The Separatrix Algorithm addresses two main sub-problems.

<p>The first is to use observed binary outcomes (top) to estimate the probability of success (bottom), and the second is to choose new points to sample. This is done so as to identify a particular isocline, called the separatrix, as illustrated by the dashed gray line.</p

Two-dimensional hyperbolic tangent performance.

<p>The Separatrix Algorithm again outperforms Latin hypercube sampling on the mean log likelihood metric, which was evaluated at points spaced evenly in arc-length along the separatrix.</p

Parameters values.

<p>Separatrix parameter values used in the three example presented in this paper.</p

One-dimensional hyperbolic tangent performance.

<p>For the one-dimensional hyperbolic tangent test function (18), the Separatrix Algorithm outperforms Latin hypercube sampling and traditional BDOE on a likelihood-based performance metric (19).</p

Malaria model separatrix results.

<p>The separatrix (A), variance (B), and samples with density (C) after simulating the malaria model times.</p

One-dimensional hyperbolic tangent analysis.

<p>(A) Shown are the true success probability function (dashed line), LHS samples (full and empty circles), the inferred distribution (hypercolor), and the most likely value (black line). The vertical magenta line is at the separatrix corresponding to an interest level of . (B) The probability density after observing samples using the Separatrix Algorithm. Note that the estimate is tight near the separatrix. (C) The inner workings of the igBDOE algorithm. First, test and sample points are loaded from the previous iteration in which they were sampled from the variance of the interest distribution, solid black (left axis), which in turn is computed from the interest distribution: is in blue-dash and is in red dash-dot. The expected KL divergence is plotted for each of the candidate sample points (green circles, right axis). The best of these candidates, indicated by red crosses, will be selected. (D) The final density estimate shows that the igBDOE algorithm was placing samples in and around the separatrix. Ticks on the x-axis represent samples.</p

Distribution of the fraction of unique reads over 261 <i>E</i>. <i>coli</i> samples.

<p>Samples had between 0.2 and 2.8 million reads with 90% of samples having over 1 million reads. Raw reads were filtered and then aligned to a reference genome using bowtie2. Unique reads are those that appear only once in the alignment for a particular sample. These are the reads that remain after use of the rmdup tool in samtools. Non-unique reads arise primarily when the same tagmented fragment is amplified during PCR. A low fraction of non-unique reads implies a diversity of fragments after tagmentation, and that errors introduced during PCR will not reach high frequencies.</p

Correspondence between BioAnalyzer traces and the length distribution of aligned reads.

<p>Panels A-C show three representative BioAnalyzer traces from three sample preparations of <i>S</i>. <i>maltophilia</i>. Panels D-F show the corresponding estimated fragment-size distributions (black) and the actual distributions of fragment lengths imputed from alignment to the reference genome (blue). A BioAnalyzer trace <i>f(x)</i> shows fluorescence <i>f</i> at fragment length <i>x</i>. However, we are interested in <i>n(x)</i>, the (relative) number of fragments <i>n</i> of length <i>x</i>. Since fluorescence of a DNA fragment is proportional to its length, <i>n(x)</i> ∝ <i>f(x) / x</i>. Note that sequencing can be successful despite the presence of apparently very long fragments (which are likely heteroduplexes) in the BioAnalyzer traces (Panels C and F).</p

Additional file 2 of Lineage abundance estimation for SARS-CoV-2 in wastewater using transcriptome quantification techniques

Additional file 2. Review history

Additional file 1 of Lineage abundance estimation for SARS-CoV-2 in wastewater using transcriptome quantification techniques

Additional file 1. Includes all supplementary information, supplementary figures and supplementary tables