Browsing by Subject "convergence"

Now showing 1 - 3 of 3

On the Construction of the Non-Uniformly Convergent Series
(University of Texas at Austin, 1912-03-08) University of Texas at Austin
On Waves, Clusters, and Diffusion: A Conceptual Framework
(2005) Elkins, Zachary; Simmons, Beth
This article makes a conceptual and theoretical contri- bution to the study of diffusion. The authors suggest that the concept of diffusion be reserved for processes (not outcomes) characterized by a certain uncoordinated interdependence. Theoretically, the authors identify the principal sources of clustered policy reforms. They then clarify the characteristics specific to diffusion mecha- nisms and introduce a categorization of such processes. In particular, they make a distinction between two types of diffusion: adaptation and learning. They argue that this categorization adds conceptual clarity and distinguishes mechanisms with distinct substantive consequences.
Opinion dynamics of random-walking agents on a lattice
(2011-05) Ree, Suhan; Ree, Suhan
The opinion dynamics of random-walking agents on finite two-dimensional lattices is studied. In the model, the opinion is continuous, and both the lattice and the opinion can be either periodic or nonperiodic. At each time step, all agents move randomly on the lattice, and update their opinions based on those of neighbors with whom the differences of opinion are not greater than a given threshold. Due to the effect of repeated averaging, opinions first converge locally, and eventually reach steady states. As in other models with bounded confidence, steady states in general are those with one or more opinion groups in which all agents have the same opinion. When both the lattice and the opinion are periodic, however, metastable states can emerge, in which the whole spectrum of location-dependent opinions can coexist. This result shows that, when a set of continuous opinions forms a structure like a circle, unlike the typically used linear opinions, rich dynamic behavior can arise. When there are geographical restrictions in real situations, a complete consensus is rarely reached, and metastable states here might be one of the explanations for these situations, especially when opinions are not linear.