Random action of compact Lie groups and minimax estimation of a mean pattern

This paper considers the problem of estimating a mean pattern in the setting of Grenander's pattern theory. Shape variability in a data set of curves or images is modeled by the random action of elements in a compact Lie group on an infinite dimensional space. In the case of observations contaminated by an additive Gaussian white noise, it is shown that estimating a reference template in the setting of Grenander's pattern theory falls into the category of deconvolution problems over Lie groups. To obtain this result, we build an estimator of a mean pattern by using Fourier deconvolution and harmonic analysis on compact Lie groups. In an asymptotic setting where the number of observed curves or images tends to infinity, we derive upper and lower bounds for the minimax quadratic risk over Sobolev balls. This rate depends on the smoothness of the density of the random Lie group elements representing shape variability in the data, which makes a connection between estimating a mean pattern and standard deconvolution problems in nonparametric statistics

Fractal initial conditions and natural parameter values in hybrid inflation

We show that the initial field values required to produce inflation in the two fields original hybrid model, and its supergravity F-term extension, do not suffer from any fine-tuning problem, even when the fields are restricted to be sub-planckian and for almost all potential parameter values. This is due to the existence of an initial slow-roll violating evolution which has been overlooked so far. Due to the attractor nature of the inflationary valley, these trajectories end up producing enough accelerated expansion of the universe. By numerically solving the full non-linear dynamics, we show that the set of such successful initial field values is connected, of dimension two and possesses a fractal boundary of infinite length exploring the whole field space. We then perform a Monte-Carlo-Markov-Chain analysis of the whole parameter space consisting of the initial field values, field velocities and potential parameters. We give the marginalised posterior probability distributions for each of these quantities such that the universe inflates long enough to solve the usual cosmological problems. Inflation in the original hybrid model and its supergravity version appears to be generic and more probable by starting outside of the inflationary valley. Finally, the implication of our findings in the context of the eternal inflationary scenario are discussed.Comment: 16 pages, 16 figures, uses RevTeX. Lyapunov exponents and references added, matches published versio

Exponential mixing for the Teichmuller flow

We study the dynamics of the Teichmuller flow in the moduli space of Abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Holder observables. A geometric consequence is that the \SL(2,\R) action in the moduli space has a spectral gap.Comment: 49 page

Agricultural Trade Liberalization: Assessing the Consequences for Developing Countries

Recent analyses suggest that the impact of agricultural trade liberalization on developing countries will be very uneven. Simulations suggest that the effects of agricultural trade liberalization will be small, overall, and are likely to be negative for a significant number of developing countries. The Doha Round focuses on tariff issues, but these countries currently have practically duty-free access to European and North American markets under preferential regimes. Multilateral liberalization will erode the benefits of these preferences, which are presently rather well utilized in the agricultural sector. The main obstacles to the exports of the poorest countries appear to be in the non-tariff area (sanitary, phytosanitary standards) which increasingly originate from the private sector and are not dealt with under the Doha framework (traceability requirements, etc.). An agreement in Doha is unlikely to solve these problems and open large markets for the poorest countries. While this is not an argument to give up multilateral liberalization, a more specific and differentiated treatment should be considered in WTO rules, and corrective measures should be implemented.agricultural trade liberalization, WTO, developing countries, International Development, International Relations/Trade, F13, Q17,

The Consequences of Agricultural Trade Liberalization for Developing Countries

International Relations/Trade,

Thickness effect of Naca foils on hydrodynamic global parameters, boundary layer states and stall establishment

The present study investigates experimentally the hydrodynamic behavior of 2D NACA (15, 25, 35%) symmetric hydrofoils at Reynolds number 0.5 106 . A particular attention is paid on the hysteretic behavior at static stall angle and a detailed cartography of boundary layer structures (integral quantities and velocity profiles) is given in order to put in evidence the mechanism of the detachment and the onset of von Karman instability for thick profil