Structurally Recursive Method computations

The Structurally Recursive Method is then expanded, and a second, non-recursive algorithm fw the manipulator inertia matrix is derived from it A finite summation, which is a function of individual link inertia matrices and columns of the propriate Jacobian matrices, is defined fw each element of the joint space inertia matrix in the Inertia Projection Method. Further manipulation of this expression and application of the composite-rigid-body inertia concept [42] are used to obtain two additional algwithms, the Modified Composite-Rigid-Body Method and the Spatial Composite-Rigid-Body Method, also in the fourth section. These algorithms do make use of recursive expressions and are more computationally efficient. 

Four algorithms for computing the joint space inertia matrix of a manipulator are presented in this section. We begin with the most physically intuitive algorithm the Structurally Recursive Method. Development of the remaining three methods, namely, the Inertia Projection Method, the Modified Composite-Rigid-Body Method, arid the Spatial Composite-Rigid-Body Method, follows directly from the results of this tot intuitive derivation. 

Selecting an optimum group of descriptors is both an important and time-consuming phase in developing a predictive QSAR model. Frohlich, Wegner, and Zell introduced the incremental regularized risk minimization procedure for SVM classification and regression models, and they compared it with recursive feature elimination and with the mutual information procedure. Their first experiment considered 164 compounds that had been tested for their human intestinal absorption, whereas the second experiment modeled the aqueous solubility prediction for 1297 compounds. Structural descriptors were computed by those authors with JOELib and MOE, and full cross-validation was performed to compare the descriptor selection methods. The incremental... 

The time scales of the structural transitions in (NaCl)35Cl mean that it is impossible to use conventional molecular dynamics to investigate the interfunnel dynamics. Instead we use the master equation method outlined in Section III.D. To reduce the computational expense and numerical difficulties we recursively removed from our sample those minima that are only connected to one other minimum—these dead-end minima do not contribute directly to the probability flow between different regions of the PES. The resulting pruned sample had 1624 minima and 2639 transition states. RRKM theory in the harmonic approximation was used to model the individual rate constants,. ... 

G(R,Rq) is not known explicitly (or by quadrature) for any but the most simple (and uninteresting problems). But it is clearly related to the solution of a diffusion problem for a particle starting at Rq in a 3N dimension space and subject to absorption probability V(R) + Vq per unit time. We therefore expect to be able to sample points R from G(R,Rq) conditional on Rq. It turns out to be possible by means of a recursive random walk in which each step is drawn from a known Green s function for a simple subdomain of the full space for the wavefunction. References ( 4) and ( ) contain a thorough discussion of this essential technical point, and also of the methods which permit the accurate computation of the energy and other quantum expectations such as the structure function, momentum density, Bose-Einstein condensate fraction, and... 

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