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o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
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/* Font Definitions */
@font-face
        {font-family:Wingdings;
        panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
        {font-family:Wingdings;
        panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
        {font-family:Cambria;
        panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
        {font-family:Calibri;
        panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
        {margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";}
h1
        {mso-style-priority:9;
        mso-style-link:"Heading 1 Char";
        margin-top:24.0pt;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        mso-add-space:auto;
        font-size:14.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
h1.CxSpFirst
        {mso-style-priority:9;
        mso-style-link:"Heading 1 Char";
        mso-style-type:export-only;
        margin-top:24.0pt;
        margin-right:0in;
        margin-bottom:0in;
        margin-left:0in;
        margin-bottom:.0001pt;
        mso-add-space:auto;
        font-size:14.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
h1.CxSpMiddle
        {mso-style-priority:9;
        mso-style-link:"Heading 1 Char";
        mso-style-type:export-only;
        margin:0in;
        margin-bottom:.0001pt;
        mso-add-space:auto;
        font-size:14.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
h1.CxSpLast
        {mso-style-priority:9;
        mso-style-link:"Heading 1 Char";
        mso-style-type:export-only;
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        mso-add-space:auto;
        font-size:14.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
h2
        {mso-style-priority:9;
        mso-style-link:"Heading 2 Char";
        margin-top:10.0pt;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        font-size:13.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
h3
        {mso-style-priority:9;
        mso-style-link:"Heading 3 Char";
        margin-top:10.0pt;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        line-height:110%;
        font-size:12.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
h4
        {mso-style-priority:9;
        mso-style-link:"Heading 4 Char";
        margin-top:10.0pt;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        font-size:12.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;
        font-style:italic;}
h5
        {mso-style-priority:9;
        mso-style-link:"Heading 5 Char";
        margin-top:10.0pt;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        font-size:12.0pt;
        font-family:"Cambria","serif";
        color:#7F7F7F;
        font-weight:bold;}
h6
        {mso-style-priority:9;
        mso-style-link:"Heading 6 Char";
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        line-height:110%;
        font-size:12.0pt;
        font-family:"Cambria","serif";
        color:#7F7F7F;
        font-weight:bold;
        font-style:italic;}
p.MsoHeading7, li.MsoHeading7, div.MsoHeading7
        {mso-style-priority:9;
        mso-style-link:"Heading 7 Char";
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        font-size:12.0pt;
        font-family:"Cambria","serif";
        font-style:italic;}
p.MsoHeading8, li.MsoHeading8, div.MsoHeading8
        {mso-style-priority:9;
        mso-style-link:"Heading 8 Char";
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        font-size:10.0pt;
        font-family:"Cambria","serif";}
p.MsoHeading9, li.MsoHeading9, div.MsoHeading9
        {mso-style-priority:9;
        mso-style-link:"Heading 9 Char";
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        font-size:10.0pt;
        font-family:"Cambria","serif";
        letter-spacing:.25pt;
        font-style:italic;}
p.MsoTitle, li.MsoTitle, div.MsoTitle
        {mso-style-priority:10;
        mso-style-link:"Title Char";
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        mso-add-space:auto;
        font-size:26.0pt;
        font-family:"Cambria","serif";
        letter-spacing:.25pt;}
p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
        {mso-style-priority:10;
        mso-style-link:"Title Char";
        mso-style-type:export-only;
        margin:0in;
        margin-bottom:.0001pt;
        mso-add-space:auto;
        font-size:26.0pt;
        font-family:"Cambria","serif";
        letter-spacing:.25pt;}
p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
        {mso-style-priority:10;
        mso-style-link:"Title Char";
        mso-style-type:export-only;
        margin:0in;
        margin-bottom:.0001pt;
        mso-add-space:auto;
        font-size:26.0pt;
        font-family:"Cambria","serif";
        letter-spacing:.25pt;}
p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
        {mso-style-priority:10;
        mso-style-link:"Title Char";
        mso-style-type:export-only;
