<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Ooops, didn't read all the way through the previous discussion ... source analysis does that anyway, and as Robert points out the power estimate is not correct, either (however, depending on the analysis that need not be a problem). Please disregard my previous comment.<DIV>Christian</DIV><DIV><BR class="khtml-block-placeholder"><DIV><BR class="khtml-block-placeholder"><DIV><DIV><DIV>On 15 Nov 2006, at 17:59, Christian Hesse wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV>Hi Dasha,</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>you could try averaging the single trial covariance matrices (preserving the spatial correlation structure of both time-locked and non-time-locked activity). Then replace the single-trial covariance matrices in your timelock data structure with that average and call lcmv with cfg.rawtrial = 'yes';</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>However don't expect miracles, because:</DIV><DIV>a) single trial estimates will always be noisy</DIV><DIV>b) if there is significant head-movement between trials, then using the average covaraiance matrix may not do much better than single trial covariance estimates (because you effectively havve moving sources)</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Hope this helps.</DIV><DIV>Christian</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><BR><DIV><DIV>On 15 Nov 2006, at 17:31, Daria Osipova wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hi</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">In continuation of this discussion...</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I would like to use the lcmv method to localize sources of (band-pass</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">filtered) ongoing alpha which I can use as spatial filters for my</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(unfiltered) data.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">From the previous discussions on lcmv it seems that most people try to</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">estimate covariance matrix from the average since they are doing ERFs.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">In my case data is not time-locked so I have to estimate it from single</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">trials and not from the average (I would think).</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">But judging from your response, Robert, it seems that cfg.rawtrial = 'yes'</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(which uses covariance matrix from single trials and applies it to single</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">trials) produces a noisy estimate.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Is there a workaround then?</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Thanks in advance</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Best regards,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Dasha</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">PS I need time-domain data</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">-----Original Message-----</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">From: FieldTrip discussion list [<A href="mailto:FIELDTRIP@NIC.SURFNET.NL">mailto:FIELDTRIP@NIC.SURFNET.NL</A>] On Behalf</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Of Robert Oostenveld</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Sent: Tuesday, May 23, 2006 12:13 PM</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">To: <A href="mailto:FIELDTRIP@NIC.SURFNET.NL">FIELDTRIP@NIC.SURFNET.NL</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Subject: Re: [FIELDTRIP] Beamformer time course</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hi Marie,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">On 22 May 2006, at 17:18, Marie Smith wrote:</DIV> <BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I have been trying out the various methods as discussed and have <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">come across a problem.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">When I select cfg.singletrials = 'yes'<SPAN class="Apple-converted-space"> </SPAN>I get a number of error <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">messages saying</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">error('this option contains a bug, and is therefore not supported <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">at the moment');</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I am using the toolbox<SPAN class="Apple-converted-space"> </SPAN>fieldtrip-20060516.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I noticed however, if I select cfg.rawtrials = 'yes' the function <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">will run.</DIV> </BLOCKQUOTE><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I recall disabling this functionality, since it was rarely used and <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">since I was concerned that it would not be correct. I now had a more <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">detailled look at the code.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">If you do rawtrial=yes, beamformer uses the single-trial covariance <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">to construct the filter and also applies it to the single trial <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">covariance/csd. That results in a very poorly estimated filter in <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">each trial, hence projecting large amounts of noise and a lot of <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">variance over trials. Therefore we found it not to be very usefull on <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">real data, although conceptually and in the code it is correct.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The idea behind singletrial=yes is that beamformer uses the average <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">covariance to construct the filter and applies it to the single trial <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">covariance/csd. The problem in the code however is that beamformer <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">would use the averaged covariance/csd to estimate the power and not <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">the single trial covariance/csd. The estimated single-trial <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">timecourse would be correct, but the power would not be correct. <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Therefore I disabled that option in the code.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The solution is something that you can do yourself in two subsequent <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">runs of sourceanalysis: you can do sourceanalysis on the average <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(i.e. do not specify any of singletrial/rawtrial options) and specify <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">keepfilter=yes. That will give you the filter, computed on the <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">average covariance. Subsequently do cfg.grid=source2grid(source), and <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">use the resulting grid (including the filters) in the second run of <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">sourceanalysis, in which you specify cfg.rawtrial=yes. In the second <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">run, the previous (based on average covariance) filters will be <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">applied to the unaveraged data, resulting in the desired single-trial <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">power and dipole moment.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">best regards,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Robert</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV> </BLOCKQUOTE></DIV><BR><DIV> <SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><DIV>----------------------------------------------------------------------</DIV><DIV>Christian Hesse, PhD, MIEEE</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">F.C. Donders Centre for Cognitive Neuroimaging </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">P.O. Box 9101 </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">NL-6500 HB Nijmegen </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The Netherlands</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Tel.: +31 (0)24 36 68293</DIV><DIV>Fax: +31 (0)24 36 10989</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Email: <A href="mailto:c.hesse@fcdonders.ru.nl">c.hesse@fcdonders.ru.nl</A></DIV><DIV>Web: <A href="http://www.fcdonders.ru.nl">www.fcdonders.ru.nl</A></DIV><DIV>----------------------------------------------------------------------</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "></SPAN><BR class="Apple-interchange-newline"></SPAN></SPAN></SPAN></SPAN></SPAN> </DIV><BR></BLOCKQUOTE></DIV><BR><DIV> <SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><DIV>----------------------------------------------------------------------</DIV><DIV>Christian Hesse, PhD, MIEEE</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">F.C. Donders Centre for Cognitive Neuroimaging </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">P.O. Box 9101 </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">NL-6500 HB Nijmegen </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The Netherlands</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Tel.: +31 (0)24 36 68293</DIV><DIV>Fax: +31 (0)24 36 10989</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Email: <A href="mailto:c.hesse@fcdonders.ru.nl">c.hesse@fcdonders.ru.nl</A></DIV><DIV>Web: <A href="http://www.fcdonders.ru.nl">www.fcdonders.ru.nl</A></DIV><DIV>----------------------------------------------------------------------</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "></SPAN><BR class="Apple-interchange-newline"></SPAN></SPAN></SPAN></SPAN></SPAN> </DIV><BR></DIV></DIV></DIV></BODY></HTML>