Procedural algorithm

A common feature of the various methods that we have developed for the calculation of electronic effects in organic molecules is that they start from fundamental atomic data such as atomic ionization potentials and electron affinities, or atomic polarizability parameters. These atomic data are combined according to specific physical models, to calculate molecular descriptors which take account of the network of bonds. In other words, the constitution of a molecule (the topology) determines the way the procedures (algorithms) walk through the molecule. Again, as previously mentioned, the calculations are performed on the entire molecule. 

It follows from the above that a distinction must be made between problems and exercises, with the latter requiring for their solution only the application of well-known and practiced procedures (algorithms). The skills that are necessary for the solution of exercises are, as a rule, lower-order cognitive skills (LOCS). On the other hand, a real/novel problem requires that the solver must be able to use what have been termed as higher-order cognitive skills (HOCS) (109, 110). 

This is a procedural algorithm that is performed in a sequential manner and leads to an explicit answer. The program code may be called from another code and may include function calls, such as the square root function sqrt. 

Quantile estimators are biased in general, but the bias (as well as the variance) of the estimator decreases as the number of replications increases. The procedure algorithm quantile estimation interpolates between order statistics to reduce bias. 

The procedure algorithm cusum assumes that all of the outputs y[t are available before generating the plot. If an additional batch average, + 1], is generated, then the plot veilues can be updated using the foUovtdng steps ... 

There are no foolproof procedural algorithms in the field of pollution studies enviromnental scientists must employ all their skills to foresee the consequences of even seemingly benign or neutral alterations in the chemical environment, and each pollutant substance has its own particular chemical features. That such foresight is possible was demonstrated by the prediction of deleterious effects on the earth s ozone layer due to the use of CFCs (see Section III.C. 1) well in advance of the observation of such effects for this work Crutzen, Mohna, and Rowland were awarded the Nobel Prize in chemistry in 1995. 

An algorithm is a mathematieal proeedure that produees the solution to a problem in a finite number of steps. An algorithm that leads to a yes or no answer is a decision procedure. An algorithm that leads to a numerical answer is a computational procedure. Algorithms are loeated in ROM. 

Procedural, algorithmic transformations such as removing a dummy loop. 

Fig. 4 shows an instance of the pattern derived by applying our generic pattern instantiation procedure (Algorithm 2) and using the P-table (Table 1). It highUghts the repetition of boilerplate nodes" after multiplicity, and illustrates how a join point connects two row instance fragments. 

To search for the forms of potentials we are considering here simple mechanical models. Two of them, namely cluster support algorithm (CSA) and plane support algorithm (PSA), were described in details in [6]. Providing the experiments with simulated and experimental data, it was shown that the iteration procedure yields the sweeping of the structures which are not volumetric-like or surface-like, correspondingly. While the number of required projections for the reconstruction is reduced by 10 -100 times, the quality of reconstruction estimated quantitatively remained quite comparative (sometimes even with less artefacts) with that result obtained by classic Computer Tomography (CT). 

Because the pseudo-inverse filter is chosen from the class of additive filters, the regularization can be done without taking into account the noise, (n). At the end of this procedure the noise is transformed to the output of the pseudo-inverse filter (long dashed lines on Fig. 1). The regularization criteria F(a,a) has to fulfill the next conditions (i) leading to an additive filter algorithm, (ii) having the asymptotic property a, —> a, for K,M... 

Two different types of calibration marks are used in our experiments, planar circles and circular balls. The accuracy of the calibration procedure depends on the accuracy of the feature detection algorithms used to detect the calibration marks in the images. To take this in account, a special feature detection procedure based on accurate ellipses fitting has been developed. Detected calibration marks are rejected, if the feature detection procedure indicates a low reliability. 

Software base complexes are used for this purpose, which realize analytical restoration algorithms and various procedures of tomograms processing Program complexes ensure the control of a measuring process and dialoguing with the operator. 

The algorithm contains five minimisation procedures which are performed the same way as in the method " i.e. by minimisation of the RMS between the measured unidirectional distribution and the corresponding theoretical distribution of die z-component of the intensity of the leakage field. The aim of the first minimisation is to find initial approximations of the depth d, of the crack in the left half of its cross-section, die depth d in its right half, its half-width a, and the parameter c. The second minimisation gives approximations of d, and d and better approximations of a and c based on estimation of d,= d, and d,= d,j. Improved approximations of d] and d4 are determined by the third minimisation while fixing new estimations of d dj, dj, and dj. Computed final values dj , d/, a and c , whieh are designated by a subscript c , are provided by the fourth minimisation, based on improved estimations of d, dj, dj, and d . The fifth minimisation computes final values d, , d, dj, d while the already computed dj , d/, a and c are fixed. 

Fig.3 The algorithm for sizing of cracks with complex cross-sections and unknown shapes. The five minimisation procedures are numbered consecutively.

The simplest way to add a non-adiabatic correction to the classical BO dynamics method outlined above in Section n.B is to use what is known as surface hopping. First introduced on an intuitive basis by Bjerre and Nikitin [200] and Tully and Preston [201], a number of variations have been developed [202-205], and are reviewed in [28,206]. Reference [204] also includes technical details of practical algorithms. These methods all use standard classical trajectories that use the hopping procedure to sample the different states, and so add non-adiabatic effects. A different scheme was introduced by Miller and George [207] which, although based on the same ideas, uses complex coordinates and momenta. 

In order to summarize the procedures used for computing ionization constants of titratable residues in proteins, the steps used in our algorithm will be enumerated below ... 

The procedure Split selects the internal displacement coordinates, q, and momenta, tt, (describing vibrations), the coordinates, r, and velocities, v, of the centers of molecular masses, angular velocities, a>, and directional unit vectors, e, of the molecules from the initial Cartesian coordinates, q, and from momenta, p. Thus, the staring values for algorithm loop are prepared. Step 1 Vibration... 

Following the procedure defined by (23) the fourth order SISM for MD simulations written explicitly can be found In ref. [22]. In the fourth order SISM additional steps in the algorithm occur due to additional force evaluations. 

A substructure search algorithm is usually the first step in the implementation of other important topological procedures for the analysis of chemical structures such as identification of equivalent atoms, determination of maximal common substructure, ring detection, calculation of topological indices, etc. 

All of these effects can be accounted for by extensions of an additivity scheme, when special increments are attributed to monocyclic structures and the combination of two ring systems having one, two, or three atoms in common [23]. Combination of a table containing values for these ring fragments with an algorithm for the determination of the smallest set of smallest rings (SSSR) [24] (see also Section 2.5.1) allows such a procedure to be performed automatically. 

Problems involving routine calculations are solved much faster and more reliably by computers than by humans. Nevertheless, there are tasks in which humans perform better, such as those in which the procedure is not strictly determined and problems which are not strictly algorithmic. One of these tasks is the recognition of patterns such as feces. For several decades people have been trying to develop methods which enable computers to achieve better results in these fields. One approach, artificial neural networks, which model the functionality of the brain, is explained in this section. 

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