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        mso-add-space:auto;
        font-size:26.0pt;
        font-family:"Cambria","serif";
        letter-spacing:.25pt;}
p.MsoSubtitle, li.MsoSubtitle, div.MsoSubtitle
        {mso-style-priority:11;
        mso-style-link:"Subtitle Char";
        margin-top:0in;
        margin-right:0in;
        margin-bottom:30.0pt;
        margin-left:0in;
        font-size:12.0pt;
        font-family:"Cambria","serif";
        letter-spacing:.65pt;
        font-style:italic;}
a:link, span.MsoHyperlink
        {mso-style-priority:99;
        color:blue;
        text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
        {mso-style-priority:99;
        color:purple;
        text-decoration:underline;}
em
        {mso-style-priority:20;
        letter-spacing:.5pt;
        border:none windowtext 1.0pt;
        padding:0in;
        font-weight:bold;}
p
        {mso-style-priority:99;
        mso-margin-top-alt:auto;
        margin-right:0in;
        mso-margin-bottom-alt:auto;
        margin-left:0in;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";}
p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
        {mso-style-priority:1;
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
        {mso-style-priority:34;
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:.5in;
        mso-add-space:auto;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";}
p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
        {mso-style-priority:34;
        mso-style-type:export-only;
        margin-top:0in;
        margin-right:0in;
        margin-bottom:0in;
        margin-left:.5in;
        margin-bottom:.0001pt;
        mso-add-space:auto;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";}
p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
        {mso-style-priority:34;
        mso-style-type:export-only;
        margin-top:0in;
        margin-right:0in;
        margin-bottom:0in;
        margin-left:.5in;
        margin-bottom:.0001pt;
        mso-add-space:auto;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";}
p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
        {mso-style-priority:34;
        mso-style-type:export-only;
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:.5in;
        mso-add-space:auto;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";}
p.MsoQuote, li.MsoQuote, div.MsoQuote
        {mso-style-priority:29;
        mso-style-link:"Quote Char";
        margin-top:10.0pt;
        margin-right:.25in;
        margin-bottom:4.0pt;
        margin-left:.25in;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";
        font-style:italic;}
p.MsoIntenseQuote, li.MsoIntenseQuote, div.MsoIntenseQuote
        {mso-style-priority:30;
        mso-style-link:"Intense Quote Char";
        margin-top:10.0pt;
        margin-right:.8in;
        margin-bottom:14.0pt;
        margin-left:.7in;
        text-align:justify;
        font-size:12.0pt;
        font-family:"Times New Roman","serif";
        font-weight:bold;
        font-style:italic;}
span.MsoSubtleEmphasis
        {mso-style-priority:19;
        font-style:italic;}
span.MsoIntenseEmphasis
        {mso-style-priority:21;
        font-weight:bold;}
span.MsoSubtleReference
        {mso-style-priority:31;
        font-variant:small-caps;}
span.MsoIntenseReference
        {mso-style-priority:32;
        font-variant:small-caps;
        letter-spacing:.25pt;
        text-decoration:underline;}
span.MsoBookTitle
        {mso-style-priority:33;
        font-variant:small-caps;
        letter-spacing:.25pt;
        font-style:italic;}
p.MsoTocHeading, li.MsoTocHeading, div.MsoTocHeading
        {mso-style-priority:39;
        margin-top:24.0pt;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        mso-add-space:auto;
        font-size:14.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
p.MsoTocHeadingCxSpFirst, li.MsoTocHeadingCxSpFirst, div.MsoTocHeadingCxSpFirst
        {mso-style-priority:39;
        mso-style-type:export-only;
        margin-top:24.0pt;
        margin-right:0in;
        margin-bottom:0in;
        margin-left:0in;
        margin-bottom:.0001pt;
        mso-add-space:auto;
        font-size:14.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
p.MsoTocHeadingCxSpMiddle, li.MsoTocHeadingCxSpMiddle, div.MsoTocHeadingCxSpMiddle
        {mso-style-priority:39;
        mso-style-type:export-only;
        margin:0in;
        margin-bottom:.0001pt;
        mso-add-space:auto;
        font-size:14.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
p.MsoTocHeadingCxSpLast, li.MsoTocHeadingCxSpLast, div.MsoTocHeadingCxSpLast
        {mso-style-priority:39;
        mso-style-type:export-only;
        margin-top:0in;
        margin-right:0in;
        margin-bottom:4.0pt;
        margin-left:0in;
        mso-add-space:auto;
        font-size:14.0pt;
        font-family:"Cambria","serif";
        font-weight:bold;}
span.Heading1Char
        {mso-style-name:"Heading 1 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 1";
