Analytical information dimensionality

The second question concerns the quality of the chemical control, directed more at the chemical analysis proper and its procedure. Important factors here are sufficient specificity and accuracy together with a short analysis time. In connection with accuracy, we can possible consider the quantization of the analytical information obtainable. For instance, from the above example of titration, if we assume for the pH measurement an accuracy of 0.02, an uncertainty remains of 0.04 over a total range of 14.0, which means a gain in information of n1 = 14.0/0.04 = 350 (at least 8 bits) with an accuracy of 5% as a mean for the titration end-point establishment of both acids, the remaining uncertainty of 1% over a range of 2 x 100% means a gain in information of n2 = 200 (at least 7 bits), so that the two-dimensional presentation of this titration represents a quantity of information I = 2log nx n2 = 15 bits at least. 

MSn are of particular interest. MSn stands for the n-fold coupling of mass spectrometers, alternatively serving as separation and detection instrument. By hyphenated techniques the dimensionality of analytical information (see Sect. 3.4) and, therefore, also the information amount (see Sect. 9.3) is significantly increased (Eckschlager and Danzer [1994]). 

A classification of the basis of these analytical quantities with regard to their mutual relationships and dependencies from physical quantities like space co-ordinates and time will be given in Sect. 3.4 according to the dimensionality of analytical information. 

As a result of analytical measurements, signals are obtained and, in the case of instrumental measurements, signals functions, y = f(z). The record of the signal intensity as a function of the signal position, Fig. 3.8, represents a two-dimensional signal function which can be back-transformed into two-dimensional analytical information, x = /(Q). 

Fig. 3.8. Two-dimensional analytical information in form of a signal function... 

Alternative characterization of the dimensionality. The SIMS example demonstrates that the dimensionality of analytical information and of signal functions occasionally follow other principles than those given above, where the dimensionality of a functional relationship is determined by the number of dependent and independent variables in such a function. 

Multispecies analyses require two-dimensional analytical information y = f(x)y see Sect. 3.4, mostly in the form of spectra and chromatograms. By evaluation of various signals or the entire signal function, simultaneous information on several sample components can be obtained (in the extreme case on all the constituents contained in the sample). The relevant quantity that characterizes multicomponent analyses is the information amount,... 

Figure 1.3 — (A) Dimensionality of analytical information. (B) Frequency ordering of the different types of information produced (and used) in connection with sensors.

Figure 1.3.A shows the scheme for another analytical information hierarchy that is complementary to the previous ones. Thus, gravimetries, titrimetries, classical qualitative analyses and sensors provide onedimensional information of the form F = where x is the signal concerned. On the other hand, instrumental techniques provide two-dimensional information that can be of two types depending on whether the signal (x) is combined with an instrumental parameter (y), time (f) or space (s). Some modem analytical techniques (several of which use hybrid instruments) furnish three-dimensional information by combining signals with one or two instrumental parameters (y, z), time and space. The great...

The goal of this section is the preparation and measurement of a number of calibration standards that contain the ammonium ion, the potassium ion or both ions simultaneously. These two-dimensional combined standards will be generated systematically, trying to provide the maximum variability to the system. The analytical information will be obtained using the array of three potentiometric PVC membrane... 

Cafiete et al. have recently elaborated on this approach by implementation of normal and derivative cyclic voltammetry. Pointing out that these types of three-dimensional analytical information is very powerful indeed (being similar to that provided by image detectors such as diode arrays), offering, besides theoretical studies, interesting practical possibilities especially in the multidetection of electroactive compounds, the authors used their cyclic... 

Possibility of obtaining analytical information from microscopic sample areas combined with linear or two-dimensional automatic scanning over the sample surface. 

Fig. 3.9. One-dimensional information (in y-direction) of a single signal at a fixed z-value (left-hand side) and quasi-multidimensional information on several analytes AyBy...,N as a sequence of one-dimensional information (right-hand side)... 

Time-dependent analytical measurements, which give three-dimensional information of the type y = f(zy t) as shown schematically in Fig. 3.11a. The same characteristic holds for distribution analysis in one spatial direction, i.e., line scans, y = f(zylx). Such signal functions are frequently represented in form of multiple diagrams as shown in Fig. 3.11b. 

For the simultaneous analysis of n components, at least N > n useful signals must be available. Instrumental-analytical methods produce as a rule two-dimensional information y = /(z), e.g., in form of spectra, chromatograms etc., as schematically shown in Fig. 7.11. 

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