Pair Of Clusters Research Articles

A framework for crime data analysis using relationship among named entities

Many crime reports are available online in various blogs and Newswire. Though manual annotation of these massive reports is quite tedious for crime data analysis, it gives an overall crime scenario of all over the world. This motivates us to propose a framework for crime data analysis based on the online reports. Initially, the method extracts the crime reports and identifies named entities. The intermediate sequence of context words between every consecutive pair of named entities is termed as a crime vector that provides relationships between the entities. The feature vectors for each entity pair are generated from these crime vectors using the Word2Vec model. The paper considers three different types of named entity pairs to facilitate the major crime data analysis task, and for each type, similarity between every pair of entities is measured using respective feature vectors. For each type of named entity pair, a separate weighted graph is generated with entity pairs as vertices and similarity score between them as the weight of the corresponding edge. Then, Infomap, a graph-based clustering algorithm, is applied to obtain optimal set of clusters of entity pairs and a representative entity pair of each cluster. Each cluster is labelled by the relationship, represented by the crime vector, of its representative entity pair. In reality, all the entity pairs in a cluster may not reflect contextual similarity with their representative entity pair. So the clusters are further partitioned into subclusters based on WordNet-based path similarity measure which makes the entity pairs in each subcluster more contextually similar compared to their original cluster. These subclusters provide us various statistical crime information over the time period. The method is experimented only using the crime reports related to crime against women in India. The experimental results demonstrate the effectiveness and superiority of the method compared to others for analysing the crime data.

Open cluster kinematics with Gaia DR2 (Corrigendum)

Context. Open clusters are very good tracers of the evolution of the Galactic disc. Thanks to Gaia, their kinematics can be investigated with an unprecedented precision and accuracy. Aims. The distribution of open clusters in the 6D phase space is revisited with Gaia DR2. Methods. The weighted mean radial velocity of open clusters was determined, using the most probable members available from a previous astrometric investigation that also provided mean parallaxes and proper motions. Those parameters, all derived from Gaia DR2 only, were combined to provide the 6D phase space information of 861 clusters. The velocity distribution of nearby clusters was investigated, as well as the spatial and velocity distributions of the whole sample as a function of age. A high quality subsample was used to investigate some possible pairs and groups of clusters sharing the same Galactic position and velocity. Results. For the high quality sample that has 406 clusters, the median uncertainty of the weighted mean radial velocity is 0.5 km/s. The accuracy, assessed by comparison to ground-based high resolution spectroscopy, is better than 1 km/s. Open clusters nicely follow the velocity distribution of field stars in the close Solar neighbourhood previously revealed by Gaia DR2. As expected, the vertical distribution of young clusters is very flat but the novelty is the high precision to which this can be seen. The dispersion of vertical velocities of young clusters is at the level of 5 km/s. Clusters older than 1 Gyr span distances to the Galactic plane up to 1 kpc with a vertical velocity dispersion of 14 km/s, typical of the thin disc. Five pairs of clusters and one group with five members are possibly physically related. Other binary candidates previously identified turn out to be chance alignment.

Phylogeography of Schisandra chinensis (Magnoliaceae) Reveal Multiple Refugia With Ample Gene Flow in Northeast China.

Temperate conifers and broadleaved mixed forests in northeast China are ideal to investigate the genetic consequences of climate changes during the last glacial maximum (LGM), 29 – 16 kya. As previous studies were focused on tree species with long generation time; here, the evolutionary history of Schisandra chinensis, a climber species with a generation time of five years, was investigated using chloroplast DNA (cpDNA), nuclear single copy gene (nSCG), and nuclear single sequence repeats (nSSRs, i.e., microsatellite) markers, along with ecological niche modeling (ENM), which predicted a suitable habitat in Korea Peninsula (KP) during the LGM. Private haplotypes and high genetic diversity of both cpDNA and nSCG were mainly found in KP and Changbai Mt. (CB). Although no significant phylogeographic structure was detected in the cpDNA and nSCG, three nSSRs clusters roughly distributed in west (CB and KP), east (north China), and north (Xiaoxing’an Range, XR) regions were found in Structure analysis. The approximate Bayesian computation analysis showed the west cluster diverged at 35.45 kya, and the other two clusters at 19.85 kya. The genetic diversity calculated for each of the three markers showed no significant correlation with latitude. Genetic differentiation of nSSRs was also not correlated with geographic distance. Migrate analysis estimated extensive gene flow between almost all genetic cluster pairs and BOTTLENECK analysis showed that few populations experienced severe bottlenecks. Overall, results indicate that S. chinensis survived the LGM in situ in multiple refugia, which likely include two macrorefugia (KP and CB) and two microrefugia (XR and north China). Extensive postglacial gene flow among the three nSSRs clusters led to uniformly distributed genetic diversity and low genetic differentiation.

