Facile synthesis of hierarchical NaX zeolite from natural kaolinite for efficient Knoevenagel condensation

Zeolite catalysts have found extensive applications in the synthesis of various fine chemicals.However,the micropores of zeolites impose diffusion limitations on bulky molecules,greatly reducing the catalytic efficiency.Herein,we explore an economic and environmentally friendly method for synthesizing hierarchical NaX zeolite that exhibits improved catalytic performance in the Knoevenagel condensation reaction for producing the useful fine chemical 2-cyano-3-phenylacrylate.The synthesis was achieved via a low-temperature activation of kaolinite and subsequent in-situ transformation strategy without any template or seed.Systematic characterizations reveal that the synthesized NaX zeolite has both intercrystalline and intra-crystalline mesopores,smaller crystal size,and larger external specific surface area compared to commercial NaX zeolite.Detailed mechanism investigations show that the inter-crystalline mesopores are generated by stacking smaller crystals formed from in-situ crystallization of the depolymerized kaolinite,and the intra-crystalline mesopores are inherited from the pores in the depolymerized kaolinite.This synthesis strategy provides an energy-saving and effective way to construct hierarchical zeolites,which may gain wide applications in fine chemical manufacturing.

Kinetic-Thermodynamic Promotion Engineering toward High-Density Hierarchical and Zn-Doping Activity-Enhancing ZnNiO@CF for High-Capacity Desalination

Despite the promising potential of transition metal oxides(TMOs)as capacitive deionization(CDI)electrodes,the actual capacity of TMOs electrodes for sodium storage is significantly lower than the theoretical capacity,posing a major obstacle.Herein,we prepared the kinetically favorable Zn_(x)Ni_(1−x)O electrode in situ growth on carbon felt(Zn_(x)Ni_(1−x)O@CF)through constraining the rate of OH^(−)generation in the hydrothermal method.Zn_(x)Ni_(1−x)O@CF exhibited a high-density hierarchical nanosheet structure with three-dimensional open pores,benefitting the ion transport/electron transfer.And tuning the moderate amount of redox-inert Zn-doping can enhance surface electroactive sites,actual activity of redox-active Ni species,and lower adsorption energy,promoting the adsorption kinetic and thermodynamic of the Zn_(0.2)Ni_(0.8)O@CF.Benefitting from the kinetic-thermodynamic facilitation mechanism,Zn_(0.2)Ni_(0.8)O@CF achieved ultrahigh desalination capacity(128.9 mgNaCl g^(-1)),ultra-low energy consumption(0.164 kW h kgNaCl^(-1)),high salt removal rate(1.21 mgNaCl g^(-1) min^(-1)),and good cyclability.The thermodynamic facilitation and Na^(+)intercalation mechanism of Zn_(0.2)Ni_(0.8)O@CF are identified by the density functional theory calculations and electrochemical quartz crystal microbalance with dissipation monitoring,respectively.This research provides new insights into controlling electrochemically favorable morphology and demonstrates that Zn-doping,which is redox-inert,is essential for enhancing the electrochemical performance of CDI electrodes.

Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

The Immense Impact of Reverse Edges on Large Hierarchical Networks

Hierarchical networks are frequently encountered in animal groups,gene networks,and artificial engineering systems such as multiple robots,unmanned vehicle systems,smart grids,wind farm networks,and so forth.The structure of a large directed hierarchical network is often strongly influenced by reverse edges from lower-to higher-level nodes,such as lagging birds’howl in a flock or the opinions of lowerlevel individuals feeding back to higher-level ones in a social group.This study reveals that,for most large-scale real hierarchical networks,the majority of the reverse edges do not affect the synchronization process of the entire network;the synchronization process is influenced only by a small part of these reverse edges along specific paths.More surprisingly,a single effective reverse edge can slow down the synchronization of a huge hierarchical network by over 60%.The effect of such edges depends not on the network size but only on the average in-degree of the involved subnetwork.The overwhelming majority of active reverse edges turn out to have some kind of“bunching”effect on the information flows of hierarchical networks,which slows down synchronization processes.This finding refines the current understanding of the role of reverse edges in many natural,social,and engineering hierarchical networks,which might be beneficial for precisely tuning the synchronization rhythms of these networks.Our study also proposes an effective way to attack a hierarchical network by adding a malicious reverse edge to it and provides some guidance for protecting a network by screening out the specific small proportion of vulnerable nodes.

