By K. Sundermeyer

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**Extra resources for Constrained Dynamics - With Applns to Yang-Mills Theory...**

**Sample text**

In order to quantitatively understand how this distortion affects our observations, let us first consider a simple example. Assume that the distribution of sequences that we want to measure consists of one unique sequence of length L that appears in a pool N times. Let us assume that the probability of reading a nucleotide correctly, p, is constant. If p < 1, then there is a non-zero probability that the sequence we think we are observing differs from the sequence that is actually in the pool. Smaller values of p, lead to larger numbers of erroneous unique sequences generated by misreadings (or mutations).

This result is quite intuitive. It is clear that the more parameters a model has, the better we can fit the model to a given set of data. But, from a practical viewpoint, we are more interested in models with fewer parameters. Statistical Information Criteria allow us to identify the models that provide the best balance between fitting experimental data well and using the fewest number of parameters. , can change at any step of the synthesis process, either by some external change in conditions (like temperature, for instance, which would directly affect the reactivities among nucleotides and, therefore, parameters ri;j , ri;j;k , etc), or by a change in the concentrations of nucleotides in solution, either intentionally or unintentionally (for instance, due to the natural degradation of nucleotides in solution).

This significant difference between the frequencies of the most and least abundant sequences in a pool also plays an important role in determining when we can reasonably assume that all possible 4L unique sequences are present. Assuming there Quantitative Analysis of Synthesized Nucleic Acid Pools 31 is no mutagenesis (for example, via PCR amplification), then if some sequences are initially absent, they cannot be selected upon by any selection experiment, even if they happen to be the best (most functional or selectable) sequences.