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

The art of spacecraft design: A multidisciplinary challenge

Actual design turn-around time has become shorter due to the use of optimization techniques which have been introduced into the design process. It seems that what, how and when to use these optimization techniques may be the key factor for future aircraft engineering operations. Another important aspect of this technique is that complex physical phenomena can be modeled by a simple mathematical equation. The new powerful multilevel methodology reduces time-consuming analysis significantly while maintaining the coupling effects. This simultaneous analysis method stems from the implicit function theorem and system sensitivity derivatives of input variables. Use of the Taylor's series expansion and finite differencing technique for sensitivity derivatives in each discipline makes this approach unique for screening dominant variables from nondominant variables. In this study, the current Computational Fluid Dynamics (CFD) aerodynamic and sensitivity derivative/optimization techniques are applied for a simple cone-type forebody of a high-speed vehicle configuration to understand basic aerodynamic/structure interaction in a hypersonic flight condition

Data assimilation insights on selecting the most valuable atmospheric measurements

We discuss how objective guidance on selecting the most valuable atmospheric measurements on future Mars spacecraft missions can be provided through already developed Martian atmospheric data assimilation systems, and in particular through Observing System Simulation Experiments (OSSEs) which are widely used to design instruments for the Earth’s atmosphere

Tailoring teleportation to the quantum alphabet

We introduce a refinement of the standard continuous variable teleportation measurement and displacement strategies. This refinement makes use of prior knowledge about the target state and the partial information carried by the classical channel when entanglement is non-maximal. This gives an improvement in the output quality of the protocol. The strategies we introduce could be used in current continuous variable teleportation experiments.Comment: 16 pages, 6 figures, RevTeX, made changes as recommended by referee, other minor textual corrections, resubmitted to Phys. Rev.

Variational assimilation of Lagrangian data in oceanography

We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional space-time circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover it is very robust with respect to increase of time-sampling period of observations. We have run many twin experiments in order to analyze the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We compare also the performances of the Lagrangian method to that of the classical Eulerian one. Finally we study the impact of errors on observations.Comment: 31 page

Prise En Charge Des Anévrismes Artériels Dans Un Centre Africain Non Spécialisée

Introduction: Arterial aneurysms affect 7 to 8% of people over 65 in the West and are the 2nd leading cause of death in these countries. In Africa this frequency is poorly evaluated. The objective of this work is to report the management of arterial aneurysms at the National Hospital of Niamey (HNN). Patients and methods: This was a retrospective, descriptive study over a period of eight (8) years from January 2009 to December 2016, performed in the surgical departments of the National Hospital of Niamey. Included in the study were patients of both sexes, hospitalized and / or operated for arterial aneurysm. Not included were patients treated for arterial aneurysm with incomplete records or those concerning the neurosurgical sphere. Results: During the study period, 17,748 patients were hospitalized in the general surgery departments, including 16 patients for arterial aneurysm, or 0.09% of surgical pathologies. There were 13 men (81.25%) and 3 women (18.75%), or a sex ratio of 4.33. The average age was 55.75 years with extremes ranging from 25 years old to 90 years old. The circumstances of discovery of the aneurysms were swelling of the antero-internal aspect of the thigh in 7 cases (43.75%), abdominal mass 6 cases (37.50%), then 2 cases (12.50%) of chest pain and incidental discovery in 1cas (6.25%). The most common risk factor was high blood pressure with 43.75% (7 cases). The aneurysm sat on the femoral artery in 43.75% (n = 7), of which 6 on the deep femoral and 1 on the superficial femoral, on the infrarenal aorta in 31.25% (n = 5), on thoracic aorta 12.50% (n = 2), on the iliac artery 12.50% (n = 2). For the diagnosis the angioscanner is realized in all the patients and in addition Doppler ultrasound in 43, 75% of cases. Twelve (12) patients benefited from curative surgical intervention by prosthetic graft by PTFE in 58.33% of cases and by Dacron in 41.66%. The average stay was 29.75 days and the immediate operative followup was complicated by thrombosis in 12.5% and parietal suppurations in 6.25%. We recorded two (2) deaths, ie 12.5% among non-operated patients. Conclusion: Arterial aneurysms are rare diseases at the HNN. Conventional surgery is the treatment performed in our patients. The postoperative course was simple in most cases

