Mean held approach

Mean-field theory can be used to predict the effects of mutation rate and parent fitness on the moments of the mutant fitness distribution (Voigt et al, 2000a). In this analysis, only the portion of the mutant distribution that is not dead (zero fitness) or parent (unmutated) is considered. The mutant effects are averaged over the transition probabilities without the cases of mutations to stop codons or when no mutations are made on a sequence. In order to obtain the fitness distribution, two probabilities are required (1) the probability pi(a) that a particular amino-acid identity a exists at a residue i, and (2) the transition probability that one amino acid will mutate into another Q = 1 — (1 — pm)3. The probability vectors p a) can be determined through a mean-held approach (Lee, 1994 Koehl and Delarue, 1996 Saven and Wolynes, 1997). The amino acid transition probabilities Q are calculated based on the special connectivity of the genetic code and the per-nucleotide mutation rate. Removing transitions to stop codons and unmutated sequences only requires the proper normalization of the probabilities pi and the moments. For example, the first moment of the fitness improvement w of the uncoupled fitness function is written as... 

The exact relations (21) and (23) are quite simple but different from those corresponding to the mean held approach given in (8) and (9). 

A model-independent conclusion The general behaviour of the in-plane paraconductivity is not affected, even up to T°, by doping. The SCF effects in L l eSr CuCU thin films seem to be not related to the pseudogap. t From the comparison of the measured paraconductivity with the ex-ended GGL approach i) The measured l c is a good mean-held critical temperature for the GGL approach, ii) Both the relaxation time of the SCF and the reduced temperature, e°, where the SCF vanish, are doping-independent and they take values close to those of BCS superconductors. This last result demands further studies. 

We observe at this point that Eq. (S.S9) supplemented by Eq. (S.S8) expresses the most recent analytical result obtained to account for the effects of nonlinear excitation. Note, however, that the perturbation approach behind this equation means that it is unable to account for large deviations from linear response theory. In other words, both the intrinsically nonlinear statistics of the system under study and the intensity of the external excitation have to be assumed to be quite small. The rotational coimterpart of Eq. (S.S8) (< is replaced by the angular velocity comparison with the results obtained by applying the continued fraction procedure (CPF) (see Chapters III and IV). It has been shown that the deviation of the linear response theory from the CFP is intermediate between that predicted by Eq. (5.59) and that based on Suzuki s mean held approximation (Chapter V). (In agreement with the CFP, however, both predict that the decay of becomes slower with increases in the excitation parameter r = ( )exc/ " )eq -1.)... 

Equation (108) also illustrates the well-known fact that in d = 4, mean held theory would be valid up to the critical point, at least if logarithmic corrections are disregarded [74], But what is most interesting in the present context, is that Eq. (106) also describes how closely one can approach the spinodal curve... 

In the same way, employing the principle of corresponding states and scaling plots, de Gennes has obtained Equations 11 and 12 in the mean held approximation. The equations differed essentially from Debye s results (section 3.3.1.2). Debye took a different approach within the framework of the mean hefd approximation (see the end of section 4.3, Equations 4.3-148 and further). 

Because the AIMS method associates a unique nuclear wavefunction with each electronic state, one has direct access to dynamical quantities on individual states. This is unlike mean-held based approaches that use only one nuclear wavefunction for all electronic states [59]. One can therefore calculate branching ratios... 

The factors 3 and 7 are statistical factors. If the rule of the geometric mean held and there were no secondary effects, then = I2 = However, if successive substitution on L2O has a secondary effect, it is likely that there will be a similar effect on L30. We follow the approach of preserving the simple form of the theory. 

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