On dimension reduction in Gaussian filters

A priori dimension reduction is a widely adopted technique for reducing the computational complexity of stationary inverse problems. In this setting, the solution of an inverse problem is parameterized by a low-dimensional basis that is often obtained from the truncated Karhunen-Loeve expansion of the prior distribution. For high-dimensional inverse problems equipped with smoothing priors, this technique can lead to drastic reductions in parameter dimension and significant computational savings. In this paper, we extend the concept of a priori dimension reduction to non-stationary inverse problems, in which the goal is to sequentially infer the state of a dynamical system. Our approach proceeds in an offline-online fashion. We first identify a low-dimensional subspace in the state space before solving the inverse problem (the offline phase), using either the method of "snapshots" or regularized covariance estimation. Then this subspace is used to reduce the computational complexity of various filtering algorithms - including the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within a novel subspace-constrained Bayesian prediction-and-update procedure (the online phase). We demonstrate the performance of our new dimension reduction approach on various numerical examples. In some test cases, our approach reduces the dimensionality of the original problem by orders of magnitude and yields up to two orders of magnitude in computational savings

Oracle-based optimization applied to climate model calibration

In this paper, we show how oracle-based optimization can be effectively used for the calibration of an intermediate complexity climate model. In a fully developed example, we estimate the 12 principal parameters of the C-GOLDSTEIN climate model by using an oracle- based optimization tool, Proximal-ACCPM. The oracle is a procedure that finds, for each query point, a value for the goodness-of-fit function and an evaluation of its gradient. The difficulty in the model calibration problem stems from the need to undertake costly calculations for each simulation and also from the fact that the error function used to assess the goodness-of-fit is not convex. The method converges to a Fbest fit_ estimate over 10 times faster than a comparable test using the ensemble Kalman filter. The approach is simple to implement and potentially useful in calibrating computationally demanding models based on temporal integration (simulation), for which functional derivative information is not readily available

Abundances of the elements in the solar system

A review of the abundances and condensation temperatures of the elements and their nuclides in the solar nebula and in chondritic meteorites. Abundances of the elements in some neighboring stars are also discussed.Comment: 42 pages, 11 tables, 8 figures, chapter, In Landolt- B\"ornstein, New Series, Vol. VI/4B, Chap. 4.4, J.E. Tr\"umper (ed.), Berlin, Heidelberg, New York: Springer-Verlag, p. 560-63

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC

Seasonal-to-decadal predictions with the ensemble Kalman filter and the Norwegian Earth System Model: a twin experiment

Here, we firstly demonstrate the potential of an advanced flow dependent data assimilation method for performing seasonal-to-decadal prediction and secondly, reassess the use of sea surface temperature (SST) for initialisation of these forecasts. We use the Norwegian Climate Prediction Model (NorCPM), which is based on the Norwegian Earth System Model (NorESM) and uses the deterministic ensemble Kalman filter to assimilate observations. NorESM is a fully coupled system based on the Community Earth System Model version 1, which includes an ocean, an atmosphere, a sea ice and a land model. A numerically efficient coarse resolution version of NorESM is used. We employ a twin experiment methodology to provide an upper estimate of predictability in our model framework (i.e. without considering model bias) of NorCPM that assimilates synthetic monthly SST data (EnKF-SST). The accuracy of EnKF-SST is compared to an unconstrained ensemble run (FREE) and ensemble predictions made with near perfect (i.e. microscopic SST perturbation) initial conditions (PERFECT). We perform 10 cycles, each consisting of a 10-yr assimilation phase, followed by a 10-yr prediction. The results indicate that EnKF-SST improves sea level, ice concentration, 2 m atmospheric temperature, precipitation and 3-D hydrography compared to FREE. Improvements for the hydrography are largest near the surface and are retained for longer periods at depth. Benefits in salinity are retained for longer periods compared to temperature. Near-surface improvements are largest in the tropics, while improvements at intermediate depths are found in regions of large-scale currents, regions of deep convection, and at the Mediterranean Sea outflow. However, the benefits are often small compared to PERFECT, in particular, at depth suggesting that more observations should be assimilated in addition to SST. The EnKF-SST system is also tested for standard ocean circulation indices and demonstrates decadal predictability for Atlantic overturning and sub-polar gyre circulations, and heat content in the Nordic Seas. The system beats persistence forecast and shows skill for heat content in the Nordic Seas that is close to PERFECT

