Statistics accuracy

Although energy resolution is rarely employed in positron camera systems, scatter is not normally a problem. This is because of the very short time window within which two photons must arrive in order to be counted. At low decay rates, the incidence of accidental events is very low, rising only slightly for those that occur as the result of scatter. Some systems employ time-of-flight measurements of the time difference between the arrival of the two photons to obtain additional information about the location of an annihilation along the line. This has been used to improve resolution and statistical accuracy. Resolution is in the range of 3—4 mm and is less dependent on position than is SPECT (16). 

With the Industrial Revolution, life became more complex but it was not until World War II that reliability engineering was needed to keep the complex airplanes, tanks, vehicles and ships operating. Of particular concern was the reliability of radar. Prior to this time equipment was known qualitatively to be reliable or unreliable. To quantify reliability requires collecting statistics on part failures in order to calculate the mean time to failure and the mean time to repair. Since then, NASA and the military has included reliability specifications in procurements thereby sustaining the collection and evaluation of data build statistical accuracy although it adds to the cost. 

Fig. 5(a) contains the oxygen and hydrogen density profiles it demonstrates clearly the major differences between the water structure next to a metal surface and near a free or nonpolar surface (compare to Fig. 3). Due to the significant adsorption energy of water on transition metal surfaces (typically of the order of 20-50kJmoP see, e.g., [136]), strong density oscillations are observed next to the metal. Between three and four water layers have also been identified in most simulations near uncharged metal surfaces, depending on the model and on statistical accuracy. Beyond about...

The first equation expresses a scaling idea as in Eq. (18), introducing the arbitrary factor 2/3 instead of unity for numerical convenience—the problem of statistical accuracy becomes easier, and numerical prefactors should not matter in statistical considerations. 

Of the gas holdup tine are obtained by regression procedures after testing the linearity of the hoaologous series plot and selecting an appropriate nuadser of standards to give the required statistical accuracy In the calculation procedure (353,354. ... 

Fig. 2.1. Po(AU), the Boltzmann factor exp (—/3AU) and their product, which is the integrand in (2.12). The Iovj-AU tail of the integrand, marked with stripes is poorly sampled with Po(AU) and, therefore, is known with low statistical accuracy. However, it provides an important contribution to the integral...

In practice, this simple formula will hardly ever work, especially if the free energy changes appreciably with . Consider, for example, two states of the systems, , and j such that A,1 f <) - AA( j) = 5/, BT. Then, on average, the former state is sampled only seven times for every 1,000 configurations sampled from the latter state. Such nonuniform sampling is undesirable, as it leads to a considerable loss of statistical accuracy. For the free energy profile shown in Fig. 3.1, transitions between... 

The radon in the air i/as measured continuously by electroprecipitation of the positively charged Po-218 ions in an electric field (10 kV) on a surface barrier detector (Porstendorfer, et al., 1980). For this purpose the air i/as dried, filtered and sucked into an aluminium sphere ( 2 1) with a flowrate of 0.5 lmin-1. The counts due to Po-218 and Po-214 were proportional to the radon activity concentration. Their disintegrations were directly detected by alpha spectroscopy with an energy resolution of about 80 keV. The monitor could detect down to 5 Bq m 3 with a two hour counting time and 30 % statistical accuracy. 

A collaborative study conducted by Britton et al. (1984) to determine the most reliable method among the three most commonly used methods (two colorimetric methods and the specific ion electrode method) showed that both pyridine-barbituric acid and pyridine-pyrazolone have similar statistical accuracy. The pyridine-barbituric acid method was preferred by Britton et al. (1984) over the pyridine-pyrazolone method for its convenience (quicker analysis time) rather than the statistical accuracy of data. The electrode method had higher data variability. 

The FPA experiment can also be performed by exciting into the S2band of ethidium using 315-nm radiation and detecting at 630 nm (J. H. Shibata, J. C. Thomas, and J. M. Schurr, unpublished results). Substantial cancellation of the two main relaxing terms (n = 1, 2) in r(t) considerably diminishes the statistical accuracy of the best-fit a., but nevertheless it remains the same as found for excitation into S, which provides a reassuring check. Using intercalated quinacrine as the probe dye, Fan et al. recently obtained a... 

The precision structure analysis of crystals and quantitative reconstruction of ESP requires the maximum possible set of structure amplitudes, which would provide a precise scaling factor, information on the thermal atomic motion and the high resolution of the ESP with good statistical accuracy being at least 1-2%. Such an experimental data set can be collected by an electron diffractometer which was designed on the basis of EMR-102 [3] (Fig. 3). 

The reflection intensities can be measured as the sums of the intensities recorded at each point of the scanned profile. The computer of the system can carry out the measurement in both accumulation mode (to achieve the same required statistical accuracy for all reflections either strong or weak) or in constant time mode. Although in accumulation mode, precision of the order of 1% can be achieved for all reflections in the ED pattern (dynamical range of 10 ), measurement time is within the order of 10 min up to now. However, it is foreseen that in near future, measurement times of 1 min can be achieved for up to 50 reflections. 

Now the specimen is perfectly aligned and it remains to measure the rocking curve. This is normally done by selecting a step size on the axis and a counting time per step for the detector. Some systems will allow instead the selection of a total number of counts at each step, so that constant statistical accuracy is... 

Flow cytometry (FCM) is a high-precision technique for rapid analysis and sorting of cells and particles. In theory, it can be used to measure any cell component, provided that a fluorescent tracer is available that reacts specifically and stoichiometrically with that constituent. The technique provides statistical accuracy, reproducibility, and sensitivity. 

The extraction of more complex particle size distributions from PCS data (which is not part of the commonly performed particle size characterization of solid lipid nanoparticles) remains a challenging task, even though several corresponding mathematical models and software for commercial instruments are available. This type of analysis requires the user to have a high degree of experience and the data to have high statistical accuracy. In many cases, data obtained in routine measurements, as are often performed for particle size characterization, are not an adequate basis for a reliable particle size distribution analysis. 

Figure 1. Typical ESR growth curve. Aliquots of enamel or other sample material are irradiated artificially and the increase in intensity measured A minimum of 10-12 points is required to provide statistical accuracy. The extrapolation of the growth curve to the x-axis gives the accumulated dose, AD.

There remains the problem of statistical accuracy, since the total count in the 239Pu peak, assuming a dosage of 0.008 Bqh m-3 and a counter efficiency of 32%, is less than 3 cpm. A statistical problem of another kind lies in the fact that the D.A.C. of 239Pu in air is equivalent to one Pu02 particle of diameter 1.6 jum Per m3 °f air. At a sampling rate of 301 min-1, one such particle would be sampled in half an hour. 

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