https://curiouscoding.nl/tags/sus-anchors/Recent content in Sus-Anchors on CuriousCodingHugoenWed, 02 Sep 2026 00:00:00 +0200https://curiouscoding.nl/slides/sus-anchors-text/Wed, 02 Sep 2026 00:00:00 +0200https://curiouscoding.nl/slides/sus-anchors-text/<script src="https://curiouscoding.nl/livereload.js?mindelay=10&amp;v=2&amp;port=1313&amp;path=livereload" data-no-instant defer></script> <h2 id="minimizer-schemes"> Minimizer schemes <a class="heading-link" href="#minimizer-schemes"> <i class="fa-solid fa-link" aria-hidden="true" title="Link to heading"></i> <span class="sr-only">Link to heading</span> </a> </h2> <p>Input: a window \(W\in \Sigma^{w+k-1}\)</p> <p><strong>Minimizer scheme</strong>: Sample the \(k\)-mer with the one with smallest hash: \[f(W) = \mathrm{argmin}_{0\leq i\lt w\ \ } h(W_{i\dots i+k}).\]</p> <p><strong>Sampling scheme</strong>: <font color="green">Arbitrary</font> function \(f: \Sigma^{w+k-1}\to \{0, \dots, w-1\}.\)</p> <p><strong>Density</strong>: The expected fraction of sampled \(k\)-mers in a random string:</p> <ul> <li><code>E</code>​<font color="red"><code>A</code></font>​<code>DCAE.....</code></li> </ul> <!--listend--> <ul> <li><code>.</code>​<font color="red"><code>A</code></font>​<code>DCAEB....</code></li> </ul> <!--listend--> <ul> <li><code>..DC</code>​<font color="red"><code>A</code></font>​<code>EBE...</code></li> </ul> <!--listend--> <ul> <li><code>...C</code>​<font color="red"><code>A</code></font>​<code>EBEC..</code></li> </ul> <!--listend--> <ul> <li><code>....</code>​<font color="red"><code>A</code></font>​<code>EBECD.</code></li> </ul> <!--listend--> <ul> <li><code>.....E</code>​<font color="red"><code>B</code></font>​<code>ECDC</code></li> </ul> <!--listend--> <ul> <li><code>E</code>​<font color="red"><code>A</code></font>​<code>DC</code>​<font color="red"><code>A</code></font>​<code>E</code>​<font color="red"><code>B</code></font>​<code>ECDC</code></li> </ul> <h2 id="density-bounds"> Density bounds <a href="#citeproc_bib_item_2">Kille et al. 2024</a> <a class="heading-link" href="#density-bounds"> <i class="fa-solid fa-link" aria-hidden="true" title="Link to heading"></i> <span class="sr-only">Link to heading</span> </a> </h2> <p>Conjecture: Optimal schemes exist for \(k\equiv 1\pmod w\)?</p>