Cluster Topology Research Articles

Deciphering the Role of Vinylene Carbonate in Shaping CO2 Cluster Growth and Stability via Wavelet-Enhanced Microwave Spectroscopy.

This study presents the first integration of wavelet denoising with resonator-enhanced microwave spectroscopy to explore the formation and characteristics of gas-phase heterogeneous vinylene carbonate-(CO2)1-5 clusters. Through this innovative approach, faint spectral lines were detected with efficiency, enhancing our understanding of complex interaction patterns that govern the growth and stability of these molecular clusters. It was found that CO2 aggregates preferentially around the vinylene carbonate molecule through C···O tetrel bonds at the carbonyl and ether groups, altering the typical self-aggregation topology of free CO2 clusters. This leads to more symmetrical growth around the vinylene carbonate monomer. Our findings provide insights into the solvation mechanisms of compounds in supercritical CO2 thereby advancing the understanding of subnanoscale CO2 aggregation patterns.

Prevalence and phylogenetic analysis of cytomegalovirus (Orthoherpesviridae: Cytomegalovirus: Cytomegalovirus humanbeta5) genetic variants from children and immunocompromised patients in central Russia

Cytomegalovirus (CMV) is a DNA-containing virus that is widespread worldwide and is of great importance in infectious pathology of children and adults. The aim of this study is to evaluate the prevalence of CMV among children and immunocompromised patients in the Nizhny Novgorod region (central Russia) and to perform a phylogenetic analysis of the identified strains. DNA samples of CMV detected in frequently ill children and adult recipients of solid organs were studied. The genetic diversity of CMV was assessed for two variable genes: UL55(gB) and UL73(gN), using NGS technology on the Illumina platform. Phylogenetic trees were constructed in the MEGA X program, the reliability of the cluster topology on the trees was confirmed using the rapid bootstrap method based on the generation of 500 pseudo-replicas. Circulation of 5 CMV genotypes by gene UL55(gB) and 5 genotypes by gene UL73(gN) was established in the territory of the Nizhny Novgorod region. While genotypes gB1 and gB2 dominated both in children and in adults, genotype gB5 was detected only in children. The spectrum of gN genotypes was more diverse: genotypes gN4a and gN3b prevailed in children, and gN1 and gN4b genotypes were predominant in adults. The obtained results allowed us to establish the similarity of the landscape of CMV genotypes circulating in Russia (Nizhny Novgorod region), Brazil, China and the USA. The obtained data indicate the similarity of the landscape of CMV genotypes circulating in Russia (Nizhny Novgorod region), Brazil, China and the USA: in children, the predominant genotypes are gB1 (40.0%), gB2 (33.3%), gN4a (42.8%), and gN3b (28.6%), while in adults (recipients of solid organs) genotypes gB1 (37.5%), gB2 (37.5%), gN1 (26.3%), and gN4b (26.3%) are prevailed.

Towards Effective Clustered Federated Learning: A Peer-to-Peer Framework With Adaptive Neighbor Matching

In federated learning (FL), clients may have diverse objectives, and merging all clients' knowledge into one global model will cause negative transfer to local performance. Thus, clustered FL is proposed to group similar clients into clusters and maintain several global models. In the literature, centralized clustered FL algorithms require the assumption of the number of clusters and hence are not effective enough to explore the latent relationships among clients. In this paper, without assuming the number of clusters, we propose a peer-to-peer (P2P) FL algorithm named PANM. In PANM, clients communicate with peers to adaptively form an effective clustered topology. Specifically, we present two novel metrics for measuring client similarity and a two-stage neighbor matching algorithm based Monte Carlo method and Expectation Maximization under the Gaussian Mixture Model assumption. We have conducted theoretical analyses of PANM on the probability of neighbor estimation and the error gap to the clustered optimum. We have also implemented extensive experiments under both synthetic and real-world clustered heterogeneity. Theoretical analysis and empirical experiments show that the proposed algorithm is superior to the P2P FL counterparts, and it achieves better performance than the centralized cluster FL method. PANM is effective even under extremely low communication budgets.

