39 citations · 72 across the 24 of their papers we have counts for
27 papers
Non-freezing of the proximity digraph and non-pseudostable convergence in heterogeneous Hegselmann--Krause models: Counterexamples to conjectures and results of Mirtabatabaei and Bullo
Peter Hegarty, Damiano Ognissanti, Edvin Wedin
In 2012, Mirtabatabaei and Bullo studied heterogeneous Hegselmann--Krause models of opinion dynamics, where different agents may have different confidence or influence bounds. They…
The "No Justice in the Universe" phenomenon: why honesty of effort may not be rewarded in tournaments
Peter Hegarty, Anders Martinsson, Edvin Wedin
In 2000 Allen Schwenk, using a well-known mathematical model of matchplay tournaments in which the probability of one player beating another in a single match is fixed for each pai…
Permutations destroying arithmetic progressions in finite cyclic groups
Peter Hegarty, Anders Martinsson
A permutation πof an abelian group G is said to destroy arithmetic progressions (APs) if, whenever (a,b,c) is a non-trivial 3-term AP in G, that is c-b=b-a and a,b,c are not all eq…
The Hegselmann-Krause dynamics on the circle converge
Peter Hegarty, Anders Martinsson, Edvin Wedin
We consider the Hegselmann-Krause dynamics on a one-dimensional torus and provide the first proof of convergence of this system. The proof requires only fairly minor modifications…
The Hegselmann-Krause dynamics for equally spaced agents
Peter Hegarty, Edvin Wedin
We consider the Hegselmann-Krause bounded confidence dynamics for n equally spaced opinions on the real line, with gaps equal to the confidence bound r, which we take to be 1. We p…
A quadratic lower bound for the convergence rate in the one-dimensional Hegselmann-Krause bounded confidence dynamics
Edvin Wedin, Peter Hegarty
Let f_{k}(n) be the maximum number of time steps taken to reach equilibrium by a system of n agents obeying the k-dimensional Hegselmann-Krause bounded confidence dynamics. Previou…