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Kalman filter (KF)-based methods for 3D multi-object tracking (MOT) in autonomous driving often face challenges when detections are missed due to occlusions, sensor noise, or objects moving out of view. This leads to data association failures and cumulative errors in the update stage, as traditional Kalman filters rely on linear state estimates that can drift significantly without measurement updates. To address this issue, we propose an enhanced Kalman filter with dummy nodes and prediction confidence (KDPBTracker) to improve tracking continuity and robustness in these challenging scenarios. First, we designed dummy nodes to act as pseudo-observations generated from past and nearby frame detections in cases of missed detection, allowing for stable associations within the data association matrix when real detections were temporarily unavailable. To address the uncertainty in these dummy nodes, we then proposed a prediction confidence score to reflect their reliability in data association. Additionally, we modified a constant acceleration motion model combined with position-based heading estimation to better control high-dimensional numerical fluctuations in the covariance matrix, enhancing the robustness of the filtering process, especially in highly dynamic scenarios. We further designed bipartite graph data association to refine Kalman filter updates by integrating geometric and motion information weighted by the prediction confidence of the dummy nodes. Finally, we designed a confidence-based retention track management module to dynamically manage track continuity and deletion based on temporal and reliability thresholds, improving tracking accuracy in complex environments. Our method achieves state-of-the-art performance on the nuScenes validation set, improving AMOTA by 1.8% over the baseline CenterPoint. Evaluation on the nuScenes dataset demonstrates that KDPBTracker significantly improves tracking accuracy, reduces ID switches, and enhances overall tracking continuity under challenging conditions. [ABSTRACT FROM AUTHOR]

We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity as well as the full spectrum distribution. For an integer d ∈ 3 , 7 , we find families of random semi-regular graphs that have higher algebraic connectivity than random d-regular graphs with the same number of vertices and edges. On the other hand, we show that regular graphs beat semi-regular graphs when d ≥ 8 . More generally, we study random semi-regular graphs whose average degree is d, not necessarily an integer. This provides a natural generalization of a d-regular graph in the case of a non-integer d . We characterize their algebraic connectivity in terms of a root of a certain sixth-degree polynomial. Finally, we construct a small-world-type network of an average degree of 2.5 with relatively high algebraic connectivity. We also propose some related open problems and conjectures. [ABSTRACT FROM AUTHOR]

The threshold protocol game is a graphical game that models the adoption of an idea or product through a population. There are two states players may take in the game, and the goal of the game is to motivate the state that begins in the minority to spread to every player. Here, the threshold protocol game is defined, and existence results are studied on infinite graphs. Many generalizations are proposed and applied. This work explores the impact of graph topology on the outcome of the threshold protocol game and consequently considers finite graphs. By exploiting the well-known topologies of complete and complete bipartite graphs, the outcome of the threshold protocol game can be fully characterized on these graphs. These characterizations are ideal, as they are given in terms of the game parameters. More generally, initial conditions in terms of game parameters that cause the preferred game outcome to occur are identified. It is shown that the necessary conditions differ between non-bipartite and bipartite graphs because non-bipartite graphs contain odd cycles while bipartite graphs do not. These results motivate the primary result of this work, which is an exhaustive list of achievable game outcomes on bipartite graphs. While possible outcomes are identified, it is noted that a complete characterization of when game outcomes occur is not possible on general bipartite graphs. [ABSTRACT FROM AUTHOR]

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel Graph Neural Network model designed to efficiently address complex matching problems at scale. HybridGNN leverages a combination of Graph Attention Networks (GATv2), Graph SAGE (SAGEConv), and Graph Isomorphism Networks (GIN) layers to enhance computational efficiency and model performance. Through extensive ablation experiments, we identify that while the SAGEConv layer demonstrates suboptimal performance in terms of accuracy and F1-score, configurations incorporating GATv2 and GIN layers show significant improvements. Specifically, in six-layer GNN architectures, the combinations of GATv2 and GIN layers with ratios of 4:2 and 5:1 yield superior accuracy and F1-score. Therefore, we name these GNN configurations HybridGNN1 and HybridGNN2. Additionally, techniques such as mixed precision training, gradient accumulation, and Jumping Knowledge networks are integrated to further optimize performance. Evaluations on an email communication dataset reveal that HybridGNNs outperform traditional algorithms such as the Hopcroft–Karp algorithm, the Hungarian algorithm, and the Blossom/Edmonds' algorithm, particularly for large and complex graphs. These findings highlight HybridGNN's robust capability to solve maximum matching problems in bipartite graphs, making it a powerful tool for analyzing large-scale and intricate graph data. Furthermore, our study aligns with the goals of the Symmetry and Asymmetry Study in Graph Theory special issue by exploring the role of symmetry in bipartite graph structures. By leveraging GNNs, we address the challenges related to symmetry and asymmetry in graph properties, thereby improving the reliability and fault tolerance of complex networks. [ABSTRACT FROM AUTHOR]

Matrix factorization has demonstrated outstanding performance in machine learning. Recently, graph-based matrix factorization has gained widespread attention. However, graph-based methods are only suitable for handling small amounts of data. This paper proposes a fast semi-supervised learning method using only matrix factorization, which considers both global and local information. By introducing bipartite graphs into symmetric matrix factorization, the technique can handle large datasets effectively. It is worth noting that by utilizing tag information, the proposed symmetric matrix factorization becomes convex and unconstrained, i.e., the non-convex problem min x (1 − x 2) 2 is transformed into a convex problem. This allows it to be optimized quickly using state-of-the-art unconstrained optimization algorithms. The computational complexity of the proposed method is O (n m d) , which is much lower than that of the original symmetric matrix factorization, which is O (n 2 d) , and even lower than that of other anchor-based methods, which is O (n m d + m 2 n + m 3) , where n represents the number of samples, d represents the number of features, and m ≪ n represents the number of anchors. The experimental results on multiple public datasets indicate that the proposed method achieves higher performance in less time. [ABSTRACT FROM AUTHOR]

The identification of drug–target interaction (DTI) is crucial for drug discovery. However, how to reduce the graph neural network's false positives due to its bias and negative transfer in the original bipartite graph remains to be clarified. Considering that the impact of heterogeneous auxiliary information on DTI varies depending on the drug and target, we established an adaptive enhanced personalized meta-knowledge transfer network named Meta Graph Association-Aware Contrastive Learning (MGACL), which can transfer personalized heterogeneous auxiliary information from different nodes and reduce data bias. Meanwhile, we propose a novel DTI association-aware contrastive learning strategy that aligns high-frequency drug representations with learned auxiliary graph representations to prevent negative transfer. Our study improves the DTI prediction performance by about 3%, evaluated by analyzing the area under the curve (AUC) and area under the precision–recall curve (AUPRC) compared with existing methods, which is more conducive to accurately identifying drug targets for the development of new drugs. [ABSTRACT FROM AUTHOR]

