Parametric algorithms

In general, this approach generates a parametric algorithm for a p-RDM with p — 3 associated arbitrary parameters leading to a whole family of approximations. In what follows this unifying algorithm is denoted by UA. 

This scheme works the other way around. Here, the tiles are sequentially processed on a fixed-size array that executes the operations of a single tile in parallel. It needs memory external to the array to store data for another tile. Typically, LPGS is used to execute huge and parametrized algorithms on a relatively small and fixed size array. 

The distribution of laser points in the image is discrete and it is difficult to locate points directly with a maximum density around. The mean shift presented by Comaniciu and Meer [COM 99] is a powerful non-parametric algorithm that allows us to find the local maximum of a function of the underlying density. It estimates the feature space as an empirical probability density function. For each data point, the mean shift defines a window and calculates the average of data within the window. Then it moves the center of the window to the average in the direction of the... 

C. G. Lambert, Multipole-based Algorithms in Molecular Biophysics and Non-parametric Statistics, Ph.D. Dissertation, Duke University Department of Computer Science, 1997. 

The only problem with the foregoing approach to molecular interactions is that the accurate solution of Schrddinger s equation is possible only for very small systems, due to the limitations in current algorithms and computer power. Eor systems of biological interest, molecular interactions must be approximated by the use of empirical force fields made up of parametrized tenns, most of which bear no recognizable relation to Coulomb s law. Nonetheless the force fields in use today all include tenns describing electrostatic interactions. This is due at least in part to the following facts. 

Zecchin AC, Simpson AR, Maier HR, Nixon JB (2005) Parametric study for an ant algorithm applied to water distribution system optimization, IEEE Trans. Evol Comput 9 175-190... 

Optimisation may be used, for example, to minimise the cost of reactor operation or to maximise conversion. Having set up a mathematical model of a reactor system, it is only necessary to define a cost or profit function and then to minimise or maximise this by variation of the operational parameters, such as temperature, feed flow rate or coolant flow rate. The extremum can then be found either manually by trial and error or by the use of numerical optimisation algorithms. The first method is easily applied with MADONNA, or with any other simulation software, if only one operational parameter is allowed to vary at any one time. If two or more parameters are to be optimised this method becomes extremely cumbersome. To handle such problems, MADONNA has a built-in optimisation algorithm for the minimisation of a user-defined objective function. This can be activated by the OPTIMIZE command from the Parameter menu. In MADONNA the use of parametric plots for a single variable optimisation is easy and straight-forward. It often suffices to identify optimal conditions, as shown in Case A below. 

Furthermore, the effects of strained rings and of aromatic compounds must be considered (7), and algorithms that perform these tasks have been developed (, 9 ). Values on bond dissociation energies can be calculated by extending the parametrization to radicals (10). 

The NYM algorithm is therefore a particular case for < = 2 of Alcoba s parametric expression. It must be noted, that as happens with the NY and the VTP, the UA does not correct the error in the elements whose indices correspond to a three-body elemental excitation. 

A multiscale system where every two constants have very different orders of magnitude is, of course, an idealization. In parametric families of multiscale systems there could appear systems with several constants of the same order. Hence, it is necessary to study effects that appear due to a group of constants of the same order in a multiscale network. The system can have modular structure, with different time scales in different modules, but without separation of times inside modules. We discuss systems with modular structure in Section 7. The full theory of such systems is a challenge for future work, and here we study structure of one module. The elementary modules have to be solvable. That means that the kinetic equations could be solved in explicit analytical form. We give the necessary and sufficient conditions for solvability of reaction networks. These conditions are presented constructively, by algorithm of analysis of the reaction graph. 

Two non-parametric methods for hypothesis testing with PCA and PLS are cross-validation and the jackknife estimate of variance. Both methods are described in some detail in the sections describing the PCA and PLS algorithms. Cross-validation is used to assess the predictive property of a PCA or a PLS model. The distribution function of the cross-validation test-statistic cvd-sd under the null-hypothesis is not well known. However, for PLS, the distribution of cvd-sd has been empirically determined by computer simulation technique [24] for some particular types of experimental designs. In particular, the discriminant analysis (or ANOVA-like) PLS analysis has been investigated in some detail as well as the situation with Y one-dimensional. This simulation study is referred to for detailed information. However, some tables of the critical values of cvd-sd at the 5 % level are given in Appendix C. 

The database of an environmental monitoring system does not always meet the requirement of parametric saturation demanded by GIMS technology. Therefore, an algorithm to parameterize the functions of the system of a selected territory, which... 

At the present time, the theory of electrochemical impedance of electrodes with distributed potentials is not yet completed, and algorithms of parametrical and structural identification procedures are not available. In addition, the interpretation of the results is very complicated. For this reason, in this work we analyzed only the frequency characteristics of impedance s components in the modified electrode system. As a result, we obtained a set of response peculiarities in the frequency range under investigation. Rather low frequency dispersion was observed in a solution containing a ferri-ferrocyanide system for both active (Fig.3, curve 2) and reactive (Fig.4, curve 3) components. In our opinion, this fact confirms that the independent on frequency resistance of charge transfer determines the main contribution to the impedance. 

In quasi-Newton methods, a parametrized estimate of F or G is used initially, then updated at each iterative step. Saved values of q, p can be used in standard algorithms such as BFGS, described above. 

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