Variational data assimilation using targetted random walks

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces

A framework for automatically checking anonymity with μ CRL

We present a powerful and flexible method for automatically checking anonymity in a possibilistic general-purpose process algebraic verification toolset. We propose new definitions of a choice anonymity degree and a player anonymity degree, to quantify the precision with which an intruder is able to single out the true originator of a given event or to associate the right event to a given protocol participant. We show how these measures of anonymity can be automatically calculated from a protocol specification in µCRL, by using a combination of dedicated tools and existing state-of-the-art µCRL tools. To illustrate the flexibility of our method we test the Dining Cryptographers problem and the FOO 92 voting protocol. Our definitions of anonymity provide an accurate picture of the different ways that anonymity can break down, due for instance to coallitions of inside intruders. Our calculations can be performed on a cluster of machines, allowing us to check protocols for large numbers of participants

A TV-Gaussian prior for infinite-dimensional Bayesian inverse problems and its numerical implementations

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, choosing an appropriate prior distribution is an important task. In particular we consider problems where the function to infer is subject to sharp jumps which render the commonly used Gaussian measures unsuitable. On the other hand, the so-called total variation (TV) prior can only be defined in a finite dimensional setting, and does not lead to a well-defined posterior measure in function spaces. In this work we present a TV-Gaussian (TG) prior to address such problems, where the TV term is used to detect sharp jumps of the function, and the Gaussian distribution is used as a reference measure so that it results in a well-defined posterior measure in the function space. We also present an efficient Markov Chain Monte Carlo (MCMC) algorithm to draw samples from the posterior distribution of the TG prior. With numerical examples we demonstrate the performance of the TG prior and the efficiency of the proposed MCMC algorithm

Satisfaction with hearing aids based on technology and style among hearing impaired persons

Introduction: Hearing loss is one of the most disabling impairments. Using a hearing aid as an attempt to improve the hearing problem can positively affect the quality of life for these people. This research was aimed to assess satisfaction of hearing impaired patients with their hearing aids regarding the employed technology and style. Materials and Methods: This descriptive-analytic cross-sectional research was conducted on 187 subjects with hearing loss who were using a hearing aid. The subjects were over 18 years of age and were using a hearing aid for at least 6 months. The Persian version of Satisfaction with Amplification in Daily Life (SADL) questionnaire was the instrument which was used for assessing satisfaction with the hearing aid. Cronbach's alpha was calculated to be 0.80 for instrument reliability. Results: A significant difference was observed among satisfaction subscales' mean scores with hearing aid technology. Also a significant difference was observed between the total satisfaction score and the hearing aid model. With respect to the analysis of satisfaction with the hearing aid and its style, cost and services was the only subscale which showed a significant difference (P=0.005). Conclusion: Respondents using hearing aids with different technology and style were estimated to be quite satisfied. Training audiologists in using more appropriate and fitting hearing aids in addition to using self-reporting questionnaires like SADL for estimating patients' social condition and participation in their life can essentially change their disability condition and countervail their hearing loss

An elementary proof of uniqueness of the particle trajectories for solutions of a class of shear-thinning non-Newtonian 2D fluids

We prove some regularity results for a class of two dimensional non-Newtonian fluids. By applying results from [Dashti and Robinson, Nonlinearity, 22 (2009), 735-746] we can then show uniqueness of particle trajectories

Optical Spectral Variability of the Very-High-Energy Gamma-Ray Blazar 1ES 1011+496

We present results of five years of optical (UBVRI) observations of the very-high-energy gamma-ray blazar 1ES 1011+496 at the MDM Observatory. We calibrated UBVRI magnitudes of five comparison stars in the field of the object. Most of our observations were done during moderately faint states of 1ES 1011+496 with R > 15.0. The light curves exhibit moderate, closely correlated variability in all optical wavebands on time scales of a few days. A cross-correlation analysis between optical bands does not show significant evidence for time lags. We find a positive correlation (Pearson's r = 0.57; probability of non-correlation P(>r) ~ 4e-8) between the R-band magnitude and the B - R color index, indicating a bluer-when-brighter trend. Snap-shot optical spectral energy distributions (SEDs) exhibit a peak within the optical regime, typically between the V and B bands. We find a strong (r = 0.78; probability of non-correlation P (>r) ~ 1e-15) positive correlation between the peak flux and the peak frequency, best fit by a relation $\nu F_{\nu}^{\rm pk} \propto \nu_{\rm pk}^k$ with k = 2.05 +/- 0.17. Such a correlation is consistent with the optical (synchrotron) variability of 1ES 1011+496 being primarily driven by changes in the magnetic field.Comment: Accepted for publication in ApJ. 16 pages, including 7 figure

Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page

Remote Sensing of Drylands: Applications of Canopy Spectral Invariants

Remote sensing plays an important role in understanding the structure and function of global terrestrial ecosystems. In this project our research focus was to characterize the dryland vegetation structure and function in the western US. Sparse distribution of vegetation, low amount of leaves on the canopies and the bright soil underneath the canopy make remote sensing of drylands a challenging task. To achieve our research goal we collected aerial and ground based optical hyperspectral and lidar data concurrent to our field campaign. We studied the potential and limitations of these sensors to retrieve canopy biochemistry and structure and to map the vegetation cover at species level