Recently, considerable attention has been directed toward graph-based semi-supervised learning (GSSL) as an effective approach for data labeling. Despite the progress achieved by current methodologies, several limitations persist. Firstly, many studies treat all samples equally in terms of weight and influence, disregarding the potential increased importance of samples near decision boundaries. Secondly, the detection of outlier-labeled data is crucial, as it can significantly impact model performance. Thirdly, existing models often struggle with predicting labels for unseen test data, restricting their utility in practical applications. Lastly, most graph-based algorithms rely on affinity matrices that capture pairwise similarities across all data points, thus limiting their scalability to large-scale databases. In this paper, we propose a novel GSSL algorithm tailored for large-scale databases, leveraging anchor points to mitigate the challenges posed by large affinity matrices. Additionally, our method enhances the influence of nodes near decision boundaries by assigning different weights based on their importance and using a mapping function from feature space to label space. Leveraging this mapping function enables direct label prediction for test samples without requiring iterative learning processes. Experimental evaluations on two extensive datasets (Norb and Covtype) demonstrate that our approach is scalable and outperforms existing GSSL methods in terms of performance metrics. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an efficient and effective algorithm for Graph-based Semi-Supervised Learning (GSSL). Unlike other GSSL methods, our proposed algorithm achieves efficiency by constructing a bipartite graph, which connects a small number of representative points to a large volume of raw data by capturing their underlying manifold structures. This bipartite graph, with a sparse and anti-diagonal affinity matrix which is symmetrical, serves as a low-rank approximation of the original graph. Consequently, our algorithm accelerates both the graph construction and label propagation steps. In particular, on the one hand, our algorithm computes the label propagation in closed-form, reducing its computational complexity from cubic to approximately linear with respect to the number of data points; on the other hand, our algorithm calculates the soft label matrix for unlabeled data using a closed-form solution, thereby gaining additional acceleration. Comprehensive experiments performed on six real-world datasets demonstrate the efficiency and effectiveness of our algorithm in comparison to five state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we present a noise-robust approach for the 3D pose estimation of multiple people using appearance similarity. The common methods identify the cross-view correspondences between the detected keypoints and determine their association with a specific person by measuring the distances between the epipolar lines and the joint locations of the 2D keypoints across all the views. Although existing methods achieve remarkable accuracy, they are still sensitive to camera calibration, making them unsuitable for noisy environments where any of the cameras slightly change angle or position. To address these limitations and fix camera calibration error in real-time, we propose a framework for 3D pose estimation which uses appearance similarity. In the proposed framework, we detect the 2D keypoints and extract the appearance feature and transfer it to the central server. The central server uses geometrical affinity and appearance similarity to match the detected 2D human poses to each person. Then, it compares these two groups to identify calibration errors. If a camera with the wrong calibration is identified, the central server fixes the calibration error, ensuring accuracy in the 3D reconstruction of skeletons. In the experimental environment, we verified that the proposed algorithm is robust against false geometrical errors. It achieves around 11.5% and 8% improvement in the accuracy of 3D pose estimation on the Campus and Shelf datasets, respectively. [ABSTRACT FROM AUTHOR]

Simple Summary: This study investigates the complex interactions between quill mites of the family Syringophilidae and starlings. We identified five species of quill mites infesting 24 species of starlings, uncovering intricate host–parasite dynamics across the Palaearctic, Afrotropical, Oriental, and Oceanian zoogeographical regions. A detailed statistical analysis of the Picobiinae–Sturnidae network revealed low connectivity but high modularity, indicating specific relationships between the mites and their starling hosts. The network structure demonstrated four distinct modules, highlighting the specialised and compartmentalised characteristics of these associations. Furthermore, the distribution of Picobia mites was found to align with the phylogeny of their starling hosts, with particular mites targeting specific starling clades. The social and breeding behaviours of starlings were observed to contribute to the high prevalence of these mites. This comprehensive network analysis provides new insights into the ecological dynamics of host–parasite interactions. The subfamily Picobiinae (Acariformes: Syringophilidae) comprises obligate and permanent parasites of birds found exclusively in the quills of contour feathers. We studied associations of picobiine mites with birds of the family Sturnidae (Aves: Passeriformes) across the Palaearctic, Afrotropical, Oriental, and Oceanian zoogeographical regions. Among the 414 examined bird individuals belonging to 44 species (35.2% of all sturnids), 103 individuals from 24 species (54.5% of examined species) were parasitised by quill mites. The diversity of mites was represented by five species, including one newly described, Picobia malayi Patan and Skoracki sp. n. Statistical analysis of the Picobiinae–Sturnidae bipartite network demonstrated a low connectance value (Con = 0.20) and high modularity, with significant differences in the H2′ specialisation index compared to null model values. The network structure, characterised by four distinct modules, highlighted the specificity and limited host range of the Picobiinae–Sturnidae associations. The distribution of Picobia species among starlings was congruent with the phylogeny of their hosts, with different mites parasitising specific clades of starlings. Additionally, the findings suggest that the social and breeding behaviours of starlings influence quite a high prevalence. Finally, our studies support the validity of museum collections to study these parasitic interactions. [ABSTRACT FROM AUTHOR]

Innovative Industrial Clusters (IIC), characterized by geographical aggregation and technological collaboration among technology enterprises and institutions, serve as pivotal drivers of regional economic competitiveness and technological advancements. Prior research on cluster identification, crucial for IIC analysis, has predominantly emphasized geographical dimensions while overlooking technological proximity. Addressing these limitations, this study introduces a comprehensive framework incorporating multiple indices and methods for accurately identifying IIC using patent data. To unearth latent technological insights within patent documents, Latent Dirichlet Allocation (LDA) is employed to generate topics from a collection of terms. Utilizing the applicants' names and addresses recorded in patents, an Application Programming Interface (API) map systems facilitates the extraction of geographic locations. Subsequently, a Multivariate Density-Based Spatial Clustering of Applications with Noise (MDBSCAN) algorithm, which accounts for both technological and spatial distances, is deployed to delineate IIC. Moreover, a bipartite network model based on patent geographic information collected from the patent is constructed to analyze the technological distribution on the geography and development mode of IIC. The utilization of the model and methodologies is demonstrated through a case study on the China flexible electronics industry (FEI). The findings reveal that the clusters identified via this novel approach are significantly correlated with both technological innovation and geographical factors. Moreover, the MDBSCAN algorithm demonstrates notable superiority over other algorithms in terms of computational precision and efficiency, as evidenced by the case analysis. [ABSTRACT FROM AUTHOR]

The bipartite polarization problem is an optimization problem where the goal is to find the highest polarized bipartition on a weighted and labeled graph that represents a debate developed through some social network, where nodes represent user's opinions and edges agreement or disagreement between users. This problem can be seen as a generalization of the maxcut problem, and in previous work, approximate solutions and exact solutions have been obtained for real instances obtained from Reddit discussions, showing that such real instances seem to be very easy to solve. In this paper, we further investigate the complexity of this problem by introducing an instance generation model where a single parameter controls the polarization of the instances in such a way that this correlates with the average complexity to solve those instances. The average complexity results we obtain are consistent with our hypothesis: the higher the polarization of the instance, the easier is to find the corresponding polarized bipartition. In view of the experimental results, it is computationally feasible to implement transparent mechanisms to monitor polarization on online discussions and to inform about solutions for creating healthier social media environments. [ABSTRACT FROM AUTHOR]

In the paper, we introduce the signless Laplacian A B C -matrix Q ̃ (G) = D ¯ (G) + A ̃ (G) , where D ¯ (G) is the diagonal matrix of A B C -degrees and A ̃ (G) is the A B C -matrix of G. The eigenvalues of the matrix Q ̃ (G) are the signless Laplacian A B C -eigenvalues of G. We give some basic properties of the matrix Q ̃ (G) , which includes relating independence number and clique number with signless Laplacian A B C -eigenvalues. For bipartite graphs, we show that the signless Laplacian A B C -spectrum and the Laplacian A B C -spectrum are the same. We characterize the graphs with exactly two distinct signless Laplacian A B C -eigenvalues. Also, we consider the problem of the characterization of the graphs with exactly three distinct signless Laplacian A B C -eigenvalues and solve it for bipartite graphs and, in some cases, for non-bipartite graphs. We also introduce the concept of the trace norm of the matrix Q ̃ (G) − t r (Q ̃ (G)) n I , called the signless Laplacian A B C -energy of G. We obtain some upper and lower bounds for signless Laplacian A B C -energy and characterize the extremal graphs attaining it. Further, for graphs of order at most 6, we compare the signless Laplacian energy and the A B C -energy with the signless Laplacian A B C -energy and found that the latter behaves well, as there is a single pair of graphs with the same signless Laplacian A B C -energy unlike the 26 pairs of graphs with same signless Laplacian energy and eight pairs of graphs with the same A B C -energy. [ABSTRACT FROM AUTHOR]

Three-dimensional multi-object tracking (MOT) using lidar point cloud data is crucial for applications in autonomous driving, smart cities, and robotic navigation. It involves identifying objects in point cloud sequence data and consistently assigning unique identities to them throughout the sequence. Occlusions can lead to missed detections, resulting in incorrect data associations and ID switches. To address these challenges, we propose a novel point cloud multi-object tracker called GBRTracker. Our method integrates an intra-frame graph structure into the backbone to extract and aggregate spatial neighborhood node features, significantly reducing detection misses. We construct an inter-frame bipartite graph for data association and design a sophisticated cost matrix based on the center, box size, velocity, and heading angle. Using a minimum-cost flow algorithm to achieve globally optimal matching, thereby reducing ID switches. For unmatched detections, we design a motion-based re-identification (ReID) feature embedding module, which uses velocity and the heading angle to calculate similarity and association probability, reconnecting them with their corresponding trajectory IDs or initializing new tracks. Our method maintains high accuracy and reliability, significantly reducing ID switches and trajectory fragmentation, even in challenging scenarios. We validate the effectiveness of GBRTracker through comparative and ablation experiments on the NuScenes and Waymo Open Datasets, demonstrating its superiority over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Most existing collaborative filtering-based recommender systems rely solely on available user–item interactions for user and item representation learning. Their performance often suffers significantly when interactions are sparse, as limited user and item interactions are insufficient for learning robust representations. To address this issue, recent research has explored additional information between users and items by leveraging the user–item bipartite graph. However, these methods have not fully exploited high-order neighborhood information, primarily using sampled interactions to enrich training data rather than integrating this information directly into representation learning. In this paper, we propose a novel model, EIR-GCN (Embedding Integration with Relational Graph Convolutional Network), which directly incorporates various types of collaborative relations, such as user–user and item–item interactions, into the embedding function for user preference modeling. Specifically, our model employs advanced graph convolutional network (GCN) techniques to integrate user–item, user–user, and item–item relations for comprehensive representation learning. EIR-GCN initially selects the most influential second-order neighbors from the user–item bipartite graph to form user–user and item–item connections. With these enriched connections, a message-passing method is adopted to learn node representations by aggregating messages from directly linked nodes, including first-order item neighbors and selected second-order user neighbors. Extensive experiments on several public datasets demonstrate that EIR-GCN outperforms strong baselines, including recent GCN-based models and those exploiting high-order information. Our results show that EIR-GCN achieves state-of-the-art performance and effectively addresses the sparsity issue, highlighting its robustness and efficacy in recommendation tasks. [ABSTRACT FROM AUTHOR]

This paper explores: How has wisdom pedagogy research emerged in higher education during 1980–2022? This study is the first to explore the emergence of wisdom pedagogy research in higher education applying Bipartite network analysis for detecting clusters of 24 wisdom pedagogy articles of 53 authors and 161 keywords. Results are visualized with WoS analytics, word-clouds, and with Bipartite network. Wisdom research in higher education is two decades late compared with other disciplines. In higher education n = 524 wisdom, n = 33 wisdom pedagogy publications were detected in the Web of Science Core Collection database. This paper analyzed n = 24 wisdom pedagogy articles published during the 1980–2022 period. There were only two articles found dealing directly with wisdom pedagogy. Therefore, this study has several further research implications for educational researchers. Firstly, they need to conduct a more comprehensive search for wisdom pedagogy models by extending the scope of this study to other databases, books, book chapters, and to conference papers. Secondly, they need to synthesize and theorize their findings by building a wisdom pedagogy model. Thirdly, researchers need to develop detailed guidelines for educational practitioners on how to apply wisdom pedagogy in practice. This study is only at the beginning of this journey. However, it would be important for educating students with wisdom pedagogy in higher education because it would facilitate students' thinking, judgements, and actions based on their moral and ethical values in a highly interconnected and complex world. [ABSTRACT FROM AUTHOR]

This paper aims to study the distributed control problems of heterogeneous signed networks whose communication topologies are undirected. A distributed control protocol is designed based on neighboring state information. With this protocol be employed, the convergence results of the heterogeneous signed network are provided. It is shown that the heterogeneous signed network can achieve the static bipartite consensus (respectively, state stability) if and only if the signed graph is structurally balanced (respectively, unbalanced). The associated convergence analyses can be developed by constructing a suitable Lyapunov function. In addition, two simulation examples are presented to validate the correctness of the obtained results. [ABSTRACT FROM AUTHOR]

