Number Of Nodes Research Articles

Elucidation of characteristics of networks where every node has its own lifetime

Growth is regarded as an important mechanism for explaining the structures of real networks. However, when the increase in the number of nodes is suppressed owing to their lifetime, the growth property alone is not sufficient to explain even fundamental network properties, such as the scale-free property. In this paper, we propose a network model that considers the lifetime of nodes and the excess addition of local internal links as a mechanism that supports network structures. By investigating the model network, we aimed to elucidate the network characteristics supported by local interactions between nodes via their common neighbors even when the rates of node addition and deletion were balanced. We found that the stationary state of the number of nodes is characterized by a scale-free property with the power-law exponent γ≃1 and localization of the peaks at l=2 in the distance distributions of neighboring nodes (DDN) as the node degree k increases. The specific behavior of the DDN explains the very slow decrease in the clustering strength C(k) with k compared with the normal behavior C(k)∼k−1 and the accelerated growth of the neighborhood graph of each node. Moreover, we showed that some real networks share local structures similar to those of the model network. These findings suggest that the same mechanism as that of the proposed model plays an essential role in supporting the local structures of some real networks.

Equilibrium seeking of higher-order networks under facet cover constraints.

Agent intelligence involves specific requirements for social attributes. Intelligent agents make their decisions based on the groups they are part of, tend to satisfy co-members, and enlarge their own benefits. A fundamental question is whether this form of subgroup decision-making accommodate each individual's preferences. In this paper, we examine the evolution of an anticoordination game on a higher-order network in the form of a simplicial complex in relation to the facet cover problem, which ensures that each subgroup yields a positive benefit. We introduce and apply the facet update rule to regulate nodes' group-based interactions. We identify the payoff parameter condition that a strict Nash equilibrium (SNE) satisfies a facet cover. The proposed facet update rule enables the activated facet to reach a facet equilibrium, and all nodes would converge to an SNE with no more than 2m strategy switches, where m is the number of nodes in the simplicial complex. Additionally, we analyze the convergence of the asynchronous update rule, which can be seen as a special case of the facet update rule. Our simulations and extensive examples reveal that the SNE achieved by the facet update rule, on average, covers fewer nodes compared to the asynchronous update rule.

Explaining results of path queries on graphs: Single-path results for context-free path queries

Many graph query languages use, at their core, path queries that yield node pairs (m,n) that are connected by a path of interest. For the end-user, such node pairs only give limited insight as to why this result is obtained, as the pair does not directly identify the underlying path of interest.In this paper, we propose the single-path semantics to address this limitation of path queries. Under single-path semantics, path queries evaluate to a single path connecting nodes m and n and that satisfies the conditions of the query. To put our proposal in practice, we provide an efficient algorithm for evaluating context-free path queries using the single-path semantics. Additionally, we perform a short evaluation of our techniques that shows that the single-path semantics is practically feasible, even when query results grow large.In addition, we explore the formal relationship between the single-path semantics we propose the problem of finding the shortest string in the intersection of a regular language (representing a graph) and a context-free language (representing a path query). As our formal results show, there is a distinction between the complexity of the single-path semantics for queries that use a single edge label and queries that use multiple edge labels: for queries that use a single edge label, the length of the shortest path is linearly upper bounded by the number of nodes in the graph; whereas for queries that use multiple edge labels, the length of the shortest path has a worst-case quadratic lower bound.

