Types Of Clusters Research Articles

Exploring meta-heuristics for partitional clustering: methods, metrics, datasets, and challenges

Partitional clustering is a type of clustering that can organize the data into non-overlapping groups or clusters. This technique has diverse applications across the different various domains like image processing, pattern recognition, data mining, rule-based systems, customer segmentation, image segmentation, and anomaly detection, etc. Hence, this survey aims to identify the key concepts and approaches in partitional clustering. Further, it also highlights its widespread applicability including major advantages and challenges. Partitional clustering faces challenges like selecting the optimal number of clusters, local optima, sensitivity to initial centroids, etc. Therefore, this survey describes the clustering problems as partitional clustering, dynamic clustering, automatic clustering, and fuzzy clustering. The objective of this survey is to identify the meta-heuristic algorithms for the aforementioned clustering. Further, the meta-heuristic algorithms are also categorised into simple meta-heuristic algorithms, improved meta-heuristic algorithms, and hybrid meta-heuristic algorithms. Hence, this work also focuses on the adoption of new meta-heuristic algorithms, improving existing methods and novel techniques that enhance clustering performance and robustness, making partitional clustering a critical tool for data analysis and machine learning. This survey also highlights the different objective functions and benchmark datasets adopted for measuring the effectiveness of clustering algorithms. Before the literature survey, several research questions are formulated to ensure the effectiveness and efficiency of the survey such as what are the various meta-heuristic techniques available for clustering problems? How to handle automatic data clustering? What are the main reasons for hybridizing clustering algorithms? The survey identifies shortcomings associated with existing algorithms and clustering problems and highlights the active area of research in the clustering field to overcome these limitations and improve performance.

Zol & fai: large-scale targeted detection and evolutionary investigation of gene clusters.

Many universally and conditionally important genes are genomically aggregated within clusters. Here, we introduce fai and zol, which together enable large-scale comparative analysis of different types of gene clusters and mobile-genetic elements (MGEs), such as biosynthetic gene clusters (BGCs) or viruses. Fundamentally, they overcome a current bottleneck to reliably perform comprehensive orthology inference at large scale across broad taxonomic contexts and thousands of genomes. First, fai allows the identification of orthologous instances of a query gene cluster of interest amongst a database of target genomes. Subsequently, zol enables reliable, context-specific inference of ortholog groups for individual protein-encoding genes across gene cluster instances. In addition, zol performs functional annotation and computes a variety of evolutionary statistics for each inferred ortholog group. Importantly, in comparison to tools for visual exploration of homologous relationships between gene clusters, zol can scale to thousands of gene cluster instances and produce detailed reports that are easy to digest. To showcase fai and zol, we apply them for: (i) longitudinal tracking of a virus in metagenomes, (ii) discovering novel population-level genetic insights of two common BGCs in the fungal species Aspergillus flavus, and (iii) uncovering large-scale evolutionary trends of a virulence-associated gene cluster across thousands of genomes from a diverse bacterial genus.

Pollution Characterization and Source Apportionment of Volatile Organic Compounds and Their Odor-causing Species in Industrial Parks