The Susceptible–Infected–Susceptible (SIS) model in complex networks is one of the critical models employed in the modeling of virus spread. The study of the heterogeneous SIS model with a non-homogeneous nodal infection rate in finite-size networks has attracted little attention. Investigating the statistical properties of heterogeneous SIS epidemic dynamics in finite networks is thus intriguing. In this paper, we focus on the measure of variability in the number of infected nodes for the heterogeneous SIS epidemic dynamics in finite-size bipartite graphs and star graphs. Specifically, we investigate the metastable-state variance of the number of infected nodes for the SIS epidemic process in finite-size bipartite graphs and star graphs with heterogeneous nodal infection rates. We employ an extended individual-based mean-field approximation to analyze the heterogeneous SIS epidemic process in finite-size bipartite networks and star graphs. We derive the approximation solutions of the variance of the infected number. We verify the proposed theory by simulations. The proposed theory has the potential to help us better understand the fluctuations of SIS models like epidemic dynamics with a non-homogeneous infection rate. [ABSTRACT FROM AUTHOR]

In this paper, we study the knapsack problem with conflict pair constraints. After a thorough literature survey on the topic, our study focuses on the special case of bipartite conflict graphs. For complete bipartite (multipartite) conflict graphs, the problem is shown to be NP-hard but solvable in pseudo-polynomial time, and it admits an FPTAS. Extensions of these results to more general classes of graphs are also presented. Further, a class of integer programming models for the general knapsack problem with conflict pair constraints is presented, which generalizes and unifies the existing formulations. The strength of the LP relaxations of these formulations is analyzed, and we discuss different ways to tighten them. Experimental comparisons of these models are also presented to assess their relative strengths. This analysis disclosed various strong and weak points of different formulations of the problem and their relationships to different types of problem data. This information can be used in designing special purpose algorithms for KPCC involving a learning component. [ABSTRACT FROM AUTHOR]

We use Category Theory to construct a 'bridge' relating directed graphs with undirected graphs, such that the notion of direction is preserved. Specifically, we provide an isomorphism between the category of simple directed graphs and a category we call 'prime graphs category'; this has as objects labeled undirected bipartite graphs (which we call prime graphs), and as morphisms undirected graph morphisms that preserve the labeling (which we call prime graph morphisms). This theoretical bridge allows us to extend undirected graph techniques to directed graphs by converting the directed graphs into prime graphs. To give a proof of concept, we show that our construction preserves topological features when applied to the problems of network alignment and spectral graph clustering. [ABSTRACT FROM AUTHOR]

Underwriters play a pivotal role in the IPO process. Information entropy, a tool for measuring the uncertainty and complexity of information, has been widely applied to various issues in complex networks. Information entropy can quantify the uncertainty and complexity of nodes in the network, providing a unique analytical perspective and methodological support for this study. This paper employs a bipartite network analysis method to construct the relationship network between underwriters and accounting firms, using the centrality of underwriters in the network as a measure of their influence to explore the impact of underwriters' influence on the distribution of interests and audit outcomes. The findings indicate that a more pronounced influence of underwriters significantly increases the ratio of underwriting fees to audit fees. Higher influence often accompanies an increase in abnormal underwriting fees. Further research reveals that companies underwritten by more influential underwriters experience a decline in audit quality. Finally, the study reveals that a well-structured audit committee governance and the rationalization of market sentiments can mitigate the negative impacts of underwriters' influence. The innovation of this paper is that it enriches the content related to underwriters by constructing the relationship network between underwriters and accounting firms for the first time using a bipartite network through the lens of information entropy. This conclusion provides new directions for thinking about the motives and possibilities behind financial institutions' cooperation, offering insights for market regulation and policy formulation. [ABSTRACT FROM AUTHOR]

The canonical decomposition of a bipartite graph is a new decomposition method that involves three operators: parallel, series, and K ⨁   S . The class of weak-bisplit graphs is the class of totally decomposable graphs with respect to these operators, and the class of bicographs is the class of totally decomposable graphs with respect to parallel and series operators. We prove in this paper that the class of bipartite (P 6 , C 6) -free graphs is the class of bipartite graphs that are totally decomposable with respect to parallel and K ⨁ S operators. We present a linear time recognition algorithm for (P 6 , C 6) -free graphs that is symmetrical to the linear recognition algorithms of weak-bisplit graphs and s t a r 1,2 , 3 -free bipartite graphs. As a result of this algorithm, we present efficient solutions in this class of graphs for two optimization graph problems: the maximum balanced biclique problem and the maximum independent set problem. [ABSTRACT FROM AUTHOR]

We construct an infinite family of bounded-degree bipartite unique neighbour expander graphs with arbitrarily unbalanced sides. Although weaker than the lossless expanders constructed by Capalbo et al., our construction is simpler and may be closer to being implementable in practice, due to the smaller constants. We construct these graphs by composing bipartite Ramanujan graphs with a fixed-size gadget in a way that generalises the construction of unique neighbour expanders by Alon and Capalbo. For the analysis of our construction, we prove a strong upper bound on average degrees in small induced subgraphs of bipartite Ramanujan graphs. Our bound generalises Kahale's average degree bound to bipartite Ramanujan graphs, and may be of independent interest. Surprisingly, our bound strongly relies on the exact Ramanujan-ness of the graph and is not known to hold for nearly-Ramanujan graphs. [ABSTRACT FROM AUTHOR]

Soil salinization poses a global threat to terrestrial ecosystems. Soil microorganisms, crucial for maintaining ecosystem services, are sensitive to changes in soil structure and properties, particularly salinity. In this study, contrasting dynamics within the rhizosphere and bulk soil were focused on exploring the effects of heightened salinity on soil microbial communities, evaluating the influences shaping their composition in saline environments. This study observed a general decrease in bacterial alpha diversity with increasing salinity, along with shifts in community structure in terms of taxa relative abundance. The size and stability of bacterial co-occurrence networks declined under salt stress, indicating functional and resilience losses. An increased proportion of heterogeneous selection in bacterial community assembly suggested salinity's critical role in shaping bacterial communities. Stochasticity dominated fungal community assembly, suggesting their relatively lower sensitivity to soil salinity. However, bipartite network analysis revealed that fungi played a more significant role than bacteria in intensified microbial interactions in the rhizosphere under salinity stress compared to the bulk soil. Therefore, microbial cross-domain interactions might play a key role in bacterial resilience under salt stress in the rhizosphere. [ABSTRACT FROM AUTHOR]

