods, all unobserved associations are ranked by their similarity scores. Higher score indicates higher probability of existence. However, most previous studies mainly focus on designing advanced methods to improve the prediction accuracy while neglect to investigate the link predictability of the networks that present the miRNAs and diseases associations. In this work, we construct a bilayer network by integrating the miRNA-disease network, the miRNA similarity network and the disease similarity network. We use structural consistency as an indicator to estimate the link predictability of the related networks. On the basis of the indicator, a derivative algorithm, called structural perturbation method (SPM), is applied to predict potential associations between miRNAs and diseases. Results: The link predictability of bilayer network is higher than that of miRNA-disease network, indicating that the prediction of potential miRNAs-diseases associations on bilayer network can achieve higher accuracy than based merely on the miRNA-disease network. A comparison between the SPM and other algorithms reveals the reliable performance of SPM which performed well in a 5-fold cross-validation. We test fifteen networks. The AUC values of SPM are higher than some well-known methods, indicating that SPM could serve as a useful computational method for improving the identification accuracy of miRNA‒disease associations. Moreover, in a case study on breast neoplasm, 80% of the top-20 predicted miRNAs have been manually confirmed by previous experimental studies. Availability and implementation: https://github.com/lecea/SPM-code.git. Supplementary information: Supplementary data are available at Bioinformatics online.

Link Prediction in Bipartite Nested Networks.

Real networks typically studied in various research fields-ecology and economic complexity, for example-often exhibit a nested topology, which means that the neighborhoods of high-degree nodes tend to include the neighborhoods of low-degree nodes. Focusing on nested networks, we study the problem of link prediction in complex networks, which aims at identifying likely candidates for missing links. We find that a new method that takes network nestedness into account outperforms well-established link-prediction methods not only when the input networks are sufficiently nested, but also for networks where the nested structure is imperfect. Our study paves the way to search for optimal methods for link prediction in nested networks, which might be beneficial for World Trade and ecological network analysis.

Efficient network disintegration under incomplete information: the comic effect of link prediction.

The study of network disintegration has attracted much attention due to its wide applications, including suppressing the epidemic spreading, destabilizing terrorist network, preventing financial contagion, controlling the rumor diffusion and perturbing cancer networks. The crux of this matter is to find the critical nodes whose removal will lead to network collapse. This paper studies the disintegration of networks with incomplete link information. An effective method is proposed to find the critical nodes by the assistance of link prediction techniques. Extensive experiments in both synthetic and real networks suggest that, by using link prediction method to recover partial missing links in advance, the method can largely improve the network disintegration performance. Besides, to our surprise, we find that when the size of missing information is relatively small, our method even outperforms than the results based on complete information. We refer to this phenomenon as the "comic effect" of link prediction, which means that the network is reshaped through the addition of some links that identified by link prediction algorithms, and the reshaped network is like an exaggerated but characteristic comic of the original one, where the important parts are emphasized.

Predicting missing links and identifying spurious links via likelihood analysis.

Real network data is often incomplete and noisy, where link prediction algorithms and spurious link identification algorithms can be applied. Thus far, it lacks a general method to transform network organizing mechanisms to link prediction algorithms. Here we use an algorithmic framework where a network's probability is calculated according to a predefined structural Hamiltonian that takes into account the network organizing principles, and a non-observed link is scored by the conditional probability of adding the link to the observed network. Extensive numerical simulations show that the proposed algorithm has remarkably higher accuracy than the state-of-the-art methods in uncovering missing links and identifying spurious links in many complex biological and social networks. Such method also finds applications in exploring the underlying network evolutionary mechanisms.

The H-index of a network node and its relation to degree and coreness.

Identifying influential nodes in dynamical processes is crucial in understanding network structure and function. Degree, H-index and coreness are widely used metrics, but previously treated as unrelated. Here we show their relation by constructing an operator , in terms of which degree, H-index and coreness are the initial, intermediate and steady states of the sequences, respectively. We obtain a family of H-indices that can be used to measure a node's importance. We also prove that the convergence to coreness can be guaranteed even under an asynchronous updating process, allowing a decentralized local method of calculating a node's coreness in large-scale evolving networks. Numerical analyses of the susceptible-infected-removed spreading dynamics on disparate real networks suggest that the H-index is a good tradeoff that in many cases can better quantify node influence than either degree or coreness.

Empirical Studies on the Network of Social Groups: The Case of Tencent QQ.

BACKGROUND: Participation in social groups are important but the collective behaviors of human as a group are difficult to analyze due to the difficulties to quantify ordinary social relation, group membership, and to collect a comprehensive dataset. Such difficulties can be circumvented by analyzing online social networks. METHODOLOGY/PRINCIPAL FINDINGS: In this paper, we analyze a comprehensive dataset released from Tencent QQ, an instant messenger with the highest market share in China. Specifically, we analyze three derivative networks involving groups and their members-the hypergraph of groups, the network of groups and the user network-to reveal social interactions at microscopic and mesoscopic level. CONCLUSIONS/SIGNIFICANCE: Our results uncover interesting behaviors on the growth of user groups, the interactions between groups, and their relationship with member age and gender. These findings lead to insights which are difficult to obtain in social networks based on personal contacts.

Toward link predictability of complex networks.

The organization of real networks usually embodies both regularities and irregularities, and, in principle, the former can be modeled. The extent to which the formation of a network can be explained coincides with our ability to predict missing links. To understand network organization, we should be able to estimate link predictability. We assume that the regularity of a network is reflected in the consistency of structural features before and after a random removal of a small set of links. Based on the perturbation of the adjacency matrix, we propose a universal structural consistency index that is free of prior knowledge of network organization. Extensive experiments on disparate real-world networks demonstrate that (i) structural consistency is a good estimation of link predictability and (ii) a derivative algorithm outperforms state-of-the-art link prediction methods in both accuracy and robustness. This analysis has further applications in evaluating link prediction algorithms and monitoring sudden changes in evolving network mechanisms. It will provide unique fundamental insights into the above-mentioned academic research fields, and will foster the development of advanced information filtering technologies of interest to information technology practitioners.