To improve the phenomenon of the volatile organic compounds （VOCs） odor pollution nuisance in industrial parks and to promote the synergistic control of atmospheric VOCs and their odor-causing substances, based on the field observation of atmospheric VOCs in residential living areas and five different types of industrial clusters in industrial parks, we analyzed the pollution characteristics of atmospheric VOCs and their odor-causing volatile organic compounds （O-VOCs） in the residential living areas and each industrial cluster, evaluated the characteristics of the odor activity of the O-VOCs in the industrial parks, and identified the key odor-causing species and their main sources. The results showed that the mean values of atmospheric φ （TVOCs） and φ（O-VOCs） in the residential living area of the industrial park were 102.57×10-9 and 72.33×10-9, respectively. φ（TVOCs） and φ（O-VOCs） were significantly higher in the industrial clusters of basic chemical industry and pharmaceutics than in the other industrial clusters, and the sum （OAVsum） and maximum （OAVmax） of the odor activity values of these two clusters were relatively high, with a potential risk of odor nuisance. Overall, the O-VOCs species with higher odor intensity were similar in residential living areas and the five industrial clusters, and effective control of O-VOCs species such as acrolein, p-diethylbenzene, p-xylene, and 1,3-diethylbenzene is essential to mitigate or eliminate organic odor pollution. The results of the source apportionment of O-VOCs in the residential area showed that the sources of O-VOCs in the residential area were mainly influenced by natural gas chemical and pharmaceutics, and the coefficients of divergence （CDO-VOCs） between the O-VOC chemical profiles from residential areas and those from natural gas chemical and pharmaceutics were 0.31 and 0.38, respectively. Principal component analysis （PCA） also confirmed this result, with residential O-VOCs mainly originating from natural gas chemicals and pharmaceutics, followed by iron and steel manufacturing and automobile manufacturing, with the lowest contribution from the basic chemicals.

The spatiotemporal patterns and regional characteristics of extreme heat disaster risk in China at the county level

Under the compound effect of continuous global warming and rapid urbanization, China is experiencing extreme heat events with increased intensity, frequency, and duration, which pose a significant threat to human society. Nonetheless, research on the spatiotemporal patterns and regional characteristics of extreme heat disaster risk (EHDR) at the county level in China remains scarce. To address this gap, we have developed an analytical framework for extreme heat disaster systems and an evaluation system for EHDR indicators. This framework measures the extent of EHDR and examines the dominant subsystems and their transformation processes across different regions. The results show that: (1) The spatial clustering types of EHDR in China's counties are mainly "High-High" and "Low-Low", forming a significant northeast-southwest low-value belt and a northwest-southeast high-value center; (2) In China, 91.49% of counties exhibited an increasing trend in EHDR from 2000 to 2018, while the counties experiencing reduced disaster risk are predominantly located in northern China; (3) The average values of EHDR and its subsystems are significantly higher in the Northwest and the Middle and Lower reaches of the Yangtze River compared to other regions, establishing these areas as high-value clusters; (4) The transformation of dominant subsystems across regions reveals significant geographic differences. In Western China, the environment predominates; in the northern regions, environment-exposure is dominant; and in the southern regions, the hazard is the primary factor. Notably, the causes of disaster risk in the Middle reaches of the Yellow River and the Lower reaches of the Yangtze River are more complex. These findings enhance the understanding of EHDR dynamics within the framework of rapid urbanization and climate change.

Exploring the Diversity and Specificity of Secondary Biosynthetic Potential in Rhodococcus.

The actinomycete genus Rhodococcus is known for its diverse biosynthetic enzymes, with potential in pollutant degradation, chemical biocatalysis, and natural product exploration. Comparative genomics have analyzed the distribution patterns of non-ribosomal peptide synthetases (NRPSs) in Rhodococcus. The diversity and specificity of its secondary metabolism offer valuable insights for exploring natural products, yet remain understudied. In the present study, we analyzed the distribution patterns of biosynthetic gene clusters (BGCs) in the most comprehensive Rhodococcus genome data to date. The results show that 86.5% of the gene cluster families (GCFs) are only distributed in a specific phylogenomic-clade of Rhodococcus, with the most predominant types of gene clusters being NRPS and ribosomally synthesized and post-translationally modified peptides (RiPPs). In-depth mining of RiPP gene clusters revealed that Rhodococcus encodes many clade-specific novel RiPPs, with thirteen core peptides showing antibacterial potential. High-throughput elicitor screening (HiTES) and non-targeted metabolomics revealed that a marine-derived Rhodococcus strain produces a large number of new aurachin-like compounds when exposed to specific elicitors. The present study highlights the diversity and specificity of secondary biosynthetic potential in Rhodococcus, and provides valuable information for the targeted exploration of novel natural products from Rhodococcus, especially for phylogenomic-clade-specific metabolites.

