Statistical clustering

Matsushita, M Hayakawa, Y. and Sawada, Y. (1985) Fractal structure and cluster statistics of zinc-metal trees deposited on a line electrode. Phys. Rev. A, 32, 3814-3816. 

In the striatum, postischemic proliferation was also increased. As in the frontal cortex, the BrdU+ cells were either single cells or doublets, but were not in clusters. Statistical analysis revealed that the density of BrdU+ cells in the monkeys... 

R. Blanc, J. L. Bouillot, C. Camoin, and M. Belzons, Cluster Statistics in a Bidimensional Suspension Comparison with Percolation, Rheol. Acta, 22, 505-511 (1983). 

As mentioned before, the disordered solids will be mostly modelled in this book using randomly diluted site or bond lattice models. A knowledge of percolation cluster statistics will therefore be necessary and widely employed. Although this lattice percolation kind of disorder will not be the only kind of disorder used to model such solids, as can be seen later in this book, the widely established results for percolation statistics have been employed successsfully to understand and formulate analytically various breakdown properties of disordered solids. We therefore give here a very brief introduction to the percolation theory. For details, see the book by Stauffer and Aharony (1992). 

Several attempts have been made to relate these conductivity exponents tc or Sc with the percolation cluster statistical exponents discussed earlier. For example, in the node-link-blob model, the conductivity E of the network is proportional to the number of parallel links, while the... 

As discussed earlier, the percolation theory or similar theories of the cluster statistics in disordered solids can give us the probability density g l) of the defect clusters of linear size 1 ... 

For use of these cluster statistics g l) in eqn (1.22) for the failure probability F a), one needs to relate the breaking stress cr to the length I of a crack, and extract g a) from g l). This is usually done using the stress concentration formula (1.21), or some generalised versions of it like the Griffith (1920) formula discussed later in Chapter 3. Let us write... 

Auf der Heyde, T, P. E., and Biirgi, H.-B. Molecular geometry of d five-coordination. 2. Cluster analysis, archetypal geometries, and cluster statistics. Inorg. Chem. 28, 3970-3981 (1989),... 

Studies on each of the hypotheses presented in this section can directly employ spatio-temporal analyses of climate data [9] and spatial analyses, such as spatial cluster statistics [12, 22], for fly-animal relationships. 

Carr D. B., Somogyi R., Michaels G. (1997) Templates for looking at gene expression clustering. Statistical Computing and Graphics Newsletter 8(1), 20-29. 

Auf der Heyde, T.P.E., Buergi, H.-B. Molecular Geometry of d Five Co-ordination. 2 Cluster Analysis, Archet3rpal (Geometries and Cluster Statistics. Inorg. Chem. 1989,25, 3970-3981. 

The MSE appears to point toward photoionization/pooling primary ionization models, because of inconsistency with preformed/cluster models. Although secondary matrix-analyte reactions occur in clusters, observation of complete matrix suppression would require that there are never more preformed ions than analyte molecules in any randomly formed cluster. Statistics would seem to exclude this, especially since the analyte is often inhomogeneously distributed. Diffusion of ions in the plume is better able to explain the MSE, since ion mobility and mixing is much better than in clusters. 

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