VADOR Events Calendar

We frequently host one off lectures on topics relating to variational analysis, dynamics and operations research.  In term-time, we host different speakers at our weekly AKOR seminar.  Seminars take place most Thursdays at 3pm in Sem. R. DB gelb 04.  Once a month, the AKOR seminar will be replaced by the Vienna Seminar on Optimization, opens an external URL in a new window - a joint venture with Radu Bot and Yurii Malitskyi of the University of Vienna

We organise the Viennese Conference on Optimal Control and Dynamic Games, typically every three years.  The next iteration - VC2025 - will take place in July 2025.  For further details on this conference, and its forerunners, please visit the VC2025, opens an external URL in a new window website.

Topics and speakers for all forthcoming events will be posted below.

05. December 2024, 15:00 until 17:00

Vienna Seminar on Optimization: Mean-Field Opinion Dynamics in Random Graphs

Seminar

David Salas, Associate Professor, University O´Higgins, Chile

We consider a set of agents in a network having different opinions over a binary subject. The network is encoded as a (undirected or directed) graph, and each opinion is represented as a value between 0 and 1. At each (discrete) stage, each agent updates her opinion as a convex combination between the average opinion of her neighbors and her intrinsic opinion (which coincides with its initial opinion). It is well known that such dynamic converges to a stable opinion, which can be computed by inverting a matrix associated with the adjacency matrix of the network. When the network itself is a random graph, the stable opinion becomes a random variable, and when the number of agents is large, computing the expected value of the stable opinion by sampling methods can become prohibitively expensive: indeed, for each sample, it is necessary to invert a large matrix. In this talk, we study the pertinence of considering a mean-field model to approximate the expected value of the stable opinion. That is, by considering an “average network”, we study the gap between the expected value of stable opinions and the stable opinion over the average network. We show, under mild hypotheses, that for undirected Erdös-Rényi random graphs the gap measured with the $\ell_{\infty}$-norm vanishes as the size of the network grows to infinity. Moreover, we show that for directed Erdös-Rényi random graphs, the same result holds for the gap measured with any $\ell_{\rho}$-norm, for $\rho \in (1,\infty]$. This talk is based on a joint work with Javiera Gutiérrez-Ramírez (Universidad de Chile) and Víctor Verdugo (Pontificia Universidad Católica de Chile).

Calendar entry

Event location

Sem. R DB gelb 04, TU Wien
1040 Wien
Wiedner Hauptstraße 8 E105-4

 

Organiser

TU Wien/University Wien

 

Public

No

 

Entrance fee

No

 

Registration required

No

Vienna Seminar on Optimization: Mean-Field Opinion Dynamics in Random Graphs

David Salas, Associate Professor, University O´Higgins, Chile

We consider a set of agents in a network having different opinions over a binary subject. The network is encoded as a (undirected or directed) graph, and each opinion is represented as a value between 0 and 1. At each (discrete) stage, each agent updates her opinion as a convex combination between the average opinion of her neighbors and her intrinsic opinion (which coincides with its initial opinion). It is well known that such dynamic converges to a stable opinion, which can be computed by inverting a matrix associated with the adjacency matrix of the network. When the network itself is a random graph, the stable opinion becomes a random variable, and when the number of agents is large, computing the expected value of the stable opinion by sampling methods can become prohibitively expensive: indeed, for each sample, it is necessary to invert a large matrix. In this talk, we study the pertinence of considering a mean-field model to approximate the expected value of the stable opinion. That is, by considering an “average network”, we study the gap between the expected value of stable opinions and the stable opinion over the average network. We show, under mild hypotheses, that for undirected Erdös-Rényi random graphs the gap measured with the $\ell_{\infty}$-norm vanishes as the size of the network grows to infinity. Moreover, we show that for directed Erdös-Rényi random graphs, the same result holds for the gap measured with any $\ell_{\rho}$-norm, for $\rho \in (1,\infty]$. This talk is based on a joint work with Javiera Gutiérrez-Ramírez (Universidad de Chile) and Víctor Verdugo (Pontificia Universidad Católica de Chile).