Data assimilation refers to any methodology that uses partialobservational data and the dynamics of a system for estimating themodel state or its parameters. We consider here a non classicalapproach to data assimilation based in null controllabilityintroduced in [Puel, C. R. Math. Acad. Sci. Paris 335 (2002) 161–166] and [Puel, SIAM J. Control Optim.48 (2009) 1089–1111] and we apply it to oceanography.More precisely, we are interested in developing this methodologyto recover the unknown final state value (state value at the end of the measurement period) in a quasi-geostrophicocean model from satellite altimeter data, which allows in fact tomake better predictions of the ocean circulation. The main idea ofthe method is to solve several null controllability problems for the adjoint system inorder to obtain projections of the final state on a reduced basis.Theoretically, we have to prove the well posedness of theinvolved systems associated to the method and we also need anobservability property to show the existence of null controls for the adjoint system. Tothis aim, we use a global Carleman inequality for the associatedvelocity-pressure formulation of the problem which was previouslyproved in [Fernández-Cara et al., J. Math. Pures Appl.83(2004) 1501–1542]. We present numerical simulations using a regularizedversion of this data assimilation methodology based on nullcontrollability for elements of a reduced spectral basis.After proving the convergence of the regularized solutions, weanalyze the incidence of the observatory size and noisy data inthe recovery of the initial value for a quality prediction.

The present study was designed to evaluate the effect of olive oil and its main polyphenol (oleuropein) in ovariectomised rats with or without inflammation. Rats (6 months old) were ovariectomised or sham-operated as control. Ovariectomised rats were separated into three groups receiving different diets for 3 months: a control diet with 25 g peanut oil and 25 g rapeseed oil/kg (OVX), the control diet with 50 g olive oil/kg or the control diet with 0·15 g oleuropein/kg. The sham-operated group was given the same control diet as OVX. Inflammation was induced 3 weeks before the end of the experiment by subcutaneous injections of talc (magnesium silicate) in one-half of each group. The sucess of ovariectomy was verified at necropsy by the atrophy of uterine horns. Inflammation, oleuropein or olive oil intakes did not have any uterotrophic activity, as they had had no effect on uterus weight. The plasma concentration of α-1-acid glycoprotein (an indicator of inflammation) was increased in OVX rats with inflammation. With regard to bone variables, osteopenia in OVX was exacerbated by inflammation, as shown by a decrease in metaphyseal and total femoral mineral density. Both oleuropein and olive oil prevented this bone loss in OVX rats with inflammation. At necropsy, oleuropein and olive oil consumption had had no effect on plasma osteocalcin concentrations (marker of bone formation) or on urinary deoxypyridinoline excretion (marker of bone resorption). In conclusion, oleuropein and olive-oil feeding can prevent inflammation-induced osteopenia in OVX rats.