Search Results (14)

This work is framed as an application of static and small exponential random graph models for complex networks in multiple layers. This document revisits the small network and exhibits its potential. Examining the bibliography reveals considerable interest in large and dynamic complex networks. This research examines the application of small networks (50,000 population) for analyzing global commerce, conducting a comparative graph structure of the tariffs, and importing multilayer networks. The authors created and described the scenario where the readers can compare the graph models visually, at a glance. The proposed methodology represents a significant contribution, providing detailed descriptions and instructions, thereby ensuring the operational effectiveness of the application. The method is organized into five distinct blocks (Bn) and an accompanying appendix containing reproduction notes. Each block encompasses a primary task and associated sub-tasks, articulated through a hierarchical series of steps. The most challenging mathematical aspects of a small network analysis pertain to modeling and sample selection (sel_p). This document describes several modeling tasks that confirm that sel_p = 10 is the best option, including modeling the edges and the convergence and covariance model parameters, modeling the node factor by vertex names, Pearson residual distributions, goodness of fit, and more. This method establishes a foundation for addressing the intricate questions derived from the established hypotheses. It provides eight model specifications and a detailed description. Given the scope of this investigation, a historical examination of the relationships between different network actors is deemed essential, providing context for the study of actors engaged in global trade. Various analytical perspectives (six), encompassing degree analyses, diameter and edges, hubs and authority, co-citation and cliques in mutual and collapse approaches, k-core, and clustering, facilitate the identification of the specific roles played by actors within the importation network in comparison to the tariff network. This study focuses on the Latin American and Caribbean region. Full article

We consider the problem of finding the largest clique of a graph. This is an NP-hard problem and no exact algorithm to solve it exactly in polynomial time is known to exist. Several heuristic approaches have been proposed to find approximate solutions. Markov Chain Monte Carlo is one of these. In the context of Markov Chain Monte Carlo, we present a class of “parallel dynamics”, known as Probabilistic Cellular Automata, which can be used in place of the more standard choice of sequential “single spin flip” to sample from a probability distribution concentrated on the largest cliques of the graph. We perform a numerical comparison between the two classes of chains both in terms of the quality of the solution and in terms of computational time. We show that the parallel dynamics are considerably faster than the sequential ones while providing solutions of comparable quality. Full article

Three-dimensional point cloud registration is a critical task in 3D perception for sensors that aims to determine the optimal alignment between two point clouds by finding the best transformation. Existing methods like RANSAC and its variants often face challenges, such as sensitivity to low overlap rates, high computational costs, and susceptibility to outliers, leading to inaccurate results, especially in complex or noisy environments. In this paper, we introduce a novel 3D registration method, CL-PCR, inspired by the concept of maximal cliques and built upon the SC²-PCR framework. Our approach allows for the flexible use of smaller sampling subsets to extract more local consensus information, thereby generating accurate pose hypotheses even in scenarios with low overlap between point clouds. This method enhances robustness against low overlap and reduces the influence of outliers, addressing the limitations of traditional techniques. First, we construct a graph matrix to represent the compatibility relationships among the initial correspondences. Next, we build clique-likes subsets of various sizes within the graph matrix, each representing a consensus set. Then, we compute the transformation hypotheses for the subsets using the SVD algorithm and select the best hypothesis for registration based on evaluation metrics. Extensive experiments demonstrate the effectiveness of CL-PCR. In comparison experiments on the 3DMatch/3DLoMatch datasets using both FPFH and FCGF descriptors, our Fast-CL-PCRv1 outperforms state-of-the-art algorithms, achieving superior registration performance. Additionally, we validate the practicality and robustness of our method with real-world data. Full article

Clique counts are crucial in applications like detecting communities in social networks and recurring patterns in bioinformatics. Counting k-cliques—a fully connected subgraph with k nodes, where each node has a direct, mutual, and symmetric relationship with every other node—becomes computationally challenging for larger k due to combinatorial explosion, especially in large, dense graphs. Existing exact methods have difficulties beyond k = 10, especially on large datasets, while sampling-based approaches often involve trade-offs in terms of accuracy, resource utilization, and efficiency. This difficulty becomes more pronounced in dense graphs as the number of potential k-cliques grows exponentially. We present Boundary-driven approximations of k-cliques (BDAC), a novel algorithm that approximates k-clique counts without using recursive procedures or sampling methods. BDAC offers both lower and upper bounds for k-cliques at local (per-vertex) and global levels, making it ideal for large, dense graphs. Unlike other approaches, BDAC’s complexity remains unaffected by the value of k. We demonstrate its effectiveness by comparing it with leading algorithms across various datasets, focusing on k values ranging from 8 to 50. Full article

