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Research - Revision history
2024-03-28T15:30:29Z
Revision history for this page on the wiki
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MarcRiedel: /* Computing with Molecules */
2024-02-07T21:26:01Z
<p><span dir="auto"><span class="autocomment">Computing with Molecules</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:26, 7 February 2024</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- valign="top"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- valign="top"</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| '''<del style="font-weight: bold; text-decoration: none;">to appear </del>in''':</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| '''<ins style="font-weight: bold; text-decoration: none;">appeared </ins>in''':</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| [https://<del style="font-weight: bold; text-decoration: none;">www</del>.springer.com/<del style="font-weight: bold; text-decoration: none;">journal</del>/<del style="font-weight: bold; text-decoration: none;">11047 </del>Natural Computing], 2023</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| [https://<ins style="font-weight: bold; text-decoration: none;">link</ins>.springer.com/<ins style="font-weight: bold; text-decoration: none;">article</ins>/<ins style="font-weight: bold; text-decoration: none;">10.1007/s11047-023-09964-z </ins>Natural Computing], 2023</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| '''presented&nbsp;at''':</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| '''presented&nbsp;at''':</div></td></tr>
</table>
MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=330784&oldid=prev
MarcRiedel: /* Storing Data with Molecules */
2024-02-07T21:22:44Z
<p><span dir="auto"><span class="autocomment">Storing Data with Molecules</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:22, 7 February 2024</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|'''appeared in''':</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|'''appeared in''':</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|[https://pubs.rsc.org/en/content/articlepdf/2023/DD/D3DD00083D?page=search Royal Society of Chemistry &ndash; Digital Discovery], Vol. 2, pp. 1436<del style="font-weight: bold; text-decoration: none;">--</del>1451, 2023</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|[https://pubs.rsc.org/en/content/articlepdf/2023/DD/D3DD00083D?page=search Royal Society of Chemistry &ndash; Digital Discovery], Vol. 2, pp. 1436<ins style="font-weight: bold; text-decoration: none;">&ndash;</ins>1451, 2023</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| width="70" align="center" |<span class="plainlinks"> [https://mriedel.ece.umn.edu/wiki/images/8/8f/Manicka_Stephan_Chari_Mendonsa_Okubo_Stolzberg-Schray_Reddy_Riedel_Automated_Routing_of_Droplets_for_DNA_Storage_on_a_Digital_Microfluidics_Platform.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| width="70" align="center" |<span class="plainlinks"> [https://mriedel.ece.umn.edu/wiki/images/8/8f/Manicka_Stephan_Chari_Mendonsa_Okubo_Stolzberg-Schray_Reddy_Riedel_Automated_Routing_of_Droplets_for_DNA_Storage_on_a_Digital_Microfluidics_Platform.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> </div></td></tr>
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MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=330783&oldid=prev
MarcRiedel: /* Storing Data with Molecules */
2024-02-07T21:22:20Z
<p><span dir="auto"><span class="autocomment">Storing Data with Molecules</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:22, 7 February 2024</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l28">Line 28:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Peyton Okubo, John Stolzberg-Schray, Anil Reddy, and [http://mriedel.ece.umn.edu/wiki/index.php/Marc_Riedel Marc Riedel]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Peyton Okubo, John Stolzberg-Schray, Anil Reddy, and [http://mriedel.ece.umn.edu/wiki/index.php/Marc_Riedel Marc Riedel]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- valign="top"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- valign="top"</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|'''<del style="font-weight: bold; text-decoration: none;">to appear </del>in''':</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|'''<ins style="font-weight: bold; text-decoration: none;">appeared </ins>in''':</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|[https://pubs.rsc.org/en/content/articlepdf/2023/DD/D3DD00083D?page=search Royal Society of Chemistry &ndash; Digital Discovery], 2023</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|[https://pubs.rsc.org/en/content/articlepdf/2023/DD/D3DD00083D?page=search Royal Society of Chemistry &ndash; Digital Discovery]<ins style="font-weight: bold; text-decoration: none;">, Vol. 2, pp. 1436--1451</ins>, 2023</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| width="70" align="center" |<span class="plainlinks"> [https://mriedel.ece.umn.edu/wiki/images/8/8f/Manicka_Stephan_Chari_Mendonsa_Okubo_Stolzberg-Schray_Reddy_Riedel_Automated_Routing_of_Droplets_for_DNA_Storage_on_a_Digital_Microfluidics_Platform.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| width="70" align="center" |<span class="plainlinks"> [https://mriedel.ece.umn.edu/wiki/images/8/8f/Manicka_Stephan_Chari_Mendonsa_Okubo_Stolzberg-Schray_Reddy_Riedel_Automated_Routing_of_Droplets_for_DNA_Storage_on_a_Digital_Microfluidics_Platform.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> </div></td></tr>
