Sequential approaches

There is little difference between the two methods in the current example since the data are of high quality. However, the sequential approach of first minimizing and then minimizing is somewhat better for this example and is preferred in general. Figure 7.4 shows the correlation. It is theoretically possible to fit both kj and kn by minimizing S, but this is prone to great error. 

Abt M, Lim Y-B, Sacks J, Xie M, Young SS. A sequential approach for identifying lead compounds in large chemical databases. Stat Sci 2001 16 154-68. 

According to the preceding results we cannot determine the steady state of the system using the sequential approach suggested by Woodley [27]. This method involves sequential study of two phenomena reactant transfer in biphasic medium and enzyme kinetics in the aqueous medium. In the steady state, substrate transfer rate is equal to the reaction rate. 

Equation based programs in which the entire process is described by a set of differential equations, and the equations solved simultaneously not stepwise, as in the sequential approach. Equation based programs can simulate the unsteady-state operation of processes and equipment. 

We have broadened the scope of this reverse addition protocol to prepare a variety of boronic acids bearing different functional groups for use in Suzuki coupling reactions. The yield and quality of the boronic acid prepared by this reverse addition protocol is usually better than the sequential approach. The boronic acids can be used without further purification (formation of pinacols) in Suzuki coupling reactions. 

A recursive procedure is presented that exhibits some advantages over classical batch processing since it avoids the inversion of large matrices. It is shown that when only one equation is processed at a time, the inversion degenerates into the computation of the reciprocal of a scalar. Furthermore, this sequential approach can also be used to isolate systematic errors that may be present in the data set (Romagnoli and Stephanopoulos, 1981 Romagnoli, 1983). 

The simultaneous solution strategy offers several advantages over the sequential approach. A wide range of constraints may be easily incorporated and the solution of the optimization problem provides useful sensitivity information at little additional cost. On the other hand, the sequential approach is straightforward to implement and also has the advantage of well-developed error control. Error control for numerical integrators (used in the sequential approach) is relatively mature when compared, for example, to that of orthogonal collocation on finite elements (a possible technique for a simultaneous approach). 

In this section the sequential approach discussed in Chapter 6 will be extended to parameter estimation. An initial estimate of 0 can be obtained from a minimal data set for which the number of observations is equal to the number of components of 0. Let yo denote an observation at time t = to if 9 has n components, the minimal data set is symbolized by the vector... 

Product-process design are linked and in specific cases, there is an advantage to look at integrated solution approaches rather than sequential approaches. 

The Reverse Sequential Approach Profiling before Screening. 130... 

Chiral method development is often referred to as one of the most difficult fields in terms of development time. Interaction with a chiral selector is required to achieve separation but the enantioselectivity of a given selector for a given chiral molecule is a priori unknown. For some compounds, it can take several days to find suitable separation conditions when using sequential approaches. Therefore, industry most often defines generic separation strategies, which are often kept internally or are... 

Scheme 12.17 shows a representative example of the covalent attachment of a molecular catalyst to an inorganic support material via a hnker ( tether ) [165]. Here the sequential approach was exploited to immobihze catalyticaUy valuable rare-earth metal BINOL complexes [166]. An alkoxysilane funchonalized (R)-BINOL was obtained by a four-step reaction sequence involving brominahon at the 6-position, protechon of the phenohc groups by O-methylahon with CH3I,... 

We start with examples of the sequential approach. With this approach, you begin with more routine experiments, ones that are reasonably likely to succeed (e.g., calibration or optimization procedures). The initial set of experiments can also serve as a test case and/or show that you can reproduce literature values. For example, Aga (P6) proposes first to explore conditions that will optimize immunoassay sensitivity, and Spain (P7) proposes to begin with a study of topography, using published methods and a self-assembled monolayer with a known structure. 

