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

Identification of novel components of Trypanosoma brucei editosomes

The editosome is a multiprotein complex that catalyzes the insertion and deletion of uridylates that occurs during RNA editing in trypanosomatids. We report the identification of nine novel editosome proteins in Trypanosoma brucei. They were identified by mass spectrometric analysis of functional editosomes that were purified by serial ion exchange/gel permeation chromatography, immunoaffinity chromatography specific to the TbMP63 editosome protein, or tandem affinity purification based on a tagged RNA editing ligase. The newly identified proteins have ribonuclease and/or RNA binding motifs suggesting nuclease function for at least some of these. Five of the proteins are interrelated, as are two others, and one is related to four previously identified editosome proteins. The implications of these findings are discussed

R-Mode Oscillations in Rotating Magnetic Neutron Stars

We show that r-mode oscillations distort the magnetic fields of neutron stars and that their occurrence is likely to be limited by this interaction. If the field is gtrsim 10^{16} (Omega/Omega_B) G, where Omega and Omega_B are the angular velocities of the star and at which mass shedding occurs, r-mode oscillations cannot occur. Much weaker fields will prevent gravitational radiation from exciting r-mode oscillations or damp them on a relatively short timescale by extracting energy from the modes faster than gravitational wave emission can pump energy into them. For example, a 10^{10} G poloidal magnetic field that threads the star's superconducting core is likely to prevent the ell=2 mode from being excited unless Omega exceeds 0.35 Omega_B. If Omega is larger than 0.35 Omega_B initially, the ell=2 mode may be excited but is likely to decay rapidly once Omega falls below 0.35 Omega_B, which happens in lesssim 15^d if the saturation amplitude is gtrsim 0.1. The r-mode oscillations may play an important role in determining the structure of neutron star magnetic fields.Comment: 4 pages, 1 postscript figure, uses emulateapj; submitted to ApJ Letters 1999 Nov 8; accepted 2000 Jan 25; this version is essentially identical to the original version except that Figure 2 was deleted in order to fit within the ApJ Letters page limi

Variants within the MMP3 gene are associated with achilles tendinopathy: possible interaction with the COL5A1 gene

Objectives: Sequence variation within the COL5A1 and TNC genes are known to associate with Achilles tendinopathy. The primary aim of this case-control genetic association study was to investigate whether variants within the matrix metalloproteinase 3 (MMP3) gene also contributed to both Achilles tendinopathy and Achilles tendon rupture in a Caucasian population. A secondary aim was to establish whether variants within the MMP3 gene interacted with the COL5A1 rs12722 variant to raise risk of these pathologies. Methods: 114 subjects with symptoms of Achilles tendon pathology and 98 healthy controls were genotyped for MMP3 variants rs679620, rs591058 and rs650108. Results: As single markers, significant associations were found between the GG genotype of rs679620 (OR = 2.5, 95% CI 1.2 to 4.90, p = 0.010), the CC genotype of rs591058 (OR = 2.3, 95% CI 1.1 to 4.50, p = 0.023) and the AA genotype of rs650108 (OR = 4.9, 95% CI 1.0 to 24.1, p = 0.043) and risk of Achilles tendinopathy. The ATG haplotype (rs679620, rs591058, and rs650108) was under-represented in the tendinopathy group when compared to the control group (41% vs 53%, p = 0.038). Finally, the G allele of rs679620 and the T allele of COL5A1 rs12722 significantly interacted to raise risk of AT (p = 0.006). No associations were found between any of the MMP3 markers and Achilles tendon rupture. Conclusion: Variants within the MMP3 gene are associated with Achilles tendinopathy. Furthermore, the MMP3 gene variant rs679620 and the COL5A1 marker rs12722 interact to modify the risk of tendinopathy. These data further support a genetic contribution to a common sports related injur

Digging deeper : in search of the mechanisms of carbon and nitrogen exchange in ectomycorrhizal symbioses

Symbiosis with ectomycorrhizal (ECM) fungi is an advantageous partnership for trees in nutrient-limited environments. Ectomycorrhizal fungi colonize the roots of their hosts and improve their access to nutrients, usually nitrogen (N) and, in exchange, trees deliver a significant portion of their photosynthetic carbon (C) to the fungi. This nutrient exchange affects key soil processes and nutrient cycling, as well as plant health, and is therefore central to forest ecosystem functioning. Due to their ecological importance, there is a need to more accurately understand ECM fungal mediated C and N movement within forest ecosystems such that we can better model and predict their role in soil processes both now and under future climate scenarios. There are a number of hurdles that we must overcome, however, before this is achievable such as understanding how the evolutionary history of ECM fungi and their inter- and intra- species variability affect their function. Further, there is currently no generally accepted universal mechanism that appears to govern the flux of nutrients between fungal and plant partners. Here, we consider the current state of knowledge on N acquisition and transport by ECM fungi and how C and N exchange may be related or affected by environmental conditions such as N availability. We emphasize the role that modern genomic analysis, molecular biology techniques and more comprehensive and standardized experimental designs may have in bringing cohesion to the numerous ecological studies in this area and assist us in better understanding this important symbiosis. These approaches will help to build unified models of nutrient exchange and develop diagnostic tools to study these fungi at various scales and environments