Systematic scoping review of cluster randomised trials conducted exclusively in low-income and middle-income countries between 2017 and 2022

ObjectiveCluster randomised trials (CRTs) are used for evaluating health-related interventions in low-income and middle-income countries (LMICs) but raise complex ethical issues. To inform the development of future ethics guidance, we...

Metagenomic mining of two Egyptian Red Sea sponges associated microbial community

The Red Sea is a promising habitat for the discovery of new bioactive marine natural products. Sponges associated microorganisms represent a wealthy source of compounds with unique chemical structures and diverse biological activities. Metagenomics is an important omics-based culture-independent technique that is used as an effective tool to get genomic and functional information on sponge symbionts. In this study, we used metagenomic analysis of two Egyptian Red Sea sponges Hyrtios erectus and Phorbas topsenti microbiomes to study the biodiversity and the biosynthetic potential of the Red Sea sponges to produce bioactive compounds. Our data revealed high biodiversity of the two sponges’ microbiota with phylum Proteobacteria as the most dominant phylum in the associated microbial community with an average of 31% and 70% respectively. The analysis also revealed high biosynthetic potential of sponge Hyrtios erectus microbiome through detecting diverse types of biosynthetic gene clusters (BGCs) with predicted cytotoxic, antibacterial and inhibitory action. Most of these BGCs were predicted to be novel as they did not show any similarity with any MIBiG database known cluster. This study highlights the importance of the microbiome of the collected Red Sea sponge Hyrtios erectus as a valuable source of new bioactive natural products.

Assessment of swallowing performance in patients with neurodegenerative disease: A hierarchical cluster analysis.

Swallowing is a complex process that alters with age and neurological diseases; swallowing disorders can be a consequence of both of them. As an advanced multivariate statistical method, hierarchical cluster analysis (HCA) was utilized to make the dendrograms, which was used to find the relationship between the variables. The purpose of this study is to ascertain the type of clustering exhibited by the variables using HCA and to evaluate the approach to major neurodegenerative diseases (MND) with swallowing disorders based on the results obtained. Data were collected from a total of 173 patients from various neurological diagnoses, such as dementia, Parkinson's disease, stroke and polyneuropathy, aging between 42 and 104 (mean of age 72.85) by using the Montreal Cognitive Assessment, the Edinburgh Feeding Evaluation Scale (EdFED), the Eating Assessment Tool (EAT-10), and the Modified Mann Swallowing Ability test. From the collected data, dendrograms were formed by using HCA with Ward linkage method. Based on cluster analysis results, clusters demonstrate statistical significance. They center around EdFED, EAT-10, and age in each MND. In healthy individuals, variables are not clustered as in the patient group. This study holds importance as it can give clinicians a different perspective on determining and managing the elderly population's swallowing problems. The HCA method explicitly proposes which variables should be examined concurrently in the clinic for MND. This research is one of the pioneering studies conducted by using the HCA method.

A pangenomic atlas reveals eco-evolutionary dynamics that shape type VI secretion systems in plant-pathogenic Ralstonia.