Learning multi-level topology representation for multi-view clustering with deep non-negative matrix factorization

Clustering of multi-view data divides objects into groups by preserving structure of clusters in all views, requiring simultaneously takes into consideration diversity and consistency of various views, corresponding to the shared and specific components of various views. Current algorithms fail to fully characterize and balance diversity and consistency of various views, resulting in the undesirable performance. Here, a novel Multi-View Clustering with Deep non-negative matrix factorization and Multi-Level Representation (MVC-DMLR) learning is proposed, which integrates feature learning, multi-level topology representation, and clustering of multi-view data. Specifically, MVC-DMLR first learns multi-level representation (also called deep features) of objects with deep nonnegative matrix factorization (DNMF), facilitating the exploitation of hierarchical structure of multi-view data. Then, it learns multi-level graphs for each view from multi-level representation, where relations between diversity and consistency are addressed at various resolutions. MVC-DMLR integrates multi-level representation learning, multi-level topology representation learning and clustering, which is formulated as an optimization problem. Experimental results show the superiority of MVC-DMLR to baselines in terms of accuracy, F1-score, normalized mutual information and adjusted rand index.

Energy efficient mobile sink driven data collection in wireless sensor network with nonuniform data

In wireless sensor network, mobile sink is used to collect data from sensor nodes by periodically traversing the network to prevent hotspot problem. However, when sensor nodes generate data non-uniformly, the efficiency of data collection is constrained by rendezvous points and network topology. It becomes more challenging under network energy consumption constraint. Thus, this paper investigates non-uniform data generation in wireless sensor network and proposes an innovative approach: Optimal Clustering and Network Topology for Mobile Sink-Driven Data Collection, called OCNTMS. It focuses on determining optimal rendezvous points and their associated clusters. Through innovative methods such as weight-balanced clustering, cost function optimization, load-balanced link construction, and node forwarding selection, the OCNTMS can efficiently construct link sets within clusters and accurately plan the mobile sink’s traversal of rendezvous points. Simulation results show that the OCNTMS reduces energy consumption by 18% and increases network lifetime by 40% compared with existing approaches under the constraint of non-uniform data generation. This greatly improves the network energy efficiency and data transmission efficiency.

Nonlinear time series analysis of state-wise COVID-19 in Malaysia using wavelet and persistent homology

The nonlinear progression of COVID-19 positive cases, their fluctuations, the correlations in amplitudes and phases across different regions, along with seasonality or periodicity, pose challenges to thoroughly examining the data for revealing similarities or detecting anomalous trajectories. To address this, we conducted a nonlinear time series analysis combining wavelet and persistent homology to detect the qualitative properties underlying COVID-19 daily infection numbers at the state level from the pandemic’s onset to June 2024 in Malaysia. The first phase involved investigating the evolution of daily confirmed cases by state in the time-frequency domain using wavelets. Subsequently, a topological feature-based time series clustering is performed by reconstructing a higher-dimensional phase space through a delay embedding method. Our findings reveal a prominent 7-day periodicity in case numbers from mid-2021 to the end of 2022. The state-wise daily cases are moderately correlated in both amplitudes and phases during the Delta and Omicron waves. Biweekly averaged data significantly enhances the detection of topological loops associated with these waves. Selangor demonstrates unique case trajectories, while Pahang shows the highest similarity with other states. This methodological framework provides a more detailed understanding of epidemiological time series data, offering valuable insights for preparing for future public health crises.

TopoSinGAN: Learning a Topology-Aware Generative Model from a Single Image

Generative adversarial networks (GANs) have significantly advanced synthetic image generation, yet ensuring topological coherence remains a challenge. This paper introduces TopoSinGAN, a topology-aware extension of the SinGAN framework, designed to enhance the topological accuracy of generated images. TopoSinGAN incorporates a novel, differentiable topology loss function that minimizes terminal node counts along predicted segmentation boundaries, thereby addressing topological anomalies not captured by traditional losses. We evaluate TopoSinGAN using agricultural and dendrological case studies, demonstrating its capability to maintain boundary continuity and reduce undesired loop openness. A novel evaluation metric, Node Topology Clustering (NTC), is proposed to assess topological attributes independently of geometric variations. TopoSinGAN significantly improves topological accuracy, reducing NTC index values from 15.15 to 3.94 for agriculture and 14.55 to 2.44 for dendrology, compared to the baseline SinGAN. Modified FID evaluations also show improved realism, with lower FID scores: 0.1914 for agricultural fields compared to 0.2485 for SinGAN, and 0.0013 versus 0.0014 for dendrology. The topology loss enables end-to-end training with direct topological feedback. This new framework advances the generation of topologically accurate synthetic images, with applications in fields requiring precise structural representations, such as geographic information systems (GIS) and medical imaging.

