Formation Of Clusters Research Articles

Influence of hydrogen bonds on state diagrams of cryoprotectant solutions

BACKGROUND: Transformation of state diagrams of cryoprotectant solutions under the influence of weak intramolecular interactions was considered. MATERIALS AND METHODS: Phase states of aqueous glycerol and DMSO solutions within temperature range +25???−150 °?? were studied using method of volumetric scanning tensodilatometry. Temperatures below which hydrogen bonds significantly affect crystallization-melting kinetics of such solutions were determined. RESULTS: Principles for plotting of state diagram for binary solutions with weak intermolecular interaction of the components were set up. The study demonstrates that in such solutions formation of clusters based on ice microcrystals and cryoprotectant occurs. Based on the obtained results, state diagrams for glycerol and DMSO aqueous solutions were plotted. These diagrams include area of cluster phase existence and differ fundamentally from those describing eutectic crystallization. CONCLUSION: Nanostructures occurring in cryoprotectant solutions during their cooling were analyzed. Difference between these structures and classical solid phase eutectics were demonstrated.

A Two-Pronged Delivery Strategy Disrupting Positive Feedback Loop of Neutrophil Extracellular Traps for Metastasis Suppression.

Neutrophil extracellular traps (NETs) severely affect tumor metastasis through a self-perpetuating feedback loop involving two key steps: (1) mitochondrial aerobic respiration-induced hypoxia promotes NET formation and (2) NETs enhance mitochondrial metabolism to exacerbate hypoxia. Herein, we propose a two-pronged approach with the activity of NET-degrading and mitochondrion-damaging by simultaneously targeting drugs to NETs and tumor mitochondria of this loop. In addition to specifically recognizing and eliminating extant NETs, the NET-targeting nanoparticle also reduces NET-induced mitochondrial biogenesis, thus inhibiting the initial step of the feedback loop and mitigating extant NETs' impact on tumor metastasis. Simultaneously, the mitochondrion-targeting system intercepts mitochondrial metabolism and alleviates tumor hypoxia, inhibiting neutrophil infiltration and subsequent NET formation, which reduces the source of NETs and disrupts another step of the self-amplifying feedback loop. Together, the combination significantly reduces the formation of NET-tumor cell clusters by disrupting the interaction between NETs and tumor mitochondria, thereby impeding the metastatic cascade including tumor invasion, hematogenous spread, and distant colonization. This work represents an innovative attempt to disrupt the feedback loop in tumor metastasis, offering a promising therapeutic approach restraining NET-assisted metastasis.

RhRu Bimetallic Oxide Cluster Catalysts for Cross-Dehydrogenative Coupling of Arenes and Carboxylic Acids.

Noble-metal-based bimetallic oxide clusters are promising novel catalysts. In this study, we developed carbon-supported RhRu bimetallic oxide clusters (RhRuOx/C) with a mean diameter of 1.2 nm, which showed remarkable catalytic activity for the cross-dehydrogenative coupling (CDC) of arenes and carboxylic acids with O2 as the sole oxidant. RhRu bimetallic oxide cluster formation was confirmed by aberration-corrected high-angle annular dark-field scanning transmission electron microscopy with energy-dispersive X-ray spectroscopy and synchrotron X-ray absorption spectroscopy. Kinetic isotope and substituent effects indicated that arene C-H bond cleavage was the rate-determining step and proceeded via electrophilic concerted metalation-deprotonation mechanism, with a carboxylate as an internal base. Density functional theory calculations supported the proposed mechanism and indicated that the active center for C-H bond activation was Rh(V) rather than Rh(III), while Ru enhanced the electrophilicity of the Rh(V) site by decreasing the negative charge of the surrounding oxygen atoms. Electron-rich arenes showed relatively high reactivity for the RhRuOx/C-catalyzed CDC reaction, and both aliphatic and aromatic carboxylic acids were applicable to the reaction. The RhRuOx/C catalyst is promising for the CDC reaction of arenes and carboxylic acids to produce aryl esters. This work promotes the development of noble-metal-based bimetallic oxide clusters for C-H bond activation reactions.

