Shape Of Clusters Research Articles

Detection of Dopamine Using Hybrid Materials Based on NiO/ZnO for Electrochemical Sensor Applications

Dopamine is a neurotransmitter which is classified as a catecholamine. It is also one of the main metabolites produced by some tumor types (such as paragangliomas and neoblastomas). As such, determining and monitoring the level of dopamine is of the utmost importance, ideally using analytical techniques that are sensitive, simple, and low in cost. Due to this, we have developed a non-enzymatic dopamine sensor that is highly sensitive, selective, and rapidly detects the presence of dopamine in the body. A hybrid material fabricated with NiO and ZnO, based on date fruit extract, was synthesized by hydrothermal methods and using NiO as a precursor material. This paper discusses the role of date fruit extracts in improving NiO’s catalytic performance with reference to ZnO and the role that they play in this process. An X-ray powder diffraction study, a scanning electron microscope study, and a Fourier transform infrared spectroscopy study were performed in order to investigate the structure of the samples. It was found that, in the composite NiO/ZnO, NiO exhibited a cubic phase and ZnO exhibited a hexagonal phase, both of which exhibited well-oriented aggregated cluster shapes in the composite. A hybrid material containing NiO and ZnO has been found to be highly electro-catalytically active in the advanced oxidation of dopamine in a phosphate buffer solution at a pH of 7.3. It has been found that this can be accomplished without the use of enzymes, and the range of oxidation used here was between 0.01 mM and 4 mM. The detection limit of non-enzymatic sensors is estimated to be 0.036 μM. Several properties of the non-enzymatic sensor presented here have been demonstrated, including its repeatability, selectivity, and reproducibility. A test was conducted on Sample 2 for the detection of banana peel and wheat grass, and the results were highly encouraging and indicated that biomass waste may be useful for the manufacture of medicines to treat chronic diseases. It is thought that date fruit extracts would prove to be valuable resources for the development of next-generation electrode materials for use in clinical settings, for energy conversion, and for energy storage.

Control of Permanent Porosity in Type 3 Porous Liquids via Solvent Clustering.

Porous liquids (PLs) are an exciting new class of materials for carbon capture due to their high gas adsorption capacity and ease of industrial implementation. They are composed of sorbent particles suspended in a nonadsorbed solvent, forming a liquid with permanent porosity. While PLs have a vast number of potential compositions based on the number of solvents and sorbent materials available, most of the research has been focused on the selection of the sorbent rather than the solvent. Therefore, PL design criteria on the supramolecular structures of the solvent are explored to create a fundamental understanding of how the solvent enables PL formation for rapid discovery of new PL compositions. Atomistic molecular dynamics simulation of eight solvents with a range of molecular sizes, shapes, and intramolecular bonding was performed, identifying that the shape and size of molecular clusters formed in the solvent are the driving predictor of PL formation rather than the size of the individual solvent molecule. The results demonstrate a significant departure from common approaches to PL formation based on the steric exclusion of solvent molecules from the sorbent via the size of the pore aperture. A modeling and experimental validation study further supports these findings. Through this computational material design study, a previously unexplored mechanism in PL formation, solvent-solvent clustering, is identified as a critical factor for the accelerated discovery of liquid phase carbon capture materials.

Clustering explanation based on multi-hyperrectangle

Clustering plays a crucial role in data mining and pattern recognition, but the interpretation of clustering results is often challenging. Existing interpretation methods usually lack an intuitive and accurate description of irregular shapes and high dimensional datas. This paper proposes a novel clustering explanation method based on a Multi-HyperRectangle(MHR), for extracting post hoc explanations of clustering results. MHR first generates initial hyperrectangles to cover each cluster, and then these hyper-rectangles are gradually merged until the optimal shape is obtained to fit the cluster. The advantage of this method is that it recognizes the shape of irregular clusters and finds the optimal number of hyper-rectangles based on the hierarchical tree structure, which discovers structural relationships between rectangles. Furthermore, we propose a refinement method to improve the tightness of the hyperrectangles, resulting in more precise and comprehensible explanations. Experimental results demonstrate that MHR significantly outperforms existing methods in both the tightness and accuracy of cluster interpretation, highlighting its effectiveness and innovation in addressing the challenges of clustering interpretation.

