Representations reduction

The continuous line in Figure 16 shows results from fitting a single tie line in addition to the binary data. Only slight improvement is obtained in prediction of the two-phase region more important, however, prediction of solute distribution is improved. Incorporation of the single ternary tie line into the method of data reduction produces only a small loss of accuracy in the representation of VLE for the two binary systems. 

The primary purpose for expressing experimental data through model equations is to obtain a representation that can be used confidently for systematic interpolations and extrapolations, especially to multicomponent systems. The confidence placed in the calculations depends on the confidence placed in the data and in the model. Therefore, the method of parameter estimation should also provide measures of reliability for the calculated results. This reliability depends on the uncertainties in the parameters, which, with the statistical method of data reduction used here, are estimated from the parameter variance-covariance matrix. This matrix is obtained as a last step in the iterative calculation of the parameters. 

Number of polygons in the outer Isosurface hull (wireframe representation) before and after two stages of polygon reduction... 

Figure 2-17. a) The redundanl bond malrix of ethanal with ihe zero values omitted, b) It can be compressed by reduction to the top right triangle, c) Omitting the hydrogen atoms provides the simplest non-redundant matrix representation. 

Data reduction. The process of transforming the initial digital or analog representation of output from a spectrometer into a form that is amenable to interpretation, e.g., a bar graph, a table of masses versus intensities. 

Preprocessor. A device in a data-acquisition system that performs a significant amount of data reduction by extracting specific information from raw signal representations in advance of the main processing operation. A preprocessor can constitute the whole of a data-acquisition interface, in which case it must also perform the data-acquisition task (conversion of spectrometer signal to computer representation), or it can specialize solely in data treatment. 

In describing the various mechanical properties of polymers in the last chapter, we took the attitude that we could make measurements on any time scale we chose, however long or short, and that such measurements were made in isothermal experiments. Most of the experimental results presented in Chap. 3 are representations of this sort. In that chapter we remarked several times that these figures were actually the result of reductions of data collected at different temperatures. Now let us discuss this technique our perspective, however, will be from the opposite direction taking an isothermal plot apart. 

The reduction of the x representation, like all such reductions, gives a unique set of irreducible representations which is... 

Figure 25-2 provides a more detailed schematic representation of the two preferred pollution prevention techniques (i.e., source reduction ana recychng). 

Another source of departure from stoichiometry occurs when cations are reduced, as for example in tire reduction of zinc oxide to yield an oxygen-defective oxide. The zinc atoms which are formed in tlris process dissolve in the lattice, Zn+ ions entering interstitial sites and the coiTesponding number of electrons being released from these dissolved atoms in much the same manner as was found when phosphorus was dissolved in the Group IV semiconductors. The Kroger-Viirk representation of dris reduction is... 

The human-machine interface (usually abbreviated to interface) is a major focus of interest for the HF/E approach to the reduction of human error. A representation of the interface in a CPI context is provided in Figure 2.2. The interface is the boimdary across which information from the process is transduced by sensors and then displayed in a form that can be utilized by the... 

The representation of the results from slow strain-rate tests may be through the usual ductility parameters such as reduction in area, the maximum load achieved, the crack velocity or even the time to failure, although as with all tests, metallographic or fractographic examination, whilst not readily quantifiable, should also be involved. Since stress-corrosion failures are usually associated with relatively little plastic deformation, the ductility... 

Fig. 16-10 A schematic representation of how the oxygen reduction and production rate, dnojdt combine to determine the size of the global oxygen reservoir. (Adapted from Holland, 1978.)...

The transformation of the irreducible representations of the molecular point group to those of the site is connected with a reduction of the symme-... 

Just as mass and energy must be conserved, so also must electrical charge. Yet free electrons are not found stable in nature under the conditions of chentistry on earth, so caimot appear as reactants or products in representations of chemical reactions. Example 11 is a half-equation , something that represents a common pattern in chemical reactions, but only occms when coupled to another suitable half-equation (i.e., this reduction process must be paired with an oxidation process that releases electrons), e.g. 

Figure 3.6 Schematic representation of deposition-reduction (DR) method (a) positiveiy charged supports and (b) negativeiy charged supports.