A cluster-of-functional-groups approach for studying organic enhanced atmospheric cluster formation

Abstract. The role of organic compounds in atmospheric new particle formation is difficult to disentangle due to the myriad of potentially important oxygenated organic molecules (OOMs) present in the atmosphere. Using state-of-the-art quantum chemical methods, we here employ a novel approach, denoted the “cluster-of-functional-groups” approach, for studying the involvement of OOMs in atmospheric cluster formation. Instead of the usual “trial-and-error” approach of testing the ability of experimentally identified OOMs to form stable clusters with other nucleation precursors, we here study which, and how many, intermolecular interactions are required in a given OOM to form stable clusters. In this manner we can reverse engineer the elusive structure of OOM candidates that might be involved in organic enhanced atmospheric cluster formation. We calculated the binding free energies of all combinations of donor and acceptor organic functional groups to investigate which functional groups most preferentially bind with each other and with other nucleation precursors such as sulfuric acid and bases (ammonia, methyl-, dimethyl- and trimethylamine). We find that multiple carboxyl groups lead to substantially more stable clusters compared to all other combinations of functional groups. Employing cluster dynamics simulations, we investigate how a hypothetically OOM composed of multiple carboxyl groups can stabilize sulfuric acid–base clusters and provide recommendations for potential atmospheric multi-carboxylic acid tracer compounds that should be explicitly studied in the future. The presented “cluster-of-functional-groups” approach is generally applicable and can be employed in many other applications, such as ion-induced nucleation and potentially in elucidating the structural patterns in molecules that facilitate ice nucleation.

Energy-Efficient Secure Routing for a Sustainable Heterogeneous IoT Network Management

The Heterogeneous Internet of Things (H-IoT) is considered as the upcoming industrial and academic revolution in the technological world, having billions of things and devices connected to the Internet. This H-IoT has a major issue of energy consumption during data transmission which leads to low scalability. Additionally, anomalies in the data create a serious threat to energy in H-IoT. To overcome these issues, a novel approach has been proposed in this study termed as the Energy-Efficient Memetic Clustering Method (EEMCM), which combines the Parallelized Memetic Algorithm (PMA) with the AlexNet architecture to improve anomaly detection efficiency in IoT WSNs. Initially, cluster formation and CH selection are carried out using PMA. This is followed by routing path generation, and the data are prepared for high-level feature extraction. The extracted features are classified to identify anomalies. For anomaly detection, high-level features were collected that contain data relevant to the model given as input into the AlexNet architecture, which detects anomalies and identifies normal or potential attacks within the IoT WSNs. The proposed EEMCM model has been implemented in the MATLAB platform and obtained an accuracy of 99.11%. As a result, the overall performance of the network is improved.

Chromosome-level genome assemblies of 2 hemichordates provide new insights into deuterostome origin and chromosome evolution.

Deuterostomes are a monophyletic group of animals that includes Hemichordata, Echinodermata (together called Ambulacraria), and Chordata. The diversity of deuterostome body plans has made it challenging to reconstruct their ancestral condition and to decipher the genetic changes that drove the diversification of deuterostome lineages. Here, we generate chromosome-level genome assemblies of 2 hemichordate species, Ptychodera flava and Schizocardium californicum, and use comparative genomic approaches to infer the chromosomal architecture of the deuterostome common ancestor and delineate lineage-specific chromosomal modifications. We show that hemichordate chromosomes (1N = 23) exhibit remarkable chromosome-scale macrosynteny when compared to other deuterostomes and can be derived from 24 deuterostome ancestral linkage groups (ALGs). These deuterostome ALGs in turn match previously inferred bilaterian ALGs, consistent with a relatively short transition from the last common bilaterian ancestor to the origin of deuterostomes. Based on this deuterostome ALG complement, we deduced chromosomal rearrangement events that occurred in different lineages. For example, a fusion-with-mixing event produced an Ambulacraria-specific ALG that subsequently split into 2 chromosomes in extant hemichordates, while this homologous ALG further fused with another chromosome in sea urchins. Orthologous genes distributed in these rearranged chromosomes are enriched for functions in various developmental processes. We found that the deeply conserved Hox clusters are located in highly rearranged chromosomes and that maintenance of the clusters are likely due to lower densities of transposable elements within the clusters. We also provide evidence that the deuterostome-specific pharyngeal gene cluster was established via the combination of 3 pre-assembled microsyntenic blocks. We suggest that since chromosomal rearrangement events and formation of new gene clusters may change the regulatory controls of developmental genes, these events may have contributed to the evolution of diverse body plans among deuterostomes.

