<div dir="ltr"><div dir="auto"><span style="color:rgb(0,0,0)">For the <i>next appointment</i> of the series of seminars "Insalate di Matematica", <b>Anna Gallo</b> (Scuola IMT Alti Studi Lucca) will give a talk. </span></div><div dir="auto"><span style="color:rgb(0,0,0)">The speaker will deliver the talk <u>in presence</u> and the meeting will also be broadcasted <u>online</u> (see below for more information).</span></div><div dir="auto"><span style="color:rgb(0,0,0)"><br></span></div><div dir="auto"><div dir="auto"><span style="color:rgb(0,0,0)"><u>Date and time</u>: <b>29th of November 2023, 3:30 pm (CET)</b></span></div><div dir="auto"><br></div><div dir="auto"><div dir="auto"><font color="#000000"><u>Title</u>: <span style="background-color:rgb(255,229,153)">"</span></font><span style="background-color:rgb(255,229,153)">Strong, weak or no balance? Testing structural hypotheses in real heterogeneous networks</span><font color="#000000"><span style="background-color:rgb(255,229,153)">"</span></font></div><br></div><div dir="auto"><div dir="auto"><font color="#000000"><u>Abstract</u>:</font> The abundance of data about social, economic and political relationships allows social theories to be tested against empirical evidence and human behaviour to be analyzed just as any other natural phenomenon. Here we focus on balance theory, stating that actors in signed, social networks tend to avoid the formation of cycles with an odd number of negative links. This statement, however, can be supported statistically only after a comparison with a null model. Since the existing benchmarks do not account for actors’ heterogeneity, here we extend the Exponential Random Graphs framework to signed networks with both global (homogeneous) and local (heterogeneous) constraints and employ them to assess the significance of unbalanced patterns in several real-world networks. We find that the nature and level of balance in social networks crucially depends on the null model employed: while homogeneous benchmarks favour the weak balance theory, according to which only triangles with one negative link should be under-represented, heterogeneous benchmarks favour the strong balance theory, according to which also triangles with all negative links should be under-represented. Biological networks, instead, display almost inverted patterns and strong frustration under any benchmark, confirming that structural bal- ance inherently distinguishes social networks from other signed networks.</div><div dir="auto"><br></div><div><u>Keywords:</u> Probability theory, Graph theory, Null models, Statistical mechanics, Entropy, Balance theory.</div><div><br></div><div><div id="m_-5411829806841061073gmail-:1l1" style="direction:ltr;margin:8px 0px 0px;padding:0px;font-size:0.875rem"><div id="m_-5411829806841061073gmail-:15w" style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:small;line-height:1.5;overflow:hidden"><div dir="ltr"><div dir="auto"><div dir="auto"><div dir="auto"><u><b>Information to attend in room 3014</b></u></div><div dir="auto">The seminar will take place in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.</div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto"><u><b>Information to attend online<br></b></u></div><div dir="auto"><a href="https://unimib.webex.com/unimib/j.php?MTID=m3c536ba5a33f71bb9d6a3bc9b00992ad" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=m3c536ba5a33f71bb9d6a3bc9b00992ad</a> (password: Insalate, 46725283 from phones)</div><div dir="auto"><br></div><div dir="auto"><div dir="auto">You can find the poster of the event in the attachment. </div><div dir="auto">We are looking forward to seeing you! </div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">insalate.matematica@unimib.it</a>. Find us also on our Instagram page: <a href="https://www.instagram.com/insalate_di_matematica22/" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://www.instagram.com/insalate_di_matematica23/</a></div><div dir="auto"><br></div><div dir="auto"><div dir="auto"><font color="#000000">The organizers: Ettore Marmo, Simone Gallivanone, Fabio Mastrogiacomo, Marco Fusari, Tommaso Toti and Matteo Tarocchi.</font></div></div></div></div></div></div></div></div><div id="m_-5411829806841061073gmail-:1ld" style="font-size:0.875rem;margin:15px 0px;clear:both"><div id="m_-5411829806841061073gmail-:1lf" style="margin:12px 0px;font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif"><span style="font-weight:bold;height:20px;line-height:20px;font-size:0.875rem;display:flex"><br>
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