Stability Of Networks Research Articles

Local set stability and target control of probabilistic Boolean networks

This paper analyzes the local set stability of probabilistic Boolean networks (PBNs), including local finite-time set stability with probability one (FSSPO) and local asymptotic set stability with probability one (ASSPO). Firstly, a necessary and sufficient condition is proposed for the local FSSPO of PBNs. Then, a reachable set with probability one is constructed, based on which, the largest domain of attraction for the local FSSPO of PBNs is determined. Secondly, by constructing two parameterized sets, the transition probability matrix of PBNs is properly partitioned, and the largest domain of attraction for the ASSPO is depicted. Finally, for PBNs which are locally stable, the target control is introduced to achieve the global FSSPO and global ASSPO of PBNs, respectively.

The Network Structure of School Principal Resilience: Gender Differences

ABSTRACTThe ability of school principals to demonstrate resilience enables them to effectively lead, adapt and thrive amidst the ever‐changing landscape of educational challenges and transformations. Despite its necessity, research on principal resilience remains largely underdeveloped and is still in its early stages. The current study aims to fill this gap using network analysis to examine the inter‐structural principal resilience network and gender differences in terms of network estimation, centrality indices, network stability and network comparison using a sample of 1274 principals from China. The results reveal a comprehensive understanding of the dynamic network and gender effects on school principal resilience at the dimension and item levels. It is noted that social resilience exhibits the highest strength, indicating the critical importance of social support networks and relationships. The gender analysis indicated that spiritual resilience emerged as a central dimension in the resilience network of female principals, while emotional and psychological resilience was the central dimension in the resilience network of male principals. This study advances the conceptual and practical understandings of school principal resilience by examining the interactions among different dimensions and items, thereby contributing to the maturity of knowledge production and intervention efforts in the field.

Nested patterns of commensals and endosymbionts in microbial communities of mosquito vectors

BackgroundMosquitoes serve as vectors for numerous pathogens, posing significant health risks to humans and animals. Understanding the complex interactions within mosquito microbiota is crucial for deciphering vector-pathogen dynamics and developing effective disease management strategies. Here, we investigated the nested patterns of Wolbachia endosymbionts and Escherichia-Shigella within the microbiota of laboratory-reared Culex pipiens f. molestus and Culex quinquefasciatus mosquitoes. We hypothesized that Wolbachia would exhibit a structured pattern reflective of its co-evolved relationship with both mosquito species, while Escherichia-Shigella would display a more dynamic pattern influenced by environmental factors.ResultsOur analysis revealed different microbial compositions between the two mosquito species, although some microorganisms were common to both. Network analysis revealed distinct community structures and interaction patterns for these bacteria in the microbiota of each mosquito species. Escherichia-Shigella appeared prominently within major network modules in both mosquito species, particularly in module P4 of Cx. pipiens f. molestus, interacting with 93 nodes, and in module Q3 of Cx. quinquefasciatus, interacting with 161 nodes, sharing 55 nodes across both species. On the other hand, Wolbachia appeared in disparate modules: module P3 in Cx. pipiens f. molestus and a distinct module with a single additional taxon in Cx. quinquefasciatus, showing species-specific interactions and no shared taxa. Through computer simulations, we evaluated how the removal of Wolbachia or Escherichia-Shigella affects network robustness. In Cx. pipiens f. molestus, removal of Wolbachia led to a decrease in network connectivity, while Escherichia-Shigella removal had a minimal impact. Conversely, in Cx. quinquefasciatus, removal of Escherichia-Shigella resulted in decreased network stability, whereas Wolbachia removal had minimal effect.ConclusionsContrary to our hypothesis, the findings indicate that Wolbachia displays a more dynamic pattern of associations within the microbiota of Culex pipiens f. molestus and Culex quinquefasciatus mosquitoes, than Escherichia-Shigella. The differential effects on network robustness upon Wolbachia or Escherichia-Shigella removal suggest that these bacteria play distinct roles in maintaining community stability within the microbiota of the two mosquito species.

