Meshless Methods in Conformation Dynamics by Weber M.

By Weber M.

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By Weber M.

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Because of the convexity of co(X ), finally, a vertex A ∈ v(FA ) is characterized by the fact that a facet of the corresponding simplex σnC includes a facet of co(X ). Therefore, the choice of such facets is unique (except for permutation) if and only if co(X ) is a simplex, see also Figure 3. e. the initial guess χdisc = XA is feasible. 38 3 ROBUST PERRON CLUSTER ANALYSIS ii) A ∈ v(FA ) is unique. e. for every i = 1, . . , nC there is an l ∈ {1, . . , s} with maximal degree of membership χdisc (l, i) = 1.

1 Metastability vs. 3. In equation (13) the propagator P τ is constructed according to a short-time Hamiltonian dynamics (MD) simulation, which leads to L2 (π)-self-adjointness of P τ . The time dependence of P τ is not very realistic, however. In a realistic model of molecular transition probabilities in a heat bath, one would expect that the underlying Markov process is homogenous and that the famous Chapman-Kolmogorov equation P (τ1 +τ2 ) = P τ2 ◦ P τ1 (47) for different simulation lengths τ1 , τ2 > 0 is satisfied.

In SOBM the Kohonen particles become centers of boxes for a discretization of Ω. The problem of this method is to keep balance between small overlap of these boxes and preferably complete overlay of the configuration space, which works hardly for high-dimensional spaces. All these methods use meshes (boxes, intervals) in some way, which can cause the curse of dimensionality. g. [79, 45, 115, 80]. In the last decade meshless particle methods have become of more and more interest, see Li and Liu [79].

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