Cluster example

With only 2 metal-metal bonds, it is no longer possible to bond directly four metal atoms and we enter the border area between cage compounds and clusters. Examples of these compounds are Co4Cp4(ju3-P)4 222 and Co4 (C0)4 0u2 -SEt)8 244 the last structure being shown in Fig. 21. 

FIGURE 6.16 Cluster evaluation for model-based clustering (example from Figure 6.9) using different types of models (see text and legend) and different numbers of clusters. That model and that number of clusters with the largest BIC value will be taken three clusters with different volume, shape, and orientation (type VVV ). 

The water cluster examples in Table 6 are meant to illustrate a somewhat more difficult minimization problem. Optimal cluster-network geometries are more difficult to locate not only because of the difficulty in constructing good starting points the optimal configurations are dominated by long-range nonbonded forces that are computationally not feasible to consider in preconditioners. 

These first applications were simply too inefficient, and the cluster examples chosen were too small, for them to be serious competition for established methods like simulated annealing (SA) (see Sect. 4) therefore, they went largely unnoticed, and the following year, 1994, did not see much activity in this field at all. 

While the capping and fusion rules significantly increase the power of the PSEP model for clusters whose atoms have relatively high metal-metal connectivity, the newest extentions apply the model to lower connectivity clusters. For transition metals, 15n electrons (where n is the number of vertices) are expected for clusters whose metal atoms are connected to three other metal atoms (that is, three-connected clusters). " Examples include tetrahedra, cubes, and cuneanes. In the four-connected clusters, such as octahedra, square antiprisms, and cuboctahedra, the electron count can range from 14n to 14n -I- 4, depending on the nature of the polyhedron. ... 

The following document-clustering examples utilize Oracle Text k-Means clustering, document gist, and theme extraction. Searching MEDLINE with two distinct queries in the article titles and selecting the top 300 documents for each query provided the 600 documents for this clustering example. The queries were lymphoma and Alzheimer s disease. ... 

This simple example can be expanded by requesting 10 clusters from the k-Means algorithm. Because the algorithm is hierarchical in nature, the initial split of the root cluster is identical to the 2-cluster example. Further splitting steps are performed until 10 clusters are obtained while maximizing the relative cluster centroid distances and intercluster quality. Figure 6.13 shows the hierarchy of the final... 

Note A. Cluster attributes for a two-cluster example. Cluster Quality is the average percent similarity of a document in the cluster from the cluster centroid. Cluster tokens are the individual words/terms that statistically distinguish each cluster. The most significant terms are listed first. A non-expert cannot easily define a more general theme of each cluster. B. Cluster themes and gist better defines the biological content of the clustered documents. It becomes clear that cluster 1 is related to Alzheimer s disease while cluster 2 contains Lymphoma documents. 

FIGURE 6.13 Clustering example—cluster hierarchy. Document cluster hierarchy separating documents about lymphoma from those about Alzheimer s disease. The cluster node names signify the most significant term for all documents within that cluster. 

Note Continued grouping of the documents from the two-cluster example identifies a range of subtopics within each disease document set. 

FIGURE 6.14 Clustering example—cluster theme heatmap. The top themes/concepts for each cluster are displayed in a heatmap. Biological themes distinguishing the two main topics are clearly distinct. The few shared themes between clusters of the two unrelated diseases, lymphoma (L) and Alzheimer s disease (AD), are analysis, disease, evaluation, groups, and relation. 

If the branching is on a ring cluster (peri-fused rings), use FrCI = —0. 45. This factor is used only once per ring cluster. [Example 1-23]... 

There are numerous /i4-carbide- and nitride-containing clusters examples from the iron-triad include [M4C(CO)i3] (M = Fe, and [M4N(CO)i2] (M = Fe,... 

The thiomolybdate(VI) anions [MoO S4 ] (n = 0-3) have been prepared by a number of methods and, with the exception of [MoOsS] ", act as versatile ligands to a wide variety of metal ions (see Table 1). In each of the compounds listed in this table, the [MoO S4- p ion acts as a bidentate ligand to the metal and the resultant structural versatility has been clearly demonstrated for copper(I) (Table 2). In addition, thiomolybdate(VI) anions are of interest since they have special relevance to aspects of bioinorganic chemistry. Thus, [MoS4] has been widely used in the synthesis of Fe—Mo—S clusters, examples of which serve as spectroscopic analogues for the iron-molybdenum cofactor of the nitrogenases (see Section 36.6.2), and Cu—Mo—S aggregates, which are relevant to the copper deficiency induced by molybdenum in ruminant animals. 

Fig. 22.1. PCA and hierarchical clustering example shown on a kidney sample, (a) Optical image of the kidney section prior to matrix application, (b) Scores of first principal component. The image is in agreement with the anatomy of the kidney, with the renal pelvis and part of the cortex showing the hot colors, (c) Clustering result Renal cortex, medulla, and pelvis are defined by the highest level clusters. The advantage of this type of analysis is that the dendrogram nodes can be expanded and highlighted until the desired molecular structure is found. Scale bar 2 mm.

Cluster geometry Atoms Atomic (N) orbitals (9N) High laying Cluster Cluster Examples 1 antibonding valence valence orbitals molecular electrons orbitals ... 

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