Direct binary search

M.A. Seldowitz, J.P. Allebach, D.W. Sweeney, Synthesis of digital holograms by direct binary search. Appl. Opt. 26, 2788-2798 (1987)... 

A more rigorous solution based on marching ahead in enthalpy according to Equation 7.42 is given in the next 16 lines of code. The temperature is found from the enthalpy using a binary search. The code is specific to the initial conditions of this problem. Results are very similar to those for marching temperature directly. 

More recently, flow titrations have been implemented in multi-commuted flow systems. With these systems, the exact amounts of the solutions involved can be modified in real time according to a concentration-oriented feedback mechanism. The flow titration really mimics a true titration because an analytical curve is not needed. A flow system exploiting a binary search to define the end point of an acid—base titration [324] is a good example of this approach. Stream directing solenoid valves were used to modify the sample and titrant volumes after every measurement via a feedback mechanism. Samples with concentrations within a range of two orders of magnitude could be titrated without modifying the flow manifold. 

Solution To determine the location of the azeotrope for a specified pressure, the liquid composition has to be varied and a bubble-point calculation performed at each liquid composition until a composition is identified, whereby X = y,-. Alternatively, the vapor composition could be varied and a dew-point calculation performed at each vapor composition. Either way, this requires iteration. Figure 4.5 shows the x—y diagram for the 2-propanol-water system. This was obtained by carrying out a bubble-point calculation at different values of the liquid composition. The point where the x—y plot crosses the diagonal line gives the azeotropic composition. A more direct search for the azeotropic composition can be carried out for such a binary system in a spreadsheet by varying T and x simultaneously and by solving the objective function (see Section 3.9) ... 

This relationship is used in an application to a simple binary system to balance the trade-offs between inefficiency (fuel costs) and capital investment. The Second Law optimization yields results identical to those obtained from a traditional direct-search technique. 

This paper has provided a framework for further application of Second Law based design methodology to separation systems. It has done so by providing a relationship that gives the available-energy destruction for a binary separation as a function of the process variables for the case in which the entropy production is primarily due to mass transfer effects. The Second Law methodology has been described and applied to a simple binary separation system. The method yields results identical to those obtained from a traditional direct search technique, and accurately indicates the respective trade-offs between fuel costs and capital investment. 

Another set of early studies came from the work of Judson and coworkers [35, 36], which emphasized using GAs for search problems on small molecules and peptides, especially cyclic peptides. A dihedral angle representation was used for the peptides with values encoded as binary strings, and the energy function used the standard CHARMM force field. Mutations were implemented as bit flips and crossovers were introduced by a cut-and-paste of the strings. The small size of the system enabled a detailed investigation of the various parameters and policies chosen. In Ref. [37], a comparison between a GA and a direct search minimization was performed and showed the advantages and weaknesses of each method. As many concepts are shared between search problems on small peptides and complete proteins, these studies have contributed to subsequent attempts on full proteins. 

Although binary pattern descriptors exclusively contain information about the presence or absence of distances, frequency pattern descriptors additionally contain the frequency of distances. Frequency pattern descriptors are valuable for direct comparison of structural similarities. For instance, a substructure can be assumed to exist if the frequencies in a substructure pattern occur in the query descriptor. Bond patterns can be used in a similar pattern search approach to determine structural similarities. In this case bond-path RDF descriptors are used. 

If a training has been performed in reverse mode, a descriptor command will be available — instead of a property command — which opens a chart containing a comparison of two descriptors. In contrast to a property vector, a descriptor can be directly searched for in a binary descriptor database (e.g., to search for corresponding structures). The result window contains then a hit list and two three-dimensional molecule models one displaying the original molecule of the test set entry (if available), and the other showing the molecule of the actually selected entry in the hit list of similar molecules. 

In terms of coding method, it is necessary to depend on the situation of practice to set up the appropriate encoding and decoding scheme in order to overcome the shortcomings of the binary code. When variables are real vectors, we can directly use code by real number to inject heuristic information relevant to the field of problem in order to increase the search ability of GA. 

There are many opportunities to be explored in the area of binary, ternary and quaternary anode catalyst formulations for methanol oxidation. Most of the studies to date, with the exception of the work by Gurau et al. on PtRuIrOs [122], explored a rather limited number of catalyst compositions, typically less than five. In order to search and discover the optimum formulation and composition, fast and efficient electrocatalyst screening techniques are required that are able to provide electrochemieal performance evaluations under conditions directly applicable to... 

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