# Integrating ISA and Part-of Domain Knowledge into Process Model Discovery
## Appendix A Experimental Comparison
The box containing the symbol “#” indicates the entry point of the model, while the “$” box represents the ending (final) action of the model.  
A qualitative analysis of the models above reveals the additional aspects and problems to be reported. In the following, we will analyze the most notable issues.  
The model obtained by the alpha miner (Figure 11) has a number of nodes that are only marginally higher than the SIM model, but the presence of many edges between the nodes/transitions/activities involved, and the constraints introduced by the syntax of Petri nets (a transition/activity is activated only when all the incoming places contain a token) make it extremely difficult to identify the therapeutic paths. While the understanding of the initial phases (\(CT\) and \(BT\), executed in parallel, with their output places enabling _Eval_) is straightforward, the identification of other paths is not. For example, if we aim to understand the contexts where the activity \(ASA\) is performed, we need to identify and list all the execution steps able to put a token in all the four \(ASA\) input places to activate it. Starting with the first activity #, an AND split generates two tokens, activating both \(CT\) and \(BT\). When enabled, \(BT\) fires a token in a place, which is input to _Eval_, while \(CT\) fires two tokens: one as input to _Eval_, and one as input to \(ASA\). _Eval_ is then activated, firing four tokens in its AND split output. Two of them end up as input to \(ASA\), and one can activate (XOR) \(ASA\) or \(MR\)\(DW\). In the first case, all the above steps generate the simple _Eval_--\(ASA\) sequence; in the second case, it is necessary to study what happens after the activation of \(MR\)\(DW\). Here, \(MR\)\(DW\) fires a token in a place which, together with the other input place, already containing a token previously fired by _Eval_, activates the \(ECG\) activity. The latter fires a token that activates \(MR\), which, in turn, generates two tokens that, in combination with the previously fired ones, activate \(ASA\). Following these steps, we can conclude that \(ASA\) can be executed in a second context, described by the _Eval_--\(MR\)\(DW\)-\(ECG\)-\(MR\)-\(ASA\) sequence. This level of complication, and the need to simulate all the possible execution steps to retrieve the treatment paths, requires the central role of an expert analyst, since a physician would not be able to read and identify the procedures hidden in the model in Figure 11. A process model such as the one in Figure 15, on the other hand, makes the interpretation task a much easier operation. Furthermore, the model in Figure 11 shows that this miner, with the default settings, is not able to integrate the _r_-\(TPA\) activity in any execution context, thus avoiding the user's obtaining information about the therapeutic steps to be performed while administering this life-saving treatment.  
The model produced by the fuzzy miner (Figure 11) is much more intuitive and easier to read than the above one (Figure 11). However, it presents some activities that cycle on themselves and some cyclical paths that are difficult to explain from a medical point of view. For example, a cycle between \(ECG\) and _r_-\(TPA\) can be seen in the lower right part of the model, suggesting that this therapy can be administered multiple times to the same patient. The same happens in the _ASA-AngioCT-TPA ia-ECG-MR-ASA_ cycle. Thromolysis therapies are administered to the patient only once, given their severe counter-indications, such as the risk of hemorrhagic episodes. Administering a single _TPA ia_ is allowed after an ineffective _r-TPA_, but repeating the same TPA treatment is not allowed.  
The model generated by the heuristic miner (Figure A3) has strengths and weaknesses that are similar to that of the model illustrated above (Figure A2). The model is simple to read and interpret. However, even in this case, there are cycles that are not allowed, from the medical point of view, such as _ECG-r-TPA-ECG_. In addition, arcs allow some therapeutic paths to return to the _ECG_ activity, potentially re-starting the same therapy several times. As a final remark, path #-_CT-ASA_ suggests that some therapies should be started before the patient has been evaluated by a neurologist (_Eval_).  
The ILP model (Figure A4) shares the difficulties of interpretation that have already been seen in the process generated by the alpha miner (Figure A1). Additionally, in this case, the analyst must simulate the evolution of the tokens across the model, in order to extract the therapeutic paths hidden in the complexity of the high number of edges. Furthermore, the model describes situations that are not acceptable from the medical point of view. For example, after the start activity (#), an AND split generates two outgoing tokens. Among these, one activates the _BT_ activity, while the other one activates a single activity (XOR split), chosen from _CT_, _r-TPA_, and _MR_. This means that a patient can undergo an _r-TPA_ without neurological evaluation (_Eval_) and with no preliminary evaluation tests or preparation activities. Problems also arise from the structural point of view, since the model is not sound. For example, after executing the activity start (#) and the AND split that follows, the token activating _BT_ can continue to travel inside the paths described by the model. At the same time, the second token can cross the path _r-TPA_\(\rightarrow\)\(ASA\rightarrow\)\(Rehab\rightarrow\)\(\$\) to enter the final place (\(E\)), ending the treatment process for the given patient.