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Series</span></h1></div></div></div></div></div></div></div></div></div></section><section id="h.18fdaab34fa48592_17" class="yaqOZd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.18fdaab34fa48592_14" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><div id="h.n7v1loiqgk5v" class="GV3q8e yMxPgf aP9Z7e"></div><h3 id="h.n7v1loiqgk5v_l" dir="ltr" class="zfr3Q OmQG5e CDt4Ke " style="text-align: center;"><div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" class="CjVfdc"><div class="PPhIP rviiZ" jsname="haAclf"><div role="presentation" class="U26fgb mUbCce fKz7Od LRAOtb Znu9nd M9Bg4d" jscontroller="mxS5xe" jsaction="click:cOuCgd; mousedown:UX7yZ; mouseup:lbsD7e; mouseenter:tfO1Yc; mouseleave:JywGue; focus:AHmuwe; blur:O22p3e; contextmenu:mg9Pef;" jsshadow aria-describedby="h.n7v1loiqgk5v_l" aria-label="Copy heading link" aria-disabled="false" data-tooltip="Copy heading link" aria-hidden="true" data-tooltip-position="top" data-tooltip-vertical-offset="12" data-tooltip-horizontal-offset="0"><a class="FKF6mc TpQm9d" href="#h.n7v1loiqgk5v" aria-label="Copy heading link" jsname="hiK3ld" role="button" aria-describedby="h.n7v1loiqgk5v_l"><div class="VTBa7b MbhUzd" jsname="ksKsZd"></div><span jsslot class="xjKiLb"><span class="Ce1Y1c" style="top: -11px"><svg class="OUGEr QdAdhf" width="22px" height="22px" viewBox="0 0 24 24" fill="currentColor" focusable="false"><path d="M0 0h24v24H0z" fill="none"/><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7c-2.76 0-5 2.24-5 5s2.24 5 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1zM8 13h8v-2H8v2zm9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1s-1.39 3.1-3.1 3.1h-4V17h4c2.76 0 5-2.24 5-5s-2.24-5-5-5z"/></svg></span></span></a></div></div><span class="C9DxTc " style="font-family: Lato, Arial; font-weight: 700;">Besides the regular lectures given by our researchers and professors within the IMT School's </span><a class="XqQF9c" href="https://sys.imtlucca.it/" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-family: Lato, Arial; font-weight: 700; text-decoration: underline;">PhD program in Systems Science</span></a><span class="C9DxTc " style="font-family: Lato, Arial; font-weight: 700;"> and other PhD tracks, NETWORKS hosts special lecture series and workshops by our </span><a class="XqQF9c" href="/visiting-professors-guest-scholars" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-family: Lato, Arial; font-weight: 700; text-decoration: underline;">Visiting Professors & Guest Scholars</span></a></div></h3></div></div></div></div></div></div></div></div></div></section><section id="h.38d4f2055fc68c1b_80" class="yaqOZd lQAHbd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.38d4f2055fc68c1b_77" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: center;"><span class="C9DxTc " style="font-style: italic;">23</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/</span><span class="C9DxTc " style="font-style: italic;">11</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/2023, IMT School of Advanced Studies Lucca, </span><span class="C9DxTc " style="font-style: italic;">San Francesco complex</span></p><div id="h.sz4dk23t7tf0" class="Ap4VC yMxPgf aP9Z7e"></div><h1 id="h.sz4dk23t7tf0_l" dir="ltr" class="zfr3Q duRjpb CDt4Ke " style="text-align: center;"><div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" class="CjVfdc"><div class="PPhIP rviiZ" jsname="haAclf"><div role="presentation" class="U26fgb mUbCce fKz7Od LRAOtb Znu9nd M9Bg4d" jscontroller="mxS5xe" jsaction="click:cOuCgd; mousedown:UX7yZ; mouseup:lbsD7e; mouseenter:tfO1Yc; mouseleave:JywGue; focus:AHmuwe; blur:O22p3e; contextmenu:mg9Pef;" jsshadow aria-describedby="h.sz4dk23t7tf0_l" aria-label="Copy heading link" aria-disabled="false" data-tooltip="Copy heading link" aria-hidden="true" data-tooltip-position="top" data-tooltip-vertical-offset="12" data-tooltip-horizontal-offset="0"><a class="FKF6mc TpQm9d" href="#h.sz4dk23t7tf0" aria-label="Copy heading link" jsname="hiK3ld" role="button" aria-describedby="h.sz4dk23t7tf0_l"><div class="VTBa7b MbhUzd" jsname="ksKsZd"></div><span jsslot class="xjKiLb"><span class="Ce1Y1c" style="top: -11px"><svg class="OUGEr QdAdhf" width="22px" height="22px" viewBox="0 0 24 24" fill="currentColor" focusable="false"><path d="M0 0h24v24H0z" fill="none"/><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7c-2.76 0-5 2.24-5 5s2.24 5 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1zM8 13h8v-2H8v2zm9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1s-1.39 3.1-3.1 3.1h-4V17h4c2.76 0 5-2.24 5-5s-2.24-5-5-5z"/></svg></span></span></a></div></div><span class="C9DxTc " style="">A random day on random graphs and random walks</span></div></h1><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: center;"><span class="C9DxTc " style="">The NETWORKS Unit hosts two seminars by mathematicians Rajat Hazra and Luca Avena</span></p></div></div></div></div></div></div></div></div></div></section><section id="h.38d4f2055fc68c1b_60" class="yaqOZd lQAHbd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.18fdaab34fa48592_39" class="hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="t3iYD"><img src="https://lh4.googleusercontent.com/DYfmse3Y27WV4yWUmwTFbZBZ_nDCLINRwMX_JYeymn0RBypoTGQNcqQTAbCkEH4YKAY9BS8o6OcsWwv-Ul4cgdFa9RxYI_uCqH-XLyyL0NK_7uWdRgeyLibfcVmfuqvoIQ=w1280" class="CENy8b" role="img"></div></div></div></div></div><div