Selection of validated hypervariable regions is crucial in 16S-based microbiota studies of the female genital tract

Next-generation sequencing-based methods are extensively applied in studies of the human microbiota using partial 16 S rRNA gene amplicons. However, they carry drawbacks that are critical to consider when interpreting results, including differences in outcome based on the hypervariable region(s) used. Here, we show that primers spanning the V3/V4 region identify a greater number of taxa in the vaginal microbiota than those spanning the V1/V2 region. In particular, taxa such as Gardnerella vaginalis, Bifidobacterium bifidum and Chlamydia trachomatis, all species that influence vaginal health and disease, are not represented in V1/V2-based community profiles. Accordingly, missing or underestimating the frequency of these species overestimates the abundance of other taxa and fails to correctly assess the bacterial diversity in the urogenital tract. We elaborate that covering these taxa using the V3/V4 region leads to profound changes in the assignment of community state types. Altogether, we show that the choice of primers used for studying the vaginal microbiota has deep implications on the biological evaluation of the results

On the Regularity of Optimal Transportation Potentials on Round Spheres

In this paper the regularity of optimal transportation potentials defined on round spheres is investigated. Specifically, this research generalises the calculations done by Loeper, where he showed that the strong (A3) condition of Trudinger and Wang is satisfied on the round sphere, when the cost-function is the geodesic distance squared. In order to generalise Loeper's calculation to a broader class of cost-functions, the (A3) condition is reformulated via a stereographic projection that maps charts of the sphere into Euclidean space. This reformulation subsequently allows one to verify the (A3) condition for any case where the cost-fuction of the associated optimal transportation problem can be expressed as a function of the geodesic distance between points on a round sphere. With this, several examples of such cost-functions are then analysed to see whether or not they satisfy this (A3) condition.Comment: 24 pages, 4 figure

Representation of Markov chains by random maps: existence and regularity conditions

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including extended discussion of many detail

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

Rectifiability of Optimal Transportation Plans

The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations

We establish a connection between Optimal Transport Theory and classical Convection Theory for geophysical flows. Our starting point is the model designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal Transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized Hydrostatic-Boussinesq equations) to various models involving Optimal Transport (and the related Monge-Ampere equation. This includes the 2D semi-geostrophic equations and some fully non-linear versions of the so-called high-field limit of the Vlasov-Poisson system and of the Keller-Segel for Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology

Dietary Silicon Deficiency Does Not Exacerbate Diet-Induced Fatty Lesions in Female ApoE Knockout Mice.

BACKGROUND: Dietary silicon has been positively linked with vascular health and protection against atherosclerotic plaque formation, but the mechanism of action is unclear. OBJECTIVES: We investigated the effect of dietary silicon on 1) serum and aorta silicon concentrations, 2) the development of aortic lesions and serum lipid concentrations, and 3) the structural and biomechanic properties of the aorta. METHODS: Two studies, of the same design, were conducted to address the above objectives. Female mice, lacking the apolipoprotein E (apoE) gene, and therefore susceptible to atherosclerosis, were separated into 3 groups of 10-15 mice, each exposed to a high-fat diet (21% wt milk fat and 1.5% wt cholesterol) but with differing concentrations of dietary silicon, namely: silicon-deprived (-Si; <3-μg silicon/g feed), silicon-replete in feed (+Si-feed; 100-μg silicon/g feed), and silicon-replete in drinking water (+Si-water; 115-μg silicon/mL) for 15-19 wk. Silicon supplementation was in the form of sodium metasilicate (feed) or monomethylsilanetriol (drinking water). RESULTS: The serum silicon concentration in the -Si group was significantly lower than in the +Si-feed (by up to 78%; P < 0.003) and the +Si-water (by up to 84%; P < 0.006) groups. The aorta silicon concentration was also lower in the -Si group than in the +Si-feed group (by 65%; P = 0.025), but not compared with the +Si-water group. There were no differences in serum and aorta silicon concentrations between the silicon-replete groups. Body weights, tissue wet weights at necropsy, and structural, biomechanic, and morphologic properties of the aorta were not affected by dietary silicon; nor were the development of fatty lesions and serum lipid concentrations. CONCLUSIONS: These findings suggest that dietary silicon has no effect on atherosclerosis development and vascular health in the apoE mouse model of diet-induced atherosclerosis, contrary to the reported findings in the cholesterol-fed rabbit model

Analysis of Oscillations and Defect Measures for the Quasineutral Limit in Plasma Physics

We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma represented by the Navier Stokes Poisson system in $3-D$. We show that as $\lambda\to 0$ the velocity field $u^{\lambda}$ strongly converges towards an incompressible velocity vector field $u$ and the density fluctuation $\rho^{\lambda}-1$ weakly converges to zero. In general the limit velocity field cannot be expected to satisfy the incompressible Navier Stokes equation, indeed the presence of high frequency oscillations strongly affects the quadratic nonlinearities and we have to take care of self interacting wave packets. We shall provide a detailed mathematical description of the convergence process by using microlocal defect measures and by developing an explicit correctors analysis. Moreover we will be able to identify an explicit pseudo parabolic pde satisfied by the leading correctors terms. Our results include all the previous results in literature, in particular we show that the formal limit holds rigorously in the case of well prepared data.Comment: Submitted pape

First steps towards a fast-neutron therapy planning program

<p>Abstract</p> <p>Background</p> <p>The Monte Carlo code GEANT4 was used to implement first steps towards a treatment planning program for fast-neutron therapy at the FRM II research reactor in Garching, Germany. Depth dose curves were calculated inside a water phantom using measured primary neutron and simulated primary photon spectra and compared with depth dose curves measured earlier. The calculations were performed with GEANT4 in two different ways, simulating a simple box geometry and splitting this box into millions of small voxels (this was done to validate the voxelisation procedure that was also used to voxelise the human body).</p> <p>Results</p> <p>In both cases, the dose distributions were very similar to those measured in the water phantom, up to a depth of 30 cm. In order to model the situation of patients treated at the FRM II MEDAPP therapy beamline for salivary gland tumors, a human voxel phantom was implemented in GEANT4 and irradiated with the implemented MEDAPP neutron and photon spectra. The 3D dose distribution calculated inside the head of the phantom was similar to the depth dose curves in the water phantom, with some differences that are explained by differences in elementary composition. The lateral dose distribution was studied at various depths. The calculated cumulative dose volume histograms for the voxel phantom show the exposure of organs at risk surrounding the tumor.</p> <p>Conclusions</p> <p>In order to minimize the dose to healthy tissue, a conformal treatment is necessary. This can only be accomplished with the help of an advanced treatment planning system like the one developed here. Although all calculations were done for absorbed dose only, any biological dose weighting can be implemented easily, to take into account the increased radiobiological effectiveness of neutrons compared to photons.</p