Soil carbon pools and microbial network stability depletion associated with wetland conversion into aquaculture ponds in Southeast China

Wetlands, which are ecosystems with the highest soil surface carbon density, have been severely degraded and replaced by artificial reclamation for fish and shrimp ponds in recent years. This transformation is causing intricate shifts in soil carbon pools and microbial stability. In this study, we examined natural wetlands and reclaimed aquaculture ponds in Southeast China to analyze the structure and network stability of soil microbial communities following the reclamation of estuarine wetlands and to elucidate the microbial-mediated mechanisms for regulating soil organic carbon (SOC). The aquaculture ponds presented significantly less average SOC content than the natural wetlands (p < 0.05). ACE, Chao1, and Shannon's indices of bacteria and fungi were decreased in aquaculture ponds. Less numbers of nodes and edge links in the co-occurrence network of soil fungi and bacteria in aquaculture ponds. This suggests reduced correlation and stability within the microbial network of aquaculture ponds. Decomposers in soil fungi (e.g. Dung Saprotroph) reduced. Reduced proportions of key phyla Ascomycota, Basidiomycota and Rozellomycota in the soil fungal network. Reduced proportions of key phyla Proteobacteria, Chloroflexi and Desulfobacterota in the soil bacterial network. In conclusion, our results suggest that converting wetland paddocks to intensive aquaculture ponds results in carbon pool loss and reduces soil microbial network stability. The results highlight the importance of protecting or moderately restoring mangrove wetlands along the coast of southeastern China. It is also predicted that such measures may enhance the storage capacity of soil carbon pools and improve the stability of carbon sequestration by soil microorganisms, thus offering a potential solution for mitigating global climate change.

Robustness of multilayer interdependent higher-order network

In real-world complex systems, most networks are interconnected with other networks through interlayer dependencies, forming multilayer interdependent networks. In each system, the interactions between nodes are not limited to pairwise but also exist in a higher-order interaction composed of three or more individuals, thus inducing a multilayer interdependent higher-order network (MIHN). First, we build four types of artificial MIHN models (i.e., chain-like, tree-like, star-like and ring-like), in which the higher-order interactions are described by the simplicial complexes, and the interlayer dependency is built via a one-to-one matching dependency link. Then, we propose a cascading failure model on MIHN and suggest a corresponding percolation-based theory to study the robustness of MIHN by investigating the giant connected components (GCC) and percolation threshold. We find that the density of the simplicial complexes and the number of layers of the network affect its penetration behavior. When the density of simplicial complexes exceeds a certain threshold, the network has a double transition, and the increase in network layers significantly enhances the vulnerability of MIHN. By comparing the simulation results of MIHNs with four types, we observe that under the same density of simplicial complexes, the size of the GCC is independent of the topological structures of MIHN after removing a certain number of nodes. Although the cascading failure process of MIHNs with different structures is different, the final results tend to be the same. We further analyze in detail the cascading failure process of MIHN with different structures and elucidate the factors influencing the speed of cascading failures. Among these four types of MIHNs, the chain-like MIHN has the slowest cascading failure rate and more stable robustness compared to the other three structures, followed by the tree-like MIHN and star-like MIHN. The ring-like MIHN has the fastest cascading failure rate and weakest robustness due to its ring structure. Finally, we give the time required for the MIHN with different structures to reach the stable state during the cascading failure process and find that the closer to the percolation threshold, the more time the network requires to reach the stable state.

Evaluation of lymph node ratios and log odds of positive nodes as prognostic indicators in primary organ malignancy

BackgroundStaging of malignant tumours based on positive lymph node number and not taking into account the actual number of examined lymph nodes during surgery may lead to bias and fallacious results. The ratio of positive and resected lymph nodes (LNR) and log odds of positive nodes (LODDS) emerged as novel prognostic markers in deciding the future course of management better than the parameter pN in predicting cancer-specific survival. We aim to evaluate and compare the prognostic value of pN, LNR and LODDS in common primary organ malignancies like breast, head and neck, gastric and cervical cancers. MethodsThis was an ambidirectional observational study conducted from September 2018 to August 2021 with one year (from 2017 to 2018) for retrospective data collection archived from records. It included patients affected by breast, head and neck, gastric and cervical cancers and were followed up for a period of 3 years from the date of diagnosis to perform a holistic survival analysis. The sample was grouped by American Joint Committee on Cancer N stage, LNR and LODDS, and analysed using Kaplan–Meier and multivariate Cox proportional hazard models. ResultsThe study included 202 breast cancer patients, 85 head and neck cancer patients, 100 gastric cancer patients and 52 cervical cancer patients. Multivariate Cox regressions analysis demonstrated a lower Akaike Information Criterion (AIC) value for LODDS and LNR followed by pN stage. ConclusionThe novel indicators LNR and LODDS better predicted the biological behaviour irrespective of lymph node number and allowed clinicians to correctly stratify patients for better postoperative management.

