Assignment flows denote a class of dynamical models for contextual data labelling (classification) on graphs. We derive a novel parametrisation of assignment flows that reveals how the underlying information geometry induces two processes for assignment regularisation and for gradually enforcing unambiguous decisions, respectively, that seamlessly interact when solving for the flow. Our result enables to characterise the dominant part of the assignment flow as a Riemannian gradient flow with respect to the underlying information geometry. We consider a continuous-domain formulation of the corresponding potential and develop a novel algorithm in terms of solving a sequence of linear elliptic partial differential equations (PDEs) subject to a simple convex constraint. Our result provides a basis for addressing learning problems by controlling such PDEs in future work.

This paper provides a survey of the applications of evolutionary algorithms in macroeconomic models. Discussion is organized around the issues related to stability of equilibria, equilibrium selection, transitional dynamics, and the long-run evolutionary dynamics different from rational-expectations equilibrium outcomes. The survey also discusses criteria that can be used to evaluate the performance and usefulness of evolutionary algorithms in the macroeconomic context.