Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

Variational Principles for Monotone and Maximal Bifunctions

2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Two parallel, pragmatic, UK multicentre, randomised controlled trials comparing surgical options for upper compartment (vault or uterine) pelvic organ prolapse (the VUE Study) : study protocol for a randomised controlled trial

The VUE study is funded by the National Institute for Health Research Health Technology Assessment programme (project number 11/129/183).

The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.

Geometric Hamiltonian formulation of a variational problem depending on the covariant acceleration

We consider a second-order variational problem depending on the covariant acceleration, which is related to the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of Pontryagin’s maximum principle, allows us to study the dynamics of the control problem.

Technique and outcomes about a new laparoscopic procedure: the Pelvic Organ Prolapse Suspension (POPS)

Pelvic organ prolapse suspension (POPS) is a recent surgical procedure for one-stage treatment of multiorgan female pelvic prolapse. This study evaluates the preliminary results of laparoscopic POPS in 54 women with a mean age of 55.2 and a BMI of 28.3. Patients underwent at the same time stapled transanal rectal resection (STARR) to correct the residual rectal prolapse. We had no relapses and the preliminary results were excellent. We evaluated the patients after 1 year follow-up and we confirmed the validity of our treatment. The technique is simplier than traditional treatments with an important reduction or completely disappearance of the pre-operative symptomatology.

A scale variational principle of Herglotz

The Herglotz problem is a generalization of the fundamental problem of the calculus of variations. In this paper, we consider a class of non-differentiable functions, where the dynamics is described by a scale derivative. Necessary conditions are derived to determine the optimal solution for the problem. Some other problems are considered, like transversality conditions, the multi-dimensional case, higher-order derivatives and for several independent variables.

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Fractional variational problems depending on indefinite integrals and with delay

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example, where we nd analytically the minimizer.

Higher-order variational problems of Herglotz type

We obtain a generalized Euler–Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given.

Conservative management for female urinary incontinence and pelvic organ prolapse review 2013 : summary of the 5th International Consultation on Incontinence

Aims The objective of the 5th International Consultation on Incontinence (ICI) chapter on Adult Conservative Management was to review and summarize the new evidence on conservative management of urinary incontinence (UI) and pelvic organ prolapse (POP) in order to compile a current reference source for clinicians, health researchers, and service planners. In this paper, we present the review highlights and new evidence on female conservative management. Methods Revision and updates of the 4th ICI Report using systematic review covering years 2008–2012. Results Each section begins with a brief definition and description of the intervention followed by a summary, where possible, of both the state and level of evidence for prevention and treatment, and ends with a “grade of recommendation.” The paper concludes with areas identified as requiring further research. Conclusions For UI, there are no prevention trials on lifestyle interventions. There are, however, few new intervention trials of lifestyle interventions involving weight loss and fluid intake with improved levels of evidence and grade of recommendation. Outside of pre- and post-natal pelvic floor muscle training (PFMT) trials for the prevention of female UI, there is a dearth of PFMT prevention trials for women with UI. PFMT remains the first-line treatment for female UI with high levels of evidence and grades of recommendation. Bladder training levels of evidence and grades of recommendation are maintained. For POP, new evidence supports the effectiveness of physiotherapy in the treatment of POP and there are now improved levels of evidence and grades of recommendation.

Variational mean-field approach to the double-exchange model

It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first- and second-order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational mean-field approach that leads to these results. We also show that the effect of the Berry phase turns out to be crucial to produce first-order paramagnetic-ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial facts: the use of a mean-field ansatz that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the mean-field techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins.

Conservative management for female urinary incontinence and pelvic organ prolapse review 2013 : summary of the 5th International Consultation on Incontinence

Aims The objective of the 5th International Consultation on Incontinence (ICI) chapter on Adult Conservative Management was to review and summarize the new evidence on conservative management of urinary incontinence (UI) and pelvic organ prolapse (POP) in order to compile a current reference source for clinicians, health researchers, and service planners. In this paper, we present the review highlights and new evidence on female conservative management. Methods Revision and updates of the 4th ICI Report using systematic review covering years 2008–2012. Results Each section begins with a brief definition and description of the intervention followed by a summary, where possible, of both the state and level of evidence for prevention and treatment, and ends with a “grade of recommendation.” The paper concludes with areas identified as requiring further research. Conclusions For UI, there are no prevention trials on lifestyle interventions. There are, however, few new intervention trials of lifestyle interventions involving weight loss and fluid intake with improved levels of evidence and grade of recommendation. Outside of pre- and post-natal pelvic floor muscle training (PFMT) trials for the prevention of female UI, there is a dearth of PFMT prevention trials for women with UI. PFMT remains the first-line treatment for female UI with high levels of evidence and grades of recommendation. Bladder training levels of evidence and grades of recommendation are maintained. For POP, new evidence supports the effectiveness of physiotherapy in the treatment of POP and there are now improved levels of evidence and grades of recommendation.

Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms.