Dissimilarity

All petroleum energy products, as distinct and dissimilar as they can be, are subjected to the process of flame combustion. It is helpful at this point to bring to mind some definitions and general laws of thermochemistry. 

Partitional clustering using Euclidean distance as a measure of dissimilarity between pattern classes has been selected for the grouping of AE hits. 

In many cases, the methods used to solve identification problems are based on an iterative minimization of some performance criterion measuring the dissimilarity between the experimental and the synthetic data (generated by the current estimate of the direct model). In our case, direct quantitative comparison of two Bscan images at the pixels level is a very difficult task and involves the solution of a very difficult optimization problem, which can be also ill-behaved. Moreover, it would lead to a tremendous amount of computational burden. Segmented Bscan images may be used as concentrated representations of the useful... 

The parameters of equivalent planar OSD are then obtained by iterative minimization of a specifie dissimilarity eriterion measuring the degree of matching between the parametric descriptions of the observed segmented Bscan image Y° = s" = n = 1,..,jV and... 

Figure 2 Schematic flow chart of the OSD parameters identification method Our specific dissimilarity criterion is defined as ...

Defect Evaluation in Diffusion Bonding Interface of Dissimilar Metals Using Ultrasonic Testing Method. 

Evaluation of Bonding Process in Diffusion Bonding Joints of Dissimilar Metals using Ultrasonic Testing Method. 

BE-7301 Life optimization of dissimilar metal welds for high temperature components Mr. V. Bicego CISE SpA... 

FlOiei Evaluation of techniques for assessing corrosion cracking In dissimilar metal welds Dr D.R. Tice AEA Technology... 

Ultrasonic Testing of Austenitic and Dissimilar Metal Welds,... 

When two dissimilar metals are connected, as illustrated in Fig. V-16, ]here is a momentary flow of electrons from the metal with the smaller work function to the other so that the electrochemical potential of the electrons becomes the same. For the two metals a and /3... 

The statement was made that the work of adhesion between two dissimilar substances should be larger than the work of cohesion of the weaker one. Demonstrate a basis on which this statement is correct and a basis on which it could be argued that the statement is incorrect. 

Some of the most interesting and important chemical and physical interactions occur when dissimilar materials meet, i.e. at an interface. The understanding of the physics and chemistry at interfaces is one of the most challenging and important endeavors in modem science. 

This type of corrosive attack occurs when dissimilar metals (i.e., with a different are in direct electrical... 

As an illustration, we consider a simple example of a top with a fixed point at the center of mass moving in an applied field not dissimilar from those encountered in molecular simulations. Specifically, we used... 

Next, we select some pillar" compounds inside each or some of those subclasses, i.e., those having the highest norm of the characteristic vector. We can employ two pillars, the lowest (that with the lowest norm) along with the highest , and keep only those compounds which are reasonably dissimilar to the pillar (or to both pillars). The threshold of reasonability" is to be set by the user. 

Accordingly, dissimilarity Da,b between two objects A and B is estimated by the number of mismatches or the difference between the objects, with respect to one or more of their characteristics j = 1. 2,. ..n. For identical objects, the... 

Similarity is often used as a general term to encompass either similarity or dissimilarity or both (see Section 6.4.3, on similarity measures, below). The terms "proximity" and distance are used in statistical software packages, but have not gained wide acceptance in the chemical literature. Similarity and dissimilarity can in principle lead to different rankings. 

Usually, the denominator, if present in a similarity measure, is just a normalizet it is the numerator that is indicative of whether similarity or dissimilarity is being estimated, or both. The characteristics chosen for the description of the objects being compared are interchangeably called descriptors, properties, features, attributes, qualities, observations, measurements, calculations, etc. In the formiilations above, the terms matches and mismatches" refer to qualitative characteristics, e.g., binary ones (those which take one of two values 1 (present) or 0 (absent)), while the terms overlap and difference" refer to quantitative characteristics, e.g., those whose values can be arranged in order of magnitude along a one-dimensional axis. 

Following Bradshaw [17], we can give the definition of a similarity measure as follows Consider two objects A and B, a is the number of features (characteristics) present in A and absent in B, b is the number of features absent in A and present in B, c is the number of features common to both objects, and d is the number of features absent from both objects. Thus, c and d measure the present and the absent matches, respectively, i.e., similarity while a and b measure the corresponding mismatches, i.e., dissimilarity. The total ntunber of features is n = a + b + c + d. 

The total number of bits set on A is a + c. and the total number of bits set on B is b + c. These totals form the basis of an alternative notation that uses a instead of a + c, and b instead oib + c [16]. This notation, however, lumps together similarity and dissimilarity components" - a disadvantage when interpreting a similarity measure. 

To construct dissimilarity measures, one uses mismatches Here a + b is the Hamming (Manhattan, taxi-cab, city-block) distance, and a + h) is the Euclidean distance. 

We should mention here that using just similarity or dissimilarity in a similarity measure might be misleading. Therefore, some composite measures using both similarity and dissimilarity have been developed. These are the Hamann and the Yule measures (Table 6-2). A simple product of (1 - Tanimoto) and squared Eucli-... 

Asymmetry in a similarity measure is the result of asymmetrical weighing of a dissimilarity component - multiplication is commutative by definition, difference is not. By weighing a and h, one obtains asymmetric similarity measures, including the Tversky similarity measure c j aa 4- fih + c), where a and fi are user-defined constants. The Tversky measure can be regarded as a generalization of the Tanimoto and Dice similarity measures like them, it does not consider the absence matches d. A particular case is c(a + c), which measures the number of common features relative to all the features present in A, and gives zero weight to h. 

Once we have the measures, we have to apply them to chemical objects. Objects of interest to a chemist include molecules, reactions, mbrtures, spectra, patents, journal articles, atoms, functional groups, and complex chemical systems. Most frequently, the objects studied for similarity/dissimilarity are molecular structures. 

The frequencies a and d reflect the similarity between two object s and t, whereas h and c provide information about their dissimilarity (Eqs. (6)- 8)) ... 

For a pair of feature values a similarity value within the range from 0 (dissimilar) to 1 (identical) is calculated. For the comparison of two feature trees, the trees have to be matched against each other. The similarity value of the feature trees results from a weighted average of the similarity values of all matches within the two feature trees to be compared. 

Initially, the first two principal components were calculated. This yielded the principal components which are given in Figure 9-9 (left) and plotted in Figure 9-9 (right). The score plot shows which mineral water samples have similar mineral concentrations and which are quite different. For e3oimple, the mineral waters 6 and 7 are similar whUe 4 and 7 are rather dissimilar. 

A cluster analysis requires a measure of the similarity (or dissimilarity) between pairs of objects. When comparing conformations, the RMSD would be an obviou.s measure to use. 

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