Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

We study Sobolev-type metrics of fractional order $s\geq0$ on the group \Diff_c(M) of compactly supported diffeomorphisms of a manifold $M$. We show that for the important special case $M=S^1$ the geodesic distance on \Diff_c(S^1) vanishes if and only if $s\leq\frac12$. For other manifolds we obtain a partial characterization: the geodesic distance on \Diff_c(M) vanishes for $M=\R\times N, s<\frac12$ and for $M=S^1\times N, s\leq\frac12$, with $N$ being a compact Riemannian manifold. On the other hand the geodesic distance on \Diff_c(M) is positive for $\dim(M)=1, s>\frac12$ and $\dim(M)\geq2, s\geq1$. For $M=\R^n$ we discuss the geodesic equations for these metrics. For $n=1$ we obtain some well known PDEs of hydrodynamics: Burgers' equation for $s=0$, the modified Constantin-Lax-Majda equation for $s=\frac 12$ and the Camassa-Holm equation for $s=1$.Comment: 16 pages. Final versio

Signatures of Relativistic Neutrinos in CMB Anisotropy and Matter Clustering

We present a detailed analytical study of ultra-relativistic neutrinos in cosmological perturbation theory and of the observable signatures of inhomogeneities in the cosmic neutrino background. We note that a modification of perturbation variables that removes all the time derivatives of scalar gravitational potentials from the dynamical equations simplifies their solution notably. The used perturbations of particle number per coordinate, not proper, volume are generally constant on superhorizon scales. In real space an analytical analysis can be extended beyond fluids to neutrinos. The faster cosmological expansion due to the neutrino background changes the acoustic and damping angular scales of the cosmic microwave background (CMB). But we find that equivalent changes can be produced by varying other standard parameters, including the primordial helium abundance. The low-l integrated Sachs-Wolfe effect is also not sensitive to neutrinos. However, the gravity of neutrino perturbations suppresses the CMB acoustic peaks for the multipoles with l>~200 while it enhances the amplitude of matter fluctuations on these scales. In addition, the perturbations of relativistic neutrinos generate a *unique phase shift* of the CMB acoustic oscillations that for adiabatic initial conditions cannot be caused by any other standard physics. The origin of the shift is traced to neutrino free-streaming velocity exceeding the sound speed of the photon-baryon plasma. We find that from a high resolution, low noise instrument such as CMBPOL the effective number of light neutrino species can be determined with an accuracy of sigma(N_nu) = 0.05 to 0.09, depending on the constraints on the helium abundance.Comment: 38 pages, 7 figures. Version accepted for publication in PR

Scale issues in soil moisture modelling: problems and prospects

Soil moisture storage is an important component of the hydrological cycle and plays a key role in land-surface-atmosphere interaction. The soil-moisture storage equation in this study considers precipitation as an input and soil moisture as a residual term for runoff and evapotranspiration. A number of models have been developed to estimate soil moisture storage and the components of the soil-moisture storage equation. A detailed discussion of the impli cation of the scale of application of these models reports that it is not possible to extrapolate processes and their estimates from the small to the large scale. It is also noted that physically based models for small-scale applications are sufficiently detailed to reproduce land-surface- atmosphere interactions. On the other hand, models for large-scale applications oversimplify the processes. Recently developed physically based models for large-scale applications can only be applied to limited uses because of data restrictions and the problems associated with land surface characterization. It is reported that remote sensing can play an important role in over coming the problems related to the unavailability of data and the land surface characterization of large-scale applications of these physically based models when estimating soil moisture storage.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Primordial Nucleosynthesis for the New Cosmology: Determining Uncertainties and Examining Concordance

Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) have a long history together in the standard cosmology. The general concordance between the predicted and observed light element abundances provides a direct probe of the universal baryon density. Recent CMB anisotropy measurements, particularly the observations performed by the WMAP satellite, examine this concordance by independently measuring the cosmic baryon density. Key to this test of concordance is a quantitative understanding of the uncertainties in the BBN light element abundance predictions. These uncertainties are dominated by systematic errors in nuclear cross sections. We critically analyze the cross section data, producing representations that describe this data and its uncertainties, taking into account the correlations among data, and explicitly treating the systematic errors between data sets. Using these updated nuclear inputs, we compute the new BBN abundance predictions, and quantitatively examine their concordance with observations. Depending on what deuterium observations are adopted, one gets the following constraints on the baryon density: OmegaBh^2=0.0229\pm0.0013 or OmegaBh^2 = 0.0216^{+0.0020}_{-0.0021} at 68% confidence, fixing N_{\nu,eff}=3.0. Concerns over systematics in helium and lithium observations limit the confidence constraints based on this data provide. With new nuclear cross section data, light element abundance observations and the ever increasing resolution of the CMB anisotropy, tighter constraints can be placed on nuclear and particle astrophysics. ABRIDGEDComment: 54 pages, 20 figures, 5 tables v2: reflects PRD version minor changes to text and reference

Genome-wide meta-analyses reveal novel loci for verbal short-term memory and learning

Understanding the genomic basis of memory processes may help in combating neurodegenerative disorders. Hence, we examined the associations of common genetic variants with verbal short-term memory and verbal learning in adults without dementia or stroke (N = 53,637). We identified novel loci in the intronic region of CDH18, and at 13q21 and 3p21.1, as well as an expected signal in the APOE/APOC1/TOMM40 region. These results replicated in an independent sample. Functional and bioinformatic analyses supported many of these loci and further implicated POC1. We showed that polygenic score for verbal learning associated with brain activation in right parieto-occipital region during working memory task. Finally, we showed genetic correlations of these memory traits with several neurocognitive and health outcomes. Our findings suggest a role of several genomic loci in verbal memory processes

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele