Similarity of patterns

As well as the Euclidean distance, other metrics have been proposed and employed to measure similarities of pattern vectors between objects. One method used for comparing and classifying spectroscopic data is the Hamming distance. For two pattern vectors i and X2 defined by Equation (38), the... 

Figure 5.13 Topology of a SOM with 6x6 output neurons. The input vectors are connected to the output neurons (the connections to neuron j is shown in the figure). The output layer in the SOM structure displays the similarity of pattern so that the similar patterns are adjacent, and different ones are well separated.

Separation of families by merely increasing the resolution evidently can not be used when the two chemical families have the same molecular formula. This is particularly true for naphthenes and olefins of the formula, C H2 , which also happen to have very similar fragmentation patterns. Resolution of these two molecular types is one of the problems not yet solved by mass spectrometry, despite the efforts of numerous laboratories motivated by the refiner s major interest in being able to make the distinction. Olefins are in fact abundantly present in the products from conversion processes. 

The breaking of a strategic bond and the generation of synthesis precursors defines a synthesis reaction. In the simplest case, the reaction is already known from literature. In most cases, however, the rcaaion step obtained has to be generalised in order to find any similar and successfully performed reactions with a similar substituent pattern or with a similar rearrangement of bonds. One way of generalizing a reaction is to identify the reaction center and the reaction substructure of the reaction. This defines a reaction type. 

The stability of the alkali metal ozonides increases from Li to Cs alkaline-earth ozonides exhibit a similar stability pattern. Reaction of metal ozonides with water proceeds through the intermediate formation of hydroxyl radicals. 

Figure 1 shows the decomposition sequence for several hydrous precursors and indicates approximate temperatures at which the activated forms occur (1). As activation temperature is increased, the crystal stmctures become more ordered as can be seen by the x-ray diffraction patterns of Figure 2 (2). The similarity of these patterns combined with subtie effects of precursor crystal size, trace impurities, and details of sample preparation have led to some confusion in the Hterature (3). The crystal stmctures of the activated aluminas have, however, been well-documented by x-ray diffraction (4) and by nmr techniques (5).

The successful appHcation of pattern recognition methods depends on a number of assumptions (14). Obviously, there must be multiple samples from a system with multiple measurements consistendy made on each sample. For many techniques the system should be overdeterrnined the ratio of number of samples to number of measurements should be at least three. These techniques assume that the nearness of points in hyperspace faithfully redects the similarity of the properties of the samples. The data should be arranged in a data matrix with one row per sample, and the entries of each row should be the measurements made on the sample, as shown in Figure 1. The information needed to answer the questions must be implicitly contained in that data matrix, and the data representation must be conformable with the pattern recognition algorithms used. 

Several silk fibroin genes have been cloned and sequenced and they all show a similar sequence pattern variable domains at the N- and C-termini flank a large region of repetitive short sequences of alternating poly-Ala (8 to 10 residues) and Gly-Gly-X repeats (where X is usually Ser, Tyr, or Gin). This middle region varies in length and may comprise up to 800 residues. 

Air supplied in confined space by downward vertical jets creates a similar flow pattern as in the case of air supply by horizontal nonattached jets. With vertical air supply, the occupied zone is ventilated directly by air jets. Grimitlyn suggests that the area of occupied zone ventilated by one jet be sized based on the jet s cross-sectional area at the point it enters the occupied zone. The jet cross-sectional area and configuration depend upon the height of the air supply, the type of air jet, and diffuser characteristics ( K, and K, ). 

Although CNTs showed similar EELS pattern in plasmon-loss and core-loss regions to graphite, SWCNT and fine MWCNT with a diameter less than 5 nm had different features. Furthermore, it has been found out that the angular-dependent EELS along the direction normal to the longitudinal axis of CNT shows stronger contribution from Jt electrons than [Pg.38]

Ketones and aldehydes ean be eonverted into a number of nucleophilie moleeules with similar reaetivity patterns. 

As an indication of the changes in deformation modes that can be produced in ionomers by increase of ion content, consider poly(styrene-co-sodium methacrylate). In ionomers of low ion content, the only observed deformation mode in strained thin films cast from tetra hydrofuran (THF), a nonpolar solvent, is localized crazing. But for ion contents near to or above the critical value of about 6 mol%, both crazing and shear deformation bands have been observed. This is demonstrated in the transmission electron microscope (TEM) scan of Fig. 3 for an ionomer of 8.2 mol% ion content. Somewhat similar deformation patterns have also been observed in a Na-SPS ionomer having an ion content of 7.5 mol%. Clearly, in both of these ionomers, the presence of a... 

In our discussion of Hopfield nets in section 10.6, we found that the maximal number of patterns that can be stored before their stability is impaired is some linear function of the size of the net n, ax aN, where 0 < a < 1 and N is the number of neurons in the net (see sections 10.6.6 and 10.7). A similar question can of course be asked of perceptroiis How many input-output fact pairs can a perceptron of given size learn ... 

Figure 3.1 The reactions of ethylene and menthene with bromine. In both molecules, the carbon-carbon doublebond functional group has a similar polarity pattern, so both molecules react with Br2 in the same way. The size and complexity of the remainders of the molecules are not important.

Figure 14-15 shows three X-ray diffraction patterns obtained from small crystalline particles of metallic copper, aluminum, and sodium. The qualitative similarity of the patterns given by copper and aluminum shows that they have the same crystal packing. Careful measurements of the spacing of the lines indicate that the atoms... 

Clathrate structures have been recently obtained also for s-PS [8] and s-PPMS [10]. In particular for s-PS, the treatment of amorphous samples, as well as of crystalline samples in the a or in the y form, produces clathrate structures including helices having s (2/1)2 symmetries, which present similar diffraction patterns, independently of the considered solvent. The treatment of samples of s-PPMS with suitable solvents also produces clathrate structures including s(2/l)2 helices however, the large differences in the X-ray diffraction patterns suggest different modes of packing, depending on the included solvent. 

Fig. 12 presents the variation of the mesophase moduli, Ej(r), for the various inclusion-volume fractions, versus the extent of the mesophase Ar, normalized to the highest inclusion-volume fraction of 25 percent. This was done in order to show the similarity of variation of the Ermodulus for the various values of uf for this series of composites, possessing the same adhesion properties between them. These normalized patterns are equivalent with those presented in Fig. 11 for the three-term unfolding model, since the differences between corresponding values of the two versions of the model are insignificant. 

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