# Connection techniques summary

In this chapter the topic of connectors in MOSAICmodeling is summarized. When you combine equations to an equation system you have to select a connection policy (‘integrate’ or ‘encapsulate’) and you have to decide whether to use a connector or not – that has to be specified for each single connected element (being an equation or an equation system) .

The combination of the above options leads to the following diagram:

In the last example the differences of all four cases from A to D are demonstrated.

The equations:

(1) a = \beta \cdot x        (namespace: e1)

(2) a = \beta \cdot y        (namespace: e2)

The connectors:

(I)  a->b,  x->z                (may be applied on equation 1)

(II) a->c,  y->z                (may be applied on equation 2)

Case A (integrate+connectors):

The resulting equation system:

(3) e0.b = e0.\beta \cdot e0.z

(4) e0.c = e0.\beta \cdot e0.z

As you can see, the policy ‘integrate’ caused all variables to have the same namespace. The connectors renamed the variables a, x, and y. Please note that the x of the first equation and the y of the second equation became the same variable z in the final equation system. The final system contains four distinguishable variables (b, c, \beta, and z).

Case B (integrate):

The resulting equation system:

(5) e0.a = e0.\beta \cdot e0.x

(6) e0.a = e0.\beta \cdot e0.y

As you can see, the policy ‘integrate’ caused all variables to have the same namespace. The final equation system contains four distinguishable variables (a, \beta, x, and y).

Case C (encapsulate+connectors):

The resulting equation system:

(7) e0.b = e0e1.\beta \cdot e0.z

(8) e0.c = e0e2.\beta \cdot e0.z

As you can see, the policy ‘encapsulate’ caused the variables to have different namespaces. The connectors renamed the variables a, x, and y to be part of the top level namespace (e0), while the unconnected variables (\beta) got lower level namespaces (e0e1, e0e2). The final equation system contains five distinguishable variables (b, c, e0e1.\beta, eoe2.\beta, and z).

Case D (encapsulate):

The resulting equation system:

(9)   e1.a = e1.\beta \cdot e1.x

(10) e2.a = e2.\beta \cdot e2.y

As you can see, the policy ‘encapsulate’ caused the variables to have different namespaces. Each variable got the namespace of its original equation. The final equation system contains six distinguishable variables (e1.a, e1.\beta, e1.x, e2.a, e2.\beta, and e2.y).