Verifying hierarchical network nonlocality in general quantum networks

Recently, a class of innovative notions on quantum network nonlocality(QNN), called full quantum network nonlocality(FQNN), have been proposed in Phys. Rev. Lett. 128 010403(2022). As the generalization of full network nonlocality(FNN), l-level quantum network nonlocality(l-QNN) was defined in arxiv. 2306.15717 quant-ph(2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.

A Shared Natural Neighbors Based-Hierarchical Clustering Algorithm for Discovering Arbitrary-Shaped Clusters

In clustering algorithms,the selection of neighbors significantly affects the quality of the final clustering results.While various neighbor relationships exist,such as K-nearest neighbors,natural neighbors,and shared neighbors,most neighbor relationships can only handle single structural relationships,and the identification accuracy is low for datasets with multiple structures.In life,people’s first instinct for complex things is to divide them into multiple parts to complete.Partitioning the dataset into more sub-graphs is a good idea approach to identifying complex structures.Taking inspiration from this,we propose a novel neighbor method:Shared Natural Neighbors(SNaN).To demonstrate the superiority of this neighbor method,we propose a shared natural neighbors-based hierarchical clustering algorithm for discovering arbitrary-shaped clusters(HC-SNaN).Our algorithm excels in identifying both spherical clusters and manifold clusters.Tested on synthetic datasets and real-world datasets,HC-SNaN demonstrates significant advantages over existing clustering algorithms,particularly when dealing with datasets containing arbitrary shapes.

Structural Engineering of Hierarchical Magnetic/Carbon Nanocomposites via In Situ Growth for High-Efficient Electromagnetic Wave Absorption

Materials exhibiting high-performance electromagnetic wave absorption have garnered considerable scientific and technological attention,yet encounter significant challenges.Developing new materials and innovative structural design concepts is crucial for expanding the application field of electromagnetic wave absorption.Particularly,hierarchical structure engineering has emerged as a promising approach to enhance the physical and chemical properties of materials,providing immense potential for creating versatile electromagnetic wave absorption materials.Herein,an exceptional multi-dimensional hierarchical structure was meticulously devised,unleashing the full microwave attenuation capabilities through in situ growth,selfreduction,and multi-heterogeneous interface integration.The hierarchical structure features a three-dimensional carbon framework,where magnetic nanoparticles grow in situ on the carbon skeleton,creating a necklace-like structure.Furthermore,magnetic nanosheets assemble within this framework.Enhanced impedance matching was achieved by precisely adjusting component proportions,and intelligent integration of diverse interfaces bolstered dielectric polarization.The obtain Fe_(3)O_(4)-Fe nanoparticles/carbon nanofibers/Al-Fe_(3)O_(4)-Fe nanosheets composites demonstrated outstanding performance with a minimum reflection loss(RLmin)value of−59.3 dB and an effective absorption bandwidth(RL≤−10 dB)extending up to 5.6 GHz at 2.2 mm.These notable accomplishments offer fresh insights into the precision design of high-efficient electromagnetic wave absorption materials.