Assimilating Seizure Dynamics

Observability of a dynamical system requires an understanding of its state—the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics

Attitudes to colorectal cancer screening among ethnic minority groups in the UK

Background: Colorectal screening by Flexible Sigmoidoscopy (FS) is under evaluation in the UK. Evidence from existing cancer screening programmes indicates lower participation among minority ethnic groups than the white-British population. To ensure equality of access, it is important to understand attitudes towards screening in all ethnic groups so that barriers to screening acceptance can be addressed.Methods: Open- and closed-ended questions on knowledge about colorectal cancer and attitudes to FS screening were added to Ethnibus (TM) - a monthly, nationwide survey of the main ethnic minority communities living in the UK (Indian, Pakistani, Bangladeshi, Caribbean, African, and Chinese). Interviews (n = 875) were conducted, face-to-face, by multilingual field-workers, including 125 interviews with white-British adults.Results: All respondents showed a notable lack of knowledge about causes of colorectal cancer, which was more pronounced in ethnic minority than white-British adults. Interest in FS screening was uniformly high (> 60%), with more than 90% of those interested saying it would provide 'peace of mind'. The most frequently cited barrier to screening 'in your community' was embarrassment, particularly among ethnic minority groups.Conclusion: Educational materials should recognise that non-white groups may be less knowledgeable about colorectal cancer. The findings of the current study suggest that embarrassment may be a greater deterrent to participation to FS screening among ethnic minority groups, but this result requires exploration in further research

Perivascular-like cells contribute to the stability of the vascular network of osteogenic tissue formed from cell sheet-based constructs

In recent years several studies have been supporting the existence of a close relationship in terms of function and progeny between Mesenchymal Stem Cells (MSCs) and Pericytes. This concept has opened new perspectives for the application of MSCs in Tissue Engineering (TE), with special interest for the pre-vascularization of cell dense constructs. In this work, cell sheet technology was used to create a scaffold-free construct composed of osteogenic, endothelial and perivascular-like (CD146+) cells for improved in vivo vessel formation, maturation and stability. The CD146 pericyte-associated phenotype was induced from human bone marrow mesenchymal stem cells (hBMSCs) by the supplementation of standard culture medium with TGF-b1. Co-cultured cell sheets were obtained by culturing perivascular-like (CD146+) cells and human umbilical vein endothelial cells (HUVECs) on an hBMSCs monolayer maintained in osteogenic medium for 7 days. The perivascular-like (CD146+) cells and the HUVECs migrated and organized over the collagen-rich osteogenic cell sheet, suggesting the existence of cross-talk involving the co-cultured cell types. Furthermore the presence of that particular ECM produced by the osteoblastic cells was shown to be the key regulator for the singular observed organization. The osteogenic and angiogenic character of the proposed constructs was assessed in vivo. Immunohistochemistry analysis of the explants revealed the integration of HUVECs with the host vasculature as well as the osteogenic potential of the created construct, by the expression of osteocalcin. Additionally, the analysis of the diameter of human CD146 positive blood vessels showed a higher mean vessel diameter for the co-cultured cell sheet condition, reinforcing the advantage of the proposed model regarding blood vessels maturation and stability and for the in vitro pre-vascularization of TE constructs.Funding provided by Fundacao para a Ciencia e a Tecnologia project Skingineering (PTDC/SAU-OSM/099422/2008). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript