Hamming

The hamming function is used to compute the hamming similarity of two bit strings. The input bit strings would have been computed with the publicl66keys function or another equivalent fragment key or fingerprint function. 

The nbits set function returns the number of bits set to 1 in a bit string. This function is written here using python. Another C language version of this function is shown later in this Appendix. 

Create Or Replace Function nbits set(bits bit) Returns Integer As EOPY  

This function computes the average molecular weight of an input SMILES structure. It uses the table of atomic weights and SMARTS shown in Table A.2. It relies on the count matches function described in Chapter 7. 

Select sum(weight count matches( 1,smarts)) From amw EOSQL Language SQL  

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This distinction between 7 s and 7svo seems first to have been made by Bang-ham and Razouk [33] it was also stressed by Harkins and Livingstone [34]. Another quantity, introduced by Bartell and co-workers [35] is the adhesion tension A, which will be defined here as... 

The first stoand of Ham s argument [11] is that V(c()) supports continuous bands of Floquet states, with wave functions of the form... 

F. S. Ham, Jahn-Teller Effects in Electron Paramagnetic Spectra, Plenum Press, New York, 1971,... 

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. 

Hamming, Manhattan, taxi-cab, city-block distance (a + fc) ... 

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). 

Presell is the basic theory of tjuaiiHim mechanics, particularly, semi-empirical molecular orbital theory. The authors detail and justify the approximations inherent in the semi-empirical Ham illoTi ian s. Includes useful discussion s of th e appiicaliori s of these methods to specific research problems. 

Because of liiTi itation s iu corn pu ter poxver an d time, it is frequen tly impractical to run a constant energy molecular dynaniics simulation. -Several approxirn ation s to th e eu ergy (usually to th e poteu -tial en ergy) are possible, wh ieh require m odifyiri g th e Ham ilto-... 

Th c in pin, th e Ham ilton ian describes th e particles of the system the output, H, is the total energy of the system and the wave function, 4, con stitn tes all we can know ami learn about the particn lar molecular system represented by... 

Specification of the CUT Ham ikon ian matrix elements limn in Ih e auinnc orbital basis set. 

The diagonal elements of the core Ham iltonian simply represent theenergy ofan electron in an atom ic orbital of the correspondin g atom, plus the attraction ofan electron in th at atom ic orbital (on atom A) for the other nuclei (atoms D). 

Euclidean and Hamming distance measures of torsional similarity. 

The differences between the Soergel and Hamming distance nieasures for various molecules (see text). 

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