Generic identifiability and second-order sufficiency in tame convex optimization

We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, "tame"). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the feasible region is "partly smooth", ensuring finite identification of the manifold by many optimization algorithms. Furthermore, second-order optimality conditions hold, guaranteeing smooth behavior of the optimal solution under small perturbations to the objective

Cosmological parameters from CMB and other data: a Monte-Carlo approach

We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including sigma_8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass (m_nu < 0.3eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendices we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters

Modelling Martian dust storms: feedbacks between dust and atmospheric circulation at a hierarchy of scales

We employ numerical models of Mars at spatial scales ranging from global to a few metres in order to investigate both the impact of increasing dust loading on atmospheric circulations and the role of different atmospheric circulation components on dust lifting, transport and on dust storm decay

Size-dependent oxygen-related electronic states in silicon nanocrystals

Silicon nanocrystals embedded in SiO2 were isolated with a selective etching procedure, and the isolated nanocrystals' excitonic emission energy was studied during controlled oxidation. Nanocrystals having initial diameters, d(0), of similar to 2.9-3.4 nm showed a photoluminescence (PL) blueshift upon oxidatively induced size reduction, as expected from models of quantum confinement. Oxidation of smaller Si nanocrystals (d(0)similar to 2.5-2.8 nm) also initially resulted in a PL blueshift, but a redshift in the PL was then observed after growth of similar to 0.3 monolayers of native oxide. This decrease in excitonic emission energy during oxidation is consistent with the theoretically predicted formation of an oxygen-related excitonic recombination state