The sequential approach is also common in proposals written by synthetic chemists (a multistep synthesis is inherently step by step). Vyvyan (excerpt 13N), for example, proposes a strategy to synthesize a select group of heliannuols (alleo-pathic natural products isolated from the sunflower) in an optically pure form. One approach that he will explore involves enantioselective cross-coupling reactions between an alkyl zinc reagent and an aryl bromide. He begins with experiments that will utilize recently developed catalysts and produce products with known optical rotation data. Subsequent reactions are described that will lead potentially to the desired stereospecific heliannuols A and D. 

The last example of a sequential approach is from Sanov (excerpt 130). A series of increasingly complex experiments is proposed to study the photochemistry of 02, and OCS . Sanov begins with the easier diatomic anions (02 and which will serve as prototypes for subsequent experiments. Next, he will study a larger, polyatomic anion (OCS ) and its cluster ions, 0CS (H20)]j. In the future, he will study even larger dimers and trimers (OCS)n (n > 2) and their hydrated counterparts. 

Based on previous success in the Pauson-Khand reaction [43], Evans demonstrated a sequential approach to the synthesis of eight-membered rings, which involved a rhodium-catalyzed aUyhc amination reaction followed by carbocyclization, to effect a three-component couphng (Scheme 12.11). To date, this transformation is only the second example of a sequential rhodium-catalyzed reaction in which only temperature is used to modulate catalytic activity. 

The rationale for concurrent chemoradiation is that the ChT can augment local-regional control by both direct tumor cell killing and radiosensitization at the same time as it addresses systemic micrometastases. Unfortunately, this also has the potential to increase radiation-related mucosal acute toxicity, predominantly esophagitis and pneumonitis. Thus, some of the early trials of concurrent therapy used either attenuated dose ChT or split course RT to ameliorate potential cotoxicity. These trials showed that concurrent therapy is feasible and, as with the sequential approach, improves outcome. 

The radiation was continuous course in the sequential approach, but there was a 2 wk split between two courses of 28 Gy/3 wk for the concurrent regimen. The ChT doses were not reduced in the concurrent arm and the split course may have conferred some protection from ChT-enhanced acute radiation toxicity, since the rate of severe esophagitis was low in both study arms. There was better short-term survival (MST... 

Zambetti M, Oriana S, Quattrone P, et al. Combined sequential approach in locally advanced breast... 

Chiral polymers can be prepared using a one-pot system, i.e., all reactants and catalysts are present at the start of the reaction and both catalysts work simultaneously. However, one can also envisage the synthesis of chiral polymers using catalysts in sequence, either in one pot or even completely independent of each other. This section will deal with the synthesis of chiral block copolymers using different catalysts in sequence. An interesting example of the synthesis of chiral polymers using catalysts in sequence is the synthesis of chiral block copolymers in a sequential approach. Both ATRP and nitroxide-mediated LFRP were evaluated for this purpose. 

For the optimization of, for instance, a tablet formulation, two strategies are available a sequential or a simultaneous approach. The sequential approach consists of a series of measurements where each new measurement is performed after the response of the previous one is knovm. The new experiment is planned according to a direction in the search space that looks promising with respect to the quality criterion which has to be optimized. Such a strategy is also called a hill-climbing method. The Simplex method is a well known example of such a strategy. Textbooks are available that describe the Simplex methods [20]. 

One way of maximizing the yield is to minimize the number of sequential steps and, whenever possible, to use parallel rather than sequential reactions. For example, suppose that we wish to synthesize a compound ABCDEF by linking together A,B,C,D,E, and F. The sequential approach would involve at least five steps as follows ... 

A summary of the sequential approach proposed by four different groups [249,252-254] is provided in Table 2.2, and this can be used to illustrate the complexity of the problem. 

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 contrast to the sequential solution method, the simultaneous strategy solves the dynamic process model and the optimization problem at one step. This avoids solving the model equations at each iteration in the optimization algorithm as in the sequential approach. In this approach, the dynamic process model constraints in the optimal control problem are transformed to a set of algebraic equations which is treated as equality constraints in NLP problem [20], To apply the simultaneous strategy, both state and control variable profiles are discretized by approximating functions and treated as the decision variables in optimization algorithms. 

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