Trees Unique

Using this ordering, we can construct a canonical representation of a given tree by reordering the children of each vertex according to the order defined above. See Figure 6. From this canonical representation, we can construct a linear code which represents the tree uniquely. There are many possible ways to do this one way is defined by the following rules. 

The Decision Forest (DF) is a DT-based consensus modeling method that was conceived as a method for combining heterogeneous yet comparable trees that fully captures the association between molecular structure and biological activity (Figure 6.4) [59], The heterogeneity requirement assures that each tree uniquely contributes to the combined prediction whereas the quality comparability requirement assures that each tree equally contributes to the combined prediction. 

Another problem for fault trees is the uniqueness of the result. Eault trees produced by two different teams of analysts most often show a different stmcture. However, this problem is reduced as the detail in the problem definition increases. 

An example of a top event expression is T= A-l- B C, where A, B, and C are comfjonent failures. This top event consists of a one-component minimal cutset (A) and a two-componcnt-minimal cutset (B C). The minimal cutsets are unique to the top event and independent nf other ways the fault tree may be drawn. 

Clearly and uniquely specify the top event to the precise requirements without ( /er-specification which might exclude important failure modes. Even if constructed by difh ent analysts, the top event specification should produce trees that have the same Boolean equatio. ... 

FTAP The Eault Tree Analysis Erogram (Willie, 1978, Section 6.4, and di.stribution disk) is a cutset generation code developed at the University of California, Berkeley Operation Research I iter. FTAP is unique in offering the user a choice of three processing methods to >wn. 

Its unique design suggests several accident scenarios that could not occur at other reactors. For example, failure to supply ECC to 1/16 of the core due to the failure of an ECC inlet valve. On the other hand, some phenomena of concern to other types of reactors seem impossible (e.g., core-concrete interactions). The list of phenomena for consideration came from previous studies, comments of an external review group and from literature review. From this, came the issues selected for the accident progression event tree (APET) according to uncertainty and point estimates. 

Appendix III of this report provides a detailed description of the reliability data used in event tree and fault tree quantification. Because of its extensive operating experience and the uniqueness of the BRP design, BRP plant-specific data was used whenever possible. Plant-specific data sources included plant maintenance orders, control room log books, surveillance tests, LERs, event reports, deviation reports, plant review committee meeting minutes, and USNRC correspondence. The plant-specific data used spanned the period from 1970 to 1979. Data before 1970 did not include maintenance orders or surveillance tests and therefore were excluded. The plant-specific data collected for BRP is presented in detail in Appendix XIII. Table III-4 summarizes 30 plant-specific component failure rates and Table 11-06 contains plant-specific maintenance unavailabilities for 20 components. These tables are a summary of the BRP component failure and maintenance outages. 

Planted trees have two types of vertices, roots and nodes, subject to two conditions a root is the unique element of its species, it has valence one. In the general case there is no restriction. The partition into species can be arbitrary and is not tied to the valence. If the number of species is equal to the number of vertices, we are dealing with individually different vertices. At the other extreme is the graph in which all the vertices are interchangeable. 

Variation within a species was examined by looking at the chemistry of Z. dipetalum specimens collected from sites on three islands, Hawaii, Kauai, and Oahu. Of the seven compounds detected in this comparison, only two, caryophyl-lene [542] and humulene [543] (see Fig. 6.5 for structures 542-546), were present in all individuals. Trees from a site on Oahu were unique in their possession of... 

Notice that T(P) is a proper tree. An execution sequence s of length n 2 2 is consistent with exactly one execution sequence s of length n-1 namely, if s consists of statements (k, k2,...,kn), then s is %, k2,...jk. The tree T(P) is finite branching for if s is an execution sequence of length n and s = (k. .., k ) we need only consider the possibilities far statement k. If it is a STOP statement, s is a complete execution sequence and has no consistent extensions so it labels a node with no sons. If kR is an assignment statement, or a farced transfer, there is exactly one statement kn+1 such that (kpk2,..., k, kn+ ) is consistent, namely the unique statement following. If is a conditional transfer (test) then, since our tests are binary,... 

Examine Scheme A in Example E - 2. Prove that it always halts and find the longest computation. Then construct the simplest strongly equivalent tree scheme you can find (its computation may or may not be shorter than those in the original scheme there is not necessarily a unique answer). 

There are many types of roots, including thick fibrous, deep tap, shallow, and tubers, all in one plant community. Some roots explore the soil to significant depth (i.e., as much as 250 cm deep), while others are shallow (i.e., only 25 cm deep). Different rooting depths are found in all plant types grasses, legumes, shrubs, and trees. Each root type will contribute its own unique exudates and characteristics to its unique volume of soil and the associated soil solution. 

The coconut is an unusual food for many reasons. It is technically a seed, produced by the coconut palm tree, and as such is one of the largest edible seeds produced by any plant. Its unusual contents also make it unique in the seed world—the interior consists of both meat and water. The meat is the white pith with which we are all familiar, as it is used extensively for cooking and flavorings the coconut water is a white liquid that is very sweet and thirst-quenching. 

Dendrons and dendrimers are the most intensely investigated subset of dendritic polymers. In the past decade over 2000 literature references have appeared on this unique class of structure controlled polymers. The term dendrimer was coined by Tomalia, et al. over 15 years ago in the first reports on poly(amidoamine) (PAMAM) dendrimers [75, 76]. It is derived from the Greek words dendri-(branch tree-like) and meros - part of). Poly(amidoamine) dendrimers constitute the first dendrimer family to be commercialized and undoubtedly represent the most extensively characterized and best understood series at this time. In view of the extensive literature information in this area, much of the remaining overview will focus on PAMAM dendrimers and will... 

Fourth lesson - combination of different compounds in unique macrostructure provides unique performance properties. Starch is used extensively in nature to store carbon and energy. Starch is readily digested and must be protected from degradation by a resistant coating, for example, a seed (e.g. com, wheat or rice) or a skin (e.g. potato). Woody materials such as trees, soft plants and grasses are composed of a complex combination of aliphatic and aromatic compounds (cellulose, hemicellulose and lignin). 

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