Hierarchical trees

The initiating event task was a detailed and systematic search for accident initiators that fail barriers to radioactive material release using dendograms (hierarchical trees). Dendograms define barriers and their failure modes in terms of J phenomena (e.g., melt,... 

A common way of visualizing such spaces is through a kind of hierarchical tree (see figure 7.3), whose leaves are identified with states and the distances between leaves - measured by counting the number of branches that must be traversed in... 

An analysis is conducted of the predicted values for each team member s factorial table to determine the main effects and interactions that would result if the predicted values were real data The interpretations of main effects and interactions in this setting are explained in simple computational terms by the statistician In addition, each team member s results are represented in the form of a hierarchical tree so that further relationships among the test variables and the dependent variable can be graphically Illustrated The team statistician then discusses the statistical analysis and the hierarchical tree representation with each team scientist ... 

Each participant is permitted to revise the predictions until satisfied that both the factorial table (which focuses on combinations of the test variables) and the associated hierarchical tree (which focuses on the individual test variables) properly reflect the scientist s views concerning the anticipated relationships among the test conditions and the predicted values of the dependent measure ... 

Agenda 6 The last agenda consists of a team review and approval of a write-up that documents the final test design The documentation must Include the consensus factorial table, hierarchical tree, and mathematical model used to fit the predicted values In addition, the documentation must Include all basic arguments and considerations, even if these considerations do not appear in explicit form in the final design The specific reasons for excluding certain test... 

Factorial tables, hierarchical trees, and associated mathematical models are elementary tools used to guide the efforts of the design team ... 

Hierarchical Trees. The hierarchical tree is constructed by the team statistician for each scientist in accord with the factorial table filled out by the scientist. To be useful for this purpose the tree must have the capability of exhibiting virtually any conceivable relation among the test factors and the dependent variable. It would be undesirable if the scientists were forced to constrain the anticipated relationships in any manner. 

Figure 1 shows the hierarchical tree that corresponds to Table I. The scale at the top of the tree corresponds to the predicted time to failure in months. The conditions at the top of the tree are given by 71 C, 72%, and 8.3 suns and correspond to an expected failure time of approximately 16 months. The first split in the tree is associated with a temperature of 95 C on the left branch and 50 C on the right branch, which correspond to average predicted lifetimes of approximately four and 27 months, respectively. The next two splits are seen to be based on relative humidity and ultraviolet radiation. 

To date every relationship anticipated by team scientists has been easily represented by a hierarchical tree. Moreover, all of the structures shown In Figure 2 have actually occurred In applications. Thus, It Is not uncommon for Interactive synerglsms to be... 

Figure 1. Hierarchical tree showing predicited life as a function of test variables.

The form of the mathematical model fitted to the consensus factorial table must be reassessed after the hierarchical tree Is pruned and the experimental design has been revised by the statistician. 

Fig. 2. The graph representation of various relations among proteins or genes. The pathway and the assembly are representations of biochemical knowledge about the network of molecular interactions. The genome represents the positional correlations of genes. The neighbor, cluster, and hierarchical tree are computationally obtained from a set of binary relations, namely, similarity relations of protein pairs or gene pairs.

The sequence rules do not suffice to deal with constitutional properties, as these are not fully given by the tree graph. Additional rales are required to define the relative importance of atoms or groups within the tree graph. The corresponding hierarchical tree graph is defined as follows ... 

J. Zupan, M.E. Munk, Hierarchical Tree based Storage, Retrieval, and Interpretation of Infrared Spectra, Anal. Chem., 57, (1985), 1609. 

Topologies. The traditional way of connecting smaller computers to a central mainframe system has been the star topology, sometimes in the form of hierarchical trees. Other networks have been built with many point-to-point connections and... 

Extension of the atom-bond-configuration Hierarchical Tree... 

Six basic modeling classes presented in Section IV. A are the root-classes for expanded trees of modeling subclasses. Whereas the six basic elements are designed to possess generic attributes and methods, independent of the particular domain they represent, the hierarchical trees emanating from... 

Figure 26 provides a different view of the ConceptDesigner"s structure. It shows that every project generates a series of distinct process flowsheets, all of which are handled by a file management system, which is organized in a hierarchical tree to reflect the evolution of the design and the various alternative designs. It also depicts the various sources of data... 

The hierarchical clustering techniques have been applied to many studies of gene expression patterns with some success.57 However, the hierarchical tree cannot determine the optimal number of clusters in the dataset. The limitation of the hierarchical algorithms is that the number of classes is determined by cutting the tree structure at an ad hoc level selected by the user. Such an ad hoc level does not necessarily reflect the true nature of the underlying structure of the gene expression data. 

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