Holonomy on D-Branes

This paper shows how to construct anomaly free world sheet actions in string theory with $D$-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to $D$-branes and connections on them. The holonomy of these connections can be used to cancel global anomalies in the world sheet action.Comment: Corrections made and some typographical errors remove

Properties of r modes in rotating magnetic neutron stars. II. Evolution of the r modes and stellar magnetic field

The evolution of the r-mode instability is likely to be accompanied by secular kinematic effects which will produce differential rotation with large scale drifts of fluid elements, mostly in the azimuthal direction. As first discussed by Rezzolla, Lamb and Shapiro 2000, the interaction of these secular velocity fields with a pre-existing neutron star magnetic field could result in the generation of intense and large scale toroidal fields. Following their derivation in the companion paper, we here discuss the numerical solution of the evolution equations for the magnetic field. The values of the magnetic fields obtained in this way are used to estimate the conditions under which the r-mode instability might be prevented or suppressed. We also assess the impact of the generation of large magnetic fields on the gravitational wave detectability of r-mode unstable neutron stars. Our results indicate that the signal to noise ratio in the detection of gravitational waves from the r-mode instability might be considerably decreased if the latter develops in neutron stars with initial magnetic fields larger than 10^10 G.Comment: 16 pages, 12 figures. To appear in Phys. Rev.

Can a Bose gas be saturated?

Bose-Einstein condensation is unique among phase transitions between different states of matter in the sense that it occurs even in the absence of interactions between particles. In Einstein's textbook picture of an ideal gas, purely statistical arguments set an upper bound on the number of particles occupying the excited states of the system, and condensation is driven by this saturation of the quantum vapour. Dilute ultracold atomic gases are celebrated as a realisation of Bose-Einstein condensation in close to its purely statistical form. Here we scrutinise this point of view using an ultracold gas of potassium (39K) atoms, in which the strength of interactions can be tuned via a Feshbach scattering resonance. We first show that under typical experi-mental conditions a partially condensed atomic gas strongly deviates from the textbook concept of a saturated vapour. We then use measurements at a range of interaction strengths and temperatures to extrapolate to the non-interacting limit, and prove that in this limit the behaviour of a Bose gas is consistent with the saturation picture. Finally, we provide evidence for the universality of our observations through additional measurements with a different atomic species, 87Rb. Our results suggest a new way of characterising condensation phenomena in different physical systems.Comment: 6 pages, 5 figure

CydDC-mediated reductant export in Escherichia coli controls the transcriptional wiring of energy metabolism and combats nitrosative stress

The glutathione/cysteine exporter CydDC maintains redox balance in Escherichia coli. A cydD mutant strain was used to probe the influence of CydDC upon reduced thiol export, gene expression, metabolic perturbations, intracellular pH homeostasis, and tolerance to nitric oxide (NO). Loss of CydDC was found to decrease extracytoplasmic thiol levels, whereas overexpression diminished the cytoplasmic thiol content. Transcriptomic analysis revealed a dramatic up-regulation of protein chaperones, protein degradation (via phenylpropionate/phenylacetate catabolism), ?-oxidation of fatty acids, and genes involved in nitrate/nitrite reduction. 1H NMR metabolomics revealed elevated methionine and betaine and diminished acetate and NAD+ in cydD cells, which was consistent with the transcriptomics-based metabolic model. The growth rate and ?pH, however, were unaffected, although the cydD strain did exhibit sensitivity to the NO-releasing compound NOC-12. These observations are consistent with the hypothesis that the loss of CydDC-mediated reductant export promotes protein misfolding, adaptations to energy metabolism, and sensitivity to NO. The addition of both glutathione and cysteine to the medium was found to complement the loss of bd -type cytochrome synthesis in a cydD strain (a key component of the pleiotropic cydDC phenotype), providing the first direct evidence that CydDC substrates are able to restore the correct assembly of this respiratory oxidase. These data provide an insight into the metabolic flexibility of E. coli , highlight the importance of bacterial redox homeostasis during nitrosative stress, and report for the first time the ability of periplasmic low molecular weight thiols to restore haem incorporation into a cytochrome complex