Development and germination of Sandersonia aurantiaca (Hook.) seeds : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Plant Biology and Biotechnology at Massey University

Sandersonia aurantiaca (Hook.) has recently become an important horticultural crop through its economic value for export of its cut flowers and tubers. Little information however is available on seed structure, morphology, development and propagation. The main objectives of this study were to investigate the pattern of seed development, to find satisfactory methods of improving the seed germination and to assess possible mechanisms of seed dormancy of Sandersonia aurantiaca (Hook.). Seed development was investigated by fixing plant material in FAA solution, embedding in paraffin, and staining with safranin-fast green. A series of sections were examined and photographed under a microscope. Both embryo and endosperm development in Sandersonia show close similarity to development in Allium fistulosum (Alliaceae). Embryo development passes through early globular, late globular, elongated spheroidal and linear embryo development stages. Endosperm development conforms to the Nuclear type. Freely-growing walls between the endosperm nuclei may be associated with the embryo sac wall as projections. The structure of the mature seeds is very similar to that of Iris (Iridaceae) seeds. The small, linear embryo is embedded in the endosperm which constitutes most of the seed volume. Such small, linear embryos may be one reason for embryo dormancy in Sandersonia seed. A special structure (a conical or cylindrical protuberance) is observed in the inner part of the seed coat, which may combine with a lignified layer (and perhaps including the endosperm) to contribute to the coat-imposed domancy in this species. Eighty five treatments were firstly used to improve the germination percentage of Sandersonia seed. Only the treatment in which seeds scarified firstly with sandpaper for 1 min and then nicked near the radicle end showed increased germination from 0 to 10.6% by 30 days, at 20°C. Based on this result, 31 new treatment methods were designed in germination experiment 2. Water uptake patterns, allelopathic effect on lettuce seeds and embryo rescue of Sandersonia seed were also studied for assessing the possible mechanisms of dormancy. The findings of the present study suggest that the Sandersonia seeds have double dormancy. The dormancy mechanism is located in both the seed coat and the embryo and it consists of at least two steps that must be activated in sequence before germination can occur. The first step can be activated prematurely by scarifying and nicking the seeds, thus allowing the seed coat to become permeable to water, oxygen or to reduced mechanical restriction. The second step can be activated directly GA3 which stimulates embryo growth. This germination-promoting technique has great potential for Sandersonia for improvement of the germination percentage of seeds from 0 to about 70%, but development on a commercial scale needs further studies

Schlichting's Theorem for Approximate Subgroups

We prove Schlichting's theorem for approximate subgroups: if $\mathcal{X}$ is a uniform family of commensurable approximate subgroups in some ambient group, then there exists an invariant approximate subgroup commensurable with $\mathcal{X}$

Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids

Topological crystalline insulators (TCIs) are nontrivial quantum phases of matter protected by crystalline (and other) symmetries. They are originally predicted by band theories, so an important question is their stability under interactions. In this paper, by directly studying the physical bulk properties of several band-theory-based nontrivial TCIs that are conceptually interesting and/or experimentally feasible, we show they are stable under interactions. These TCIs include (1) a weak topological insulator, (2) a TCI with a mirror symmetry and its time-reversal symmetric generalizations, (3) a doubled topological insulator with a mirror symmetry, and (4) two TCIs with symmetry-enforced-gapless surfaces. We describe two complementary methods that allow us to determine the properties of the magnetic monopoles obtained by coupling these TCIs to a U(1) gauge field. These methods involve studying different types of surface states of these TCIs. Applying these methods to our examples, we find all of them have nontrivial monopoles, which proves their stability under interactions. Furthermore, we discuss two levels of relations between these TCIs and symmetry enriched U(1) quantum spin liquids (QSLs). First, these TCIs are directly related to U(1) QSLs with crystalline symmetries. Second, there is an interesting correspondence between U(1) QSLs with crystalline symmetries and U(1) QSLs with internal symmetries. In particular, the TCIs with symmetry-enforced-gapless surfaces are related to the "fractional topological paramagnets" introduced in Ref. 1 by Zou et al.Comment: 10 pages + appendices + reference