Modified simples algorithm

A simple algorithm based on an arbitrary adjustment of /3 (a modified Mar-quardt s method) is listed in Table 6.1. 

PLS has been introduced in the chemometrics literature as an algorithm with the claim that it finds simultaneously important and related components of X and of Y. Hence the alternative explanation of the acronym PLS Projection to Latent Structure. The PLS factors can loosely be seen as modified principal components. The deviation from the PCA factors is needed to improve the correlation at the cost of some decrease in the variance of the factors. The PLS algorithm effectively mixes two PCA computations, one for X and one for Y, using the NIPALS algorithm. It is assumed that X and Y have been column-centred as usual. The basic NIPALS algorithm can best be demonstrated as an easy way to calculate the singular vectors of a matrix, viz. via the simple iterative sequence (see Section 31.4.1) ... 

While this chapter has described two examples of our efforts in bacterial strain identification, a number of other groups have contributed to this research area. It remains to be seen whether mathematical algorithms such as the modified correlation approach described herein are always more effective for strain assignments than the simple use of distinctive biomarker peaks. Nilsson reported MALDI mass spectra of Helicobacter pylori with three different matrices and solvent conditions.59 She showed that some strains of this bacteria yield rather similar mass spectra while others are quite different. Nevertheless, each strain appears to exhibit some unique peaks that might be used for distinguishing strains. 

Unfortunately, if rank(A) < n, then the Q-R factorization does not necessarily produce an orthonormal basis for R(A). However, the Q-R decomposition can be modified in a simple way so as to produce an orthonormal basis for A s range. The modified algorithm computes the factorization... 

Fairbanks, Everitt and Jaeger s modified tape recorder [Fairbanks et al., 1954] is the simplest and oldest example of a pitch-independent time-domain time or pitch scaling system. Although Pitch independent methods are no longer used in practice, they offer a simple illustration of the basic principles underlying most of the more recent algorithms. 

This restriction is not demanded. It is a simple way to satisfy the Pauli exclusion principle, but it is not the only means for doing so. In an unrestricted wavefunction, the spin-up electron and its spin-down partner do not have the same spatial description. The Hartree-Fock-Roothaan procedure is slightly modified to handle this case by creating a set of equations for the a electrons and another set for the p electrons, and then an algorithm similar to that described above is implemented. 

All the particles in the PSO have memory and they modify these memorized values as the optimisation routine advances. The recorded values are velocity (f), position (p), best previous performance (pbesf) and best group performance (gbesf). The velocity describes how fast a particle should move from its current position which contains the coordinates of the particle. The last two parameters are the recorded best values that have been formd during the iterations. A simple PSO algorithm is expressed as [9] ... 

On the basis of the model of a heterogeneous membrane, it is possible to create a simulation scheme based on dynamic Monte Carlo computer simulations of the adsorption and desorption process on heterogeneous surfaces to extract the involved rate constants as a function of the calcium ion concentration. A simple simulation based on a modified, partly reversible, random sequential adsorption (RSA) algorithm provides very good accordance between experiment and measurement. Figure 8 schematically depicts the assumed model. 

---