The cost of uniqueness in groundwater model calibration

Calibration of a groundwater model requires that hydraulic properties be estimated throughout a model domain. This generally constitutes an underdetermined inverse problem, for which a Solution can only be found when some kind of regularization device is included in the inversion process. Inclusion of regularization in the calibration process can be implicit, for example through the use of zones of constant parameter value, or explicit, for example through solution of a constrained minimization problem in which parameters are made to respect preferred values, or preferred relationships, to the degree necessary for a unique solution to be obtained. The cost of uniqueness is this: no matter which regularization methodology is employed, the inevitable consequence of its use is a loss of detail in the calibrated field. This, ill turn, can lead to erroneous predictions made by a model that is ostensibly well calibrated. Information made available as a by-product of the regularized inversion process allows the reasons for this loss of detail to be better understood. In particular, it is easily demonstrated that the estimated value for an hydraulic property at any point within a model domain is, in fact, a weighted average of the true hydraulic property over a much larger area. This averaging process causes loss of resolution in the estimated field. Where hydraulic conductivity is the hydraulic property being estimated, high averaging weights exist in areas that are strategically disposed with respect to measurement wells, while other areas may contribute very little to the estimated hydraulic conductivity at any point within the model domain, this possibly making the detection of hydraulic conductivity anomalies in these latter areas almost impossible. A study of the post-calibration parameter field covariance matrix allows further insights into the loss of system detail incurred through the calibration process to be gained. A comparison of pre- and post-calibration parameter covariance matrices shows that the latter often possess a much smaller spectral bandwidth than the former. It is also demonstrated that, as all inevitable consequence of the fact that a calibrated model cannot replicate every detail of the true system, model-to-measurement residuals can show a high degree of spatial correlation, a fact which must be taken into account when assessing these residuals either qualitatively, or quantitatively in the exploration of model predictive uncertainty. These principles are demonstrated using a synthetic case in which spatial parameter definition is based oil pilot points, and calibration is Implemented using both zones of piecewise constancy and constrained minimization regularization. (C) 2005 Elsevier Ltd. All rights reserved.

Investigating the performance analysis of EASI algorithm and EKENS algorithm in nonlinear model

This paper investigates the performance of EASI algorithm and the proposed EKENS algorithm for linear and nonlinear mixtures. The proposed EKENS algorithm is based on the modified equivariant algorithm and kernel density estimation. Theory and characteristic of both the algorithms are discussed for blind source separation model. The separation structure of nonlinear mixtures is based on a nonlinear stage followed by a linear stage. Simulations with artificial and natural data demonstrate the feasibility and good performance of the proposed EKENS algorithm.

Development of an in-vitro model system to investigate the mechanism of muscle protein catabolism induced by proteolysis-inducing factor

The mechanism of muscle protein catabolism induced by proteolysis-inducing factor, produced by cachexia-inducing murine and human tumours has been studied in vitro using C2C12 myoblasts and myotubes. In both myoblasts and myotubes protein degradation was enhanced by proteolysis-inducing factor after 24 h incubation. In myoblasts this followed a bell-shaped dose-response curve with maximal effects at a proteolysis-inducing factor concentration between 2 and 4 nM, while in myotubes increased protein degradation was seen at all concentrations of proteolysis-inducing factor up to 10 nM, again with a maximum of 4 nM proteolysis-inducing factor. Protein degradation induced by proteolysis-inducing factor was completely attenuated in the presence of cycloheximide (1 μM), suggesting a requirement for new protein synthesis. In both myoblasts and myotubes protein degradation was accompanied by an increased expression of the α-type subunits of the 20S proteasome as well as functional activity of the proteasome, as determined by the 'chymotrypsin-like' enzyme activity. There was also an increased expression of the 19S regulatory complex as well as the ubiquitin-conjugating enzyme (E214k), and in myotubes a decrease in myosin expression was seen with increasing concentrations of proteolysis-inducing factor. These results show that proteolysis-inducing factor co-ordinately upregulates both ubiquitin conjugation and proteasome activity in both myoblasts and myotubes and may play an important role in the muscle wasting seen in cancer cachexia. © 2002 Cancer Research UK.

Web based expert elicitation of uncertainties in environmental model inputs

When constructing and using environmental models, it is typical that many of the inputs to the models will not be known perfectly. In some cases, it will be possible to make observations, or occasionally physics-based uncertainty propagation, to ascertain the uncertainty on these inputs. However, such observations are often either not available or even possible, and another approach to characterising the uncertainty on the inputs must be sought. Even when observations are available, if the analysis is being carried out within a Bayesian framework then prior distributions will have to be specified. One option for gathering or at least estimating this information is to employ expert elicitation. Expert elicitation is well studied within statistics and psychology and involves the assessment of the beliefs of a group of experts about an uncertain quantity, (for example an input / parameter within a model), typically in terms of obtaining a probability distribution. One of the challenges in expert elicitation is to minimise the biases that might enter into the judgements made by the individual experts, and then to come to a consensus decision within the group of experts. Effort is made in the elicitation exercise to prevent biases clouding the judgements through well-devised questioning schemes. It is also important that, when reaching a consensus, the experts are exposed to the knowledge of the others in the group. Within the FP7 UncertWeb project (http://www.uncertweb.org/), there is a requirement to build a Webbased tool for expert elicitation. In this paper, we discuss some of the issues of building a Web-based elicitation system - both the technological aspects and the statistical and scientific issues. In particular, we demonstrate two tools: a Web-based system for the elicitation of continuous random variables and a system designed to elicit uncertainty about categorical random variables in the setting of landcover classification uncertainty. The first of these examples is a generic tool developed to elicit uncertainty about univariate continuous random variables. It is designed to be used within an application context and extends the existing SHELF method, adding a web interface and access to metadata. The tool is developed so that it can be readily integrated with environmental models exposed as web services. The second example was developed for the TREES-3 initiative which monitors tropical landcover change through ground-truthing at confluence points. It allows experts to validate the accuracy of automated landcover classifications using site-specific imagery and local knowledge. Experts may provide uncertainty information at various levels: from a general rating of their confidence in a site validation to a numerical ranking of the possible landcover types within a segment. A key challenge in the web based setting is the design of the user interface and the method of interacting between the problem owner and the problem experts. We show the workflow of the elicitation tool, and show how we can represent the final elicited distributions and confusion matrices using UncertML, ready for integration into uncertainty enabled workflows.We also show how the metadata associated with the elicitation exercise is captured and can be referenced from the elicited result, providing crucial lineage information and thus traceability in the decision making process.