Cluster-Cation Pairs Mediated Assembly of Subnanometer Polyoxometalates Superstructures.

Superstructures assembled by subnanometer polyoxometalate (POM) clusters are interesting for their attractive structures and excellent properties. However, the complex interactions between clusters and cations make it challenging to control the assembly of POM clusters at the subnanometer scale. Here, 20 cluster-assembled superstructures built by two types of MP2W17O61 (M = La-Lu) clusters are successfully synthesized. The precise structures and configurations of the subnanostructures, including nanowires, tetragonal nanosheets, and rectangular nanosheets, are characterized and presented. Molecular dynamics (MD) simulations reveal that the difference in interactions of POM clusters and cations leads to the formation of distinct superstructures. Two mechanisms of superstructure formation are proposed. Furthermore, the EuP2W17 nanosheet behaves with a high Faradaic efficiency of 90.2% and selectivity of 87.3% for glycolic acid in the electrocatalytic ethylene glycol oxidation reaction, which is much higher than that of isolated cluster components. This work connects the cluster topologies and cluster-cation pairs to the superstructures of cluster assemblies, providing general guidelines for the supramolecular self-assembly of POM clusters.

Identification and classification of clusters of dipolar colloids in an external field.

Colloids can acquire a dipolar interaction in the presence of an external AC electric field. At high field strength, the particles form strings in the field direction. However, at weaker field strength, competition with isotropic interactions is expected. One means to investigate this interplay between dipolar and isotropic interactions is to consider clusters of such particles. Therefore, we have identified, using the GMIN basin-hopping tool, a rich library of lowest energy clusters of a dipolar colloidal system, where the dipole orientation is fixed to lie along the z axis and the dipole strength is varied for m-membered clusters of 7 ≤ m ≤ 13. In the regime where the isotropic and dipolar interactions are comparable, we find elongated polytetrahedral, octahedral, and spiral clusters as well as a set of non-rigid clusters, which emerge close to the transition to strings. We further implement a search algorithm that identifies these minimum energy clusters in bulk systems using the topological cluster classification [J. Chem. Phys. 139 234506 (2013)]. We demonstrate this methodology with computer simulations, which show instances of these clusters as a function of dipole strength.

Neuro‐fuzzy‐based cluster formation scheme for energy‐efficient data routing in IOT‐enabled WSN

SummaryInternet of things–enabled wireless sensor networks face challenges like inflexibility, poor scalability, suboptimal cluster head selection, and energy inefficiencies. This is due to the faster data transmission rates between cluster nodes during data packet routing. This creates unnecessary energy consumption burdens for those actively transmitting nodes. Conceptually, an effective cluster formation phase supports better data routing mechanisms, while sustaining the energy efficiency of individual nodes. This paper proposes a Neuro‐Fuzzy based Cluster Formation (NFCF) scheme to facilitate adaptive and energy‐efficient cluster topologies. NFCF utilizes fuzzy logic and neural networks to identify optimal super nodes for flexible cluster formations. This approach enables configurable cluster sizes along with inclusion/exclusion criteria for member nodes based on energy thresholds. Parameters evaluated for node selection include the degree of super node, expected energy per cluster, energy variance, and residual energy. Nodes not meeting the thresholds are excluded. The neural network updates fuzzy rules to guide optimal clustering decisions based on anticipated energy dynamics under different conditions. The performance of the proposed NFCF scheme is evaluated based on objective function changes related to data transmission, individual node energy variation, energy variance before and after transmissions, and averaged end‐to‐end delay across transmission cycles. Results are compared against genetic fuzzy clustering, fuzzy energy‐aware clustering, fuzzy‐based distributed clustering, fuzzy logic‐based multi‐hop clustering, and fuzzy weighted k‐means clustering.

Non-local interaction in discrete Ricci curvature-induced biological aggregation

We investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods. We find that even a single effective topological neighbour suffices for significant order in a system with non-local topological interactions. We also explore topological information flow patterns and clustering dynamics using Hodge spectral entropy and mean Forman–Ricci curvature.

Delocalization-ratio analysis of 3-center bonding in position-space for closo-boranes and related systems: Approaching the styx picture and beyond.