Optimal Energy Management Systems and Voltage Stabilization of Renewable Energy Networks

This paper addresses the challenge of integrating multiple energy sources into a single-domain microgrid, commonly found in urban buildings, while also providing a platform for energy management. A Lyapunov stability analysis of a simple boost converter was used as a basis for designing the dual control loop of the grid. The versatility of the developed control structure allows for the incorporation of an arbitrary number of sources hence achieving scalability. Next, the energy in the microgrid was separated into exogenous energy and actuator energy. This yielded a description of the system that quantified the condition of stability independent of the decision made by a would-be energy management system. This, in turns, liberates the process of designing an optimized energy management system from stability concerns. The acquired theoretical findings were then translated to a simulation model, where multiple components of the grid were simulated under a typical scenario of operation. Once the simulation phase was concluded, a prototype of the designed grid was constructed to emulate the theoretical results. The prototype exhibited promising performance, matching the simulation predictions to a reasonable degree.

A highly naturalistic facial expression generation method with embedded vein features based on diffusion model

Abstract Facial expression generation technology has achieved notable progress in computer vision and artificial intelligence. However, challenges persist regarding background consistency, expression clarity, and detailed representation. Additionally, the instability of generative adversarial networks (GANs) during training affects both image quality and diversity. While diffusion models have demonstrated potential advantages over GANs, research on controllable expression generation remains limited. To address these challenges, this paper proposes a highly natural facial expression generation method based on denoising diffusion implicit models (DDIM) with embedded vein features. This approach avoids adversarial training by employing gradual diffusion to generate specific expressions, thereby enhancing both the diversity and authenticity of the images. Vein features are introduced and embedded within the generated expression images to protect the intellectual property of algorithm-generated digital resources. Firstly, image and expression text guide words are combined as conditional inputs to improve the authenticity and diversity of the generated images. Secondly, a classification coding network is introduced to guide expression generation, thus enhancing the accuracy and consistency of the produced expressions. Furthermore, this paper proposes a vein feature fusion method based on multi-directional local dynamic feature coding operator (MLDFO) and integrates DDIM with frequency-domain watermarking technology to achieve image intellectual property protection. Experimental results demonstrate the effectiveness of this method across several public datasets, including FFHQ, CelebA, FV-USM, and SDUMLA-HMT. Notably, in the CelebA dataset, the average expression recognition rate increased by 11.41%, with a 100.00% recognition rate for happy expressions. The generated expression images exhibit a high degree of authenticity and consistency, and the video conversion tests reveal a natural and smooth effect. These results confirm that this method not only advances facial expression generation technology but also significantly enhances the steganographic protection of images.

Environmental Enrichment and Health Outcomes Among Low-Grade Glioma Brain Tumor Survivors.

BACKGROUND: Brain tumor survivors who received radiotherapy (RT) are at a disproportionately increased risk of accelerated aging and symptom burden. We aim to examine the association between environmental enrichment (EE) and health outcomes among low-grade glioma survivors who received brain RT. METHODS: The study used a cross-sectional cohort design, enrolling participants approximately 5 years from diagnosis. The construct of EE consisted of social network, physical activity, employment status, and financial stability. Berkman-Syme Social Network Index, International Physical Activity Questionnaire, Vocational Index Scale, and a Socioeconomic Questionnaire were used to measure the construct of EE. Health outcome measures included the Montreal Cognitive Assessment, Symbol Digit Modality Test, clinical brain magnetic resonance images (pre-RT, approximately 2-3 years after RT, and approximately 5 years after RT), Karnofsky Performance Status Scale, and the MD Anderson Symptom Inventory Brain Tumor Module. Ordinal logistic regression estimated the association between levels of EE and health outcomes. RESULTS: Thirty-nine participants completed the study and experienced varying levels of EE. The median age was 44 years old, ranging from 26 to 78 years old. Nineteen individuals were diagnosed with oligodendroglioma, and 18 were diagnosed with astrocytoma. Thirteen participants had low EE, 17 had moderate EE, and 9 had high EE. Although not statistically significant, we observed patterns of increasing health outcomes (Montreal Cognitive Assessment, Symbol Digit Modality Test, and Karnofsky Performance Status Scale) related to increasing levels of EE. CONCLUSION: This study is an initial exploration into the role of EE in health outcomes and survivorship programs for persons with glioma. Future research should assess EE before treatment or at the time of diagnosis and be longitudinal to accurately ascertain the association between EE and health outcomes. Comprehensive neuro-oncology survivorship programs structured to facilitate EE may reduce symptom burden, promote neuroplasticity, and improve cognitive and functional outcomes after brain radiation.

