General Spectral Flow Formula for Fixed Maximal Domain

We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous family of (unbounded) self-adjoint Fredholm operators in terms of the Maslov index of two related curves of Lagrangian spaces. One curve is given by the varying domains, the other by the Cauchy data spaces. We provide rigorous definitions of the underlying concepts of spectral theory and symplectic analysis and give a full (and surprisingly short) proof of our General Spectral Flow Formula for the case of fixed maximal domain. As a side result, we establish local stability of weak inner unique continuation property (UCP) and explain its role for parameter dependent spectral theory.Comment: 22 page

Reconstructing the deep-branching relationships of the papilionoid legumes

Resolving the phylogenetic relationships of the deep nodes of papilionoid legumes (Papilionoideae) is essential to understanding the evolutionary history and diversification of this economically and ecologically important legume subfamily. The early-branching papilionoids include mostly Neotropical trees traditionally circumscribed in the tribes Sophoreae and Swartzieae. They are more highly diverse in floral morphology than other groups of Papilionoideae. For many years, phylogenetic analyses of the Papilionoideae could not clearly resolve the relation- ships of the early-branching lineages due to limited sampling. In the eight years since the publication of Legumes of the World, we have seen an extraordinary wealth of new molecular data for the study of Papilionoideae phylogeny, enabling increasingly greater resolution and many surprises. This study draws on recent molecular phylogenetic studies and a new comprehensive Bayesian phylogenetic analysis of 668 plastid matK sequences. The present matK phylogeny resolves the deep-branching relationships of the papilionoids with increased support for many clades, and suggests that taxonomic realignments of some genera and of numerous tribes are necessary. The potentially earliest-branching papilionoids fall within an ADA clade, which includes the recircumscribed monophyletic tribes Angylocalyceae, Dipterygeae, and Amburanae. The genera Aldina and Amphimas represent two of the nine main but as yet unresolved lineages comprising the large 50-kb inversion clade. The quinolizidine-alkaloid-accumulating Genistoid s.l. clade is expanded to include Dermatophyllum and a strongly supported and newly circumscribed tribe Ormosieae. Sophoreae and Swartzieae are dramatically reorganized so as to comprise mono-phyletic groups within the Core Genistoid clade and outside the 50-kb inversion clade, respectively. Acosmium is excluded from the Genistoids s.l. and strongly resolved within the newly circumscribed tribe Dalbergieae. By providing a better resolved phylogeny of the earliest-branching papilionoids, this study, in combination with other recent evidence, will lead to a more stable phylogenetic classification of the Papilionoideae.Web of Scienc

Genome-wide meta-analysis of myopia and hyperopia provides evidence for replication of 11 loci

Refractive error (RE) is a complex, multifactorial disorder characterized by a mismatch between the optical power of the eye and its axial length that causes object images to be focused off the retina. The two major subtypes of RE are myopia (nearsightedness) and hyperopia (farsightedness), which represent opposite ends of the distribution of the quantitative measure of spherical refraction. We performed a fixed effects meta-analysis of genome-wide association results of myopia and hyperopia from 9 studies of European-derived populations: AREDS, KORA, FES, OGP-Talana, MESA, RSI, RSII, RSIII and ERF. One genome-wide significant region was observed for myopia, corresponding to a previously identified myopia locus on 8q12 (p = 1.25610-8), which has been reported by Kiefer et al. as significantly associated with myopia age at onset and Verhoeven et al. as significantly associated to mean spherical-equivalent (MSE) refractive error. We observed two genomewide significant association

Plastome Structural Evolution and Homoplastic Inversions in Neo-Astragalus (Fabaceae)

The plastid genomes of photosynthetic green plants have largely maintained conserved gene content and order as well as structure over hundreds of millions of years of evolution. Several plant lineages, however, have departed from this conservation and contain many plastome structural rearrangements, which have been associated with an abundance of repeated sequences both overall and near rearrangement endpoints. We sequenced the plastomes of 25 taxa of Astragalus L. (Fabaceae), a large genus in the inverted repeat-lacking clade of legumes, to gain a greater understanding of the connection between repeats and plastome inversions. We found plastome repeat structure has a strong phylogenetic signal among these closely related taxa mostly in the New World clade of Astragalus called Neo-Astragalus. Taxa without inversions also do not differ substantially in their overall repeat structure from four taxa each with one large-scale inversion. For two taxa with inversion endpoints between the same pairs of genes, differences in their exact endpoints indicate the inversions occurred independently. Our proposed mechanism for inversion formation suggests the short inverted repeats now found near the endpoints of the four inversions may be there as a result of these inversions rather than their cause. The longer inverted repeats now near endpoints may have allowed the inversions first mediated by shorter microhomologous sequences to propagate, something that should be considered in explaining how any plastome rearrangement becomes fixed regardless of the mechanism of initial formation. © The Author(s) 2021. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

A molecular phylogeny reveals the Cuban enigmatic genus Behaimia as a new piece in the Brongniartieae puzzle of papilionoid legumes

The papilionoid legume tribe Brongniartieae comprises a collection of 15 genera with disparate morphologies that were previously positioned in at least four remotely related tribes. The Brongniartieae displays a wide geographical disjunction between Australia and the New World and previous phylogenetic studies had provided conflicting results about the relationships between the American and Australian genera. We carry out phylogenetic analyses of (1) a plastid matK dataset extensively sampled across legumes to solve the enigmatic relationship of the Cuban-endemic monospecific genus Behaimia; and (2) multilocus datasets with focus on all genera ever referred to Brongniartieae. These analyses resulted in a well-resolved and strongly-supported phylogenetic tree of the Brongniartieae. The monophyly of all American genera of Brongniartieae is strongly supported. The doubtful position of the Australian genus Plagiocarpus is resolved within a clade comprising all Australian genera. Behaimia has been traditionally classified in tribe Millettieae, but our new molecular data and re-assessment of morphological traits have resolved the genus within the early-branching papilionoid tribe Brongniartieae. Characters including the pinnately multifoliolate (vs. unifoliolate) leaves, a sessile (vs. stipitate) ovary, and an indehiscent or late dehiscent one-seeded pod distinguish Behaimia from its closer relatives, the South American genera Cyclolobium and Limadendron

Perturbation of sectorial projections of elliptic pseudo-differential operators

Over a closed manifold, we consider the sectorial projection of an elliptic pseudo-differential operator A of positive order with two rays of minimal growth. We show that it depends continuously on A when the space of pseudo-differential operators is equipped with a certain topology which we explicitly describe. Our main application deals with a continuous curve of arbitrary first order linear elliptic differential operators over a compact manifold with boundary. Under the additional assumption of the weak inner unique continuation property, we derive the continuity of a related curve of Calderon projections and hence of the Cauchy data spaces of the original operator curve. In the Appendix, we describe a topological obstruction against a verbatim use of R. Seeley's original argument for the complex powers, which was seemingly overlooked in previous studies of the sectorial projection.Comment: 30 pages, 2 figures; v3: major revision, shortened, several references added, some material moved into an appendix; v4: final version, accepted for publication in Journal of Pseudo-Differential Operators and Application