Network Structure Research Articles

Predicting the thickness loss and recovery of acrylic carpet pile imposed to UV exposure using artificial intelligence

One of the metrics that establishes the carpet quality is its compress and decompress behaviors. In a research, addressed later in the paper, carpet samples with the acrylic pile were exposed to the ultraviolet (UV) exposure for 0, 8, 12, 16, and 20 h. The wear test was then carried out using drum revolutions of 0, 4000, 6000, and 8000. Following that, the samples were subjected to a static stress of 700 KPa for 2 h. After removing the load, the sample thickness was measured every 2 min. Finally, the thickness loss and recovery features were determined. Now in this study, the statistical analysis demonstrated the significance of recovery time, UV exposure, and drum revolutions on the features mentioned above, and in the next step, they were modeled using an artificial neural network (ANN) structure. The genetic algorithm, particle swarm optimization, and gray wolf optimization (GWO) were applied as the alternatives to the backpropagation (BP) algorithm for updating the weights and biases of ANN. In the end, it was found that the thickness loss and recovery could be predicted with 6.92 and 9.14% errors, using ANN-GWO and ANN-BP-GWO, respectively.

Pattern formation in reaction-diffusion information propagation model on multiplex simplicial complexes

Turing patterns for explaining spatial distribution in nature mostly focus on continuous media and existing networks, but only few attempts exist to study them on systems with high-order interactions. Considering that high-order interactions have a particularly significant impact on rumor propagation, this study establishes a generalized reaction-diffusion rumor propagation model based on a multiplex network, where simplicial complexes are employed to describe high-order structures. It aims to provide the spatial distribution patterns of the population participating in rumor propagation and identify the structural factors that affect such patterns. We theoretically provide the necessary conditions for Turing instability in single-layer and multiplex networks by considering high-order interactions. In the numerical simulation, we demonstrate that the Turing pattern could be controlled by adjusting the diffusion coefficient, high-order structure intensity, and average degree of the network. The results indicate that: (i) in a single-layer network, the Turing pattern only exists when high-order interactions appear, and the difference in diffusion rate plays a decisive role, (ii) in a multiplex network, the Turing pattern can still be observed under the same diffusion rates, which are affected by the difference in higher-order intensity between the two layers, and (iii) in existing networks, the average degree of the network has an important impact on Turing pattern. These findings contribute toward comprehending the impact of network structure on pattern formation, particularly the high-order interactions on the Turing pattern.

Dynamics of personal financial management: a bibliometric and systematic review on financial literacy, financial capability and financial behavior

PurposeFinancial literacy, capability and behavior are crucial factors in personal financial management, which in turn plays a significant role in individual and societal financial well-being. The objective of this investigation is to explain critical factors and dimensions of personal financial management systems by employing a hybrid approach that encompasses a bibliometric analysis and a systematic review of the literature.Design/methodology/approachThe research team carefully evaluated a selection of 606 scholarly articles from the Scopus database and studied the evolution of personal financial management behavior over 38 years (1986–2023). This research adopted several graphical representations and network structures to comprehend publishing tendencies, high-impact papers, theoretical frameworks, intellectual constructs as well as the current state of research collaboration.FindingsFour major clusters were identified in the field of personal financial management behavior: the relationship between financial literacy and financial capability, factors influencing financial behavior, the impact of financial behavior on financial well-being and the financial behavior of different demographic groups. In addition, by performing content analysis on papers published within the last five years, new themes in personal financial management behavior were identified.Practical implicationsThis investigation serves to equip financial advisors, policy architects and scholarly investigators with a deeper insight into the intricacies of personal financial management behavior and aids in pinpointing prospective domains for forthcoming research.Originality/valueThis study seeks to address a significant vacuum in the current body of research by providing a thorough bibliometric analysis that specifically examines financial literacy, ability and conduct. To the best of our knowledge, no previous research has conducted such a comprehensive investigation in this field. This research aims to identify important researchers and influential works in the subject by using a mixed-methods approach that combines qualitative and quantitative methodologies, including content analysis. The purpose of doing this is to provide exclusive insights and expertise that can be highly valuable to scholars, practitioners, policymakers and other stakeholders who are interested in furthering the comprehension and encouragement of financial literacy and responsible financial behavior.

