Global matching function

As discussed by Andersen [9, 10] for muffin-tin orbitals, the locally regular components y defined in each muffin-tin sphere are cancelled exactly if expansion coefficients satisfy the MST equations (the tail-cancellation condition) [9, 384], The standard MST equations for space-filling cells can be derived by shrinking the interstitial volume to a honeycomb lattice surface that forms a common boundary for all cells. The wave function and its normal gradient evaluated on this honeycomb interface define a global matching function %(cr). 

The coefficients ft = Sy are the expansion coefficients of the global matching function (cr) = Jft, l nl (G ) l - Defining t = —SiSUjy Sft which reduces to t = —SC l for square matrices [281], EIIV takes the standard MST form I — tg, without implying inversion of a rectangular matrix. Using these closed forms, the coefficients ft and y are related by... 

For an exact solution, the external function ijrv would be identical to the global matching function on each interface. An alternative algorithm can be based on fitting a linear combination of basis functions in each cell to %, which is uniquely determined. The VCM equations for an orbital basis at fixed energy reduce to [282]... 

These difficulties with the linearized VCM can be resolved by using the extended functional, defined over the global matching surface a in Subsection 7.2.4, above,... 

Before we discuss the solution in the inner part of the potential, let us first consider the matching conditions at the dividing surface. Suppose a solution r, 7) for i < s is found. The global wave function in the... 

Through this method, it is possible to find structural (and, presumably, functional) relationships between proteins in cases that may lack overt sequence similarity. The resultant alignment need not be global matches may be between individual domains of different proteins. 

Maxwell theory, soliton flows are Hamiltonian flows. Such Hamiltonian functions define symplectic structures6 for which there is an absence of local invariants but an infinite-dimensional group of diffeomorphisms which preserve global properties. In the case of solitons, the global properties are those permitting the matching of the nonlinear and dispersive characteristics of the medium through which the wave moves. 

Figure 5 (a) Stimulated photon echo signal of the azide ion (N3 ) in D2O at 2043 cm-1 as a function of r and T for the — kj + k2 + k3 (gray surface) and the +ki — k2 + k3 (white surface) phase matching directions, (b) Representative traces for four selected values of T. The solid lines represent a global fit of all the scans to the model correlation function Equation (20). (From Ref. 41.)... 

Each member in an ensemble uses a local aggregation function (such as average) to generate a schema matching similarity measure from the similarity measures of the attribute correspondences. Local similarity measures can then be aggregated using a global similarity measure (e.g., max) to become the ensemble similarity... 

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