class="oKdM2c ZZyype"><div id="h.38d4f2055fc68c1b_65" class="hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><div id="h.k8kx24pg1sao" class="CobnVe yMxPgf aP9Z7e"></div><h2 id="h.k8kx24pg1sao_l" dir="ltr" class="zfr3Q JYVBee CDt4Ke " style="text-align: center;"><div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" class="CjVfdc"><div class="PPhIP rviiZ" jsname="haAclf"><div role="presentation" class="U26fgb mUbCce fKz7Od LRAOtb Znu9nd M9Bg4d" jscontroller="mxS5xe" jsaction="click:cOuCgd; mousedown:UX7yZ; mouseup:lbsD7e; mouseenter:tfO1Yc; mouseleave:JywGue; focus:AHmuwe; blur:O22p3e; contextmenu:mg9Pef;" jsshadow aria-describedby="h.k8kx24pg1sao_l" aria-label="Copy heading link" aria-disabled="false" data-tooltip="Copy heading link" aria-hidden="true" data-tooltip-position="top" data-tooltip-vertical-offset="12" data-tooltip-horizontal-offset="0"><a class="FKF6mc TpQm9d" href="#h.k8kx24pg1sao" aria-label="Copy heading link" jsname="hiK3ld" role="button" aria-describedby="h.k8kx24pg1sao_l"><div class="VTBa7b MbhUzd" jsname="ksKsZd"></div><span jsslot class="xjKiLb"><span class="Ce1Y1c" style="top: -11px"><svg class="OUGEr QdAdhf" width="22px" height="22px" viewBox="0 0 24 24" fill="currentColor" focusable="false"><path d="M0 0h24v24H0z" fill="none"/><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7c-2.76 0-5 2.24-5 5s2.24 5 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1zM8 13h8v-2H8v2zm9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1s-1.39 3.1-3.1 3.1h-4V17h4c2.76 0 5-2.24 5-5s-2.24-5-5-5z"/></svg></span></span></a></div></div><span class="C9DxTc " style="">Rajat Hazra</span></div></h2><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: center;"><span class="C9DxTc " style="font-variant: normal;">Ass</span><span class="C9DxTc " style="">ociate</span><span class="C9DxTc " style="font-variant: normal;"> Professor, University of Leiden</span><span class="C9DxTc " style="">, The Netherlands</span></p></div></div></div></div></div></div></div><div class="hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.38d4f2055fc68c1b_43" class="hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="t3iYD"><img src="https://lh5.googleusercontent.com/NhbJqEdfOidsCnAcoXPKpYGUBGJvKdIQS3bCIN2Po3pbKsMqAjQgON6daTU-T3-D4Fy3wABFFJNI0iGb5ZjVe1MgdU3cY4FxbS2LG4NAOCiZPaRiuLOgbz5lrfIun1fxJA=w1280" class="CENy8b" role="img"></div></div></div></div></div><div class="oKdM2c ZZyype"><div id="h.38d4f2055fc68c1b_72" class="hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><div id="h.cvtegw9qcdj6" class="CobnVe yMxPgf aP9Z7e"></div><h2 id="h.cvtegw9qcdj6_l" dir="ltr" class="zfr3Q JYVBee CDt4Ke " style="text-align: center;"><div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" class="CjVfdc"><div class="PPhIP rviiZ" jsname="haAclf"><div role="presentation" class="U26fgb mUbCce fKz7Od LRAOtb Znu9nd M9Bg4d" jscontroller="mxS5xe" jsaction="click:cOuCgd; mousedown:UX7yZ; mouseup:lbsD7e; mouseenter:tfO1Yc; mouseleave:JywGue; focus:AHmuwe; blur:O22p3e; contextmenu:mg9Pef;" jsshadow aria-describedby="h.cvtegw9qcdj6_l" aria-label="Copy heading link" aria-disabled="false" data-tooltip="Copy heading link" aria-hidden="true" data-tooltip-position="top" data-tooltip-vertical-offset="12" data-tooltip-horizontal-offset="0"><a class="FKF6mc TpQm9d" href="#h.cvtegw9qcdj6" aria-label="Copy heading link" jsname="hiK3ld" role="button" aria-describedby="h.cvtegw9qcdj6_l"><div class="VTBa7b MbhUzd" jsname="ksKsZd"></div><span jsslot class="xjKiLb"><span class="Ce1Y1c" style="top: -11px"><svg class="OUGEr QdAdhf" width="22px" height="22px" viewBox="0 0 24 24" fill="currentColor" focusable="false"><path d="M0 0h24v24H0z" fill="none"/><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7c-2.76 0-5 2.24-5 5s2.24 5 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1zM8 13h8v-2H8v2zm9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1s-1.39 3.1-3.1 3.1h-4V17h4c2.76 0 5-2.24 5-5s-2.24-5-5-5z"/></svg></span></span></a></div></div><span class="C9DxTc " style="">Luca Avena</span></div></h2><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: center;"><span class="C9DxTc " style="font-variant: normal;">Associate Professor, University of </span><span class="C9DxTc " style="">Florence, Italy</span></p></div></div></div></div></div></div></div></div></div></section><section id="h.369e446412f6dcc2_0" class="yaqOZd qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.369e446412f6dcc2_8" class="hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="t3iYD"><img src="https://lh4.googleusercontent.com/89iWTypDkz4ux8IAANPKikei6DQSyOdjUypBVOBiPOCysle-ZI9he3a6YjXy5JGWg2XbsJXu3wp1q1QJMTTIPXhekSr5xHtjnDafYZi8tXPPJAHxjSDh0XxaeQg83TRMRA=w1280" class="CENy8b" role="img"></div></div></div></div></div></div></div></div><div class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.369e446412f6dcc2_3" class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700;">Seminar by Rajat Hazra: </span><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700; text-decoration: underline;">Spectra of inhomogeneous random graphs</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">23</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/11/2024, 9:30-11:00 (Sagrestia, San Francesco complex).