Measuring Similarity

To determine whether sample patterns in a database are similar to one another, the values of each of the n parameters that define the sample must be compared. Because it is not possible to check whether points form clusters by actually looking into the n-dimensional space—unless n is very small— some mathematical procedure is needed to identify clustered points. Points that form clusters are, by definition, close to one another, therefore, provided that we can pin down what we mean by close to one another, it should be possible to spot mathematically any clusters and identify the points that comprise them. 

We shall start by clustering animals and scientists (separately). Living creatures display a remarkable diversity some species have few features in common, while others are very alike. An elephant is not much like an amoeba, beyond the fact that they are both alive, but leopards and cheetahs share many characteristics. 

We can group animals into clusters according to how similar they are, comparing their key characteristics the more closely those characteristics match, the more similar are the two species. The choice of characteristics is inherently arbitrary, but we might include the number of legs, covered in fur or feathers, the speed of movement, size, color, carnivore/ vegetarian, and so on  

Lion legs = 4, covering = fur, speed = fast, size = big.  

Anaconda legs = 0, covering = skin, speed = moderate, size = moderate.  

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This section attempts a brief review of several areas of research on the significance of phases, mainly for quantum phenomena in molecular systems. Evidently, due to limitation of space, one cannot do justice to the breadth of the subject and numerous important works will go unmentioned. It is hoped that the several cited papers (some of which have been chosen from quite recent publications) will lead the reader to other, related and earlier, publications. It is essential to state at the outset that the overall phase of the wave function is arbitrary and only the relative phases of its components are observable in any meaningful sense. Throughout, we concentrate on the relative phases of the components. (In a coordinate representation of the state function, the phases of the components are none other than the coordinate-dependent parts of the phase, so it is also true that this part is susceptible to measurement. Similar statements can be made in momentum, energy, etc., representations.)... 

A positive ion formed on such a tip held at a high positive potential is repelled and flies olf the tip almost immediately after formation and into the mass spectrometer, where its m/z value is measured. Similarly, negative ions can be mass measured. 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Any main CT that is itndeiioaded will also add to the error in the measurement. Similarly, if provision is tnade in the primary of the summation CT to accommodate fntnre circuits but is not being utilized it tnust be left open, otherwise it will also add to the error. The impedance of the shorting terminals will add to the impedance of the circuit and will increase the total error. 

In all electrical measurements, current and voltage measuring instruments with two terminals are employed. The object being measured similarly has two termi-... 

Depending on use, the tighmess and containment of the box can be tested with a tracer gas or with generated contaminants. Since the pressure inside the box is lower than the pressure outside it could be easier to check the tightness without the exhaust airflow. Measurements similar to those for fume cupboards can be used. 

Pulsed hot wire anemometer A device used for gas flow measurement, similar to the hot grid anemometer, in which measurement, are made by pulses of hot air at a downstream sensor. 

The CV is 3.4%. Note Had measurements similar to those in vector 4 been made, the CV of 5.6% would have come close to the 6% limit stipulated by the USP 1985, which would have necessitated a retest. There are no individual values outside the 85-115% range that would signal retest and perhaps rejection. 

Over the years, chemists have carried out many measurements similar to the one depicted in Figure 19-14. The resulting values for standard reduction potentials are tabulated in reference sources such as the CRC Handbook of Chemistry and Physics. Many values appear in Appendix F, and some representative values appear in Table 19-1. 

Unreacted monomers In AN/M latex solutions were measured similarly. Methylacrylate Is a relatively strong UV absorber In the 225-250 nm range while acrylonitrile does not significantly absorb UV radiation at wavelengths above about 220 nm. At 230 nm, the wavelength used, the UV detector responded only to methylacrylate. And the refractive Indices of the two monomers are such that. In the 75/25 AN/MA proportions used, the refrac-tometer was Insensitive to methylacrylate. The reiErac tome ter therefore functioned as a selective detector for acrylonitrile In the presence of methylacrylate. 

As will be shown in Section 4.2, published data are available on the application of societal risk measures, including the development of risk tolerability limits for F-N curves. However, much of this guidance has been developed for characterizing risks to the general public and would not normally be considered as a basis for assessing risks to on-site personnel. It is appropriate, therefore, to suggest another risk measure, similar in concept to societal risk, for on-site applications to process plant buildings ... 

The difference in the outer potentials between the metal and the electrolyte solution is measured similarly. In Fig. 3.6, phase jS will now designate an electrolyte solution in contact with the metal phase oc. Also here tue(a) = jue(cc ) and ip(oc ) = (/ ), and U is again expressed by Eq. (3.1.30) however, fie(oc) = as the communicating species between... 

XPS has been used by several authors to identify the surface and bulk composition of ruthenium based, valve metal stabilized DSA electrodes for chlorine evolution. Augustynski et al. [45] investigated the composition of Ru02-Ti02 electrodes before and after electrochemical treatment. They found a surface composition which deviated significantly from that of the bulk. The Ru/Ti ratio corresponded to 0.15 at the surface while in the bulk 0.28 was measured. Similar results were obtained by De Battisti et al. [46] for Ru02-Ti02 electrodes with different composition ratios on Ti substrates. Fig. 10 shows the Ru/Ti ratio for different solution compositions as a function of the depth. 

Figure 8.1 The duration of NREM sleep and delta activity during NREM sleep following saline (open circles) or 0.5mg/kg MK-801 (filled circles), administered 6h after the start of the dark period. MK-801 initially produced a period of wakefulness approximately 3 h long. In the subsequent light period, NREM sleep duration (A), total integrated amplitude (TIA, a period amplitude measure similar to power) of NREM sleep delta (B), and NREM sleep delta integrated amplitude per minute (IA/min) (C) were all significantly increased above control levels.

Porstendorfer, 1984). Knutson et al. (1983) measured similar results in their chamber investigation. The results show that the values of the deposition velocity of the free radon daughters are about 100 times those of the aerosol radon progeny. But there are no information about the effective deposition surface S of a furnished room for the calculation of the plateout rates qf and qa by means of Vg and Vg. For this reason the direct measurements of the plateout rates in rooms are necessary. Only Israeli (1983) determined the plateout rates in houses with values between qf = 3-12 h"1 and qa = 0.4-2.0 h"1, which give only a low value of the... 

Baxendale and Wardman (1973) note that the reaction of es with neutrals, such as acetone and CC14, in n-propanol is diffusion-controlled over the entire liquid phase. The values calculated from the Stokes-Einstein relation, k = 8jtRT/3jj, where 7] is the viscosity, agree well with measurement. Similarly, Fowles (1971) finds that the reaction of es with acid in alcohols is diffusion-controlled, given adequately by the Debye equation, which is not true in water. The activation energy of this reaction should be equal to that of the equivalent conductivity of es + ROH2+, which agrees well with the observation of Fowles (1971). 

Figure 27 shows the pyroelectric current trace and the temperature cycle around 20 °C applied to the pyroelectric measurement of the alternating film consisting of the barium salt of Compound II and stearic acid. As the temperature increased, positive current flowed through the circuit to reach an almost constant value. When the temperature started to decrease, the current immediately changed its flow direction to negative until it reached an almost constant value. This square wave pattern of the current flow did not vary during continuous one-hour measurement. Similar current... 

The second category, time-dependent behaviour, is common but difficult to deal with. The best known type is the thixotropic fluid, the characteristic of which is that when sheared at a constant rate (or at a constant shear stress) the apparent viscosity decreases with the duration of shearing. Figure 1.21 shows the type of flow curve that is found. The apparent viscosity continues to fall during shearing so that if measurements are made for a series of increasing shear rates and then the series is reversed, a hysteresis loop is observed. On repeating the measurements, similar behaviour is seen but at lower values of shear stress because the apparent viscosity continues to fall. 

Tear strength is only applicable to flexible materials and is very little used to monitor ageing simply because tensile strength will serve perfectly well. There are circumstances where compression stress-strain properties would be relevant but the relatively bulky test pieces will be subject to the limitation of oxygen diffusion in any accelerated tests and changes can probably be estimated from tensile measurements. Similarly, shear stress-strain is very rarely used for monitoring ageing. 

The plateau region corresponds to effectively complete N-protonation. The pK value measured spectrophotometrically (1.90) agreed with that derived from the kinetic measurements. Similar good agreement was obtained for the N-Et and 4-Me reactants and also for the unsubstituted phenylhydroxylamine in D2O. The measured solvent KIE was also in agreement with the mechanism in Scheme 7. Acid catalysis at high acidity is believed... 

Surface and volume resistivity measurements have been performed on films of polymer alone and polymer with Al(acac) added. Special care was taken to insure that only films of uniformly high quality were measured. Regardless of the film pretreatment, volume resistivities on two independently cast films of polymer alone fall in the 10- - ohm-cm range. No previously published resistivity is available on this particular polymer although upon surveying several ether polyimides from independent sources we measured similar volume resistivities. 

The comparison of "numbers of reactive bonds" crudely measures similarity. A more appropriate but complex approach would evaluate similarity in terms of known functional groups or discovered reactive substructures shared or not shared by two reactions. Both these approaches to validity estimation are limited because they are entirely based on structure. The expert will use other factors, including theoretical considerations, to refine validity. 

The reactions of the species H3O+, NO+, and O2+ with a range of aldehydes and ketones have been studied by the selected ion flow tube (SIFT) method. H3O+ protonates ketones and aldehydes, with the latter eliminating water under the conditions of measurement. Similarly, NO+ associates with ketones, but this is followed by hydride transfer for the aldehydes. O2+ reactions typically produce several ionic products. 

Referee Laboratories and Spike Recovery Testing. Outside laboratories, with demonstrated performance records, can be used to evaluate the suitability of a candidate method when none of the other accuracy testing options is feasible. However, This technique provides a very weak form of accuracy assessment. Indeed, it provides a comparability check, not an accuracy measure. Similarly, spike recovery tests provide only weak evidence of method accuracy. Quantitative spike recovery only indicates that the added form of the analyte was recovered. If the added form responds differently toward sample preparation or detection the utility of spike recovery testing remains doubtful. 

Five different types of rate constants are of concern in radical chain polymerization—those for initiation, propagation, termination, chain transfer, and inhibition. The use of polymerization data under steady-state conditions allows the evaluation of only the initiation rate constant kd (or kt for thermal initiation). The ratio kp/k J2 or kp/kl can be obtained from Eq. 3-25, since Rp, Rj, and [M] are measurable. Similarly, the chain-transfer constant k /kp and the inhibition constant kz/kp can be obtained by any one of several methods discussed. However, the evaluation of the individual kp, k ktr, and kz values under steady-state conditions requires the accurate determination of the propagating radical concentration. This would allow the determination of kp from Eq. 3-22 followed by the calculation of kt, kIr, and kz from the ratios kp/ltj2, ktr/kp, and kz/kp. 

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