Complex organic molecules uncover deeply embedded precursors of hot cores

Context. During the process of star formation, the dense gas undergoes significant chemical evolution leading to the emergence of a rich variety of molecules associated with hot cores and hot corinos. However, the physical conditions and the chemical processes involved in this evolution are poorly constrained. In particular, the early phases, corresponding to a stage prior to the emergence of any strong ionising emission from the protostar, are still poorly studied. Aims. In this work, we provide a full inventory of the emission from complex organic molecules (COMs) to investigate the physical structure and chemical composition of six high-mass protostellar envelopes. We aim to investigate the conditions for the emergence of COMs in hot cores. Methods. We performed an unbiased spectral survey towards six infrared-quiet massive clumps between 159 GHz and 374 GHz with the APEX 12 m telescope, covering the entire atmospheric windows at 2 mm, 1.2 mm, and 0.8 mm. To identify the spectral lines, we used rotational diagrams and radiative transfer modelling assuming local thermodynamic equilibrium. Results. We detect up to 11 COMs plus three isotopologues, of which at least five COMs (CH3OH, CH3CN, CH3OCHO, CH3OCH3, and CH3CHO) are detected towards all sources. Towards all the objects, most of the COM emission is found to be cold, with respect to the typical temperatures at which COMs are found, with a temperature of 30 K and extended with a size of ~0.3 pc. Although the bulk of the gas for our sample of young massive clumps has a cold temperature, we also detect emission from COMs originating from the immediate vicinity of the protostar. This warm component of the envelope is best traced by methanol and methyl cyanide, in particular methyl cyanide traces a compact (~1″) and the hottest (T ~200 K) component of the envelope. Only three out of the six sources exhibit a robustly detected hot gas component (T > 100 K) traced by several COMs. We find a gradual emergence of the warm component in terms of size and temperature, together with an increasing molecular complexity, allowing us to establish an evolutionary sequence for our sample based on COMs. While they can already be well characterised by an emerging molecular richness, gas temperatures of COMs in the hot gas and molecular abundances suggest that COMs may become abundant in the gas phase at temperatures below the thermal desorption temperature. Conclusions. Our findings confirm that the sources of our sample of infrared-quiet massive clumps are in an early evolutionary stage during which the bulk of the gas is cold. The presence of COMs is found to be characteristic of these early evolutionary stages accompanying high-mass star and cluster formation. While the extent of the compact heated regions resembles that of hot cores, the molecular abundances, except for complex cyanides, resemble those of hot corinos and are lower than the peak COM abundances of hot cores. We suggest that the emergence of hot cores is preceded by a phase in which mostly O-bearing COMs appear first with similar abundances to hot corinos albeit with larger source sizes.

