## 3 Conceptual Discovery Framework
### Work Transference Network Model  
As described above, we confirmed that a TWTM can be constructed for each workflow instance by combining the corresponding TWC and TWT. At this stage, one step remains for amalgamating all TWTMs into the workflow transference network model (WTNM) that we ultimately aim to discover. A WTNM reveals the real form of the work transference relationships among the performers after a lapse of a certain time since deploying the corresponding workflow model and it is discovered from the event logs shaped in the form of a workflow warehouse. As shown on the right side of Figure 2, as the final outcome of the framework, a WTNM has the formal and graphical structure of a directed graph (digraph) model to represent the performers and work transferences among them. Each node represents a performer, and each ordered pair of nodes (or a directed edge) represents a work transference relationship. Edges contain the intermediate activities and their occurrences; for example, the performer \(p_{2}\) has completed the work items of activity C 20 times and has transferred those outcomes to the performer \(p_{11}\).  
As a formal representation of such knowledge regarding the work transferences, we define the WTNM through Definition 6. Using the formal notation of \(\sigma(=\sigma_{i}\cup\sigma_{o})\), we define the work transference relationships, in which the two nodes of a directed edge represent the predecessor and successor of the work items. In addition, we define the formal notation of \(\psi(=\psi_{i}\cup\psi_{o})\) for the work association relationships by labelling each directed edge with the activity names and occurrences corresponding the work items that are transferred to the successor and received from the predecessor of the corresponding work transference relationship concurrently.  
**Definition 6** (Work Transference Network Model).: _A work transference network model is formally defined as \(\Lambda^{R}\) = (\(\sigma\), \(\psi\), \(F_{r}\), \(T_{o}\)), over a set \(\mathbf{P}\) of performer nodes, \(\eta_{p}^{\tau[\cdot,\phi]}\), and a set \(\mathbf{A}\) of activity nodes, \(\eta_{\alpha}^{\tau[\cdot,\phi]}\), in a set of event traces logged from enacting the underlying workflow model, where:_  
* \(F_{r}\) _is a coordinators or a coordinator-group linked from some external work transference networks;_
* \(T_{o}\) _is a coordinators or a coordinator-group linked to some external work transference networks;_
* \(\sigma=\sigma_{i}\cup\sigma_{o}\) _'Work Transferences */_
* \(\sigma_{i}:\mathbf{P}\longrightarrow\wp(\mathbf{P})\) _is a multi-valued function mapping a performer to its set of immediate predecessors;_
* \(F_{r}\) _is a coordinators or a coordinator-group linked to some external work transference networks;_
* \(T_{o}\) _is a coordinators or a coordinator-group linked to some external work transference networks;_
* \(\sigma=\sigma_{i}\cup\sigma_{o}\) _'Work Transferences */_
* \(\sigma_{i}:\mathbf{P}\longrightarrow\wp(\mathbf{P})\) _is a multi-valued function mapping a performer to its set of immediate predecessors;_
* \(F_{r}\) _is a coordinators or a coordinator-group linked to some external work transference networks;_  
\(\sigma_{o}:\mathbf{P}\longrightarrow\wp(\mathbf{P})\) is a multi-valued function mapping a performer to its set of immediate successors;
* \(\psi=\psi_{i}\cup\psi_{o}\) /
* Work Associations */
* \(\psi_{i}:(\mathbf{P}\times\mathbf{P})\longrightarrow[\wp(\mathbf{A}),\mathbb{N}]\) is a multi-valued function returning a paired list of receiving work items and their occurrences on ordered pairs of performers, \((\sigma_{i}(p),p)\), \(p\in\mathbf{P}\), from \(\sigma_{i}(p)\) to \(p\);
* \(\psi_{o}:(\mathbf{P}\times\mathbf{P})\longrightarrow[\wp(\mathbf{A}),\mathbb{N}]\) is a multi-valued function returning a paired list of transferring work items and their occurrences on ordered pairs of performers, \((p,\sigma_{o}(p))\), \(p\in\mathbf{P}\), from \(p\) to \(\sigma_{o}(p)\);