Heterogeneity modeling is crucial for developing tailored interventions and policies in medicine, economics, and social sciences. Traditional subgroup analysis methods often impose restrictive distributional or structural assumptions, require high computational costs, or lack direct predictive utility. In this paper, we propose a novel subgroup analysis framework for regression settings that substantially relaxes conventional distributional and pre-specified subgroup assumptions. The proposed method detects subgroup structure of heterogeneous regression coefficients efficiently using a minimum spanning tree (MST)-based regularization approach, estimates the regression coefficients via a post-group estimator based on the estimated subgroup structure, and predicts the subgroup memberships of new subjects via support vector machine (SVM) classifiers. We establish strong consistency of the subgroup membership detection, asymptotic normality of the post-group estimator for regression coefficients, and theoretical properties of the SVM classifier for prediction. We demonstrate the merit of the proposed method through simulation studies and analyses of the National Health and Nutrition Examination Survey.

High-mass stars and star clusters form from the fragmentation of massive dense clumps driven by gravity, turbulence, and magnetic fields. The extent to which each of these agents impacts the fragmentation depending on the clump mass, density, and evolutionary stage is still largely unknown. The ALMA evolutionary study of high-mass protocluster formation in the GALaxy (ALMAGAL) project, with sim1000 clumps observed at ∼1000,au resolution, allows a statistically significant characterization of the fragmentation process over a large range of clump physical parameters and evolutionary stages. Our goal is to characterize where and how the dense cores revealed by ALMA are distributed in massive potentially cluster-forming clumps to trace how fragmentation is initially set and how it proceeds before gas dispersal due to stellar feedback. We characterized the spatial distribution of dense cores in the 514 ALMAGAL clumps that host at least four cores, using a set of quantitative descriptors that we evaluated against the clump bolometric luminosity-to-mass ratio, which we adopted as an indicator of the evolution of the system. We measured the separations between cores with the minimum spanning tree (MST) method, which we compared with the predictions of gravitational fragmentation from Jeans theory. We investigated whether cores have specific arrangements using the Q parameter or variations due to their masses with the mass segregation ratio, Λ_MSR. ALMAGAL cores are distributed throughout the entire area of the clump, usually arranged in elliptical groups with an axis ratio e _ although high values with e,≥,5 are also observed. We found a single characteristic core separation per clump in sim76% of cases, suggesting that multiple fragmentation lengths may be frequently present. Typical core separations are compatible with the clump-averaged thermal Jeans length, łambda^ th J . However, we found an additional population of cores, typical of low-fragmented and young clumps, which are on average more widely separated with l,≈,3 _ th J . By stacking the distributions of the core separations in clumps of similar evolutionary stage, we also found that the separation decreases on average from l in younger systems to l in more evolved ones. The ALMAGAL cores are typically distributed in fractal-type subclusters, while centrally concentrated patterns appear only at later stages, but we do not observe a progressive transition between these configurations with evolution. Finally, we also found 110 ALMAGAL systems with a signature of mass segregation, with an occurrence that increases with evolution.

A novel physically interpretable approach for drought diagnosis: the state-space gradient drought index from a Gaussian Mixture Model–Minimum Spanning Tree (GMM–MST) framework

Emergency vehicles (EVs) often experience delays at congested intersections, undermining time-critical rescue operations. Enabled by connected and automated vehicle (CAV) technologies and Vehicle-to-Everything (V2X) communication, intersections can be managed cooperatively, but EV priority that balances EV efficiency and surrounding traffic performance remains underexplored. This paper proposes MILP-LC, a mixed-integer linear programming (MILP) approach integrating a lane-changing yielding strategy. Vehicles ahead of the EV are instructed to proactively change lanes to create space, while the MILP model optimises vehicle passing orders to minimise disruption to surrounding traffic. A level-based control algorithm executes the plan to ensure orderly movement through the intersection. Simulation results show that, compared with a heuristic depth-first spanning tree algorithm and conventional EV signal preemption, MILP-LC significantly reduces EV travel time while maintaining overall traffic efficiency with only a slight increase in fuel consumption. Benefits are more pronounced under high traffic volumes and short time headways.