The mathematical side of applied problems in multiple subject areas (biology, pattern recognition, etc.) is reduced to the problem of discrete optimization in the following mathematical method. We were provided a network and graphs in its leaves, for which we needed to find a rearrangement of graphs by non-leaf nodes, in which the given functional reached its minimum. Such a problem, even in the simplest case, is NP-hard, which means unavoidable restrictions on the network, on graphs, or on the functional. In this publication, this problem is addressed in the case of all graphs being so-called "structures", meaning directed-loaded graphs consisting of paths and cycles, and the functional as the sum (over all edges in the network) of distances between structures at the endpoints of every edge. The distance itself is equal to the minimal length of sequence from the fixed list of operations, the composition of which transforms the structure at one endpoint of the edge into the structure at its other endpoint. The list of operations (and their costs) on such a graph is fixed. Under these conditions, the given discrete optimization problem is called the reconstruction problem. This paper presents novel algorithms for solving the reconstruction problem, along with full proofs of their low error and low polynomial complexity. For example, for the network, the problem is solved with a zero error algorithm that has a linear polynomial computational complexity; and for the tree the problem is solved using an algorithm with a multiplicative error of at most two, which has a second order polynomial computational complexity. [ABSTRACT FROM AUTHOR]

The state-owned power Electricity Generating Authority of Thailand (EGAT), a monopoly market in charge of producing, distributing, and wholesaling power, is the focal point of Thailand's electricity market. Although the government has encouraged people to install on-grid solar panels to sell electricity as producers and retail consumers, the price mechanism, i.e., purchasing price and selling prices, is still unilaterally determined by the government. Therefore, we are interested in studying the case where blockchain can be used as a free trading platform. Without involving buying or selling from the government, this research presents a model of fully traded price mechanisms. Based on the study results of the double auction system, data on buying and selling prices of electrical energy in Thailand were used as the initial data for the electricity peer-to-peer free-trading model. Then, information was obtained to analyze the trading price trends by using the law of demand and supply in addition to the principle of the bipartite graph. The price trend results agree well with those of price equilibrium equations. Therefore, we firmly believe that the model we offer can be traded in a closed system of free-trade platforms. In addition, the players in the system can help to determine the price trend that will occur according to various parameters and will cause true fairness in the sustainable electricity supply chain industry in Thailand. [ABSTRACT FROM AUTHOR]

Existing contour-based building-reconstruction methods face the challenge of producing low-poly results. In this study, we introduce a novel iterative contour-based method to reconstruct low-poly meshes with only essential details from mesh soups. Our method focuses on two primary targets that determine the quality of the results: reduce the total number of contours, and generate compact surfaces between contours. Specifically, we implemented an iterative pipeline to gradually extract vital contours by loss and topological variance, and potential redundant contours will be removed in a post-processing procedure. Based on these vital contours, we extracted the planar primitives of buildings as references for contour refinement to obtain compact contours. The connection relationships between these contours are recovered for surface generation by a contour graph, which is constructed using multiple bipartite graphs. Then, a low-poly mesh can be generated from the contour graph using our contour-interpolation algorithm based on polyline splitting. The experiments demonstrated that our method produced satisfactory results and outperformed the previous methods. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) have recently been widely employed as effective wireless platforms for aiding users in various situations, particularly in hard-to-reach scenarios like post-disaster relief efforts. This study employs multiple UAVs to cover users in overlapping locations, necessitating the optimization of UAV-user association to maximize the spectral and energy efficiency of the UAV network. Hence, a connected bipartite graph is formed between UAVs and users using graph theory to accomplish this goal. Then, a maximum weighted matching-based maximum flow (MwMaxFlow) optimization approach is proposed to achieve the maximum data rate given users' demands and the UAVs' maximum capacities. Additionally, power control is applied using the M -matrix theory to optimize users' transmit powers and improve their energy efficiency. The proposed strategy is evaluated and compared with other benchmark schemes through numerical simulations. The simulation outcomes indicate that the proposed approach balances spectral efficiency and energy consumption, rendering it suitable for various UAV wireless applications, including emergency response, surveillance, and post-disaster management. [ABSTRACT FROM AUTHOR]

This paper concentrates on bipartite formation control for nonlinear leader-following multi-agent systems (MASs) with fixed and switching topologies under aperiodic Denial-of-Service (DoS) attacks. Firstly, distributed control protocols are proposed under the aperiodic DoS attacks based on fixed and switching topologies. Then, considering control gains, as well as attack frequency and attack length ratio of the aperiodic DoS attacks, using algebraic graph theory and the Lyapunov stability method, some criteria are acquired to ensure that the nonlinear leader-following MASs with either fixed or switching topologies can realize bipartite formation under aperiodic DoS attacks. Finally, numerical simulations are carried out to validate the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This study presents a novel approach that synergizes community detection algorithms with various Graph Neural Network (GNN) models to bolster link prediction in scientific literature networks. By integrating the Louvain community detection algorithm into our GNN frameworks, we consistently enhanced the performance across all models tested. For example, integrating the Louvain model with the GAT model resulted in an AUC score increase from 0.777 to 0.823, exemplifying the typical improvements observed. Similar gains were noted when the Louvain model was paired with other GNN architectures, confirming the robustness and effectiveness of incorporating community-level insights. This consistent increase in performance—reflected in our extensive experimentation on bipartite graphs of scientific collaborations and citations—highlights the synergistic potential of combining community detection with GNNs to overcome common link prediction challenges such as scalability and resolution limits. Our findings advocate for the integration of community structures as a significant step forward in the predictive accuracy of network science models, offering a comprehensive understanding of scientific collaboration patterns through the lens of advanced machine learning techniques. [ABSTRACT FROM AUTHOR]

The vertex quadrangulation Q G of a 4-regular graph G visually looks like a graph whose vertices are depicted as empty squares, and the connecting edges are attached to the corners of the squares. In a previous work [JOMC 59, 1551–1569 (2021)], the question was posed: does the spectrum of an arbitrary unweighted graph Q G include the full spectrum { 3 , (− 1) 3 } of the tetrahedron graph (complete graph K 4 )? Previously, many bipartite and nonbipartite graphs Q G with such a subspectrum have been found; for example, a nonbipartite variant of the graph Q K 5 . Here, we present one of the variants of the nonbipartite vertex quadrangulation Q O of the octahedron graph O, which has eigenvalue (− 1) of multiplicity 2 in the spectrum, while the spectrum of the bipartite variant Q O contains eigenvalue (− 1) of multiplicity 3. Thus, in the case of nonbipartite graphs, the answer to the question posed depends on the particular graph Q G . Here, we continue to explore the spectrum of graphs Q G . Some possible connections of the mathematical theme to chemistry are also noted. [ABSTRACT FROM AUTHOR]