Measurement Dependence can Affect Security in a Quantum Network

AbstractNetwork Nonlocality is an advanced study of quantum nonlocality that comprises network structure beyond Bell's theorem. The development of quantum networks has the potential to bring a lot of technological applications in several quantum information processing tasks. Here, the focus is on how the role of the independence of the measurement choices by the end parties in a network works and can be used to affect the security in a quantum network. In both three‐parties two‐sources bilocal network and four‐parties three‐sources star network scenarios, this study is able to show, a practical way to understand the relaxation of the assumptions to enhance a real security protocol if someone wants to breach in a network communication. Theoretically, it have been proved that by relaxing the independence of the measurement choices of only one end party, a Standard Network Nonlocality (SNN) and more stronger Full Network Nonlocality (FNN) can be created and the maximum quantum violation by the classical no‐signalling local model can be obtained. The distinguish between two types of network nonlocality, SNN and FNN, can also be made. It has been shown that FNN is a stronger correlation than SNN in the sense that the former comes in a scenario where all the sources must be nonlocal in nature.

Unidimensional community detection: A monte carlo simulation, grid search, and comparison.

Unidimensionality is fundamental to psychometrics. Despite the recent focus on dimensionality assessment in network psychometrics, unidimensionality assessment remains a challenge. Community detection algorithms are the most common approach to estimate dimensionality in networks. Many community detection algorithms maximize an objective criterion called modularity. A limitation of modularity is that it penalizes unidimensional structures in networks, favoring two or more communities (dimensions). In this study, this penalization is discussed and a solution is offered. Then, a Monte Carlo simulation using one- and two-factor models is performed. Key to the simulation was the condition of model error or the misfit of the population factor model to the generated data. Based on previous simulation studies, several community detection algorithms that have performed well with unidimensional structures (Leading Eigenvalue, Leiden, Louvain, and Walktrap) were compared. A grid search was performed on the tunable parameters of these algorithms to determine the optimal trade-off between unidimensional and bidimensional recovery. The best-performing parameters for each algorithm were then compared against each other as well as maximum likelihood factor analysis and parallel analysis (PA) with mean and 95th percentile eigenvalues. Overall, the Leiden and Louvain algorithms and PA methods were the most accurate methods to recover unidimensional and bidimensional structures and were the most robust to model error. More nuanced method recommendations for specific unidimensional and bidimensional conditions are provided. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Molecular clouds as hubs in spiral galaxies : gas inflow and evolutionary sequence

Abstract We decomposed the molecular gas in the spiral galaxy NGC 628 (M74) into multi-scale hub-filament structures using the CO (2−1) line by the dendrogram algorithm. All leaf structures as potential hubs were classified into three categories, i.e. leaf-HFs-A, leaf-HFs-B and leaf-HFs-C. leaf-HFs-A exhibit the best hub-filament morphology, which also have the highest density contrast, the largest mass and the lowest virial ratio. We employed the FILFINDER algorithm to identify and characterize filaments within 185 leaf-HFs-A structures, and fitted the velocity gradients around the intensity peaks. Measurements of velocity gradients provide evidence for gas inflow within these structures, which can serve as a kinematic evidence that these structures are hub-filament structures. The numbers of the associated 21 μm and Hα structures and the peak intensities of 7.7 μm, 21 μm and Hα emissions decrease from leaf-HFs-A to leaf-HFs-C. The spatial separations between the intensity peaks of CO and 21 μm structures of leaf-HFs-A are larger than those of leaf-HFs-C. These evidence indicate that leaf-HFs-A are more evolved than leaf-HFs-C. There may be an evolutionary sequence from leaf-HFs-C to leaf-HFs-A. Currently, leaf-HFs-C lack a distinct gravitational collapse process that would result in a significant density contrast. The density contrast can effectively measure the extent of the gravitational collapse and the depth of the gravitational potential of the structure which, in turn, shapes the hub-filament morphology. Combined with the kinematic analysis presented in previous studies, a picture emerges that molecular gas in spiral galaxies is organized into network structures through the gravitational coupling of multi-scale hub-filament structures. Molecular clouds, acting as knots within these networks, serve as hubs, which are local gravitational centers and the main sites of star formation.