Antimicrobial resistance (AMR) in Neisseria gonorrhoeae severely limits treatment options, with increasing resistance even to first-line and last-line ceftriaxone (CRO), posing a major global public health threat. In this study, we systematically identified 53 significantly different mutations between ceftriaxone-resistant and susceptible strains in multiple proteins through bioinformatics analysis. Among these, 33 mutations were identified for the first time, notably including the PorB Q143K via structural analysis. Minimum spanning tree (MST) analysis based on these mutations marked improved sensitivity and specificity for identifying ceftriaxone-resistant strains compared to traditional sequence typing of PenA, PonA, PorB, and MtrR (68.4% vs. 53.2%; 77.3% vs. 57.5%, respectively). Furthermore, analysis of PenA sequences from global 8,325 strains (470 MLST types) revealed that mutation frequencies at key PenA sites are highly associated with MLST types, with 34 high-frequency MLST types (STs) identified. The proportions of these 34 STs were 88.38% in 611 decreased susceptibility to ceftriaxone (CRO-DS) strains and 33.09% in 8,325 background strains, respectively, revealing an extremely significant association between 34 high-frequency STs and CRO-DS (P < 0.0001). In conclusion, this work provides further insights into the molecular mechanisms of CRO resistance while offering significant value for monitoring and predicting emerging CRO-DS-associated MLST types.

Traditional association rule analysis is effective at uncovering co-purchase patterns but fails to provide a global structural view of the market, which often results in fragmented and isolated insights. This study proposes a hybrid framework that integrates the Apriori algorithm with a Minimum Spanning Tree (MST) in order to validate and contextualize association rules within a single structural backbone. Transaction data from a retail store are transformed into a weighted, undirected product graph using an inverse-support function, and an MST is then extracted to represent the market backbone, while frequent itemsets and strong rules are obtained using Apriori. Experimental results on 236 multi-item transactions show that the MST backbone comprises 10 products and 9 fundamental links, with 66.67% of these links being confirmed by strong association rules, indicating a substantial coherence between statistical and structural evidence. The proposed model identifies 41 Apriori patterns that can be embedded in the MST and ranks them using a new metric, Structural Distance, which enables the categorization of Core Patterns, Bridge Patterns, and Complex Patterns according to their structural tightness. This hybrid perspective distinguishes dense, strategically meaningful bundles from anomalous but frequent combinations that are structurally peripheral, thereby offering a more holistic and actionable alternative to conventional Market Basket Analysis. The validated framework can support various applications, including store layout optimization, cross-selling strategies, and the design of path-based recommender systems, and it opens avenues for future extensions based on dynamic graphs and Graph Neural Networks.

The modernization of power distribution grids, driven by the integration of DER, necessitates advanced modelling capabilities. A critical challenge is the semantic gap between the extensive geospatial asset data and the detailed electrical models required for engineering analysis. This data is often stored in static, unstructured KMZ formats that contain inherent topological errors. To address this, this paper presents a novel low-cost, Python framework that fully automates the conversion of this raw GIS data into solvable mathematical models for computation. This process generates executable files for industry-standard, script-based simulators such as MATPOWER and OpenDSS. The framework's core technical contributions include an XPath and Regex-based engine for metadata extraction. A graph-theory pipeline then utilizes a Minimum Spanning Tree (MST) algorithm to algorithmically heal topological disconnections. A Dijkstra-based method is then used for model abstraction. The core methodology was first validated using a bidirectional, reverse-engineering process on a 4-bus test case. This confirmed a lossless round-trip conversion to and from a data-rich KMZ format. Subsequently, it was applied to a complex, real-world 11 kV Kenyan distribution feeder. The generated model converged in a Newton-Raphson power flow. This demonstrated its utility as a powerful diagnostic instrument by enabling detailed feeder voltage profiling and loss analysis. Results were cross-validated against DIgSILENT PowerFactory, a graphic-based simulator, showing excellent numerical agreement. This study validates a scalable framework that transforms static, error-prone GIS data into dynamic, multi-platform diagnostic models. This approach provides a feasible pathway to accelerate grid modernization.

This paper presents a high-level system architecture that integrates the Software Defined Networking (SDN) paradigm in 5G/6G networks with the aim of supporting the requirements expected for Industrial Internet of Things (IIoT) devices and services. To this purpose, we include multiple Reconfigurable Intelligent Surfaces (RISs) systems and provide for them an abstract representation consistent with the OpenFlow interface and messaging framework. The main contribution of this is firstly focused on designing a comprehensive framework that specifies the modules, components, interfaces, protocols, and message exchanges across the typical three layers SDN architecture. In addition, we characterize the Network Discovery (ND) and Host Discovery (HD) protocols that enable the SDN Controller to achieve a global and updated view of the network. Then, the RIS Placement and Selection Problem (RPSP) is formulated by using two graph-theory approaches, i.e., Set Covering (SC) and Minimum Spanning Tree (MST). Finally, we conduct an extensive simulation campaign that evaluates the performance of the discovery phases and the RIS placement/selection algorithms in realistic industrial environments. The results highlight the advantages achieved in terms of coverage and complexity.

