Independent counting

Figure 5. Potential of PARG MEFs for immortalization. Cells with indicated genotypes were seeded at 10 cells/well and immortalized following a 3T3 protocol. Every 3 days cells were trypsinized, counted and replated. Data represent the mean of two independent counts. These data represent one of three independent experiments.

We used a LB 9505 multidetector unit for the simultaneous and continuous recording of luminescence from six samples (Berthold and Maly 1987). This instrument is equipped with six rubidium-bialkali photomultiplier tubes placed in close proximity to the vials inside six independent counting chambers. Reflectors ensure optimum counting efficiency. Each measuring chamber has its own temperature control. Since the results from all six detectors should allow direct comparison, they were standardised by determination of its individual sensitivity constant (X-factor). 

In order to consider the 3D structure but make the chirality code independent of a specific conformer, r- is taken as the sum of the bond lengths between atoms i and j on the path with a minimum number of bond counts. 

First, solutes with larger electrophoretic mobilities (in the same direction as the electroosmotic flow) have greater efficiencies thus, smaller, more highly charged solutes are not only the first solutes to elute, but do so with greater efficiency. Second, efficiency in capillary electrophoresis is independent of the capillary s length. Typical theoretical plate counts are approximately 100,000-200,000 for capillary electrophoresis. 

Aperture impedance and most other automated counters measure MCV and RBC independently, in contrast to the manual methods where MCV and MCH accuracies depend on hemocytometer red cell count accuracy. 

The chi-square distribution can be applied to other types of apph-catlon which are of an entirely different nature. These include apph-cations which are discussed under Goodness-of-Fit Test and Two-Way Test for Independence of Count Data. In these applications, the mathematical formulation and context are entirely different, but they do result in the same table of values. 

A similar formalism is used by Thompson and Goldstein [90] to predict residue accessibilities. What they derive would be a very useful prior distribution based on multiplying out independent probabilities to which data could be added to form a Bayesian posterior distribution. The work of Arnold et al. [87] is also not Bayesian statistics but rather the calculation of conditional distributions based on the simple counting argument that p(G r) = p(a, r)lp(r), where a is some property of interest (secondary structure, accessibility) and r is the amino acid type or some property of the amino acid type (hydro-phobicity) or of an amino acid segment (helical moment, etc). 

Consider, for definiteness, a set of otherwise identical lowest-level components of a system, so that the hierarchy is a tree of constant depth. Since we assume that the components are all identical, the only distinction among the various nodes of the hierarchy consists of the structure of the subtrees. Now suppose we have a tree T that consists of /3 subtrees branching out from the root at the top level. We need to determine the number of different interactions that can occur on each level, independent of the structure of each subtree i.e. isomorphic copies of trees do not contribute to our count. We therefore need to find the number of nonisomorphic subtrees. We can do this recursively. 

Because the Geiger counter produces pulses independent in size of x-ray wavelength, it is the best detector for the method of counting that employs a capacitor to accumulate the individual counts (2.3, 2.10). 

For the usual accurate analytical method, the mean f is assumed identical with the true value, and observed errors are attributed to an indefinitely large number of small causes operating at random. The standard deviation, s, depends upon these small causes and may assume any value mean and standard deviation are wholly independent, so that an infinite number of distribution curves is conceivable. As we have seen, x-ray emission spectrography considered as a random process differs sharply from such a usual case. Under ideal conditions, the individual counts must lie upon the unique Gaussian curve for which the standard deviation is the square root of the mean. This unique Gaussian is a fluctuation curve, not an error curve in the strictest sense there is no true value of N such as that presumably corresponding to a of Section 10.1—there is only a most probable value N. 

In other words, if we assume that the counting function N(t) has statistically independent increments (Eq. (3-237)), and has the property that the probability of a single jump occurring in a small interval of length h is approximately nh but the probability of more than one jump is zero to within terms of order h, (Eq. (3-238)), then it can be shown 51 that its probability density functions must be given by Eq. (3-231). It is the existence of theorems of this type that accounts for the great... 

Singh KK, Hughes MD, Chen J, Spector SA (2005) Genetic polymorphisms in CX3CR1 predict HIV-1 disease progression in children independently of CD4-I- lymphocyte count and HIV-1 RNA load. J Infect Dis 191 1971-1980... 

Since cigarette tobacco already contains several micrograms of the TSNA, we determined the transfer rate of NNN into the smoke by spiking the tobacco column with NNN-2 - C. The smoke from such radiolabeled cigarettes is then analyzed by HPLC and the amount of unchanged NNN-2 - C is determined by liquid scintillation counting. Independent of the smoke pH, about 11% of the radioactive NNN is found in the mainstream smoke thus 41-46% of mainstream smoke NNN stems from the tobacco NNN and 54-59% are pyrosynthesized (11). 

Radioisotope-labeled nitrosamines have proven valuable in development of analytical methods and for demonstrating efficiency of recovery of nitrosamines from tobacco products and smoke (37-39). The very high specific activity required for low part-per-billion determinations has discouraged most analysts from using this approach. Unless a radiochromatographic detector with adequate sensitivity is available, samples must be counted independently of the final chromatographic determination, and one of the advantages of internal standardization, correction for variation in volume injected, is lost. 

Figure 6. Schematic outline of the first commercially available multiple collector ICPMS, the Plasma 54, after Halhday et al. (1995). This instrument uses Nier-Johnson double-focusing and is equipped with eight independently adjustable Faraday collectors. The axial collector can be wound down to provide access to a Daly detector equipped with ion counting capabilities and a second-stage energy filter for high abundance sensitivity measurements. The sample may be introduced to the plasma source by either solution aspiration or laser ablation.

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