Closo-boron hydrides BnHn 2- (n = 5-12) are a conceptually well understood class of compounds. For these and a few related prototype compounds, both the local and the global picture of 3-center bonding are extracted from position-space quantities based on the electron density and the pair density. For this purpose, three-center delocalization indices between quantum theory of atoms in molecules (QTAIM) atoms in position space are used to develop a consistent set of local bond and triangle, and global cluster delocalization ratios (DRs), which are quantitatively compared with conceptual Γ values derived from the styx code for each cluster. Combination of the cluster DRs with associated effective numbers of skeletal electron sharing (SES) for selected cluster surface edges, triangles, or the whole cluster yields effective styx type values describing the trend and even the size of the conceptual styx codes for closo-boranes BnHn 2- and related systems with increasing cluster size n reasonably well. For nonuniform cluster topologies, the different vertex degrees are shown to cause systematic 3-center wise bond delocalization effects for the associated edges and triangles of different average vertex degrees. Extension of DR analysis beyond the styx type triangular cluster-surface bonding corresponds to a triangulation of multicentric bonding. The cluster-wise results keep indicating consistency with the mixed 2- and 3-center bonding approach. The successfully established chemical meaning of the local edge, triangle, and global cluster DRs and their associated SES values constitutes the basis for systematic investigations of mixed 2- and 3-center bonding scenarios in particular in intermetallic and related (endohedral) cluster compounds in the future.

Exploring mesophase formation: Structural characterization approaches in a soft sphere model

This study employs Molecular Dynamics simulations to enhance the structural characterization of sphere mixture systems, focusing on local order parameters to identify order-disorder transitions within lamellar and hexagonal mesophases. The structural characterization included the use of neural networks and the search for clusters with topological order. We have identified the order-disorder transition at a characteristic temperature TOD, effectively captured by the structural parameters analyzed. Below TOD, the system organizes into an ordered mesophase, while above this temperature, it transitions into an isotropic liquid state. Moreover, within the isotropic region, we observe that the liquid begins to form clusters. This clustering phenomenon becomes evident below a specific temperature, denoted as T⁎. At T⁎, there are noticeable changes in the volume versus temperature curves, indicating a process of micellization or clustering in the system. The structural parameters used in our study also register this behavioral change at T⁎, further supporting the occurrence of this phenomenon. Additionally, our analysis of the overlap in detecting ordered particles between the two structural parameters using the Sørensen-Dice similarity coefficient reveals a significant spatial correlation in the isotropic phase, with a correlation higher than what would be expected in a random case. This indicates that both neural networks and topological cluster classification detect statistically similar ordered regions in the isotropic phase, highlighting the clustering. Our findings reveal that the structural parameters effectively capture both the order-disorder transition at TOD and the clustering process at T⁎. These results provide valuable insights into the self-assembly mechanisms and phase behavior in this soft-sphere model, advancing our understanding of self-assembly processes in material science, particularly in exploring phase behavior in mesogenic nanoparticle systems.

Structural regression modelling of peptide based drug delivery vectors for targeted anti-cancer therapy.

Drug resistance in cancer poses a serious challenge in finding an effective remedy for cancer patients, because of the multitude of contributing factors influencing this complex phenomenon. One way to counter this problem is using a more targeted and dose-limiting approach for drug delivery, rather than relying on conventional therapies that exhibit multiple pernicious side-effects. Stability and specificity have traditionally been the core issues of peptide-based delivery vectors. In this study, we employed a structural regression modelling approach in the design, synthesis and characterization of a series of peptides that belong to approximately same topological cluster, yet with different electrostatic signatures encoded as a result of their differential positioning of amino acids in a given sequence. The peptides tagged with the fluorophore 5(6)-carboxyfluorescein, showed higher uptake in cancer cells with some of them colocalizing in the lysosomes. The peptides tagged with the anti-cancer drug methotrexate have displayed enhanced cytotoxicity and inducing apoptosis in triple-negative breast cancer cells. They also showed comparable uptake in side-population cells of lung cancer with stem-cell like properties. The most-optimized peptide showed accumulation in the tumor resulting in significant reduction of tumor size, compared to the untreated mice in in-vivo studies. Our results point to the following directives; (i) peptides can be design engineered for targeted delivery (ii) stereochemical engineering of peptide main chain can resist proteolytic enzymes and (iii) cellular penetration of peptides into cancer cells can be modulated by varying their electrostatic signatures.