Design and Implementation of Energy-Aware Integration Mechanisms for IoT-Cloud Architectures: Enhancing Efficiency in Resource-Constrained Environments

This study paper suggests a way for the Internet of Things (IoT) and Cloud computing to work together that is smart about energy use. The goal is to solve the problem of IoT-Cloud integration's energy efficiency, which is important for making sensor nodes last longer and making sure that data transfer continues over time. The first step in the process is to plan the IoT nodes and give each sensor node a unique ID and a starting energy level. To make data safer, a homomorphic encryption method is used to make public and private keys. The integration process uses a good Cluster Head Selection Technique that has Random, Energy-Based, Distance-Based, and Density-Based methods to make sure that the sensor nodes are grouped together in the best way possible. The sensor nodes send data to the base station through cluster heads, which use homomorphic encryption to make the connection safe. The public key is used to hash each data packet before it is sent to the cluster head. The cluster head then sends the packets to the base station through the Cloud. At the base station, the data hash is checked one at a time, and then the data is decrypted. This makes sure that the data is correct and safe while it is being sent. Comparing time and energy use across different systems and node numbers is part of the performance assessment. The results show that System 4 did better than the others in terms of how much energy it used and how efficiently it transferred data. This shows that the proposed system can effectively handle IoT-Cloud integration. System 4 kept 28,848 units of energy after starting with 29,442 units, showing that it was much more energy efficient. The results show that using techniques that are aware of energy in IoT-Cloud systems can greatly improve performance. This study adds to the growing body of research on integrating IoT and the cloud by showing a safe, effective, and energy-conscious method that sends data while using the least amount of energy possible.

A Novel Approach to Node Coverage Enhancement in Wireless Sensor Networks Using Walrus Optimization Algorithm

Wireless Sensor Networks (WSNs) are crucial components of modern technology, supporting applications like healthcare, industrial automation, and environmental monitoring. This research aims to design intelligent and adaptive sensor networks by integrating metaheuristics with node coverage optimization in WSNs. By incorporating metaheuristics and optimizing node coverage, WSNs can become more resilient and robust, leading to the development of self-adapting, self-organizing networks capable of efficiently covering dynamic and diverse environments. This research introduces the Walrus Optimization Algorithm for Node Coverage Enhancement in WSNs, called the WaOA-NCEWSN technique. The primary goal of this technique is to optimize the coverage of a target region using a limited number of Sensor Nodes (SNs) and by improving their placement. The WaOA is inspired by walrus behaviours like feeding, migrating, breeding, escaping, roosting, and gathering in response to environmental signals. The WaOA-NCEWSN technique uses an objective function that defines the coverage ratio, representing the maximum probability of coverage in a 2D-WSN monitoring area. Comparative analysis with other models using 50, 75, 100, and 200 nodes shows that the WaOA-NCEWSN technique performs better. The compilation times for the WaOA-NCEWSN technique are 5.14s, 6.48s, 6.54s, and 7.47s for 50, 75, 100, and 200 nodes, respectively. Experimental results indicate that the WaOA-NCEWSN technique offers superior coverage performance compared to other models.

