Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems

Motivated by the theory of Painlev\'e equations and associated hierarchies, we study non-autonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of Hamiltonian vector fields can be deformed to a time-dependent Lie algebra of Frobenius integrable vector fields spanning the same distribution as the original algebra. The results are applied to quasi-St\"ackel systems.Comment: 14 pages, no figures. We repaired Example 5 and also made some minor amendments in the tex

Modularity and Openness in Modeling Multi-Agent Systems

We revisit the formalism of modular interpreted systems (MIS) which encourages modular and open modeling of synchronous multi-agent systems. The original formulation of MIS did not live entirely up to its promise. In this paper, we propose how to improve modularity and openness of MIS by changing the structure of interference functions. These relatively small changes allow for surprisingly high flexibility when modeling actual multi-agent systems. We demonstrate this on two well-known examples, namely the trains, tunnel and controller, and the dining cryptographers. Perhaps more importantly, we propose how the notions of multi-agency and openness, crucial for multi-agent systems, can be precisely defined based on their MIS representations.Comment: In Proceedings GandALF 2013, arXiv:1307.416