Statistical signatures

The reconstructed structures are characterized by a two-point correlation function and their pore size distribution. The two-point correlation function S2) of an homogeneous medium can be obtained by randomly tossing a line segment of r length with a specific orientation and counting the number of times that the beginning (x) and the end (x -F r) of the line fall in phase j, as described by  

Using orthogonal coordinates, the two-point correlation function is employed to characterize the generated structures and it becomes  

The pore size is determined by the distribution of spheres of different racUi in the porous structure, where the pore radius is equal to the radius of the sphere that in its inside is formed by the empty phase (Schulz et al, 2007). To avoid that large spaces are fractioned into smaller spaces, the spheres radii begin to be modified from a maximum limit to unity. The characterized spaces are identified by the following index function  

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Room-temperature fluorescence (RTF) has been used to determine the emission characteristics of a wide variety of materials relative to the wavelengths of selected Fraunhofer lines in support of the Fraunhofer luminescence detector remote-sensing instrument. RTF techniques are now used in the compilation of excitation-emission-matrix (EEM) fluorescence "signatures" of materials. The spectral data are collected with a Perkin-Elraer MPF-44B Fluorescence Spectrometer interfaced to an Apple 11+ personal computer. EEM fluorescence data can be displayed as 3-D perspective plots, contour plots, or "color-contour" images. The integrated intensity for selected Fraunhofer lines can also be directly extracted from the EEM data rather than being collected with a separate procedure. Fluorescence, chemical, and mineralogical data will be statistically analyzed to determine the probable physical and/or chemical causes of the fluorescence. 

Because dissociation on So is barrierless, the product state distributions should be well approximated by statistical theories, especially when the excess energy is small, as in the Valachovic study. Product state distributions arising from the So pathway should be characterized by small translational energy release, but significant rovibrational excitation of HCO. This signature is demonstrated in the top panel of Fig. 17, which shows a HRTOF spectrum with... 

CFR - Part 77 is a federal law that regulates the submission of electronic records and electronic signatures to the FDA. Of particular interest to the statistical programmer are the following requirements of Part 11 ... 

Statistical studies of MALDI MS applied to bacterial samples show that some biomarker peaks are highly reproducible and appear very consistently, while others appear much less reliably.1719 In Jarman et al.20 and Wahl et al.21 a probability model for MALDI signatures is proposed that takes into account the variability in appearance of biomarker peaks. This method constructs MALDI reference signatures from the set of peak locations for reproducible biomarker peaks, along with a measure of the reproducibility of each peak. 

Inclusions of the CV3 led to the search for isotopic signatures of individual nucleosynthetic processes, or at least for components closer to the original signature than average solar compositions. They have also begun to demonstrate the isotopic variability of matter emerging from these processes in agreement with astrophysical and astronomical expectations. The principal features of inclusions are an up to 4% 0 enriched reservoir in the early solar system, variations in a component produced in a nuclear neutron-rich statistical equilibrium, and variations in the contribution of p- and r-process products to the heavy elements. 

It is vitally important that the multivariate nature of data related to a process be assessed to develop an understanding of a process and to assess quality. Process data together with appropriate chemometric models can provide information about (1) product quality inferentially from process conditions (2) process consistency (process signature, statistical process control) (3) analyzer reliability and (4) operational knowledge that can aid in scale-up and process transfers. ... 

Unfortunately, amendments to the approved protocol are frequent. These will require the same sign-off/approval of signatures as required for the original protocol. If the amendment has any impact on the clinical trial, either medically or statistically, it will need to be approved by an lEC. 

The date of approval of the protocol by the sponsor and the dated signature of the study director A statement of the proposed statistical methods to be used... 

Fig. 16.4. Three methods of obtaining Raman-based estimates of biofluid concentrations in vivo, a Confocal isolation of a subsurface volume occupied by a blood vessel, enabling direct measurement of a blood spectrum, b Difference measurement between tissue in two states, one with more blood in the sampling volume (in this case, due to pressure modulation by the subject [6]). Computing the difference removes the bulk tissue contributions to the spectral measurement and emphasizes the contribution from blood, c Statistical correlation approach of measuring many volunteers tissue in a region where sufficient blood is present (e.g., the forearm as shown here) and obtaining a correlated reference value from a blood sample drawn at the same time. Multivariate calibration is then used to find correlations between the reference value and the spectral data vector. Unlike the previous two methods, this does not intrinsically isolate the blood chemicals Raman signatures from those of the surrounding tissue volume...

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