Selective collaboration in distributed FxLMS active noise control systems

This paper addresses the selection of the collaboration configuration on distributed active noise control (ANC) systems. ANC systems aim to cancel out acoustic noise within a listening area. In distributed systems, the control task is delegated among multiple acoustic control nodes that generate the control signals by filtering a noise reference signal. The coefficients of each node filter are iteratively calculated using the filtered-X LMS algorithm. The stability is achieved when the adaptive filters computed in each node converge to finite values. However, acoustic coupling among nodes could lead to instability (i.e., divergence). Collaboration among selected nodes may avoid this phenomenon, although not just any collaboration configuration guarantees network stability. On the other hand, a collaborative distributed system presents two drawbacks: the stability assessment is computationally expensive, and communication requirements increase with the number of collaborations among nodes. In this paper, we propose and discuss several methods to establish a collaboration configuration that ensures system stability. The optimal configuration, which is characterized by the minimal number of necessary collaborations between nodes, can be identified through exhaustive search. However, this approach incurs a high computational cost, particularly in networks with many nodes. To address this challenge, we introduce several heuristic methods aimed at efficiently obtaining stable configurations.

Design and preparation of composite bipolar plates with synergistic conductive networks of graphite and metal foam

Graphite composite bipolar plate (BP) have limited conductivity, which makes them less than ideal for extensive application in proton exchange membrane fuel cell (PEMFC). In traditional graphite composite BP, the construction process of the conductive network is entirely random. To enhance conductivity, it is typically necessary to increase the content of conductive fillers or incorporate high aspect ratio carbon nanomaterials to optimize the density of the conductive network. In this work, we manufactured a highly conductive composite bipolar plate with synergistic conductive networks of graphite and metal foam (MF). With a synergistic conductive network, the ASR of CuG80-20ppi decreased to 7.7 mΩ cm2. Additionally, thermal conductivity increased to 24.76 W/(m·K), and in-plane conductivity reached 294.1 S/cm at 80 wt% mass fractions of conductive filler, using 20 ppi copper foam as the metallic conductive network. CuG80-20ppi exhibited a flexural strength of 52.2 MPa. G80 and CuG80-20ppi have the 80 wt% conductive filler and are molded into BP with parallel flow fields. CuG80-20ppi enhances the current density of PEMFC by 0.132 W/cm2 and reduces the ohmic impedance by 5.25%. Therefore, the findings of this study offer valuable insights for the enhancement of composite BP conductivity, while simultaneously ensuring the stability and continuity of the synergistic conductive network. A novel approach is presented to enhance the electrical conductivity of graphite composite bipolar plate (BP) for proton exchange membrane fuel cells (PEMFCs). By embedding metal foam as a supplementary conductive network within the graphite matrix, a synergistic conductive architecture is achieved. This innovation significantly reduces the area specific resistance (ASR) to 7.7 mΩ cm2 and boosts thermal conductivity to 24.76 W/(m·K). The resulting CuG80-20ppi BP, with 80 wt% conductive filler, exhibits improved mechanical strength and conductivity, contributing to a 0.132 W/cm2 increase in PEMFC current density and a 5.25% reduction in ohmic impedance. This work highlights the potential of metal foam integration to enhance BP conductivity and PEMFC performance.

The structure and function of rhizosphere bacterial communities: impact of chemical vs. bio-organic fertilizers on root disease, quality, and yield of Codonopsis pilosula

IntroductionLong-term use of chemical fertilizers (CFs) can cause soil compaction and acidification. In recent years, bio-organic fertilizers (BOFs) have begun to replace CFs in some vegetables and cash crops, but the application of CFs or BOFs has resulted in crop quality and disease occurrence.MethodsThis study aimed to analyze the microbial mechanism of differences between CFs and BOFs in root disease, quality, and yield of tuber Chinese herbal medicine. We studied the effects of CFs, organic fertilizers, commercial BOFs, biocontrol bacteria BOFs, and biocontrol fungi BOFs on rhizosphere microbial community structure and function, root rot, quality, and yield of Codonopsis pilosula at different periods after application and analyzed the correlation.Results and discussionCompared to CFs, the emergence rate and yield in BOF treatments were increased by 21.12 and 33.65%, respectively, and the ash content, water content, and disease index in the BOF treatments were decreased by 17.87, 8.19, and 76.60%, respectively. The structural equation model showed that CFs promoted the quality and yield of C. pilosula by influencing soil environmental factors, while BOFs directly drove soil bacterial community to reduce disease index and improve the quality and yield of C. pilosula. There was a stronger interaction and stability of soil microbial networks after BOF treatments. Microlunatus, Rubrobacter, Luteitalea, Nakamurella, and Pedomicrobium were identified as effector bacteria, which were related to disease prevention and yield and quality increase of C. pilosula. Microbial functional analysis indicated that the signal transduction and amino acid metabolism of soil bacteria might play a major role in improving the quality and yield of C. pilosula in the early and middle growth stages. In conclusion, compared to CFs, BOFs obtained a lower disease index of root rot and a higher quality and yield of C. pilosula by changing the structure and function of the rhizosphere bacterial community.

