<div dir="ltr"><p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration-line:underline"><span style="font-size:18pt;font-family:"Times New Roman",serif">SEMINARIO
DI MATEMATICA</span></p>

<p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration-line:underline"><span style="font-size:10pt;font-family:"Times New Roman",serif"><span style="text-decoration-line:none"> </span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span style="font-size:16pt;font-family:"Times New Roman",serif">Giovedì 21 marzo 2019</span></b><b><span style="font-size:16pt;font-family:"Times New Roman",serif"></span></b></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">ore 15:00</span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"> </span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><u><span style="font-size:16pt;font-family:"Times New Roman",serif">Scuola Normale Superiore</span></u></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Pisa</span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-size:16pt;font-family:"Times New Roman",serif">Aula Mancini</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><u><span lang="EN-US" style="font-size:10pt;font-family:"Times New Roman",serif"><span style="text-decoration-line:none"> </span></span></u></b></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span lang="EN-US" style="font-size:22pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Vladimir Druskin</span> </b><b><span lang="EN-US" style="font-size:22pt;font-family:"Times New Roman",serif"></span></b></p>

<h4 align="center" style="margin:0cm 0cm 0.0001pt;text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;break-after:avoid;font-size:12pt;font-family:Cambria,serif;color:rgb(79,129,189);font-style:italic"><span lang="EN-US" style="font-family:"Times New Roman",serif;color:windowtext;font-weight:normal;font-style:normal">(</span><span lang="EN-US" style="font-family:"Times New Roman",serif;color:rgb(34,34,34);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-weight:normal">Worcester Polytechnic Institute</span><span lang="EN-US" style="font-family:"Times New Roman",serif;color:windowtext;font-weight:normal;font-style:normal">)</span></h4>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><i><span lang="EN-US" style="font-family:"Times New Roman",serif"> </span></i></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Terrà un
seminario dal titolo:</span></p>

<p align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;margin-right:0cm;margin-left:0cm;font-size:12pt;font-family:"Times New Roman",serif"><b><span lang="EN-US" style="font-size:18pt">“<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Embedding properties of network
realizations of reduced order models with applications to inverse scattering
and data science</span></span></b><b><span lang="EN-US" style="font-size:18pt">”</span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><i><span lang="EN-US" style="font-size:10pt;font-family:"Times New Roman",serif"> </span></i></b></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><i><span lang="EN-US" style="font-size:10pt;font-family:"Times New Roman",serif">Abstract:</span></i></b></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Continued fractions are known since antiquity as the
most compact representations of numbers. At the end of the 19th century
Stieltjes </span>connected them with physics. This connection gave rise to
network syntheses in the first half of the 20th century that was at the base of modern
electronics design and consecutively to model order reduction (MOR) that
tremendously impacted many areas of engineering by enabling
efficient compression of the underlining dynamical systems. In his seminal
1950s works, Krein realized that in addition to their compressing
properties, Stieltjes continued fractions can be used to embed the data back
into the state space of the underlying dynamical system via special
mechanical networks known as Stieltjes strings. Such networks can  learn
the underlying PDE system from the data (transfer function) via
rigorously chosen hyper-parameters. Among many application of this powerful</p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">approach we discuss the following two: </span><span lang="EN-US" style="font-family:"Times New Roman",serif"></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1. Imaging in   strongly scattering media
with waves (e.g.,seismic exploration) via data-driven MOR. </span><span lang="EN-US" style="font-family:"Times New Roman",serif"><br style="text-align:start">
<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="text-align:start">2. Reduced order graph-Laplacians and efficient cluster
analysis of big data sets.</span></span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"> </span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Tutti gli
interessati sono invitati a partecipare.</span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"> </span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Classe di
Scienze</span></p><p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><br></span></p><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div>Valeria Giuliani</div><div>Scuola Normale Superiore</div><div>Servizio alla Didattica e Allievi</div><div>tel. 050 509260</div><div>Piazza dei Cavalieri, 7</div><div>56126 Pisa</div><div>E-mail: <a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a></div><div>E-mail: <a href="mailto:classi@sns.it" target="_blank">classi@sns.it</a></div></div></div></div></div>

<p></p>

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