</table>
MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=317181&oldid=prev
MarcRiedel: /* Storing Data with Molecules */
2023-08-23T19:29:39Z
<p><span dir="auto"><span class="autocomment">Storing Data with Molecules</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:29, 23 August 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l28">Line 28:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Peyton Okubo, John Stolzberg-Schray, Anil Reddy, and [http://mriedel.ece.umn.edu/wiki/index.php/Marc_Riedel Marc Riedel]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Peyton Okubo, John Stolzberg-Schray, Anil Reddy, and [http://mriedel.ece.umn.edu/wiki/index.php/Marc_Riedel Marc Riedel]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- valign="top"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- valign="top"</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|'''<del style="font-weight: bold; text-decoration: none;">under revision</del>''':</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|'''<ins style="font-weight: bold; text-decoration: none;">to appear in</ins>''':</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|[https://<del style="font-weight: bold; text-decoration: none;">arxiv</del>.org/<del style="font-weight: bold; text-decoration: none;">abs</del>/<del style="font-weight: bold; text-decoration: none;">2211.15494 </del>Royal Society of Chemistry &ndash; Digital Discovery], 2023</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|[https://<ins style="font-weight: bold; text-decoration: none;">pubs.rsc</ins>.org/<ins style="font-weight: bold; text-decoration: none;">en/content/articlepdf/2023</ins>/<ins style="font-weight: bold; text-decoration: none;">DD/D3DD00083D?page=search </ins>Royal Society of Chemistry &ndash; Digital Discovery], 2023</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| width="70" align="center" |<span class="plainlinks"> [https://mriedel.ece.umn.edu/wiki/images/8/8f/Manicka_Stephan_Chari_Mendonsa_Okubo_Stolzberg-Schray_Reddy_Riedel_Automated_Routing_of_Droplets_for_DNA_Storage_on_a_Digital_Microfluidics_Platform.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| width="70" align="center" |<span class="plainlinks"> [https://mriedel.ece.umn.edu/wiki/images/8/8f/Manicka_Stephan_Chari_Mendonsa_Okubo_Stolzberg-Schray_Reddy_Riedel_Automated_Routing_of_Droplets_for_DNA_Storage_on_a_Digital_Microfluidics_Platform.pdf http://mriedel.ece.umn.edu/wiki/images/0/04/Pdf.jpg]</span> </div></td></tr>
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MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=312810&oldid=prev
MarcRiedel: /* Computing with Random Bit Streams */
2023-07-16T21:01:59Z
<p><span dir="auto"><span class="autocomment">Computing with Random Bit Streams</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:01, 16 July 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l273">Line 273:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''<big>A Deterministic Approach</big>'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''<big>A Deterministic Approach</big>'''</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Having <del style="font-weight: bold; text-decoration: none;">pioneered the field of </del>stochastic logic, we decided to reexamine its foundations. Why can complex functions be computed with such simple circuits when we compute on probabilities? Intuition might suggest that somehow we are harnessing deep aspects of probability theory. ''This intuition is <u>wrong</u>''.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Having <ins style="font-weight: bold; text-decoration: none;">championed </ins>stochastic logic <ins style="font-weight: bold; text-decoration: none;">for many years</ins>, we decided to reexamine its foundations. Why can complex functions be computed with such simple circuits when we compute on probabilities? Intuition might suggest that somehow we are harnessing deep aspects of probability theory. ''This intuition is <u>wrong</u>''.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The keys is that we operate on uniform representation rather than a positional one. We showed that '''we can compute deterministically using the same structures that we use when computing stochastically.''' ''There is no need to do anything randomly!'' This upended the field that we had pioneered.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The keys is that we operate on uniform representation rather than a positional one. We showed that '''we can compute deterministically using the same structures that we use when computing stochastically.''' ''There is no need to do anything randomly!'' This upended the field that we had pioneered.</div></td></tr>
</table>
MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=312762&oldid=prev
MarcRiedel: /* Computing with Molecules */
2023-07-16T15:53:29Z
