BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Des Higham (University of Edinburgh) DTSTART:20201111T150000Z DTEND:20201111T160000Z DTSTAMP:20260423T022920Z UID:E-NLA/20 DESCRIPTION:Title: C oncepts and Algorithms for Higher Order Networks: Beyond Pairwise Interact ions\nby Des Higham (University of Edinburgh) as part of E-NLA - Onlin e seminar series on numerical linear algebra\n\n\nAbstract\nNetwork scient ists have shown that there is great value in studying pairwise interaction s between components in a system. From a linear algebra point of view\, th is involves defining and evaluating functions of the associated adjacency matrix. Recently\, there has been increased interest in the idea of accoun ting directly for higher order features. Such features may be built from t he adjacency matrix---for example\, a triangle involving nodes i\, j and k arises when the three edges\, i<->j\, j<->k and k<->i are present. In oth er contexts\, higher order information appears explicitly---for example\, in a coauthorship network\, a document involving three authors forms a nat ural triangle. I will discuss the use of tensor-based definitions and algo rithms to exploit such higher order information. The algorithms also incor porate nonlinearities that increase flexibility. I will focus on spectral methods that extend classical concepts of node centrality and clustering coefficients. The underlying object of study will be a constrained nonline ar eigenvalue problem associated with a tensor. Using recent results from nonlinear Perron--Frobenius theory\, we can establish existence and unique ness under mild conditions\, and show that such spectral measures can be c omputed efficiently and robustly with a nonlinear power method.\n\nThe tal k is based on joint work with Francesca Arrigo (University of Strathclyde) and Francesco Tudisco (Gran Sasso Science Institute).\n LOCATION:https://researchseminars.org/talk/E-NLA/20/ END:VEVENT END:VCALENDAR