Boolean distance

As an example, consider the truth tables that are appropriate for the toggle switch with two variables, and the repressilator, shown in Table I. The associated A-cubes are shown in Fig. 3. The orientations on edges are determined using the following algorithm. First define the Hamming distance between two Boolean... 

An alternative way to think of Definition 9.14 is the following. Assume that we have n data points and N landmark points. Every data point induces an order on the landmark points just sort them with respect to their distances to that point. Every such ordering can be visualized as a path in the Hasse diagram of the Boolean lattice starting from the point nearest to the chosen data point, then proceeding to the union of the two closest ones, then on to the three closest ones, and so on. Now, the witness complex W(A, B) is the maximal abstract sirnplicial complex whose face poset is contained in the union of these paths. 

Along with AND, OR and NOT there are more operators for restricting a query. Using Boolean logic, the distance between search terms is not defined. In many cases it will be necessary to determine more precisely the proximity between two search terms in order to catch them in the same context. Other important proximity operators are listed below ... 

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