Deep learning technology has greatly propelled the development of intelligent and information-driven research on ship infrared automatic target recognition (SIATR). In future scenarios, there will be various recognition models with different mechanisms to choose from. However, in complex and dynamic environments, ship infrared (IR) data exhibit rich feature space distribution, resulting in performance variations among SIATR models, thus preventing the existence of a universally superior model for all recognition scenarios. In light of this, this study proposes a model-matching method for SIATR tasks based on bipartite graph theory. This method establishes evaluation criteria based on recognition accuracy and feature learning credibility, uncovering the underlying connections between IR attributes of ships and candidate models. The objective is to selectively recommend the optimal candidate model for a given sample, enhancing the overall recognition performance and applicability of the model. We separately conducted tests for the optimization of accuracy and credibility on high-fidelity simulation data, achieving Accuracy and EDMS (our credibility metric) of 95.86% and 0.7781. Our method improves by 1.06% and 0.0274 for each metric compared to the best candidate models (six in total). Subsequently, we created a recommendation system that balances two tasks, resulting in improvements of 0.43% (accuracy) and 0.0071 (EDMS). Additionally, considering the relationship between model resources and performance, we achieved a 28.35% reduction in memory usage while realizing enhancements of 0.33% (accuracy) and 0.0045 (EDMS). [ABSTRACT FROM AUTHOR]

As an analogous concept of a nowhere-zero flow for directed graphs, zero-sum flows and constant-sum flows are defined and studied in the literature. For an undirected graph, a zero-sum flow (constant-sum flow resp.) is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero (constant h resp.), and we call it a zero-sum k-flow (h-sum k-flow resp.) if the values of the edges are less than k. We extend these concepts to general constant-sum A-flow, where A is an Abelian group, and consider the case A = Z k the additive Abelian cyclic group of integer congruences modulo k with identity 0. In the literature, a graph is alternatively called Z k -magic if it admits a constant-sum Z k -flow, where the constant sum is called a magic sum or an index for short. We define the set of all possible magic sums such that G admits a constant-sum Z k -flow to be I k (G) and call it the magic sum spectrum, or for short, the index set of G with respect to Z k . In this article, we study the general properties of the magic sum spectrum of graphs. We determine the magic sum spectrum of complete bipartite graphs K m , n for m ≥ n ≥ 2 as the additive cyclic subgroups of Z k generated by k d , where d = g c d (m − n , k) . Also, we show that every regular graph G with a perfect matching has a full magic sum spectrum, namely, I k (G) = Z k for all k ≥ 3 . We characterize a 3-regular graph so that it admits a perfect matching if and only if it has a full magic sum spectrum, while an example is given for a 3-regular graph without a perfect matching which has no full magic sum spectrum. Another example is given for a 5-regular graph without a perfect matching, which, however, has a full magic sum spectrum. In particular, we completely determine the magic sum spectra for all regular graphs of even degree. As a byproduct, we verify a conjecture raised by Akbari et al., which claims that every connected 4 k -regular graph of even order admits a 1-sum 4-flow. More open problems are included. [ABSTRACT FROM AUTHOR]

The Diannong River, a valuable river and lake resource of the northern Ningxia Yellow River Irrigation Area, plays an instrumental role in regional flood control, drought resistance, climate regulation, and biodiversity conservation. Phytoplankton and zooplankton, as crucial elements of the aquatic ecosystem, have their distribution patterns evaluated and potential influencing factors identified, thereby enhancing the understanding of community distribution patterns. Nested structures and interspecies interaction relationships bear significant implications for community distribution patterns, functions, and stability. The upstream section of the Diannong River in Yinchuan City was chosen as the study object. Water samples were collected in January, April, July, and October 2021, and the community composition of phytoplankton and zooplankton was analyzed using relative abundance, density, and biomass. The distribution matrix temperature and bipartite network methodologies were deployed to investigate their nested pattern and interaction network seasonal characteristics. The findings indicate that the water environment of the Diannong River's upstream section displays pronounced spatiotemporal heterogeneity, characterized by weak alkalinity and high fluoride content. The plankton community composition and relative abundance showed marked differences among the distinct sampling periods. The temperature of the random distribution matrix shows a significant difference compared to the zero-sum model, revealing a notable nested pattern in plankton in the Diannong River's upstream section. The bipartite network suggests that the plankton composition was the simplest in January and the most complex in July, with the fiercest species competition observed in January and the lowest levels of species specificity, vulnerability, and generality. Water temperature (WT), dissolved oxygen (DO), total phosphorus (TP), available phosphorus (AP), CODCr, F−, and Cl− constitute the environmental parameters influencing the overall structure of the phytoplankton community in the Diannong River's upstream section, whereas zooplankton did not present a significant correlation with water environmental factors. [ABSTRACT FROM AUTHOR]

The intention of this paper is to explore the distributed control issues for directed signed networks in the face of external disturbances under strongly connected topologies. A new class of nonsingular transformations is provided by introducing an output variable, with which the consensus can be equivalently transformed into the output stability regardless of whether the associated signed digraphs are structurally balanced or not. By taking advantage of the standard robust H ∞ control theory, the bipartite consensus and state stability results can be built for signed networks under structurally balanced and unbalanced conditions, respectively, in which the desired disturbance rejection performances can also be satisfied. Furthermore, the mathematical expression can be given for the terminal states of signed networks under the influence of external disturbances. In addition, two simulations are presented to verify the correctness of our developed results. [ABSTRACT FROM AUTHOR]

We consider a point process (PP) generated by superimposing an independent Poisson point process (PPP) on each line of a 2D Poisson line process (PLP). Termed PLP-PPP, this PP is suitable for modeling networks formed on an irregular collection of lines, such as vehicles on a network of roads and sensors deployed along trails in a forest. Inspired by vehicular networks in which vehicles connect with their nearest wireless base stations (BSs), we consider a random bipartite associator graph in which each point of the PLP-PPP is associated with the nearest point of an independent PPP through an edge. This graph is equivalent to the partitioning of PLP-PPP by a Poisson Voronoi tessellation (PVT) formed by an independent PPP. We first characterize the exact distribution of the number of points of PLP-PPP falling inside the ball centered at an arbitrary location in R 2 as well as the typical point of PLP-PPP. Using these distributions, we derive cumulative distribution functions (CDFs) and probability density functions (PDFs) of kth contact distance (CD) and the nearest neighbor distance (NND) of PLP-PPP. As intermediate results, we present the empirical distribution of the perimeter and approximate distribution of the length of the typical chord of the zero-cell of this PVT. Using these results, we present two close approximations of the distribution of node degree of the random bipartite associator graph. In a vehicular network setting, this result characterizes the number of vehicles connected to each BS, which models its load. Since each BS has to distribute its limited resources across all the vehicles connected to it, a good statistical understanding of load is important for an efficient system design. Several applications of these new results to different wireless network settings are also discussed. [ABSTRACT FROM AUTHOR]

