Three-dimensional ordered-subset expectation maximization iterative protocol for evaluation of left ventricular volumes and function by quantitative gated SPECT: a dynamic phantom study.

The purposes of this study were to characterize the performance of a 3-dimensional (3D) ordered-subset expectation maximization (OSEM) algorithm in the quantification of left ventricular (LV) function with (99m)Tc-labeled agent gated SPECT (G-SPECT), the QGS program, and a beating-heart phantom and to optimize the reconstruction parameters for clinical applications. METHODS: A G-SPECT image of a dynamic heart phantom simulating the beating left ventricle was acquired. The exact volumes of the phantom were known and were as follows: end-diastolic volume (EDV) of 112 mL, end-systolic volume (ESV) of 37 mL, and stroke volume (SV) of 75 mL; these volumes produced an LV ejection fraction (LVEF) of 67%. Tomographic reconstructions were obtained after 10-20 iterations (I) with 4, 8, and 16 subsets (S) at full width at half maximum (FWHM) gaussian postprocessing filter cutoff values of 8-15 mm. The QGS program was used for quantitative measurements. RESULTS: Measured values ranged from 72 to 92 mL for EDV, from 18 to 32 mL for ESV, and from 54 to 63 mL for SV, and the calculated LVEF ranged from 65% to 76%. Overall, the combination of 10 I, 8 S, and a cutoff filter value of 10 mm produced the most accurate results. The plot of the measures with respect to the expectation maximization-equivalent iterations (I x S product) revealed a bell-shaped curve for the LV volumes and a reverse distribution for the LVEF, with the best results in the intermediate range. In particular, FWHM cutoff values exceeding 10 mm affected the estimation of the LV volumes. CONCLUSION: The QGS program is able to correctly calculate the LVEF when used in association with an optimized 3D OSEM algorithm (8 S, 10 I, and FWHM of 10 mm) but underestimates the LV volumes. However, various combinations of technical parameters, including a limited range of I and S (80-160 expectation maximization-equivalent iterations) and low cutoff values (< or =10 mm) for the gaussian postprocessing filter, produced results with similar accuracies and without clinically relevant differences in the LV volumes and the estimated LVEF.

Formule sanguine: intérêt des nouveaux paramètres [Complete blood counts: new parameters].

Performing a complete blood count analysis is a daily routine necessary for a good care of patients. Nowadays, modern blood analyzers provide on top of classical blood values, several additional parameters. In this paper, using short case presentations, we discuss how to interpret these results and integrate them in the clinical context.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

Prevalence of cardiovascular risk factors in a middle-income country and estimated cost of a treatment strategy.

BACKGROUND: We assessed the prevalence of risk factors for cardiovascular disease (CVD) in a middle-income country in rapid epidemiological transition and estimated direct costs for treating all individuals at increased cardiovascular risk, i.e. following the so-called "high risk strategy". METHODS: Survey of risk factors using an age- and sex-stratified random sample of the population of Seychelles aged 25-64 in 2004. Assessment of CVD risk and treatment modalities were in line with international guidelines. Costs are expressed as USD per capita per year. RESULTS: 1255 persons took part in the survey (participation rate of 80.2%). Prevalence of main risk factors was: 39.6% for high blood pressure (> or =140/90 mmHg or treatment) of which 59% were under treatment; 24.2% for high cholesterol (> or =6.2 mmol/l); 20.8% for low HDL-cholesterol (<1.0 mmol/l); 9.3% for diabetes (fasting glucose > or =7.0 mmol/l); 17.5% for smoking; 25.1% for obesity (body mass index > or =30 kg/m2) and 22.1% for the metabolic syndrome. Overall, 43% had HBP, high cholesterol or diabetes and substantially increased CVD risk. The cost for medications needed to treat all high-risk individuals amounted to USD 45.6, i.e. 11.2 dollars for high blood pressure, 3.8 dollars for diabetes, and 30.6 dollars for dyslipidemia (using generic drugs except for hypercholesterolemia). Cost for minimal follow-up medical care and laboratory tests amounted to 22.6 dollars. CONCLUSION: High prevalence of major risk factors was found in a rapidly developing country and costs for treatment needed to reduce risk factors in all high-risk individuals exceeded resources generally available in low or middle income countries. Our findings emphasize the need for affordable cost-effective treatment strategies and the critical importance of population strategies aimed at reducing risk factors in the entire population.

