Semigroup Expansions for Autobiographic

Semigroup Expansions for Autobiographic Agents

Regularized traces and Taylor expansions for the heat semigroup

We study heat trace asymptotics for Schrödinger operators using commutator expansions due to Agmon-Kannai and Melin. Closed formulas for coefficients of the scattering phase asymptotics in the short-range case are presented. In the long-range case, following Melin, we consider regularized traces and compute coefficients in their asymptotic expansions. These can be thought of as heat invariants ...

On Finitely Presented Expansions of Computably Enumerable Semigroups

Every computable universal algebra has a finitely presented expansion, but there are examples of finitely generated, computably enumerable universal algebras with no finitely presented expansions. It is natural to ask whether such examples can be found in well-known classes of algebras such as groups and semigroups. In this paper, we build an example of a finitely generated, infinite, computabl...

Geometric Semigroup Theory

Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups and automata lead to simplifications of the graphs on which the corresponding finite semigroups act. We show in particular that every finite semigroup can b...

Comparing Different Control Architectures for Autobiographic Agents in Static Virtual Environments

This paper highlights the effectiveness of autobiographic memory applied to an autonomous agent from an Artificial Life perspective. A virtual experimental based approach deals with different implementations of control architectures for autobiographic agents, including detailed measurements of the agent’s lifetimes compared with a Purely Reactive agent, running in two distinct static environmen...