Rigidity around Poisson Submanifolds

We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash-Moser fast convergence method. In the case of one-point submanifolds (fixed points), this immediately implies a stronger version of Conn's linearization theorem, also proving that Conn's theorem is, indeed, just a manifestation of a rigidity phenomenon; similarly, in the case of arbitrary symplectic leaves, it gives a stronger version of the local normal form theorem; another interesting case corresponds to spheres inside duals of compact semisimple Lie algebras, our result can be used to fully compute the resulting Poisson moduli space.Comment: 43 pages, v3: published versio

Simple choreographies of the planar Newtonian NN-body Problem

In the $N$-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are at least $2^{N-3} + 2^{[(N-3)/2]}$ different main simple choreographies. This confirms a conjecture given by Chenciner and etc. in \cite{CGMS02}.Comment: 31pages, 6 figures. Refinements in notations and proof

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Molecular and Historical Aspects of Corn Belt Dent Diversity

Tens-of-thousands of open-pollinated cultivars of corn (Zea mays L.) are being maintained in germplasm banks. Knowledge of the amount and distribution of genetic variation within and among accessions can aid end users in choosing among them. We estimated molecular genetic variation and looked for influences of pedigree, adaptation, and migration in the genetic makeup of conserved Corn-Belt Dent-related germplasm. Plants sampled from 57 accessions representing Corn-Belt Dents, Northern Flints, Southern Dents, plus 12 public inbreds, were genotyped at 20 simple sequence repeat (SSR) loci. For 47 of the accessions, between 5 and 23 plants per accession were genotyped (mean = 9.3). Mean number of alleles per locus was 6.5 overall, 3.17 within accessions, and 3.20 within pooled inbreds. Mean gene diversity was 0.53 within accessions and 0.61 within pooled inbreds. Open-pollinated accessions showed a tendency toward inbreeding (FIS = 0.09), and 85% of genetic variation was shared among them. A Fitch-Margoliash tree strongly supported the distinctiveness of flint from dent germplasm but did not otherwise reveal evidence of genetic structure. Mantel tests revealed significant correlations between genetic distance and geographical (r = 0.54, P= 0.04) or maturity zone (r = 0.33, P = 0.03) distance only if flint germplasm was included in the analyses. A significant correlation (r = 0.76, P \u3c 0.01) was found between days to pollen shed and maturity zone of accession origin. Pedigree, rather than migration or selection, has most influenced the genetic structure of the extant representatives of the open-pollinated cultivars at these SSR loci

A mouse-adapted model of SARS-CoV-2 to test COVID-19 countermeasures

Coronaviruses are prone to emergence into new host species most recently evidenced by SARS-CoV-2, the causative agent of the COVID-19 pandemic1. Small animal models that recapitulate SARS-CoV-2 disease are desperately needed to rapidly evaluate medical countermeasures (MCMs)2,3. SARS-CoV-2 cannot infect wildtype laboratory mice due to inefficient interactions between the viral spike (S) protein and the murine ortholog of the human receptor, ACE24. We used reverse genetics5 to remodel the interaction between S and mACE2 resulting in a recombinant virus (SARS-CoV-2 MA) that could utilize mACE2 for entry. SARS-CoV-2 MA replicated in both the upper and lower airways of both young adult and aged BALB/c mice. Importantly, disease was more severe in aged mice, and showed more clinically relevant phenotypes than those seen in HFH4-hACE2 transgenic mice. We then demonstrated the utility of this model through vaccine challenge studies in immune competent mice with native expression of mACE2. Lastly, we show that clinical candidate interferon (IFN) lambda-1a can potently inhibit SARS-CoV-2 replication in primary human airway epithelial cells in vitro, and both prophylactic and therapeutic administration diminished replication in mice. Our mouse-adapted SARS-CoV-2 model demonstrates age-related disease pathogenesis and supports the clinical use of pegylated IFN lambda-1a treatment in human COVID-19 infections

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions

Genome-wide meta-analysis of common variant differences between men and women

The male-to-female sex ratio at birth is constant across world populations with an average of 1.06 (106 male to 100 female live births) for populations of European descent. The sex ratio is considered to be affected by numerous biological and environmental factors and to have a heritable component. The aim of this study was to investigate the presence of common allele modest effects at autosomal and chromosome X variants that could explain the observed sex ratio at birth. We conducted a large-scale genome-wide association scan (GWAS) meta-analysis across 51 studies, comprising overall 114 863 individuals (61 094 women and 53 769 men) of European ancestry and 2 623 828 common (minor allele frequency >0.05) single-nucleotide polymorphisms (SNPs). Allele frequencies were compared between men and women for directly-typed and imputed variants within each study. Forward-time simulations for unlinked, neutral, autosomal, common loci were performed under the demographic model for European populations with a fixed sex ratio and a random mating scheme to assess the probability of detecting significant allele frequency differences. We do not detect any genome-wide significant (P < 5 × 10−8) common SNP differences between men and women in this well-powered meta-analysis. The simulated data provided results entirely consistent with these findings. This large-scale investigation across ∼115 000 individuals shows no detectable contribution from common genetic variants to the observed skew in the sex ratio. The absence of sex-specific differences is useful in guiding genetic association study design, for example when using mixed controls for sex-biased trait