Node-labeled tree structure

The scheme in P in Example IV-2 is not tree-like. (Here we let A,B,C,D,E stand for arbitrary assignment statements or sets of assignment statements, in order to exhibit the structure of the example uncluttered by extraneous formulae.) The direct connection from the node labelled T(x ) following the node labelled D up to the node labelled B is anomalous since the path START A T(x ) D T(x ) does not contain B and the path START A T(x- ) B does not contain the node labelled T(x- ) following D. Similarly the two direct connections at the bottom of the diagram, from test T(x2) to test T(x ) and from test T(x ) to E are anomalous. The other direct connections in the graph are not anomalous. For example, the direct connection from test T(x2> up to the node labelled A is not anomalous since A is an ancestor of every node in the graph except START. 

Meiss and Ott [36] have developed these arguments further and proposed a model based on the Markov tree structure. They have also assumed that partial barriers are formed and cantori with small gaps divide the region around the outermost KAM torus into infinitely many states. An essential point in their argument is to give a labeling scheme to these states and to specify transition probabilities between adjacent states. In particular, each state is viewed as the node of tree, and the transition between these states is assumed to obey the Markov process. 

CandidTree shows the sub-free sfrueture uncertainty of a node by transparency (of the node label). To make the node readable, even if uncertainty is very high, CandidTree uses 128 as a minimum alpha value (50% transparent). From the usability study, we learned that it is difficult to distinguish small differences (e.g., the difference between 1 and. 9). To help users distinguish the 100% certain information from less certain data, CandidTree uses a solid link only when the sub-tree structure uncertainty is 0. For example, in Fig. 1, among the children of Megapodiidae, the sub-tree structure uncertainty of Leipoa and Macrocephalon is 0 and that of the others is non-0. 

Results. Overall ease of use improved slightly over the usability study (Table 1). Still, transparency as an indicator of the sub-tree structure change scored particularly low. Color representing the node location change was clear and It was easy to read the labels of the nodes also received relatively low scores. 

There are two possible approaches. In one approach we in effect build the execution sequence tree for P. We start with node (1,0) labelled START. A node (k,r) will be at level r of the new tree-like structure and be labelled with the instruction named by k. Suppose statement k in P is connected by an arrow (with or without a label) to statement p in P and that we have constructed node (k,r) in P to date. If (k,r) has no ancestor of the form (p,r ), r < r, place node (p,r+l) labelled by statement p on the tree, with an arrow from (k,r) to (p,r+l) which contains any label on the arrow from k to p. If there is already an ancestor (p,rT), r < r, of (k,r) on the tree, then do not create (p,r+l) but instead add an arrow from (k,r) back to (p,r ) containing any label also on the arrow from k to p. If P has N statements, this process must terminate in a scheme P with at most N levels. Clearly P is tree-like and is strongly equivalent to P. This transformation is global and structure preserving. In fact P is a strong homomorphic image of P under the homomorphism h taking each (k,r>) back into k. ... 

Applications. CART is not generally established yet, and as a consequence, not many applications for electrophoretic or similar data in the pharmaceutical held are found. Put et al. (52) apphed CART in a quantitative structure-retention relationship context on a retention data set of 83 structurally diverse drugs, in order to predict chromatographic retention. There were 266 molecular descriptors calculated and used as explanatory variables (X matrix). The considered response (y) was the retention factor of the compounds, predicted for a pure aqueous mobile phase. The total sum of squares of the response values about the mean of the node was applied as impurity measure. From all descriptors, three were selected to describe and predict the retention, and four terminal nodes were obtained (Fig. 13.11b). Arbitrarily, the drugs were then divided into hve retention classes. Each terminal node was then labeled with either one or two class names. The regression tree thus becomes a classihcation tree. From CV, it was concluded that only 9% serious misclassihcations were observed. 

Stress can be graphically represented in the sort of tree used to describe syllable constituent structure. In our previous example the nodes at the syllable level were unlabelled we can now show the same tree but with stress labels at the nodes ... 

In order to program this hypothesis we devised a representation technique called Abstract Sound Schema (ASS). The ASS is a tree-like abstract structure consisting of nodes, slots and links. Nodes and slots are components and links correspond to the relations between them. Both components and relations are labelled on the ASS. Slots are grouped bottom-up into higher-level nodes, which in turn are grouped into higher-level nodes and so on until the top node (Figure 7.2). 

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