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This paper describes a model-based flow for the development of Interlocking Systems. The flow starts from a set of specifications in Controlled Natural Language (CNL), that are close to the jargon adopted in by domain experts, but fully formal. From the CNL, a complete SysML specification is extracted, leveraging various forms of diagrams, and enabling automated code generation. Several formal verification methods are supported. A complementary part of the flow supports the extraction of formal properties from legacy Interlocking Systems designed as Relay circuits. The flow is implemented in a comprehensive toolset, and is currently used by railway experts.

We introduce a notion of noncommutative Poisson-Nijenhuis structure on the path algebra of a quiver. In particular, we focus on the case when the Poisson bracket arises from a noncommutative symplectic form. The formalism is then applied to the study of the Calogero-Moser and Gibbons-Hermsen integrable systems. In the former case, we give a new interpretation of the bihamiltonian reduction performed in [3]., Comment: 23 pages

The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory associative geometry. We argue that this formalism sheds a new light on some classic solution methods in the theory of finite-dimensional integrable dynamical systems., Comment: Review article, 45 pages. To appear in Journal of Geometry and Physics

We introduce a family of quivers $Z_{r}$ (labeled by a natural number $r\geq 1$) and study the non-commutative symplectic geometry of the corresponding doubles $\mathbf{Q}_{r}$. We show that the group of non-commutative symplectomorphisms of the path algebra $\mathbb{C}\mathbf{Q}_{r}$ contains two copies of the group $\mathrm{GL}_{r}$ over a ring of polynomials in one indeterminate, and that a particular subgroup $\mathcal{P}_{r}$ (which contains both of these copies) acts on the completion $\mathcal{C}_{n,r}$ of the phase space of the $n$-particles, rank $r$ Gibbons-Hermsen integrable system and connects each pair of points belonging to a certain dense open subset of $\mathcal{C}_{n,r}$. This generalizes some known results for the cases $r=1$ and $r=2$., 29 pages. v3: keeps some introductory material left out of the journal version

We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discussed., 15 pages, no figures