</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">Also online at </span><a class="XqQF9c" href="http://imt.lu/sagrestia" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-style: italic; font-variant: normal; text-decoration: underline;">http://imt.lu/sagrestia</span></a><span class="C9DxTc " style="font-style: italic; font-variant: normal;">.</span></p></div></div></div></div><div class="oKdM2c ZZyype"><div id="h.369e446412f6dcc2_5" class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Abstract: I will describe some results on the bulk of the spectrum of sparse and dense inhomogeneous random graphs and how the two spectrums are related. In the second part of the talk, I will focus on the edge on the spectrum and describe properties of the largest eigenvalue, eigenvectors and some related large deviation results.</span></p></div></div></div></div></div></div></div></div></div></section><section id="h.369e446412f6dcc2_20" class="yaqOZd WxWicb qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.369e446412f6dcc2_23" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="iwQgFb" role="presentation"></div></div></div></div></div></div></div></div></div></div></section><section id="h.369e446412f6dcc2_11" class="yaqOZd qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.369e446412f6dcc2_14" class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700;">Seminar by Luca Avena:</span><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700;"> </span><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700; text-decoration: underline;">Meetings of random walks & consensus dynamics on sparse random digraphs</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">23</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/11/2023, 16:00-17:30 (Aula 1, San Francesco complex).</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">Also online at </span><a class="XqQF9c" href="http://imt.lu/aula1" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-style: italic; font-variant: normal; text-decoration: underline;">http://imt.lu/aula1</span></a><span class="C9DxTc " style="font-style: italic; font-variant: normal;">.</span></p></div></div></div></div><div class="oKdM2c ZZyype"><div id="h.369e446412f6dcc2_16" class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="font-variant: normal;">Abstract: I will first discuss the general relation between meeting time of random walks and consensus time in Markovian opinion dynamics on finite networks. I will then focus on sparse random directed graphs and give an account on a recent result in which we characterize in such directed setup how random walks meet and related implications for opinion dynamics. I will in particular discuss how the directed degree structure of the underlying network may speed up or slow down meetings of different random walks.</span></p></div></div></div></div></div></div></div><div class="hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.369e446412f6dcc2_19" class="hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="t3iYD"><img src="https://lh3.googleusercontent.com/gfmyYvlBv-ofLV-8Uld9ZR1M5BItvrGjCGNBFrSdrXmjp8akQyVELwGvfZKwAlricvpf_K-yDkj0CcpO01bSO1JonhwURy0MXwH81YsgWJJJ6iDfDhYEdjnEBJfGvOI0=w1280" class="CENy8b" role="img"></div></div></div></div></div></div></div></div></div></div></section><section id="h.38d4f2055fc68c1b_22" class="yaqOZd lQAHbd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.38d4f2055fc68c1b_25" class="hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="t3iYD"><img src="https://lh5.googleusercontent.com/-zLnjzwVK7L5pflbsRdYy27fauNS6FRAVdITx1D4Zzwuno4INxoRZgmNq3XGjSB01wzKfPuuyXR_AhxQuurFiyth91B8ylC9-_ccLCaarHS3Ump6SSmzUavM4RbikHlytg=w1280" class="CENy8b" role="img"></div></div></div></div></div></div></div></div><div class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.38d4f2055fc68c1b_28" class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">14/04/2023 - 26/05/2023, IMT School of Advanced Studies Lucca </span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">(also online at </span><a class="XqQF9c" href="http://imt.lu/seminar" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-style: italic; font-variant: normal; text-decoration: underline;">http://imt.lu/seminar</span></a><span class="C9DxTc " style="font-style: italic; font-variant: normal;">).</span></p><div id="h.zdrnnntwuksj" class="CobnVe yMxPgf aP9Z7e"></div><h2 id="h.zdrnnntwuksj_l" dir="ltr" class="zfr3Q JYVBee CDt4Ke " style="line-height: 1.2;"><div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" class="CjVfdc"><div class="PPhIP rviiZ" jsname="haAclf"><div role="presentation" class="U26fgb mUbCce fKz7Od LRAOtb Znu9nd M9Bg4d" jscontroller="mxS5xe" jsaction="click:cOuCgd; mousedown:UX7yZ; mouseup:lbsD7e; mouseenter:tfO1Yc; mouseleave:JywGue; focus:AHmuwe; blur:O22p3e; contextmenu:mg9Pef;" jsshadow aria-describedby="h.zdrnnntwuksj_l" aria-label="Copy heading link" aria-disabled="false" data-tooltip="Copy heading link" aria-hidden="true" data-tooltip-position="top" data-tooltip-vertical-offset="12" data-tooltip-horizontal-offset="0"><a class="FKF6mc TpQm9d" href="#h.zdrnnntwuksj" aria-label="Copy heading link" jsname="hiK3ld" role="button" aria-describedby="h.zdrnnntwuksj_l"><div class="VTBa7b MbhUzd" jsname="ksKsZd"></div><span jsslot class="xjKiLb"><span