Aggregate Functions

General indices method comprises formation of an aggregative function with the weighted arithmetic mean as the synthesizing function defined as ... 

The single parameter assessment for each indicator is demonstrated as the traditional approach in the evaluation of the option under consideration that reflects a biased result depending on the selected indicator. In order to apply the multicriteria approach to the hydrogen systems, it is necessary to use the multi-criteria procedure based on the sustainability index rating composed of linear aggregative functions of all indicators with respective weighting functions. 

The call back queries used in these steps are not purely queries to source databases. For example, the needed simulation results of the reactor are results of an aggregation function. In this sense the results are the results of a (highly complex) query on the data warehouse store. As simulating is a time consuming and expensive task we also store the results in the data warehouse for reuse. To gain access to the units the DB trader contains meta information about the CAPE-OPEN components. As a result of the usage of the CAPE-OPEN compliant units we do not need to handle very different simulators such as Aspen Plus, Pro/II or gPROMS, but only have to create the CAPE-OPEN objects used by the units. This especially concerns the material object for each substance contained in the input ports of the unit. The process data warehouse produces these CORBA objects and is then able to start the simulation of the unit. 

Each member in an ensemble uses a local aggregation function (such as average) to generate a schema matching similarity measure from the similarity measures of the attribute correspondences. Local similarity measures can then be aggregated using a global similarity measure (e.g., max) to become the ensemble similarity... 

Similarity measures are the basic components of schema matchers. They can be used as individual algorithms or combined with an aggregation function. Consequently, they may have internal parameters. In most cases, schema matchers do not enable users to tune such low-level parameters. Another parameter applied to similarity measures is the threhold. It filters the pair of schema elements in different categories (e.g., is a correspondence, or should apply another type of similarity measure) based on the output of the similarity measures. The last part of this section is dedicated to parameters specific to one or several matchers. 

A simple example of aggregation function is demonstrated with BMatch [Duchateau et al. 2008b] or Cupid [Madhavan et al. 2001], Their authors aggregate the results of terminological measure with the ones computed by a structural measure by varying the weights applied to each measure ( and and , etc.). 

Aggregate functions operate on a group of values rather than individual values as ordinary (or scalar) functions do. SQL has several standard aggregate functions, for example, sum, average, and max. The following SQL would likely return multiple rows. 

Another use of an aggregate function depends on the use of the Group by clause of SQL. The following SQL will return multiple rows. 

The SQL aggregate function sum and the multiplication in the above statement effectively carry out the computation according to Formula 12.1 shown earlier. The constant value 0.262592 is the intercept from the lm fit shown above. A glogp function can be defined as follows. 

The use of the group by clause causes all identical values of isosmiles to be grouped together and processed by the aggregate function count. For duplicate values of isosmiles, the count will be greater than 1. The above SQL statement will select these isosmiles. 

Any <-relation of the original poset will be maintained by this kind of aggregation. This is generally true if as aggregation function positive weak monotonous functions with respect to the attributes are applied. 

Fig. 4.14 Plot of the results of a calculation of the steady-state concentration of frnctose 6-phosphate for the system shown in fig. 4.13. The enzyme models are either based on Michaelis-Menten formalisms or modifications of multiple allosteric effector equations. The gate exhibits a function with both AND and OR properties. At low concentrations of both inpnts, the mechanism functions similarly to an OR gate, while at simultaneously high concentrations of the inpnt species (citrate and cAMP), the output behavior more closely resembles a fuzzy logic AND gate. The mechanism satisfies the requirements for a fuzzy aggregation function. (From [7].)...

The data is often available only in the form of rj collective failures observed 2 cumulative hours with no further delineation or detail available (see (Coit Jin (2000))). Quantities rj and Tj are known but the individual failure times are not. Analysts may have many of these merged data records available for the same component. In our paper we provide a general approach for the missing data by relaxing an aggregation function on the complete data sample. To be more specific, we consider that instead of observing a complete sample y = (y],...,y ) of times-to-failure, we observe a smooth missing function of it, i.e. i(yi,..., y ),... 

All of the set-based similarity functions in Table 15.3 are symmetric, have identical numerators, and are bounded by 0 and 1. Except for the Tanimoto similarity function, the denominators of and 5 are aggregation functions [50, 90] that... 

Behakov G, Pradera A, Calvo T. Aggregation Functions A Guide for Practioners. New York Springer 2010. 

To keep the molecules far apart from each other and counteract aggregation, functionalization with bulky substituents is required. When soluble and larger sized all-oxidized oligothiophene-5,5-dioxides... 

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