Cataractogenesis after total body irradiation.

PURPOSE: To evaluate the prognostic factors and the ophthalmologic follow-up on cataract formation following total body irradiation (TBI) prior to bone marrow transplantation (BMT). METHODS AND MATERIALS: Between 1980 and 1992, 494 patients were referred to our department for TBI prior to BMT. The mean age was 32 +/- 11 (median: 32, range: 2-63) years and the male to female ratio was 1.6 (304:190). The majority of patients were treated for acute leukemia (lymphoblastic, n = 177, 36%; or nonlymphoblastic , n = 139, 28%); 80 (16%) for chronic myeloid leukemia, 60 (12%) for non-Hodgkin's lymphoma, 23 (5%) for multiple myeloma, and 15 (3%) for other malignancies. Two hundred and fifty-four (51%) patients were grafted in the first complete remission (CR), 118 (24%) in second CR. Allogenic BMT was performed in 210 (43%) patients, and autologous BMT in 284 (57%). Methotrexate combined to steroids (n = 47, 22%) or to cyclosporine (n = 163, 78%) was administered for graft-versus-host disease (GvHD) prophylaxis. In 188 patients (38%), heparin was used in the prevention of veno-occlusive disease (VOD) of the liver. Furthermore, steroid administration was registered in 223 (45%). The conditioning chemotherapy consisted of cyclophosphamide (Cy) alone in 332 (67%) patients. Total-body irradiation was administered either in single dose (STBI; 10 Gy in 1 day, n = 291) or in six fractions (FTBI; 12 Gy over 3 consecutive days, n = 203) before BMT. The mean instantaneous dose rate was 0.0574 +/- 0.0289 Gy/min (0.024-0.1783). It was < 0.048 Gy/min in 157 patients (LOW group), > or = 0.048 Gy/min and <0.09 Gy/min in 301 patients (MEDIUM group), and > or = 0.09 Gy/min in 36 patients (HIGH group). RESULTS: When considering all patients, 42 (8.5%) patients developed cataracts after 13 to 72 months (median: 42 months) with a 5-year estimated cataract incidence (ECI) of 23%. Thirty-three (11.3%) out of 291 patients in the STBI group, and 9 (4.4%) out of 203 patients in the FTBI group developed cataracts with 5-year estimated incidences of 34 and 11%, respectively (p = 0.0004). Seven (19.4%) out of 36 patients in the HIGH group, 33 (10.9%) out of 301 in the MEDIUM group, and 2 (1.2%) out of 157 in the LOW group developed cataracts with respective 5-year cataract incidences of 54%, 30%, and 3.5% (HIGH vs. MEDIUM, p = 0.07; MEDIUM vs. LOW, p = 0.0001; HIGH vs. LOW, p < 0.0001). On the other hand, patients who received heparin as prophylactic treatment against VOD of the liver had less cataracts than those who did not receive (5-year ECI of 16% vs. 28%, respectively; p = 0.01). There was no statistically significant difference in terms of 5-year ECI according to age, sex, administration of steroids, GvHD prophylaxis, type of BMT, or previous cranial radiotherapy in children. Multivariate analysis revealed that the instantaneous dose rate (p = 0.001), and the administration of heparin against VOD (p = 0.05) were the two independent factors influencing the cataract incidence, while age, fractionation, and use of steroids were not. Among the 42 patients who developed cataracts, 38 had bilateral extracapsular cataract extraction and intraocular lens implantation, and only 4 (10%) developed secondary cataracts in a median follow-up period of 39 months. CONCLUSION: Among the abovementioned TBI parameters, high instantaneous dose rate seems to be the main risk factor of cataract formation, and the administration of heparin appears to have a protective role in cataractogenesis. On the other hand, ionizing radiation seems to have a protective effect on posterior capsule opacification following extracapsular cataract extraction and intraocular lens implantation.

Correlations between trabecular bone score, measured using anteroposterior dual-energy x-ray absorptiometry acquisition, and 3-dimensional parameters of bone microarchitecture: an experimental study on human cadaver vertebrae.

