In Spivak's work, dynamical systems are described in terms of their inputs and outputs in a pictorial way using an operad of wiring diagrams. Each dynamical system is a box with certain inputs and outputs, and multiple dynamical systems are linked together using wiring diagrams, which describe how the outputs of one dynamical system to the inputs of another. By describing dynamical systems in this way, we can decompose a large dynamical system as a collection of smaller, simpler dynamical… Expand

Two forms of semantics for open Petri nets are described using symmetric monoidal double functors out of pen(Petri), including an operational semantics and a reachability semantics that simply says which markings of the outputs can be reached from a given marking of the inputs.Expand

Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way.… Expand

In some bicategories, the 1-cells are `morphisms' between the 0-cells, such as functors between categories, but in others they are `objects' over the 0-cells, such as bimodules, spans, distributors,… Expand

We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently… Expand