A New Microbial Pathway for Organophosphonate Degradation Catalyzed by Two Previously Misannotated Non-Heme-Iron Oxygenases.

The assignment of biochemical functions to hypothetical proteins is challenged by functional diversification within many protein structural superfamilies. This diversification, which is particularly common for metalloenzymes, renders functional annotations that are founded solely on sequence and domain similarities unreliable and often erroneous. Definitive biochemical characterization to delineate functional subgroups within these superfamilies will aid in improving bioinformatic approaches for functional annotation. We describe here the structural and functional characterization of two non-heme-iron oxygenases, TmpA and TmpB, which are encoded by a genomically clustered pair of genes found in more than 350 species of bacteria. TmpA and TmpB are functional homologues of a pair of enzymes (PhnY and PhnZ) that degrade 2-aminoethylphosphonate but instead act on its naturally occurring, quaternary ammonium analogue, 2-(trimethylammonio)ethylphosphonate (TMAEP). TmpA, an iron(II)- and 2-(oxo)glutarate-dependent oxygenase misannotated as a γ-butyrobetaine (γbb) hydroxylase, shows no activity toward γbb but efficiently hydroxylates TMAEP. The product, ( R)-1-hydroxy-2-(trimethylammonio)ethylphosphonate [( R)-OH-TMAEP], then serves as the substrate for the second enzyme, TmpB. By contrast to its purported phosphohydrolytic activity, TmpB is an HD-domain oxygenase that uses a mixed-valent diiron cofactor to enact oxidative cleavage of the C-P bond of its substrate, yielding glycine betaine and phosphate. The high specificities of TmpA and TmpB for their N-trimethylated substrates suggest that they have evolved specifically to degrade TMAEP, which was not previously known to be subject to microbial catabolism. This study thus adds to the growing list of known pathways through which microbes break down organophosphonates to harvest phosphorus, carbon, and nitrogen in nutrient-limited niches.

Clustered Planarity with Pipes

We study the version of the C-Planarity problem in which edges connecting the same pair of clusters must be grouped into pipes, which generalizes the Strip Planarity problem. We give algorithms to decide several families of instances for the two variants in which the order of the pipes around each cluster is given as part of the input or can be chosen by the algorithm.

On collision course: The nature of the binary star cluster NGC2006/SL 538

Context. The Large Magellanic Cloud (LMC) is known to be the host of a rich variety of star clusters of all ages. A large number of them is seen in close projected proximity. Ages have been derived for few of them showing differences up to few million years, hinting at being binary star clusters. However, final confirmation through spectroscopy measurements and dynamical analysis is needed. Aims. In the present work we focus on one of these LMC cluster pairs (NGC 2006–SL 538) and aim to determine whether the star cluster pair is a bound entity and, therefore, a binary star cluster or a chance alignment. Methods. We used the Magellan Inamori Kyocera Echelle (MIKE) high-resolution spectrograph on the 6.5 m Magellan-II Clay telescope at Las Campanas Observatory to acquire integrated-light spectra of the two clusters, measuring their radial velocities with individual absorption features and cross-correlation of each spectrum with a stellar spectral library. Results. We measured radial velocities by two methods: first by direct line-profile measurement yields νr = 300.3 ± 5 ± 6 km s−1 for NGC 2006 and νr = 310.2 ± 4 ± 6 km s−1 for SL 538. The second one is derived by comparing observed spectra with synthetic bootstrapped spectra yielding νr = 311.0 ± 0.6 km s−1 for NGC 2006 and νr = 309.4 ± 0.5 km s−1 for SL 538. Finally when spectra are directly compared, we find a Δν = 1.08 ± 0.47 km s−1. Full-spectrum spectral energy distribution fits reveal that the stellar population ages of both clusters lie in the range 13–21 Myr with a metallicity of Z = 0.008. We find indications for differences in the chemical abundance patterns as revealed by the helium absorption lines between the two clusters. The dynamical analysis of the system shows that the two clusters are likely to merge within the next ∼150 Myr to form a star cluster with a stellar mass of ∼104 M⊙. Conclusions. The NGC 2006–SL 538 cluster pair shows radial velocities, stellar population and dynamical parameters consistent with a gravitational bound entity and, considering that the velocity dispersion of the stars in LMC is ≲20 km s−1, we reject them as a chance alignment. We conclude that this is a genuine binary cluster pair, and we propose that their differences in ages and stellar population chemistry is most likely due to variances in their chemical enrichment history within their environment. We suggest that they may have formed in a loosely bound star-formation complex which saw initial fragmentation but then had its clusters become a gravitationally bound pair by tidal capture.