Developing a novel technique for the efficient, noninvasive clinical evaluation of bone microarchitecture remains both crucial and challenging. The trabecular bone score (TBS) is a new gray-level texture measurement that is applicable to dual-energy X-ray absorptiometry (DXA) images. Significant correlations between TBS and standard 3-dimensional (3D) parameters of bone microarchitecture have been obtained using a numerical simulation approach. The main objective of this study was to empirically evaluate such correlations in anteroposterior spine DXA images. Thirty dried human cadaver vertebrae were evaluated. Micro-computed tomography acquisitions of the bone pieces were obtained at an isotropic resolution of 93μm. Standard parameters of bone microarchitecture were evaluated in a defined region within the vertebral body, excluding cortical bone. The bone pieces were measured on a Prodigy DXA system (GE Medical-Lunar, Madison, WI), using a custom-made positioning device and experimental setup. Significant correlations were detected between TBS and 3D parameters of bone microarchitecture, mostly independent of any correlation between TBS and bone mineral density (BMD). The greatest correlation was between TBS and connectivity density, with TBS explaining roughly 67.2% of the variance. Based on multivariate linear regression modeling, we have established a model to allow for the interpretation of the relationship between TBS and 3D bone microarchitecture parameters. This model indicates that TBS adds greater value and power of differentiation between samples with similar BMDs but different bone microarchitectures. It has been shown that it is possible to estimate bone microarchitecture status derived from DXA imaging using TBS.

Estimated Target for Construction Lettings, May 17, 2011

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Estimated Target for Construction Lettings,2011

Estimated Target for Construction Lettings,(Primary, Interstate, Local, and Institutional)

Improved multiexponential transient spectroscopy by iterative deconvolution

The analysis of multiexponential decays is challenging because of their complex nature. When analyzing these signals, not only the parameters, but also the orders of the models, have to be estimated. We present an improved spectroscopic technique specially suited for this purpose. The proposed algorithm combines an iterative linear filter with an iterative deconvolution method. A thorough analysis of the noise effect is presented. The performance is tested with synthetic and experimental data.

Microinductive signal conditioning with resonant differential filters: high-sensitivity biodetection applications

Inductive-based devices integrated with Si technology for biodetection applications are characterized, using simple resonant differential filter configurations. This has allowed the corroboration of the viability of the proposed circuits, which are characterized by their very high simplicity, for microinductive signal conditioning in high-sensitivity sensor devices. The simulation of these simple circuits predicts sensitivities of the differential output voltage which can achieve values in the range of 0.1-1 V/nH, depending on the coil parameters. These very high-sensitivity values open the possibility for the experimental detection of extremely small inductance changes in the devices. For real microinductive devices, both series resistance and parasitic capacitive components contribute to the decrease of the differential circuit sensitivity. Nevertheless, measurements performed using micro-coils fabricated with relatively high series resistance and coupling parasitic effects have allowed detection of changes in the range of 2 nH. which are compatible with biodetection applications with estimated detection limits below the picomolarity range.

Were Spanish migrants attracted by industrial agglomerations?: an analysis for the interwar years in the light of the new economic geography

In this paper we examine whether access to markets had a significant influence onmigration choices of Spanish internal migrants in the inter-war years. We perform astructural contrast of a New Economic Geography model that focus on the forwardlinkage that links workers location choice with the geography of industrial production,one of the centripetal forces that drive agglomeration in the NEG models. The resultshighlight the presence of this forward linkage in the Spanish economy of the inter-warperiod. That is, we prove the existence of a direct relation between workers¿ localizationdecisions and the market potential of the host regions. In addition, the direct estimationof the values associated with key parameters in the NEG model allows us to simulatethe migratory flows derived from different scenarios of the relative size of regions andthe distances between them. We show that in Spain the power of attraction of theagglomerations grew as they increased in size, but the high elasticity estimated for themigration costs reduced the intensity of the migratory flows. This could help to explainthe apparently low intensity of internal migrations in Spain until its upsurge during the1920s. This also explains the geography of migrations in Spain during this period,which hardly affected the regions furthest from the large industrial agglomerations (i.e.,regions such as Andalusia, Estremadura and Castile-La Mancha) but had an intenseeffect on the provinces nearest to the principal centres of industrial development.

