<div dir="ltr"><div dir="ltr"><div class="gmail_default" style=""><div class="gmail_default" style=""><div class="gmail_default" style=""><div class="gmail_default" style="font-size:small;color:rgb(80,0,80)"><b style="color:rgb(34,34,34)"><font color="#ff0000" face="tahoma, sans-serif">Please note that this <span class="gmail-il">talk</span> has been CANCELED!</font></b></div><div class="gmail_default" style="font-size:small;color:rgb(80,0,80)"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b><br></b></font></font></div><div class="gmail_default" style="font-size:small;color:rgb(80,0,80)"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b> </font></font><font style="font-family:arial,sans-serif;vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(0,0,0)"> Thurs</font><span class="gmail_default" style="color:rgb(0,0,0)">day, April 11<span class="gmail_default">, </span>2024</span><font style="color:rgb(0,0,0)"> at</font><b style="color:rgb(0,0,0)"> <span style="background-color:rgb(255,255,0)"><u>11:00</u></span></b><b><u><font color="#000000" style="background-color:rgb(255,255,0)"> am</font></u></b><b><u><font color="#000000" style="background-color:rgb(255,255,0)"> CT</font></u><font color="#000000"><u> </u> </font></b></font></font><br></div><div class="gmail_default" style="font-size:small"><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b style="font-family:arial,sans-serif"><font color="#500050"><br></font></b></p><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b style="font-family:arial,sans-serif"><font color="#500050">Where: </font></b><font color="#000000" style="font-family:arial,sans-serif">Talk will be given </font><font color="#000000" style="font-family:arial,sans-serif;font-weight:bold"><u>live, in-person</u></font><font style="font-family:arial,sans-serif;font-weight:bold"> </font><span style="font-family:arial,sans-serif">at</span><br></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font color="#500050"> </font><font color="#000000"> TTIC, 6045 S. Kenwood Avenue</font></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif" color="#000000"> 5th Floor, Room 530<b> </b></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><b><span style="color:black"><br></span></b></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="color:rgb(60,64,67);letter-spacing:0.2px"><font face="georgia, serif"><b><font size="1"> </font></b></font></span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font style="color:rgb(80,0,80);font-family:arial,sans-serif;vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b> <font color="#500050"> </font><font color="#000000"><font color="#500050"> </font></font></font></font>Elchanan Mossel, MIT</p></div></div><div class="gmail_default" style="font-size:small"><div dir="ltr"><div><div class="MsoNormal" align="center" style="margin:0in 0in 8pt;text-align:center;line-height:15.6933px;font-size:11pt;font-family:Calibri,sans-serif"><hr size="3" width="100%" noshade align="center" style="color:rgb(46,116,181)"></div></div><div><div dir="ltr"><b>Title:</b> Reconstructing the Geometry of Random Geometric Graphs<div><br></div><div><span style="font-family:Arial,sans-serif;font-size:13px"><b>Abstract:</b> Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance, independently among pairs. In this work, we show how to efficiently reconstruct the geometry of the underlying space from the sampled graph under the manifold assumption, i.e., assuming that the underlying space is a low dimensional manifold and that the connection probability is a strictly decreasing function of the Euclidean distance between the points in a given embedding of the manifold in </span><span style="font-family:Arial,sans-serif;font-size:13px">. Our work complements a large body of work much of on manifold learning, an area of research where TTI played a major role. In Manifold Learning the goal is to recover a manifold from sampled points sampled in the manifold along with their (approximate) distances. Based on joint work with </span><br></div>Han Huang and Pakawut Jiradilok: <a href="https://arxiv.org/html/2402.09591v1" target="_blank">https://arxiv.org/html/2402.09591v1</a></div><div dir="ltr"><br></div><b> Host: </b><a href="http://lirenshan@ttic.edu/" target="_blank">Liren Shan</a></div></div></div></div><div class="gmail_default" style="font-size:small"><br></div><div class="gmail_default" style="font-size:small"><br></div><div class="gmail_default" style="font-size:small"><br></div><div class="gmail_default" style="font-size:small"><br></div></div><div><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><span style="font-family:arial,helvetica,sans-serif;font-size:x-small">Mary C. Marre</span><br></div><div><div><font face="arial, helvetica, sans-serif" size="1">Faculty Administrative Support</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1">6045 S. Kenwood Avenue, Rm 517</font></i></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL 60637</font></i><br></font></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">773-834-1757</font></i></font></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif" size="1">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Apr 8, 2024 at 2:23 PM Mary Marre <<a href="mailto:mmarre@ttic.edu">mmarre@ttic.