Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

Matching Schur complement approximations for certain saddle-point systems

The solution of many practical problems described by mathematical models requires approximation methods that give rise to linear(ized) systems of equations, solving which will determine the desired approximation. This short contribution describes a particularly effective solution approach for a certain class of so-called saddle-point linear systems which arises in different contexts

On Block Triangular Preconditioners for the Interior Point Solution of PDE-Constrained Optimization Problems

We consider the numerical solution of saddle point systems of equations resulting from the discretization of PDE-constrained optimization problems, with additional bound constraints on the state and control variables, using an interior point method. In particular, we derive a Bramble-Pasciak Conjugate Gradient method and a tailored block triangular preconditioner which may be applied within it. Crucial to the usage of the preconditioner are carefully chosen approximations of the (1,1)-block and Schur complement of the saddle point system. To apply the inverse of the Schur complement approximation, which is computationally the most expensive part of the preconditioner, one may then utilize methods such as multigrid or domain decomposition to handle individual sub-blocks of the matrix system

Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms

PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\rm L^1$ term within the objective function requires sophisticated optimization methods. We propose the use of an Interior Point scheme applied to a smoothed reformulation of the discretized problem, and illustrate that such a scheme exhibits robust performance with respect to parameter changes. To increase the potency of this method we introduce fast and efficient preconditioners which enable us to solve problems from a number of PDE applications in low iteration numbers and CPU times, even when the parameters involved are altered dramatically

Evidence for a pervasive 'idling-mode' activity template in flying and pedestrian insects

This is the final version. Available on open access from the Royal Society via the DOI in this recordUnderstanding the complex movement patterns of animals in natural environments is a key objective of 'movement ecology'. Complexity results from behavioural responses to external stimuli but can also arise spontaneously in their absence. Drawing on theoretical arguments about decision-making circuitry, we predict that the spontaneous patterns will be scale-free and universal, being independent of taxon and mode of locomotion. To test this hypothesis, we examined the activity patterns of the European honeybee, and multiple species of noctuid moth, tethered to flight mills and exposed to minimal external cues. We also reanalysed pre-existing data for Drosophila flies walking in featureless environments. Across these species, we found evidence of common scale-invariant properties in their movement patterns; pause and movement durations were typically power law distributed over a range of scales and characterized by exponents close to 3/2. Our analyses are suggestive of the presence of a pervasive scale-invariant template for locomotion which, when acted on by environmental cues, produces the movements with characteristic scales observed in nature. Our results indicate that scale-finite complexity as embodied, for instance, in correlated random walk models, may be the result of environmental cues overriding innate behaviour, and that scale-free movements may be intrinsic and not limited to 'blind' foragers as previously thought.Rothamsted research receives grant aided support from the Biotechnology and Biological Sciences Research Council. S.W. was funded jointly by a grant from BBSRC, Defra, NERC, the Scottish Government and the Wellcome Trust, under the Insect Pollinators Initiative (grant nos. BB/I00097/1). A.J.P. was funded by a BBSRC Doctoral Training Partnership in Food Security awarded to K.W. and J.W.C. H.B.C.J. was funded by a BBSRC Quota studentship awarded to J.W.C. and J.K.

A short-term mouse model that reproduces the immunopathological features of rhinovirus-induced exacerbation of COPD

© 2015 The Author(s). Viral exacerbations of chronic obstructive pulmonary disease (COPD), commonly caused by rhinovirus (RV) infections, are poorly controlled by current therapies. This is due to a lack of understanding of the underlying immunopathological mechanisms. Human studies have identified a number of key immune responses that are associated with RV-induced exacerbations including neutrophilic inflammation, expression of inflammatory cytokines and deficiencies in innate anti-viral interferon. Animal models of COPD exacerbation are required to determine the contribution of these responses to disease pathogenesis. We aimed to develop a short-term mouse model that reproduced the hallmark features of RV-induced exacerbation of COPD. Evaluation of complex protocols involving multiple dose elastase and lipopolysaccharide (LPS) administration combined with RV1B infection showed suppression rather than enhancement of inflammatory parameters compared with control mice infected with RV1B alone. Therefore, these approaches did not accurately model the enhanced inflammation associated with RV infection in patients with COPD compared with healthy subjects. In contrast, a single elastase treatment followed by RV infection led to heightened airway neutrophilic and lymphocytic inflammation, increased expression of tumour necrosis factor (TNF)-α, C-X-C motif chemokine 10 (CXCL10)/IP-10 (interferon γ-induced protein 10) and CCL5 [chemokine (C-C motif) ligand 5]/RANTES (regulated on activation, normal T-cell expressed and secreted), mucus hypersecretion and preliminary evidence for increased airway hyper-responsiveness compared with mice treated with elastase or RV infection alone. In summary, we have developed a new mouse model of RV-induced COPD exacerbation that mimics many of the inflammatory features of human disease. This model, in conjunction with human models of disease, will provide an essential tool for studying disease mechanisms and allow testing of novel therapies with potential to be translated into clinical practice

Transplantation of Photoreceptor Precursors Isolated via a Cell Surface Biomarker Panel From Embryonic Stem Cell-Derived Self-Forming Retina.

