Ranking function

Most automated pharmacophore model generators are equipped with an internal scoring method to rank different hypotheses (here termed ranking function ) and provide the expert with the most relevant solutions. Indeed, real-life... 

Ranking function Its internal scoring function depends on the displacement in the alignment of the input molecules and the uniqueness of the pharmacophore (e.g. other things being equal, a positive ionizable feature is more unique than a hydrophobe feature). 

Ranking function DISCO outputs all possible solutions. It is up to the user to decide their relevance further [14],... 

Ranking function The fitness function is the weighted sum of three terms number and similarity of overlaid elements, common volume of all molecules and internal van der Waals energy of each molecule. 

Ranking function The scoring function is made of the weighted contributions of three aspects quality of the alignment, similarity (common volume/total volume) and selectivity (rarity). 

The MCS of a set of N compounds, however, may be very small or may not even exist if an exotic structure is contained in the set. TTierefore, the common structural characteristics of a set of structures are better described by a set of MCS, each of them being the MCS of a pair of structures. Such a set is obtained by determining the MCS for all the N(N-l)/2 pairs of compounds then the number N, of occurrences of each different MCS is counted in the set. Finally, an ordered set of MCS is obtained by a ranking function which consideres both frequency and size of the MCS ... 

In the above advices 1-6, the rule 4 needs additional explanations. In order to do this, we introduce first the concept of graduation and of the rank-function, respectively. If there is a rank function r, then for any element of the ground set the levels are uniquely found. Hence, a poset is graded or possesses a rank function if ... 

In the case, shown in Fig. 11 (a) such a rank function exists, whereas in Fig. 11 (b) one cannot find a function r. Obviously, for the Hasse diagram in Fig. 11 (a) all five objects are located at specific levels, whereas the hatched object in the diagram in Fig. 11 (b) may be located either at the level of x or the level of y, respectively. However, corresponding to the level construction the element u belongs to MAX2. The elements u and z have therefore the same vertical position and are below the top element, which belongs to MAXi. 

If a specific element, say xe is selected then its spectrum is of interest (Atkinson 1990). It should be noted that other authors (for example Trotter 1991, Schroder 2003) also call the spectrum a projection. However, we favour "spectrum" as the more suitable name for the following construction. Thus, let LT be the number of linear extensions of a poset, then we can find the rank of an element x in the ith linear extension rank(i, x). Note that this construction should not be confused with the rank function, we discussed above. Conventionally, the bottom element of a linear extension is given the rank 1, thus the top element has the rank n (card E = n). However, if appropriate the top element may be assigned the first priority, such that bottom elements will get numbers > 1 (see for example chapter by Carlsen, p. 163). We call A,k(x) the frequency, how often x e E gets the rank k. The spectrum spec(x) is a tuple containing n components (Ii(x), I2(x),. .., A,n(x)). Thus for example the spectrum of element b in Fig. 14 as follows spec(b) = (0, 0, 3, 6, 5, 0). (i) There is no linear extension, where the rank of b is 1, 2 or 6. (ii) There are 3 linear extensions, where the rank of b is 3. (iii) There are 6 linear extensions, where the rank of b is 4. (iv) There are 5 linear extensions, where the rank of b is 5. Obviously ... 

Thus, the ranking model is given by the chosen ranking function and the ordered training set. 

We say that X, is d-connected if X, consists of one connected component (note that the word connected is reserved for componentwise connectedness). If X, is locally noetherian, then a connected component of X, is a closed open subdiagram of schemes in a natural way. If this is the case, the rank function i, x) i—> ranko y, of a locally free sheaf IF is constant on... 

In addition to these ranking functions, we can also consider using various functions available in external statistical software packages such as R, Excel, SAS, and so on. In that case, the first method can be used, or it is possible to implement a wrapper function that has the prototype as in the second method and performs a filtering operation. 

Order of precedence of functional groups A system for ranking functional groups in order of priority for the purposes of IUPAC nomenclature. 

A database of elucidated spectra is indispensable for both quality assessment of ranking functions and for calculation of MS classifiers. Here, we use spectra and structures from the NIST MS library [224]. This 1998 version of NIST contains 107,888 spectra of 107,812 structures. Spectra and structures are two separate files, linked by numerical identifiers. 

If there was a match value that fulfilled the above conditions, the verification step of our structure elucidation problem would be solved. Unfortunately, there is no ranking function for real mass spectra that fulfils the latter two requirements in general. However, if we assume an exact recording of mass spectra intensities we can at least define a ranking function for molecular formulas that satisfies requirements (R) and (T). 

By normalizing the above we can define a ranking function that satisfies requirement (R), and, for mass spectra measured at infinite precision, also (T) ... 

Here, the square root results in a more even distribution of match values, since the minimum from Equation (8.5) usually is closer to zero than to the upper interval limit. In addition, we justify the expression explained fraction of total intensity for our ranking function. 

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