8 Diagrams

Let $V$ be the space of infinitely differentiable functions $f:(0,\mathrm{\infty })\to 𝐂$. Let $u\in V$ be the input, $y\in V$ be the output. A diagram is a graph built up from vertices $u,y$ and others chosen from

which are connected by directed edges, drawn as arrows.

(1) $u$ is the input and $y$ is the output. The vertices $u$ and $y$ have degree one; whereas all other vertices have degree two or three with one or two arrows pointing into the vertex, and one or two pointing out.

(2) The graph is simple, so there are no loops or multiple edges. All the vertices lie on some directed path consisting of consecutive arrows from $u$ to $y$.

(3) If the diagram contains a circuit, then we say that there is feedback.