Loss of photoreceptors due to retinal degeneration is a major cause of untreatable blindness. Cell replacement therapy, using pluripotent stem cell-derived photoreceptor cells, may be a feasible future treatment. Achieving safe and effective cell replacement is critically dependent on the stringent selection and purification of optimal cells for transplantation. Previously, we demonstrated effective transplantation of post-mitotic photoreceptor precursor cells labelled by fluorescent reporter genes. As genetically labelled cells are not desirable for therapy, here we developed a surface biomarker cell selection strategy for application to complex pluripotent stem cell differentiation cultures. We show that a five cell surface biomarker panel CD73(+)CD24(+)CD133(+)CD47(+)CD15(-) facilitates the isolation of photoreceptor precursors from three-dimensional self-forming retina differentiated from mouse embryonic stem cells. Importantly, stem cell-derived cells isolated using the biomarker panel successfully integrate and mature into new rod photoreceptors in the adult mouse retinae after subretinal transplantation. Conversely, unsorted or negatively selected cells do not give rise to newly integrated rods after transplantation. The biomarker panel also removes detrimental proliferating cells prior to transplantation. Notably, we demonstrate how expression of the biomarker panel is conserved in the human retina and propose that a similar selection strategy will facilitate isolation of human transplantation-competent cells for therapeutic application. Stem Cells 2015;33:2469-2482

Developing Prognosis Tools to Identify Learning Difficulties in Children Using Machine Learning Technologies

The Mental Attributes Profiling System was developed in 2002 (Laouris and Makris, Proceedings of multilingual & cross-cultural perspectives on Dyslexia, Omni Shoreham Hotel, Washington, D.C, 2002), to provide a multimodal evaluation of the learning potential and abilities of young children’s brains. The method is based on the assessment of non-verbal abilities using video-like interfaces and was compared to more established methodologies in (Papadopoulos, Laouris, Makris, Proceedings of IDA 54th annual conference, San Diego, 2003), such as the Wechsler Intelligence Scale for Children (Watkins et al., Psychol Sch 34(4):309–319, 1997). To do so, various tests have been applied to a population of 134 children aged 7–12 years old. This paper addresses the issue of identifying a minimal set of variables that are able to accurately predict the learning abilities of a given child. The use of Machine Learning technologies to do this provides the advantage of making no prior assumptions about the nature of the data and eliminating natural bias associated with data processing carried out by humans. Kohonen’s Self Organising Maps (Kohonen, Biol Cybern 43:59–69, 1982) algorithm is able to split a population into groups based on large and complex sets of observations. Once the population is split, the individual groups can then be probed for their defining characteristics providing insight into the rationale of the split. The characteristics identified form the basis of classification systems that are able to accurately predict which group an individual will belong to, using only a small subset of the tests available. The specifics of this methodology are detailed herein, and the resulting classification systems provide an effective tool to prognose the learning abilities of new subjects

RNAi-mediated suppression of vimentin or glial fibrillary acidic protein prevents the establishment of Müller glial cell hypertrophy in progressive retinal degeneration.

Gliosis is a complex process comprising upregulation of intermediate filament (IF) proteins, particularly glial fibrillary acidic protein (GFAP) and vimentin, changes in glial cell morphology (hypertrophy) and increased deposition of inhibitory extracellular matrix molecules. Gliosis is common to numerous pathologies and can have deleterious effects on tissue function and regeneration. The role of IFs in gliosis is controversial, but a key hypothesized function is the stabilization of glial cell hypertrophy. Here, we developed RNAi approaches to examine the role of GFAP and vimentin in vivo in a murine model of inherited retinal degeneration, the Rhodopsin knockout (Rho-/- ) mouse. Specifically, we sought to examine the role of these IFs in the establishment of Müller glial hypertrophy during progressive degeneration, as opposed to (more commonly assessed) acute injury. Prevention of Gfap upregulation had a significant effect on the morphology of reactive Müller glia cells in vivo and, more strikingly, the reduction of Vimentin expression almost completely prevented these cells from undergoing degeneration-associated hypertrophy. Moreover, and in contrast to studies in knockout mice, simultaneous suppression of both GFAP and vimentin expression led to severe changes in the cytoarchitecture of the retina, in both diseased and wild-type eyes. These data demonstrate a crucial role for Vimentin, as well as GFAP, in the establishment of glial hypertrophy and support the further exploration of RNAi-mediated knockdown of vimentin as a potential therapeutic approach for modulating scar formation in the degenerating retina