        font-family:"Cambria","serif";
        font-weight:bold;}
span.Heading2Char
        {mso-style-name:"Heading 2 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 2";
        font-family:"Cambria","serif";
        font-weight:bold;}
span.Heading3Char
        {mso-style-name:"Heading 3 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 3";
        font-family:"Cambria","serif";
        font-weight:bold;}
span.Heading4Char
        {mso-style-name:"Heading 4 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 4";
        font-family:"Cambria","serif";
        font-weight:bold;
        font-style:italic;}
span.Heading5Char
        {mso-style-name:"Heading 5 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 5";
        font-family:"Cambria","serif";
        color:#7F7F7F;
        font-weight:bold;}
span.Heading6Char
        {mso-style-name:"Heading 6 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 6";
        font-family:"Cambria","serif";
        color:#7F7F7F;
        font-weight:bold;
        font-style:italic;}
span.Heading7Char
        {mso-style-name:"Heading 7 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 7";
        font-family:"Cambria","serif";
        font-style:italic;}
span.Heading8Char
        {mso-style-name:"Heading 8 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 8";
        font-family:"Cambria","serif";}
span.Heading9Char
        {mso-style-name:"Heading 9 Char";
        mso-style-priority:9;
        mso-style-link:"Heading 9";
        font-family:"Cambria","serif";
        letter-spacing:.25pt;
        font-style:italic;}
span.TitleChar
        {mso-style-name:"Title Char";
        mso-style-priority:10;
        mso-style-link:Title;
        font-family:"Cambria","serif";
        letter-spacing:.25pt;}
span.SubtitleChar
        {mso-style-name:"Subtitle Char";
        mso-style-priority:11;
        mso-style-link:Subtitle;
        font-family:"Cambria","serif";
        letter-spacing:.65pt;
        font-style:italic;}
span.QuoteChar
        {mso-style-name:"Quote Char";
        mso-style-priority:29;
        mso-style-link:Quote;
        font-style:italic;}
span.IntenseQuoteChar
        {mso-style-name:"Intense Quote Char";
        mso-style-priority:30;
        mso-style-link:"Intense Quote";
        font-weight:bold;
        font-style:italic;}
span.EmailStyle44
        {mso-style-type:personal-compose;
        font-family:"Times New Roman","serif";}
.MsoChpDefault
        {mso-style-type:export-only;
        font-size:10.0pt;}
@page WordSection1
        {size:8.5in 11.0in;
        margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
        {page:WordSection1;}
/* List Definitions */
@list l0
        {mso-list-id:1993093905;
        mso-list-type:hybrid;
        mso-list-template-ids:-1828260418 67698689 67698691 67698693 67698689 67698691 67698693 67698689 67698691 67698693;}
@list l0:level1
        {mso-level-number-format:bullet;
        mso-level-text:\F0B7;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:Symbol;}
@list l0:level2
        {mso-level-number-format:bullet;
        mso-level-text:o;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:"Courier New";}
@list l0:level3
        {mso-level-number-format:bullet;
        mso-level-text:\F0A7;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:Wingdings;}
@list l0:level4
        {mso-level-number-format:bullet;
        mso-level-text:\F0B7;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:Symbol;}
@list l0:level5
        {mso-level-number-format:bullet;
        mso-level-text:o;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:"Courier New";}
@list l0:level6
        {mso-level-number-format:bullet;
        mso-level-text:\F0A7;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:Wingdings;}
@list l0:level7
        {mso-level-number-format:bullet;
        mso-level-text:\F0B7;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:Symbol;}
@list l0:level8
        {mso-level-number-format:bullet;
        mso-level-text:o;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:"Courier New";}
@list l0:level9
        {mso-level-number-format:bullet;
        mso-level-text:\F0A7;
        mso-level-tab-stop:none;
        mso-level-number-position:left;
        text-indent:-.25in;
        font-family:Wingdings;}
ol
        {margin-bottom:0in;}
ul
        {margin-bottom:0in;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><table class=MsoNormalTable border=0 cellpadding=0 width=600 style='width:6.25in'><tr><td style='padding:.75pt .75pt .75pt .75pt'><div style='margin-bottom:4.0pt'><div class=MsoNormal align=center style='margin-bottom:0in;margin-bottom:.0001pt;text-align:center'><span style='font-size:11.0pt'><hr size=2 width="100%" align=center></span></div></div><p align=center style='text-align:center'><span style='font-size:11.0pt'>Boston University -- Computer Science Department<br><br><strong>P H D&nbsp;&nbsp;&nbsp; D E F E N S E</strong><br><br>Tuesday&nbsp;June 21, 2011/ 10:00am - 11:30am<br></span><span style='font-size:11.0pt'>SMG-324 (<a href="http://www.bu.edu/maps/?id=266">http://www.bu.edu/maps/?id=266</a>)</span><span style='font-size:11.0pt'><br><br><o:p></o:p></span></p><div style='margin-bottom:4.0pt'><div class=MsoNormal align=center style='margin-bottom:0in;margin-bottom:.0001pt;text-align:center'><span style='font-size:11.0pt;color:blue'><hr size=2 width="100%" align=center></span></div></div></td></tr><tr><td style='padding:.75pt .75pt .75pt .75pt'><p align=center style='text-align:center'><b><span style='font-size:11.0pt'>ANALYZING PROBABILISTIC GRAPHS<o:p></o:p></span></b></p><p align=center style='text-align:center'><strong><span style='font-size:11.0pt'>Michalis Potamias</span></strong><span style='font-size:11.0pt'><br><strong><span style='font-weight:normal'><a href="http://cs-people.bu.edu/mp/">http://cs-people.bu.edu/mp/</a> </span></strong><b><o:p></o:p></b></span></p><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><p class=MsoNormal><strong><span style='font-size:11.0pt'>Abstract:</span></strong><span style='font-size:11.0pt'> Large probabilistic graphs appear in many diverse application domains such as social, biological, and mobile ad-hoc networks. Similar to standard graphs, probabilistic graphs may be weighted or un-weighted, and directed or undirected; the difference is that their components are also associated with uncertainty. This thesis focuses on analyzing graphs whose edges are labeled with probability values.&nbsp;Assuming that the probabilistic graph is known a priori, we revisit well known graph mining problems. In particular, we study the problems of defining distance functions between two nodes, answering k-nearest neighbors queries, and clustering the probabilistic graph into partitions. Contrary to mining tasks, in learning tasks the probabilistic graph is unknown - it is the objective of the analysis. In this thesis we propose models and design algorithms to infer probabilistic graphs. In particular we infer probabilistic graphs that explain the observed spread of information in social networks.&nbsp;We analyze probabilistic graphs both theoretically and experimentally. The theoretical analysis consists of defining analytical tasks, studying their computational complexity, and designing algorithms to address them. In the experimental analysis, we apply our techniques to synthetic data as well as to real-world data from biological and online social networks. This analysis shows the computational efficiency and the analytical efficacy of the proposed techniques.<o:p></o:p></span></p><p><b><span style='font-size:11.0pt'>Examination Committee:</span></b><span style='font-size:11.0pt'>.<o:p></o:p></span></p><p class=MsoListParagraphCxSpFirst style='mso-margin-top-alt:5.0pt;margin-right:.5in;margin-bottom:5.0pt;margin-left:.5in;mso-add-space:auto;text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:Symbol'><span style='mso-list:Ignore'>&middot;<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span style='font-size:11.0pt'>George Kollios (First Reader and Major Advisor)<o:p></o:p></span></p><p class=MsoListParagraphCxSpMiddle style='mso-margin-top-alt:5.0pt;margin-right:.5in;margin-bottom:5.0pt;margin-left:.5in;mso-add-space:auto;text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:Symbol'><span style='mso-list:Ignore'>&middot;<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span style='font-size:11.0pt'>Evimaria Terzi (Second Reader)<o:p></o:p></span></p><p class=MsoListParagraphCxSpMiddle style='mso-margin-top-alt:5.0pt;margin-right:.5in;margin-bottom:5.0pt;margin-left:.5in;mso-add-space:auto;text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:Symbol'><span style='mso-list:Ignore'>&middot;<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span style='font-size:11.0pt'>John Byers (Third Reader)<o:p></o:p></span></p><p class=MsoListParagraphCxSpMiddle style='mso-margin-top-alt:5.0pt;margin-right:.5in;margin-bottom:5.0pt;margin-left:.5in;mso-add-space:auto;text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:Symbol'><span style='mso-list:Ignore'>&middot;<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span style='font-size:11.0pt'>Aristides Gionis (External Committee Member)<o:p></o:p></span></p><p class=MsoListParagraphCxSpLast style='mso-margin-top-alt:5.0pt;margin-right:.5in;margin-bottom:5.0pt;margin-left:.5in;mso-add-space:auto;text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:Symbol'><span style='mso-list:Ignore'>&middot;<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span style='font-size:11.0pt'>Azer Bestavros (Committee Chair)<o:p></o:p></span></p></blockquote></td></tr><tr><td style='padding:.75pt .75pt .75pt .75pt'><div style='margin-bottom:4.0pt'><div class=MsoNormal align=center style='margin-bottom:0in;margin-bottom:.0001pt;text-align:center'><span style='font-size:11.0pt;color:blue'><hr size=2 width="100%" align=center></span></div></div></td></tr></table><p><span style='font-size:11.0pt'>&nbsp;<o:p></o:p></span></p></div></body></html>