18 research outputs found
A centrality measure for cycles and subgraphs II
In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe’s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexe
Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions
We compute the stable homology of the braid group with coefficients in any
Schur functor applied to the integral reduced Burau representation. This may be
considered as a hyperelliptic analogue of the Mumford conjecture (Madsen-Weiss
theorem) with twisted coefficients. We relate the result to the function field
case of conjectures of Conrey-Farmer-Keating-Rubinstein-Snaith on moments of
families of quadratic L-functions. In particular, we formulate a purely
topological homological stability conjecture, which when combined with our
calculations would imply a precise asymptotic formula for all moments in the
rational function field case.Comment: 91 page
International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022
Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022.
Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress.
The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum