Geometrical Insights for Implicit Generative Modeling

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by these distances on the space of probability measures reveals interesting differences. In particular, we can establish surprising approximate global convergence guarantees for the $1$-Wasserstein distance,even when the parametric generator has a nonconvex parametrization.Comment: this version fixes a typo in a definitio

Allergic Rhinitis and its Associated Co-Morbidities at Bugando Medical Centre in Northwestern Tanzania; A Prospective Review of 190 Cases.

Allergic rhinitis is one of the commonest atopic diseases which contribute to significant morbidity world wide while its epidemiology in Tanzania remains sparse. There was paucity of information regarding allergic rhinitis in our setting; therefore it was important to conduct this study to describe our experience on allergic rhinitis, associated co-morbidities and treatment outcome in patients attending Bugando Medical Centre. This was descriptive cross-sectional study involving all patients with a clinical diagnosis of allergic rhinitis at Bugando Medical Centre over a three-month period between June 2011 and August 2011. Data was collected using a pre-tested coded questionnaire and analyzed using SPSS statistical computer software version 17.0. A total of 190 patients were studied giving the prevalence of allergic rhinitis 14.7%. The median age of the patients was 8.5 years. The male to female ratio was 1:1. Adenoid hypertrophy, tonsillitis, hypertrophy of inferior turbinate, nasal polyps, otitis media and sinusitis were the most common co-morbidities affecting 92.6% of cases and were the major reason for attending hospital services. Sleep disturbance was common in children with adenoids hypertrophy (χ2 = 28.691, P = 0.000). Allergic conjunctivitis was found in 51.9%. The most common identified triggers were dust, strong perfume odors and cold weather (P < 0.05). Strong perfume odors affect female than males (χ2 = 4.583, P = 0.032). In this study family history of allergic rhinitis was not a significant risk factor (P =0.423). The majority of patients (68.8%) were treated surgically for allergic rhinitis co morbidities. Post operative complication and mortality rates were 2.9% and 1.6% respectively. The overall median duration of hospital stay of in-patients was 3 days (2 - 28 days). Most patients (98.4%) had satisfactory results at discharge. The study shows that allergic rhinitis is common in our settings representing 14.7% of all otorhinolaryngology and commonly affecting children and adolescent. Sufferers seek medical services due to co-morbidities of which combination of surgical and medical treatment was needed. High index of suspicions in diagnosing allergic rhinitis and early treatment is recommended

Solid-liquid iron partitioning in Earth's deep mantle

International audienceMelting processes in the deep mantle have important implications for the origin of the deep-derived plumes believed to feed hotspot volcanoes such as those in Hawaii(1). They also provide insight into how the mantle has evolved, geochemically and dynamically, since the formation of Earth(2). Melt production in the shallow mantle is quite well understood, but deeper melting near the core-mantle boundary remains controversial. Modelling the dynamic behaviour of deep, partially molten mantle requires knowledge of the density contrast between solid and melt fractions. Although both positive and negative melt buoyancies can produce major chemical segregation between different geochemical reservoirs, each type of buoyancy yields drastically different geodynamical models. Ascent or descent of liquids in a partially molten deep mantle should contribute to surface volcanism or production of a deep magma ocean, respectively. We investigated phase relations in a partially molten chondritic-type material under deep-mantle conditions. Here we show that the iron partition coefficient between aluminium-bearing (Mg,Fe)SiO3 perovskite and liquid is between 0.45 and 0.6, so iron is not as incompatible with deep-mantle minerals as has been reported previously(3). Calculated solid and melt density contrasts suggest that melt generated at the core-mantle boundary should be buoyant, and hence should segregate upwards. In the framework of the magma oceans induced by large meteoritic impacts on early Earth, our results imply that the magma crystallization should push the liquids towards the surface and form a deep solid residue depleted in incompatible elements