64 research outputs found
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 , 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 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
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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 atmosphereâocean 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
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