Hamming coefficient

If the binary descriptors for the objects s and t are substructure keys the Hamming distance Eq. (6)) gives the number of different substructures in s and t (components that are 1 in either s or but not in both). On the other hand, the Tanimoto coefficient (Eq. (7)) is a measure of the number of substructures that s and t have in common (i.e., the frequency a) relative to the total number of substructures they could share (given by the number of components that are 1 in either s or t). 

Volatile nitroso compounds were determined in hams processed in elastic rubber nettings by SPE and GC-CLD577. By a similar method A-n i tro sodi ben zy lamine (278b), a semivolatile nitrosamine, was determined in these products by SPE followed by GC interfaced to a nitrosamine-specific TEA-CLD detector the coefficient of variation was 10.6% at the 2.1 ppb level578. The nitrosamines detected in ham most likely originate from the amine precursors in rubber and from the nitrite commonly used in the meat curing process. 

This is the simplest version of the rate coefficient which can be derived. Ham suggested that a better approximation to the eigen-function A0 can be obtained from the variational integral... 

The very simple analysis of Ham [508] for the first correction to the rate coefficient to account for the effect of neighbouring sinks on the diffusing species concentration [i.e. eqn. (270)] is an excellent approximation to the exact result of Lebenhaft and Kapral. Even the variation calculation is quite a satisfactory upper bound. That of Reck and Prager [507] is rather smaller. 

Incidentially, it is worth recalling that Ham was interested in the rate of accretion of the diffusing species on to the surface of the sink when the sinks were randomly distributed. In such cases, Felderhof and Deutch [25] and Lebenhaft and Kapral [492] have found that the correction term to the rate coefficient is of the form 1 + (3e)1/2 rather than (1 + 9c1/3/5). The original assumption by Ham that the random distribution of sinks could be approximated by a regular cubic lattice is satisfactory numerically, but leads to the wrong power of the volume fraction of sinks. 

Compute similarity coefficients (Tanimoto, Dice, Ochia, Hamming) between the active site fingerprint and the fingerprint for each molecule in the Catalyst database. The top N% of compounds can be selected by ranking the compound collection in descending order based on the similarity coefficient. 

The non-binary all feature combination of the 3D fingerprint and interaction feature was able to retrieve -90% of the actives on screening 20% of the database. The Ochiai coefficient was slightly better than Tanimoto and significantly better than Dice and Hamming in retrieving actives. All features for the enzyme... 

Other similarity coefficients used in similarity studies include the cosine coefficient, and the Hamming and Euclidean distance measures [7], Similarity coefficients can also be applied to vectors of attributes where the attributes are real numbers, for example, topological indices or physiochemical properties. 

Other metrics include the Hamming distance metric, given by (6). XOR is the bitwise exclusive or operation (a bit in the result is set if the corresponding bits in the two operands are different), and N the number of bits in each set. The Dice coefficient is defined by (7). 

Ham et al. (1990) used Eqs. (30) and (31) and estimated the values of the solid phase dispersion coefficient using the experimental results on transition in solid-liquid fluidized beds. However, the estimated values of deviate from the experimental values of obtained by Dorgelo et al. (1985). It may be noted that the RTD based experimental values includes gross nonidealities in addition to the turbulent dispersion. 

According to equation (12.17), the fluxes of electrons and holes are driven by concentration and potential gradients. This distinction is a result of the separation of the chemical and electrical contributions given in equation (12.15). If desired, degenerate semiconductor conditions can be modeled by calculating the value of the activity coefficients f for electrons and holes as described by Hwang and Brews and Bor ham and Orazem. The flux expression for species i is constrained by the equation of continuity, i.e.. 

The most popular measures are Hamming and Tanimoto coefficients, which are listed below, together with other important distance measures on binary variables ... 

There are many different types of similarity indexes, including the association coefficients (e.g., Tanimoto coefficient [27], Jaccard coefficient [38], Hodgkin-Richards coefficient [39,40]), the correlation coefficients or cosinelike indexes, and the distance coefficients or dissimilarity indexes (e.g., Hamming distance) [26],... 

Hamming similarity coefficient similarity/diversity (0 Table S9)... 

Another weighted measure for binary variables is the azzoo similarity coefficient, which is a weighted Hamming similarity coefficient and aims at weighing the contribution of the term d as... 

It must be noted that comparing distances for binary and continuous variables, the Hamming distance coincides vith the Manhattan distance, square root Hamming distance is the Euclidean distance, Tanimoto distance coincides vdth average Manhattan distance and squared Tanimoto vith the average Euclidean distance. Moreover, the Watson nonmetric distance corresponds to the Lance-Williams distance and is the complement of the Sorenson coefficient the Soergel binary distance corresponds to the Soergel distance and is the complement of the Jaccard/ Tanimoto coefficient. 

Fig. 31. Gas-to-solid mass transfer characteristics of various regimes of operation for FCC regenerators. R-2, R-4, and R-4 refer to the regimes sketched in Fig. 11. The kinetic data for coke burn off is taken from Hano et al. (1975). The gas-solids mass transfer coefficient for riser reactors is estimated from the Van der Ham et al. (1993) correlation. The estimation of volumetric mass transfer coefficient in fluid beds is from the model of Krishna (1981). Further details of the calculations presented in this figure can be found in Krishna (1993).

FIGURE 15.136 (Continued) Fost-CHF heat transfer coefficient as a function of equilibrium quality (from Ham-... 

Fluorescence decay of 9-methylanthracene has been used by Tan and Treloar to study the coiling of poly(methacrylic acid) in water. Hara and Ware have studied the influence of solvent on the radiative probablity from the i state of pyrene. The fraction of fluorescence in the 0-0 parallels the extinction coefficient change for the 0-0 band. The Ham band also decreased with temperature, an effect correlated with the decrease in dielectric constant with temperature. There is also evidence that a solvent-solute interaction is involved in Ham band effects in alcohols and aromatic solvents. Use of the integrating sphere eliminates any uncertainty in the conventional instrumental refractive index correction. Some of the data obtained is given in Table 4. 

Here we will introduce three similarity coefficients that have been widely used for both realvalued (i.e. continuous) and binary (dichotomous) descriptors the Tanimoto coefficient, the Dice coefficient and the Cosine coefficient The formulae used to compute these coefficients are given in Table 12.3, where, for completeness, we have also provided the Euclidean and Hamming expressions that were introduced in Section 9.13. Different expressions are used for real-valued data (where the molecule is represented by a vector containing N real values Xj) and for binary data (where each molecule is represented by N binary values). For binary data, we additionally define a to be the number of bits on in the bitstring for A, b to be the number of bits on in the bitstring for B, and c to be the number of bits that are on in both A and B (calculated using the AND operator). 

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