Improving I-ELM structure through optimal addition of hidden nodes: Compact I-ELM

Incremental extreme learning machines (I-ELMs) can automatically determine the structure of neural networks and achieve high learning speeds. However, during the process of adding hidden nodes, unnecessary hidden nodes that have little relevance to the target may be added. Several studies have proposed methods to overcome this problem by measuring the relevance between hidden nodes and outputs and adding or removing hidden nodes accordingly. Random hidden nodes have the advantage of creating diverse patterns, but they encounter a problem in which hidden nodes that generate patterns with little or no relevance to the target can be added, thereby increasing the number of hidden nodes. Unlike in existing I-ELMs, which use random hidden nodes, we propose a compact I-ELM algorithm that initially adds linear regression nodes and subsequently applies a method to ensure that the hidden nodes have patterns differing from the existing ones. Based on benchmark data, we confirmed that the proposed method constructs a compact neural network structure with fewer hidden nodes compared to the existing I-ELM systems.

Pinning control design for the output regulation of Boolean networks

In previous studies, the output regulation problem (ORP) of Boolean networks (BNs) is usually studied by the augmented system method, however, the state transition matrix dimension of augmented system is growing exponentially as the number of network nodes increases. To reduce the computational complexity, a new method to solve the ORP is adopted in this paper. Firstly, the relationship among the attractors of two BNs and their augmented system is studied, based on which, the ORP is converted into the set stabilisation problem of the original BN, and some necessary and sufficient conditions are given to detect the solvability of the ORP. Secondly, a pinning control for the ORP is considered according to the attractors of the original BNs, and an algorithm to design this kind of controls is provided. Finally, a practical example of signal transduction network is given to illustrate the effectiveness of the method in this paper.

Prognostic impact of log odds of positive lymph nodes (LODDS) in the stratification of patients with rectal cancer

IntroductionThe use of the N category of the TNM staging system, lymph node ratio (LNR) and log odds of positive lymph nodes (LODDS) in predicting overall survival (OS) and disease-free survival (DFS) in patients with rectal cancer is still controversial. Material and methodsA retrospective study of 445 patients with rectal cancer who underwent surgery between 2008 and 2017 in the University Complex Hospital was performed. Patients were stratified according to number of lymph nodes examined (NLNE), N staging, LNR and LODDS. The analysis was performed using the log-rank test, Kaplan-Meier functions, Cox regression and ROC curves. ResultsFive-year OS and DFS were 73.7% and 62.5%, respectively. No statistically significant differences were observed depending on NLNE. Increased LNR and LODDS were associated with shorter OS and DFS, independently of NLNE.Multivariate analysis showed that N stage, LNR and LODDS were independently associated with OS and DFS; however, the LODDS system obtained the best area under the curve, with greater predictive capacity for OS (AUC: 0.679) and DFS (AUC: 0.711). ConclusionLODDS and LNR give prognostic information that is not related to NLNE. LODDS provides better prognostic accuracy in patients with negative nodes than LNR and N stage.

A Dynamic Path Planning Method for UAVs Based on Improved Informed-RRT* Fused Dynamic Windows

In recent years, navigating rotor drones in complex and dynamic environments has been a significant challenge. This paper proposes an improved path planning method by integrating the enhanced Informed-RRT* algorithm with the Dynamic Window Approach (DWA) algorithm. Firstly, the probability weight function for sampling direction is dynamically adjusted based on the Euclidean distance between the start and goal points to obtain higher-quality sampling points. Secondly, the Artificial Potential Field (APF) concept is introduced during the generation of new nodes, applying the improved APF method to the elliptical sampling area to guide the direction of new node generation. This significantly reduces the number of redundant nodes, enhances the convergence speed, and improves the obstacle avoidance efficiency. Then, a polynomial fitting method is employed to optimize the path, yielding a smoother trajectory. Finally, the improved DWA algorithm is integrated. Initially, the Informed-RRT* algorithm generates an optimal path from the starting point to the goal point in the global space, which is then provided as an initial reference path to the DWA algorithm. During actual operation, the DWA algorithm dynamically adjusts control inputs based on the current position, speed, and reference path of the drone, ensuring that the drone can avoid dynamic obstacles and unknown static obstacles in real time while staying as close to the reference path as possible.

Laparoscopic segmental colectomy with extensive D3 lymph node dissection for right transverse colon cancer.