Morphology and properties of carbon black‐filled thermoplastic vulcanizate (TPV) composites based on hydrogenated acrylonitrile butadiene rubber and thermoplastic polyester elastomer

AbstractThe unique morphology of thermoplastic vulcanizates (TPVs) reveals a significant correlation between the microstructure and performance, and the development of high‐performance TPV composites for specialized applications has become a current research priority. This study is devoted to developing heat‐ and oil‐resistant TPV composites filled with carbon black (CB) based on hydrogenated acrylonitrile butadiene rubber (HNBR) and thermoplastic polyester elastomer (TPEE) following the masterbatch procedure of dynamic vulcanization. Herein, it focuses on the effects of CB content on the morphology, filler network structure, and properties of the TPV/CB composites. As observed by morphological studies, CB nanoparticles are interconnected and aggregated to form a dual network structure of rubber and CB particles in the composite. With the increasing CB content, it's demonstrated that dual networks have enhanced and shifted to rigid. Consequently, the hardness, thermal stability, and oil resistance of TPV/CB composites are improved, with a 104% elevation in the stress at 300% strain. The flowability in the molten state, toughness (the elongation at break decreased from 690% to 310%), and elasticity deteriorated by oversized (0.5 ~ 1.2 μm) CB agglomerates and rigid rubber particles. This study gives new insight into the microstructure‐properties relationship of TPVs, offering theoretical guidance for fabricating HNBR‐based TPV composites.

Local and regional processes drive distance decay in structure in a spatial multilayer plant-pollinator network.

Understanding spatial variation in species distribution and community structure is at the core of community ecology. Nevertheless, the effect of distance on metacommunity structure remains little studied. We examine how plant-pollinator community structure changes across geographical distances at a regional scale and disentangle its underlying local and regional processes. We use a multilayer network to represent linked plant-pollinator communities as a metacommunity in the Canary Islands. We used modularity (i.e. the extent to which the community is partitioned into groups of densely interacting species) to quantify distance decay in structure across space. In multilayer modularity, the same species can belong to different modules in different communities, and modules can span communities. This enabled quantifying how similarity in module composition varied with distance between islands. We developed three null models, each controlling for a separate component of the multilayer network, to disentangle the role of species turnover, interaction rewiring and local factors in driving distance decay in structure. We found a pattern of distance decay in structure, indicating that islands tended to share fewer modules with increasing distance. Species turnover (but not interaction rewiring) was the primary regional process triggering distance decay in structure. Local interaction structure also played an essential role in determining the structure similarity of communities at a regional scale. Therefore, local factors that determine species interactions occurring at a local scale drive distance decay in structure at a regional scale. Our work highlights the interplay between local and regional processes underlying community structure. The methodology, and specifically the null models, we developed provides a general framework for linking communities in space and testing different hypotheses regarding the factors generating spatial structure.

Multi-objective topology optimization of macro structure and microtubule network structure for self-healing material

Abstract Self-healing materials possess the capability to promptly repair minor damages occurring during service, thereby effectively preventing safety accidents. This paper investigates a multi-objective topology optimization method for the macro structure and microtubule network of self-healing materials around pure epoxy resin materials, aiming to enhance the damage healing capability of the microtubule network while meeting the mechanical performance requirements of the macro structure. By introducing the design variables of macro structure and microtubule network, the corresponding topological description functions are established respectively. And study applies logical operations and post-processing techniques to generate an embedded microtubule network structure description. The objective functions include the flexibility of the macro structure, the along-travel head loss, and the total length of the microtubule network, with material volume serving as a constraint. In order to determine the head loss of the three-dimensional microtubule network structure, a Hardy-Cross method based on flow initialization and loop search is proposed. Multi-objective topology optimization is designed based on moving morphable components algorithm, enumeration method and Pareto principle. Develop iterative termination conditions by assessing the disparity between Pareto solution sets in each generation, thereby ensuring algorithm convergence. The numerical example of the Messerschmitt–Bölkow–Blohm (MBB) beamyields a flexibility of 0.059 without a carrier and 0.0728 with a carrier the macrostructural flexibility without a carrier is 81.0% compared to with a carrier, and the macrostructural profiles and the overall flexibility of the MBB beams with/without a carrier are close to each other. This method serves as a reference for optimizing large-scale self-healing structures.

Improved YOLOv8 garment sewing defect detection method based on attention mechanism

For the garment sewing defect detection method, this paper proposes an improved YOLOv8-FPCA scheme based on the YOLOv8 algorithm, which improves the YOLOv8 target detection head to enhance the information extraction of small target defects, then introduces Focal Loss to optimize the loss function to guide the network to better handle target data sets with different difficulties and imbalances. Finally, the attention mechanism CA is added to the YOLOv8 network structure to achieve multi-scale feature fusion extraction, and the attention mechanisms CABM and SENet are added at the same locations for experimental comparison. The results show that after increasing the attention mechanisms of CBAM and SENet, the mAP@0.5 model increased by 1.7 % and 1.9 % respectively. The CA attention mechanism emphasizes the importance of location information, and the model has better accuracy and recall after adding the CA attention mechanism, with a 3.7 % increase in mAP@0.5, indicating that YOLOv8-CA has better performance in sewing defect detection.

