Tree interpretation

They reason as follows let S denote the average size of the trees, interpreted as the total surface area of the branches in a stand. Then the carrying capacity K should be proportional to the available foliage, so K = K S. Similarly, the halfsaturation parameter A in the predation term should be proportional to S predators such as birds search units of foliage, not acres of forest, and so the relevant quantity A must have the dimensions of budworms per unit of branch area. Hence A = A S and therefore... 

TREE INTERPRETATION—THE IMPORTANCE OF IDENTIFYING PARALOGS AND ORTHOLOGS... 

A series of monographs and correlation tables exist for the interpretation of vibrational spectra [52-55]. However, the relationship of frequency characteristics and structural features is rather complicated and the number of known correlations between IR spectra and structures is very large. In many cases, it is almost impossible to analyze a molecular structure without the aid of computational techniques. Existing approaches are mainly based on the interpretation of vibrational spectra by mathematical models, rule sets, and decision trees or fuzzy logic approaches. 

This paper presents a continuation of work done by Cayley. Cayley has repeatedly investigated combinatorial problems regarding the determination of the number of certain treesK Some of his problems lend themselves to chemical interpretation the number of trees in question is equal to the number of certain (theoretically possible) chemical compounds. 

Pursuing this correspondence between a C-H graph and the corresponding C-graph we find a new interpretation of the numbers p and R p is the number of topologically different free C-trecs with n vertices, R is the number of planted C-trees with n nodes. In other words ... 

It was largely this chemical interpretation which led Cayley to enumerate various kinds of trees. He gave (without much of a proof) the formula for the number of trees on n labelled vertices [CayA89], and the equation... 

Lowdin, P.-O., Phys. Rev. 97, 1474, 1490, 1509, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals and convergence problems in the method of configuration interaction. II. Study of the ordinary Hartree-Fock approximation. III. Extension of the Har-tree-Fock scheme to include degenerate systems and correlation effects. ... 

The model induced via the decision tree is not a blackbox, and provides explicit and interpretable rules for solving the pattern classification problem. The most relevant variables are also clearly identified. For example, for the data in Table I, the value of the temperature are not necessary for obtaining good or bad quality, as is clearly indicated by the decision tree in Fig. 22. 

The analysis of the branching structure turns the preceding deduction process around. We have all the facts available to us at the end of the solution synthesis, i.e., at the end of solving a particular problem. Our task is to select and connect subsets of those facts to prove new results that are useful for deriving new control information. In essence, we have to turn facts about solutions and partial solutions at lower levels in the tree, into constraints on the properties of states and alphabet interpretations higher in the tree. 

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 ... 

With the view that a KBS interpreter is a method for mapping from input data in the form of intermediate symbolic state descriptions to labels of interest, four families of approaches are described here, each offering inference mechanisms and related knowledge representations that can be used to solve interpretation problems namely, model-based approaches, digraphs, fault trees, and tables. These methods have been heavily used... 

It is not only the vast difference of about 1.8 billion years which is so surprising the timescale for the separation point of the main branches of the tree of life is clearly shifted. The catastrophe hypothesis put forward to explain this difference appears unlikely, since there are no signs of such a phenomenal obliteration of all life on Earth. Another explanation could be that the data from the amino acid sequences provide only information on the way in which life forms diverged, but not on the timescale (Schopf, 1998). This interpretation of the Doolittle event by Schopf was provided at a time when doubts had not yet been cast on the dating of the first fossils at 3.45 billion years, published by him in 1993. 

Let P be any program scheme. Using our algorithm for testing whether a path is an execution sequence, we construct a tree T(P) of all possible execution sequences for P under free interpretations. The tree T(P) may be finite or infinite our main result on the subject will say that T(P) is finite if and only if P is always halting. The nodes of T(P) are labelled with execution sequences. At level n (declaring the root or initial node to be at level 1)... 

If the flowchart P has a loop-free graph - if P is a tree - then the construction of W(P,A,B) is now quite simple. If P is loop-free there are only a finite number of paths 0, ...,on from START to STOP which are consistent and hence execution sequences. The input condition A(X) is a function only of the inputs, of course, while the output condition B(X,Y) can be regarded as a function of the input and of the final values of all the program variables (some of these values, of course, may play no role in the statement of the condition). Notice that under these conditions, when is a complete execution sequence from START to STOP, the path verification condition VCPjO AB, ) for any interpretation I is a function of the input X alone. 

Statements (l)-(4) are equivalent since we saw before that if a scheme halts for any interpretation, it halts for some finite interpretation. Further, if P halts for any input under any interpretation, (P,I,x) converges for some free interpretation I and we can discover this by building the (possibly infinite) execution sequence tree and seeing whether STOP ever appears. Hence CD—(M-) are partially decidable. 

SUBLEMMA Let P be any program scheme and I any free interpretation. If (P,I) ever constructs a full binary tree of depth N with distinct leaves, then P must have at least N+l storage locations (variables). 

PROPOSITION 7.7 If S is a recursion scheme such that for each n there is a free interpretation I for which the computation of val(S,I, x) requires constructing a full binary tree of depth n or greater with distinct leaves, then S is not flowchartable. 

Construct a recursion augmented scheme P without iteration (the main scheme and all procedure bodies are trees - no loops) and an interpretation I with domain the nonnegative integers and using only dyadic function,... 

Keeling interprets these seasonal isotopic variations as caused by trees preferentially removing 12C02 from the atmosphere in summer when they are growing but not in winter when they are dormant. 

If the stable isotope ratio of 13C/12C is to be further measured in tree rings and interpreted as an indicator of climate variation, (and we have barely begun to initiate its use as a thermometer in the present work, confining our measurements to the stable isotopes in water, because water is so abundant compared to carbon dioxide and because the dependence of its isotope ratios is relatively simple compared with those of carbon dioxide), some more sophisticated considerations must be given to the distribution of carbon dioxide among the reservoirs on the surface of the earth. 

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