We herein propose a novel approach, laparoscopic segmental colectomy with extensive D3 lymph node dissection (ED3LND), for right-sided transverse colon cancer (TCC). Forty-two patients with right-sided TCC were randomly assigned to two groups: Group 1 (segmental colectomy with D3LND) and Group 2 (segmental colectomy with ED3LND). Clinical characteristics, surgical and pathological outcomes, and oncological outcomes were retrospectively compared between the two groups. The number of lymph nodes retrieved, apical lymph nodes retrieved, and apical lymph node metastases were significantly lower in Group 1 than in Group 2. No significant differences were observed in the operation time, length of hospital stay, estimated blood loss, lymph node metastases, postoperative lymphoceles, or other Clavien-Dindo grade ≥III postoperative complications between the two groups. The 3-year disease-free survival rate was 82.6% in Group 1 and 84.2% in Group 2, with no significant difference. Laparoscopic segmental colectomy with ED3LND for right-sided TCC may offer better oncological outcomes than D3LND. A large-scale prospective randomized controlled study is needed to further validate the oncological benefits of this novel procedure.

Rational cuts? The local impact of closing undersized schools

The availability of public education services can influence residential choices. Therefore, policies aimed at ‘rationalising’ service provision by reducing the number of undersized nodes in the public school network can lead to population decline, especially in spatially isolated areas lacking valid alternatives to the removed services. This paper examines the demographic and income effects of primary school closures by exploiting an Italian education reform that resulted in the contraction of the school network. We assess whether school closures impact households’ residential choices, over and above preexisting negative population trends that motivate school closures. Our findings indicate that municipalities affected by school closures experience significant reductions in population and income. The effect is primarily driven by peripheral municipalities located far away from economic centres and distant from the next available primary school. This evidence indicates that school ‘rationalisation policies’, by fostering depopulation of peripheral areas, have an influence on the spatial distribution of households and income, thus affecting territorial disparities.

A novel meshless method for numerical simulation of fractured-vuggy reservoirs

This paper proposes a novel meshless numerical simulation method for fractured-vuggy reservoirs. Initially, model discretization involves extracting fracture and vug feature nodes along the contours of the reservoir bodies and in alignment with fracture orientations, tailored to the characteristics of the fractured-vuggy oil deposit. Subsequently, a connection element model is established within the influence domain. Based on the seepage equations of the connection system, a computational method for the parameters of the connection elements (connection transmissibility and connection volume) is defined. In addition, a sequential method is employed to solve for the pressure and saturation, achieving rapid prediction of the reservoir's production dynamics. On this basis, an automatic history matching algorithm is utilized for real-time fitting of oil–water dynamic indicators, inverting the characteristic parameters of the connection element model, and quantitatively characterizing the injection–production connection elements. The research findings indicate that the method is capable of rapidly fitting and predicting the dynamics of oil reservoir production. Furthermore, conceptual model examples have substantiated that it achieves comparable computational efficiency and superior computational accuracy when compared to the traditional finite difference (volume) method under the same nodal conditions. Additionally, the node arrangement for fractures and vugs is comparatively flexible, and it can ensure the integrity of the flow paths with a limited number of nodes to enhance predictive accuracy. Therefore, this method can effectively meet the rapid prediction requirements for fractured-vuggy reservoirs and also provides a novel meshless computational approach for the numerical simulation of such reservoirs.

High-speed turbulent flows towards the exascale: STREAmS-2 porting and performance

