Sequential methods

The parameterization process may be done sequentially or in a combined fashion. In the sequential method a certain class of compound, such as hydrocarbons, is parameterized first. These parameters are held fixed, and a new class of compound, for example alcohols and ethers, is then parameterized. Tins method is in line with the basic assumption of force fields parameters are transferable. The advantage is that only a fairly small number of parameters are fitted at a time. The ErrF is therefore a relatively low-dimensional function, and one can be reasonably certain that a good minimum has been found (although it may not be the global minimum). The disadvantage is that the final set of parameters necessarily provides a poorer fit (as defined from the value of the ErrF) than if all the parameters are fitted simultaneously. 

Fu, K., Sequential Methods in Pattern Recognition and Machine Learning. Academic Press, New York, 1968. 

These methods move one step at a time. A strategy that delineates the particular method dictates how to proceed once the results of the most recent tests are available. The one-at-a-time method is an example of an algebraic sequential procedure. The goal of the algebraic sequential methods is to find and follow a path to the summit. The geometric sequential methods attempt to isolate the area in which the maximum may exist. 

Perhaps the biggest gap in terms of effective models is the capability of simultaneously handling changeovers, inventories and resource constraints. Sequential methods can handle well the first, while discrete time models (e.g., STN, RTN), can handle well the last two. While continuous-time models with global time intervals can theoretically handle all of the three issues, they are at this point still much less efficient than discrete time models, and therefore require further research. 

Accordingly, FDA has developed a sequential method of evaluating and dealing with reproductive and developmental analysis. This is called Wedge Analysis and is demonstrated in Figures 8.9 through 8.11. 

The German guidelines advise an interval of 15 seconds if a sequential method is used. This means a series of dilutions commencing below the threshold in rising order. If the set of dilutions is presented in random order the interval should be 1 minute. The Dutch guidelines allow only the sequential method with increasing concentrations. 

In France random and sequential method is possible with intervals of 3 minutes. In Warren Spring it is the experience that more consistent results are obtained in starting from a high concentration. There should be at least one minute between each exposure. 

The temperature-sensitive poly(A-isopropyl acrylamide) and pH-sensitive poly(methacrylic acid) were used as the two component networks in the IPN system. Since both A-isopropyl acrylamide (NIPAAm) (Fisher Scientific, Pittsburgh, PA) and methacrylic acid (MAA) (Aldrich, Milwaukee, Wl) react by the same polymerization mechanism, a sequential method was used to avoid the formation of a PNIPAAm/PMAA copolymer. A UV-initiated solution-polymerization technique offered a quick and convenient way to achieve the interpenetration of the networks. Polymer network I was prepared and purified before polymer network II was synthesized in the presence of network I. Figure I shows the typical IPN structure. 

Pocock SJ. Group sequential methods in the design and analysis of clinical trials. Biometrika 1977 64 191-99. 

The one-pot sequential method has the disadvantage that the propagation of the second monomer involves a mixture of the second monomer plus unreacted first monomer. The second block is actually a random copolymer. The isolated macroinitiator method is the method of choice to avoid this contamination of the second block. The isolated macroinitiator... 

The three methods described in the preceding paragraphs each offer distinct advantages and disadvantages. The first and most obvious difference between the methods is the distinction between the sequential methods (sequential simplex and prisma method) and the simultaneous method (mixture design). With the sequential method some experiments are performed, these are evaluated, and on the basis of this evaluation new design points are selected, these are evaluated etc. With the simultaneous... 

Although application of chemometrics in sample preparation is very uncommon, several optimisation techniques may be used to optimise sample preparation systematically. Those techniques can roughly be divided into simultaneous and sequential methods. The main restrictions of a sequential simplex optimisation [6,7] find their origin in the complexity of the optimisation function needed. This function is a predefined function, often composed of several criteria. Such a composite criterion may lead to ambiguous results [8]. Other important disadvantages of simplex optimisation methods are that not seldom local optima are selected instead of global optima and that the number of experiments needed is not known beforehand. 

This method will soon replace the sequential method for 1R spectrometers (Fig. 10.13). 

Figure 13.9—Schematic of a sequential, crystal-based spectrometer and the spectrum obtained using the sequential method with an instrument having a goniometer. The Soller slit collimator, made of metallic parallel sheets, collimates the primary X-ray beam emitted by a high power source (SRS 300 instrument, reproduced by permission of Siemens). A typical spectrum of an alloy, obtained by an instrument of this category, having an LiF crystal (200) with 26 angle in degrees as the abscissa and intensity in Cps as the ordinate). Model Philips PW2400 Spectrum, reproduced with permission of VALDI-France.

SEQUENTIAL ANALYSIS. The analysis of material derived by a sequential method of sampling, that is to say, it is tile data, not tile analysis, which are sequential. 

Optimization methods can be classified in several ways, and the choice is largely subjective. For our purposes, it is convenient to categorize them as sequential or simultaneous. A sequential method is one in which the experimental and evaluation stages alternate throughout the procedure, with the results of previous experiments being used to predict further experiments in search of the optimum. In contrast, with a simultaneous optimization strategy, most if not all experiments are completed prior to evaluation. (Note that simultaneous has a different meaning here than in the previous section.)... 

Screening in stationary mode will only give information about the activity of a single catalyst or a catalyst mixture. When a proper catalyst for a certain reaction is found, the next important information is the reaction kinetics. To obtain this information, several methods and reactors are recommended in the literature [66-73]. Most of them apply transient reactor operations to find detailed kinetic information. Microreactors are particularly suited for such an operation since their low internal reaction volumes enable a fast response to process parameter changes, e.g., concentration or temperature changes. This feature was already applied by some authors to increase the product yield in microreactors [70, 74, 75]. De Belle-fon [76] reported a dynamic sequential method to screen liquid-liquid and liquid-... 

One advantage in the sequential approach is that only the parameters that are used to discretize the control variable profile are considered as the decision variables. The optimization formulated by this approach is a small scale NLP that makes it attractive to apply for solving the optimal control with large dimensional systems that are modeled by a large number of differential equations. In addition, this approach can take the advantage of available IVP solvers. However, the limitation of the sequential method is a difficulty to handle a constraint on state variables (path constraint). This is because the state variables are not directly included in NLP. 

In order to link the section on exactly planned experiments and the section on pure sequential methods let us roughly describe the method of BOX and WILSON [1951] with two factors under study. 

In the first case (1) and when the user wants to ensure optimum conditions for regression modeling and analysis of variance, the family of methods comprising statistical, experimental, and factorial designs should be consulted. In the second case (2) an appropriate procedure from the sequential method family should be selected. 

In this context, a new concept for high-throughput screening was developed [109], De Bellefon et al. [109] reported a dynamic sequential method to screen liquid/ liquid- and liquid/gas-phase catalytic reactions by applying the method of the injection of different samples followed by barrier liquid. Although the pulsed input to establish spatially separated samples, this method might also be applicable to the study of the dynamic behavior in gas-phase reactions. 

Statistics. Where appropriate, the data in each experiment were subjected to analysis of variance. Means were tested for significant differences (P < 0.05) by the sequential methods of Newman and Keuls multiple range test. 

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