The Minimum Vertex Weighted Coloring (MinVWC) problem is an important generalization of the classic Minimum Vertex Coloring (MinVC) problem which is NP-hard. Given a simple undirected graph $G=(V,E)$, the MinVC problem is to find a coloring s.t. any pair of adjacent vertices are assigned different colors and the number of colors used is minimized. The MinVWC problem associates each vertex with a positive weight and defines the weight of a color to be the weight of its heaviest vertices, then the goal is the find a coloring that minimizes the sum of weights over all colors. Among various approaches, reduction is an effective one. It tries to obtain a subgraph whose optimal solutions can conveniently be extended into optimal ones for the whole graph, without costly branching. In this paper, we propose a reduction algorithm based on maximal clique enumeration. More specifically our algorithm utilizes a certain proportion of maximal cliques and obtains lower bounds in order to perform reductions. It alternates between clique sampling and graph reductions and consists of three successive procedures: promising clique reductions, better bound reductions and post reductions. Experimental results show that our algorithm returns considerably smaller subgraphs for numerous large benchmark graphs, compared to the most recent method named RedLS. Also, we evaluate individual impacts and some practical properties of our algorithm. Furthermore, we have a theorem which indicates that the reduction effects of our algorithm are equivalent to that of a counterpart which enumerates all maximal cliques in the whole graph if the run time is sufficiently long. Full article

Background: Insulin resistance (IR) is a major contributing factor to the pathogenesis of metabolic syndrome and type 2 diabetes mellitus (T2D). Adipocyte metabolism is known to play a crucial role in IR. Therefore, the aims of this study were to identify metabolism-related proteins that could be used as potential biomarkers of IR and to investigate the role of N⁶-methyladenosine (m⁶A) modification in the pathogenesis of this condition. Methods: RNA-seq data on human adipose tissue were retrieved from the Gene Expression Omnibus database. The differentially expressed genes of metabolism-related proteins (MP-DEGs) were screened using protein annotation databases. Biological function and pathway annotations of the MP-DEGs were performed through Gene Ontology and Kyoto Encyclopedia of Genes and Genomes pathway analyses. Key MP-DEGs were screened, and a protein–protein interaction (PPI) network was constructed using STRING, Cytoscape, MCODE, and CytoHubba. LASSO regression analysis was used to select primary hub genes, and their clinical performance was assessed using receiver operating characteristic (ROC) curves. The expression of key MP-DEGs and their relationship with m⁶A modification were further verified in adipose tissue samples collected from healthy individuals and patients with IR. Results: In total, 69 MP-DEGs were screened and annotated to be enriched in pathways related to hormone metabolism, low-density lipoprotein particle and carboxylic acid transmembrane transporter activity, insulin signaling, and AMPK signaling. The MP-DEG PPI network comprised 69 nodes and 72 edges, from which 10 hub genes (FASN, GCK, FGR, FBP1, GYS2, PNPLA3, MOGAT1, SLC27A2, PNPLA3, and ELOVL6) were identified. FASN was chosen as the key gene because it had the highest maximal clique centrality (MCC) score. GCK, FBP1, and FGR were selected as primary genes by LASSO analysis. According to the ROC curves, GCK, FBP1, FGR, and FASN could be used as potential biomarkers to detect IR with good sensitivity and accuracy (AUC = 0.80, 95% CI: 0.67–0.94; AUC = 0.86, 95% CI: 0.74–0.94; AUC = 0.83, 95% CI: 0.64–0.92; AUC = 0.78, 95% CI: 0.64–0.92). The expression of FASN, GCK, FBP1, and FGR was significantly correlated with that of IGF2BP3, FTO, EIF3A, WTAP, METTL16, and LRPPRC (p < 0.05). In validation clinical samples, the FASN was moderately effective for detecting IR (AUC = 0.78, 95% CI: 0.69–0.80), and its expression was positively correlated with the methylation levels of FASN (r = 0.359, p = 0.001). Conclusion: Metabolism-related proteins play critical roles in IR. Moreover, FASN and GCK are potential biomarkers of IR and may be involved in the development of T2D via their m⁶A modification. These findings offer reliable biomarkers for the early detection of T2D and promising therapeutic targets. Full article