Soilborne Ralstonia solanacearum species complex (RSSC) pathogens disrupt microbial communities as they invade roots and fatally wilt plants. RSSC pathogens secrete antimicrobial toxins using a type VI secretion system (T6SS). To investigate how evolution and ecology have shaped the T6SS of these bacterial pathogens, we analyzed the T6SS gene content and architecture across the RSSC and their evolutionary relatives. Our analysis reveals that two ecologically similar Burkholderiaceae taxa, xylem-pathogenic RSSC and Paracidovorax, have convergently evolved to wield large arsenals of T6SS toxins. To understand the mechanisms underlying genomic enrichment of T6SS toxins, we compiled an atlas of 1,066 auxiliary T6SS toxin clusters ("aux" clusters) across 99 high-quality RSSC genomes. We classified 25 types of aux clusters with toxins that predominantly target lipids, nucleic acids, or unknown cellular substrates. The aux clusters were located in diverse genetic neighborhoods and had complex phylogenetic distributions, suggesting frequent horizontal gene flow. Phages and other mobile genetic elements account for most of the aux cluster acquisition on the chromosome but very little on the megaplasmid. Nevertheless, RSSC genomes were more enriched in aux clusters on the megaplasmid. Although the single, ancestral T6SS was broadly conserved in the RSSC, the T6SS has been convergently lost in atypical, non-soilborne lineages. Overall, our data suggest dynamic interplay between the lifestyle of RSSC lineages and the evolution of T6SSes with robust arsenals of toxins. This pangenomic atlas poises the RSSC as an emerging, tractable model to understand the role of the T6SS in shaping pathogen populations.IMPORTANCEWe explored the eco-evolutionary dynamics that shape the inter-microbial warfare mechanisms of a globally significant plant pathogen, the Ralstonia solanacearum species complex. We discovered that most Ralstonia wilt pathogens have evolved extensive and diverse repertoires of type VI secretion system-associated antimicrobial toxins. These expansive toxin arsenals potentially enhance the ability of Ralstonia pathogens to invade plant microbiomes, enabling them to rapidly colonize and kill their host plants. We devised a classification system to categorize the Ralstonia toxins. Interestingly, many of the toxin gene clusters are encoded on mobile genetic elements, including prophages, which may be mutualistic symbionts that enhance the inter-microbial competitiveness of Ralstonia wilt pathogens. Moreover, our findings suggest that the convergent loss of this multi-gene trait contributes to genome reduction in two vector-transmitted lineages of Ralstonia pathogens. Our findings demonstrate that the interplay between microbial ecology and pathogen lifestyle shapes the evolution of a genetically complex antimicrobial weapon.

Fumasep FAA-3-PK-130: Exploiting multinuclear solid-state NMR to shed light on undisclosed structural properties

Fumasep FAA-3-PK-130 is considered the state-of-the-art among the different commercially available Anion Exchange Membranes (AEMs). It is produced by Fumatech GmbH as a cost-effective blend of polyetheretherketone (PEEK) and poly (phenylene oxide) (PPO) characterized by high hydroxyl ions conductivity, high thermal and chemical resistance, and high dimensional stability. Nevertheless, the chemical structure of the anion exchange sites and their contents were unknown so far.In this paper, we report a detailed structural characterization of Fumasep FAA-3-PK-130 to identify the material phase composition, the nature of the conducting moieties and their interactions with the adsorbed water molecules. A complete phase segregation between PPO and PEEK was found on a micrometric scale from 1H spin-lattice relaxation times and micro-ATR analysis. Multinuclear (1H, 13C, 19F) Solid-State NMR spectra, combined with nuclear spin relaxation measurements, allowed us to identify the anion exchange moiety with benzyl-ethyl-dimethylammonium. This is present as functionalizing group of PPO monomers with a functionalization degree of about 40 %. Moreover, the mobility of water absorbed in the membrane was studied by 2H Solid-State NMR on samples hydrated with deuterated water under controlled relative humidity: at low relative moisture, two different types of environments were found for water molecules, compatible with two types of water-ion clusters, one of which contains water molecules with a restricted mobility, limited to C2 jumps, due to strong interactions with ions.

Spatial dynamics of transport accessibility and regional efficiency in the Yangtze River Delta Urban Agglomeration

