By using a first order Markov Chain, P [D1 U2 D3 U4]), for example, is computed as follows: where,, and.
This last functionality can for example be used to compute dot products, where it is important not to perform computations twice on overlapping regions.
The first two examples were chosen to demonstrate the algorithm's accuracy against the exact solution, which for these examples can be computed using the master equation or the infinitesimal generator matrix [ 1].
Can average directionality be computed?
We often require a scalar value for the entire matrix or vector, and one example that can be computed is the so-called matrix or vector norm.
This matrix square root can be computed, for example, with Cholesky decomposition.
where P(δ i ) is probability associated with knowledge unit δ i and n is the number of KUs in Δ. Global mastery of the domain Δ can be computed, for example, as: frac{sum P delta_{i})}{n} (8).
This (mathsf{hocolim}_I) can be computed for example by Proposition 9.13, and then it is clear that it lies in any triangulated subcategory in ({text {Ho}}(mathsf{Ind},mathcal {C})) that contains ({text {Ho}}(mathsf{Ind},mathcal {C})) and is closed under all sums.
This way, the ultimate capacity limits can be computed (see, for example, [4, 5]).
