By Weber M.
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9. Only the positivity constraint may be violated. 9 provides very good solutions, which are almost feasible. Therefore, further investigations are not neccessary. But in order to be mathematically rigorous, a feasible solution is derived in the following. From infeasible to feasible solutions. We now aim at a projection algorithm from an arbitrary matrix A ∈ IRnC ×nC to a feasible transformation matrix A. 7, theoretically, we can restrict our search of transformation matrices to vertices of the feasible set A ∈ v(FA ).
60 is projected to IR2 . The I1 -optimal simplex σ3 spanned by the vertices v1 , . . , vnC is shown. 8 provides X(ind(1), :) as an approximation of v1 = A−1 (1, :). we get vj = X(ind(j), :) , j = 1, . . , nC . If the maximality assumption nearly holds, see Fig. 2, then the following routine  finds an index mapping for an approximation of the simplex σnC . Its “vertices” are determined successively among the rows of X: Once one has found a vertex subset, the hyperplane of minimal dimension is constructed, which includes these vertices.
5 . 99 In this matrix the second row can be seen as a transition state. e. 49. The bad estimation is implied by the fact that the transition state (2nd row of P ) cannot be assigned to one of the other two states keeping small. In conformation dynamics the occurrence of transition states is generic. In fact, this observation was the reason for introducing a “soft”-clustering method, see . The MINVAL indicator is necessary but not sufficient for fixing nC . Further investigations are essential.
Meshless Methods in Conformation Dynamics by Weber M.