it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

Abstract We initiate a study of the Euclidean distance degree in context sparse polynomials. Specifically, we consider hypersurface $$f=0$$ f = 0 defined by polynomial f that is general given its support, such support contains origin. show equals mixed ...

Although the voxel-based morphometry (VBM) has been widely used in quantifying the amount of gray matter of the human brain, the optimal amount of registration that should be used in VBM has not been addressed. In this paper, we present a novel multi-scale VBM using the weighted spherical harmonic (SPHARM) representation to address the issue. The weighted-SPHARM provides the explicit smooth fun...

A standard method to perform skeletonisation is to use a distance transform. Unfortunately such an approach has the drawback that only the Symmetric axis transform can be computed and not the more practical smoothed local symmetries or the more general symmetry set. Using singularity theory we introduce an extended distance transform which may be used to capture more of the symmetries of a shap...