One-at-a-time method

Current proteomics studies rely almost exclusively on 2D gel electrophoresis to resolve proteins before MALDI-TOF or ESI-MS/MS approaches. A drawback of the 2D gel approach is that it is relatively slow and work intensive. In addition, the in-gel proteolytic digestion of spots followed by mass spectrometry is a one-at-a-time method that is not well suited for high throughput studies. Therefore, considerable effort is being directed towards alternate methods for higher throughput protein characterization. 

For this last stage, the one-at-a-time procedure may be a very poor choice. At Union Carbide, use of the one-at-a-time method increased the yield in one plant from 80 to 83% in 3 years. When one of the techniques, to be discussed later, was used in just 15 runs the yield was increased to 94%. To see why this might happen, consider a plug flow reactor where the only variables that can be manipulated are temperature and pressure. A possible response surface for this reactor is given in Figure 14-1. The response is the yield, which is also the objective function. It is plotted as a function of the two independent variables, temperature and pressure. The designer does not know the response surface. Often all he knows is the yield at point A. He wants to determine the optimum yield. The only way he usually has to obtain more information is to pick some combinations of temperature and pressure and then have a laboratory or pilot plant experimentally determine the yields at those conditions. 

The one-at-a-time method is to pick one of the variables and make a number of tests until the optimum for that variable is obtained at a constant level of the other variables. If the temperature is held constant at 250°F in Figure 14-1, the optimum value of the pressure would be 51 psia (point B). 

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. 

Figure 7.7 Contour diagram a situation in which the one-at-a-time method fails to locate the...

The ability to make optical measurements on individual molecules and submicroscopic aggregates, one at a time, is a valuable new tool in several areas of molecular science. By eliminating inlromogeneous broadening it allows pure spectroscopy to be perfonned witli unprecedented precision in certain condensed phase systems. As an analytical method it pennits tire rapid detection of certain analytes witli unmatched sensitivity. Finally, it is revolutionizing our... 

Vitha, M. F. Carr, P. W. A Laboratory Exercise in Statistical Analysis of Data, /. Chem. Educ. 1997, 74, 998-1000. Students determine the average weight of vitamin E pills using several different methods (one at a time, in sets of ten pills, and in sets of 100 pills). The data collected by the class are pooled together, plotted as histograms, and compared with results predicted by a normal distribution. The histograms and standard deviations for the pooled data also show the effect of sample size on the standard error of the mean. 

A variation on the use of pseudo-ordered reactions is the initial rate method. In this approach to determining a reaction s rate law, a series of experiments is conducted in which the concentration of those species expected to affect the reaction s rate are changed one at a time. The initial rate of the reaction is determined for each set of conditions. Comparing the reaction s initial rate for two experiments in which the concentration of only a single species has been changed allows the reaction order for that species to be determined. The application of this method is outlined in the following example. 

Implementation Issues A critical factor in the successful application of any model-based technique is the availability of a suitaole dynamic model. In typical MPC applications, an empirical model is identified from data acquired during extensive plant tests. The experiments generally consist of a series of bump tests in the manipulated variables. Typically, the manipulated variables are adjusted one at a time and the plant tests require a period of one to three weeks. The step or impulse response coefficients are then calculated using linear-regression techniques such as least-sqiiares methods. However, details concerning the procedures utihzed in the plant tests and subsequent model identification are considered to be proprietary information. The scaling and conditioning of plant data for use in model identification and control calculations can be key factors in the success of the apphcation. 

Various procedures for solving Eqs. (13-149) to (13-161), ranging from a complete tearing method to solve the equations one at a time, as shown by Distefano, to a complete simultaneous method, have been studied. Regardless of the method used, the following considerations generally apply ... 

Replace the holdup derivatives in Eqs. (13-149) to (13-151) by total-stage material-balance equations (e.g., dMj/dt = Vj + i + Ej- — Vj — Lj) and solve the resulting equations one at a time by the predictor step of an explicit integration method for a time increment that is determined by stability and truncation considerations. If the mole fraclions for a particular stage do not sum to 1, normalize them. 

An additional capacity control method is the unloader. This method can be used in conjunction with clearance pockets to extend the range of control to zero capacity. On double-acting cylinders, unloading the individual sides one at a time will provide a two-step unloading of the cylinder. On multicylinder arrangements, the cylinders can be unloaded one at a time providing as many steps as cylinders operating in parallel. The unloaders can also be used to totally unload the compressor, as is necessary for electric motor driver startup. 

The Locally Updated Plane.s- (LUP) minimization is related to the chain method, but the relaxation is here done in the hyperplane perpendieular to the reaction coordinate, rather than along a line defined by the gradient. Furthermore, all the points are moved in each iteration, rather than one at a time. 

Using experimental design such as Surface Response Method optimises the product formulation. This method is more satisfactory and effective than other methods such as classical one-at-a-time or mathematical methods because it can study many variables simultaneously with a low number of observations, saving time and costs [6]. Hence in this research, statistical experimental design or mixture design is used in this work in order to optimise the MUF resin formulation. 

One may clearly extend the technique to include as many reactions as desired. The irreversibility of the reactions permits one to solve the rate expressions one at a time in recursive fashion. If the first reaction alone is other than first-order, one may still proceed to solve the system of equations in this fashion once the initial equation has been solved to determine A(t). However, if any reaction other than the first is not first-order, one must generally resort to numerical methods to obtain a solution. 

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