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<h1 class="ltx_title_section"><div><br></div><div>Results<br></div></h1><h2 class="ltx_title_subsection"><br></h2><p>Genetic Algorithm Results<br></p><p><br></p><div>To assess the capabilities of a genetic algorithm similar to
one used by Lynch and Houghton (2015), we generated a 2400ms spike train
derived from a DSTRF HR-neuron model with known parameters (table X). For the <b>r(t)</b> parameter, we convolved gaussian random
noise with a filter <b>h(t) </b>presented
below of size 50ms, where τ = 5.<br></div><div><br></div><div><i>h(t)</i><b> = </b>t/(τ^2)*exp(-t/τ) <br></div><div><br></div><div>We then created populations of size 50, with each individual
having 7 parameters associated with HR-neuron parameters a, b, c, d, r, x0 and
s. A single parameter (sc) is associated with a scaling constant for the <b>r(t)</b> parameter and 50 parameter
estimates for <b>h(t)</b> for each <b>t</b>. Each population of parameter estimates
was evolved 10 times , with <b>fit(I)</b> being spike distance measured by SPIKy,<b> </b>for the HR-neuron parameters before switching to evolving
filter estimates for 10 times. This back and forth process was repeated 10
times. We ran this same algorithm 10 times in total and took the median values
as our estimates for the DSTRF neuron model. <br></div><p><br></p><div><div><table class="ltx_tabular ltx_tabular_fullpage" contenteditable="false"><tbody><tr><td class="ltx_framed ltx_align_center">Table X</td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
</tr>
<tr>
<td class="ltx_framed ltx_align_center">Genetic algorithm estimates of an HR-neuron with known parameters</td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
<td class="ltx_framed ltx_align_center"></td>
</tr><tr><td></td><td></td><td></td><td></td><td>Parameters</td><td><span class="authorea-table"></span><br></td><td><br></td><td><br></td></tr>
<tr>
<td class="ltx_framed ltx_align_center"><br></td>
<td class="ltx_framed ltx_align_center">a</td>
<td class="ltx_framed ltx_align_center">b</td>
<td class="ltx_framed ltx_align_center">c</td>
<td class="ltx_framed ltx_align_center">d</td>
<td class="ltx_framed ltx_align_center">x0<br></td>
<td class="ltx_framed ltx_align_center">r</td>
<td class="ltx_framed ltx_align_center">s</td>
</tr>
<tr>
<td class="ltx_framed ltx_align_center">Real</td>
<td class="ltx_framed ltx_align_center">1</td>
<td class="ltx_framed ltx_align_center">6</td>
<td class="ltx_framed ltx_align_center">4</td>
<td class="ltx_framed ltx_align_center">5</td>
<td class="ltx_framed ltx_align_center">-1.5</td>
<td class="ltx_framed ltx_align_center">0.001</td>
<td class="ltx_framed ltx_align_center">7</td>
</tr>
<tr>
<td class="ltx_framed ltx_align_center">Search Range</td>
<td class="ltx_framed ltx_align_center">0 - 8</td>
<td class="ltx_framed ltx_align_center">0 - 8</td>
<td class="ltx_framed ltx_align_center">0 - 6</td>
<td class="ltx_framed ltx_align_center">0 - 6</td>
<td class="ltx_framed ltx_align_center">-2 - 0</td>
<td class="ltx_framed ltx_align_center">0 - 0.005</td>
<td class="ltx_framed ltx_align_center"> 0 - 8</td>
</tr>
<tr>
<td class="ltx_framed ltx_align_center">Estimate (SD)</td>
<td class="ltx_framed ltx_align_center">.68 (1.30)</td>
<td class="ltx_framed ltx_align_center">4.92 (1.61)</td>
<td class="ltx_framed ltx_align_center">3.91 (1.01)</td>
<td class="ltx_framed ltx_align_center">5.22 (0.54)</td>
<td class="ltx_framed ltx_align_center">-1.62 (0.27)</td>
<td class="ltx_framed ltx_align_center">0.0013 (0.0002)</td>
<td class="ltx_framed ltx_align_center">7.14 (0.89)</td>
</tr>
</tbody></table><br></div><div><br></div><br></div><h2 id="auto-label-subsection-810535" class="ltx_title_subsection"><div>MCMC Results<br></div></h2><div><div><br></div><div>We tested our MCMC data assimilation technique in a similar manner. We simulated the response of two DSTRF-HR model neurons with a 50-step bandpass filter to a 1200ms of random noise. The parameters of the neurons were set to produce different behaviors, with one set for burst firing and the other set to not burst. Because the SPIKE synchronization fitness metric considers only spike-times and not spike shapes, we fixed the the spike shape determining HR parameters, a and b, to 1 and 6 respectively. Preliminary results showed that it is possible to fit spike shapes with another type of cost function, such as least squares, but we found it more simple and time efficient to just set these parameters by hand to values known to produce the desired shape.<br></div><div><br></div><div>Parameter estimates for the non-bursting HR model are shown in Figure 1 and Table 2, and the filter estimate is in Figure 2. Wile the estimates for most parameters were close to the true values, the estimate for s was quite off. The wide posterior distribution for this parameter exemplifies the uncertainty of the estimate. However, as shown in Figure 3, these parameter estimates produce a voltage trace and spike train that matches the data with which it was assimilated perfectly (100% spike synchrony). As shown in Figure 4, the simulated response of the estimated parameter values to a novel stimulus is close to that of the original parameters, but not perfect (91% spike synchrony). Given this result, we hypothesis that assimilating more data with more spikes will constrain the model more and produce better estimates.<br></div><div><br></div><div>Results for the bursting HR model neuron were very similar, though it reached 99% spike synch during assimilation and 85% spike synch when responding to a novel stimulus. Parameter estimates for it are shown in Figure 5, Figure 6, and Table 3, the data assimilation result in Figure 7, and the response to a novel stimulus in Figure 8. <br></div><br></div><div><br></div>
