Bayesian data assimilation in shape registration

In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem

Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups

In the framework of large deformation diffeomorphic metric mapping (LDDMM), we develop a multi-scale theory for the diffeomorphism group based on previous works. The purpose of the paper is (1) to develop in details a variational approach for multi-scale analysis of diffeomorphisms, (2) to generalise to several scales the semidirect product representation and (3) to illustrate the resulting diffeomorphic decomposition on synthetic and real images. We also show that the approaches presented in other papers and the mixture of kernels are equivalent.Comment: 21 pages, revised version without section on evaluatio

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul tivariate background error covariance matrix $\textbf{B}_r$, and an important decrease of the computational burden o f the method, due to the drastic reduction of the dimension of the control space. % An illustration of the feasibility and the effectiveness of this method is given in the academic framework of twin experiments for a model of the equatorial Pacific ocean. It is shown that the multivariate aspect of $\textbf{B}_r$ brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method

Un-reduction

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.Comment: 25 pages, revised versio

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

Dpb11 coordinates Mec1 kinase activation with cell cycle-regulated Rad9 recruitment

Cyclin-dependent kinase phosphorylation of the replication checkpoint mediator Rad9 controls its association with Dpb11, a key activator of the yeast ATR homologue Mec1, thus conferring cell-cycle dependence to checkpoint signalling

Identifying causes of Western Pacific ITCZ drift in ECMWF System 4 hindcasts

The development of systematic biases in climate models used in operational seasonal forecasting adversely affects the quality of forecasts they produce. In this study, we examine the initial evolution of systematic biases in the ECMWF System 4 forecast model, and isolate aspects of the model simulations that lead to the development of these biases. We focus on the tendency of the simulated intertropical convergence zone in the western equatorial Pacific to drift northwards by between 0.5° and 3° of latitude depending on season. Comparing observations with both fully coupled atmosphere–ocean hindcasts and atmosphere-only hindcasts (driven by observed sea-surface temperatures), we show that the northward drift is caused by a cooling of the sea-surface temperature on the Equator. The cooling is associated with anomalous easterly wind stress and excessive evaporation during the first twenty days of hindcast, both of which occur whether air-sea interactions are permitted or not. The easterly wind bias develops immediately after initialisation throughout the lower troposphere; a westerly bias develops in the upper troposphere after about ten days of hindcast. At this point, the baroclinic structure of the wind bias suggests coupling with errors in convective heating, although the initial wind bias is barotropic in structure and appears to have an alternative origin

Chromosome microarray analysis as first-line test in pregnancies with a priori low risk for detection of submicroscopic chromosomal abnormalities

n this study, we aimed to explore the utility of chromosomal microarray analysis (CMA) in groups of pregnancies with a priori low risk for detection of submicroscopic chromosome abnormalities, usually not considered an indication for testing, in order to assess whether CMA improves the detection rate of prenatal chromosomal aberrations. A total of 3000 prenatal samples were processed in parallel using both whole-genome CMA and conventional karyotyping. The indications for prenatal testing included: advanced maternal age, maternal serum screening test abnormality, abnormal ultrasound findings, known abnormal fetal karyotype, parental anxiety, family history of a genetic condition and cell culture failure. The use of CMA resulted in an increased detection rate regardless of the indication for analysis. This was evident in high risk groups (abnormal ultrasound findings and abnormal fetal karyotype), in which the percentage of detection was 5.8% (7/120), and also in low risk groups, such as advanced maternal age (6/1118, 0.5%), and parental anxiety (11/1674, 0.7%). A total of 24 (0.8%) fetal conditions would have remained undiagnosed if only a standard karyotype had been performed. Importantly, 17 (0.6%) of such findings would have otherwise been overlooked if CMA was offered only to high risk pregnancies.The results of this study suggest that more widespread CMA testing of fetuses would result in a higher detection of clinically relevant chromosome abnormalities, even in low risk pregnancies. Our findings provide substantial evidence for the introduction of CMA as a first-line diagnostic test for all pregnant women undergoing invasive prenatal testing, regardless of risk factors