class="Ce1Y1c" style="top: -11px"><svg class="OUGEr QdAdhf" width="22px" height="22px" viewBox="0 0 24 24" fill="currentColor" focusable="false"><path d="M0 0h24v24H0z" fill="none"/><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7c-2.76 0-5 2.24-5 5s2.24 5 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1zM8 13h8v-2H8v2zm9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1s-1.39 3.1-3.1 3.1h-4V17h4c2.76 0 5-2.24 5-5s-2.24-5-5-5z"/></svg></span></span></a></div></div><span class="C9DxTc " style="font-variant: normal;">Dynamics, heterogeneity and fluctuations</span></div></h2><div id="h.41dak6tin7cn" class="GV3q8e yMxPgf aP9Z7e"></div><h3 id="h.41dak6tin7cn_l" dir="ltr" class="zfr3Q OmQG5e CDt4Ke " style="line-height: 1.2;"><div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" class="CjVfdc"><div class="PPhIP rviiZ" jsname="haAclf"><div role="presentation" class="U26fgb mUbCce fKz7Od LRAOtb Znu9nd M9Bg4d" jscontroller="mxS5xe" jsaction="click:cOuCgd; mousedown:UX7yZ; mouseup:lbsD7e; mouseenter:tfO1Yc; mouseleave:JywGue; focus:AHmuwe; blur:O22p3e; contextmenu:mg9Pef;" jsshadow aria-describedby="h.41dak6tin7cn_l" aria-label="Copy heading link" aria-disabled="false" data-tooltip="Copy heading link" aria-hidden="true" data-tooltip-position="top" data-tooltip-vertical-offset="12" data-tooltip-horizontal-offset="0"><a class="FKF6mc TpQm9d" href="#h.41dak6tin7cn" aria-label="Copy heading link" jsname="hiK3ld" role="button" aria-describedby="h.41dak6tin7cn_l"><div class="VTBa7b MbhUzd" jsname="ksKsZd"></div><span jsslot class="xjKiLb"><span class="Ce1Y1c" style="top: -11px"><svg class="OUGEr QdAdhf" width="22px" height="22px" viewBox="0 0 24 24" fill="currentColor" focusable="false"><path d="M0 0h24v24H0z" fill="none"/><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7c-2.76 0-5 2.24-5 5s2.24 5 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1zM8 13h8v-2H8v2zm9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1s-1.39 3.1-3.1 3.1h-4V17h4c2.76 0 5-2.24 5-5s-2.24-5-5-5z"/></svg></span></span></a></div></div><span class="C9DxTc " style="font-variant: normal;">Prof. Roberto Livi</span></div></h3><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 13.5pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt;"><a class="XqQF9c" href="/visiting-professors-guest-scholars" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-variant: normal; text-decoration: underline;">IMT Visiting Professor</span></a><span class="C9DxTc " style="font-variant: normal;"> & Honorary Professor, University of Florence; </span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">President of the </span><a class="XqQF9c" href="https://www.fisicastatistica.org" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-variant: normal; text-decoration: underline;">Italian Statistical Physics Society (SIFS)</span></a><span class="C9DxTc " style="font-variant: normal;">.</span></p></div></div></div></div><div class="oKdM2c ZZyype"><div id="h.38d4f2055fc68c1b_30" class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="font-variant: normal;">This series aims at introducing the audience to the theory of dynamical systems, encompassing deterministic, disordered, stochastic and irreversible systems, providing a unified description in terms of various statistical indicators, typically associated with the solution of spectral problems. The series consists of four self-contained daily blocks, where each block has a first 2-hour introductory lecture intended for a broader audience (11:00 - 13:00) and a second 2-hour lecture providing a more detailed illustration of useful methods and applications (14:00 - 16:00). </span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="font-variant: normal;">Useful resources </span><a class="XqQF9c" href="https://drive.google.com/drive/folders/1M9wUjINSccqLYVwAkRQahW2gEOSSAD53?usp=sharing" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-variant: normal; text-decoration: underline;">at this link</span></a><span class="C9DxTc " style="font-variant: normal;">.</span></p></div></div></div></div></div></div></div></div></div></section><section id="h.47a4c759a6bec1f4_3" class="yaqOZd qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.47a4c759a6bec1f4_0" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700;">Block 1. </span><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700; text-decoration: underline;">Deterministic dynamical systems: tools and methods</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">14/04/2023, 11:00-13:00 (Sagrestia, San Francesc</span><span class="C9DxTc " style="font-style: italic;">o complex</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">) and 14:00-16:00 (Sagrestia, San Francesco </span><span class="C9DxTc " style="font-style: italic;">c</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">omplex). </span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">Also online at </span><a class="XqQF9c" href="http://imt.lu/seminar" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-style: italic; font-variant: normal; text-decoration: underline;">http://imt.lu/seminar</span></a><span class="C9DxTc " style="font-style: italic;">.