Exascale High Performance Computing (HPC) represents a tremendous opportunity to push the boundaries of Computational Fluid Dynamics (CFD), but despite the consolidated trend towards the use of Graphics Processing Units (GPUs), programmability is still an issue. STREAmS-2 (Bernardini et al. Comput. Phys. Commun. 285 (2023) 108644) is a compressible solver for canonical wall-bounded turbulent flows capable of harvesting the potential of NVIDIA GPUs. Here we extend the already available CUDA Fortran backend with a novel HIP backend targeting AMD GPU architectures. The main implementation strategies are discussed along with a novel Python tool that can generate the HIP and CPU code versions allowing developers to focus their attention only on the CUDA Fortran backend. Single GPU performance is analysed focusing on NVIDIA A100 and AMD MI250x cards which are currently at the core of several HPC clusters. The gap between peak GPU performance and STREAmS-2 performance is found to be generally smaller for NVIDIA cards. Roofline analysis allows tracing this behavior to unexpectedly different computational intensities of the same kernel using the two cards. Additional single-GPU comparisons are performed to assess the impact of grid size, number of parallelized loops, thread masking and thread divergence. Parallel performance is measured on the two largest EuroHPC pre-exascale systems, LUMI (AMD GPUs) and Leonardo (NVIDIA GPUs). Strong scalability reveals more than 80% efficiency up to 16 nodes for Leonardo and up to 32 for LUMI. Weak scalability shows an impressive efficiency of over 95% up to the maximum number of nodes tested (256 for LUMI and 512 for Leonardo). This analysis shows that STREAmS-2 is the perfect candidate to fully exploit the power of current pre-exascale HPC systems in Europe, allowing users to simulate flows with over a trillion mesh points, thus reducing the gap between the Reynolds numbers achievable in high-fidelity simulations and those of real engineering applications.

SCVAN- BKM: Swarm clustering for vehicular ad hoc network with a secure blockchain-based key management scheme

The advancements in telematics and communication technology for automobiles have contributed to the development of Vehicular ad Hoc Networks (VANETs). These networks serve as the foundation for Intelligent Transportation Systems (ITS). Communication across various VANET entities is challenging due to the open communication environment and the highly dynamic nature of VANETs. One of the major challenges in VANETs is ensuring stable and secure transmission. To address these factors, several studies have been conducted. The article discusses a clustering algorithm for VANETs that leverages SCVAN-DPSO to create stable clusters and provide secure communication for mitigating malicious nodes. Additionally, Hyperelliptic Curve Cryptography (HECC) with signcryption in blockchain is proposed. This algorithm is designed to identify and mitigate malicious nodes, ensuring robust and secure communication within the network. To verify vehicles in VANETs, this study also suggests a safe and reliable key management method that generates and stores cryptographic keys using blockchain’s distributed ledger technology. By doing so, the risk of rogue nodes is reduced, and a safe, stable connection between vehicles is guaranteed. This work has been implemented using NS 3.34 simulation with the SUMO real-time traffic mobility simulator, and its performance has been evaluated. The proposed algorithm SCVAN-BKM provides a 99.6 % packet delivery ratio for 20 nodes, 0.4 % packet loss, end-to-end delay of 32.65 ms, throughput of 9.522 Mbps, and a cluster lifetime of 105 s. As the number of nodes increases in the communication zone, stable communication is maintained due to the clustering algorithm used in the proposed approach, as cluster formation supports stability in the high-mobility nature of vehicles, while secure communication is ensured using blockchain technology. The findings demonstrate that our approach is more effective and yields better outcomes than existing systems.

Progressive Supervision via Label Decomposition: An long-term and large-scale wireless traffic forecasting method

Long-term and Large-scale Wireless Traffic Forecasting (LL-WTF) is pivotal for strategic network management and comprehensive planning on a macro scale. However, LL-WTF poses greater challenges than short-term ones due to the pronounced non-stationarity of extended wireless traffic and the vast number of nodes distributed at the city scale. To cope with this, we propose a Progressive Supervision method based on Label Decomposition (PSLD). Specifically, we first introduce a Random Subgraph Sampling (RSS) algorithm designed to sample a tractable subset from large-scale traffic data, thereby enabling efficient network training. Then, PSLD employs label decomposition to obtain multiple easy-to-learn components, which are learned progressively at shallow layers and combined at deep layers to effectively cope with the non-stationary problem raised by LL-WTF tasks. Finally, we compare the proposed method with various state-of-the-art (SOTA) methods on three large-scale WT datasets. Extensive experimental results demonstrate that the proposed PSLD significantly outperforms existing methods, with an average 2%, 4%, and 11% performance improvement on three WT datasets, respectively. In addition, we built an open source library for WT forecasting (WTFlib) to facilitate related research, which contains numerous SOTA methods and provides a strong benchmark. Experiments can be reproduced through https://github.com/Anoise/WTFlib.