Inverse Problem of Permeability Field under Multi-Well Conditions Using TgCNN-Based Surrogate Model

Under the condition of multiple wells, the inverse problem of two-phase flow typically requires hundreds of forward runs of the simulator to achieve meaningful coverage, leading to a substantial computational workload in reservoir numerical simulations. To tackle this challenge, we propose an innovative approach leveraging a surrogate model named TgCNN (Theory-guided Convolutional Neural Network). This method integrates deep learning with computational fluid dynamics simulations to predict the behavior of two-phase flow. The model is not solely data-driven but also incorporates scientific theory. It comprises a coupled permeability module, a pressure module, and a water saturation module. The accuracy of the surrogate model was comprehensively tested from multiple perspectives in this study. Subsequently, efforts were made to address the permeability-field inverse problem under multi-well conditions by combining the surrogate model with the Ensemble Random Maximum Likelihood (EnRML) algorithm. The research findings indicate that modifying the network structure allows for improved integration of the outputs, resulting in prediction accuracy and computational efficiency. The TgCNN surrogate model demonstrated outstanding predictive performance and computational efficiency in two-phase flow. By combining the surrogate model with the EnRML algorithm, the inversion results closely aligned with those from the commercial simulation software, significantly improving the computational efficiency.

Ethanediamine Intercalation Induced Hydrogen Bond Network in Vanadium Oxide for Ultralong‐Life Aqueous Ammonium Ion Batteries

AbstractAqueous ammonium‐ion batteries (AAIBs) have received tremendous attention as a potential energy technology, but their development is severely challenged by the fact that the as‐reported electrode materials are usually unable to meet the requirements of high capacity and high stability simultaneously. Herein, an organic‐inorganic hybrid material of ethanediamine (EDA) intercalated vanadium oxide (VO‐EDA) is synthesized as a high‐performance anode material for AAIBs. The intercalated EDA molecules not only act as an electron donor to bind with NH4+, but also form hydrogen bonding network structures with vanadium oxides to facilitate charge/ion transfer. As a result, this hybrid material provides a high specific capacity of 104.4 mAh g−1 at 0.5 A g−1 and good cycling stability after 5000 cycles 10 A g−1 with a coulombic efficiency of ~100 %. Moreover, the ammonium‐ion full cell based on VO‐EDA anode and NiHCF cathode achieves a specific capacity of 55 mAh g−1 at 0.1 A g−1 and impressive cycling stability with 88.6 % capacity retention after 10000 cycles at 5 A g−1.

Controllable In situ Polymerization of 1,3‐Dioxolane via Sustained‐Release Effect for Solid‐State Lithium Metal Batteries

AbstractIn situ formed poly(1,3‐dioxolane) (PDOL) electrolytes are of great interest due to the facile process and the improved interface contact. However, the practical application of in situ PDOL electrolytes is still plagued by fast solidification time (liquid state) and poor high‐voltage stability (solid state). Herein, the slow‐release carriers triglycidyl isocyanurate (TGIC), which play dual roles as initiator sustained‐release and network confinement, can tune DOL curing time and cathode/electrolyte interface chemistry is demonstrated. Specifically, the electronegative C≐O and epoxy groups in TGIC have an affinity with BF3, the decomposition product of lithium bis(oxalate)borate (LiDFOB), delaying BF3 protonation reaction and thus extending DOL solidification time. In addition, the epoxy groups in TGIC serve as crosslinking sites to form in situ crosslinked polymer electrolytes (TPDOL@FEC). The corresponding network structure suppresses the contact reaction between high‐fluidity organic components and cathodes, generating a uniform and thin cathode electrolyte interface layer. As a result, the TPDOL@FEC precursor solution can remain its liquid state even after resting 24 h at room temperature. The assembled LiNi0.6Co0.2Mn0.2O2||TPDOL@FEC||Li cells display an impressive capacity retention of 91.5% after 100 cycles at 4.4 V (0.5 C). This study is expected to be a leap in the pursuit of practically feasible in situ formed PDOL electrolytes.

