On the convexity theory of generating functions

In this paper, we extend our convexity theory for $C^2$ cost functions in optimal transportation to more general generating functions, which were originally introduced by the second author to extend the framework of optimal transportation to embrace near field geometric optics. In particular we provide an alternative geometric treatment to the previous analytic approach using differential inequalities, which also gives a different derivation of the invariance of the fundamental regularity conditions under duality. We also extend our local theory to cover the strict version of these conditions for $C^2$ cost and generating functions.Comment: Some typos corrected in previous version and comments adde

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

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

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

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

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

The Structure of Hyperalkaline Aqueous Solutions Containing High Concentrations of Gallium - a Solution X-ray Diffraction and Computational Study

Highly concentrated alkaline NaOH/Ga(OH)3 solutions with 1.18 M Ga(III)T 2.32 M and 2.4 M NaOHT 4.9 M (where the subscript T denotes total or analytical concentrations) have been prepared and investigated by solution X-ray diffraction and also by ab initio quantum chemical calculations. The data obtained are consistent with the presence of only one predominant Ga(III)-bearing species in these solutions, that is the tetrahedral hydroxo complex Ga(OH)4–. This finding is in stark contrast to that found for Al(III)-containing solutions of similar concentrations, in which, besides the monomeric complex, an oxo-bridged dimer was also found to form. From the solution X-ray diffraction measurements, the formation of the dimeric (OH)3Ga–O–Ga(OH)32– could not unambiguously be shown, however, from the comparison of experimental IR, Raman and 71Ga NMR spectra with calculated ones, its formation can be safely excluded. Moreover, higher mononuclear stepwise hydroxo complexes, like Ga(OH)63–, that have been claimed to exist by others in the literature, was not possible to experimentally detect in these solutions with any of the spectroscopic techniques used

Efficacy and complications of neurosurgical treatment of acromegaly

The aim of the study was to evaluate the frequency of occurrence of pituitary failure following neurosurgery and the efficacy of transsphenoidal tumour resection in acromegalic patients. We retrospectively evaluated 85 patients (60 female and 25 male), of mean age 43.9 ± 13.2 years, treated by transsphenoidal neurosurgery. Macroadenoma and microadenoma of pituitary were found in 66 (77.6%) and 19 (22.4%) of these patients, respectively. Criteria of cure following neurosurgery were: basal GH < 2.5 μg/l, GH at 120 min in OGTT < 1.0 μg/l and serum concentration of IGF-1 within normal ranges for age and sex. After surgery 32 patients (37.6%) were cured and 53 patients (62.4%) required somatostatin analogue treatment. In patients cured by surgery, lower levels of basal GH (P < 0.05), IGF-1 (P < 0.001), GH at 120 min in OGTT and smaller size of pituitary tumour (P < 0.05) were found at diagnosis, as compared to patients in whom surgery was unsuccessful. Significant correlation between basal serum level of GH at diagnosis and size of pituitary tumour was found (P < 0.001). Invasive tumours were found in 45 of 53 (84.9%) patients not cured and in only 8 of 32 (25.0%) patients cured (P < 0.001). Impaired function of pituitary anterior lobe after surgery was observed in 30% and 4% of patients with macro- and microadenoma, respectively (P < 0.05). The efficacy of neurosurgery is affected by concentration of basal serum GH and IGF-1, GH at 120 min in OGTT, tumour size and invasiveness. Hypopituitarism after surgery is more frequent in patients with macroadenoma. Pituitary insufficiency, as a consequence of surgery, was found in 21% of patients with normal pituitary function prior to operation