Preference functions

The parent that includes the functional group most preferred by general principles of organic nomenclature [13,14], If there is a choice, it is made on the basis of the greatest number of occurrences of the most preferred functional group. Thus aldaric acid > uronic acid/ketoaldonic acid/aldonic acid > dialdose > ketoal-dose/aldose > diketose > ketose. 

PROMETHEE evaluates discrete alternatives based on pairwise comparisons for each sub-objective. However, these comparisons are not performed "manually". Instead, partial preference functions, usually using the difference between two alternatives attribute values as data input, are used to perform the pairwise comparisons. These partial preference functions have to be defined for each sub-objective as a first step of using PROMETHEE. They are used to determine the decision maker s strength of preference for an alternative (with 0 assigned for indifference, 1 for strict preference and values between 0 and 1 for intermittent preference values). 

Defining partial preference functions which require up to three different threshold parameters for each sub-objective makes using PROMETHEE a relatively complex task. Estimating these parameters might be diffi-cult/impossible in many decision environments. Even if the parameters can be specified it is often hard to provide a sound analytical foundation for doing so. Additionally, partial preference rankings are more difficult to understand than additive preference functions and hence the results obtained are more difficult to communicate to stakeholders. 

Table III gives a summary of the results of using Equation 14 as a representation of the energies of atomization for the 62 test molecules. Results are quoted for both polarity functions, fp and f°. When the entire set of molecules is tested, fc seems to be the preferred function however, fp is definitely superior for the compounds without carbon, and f° and the alternate electronegativities are superior for the carbon compounds. For extrapolations to other molecules it would seem desirable to use fp for compounds without carbon and fc and the alternate electronegativities...

Some formulations of jointly NO3/NH4 limited growth have not relied on inhibition. For example, Jamart et al. (1977) defined preference functions that divided the N sink between NH4 and NO3, while the two jointly regulate the phytoplankton growth rate by a single Monod function of their aggregate concentration. Similarly, Frost (1993) defined a Monod function for NH4 uptake, but assumed that N is not limiting to phytoplankton growth, and that any additional N requirements would be met by NO3. 

This approach is particularly efficient when combined with the Cosine coefficient (69) and was used by Pickett et al. in combination with pharmacophore descriptors (70). In lower dimensional spaces the maxsum measure tends to force selection from the comers of diversity space (6b, 71) and hence maxmin is the preferred function in these cases. A similar conclusion was drawn from a comparison of algorithms for dissimilarity-based compound selection (72). 

We first review briefly some of the consumer preference functions. We then compute a net present value as a function of price for different qualities as suggested by Bagajewicz (2007). Finally, we discuss the uncertainty associated to the model and suggest means to deal with uncertainty. 

Finally, is a positive coefficient that relates how much more appealing the consumer will find the product of interest in comparison to the competing product. It is defined as the ratio of the consumer preference functions p = In turn, the consumer... 

The site preference function only describes the propaisity for adsorption of the coke precursor on a given site, but not the loss of sites due to coke. A deactivation function is now needed to describe the sites remaining at a particular degree of deactivation. The deactivation Emotion, p(E), must meet the following criteria ... 

Torrance GW, Furlong W, Feeny D, Boyle M. Multiattribute preference functions. Health Utilities Index. Pharmacoeconomics. 1995 7 503-20. 

In contrast to HDT, when using the Utility Function, each (normalized to the scale [0,1] and then called instead of q now p,) descriptor is given a weight indicating the relative importance of that particular descriptor. More complex assumption, how a descriptor can be transformed into an "individual" preference function can be found by Schneeweiss (1991), where also the axiomatic foundation of this method is discussed. Instead of the simultaneous consideration of the descriptors the function... 

In contrast to the utility function approach the various descriptors of each substances are not aggregated. However a preference function pr, will be constructed based on the mutual comparison with respect to one descriptor q (note that we return to the original attributes q ) of any two substances. The preference function needs -as in the utility function approach-weights and information about the significance of numerical differences between the descriptor values of two substances, here called Aq°. Any difference qj(xi) - q,(xk) will be assigned to the preference function pr . i and k are ranging from 1 to m. In the simplest case the preference function may be formulated as follows ... 

In case S, the result depends on the algorithm used, on weights, on the use of preference functions discrepancies to HDT are due to the specific choices within the MCAs. Therefore in the case of uncertainties in the selection of weights, preference functions, it seems that HDT is transparent displaying the ranking interval. (HDT may be on the safe side in priority setting exercises.)... 

Protein transmembrane structure recognition and prediction by using hydrophobicity scales through preference functions... 

Figure 1 Very strong dependence of the a-helix conformational preferences on average hydrophobic sequence environment. Standard training procedure (Methods) was used. Observed preferences for glycine (Figure lA) and leucine (Figure IB) are shown as open points. Confidence limits, shown as bars above and below preference points, were calculated as described by Ptitsyn [51] so that it was 67.5% certain that observed preferences would fell between these values, The preference functions for leucine and glycine are shown as full lines.

Preference functions were extracted from the data base of 63 membrane proteins selected by Rost et al. [9] and 37 soluble proteins of the P-class (SOLBl, Methods) by using the PREF algorithm versions with sliding window length from 7 to 19 residues. 

The extraction of preference functions, as the training procedure, is not a very powerful training procedure and it is not expected to lead to overtraining. We shall test this assumption by performing still another two-times cross-validation test in which 168 membrane proteins are divided into 63 proteins used by Rost et al. [9] and 105 proteins used by us. Table 9 lists performance results for different combinations of training and testing procedures... 

The observation that conformational preferences are specified by the contexts - local segment primary structure, amino acid attributes, the three-dimensional environment in protein and environmental media, has been discussed before [102-105] Algorithms that do take into account context-dependence of preferences [106] generally perform better for secondary structure prediction In this report simple mathematical representation of context dependence is obtained through preference flmctions that are analytical fiinctions of the surrounding sequence hydrophobicity or of any other amino acid attribute. Furthermore, preference functions are used to predict secondary structure motifs. It has turned out that for integral membrane proteins preference functions are excellent predictors of transmembrane segments in helical conformation In fact preference functions are much better predictors than the hydrophobicity scale chosen to extract these functions. 

The main goal of this work was accurate prediction of transmembrane helical structures, but we do realize that membrane proteins may exist that have both a-helices and P-strands as transmembrane structure. Preference function method is capable of predicting separately a-helical and P-strand conformation of segments that have potential to become... 

Availability of the prediction with preference functions. We have set up an automatic electronic mail server at the Internet address predict drava.etfos.hr. The server will return complete prediction results, such as given in Table 6, when provided with the sequence of your protein For further information, send the word help to the server Questions, comments and suggestions should be sent to juretic mapmf pmfst hr or zucic mia os.camet.hr. 

Two data bases of soluble proteins of known structure used to find false positive prediction results (Table I and Table II). Gaussian parameters needed for evaluation of preference functions based on the Kyte-Doolittle hydropathy scale [17] (Table III). Table with detailed prediction results for transmembrane helices in 168 integral membrane proteins (Table IV). Table with a detailed comparison of prediction results for 10 best known membrane proteins for our and three other algorithms (Table V). All these tables together with the FORTRAN 77 source code are available from the anonymous ftp server mia.os.camet.hr in the /pub/pssp directory. The anonymous login is ftp and the e-mail address is accepted as password. The list of files with short descriptions is contained in the 00index.txt file. 

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