Unweighted Averaging

While the majority of moleeules may be adequately represented by a single resonanee eontributor, there are numerous situations where two or more eontributors are needed. The simplest ease is where all the eontributing resonance struetures are equivalent. Here, the proper deseription is in terms of an unweighted average. 

Fig. 4. The dependence of the unweighted average fraction on the fold rank for the 22 complete proteomes. The unweighted average fraction of folds is shown separately for bacterial, archaeal, and eukaryotic proteomes and for the entire collection. The broken blue line shows the best-fitting power-law approximation, the analytic form of which is also shown (k is the fold rank).

With the exception of the orientation factor, all the parameters in this equation may be obtained within reasonable error by direct experimental measurement or by estimation. The problem of setting reasonable values for k2, which may vary from 0 to 4 for orientations in which the dipole moments are orthogonal or parallel, respectively, is nontrivial. A value of , which is an unweighted average over all orientations, is often used. Dale et al.(53) have examined this problem in great detail and have shown that a k2 value of is never justified for energy transfer in macromolecules because it is impossible for the donors and acceptors to achieve a truly isotropic distribution. They do provide an experimental approach, using polarized emission spectroscopy, to estimate the relative freedom of motion for the donor and acceptor that allows reasonable limits to be set for k2. 

For odd m, is an integral of an odd function over a symmetric interval and hence = 0. To calculate the susceptibility and specific heat to second order in we require I2 and I4, which will be calculated using symmetry arguments similar to those employed to derive the a = 0 unweighted averages (see, e.g., arguments in Ref. 135). 

The proportion of ATS abuse related treatment is highest in Asia (19%), notably in East South-East Asia (unweighted average of 37 % in 2005), the Oceania... 

Fig. 48 Perceived availability of cocaine among US high school students, 1998-2006 (unweighted average of 8th, 10th and 12th grade students reporting that it is fairly easy or very easy to obtain cocaine powder)...

Previous comparative school surveys, undertaken under the auspices of OAS/CICAD in Central America in 2001/02 found an (unweighted) average life-time prevalence rate among 15-16 year old students of 1.5 per cent. Only Guatemala reported above average cocaine use levels (2.3%).17 The perception of lower levels of cocaine use in Central America could, however, be misleading as one cannot exclude the possibility that cocaine use increased substantially over the last few years in this region. 

The yields reported by Member States varied substantially, from as low as 5 kg/ha to 17,500 kg/ha. This is a reflection of the wide ranges of cannabis yields, e.g. from wild cannabis to hydroponically grown cannabis. Within reported estimates the median cannabis yield was 730 kg/ha and the (unweighted) average yield was 2,070 kg/ha. Despite the large difference, such yield fig-... 

Australia unweighted average of results from all sites... 

Fig. 2.4 Crude estimates of the coefficients of the n orbitals of a Z-substituted alkene as an unweighted average of the coefficients of an allyl cation 2.2 and butadiene 2.3...

Unweighted Averaging.—One oftra has to deal with systems exhibiting no interaction between the microsystems (l/j, = 0), when the potential energy does not depend explicitly on the configurational variables t. The statistical function (96) now reduces simply to ... 

In equation (2), P is the bulk gas saturation pressure P(- is the pore filling pressure R is the gas constant and T is the temperature. In the original HK method, the mean heat of adsorption is computed from an unweighted average of the gas-solid interaction potential taken over the accessible volume of the pore ... 

Thus, the average value of k obtained graphically using a set of observations made at equally spaced time intervals is determined by the ratio of the difference between the value of f( o) and the unweighted average of the f(a ) to the time elapsed to exactly midway in the experiment. 

Since the nature of the data set is not always clear, a good approach in prediction is to build a consensus model using a combination of several methods. There are different ways of achieving this. One is to run the same approach, for example, a neural network, many times and build an ensemble or committee model. The other is to use several approaches, for example, PLS, RE, NN, and calculate the weighted or unweighted average in a consensus model. The advantage is that you cover various aspects of the nature of the data and each individual model uses a potentially different descriptor subset. 

---