<html>
<head>
<style><!--
.hmmessage P
{
margin:0px;
padding:0px
}
body.hmmessage
{
font-size: 10pt;
font-family:Tahoma
}
--></style>
</head>
<body class='hmmessage'><div dir='ltr'>
<div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">PCA depend of the number of frames?</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">Dear users</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> </span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">I did a test with three sets of frames</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">(1) 13 frames From X-ray</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">(2) 28 frames From X-ray</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">(3) 1000 frames From MD</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">In each case translations and rotations were eliminated.</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">then g_covar was applied to obtain the covariance matrix</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> g_covar -f sample.xtc -s representative.tpr -o eig_sample.xvg -xpm covar_sample.xpm</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> </span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">For the case (1) and (2) the most representative structure was used in the option -s ( One that has the lowest rmsd with respect to the average of each cluster).</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">In case (3) the initial structure of the MD was used in the option -s.</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">When I look the eigenvalues for the case (1) and (2), I found that the eigenvalue is zero only after index="number of frames" (see below)</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">In the case (3) the distribution is smooth</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">I could expect a similar distribution for the case (1) and (2), because the frames are representative of the dymanics of the protein.</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">Why this difference?</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">PCA depend of the number of frames?</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">A plot with the eigenvalues and cumulative number is available in this limk.</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">http://www.4shared.com/file/c4sQQd9U/cumulative.html?</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">In the plot Cluster (1) is case (1)</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> Cluster (2) is case (2) </span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> X1 is case (3)</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">Sincerely yours</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">Ricardo</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">caso (1)</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ title "Eigenvalues of the covariance matrix"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ xaxis label "Eigenvector index"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ yaxis label "(nm\S2\N)"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@TYPE xy</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 1 3.21824</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 2 1.59207</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 3 0.7186</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 4 0.603902</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 5 0.555743</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 6 0.479754</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 7 0.412325</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 8 0.345979</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 9 0.282516</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 10 0.269861</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 11 0.260193</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 12 0.209889</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 13 1.96752e-15 *IN THIS INDEX THE EIGENVALUES IS CLOSE TO ZEROM COINCIDENT WITH THE NUMBER OF FRAMES</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 14 1.62777e-15</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 15 1.5654e-15</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 16 1.3087e-15</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 17 9.35402e-16</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 18 9.04299e-16</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 19 6.71342e-16</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 20 6.64882e-16</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">caso (2) Obtained from X-ray</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ title "Eigenvalues of the covariance matrix"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ xaxis label "Eigenvector index"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ yaxis label "(nm\S2\N)"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@TYPE xy</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 1 0.283967</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 2 0.0952257</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 3 0.0743586</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 4 0.0598192</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 5 0.0450539</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 6 0.0410722</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 7 0.0301708</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 8 0.0262085</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 9 0.0240471</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 10 0.0175948</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 11 0.0147602</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 12 0.0140895</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 13 0.011544</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 14 0.0107718</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 15 0.00884784</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 16 0.00851068</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 17 0.00748592</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 18 0.00662536</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 19 0.00645983</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 20 0.00609032</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 21 0.00516941</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 22 0.00404203</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 23 0.00373644</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 24 0.00336767</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 25 0.00299449</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 26 0.00227847</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 27 0.00156805</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 28 -3.86967e-05 *IN THIS INDEX THE EIGENVALUES IS CLOSE TO ZEROM COINCIDENT WITH THE NUMBER OF FRAMES</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 29 1.04056e-07</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 30 -2.72851e-08</span></font></div><div><span class="Apple-tab-span" style="white-space: pre; font-size: 13px;"><font class="Apple-style-span" face="Tahoma"> </font></span></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">caso (3)</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"><br></span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ title "Eigenvalues of the covariance matrix"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ xaxis label "Eigenvector index"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@ yaxis label "(nm\S2\N)"</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">@TYPE xy</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 1 3.03786</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 2 1.27271</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 3 0.53899</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 4 0.423554</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 5 0.27003</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 6 0.260328</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 7 0.220423</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 8 0.191197</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 9 0.168856</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 10 0.152404</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 11 0.128236</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 12 0.126204</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 13 0.110368</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 14 0.092775</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 15 0.0885705</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 16 0.0750595</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 17 0.0696554</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 18 0.0627624</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 19 0.0532074</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 20 0.0513393</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 21 0.0474214</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 22 0.0463299</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 23 0.0432387</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 24 0.0403574</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 25 0.0392867</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 26 0.0352699</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 27 0.0333476</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 28 0.0319553</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 29 0.0308987</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 30 0.0306235</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 31 0.027971</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 32 0.0268982</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 33 0.0258224</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 34 0.0249171</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 35 0.0234315</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 36 0.0221298</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 37 0.0217099</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 38 0.0202486</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 39 0.0196283</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 40 0.0191729</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 41 0.018719</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 42 0.0185378</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 43 0.0176382</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 44 0.0174487</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 45 0.0165635</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 46 0.0161611</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 47 0.015876</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 48 0.0155579</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 49 0.0147515</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;"> 50 0.0139361</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">.</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">.</span></font></div><div><font class="Apple-style-span" face="Tahoma"><span class="Apple-style-span" style="font-size: 13px;">.</span></font></div><div style="font-family: Tahoma; font-size: 10pt; "><br></div><br><div style="font-family: Tahoma; font-size: 10pt; "><br></div> </div></body>
</html>