Flattened Pt clusters constructed on CeO2 for efficient selective oxidation of NH3

In the field of environmental catalysis, the effective elimination of pollutants with limited generation of harmful byproducts is a general requirement for environmental pollutant elimination catalysts. Recently, the efficient selective catalytic oxidation of NH3 (NH3-SCO) with high N2 selectivity has become a research hotspot. In this work, based on the understanding of the structure-activity relationship for Pt/CeO2 catalysts in NH3-SCO reaction, a novel flattened Pt cluster catalyst supported on CeO2 (FC-Pt/CeO2) was synthesized by the solution combustion method. In comparison to CeO2-supported bulky (three-dimensional) Pt cluster/particle catalyst prepared by the conventional incipient wetness impregnation method, flattened Pt clusters with more Pt-O-Ce structure could better facilitate the activation of adsorbed NH3 at low temperatures, thus achieving superior low temperature NH3 oxidation activity. It was also revealed that the NH3-SCO reaction on FC-Pt/CeO2 was proceeded by i-SCR pathway, in which NO generated by the deep oxidation of NH3 would react with adsorbed NH3 or -NH2/-NH. This work provided new insights into constructing robust cluster catalysts from an aspect of cluster shape control, which would significantly benefit the environmental catalysis community.

Geochemical Anomaly Detection and Pattern Recognition: A Combined Study of the Apriori Algorithm, Principal Component Analysis, and Spectral Clustering

This study demonstrates the effectiveness of combining Principal Component Analysis (PCA) and the Apriori algorithm for feature selection, alongside Spectral clustering, to detect geochemical anomalies in Mississippi Valley-Type (MVT) Pb-Zn deposits in western Iran. First, PCA and Apriori enabled the identification of both syngenetic and epigenetic components, which helped in recognizing elements associated with mineralization. These elements were then modeled using Spectral clustering to detect geochemical anomalies. Unlike traditional methods like k-means, Spectral clustering does not require spherical clusters and is adept at identifying clusters of arbitrary shapes. This made it particularly suitable for analyzing the irregular shapes of geochemical anomalies in the study area. By incorporating Spectral clustering, the method effectively separated geochemical groups, revealing the underlying structure of the data. This was crucial for identifying anomalous geochemical zones and delineating areas with a high potential for Pb-Zn mineralization. The performance of the Spectral clustering algorithm was thoroughly evaluated using the Silhouette Score, the Davies–Bouldin Index, and Dunn Index. Subsampling was employed to assess the algorithm’s stability, providing a comprehensive evaluation of its effectiveness in identifying geochemical anomalies and mapping mineralization potential.

Development of a Universal Material Characterization, Evaluation and Estimation System via Microstructure Construction

In recent decades, advancements in material-scanning technologies have enabled detailed acquisition of microstructural data, yet direct integration of this data into simulation models remains challenging. This study develops a system that utilizes scanning electron microscope (SEM) micrographs to construct a 2D spatial map, which categorizes microstructural attributes. Employing the Marching Cubes algorithm, we create the contours and shapes of grain clusters based on consistent grey values, facilitating the precise generation of grain areas in simulation software. This generated model is then applied to simulate a uniaxial tensile test, revealing irregular principal stress distributions along grain boundaries and notable stress concentrations at void-grain interfaces. These results emphasize the system’s efficacy in providing precise material characterization, evaluation, and estimation. Additionally, the system accommodates further refinements, such as incorporating crystal orientations and conducting analyses like creep deformation and electrical property evaluation. Ultimately, this approach supports a comprehensive pipeline for material design, testing, analysis, and simulation, thereby enhancing the potential for targeted material improvements. Figure 1

Ag108(PEt3)24Cl6: A Hexagonal Prismatic Metalloid Cluster.