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><div><div style="font-size:small"><div style="color:rgb(80,0,80)"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b> </font></font><font style="font-family:arial,sans-serif;vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(0,0,0)"> Thurs</font><span class="gmail_default" style="color:rgb(0,0,0)">day, April 11<span class="gmail_default">, </span>2024</span><font style="color:rgb(0,0,0)"> at</font><b style="color:rgb(0,0,0)"> <span style="background-color:rgb(255,255,0)"><u>11<font>:00</font></u></span></b><b><u><font color="#000000" style="background-color:rgb(255,255,0)"> am</font></u></b><b><u><font color="#000000" style="background-color:rgb(255,255,0)"> CT</font></u><font color="#000000"><u> </u> </font></b></font></font><br></div><div><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b style="font-family:arial,sans-serif"><font color="#500050"><br></font></b></p><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b style="font-family:arial,sans-serif"><font color="#500050">Where: </font></b><font color="#000000" style="font-family:arial,sans-serif">Talk will be given </font><font color="#000000" style="font-family:arial,sans-serif;font-weight:bold"><u>live, in-person</u></font><font style="font-family:arial,sans-serif;font-weight:bold"> </font><span style="font-family:arial,sans-serif">at</span><br></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font color="#500050"> </font><font color="#000000"> TTIC, 6045 S. Kenwood Avenue</font></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif" color="#000000"> 5th Floor, Room 530<b> </b></font></p><p class="MsoNormal" style="margin:0in;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><b><span style="color:black"><br></span></b></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="color:rgb(60,64,67);letter-spacing:0.2px"><font face="georgia, serif"><b><font size="1"> </font></b></font></span></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font style="color:rgb(80,0,80);font-family:arial,sans-serif;vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b> <font color="#500050"> </font><font color="#000000"><font color="#500050"> </font></font></font></font>Elchanan Mossel, MIT</p></div></div><div><div dir="ltr"><div style="font-size:small"><div class="MsoNormal" align="center" style="margin:0in 0in 8pt;text-align:center;line-height:15.6933px;font-size:11pt;font-family:Calibri,sans-serif"><hr size="3" width="100%" noshade align="center" style="color:rgb(46,116,181)"></div></div><div><div dir="ltr"><b>Title:</b> Reconstructing the Geometry of Random Geometric Graphs<div style="font-size:small"><br></div><div style="font-size:small"><span style="font-family:Arial,sans-serif;font-size:13px"><b>Abstract:</b> Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance, independently among pairs. In this work, we show how to efficiently reconstruct the geometry of the underlying space from the sampled graph under the manifold assumption, i.e., assuming that the underlying space is a low dimensional manifold and that the connection probability is a strictly decreasing function of the Euclidean distance between the points in a given embedding of the manifold in </span><span style="font-family:Arial,sans-serif;font-size:13px">. Our work complements a large body of work much of on manifold learning, an area of research where TTI played a major role. In Manifold Learning the goal is to recover a manifold from sampled points sampled in the manifold along with their (approximate) distances. Based on joint work with </span><br></div>Han Huang and Pakawut Jiradilok: <a href="https://arxiv.org/html/2402.09591v1" style="font-size:small" target="_blank">https://arxiv.org/html/2402.09591v1</a></div><div dir="ltr"><br></div><b> Host: </b><a href="http://lirenshan@ttic.edu" target="_blank">Liren Shan</a></div></div></div></div><div style="font-size:small"><br></div><div style="font-size:small"><br></div><div style="font-size:small"><br></div><div style="font-size:small"><br></div></div><div><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><span style="font-family:arial,helvetica,sans-serif;font-size:x-small">Mary C. Marre</span><br></div><div><div><font face="arial, helvetica, sans-serif" size="1">Faculty Administrative Support</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1">6045 S. Kenwood Avenue, Rm 517</font></i></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL 60637</font></i><br></font></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">773-834-1757</font></i></font></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif" size="1">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div>
</blockquote></div></div>