The importance of school leadership and workplace stress is a recurring theme in education-based research. The literature reports that workplace stress in teaching is a difficult matter to resolve, with mixed outcomes from interventions. The aim of this initial scoping study was to report on the experiences of school leaders with interpersonal conflict (IPC), a known cause of this workplace stress. Accordingly, a sample of twelve school leaders working in Irish post primary schools were recruited to participate in this study using semi-structured interviews. All twelve participants reported experiencing workplace stress and linked other people as a source of this stress. Nine out of twelve had experienced IPC as a school leader. School leaders also noted a fear of reporting workplace stress. Half of the participants reported becoming ill from workplace stress and had taken time off from work. Participants also reported ‘balkanisation’ of like-minded cliques that tried to exert control over other groups. None of the participants expressed confidence in organisational strategies to resolve workplace stress or IPC. This study demonstrates that resolutions for IPC were scant. Further research is needed to conceptualise this phenomenon in the school environment and to support school leaders to effectively manage IPC as a cause of workplace stress. Full article

Forest fragments are characteristic features of many megacities that have survived the urbanisation process and are often represented by unique assemblages of flora and fauna. Such woodlands are representations of nature in the city—often dominated by non-native and invasive species that coexist with resilient native congeners and purposefully introduced flora. These forest fragments also provide significant ecosystem services to urban society and therefore, understanding their compositional patterns is of considerable importance for conservation and management. In this work, we use a complex network approach to investigate species assemblages across six distinct urban forest fragments in the South Delhi Ridge area of the National Capital Territory, India. We generate bipartite ecological networks using conventional vegetation sampling datasets, followed by network partitioning to identify multiple cliques across the six forest fragments. Our results show that urban woodlands primarily form invasive–native associations, and that major invasive species, such as Prosopis juliflora and Lantana camara exclude each other while forming cliques. Our findings have implications for the conservation of these urban forests and highlight the importance of using network approaches in vegetation analysis. Full article

The present study aimed to identify potential therapeutic targets for esophageal squamous cell carcinoma (ESCC). The gene expression profile GSE161533 contained 84 samples, in that 28 tumor tissues and 28 normal tissues encoded as ESCC patients were retrieved from the Gene Expression Omnibus database. The obtained data were validated and screened for differentially expressed genes (DEGs) between normal and tumor tissues with the GEO2R tool. Next, the protein–protein network (PPI) was constructed using the (STRING 2.0) and reconstructed with Cytoscape 3.8.2, and the top ten hub genes (HGsT10) were predicted using the Maximal Clique Centrality (MCC) algorithm of the CytoHubba plugin. The identified hub genes were mapped in GSE161533, and their expression was determined and compared with The Cancer Genome Atlas (TCGA.) ESCC patient’s samples. The overall survival rate for HGsT10 wild and mutated types was analyzed with the Gene Expression Profiling Interactive Analysis2 (GEPIA2) server and UCSC Xena database. The functional and pathway enrichment analysis was performed using the WebGestalt database with the reference gene from lumina human ref 8.v3.0 version. The promoter methylation for the HGsT10 was identified using the UALCAN server. Additionally, the miRNA-HGsT10 regulatory network was constructed to identify the top ten hub miRNAs (miRT10). Finally, we identified the top ten novel driving genes from the DEGs of GSE161533 ESCC patient’s sample using a multi-omics approach. It may provide new insights into the diagnosis and treatment for the ESCC affected patients early in the future. Full article

In 1943, McCulloch and Pitts introduced a discrete recurrent neural network as a model for computation in brains. The work inspired breakthroughs such as the first computer design and the theory of finite automata. We focus on learning in Hopfield networks, a special case with symmetric weights and fixed-point attractor dynamics. Specifically, we explore minimum energy flow (MEF) as a scalable convex objective for determining network parameters. We catalog various properties of MEF, such as biological plausibility, and then compare to classical approaches in the theory of learning. Trained Hopfield networks can perform unsupervised clustering and define novel error-correcting coding schemes. They also efficiently find hidden structures (cliques) in graph theory. We extend this known connection from graphs to hypergraphs and discover n-node networks with robust storage of $2^{\mathsf{\Omega }\left(n^{1-ϵ}\right)}$ memories for any $ϵ>0$. In the case of graphs, we also determine a critical ratio of training samples at which networks generalize completely. Full article

