Constraints on Cold H_2 Clouds from Gravitational Microlensing Searches

It has been proposed that the Galaxy might contain a population of cold clouds in numbers sufficient to account for a substantial fraction of the total mass of the Galaxy. These clouds would have masses of the order of 10^{-3} Solar mass and sizes of the order of 10 AU. We consider here the lensing effects of such clouds on the light from background stars. A semianalytical formalism for calculation of the magnification event rate produced by such gaseous lensing is developed, taking into account the spatial distribution of the dark matter in the Galaxy, the velocity distribution of the lensing clouds and source stars, and motion of the observer. Event rates are calculated for the case of gaseous lensing of stars in the Large Magellanic Cloud and results are directly compared with the results of the search for gravitational microlensing events undertaken by the MACHO collaboration. The MACHO experiment strongly constrains the properties of the proposed molecular clouds, but does not completely rule them out. Future monitoring programs will either detect or more strongly constrain this proposed population.Comment: 36 pages, 9 figures, 1 table, typos corrected, minor change

Certification of Bounds of Non-linear Functions: the Templates Method

The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of inequalities. We introduce an approximation algorithm, which combines ideas of the max-plus basis method (in optimal control) and of the linear templates method developed by Manna et al. (in static analysis). This algorithm consists in bounding some of the constituents of the function by suprema of quadratic forms with a well chosen curvature. This leads to semialgebraic optimization problems, solved by sum-of-squares relaxations. Templates limit the blow up of these relaxations at the price of coarsening the approximation. We illustrate the efficiency of our framework with various examples from the literature and discuss the interfacing with Coq.Comment: 16 pages, 3 figures, 2 table

From Double Chooz to Triple Chooz - Neutrino Physics at the Chooz Reactor Complex

We discuss the potential of the proposed Double Chooz reactor experiment to measure the neutrino mixing angle $\sin^2 2\theta_{13}$. We especially consider systematical uncertainties and their partial cancellation in a near and far detector operation, and we discuss implications of a delayed near detector startup. Furthermore, we introduce Triple Chooz, which is a possible upgrade scenario assuming a second, larger far detector, which could start data taking in an existing cavern five years after the first far detector. We review the role of the Chooz reactor experiments in the global context of future neutrino beam experiments. We find that both Double Chooz and Triple Chooz can play a leading role in the search for a finite value of $\sin^2 2\theta_{13}$. Double Chooz could achieve a sensitivity limit of $\sim 2 \cdot 10^{-2}$ at the 90%~confidence level after 5~years while the Triple Chooz setup could give a sensitivity below $10^{-2}$.Comment: 18 pages, 6 figure

Existing opportunities to adapt the Rio Grande/Bravo Basin Water Resources Allocation Framework

The study of the Rio Grande/Bravo (RGB) Basin water allocation demonstrates how the United States (U.S.) and Mexico have consolidated a transboundary framework based on water sharing. However, the water supply no longer meets the ever-increasing demand for water or the expectations of different stakeholders. This paper explores opportunities for an enhanced management regime that will address past problems and better examine how to balance demands for a precious resource and environmental needs. Based on an overview of the RGB Basin context and the water allocation framework, as well as a discussion on stakeholders’ ability to achieve solutions, this paper explores three key questions: (1) Does the current binational water allocation framework meet current and future human and environmental needs? (2) How can the U.S.-Mexico water allocation framework be adapted to balance social and environmental water demands so it can support and preserve the RGB Basin ecosystem? (3) What are the main opportunities to be explored for expanding the U.S.-Mexico water resources allocation framework? The U.S.-Mexico water resources framework is subject to broad interpretation and may be adapted to the circumstances taking the fullest advantage of its flexibility. Policy recommendations highlight the existing flexibility of the binational framework, the potential to move forward with an ad hoc institutional arrangement, and the creation of political will to achieve change through stakeholders recommendations