ABC, an efficient heuristic method based on swarm intelligence, is used to select the optimal subset of dimensions from the original high-dimensional data while retaining a subset that satisfies the defined objective.
For a given set of geometric parameters defining the product shapes, parameter relationships (i.e., geometric constraints), and parameter ranges, a particle tracing (PT) algorithm is proposed to find product shapes that satisfy the defined geometric constraints in the shape space.
After no more markers could be inserted that satisfied the criteria defined above, and the algorithms did not reveal a more likely marker order from the reduced data, the full data set was used to finalize the set of markers on the multi-point map, then order and position those markers.
CB is a choice function (i.e. satisfies the defining criteria for a choice function given in section 3.1) if and only if ≽ is complete and acyclical.
So, the process arising in the context of this model, satisfies the defining conditions of the generalized Waring process.
Using the intertwining relations of differential operators (i.e., differential operators satisfy the defining relations of the Lie algebra (see [20])), we overcome the noncommutative properties between functions.
Given an estimated essential matrix it is possible to investigate whether a set of corresponding image points satisfy the defining epipolar constraint in image plane.
In our example, both P1 and N1 have degree 3. A case C is said to 'display' a pattern, or to be 'covered' by it, if the corresponding intensity levels of the gene expressions satisfy the defining conditions of that pattern.
This requirement is practically not satisfied for the defined standards.
One service can represent multiple traffic flows in the network as long as those traffic flows can satisfy the conditions defined in the properties set.