Dimension Reduction of Multidimensional Structured and Unstructured Datasets through Ensemble Learning of Neural Embeddings

Dimension reduction aims to project a high‐dimensional dataset into a low‐dimensional space. It tries to preserve the topological relationships among the original data points and/or induce clusters. NetDRm, an online dimensionality reduction method based on neural ensemble learning that integrates different dimension reduction methods in a synergistic way, is introduced. NetDRm is designed for datasets of multidimensional points that can be either structured (e.g., images) or unstructured (e.g., point clouds, tabular data). It starts by training a collection of deep residual encoders that learn the embeddings induced by multiple dimension reduction methods applied to the input dataset. Subsequently, a dense neural network integrates the generated encoders by emphasizing topological preservation or cluster induction. Experiments conducted on widely used multidimensional datasets (point‐cloud manifolds, image datasets, tabular record datasets) show that the proposed method yields better results in terms of topological preservation ( curves), cluster induction (V measure), and classification accuracy than the most relevant dimension reduction methods.

Transcriptomics and weighted protein network analyses of the LRRK2 protein interactome reveal distinct molecular signatures for sporadic and LRRK2 Parkinson’s Disease

Mutations in the LRRK2 gene are the most common genetic cause of familial Parkinson’s Disease (LRRK2-PD) and an important risk factor for sporadic PD (sPD). Multiple clinical trials are ongoing to evaluate the benefits associated with the therapeutical reduction of LRRK2 kinase activity. In this study, we described the changes of transcriptomic profiles (whole blood mRNA levels) of LRRK2 protein interactors in sPD and LRRK2-PD cases as compared to healthy controls with the aim of comparing the two PD conditions. We went on to model the protein-protein interaction (PPI) network centred on LRRK2, which was weighted to reflect the transcriptomic changes on expression and co-expression levels of LRRK2 protein interactors. Our results showed that LRRK2 interactors present both similar and distinct alterations in expression levels and co-expression behaviours in the sPD and LRRK2-PD cases; suggesting that, albeit being classified as the same disease based on clinical features, LRRK2-PD and sPD display significant differences from a molecular perspective. Interestingly, the similar changes across the two PD conditions result in decreased connectivity within a topological cluster of the LRRK2 PPI network associated with protein metabolism/biosynthesis and ribosomal metabolism suggesting protein homoeostasis and ribosomal dynamics might be affected in both sporadic and familial PD in comparison with controls.

Topological Octet-Rule Implementation for Deltahedral Boron Hydrides and Related Zintl Clusters of the Main-Group Elements: Flexible Octet-Rule Fulfillment by Mixed 2- and 3-Center Fractional Bonding Scenarios.

In the large class of main-group Zintl phases, the octet rule plays a key role for the polyanions following the pseudoatom concept and the 8-N rule, such that a unique correspondence between atomic partial structure and its electron count results. In the conceptual framework of the Wade's type of clusters the relations to the octet rule are less obvious, and its structural implications are not clear. For this purpose, a topological implementation of the octet rule (TORI) within a delocalized bonding scenario is introduced. It is based on the average topology of the deltahedral cluster skeletons and the octet rule applied to delocalized fractional 2- and 3-center bond distributions. For a given skeletal electron pair count SEP, TORI yields values (ttoc, ytoc) similar to the styx approach. Two hierarchically different types of octet-rule fulfillment are identified, the cluster-wise and the local one. The local octet-rule fulfillment always implies the cluster-wise one, while the converse is not true. Deltahedral clusters with different skeletal shapes but the same Wade's SEP count can be distinguished with respect to different octet-rule fulfillment. The TORI approach opens a perspective to compare Zintl phases containing Wade-type clusters with those containing 8-N type of partial structures on the basis of octet-rule implications. The main difference to the 8-N type of partial structures identified is the more flexible way of octet-rule fulfillment in the Wade's type clusters, which does not prevent them from realizing the same cluster topology with different SEP counts. The TORI approach works with delocalized fractional bonds and is consistent with the concept of PSEPT; it just adds an additional facet.