The ligands used for the protection of metalloid clusters heavily influence the resulting structure and shape. For silver, thiolate and alkynyl ligands are commonly used, while phosphines usually play a minor role as co-ligands. Herein, we report the synthesis and structural characterization of Ag108(PEt3)24Cl6 (1), the largest structurally characterized metalloid silver cluster with phosphines and halides as sole ligands. Instead of the frequently observed spherical shape of metalloid clusters, 1's structure resembles a hexagonal prism. The highly light and temperature sensitive compound features many similarities to its smaller congener Ag64(PnBu3)16Cl6, though there are distinct structural and electronic differences present. Within 1, a Ag64 subunit can be found, which identifies these clusters as molecular seeds for the formation of faceted nanoparticles.

Global Optimization of Molybdenum Subnanoclusters on Graphene: A Consistent Approach toward Catalytic Applications.

The development of novel subnanometer clusters (SNCs) catalysts with superior catalytic performance depends on the precise control of clusters' atomistic sizes, shapes, and accurate deposition onto surfaces. The intrinsic complexity of the adsorption process complicates the ability to achieve an atomistic understanding of the most relevant structure-reactivity relationships hampering the rational design of novel catalytic materials. In most cases, existing computational approaches rely on just a few structures to draw conclusions on clusters' reactivity thereby neglecting the complexity of the existing energy landscapes thus leading to insufficient sampling and, most likely, unreliable predictions. Moreover, modeling of the actual experimental procedure that is responsible for the deposition of SNCs on surfaces is often not done even though in some cases this procedure may enhance the significance of certain (e.g., metastable) adsorption geometries. This study proposes a novel systematic approach that utilizes global search techniques, specifically, the particle swarm optimization (PSO) method, in conjunction with ab initio calculations, to simulate all stages in the beam experiments, from predicting the most relevant SNCs structures in the beam and on a surface, to their reactivity. To illustrate the main steps of our approach, we consider the deposition of Molybdenum SNC of 6 Mo atoms on a free-standing graphene surface, as well as their catalytic properties with respect to the CO molecule dissociation reaction. Even though our calculations are not exhaustive and serve only to produce an illustration of the method, they are still able to provide insight into the complicated energy landscape of Mo SNCs on graphene demonstrating the catalytic activity of Mo SNCs and the importance of performing statistical sampling of available configurations. This study establishes a reliable procedure for performing theoretical rational design predictions.

Implementation of K-Nearest Neighbor Algorithm on Density-Based Spatial Clustering Application with Noise Method on Stunting Clustering

This paper studies the implementation of the K-Nearest Neighbor (KNN) algorithm on Density-Based Spatial Clustering Application with Noise (DBSCAN) method on stunting Clustering in the eastern region of Indonesia in 2022. The DBSCAN method is used because it is more efficient to perform the Clustering process for irregular Clustering shapes. The main objective of this study is to apply the KNN algorithm to the DBSCAN Clustering technique in 161 Districts/Cities in 11 provinces in eastern Indonesia. A comparison of the performance evaluation of the DBSCAN Clustering technique is done by considering the value of the Silhouette score, BetaCV score, and Davies-Bouldin score indicating the quality of the Clusters formed with the lowest results scores of 0.67 and 1.84 with epsilon value = 3.4 and minimum point value = 2 resulting in 4 Clusters. The results of Clustering 161 Districts and Cities based on the factors that cause stunting formed 4 Clusters where Cluster 0 consists of 119 Districts and Cities with very high stunting characteristics, Cluster 1 consists of 3 Districts and Cities with high stunting characteristics, the results of Cluster 2 consist of 2 Districts and Cities with low stunting characteristics, then the results of Cluster 2 consist of 2 Districts and Cities with low stunting characteristics and Cluster 3 consists of 2 Cities with very low stunting characteristics.

