Phylogeny of Miliusa (Magnoliales: Annonaceae: Malmeoideae: Miliuseae), with descriptions of two new species from Malesia

The molecular phylogeny of Miliusa (Annonaceae) is reconstructed, with 27 (of ca. 50) species included, using a combination of seven plastid markers (rbcL exon, trnL intron, trnL-F spacer, matK exon, ndhF exon, psbA-trnH spacer, and ycf1 exon) constituting ca. 7 kb. In addition, two new species of Miliusa are described from the Malesian area: M. butonensis sp. nov. from Buton Island, Indonesia and M. viridifl ora sp. nov. from Papua New Guinea. The former is included in the molecular phylogenetic analysis. The reconstructed phylogeny corresponds well to the informal morphological grouping proposed earlier. A revised key to 13 Austro-Malesian species of Miliusa is provided

Singular Euler-Maclaurin expansion on multidimensional lattices

We extend the classical Euler-Maclaurin expansion to sums over multidimensional lattices that involve functions with algebraic singularities. This offers a tool for the precise quantification of the effect of microscopic discreteness on macroscopic properties of a system. First, the Euler-Maclaurin summation formula is generalised to lattices in higher dimensions, assuming a sufficiently regular summand function. We then develop this new expansion further and construct the singular Euler-Maclaurin (SEM) expansion in higher dimensions, an extension of our previous work in one dimension, which remains applicable and useful even if the summand function includes a singular function factor. We connect our method to analytical number theory and show that all operator coefficients can be efficiently computed from derivatives of the Epstein zeta function. Finally we demonstrate the numerical performance of the expansion and efficiently compute singular lattice sums in infinite two-dimensional lattices, which are of high relevance in solid state and quantum physics. An implementation in Mathematica is provided online along with this article

On the Efficient Computation of Large Scale Singular Sums with Applications to Long-Range Forces in Crystal Lattices

We develop a new expansion for representing singular sums in terms of integrals and vice versa. This method provides a powerful tool for the efficient computation of large singular sums that appear in long-range interacting systems in condensed matter and quantum physics. It also offers a generalised trapezoidal rule for the precise computation of singular integrals. In both cases, the difference between sum and integral is approximated by derivatives of the non-singular factor of the summand function, where the coefficients in turn depend on the singularity. We show that for a physically meaningful set of functions, the error decays exponentially with the expansion order. For a fixed expansion order, the error decays alge braically both with the grid size, if the method is used for quadrature, or the characteristic length scale of the summand function in case the sum over a fixed grid is approximated by an integral. In absence of a singularity, the method reduces to the Euler–Maclaurin summation formula. We demonstrate the numerical performance of our new expansion by applying it to the computation of the full nonlinear long-range forces inside a domain wall in a macro scopic one-dimensional crystal with 2 × 1010 particles. The code of our implementation in Mathematica is provided online. For particles that interact via the Coulomb repulsion, we demonstrate that finite size effects remain relevant even in the thermodynamic limit of macro scopic particle numbers. Our results show that widely-used continuum limits in condensed matter physics are not applicable for quantitative predictions in this case

‘Elite’ and ‘Excellence’ from the perspective of young people and their peers

info:eu-repo/semantics/acceptedVersio

Phylogeny of Miliusa (Magnoliales: Annonaceae: Malmeoideae: Miliuseae), with descriptions of two new species from Malesia – Corrigendum

Corrigendum: The third author has been added to paper No. 54 (http://dx.doi.org/10.5852/ejt.2013.5

Phylogeny of Miliusa (Magnoliales: Annonaceae: Malmeoideae: Miliuseae), with descriptions of two new species from Malesia – Corrigendum

Corrigendum: The third author has been added to paper No. 54 (http://dx.doi.org/10.5852/ejt.2013.5