Universal architecture and defect engineering dual strategy for hierarchical antimony phosphate composite toward fast and durable sodium storage

Antimony(Sb)-ba sed anode materials are feasible candidates for sodium-ion batteries(SIBs) due to their high theoretical specific capacity and excellent electrical conductivity.However,they still suffer from volume distortion,structural collapse,and ionic conduction interruption upon cycling.Herein,a hierarchical array-like nanofiber structure was designed to address these limitations by combining architecture engineering and anion tuning strategy,in which SbPO_(4-x) with oxygen vacancy nanosheet arrays are anchored on the surface of interwoven carbon nanofibers(SbPO_(4-x)@CNFs).In particular,bulky PO_(4)^(3-) anions mitigate the large volume distortion and generate Na_(3)PO_(4) with high ionic conductivity,collectively improving cyclic stability and ionic transport efficiency.The abundant oxygen vacancies substantially boost the intrinsic electronic conductivity of SbPO_4,further accelerating the reaction dynamics.In addition,hierarchical fibrous structures provide abundant active sites,construct efficient conducting networks,and enhance the electron/ion transport capacity.Benefiting from the advanced structural design,the SbPO_(4-x)@CNFs electrodes exhibit outstanding cycling stability(1000 cycles at 1.0 A g^(-1) with capacity decay of 0.05% per cycle) and rapid sodium storage performance(293.8 mA h g^(-1) at 5.0 A g^(-1)).Importantly,systematic in-/ex-situ techniques have revealed the "multi-step conversion-alloying" reaction process and the "battery-capacitor dual-mode" sodium-storage mechanism.This work provides valuable insights into the design of anode materials for advanced SIBs with elevated stability and superior rate performance.

Leveraging Uncertainty for Depth-Aware Hierarchical Text Classification

Hierarchical Text Classification(HTC)aims to match text to hierarchical labels.Existing methods overlook two critical issues:first,some texts cannot be fully matched to leaf node labels and need to be classified to the correct parent node instead of treating leaf nodes as the final classification target.Second,error propagation occurs when a misclassification at a parent node propagates down the hierarchy,ultimately leading to inaccurate predictions at the leaf nodes.To address these limitations,we propose an uncertainty-guided HTC depth-aware model called DepthMatch.Specifically,we design an early stopping strategy with uncertainty to identify incomplete matching between text and labels,classifying them into the corresponding parent node labels.This approach allows us to dynamically determine the classification depth by leveraging evidence to quantify and accumulate uncertainty.Experimental results show that the proposed DepthMatch outperforms recent strong baselines on four commonly used public datasets:WOS(Web of Science),RCV1-V2(Reuters Corpus Volume I),AAPD(Arxiv Academic Paper Dataset),and BGC.Notably,on the BGC dataset,it improvesMicro-F1 andMacro-F1 scores by at least 1.09%and 1.74%,respectively.

A hierarchical salt-rejection strategy for sustainable and high-efficiency solar-driven desalination

Solar steam generation(SSG)is widely regarded as one of the most sustainable technologies for seawater desalination.However,salt fouling severely compromises the evaporation performance and lifetime of evaporators,limiting their practical applications.Herein,we propose a hierarchical salt-rejection(HSR)strategy to prevent salt precipitation during long-term evaporation while maintaining a rapid evaporation rate,even in high-salinity brine.The salt diffusion process is segmented into three steps—insulation,branching diffusion,and arterial transport—that significantly enhance the salt-resistance properties of the evaporator.Moreover,the HSR strategy overcomes the tradeoff between salt resistance and evaporation rate.Consequently,a high evaporation rate of 2.84 kg m^(-2) h^(-1),stable evaporation for 7 days cyclic tests in 20 wt%NaCl solution,and continuous operation for 170 h in natural seawater under 1 sun illumination were achieved.Compared with control evaporators,the HSR evaporator exhibited a>54%enhancement in total water evaporation mass during 24 h continuous evaporation in 20 wt%salt water.Furthermore,a water collection device equipped with the HSR evaporator realized a high water purification rate(1.1 kg m^(-2) h^(-1)),highlighting its potential for agricultural applications.