Great Balls of FIRE

Context. Despite the nearly hundred gravitational-wave detections reported by the LIGO-Virgo-KAGRA Collaboration, the question of the cosmological origin of merging binary black holes (BBHs) remains open. The two main formation channels generally considered are from isolated field binaries or via dynamical assembly in dense star clusters. Aims. Here we focus on understanding the dynamical formation of merging BBHs within massive clusters in galaxies of different masses. Methods. To this end, we applied a new framework to consistently model the formation and evolution of massive star clusters in zoom-in cosmological simulations of galaxies. Each simulation, taken from the FIRE project, provides a realistic star formation environment, with a unique star formation history, that hosts realistic giant molecular clouds that constitute the birthplace of star clusters. Combined with the code for star cluster evolution CMC, we are able to produce populations of dynamically formed merging BBHs across cosmic time in different environments. Results. As the most massive star clusters preferentially form in dense massive clouds of gas, we find that, despite their low metallicities favouring the creation of black holes, low-mass galaxies contain few massive clusters and therefore make a limited contribution to the global production of dynamically formed merging BBHs. Furthermore, we find that massive clusters can host hierarchical BBH mergers with clear, identifiable physical properties. Looking at the evolution of the BBH merger rate in different galaxies, we find strong correlations between BBH mergers and the most extreme episodes of star formation. Finally, we discuss the implications for future LIGO-Virgo-KAGRA gravitational wave observations.

Simulations predict intermediate-mass black hole formation in globular clusters.

Intermediate-mass black holes (IMBHs) are those between 100 and 105 solar masses (M⨀); their formation process is debated. One potential origin is the growth of less massive black holes, by merging with stars and compact objects within globular clusters (GCs). However, previous simulations have indicated that this process only produces IMBHs <500 M⨀, before gravitational wave recoil ejects them from the GC. We perform star-by-star simulations of GC formation, finding that high-density star formation in a GC's parent giant molecular cloud can produce sufficient mergers of massive stars to overcome that mass threshold. We conclude that GCs can form with IMBHs ≳103M⨀, which is sufficiently massive to be retained within the GC even with the expected gravitational wave recoil.

Emergent Synchronous Volumetric Oscillation in Hierarchically Structured Self-Oscillating Gel Clusters.

Emergent properties accompanying synchronization among oscillators are vital characteristics in biological systems. Belousov-Zhabotinsky (BZ) oscillators are an artificial model to study the emergence and synchronization in life. This research represents a self-oscillating gel system with clusterable properties to experimentally examine synchronous and emergent properties at a fundamental hierarchical level. Incorporating acrylic acid (AAc) moieties within the gel network facilitates cluster formation through hydrogen bonding in an acidic BZ substrate solution. Upon clustering, both homogeneous and heterogeneous gel assemblies─ranging from double to quadruple clusters─exhibit increased and synchronized periods and amplitudes during the BZ reaction. Notably, in heterogeneous clusters, gel units with initially short periods and small volumetric amplitudes display a significant increase, aligning with the lonfger periods and larger amplitudes of other elements within the cluster, an emergent property. This research can pave the way for a better understanding of synchronous and emergent properties in biological oscillators such as cardiomyocytes.

Kinematics and Star Formation in the Hub–Filament System G6.55-0.1

Hub–filament systems (HFSs) being the potential sites of formation of star clusters and high-mass stars, provide a testbed for the current theories that attempt to explain star formation globally. It is thus important to study a large number of HFSs using both intensity and velocity information to constrain these objects better observationally. Here, we present a study of the HFS associated with G6.55-0.1 using newly obtained observations of the radio continuum and the J = 2–1 transition of CO, 13CO, and C18O. The radio continuum maps show multiple peaks that coincide with far-infrared dust continuum peaks, indicating the presence of more than one young massive star in the hub of the HFS. We used the velocity information from the C18O(2–1) map to (a) show that the source G6.55-0.1 is not physically associated with the supernova remnant W28 and (b) disentangle and identify the velocity components genuinely associated with G6.55-0.1. Among the velocity-coherent structures identified in the region, we conclude that only the two filaments at 13.8 and 17.3 km s−1 contribute a total mass accretion rate of 3000 M ⊙ Myr−1 to the hub. Both the filaments also show a V-shaped structure, characteristic of gravitational collapse, in their velocity profile at the location of the hub. The estimated mass per unit length of the segments of the filaments is smaller than the critical line masses derived from virial equilibrium considerations. This suggests that the filaments are not gravitationally collapsing as a whole, although their inner parts clearly show evidence of collapse in the form of young star-forming cores. We further conclude that the observed velocity gradients are consistent with the gravitational collapse of the main source in the region as estimated from its mass and size.

