Vector sequences which are stationary with respect to polynomial hypergroups arise in various fields, such as stochastic processes and difference equations. In this paper, we discuss analytic properties of these sequences, namely the representation and complexification of the vector sequence.

Let GR denote the real points of a connected complex reductive algebraic group defined over R). (For the basic results on cells below, this class of groups is unnecessarily restrictive. But we shall need the assumption when we discuss unipotent representations below.) Let gR denote the Lie algebra of GR and write g for the complexification of gR. Let KR denote a maximal compact subgroup in G, a...

Consumers’ attention limitations give firms incentives to manipulate prospective buyers’ allocation of attention. This paper models such attention manipulation and shows that it limits the ability of disclosure regulation to improve consumer welfare. Competitive information supply, from firms competing for attention, can reduce consumers’ knowledge by causing information overload. A single firm...

Complex systems such as ecosystems, electronic circuits, lasers or chemical reactions can be modelled by dynamical which typically experience bifurcations. Transients suffer extremely long delays at the vicinity of bifurcations and it is also known that these transients follow scaling laws bifurcation parameter gets closer value in deterministic systems. The mechanisms involved local are well-k...

This paper focuses on parameter search for multi-agent based models using evolutionary algorithms. Large numbers and variable dimensions of parameters require a search method which can efficiently handle a high dimensional search space. We are proposing the use of complexification as it emulates the natural way of evolution by starting with a small constrained search space and expanding it as t...

An appropriate but challenging goal for evolutionary computation (EC) is to evolve systems of biological complexity. However, specifying complex structures requires many genes, and searching for a solution in such a highdimensional space can be intractable. In this paper, we propose a method for finding high-dimensional solutions incrementally, by starting with an initial population of very sma...

We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of the Aand B-models which involves a doubling of coordinates, and can be understood as a complexification of the Poisson σ-model underlying these. In the flat space limit the construction contains models obtained by twisting an N=2 supersymmetric σ-model on Hull’s doubled geometry. The curved space gen...