Isomerism in Titanium-Oxo Clusters: Molecular Anatase Model with Atomic Structure and Improved Photocatalytic Activity.

Phase isomerism is a common and important phenomenon in inorganic materials, but the molecular isomerism of their nanocluster models is still rare. In this work, we report the first pair of isomeric titanium-oxo clusters. Through combining pentagonal {Ti(Ti5 )} building units in corner-sharing or edge-sharing forms, the two obtained Ti20 -oxo clusters take vertical and horizontal core configurations, respectively, which are both functionalized by the same organic ligands. More interestingly, the vertical type Ti20 -oxo core contains an identical {Ti8 O14 } moiety as anatase, making it the first molecular model of anatase TiO2 . As a result, the vertical type cluster exhibits better photocatalytic H2 evolution activity, higher photocurrent response and faster charge transfer to external acceptors than its horizontal isomer. Thus, this work provides a cluster isomer method to understand the structure-property relationship of import titanium oxide materials.

Simulations of the Polarized Sky for the SKA: How to Constrain Intracluster Magnetic Fields

The advent of the Square Kilometer Array (SKA) will have unprecedented impact on the study of magnetic fields in galaxy clusters. This instrument will be able to perform all-sky surveys in polarization, allowing us to build a rotation-measure (RM) grid based on an enormous number of sources. However, it is not always obvious how to extract correct information about the strength and the structure of magnetic fields from the RM grid. The simulations presented here help us to investigate this topic as they consist of full-Stokes idealized (because we did not add thermal noise) images of a pair of galaxy clusters between 950–1760 GHz, i.e., the SKA1-MID band 2. These images include not just cluster-embedded radio sources but also foreground and background discrete radio sources populating the simulated portion of the universe. To study the magnetic fields of the simulated galaxy clusters, we applied the RM synthesis technique on the simulated images and compared the “true” cluster RM values with those inferred from RM synthesis. The accuracy of our methodology is guarantee by the excellent agreement that we observed when we considered only the signal from the background radio sources. The presence of a Faraday screen, foreground, and cluster sources, introduces degeneracies and/or ambiguities that make the interpretation of the results more difficult.

An edge priority‐based clustering algorithm for multiprocessor environments

SummaryIn multiprocessor environments, the scheduling algorithms play a significant role in maximizing system performance. In this paper, we propose a clustering‐based task scheduling algorithm called Edge Priority Scheduling (EPS) for multiprocessor environments. The proposed algorithm extends the idea of edge zeroing heuristic and uses the concept of edge priority to minimize the makespan of the task graph. The complexity of the EPS algorithm is O(|V||E|(|V| + |E|)), where |E| represents the number of edges and |V| denotes the number of nodes in the task graph. The experiments are performed for random task graphs and the task graphs generated from some representative real‐world applications such as Gaussian Elimination and Fast Fourier Transform. The performance of the EPS algorithm is compared with six well‐known algorithms such as EZ (Edge Zeroing), LC (Linear Clustering), CPPS (Cluster Pair Priority Scheduling), DCCL (Dynamic Computation Communication Load), RDCC (Randomized Dynamic Computation Communication), and LOCAL. The results show that the EPS algorithm outperforms the compared algorithms in terms of the normalized schedule length and speedup.

Long-term impact of community-based participatory women’s groups on child and maternal mortality and child disability: follow-up of a cluster randomised trial in rural Nepal

BackgroundCommunity-based women’s groups practising participatory learning and action (PLA) can reduce maternal and neonatal mortality in low-income countries. However, it is not clear whether these reductions are associated with subsequent...