An optimized method for AUV trajectory model in benthonic hydrothermal area based on improved slime mold algorithm

The optimization of the desired autonomous underwater vehicle (AUV) trajectory modeling and AUV trajectory tracking control in the benthonic hydrothermal area were studied. In the conventional trajectory tracking model construction methods, the time points were roughly combined with the position points of the planned path, making it difficult to produce a smooth trajectory. Although the spline interpolation method was an ideal option for smooth curves, a great number of points were needed for a complex desired trajectory mode. In response to the demanding requirements of AUV trajectory tracking control in the benthonic hydrothermal area, an under-actuated test platform was first established, and the cubic spline interpolation was adopted to process the preset path points for a smooth desired trajectory. An improved slime mold algorithm (SMA) was put forward to optimize the interpolating points used in the trajectory modeling. The Levy flight technology and the compactness technique to speed up the search process and increase the search accuracy. The simulation experiments were conducted in comparison with the artificial fish swarm algorithm (AFSA), the particle swarm optimization (PSO), and the compact cuckoo search (CCS). The results showed that the improved SMA shortened the search process, effectively avoided the local extreme values, and generated a high-precision desired trajectory model in a shorter time. The pool test also verified the feasibility and effectiveness of the proposed method. The method proposed in this study can satisfy the modeling of benthonic hydrothermal trajectory with a fewer number of nodes, faster search progress and search accuracy.

Excluding Upper Axillary Level 1 in Regional Nodal Irradiation Does Not Increase Axillary Recurrence Risk in Patients With Breast Cancer

PurposeThe optimal extent of regional nodal irradiation (RNI) in postoperative radiotherapy for breast cancer, particularly regarding axillary level 1 (AXL1), remains uncertain. This study aims to compare clinical outcomes between extensive RNI including the entire axilla and limited RNI excluding the upper AXL1 in patients with breast cancer. MethodsA retrospective analysis included 1,780 women with non-metastatic unilateral breast cancer who underwent RNI during postoperative radiotherapy between 2007 and 2018. Patients were classified into extensive and limited RNI groups based on the upper AXL1 inclusion in the radiation field. Propensity score matching yielded a cohort of 1,020 patients. Non-inferiority of limited RNI compared to extensive RNI was assessed with a defined margin of ≤2% in the 5-year axillary recurrence rate. ResultsAfter a median follow-up of 67.9 months, the 5-year axillary recurrence rates were similar between extensive and limited RNI groups (1.2% vs. 1.6%; Plog-rank=0.790). Limited RNI demonstrated non-inferiority with a 0.4% difference (95% confidence interval, -1.1%–1.9%; Pnon-inferiority=0.019). Disease-free survival (87.9% vs. 91.5%; Plog-rank=0.122) and overall survival (94.1% vs. 96.9%; Plog-rank=0.260) at 5 years were not significantly different between extensive and limited RNI groups. Multivariable analysis revealed that lymphovascular invasion (hazard ratio [HR], 5.17; P=0.02) and negative hormone receptor status (HR, 11.73; P=0.002) were associated with a higher risk of axillary recurrence, while limited RNI showed no significant association (HR, 1.35; P=0.652). Subgroup analysis demonstrated that extensive RNI did not improve axillary control in patients with lymphovascular invasion, hormone receptor negativity, positive lymph node metastasis, or a small number of nodes removed. ConclusionLimited RNI, excluding the upper AXL1 from the radiation field, demonstrated axillary recurrence rates comparable to those of extensive RNI in patients with breast cancer. The study suggests that extensive RNI may not provide additional therapeutic benefits, while limited RNI appears to be a valid option for regional control.