Approximation of Bayesian inverse problems for PDEs

Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at the level of probability measures. The stability which results from this well posedness may be used as the basis for quantifying the approximation, in finite dimensional spaces, of inverse problems for functions. This paper contains a theory which utilizes this stability property to estimate the distance between the true and approximate posterior distributions, in the Hellinger metric, in terms of error estimates for approximation of the underlying forward problem. This is potentially useful as it allows for the transfer of estimates from the numerical analysis of forward problems into estimates for the solution of the related inverse problem. It is noteworthy that, when the prior is a Gaussian random field model, controlling differences in the Hellinger metric leads to control on the differences between expected values of polynomially bounded functions and operators, including the mean and covariance operator. The ideas are applied to some non-Gaussian inverse problems where the goal is determination of the initial condition for the Stokes or Navier–Stokes equation from Lagrangian and Eulerian observations, respectively

Non-perturbative renormalization of meson decay constants in quenched QCD for a renormalization group improved gauge action

Renormalization constants ($Z$-factors) of vector and axial-vector currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schr\"odinger functional method. Non-perturbative values of $Z$-factors turn out to be smaller than one-loop perturbative values by $O(15$ at lattice spacing of $a^{-1}\approx$ 1 GeV. The pseudoscalar and vector meson decay constants calculated with the non-perturbative $Z$-factors show a much better scaling behavior compared to previous results obtained with tadpole improved one-loop $Z$-factors. In particular, the non-perturbative $Z$-factors normalized at infinite physical volume show that scaling violation of the decay constants are within about 10% up to the lattice spacing $a^{-1}\sim 1$ GeV. The continuum estimates obtained from data in the range $a^{-1}=$ 1 -- 2 GeV agree with those determined from finer lattices ($a^{-1}\sim 2-4$ GeV) with the standard action.Comment: 19 pages, 18 eps figures. Corrected addres

Ileus Biliaire : A Propos D’un Cas Clinique

Introduction: Gallstone ileus is a rare mechanical occlusion. It is caused by the enclosure of biliary macro lithiasis in a portion of the digestive tract resulting from a digestive bile fistula. We report a clinical case to discuss therapeutic modalities through a review of the literature. Medical observation: We report the case of a 77-year-old patient who was hospitalized in the Nephrology department of the university hospital in Montpellier for functional kidney failure and dehydration from vomiting and diarrhea. The none-injected abdominal-pelvic CT scan showed a gallstone ileus with 5 enclaved duodenum, jejunum and ileum lithiasis resulting into a small bowel obstruction. There are no signs of acute cholecystitis. The management was simple by enterolithotomy surgery alone after fixing of hydro electrolyte imbalance. The after surgery sequence was simple. Conclusion: Gallstone ileus is a rare surgical condition. The high mortality rate in the management of this condition makes enterolithotomy the least invasive and recommended method

Non-perturbative renormalization of vector and axial vector currents in quenched QCD for a renormalization group improved gauge action

Renormalization constants of vector ($Z_V$) and axial-vector ($Z_A$) currents are determined non-perturbatively in quenched QCD for an RG-improved gauge action and a tadpole-improved clover quark action using the Schr\"odinger functional method. Meson decay constants $f_\rho$ and $f_\pi$ show much better scaling when $Z_V$ and $Z_A$ estimated for infinite physical volume are used instead of $Z$-factors from tadpole-improved one-loop perturbation theory.Comment: Lattice2003(improve), 3 page

The measurement of aircraft performance and stability and control after flight through natural icing conditions

The effects of airframe icing on the performance and stability and control of a twin-engine commuter-class aircraft were measured by the NASA Lewis Research Center. This work consisted of clear air tests with artificial ice shapes attached to the horizontal tail, and natural icing flight tests in measured icing clouds. The clear air tests employed static longitudinal flight test methods to determine degradation in stability margins for four simulated ice shapes. The natural icing flight tests employed a data acquisition system, which was provided under contract to NASA by Kohlman Systems Research Incorporated. This system used a performance modeling method and modified maximum likelihood estimation (MMLE) technique to determine aircraft performance degradation and stability and control. Flight test results with artificial ice shapes showed that longitudinal, stick-fixed, static margins are reduced on the order of 5 percent with flaps up. Natural icing tests with the KSR system corroborated these results and showed degradation in the elevator control derivatives on the order of 8 to 16 percent depending on wing flap configuration. Performance analyses showed the individual contributions of major airframe components to the overall degration in lift and drag

Non-perturbative renormalization for a renormalization group improved gauge action

Renormalization constants of vector ($Z_V$) and axial-vector ($Z_A$) currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schr\"odinger functional method. Non-perturbative values of $Z_V$ and $Z_A$ turn out to be smaller than the one-loop perturbative values by $O(10$ at $a^{-1}\approx 1$ GeV. A sizable scaling violation of meson decay constants $f_\pi$ and $f_\rho$ observed with the one-loop renormalization factors remains even with non-perturbative renormalization.Comment: Lattice2001(improvement), 3 pages, 7 figure

Crystal growth of ice Ih by revapor-deposition and diffusion suppression of monomolecular water in a polymer solid: spectroscopic observation of phase transition of water sorbed into solid polystyrene.

Monomolecular water in a solid polymer, which has no effective hydrogen bonding sites, was revealed by temperature-variable Fourier transform infrared spectroscopy to be condensable and crystallizable. Ice Ih formed in the polymer matrix was grown by vapor deposition and was reduced by sublimation. Moreover, rapid cooling induced crystal growth by vapor deposition during heating (revapor-deposition). These results indicate the requirement of a change in the generally accepted understanding of the thermal responses of water in a polymer matrix and give rise to a problem for general interpretation of the category of water in a polymer matrix based on calorimetrical analysis at very low water contents

Aged garlic extract therapy for sickle cell anemia patients

BACKGROUND: Sickle cell anemia is one of the most prevalent hereditary disorders with prominent morbidity and mortality. With this disorder oxidative, phenomena play a significant role in its pathophysiology. One of the garlic (Allium sativum L.) formulations, aged garlic extract (AGE), has been reported to exert an anti-oxidant effect in vitro, we have evaluated the anti-oxidant effect of AGE on sickle red blood cells (RBC). METHODS: Five patients (two men and three women, mean age 40 ± 15 years, range 24–58 years) with sickle cell anemia participated in the study. AGE was administered at a dose of 5 ml a day. Whole blood samples were obtained at baseline and at 4 weeks for primarily Heinz body analysis. RESULTS: The data were consistent with our hypothesis. In all patients, the number of Heinz bodies decreased over the 4 week period (58.9 ± 20.0% at baseline to 29.8 ± 15.3% at follow-up, p = 0.03). CONCLUSIONS: These data suggest that there is a significant anti-oxidant activity of AGE on sickle RBC. AGE may be further evaluated as a potential therapeutic agent to ameliorate complications of sickle cell anemia