Polarized Light from Massive Protoclusters (POLIMAP). I. Dissecting the Role of Magnetic Fields in the Massive Infrared Dark Cloud G28.37+0.07

Magnetic fields may play a crucial role in setting the initial conditions of massive star and star cluster formation. To investigate this, we report SOFIA-HAWC+ 214 μm observations of polarized thermal dust emission and high-resolution GBT-Argus C18O(1-0) observations toward the massive Infrared Dark Cloud (IRDC) G28.37+0.07. Considering the local dispersion of B-field orientations, we produce a map of the B-field strength of the IRDC, which exhibits values between ∼0.03 and 1 mG based on a refined Davis–Chandrasekhar–Fermi method proposed by Skalidis & Tassis. Comparing to a map of inferred density, the IRDC exhibits a B–n relation with a power-law index of 0.51 ± 0.02, which is consistent with a scenario of magnetically regulated anisotropic collapse. Consideration of the mass-to-flux ratio map indicates that magnetic fields are dynamically important in most regions of the IRDC. A virial analysis of a sample of massive, dense cores in the IRDC, including evaluation of magnetic and kinetic internal and surface terms, indicates consistency with virial equilibrium, sub-Alfvénic conditions, and a dominant role for B-fields in regulating collapse. A clear alignment of magnetic field morphology with the direction of the steepest column density gradient is also detected. However, there is no preferred orientation of protostellar outflow directions with the B-field. Overall, these results indicate that magnetic fields play a crucial role in regulating massive star and star cluster formation, and therefore they need to be accounted for in theoretical models of these processes.

Sex differences in entrapment in a multinational sample: a network analysis perspective.

The concept of entrapment has been highlighted as a transdiagnostic element that manifests itself in disorders such as depression, anxiety, and suicidal ideation. Although research has been conducted in different contexts independently, a comprehensive multi-country study to assess gender differences in entrapment through network analysis has not yet been carried out. The objective of this study was to evaluate the entrapment network in men and women at the multinational level. A sample of 2,949 participants, ranging in age from 18 to 73 years from six countries (Germany, Iran, Spain, Slovakia, El Salvador, and Peru), was considered. They completed the entrapment scale. A network analysis was performed for both men and women to identify the connectivity between indicators and the formation of clusters and domains, in addition to the centrality assessment in both sex groups. The study findings revealed the presence of a third domain focused on external interpersonal entrapment in the network of men and women. However, in relation to the interconnectivity between domains, variations were evidenced in both networks, as well as in centrality, it was reported that men present a greater generalized entrapment in various aspects of life, while women tend to experience a more focused entrapment in expressions of intense emotional charge. The multinational study identified variations in the structure of entrapment between genders, with three domains (internal, external, and external-interpersonal) and differences in the interaction of indicators and groupings, as well as discrepancies in centrality.

Hidden Gems on a Ring: Infant Massive Clusters and Their Formation Timeline Unveiled by ALMA, HST, and JWST in NGC 3351

We use 0.1″ observations from the Atacama Large Millimeter Array (ALMA), Hubble Space Telescope (HST), and JWST to study young massive clusters (YMCs) in their embedded “infant” phase across the central starburst ring in NGC 3351. Our new ALMA data reveal 18 bright and compact (sub-)millimeter continuum sources, of which 8 have counterparts in JWST images and only 6 have counterparts in HST images. Based on the ALMA continuum and molecular line data, as well as ancillary measurements for the HST and JWST counterparts, we identify 14 sources as infant star clusters with high stellar and/or gas masses (∼105 M ⊙), small radii (≲ 5 pc), large escape velocities (6–10 km s−1), and short freefall times (0.5–1 Myr). Their multiwavelength properties motivate us to divide them into four categories, likely corresponding to four evolutionary stages from starless clumps to exposed H ii region–cluster complexes. Leveraging age estimates for HST-identified clusters in the same region, we infer an evolutionary timeline, ranging from ∼1–2 Myr before cluster formation as starless clumps, to ∼4–6 Myr after as exposed H ii region–cluster complexes. Finally, we show that the YMCs make up a substantial fraction of recent star formation across the ring, exhibit a nonuniform azimuthal distribution without a very coherent evolutionary trend along the ring, and are capable of driving large-scale gas outflows.