AVA-YOLO: Image-based Multiscale Feature Fusion Enhanced Perception Model for Snow Avalanche Detection

Abstract The global climate change has led to frequent occurrences of snow avalanche disasters. However, the significant variations in scale and shape during the avalanche process, and complex background imagery pose significant challenges to automated detection efforts. There is an urgent need to combine advanced deep learning technology to research automatic detection and recognition of avalanches in the field. In this paper, a novel deep learning model based on YOLOv8 improved multi-scale detection called AVA-YOLO is proposed to solve this problem. In AVA-YOLO, a key component, AKA (AKConv Combined Attention)module was designed and developed. This module combines the deformable convolutional properties of AKconvwith the state-of-the-art self-attention module EMA(Exponential Moving Average), aiming to better perceive the feature map information of different shaped avalanches and to enhance the global relevance, thus improving the utilization of the information. Secondly, a new multi-scale sensing network structure was designed by increasing the number of detection heads to four and introducing the AKA module into the key positions of the network, while the association between model layers was newly designed to enhance the fusion of shallow and deep information to improve the detection accuracy. Experimental results demonstrated the effectiveness of AVA-YOLO, achieving 95.7% mAP50 and 75.6% mAP50:95 detection accuracies, as well as an F1 score of 0.92. Finally, a number of experiments were conducted to demonstrate the superior performance of the proposed model in comparison to other versions of YOLO, which will further exploit the potential of webcams as an underutilized technical capability in snow avalanche intelligence and portable monitoring.

Effects of different oxidation methods on the functional properties and gel characteristics of hazelnut proteins

SummaryThis study aimed to investigate the effects of different oxidation modes on the functional and gel properties of hazelnut proteins. The solubility of hazelnut protein showed a small trend when the oxidation level was low, and it decreased significantly with the increase in concentration. The maximum value of water‐holding capacity (WHC), emulsifying activity index (EAI), and emulsion stability index (ESI) was 343.33%, 56.00 m2 g−1, and 75.85 min at AAPH concentration of 1.0 mmol L−1, respectively. The functional properties of hazelnut proteins, except oil‐holding capacity (OHC), gradually reduced with the increase in malondialdehyde (MDA) concentration. H2O2 modified improved OHC, foaming capacity, foam stability, and EAI of hazelnut proteins, whereas WHC and ESI gradually decreased. The results of the secondary structure of hazelnut protein gels indicated a high ratio of α‐helix and β‐fold of the gels. Also, the increase in oxidation led to an increase in the gels' voids. Also, oxidation led to a rough and loose network structure of hazelnut protein gels. These results suggested that peroxyl radical, hydroxyl radical, and MDA produced during lipid peroxidation affected the interfacial properties of hazelnut protein and disrupted the formation of hazelnut protein gel, thus affecting the quality of hazelnut protein.

Fast Responsive and Highly Sensitive Ethanol Gas Sensors Designed by Agar‐Laponite Hybrid Hydrogels

AbstractLaponite, a synthetic nanosilicate clay and agar, a natural polysaccharide, both imbibe large amount of water and form into hydrogels. Various physical and chemical stimuli elicit the hydrogel response, which has been applied in designing diverse sensors and biomedical systems. In this work, we exploit the change in hydrogel's ionic conductivity due to volatile organic compounds (VOCs) (e. g. ethanol) interaction with the surfaces of Laponite‐Agar hybrid hydrogel films. Gas sensing studies are carried out on silicon (Si) and flexible polyethylene terephthalate (PET) substrates by monitoring the resistance changes. Pristine Laponite hydrogel has shown increase in resistance as it interacted with the ethanol, whereas pure agar and Laponite‐Agar have shown decrease in resistance. Moreover, Laponite‐Agar gel films have exhibited high sensitivity, fast response (4 s) and recovery time (15 s) with lowest detection limit of 6 ppm. Selectivity test carried shows high ethanol sensing response and exhibited very good reproducibility. Observed responses and sensing mechanism are discussed based on changes in ionic conduction resulted due to interacting ethanol with the gel surface network structure. Present study paves the way for understanding and designing low cost, soft and flexible hydrogel gas sensors.

