Node Merging Research Articles

Stability of Weyl Node Merging Processes under Symmetry Constraints

Stability of Weyl Node Merging Processes under Symmetry Constraints

Two-Step Clustering for Mineral Prospectivity Mapping: A Case Study from the Northeastern Edge of the Jiaolai Basin, China

The advancement of geological big data has rendered data-driven methodologies increasingly vital in Mineral Prospectivity Mapping. The effective integration of quantitative and qualitative data, including experiential and knowledge-based insights, is crucial in geological data fusion. Specifically, the conversion of raw data into samples and the selection of predictive methods are two core issues that constitute the focus of this study. Traditional clustering methods require the user to specify the number of clusters in advance. The two-step clustering can automatically determine the clustering result ‘k’ while analyzing both continuous and categorical variables, by building a Cluster Feature (CF) and using information criteria to merge nodes. In this study, we conducted an analysis utilizing stream sediment element data, residual gravity anomalies, and fault distribution through the two-step clustering method. Factor analysis (FA) was employed to reduce 16 elemental variables from stream sediments into five uncorrelated continuous variables; additionally, residual gravity anomalies were transformed from continuous to categorical variables via an interval-based method before being combined with fault distribution, resulting in seven variables for clustering. The research findings indicate that categorical variables significantly influence clustering results; concurrently, as the importance of continuous variables within the cluster increases, so does k. When only one categorical variable is present, residual gravity anomalies show significantly better clustering than fault distribution; however, when two categorical variables are involved, it is essential to consider the quantity of categories: more categories lead to poorer quality. The results from the Jiaolai Basin’s northeastern margin indicate a significant correlation with known gold deposits; two-step clustering is a promising and effective method for improving mineral prospecting efforts.

TC-Match: Fast Time-Constrained Continuous Subgraph Matching

Continuously monitoring structural patterns in streaming graphs is a critical task in many real-time graph-based applications. In this paper, we study the problem of time-constrained continuous subgraph matching (shorted as TCSM) over streaming graphs. Given a query graph Q with timing order constraint and a data graph stream G , TCSM aims to report all incremental matches of Q in G for each update of G , where a match should obey both structure constraint (i.e., isomorphism) and timing order constraint of Q. Although TCSM has a wide range of applications, such as cyber-attack detection and credit card fraud detection, we note that this problem has not been well addressed. The state-of-the-art bears the limitations of high index space cost and intermediate result maintenance cost. In this paper, we propose TC-Match, an effective approach to TCSM. First, we design a space and time cost-effective index CSS, which is essentially a k -partite graph structure where a node corresponds to an edge in G. By carefully creating links between nodes, we can encapsulate into CSS the partial embedding and timing order information between edges in G. We theoretically show that CSS has polynomial space and construction time complexities. Second, based on the property of CSS, we develop an efficient incremental matching algorithm with an effective node merging optimization. Extensive experiments show that TC-Match can achieve up to 3 orders of magnitude query performance improvement over the baseline methods, and meanwhile the memory consumption is reduced by 48.7%-86.7%.

Improving Temporal Treemaps by Minimizing Crossings

AbstractTemporal trees are trees that evolve over a discrete set of time steps. Each time step is associated with a node‐weighted rooted tree and consecutive trees change by adding new nodes, removing nodes, splitting nodes, merging nodes, and changing node weights. Recently, two‐dimensional visualizations of temporal trees called temporal treemaps have been proposed, representing the temporal dimension on the x‐axis, and visualizing the tree modifications over time as temporal edges of varying thickness. The tree hierarchy at each time step is depicted as a vertical, one‐dimensional nesting relationships, similarly to standard, non‐temporal treemaps. Naturally, temporal edges can cross in the visualization, decreasing readability. Heuristics were proposed to minimize such crossings in the literature, but a formal characterization and minimization of crossings in temporal treemaps was left open. In this paper, we propose two variants of defining crossings in temporal treemaps that can be combinatorially characterized. For each variant, we propose an exact optimization algorithm based on integer linear programming and heuristics based on graph drawing techniques. In an extensive experimental evaluation, we show that on the one hand the exact algorithms reduce the number of crossings by a factor of 20 on average compared to the previous algorithms. On the other hand, our new heuristics are faster by a factor of more than 100 and still reduce the number of crossings by a factor of almost three.

