Three-dimensional data sets

One technique for high dimensional data is to reduce the number of dimensions being plotted. For example, one slice of a three-dimensional data set can be plotted with a two-dimensional technique. Another example is plotting the magnitude of vectors rather than the vectors themselves. 

MS offers the opportunity for both qualitative and quantitative analysis in a single instrument and even in a single experiment. In full-scan mode, mass spectra are continuously scanned as the gas chromatographic analysis proceeds. As shown in Fig. 14.8, GC/MS provides a three-dimensional data set with axes of time, mass-to-charge ratio and... 

Recently, however, NMR techniques have been developed that can be used to considerably accelerate the measurement of large three-dimensional data sets [31,32], These reduced-dimensionality techniques have already been successfully used in in-cell NMR applications [16]. In the future these techniques might enable the complete backbone assignment of a protein in its natural environment and might enable detailed investigation of different folding states. 

All obtainable three-dimensional data sets were used to test this methodology. They were the following Aluminium Iron alloy [20], Brucite (Mg(OH)2), CNBA, DMABC, DMACB, Copper Perchlorophthalocyanine, Poly(l-butene) form III, Polyethylene, Silicon surface, Poly (1,4- trans-cyclohexanediyl dimethylene succinate) (T-cds)... 

The mechanical scanner simply scans the array downward in 1 s to capture a full aperture ( 0.75 x 2.0 m) three-dimensional data set. This data set is then reconstructed and displayed using the computer system. 

FIGURE 6.8 (a) Different types of outliers when a three-dimensional data set is projected on a robust two-dimensional PC A subspace, with (b) the corresponding outlier map [44],... 

The term 2D NMR, which stands for two-dimensional NMR, is something of a misnomer. All the NMR spectra we have discussed so far in this book are two dimensional in the sense that they are plots of signal intensity versus frequency (or its Fourier equivalent, signal intensity versus time). By contrast, 2D NMR refers to spectroscopic data that are collected as a function of two time scales, tx (evolution and mixing) and t2 (detection). The resulting data set is then subjected to separate Fourier transformations of each time domain to give a frequency-domain 2D NMR spectrum of signal intensity versus two frequencies, Fx (the Fourier transform of the t time domain) and F2 (the Fourier transform of the t2 time domain). Thus, a 2D NMR spectrum is actually a three-dimensional data set ... 

Figure 3.1. PCs of three-dimensional data set projected on a single plane. Prom [242], reproduced with permission. Copyright 1996 AIChE.

RSSF spectroscopy provides a three-dimensional data set where, in the absorbance mode of detection, the three dimensions are absorbance, wavelength, and time. Compared to SWSF spectroscopy, RSSF spectroscopy significandy expands the set of information contained in a single experiment. This wealth of information has the potential not only for defining the kinetic pathway of a reaction, but also for allowing spectroscopic characterization and identification of transient intermediates that accumulate and decay along the pathway. 

I. In a CITS experiment the current control is released and the I-V characteristics at the particular pixel are recorded. This added information represents a three-dimensional data set of current-voltage characteristics as a function of the x, y spatial position on the image and can be displayed as a 3D map of current at a particular location at a particular voltage. At certain bias voltages, the current... 

Formation and decay of transient intermediates constitute a phenomenon that is ubiquitous to enzyme catalysis. Time-resolved UV/visible optical spectra which document the absorbance spectral changes that accompany the conversion of chromophoric reactants to final products by way of transient intermediates have the potential for identification of these transient species. The RSSF experiment provides three-dimensional data sets consisting of optical absorbance as a function of both wavelength and time. Owing to the temporal nature of the acquired data, an RSSF experiment can be a powerful tool for sorting out the timing of intermediate formation and decay with respect to other events that take place during... 

The structural details of even the best rendered data are more clear in a display mode that shows more than a single view of the three-dimensional data set. The... 

An LC—MS chromatogram is essentially a three-dimensional data set with separate chromatographic, mass-to-charge (m/z) and ion count (intensity) dimensions. The combination of chromatography and mass spectral approaches can take on many incarnations and are dependent on the nature of the metabonomics investigation. Because of the complexity of most metabonomics samples, the final solution is often a compromise between good science and expediency since the ideal analytical conditions for 1000+ metabolome components is an um-ealistic goal. In this section, we will discuss each of these elements separately with an emphasis on biomedical metabonomic applications. 

Three-dimensional data sets can be examined using different 2D and3D reconstruction techniques, starting with multiplanar reformations along three orthogonal axes and in oblique planes. 

The RAW file can be directly imported into the MIA toolbox (tee Note 16). Unit mass binning is applied to the skull file and masses from m/z=0 to 200 are selected for image PCA analysis (see Note 17). The imported data set of the skull is a three-dimensional data set of 256 (pixels)x256 (pixels)x200 (masses) elements. Each element in the data set is the ion intensity of a specific mass at a specific pixel of the skull image. 

In the early stage of X-ray CT development, a pencil beam was used with an X-ray detector in combination with linear and rotational morions of an object, followed subsequently by a fan beam with a one-dimensional array detector. A scan must, however, be performed at every individual Z plane to recon-stmct a three-dimensional image. The scan time was therefore extended to obtain a full data set in the early stages of the development. Nowadays, a two-dimensional X-ray image detector is routinely used, and three-dimensional data set is obtained with one turn of the object. 

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