A quick check of the residuals for model fit shows that residuals from a fitted mode approximate the random errors and the distribution does not deviate from normality (Fig. 1, top left).
The only difference between the two methods is the mathematical model used: Method:LMS fits the data with a 6D polynomial model, whereas Method:MODE approximates the observations with one single scalar constant, i.e. a 1D mathematical model.
As discussed below, we propose that this (rapidly attained) surface-binding mode approximates the starting point for the (slow) intercalation process observed with AT-rich DNA through optical measurements.
For frequencies less than 15 kHz, the lower order QTM and QTE modes approximate pure TM and TE modes (Wood 2004).
This study employs the method of proper orthogonal decomposition (POD), also known as the Karhunen Loeve (K L) method, to extract dominant coherent structures (modes that approximate the system behavior) from time-series data.
As defined by [ 17], the flux efficiency of each mode is related to the investment required to produce the enzyme needed to establish the mode, approximated by the sum of all absolute fluxes, because for comparable metabolite concentrations, the flux through a reaction scales linearly with the enzyme concentration.
The system is reduced to a set of two second order ordinary differential equations by using a single (axisymmetric) mode to approximate the spatial distribution of the lineal displacements.
One is the multi-moment bulk method, which predicts the integrand of each mode by approximating the modes via the gamma distribution (e.g., Milbrandt and Yau [2005b]; Seifert and Beheng [2006]): f r = K r v exp − λ r μ, where κ, λ, μ, and ν are the diagnosed parameters.
However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm.
The assumed-modes approximate method has been used in this study.