The development of an in vivo model of drug-induced terminal differentiation of Leukaemic cells

The technique of growing human leukaemic cells in diffusion chambers was developed to enable chemicals to be assessed for their ability to induce terminal differentiation. HL-60 promyelocytic leukaemia cell growth, in a lucite chamber with a Millipore filter, was optimised by use of a lateral incision site. Chambers were constructed using 0.45um filters and contained 150ul of serum-free HL-60 cells at a density of 1x106 cells/ml. The chambers were implanted into CBA/Ca mice and spontaneous terminal differentiation of the cells to granulocytes was prevented by the use of serum-free medium. Under these conditions there was an initial growth lag of 72 hours and a logarithmic phase of growth for 96 hours; the cell number reached a plateau after 168 hours of culture in vivo. The amount of drug in the plasma of the animal and in chambers that had been implanted for 5 days, was determined after a single ip injection of equitoxic doses of N-methylformamide, N-ethylformamide, tetramethylurea, N-dibutylformamide, N-tetramethylbutylformamide and hexamethylenebisacetamide. Concentrations of both TMU and HMBA were obtained in the plasma and in the chamber which were pharmacologically effective for the induction of differentiation of HL-60 cells in vitro, that is 12mM TMU and 5mM HMBA. A 4 day regime of treatment of animals implanted with chambers demonstrated that TMU and HMBA induced terminal differentiation of 50% and 35%, respectively, of the implanted HL-60 cells to granulocyte-like cells, assessed by measurement of functional and biochemical markers of maturity. None of the other agents attained concentrations in the plasma that were pharmacologically effective for the induction of differentiation of the cells in vitro and were unable to induce the terminal differentiation of the cells in vivo.

Bistable attractors in a model of convection-driven spherical dynamos

The range of existence and the properties of two essentially different chaotic attractors found in a model of nonlinear convection-driven dynamos in rotating spherical shells are investigated. A hysteretic transition between these attractors is established as a function of the rotation parameter t. The width of the basins of attraction is also estimated. © 2012 The Royal Swedish Academy of Sciences.

Monocyte urokinase-type plasminogen activator up-regulation reduces thrombus size in a model of venous thrombosis

Background - Our previous studies showed that the direct injection of an adenovirus construct expressing urokinase-type plasminogen activator (uPA) into experimental venous thrombi significantly reduces thrombus weight. The systemic use of adenovirus vectors is limited by inherent hepatic tropism and inflammatory response. As macrophages are recruited into venous thrombi, it is reasonable to speculate that these cells could be used to target the adenovirus uPA (ad-uPA) gene construct to the thrombus. The aims of this study were to determine whether macrophages transduced with ad-uPA have increased fibrinolytic activity and whether systemic injection of transduced cells could be used to target uPA expression to the thrombus and reduce its size. Methods - The effect of up-regulating uPA was examined in an immortalized macrophage cell line (MM6) and macrophages differentiated from human blood monocyte-derived macrophages (HBMMs). Cells were infected with ad-uPA or blank control virus (ad-blank). Fibrinolytic mediator expression, cell viability, and cytokine expression were measured by activity assays and enzyme-linked immunosorbent assays. Monocyte migration was measured using a modified Boyden chamber assay. A model of venous thrombosis was developed and characterized in mice with severe combined immunodeficiency (SCID). This model was used to study whether systemically administered macrophages over-expressing uPA reduced thrombus size. Uptake of HBMMs into the thrombus induced in these mice was confirmed by a combination of PKH2-labeled cell tracking and colocalization with human leukocyte antigen (HLA) by immunohistology. Results - Compared with ad-blank, treated HBMMs transduction with ad-uPA increased uPA production by >1000-fold (P = .003), uPA activity by 150-fold (P = .0001), and soluble uPA receptor (uPAR) by almost twofold (P = .043). Expression of plasminogen activator inhibitor (PAI-1) and PAI-2 was decreased by about twofold (P = .011) and threefold (P = .005), respectively. Up-regulation of uPA had no effect on cell viability or inflammatory cytokine production compared with ad-blank or untreated cells. Ad-uPA transduction increased the migration rate of HBMMs (about 20%, P = .03) and MM6 cells (>twofold, P = .005) compared with ad-blank treated controls. Human macrophage recruitment into the mouse thrombus was confirmed by the colocalization of HLA with the PKH2-marked cells. Systemic injection of uPA-up-regulated HBMMs reduced thrombus weight by approximately 20% compared with ad-blank (P = .038) or sham-treated controls (P = .0028). Conclusion - Transduction of HBBM with ad-uPA increases their fibrinolytic activity. Systemic administration of uPA up-regulated HBBMs reduced thrombus size in an experimental model of venous thrombosis. Alternative methods of delivering fibrinolytic agents are worth exploring.