Figure 3.7 Schematic representation of the reduction of Au (III) ions at the outer layer of the electric double layer in aqueous media [43].

Figure 20.6 Schematic representation of the effects of 5-HT reuptake inhibitors on serotonergic neurons, (a) 5-HT is released at the somatodendritic level and by proximal segments of serotonergic axons within the Raphe nuclei and taken up by the 5-HT transporter. In these conditions there is little tonic activation of somatodendritic 5-HTia autoreceptors. At nerve terminals 5-HTib receptors control the 5-HT synthesis and release in a local manner, (b) The blockade of the 5-HT transporter at the level of the Raphe nuclei elevates the concentration of extraneuronal 5-HT to an extent that activates somatodendritic autoreceptors (5-HTia). This leads to neuronal hyperpolarisation, reduction of the discharge rate and reduction of 5-HT release by forebrain terminals, (c) The exposure to an enhanced extracellular 5-HT concentration produced by continuous treatment with SSRIs desensitises Raphe 5-HTia autoreceptors. The reduced 5-HTia function enables serotonergic neurons to recover cell firing and terminal release. Under these conditions, the SSRI-induced blockade of the 5-HT transporter in forebrain nerve terminals results in extracellular 5-HT increases larger than those observed after a single treatment with SSRIs. (Figure and legend taken from Hervas et al. 1999 with permission)...

Ru 2,2 -bipyridine complexes can form a large number of colored compounds upon successive reduction, with the formal Ru oxidation state from +2 to -4. In the case of highly reduced complexes, proper representation of the electrochromic reaction is actually the reduction of the hgand, not that of the metal center. 

Figure 3. Schematic representation of the selective synthesis of metal nanowires and nanoparticles by the Sintering Controlled Synthesis approach, (a) Mesoporous silica, (b) impregnation of mesoporous silica with metal ions, (c) addition of water/alcohol vapors and UV-irradiation, or wet H2-reduction, (d) formation of metal nanowires, (e) dry H2-reduction, (f) formation of metal nanoparticles.

Figure 17.7 Electrocatalysis of O2 reduction by Pycnoporus cinnabarinus laccase on a 2-aminoanthracene-modified pyrolytic graphite edge (PGE) electrode and an unmodified PGE electrode at 25 °C in sodium citrate buffer (200 mM, pH 4). Red curves were recorded immediately after spotting laccase solution onto the electrode, while black curves were recorded after exchanging the electrochemical cell solution for enzyme-fiiee buffer solution. Insets show the long-term percentage change in limiting current (at 0.44 V vs. SHE) for electrocatalytic O2 reduction by laccase on an unmodified PGE electrode ( ) or a 2-aminoanthracene modified electrode ( ) after storage at 4 °C, and a cartoon representation of the probable route for electron transfer through the anthracene (shown in blue) to the blue Cu center of laccase. Reproduced by permission of The Royal Society of Chemistry fi om Blanford et al., 2007. (See color insert.)...

Figure 17.19 A membianeless ethanol/02 enz3fme fuel cell. Alcohol dehydrogenase and aldehyde dehydrogenase catalyze a stepwise oxidation of ethanol to acetaldehyde and then to acetate, passing electrons to the anode via the mediator NAD+/NADH. At the carhon cathode, electrons are passed via the [Ru(2,2 -bipyridyl)3] and biUverdin/bilimbin couples to bilirubin oxidase, which catalyzes O2 reduction to H2O. (a) Schematic representation of the reactions occruring. (b) Power/cmrent response for the ceU operating in buffered solution at pH 7.15, containing 1 mM ethanol and 1 mM NAD. Panel (b) reprinted from Topcagic and Minteer [2006]. Copyright Elsevier, 2006.

The most serious problem with input analysis methods such as PCA that are designed for dimension reduction is the fact that they focus only on pattern representation rather than on discrimination. Good generalization from a pattern recognition standpoint requires the ability to identify characteristics that both define and discriminate between pattern classes. Methods that do one or the other are insufficient. Consequently, methods such as PLS that simultaneously attempt to reduce the input and output dimensionality while finding the best input-output model may perform better than methods such as PCA that ignore the input-output relationship, or OLS that does not emphasize input dimensionality reduction. 

---