Assessing aortic morphology post aortic valve replacement using unsupervised hierarchical clustering and statistical shape modelling

Abstract Introduction There are different surgical procedures used to treat aortic valve disease such as aortic valve replacement (AVR), the Ozaki procedure, the Ross procedure, and the valve-sparing procedure. There may be postoperative side effects associated with aortic morphology. Computational analyses that assess morphology are thus necessary in such scenario. Statistical shape modelling is used to assess three-dimensional morphology, discover unique shape features, create mean shapes, and create shape modes that display morphological variability. Hierarchical cluster analysis is a machine learning method used to classify a population into subgroups. Both of these statistical methods were applied to aortic valve replacement patients to evaluate morphological variability after aortic valve replacement (AVR) surgery. Purpose The purpose of this study is to assess the aortic morphology of AVR patients, identify morphological differences between different surgical procedures, identify subgroups postoperatively using statistical shape modelling and hierarchical cluster analysis, and assessing possible correlations between the resultant clusters and function i.e. ejection fraction. Methods Computed tomography and cardiac magnetic resonance images were used to reconstruct aortas into 3D models using segmentation and 3D reconstruction software. For each patient, two models were created (i.e. ascending aorta only and aorta including the arch and the descending aorta). N=35 patients were included in the study. Statistical shape analysis was run to create templates and shape modes. Statistical environment and language software was used to run hierarchical cluster analysis. Results Overall, the hierarchical cluster analysis did not classify the aortas based on type of surgery, but most patients in the Ross group demonstrated morphological differences from the other surgical groups and many of the aortas belonging to the Ross group were clustered together in both clustering analyses. No significant differences between clusters were seen (p=0.47 for ascending, p=0.19 for whole aorta). No correlation was found between clusters and ejection fraction (p=0.75, r2<0.01), possibly indicating that post-AVR aortic morphology in this sample does not reflect overt functional changes. Conclusion Both statistical shape modelling and hierarchical cluster analyses were successful in assessing morphological variability and identifying subgroups in this population. This framework could therefore be extended to larger samples to inform on surgical decision-making allowing surgeons to choose the appropriate surgery for the patient or design prosthetic valves that are more customised to the patient’s anatomy.Cluster-Ejection Fraction Correlation

Robust Parameter Optimisation of Noise-Tolerant Clustering for DENCLUE Using Differential Evolution

Clustering samples based on similarity remains a significant challenge, especially when the goal is to accurately capture the underlying data clusters of complex arbitrary shapes. Existing density-based clustering techniques are known to be best suited for capturing arbitrarily shaped clusters. However, a key limitation of these methods is the difficulty in automatically finding the optimal set of parameters adapted to dataset characteristics, which becomes even more challenging when the data contain inherent noise. In our recent work, we proposed a Differential Evolution-based DENsity CLUstEring (DE-DENCLUE) to optimise DENCLUE parameters. This study evaluates DE-DENCLUE for its robustness in finding accurate clusters in the presence of noise in the data. DE-DENCLUE performance is compared against three other density-based clustering algorithms—DPC based on weighted local density sequence and nearest neighbour assignment (DPCSA), Density-Based Spatial Clustering of Applications with Noise (DBSCAN), and Variable Kernel Density Estimation–based DENCLUE (VDENCLUE)—across several datasets (i.e., synthetic and real). The study has consistently shown superior results for DE-DENCLUE compared to other models for most datasets with different noise levels. Clustering quality metrics such as the Silhouette Index (SI), Davies–Bouldin Index (DBI), Adjusted Rand Index (ARI), and Adjusted Mutual Information (AMI) consistently show superior SI, ARI, and AMI values across most datasets at different noise levels. However, in some cases regarding DBI, the DPCSA performed better. In conclusion, the proposed method offers a reliable and noise-resilient clustering solution for complex datasets.