Open cluster kinematics with Gaia DR2

Context. Open clusters are very good tracers of the evolution of the Galactic disc. Thanks to Gaia, their kinematics can be investigated with an unprecedented precision and accuracy. Aims. The distribution of open clusters in the 6D phase space is revisited with Gaia DR2. Methods. The weighted mean radial velocity of open clusters was determined, using the most probable members available from a previous astrometric investigation that also provided mean parallaxes and proper motions. Those parameters, all derived from Gaia DR2 only, were combined to provide the 6D phase-space information of 861 clusters. The velocity distribution of nearby clusters was investigated, as well as the spatial and velocity distributions of the whole sample as a function of age. A high-quality subsample was used to investigate some possible pairs and groups of clusters sharing the same Galactic position and velocity. Results. For the high-quality sample of 406 clusters, the median uncertainty of the weighted mean radial velocity is 0.5 km s−1. The accuracy, assessed by comparison to ground-based high-resolution spectroscopy, is better than 1 km s−1. Open clusters nicely follow the velocity distribution of field stars in the close solar neighbourhood as previously revealed by Gaia DR2. As expected, the vertical distribution of young clusters is very flat, but the novelty is the high precision to which this can be seen. The dispersion of vertical velocities of young clusters is at the level of 5 km s−1. Clusters older than 1 Gyr span distances to the Galactic plane of up to 1 kpc with a vertical velocity dispersion of 14 km s−1, typical of the thin disc. Five pairs of clusters and one group with five members might be physically related. Other binary candidates that have been identified previously are found to be chance alignments.

A coarse‐to‐fine two‐step method for semisupervised classification using quasi‐linear Laplacian SVM

This paper proposes a two‐step method to construct a nonlinear classifier based on semisupervised learning in a coarse‐to‐fine way. In the first step, a recursive density‐based spatial clustering of applications with noise clustering algorithm is first introduced to find a group of density clusters, each of which contains only one kind of class labels. An SK algorithm is then applied to pairs of density clusters containing different class labels to find a set of local linear classifiers, which forms a coarse nonlinear separating boundary crossing the low‐density areas by interpolating the local linear classifiers. In the second step, a Laplacian support vector machine (LapSVM) formulation based on graph construction is applied to further implicitly optimize the parameter set of the nonlinear coarse classifier. As a result, the fine‐tuned nonlinear classifier is constructed in exactly the same way as a standard LapSVM, using a special data‐dependent quasi‐linear kernel composed of the interpolation functions and the information of the local linear classifiers obtained in the first step. Moreover, the quasi‐linear kernel is used as a better similarity function for the graph construction. Numerical experiments on various real‐world datasets demonstrate the effectiveness of the proposed method. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Clusters of the Ionic Liquid 1-Hydroxyethyl-3-methylimidazolium Picrate: From Theoretical Prediction in the Gas Phase to Experimental Evidence in the Solid State.

Interonic interactions determine the macroscopic properties of ionic liquids (ILs). Hence, unravelling the relationships between the microscopic and macroscopic scales is key for rational design. Combining density functional theory (DFT) calculations of isolated ion pairs and vibrational spectroscopy of the condensed phase (fluid or solid) has become a very common approach. In the present work, we make a step towards understanding how the physicochemical effects in small gas phase clusters of a hydroxyl functionalized imidazolium-picrate IL relate with the molecular structure and interactions of the corresponding solid material taking 1-hydroxyethyl-3-methylimidazolium picrate, C2 OHmimPic, as an example. In the isolated ion pair, strong alkyl-OH⋅⋅⋅Pic hydrogen bonding interactions are found rather than the commonly observed hydrogen bonding interactions at the slightly acidic C(2)-H site of the imidazolium ring. However, this part of the cation plays an important role when clusters of ion pairs in the gas phase and inside a crystal lattice are considered. For example, in the dimeric ion-pair cluster, one centre (O*) with two interaction sites (C(2)-H-O* and alkyl OH-Pic) is observed. This configuration is suggested by single crystal X-ray diffraction (XRD), vibrational spectroscopy, and the dispersion-corrected DFT calculations. Hence, the study provides evidence for the appearance of theoretical gas phase clusters in an actual solidified ionic liquid. This ion pair dimer formation may be a general behavior of hydroxyl functionalized imidazolium ILs, but further research is needed to draw a final conclusion. Moreover, the Raman spectra confirm the exclusive gauche conformation of the hyroxyl functionalized alkyl chain.

