## 3 Results
### Congruence Matrices  
The congruence matrices present multidomain information by highlighting the unmapped indirect influences through logical debugging. The environment congruence matrix (\(eC_{mmn}\)) indicates the relationships of the environments that allocate the same activity or a sequence of dependent activities (Figure 7). When the relationship between the two environments has a dark blue indicator (see color legend in Table 2), it means that the physical relationship is justified by one or more of the activities that pass through these environments to be carried out. When a relationship is depicted in light blue, it means that the designations of these environments can be reallocated and replaced by the activities that interact with the activities in adjacent rooms. The red color indicates that there is potential for reallocation between uses, so it refers to contiguous spaces or spaces that are connected by a circulation process. Indications in red appear in other support activities, in which the environments where the middle activities are carried out are located far from the environment where the end activity takes place. For example, the cleaning activities exhibited a series of red indicators because the storage of materials and the parking of cleaning carts were located far from the emergency department area (matrix in S10). Figure 6: Detailed relationship matrix (\(R_{nm}\)) of the medical activities in AED (see full matrix in S8). In a context in which, when reallocating the uses of environments, the congruence indices do not fall or improve--that is, the number of predicted and fulfilled relations remains the same or increases, or the number of relations not attended to remains the same or decreases--this means that the reallocation was successful without the need for changes in the building design. In this context, the manager can explore changes in use in the environments in which the need for close environmental relationships were not detected (light blue indications). This can be used to test changes to the existing mapping, simulating alternative allocation scenarios to the existing one. However, if the congruence indices drop when reallocating the uses of the environments, this may mean that there is a need for intervention in the design. In this second context, mapping becomes a PDE tool that supports the decision to start a design and guides the definition of change requirements. Furthermore, the congruence indices can be used as a parameter to support the decision to evaluate and the decision to accept a design proposal. The activity congruence (\(aC_{mn}\)) indicates the interactions of the activities that can share the same environment while they are being performed (Figure 8). This matrix is a complementary instrument that can be used to guide the facility manager in defining the potential reallocations of activities. It presents the relationships between the activities that are not indicated in the activity map (\(A_{nm}\)), but which potentially exist due to the crossing of relations, as logically processed by the application. Figure 7: Detailed environment congruence matrix (eCmm), highlighting the relations between AED environments. Rows have been reordered to group department rooms (see the full matrix in S9). Figure 8: Detailed activity congruence matrix (\(aC_{mn}\)), highlighting the relationships between the medical activities in ESs and other activities. Rows have been reordered to show the other activities that are related to the medical activities (see the full matrix in S10). In the case that has been presented, the unattended potential relationships link the clinical activities to the support activities. These are indications that need to be analyzed and validated. The solution is not necessarily linked to the change in the allocation but it indicates that there are interfaces that have not been considered in the mapping, but which are possible because they occur in a common environment.