Nanoparticle Clustering in Supraparticles to Control Magnetic Long‐Range Interactions

AbstractTo tailor superparamagnetic iron oxide nanoparticles (SPIONs) to the specific needs of diverse application fields, it is essential to understand not only their intrinsic properties but also their interactions with each other. Theoretical models predicting/explaining the magnetization behavior of macroscopic samples containing millions of SPIONs are intricate due to the complexity of the underlying relaxation mechanisms in alternating fields. This study introduces supraparticles (SPs) as model architectures to empirically investigate magnetic interactions within and between large SPION clusters (>100 nanoparticles (NPs)). For this purpose, NP dispersions containing SPIONs and silica (SiO2)NPs as non‐magnetic building blocks are spray‐dried to form binary SPs. Selective salt‐induced agglomeration of the two building block types before spray‐drying is utilized to tailor SP architectures, including control over SPION cluster size, shape, and proximity. Magnetic particle spectroscopy (MPS), operating under ambient conditions, reveals altered magnetization behavior for different cluster structures. Not only the nearest SPION neighbors, but the whole cluster structure up to several micrometers is decisive for the magnetization behavior. This highlights the importance of long‐range magnetic interactions. This work presents a versatile approach for designing model architectures to advance empirical interaction studies between SPIONs in macroscopic samples.

Using an electrically charged mist to visualize the potential wells in “sonomaglev,” a combined diamagnetic-acoustic levitator

We use a water mist to experimentally visualize the wells in the potential energy of material levitated by a combined diamagnetic-acoustic levitator. The levitator consists of an 18.5 T superconducting magnet, which can levitate diamagnetic material, such as water, plastics, and organic materials, by applying a magnetic body force counteracting the force of gravity. Low-power ultrasound transducers operated at 37.5 kHz generate an acoustic field that spatially modulates the net force acting on the diamagnetically levitated material, making “sonomaglev” capable of levitating multiple objects in stable equilibrium. In these experiments, we levitate a mist of water droplets that are electrically charged so that they repel each other, preventing them from coalescing as a single drop in each of the local potential minima. The shapes of the potential wells are revealed by the shapes of clusters of droplets, which conform to the isosurfaces of the sum of the magnetic, gravitational, and acoustic potentials. The spacing of the droplets in a cluster is shown to depend on their charge, volume, and the force constant of the well in a simple model. Compared to acoustic levitation alone, the combination of diamagnetic and acoustic levitation allows more scope for the manipulation of levitated objects, since the acoustic field is not constrained by the requirement to balance the force of gravity. The method demonstrated here allows the influence on the potential energy of switching on the acoustic field to be observed directly.

Controlling the scatterplot shapes of 2D and 3D multidimensional projections

Multidimensional projections are effective techniques for depicting high-dimensional data. The point patterns created by such techniques, or a technique’s visual signature, depend — apart from the data themselves — on the technique design and its parameter settings. Controlling such visual signatures — something that only few projections allow — can bring additional freedom for generating insightful depictions of the data. We present a novel projection technique — ShaRP — that allows explicit control on such visual signatures in terms of shapes of similar-value point clusters (settable to rectangles, triangles, ellipses, and convex polygons) and the projection space (2D or 3D Euclidean or S2). We show that ShaRP scales computationally well with dimensionality and dataset size, provides its signature-control by a small set of parameters, allows trading off projection quality to signature enforcement, and can be used to generate decision maps to explore the behavior of trained machine-learning classifiers.

The early peak knee abduction moment waveform is a novel risk factor predicting anterior cruciate ligament injury in young athletes: A prospective study.