Kinetic-boosted CO_(2) electroreduction to formate via synergistic electric-thermal field on hierarchical bismuth with amorphous layer

Electrocatalytic converting CO_(2) into chemical products has emerged as a promising approach to achieving carbon neutrality.Herein,we report a bismuth-based catalyst with high curvature terminal and amorphous layer which fabricated via two-step electrodeposition achieves stable formate output in a wide voltage window of 600 mV.The Faraday efficiency(FE) of formate reached up to 99.4% at-0.8 V vs.RHE and it remained constant for more than 92 h at-15 mA cm^(-2).More intriguingly,FE formate of95.4% can be realized at a current density of industrial grade(-667.7 mA cm^(-2)) in flow cell.The special structure promoted CO_(2) adsorption and reduced its activation energy and enhanced the electric-thermal field and K^(+) enrichment which accelerated the reaction kinetics.In situ spectroscopy and theoretical calculation further confirmed that the introduction of amorphous structure is beneficial to adsorpting CO_(2)and stabling*OCHO intermediate.This work provides special insights to fabricate efficient electrocatalysts by means of structural and crystal engineering and makes efforts to realize the industrialization of bismuth-based catalysts.

Nano-Au-decorated hierarchical porous cobalt sulfide derived from ZIF-67 toward optimized oxygen evolution catalysis:Important roles of microstructures and electronic modulation

Enhancing both the number of active sites available and the intrinsic activity of Co-based electrocatalysts simultaneously is a desirable goal.Herein,a ZIF-67-derived hierarchical porous cobalt sulfide decorated by Au nanoparticles(NPs)(denoted as HP-Au@CoxSy@ZIF-67)hybrid is synthesized by low-temperature sulfuration treatment.The well-defined macroporous-mesoporous-microporous structure is obtained based on the combination of polystyrene spheres,as-formed CoxSy nanosheets,and ZIF-67 frameworks.This novel three-dimensional hierarchical structure significantly enlarges the three-phase interfaces,accelerating the mass transfer and exposing the active centers for oxygen evolution reaction.The electronic structure of Co is modulated by Au through charge transfer,and a series of experiments,together with theoretical analysis,is performed to ascertain the electronic modulation of Co by Au.Meanwhile,HP-Au@CoxSy@ZIF-67 catalysts with different amounts of Au were synthesized,wherein Au and NaBH4 reductant result in an interesting“competition effect”to regulate the relative ratio of Co^(2+)/Co^(3+),and moderate Au assists the electrochemical performance to reach the highest value.Consequently,the optimized HP-Au@CoxSy@ZIF-67 exhibits a low overpotential of 340 mV at 10 mA cm^(-2)and a Tafel slope of 42 mV dec-1 for OER in 0.1 M aqueous KOH,enabling efficient water splitting and Zn-air battery performance.The work here highlights the pivotal roles of both microstructural and electronic modulation in enhancing electrocatalytic activity and presents a feasible strategy for designing and optimizing advanced electrocatalysts.

Integrated adsorption and photocatalytic removal of methylene blue dye from aqueous solution by hierarchical Nb_(2)O_(5)@PAN/PVDF/ANO composite nanofibers

This work presents the development of hierarchical niobium pentoxide(Nb_(2)O_(5))-based composite nanofiber membranes for integrated adsorption and photocatalytic degradation of methylene blue(MB)pollutants from aqueous solutions.The Nb_(2)O_(5) nanorods were vertically grown using a hydrothermal process on a base electrospun nanofibrous membrane made of polyacrylonitrile/polyvinylidene fluoride/ammonium niobate(V)oxalate hydrate(Nb_(2)O_(5)@PAN/PVDF/ANO).They were characterized using field-emission scanning electron microscopy(FE-SEM),X-ray diffraction(XRD)analysis,and Fourier transform infrared(FTIR)spectroscopy.These composite nanofibers possessed a narrow optical bandgap energy of 3.31 eV and demonstrated an MB degradation efficiency of 96%after 480 min contact time.The pseudo-first-order kinetic study was also conducted,in which Nb_(2)O_(5)@PAN/PVDF/ANO nanofibers have kinetic constant values of 1.29×10^(-2) min^(-1) and 0.30×10^(-2) min^(-1) for adsorption and photocatalytic degradation of MB aqueous solutions,respectively.These values are 17.7 and 7.8 times greater than those of PAN/PVDF/ANO nanofibers without Nb_(2)O_(5) nanostructures.Besides their outstanding photocatalytic performance,the developed membrane materials exhibit advantageous characteristics in recycling,which subsequently widen their practical use in environmental remediation applications.

