Chain background

.. |a| image:: /files/equations/chain_X_subset.svg .. \mathbf{X'\subseteq X} .. \mathbf{\forall \, x,y \in X': x \perp y} .. |b| image:: /files/equations/chain_forall_perp.svg .. \mathbf{T(chain\ i, chain\ j) = \frac{\left |X' (chain\ i) \bigcap X'(chain\ j)\right |} {\left |X' (chain\ i) \bigcup X'(chain\ j)\right |}} .. |c| image:: /files/equations/chain_main.svg Chain: A subset |a|, with: |b| 1) Based on the Hasse diagram a start vertex "start" and a sink vertex "sink" is to be selected. 2) Note: start < sink, i.e. the chain module is searching for paths upwards. 3) Furthermore a selection is to be done, how many vertices should be in a chain: The corresponding variable is called maxch. 4) If “start” and "sink" and "maxch" are appropriately selected chains are identified. The result is a matrix where chain i is compared with chain j and its similarity due to the Tanimoto-Index is calculated: |c| 5) The matrix T is also displayed as bar diagram. 6) Chains which are of interest can be selected and objects belonging to the selected chain are displayed.