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<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><b><span style="font-size:12pt;line-height:115%" lang="EN-US">Probability Webinar -<span> </span>IM-UFRJ <span></span></span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US"><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Dear colleagues,<span>
</span><span></span></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Our next
online seminar will be held on Monday, <b>August
16, </b><span> </span>from <b>3 p.m. to 4 p.m</b>.
(Rio de Janeiro local time)<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">The GoogleMeet link for the seminar is </span><a href="https://meet.google.com/uew-ehhn-kby" style="color:blue;text-decoration:underline" target="_blank"><span style="font-size:12pt;line-height:115%" lang="EN-US">https://meet.google.com/uew-ehhn-kby</span></a><span style="font-size:12pt;line-height:115%" lang="EN-US">
<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Speaker:<span> </span><b>Jefferson Elbert Simões (DIA/UNIRIO)</b><span></span></span></p>
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<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Title:
</span><b><span style="font-size:12pt;line-height:115%;color:black;background:white none repeat scroll 0% 0%" lang="EN-US">Local Symmetry in Erdős–Rényi Graphs</span></b><span style="font-size:12pt;line-height:115%;color:black;background:white none repeat scroll 0% 0%" lang="EN-US"><span></span></span></p>
<p class="MsoNormal" style="background:white none repeat scroll 0% 0%;margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Abstract: </span><span style="font-size:12pt;line-height:115%" lang="EN-US"><span> </span></span><span style="font-size:12pt;line-height:115%;color:black" lang="EN-US"> Real-world
networks are often understood as being symmetrical, meaning that vertices can
be found which perform similar or equivalent structural roles (such as hubs
from different communities in social networks, or functional regions in
neuronal networks). These roles are usually associated with their topological
placement relative to its surroundings; however, traditional mathematical
formulations of graph symmetry are based on automorphism groups, which depend
fundamentally on global structure and do not account for similarities in local
structures. In this work, we introduce the concept of local symmetry, which
reflects the structural equivalence of vertices' egonets while generalizing
classical conceptualizations of symmetry such as automorphism and isomorphism.
We also study the emergence of local asymmetry in Erdős–Rényi graphs,
identifying regimes of both asymptotic local symmetry and asymptotic local
asymmetry. We find that local symmetry persists at least to an average degree
of n^{1/3} and local asymmetry emerges at an average degree not greater than
n^{1/2}, which are regimes of much larger average degree than for traditional,
global asymmetry. <span></span></span></p>
<p class="MsoNormal" style="background:white none repeat scroll 0% 0%;margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%;color:black" lang="EN-US">Joint work with
Daniel Figueiredo (COPPE/UFRJ) and Valmir Barbosa (COPPE/UFRJ).</span></p><p class="MsoNormal" style="background:white none repeat scroll 0% 0%;margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><br><span style="font-size:12pt;line-height:115%;color:black" lang="EN-US"></span><span style="font-size:12pt;line-height:115%" lang="EN-US"><span></span></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">All the talks
are held in English. <br></span></p><p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><br><span style="font-size:12pt;line-height:115%" lang="EN-US"><span></span></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">The videos of
the online seminars are available:<span></span></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">2020 -<span> </span><a href="http://www.dme.ufrj.br/?page_id=2885" target="_blank">http://www.dme.ufrj.br/?page_id=2885</a><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">2021-1<span> </span>-
<a href="http://www.dme.ufrj.br/?page_id=3027" target="_blank">http://www.dme.ufrj.br/?page_id=3027</a><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">For the second semester, a few days after each meeting
the video should be available at <a href="http://www.dme.ufrj.br/?page_id=3178" target="_blank">http://www.dme.ufrj.br/?page_id=3178</a><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Thanks for circulating this information. <span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Sincerely, <br>
Organizers: Guilherme Ost and Maria Eulalia Vares<span></span></span></p>
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