Hierarchical Privacy Protection Model in Advanced Metering Infrastructure Based on Cloud and Fog Assistance

The Advanced Metering Infrastructure(AMI),as a crucial subsystem in the smart grid,is responsible for measuring user electricity consumption and plays a vital role in communication between providers and consumers.However,with the advancement of information and communication technology,new security and privacy challenges have emerged for AMI.To address these challenges and enhance the security and privacy of user data in the smart grid,a Hierarchical Privacy Protection Model in Advanced Metering Infrastructure based on Cloud and Fog Assistance(HPPM-AMICFA)is proposed in this paper.The proposed model integrates cloud and fog computing with hierarchical threshold encryption,offering a flexible and efficient privacy protection solution that significantly enhances data security in the smart grid.The methodology involves setting user protection levels by processing missing data and utilizing fuzzy comprehensive analysis to evaluate user importance,thereby assigning appropriate protection levels.Furthermore,a hierarchical threshold encryption algorithm is developed to provide differentiated protection strategies for fog nodes based on user IDs,ensuring secure aggregation and encryption of user data.Experimental results demonstrate that HPPM-AMICFA effectively resists various attack strategies while minimizing time costs,thereby safeguarding user data in the smart grid.

Engineering hierarchical quaternary superstructure of an integrated MOF-derived electrode for boosting urea electrooxidation assisted water electrolysis

Controllable design of the catalytic electrodes with hierarchical superstructures is expected to improve their electrochemical performance.Herein,a self-supported integrated electrode(NiCo-ZLDH/NF)with a unique hierarchical quaternary superstructure was fabricated through a self-sacrificing template strategy from the metal–organic framework(Co-ZIF-67)nanoplate arrays,which features an intriguing well-defined hierarchy when taking the unit cells of the NiCo-based layered double hydroxide(NiCo-LDH)as the primary structure,the ultrathin LDH nanoneedles as the secondary structure,the mesoscale hollow plates of the LDH nanoneedle arrays as the tertiary structure,and the macroscale three-dimensional frames of the plate arrays as the quaternary structure.Notably,the distinctive structure of NiCo-ZLDH/NF can not only accelerate both mass and charge transfer,but also expose plentiful accessible active sites with high intrinsic activity,endowing it with an excellent electrochemical performance for urea oxidation reaction(UOR).Specially,it only required the low potentials of 1.335,1.368 and 1.388 V to deliver the current densities of 10,100 and 200 mA cm^(-2),respectively,much superior to those for typical NiCo-LDH.Employing NiCo-ZLDH/NF as the bifunctional electrode for both anodic UOR and cathodic HER,an energy-saving electrolysis system was further explored which can greatly reduce the needed voltage of 213 mV to deliver the current density of 100 mA cm^(-2),as compared to the conventional water electrolysis system composed of OER.This work manifests that it is prospective to explore the hierarchically nanostructured electrodes and the innovative electrolytic technologies for high-efficiency electrocatalysis.

Hybrid Hierarchical Particle Swarm Optimization with Evolutionary Artificial Bee Colony Algorithm for Task Scheduling in Cloud Computing

Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios.In this work,the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm(HPSO-EABC)has been proposed,which hybrids our presented Evolutionary Artificial Bee Colony(EABC),and Hierarchical Particle Swarm Optimization(HPSO)algorithm.The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm.Comprehensive testing including evaluations of algorithm convergence speed,resource execution time,load balancing,and operational costs has been done.The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm.Compared with the Particle Swarm Optimization algorithm,the HPSO algorithmnot only improves the global search capability but also effectively mitigates getting stuck in local optima.As a result,the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed.Moreover,it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments,effectively reducing execution time and cost,which also is verified by the ablation experimental.