Measuring conduct and cost parameters in the Spanish air transport market

This paper estimates a model of airline competition for the Spanish air transport market. I test the explanatory power of alternative oligopoly models with capacity constraints. In addition, I analyse the degree of density economies. Results show that Spanish airlines conduct follows a price-leadership scheme so that it is less competitive than the Cournot solution. I also find evidence that thin routes can be considered as natural monopolies

Seeds enriched with phosphorus and molybdenum improve the contribution of biological nitrogen fixation to common bean as estimated by 15n isotope dilution

Seeds with a high concentration of P or Mo can improve the growth and N accumulation of the common bean (Phaseolus vulgaris L.), but the effect of enriched seeds on biological N2 fixation has not been established yet. This study aimed to evaluate the effect of seeds enriched with P and Mo on growth and biological N2 fixation of the common bean by the 15N isotope dilution technique. An experiment was carried out in pots in a 2 x 3 x 2 x 2 factorial design in randomized blocks with four replications, comprising two levels of soil applied P (0 and 80 mg kg-1), three N sources (without N, inoculated with rhizobia, and mineral N), two seed P concentrations (low and high), and two seed Mo concentrations (low and high). Non-nodulating bean and sorghum were used as non-fixing crops. The substrate was 5.0 kg of a Red Latosol (Oxisol) previously enriched with 15N and mixed with 5.0 kg of sand. Plants were harvested 41 days after emergence. Seeds with high P concentration increased the growth and N in shoots, particularly in inoculated plants at lower applied P levels. Inoculated plants raised from high P seeds showed improved nodulation at both soil P levels. Higher soil P levels increased the percentage of N derived from the atmosphere (%Ndfa) in bean leaves. Inoculation with the selected strains increased the %Ndfa. High seed P increased the %Ndfa in inoculated plants at lower soil P levels. High seed Mo increased the %Ndfa at lower soil P levels in plants that did not receive inoculation or mineral N. It is concluded that high seed P concentration increases the growth, N accumulation and the contribution of the biological N2 fixation in the common bean, particularly in inoculated plants grown at lower soil P availability.

Local and global error models to improve uncertainty quantification

In groundwater applications, Monte Carlo methods are employed to model the uncertainty on geological parameters. However, their brute-force application becomes computationally prohibitive for highly detailed geological descriptions, complex physical processes, and a large number of realizations. The Distance Kernel Method (DKM) overcomes this issue by clustering the realizations in a multidimensional space based on the flow responses obtained by means of an approximate (computationally cheaper) model; then, the uncertainty is estimated from the exact responses that are computed only for one representative realization per cluster (the medoid). Usually, DKM is employed to decrease the size of the sample of realizations that are considered to estimate the uncertainty. We propose to use the information from the approximate responses for uncertainty quantification. The subset of exact solutions provided by DKM is then employed to construct an error model and correct the potential bias of the approximate model. Two error models are devised that both employ the difference between approximate and exact medoid solutions, but differ in the way medoid errors are interpolated to correct the whole set of realizations. The Local Error Model rests upon the clustering defined by DKM and can be seen as a natural way to account for intra-cluster variability; the Global Error Model employs a linear interpolation of all medoid errors regardless of the cluster to which the single realization belongs. These error models are evaluated for an idealized pollution problem in which the uncertainty of the breakthrough curve needs to be estimated. For this numerical test case, we demonstrate that the error models improve the uncertainty quantification provided by the DKM algorithm and are effective in correcting the bias of the estimate computed solely from the MsFV results. The framework presented here is not specific to the methods considered and can be applied to other combinations of approximate models and techniques to select a subset of realizations

Modeling water movement in horizontal columns using fractal theory

Fractal mathematics has been used to characterize water and solute transport in porous media and also to characterize and simulate porous media properties. The objective of this study was to evaluate the correlation between the soil infiltration parameters sorptivity (S) and time exponent (n) and the parameters dimension (D) and the Hurst exponent (H). For this purpose, ten horizontal columns with pure (either clay or loam) and heterogeneous porous media (clay and loam distributed in layers in the column) were simulated following the distribution of a deterministic Cantor Bar with fractal dimension H" 0.63. Horizontal water infiltration experiments were then simulated using Hydrus 2D software. The sorptivity (S) and time exponent (n) parameters of the Philip equation were estimated for each simulation, using the nonlinear regression procedure of the statistical software package SAS®. Sorptivity increased in the columns with the loam content, which was attributed to the relation of S with the capillary radius. The time exponent estimated by nonlinear regression was found to be less than the traditional value of 0.5. The fractal dimension estimated from the Hurst exponent was 17.5 % lower than the fractal dimension of the Cantor Bar used to generate the columns.