The corresponding dynamic system algebras (given in Table 1) were computed with the help of the computer algebra system magma [70] for up to six modes while distinguishing nearest-neighbor interactions from arbitrary translation-invariant ones.
They found that the dissimilarities between distributions of shape functions (particularly D2) provide a robust measure for discriminating between classes of objects (e.g., cars versus airplanes) in a moderately-sized database, despite the presence of arbitrary translations, rotations, scales, mirrors and model degeneracies.
The linearized response to arbitrary small-amplitude translation and rotation is analyzed using Fourier decomposition of the forcing signal.
Employing fractional and arbitrary scaling and translation factors, FAWT possesses attractive properties such as flexible time frequency (TF) covering manner, better shift-invariance and tunable oscillatory nature of the bases, offering proper wavelet frame and bases shape to match the weak fault components.
This fundamental problem in structural biology is commonly addressed by performing a superposition, which removes arbitrary differences in translation and rotation so that a set of structures is oriented in a common reference frame (Flower, 1999).
In all the cases, arbitrary unsteady span-wise translations permit to generalise as well as to exhibit helical or 3D universal motions.
The responsibility for identifying relevant premises, and for producing and coordinating academic work on ethics that adequately, and in a non-arbitrary manner, facilitates the translation of philosophically justified knowledge into practice, rests with theoretical researchers.
For affine transformation, all six parameters are arbitrary (this explains that affine transformation includes translation, etc., as noted above).
Flexibility of the ligand helps it explore six spatial degrees of freedom for rotation and translation and an arbitrary number of torsional degrees of freedom.