DNA replication stress restricts ribosomal DNA copy number

Ribosomal RNAs (rRNAs) in budding yeast are encoded by ~100–200 repeats of a 9.1kb sequence arranged in tandem on chromosome XII, the ribosomal DNA (rDNA) locus. Copy number of rDNA repeat units in eukaryotic cells is maintained far in excess of the requirement for ribosome biogenesis. Despite the importance of the repeats for both ribosomal and non-ribosomal functions, it is currently not known how “normal” copy number is determined or maintained. To identify essential genes involved in the maintenance of rDNA copy number, we developed a droplet digital PCR based assay to measure rDNA copy number in yeast and used it to screen a yeast conditional temperature-sensitive mutant collection of essential genes. Our screen revealed that low rDNA copy number is associated with compromised DNA replication. Further, subculturing yeast under two separate conditions of DNA replication stress selected for a contraction of the rDNA array independent of the replication fork blocking protein, Fob1. Interestingly, cells with a contracted array grew better than their counterparts with normal copy number under conditions of DNA replication stress. Our data indicate that DNA replication stresses select for a smaller rDNA array. We speculate that this liberates scarce replication factors for use by the rest of the genome, which in turn helps cells complete DNA replication and continue to propagate. Interestingly, tumors from mini chromosome maintenance 2 (MCM2)-deficient mice also show a loss of rDNA repeats. Our data suggest that a reduction in rDNA copy number may indicate a history of DNA replication stress, and that rDNA array size could serve as a diagnostic marker for replication stress. Taken together, these data begin to suggest the selective pressures that combine to yield a “normal” rDNA copy number

DADA: data assimilation for the detection and attribution of weather and climate-related events

A new nudging method for data assimilation, delay‐coordinate nudging, is presented. Delay‐coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each time step. Numerical experiments with a low‐order chaotic system show that the new method systematically outperforms standard nudging in different model and observational scenarios, also when using an unoptimized formulation of the delay‐nudging coefficients. A connection between the optimal delay and the dominant Lyapunov exponent of the dynamics is found based on heuristic arguments and is confirmed by the numerical results, providing a guideline for the practical implementation of the algorithm. Delay‐coordinate nudging preserves the easiness of implementation, the intuitive functioning and the reduced computational cost of the standard nudging, making it a potential alternative especially in the field of seasonal‐to‐decadal predictions with large Earth system models that limit the use of more sophisticated data assimilation procedures

No benefit of an adjunctive phototherapy protocol in treatment of periodontitis: A split-mouth randomized controlled trial

Aim: To assess the efficacy of a commercially available adjunctive phototherapy protocol (“Perio-1”) in treatment of periodontitis. Materials and Methods: In an examiner-blind, randomized, controlled, split-mouth, multicentre study, 60 periodontitis patients received root surface debridement (RSD) in sextants either alone (control sextants) or with the adjunctive phototherapy protocol (test sextants). Re-evaluation was performed at 6, 12 and 24 weeks. Results: No statistically significant differences in mean (± standard deviation) clinical attachment level (CAL) change from baseline to week 24 were observed between test (−1.00 ± 1.16 mm) and control sextants (−0.87 ± 0.79 mm) at sites with probing pocket depths (PPDs) ≥5 mm (“deep sites”) at baseline (p =.212). Comparisons between test and control sextants for all other parameters (CAL change at all sites, PPD change at deep sites/all sites, bleeding on probing, plaque scores), and for all change intervals, failed to identify any statistically significant differences. Conclusions: The phototherapy protocol did not provide any additional clinical benefits over those achieved by RSD alone. (German Clinical Trials Register DRKS00011229)