Diversity and distribution of Asian Lejeuneaceae subfamily Ptychanthoideae

A synopsis is provided of 88 species in 17 genera currently recognized in Lejeuneaceae subfamily Ptychanthoideae sensu lato (including Nipponolejeunea) of Asia. Taxonomic novelties include Thysananthus flavescens (Hatt.) comb. nov. (for Mastigolejeunea flavescens (Hatt.) Mizut.), Spruceanthus macrostipulus (Steph.) comb. nov. (for Archilejeunea macrostipula (Steph.) Verd.) and the reduction of Platylejeunea Mizut. to synonymy under Lopholejeunea

A key to the New World species of holostipous Lejeuneaceae

A synopsis and key emphasizing vegetative characters are provided for the 967species (in 36 genera) of Lejeuneaceae with undivided underleaves recorded from the New World

Threatened bryophytes of the neotropical rain forest : a status report

Tropical deforestation, inevitably, leads to the local loss of bryophyte species. Recent studies show that the degree of species loss may vary considerably and depends on the scale or amount of habitat change that has occurred. Predictably, the shade epiphytes are most seriously affected by disturbance. An estimated 10% of the bryophyte species of neotropical rain forests are under threat. Based on data from recent monographs, a first list of 19 endangered and 27 rare species of these forests is presented. Critical areas for threatened species include Costa Rica and Panama, the Greater Antilles, the Chocó, southeastern Brazil, and parts of Amazonia. Protection of as much as possible of the remaining natural rain forest area seems the best approach to the conservation of the tropical bryophyte flora

Type classes for efficient exact real arithmetic in Coq

Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. Previously, we [Krebbers/Spitters 2011] provided a fast implementation of the exact real numbers in the Coq proof assistant. Our implementation improved on an earlier implementation by O'Connor by using type classes to describe an abstract specification of the underlying dense set from which the real numbers are built. In particular, we used dyadic rationals built from Coq's machine integers to obtain a 100 times speed up of the basic operations already. This article is a substantially expanded version of [Krebbers/Spitters 2011] in which the implementation is extended in the various ways. First, we implement and verify the sine and cosine function. Secondly, we create an additional implementation of the dense set based on Coq's fast rational numbers. Thirdly, we extend the hierarchy to capture order on undecidable structures, while it was limited to decidable structures before. This hierarchy, based on type classes, allows us to share theory on the naturals, integers, rationals, dyadics, and reals in a convenient way. Finally, we obtain another dramatic speed-up by avoiding evaluation of termination proofs at runtime.Comment: arXiv admin note: text overlap with arXiv:1105.275

MultivariateResidues - a Mathematica package for computing multivariate residues

We present the Mathematica package MultivariateResidues, which allows for the efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Multivariate residues appear in several contexts of scattering amplitude computations. Examples include applications to the extraction of master integral coefficients from maximal unitarity cuts, the construction of canonical bases of loop integrals and the construction of tree amplitudes from scattering equations.Comment: 7 pages, 2 figures, contribution to the proceedings of the 13th International Symposium on Radiative Corrections (RADCOR 2017