FOA Research Lab

Known means and model of mathematics (statistics, correlation, spectral and fractal analysis, Markov chains, methods of mathematical linguistics, weighted graphs, etc) don’t take directly into account the order of the components in the studied objects. This situation is to some extent explained by the lack of formalism for an abstract object that represents the order of the elements in the symbolic sequence. In FOA that object called an "order" or "arrangement of the components".

The object of study in FOA can be: texts, nucleotide sequences, musical entries, time series and data sets in general.

FOA is based on the concept of order – specific representation of the original sequence, in which all the information is discarded except for the location of the elements. Intervals between nearest identical elements are then extracted from the order. Such interval can be called inter-element interval or distance (or internucleotide distance in case of nucleotide sequences). All characteristics of order are based on the multiplication of these intervals.

Despite the resemblance characteristic of order are not statistical. As a rule, the statistical characteristics calculated by summing the values and dividing by the number of summands (arithmetic mean). Therefore arrays with different arrangement of elements can give the same values of statistical characteristics. On the contrary, all the characteristics of order are based on a multiplication of inter-element intervals, followed by extraction of the root of degree of the factors (geometric mean interval). If the order of elements in sequence is changed it is almost always changing the factors. Therefore numerical characteristics order directly takes into account the location of elements in the array. In the logarithmic scale order characteristics are based on a simple summation of the logarithms of the intervals.