Building on recent work by others who introduced RBFs into level sets for structural topology optimisation, we introduce the concept into active models and present a new level set formulation able to handle more complex topological changes, in particular perturbation away from the evolving front. This allows the initial contour or surface to be placed arbitrarily in the image. The proposed leve...

We extend the recently proposed order-N algorithms for calculating linear- and nonlinear-response functions in time domain to the systems described by nonorthonormal basis sets.

Potential-density pair basis sets can be used for highly efficient N-body simulation codes, but they suffer from a lack of versatility, i.e. a basis set has to be constructed for each different class of stellar system. We present numerical techniques for generating a biorthonormal potential-density pair basis set which has a general specified pair as its lowest order member. We go on to demonst...

FMRI modelling requires flexible haemodynamic response function (HRF) modelling, with the HRF being allowed to vary spatially and between subjects. To achieve this flexibility, voxelwise parameterised HRFs have been proposed; however, inference on such models is very slow. An alternative approach is to use basis functions allowing inference to proceed in the more manageable General Linear Model...

We study the relationship between certain Gröbner bases for zerodimensional radical ideals, and the varieties defined by the ideals. Such a variety is a finite set of points in an affine n-dimensional space. We are interested in monomial orders that “eliminate” one variable, say z. Eliminating z corresponds to projecting points in n-space to (n − 1)-space by discarding the z-coordinate. We show...

Different types of Gaussian basis sets for accurate LCAO calculations are discussed. For calculations designed to recover a substantial portion of the correlation energy, we suggest the use of basis sets comprising natural orbitals from correlated calculations on the atoms. These basis sets have proven to be very efficient in accounting for large fractions of the molecular correlation energy. F...

An accurate description of the electrical properties of atoms and molecules is critical for quantitative predictions of the nonlinear properties of molecules and of long-range atomic and molecular interactions between both neutral and charged species. We report a systematic study of the basis sets required to obtain accurate correlated values for the static dipole (ar,), quadrupole ((Ye), and o...

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be...

The quantitative phase space similarities between the uniformly mixed ensembles of eigenstates, and the quasiclassical Thomas–Fermi distribution, are exploited in order to generate a nearly optimal basis representation for an arbitrary quantum system. An exact quantum optimization functional is provided, and the minimum of the corresponding quasiclassical functional is proposed as an excellent ...