Streptococcus pneumoniae (S. pneumoniae) is responsible for a wide range of infections. The aim of this study was to investigate the clonal diversity of S. pneumoniae in thirteen Arab countries. Multi-Locus Sequence Typing (MLST) data were extracted from PubMLST database. Genetic analysis was performed using DnaSP software version 6.0. A Minimum Spanning Tree (MST) analysis was conducted to evaluate the population structure of S. pneumoniae strains. Genetic data from 1008 Arab S. pneumoniae strains, collected over 22 years (1996–2018), were analyzed. MLST analysis identified a highly diverse population comprising 600 sequence types grouped into 87 clonal complexes and 295 singletons. Both internationally disseminated clones (e.g., ST156) and country-specific lineages (e.g., ST2307, Saudi Arabia) were observed, indicating substantial geographic structuring. Significant associations were detected between sequence types and geographical origin, decade of isolation, patient age, disease type, and serotype (p &lt; 0.05). Although recombination events were presented, the population retained a predominantly clonal structure over time (ISA = 0.0715, p &lt; 0.001). Overall, these findings demonstrated extensive genetic heterogeneity and spatiotemporal structuring of S. pneumoniae in the Arab region, providing valuable insights for regional surveillance and vaccine-related strategies.

Abstract We report the discovery of 45 compact hub-filament systems (HFSs; median size ∼2.4 pc) in infrared-dark clouds (IRDCs) in the W33 complex, located at the junction of the Scutum and Norma spiral arms. Using Spitzer 8 and 24 µ m, and unWISE 12 μ m images, HFSs are identified as regions where three or more filaments converge onto a central hub, appearing as absorption features toward IRDCs. In each IRDC, HFSs mainly lie at the intersections of elongated substructures, associated with groups of protostars and lacking radio continuum emission. Minimum Spanning Tree (MST) analysis shows that protostars are closely associated with the HFSs, with protostellar core separations of ≤0.7 pc, indicating strong clustering within fragmented structures. The HFSs form two main groupings spanning 10–15 pc, with member separations of 1–3.3 pc. Around 65% are tightly clustered (&lt;2 pc), exhibiting rich small-scale structures and emphasizing the uniqueness of the complex. MST analysis of ALMAGAL 1.38 mm continuum cores—predominantly low-mass and embedded in 10 HFSs—reveals a median core separation of ∼0.03 pc. The protostellar spacing (∼0.7 pc) significantly exceeds the thermal Jeans length (∼0.08 pc for temperature ∼18 K and density ∼10 5 cm −3 ), whereas the core spacing is smaller than the Jeans length, suggesting that thermal fragmentation may influence core formation but alone cannot explain the larger-scale protostellar distribution. All these findings together support a picture in which fragments of clouds/filaments form clumps hosting compact HFSs that facilitate efficient and clustered star formation, often yielding massive stars.

An Automatic Layer Extraction Algorithm for Ice Sounding Radar Data Based on Curvelet Transform (CT) and Minimum Spanning Tree (MST)

Most medium voltage (MV) distribution systems are structured in mesh and radially operated to distribute electric power from distribution substations to consumers (distribution transformers). The difficult decision of building a new radial MV topology is which branch should be connected to others and could save cost in constructing for the operator in the first stage of designing and bidding for the new topology. Due to that problem which always occurs during the primary stage of designing proposals for the system, many heuristic algorithms have been implemented to make a convenient to build up distribution systems and analyze costs for the new system. This paper proposes to study from scratch buildup for the new radial topology to the final stage of the project by using and comparing two methods, called Minimum Spanning Tree (MST) Algorithm and Shortest Path (SP) Algorithm to find the shortest routing connection for structuring the topology with the shortest length of conductor and the better voltage profile by using backward forward load flow to modify. In addition, after the new radial topology is built up, the reliability indicator is proposed by identifying the optimal line among the possible connections within the topology. In the final stage, the economy is estimated by considering the cost of conductors, protective devices, labor, and operational expenses over a planning study of 30 years. To validate the proposed method, the standard test distribution system (9-bus test and 25-bus test) and the real distribution system, which is located in Khsach Kandal, Kandal, Cambodia with 47-bus is selected. The result of this paper demonstrates that the radial Medium Voltage (MV) topology is constructed using the Minimum Spanning Tree (MST) algorithm. This approach results in a reduced length of conductor and a faster payback period, despite the fact that the power loss of the SP algorithm is more favorable. However, the capital expenditure (CAPEX) of the SP system remains a significant concern for many investors. In the reliability index tie line connections are selected based on their highest probability of serving as tie lines within the system.