Quantitative assessment of congestion diffusion and cascading effect under rainfall-flood disasters: A case study of Nanjing, China

Urban road networks are frequently disrupted by flooding rainfall-flood disasters, which can cause severe traffic disruptions and leading to traffic congestion due to cascading effect. This paper investigates the reliability issues under rainfall-flood conditions. A coupled model, integrating a rainfall-flood model with an improved cascading failure model, is proposed to assess how rainfall intensities and flooding will influence traffic congestion and bring network instability. Utilizing an improved Nonlinear Load-Capacity model, we quantify the impact of congestion and analyze cascading processes under various rainfall-flood conditions. The case study in Nanjing, China reveal that, when congestion causes network pressure to exceed the traffic percolation threshold, traffic congestion diffusion becomes more pronounced, putting excessive strain on other passable roads. Network cascading failures due to traffic congestion diffusion can lead to excessive focus on the remaining passable roads, resulting in a sharp increase in the average importance. The significance of this work lies in its provision of an effective method for predicting potential network disruptions and cascading failures in advance, thereby enhancing post-disaster road operations.

Depth-dependent effects of forest diversification on soil functionality and microbial community characteristics in subtropical forests

Soil microbes are critical to the maintenance of forest ecosystem function and stability. Forest diversification, such as monocultures versus mixed forests stands, can strongly influence microbial community patterns and processes, as well as their role in soil ecosystem multifunctionality, such as in subtropical forest ecosystems. However, less is known about these patterns and processes vary with soil depth. Here, we investigated the results of an eight-year forest diversification field experiment comparing the soil ecosystem multifunctionality, bacterial and fungal community assembly, and network patterns in mixed versus monoculture plantations along vertical profiles (0–80 cm depth) in a subtropical region. We found that the introduction of broadleaf trees in coniferous monocultures led to enhanced synergies between multiple functions, thus improving soil multifunctionality. The effects of mixed plantations on the functional potential in top soils were greater than in deep soils, especially for carbon degradation genes (apu, xylA, cex, and glx). Microbial community assembly in the top layer, particularly in mixed plantations, was dominated by stochastic processes, whereas deterministic were more important in the deep layer. Soil microbial network complexity and stability were higher in the top layer of mixed plantations, but in the deep layer was monoculture. Interestingly, the changes in microbial communities and multifunctionality in the top layer were mainly related to variation in nutrients, whereas those in the deep were more influenced by soil moisture. Overall, we reveal positive effects of mixed forest stands on soil microbial characteristics and functionality compared to that of monocultures. Our findings highlighted the importance of enhancing functional diversity through the promotion of tree species diversity, and managers can better develop forest management strategies to promote soil health under global change scenarios.

Exponential stability of stochastic inertial neural networks with generalised piecewise constant argument

This paper investigates the exponential stability of stochastic inertial neural networks (SINNs) with generalised piecewise constant argument. By applying variable substitution, the second-order system is transformed into a first-order system. Subsequently, several sufficient conditions are introduced to ensure the existence of a unique solution. Due to the presence of generalised piecewise constant argument, calculus theory is applied to estimate the dynamic effects of network states in current time and deviation function. The global mean-square exponential stability of SINNs with generalised piecewise constant argument is established using the Lyapunov function method. Finally, two numerical examples are provided to verify the validity of derived theoretical results.

A clustering coefficient structural entropy of complex networks

The structural entropy is a quantification of the topological structural complexity of the static complex networks, which is defined based on the structural characteristics and the Shannon entropy. For instance, the ’degree structural entropy’ is based on the network’s ’first-order’ topological properties: the degree of each node. The ’betweenness structural entropy’ is based on the betweenness centrality of nodes, which is a global topological structural property of static complex networks. The two different structural entropy give two completely different views of the network’s topological structural complexity. However, a ’mesoscopic’ structural entropy is still missing in the network theory. In this work, a clustering coefficient structural entropy of complex networks is proposed to quantify the structural complexity of static networks on the mesoscopic scale. The effectivity of the proposed ’mesoscopic’ structural entropy is verified in a series of networks that grow from two different seed networks under the Barabási–Albert and Erdős–Rényi rules. We also find that the quantification of structural entropy effectively reflects the impact of structural heterogeneity on the growth rule in the early stages of seed network growth. Finally, we observe that the structural ratio of the clustering coefficient structural entropy and degree structural entropy remains stable and unchanged when network growth reaches maturity. We also note that the convergence rate of the network’s structural entropy ratio varies under different guiding rules. These findings suggest that the differences in structural entropy can serve as a novel tool for measuring the stability of complex networks and provide fresh insights into achieving a ’balanced’ state in the dynamic evolution of complex networks.