Transport accessibility is crucial for defining urban clusters and evaluating a region's centrality and connectivity. To foster equitable growth in urban conglomerates, it is crucial to understand the relationship between transport accessibility and regional development. This study introduces the concept of 'regional efficiency'—the effectiveness of converting regional inputs into outputs—determined via the super-efficiency Data Envelopment Analysis methodology, to assess the progression of regional development. Employing a combination of bivariate spatial autocorrelation and spatial regression analysis, this research elucidates the spatial dynamics between transport accessibility and regional efficiency, both at macro and micro levels. A binary Logit model identifies the factors affecting the Moran's I correlation between regional efficiency and transport accessibility. Based on the diverse urban characteristics within a single conglomerate, tailored development strategies are suggested. Focusing on the Yangtze River Delta Urban Agglomeration in China as a case study, four distinct spatial clusters—High–High (HH), Low–Low (LL), High–Low (HL), and Low–High (LH)—are identified, based on the local correlation between regional efficiency and transport accessibility. The findings reveal that regions with a High–High Moran's I correlation between road accessibility and regional efficiency predominantly located in the eastern sectors of the Yangtze River Delta, exhibiting effective regional efficiency. These regions are characterized by superior road accessibility, aligning well with their regional efficiency metrics. For air accessibility, cities classified under the HH category, including Shanghai and its neighboring cities, demonstrate a significant spatial correlation with regional efficiency. Population density and urban tier are key predictors of the significance of the Moran's I correlation between road accessibility and regional efficiency. In contrast, for air accessibility, these factors assume an inverse role. The identified cluster types (HH, LL, LH, and HL) are proposed as predictive indicators for the significance of the Moran's I relationship between air accessibility and regional efficiency.

Evolving molecular HIV clusters revealed genotype-specific dynamics in Guangzhou, China (2008-2020)

ObjectivesThis study investigated the genotype-specific dynamics of molecular HIV clusters (MHCs) in Guangzhou, China, aiming to enhance HIV control. MethodsHIV pol sequences from people with HIV (PWH) in Guangzhou (2008-2020) were obtained for genotyping and molecular network creation. MHCs were identified and categorized into three types: emerging, growing, or stable. Clustering rates, proportions of cluster types, and members within each type were calculated and their trends were assessed using joinpoint regression. ResultsAmong 8395 PWH, the most prevalent HIV-1 genotypes were CRF07_BC (39.7%) and CRF01_AE (32.6%). The genotype composition has been stable since 2012 (Ps > 0.05). The overall clustering rate was 43.3%, with significant variations across genotypes (P < 0.001), indicating genotype-specific transmission fitness. Significant declines in overall and genotype-specific clustering rates toward the end of 2020 (Ps < 0.05), potentially offer support for HIV control efforts in reducing local infections. The continuously increasing proportions of stable clusters and the gradually decreasing proportions of emerging and growing clusters (either Ps < 0.05 or Ps > 0.05) suggest a trend toward stable molecular network structure. However, growing clusters exhibited CRF55_01B, CRF07_BC, and CRF59_01B dominance that indicate their priority for interventions. ConclusionThe evolving MHCs highlight the genotype-specific cluster dynamics, providing fresh insights for enhanced prevention and control strategies.

Characterization of methicillin resistant Staphylococcus Aureus in municipal wastewater in Finland