Graph collaborative filtering can efficiently find the hidden interests of users for recommender systems in recent years. This method can learn complex interactions between nodes in the graph, identify user preferences, and provide satisfactory recommendations. However, recommender systems face the challenge of data sparsity. To address this, recent studies have utilized contrastive learning to make use of unlabeled data structures. However, the existing positive and negative example sampling methods are not reasonable. Random-based or data augmentation-based sampling cannot make use of useful latent information. Clustering-based sampling methods ignore the semantics of node features and the relationship between global and local information. To utilize the latent structures in the data, we introduce a novel Community-Enhanced Contrastive Learning method to help the recommendation main task called CECL which uses a community detection algorithm to sample examples with semantic and global information, using both known and hidden community connections in the bipartite interaction graph. Extensive experiments are conducted on two well-known datasets, the results of which show a 12% and 8% performance improvement compared to that of the existing baseline methods. [ABSTRACT FROM AUTHOR]

Spectral graph theory is like a special tool for understanding graphs. It helps us find patterns and connections in complex networks, using the magic of eigenvalues. Let G be the graph and A (G) be its adjacency matrix, then G is singular if the determinant of the adjacency matrix A (G) is 0, otherwise it is nonsingular. Within the realm of nonsingular graphs, there is the concept of property R , where each eigenvalue's reciprocal is also an eigenvalue of G. By introducing multiplicity constraints on both eigenvalues and their reciprocals, it becomes property SR. Similarly, the world of nonsingular graphs reveals property − R , where the negative reciprocal of each eigenvalue also finds a place within the spectrum of G. Moreover, when the multiplicity of each eigenvalue and its negative reciprocal is equal, this results in a graph with a property of − SR . Some classes of unweighted nonbipartite graphs are already constructed in the literature with the help of the complete graph K n and a copy of the path graph P 4 satisfying property R but not SR. This article takes this a step further. The main aim is to construct several weighted classes of graphs which satisfy property R but not SR. For this purpose, the weight functions are determined that enable these nonbipartite graph classes to satisfy the − SR and R properties, even if the unweighted graph does not satisfy these properties. Some examples are presented to support the investigated results. These examples explain how certain weight functions make these special types of graphs meet the properties R or − SR , even when the original graphs without weights do not meet these properties. [ABSTRACT FROM AUTHOR]

We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius. From a modelling perspective, we explain how the model captures higher-order connections that arise in real data sets. Our main contribution is to study the connectivity properties of the model. In an asymptotic limit where the number of nodes and hyperedges grow in tandem, we give a condition on the radius that guarantees connectivity. [ABSTRACT FROM AUTHOR]

The current fraud risk in digital finance is increasing year by year, and the mainstream solutions rely on the inherent characteristics of users, which makes it difficult to explain fraud behaviors and fraud behavior patterns are less researched. To address these problems, we propose an integrated multiple relational graphs fraud detection model Tri-RGCN-XGBoost, which analyzes the impact of user association patterns on fraud detection by mining the behavioral associations of users. The model builds a heterogeneous information network based on real transaction data, abstracts three types of bipartite graphs (user–device, user–merchant, and user–address), aggregates the information of the user's neighbor nodes under the three types of behavioral patterns, and integrates the graph convolution classification results under the three behavioral patterns with the XGBoost model to achieve fraudulent user detection with integrated multiple relational graphs. The results show that the performance of this model in fraud identification is significantly improved, especially in reducing the fraudulent user underreporting rate. Further, the behavioral associations that play a key role in fraud user identification are analyzed in conjunction with shape value to provide a reference for fraud pattern mining. [ABSTRACT FROM AUTHOR]

In this work, alternative product formulations are represented as a bipartite graph, and mixed-integer programming is used to find a graph partitioning that identifies the most dissimilar formulations within a potentially large design space. This involves fully integrating available models for product properties and known heuristic rules for product formulation. The set of dissimilar alternative formulations thus found constitutes the best exploratory plan of experiments in the face of the available knowledge. Also in this work, a cosmetic emulsion example is explored, where some ingredients (in a non-specified number) have to be chosen from a pool of 32 possible. The number of possible combinations of ingredients is around half a million. With the new tools proposed herein, one is able to identify small sets of alternative formulations that adhere to available models and known heuristics rules, have maximum dissimilarity, and are optimal regarding a specific product design objective (cost or other), in a few minutes of computational time. [ABSTRACT FROM AUTHOR]

Small nucleolar RNAs (snoRNAs) constitute a prevalent class of noncoding RNAs localized within the nucleoli of eukaryotic cells. Their involvement in diverse diseases underscores the significance of forecasting associations between snoRNAs and diseases. However, conventional experimental techniques for such predictions suffer limitations in scalability, protracted timelines, and suboptimal success rates. Consequently, efficient computational methodologies are imperative to realize the accurate predictions of snoRNA–disease associations. Herein, we introduce GCLSDA—graph Convolutional Network and contrastive learning predict snoRNA disease associations. GCLSDA is an innovative framework that combines graph convolution networks and self-supervised learning for snoRNA–disease association prediction. Leveraging the repository of MNDR v4.0 and ncRPheno databases, we construct a robust snoRNA–disease association dataset, which serves as the foundation to create bipartite graphs. The computational prowess of the light graph convolutional network (LightGCN) is harnessed to acquire nuanced embedded representations of both snoRNAs and diseases. With careful consideration, GCLSDA intelligently incorporates contrast learning to address the challenging issues of sparsity and over-smoothing inside correlation matrices. This combination not only ensures the precision of predictions but also amplifies the model's robustness. Moreover, we introduce the augmentation technique of random noise to refine the embedded snoRNA representations, consequently enhancing the precision of predictions. Within the domain of contrast learning, we unite the tasks of contrast and recommendation. This harmonization streamlines the cross-layer contrast process, simplifying the information propagation and concurrently curtailing computational complexity. In the area of snoRNA–disease associations, GCLSDA constantly shows its promising capacity for prediction through extensive research. This success not only contributes valuable insights into the functional roles of snoRNAs in disease etiology, but also plays an instrumental role in identifying potential drug targets and catalyzing innovative treatment modalities. [ABSTRACT FROM AUTHOR]

This paper provides a survey of recent research progress in mathematical modeling and distributed control of wide-area networks. Firstly, the modeling is introduced for two types of wide-area networks, i.e., coopetitive networks and cooperative networks, with the help of algebraic graph theory. Particularly, bipartite network topologies and cluster network topologies are introduced for coopetitive networks. With respect to cooperative networks, an intermittent clustered network modeling is presented. Then, some classical distributed control strategies are reviewed for wide-area networks to ensure some desired collective behaviors, such as consensus (or synchronization), bipartite consensus (or polarization), and cluster consensus (or fragmentation). Finally, some conclusions and future directions are summarized. [ABSTRACT FROM AUTHOR]

