Recursive synthesis

Moore [Moore, 1977b] studied the effect of oscillator implementation using lookup tables and found that linear interpolation produces the least distortion and that truncation produces the worst. This result was confirmed by Hartmann [Hartmann, 1987], Another possibility is to use a recursive (HR) filter with poles located on the unit circle. This coupled form [Tierney et al., 1971] offers a alternate method that avoids using memoiy space. Frequency resolution requirements were calculated by Snell in a superpipeline oscillator design for dynamic Fourier synthesis [Snell, 1977]. 

At the end of a split synthesis, because the beads have been pooled and mixed, the exact identity of a molecule on a given bead is unknown. Likewise, the identity and structure of compounds in wells is unknown. Split synthesis is not a spatially addressable method. Fortunately, the exact structure does not need to be known unless a compound shows activity in a screen. If active, the structure of the compound in the well will need to be elucidated through a process called deconvolution. Deconvolution is generally accomplished through one of two methods recursive deconvolution21 or binary encoding.22... 

A 27-member library was prepared by split synthesis in three steps. Each step involved three different building blocks A, B, C 1, 2, 3 and a, b, c. The library afforded one hit. In a recursive deconvolution of the library, how many compounds would need to be made and tested to determine the identity of the hit For a hypothetical three-step library of steps involving x, y, and z building blocks, how many compound syntheses would be required for recursive deconvolution How many compounds would be required to deconvolve a four-step library of m, n, o, and p building blocks ... 

The Conceptual Synthesis of Chemical Processing Schemes Michael L. Mavrovouniotis, Symbolic and Quantitative Reasoning Design of Reaction Pathways through Recursive Satisfaction of Constraints Christopher Nagel and George Stephanopoulos, Inductive and Deductive Reasoning ... 

In a related strategy termed recursive deconvolution [16], samples of all sublibraries at each stage are retained. With this approach it is not necessary to repeat the entire synthesis at each stage of the deconvolution. One simply adds the previously determined preferred synthons to the reserved sublibraries. 

These techniques can be broadly split into two groups, the first of which can be represented by pooling methods, where deconvolution is obtained via various chemical steps, run in parallel or after the library synthesis. Pooling methods normally require multiple synthesis of many library members, including inactive individuals, in different pool formats. They are not single bead methods, so they are independent from analytical methods for structure determination. This group includes iterative deconvolution, recursive deconvolution, subtractive deconvolution, positional scanning and mutational... 

The second group can be represented by single bead methods, and relies on either bioanalytical methods to select the active compounds or on-bead screening to determine the beads carrying active compounds. It is limited to solid-phase chemistry and does not require chemical steps after library synthesis but does require sophisticated analytical methods to determine the structure of the active compounds. A recent hybrid deconvolution-single beaddecoding method named DRED (dual recursive deconvolution) requires both deconvolutive techniques and sophisticated analytical capacities. 

Figure 3. Liquid phase combinatorial synthesis (LPCS) and recursive deconvolution.

Given a fixed, predetermined set of elementary reactions, compose reaction pathways (mechanisms) that satisfy given specifications in the transformation of available raw materials to desired products. This is a problem encountered quite frequently during research and development of chemical and biochemical processes. As in the assembly of a puzzle, the pieces (available reaction steps) must fit with each other (i.e., satisfy a set of constraints imposed by the precursor and successor reactions) and conform with the size and shape of the board (i.e., the specifications on the overall transformation of raw materials to products). This chapter draws from symbolic and quantitative reasoning ideas of AI which allow the systematic synthesis of artifacts through a recursive satisfaction of constraints imposed on the artifact as a whole and on its components. The artifacts in this chapter are mechanisms of catalytic reactions and... 

Question A cell consists of several replicating molecules that mutually help the synthesis and keep some synchronization for replication. At least a membrane that partly separates a cell from the outside has to be synthesized, keeping some degree of synchronization with the replication of other internal chemicals. How is such recursive production maintained, while keeping diversity of chemicals Furthermore, this recursive production is not complete, and there appears a slow mutational change over generations, which leads to evolution. How is evolvability compatible with recursive production [1] ... 

Next, we discuss the mechanism of switching. In phase 3, the recursive production state is destabilized, when the population of parasitic molecules increase. For example, the number of the molecule C may be decreased due to fluctuations, while the number of some parasitic molecules (X) that are not originally in the catalytic network but are catalyzed by C may increase. Frequency of such fluctuation increases as the total population of molecules in a cell becomes smaller. If such fluctuation appears, the other molecular species in the original network loses the main source of molecules that catalyze their synthesis, successively. Then the new parasitic molecule X occupies a large portion of populations. However, the molecule s main catalyst (C) soon... 

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