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 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

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.

Monitoring Ion Channel Function In Real Time Through Quantum Decoherence

In drug discovery research there is a clear and urgent need for non-invasive detection of cell membrane ion channel operation with wide-field capability. Existing techniques are generally invasive, require specialized nano structures, or are only applicable to certain ion channel species. We show that quantum nanotechnology has enormous potential to provide a novel solution to this problem. The nitrogen-vacancy (NV) centre in nano-diamond is currently of great interest as a novel single atom quantum probe for nanoscale processes. However, until now, beyond the use of diamond nanocrystals as fluorescence markers, nothing was known about the quantum behaviour of a NV probe in the complex room temperature extra-cellular environment. For the first time we explore in detail the quantum dynamics of a NV probe in proximity to the ion channel, lipid bilayer and surrounding aqueous environment. Our theoretical results indicate that real-time detection of ion channel operation at millisecond resolution is possible by directly monitoring the quantum decoherence of the NV probe. With the potential to scan and scale-up to an array-based system this conclusion may have wide ranging implications for nanoscale biology and drug discovery.Comment: 7 pages, 6 figure

Evaluating clinical utility of subgingival and salivary endotoxin activity levels as periodontal biomarkers.

OBJECTIVES: The use of periodontal biomarkers for identification and monitoring of unique patient populations could foster better stratification of at-risk groups, increase access to treatment for those most in need, facilitate preventive measures and improve personalised care plans. The aim of this study was to examine the diagnostic and prognostic utility of oral lipopolysaccharides as bacterially-derived periodontal biomarkers. METHODS: Periodontal parameters were recorded, and saliva and subgingival plaque samples were collected at the beginning of the study from periodontally healthy volunteers and periodontitis patients, and three months after completion of conventional periodontal treatment in the periodontitis group. Endotoxin activity in the samples was measured using the recombinant factor C assay. Associations between clinical periodontal parameters and subgingival and salivary endotoxin activities were analysed using a multivariate regression model, while the ROC curve was applied to estimate the sensitivity, specificity and c-statistics for salivary and subgingival endotoxin activities as diagnostic biomarkers for periodontitis. RESULTS: Significant correlations were found between subgingival endotoxin activities, probing pocket depth and periodontal diagnosis, which were independent from patients' age, gender and smoking status. In addition, subgingival endotoxin levels had high specificity and sensitivity in detecting periodontal health and disease (0.91 and 0.85 respectively). Salivary endotoxin activity was positively associated with periodontal diagnosis, mean probing pocket depth, percentages of sites over 4 mm and full mouth bleeding score. However, it was inferior in discriminating patients with stable periodontium from those with periodontitis (sensitivity = 0.69, specificity = 0.61) compared to subgingival endotoxin activity. CONCLUSIONS: Subgingival endotoxin activity has good diagnostic and prognostic values as a site-specific periodontal biomarker and is not influenced by the patient's age, gender or smoking status. In contrast, salivary endotoxin activity, as a patient-level biomarker, is dependent on patient's age, has poorer diagnostic and prognostic capability, but shows good correlations with disease susceptibility and both its extent and severity

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

Synoptic Lagrangian maps: Application to surface transport in Monterey Bay

Here we report on an effort to describe in detail the evolution of surface water particles in Monterey Bay from the time they first enter until the time they leave. The data used for this study are objective mappings from hourly surface currents obtained from high frequency (HF) radar measurements in Monterey Bay for the period 2 June through 4 August 1999. The basic concept is simple: compute the origin and fate of a large number of particles for every hour during the analysis period. However, analyzing and displaying the enormous amount of computed trajectory information required a new data compression technique: synoptic Lagrangian maps produced by representing each trajectory by its origin/fate and its residence time. The results show unexpected complexity and variability not apparent in the Eulerian current archive. For example, the fraction of particles that escaped to the open ocean during this period varied from about 17 to more than 92 percent. Mean particle residence times ranged from 4.5 to 11 days. The distribution of particle residence times and transport pathways varied over time scales from hours to weeks, and space scales from 2 to 40 km. The wide range of variability in particle properties reported here shows that surface transport studies in Monterey Bay require detailed wind and tidal current information over the entire bay, as well as information about the flow along the open ocean boundary

Demographic and psychological predictors of community pharmacists’ cancer-related conversations with patients: a cross-sectional analysis and survey study

BACKGROUND: There is increasing interest in the role of community pharmacy in the early diagnosis and prevention of cancer. This study set out to examine how often community pharmacists (CPs) encourage patients to spot or respond to potential signs and symptoms of cancer, and how often they help people to make an informed decision about taking part in bowel cancer screening. METHODS: Data from 400 UK CPs, who completed the 2018 Cancer Research UK Healthcare Professional Tracker survey, were analysed. The primary outcomes were: ‘how often CPs encourage patients to spot or respond to potential signs and symptoms of cancer’ and ‘how often CPs encourage eligible people to make an informed decision to participate in bowel cancer screening’. Associations between behaviours and demographic and psychological variables (Capability, Opportunity and Motivation) were assessed using multivariate logistic regression. RESULTS: Most (n = 331, 82.8%) CPs reported occasionally, frequently or always encouraging patients to spot or respond to potential signs and symptoms of cancer, while only half (n = 203, 50.8%) reported occasionally, frequently or always helping people make an informed decision to participate in bowel cancer screening. Female sex (aOR: 3.20, 95%CI: 1.51, 6.81; p < 0.01) and increased Opportunity (aOR: 1.72, 95%CIs: 1.12, 2.64; p < 0.05) and Motivation (aOR: 1.76, 95%CIs: 1.37, 2.27; p < 0.001) were associated with encouraging patients to spot or respond to potential signs and symptoms of cancer; all three psychological variables were associated with helping people to make an informed decision to participate in bowel cancer screening (Capability: aOR: 1.39, 95%CIs: 1.26, 1.52, p < 0.001; Opportunity: aOR: 1.44, 95%CIs: 1.11, 1.87; p < 0.01; Motivation: aOR: 1.45, 95%CIs: 1.05, 2.00; p < 0.05). CONCLUSIONS: Most CPs encourage patients to spot or respond to potential cancer symptoms, while only half help them make an informed decision to participate in bowel cancer screening. A multifaceted approach, targeting multiple COM-B components, is required to change these behaviours

Shallow slow earthquakes to decipher future catastrophic earthquakes in the Guerrero seismic gap

海底地震計記録で読み解く地震空白域の将来 --メキシコ・ゲレロ州沖合の地震空白域のスロー地震活動の発見--. 京都大学プレスリリース. 2021-06-29.The Guerrero seismic gap is presumed to be a major source of seismic and tsunami hazard along the Mexican subduction zone. Until recently, there were limited observations at the shallow portion of the plate interface offshore Guerrero, so we deployed instruments there to better characterize the extent of the seismogenic zone. Here we report the discovery of episodic shallow tremors and potential slow slip events in Guerrero offshore. Their distribution, together with that of repeating earthquakes, seismicity, residual gravity and bathymetry, suggest that a portion of the shallow plate interface in the gap undergoes stable slip. This mechanical condition may not only explain the long return period of large earthquakes inside the gap, but also reveals why the rupture from past M < 8 earthquakes on adjacent megathrust segments did not propagate into the gap to result in much larger events. However, dynamic rupture effects could drive one of these nearby earthquakes to break through the entire Guerrero seismic gap