Six Pulse Type Segmented Thyristor Controlled Reactor with Fixed Capacitor for Reactive Power Compensation

This article presents a Six Pulse Type Segmented Thyristor Controlled Reactor (TCR) integrated with a Fixed Capacitor (FC) for reactive power compensation. The primary objective is to improve voltage stability and power factor in electrical networks, addressing issues related to reactive power imbalance and harmonic distortion. The proposed configuration combines the advantages of segmented TCR and FC, providing a flexible and efficient approach to reactive power management. The novelty of this work lies in the segmentation of the TCR, which enhances the dynamic control of reactive power by allowing more precise regulation and reduced harmonics compared to conventional TCR systems. This segmented approach also minimizes switching losses and thermal stress on thyristors, leading to enhanced reliability and longevity of the system. Additionally, the integration of a fixed capacitor optimizes the overall power factor correction, contributing to improved system efficiency. Key findings from simulation and experimental results demonstrate that the Six Pulse Type Segmented TCR with FC significantly reduces reactive power, stabilizes voltage levels, and effectively suppresses harmonics within permissible limits, adhering to IEEE standards. The system shows a marked improvement in power quality, making it a viable solution for industrial applications where reactive power control is critical. This innovative approach not only provides superior compensation characteristics but also offers a scalable and adaptable framework for modern power systems, highlighting its potential to enhance operational performance and energy efficiency in various electrical grids.

Microbial Inoculants Drive Changes in Soil and Plant Microbiomes and Improve Plant Functions in Abandoned Mine Restoration.

The application of microbial inoculants holds promise for the sustainable restoration of abandoned mine sites by affecting soil nutrients and microbial communities. However, the responses of plant microbial communities to microbial inoculants in mine restoration remain largely unknown. To bridge this knowledge gap, we conducted a 4-year field experiment at an abandoned carbonate mine site to assess the impacts of microbial inoculants on the soil-plant microbiome. Our findings revealed that microbial inoculants significantly changed roots, fine root bacterial and fungal communities. Further, no significant correlations were observed between the soil-plant nutrient content (Z-score) and microbial alpha diversity. However, a significantly positive correlation was found between the relative abundance of the keystone ecological cluster (Module #1) and soil-plant nutrient content. The application of microbial inoculants also increased complexity, albeit decreased stability of plant microbiome networks, alongside a reduction in stochastic assembly. Conversely, they decreased the complexity but increased the stability of soil microbiome networks, accompanied by an increase in stochastic assembly. Notably, the number of specifically enriched microbiome functional traits of roots and root nodules under the microbial inoculant treatments surpassed that of the control. In summary, our findings underscored the potential of microbial inoculants to enhance soil-plant functionality at abandoned mine restoration sites.

Identification and Counting of Pirapitinga Piaractus brachypomus Fingerlings Fish Using Machine Learning.

Identifying and counting fish are crucial for managing stocking, harvesting, and marketing of farmed fish. Researchers have used convolutional networks for these tasks and explored various approaches to enhance network learning. Batch normalization is one technique that improves network stability and accuracy. This study aimed to evaluate machine learning for identifying and counting pirapitinga Piaractus brachypomus fry with different batch sizes. The researchers used one thousand photographic images of Pirapitinga fingerlings, labeled with bounding boxes. They trained the adapted convolutional network model with batch normalization layers added at the end of each convolution block. They set the training to one hundred and fifty epochs and tested batch sizes of 5, 10, and 20. Furthermore, they measured network performance using precision, recall, and mAP@0.5. Models with smaller batch sizes performed less effectively. The training with a batch size of 20 achieved the best performance, with a precision of 96.74%, recall of 95.48%, mAP@0.5 of 97.08%, and accuracy of 98%. This indicates that larger batch sizes improve accuracy in detecting and counting pirapitinga fry across different fish densities.