<p><span dir="auto"><span class="autocomment">Computing with Molecules</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:53, 16 July 2023</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- valign="top"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|- valign="top"</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| '''<del style="font-weight: bold; text-decoration: none;">under review </del>in''':</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| '''<ins style="font-weight: bold; text-decoration: none;">to appear </ins>in''':</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| [https://www.springer.com/journal/11047 Natural Computing], 2023</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| [https://www.springer.com/journal/11047 Natural Computing], 2023</div></td></tr>
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</table>
MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=311795&oldid=prev
MarcRiedel: /* Computational Immunology */
2023-07-09T14:36:14Z
<p><span dir="auto"><span class="autocomment">Computational Immunology</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Computational Immunology==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Computational Immunology==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>“''<del style="font-weight: bold; text-decoration: none;">Biology </del>is the study of the <del style="font-weight: bold; text-decoration: none;">complex </del>things in the Universe. <del style="font-weight: bold; text-decoration: none;">Physics </del>is the study of the <del style="font-weight: bold; text-decoration: none;">simple </del>ones.''” </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>“''<ins style="font-weight: bold; text-decoration: none;">Physics </ins>is the study of the <ins style="font-weight: bold; text-decoration: none;">simple </ins>things in the Universe. <ins style="font-weight: bold; text-decoration: none;">Biology </ins>is the study of the <ins style="font-weight: bold; text-decoration: none;">complex </ins>ones.'' ” </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&ndash;&ndash; '''Richard Dawkins''' (1941&ndash; )</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&ndash;&ndash; '''Richard Dawkins''' (1941&ndash; )</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>We are studying a problem that computer science currently judges to be very difficult: '''''predicting cellular immunity'''''. It centers on the question of how strongly molecules binds to one another. The molecules in question are ''peptides'' – fragments of proteins from a virus – <del style="font-weight: bold; text-decoration: none;">and </del>cell-surface receptors <del style="font-weight: bold; text-decoration: none;">that have a cleft</del>. A peptide will only bind if it fits <del style="font-weight: bold; text-decoration: none;">into the cleft </del>like a key into a lock. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>We are studying a problem that computer science currently judges to be very difficult: '''''predicting cellular immunity'''''. It centers on the question of how strongly molecules binds to one another. The molecules in question are ''peptides'' – fragments of proteins from a virus – <ins style="font-weight: bold; text-decoration: none;">binding to </ins>cell-surface receptors. A peptide will only bind if it fits like a key into a lock. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| align="center"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| align="center"</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>||</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>||</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"''To invent, all you need is a pile of junk and a good imagination.''" &ndash;&ndash; '''Thomas A. Edison''' (1847&ndash;1931)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"''To invent, all you need is a pile of junk and a good imagination.''" &ndash;&ndash; '''Thomas A. Edison''' (1847&ndash;1931)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Humans are accustomed to counting in a positional number system &ndash; [http://en.wikipedia.org/wiki/Decimal decimal] radix. Nearly all computer systems operate on another <del style="font-weight: bold; text-decoration: none;">positional number system </del>&ndash; [http://en.wikipedia.org/wiki/Binary_numeral_system binary] radix. We are so accustomed to these systems that it <del style="font-weight: bold; text-decoration: none;">counter-intuitive </del>to ask: ''can we compute using a different representatio''n? and ''why would we want to''? </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Humans are accustomed to counting in a positional number system &ndash; [http://en.wikipedia.org/wiki/Decimal decimal] radix. Nearly all computer systems operate on another &ndash; [http://en.wikipedia.org/wiki/Binary_numeral_system binary] radix. We are so accustomed to these systems that it <ins style="font-weight: bold; text-decoration: none;">counterintuitive </ins>to ask: ''can we compute using a different representatio''n? and ''why would we want to''? </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Stochastic Logic ====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Stochastic Logic ====</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|} </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|} </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Using <del style="font-weight: bold; text-decoration: none;">a </del>conventional <del style="font-weight: bold; text-decoration: none;">representation</del>, building a circuit that computes, say