Discrete moving frames on lattice varieties and lattice based multispace

In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame defined on a lattice variety and the equivalence classes of global syzygies that result from the first fundamental group of the variety. In the second half, we consider the continuum limit of discrete moving frames as a local lattice coalesces to a point. To achieve a well-defined limit of discrete frames, we construct multispace, a generalization of the jet bundle that also generalizes Olver’s one dimensional construction. Using interpolation to provide coordinates, we prove that it is a manifold containing the usual jet bundle as a submanifold. We show that continuity of a multispace moving frame ensures that the discrete moving frame converges to a continuous one as lattices coalesce. The smooth frame is, at the same time, the restriction of the multispace frame to the embedded jet bundle. We prove further that the discrete invariants and syzygies approximate their smooth counterparts. In effect, a frame on multispace allows smooth frames and their discretisations to be studied simultaneously. In our last chapter we discuss two important applications, one to the discrete variational calculus, and the second to discrete integrable systems. Finally, in an appendix, we discuss a more general result concerning equicontinuous families of discretisations of moving frames, which are consistent with a smooth frame

Stroke genetics informs drug discovery and risk prediction across ancestries

Previous genome-wide association studies (GWASs) of stroke - the second leading cause of death worldwide - were conducted predominantly in populations of European ancestry(1,2). Here, in cross-ancestry GWAS meta-analyses of 110,182 patients who have had a stroke (five ancestries, 33% non-European) and 1,503,898 control individuals, we identify association signals for stroke and its subtypes at 89 (61 new) independent loci: 60 in primary inverse-variance-weighted analyses and 29 in secondary meta-regression and multitrait analyses. On the basis of internal cross-ancestry validation and an independent follow-up in 89,084 additional cases of stroke (30% non-European) and 1,013,843 control individuals, 87% of the primary stroke risk loci and 60% of the secondary stroke risk loci were replicated (P < 0.05). Effect sizes were highly correlated across ancestries. Cross-ancestry fine-mapping, in silico mutagenesis analysis(3), and transcriptome-wide and proteome-wide association analyses revealed putative causal genes (such as SH3PXD2A and FURIN) and variants (such as at GRK5 and NOS3). Using a three-pronged approach(4), we provide genetic evidence for putative drug effects, highlighting F11, KLKB1, PROC, GP1BA, LAMC2 and VCAM1 as possible targets, with drugs already under investigation for stroke for F11 and PROC. A polygenic score integrating cross-ancestry and ancestry-specific stroke GWASs with vascular-risk factor GWASs (integrative polygenic scores) strongly predicted ischaemic stroke in populations of European, East Asian and African ancestry(5). Stroke genetic risk scores were predictive of ischaemic stroke independent of clinical risk factors in 52,600 clinical-trial participants with cardiometabolic disease. Our results provide insights to inform biology, reveal potential drug targets and derive genetic risk prediction tools across ancestries.</p

CHARACTERIZATIONS AND DECOMPOSITIONS OF ALMOST STRICTLY POSITIVE MATRICES ∗

Abstract. A nonsingular matrix is called almost strictly totally positive when all its minors are nonnegative, and furthermore these minors are positive if and only if their diagonal entries are positive. In this paper we give a characterization of these matrices in terms of the positivity of a very reduced number of their minors (which are called boundary minors), improving previous characterizations that have appeared in the literature. We show the role of boundary minors in accurate computations with almost strictly totally positive matrices. Moreover, we analyze the QR factorization of these matrices, showing the differences and analogies with that of totally positive matrices. Key words. total positivity, QR factorization, almost strictly totally positive matrices AMS subject classifications. 65F25, 65F40, 15A4

Recent advances of marine ornamental fish larviculture: broodstock reproduction, live prey and feeding regimes, and comparison between demersal and pelagic spawners

Marine ornamental fish are a key component of the multimillion‐dollar marine aquarium trade industry, a controversial industry due to current heavy reliance on wild‐collected specimens. Aquaculture of marine ornamental fish is considered as a sustainable alternative, but it is still in the early stage of development. This review focuses on the current state of marine ornamental fish aquaculture, by covering topics on reef fish reproductive biology in captivity, traditional and novel live feeds, feeding regimes and visual environment in larviculture. Where possible, major differences between demersal and pelagic spawners are compared and discussed. Overall, for many ornamental fish species, natural spawning can be achieved in a captive environment without the use of hormone induction; however, sex identification and successful pairing for reef fish species could be a challenge. With the use of both traditional (rotifers and Artemia) and novel live feeds (e.g. marine copepods and ciliates), a range of breakthroughs in larval rearing of both demersal and pelagic spawning ornamental fish species have been achieved in recent years, although larval survival varies. To further improve the larval rearing success of marine ornamental fish, this review suggests that future research should focus on optimizing the use of live feed in terms of both quality and quantity, and establishment of well‐defined species‐specific larval feeding regime, as well as providing appropriate rearing condition through improved manipulation of light conditions and the 'greenwater' techniques in larval rearing