Wastewater-based surveillance (WBS) of multidrug-resistant bacteria could complement clinical data, serving as a population-level early warning tool. This study evaluated WBS as a pandemic preparedness tool, by selectively isolating and culturing methicillin-resistant Staphylococcus aureus (MRSA) with CHROMagar MRSA. Some 24-h composite wastewater samples (n = 80) were collected from ten treatment plants across Finland between February 2021 and January 2022. MRSA prevalence in wastewater samples was 27.5% (n = 22/80), showing seasonal and temporal variations. Phenotypic antimicrobial susceptibility testing (AST) with microdilution showed that over 80% of isolates were drug-resistant to clindamycin, sulfamethoxazole/trimethoprim, tetracycline, fusidic acid, and erythromycin. Four isolates (18.2%) were vancomycin-resistant. WGS revealed that 31.8% (n = 7) of the isolates belonged to the ST8-t008 and ST6-t304 spa types, respectively. In addition, two spa types (t011 and t034) belong to the CC398 complex. The mecA gene was found in all isolates (n = 22) and three tetracycline resistance determinants (tet38, tetK, and tetM) were detected with tet38 being the most abundant (81.8%, n = 18/22). Three isolates harboured the plasmid-mediated sat4 gene that confers resistance to Streptothricin. In addition, resistance determinants to macrolide antibiotics (mph (C)/msr (A) and fosfomycin (fosB) were detected in the seven isolates that belonged to spa type t008. All isolates except one harboured the SCCmec_type_IVa(2B). Six ST8 isolates harboured the LukS/F-PV genes encoding the Panton–Valentine leukocidin (PVL) and were also positive for the Arginine Catabolic Mobile Element (ACME), suggesting they belong to the USA300 clone. The Inc18 plasmid was the most abundant as it was detected in 72.7% (n = 16/22) of the isolates. Other plasmid replicons detected were the rep_trans and repA_N which were detected in 45.4% (n = 10/22) and 40.9% (n = 9/22) of the isolates respectively. Ten isolates harboured at least three plasmid replicons and no plasmid replicons were detected in four isolates (ST6/t304). The cgMLST revealed that some isolates aggregated into two genomically indistinguishable clusters: ST6/t304 belonging to cluster type CT12405 (≤20 allelic differences) and ST8/t008 belonging to cluster type CT1925 (<8 allelic differences). Overall, we found a high genotypic concordance with the national clinical bacterial resistance data. Our study demonstrates the sensitivity of culture-based wastewater surveillance for MRSA using clinical media following pre-enrichment, reliably predicting pathogen occurrence at the population level.

Attributes and types of innovation clusters in the context of digital transformation

Attributes and types of innovation clusters in the context of digital transformation

Spatial Characteristics of Brownfield Clusters and “City-Brown” Patterns: Case Studies of Resource-Exhausted Cities in China

In the post-industrial era, many cities have experienced the decline of heavy industry and traditional manufacturing, leading to the widespread emergence of brownfields. These often cluster geographically, forming “brownfield clusters” characterized by shared spatial and functional traits. Our research examined these phenomena within 10 resource-exhausted cities in China, employing kernel density analysis to explore the spatial dynamics within and among these clusters and their urban contexts. We identified three distinct spatial relationships between brownfield clusters and their host cities (coupling, juxtaposition, and encircling), with a detailed case study in Huangshi City further classifying the clusters into five categories based on their dominant factors, spatial morphologies, types of brownfields, and internal dynamics. The study reveals that the spatial configurations of brownfield clusters are significantly influenced by geographic features, transportation infrastructure, and policy frameworks. Based on these findings, we propose targeted regeneration strategies for each cluster type. This research not only enhances our understanding of brownfield challenges and opportunities in China’s resource-exhausted cities but also serves as a valuable reference for other cities and regions worldwide facing similar challenges.

Protocellular Heme and Iron-Sulfur Clusters.

ConspectusCentral to the quest of understanding the emergence of life is to uncover the role of metals, particularly iron, in shaping prebiotic chemistry. Iron, as the most abundant of the accessible transition metals on the prebiotic Earth, played a pivotal role in early biochemical processes and continues to be indispensable to modern biology. Here, we discuss our recent contributions to probing the plausibility of prebiotic complexes with iron, including heme and iron-sulfur clusters, in mediating chemistry beneficial to a protocell. Laboratory experiments and spectroscopic findings suggest plausible pathways, often facilitated by UV light, for the synthesis of heme and iron-sulfur clusters. Once formed, heme displays catalytic, peroxidase-like activity when complexed with amphiphiles. This activity could have been beneficial in two ways. First, heme could have catalytically removed a molecule (H2O2) that could have had degradative effects on a protocell. Second, heme could have helped in the synthesis of the building blocks of life by coupling the reduction of H2O2 with the oxidation of organic substrates. The necessity of amphiphiles to avoid the formation of inactive complexes of heme is telling, as the modern-day electron transport chain possesses heme embedded within a lipid membrane. Conversely, prebiotic iron-sulfur peptides have yet to be reported to partition into lipid membranes, nor have simple iron-sulfur peptides been found to be capable of participating in the synthesis of organic molecules. Instead, iron-sulfur peptides span a wide range of reduction potentials complementary to the reduction potentials of hemes. The reduction potential of iron-sulfur peptides can be tuned by the type of iron-sulfur cluster formed, e.g., [2Fe-2S] versus [4Fe-4S], or by the substitution of ligands to the metal center. Since iron-sulfur clusters easily form upon stochastic encounters between iron ions, hydrosulfide, and small organic molecules possessing a thiolate, including peptides, the likelihood of soluble iron-sulfur clusters seems to be high. What remains challenging to determine is if iron-sulfur peptides participated in early prebiotic chemistry or were recruited later when protocellular membranes evolved that were compatible with the exploitation of electron transfer for the storage of energy as a proton gradient. This problem mirrors in some ways the difficulty in deciphering the origins of metabolism as a whole. Chemistry that resembles some facets of extant metabolism must have transpired on the prebiotic Earth, but there are few clues as to how and when such chemistry was harnessed to support a (proto)cell. Ultimately, unraveling the roles of hemes and iron-sulfur clusters in prebiotic chemistry promises to deepen our understanding of the origins of life on Earth and aids the search for life elsewhere in the universe.