</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="font-variant: normal;">The first block is devoted to the description of the basic mathematical tools, needed to study determinisitic dynamical systems. As applications we discuss how to characterize the dynamics by statistical methods (symbolic representation, etc) and by its spectrum of Lyapunov exponents, making use of analytical and numerical techniques. Topics include:</span></p><ul class="n8H08c UVNKR " style="list-style-type: square; margin-left: 0; margin-right: 0; padding: 0;"><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">An introduction to dynamical systems: fluxes and maps;</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Mathematical ingredients: singular points, manifolds, Poincarè section, chaotic scenarios;</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Dissipative and conservative dynamical systems;</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Stability analysis: Lyapunov spectra (covariant definition).</span></p></li></ul></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_77" class="yaqOZd WxWicb qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_80" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="iwQgFb" role="presentation"></div></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_61" class="yaqOZd qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_64" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700;">Block 2. </span><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700; text-decoration: underline;">Dynamical evolutions in spatially extended systems</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">28</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/04/2023, 11:00-13:00 (Sagrestia, San Francesco complex) and 14:00-16:00 (Sagrestia, San Francesco complex).</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">Also online at </span><a class="XqQF9c" href="http://imt.lu/seminar" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-style: italic; font-variant: normal; text-decoration: underline;">http://imt.lu/seminar</span></a><span class="C9DxTc " style="font-style: italic; font-variant: normal;">.</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="font-variant: normal;">The second block deals with deterministic dynamical systems made of many degrees of freedom, organized on lattices and networks. Applications will be focused on the relation of hydrodynamics with the Lyapunov spectrum in conservative systems, on the spectral method for solving transport problems in disordered harmonic chains and on suitable methods (stable chaos, heterogeneous mean-field) for models of neural networks. Topics include:</span></p><ul class="n8H08c UVNKR " style="list-style-type: square; margin-left: 0; margin-right: 0; padding: 0;"><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Dynamics in systems with many degrees of freedom;</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Dynamics and disorder: transport in harmonic chains;</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Coupled maps, networks and stable chaos.</span></p></li></ul></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_81" class="yaqOZd WxWicb qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_84" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="iwQgFb" role="presentation"></div></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_65" class="yaqOZd qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_68" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700;">Block 3. </span><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700; text-decoration: underline;">Stochastic dynamics: basic ingredients</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">12</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/05/2023, 11:00-13:00 (Sagrestia, San Francesco complex) and 14:00-16:00 (Conference Room, San Ponziano complex). </span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">Also online at </span><a class="XqQF9c" href="http://imt.lu/seminar" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-style: italic; font-variant: normal; text-decoration: underline;">http://imt.lu/seminar</span></a><span class="C9DxTc " style="font-style: italic; font-variant: normal;">.</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="font-variant: normal;">The third block provides an introduction to stochastic processes in discrete-time (Markov chains) and continuous time (Langevin, Fokker-Planck). For what concerns applications we focus on simple examples of Markov processes (random walker on a ring, Monte-Carlo algorithms) and on models of anomalous diffusion. Topics include:</span></p><ul class="n8H08c UVNKR " style="list-style-type: square; margin-left: 0; margin-right: 0; padding: 0;"><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Markov Chains and their spectral properties (ergodicity);</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Stochastic dynamics: Langevin and Fokker-Planck;</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Anomalous diffusion.