Objective: The article aims to study how much digitalisation influences the systemic risk (SR) in the insurance sector of European Union (EU) countries. Research Design &amp; Methods: In this research, we introduce an innovative, quantitative method for exploring the impact of digitalisation and assessing the similarities and interconnections among all European Union countries’ insurance sectors from 2004 to 2018 within the framework of Industry 4.0. The study integrates statistical and econometric tools with network modelling techniques, focusing on the topological indicators of minimum spanning trees (MST) derived from multidimensional dynamic time warping (DTW) distances. We analysed two datasets. The first one comprises exclusively data describing insurance sectors, while the second incorporates data detailing both insurance sectors and the digitalisation processes of individual EU countries. We assessed the similarity of the sectors’ dynamics over the analysed period, examining network behaviour during subprime crises, periods of excessive public debt, and immigration-related crises in Europe. Findings: The proposed tools made it possible to determine how digitalisation contributes to the increase in systemic risk in the EU insurance sector over the periods examined and effectively measure similarity levels, and outline indirect connections between insurance sectors. Implications &amp; Recommendations: Because similarity can be a potential indirect channel for systemic risk contagion, countries with comparable insurance sectors and shared digitalisation-related behaviours may undergo similar repercussions during global financial downturns. Research endeavours in the insurance sector must consider digitalisation indicators that encompass technological advancements and consumer behaviour. Contribution &amp; Value Added: We developed a new method to examine the similarity of the insurance sectors of the European Union countries and to assess the dynamics of changes in this similarity in the era of Insurance 4.0. Such an analysis allows for a long-term assessment of the possibility of spreading threats in the insurance sector throughout the European Union.

In modern basketball, effective player spacing is critical for optimizing offensive efficiency and shot quality. This paper proposes a novel approach to quantifying spacing using graph theory. Each player is represented as a node, and the pairwise Euclidean distances between them form the weighted edges of a complete graph. We compute several spatial and structural metrics, including total spacing, convex hull area, minimum spanning tree weight, and centrality measures. Our method allows for a frame-by-frame quantitative analysis of spacing, revealing key patterns associated with successful possessions. Results demonstrate that certain geometric and network-derived properties are strong indicators of tactical efficiency.

We consider the following NP-hard generalization of the Minimum Spanning Tree problem. Given an undirected \(n\)-vertex edge-weighted complete graph and integers \(d\) and \(m\), find \(m\) edge-disjoint spanning trees of diameter at most \(d\) with minimum total weight. We propose a new polynomial-time approximation algorithm for the problem and study its performance guarantees on random inputs, that is, when the edge weights of the graph are i. i. d. random variables. We show that under mild conditions on the distribution parameters the proposed algorithm is asymptotically optimal for the case of continuous and discrete uniform distribution on \([a_n, b_n]\), \(a_n&gt;0\), the shifted exponential distribution with shift \(a_n&gt;0\), and distributions dominating the above. In contrast to a number of previous results for related problems, the new algorithm is asymptotically optimal not only if \(d\) tends to infinity with \(n\), but for constant \(d\) as well.

The development of science and technology has encouraged the utilization of graph theory in solving optimization problems, particularly in transportation systems and tourism route planning. Medan City, as a metropolitan area with dense road networks and widely dispersed tourist destinations, faces challenges in selecting efficient travel routes. This research aims to determine the optimal route between tourist destinations in Medan City using the Minimum Spanning Tree (MST) method with Prim’s Algorithm. The research was conducted using a weighted graph modeling approach, where each tourist destination is represented as a vertex and the distance between destinations is represented as an edge weight. Distance data and estimated travel time were obtained through digital mapping using Google Maps and then analyzed through iterations of Prim’s Algorithm to produce a minimum spanning tree without forming cycles. The results show that all 23 tourist destinations are successfully connected in a single MST structure with a minimum total distance of 68.97 km and a travel time of approximately 199 minutes or 3 hours and 19 minutes. This model is expected to serve as a reference for tourism planning and support urban transportation efficiency based on mathematical computation.