Hospital environment microbiome

The aim of the review is to give a brief description of the biodiversity and structure of the hospital environment microbiome based on molecular genetic research methods. Until a certain time, studies of the hospital environment microbiota for the purposes of epidemiological surveillance and control of healthcare-associated infections (HAIs) were based on routine microbiological identification of clinically relevant bacterial taxa. Discovery of DNA, the development of sequencing technologies, PCR and cloning techniques enabled the investigation of microbial communities using cultivation-independent, DNA and RNA-based approaches. At the current level of knowledge, the hospital environment can be considered as a superorganism with its own microbiome. Multiomic technologies, including meta-transcriptomic, meta-proteomic and metabolomic approaches, provide detailed information about microbial activity in the environment. Now it has been established that there is a stable core of the hospital microbiome where the vast majority of microorganisms are necessary for the functioning of the hospital ecosystem and are not classified as human pathogens. The hospital microbiome has a homogeneous structure composed by a massive dominance of a few taxa and microbial network with low connectivity forming a clustered topology. A keystone species is a taxon whose importance for maintaining community structure is relatively higher than others and its identification is of paramount importance. Due to the lack of knowledge of the hospital environment microbiome by molecular genetic technologies, there is no single shared point of view on the microbial diversity in different healthcare facilities. But there is no doubt that molecular genetic technologies will shed light on the evolution of hospital strains and determine which indicators are the most informative for monitoring and prognosis of HAIs.

Deciphering Molecular Mechanisms of Cutaneous Leishmaniasis, Pathogenesis and Drug Repurposing through Systems Biology

Cutaneous leishmaniasis (CL) is a major health problem caused by an intracellular pathogen of the genus Leishmania. CL results in morphologically distinct skin injuries, ranging from nodules to plaques and ulcers, which persist as a recuperating incessant injury depending on the type of contaminating parasite. There is still no effective treatment to reduce the skin lesions in patients infected with CL. The aim of this study was to develop strategies to treat skin lesions in CL patients. We retrieved the transcriptomic data of skin lesions from patients with CL and normal skin from the gene Expression Omnibus (GEO) database. The protein-protein interaction network (PPIN) was constructed using the STRING database and Cytoscape v3.10.1 software. Critical genes were identified by topological network analysis and cluster detection. Finally, gene ontology and repurposing drugs for critical genes were determined. CD8A, IFNG, IL-6, PTPRC, CCR7, TLR2, GSTA5, CYBB, IL-12RB2, ITGB2, FCGR3A, CTLA4, and IFNG were identified as the critical genes in PPIN and subnetworks. Enrichment analysis revealed that T-cell receptor signaling, toll-like receptor signaling, cytokine-cytokine receptor interaction, graft-versus-host disease, leishmaniasis, chemokine signaling, primary immunodeficiency, and Th17 cell differentiation were the major pathways associated with critical genes. The drug repurposing results identified cyclosporine, rituximab, infliximab, blinatumomab, and methylprednisolone as candidates for treatment of CL. After validating our model with available experimental data, we found that critical molecules and drug candidates play a crucial role in the treatment of skin lesions caused by Leishmania in prospective studies.

Distributed Batch Learning of Growing Neural Gas for Quick and Efficient Clustering

Growing neural gas (GNG) has been widely used in topological mapping, clustering and unsupervised tasks. It starts from two random nodes and grows until it forms a topological network covering all data. The time required for growth depends on the total amount of data and the current network nodes. To accelerate growth, we introduce a novel distributed batch processing method to extract the rough distribution called Distributed Batch Learning Growing Neural Gas (DBL-GNG). First, instead of using a for loop in standard GNG, we adopt a batch learning approach to accelerate learning. To do this, we replace most of the standard equations with matrix calculations. Next, instead of starting with two random nodes, we start with multiple nodes in different distribution areas. Furthermore, we also propose to add multiple nodes to the network instead of adding them one by one. Finally, we introduce an edge cutting method to reduce unimportant links between nodes to obtain a better cluster network. We demonstrate DBL-GNG on multiple benchmark datasets. From the results, DBL-GNG performs faster than other GNG methods by at least 10 times. We also demonstrate the scalability of DBL-GNG by implementing a multi-scale batch learning process in it, named MS-DBL-GNG, which successfully obtains fast convergence results. In addition, we also demonstrate the dynamic data adaptation of DBL-GNG to 3D point cloud data. It is capable of processing and mapping topological nodes on point cloud objects in real time.