</span></p></li></ul></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_85" class="yaqOZd WxWicb qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_88" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="iwQgFb" role="presentation"></div></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_69" class="yaqOZd qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_72" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700;">Block 4. </span><span class="C9DxTc " style="font-family: Lato, Arial; font-variant: normal; font-weight: 700; text-decoration: underline;">Stochastic processes, reversibility and fluctuation relations</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">26</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/05/2023, 11:00-13:00 (Sagrestia, San Francesco complex) and 14:00-16:00 (Sagrestia, San Francesco complex). </span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: justify;"><span class="C9DxTc " style="font-style: italic; font-variant: normal;">Also online at </span><a class="XqQF9c" href="http://imt.lu/seminar" target="_blank" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-style: italic; font-variant: normal; text-decoration: underline;">http://imt.lu/seminar</span></a><span class="C9DxTc " style="font-style: italic; font-variant: normal;">.</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="font-variant: normal;">The fourth block deals with the problem of “irreversibility” in stochastic processes in the framework of the Chapman Kolmogorov equation and on the basic aspects of fluctuation-dissipation relations. Applications are devoted to outline the general approach to solve “first passage problems” and also to describe Jarzinsky, Crooks and Gallavotti-Cohen relations, associated with fluctuating thermodynamics. The final comments will be about linear response theory and coupled transport. Topics include:</span></p><ul class="n8H08c UVNKR " style="list-style-type: square; margin-left: 0; margin-right: 0; padding: 0;"><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Chapman-Kolmogorov equations (first-passage problem);</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Fluctuation-dissipation and stochastic thermodynamics;</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="margin-left: 0.0pt; padding-left: 0.0pt; text-align: justify; text-indent: 0.0pt;"><span class="C9DxTc " style="font-variant: normal;">Linear response theory and transport.</span></p></li></ul></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_8" class="yaqOZd lQAHbd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_93" class="hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="t3iYD"><img src="https://lh6.googleusercontent.com/3ZIvu8ouTqiqxUznEN3rveGrLNc2Tt2GSjblq7lhwUnnc93SYl82q8MIivLZFTrVVkfc2OCl3wjlDxc6lX2rNiCKzp81O1ZQhgSpcqkLnqbSVcFK9izZGD9LO0zHF59wvw=w1280" class="CENy8b" role="img"></div></div></div></div></div></div></div></div><div class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_14" class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.2;"><span class="C9DxTc " style="font-style: italic;">25</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/</span><span class="C9DxTc " style="font-style: italic;">11</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/20</span><span class="C9DxTc " style="font-style: italic;">19,</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;"> 2</span><span class="C9DxTc " style="font-style: italic;">7</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/</span><span class="C9DxTc " style="font-style: italic;">11</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">/20</span><span class="C9DxTc " style="font-style: italic;">19</span><span class="C9DxTc " style="font-style: italic; font-variant: normal;">, IMT School of Advanced Studies Lucca</span><span class="C9DxTc " style="font-style: italic;">.</span></p><div id="h.b7h4nfwng5s6" class="CobnVe yMxPgf aP9Z7e"></div><h2 id="h.b7h4nfwng5s6_l" dir="ltr" class="zfr3Q JYVBee CDt4Ke " style="line-height: 1.2;"><div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" class="CjVfdc"><div class="PPhIP rviiZ" jsname="haAclf"><div role="presentation" class="U26fgb mUbCce fKz7Od LRAOtb Znu9nd M9Bg4d" jscontroller="mxS5xe" jsaction="click:cOuCgd; mousedown:UX7yZ; mouseup:lbsD7e; mouseenter:tfO1Yc; mouseleave:JywGue; focus:AHmuwe; blur:O22p3e; contextmenu:mg9Pef;" jsshadow aria-describedby="h.b7h4nfwng5s6_l" aria-label="Copy heading link" aria-disabled="false" data-tooltip="Copy heading link" aria-hidden="true" data-tooltip-position="top" data-tooltip-vertical-offset="12" data-tooltip-horizontal-offset="0"><a class="FKF6mc TpQm9d" href="#h.b7h4nfwng5s6" aria-label="Copy heading link" jsname="hiK3ld" role="button" aria-describedby="h.b7h4nfwng5s6_l"><div class="VTBa7b MbhUzd" jsname="ksKsZd"></div><span jsslot class="xjKiLb"><span class="Ce1Y1c" style="top: -11px"><svg class="OUGEr QdAdhf" width="22px" height="22px" viewBox="0 0 24 24" fill="currentColor" focusable="false"><path d="M0 0h24v24H0z" fill="none"/><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7c-2.76 0-5 2.24-5 5s2.24 5 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1zM8 13h8v-2H8v2zm9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1s-1.39 3.1-3.1 3.1h-4V17h4c2.76 0 5-2.24 5-5s-2.24-5-5-5z"/></svg></span></span></a></div></div><span class="C9DxTc " style="">Mathematical theory of complex networks</span></div></h2><div id="h.wc7nvysv09rw" class="GV3q8e yMxPgf aP9Z7e"></div><h3 id="h.wc7nvysv09rw_l" dir="ltr" class="zfr3Q OmQG5e CDt4Ke " style="line-height: 1.2;"><div jscontroller="Ae65rd" jsaction="touchstart:UrsOsc; click:KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;CrfLRd:SzACGe;" class="CjVfdc"><div class="PPhIP