In this study, prospective data were used to evaluate whether the early peak knee abduction moment waveform is associated with the risk of anterior cruciate ligament (ACL) injury. Biomechanical data from 84 athletes who participated in the study as adolescents were analysed after cross-referencing national health registry data to confirm ACL reconstruction in the subsequent years. The knee abduction moment waveform shape was obtained with cluster analysis for the first 100 ms of a cutting manoeuvre (1776 trials in total) and classified as either containing an early peak knee abduction moment or not, and the odds ratio for later ACL injury was then calculated. Additionally, discrete kinematic and kinetic variables were extracted, and tested against the risk of ACL injury using mixed model logistic regression. Of 84 athletes, 8 (all female) sustained a total of 13 ACL injuries in the years after motion analysis data collection. Six clusters of knee abduction moment waveform shapes were identified. Two clusters containing 446 trials were classified as an early peak knee abduction waveform. This waveform was associated with a 7.2-fold increase in the risk of ACL injury (95% confidence interval: 2.4-24.6; p < 0.001). Of the kinematic and kinetic variables tested, only the knee abduction angle at initial contact was associated with an increased risk of ACL injury (p < 0.001). This is the first study to confirm the association between the early peak knee abduction moment waveform and the risk of ACL injury. Using waveforms, instead of discrete peak values of the knee abduction moment, may better represent risky movement patterns. Replicating these findings in a larger cohort will support the use of this method to screen athletes for risk and guide targeted preventive interventions and their efficacy. Level II.

An Insight into the Mechanical Properties of Unidirectional C/C Composites Considering the Effect of Pore Microstructures via Numerical Calculation.

Pores are common defects generated during fabrication, which restrict the application of carbon/carbon (C/C) composites. To quantitatively understand the effects of pores on mechanical strength, this paper proposes a representative volume element model of unidirectional (UD) C/C composites based on the finite element method. The Hashin criterion and exponential degraded rule are used as the failure initiation and evolution of pyrolytic carbon matrices, respectively. Interfacial zones are characterized using the cohesive constitutive. At the same time, periodic boundary conditions are employed to study transverse tensile, compressive, and shear deformations of UD C/C composites. Predicted results are compared with the experimental results, which shows that the proposed model can effectively simulate the transverse mechanical behaviors of UD C/C composites. Based on this model, the effects of microstructural parameters including porosity, pore locations, the distance between two pores, pore clustering, and pore shapes on the mechanical strength are investigated. The results show that porosity markedly reduces the strength as porosity increases. When the porosity increases from 4.59% to 12.5%, the transverse tensile, compressive, and shear strengths decrease by 35.91%, 37.52%, and 30.76%, respectively. Pore locations, the distance between two pores, and pore clustering have little effect on the shear strength of UD C/C composites. For pore shapes, irregular pores more easily lead to stress concentration and matrix failure, which greatly depresses the bearing capacity of UD C/C composites.

Enhanced Parameter Estimation of DENsity CLUstEring (DENCLUE) Using Differential Evolution

The task of finding natural groupings within a dataset exploiting proximity of samples is known as clustering, an unsupervised learning approach. Density-based clustering algorithms, which identify arbitrarily shaped clusters using spatial dimensions and neighbourhood aspects, are sensitive to the selection of parameters. For instance, DENsity CLUstEring (DENCLUE)—a density-based clustering algorithm—requires a trial-and-error approach to find suitable parameters for optimal clusters. Earlier attempts to automate the parameter estimation of DENCLUE have been highly dependent either on the choice of prior data distribution (which could vary across datasets) or by fixing one parameter (which might not be optimal) and learning other parameters. This article addresses this challenge by learning the parameters of DENCLUE through the differential evolution optimisation technique without prior data distribution assumptions. Experimental evaluation of the proposed approach demonstrated consistent performance across datasets (synthetic and real datasets) containing clusters of arbitrary shapes. The clustering performance was evaluated using clustering validation metrics (e.g., Silhouette Score, Davies–Bouldin Index and Adjusted Rand Index) as well as qualitative visual analysis when compared with other density-based clustering algorithms, such as DPC, which is based on weighted local density sequences and nearest neighbour assignments (DPCSA) and Variable KDE-based DENCLUE (VDENCLUE).

