Character-state weight matrices

Character-state weight matrices have usually been estimated more or less by eye, but they can also be derived from a rate matrix. For example, if it is presumed that each of the two transitions occurs at double the frequency of each transversion, a weight matrix can simply specify, for example, that the cost of A-G is 1 and the cost of A-T is 2 (Fig. 14.5). (The parsimony method dictates that the diagonal elements of the matrix, or the cost of having the same base in different sequences, be zero. This proves to be a shortcoming of parsimony this will be discussed further below.) In the subsequent tree-building step, this set of assumptions will minimize the overall number of transversions and tend to cluster sequences differing mainly by transitions. 

Appendix 6B Data matrix used for this cladistic analysis which contained 7 taxa, 13 characters 6 trees each 20 steps long consistency index (Cl) = 0.85 homoplasy index (HI) = 0.15 Cl excluding uninformative characters = 0.81 HI excluding uninformative characters = 0.19 retention index (Rl) = 0.73 rescaled consistency index (RCI) = 0.62 unrooted tree(s) rooted using outgroup method optimality criterion = parsimony. All characters are unordered and equally weighted character-state optimisation ACCTRAN. 

An illustrative example, taken from the work of Weich, is shown in Figure 16. Both K and L emission spectra for crystalline and amorphous Si are shown. Because of the matrix element in Eq. (40), the K spectrum measures (roughly speaking) the density of electronic states weighted with the fractional p-like character of the states. Similarly, the L spectrum is weighted by the s-like character. Wiech has shown that by adding the two spectra for crystalline Si, appropriately... 

One of the important issues addressed in our simulations is the character of clusters under study. Are these clusters solid or liquid rmder experimental conditions If they arc liquid, then the distribution wc observe in the pick-up and consequently in the photodissociation simulations corresponds to a statistical distribution at a. given temperature. If, however, the cluster is solid then both in the simulations and in the cxj)eriment we observe a quasi-stationary state with a very long lifetime rather than an equilibrium thermodynamical state. This question can be resolved by means of the instantaneous normal modes (INM) density of states (DOS) spectrum. To calculate INM DOS wc construct the Hessian matrix in a mass-weighted atomic Cartesian coordinate basis of N atoms with /r=. r, y, z. The 3N eigenvectors in the form Ci -.Cjj,Cj-,C2, C2/,C2-,.c.vj.,ca/j,c.v de-... 

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