Probability, weighted

Unconditional Probability (weighted sum) that Quality of Training is high vs. low is . 254. 746 ... 

Reserve Category Total Company (boe) Probability Probability Weighted Reserve (boe)... 

The expected profit across multiple scenarios provides a more realistic picture of the future profit situation compared to one single scenario. However, scenarios are consolidated and averaged in one total number with their probability weights. The planner would have no information about potential worst case profits as a profit basis and might like to sacrifice expected profit opportunities for safety in exchange. This is addressed by the two-phase optimization approach. 

The time evolution of the probability density is induced by Hamiltonian dynamics so that it has its properties—in particular, the time-reversal symmetry. However, the solutions of Liouville s equation can also break this symmetry as it is the case for Newton s equations. This is the case if each trajectory (43) has a different probability weight than its time reversal (44) and that both are physically distinct (45). 

The classical mechanics is naturally weighting the paths according to their instability. The higher the instability, the smaller the probability weight according to... 

Of course this method requires much larger amounts of lipid than ever found, for example, in an extract from a signal transduction experiment. In the latter instance, the most expedient approach would be to use a total phosphorus value as the basis for calculation of the probable weight of the particular fraction. This will be explained in the next section. 

Accordingly, the probability-weighted contributions to the average mutual-information quantities of bonded atoms are defined in reference to... 

The multicanonical algorithms are powerful, but the probability weight factors are not a priori known and have to be determined by iterations of short trial simulations. This process can be nontrivial and very tedius for complex systems with many degreees of freedom. 

Glucose is a system in which the conformational average of multiple low energy isomers cannot be ignored. That is, the free energy of solvation is a Boltzmann probability-weighted average over conformations ... 

Equations (1.52) and (1.53) are expressions of the number and weight fractions for the most-probable distribution of molecules expected for linear condensation polymerization. The most-probable weight fraction distribution W vr(p) is compared with experimental data in Fig. 1.18. While the number fraction for the most-probable distribution is a monotonic function, the weight fraction has a maximum. The position of the maximum in... 

Comparison of the most-probable weight fraction distribution (0.991) with experimental nylon 66 data from G. B. Taylor, J. Am. Chem. Soc. 69, 638 (1947). The dashed line is the number fraction distribution W/v (0.991). 

The most-probable weight fraction distribution [Eq. (1.53)] can be approximated for large number-average degree of polymerization N by an exponential representation, utilizing the expansion of the logarithm for p near unity ln/ S/7 — 1 and Eq. (1.55) for N -... 

Thus, the most-probable weight fraction distribution can be approximated by a linear function with an exponential cutoff-----------... 

This measure is also referred to as the probability-weighted average of all possible values of c. 

The probability-weight properties p and pj are, and should be, primarily independent of the property p that dehnes the second dimension of the descriptor. In other words, the distance dimension g(r) is separated from the property dimension g(p ), and, additionally, the probability is weighted by the property p. Figure 5.17 shows an example of a 2D RDF descriptor calcnlated for a simple molecule. 

The 2D RDF shows a distance axis and a property axis showing the partial atomic charge distribution. Since the probability-weight fnnction p is omitted, the fnnction simply splits into distance space and property space. The distance axis is equivalent to a one-dimensional RDF, whereas the property axis shows the charge distribution at a certain distance. The two intense peaks represent the C-H and C-H ... 

We now extend this notion for query answering that takes p-med-schema into consideration. Intuitively, we compute query answers by first answering the query with respect to each possible mediated schema and then for each answer tuple by taking the sum of its probabilities weighted by the probabilities of the mediated schemas. 

A direct test of the vibrationally adiabatic approximation for H + H2 has also been made (Bowman et al.. 1973). This test was done by projecting accurate wavefunctions on the vibrationally adiabatic functions for zero curvature, and measuring deviations of the resulting probability weight from unity. The symmetric stretch motion was found to be adiabatic to within 10 % for total energies between 0-51 and 0-72 eV, but adiabaticity was lost at lower and higher energies. 

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