Insurance Analytics with Clustering Techniques

The K-means algorithm and its variants are well-known clustering techniques. In actuarial applications, these partitioning methods can identify clusters of policies with similar attributes. The resulting partitions provide an actuarial framework for creating maps of dominant risks and unsupervised pricing grids. This research article aims to adapt well-established clustering methods to complex insurance datasets containing both categorical and numerical variables. To achieve this, we propose a novel approach based on Burt distance. We begin by reviewing the K-means algorithm to establish the foundation for our Burt distance-based framework. Next, we extend the scope of application of the mini-batch and fuzzy K-means variants to heterogeneous insurance data. Additionally, we adapt spectral clustering, a technique based on graph theory that accommodates non-convex cluster shapes. To mitigate the computational complexity associated with spectral clustering’s O(n3) runtime, we introduce a data reduction method for large-scale datasets using our Burt distance-based approach.

Gaia DR3 reveals the complex dynamical evolution within star clusters

Context. Star clusters, composed of stars born from the same molecular cloud, serve as invaluable natural laboratories for understanding the fundamental processes governing stellar formation and evolution. Aims. This study aims to investigate correlations between the Mean Interdistance ($ \bar{D_{\mathrm{i}}} $), Mean Closest Interdistance ($ \bar{D_{\mathrm{c}}} $) and Median Weighted Central Interdistance ($ \bar{D_{\mathrm{cc}}} $) with the age of star clusters, examining their evolutionary trends and assessing the robustness of these quantities as possible age indicators. Methods. We selected a sample of open clusters in the solar region and with a representative number of members (e.g. well populated and without outliers). The interdistances are derived from the spatial distribution of member stars within a cluster. Their evolution over time allows us to use them as age indicators for star clusters. Results. Our investigation reveals a high-significant correlation between the interdistances and cluster age. Considering the full sample of clusters between 7 and 9 kpc, the relationship is very broad. This is due to uncertainties in parallax, which increase with increasing distance. In particular, we must limit the sample to a maximum distance from the Sun of about 200 pc to avoid artificial effects on cluster shape and on the spatial distribution of their stars along the line of sight. Conclusions. By conservatively restraining the distance to a maximum of ∼200 pc, we have established a relationship between the interdistances and the age of the clusters. In our sample, the relationship is mainly driven by the internal expansion of the clusters and is marginally affected by external perturbative effects. Such relation might enhance our comprehension of cluster dynamics and might be used to derive cluster dynamical ages.

Relation between the geometric shape and rotation of Galactic globular clusters

We homogeneously measured the elliptical shapes of 163 globular clusters (GCs) using the on-sky distribution of their cluster members and the third data release of the ESA mission Gaia (DR3). The astrometry enables the differentiation of stars within clusters from those in the field. This feature is particularly valuable for clusters located in densely populated areas of the sky, where conventional methods for measuring the geometry of the GCs are not applicable. The median axial ratio of our full sample is 〈b/a〉 = 0.935−0.090+0.033 and 0.986−0.004+0.009 for the subset of 11 GCs previously studied based on Hubble Space Telescope imaging. We investigated whether the minor axis of the ellipses can be interpreted as a pseudo-rotation axis by comparing it to measurements of cluster rotation. Using the radial velocities from Gaia, we detected rotation for three clusters, NGC 5139, NGC 104, and NGC 6341, and observed an alignment between the pseudo-rotation axis and the 2D projection of the real rotation axis. To expand the set of clusters for which rotation has been detected, we analyzed multiple literature references. Depending on the reference used for comparison, we observed an alignment in between 76% to 100% of the clusters. The lack of an alignment observed in some clusters may be linked to different scales analyzed in various studies. Several studies have demonstrated that the orientation of rotation varies with the distance from the center. We estimate that the next Gaia release will increase the number of stars with radial velocities in GCs from ~10 000 in Gaia DR3 to ~55 000 in Gaia DR4. This will enable the measurement of rotation and ellipticities at identical angular scales for additional clusters, which will help us to clarify whether the previously mentioned alignment occurs in all clusters.