Optimal designs using generalized estimating equations in cluster randomized crossover and stepped wedge trials.

Cluster randomized crossover and stepped wedge cluster randomized trials are two types of longitudinal cluster randomized trials that leverage both the within- and between-cluster comparisons to estimate the treatment effect and are increasingly used in healthcare delivery and implementation science research. While the variance expressions of estimated treatment effect have been previously developed from the method of generalized estimating equations for analyzing cluster randomized crossover trials and stepped wedge cluster randomized trials, little guidance has been provided for optimal designs to ensure maximum efficiency. Here, an optimal design refers to the combination of optimal cluster-period size and optimal number of clusters that provide the smallest variance of the treatment effect estimator or maximum efficiency under a fixed total budget. In this work, we develop optimal designs for multiple-period cluster randomized crossover trials and stepped wedge cluster randomized trials with continuous outcomes, including both closed-cohort and repeated cross-sectional sampling schemes. Local optimal design algorithms are proposed when the correlation parameters in the working correlation structure are known. MaxiMin optimal design algorithms are proposed when the exact values are unavailable, but investigators may specify a range of correlation values. The closed-form formulae of local optimal design and MaxiMin optimal design are derived for multiple-period cluster randomized crossover trials, where the cluster-period size and number of clusters are decimal. The decimal estimates from closed-form formulae can then be used to investigate the performances of integer estimates from local optimal design and MaxiMin optimal design algorithms. One unique contribution from this work, compared to the previous optimal design research, is that we adopt constrained optimization techniques to obtain integer estimates under the MaxiMin optimal design. To assist practical implementation, we also develop four SAS macros to find local optimal designs and MaxiMin optimal designs.

On the Identification of Solid-Like Clusters in a Crystallizing Yukawa System

The crystallization of systems with soft interaction potentials is analyzed for a Yukawa system as an example. The crystallization pathway in the plane of rotational invariants q4 and q6 is studied in detail. The recently proposed invariants bcc1 and bcc2, calculated using 12 nearest neighbors, are applied for the first time to study the crystallization. It is shown that the combination of the rotational invariant technique and the method of Voronoi polyhedra allows us to identify quite simply all types of solid-like clusters formed during the solidification of the system, including bcc-like clusters, which are hardly identified by conventional methods.

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.

Structures of Large Tin(IV) Oxo Clusters

AbstractThe article reviews and categorizes the structures of tin oxo clusters with nuclearities ≥6 and compares them with oxo clusters of the other group 4 and 14 metals. Basic construction principles of the cluster core are worked out by comparing the different cluster types and by identifying smaller building blocks. The comparison also shows how the different cluster types are influenced by the interplay between the ligands which stabilize the cluster core and the bridging oxygen atoms.