Abstract The current paper analyzes minimum cost spanning tree problems having irreducible costs while incorporating revenues. We prove that, in this context, the core of the associated cost-revenues game (the r -core) is non-empty. In particular, we find an stable allocation in the r -core, based on the CEL bankruptcy rule, that ensures fairness by distributing revenues only among agents that belong to every effective coalition. Therefore, our findings contribute to the literature by identifying structural conditions that guarantee stability in minimum cost spanning tree problems with revenues, overcoming previous results which showed that the r -core could be empty.

The development of a Mass Rapid Transit (MRT) system that interconnects multiple shopping centers has substantial potential to enhance the economic and social infrastructure of metropolitan areas. Improved connectivity not only reduces travel time and transportation costs for consumers but also increases foot traffic, alleviates urban traffic congestion, and contributes to reduced environmental pollution. This study presents a comparative performance analysis of two widely implemented Minimum Spanning Tree (MST) algorithms—Kruskal’s and Prim’s—to determine their suitability for designing optimal underground MRT routes connecting major malls in Jakarta. MST algorithms serve a critical role in graph theory by connecting all vertices with the minimum cumulative weight, while maintaining both acyclicity and full connectivity. Their application in transportation network design is essential for minimizing construction and operational expenses while simultaneously maximizing time efficiency and network reliability. The experimental results indicate that although both algorithms yield identical minimum spanning costs, Kruskal’s algorithm runs faster than Prim’s, particularly on sparse graphs that typify urban transportation systems. Despite this performance gap, both algorithms are categorized as polynomial-time algorithms, not in the nondeterministic polynomial (NP) class, as their computational processes do not exhibit exponential growth (i.e., not of the form 2ⁿ). Based on these findings, Kruskal’s algorithm is recommended for scenarios requiring faster computation in MRT network development. Nevertheless, both algorithms remain effective and applicable depending on specific graph characteristics and computational constraints.

Abstract Optimization is a fundamental requirement in modern engineering and computational systems, where efficient utilization of resources and reduction of computational cost are critical. Graph theory offers a robust mathematical framework for modeling and solving optimization problems by representing system elements as vertices and their interactions as weighted or capacitated edges. This paper investigates the application of graph-theoretic optimization techniques and their implementation using MATLAB. Classical optimization problems, including shortest path, minimum spanning tree, and maximum flow, are formulated using graph models and solved through well-established algorithms. MATLAB’s graph and network analysis tools are employed to implement these algorithms, enabling efficient computation, visualization, and validation of optimal solutions. The proposed methodology demonstrates how graph-based modeling simplifies complex optimization problems and reduces computational complexity while maintaining solution accuracy. Through illustrative examples and performance evaluation, the effectiveness of graph theory–based optimization is demonstrated in practical domains such as network design, transportation systems, and resource allocation. The results confirm that integrating graph theory with MATLAB provides a scalable and efficient framework for addressing large-scale optimization problems. This study highlights the significance of graph-theoretic approaches as reliable optimization tools for contemporary engineering and scientific applications. Keywords: Graph Theory, Optimization Techniques, Shortest Path, Minimum Spanning Tree, Maximum Flow, MATLAB

In a Wireless Sensor Network (WSN), dozens or hundreds of battery-driven sensors communicate with one another. Batteries have to be replaced frequently when nodes are deployed in unattended environments. Internet of Things (IoT) applications are becoming increasingly scalable and energy-efficient, making energy-efficient data aggregation a critical research focus. As part of this study, two hybrid data aggregation frameworks are presented and evaluated in order to optimize energy consumption and network performance. In the first framework, hierarchical clustering is performed using BIRCH (Balanced Iterative Reduction and Clustering Using Hierarchies), while mobile base station shunting is performed using Ant Colony Optimization (ACO). Using Particle Swarm Optimization (PSO), optimal cluster heads and base stations can be placed, and routing paths can be optimized using the Minimum Spanning Tree (MST) algorithm. Software-defined WSNs reduce computational overhead and improve adaptability by utilizing a software-defined architecture. According to a comparison of energy efficiency, network lifetime, control overhead, and data latency metrics, both approaches outperform traditional static clustering methods significantly; however, the BIRCH and ACO model excels in adaptive clustering and load distribution, while the PSO and MST model provides the best path optimization and the least amount of delay in data transmission.