Duality Theorems in Ergodic Transport

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose $\sigma$ is the shift acting on Bernoulli space $X=\{0,1\}^\mathbb{N}$, and, consider a fixed continuous cost function $c:X \times X\to \mathbb{R}$. Denote by $\Pi$ the set of all Borel probabilities $\pi$ on $X\times X$, such that, both its $x$ and $y$ marginal are $\sigma$-invariant probabilities. We are interested in the optimal plan $\pi$ which minimizes $\int c d \pi$ among the probabilities on $\Pi$. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on $c$. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs $c$ the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan $\pi$ by convex combinations of plans such that the support projects in periodic orbits

Age at menarche and urbanization in Cameroon : current status and secular trends

Status quo data on the age at menarche were obtained on samples of Cameroonian girls living in urban (Yaoundé) (n = 205), suburban (n = 505) and rural areas (n = 201). Mean ages at menarche, estimated by probit analysis, are 13.18 years (SD 1.08) in Yaoundé, 13.98 years (SD 1.55) in the suburban area, and 14.27 years (SD 1.65) in the rural area. The early menarcheal age observed in Yaoundé girls attending 'privileged schools' (12.72 years, SD 1.18) substantiates the hypothesis that in good environmental conditions Africans are as early-maturing as Asiatic or Mediterranean populations. Comparison with retrospective data on age at menarche during previous decades reveals the presence of a clear secular trend towards earlier maturation, at a rate of 2.5-3.2 months per decade, only in the main cities of the country (Yaoundé/Douala) and a lack of temporal variation in rural areas. The degree of urbanization influences maturational age and its evolution probably through improvements in the nutritional standards. (Résumé d'auteur

Intimate partner violence against HIV-positive Cameroonian women : prevalence, associated factors and relationship with antiretroviral therapy discontinuity-results from the ANRS-12288 EVOLCam survey

Background: Intimate partner violence in its various forms increases HIV exposure in female victims and potentially jeopardizes the HIV treatment cascade, for instance, by impeding engagement in and adherence to care. Elevated rates of HIV and intimate partner violence are reported in Central Africa. Evidence on the effect of intimate partner violence on antiviral therapy interruption is lacking in Cameroon, where only 330,000 women live with HIV and only 19% of HIV-positive people are virally suppressed. This study aimed to assess the prevalence and factors of intimate partner violence against HIV-positive women and its relationship with antiretroviral therapy interruption > 1 month. Methods: The EVOLCam cross-sectional survey was conducted in 19 hospitals in the Center and Littoral regions. The study sample comprised antiviral therapy-treated women declaring at least one sexual partner in the previous year. Scores of recent emotional, physical, extreme physical and sexual intimate partner violence were built using principal component analysis and categorized under no, occasional or frequent intimate partner violence. Multivariate logistic analyses were performed to investigate the relationship between intimate partner violence and recent antiretroviral therapy interruption > 1 month, and associated factors. Results: Among the 894 analyzed women, the prevalence of intimate partner violence was 29% (emotional), 22% (physical), 13% (extreme physical) and 18% (sexual). Frequent physical intimate partner violence was a significant risk factor of antiretroviral therapy interruption > 1 month (adjusted odds ratio = 2.42 (95% confidence interval = 1.00; 5.87)). It was also associated with HIV-related stigma (2.53 (1.58; 4.02)), living with a main partner (2.03 (1.20; 3.44) and non-defensive violence against this partner (5.75 (3.53; 9.36)). Conclusion: Intimate partner violence is a potential barrier to antiviral therapy continuity and aggravates vulnerability of Cameroonian HIV-positive women. The prevention and detection of intimate partner violence by HIV services might help to reach the last "90" of the 90-90-90 targets

Design and performance of the main amplifier system for the National Ignition Facility

This paper describes the design and performance of flashlamp-pumped, Nd:glass. Brewster-angle slab amplifiers intended to be deployed in the National Ignition Facility (NIF). To verify performance, we tested a full-size, three-slab-long, NIF prototype amplifier, which we believe to be the largest flashlamp-pumped Nd:glass amplifier ever assembled. Like the NIF amplifier design, this prototype amplifier had eight 40-cm-square apertures combined in a four-aperture-high by two-aperture-wide matrix. Specially-shaped reflectors, anti-reflective coatings on the blastshields, and preionized flashlamps were used to increase storage efficiency. Cooling gas was flowed over the flashlamps to remove waste pump heat and to accelerate thermal wavefront recovery. The prototype gain results are consistent with model predictions and provide high confidence in the final engineering design of the NIF amplifiers. Although the dimensions, internal positions, and shapes of the components in the NIF amplifiers will be slightly different from the prototype, these differences are small and should produce only slight differences in amplifier performanc