http://seancarver.org/index.php?title=Project3NewThought&feed=atom&action=historyProject3NewThought - Revision history2024-03-28T21:05:54ZRevision history for this page on the wikiMediaWiki 1.28.2http://seancarver.org/index.php?title=Project3NewThought&diff=122&oldid=prevCarver at 20:08, 28 January 20092009-01-28T20:08:00Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 20:08, 28 January 2009</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; 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 class="diffchange diffchange-inline">Here's an idea for a straightforward project that builds upon the idea for project 3 introduced the first day of class.  </del>There has been a lot of papers <del class="diffchange diffchange-inline">using </del>and applying techniques of testing whether a system is chaotic.  I don't know what the current state of the field is but the problem has been that it is difficult to tell between a chaotic system and a noisy system.  Nevertheless it has been a problem that has captivated the imagination of many researchers.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>There has been a lot of papers <ins class="diffchange diffchange-inline">developing </ins>and applying techniques of testing whether a system is chaotic.  I don't know what the current state of the field is but the problem has been that it is difficult to tell between a chaotic system and a noisy system.  Nevertheless it has been a problem that has captivated the imagination of many researchers.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>The ghostburster cell exhibits chaos for some values of the parameters and not for others.  Models that exhibit qualitatively different behavior for different parameters have a bifurcation structure that can be visualized with a bifurcation diagram (shown in the paper).  Usually, when you <del class="diffchange diffchange-inline">change </del>parameters, the qualitative properties of the cell (e.g. quiesient, bistable, tonically active, chaotic) don't change<del class="diffchange diffchange-inline">: for most small changes in the parameters, </del>the resulting models are equivalent.  Only at discrete values of the parameters do bifurcations (qualitative changes in the <del class="diffchange diffchange-inline">models</del>) occur (e.g. quiesent --> tonically active).</div></td><td class='diff-marker'>+</td><td style="color:black; 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>The ghostburster <ins class="diffchange diffchange-inline">model </ins>cell exhibits chaos for some values of the parameters and not for others.  Models that exhibit qualitatively different behavior for different parameters have a bifurcation structure that can be visualized with a bifurcation diagram (shown in the paper).  Usually, when you <ins class="diffchange diffchange-inline">make small changes to the </ins>parameters, the qualitative properties of the cell (e.g. quiesient, bistable, tonically active, chaotic) don't change <ins class="diffchange diffchange-inline">(</ins>the resulting models are equivalent<ins class="diffchange diffchange-inline">)</ins>.  Only at discrete values of the parameters do <ins class="diffchange diffchange-inline">"</ins>bifurcations<ins class="diffchange diffchange-inline">" </ins>(qualitative changes in the <ins class="diffchange diffchange-inline">model</ins>) occur (e.g. quiesent --> tonically active).</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>Let's say (<del class="diffchange diffchange-inline">GTG more later</del>...<del class="diffchange diffchange-inline">)</del></div></td><td class='diff-marker'>+</td><td style="color:black; 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>Let's say <ins class="diffchange diffchange-inline">you fix all but one </ins>(<ins class="diffchange diffchange-inline">or two) of the parameters and try to fit the one (or two) that remain.  In these situations you can actually draw both the bifurcation diagram and the likelihood function.  It would interesting to see what the relationship between the other figures are as you vary the other ("fixed") parameters</ins>. <ins class="diffchange diffchange-inline"> When will the maximum likelihood estimates of the parameters tell you in what region of the bifurcation diagram you lie?  When will  they tell you that the cell exhibits backpropagation?  When will they distiguish between a nonchaotic cell perturbed by noise and a chaotic cell perturbed by noise?</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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"> </td><td class='diff-marker'>+</td><td style="color:black; 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 class="diffchange diffchange-inline">I said in class that this project was the most risky in terms of being publishable</ins>. <ins class="diffchange diffchange-inline"> This is only because the story we would tell is not yet clear.  Sometimes the most risk involves the most potential payoff.  That is not yet clear, but it is clear that this project would be doable and interesting</ins>.</div></td></tr>
</table>Carverhttp://seancarver.org/index.php?title=Project3NewThought&diff=121&oldid=prevCarver: New page: Here's an idea for a straightforward project that builds upon the idea for project 3 introduced the first day of class. There has been a lot of papers using and applying techniques of tes...2009-01-28T18:28:42Z<p>New page: Here's an idea for a straightforward project that builds upon the idea for project 3 introduced the first day of class. There has been a lot of papers using and applying techniques of tes...</p>
<p><b>New page</b></p><div>Here's an idea for a straightforward project that builds upon the idea for project 3 introduced the first day of class. There has been a lot of papers using and applying techniques of testing whether a system is chaotic. I don't know what the current state of the field is but the problem has been that it is difficult to tell between a chaotic system and a noisy system. Nevertheless it has been a problem that has captivated the imagination of many researchers.<br />
<br />
The ghostburster cell exhibits chaos for some values of the parameters and not for others. Models that exhibit qualitatively different behavior for different parameters have a bifurcation structure that can be visualized with a bifurcation diagram (shown in the paper). Usually, when you change parameters, the qualitative properties of the cell (e.g. quiesient, bistable, tonically active, chaotic) don't change: for most small changes in the parameters, the resulting models are equivalent. Only at discrete values of the parameters do bifurcations (qualitative changes in the models) occur (e.g. quiesent --> tonically active).<br />
<br />
Let's say (GTG more later...)</div>Carver