This paper introduces the matrix of coefficients, which summarizes the physical insight into a problem. This matrix is part of a larger methodology, Order of Magnitude Scaling, which provides closed form estimations of the unknowns, their range of validity, and a set of dimensionless groups that indicate the true ratio of driving forces. These results are obtained even when the problems are des...

A time series can be decomposed into two sub-series: a magnitude series and a sign series. Here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example. We 6nd that time series having identical distributions and long-range correlation properties can exhibit quite di8erent temporal organ...

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processi...

Earthquakes span a tremendous range of scales, more than 5 orders of magnitude in length. Are earthquakes fundamentally the same across this huge range of scales, or are the great earthquakes somehow different from the small ones? We show that a robust scaling law seen in small earthquakes, with stress drops being independent of earthquake size, indeed holds for great earthquakes as well. The s...