Remarkably Enhanced Methane Sensing Performance at Room Temperature via Constructing a Self-Assembled Mulberry-Like ZnO/SnO_(2) Hierarchical Structure

Development of metal oxide semiconductors-based methane sensors with good response and low power consumption is one of the major challenges to realize the real-time monitoring of methane leakage.In this work,a self-assembled mulberry-like ZnO/SnO_(2)hierarchical structure is constructed by a two-step hydrothermal method.The resultant sensor works at room temperature with excellent response of~56.1%to 2000 ppm CH_(4)at 55%relative humidity.It is found that the strain induced at the ZnO/SnO_(2)interface greatly enhances the piezoelectric polarization on the ZnO surface and that the band bending results in the accumulation of chemically adsorbed O_(2)^(-)ions close to the interface,leading to significant improvement in the sensing performance of the methane gas sensor at room temperature.

Addressing inclusion,innovation,and sustainability challenges through the lens of economic geography:Introducing the hierarchical regional innovation system

The world is facing dramatic challenges related to environmental sustainability at an accelerating pace.In this context,the field of economic geography(EG)has been playing an important role in understanding both the socioeconomic and technological dimensions of these challenges,as it deals with a variety of complementary notions and perspectives.Departing from this lens,our aim is to explore a conceptual framework that can help us to understand environmental changes relating to multi-dimensional territorial development,notably in eco-nomic contexts where inequality is high,and stratification based on hierarchies regulate social and economic life.Based on the territory concept,we propose the original notion of a hierarchical regional innovation system(HRIS)that emphasises the pervasive role of hierarchies(powers)in regional innovation systems and illustrate its value with evidence and case studies from extant literature on sustainability transitions.The HRIS can help us understand and promote development paths considering the contribution of inclusive eco-innovations(another original conceptual amalgam).Through some empirical cases from other studies in low-carbon transitions,we show the application of the HRIS(and inclusive eco-innovation)framework.In conclusion,we provide incen-tives to explore new regional innovation systems,alongside the HRIS,adapted to different regions worldwide and centred on the inclusiveness of people and places.

A chaotic hierarchical encryption/watermark embedding scheme for multi-medical images based on row-column confusion and closed-loop bi-directional diffusion

Security during remote transmission has been an important concern for researchers in recent years.In this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is designed,and a multiimage encryption(MIE)algorithm with row and column confusion and closed-loop bi-directional diffusion is adopted in the paper.While ensuring secure communication of medical image information,people with different security levels have different levels of decryption keys,and differentiated visual effects can be obtained by using the strong sensitivity of chaotic keys.The highest security level can obtain decrypted images without watermarks,and at the same time,patient information and copyright attribution can be verified by obtaining watermark images.The experimental results show that the scheme is sufficiently secure as an MIE scheme with visualized differences and the encryption and decryption efficiency is significantly improved compared to other works.

Hierarchical Federated Learning Architectures for the Metaverse

In the context of edge computing environments in general and the metaverse in particular,federated learning(FL)has emerged as a distributed machine learning paradigm that allows multiple users to collaborate on training a shared machine learning model locally,eliminating the need for uploading raw data to a central server.It is perhaps the only training paradigm that preserves the privacy of user data,which is essential for computing environments as personal as the metaverse.However,the original FL architecture proposed is not scalable to a large number of user devices in the metaverse community.To mitigate this problem,hierarchical federated learning(HFL)has been introduced as a general distributed learning paradigm,inspiring a number of research works.In this paper,we present several types of HFL architectures,with a special focus on the three-layer client-edge-cloud HFL architecture,which is most pertinent to the metaverse due to its delay-sensitive nature.We also examine works that take advantage of the natural layered organization of three-layer client-edge-cloud HFL to tackle some of the most challenging problems in FL within the metaverse.Finally,we outline some future research directions of HFL in the metaverse.