Recent discoveries of distinct molecular subtypes have led to remarkable advances in treatment for a variety of diseases. While subtyping via unsupervised clustering has received a great deal of interest, most methods rely on basic statistical or machine learning methods. At the same time, techniques based on graph clustering, particularly clique-based strategies, have been successfully used to identify disease biomarkers and gene networks. A graph theoretical approach based on the paraclique algorithm is described that can easily be employed to identify putative disease subtypes and serve as an aid in outlier detection as well. The feasibility and potential effectiveness of this method is demonstrated on publicly available gene co-expression data derived from patient samples covering twelve different disease families. Full article

Rhabdomyosarcoma is subclassified by the presence or absence of a recurrent chromosome translocation that fuses the FOXO1 and PAX3 or PAX7 genes. The fusion protein (FOXO1-PAX3/7) retains both binding domains and becomes a novel and potent transcriptional regulator in rhabdomyosarcoma subtypes. Many studies have characterized and integrated genomic, transcriptomic, and epigenomic differences among rhabdomyosarcoma subtypes that contain the FOXO1-PAX3/7 gene fusion and those that do not; however, few investigations have investigated how gene co-expression networks are altered by FOXO1-PAX3/7. Although transcriptional data offer insight into one level of functional regulation, gene co-expression networks have the potential to identify biological interactions and pathways that underpin oncogenesis and tumorigenicity. Thus, we examined gene co-expression networks for rhabdomyosarcoma that were FOXO1-PAX3 positive, FOXO1-PAX7 positive, or fusion negative. Gene co-expression networks were mined using local maximum Quasi-Clique Merger (lmQCM) and analyzed for co-expression differences among rhabdomyosarcoma subtypes. This analysis observed 41 co-expression modules that were shared between fusion negative and positive samples, of which 17/41 showed significant up- or down-regulation in respect to fusion status. Fusion positive and negative rhabdomyosarcoma showed differing modularity of co-expression networks with fusion negative (n = 109) having significantly more individual modules than fusion positive (n = 53). Subsequent analysis of gene co-expression networks for PAX3 and PAX7 type fusions observed 17/53 were differentially expressed between the two subtypes. Gene list enrichment analysis found that gene ontology terms were poorly matched with biological processes and molecular function for most co-expression modules identified in this study; however, co-expressed modules were frequently localized to cytobands on chromosomes 8 and 11. Overall, we observed substantial restructuring of co-expression networks relative to fusion status and fusion type in rhabdomyosarcoma and identified previously overlooked genes and pathways that may be targeted in this pernicious disease. Full article

Challenges in changing school system functioning to orient them towards health are commonly underestimated. Understanding the social interactions of school staff from a complex systems perspective may provide valuable insight into how system dynamics may impede or facilitate the promotion of health and wellbeing. Ego social network analysis was employed with wellbeing leads within four diverse case study schools to identify variability in embeddedness of health and wellbeing roles. This variation, as well as the broader context, was then explored through semi-structured qualitative interviews with school staff and a Healthy Schools Coordinator, sampled from the wellbeing leads’ ego-networks. Networks varied in terms of perceived importance and frequency of interactions, centrality, brokerage and cliques. Case study schools that showed higher engagement with health and wellbeing had highly organised, distributed leadership structures, dedicated wellbeing roles, senior leadership support and outside agencies embedded within school systems. Allocation of responsibility for wellbeing to a member of the senior leadership team alongside a distributed leadership approach may facilitate the reorientation of school systems towards health and wellbeing. Ego-network analysis to understand variance in complex school system starting points could be replicated on a larger scale and utilised to design complex interventions. Full article

Social support is an important predictor of the health of a population. Few studies have analyzed the influence of caregivers’ personal networks from a gender perspective. The aim of this study was to analyze the composition, structure, and function of informal caregiver support networks and to examine gender differences. It also aimed to explore the association between different network characteristics and self-perceived health among caregivers. We performed a social network analysis study using a convenience sample of 25 female and 25 male caregivers. A descriptive analysis of the caregivers and bivariate analyses for associations with self-perceived health were performed. The structural metrics analyzed were density; degree centrality mean; betweenness centrality mean; and number of cliques, components, and isolates. The variability observed in the structure of the networks was not explained by gender. Some significant differences between men and women were observed for network composition and function. Women received help mainly from women with a similar profile to them. Men’s networks were broader and more diverse and they had more help from outside family circles, although these outcomes were not statistically significant. Our results indicate the need to develop strategies that do not reinforce traditional gender roles, but rather encourage a greater sharing of responsibility among all parties. Full article