Quasi-reproducible Experiments: Universal Fitting Function for Quantitative Description of Complex Systems Data

This paper provides the foundations of an original theory of quasi-reproducible experiments (QRE) based on the testable hypothesis that there exists an essential correlation (memory) between successive measurements. Based on this hypothesis, which the authors define for brevity as the verified partial correlation principle (VPCP), it can be proved that there exists a universal fitting function (UFF) for quasi-periodic (QP) and quasi-reproducible (QR) measurements. In other words, there is some common platform or ‘‘bridge’’ on which, figuratively speaking, a true theory (claiming to describe data from first principles or verifiable models) and an experiment offering this theory for verification measured data, maximally ‘‘cleaned’’ from the influence of uncontrollable factors and apparatus/soft wire function, meet. The proposed theory has been tested on eddy covariance ecological data, specifically measuring only the concentration of \(\textrm{CH}_{4}\) , \(\textrm{CO}_{2}\) and water vapors of \(\textrm{H}_{2}\textrm{O}\) in the local atmosphere where the corresponding detectors for measuring of the desired gases content are located. For these tested eddy covariance data associated with the presence of two gases \(\textrm{CH}_{4}\) , \(\textrm{CO}_{2}\) and \(\textrm{H}_{2}\textrm{O}\) vapors in atmosphere there is no simple hypothesis containing a minimal number of the fitting parameters, and, therefore, the fitting function that follows from this theory can serve as the only and reliable quantitative description of this kind of data belonging to the tested complex system. Applications of this theory to practical applications, the place of this theory among other alternative approaches, (especially touching the professional interests of ecologists) and its further development are discussed at the end of this paper.