Randomized incremental construction for the Hausdorff Voronoi diagram revisited and extended

This paper applies the randomized incremental construction (RIC) framework to computing the Hausdorff Voronoi diagram of a family of k clusters of points in the plane. The total number of points is n. The diagram is a generalization of Voronoi diagrams based on the Hausdorff distance function. The combinatorial complexity of the Hausdorff Voronoi diagram is O(n+m), where m is the total number of crossings between pairs of clusters. For non-crossing clusters (m=0), our algorithm works in expected O(n log n + k log n log k) time and deterministic O(n) space. For arbitrary clusters (m=O(n^2)), the algorithm runs in expected O((m+n log k) log n) time and O(m +n log k) space. When clusters cross, bisectors are disconnected curves resulting in disconnected Voronoi regions that challenge the incremental construction. This paper applies the RIC paradigm to a Voronoi diagram with disconnected regions and disconnected bisectors, for the first time.

Dynamics and stability of gap-flow interference in a vibrating side-by-side arrangement of two circular cylinders

In this work, the coupled dynamics of the gap flow and the vortex-induced vibration (VIV) of a side-by-side (SBS) arrangement of two circular cylinders is numerically investigated at Reynolds numbers $100\leqslant Re\leqslant 500$ . The influence of VIV is incorporated by allowing one of the cylinders to vibrate freely in the transverse direction, which is termed as a vibrating side-by-side (VSBS) arrangement. A comparative three-dimensional study is performed between the stationary side-by-side (SSBS) and the VSBS arrangements to examine the characteristics of the complex coupling between the VIV and the gap flow. The results are also contrasted against the isolated configurations without any proximity and gap-flow interference. Of particular interest is to establish a relationship between the VIV, the gap flow and the near-wake instability behind bluff bodies. We find that the kinematics of the VIV regulates the streamwise vorticity concentration, which accompanies a recovery of the two-dimensional hydrodynamic response at the peak lock-in. Moreover, the near-wake instability may develop around an indeterminant two-dimensional streamline saddle point along the interfaces of a pair of imbalanced counter-signed vorticity clusters. The interaction between the imbalanced vorticity clusters and the gap-flow momentum are closely interlinked with the prominence of streamwise vortical structures. In both SSBS and VSBS arrangements, the flip-flopping frequency is significantly low for the three-dimensional flow, except at the VIV lock-in for the VSBS arrangement. While an early onset of VIV lock-in is observed for the vibrating configuration, a quasi-stable deflected gap-flow regime with stably deflected gap flow is found at the peak lock-in. The increase of the gap-flow proximity interference promotes the energy transfer and stabilizes the VIV lock-in. Finally, we employ the dynamic mode decomposition procedure to characterize the space–time evolution of the vortex wake system behind the cylinders.

Evaluation of wheat genotypes (Triticum aestivum L.) for assessment of character association, path coefficient and cluster analysis

Thirty wheat genotypes (Triticum aestivum L.) were evaluated for 11 morphological and yield trait for analysis of character association (phenotypic and genotypic correlation coefficient), path analysis and cluster analysis. The experiment was conducted during rabi seasons of 2014-2015 in a randomized block design with three replication. Days to 50% heading showed positive and significant correlation with flag leaf area and number of spiklet per ear; flag leaf area showed positive and significant correlation with 1000 grain weight; Plant height showed positive and significant correlation with spike length; spike length showed positive and significant correlation with 1000 grain weight. Phenotypic path analysis showed biological yield and number of grain per spike had highly positive and direct effect on grain yield. Direct and highly positive effect on grain yield was shown by number of productive tillers, plant height, spike length, number of spikelet per spike genotypic path coefficient. Biological yield and grains yield per plant show highly positive and direct effect on yield with number of productive tillers, plant height, number of spikelet per spike and spike length. In cluster analysis the intra cluster distance ranged from 1.61 (cluster II) to 2.37 (cluster III and VI ). Thus the member of cluster II were least divergent and similarly the member of cluster III and IV were most divergent The maximum inter cluster distance was between cluster II and III followed by cluster IV and V , cluster VI and III and cluster VI and V that order therefore the accessions grouped in the five pair of cluster may be considered as most divergent.