a polynomial approximation to a trigonometric function such as ''tanh(x)'' or ''cos(x),'' requires ''thousands'' of logic gates. With stochastic logic, we have shown that we can compute such functions with about a ''dozen'' logic gates, so a 100X reduction in gate count. Our most important contribution is a '''general methodology for synthesizing polynomial functions''' with stochastic logic, one of the seminal contributions to the field: </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Using conventional <ins style="font-weight: bold; text-decoration: none;">binary</ins>, building a circuit that computes, say a polynomial approximation to a trigonometric function such as ''tanh(x)'' or ''cos(x),'' requires ''thousands'' of logic gates. With stochastic logic, we have shown that we can compute such functions with about a ''dozen'' logic gates, so a <ins style="font-weight: bold; text-decoration: none;">'''</ins>100X reduction in gate count<ins style="font-weight: bold; text-decoration: none;">'''</ins>. Our most important contribution is a '''general methodology for synthesizing polynomial functions''' with stochastic logic, one of the seminal contributions to the field: </div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>FET-like junctions that cross these develop a high or low impedance, respectively.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>FET-like junctions that cross these develop a high or low impedance, respectively.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>]]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| <del style="font-weight: bold; text-decoration: none;">&nbsp;</del>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| [[Image:percolation.gif|center|thumb|<del style="font-weight: bold; text-decoration: none;">200px</del>| In a switching network with defects, percolation can be exploited to produce robust Boolean functionality<del style="font-weight: bold; text-decoration: none;">. Unless the defect rate exceeds an error margin, with high probability no connection forms between the top and bottom plates for logical zero ("OFF"); with high probability, a connection forms for logical one ("ON")</del>.]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| [[Image:percolation.gif|center|thumb|<ins style="font-weight: bold; text-decoration: none;">260.994x260.994px</ins>| In a switching network with defects, percolation can be exploited to produce robust Boolean functionality. ]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of [http://en.wikipedia.org/wiki/Percolation_theory percolation]. With random connectivity, percolation gives rise to a sharp non-linearity in the probability of global connectivity as a function of the probability of local connectivity. We exploit this phenomenon to compute Boolean functions robustly in the presence of defects.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of [http://en.wikipedia.org/wiki/Percolation_theory percolation]. With random connectivity, percolation gives rise to a sharp non-linearity in the probability of global connectivity as a function of the probability of local connectivity. We exploit this phenomenon to compute Boolean functions robustly in the presence of defects.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"''There are two kinds of people in the world: those who divide the world into two kinds of people, and those who don't.''" &ndash;&ndash; '''Robert Charles Benchley''' (1889&ndash;1945)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"''There are two kinds of people in the world: those who divide the world into two kinds of people, and those who don't.''" &ndash;&ndash; '''Robert Charles Benchley''' (1889&ndash;1945)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Consider the task of designing a digital circuit with 256 inputs. From a mathematical standpoint, such a circuit performs mappings from a space of <math>2^{256}</math> Boolean input values to Boolean output values. (The number of rows in a [http://en.wikipedia.org/wiki/Truth_table truth table] for such a function is approximately equal to [http://en.wikipedia.org/wiki/Observable_universe#Matter_content the number of atoms in the universe] &ndash; <math>10^{77}</math> rows versus <math>10^{79}</math> atoms!) Verifying such a function, let alone designing the corresponding circuit, would seem to be an intractable problem. Circuit designers have succeeded in their endeavor largely as a result of innovations in the data structures and algorithms used to represent and manipulate [http://en.wikipedia.org/wiki/Boolean_function Boolean functions]. We have developed novel, efficient techniques for synthesizing functional dependencies based on so-called [http://en.wikipedia.org/wiki/Boolean_satisfiability_problem SAT-solving algorithms]. We use [http://en.wikipedia.org/wiki/Craig_interpolation Craig Interpolation] to generate circuits from the corresponding Boolean functions. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Consider the task of designing a digital circuit with 256 inputs. From a mathematical standpoint, such a circuit performs mappings from a space of <math>2^{256}</math> Boolean input values to Boolean output values. (The number of rows in a [http://en.wikipedia.org/wiki/Truth_table truth table] for such a function is approximately equal to [http://en.wikipedia.org/wiki/Observable_universe#Matter_content the number of atoms in the universe] &ndash; <math>10^{77}</math> rows versus <math>10^{79}</math> atoms!) Verifying such a function, let alone designing the corresponding circuit, would seem to be an intractable problem. <ins style="font-weight: bold; text-decoration: none;"> </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Circuit designers have succeeded in their endeavor largely as a result of innovations in the data structures and algorithms used to represent and manipulate [http://en.wikipedia.org/wiki/Boolean_function Boolean functions]. We have developed novel, efficient techniques for synthesizing functional dependencies based on so-called [http://en.wikipedia.org/wiki/Boolean_satisfiability_problem SAT-solving algorithms]. We use [http://en.wikipedia.org/wiki/Craig_interpolation Craig Interpolation] to generate circuits from the corresponding Boolean functions. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| align="center"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| align="center"</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| [[Image:sat-squid.jpg|center|thumb|350px|A circuit construct for SAT-based verification.]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| [[Image:sat-squid.jpg|center|thumb|350px|A circuit construct for SAT-based verification.]]</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"''Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.''" &ndash;&ndash; '''Bertrand Russell''' (1872&ndash;1970)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"''Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.''" &ndash;&ndash; '''Bertrand Russell''' (1872&ndash;1970)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Image:xkcd_disciplines_by_purity.png|center|thumb|<del style="font-weight: bold; text-decoration: none;">none|550px|Mathematics, before the era of [http://en.wikipedia.org/wiki/LaTeX LaTeX].</del>]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Image:xkcd_disciplines_by_purity.png|center|thumb|<ins style="font-weight: bold; text-decoration: none;">740x740px</ins>]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The great mathematician [http://en.wikipedia.org/wiki/John_von_Neumann John von Neumann] articulated the view that research should never meander too far down theoretical paths; it should always be guided by potential applications. This view was not based on concerns about the relevance of his profession; rather, in his judgment, real-world applications give rise to the most ''interesting'' problems for mathematicians to tackle. At their core, most of our research contributions are mathematical contributions. The tools of our trade are [http://en.wikipedia.org/wiki/Discrete_mathematics discrete math], including [http://en.wikipedia.org/wiki/Combinatorics combinatorics] and [http://en.wikipedia.org/wiki/Probability probability theory].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The great mathematician [http://en.wikipedia.org/wiki/John_von_Neumann John von Neumann] articulated the view that research should never meander too far down theoretical paths; it should always be guided by potential applications. This view was not based on concerns about the relevance of his profession; rather, in his judgment, real-world applications give rise to the most ''interesting'' problems for mathematicians to tackle. At their core, most of our research contributions are mathematical contributions. The tools of our trade are [http://en.wikipedia.org/wiki/Discrete_mathematics discrete math], including [http://en.wikipedia.org/wiki/Combinatorics combinatorics] and [http://en.wikipedia.org/wiki/Probability probability theory].</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Image:papa-handwriting.gif|center|thumb|none|550px|Mathematics, before the era of [http://en.wikipedia.org/wiki/LaTeX LaTeX].]]</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{|</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|</div></td></tr>
</table>
MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=311792&oldid=prev
MarcRiedel: /* Computing with Molecules */
2023-07-09T14:25:12Z
<p><span dir="auto"><span class="autocomment">Computing with Molecules</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:25, 9 July 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l50">Line 50:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Computing has escaped! It has gone from desktops and data centers into the wild. Embedded microcontrollers – found in our gadgets, our buildings, and even our bodies – are transforming our lives. And yet, there are limits to where silicon can go and where it can compute effectively. It is a foreign object that requires a electrical power source. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Computing has escaped! It has gone from desktops and data centers into the wild. Embedded microcontrollers – found in our gadgets, our buildings, and even our bodies – are transforming our lives. And yet, there are limits to where silicon can go and where it can compute effectively. It is a foreign object that requires a electrical power source. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>We are studying novel types of computing systems that are not foreign, but rather an integral part of their physical and chemical environments: systems that compute ''directly'' with molecules. A simple but radical idea: compute with '''acids''' and '''bases'''. An acidic solution corresponds to a "1"<del style="font-weight: bold; text-decoration: none;">, while </del>a basic solution to "0".</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>We are studying novel types of computing systems that are not foreign, but rather an integral part of their physical and chemical environments: systems that compute ''directly'' with molecules. A simple but radical idea: compute with '''acids''' and '''bases'''. An acidic solution corresponds to a "1" <ins style="font-weight: bold; text-decoration: none;">and </ins>a basic solution to "0".</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{|</div></td></tr>
</table>
MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=311704&oldid=prev
MarcRiedel: /* Computing with Nanoscale Lattices */
2023-07-09T01:43:23Z
<p><span dir="auto"><span class="autocomment">Computing with Nanoscale Lattices</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:43, 8 July 2023</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|| [[Image:percolation.gif|center|thumb|<del style="font-weight: bold; text-decoration: none;">315px</del>| In a switching network with defects, percolation can be exploited to produce robust Boolean functionality. Unless the defect rate exceeds an error margin, with high probability no connection forms between the top and bottom plates for logical zero ("OFF"); with high probability, a connection forms for logical one ("ON").]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|| [[Image:percolation.gif|center|thumb|<ins style="font-weight: bold; text-decoration: none;">200px</ins>| In a switching network with defects, percolation can be exploited to produce robust Boolean functionality. Unless the defect rate exceeds an error margin, with high probability no connection forms between the top and bottom plates for logical zero ("OFF"); with high probability, a connection forms for logical one ("ON").]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of [http://en.wikipedia.org/wiki/Percolation_theory percolation]. With random connectivity, percolation gives rise to a sharp non-linearity in the probability of global connectivity as a function of the probability of local connectivity. We exploit this phenomenon to compute Boolean functions robustly in the presence of defects.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of [http://en.wikipedia.org/wiki/Percolation_theory percolation]. With random connectivity, percolation gives rise to a sharp non-linearity in the probability of global connectivity as a function of the probability of local connectivity. We exploit this phenomenon to compute Boolean functions robustly in the presence of defects.</div></td></tr>
</table>
MarcRiedel
http://mriedel.ece.umn.edu/wiki/index.php?title=Research&diff=311703&oldid=prev
MarcRiedel: /* Time-Encoded Computing */
2023-07-09T01:42:44Z
<p><span dir="auto"><span class="autocomment">Time-Encoded Computing</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:42, 8 July 2023</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|[[File:Analog-in-time.jpg|center|thumb|<del style="font-weight: bold; text-decoration: none;">400x400px</del>|Encoding a value in time. The value represented is the fraction of the time that the signal is high in each cycle, in this case 0.687.]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|[[File:Analog-in-time.jpg|center|thumb|<ins style="font-weight: bold; text-decoration: none;">500px</ins>|Encoding a value in time. The value represented is the fraction of the time that the signal is high in each cycle, in this case 0.687.]]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>||[[File:Multiplicaiton-on-time-encoding-signals.jpg|thumb|<del style="font-weight: bold; text-decoration: none;">400x400px</del>|Multiplication with a single AND gate, operating on deterministic periodic signals. ]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>||[[File:Multiplicaiton-on-time-encoding-signals.jpg|thumb|<ins style="font-weight: bold; text-decoration: none;">500px</ins>|Multiplication with a single AND gate, operating on deterministic periodic signals. ]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>As technology has scaled and device sizes have gotten smaller, the supply voltages have dropped while the device speeds have improved. Control of the dynamic range in the voltage domain is limited; however, control of the length of pulses in the time domain can be precise. Encoding data in the time domain can be done more accurately and more efficiently than converting signals into binary radix. So we can compute ''more precisely,'' ''faster'', and with ''fewer logic gates:''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>As technology has scaled and device sizes have gotten smaller, the supply voltages have dropped while the device speeds have improved. Control of the dynamic range in the voltage domain is limited; however, control of the length of pulses in the time domain can be precise. Encoding data in the time domain can be done more accurately and more efficiently than converting signals into binary radix. So we can compute ''more precisely,'' ''faster'', and with ''fewer logic gates:''</div></td></tr>
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MarcRiedel