Construction of foam-templated Antarctic krill oil oleogel based on pea protein fibril and ι-carrageenan

Edible plant-based oleogels with zero trans-fat are promising solid fat substitutes. In this study, Antarctic krill oil (AKO) oleogels prepared from pea protein fibril (PPF) and ι-carrageenan (CG) by foam-templated method were developed for the first time. The modulation of the ratio of PPF and CG concentration on the structure and properties of foam, cryogel and oleogel was investigated and the potential formation mechanism of the foam-templated oleogel was explained. The results demonstrated that the addition of CG significantly decreased the foam size and enhanced the foam stability. The oil absorption and oil holding ability of the dense and reticular porous structure of the cryogel was demonstrated. Fourier infrared spectroscopy confirmed the interaction between PPF and CG involved in the formation of cryogels. With the addition of CG, the network structure and mechanical strength of the cryogel were reinforced, leading to more compact pores and higher capillary suction, which was appropriate for the establishment of good viscoelastic semi-solid oleogels. In addition, the oleogel was effective in masking the fishy odor of AKO. The significance of this study lies in its provision of a novel approach to the preparation of the foam-templated oleogel with PPF and CG as the oleogelators.

Exploring the network structure of coupled green-grey infrastructure to enhance urban pluvial flood resilience: A scenario-based approach focusing on ‘centralized’ and ‘decentralized’ structures

Urban pluvial floods pose a significant risk to cities, occurring when precipitation exceeds the carrying capacity of the urban drainage network. Coupled green-grey infrastructure has emerged as a sustainable solution for mitigating urban pluvial floods. This study aims to explore best practices in the network configuration of urban drainage systems coupled with low-impact development (LID) to enhance flow distribution and stormwater infiltration. To do so, we focused on two competing key concepts in network analysis: (1) Centralization and (2) Decentralization. We integrated a one-dimensional stormwater model with a rapid flood spreading model to assess the flood mitigation performance of various centralized and decentralized network configurations in the Gangnam region of Seoul, South Korea. To further assess the combined effects of green and grey infrastructure, we compared the performance of each drainage network configuration with and without identical mixed LID practices. Here we show that the centralized drainage network scenario performed best in reducing flood volume by 40.3%, the decentralized drainage network scenario performed best in shortening flood duration by 47.8%, and the LID practices scenario performed best in mitigating peak flooding rates by 4.2%, each as independent scenarios. When all three scenarios were coupled together, flood volume could be reduced by 73.5%, flood duration by 54.7%, and peak flooding rates by 19.8% in the study area. This exploratory study underscores the potential of network analysis in urban flood research, particularly the effectiveness of loosely-connected network topology. Our findings contribute to the development of best practices for coupled green-grey infrastructure, facilitating sustainable stormwater management and urban flood resilience.

How do partner selection strategies affect the amount of funding in collaborative research projects? Evidence using the dual-projection approach

The selection of partners plays a crucial role in determining the success of collaborative projects. This study makes a valuable contribution to the existing literature on collaborative research and development by examining the impact of different partner selection strategies on the funding received in collaborative research projects. Previous studies have not shown sufficiently how collaborating with new partners as opposed to existing ones influences the amount of funding received. To bridge this gap, we use the innovative dual-projection approach from Social Network Analysis. Specifically, we analyze the network structure of projects funded by Horizon 2020, the eighth European Framework Programme. Our findings show that compared to collaborating with established partners, collaborating with new ones increases the likelihood of securing more funding when entering a new project. Moreover, projects coordinated by private or public organizations rather than research centers and higher education institutions have a higher probability of obtaining greater funding. However, the significance of partner connections diminishes with decreasing proximity to the focal organization. Ultimately, our results offer valuable insights into the effectiveness of the European Research and Technological Development Policy in fostering excellent science through cross-collaboration among a diverse group of actors.

Enhancing robustness of community structure in networks against attacks with gray information

In recent years, network science has received significant attention and application. As an important mesoscale structure of networks, community structure reveals the inherent modular structure and potential functionality of networks. Therefore, maintaining the community structure during attacks is crucial. Existing studies on community robustness primarily focus on two attack behaviors: malicious attacks and random failures. However, little is known on the community robustness in the more practical situations where the attackers have limited ability to access precise network information, leading to gray information attack behaviors. Hence, in this paper, we investigate the robustness of network communities under gray information attacks and the enhancing algorithms. Following the community robustness measure for the sequential attacks, we establish a unified evaluation framework for attacks with gray information by introducing a gray attack coefficient, which treats the usual random failures and malicious attacks as the two special situations in the proposed framework. Several enhancing algorithms with local search strategy are exquisitely devised. The efficacy of our framework and algorithms which significantly improve the community robustness against gray attacks is demonstrated by the experimental results on a variety of real-world networks. Our findings have important implications not only in enhancing the community robustness of existing networks but also in designing robust ones from the scratch, which paves the way to further understand and seek strategies and solutions for network community robustness with gray information.