Formation History of Binary Clusters in the Large Magellanic Cloud

AbstractGlobal history of star or cluster formation in the Large Magellanic Cloud (LMC) has been the center of interest in several studies as it is thought to be influenced by tidal interaction with the Small Magellanic Cloud and even the Milky Way. This study focus on the formation history of the LMC in relation with the context of binary star clusters population, the apparent binary fraction (e.g., percentage of cluster pairs) in different epoch were calculated and analyzed. From the established distributions, it can be deduced that the binary clusters tend to be young (∽ 100 Myr) while their locations coincide with the locations of star forming complexes. There is an indication that the binary fraction increases as the rise of star formation rate in the last millions years. In the LMC, the increase of binary fraction at age ∽ 100 Myr can be associated to the last episode of close encounter with the Small Magellanic Cloud at ∽ 150 Myr ago. This observational evidence supports the theory of binary cluster formation through the fission of molecular cloud where the encounter between galaxies enhanced the clouds velocity dispersion which in turn increased the probability of cloud-cloud collisions that produce binary clusters.

Symptom Based Clustering of Men in the LURN Observational Cohort Study.

Conventional classification of patients with lower urinary tract symptoms into diagnostic categories based on a predefined symptom complex or predominant symptom appears inadequate. This is due to the frequent presentation of patients with multiple urinary symptoms which could not be perfectly categorized into traditional diagnostic groups. We used a novel clustering method to identify subtypes of male patients with lower urinary tract symptoms based on detailed multisymptom information. We analyzed baseline data on 503 care seeking men in the LURN (Symptoms of Lower Urinary Tract Dysfunction Research Network) Observational Cohort Study. Symptoms and symptom severity were assessed using the LUTS (Lower Urinary Tract Symptoms) Tool and the AUA SI (American Urological Association Symptom Index), which include a total of 52 questions. We used a resampling based consensus clustering algorithm to identify patient subtypes with distinct symptom signatures. Four distinct symptom clusters were identified. The 166 patients in cluster M1 had predominant symptoms of frequency, nocturia, hesitancy, straining, weak stream, intermittency and incomplete bladder emptying suggestive of bladder outlet obstruction. The 93 patients in cluster M2 mainly endorsed post-micturition symptoms (eg post-void dribbling and post-void leakage) with some weak stream. The 114 patients in cluster M3 reported mostly urinary frequency without incontinence. The 130 patients in cluster M4 reported severe frequency, urgency and urgency incontinence. Most other urinary symptoms statistically differed between cluster pairs. Patient reported outcomes of bowel symptoms, mental health, sleep dysfunction, erectile function and urological pain significantly differed across the clusters. We identified 4 data derived clusters among men seeking care for lower urinary tract symptoms. The clusters differed from traditional diagnostic categories. Further subtype refinement will be done to incorporate clinical data and nonurinary patient reported outcomes.

Behind the success of modified coupled-cluster methods: addition by subtraction

ABSTRACTModified coupled-cluster (CC) methods such as linearized coupled-cluster doubles (LinCCD), approximate coupled pair (ACP D14), 2CC (from nCC family), parameterized CCSD (pCCSD) and distinguishable cluster (DCSD) can have their advantages over general CC methods. Though these methods include connected clusters of single and double excitations at most, distinguishable cluster, parameterized CC and approximate coupled pair methods, in particular, have been shown to produce quantitatively correct results in benchmark studies. To put these methods on a stronger foothold, it is essential to understand the rationale for their success: mimicking the effect of connected triple excitations. We exploit the relation between CC and many body perturbation theory (MBPT) in general, and between CCSD and MBPT(4)/MP4 in particular, to take a step towards bringing clarity to this persisting conundrum. Our aim here is to look for numerical signs of ‘addition by subtraction’ or ‘inclusion by deletion’ effect that is likely behind the success of these modified CCD or CCSD methods. We achieve this by revisiting well-studied examples of single and multiple bond dissociation and comparing the performance of these modified CCSD methods with higher-level CC methods. Though our results are qualitative in nature, we hope this would lead to more rigorous analysis in future studies.

Structural aspects of heterotetranuclear platinum clusters-distortion isomers

Abstract This review includes 16 examples of distortion isomers of heterotetranuclear platinum clusters. The clusters are of the compositions: Pt3Sn, Pt2M2 (M=Au, Ag, W, Mo), and PtM3 (M=Os, Ru, Re). The four metal atoms are found in a distorted tetrahedral core (most common), planar-rhombohedral, spiked-triangular, and eight-membered ring skeleton. There are three pairs (Pt2W2, Pt2Au2, and Pt2Ag2) of clusters and all remainder clusters contain two crystallographically independent molecules within the same crystal. All are classical examples of distortion isomerism. Their structures are analyzed and discussed.