rviiZ" jsname="haAclf"><div role="presentation" class="U26fgb mUbCce fKz7Od LRAOtb Znu9nd M9Bg4d" jscontroller="mxS5xe" jsaction="click:cOuCgd; mousedown:UX7yZ; mouseup:lbsD7e; mouseenter:tfO1Yc; mouseleave:JywGue; focus:AHmuwe; blur:O22p3e; contextmenu:mg9Pef;" jsshadow aria-describedby="h.wc7nvysv09rw_l" aria-label="Copy heading link" aria-disabled="false" data-tooltip="Copy heading link" aria-hidden="true" data-tooltip-position="top" data-tooltip-vertical-offset="12" data-tooltip-horizontal-offset="0"><a class="FKF6mc TpQm9d" href="#h.wc7nvysv09rw" aria-label="Copy heading link" jsname="hiK3ld" role="button" aria-describedby="h.wc7nvysv09rw_l"><div class="VTBa7b MbhUzd" jsname="ksKsZd"></div><span jsslot class="xjKiLb"><span class="Ce1Y1c" style="top: -11px"><svg class="OUGEr QdAdhf" width="22px" height="22px" viewBox="0 0 24 24" fill="currentColor" focusable="false"><path d="M0 0h24v24H0z" fill="none"/><path d="M3.9 12c0-1.71 1.39-3.1 3.1-3.1h4V7H7c-2.76 0-5 2.24-5 5s2.24 5 5 5h4v-1.9H7c-1.71 0-3.1-1.39-3.1-3.1zM8 13h8v-2H8v2zm9-6h-4v1.9h4c1.71 0 3.1 1.39 3.1 3.1s-1.39 3.1-3.1 3.1h-4V17h4c2.76 0 5-2.24 5-5s-2.24-5-5-5z"/></svg></span></span></a></div></div><span class="C9DxTc " style="">Dr</span><span class="C9DxTc " style="font-variant: normal;">. </span><span class="C9DxTc " style="">Luca</span><span class="C9DxTc " style="font-variant: normal;"> </span><span class="C9DxTc " style="">Avena</span></div></h3><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.2; margin-bottom: 0.0pt; margin-top: 13.5pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt;"><a class="XqQF9c" href="/visiting-professors-guest-scholars" style="color: inherit; text-decoration: none;"><span class="C9DxTc aw5Odc " style="font-variant: normal; text-decoration: underline;">IMT Visiting Professor</span></a><span class="C9DxTc " style="font-variant: normal;"> & </span><span class="C9DxTc " style="">Assistant</span><span class="C9DxTc " style="font-variant: normal;"> Professor, University of </span><span class="C9DxTc " style="">Leiden.</span></p></div></div></div></div><div class="oKdM2c ZZyype"><div id="h.7e5f353c30879f63_16" class="hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="">This is a series of two mini-workshops. Each workshop begins with a longer lecture by the visiting professor, followed by a series of shorter seminars by IMT professors and PhD students that work on related themes. There will be plenty of time devoted to informal discussions, aimed at establishing potential lines of joint research between Dr. Avena and IMT researchers and students. </span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="text-align: justify;"><span class="C9DxTc " style="">To keep focus, each mini-workshop has a specific theme: "Network coarse-graining" (25 November, 9:00-13:00) and "Brain networks and metastability" (27 November, 9:00-13:00). Both workshops are open to all IMT members, to maximize the number and diversity of potential collaborations generated by the event. Whoever is interested in the topics discussed will have a chance of further discussing with the visiting professor during the week.</span></p></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_20" class="yaqOZd qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_17" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-family: Lato, Arial; font-weight: 700;">Workshop 1. </span><span class="C9DxTc " style="color: #222222; font-family: Lato, Arial; font-weight: 700; text-decoration: underline;">Network coarse-graining</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.38;"><span class="C9DxTc " style="color: #222222; font-style: italic; font-variant: normal;">27/11/2019, 9:00-13:00 (Aula 2, San Francesco complex)</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.56; margin-bottom: 0.0pt; margin-top: 12.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: justify;"><span class="C9DxTc " style="color: #222222;">Network coarse-graining refers to the reduction of a larger network to a smaller version of it, by keeping certain properties preserved. This procedure is needed in a diverse range of disciplines, especially when the original network is too big to be dealt with mathematically, computationally or experimentally. The mini-workshop aims at exposing different techniques that have been proposed across disciplines (most prominently mathematics, physics and computer science), and to highlight the open challenges that require a multidisciplinary approach.</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-top: 12.