The architecture of Permian glossopterid ovuliferous reproductive organs

A historical account of research on glossopterid ovuliferous reproductive structures reveals starkly contrasting interpretations of their architecture and homologies from the earliest investigations. The diversity of interpretations has led to the establishment of a multitude of genera for these fossil organs, many of the taxa being synonymous. We identify a need for taxonomic revision of these genera to clearly demarcate taxa before they can be used effectively as palaeobiogeographic or biostratigraphic indices. Our assessment of fructification features based on extensive studies of adpression and permineralized fossils reveals that many of the character states for glossopterids used in previous phylogenetic analyses are erroneous. We interpret glossopterid fertiligers to have been borne in loose strobili in which individual polysperms represent fertile cladodes of diverse morphologies subtended by a vegetative leaf or bract. Polysperms within the group are variously branched or condensed with ovule placement ranging from marginal to abaxial, in some cases occurring on recurved branchlets or in cupule-like structures. Glossopterid polysperms of all types are fringed by one or two ranks of wing-like structures that may represent the remnants of megasporophylls that were, ancestrally, developed on the fertile axillary shoot. Glossopterid fertiligers have similarities to the condensed bract/ovuliferous scale complexes of conifer cones, but comparisons with Mesozoic seed-ferns are hindered by insufficient data on the arrangement and homologies of the ovulebearing organs of the latter group. Nevertheless, glossopterid polysperms differ from the ovuliferous organs of Mesozoic seed-ferns by longitudinal versus transverse folding, respectively.Also funded by the National Science Foundation [project #1636625]; University of the Witwatersrand; Rhodes University; the DST-NRF Centre of Excellence in Palaeosciences and the NRF African Origins Platform [UID: 98822]</p

The geometric dimension of some small configurations

Recently, Jungnickel and Tonchev (Des Codes Cryptogr, doi:10.1007/s10623-012-9636-z, 2012) introduced new invariants for simple incidence structures D, which admit both a coding theoretic and a geometric description. Geometrically, one considers embeddings of D into projective geometries Π = PG(n, q), where an embedding means identifying the points of D with a point set V in Π in such a way that every block of D is induced as the intersection of V with a suitable subspace of Π. Then the new invariant, the geometric dimension geomdimq D of D, is the smallest value of n for which D may be embedded into the n-dimensional projective geometry PG(n, q). It is the aim of this paper to discuss a few additional general results regarding these invariants, and to determine them for some further examples, mainly some small configurations; this will answer some problems posed in (Des Codes Cryptogr, doi:10.1007/s10623-012-9636-z, 2012)