Motivation: Comparative genomics heavily relies on alignments of large and often complex DNA sequences. From an engineering perspective, the problem here is to provide maximum sensitivity (to find all there is to find), specificity (to only find real homology) and speed (to accommodate the billions of base pairs of vertebrate genomes).

Results: Satsuma addresses all three issues through novel strategies: (i) cross-correlation, implemented via fast Fourier transform; (ii) a match scoring scheme that eliminates almost all false hits; and (iii) an asynchronous 'battleship'-like search that allows for aligning two entire fish genomes (470 and 217 Mb) in 120 CPU hours using 15 processors on a single machine.

Availability: Satsuma is part of the Spines software package, implemented in C++ on Linux. The latest version of Spines can be freely downloaded under the LGPL license from http://www.broadinstitute.org/science/programs/genome-biology/spines/ Contact: grabherr@broadinstitute.org

Two squeeze-film gas damping models are proposed to quantify uncertainties associated with the gap size and the ambient pressure. Modeling of gas damping has become a subject of increased interest in recent years due to its importance in micro-electro-mechanical systems (MEMS). In addition to the need for gas damping models for design of MEMS with movable micro-structures, knowledge of parameter dependence in gas damping contributes to the understanding of device-level reliability. In this work, two damping models quantifying the uncertainty in parameters are generated based on rarefied flow simulations. One is a generalized polynomial chaos (gPC) model, which is a general strategy for uncertainty quantification, and the other is a compact model developed specifically for this problem in an early work. Convergence and statistical analysis have been conducted to verify both models. By taking the gap size and ambient pressure as random fields with known probability distribution functions (PDF), the output PDF for the damping coefficient can be obtained. The first four central moments are used in comparisons of the resulting non-parametric distributions. A good agreement has been found, within 1\%, for the relative difference for damping coefficient mean values. In study of geometric uncertainty, it is found that the average damping coefficient can deviate up to 13% from the damping coefficient corresponding to the average gap size. The difference is significant at the nonlinear region where the flow is in slip or transitional rarefied regimes.

Keywords: uncertainty quantification, squeeze-film damping, gPC expansion, rarefied flow

In this chapter, we present a high performance multi-scale 3D image processing framework to exploit the parallel processing power of multiple graphic processing units (Multi-GPUs) for medical image analysis. We developed GPU algorithms and data structures that can be applied to a wide range of 3D image processing applications and efficiently exploit the computational power and massive bandwidth offered by modern GPUs. Our framework helps scientists solve computationally intensive problems which previously required super computing power. To demonstrate the effectiveness of our framework and to compare to existing techniques, we focus our discussions on atlas construction - the application of understanding the development of the brain and the progression of brain diseases.

Deformable image registration in the presence of considerable contrast differences and large-scale size and shape changes represents a significant challenge for image registration. A representative driving application is the study of early brain development in neuroimaging, which requires co-registration of images of the same subject across time or building 4-D population atlases. Growth during the first few years of development involves significant changes in size and shape of anatomical structures but also rapid changes in tissue properties due to myelination and structuring that are reflected in the multi-modal Magnetic Resonance (MR) contrastmeasurements. We propose a new registration method that generates a mapping between brain anatomies represented as a multi-compartment model of tissue class posterior images and geometries.We transform intensity patterns into combined probabilistic and geometric descriptors that drive thematching in a diffeomorphic framework, where distances between geometries are represented using currents which does not require geometric correspondence. We show preliminary results on the registrations of neonatal brainMRIs to two-year old infantMRIs using class posteriors and surface boundaries of structures undergoing major changes. Quantitative validation demonstrates that our proposedmethod generates registrations that better preserve the consistency of anatomical structures over time.

Keywords: netl

In the field of uncertainty quantification, uncertainty in the governing equations may assume two forms: aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty can be characterised by known probability distributions whilst epistemic uncertainty arises from a lack of knowledge of probabilistic information. While extensive research efforts have been devoted to the numerical treatment of aleatory uncertainty, little attention has been given to the quantification of epistemic uncertainty. In this paper, we propose a numerical framework for quantification of epistemic uncertainty. The proposed methodology does not require any probabilistic information on uncertain input parameters. The method only necessitates an estimate of the range of the uncertain variables that encapsulates the true range of the input variables with overwhelming probability. To quantify the epistemic uncertainty, we solve an encapsulation problem, which is a solution to the original governing equations defined on the estimated range of the input variables. We discuss solution strategies for solving the encapsulation problem and the sufficient conditions under which the numerical solution can serve as a good estimator for capturing the effects of the epistemic uncertainty. In the case where probability distributions of the epistemic variables become known a posteriori, we can use the information to post-process the solution and evaluate solution statistics. Convergence results are also established for such cases, along with strategies for dealing with mixed aleatory and epistemic uncertainty. Several numerical examples are presented to demonstrate the procedure and properties of the proposed methodology.

Keywords: Uncertainty quantification, Epistemic uncertainty, Generalized polynomial chaos, Stochastic collocation, Encapsulation problem

The use of (a posteriori) error estimates is a fundamental tool in the application of adaptive numerical methods across a range of fluid flow problems. Such estimates are incomplete however, in that they do not necessarily indicate where to refine in order to achieve the most impact on the error, nor what type of refinement (for example h-refinement or p-refinement) will be best. This paper extends preliminary work of the authors (Comm Comp Phys, 2010;7:631–8), which uses adjoint-based sensitivity estimates in order to address these questions, to include application with p-refinement to arbitrary order and the use of practical a posteriori estimates. Results are presented which demonstrate that the proposed approach can guide both the h-refinement and the p-refinement processes, to yield improvements in the adaptive strategy compared to the use of more orthodox criteria.