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-align: justify;"><span class="C9DxTc " style="color: #222222; font-family: Lato, Arial; font-weight: 700;">Program:</span></p><ul class="n8H08c UVNKR " style="list-style-type: square; margin-left: 0; margin-right: 0; padding: 0;"><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222;">09:00 Luca Avena: "Renormalisation for graphs and signals on graphs via random walk kernels"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222;">10:30 Mirco Tribastone: "Automatic simplification of large-scale reaction networks"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222;">11:00 Coffee break</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222;">11:30 Margherita Lalli: "Spectral coarse graining of complex networks"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222;">12:00 Diego Garlaschelli: "Multiscale network renormalization: scale-invariance without geometry"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222;">12:30 Matteo Serafino: "Scale-free networks revealed from finite-size scaling"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222;">13:00 Lunch</span></p></li></ul></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_49" class="yaqOZd WxWicb qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_52" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd baZpAe"><div class="iwQgFb" role="presentation"></div></div></div></div></div></div></div></div></div></div></section><section id="h.7e5f353c30879f63_53" class="yaqOZd qeLZfd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.7e5f353c30879f63_56" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><p dir="ltr" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-family: Lato, Arial; font-variant: normal; font-weight: 700;">Workshop 2. </span><span class="C9DxTc " style="color: #222222; font-family: Lato, Arial; font-variant: normal; font-weight: 700; text-decoration: underline;">Brain networks and metastability</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.38;"><span class="C9DxTc " style="color: #222222; font-style: italic; font-variant: normal;">27/11/2019, 9:00-13:00 (Aula 2, San Francesco complex)</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.56; text-align: justify;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">Metastability is the property of systems that, before eventually reaching a completely stable state, visit a number of intermediate states that are temporarily and transiently stable. This workshop aims at introducing some mathematical aspects of metastability and discussing the potential applications to the empirical analysis of brain networks, especially in relation to the presence of possible transient neural states and/or modular functional structures.</span></p><p dir="ltr" class="zfr3Q CDt4Ke " style="line-height: 1.38; text-align: justify;"><span class="C9DxTc " style="color: #222222; font-family: Lato, Arial; font-variant: normal; font-weight: 700;">Program: </span></p><ul class="n8H08c UVNKR " style="list-style-type: square; margin-left: 0; margin-right: 0; padding: 0;"><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">09:00 Luca Avena: "Mesoscopic explorations of graphs through random rooted forests"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">10:30 Tommaso Gili: "Functional brain networks dynamics: from time series to metastability"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">11:00 Coffee break</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">11:30 Rossana Mastrandrea: "Functional brain networks in schizophrenic patients and healthy individuals"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">12:00 Virginia Gurioli: "Reconstruction of functional connectivity brain network in healthy subjects and schizophrenic patients"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">12:15 Adrian Ioan Onicaș: "Detecting task events in fMRI time series based on the topological structure of visibility graphs"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">12:30 Francesca Santucci: "Statistical inference for brain network construction"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">12:45 Diego Garlaschelli: "Communities from brain correlation matrices: functional modules without functional networks"</span></p></li><li dir="ltr" class="zfr3Q TYR86d eD0Rn " style="margin-left: 15.0pt;"><p dir="ltr" role="presentation" class="zfr3Q CDt4Ke " style="background-color: transparent; border-bottom: none; border-left: none; border-right: none; border-top: none; line-height: 1.38; margin-bottom: 0.0pt; margin-left: 0.0pt; margin-top: 0.0pt; padding-bottom: 0.0pt; padding-left: 0.0pt; padding-right: 0.0pt; padding-top: 0.0pt; text-indent: 0.0pt;"><span class="C9DxTc " style="color: #222222; font-variant: normal;">13:00 Lunch</span></p></li></ul></div></div></div></div></div></div></div></div></div></section></div><div class="Xpil1b xgQ6eb"></div><footer jsname="yePe5c"><section id="h.55c70290097ac894_3" class="yaqOZd lQAHbd"><div class="IFuOkc"></div><div class="mYVXT"><div class="LS81yb VICjCf j5pSsc db35Fc" tabindex="-1"><div class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc"><div class="JNdkSc-SmKAyb LkDMRd"><div class="" jscontroller="sGwD4d" jsaction="zXBUYb:zTPCnb;zQF9Uc:Qxe3nd;" jsname="F57UId"><div class="oKdM2c ZZyype Kzv0Me"><div id="h.55c70290097ac894_0" class="hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb"><div class="jXK9ad-SmKAyb"><div class="tyJCtd mGzaTb Depvyb baZpAe"><small id="h.yptqm42axd4e" dir="ltr" class="zfr3Q TMjjoe CDt4Ke " style="display: block;"><span class="C9DxTc " style="">© Copyright 2023 IMT School for Advanced Studies Lucca</span></small></div></div></div></div></div></div></div></div></div></section></footer><div jscontroller="j1RDQb" jsaction="rcuQ6b:rcuQ6b;MxH79b:JdcaS;FaOgy:XuHpsb;" class="dZA9kd ynRLnc" data-last-updated-at-time="1701252730530" data-is-preview="false"><div role="button" class="U26fgb JRtysb WzwrXb I12f0b K2mXPb zXBiaf ynRLnc" jscontroller="iSvg6e" jsaction="click:cOuCgd; 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