High-harmonic generation in semi-Dirac and Weyl semimetals with broken time-reversal symmetry: Exploration of the merging of Weyl nodes

High-harmonic generation in semi-Dirac and Weyl semimetals with broken time-reversal symmetry: Exploration of the merging of Weyl nodes

A large-scale graph clustering method for cell conditions spatio-temporal localization in aluminum electrolysis

Sensor nodes (industrial nodes) clustering is an efficacious method for gaining local working conditions real-timely in the production process. The existing deep graph neural networks-based industrial nodes clustering studies construct static graphs to describe the potential spatial correlation among industrial nodes, but the temporal correlation among industrial nodes is ignored, resulting in inferior real-time performance. Meanwhile, these deep learning models fail to obtain good clustering results due to the large-scale and noise-containing characteristics of industrial nodes. In this paper, a large-scale graph clustering method (LsGCM) is proposed for cell conditions spatio-temporal localization in aluminum electrolysis to address the above issues. Specifically, a spatio-temporal graph construction method based on industrial process mechanism knowledge and local working condition boundary types statistical feature fusion is proposed for capturing effective spatio-temporal correlations between industrial nodes. Then, hysteresis knowledge of industrial production system is used to guide the nodes merging, thereby avoiding the incorrect merging of time-asynchronous nodes when performing the spatio-temporal region detection of local working conditions. Finally, combined with the actual spatio-temporal location information of industrial nodes, a novel spatio-temporal information expansion method (StIEM) of the sub-spatio-temporal graph describing local working condition is proposed for obtaining spatio-temporal feature information of the neighborhood, which is beneficial to improve the performance of industrial node clustering. Validation studies on a numerical simulation example and multiple real aluminum electrolysis industrial datasets certificate the effectiveness and superiority of the proposed method. In particular, compared with existing graph clustering methods, our method improves the clustering accuracy by 7.79%.

Using Clustering to Strengthen Decision Diagram Bounds for Discrete Optimization

Offering a generic approach to obtaining both upper and lower bounds, decision diagrams (DDs) are becoming an increasingly important tool for solving discrete optimization problems. In particular, they provide a powerful and often complementary alternative to other well-known generic bounding mechanisms such as the LP relaxation. A standard approach to employ DDs for discrete optimization is to formulate the problem as a Dynamic Program and use that formulation to compile a DD top-down in a layer-by-layer fashion. To limit the size of the resulting DD and to obtain bounds, one typically imposes a maximum width for each layer which is then enforced by either merging nodes (resulting in a so-called relaxed DD that provides a dual bound) or by dropping nodes (resulting in a so-called restricted DD that provides a primal bound). The quality of the DD bounds obtained from this top-down compilation process heavily depends on the heuristics used for the selection of the nodes to merge or drop. While it is sometimes possible to engineer problem-specific heuristics for this selection problem, the most generic approach relies on sorting the layer’s nodes based on objective function information. In this paper, we propose a generic and problem-agnostic approach that relies on clustering nodes based on the state information associated with each node. In a set of computational experiments with different knapsack and scheduling problems, we show that our approach generally outperforms the classical generic approach, and often achieves drastically better bounds both with respect to the size of the DD and the time used for compiling the DD.

Spruce: a Fast yet Space-saving Structure for Dynamic Graph Storage

Dynamic graphs have been gaining increasing popularity across various application domains. With the growing size of these graphs, the update performance as well as space occupancy is becoming a crucial aspect of dynamic graph storage. Although existing dynamic graph systems can handle massive streaming updates (e.g., insertions and deletions), they cannot achieve both high throughput and low memory footprint. Drawing inspiration from the basic operations of the van Emde Boas (vEB) tree in double-logarithmic time, we designed Spruce, a high-performance yet space-saving in-memory structure to store dynamic graphs. Spruce uses a compact representation to construct the tree-like multilevel structure, which shares the common prefixes of vertices and has no merging or splitting of nodes to achieve the requirements of low memory consumption and high-efficiency dynamic operations. Furthermore, Spruce incorporates a read-optimized concurrency protocol, which refines ROWEX and Optimistic Locking, to facilitate efficient simultaneous read/write operations. Our experiment demonstrates that compared to Sortledton (the best of competitors), Spruce is up to 2.4X faster in ingesting graph updates, while saving up to 38.5% of memory space. As for graph analytics, Spruce shows high adaptability to different analytical workloads, and achieves comparable performance to other state-of-the-art dynamic graph structures.

Discrete Event Systems Theory for Fast Stochastic Simulation via Tree Expansion

Discrete Event Systems Theory for Fast Stochastic Simulation via Tree Expansion

The OREGANO knowledge graph for computational drug repurposing

Drug repositioning is a faster and more affordable solution than traditional drug discovery approaches. From this perspective, computational drug repositioning using knowledge graphs is a very promising direction. Knowledge graphs constructed from drug data and information can be used to generate hypotheses (molecule/drug - target links) through link prediction using machine learning algorithms. However, it remains rare to have a holistically constructed knowledge graph using the broadest possible features and drug characteristics, which is freely available to the community. The OREGANO knowledge graph aims at filling this gap. The purpose of this paper is to present the OREGANO knowledge graph, which includes natural compounds related data. The graph was developed from scratch by retrieving data directly from the knowledge sources to be integrated. We therefore designed the expected graph model and proposed a method for merging nodes between the different knowledge sources, and finally, the data were cleaned. The knowledge graph, as well as the source codes for the ETL process, are openly available on the GitHub of the OREGANO project (https://gitub.u-bordeaux.fr/erias/oregano).

The Computational Complexity of the ChordLink Model

In order to visualize well-clustered graphs with many intra-cluster but few inter-cluster edges, hybrid approaches have been proposed. For example, ChordLink draws the clusters as chord diagrams and embeds these into a node-link diagram that represents the overall structure of the clustered graph. The ChordLink approach consists of four steps; node replication, node permutation, node merging, and chord insertion. In this paper, we focus on the optimization problems defined by two of these steps. We show that the decision version of the problem defined by node permutation is NP-complete and present an efficient algorithm for a special case. For chord insertion, we show that it is NP-complete to decide whether a crossing-free placement of the chords exists. Moreover, it is APX-hard to minimize the number of crossings among the chords. Our results answer an open question posed by Angori, Didimo, Montecchiani, Pagliuca, and Tappini, who introduced ChordLink [TVCG 2021].

P-VERSE: Prioritization of Vehicles to Enhance Road Safety in IoT Environment

In this paper, we propose a scheme, named P-VERSE, to prioritize the emergency vehicles in the absence of a traffic signal at a multiway intersection point on a road. We consider the emergency vehicles, such as ambulance, fire trucks, or police vehicles, as prioritized vehicles and provide them safe and quick passage. The traffic signal is a traditional approach to minimize congestion, avoid collision among the vehicles, and reduce accidents. However, this results in the repetitive interruption of vehicles, thereby increasing their waiting time. To address these issues, we formulate a scheme that executes in two stages. In the first stage, we use Markov Chain to predict the future path of each vehicular nodes. Based on the predicted path, the common and emergency vehicles cooperatively form groups to avoid collision and congestion at the intersection point. On the other hand, in the second stage, we apply a cooperative coalition-based game-theoretic approach to design the strategic interactions among the vehicular nodes. These vehicular nodes act as players and dynamically form coalitions among them. Depending upon the utility of the coalition, the vehicular nodes either merge with or split out from a coalition. These nodes form a coalition to provide safe passage to the emergency vehicles. Further, we constrain our optimization problem to the Karush-Kuhn-Tucker (KKT) conditions and compute the optimal distance between the vehicular nodes. Extensive simulation-based analysis of our proposed scheme, P-VERSE, demonstrates that the energy consumption is reduced and utility is improved by 31.37% and 42.28% compared to the existing schemes proposed by Das et al. [1] and Xie et al. [2].

Circuitry optimization using genetic programming for the advancement of next generation refrigerants

In this study, a new evolutionary method, which can handle the implementation of genetic operators with unrestrained number and locations of splitting and merging nodes for the optimization of heat exchanger circuitries, is developed. Accordingly, this technique expands the search space of previous optimization studies. To this end, a finned-tube heat exchanger simulator is structured around a bijective mathematical representation of a refrigerant circuitry (the tube–tube adjacency matrix), which is used in combination with traversing algorithms from graph theory to recognize infeasible circuitries and constrain the evolutionary search to coherent and feasible offspring. The performance of three refrigerants, namely R32, R410A, and R454C, commonly used in air-conditioning applications was assessed for the optimized circuitries of a 36-tube evaporator while converging to a given cooling capacity, degree of superheating, and heat source boundary conditions. At a given output capacity and air outlet temperature, larger coefficient-of-performance improvements (up to 9.99% with reference to a common serpentine configuration) were realized for zeotropic refrigerant mixtures, such as R454C, where appropriate matching of the temperature glide with the temperature variation of the air yielded the possibility of further reducing the required compression ratio under the corresponding operating conditions. Hence, it was demonstrated that low-GWP zeotropic mixtures with temperature glide can realize a performance comparable to that of R32 and higher than that of R410A by approaching the Lorenz cycle operation.

Effects of coal bedding dip angle on hydraulic fracturing crack propagation

As a commonly used and effective technology for increasing the permeability of coal–rock reservoirs, hydraulic fracturing has been widely used in engineering sites to realize the efficient exploitation and utilization of gas resources in coal–rock reservoirs. The core of hydraulic fracturing is the initiation, propagation, and path of hydraulic cracks. In this paper, the combination of true triaxial physical test and numerical simulation is used to study the influence of coal bedding characteristics on the crack propagation of hydraulic fracturing and to discuss the important role of bedding in hydraulic crack formation. Results show that the control effect of the coal bedding dip angle on the hydraulic crack propagation under the same stress conditions is stronger than that of the maximum principal stress, and the control effect of the bedding on the crack propagation is weaker under the bedding dip angles of 0° and 90°. Reasonable fracturing fluid displacement setting is conducive to the formation of complex hydraulic fracture network structure, small displacement is conducive to the opening of primary natural fractures, and large displacement is conducive to hydraulic cracks that pass through the structural surface and the coal–rock interface. Global and local methods of finite element mesh embedding zero-thickness cohesion element and a pore-pressure node merging method to simulate fracturing are established using Python language and ABAQUS numerical analysis platform, respectively. The numerical simulation results suggest that the main fractures are formed along the principal stress direction, and the secondary branch fractures are formed along the bedding direction under the condition wherein the coal bedding dip angle is 30°. Under the conditions of different stress fields and fracturing fluid discharges, the controlling effect of bedding on hydraulic fracture is closely related to the fracturing parameters.

Graph Transformer with Reinforcement Learning for Vehicle Routing Problem

Vehicle routing problem (VRP) is one of the classic combinatorial optimization problems where an optimal tour to visit customers is required with a minimum total cost in the presence of some constraints. Recently, VRP is being solved with the use of deep reinforcement learning (DRL), with node sets considered (represented) as a graph structure. Existing Transformer based DRL solutions for VRP rely only on node information ignoring the role of information on the edges between nodes in the graph structure. In this paper, we proposed an attention‐based end‐to‐end DRL model to solve VRP which embeds edge information between nodes for rich graph representation learning. We used Transformer based encoder‐decoder framework with an edge information embedded multi‐head attention (EEMHA) layer in the encoder. The EEMHA‐based encoder learns underlying structure of the graph and generates an expressive graph topology representation by merging node and edge information. We trained our model using proximal policy optimization (PPO) with some code‐level optimization techniques. We conducted an experiment on randomly generated instances and on a real‐world data generated from road networks to verify the performance of our proposed model. The result from all experiments show that our model performs better than the existing DRL methods and most of the conventional heuristics with good generalizability from random instance training to real‐world instance testing of different problem size. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Scalable clustering by aggregating representatives in hierarchical groups

Appropriately handling the scalability of clustering is a long-standing challenge for the study of clustering techniques and is of fundamental interest to researchers in the community of data mining and knowledge discovery. In comparison to other clustering methods, hierarchical clustering demonstrates better interpretability of clustering results but poor scalability while handling large-scale data. Thus, more comprehensive studies on this problem need to be conducted. This paper develops a new scalable hierarchical clustering model called Election Tree, which can detect the most representative point for each sub-cluster via the process of node election in split data and adjust the members in sub-clusters by the operations of node merging and swap. Extensive experiments on real-world datasets reveal that the proposed computational framework has better clustering accuracy as opposed to the competing baseline methods. Meanwhile, with respect to the scalability tests on incremental synthetic datasets, the results show that the new model has a significantly lower time consumption than the state-of-the-art hierarchical clustering models such as PERCH, GRINCH, SCC and other classic baselines.

RDF Graph Summarization Based on Node Characteristic and Centrality

The explosive growth of RDF data makes it difficult to be efficiently queried, understood and used. RDF graph (RDFG) summarization aims to extract the most relevant and crucial data as summaries according to different criteria. Current summarization approaches mainly apply single strategies such as graph structure, pattern mining or relevance metrics to calculate RDFG summaries. Different to the existing approaches, this paper proposes a summarization approach to automatically generating RDFG summary, which can capture both structure and centrality information. Specifically, we present three algorithms, SumW (merging nodes based on node characteristics or similar types), SumS (merging nodes based on typed node characteristics) and SummaryFL (retrieving central nodes by combining node frequency and bridging coefficient). The three algorithms can be used by two summarization strategies: SumS or SumW only, and SumS+SummaryFL or SumW+SummaryFL. We conducted experiments over large and real-world RDF datasets to verify the effectiveness of our method with respect to time complexity, compression capability and coverage of the summary. The experiment results demonstrate that our approach outperformed the comparative algorithms.

Real Time Feature Influence Analysis Based ETL Framework for Efficient Big Data Management

The increased volume of big data introduces various challenges for its maintenance and analysis. There exist various approaches to the problem, but they fail to achieve the expected results. To improve the big data management performance, an efficient real time feature influence analysis based Extraction, Transform, and Loading (ETL) framework is presented in this article. The model fetches the big data and analyses the features to find noisy records by preprocessing the data set. Further, the method performs feature extraction and applies feature influence analysis to various data nodes and the data present in the data nodes. The method estimates Feature Specific Informative Influence (FSII) and Feature Specific Supportive Influence (FSSI). The value of FSII and FSSI are measured with the support of a data dictionary. The class ontology belongs to various classes of data. The value of FSII is measured according to the presence of a concrete feature on a tuple towards any data node, whereas the value of FSSI is measured based on the appearance of supportive features on any data point towards the data node. Using these measures, the method computes the Node Centric Transformation Score (NCTS). Based on the value of NCTS the method performs map reduction and merging of data nodes. The NCTS_FIA method achieves higher performance in the ETL process. By adapting feature influence analysis in big data management, the ETL performance is improved with the least amount of time complexity.

Low-Complexity Hyperbolic Embedding Schemes for Temporal Complex Networks

Hyperbolic embedding can effectively preserve the property of complex networks. Though some state-of-the-art hyperbolic node embedding approaches are proposed, most of them are still not well suited for the dynamic evolution process of temporal complex networks. The complexities of the adaptability and embedding update to the scale of complex networks with moderate variation are still challenging problems. To tackle the challenges, we propose hyperbolic embedding schemes for the temporal complex network within two dynamic evolution processes. First, we propose a low-complexity hyperbolic embedding scheme by using matrix perturbation, which is well-suitable for medium-scale complex networks with evolving temporal characteristics. Next, we construct the geometric initialization by merging nodes within the hyperbolic circular domain. To realize fast initialization for a large-scale network, an R tree is used to search the nodes to narrow down the search range. Our evaluations are implemented for both synthetic networks and realistic networks within different downstream applications. The results show that our hyperbolic embedding schemes have low complexity and are adaptable to networks with different scales for different downstream tasks.

NCAlt: Alternatives and Difference Visualizations for Behavior Trees in Game Development Learning

When learning how to develop AI behavior it is common for students to test different ideas before settling on a desired outcome. This functionality is not available in modern behavior tree systems beyond the traditional methods of duplication and conditional execution. We present NCAlt - a visual behavior authoring framework for exploring multiple game AI behaviors. The system also allows selective merging of nodes between multiple behavior tree alternatives and their visual differencing in the game scene and behavior tree views. We present two worked examples which demonstrate how NCAlt can improve the workflow of game development students. We have conducted a user study where NCAlt was compared against NodeCanvas for creating and using alternatives with moderately skilled game development students. Participants rated NCAlt 15% higher than NodeCanvas on the System Usability Scale (SUS). NCAlt was also rated higher on a self-developed questionnaire. We also conducted a semi-structured interview and a detailed longitudinal follow-up and obtained mostly positive feedback for NCAlt. The results suggest NCAlt has a potential to improve the types of workflows with behavior trees that involve exploration for game development students and facilitate learning, as a result. NCAlt was built on top of NodeCanvas - a plugin for the Unity Engine.