JWST’s First Glimpse of a z > 2 Forming Cluster Reveals a Top-heavy Stellar Mass Function

Clusters and their progenitors (protoclusters) at z ∼ 2 − 4, the peak epoch of star formation, are ideal laboratories to study the formation process of both the clusters themselves and their member galaxies. However, a complete census of their member galaxies has been challenging due to observational difficulties. Here we present new JWST/NIRCam observations targeting the distant cluster CLJ1001 at z = 2.51 from the COSMOS-Web program, which, in combination with previous narrowband imaging targeting Hα emitters and deep millimeter surveys of CO emitters, provide a complete view of massive galaxy assembly in CLJ1001. In particular, JWST reveals a population of massive, extremely red cluster members in the long-wavelength bands that were invisible in previous Hubble Space Telescope (HST)/F160W imaging (HST-dark members). Based on this highly complete spectroscopic sample of member galaxies, we show that the spatial distribution of galaxies in CLJ1001 exhibits a strong central concentration, with the central galaxy density already resembling that of low-z clusters. Moreover, we reveal a “top-heavy” stellar mass function for the star-forming galaxies (SFGs), with an overabundance of massive SFGs piled up in the cluster core. These features strongly suggest that CLJ1001 is caught in a rapid transition, with many of its massive SFGs likely soon becoming quiescent. In the context of cluster formation, these findings suggest that the earliest clusters form from the inside out and top to bottom, with the massive galaxies in the core assembling first, followed by the less massive ones in the outskirts.

Role of carbon substitutional and vacancy in tailoring the H2 adsorption energy over a hexagonal boron nitride monolayer: an ab initio study

The effect of the substitutional and vacancy type defects on the H2 adsorption energy over a monolayer hexagonal boron nitride (h-BN) substrate has been studied by using the van der Waals density functional theory calculations. Carbon doping at the boron site or formation of boron vacancy can be an effective way to increase the adsorption energy value of a pristine h-BN substrate. The repulsive lateral interaction present in between the two H2 molecules plays a vital role in case of multiple H2 molecule adsorption over the substrate. Also, the carbon cluster formation during doping can have a favorable effect in the overall storage capacity of the h-BN substrate.

Atomistic insights into argon clusters and nucleation dynamics

Accurate predictions of nucleation and atomic-level estimates of cluster properties in gas-phase chemical physics have proven challenging. These challenges arise from two primary sources: finite-size effects associated with nanoscopic particles and the emergence of non-standard thermodynamics, particularly at elevated temperatures. This study reexamines the formation of argon clusters using established methodologies such as atomistic simulations, configurational sampling, and statistical thermochemistry. To enhance the representation of condensed-phase argon, we employ an ab initio-based two-body potential, complemented by a three-body Axilrod–Teller potential. Additionally, we address the impact of anharmonicities on cluster stabilities using a recently developed extension to the standard statistical cluster model. The employed anharmonic model is rigorously benchmarked against molecular dynamics simulations. The subsequent analysis demonstrates a robust and consistent agreement between our model and experimental data. Our analysis covers nearly every experimental data point collected between 1971 and 2010, offering valuable insights into the predictive capabilities of the model. Moreover, in contrast to previous studies, our findings indicate that individual measurements are consistently in alignment with each other.

