Terminal node

Search trees are widely used to represent the different states that a problem cem adopt, example is shown in Figure 9.4 from which it should be clear where the name deri especially if the page is turned upside down. A tree contains nodes that are connected edges. The presence of an edge indicates that the two nodes it connects ctre related in so way. Each node represents a state that the system may adopt. The root node represents initial state of the system. Terminal nodes have no child nodes. A goal node is a special k of terminal node that corresponds to Em acceptable solution to the problem. 

Tree representation of the conformation search problem for hexane. Unlike the tree in Figure 9.4 the path gth from the root node to any of the terminal nodes is constant. 

Fig. 12.39 Tree describing the rules to differentiate active and inactive inotropic compounds. Each of the terminal nodes corresponds to the numbers of active and inactive molecules produced by the application of the preceding rules.

Define a balanced tree as any tree such that all of its leaves arc located at the same distance from its root. Let the height of a tree equal the maximum number of arcs that arc traversed while desc ending from any leaf or terminal node to the root of the tree. Let D2 N) be the maximum 2 dividing N. We state the following theorem for rule R90 for the ca.se when N is even without proof (see [martin84]) ... 

Although decision trees contain a number of attractive features, including competitive accuracy, when considered strictly as classification devices (Saraiva and Stephanopoulos, 1992a), the most important point for our purposes is that each of the tree s terminal nodes identifies a particular hyperrectangle in the decision space, X, associated with a given y value. For example, node M defines a y = excellent rectangle that corresponds to the following rule ... 

This splitting procedure is now applied reeursively to each of the children nodes just created. The successive expansion process continues until terminal nodes or leaves, over which no further partitions are performed, can be identified. 

In Fig. 4 we present the final induced decision tree, as well as the partition of the (xi,X4) plane defined by its leaves, together with a projection of all the available (x, y) pairs on the same plane. These two decision variables are clearly influencing the current performance of the refinery unit, and the decision tree leaves perform a reasonable partition of the plane. To achieve better performance, we must look for operating zones that will result in obtaining mostly y = 3 values. Terminal nodes 2... 

This follows step 2a. Only one ion remains on the column. It is now eluted, so that the terminal node is reached. 

Fig. 2.1. A tree representing the phylogeny of Wolbachia in arthropods (groups A and B) and filarial nematodes (groups C and D). Group designations correspond to those proposed by Werren etal. (1995) and by Bandi etal. (1998). The names at the terminal nodes are those of the host species. The tree is based on the ftsZgene sequence alignment used by Bandi etal. (1998). The tree was obtained using a distance matrix method (Jukes and Cantor correction neighbour-joining method).

An example of a problem solving tree for the synthesis of Darvon appears in Figure 3. The tree contains both AND nodes and OR nodes (7). The AND branches, connected by double arcs, indicate that both compounds are required to make the compound above them. The OR branches (there are three OR paths to make compound II) indicate different routes for making the compound. The terminal nodes corresponding to starting materials are enclosed in boxes. At present, a branch is terminated when the number of clauses in the clause list, the internal representation of the goal, is less than or equal to six or the clause list matches the clause list of a starting material molecule. 

The tree selected is not necessarily the best tree, even among trees of the same complexity, the same number of terminal nodes. 

The results of the recursive partitioning analysis displaying the 12 terminal nodes and their amalgamation into six classes are shown in Fig. 1. The first major nodal split was identified as patient age. For the 541 patients under age 50 the most significant split was... 

Fig. 1. Results of the recursive partitioning analysis showing the major nodal splits by prognostic factor and the amalgamation of terminal nodes into six distinct classes.

The sum of the reaction rates for the steps incident on/from each terminal node must be some stoichiometric multiple of the overall reaction rate. 

The sum of the affinities for any trail, path or walk between two terminal nodes must be the affinity of the overall reaction. 

Figure 7. Reaction route graphs for the peroxide and superoxide-peroxide mechanisms reaction steps occur on directed edges nodes n, represent the component potentials, the difference between these potentials for adjacent nodes is the affinity of the associated reaction step and terminal nodes are open, intermediate nodes, closed.

Figure 1.8. Decision tree. Shown is a rudimentary tree structure (D, descriptors T, terminal nodes) for recursive partitioning. Terminal nodes are shaded gray.

The application of CT analysis to the pH data in Table 18.4 generated a CT (Figure 18.1). The CT is interpreted by reading from the root node (node 1) at the top of the tree to the terminal nodes (nodes 3,4, and 5) at the bottom. The nodes are numbered in the top left comer. Before the splitting... 

MOGP is based on the more traditional optimisation method genetic programming (GP), which is a type of GA [53,54]. The main difference between GP and a GA is in the chromosome representation in a GA an individual is usually represented by a fixed-length linear string, whereas in GP individuals are represented by treelike structures hence, they can vary in shape and size as the population undergoes evolution. The internal nodes of the tree, typically represent mathematical operators, and the terminal nodes, typically represent variables and constant values thus, the chromosome can represent a mathematical expression as shown in Fig. 4. 

Fig. 4 In genetic programming (GP), a chromosome is a tree structure and can be used to represent a mathematical expression where the internal nodes are mathematical operators and the terminal nodes are variable or constant values...

In MoQSAR, the internal nodes include the sum, quadratic and cubic power operators and the terminal nodes consist of the molecular descriptors available for the dataset. A chromosome is translated into a QSAR in two steps (1) the expression encoded in a chromosome is extracted to determine the descriptors that will be used in the QSAR model (2) optimum values for the coefficients and the intercept are calculated using the least-squares method. 

Fig. 3. Transfonnation of the molecular forest of trees (a) into a forest of rooted trees (b) for a tri-functional monomer. node representing a monomer unit, O terminal node representing an unreacted functionality...

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