Increasing tree phylogenetic diversity stimulates microbial functional potential in a subtropical forest

Abstract Soil microbial functions are closely related to ecosystem productivity, carbon sequestration and their responses to global change. Tree phylogenetic diversity has been found to impact microbial community composition, diversity, and functions, but how it modulates the linkage between microbial community facets and functions remains unclear. Here, 45 plots covering a natural gradient of tree phylogenetic diversity (TPD) were selected in a subtropical forest of southwest China to explore how increasing TPD impacts soil microbial community facets and microbial functional potential. The microbial functional potential was evaluated based on the abundances of carbon, nitrogen, and phosphorus cycling-related functional genes. Soil fungal alpha diversity increased significantly, but bacterial alpha diversity did not change as TPD increased. Both soil microbial network complexity and stability improved significantly with increasing TPD. Ultimately, increasing TPD promoted soil microbial functional potential by stimulating soil carbon and nitrogen availability, microbial keystone diversity, and network stability collectively. These findings emphasize the critical roles of keystone taxa and network stability as microbial factors in stimulating soil microbial function in response to increasing TPD. Therefore, it is strongly recommended to increase TPD in order to stimulate soil microbial functions and other ecosystem functions when implementing afforestation or ecological restoration projects.

Enhancing Adversarial Robustness through Stable Adversarial Training

Deep neural network models are vulnerable to attacks from adversarial methods, such as gradient attacks. Evening small perturbations can cause significant differences in their predictions. Adversarial training (AT) aims to improve the model’s adversarial robustness against gradient attacks by generating adversarial samples and optimizing the adversarial training objective function of the model. Existing methods mainly focus on improving robust accuracy, balancing natural and robust accuracy and suppressing robust overfitting. They rarely consider the AT problem from the characteristics of deep neural networks themselves, such as the stability properties under certain conditions. From a mathematical perspective, deep neural networks with stable training processes may have a better ability to suppress overfitting, as their training process is smoother and avoids sudden drops in performance. We provide a proof of the existence of Ulam stability for deep neural networks. Ulam stability not only determines the existence of the solution for an operator inequality, but it also provides an error bound between the exact and approximate solutions. The feature subspace of a deep neural network with Ulam stability can be accurately characterized and constrained by a function with special properties and a controlled error boundary constant. This restricted feature subspace leads to a more stable training process. Based on these properties, we propose an adversarial training framework called Ulam stability adversarial training (US-AT). This framework can incorporate different Ulam stability conditions and benchmark AT models, optimize the construction of the optimal feature subspace, and consistently improve the model’s robustness and training stability. US-AT is simple and easy to use, and it can be easily integrated with existing multi-class AT models, such as GradAlign and TRADES. Experimental results show that US-AT methods can consistently improve the robust accuracy and training stability of benchmark models.

Mittag-Leffler Stability and Synchronization of Multi-delayed Fractional Neural Networks via Halanay Inequality

Mittag-Leffler Stability and Synchronization of Multi-delayed Fractional Neural Networks via Halanay Inequality

Coordination of smart inverter-enabled distributed energy resources for optimal PV-BESS integration and voltage stability in modern power distribution networks: A systematic review and bibliometric analysis

Integrating photovoltaic (PV) and battery energy storage systems (BESS) in modern power distribution networks presents opportunities and challenges, particularly in maintaining voltage stability and optimizing energy resources. This systematic review and bibliometric analysis investigates the coordination of smart inverter-enabled distributed energy resources (DERs) for enhancing PV-BESS integration and ensuring voltage stability. The study synthesizes recent advancements in smart inverter technologies, which provide grid support functions such as Volt/VAr control, and their applications in DER coordination. A comprehensive review of the literature is conducted to identify prevailing trends, research gaps, and emerging techniques in the field. Bibliometric analysis is employed to quantify the research landscape, highlighting key publications, citations, publications per country, and collaborative networks. The findings reveal that smart inverters play a crucial role in mitigating voltage violations and improving the hosting capacity of PV systems in distribution networks. Furthermore, optimal inverter settings, strategic placement of PV-BESS, and advanced control algorithms are identified as critical factors for effective DER integration. The study concludes by proposing future research directions, including the exploration of smart inverter interactions with legacy grid management systems and the development of robust algorithms for dynamic and adaptive DER coordination. This review serves as a valuable resource for researchers and practitioners aiming to enhance the stability and efficiency of power distribution networks through advanced DER management strategies.