Influence of a Preageing Treatment on the Cluster Formation and the Further Ageing Route in Al–Mg–Si Extrusion Alloys

Herein, the influence of one‐ and two‐step preageing treatments prior to the artificial ageing step to peak age condition for three different 6xxx alloys, from low to high alloy content, is investigated. Analysis of the preaged conditions using atom probe tomography (APT) reveals a broad distribution of Mg and Si clusters, with some instances of Guinier‐Preston I zones present. Additionally, the high alloyed system exhibits a growth of precipitates toward a needle‐like shaped. These clusters formed during the preageing treatment serve as nucleation sites in the subsequent artificial ageing treatment, leading to an increase in hardness. Microstructural analysis conducted using transmission electron microscopy and APT demonstrates a reduction in the average precipitate length and a more narrow size distribution for T6 condition. This indicates that the preageing treatment results in a decreased portion of already overaged precipitates compared to the direct aged condition. Consequently, the more narrow size distribution of the precipitates leads to more effective hardening of the material, as a higher portion of precipitates is at or close to their optimum size. The investigations highlight the significant influence and positive effect of a preageing treatment at lower temperatures on the subsequent artificial ageing treatment.

Specific surface area of mannitol rather than particle size dominant the dissolution rate of poorly water-soluble drug tablets: A study of binary mixture

The dissolution behavior of tablets, particularly those containing poorly water-soluble drugs, is a critical factor in determining their absorption and therapeutic efficacy. Traditionally, the particle size of excipients has been considered a key property affecting tablet dissolution. However, lurasidone hydrochloride (LH) tablets prepared by similar particle size mannitol, namely M200 (D90 = 209.68 ± 1.42 μm) and 160C (D90 = 195.38 ± 6.87 μm), exhibiting significant differences in their dissolution behavior. In order to find the fundamental influential factors of mannitol influencing the dissolution of LH tablets, the properties (particle size, water content, true density, bulk density, tapped density, specific surface area, circularity, surface free energy, mechanical properties and flowability) of five grades mannitol including M200 and 160C were investigated. Principal component analysis (PCA) was used to establish a relationship between mannitol properties and the dissolution behavior of LH. The results demonstrated that specific surface area (SSA) emerged as the key property influencing the dissolution of LH tablets. Moreover, our investigation based on the percolation theory provided further insights that the SSA of mannitol influences the probability of LH-LH bonding and LH infinite cluster formation, resulting in the different percolation threshold states, then led to different dissolution behaviors. Importantly, it is worth noting that these findings do not invalidate previous conclusions, as reducing particle size generally increases SSA, thereby affecting the percolation threshold and dissolution behavior of LH. Instead, this study provides a deeper understanding of the underlying role played by excipient SSA in the dissolution of drug tablets. This study provides valuable guidance for the development of novel excipients aimed at improving drug dissolution functionality.

PROVINCIAL CLUSTERING BASED ON EDUCATION INDICATORS: K-MEDOIDS APPLICATION AND K-MEDOIDS OUTLIER HANDLING

K-Medoids is a clustering algorithm that is often used because of its robustness against outliers. In this research, the focus is to cluster provinces based on educational level through several assessment indicators. This is in line with improving the quality of education in point 4 of the National Sustainable Development Goals (SDGs), namely "Quality Education". One of the points of the National Sustainable Development Goals (SDGs) that will still be improved is "Quality Education" which is the 4th point. This is because the success of a country is determined by the quality of good education. The condition of education in Indonesia still overlaps, so it is necessary to do equal distribution of education through clustering. The purpose of this research is to provide the best cluster results according to the Silhouette Index, which then the results of the clustering can be used as a consideration for advancing education in areas that still need attention, through policies or programs that can be developed by educational observers. This research was conducted in 34 provinces in Indonesia. The data source is from Statistical Publications by BPS RI. The method used is K-Medoids, because in this study there were outliers found. In addition to natural K-Medoids, the researcher also wants to compare methods by implementing K-Medoids with outlier handling in the form of imputed mean values and K-Medoids with imputed min-max values. The Silhouette Index results and cluster formation for the three comparators were 0.24 with 2 clusters, 0.26 with 8 clusters and 0.25 with 9 clusters, respectively. What differentiates this research from previous research is the type of outlier handling. Generally, K-Medoids are very indifferent to the existence of outliers. K-medoids is a widely recognized and straightforward clustering approach. Nevertheless, the algorithm's effectiveness might occasionally decline as a result of local outliers and the random selection of beginning medoids