This paper proposes a method to reduce seismogram variability as a determining factor in its interpretation, processing, and clustering. By introducing the concept of single fluctuations (SFs), the seismogram can be parsed into a sequence of random impulses with subsequent ordering. This rearrangement of SFs, if they are assigned by positive integers, represents the formal mapping of a regular string of integers into a random one, which can be represented with a bipartite random graph (bigraph). Due to its specific randomness, such a bigraph is considered a new type of random balanced bigraph. The R-envelope and RQ-envelope, its equidistant version, are defined by tracing the peak envelope over ordered SFs. The equivalence and complementariness of the RQ and bigraph are considered and discussed, forming a combined characteristic of the seismogram. The R/RQ provided a considerable reduction in seismogram variability, which was confirmed by creating and analyzing an ensemble of RQ from several seismograms. In the RQ domain, distance is defined as a possible basis for metrics and clustering, but the ensemble variability was quite narrow and not as suitable for this purpose. Otherwise, the ensemble shows high redundancy hidden in the seismogram population. As for the bigraph, the mesh of its edges is structuralized in bundles, forming a skeleton, which reflects the internal structural content of the seismogram. The distance over the domain of bigraphs is proposed to show the possibility of clustering. This means that only a combined RQ and bigraph provides a suitable frame for seismogram representation with reduced variability and, thus, the potential for more effectively organizing seismic databases and a deeper interpretation of seismograms; therefore, RQs and bigraphs can be considered as a transform of a seismogram. Many aspects of these concepts are thoroughly discussed. The similarity between concepts of SF and wavelets is briefly considered. This very complex theme is new and promises broad further research. All issues considered in the paper are abundantly illustrated. [ABSTRACT FROM AUTHOR]

Existing list recommendation methods present a list consisting of multiple items for feedback recommendation to user requests, which has the advantages of high flexibility and direct user feedback. However, the structured representation of state data limits the embedding of users and items, making them isolated from each other, missing some useful infomation for recommendation. In addition, the traditional non-end-to-end learning series takes a long time and accumulates errors. During the model training process, the results of each task can easily affect the next calculation, thus affecting the entire training effect. Aiming at the above problems, this paper proposes a Reinforcement Learning List Recommendation Model Fused with a Graph Neural Network, GNLR. The goal of this model is to maximize the recommendation effect while ensuring that the list recommendation system accurately analyzes user preferences to improve user experience. To this end, firstly, we use an user–item bipartite graph and Graph Neural Network to aggregate neighborhood information for users and items to generate graph structured representation; secondly, we adopt an attention mechanism to assign corresponding weights to neighborhood information to reduce the influence of noise nodes in heterogeneous information networks; finally, we alleviate the problems of traditional non-end-to-end methods through end-to-end training methods. The experimental results show that the method proposed in this paper can alleviate the above problems, and the recommendation hit rate and accuracy rate increase by about 10%. [ABSTRACT FROM AUTHOR]

A total perfect Roman dominating function (TPRDF) on a graph G = (V , E) is a function f from V to { 0 , 1 , 2 } satisfying (i) every vertex v with f (v) = 0 is a neighbor of exactly one vertex u with f (u) = 2 ; in addition, (ii) the subgraph of G that is induced by the vertices with nonzero weight has no isolated vertex. The weight of a TPRDF f is ∑ v ∈ V f (v) . The total perfect Roman domination number of G, denoted by γ t R p (G) , is the minimum weight of a TPRDF on G. In this paper, we initiated the study of total perfect Roman domination. We characterized graphs with the largest-possible γ t R p (G) . We proved that total perfect Roman domination is NP-complete for chordal graphs, bipartite graphs, and for planar bipartite graphs. Finally, we related γ t R p (G) to perfect domination γ p (G) by proving γ t R p (G) ≤ 3 γ p (G) for every graph G, and we characterized trees T of order n ≥ 3 for which γ t R p (T) = 3 γ p (T) . This notion can be utilized to develop a defensive strategy with some properties. [ABSTRACT FROM AUTHOR]

Matrix factorization is a long-established method employed for analyzing and extracting valuable insight recommendations from complex networks containing user ratings. The execution time and computational resources demanded by these algorithms pose limitations when confronted with large datasets. Community detection algorithms play a crucial role in identifying groups and communities within intricate networks. To overcome the challenge of extensive computing resources with matrix factorization techniques, we present a novel framework that utilizes the inherent community information of the rating network. Our proposed approach, named Community-Based Matrix Factorization (CBMF), has the following steps: (1) Model the rating network as a complex bipartite network. (2) Divide the network into communities. (3) Extract the rating matrices pertaining only to those communities and apply MF on these matrices in parallel. (4) Merge the predicted rating matrices belonging to communities and evaluate the root mean square error (RMSE). In our experimentation, we use basic MF, SVD++, and FANMF for matrix factorization, and the Louvain algorithm is used for community division. The experimental evaluation on six datasets shows that the proposed CBMF enhances the quality of recommendations in each case. In the MovieLens 100K dataset, RMSE has been reduced to 0.21 from 1.26 using SVD++ by dividing the network into 25 communities. A similar reduction in RMSE is observed for the datasets of FilmTrust, Jester, Wikilens, Good Books, and Cell Phone. [ABSTRACT FROM AUTHOR]

Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semi-definite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks where nodes share at most one source, such as all bipartite networks. [ABSTRACT FROM AUTHOR]

The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P 3 -coloring, was introduced. A simple graph is called a P 3 -colorable graph if its vertices can be colored so that all the vertices in each P 3 path of the graph have different colors; this is called the P 3 -coloring of the graph. The minimum number of colors required to form a P 3 -coloring of a graph is called the P 3 -chromatic number of the graph. The aim of this article is to determine the P 3 -chromatic number of different well-known classes of bipartite graphs such as complete bipartite graphs, tree graphs, grid graphs, and some special types of bipartite graphs. Moreover, we have also presented some algorithms to produce a P 3 -coloring of these classes with a minimum number of colors required. [ABSTRACT FROM AUTHOR]

Food safety risk, as an implicit cost of social and economic development, endangers the health of global residents, including China. To systematically understand the impact of socioeconomic development on food safety risk and to establish a sound modern governance system of food safety in China, this paper uses provincial panel data from 2011 to 2020 to explore the relationship between food safety risk and socio-economic development factors such as economic growth and income inequality by employing a two-way fixed effect model and moderating effect model. The results show that the food safety risk is a Kuznets curve, and the turning point is about RMB 58,104.59 per capita GDP (based on prices in 2011). However, under the moderating effect of income inequality, the turning point of the Kuznets curve of food safety risk will shift to the right, and the curve will be flattened. In other words, income inequality has a negative moderating effect on the "inverted U-shaped" relationship between economic growth and food safety risk. When dealing with food safety problems, the goal of stable and sustained economic growth and common prosperity should be incorporated into policy formulation to enhance the governance effectiveness of food safety risk. [ABSTRACT FROM AUTHOR]