Conditional statistics

Attention must be paid to the specific technical problems posed by measuring flow in industrial ventilating systems, such as high turbulence level and long time-variation of mean velocity. The LDA measurement conditions (statistically sufficient number of LDA data, suitably long duration of LDA measurements for recognition of long-term phenomena) must be carefully selected for an appropriate treatment of these problems. 

In one-point models for turbulent mixing, extensive use of conditional statistics is made when developing simplified models. For example, in the PDF transport equation for /++ x, r), the expected value of the velocity fluctuations conditioned on the scalars appears and is defined by... 

In theory, such information could be extracted from high-resolution experimental data. However, due to the technical challenges, conditional statistics of small-scale quantities are more readily accessible from numerical simulations. 

Statistical data can provide general information about how common a condition is, how many people have the condition, or how likely it is that a person will develop the condition. Statistics are not personalized, however—they offer estimates based on groups of people. By taking into account a person s family history, medical history, and other factors, a genetics professional can help interpret what statistics mean for a particular patient. 

Ury, H. K., and A. C. Hexter. Relating photochemical pollution to human physiological reactions under controlled conditions. Statistical procedures. Arch. Environ. Health 18 473-480, 1%9. 

The authors have studied the properties of this density in detail [24, 33] and have observed some similarities between the PF and the AMC as well as some differences. Both these methods are utilized in the context of a single-point closure. Therefore, in both cases the magnitudes of moments up to second order must be provided externally. Also, neither method accounts for migration of the scalar s bounds as mixing proceeds. This is portrayed by the evolution of the conditional statistics of the scalar namely, the conditional expected dissipation and the conditional expected diffusion [41, 42]. 

From Eq. (3.1), the correlation time xc is defined as the time constant for which the correlation function exponentially decays to zero. At a time small compared with rc, exp(—t/xc) — 1 and we expect that essentially all spins maintain their original value. Therefore, most of the products will be A. At times long with respect to rc, we expect that all spins have changed their orientations many times, so that on the average half of the spins will result with the same Ms with respect to their original values, and the other half will have the other Ms value. Under these conditions, statistically half of the products will be A and half — A, and the summation over a large number n of spins will yield zero. 

Another important aspect in validation of a new dissolution method is to investigate how sensitive the dissolution results of the product, for which the method has been developed, are for minute variations in operating conditions. Examples of factors to consider in such a test are temperature of test medium, rotational speed, volume, sampling procedure, medium compositions and testing performed by different operators. Based on such robustness tests of the method, limits can be defined for acceptable variations of test conditions. Statistical design may be useful to apply in situations such as those demonstrated earlier in this chapter. 

The first step in reduction of the frequency of accidents is to determine whether the cause of an accident belongs to the system or to some specific person or set of conditions. Statistical methods provide the only method of analysis to serve as a guide to the understanding of accidents and to then-reduction [p. 314],... 

Figure 9.7 Staphylococcus epidermidis adhesion on textured polyurethane surfaces in (a) PBS and (b) 75% PPP for 1 h under static conditions. (Statistical symbols , compared to same polyurethane without PEG modification , compared to PEG smooth polyurethane.)...

Now express the monomer conditional statistical weights in terms of matrix G ... 

In membrane research, Michael has developed a poroelectroelastic theory of water sorption and swelling together with Peter Berg (NTNU Trondheim). It rationalizes the impact of external conditions, statistical distribution of anionic head groups, and microscopic elastic properties of the polymer on water sorption and swelling. This work has opened up an intriguing research area the study of internal mechanical stresses in charged elastic media, induced by water sorption. 

Fig. D-20. The prevalence of selected chronic disorders in people of various ages in the U.S. for each of the diseases or conditions. Statistical Abstract of the United States, 1991, U.S. Dept, of Commerce, p. 120, Table 195)...

Given the lack of legislation on this issue, the researcher must always judge the necessary adaptation of work protocols, based on the promoter s requests (number of repetitions, number of volunteers, experimental conditions, statistical treatments to interpret results, etc.). 

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