An approximation algorithm for #k-SAT

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Quantitative integration of geophysical and hydraulic data : from the local towards the regional scale range

Des progrès significatifs ont été réalisés dans le domaine de l'intégration quantitative des données géophysique et hydrologique l'échelle locale. Cependant, l'extension à de plus grandes échelles des approches correspondantes constitue encore un défi majeur. Il est néanmoins extrêmement important de relever ce défi pour développer des modèles fiables de flux des eaux souterraines et de transport de contaminant. Pour résoudre ce problème, j'ai développé une technique d'intégration des données hydrogéophysiques basée sur une procédure bayésienne de simulation séquentielle en deux étapes. Cette procédure vise des problèmes à plus grande échelle. L'objectif est de simuler la distribution d'un paramètre hydraulique cible à partir, d'une part, de mesures d'un paramètre géophysique pertinent qui couvrent l'espace de manière exhaustive, mais avec une faible résolution (spatiale) et, d'autre part, de mesures locales de très haute résolution des mêmes paramètres géophysique et hydraulique. Pour cela, mon algorithme lie dans un premier temps les données géophysiques de faible et de haute résolution à travers une procédure de réduction déchelle. Les données géophysiques régionales réduites sont ensuite reliées au champ du paramètre hydraulique à haute résolution. J'illustre d'abord l'application de cette nouvelle approche dintégration des données à une base de données synthétiques réaliste. Celle-ci est constituée de mesures de conductivité hydraulique et électrique de haute résolution réalisées dans les mêmes forages ainsi que destimations des conductivités électriques obtenues à partir de mesures de tomographic de résistivité électrique (ERT) sur l'ensemble de l'espace. Ces dernières mesures ont une faible résolution spatiale. La viabilité globale de cette méthode est testée en effectuant les simulations de flux et de transport au travers du modèle original du champ de conductivité hydraulique ainsi que du modèle simulé. Les simulations sont alors comparées. Les résultats obtenus indiquent que la procédure dintégration des données proposée permet d'obtenir des estimations de la conductivité en adéquation avec la structure à grande échelle ainsi que des predictions fiables des caractéristiques de transports sur des distances de moyenne à grande échelle. Les résultats correspondant au scénario de terrain indiquent que l'approche d'intégration des données nouvellement mise au point est capable d'appréhender correctement les hétérogénéitées à petite échelle aussi bien que les tendances à gande échelle du champ hydraulique prévalent. Les résultats montrent également une flexibilté remarquable et une robustesse de cette nouvelle approche dintégration des données. De ce fait, elle est susceptible d'être appliquée à un large éventail de données géophysiques et hydrologiques, à toutes les gammes déchelles. Dans la deuxième partie de ma thèse, j'évalue en détail la viabilité du réechantillonnage geostatique séquentiel comme mécanisme de proposition pour les méthodes Markov Chain Monte Carlo (MCMC) appliquées à des probmes inverses géophysiques et hydrologiques de grande dimension . L'objectif est de permettre une quantification plus précise et plus réaliste des incertitudes associées aux modèles obtenus. En considérant une série dexemples de tomographic radar puits à puits, j'étudie deux classes de stratégies de rééchantillonnage spatial en considérant leur habilité à générer efficacement et précisément des réalisations de la distribution postérieure bayésienne. Les résultats obtenus montrent que, malgré sa popularité, le réechantillonnage séquentiel est plutôt inefficace à générer des échantillons postérieurs indépendants pour des études de cas synthétiques réalistes, notamment pour le cas assez communs et importants où il existe de fortes corrélations spatiales entre le modèle et les paramètres. Pour résoudre ce problème, j'ai développé un nouvelle approche de perturbation basée sur une déformation progressive. Cette approche est flexible en ce qui concerne le nombre de paramètres du modèle et lintensité de la perturbation. Par rapport au rééchantillonage séquentiel, cette nouvelle approche s'avère être très efficace pour diminuer le nombre requis d'itérations pour générer des échantillons indépendants à partir de la distribution postérieure bayésienne. - Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending corresponding approaches beyond the local scale still represents a major challenge, yet is critically important for the development of reliable groundwater flow and contaminant transport models. To address this issue, I have developed a hydrogeophysical data integration technique based on a two-step Bayesian sequential simulation procedure that is specifically targeted towards larger-scale problems. The objective is to simulate the distribution of a target hydraulic parameter based on spatially exhaustive, but poorly resolved, measurements of a pertinent geophysical parameter and locally highly resolved, but spatially sparse, measurements of the considered geophysical and hydraulic parameters. To this end, my algorithm links the low- and high-resolution geophysical data via a downscaling procedure before relating the downscaled regional-scale geophysical data to the high-resolution hydraulic parameter field. I first illustrate the application of this novel data integration approach to a realistic synthetic database consisting of collocated high-resolution borehole measurements of the hydraulic and electrical conductivities and spatially exhaustive, low-resolution electrical conductivity estimates obtained from electrical resistivity tomography (ERT). The overall viability of this method is tested and verified by performing and comparing flow and transport simulations through the original and simulated hydraulic conductivity fields. The corresponding results indicate that the proposed data integration procedure does indeed allow for obtaining faithful estimates of the larger-scale hydraulic conductivity structure and reliable predictions of the transport characteristics over medium- to regional-scale distances. The approach is then applied to a corresponding field scenario consisting of collocated high- resolution measurements of the electrical conductivity, as measured using a cone penetrometer testing (CPT) system, and the hydraulic conductivity, as estimated from electromagnetic flowmeter and slug test measurements, in combination with spatially exhaustive low-resolution electrical conductivity estimates obtained from surface-based electrical resistivity tomography (ERT). The corresponding results indicate that the newly developed data integration approach is indeed capable of adequately capturing both the small-scale heterogeneity as well as the larger-scale trend of the prevailing hydraulic conductivity field. The results also indicate that this novel data integration approach is remarkably flexible and robust and hence can be expected to be applicable to a wide range of geophysical and hydrological data at all scale ranges. In the second part of my thesis, I evaluate in detail the viability of sequential geostatistical resampling as a proposal mechanism for Markov Chain Monte Carlo (MCMC) methods applied to high-dimensional geophysical and hydrological inverse problems in order to allow for a more accurate and realistic quantification of the uncertainty associated with the thus inferred models. Focusing on a series of pertinent crosshole georadar tomographic examples, I investigated two classes of geostatistical resampling strategies with regard to their ability to efficiently and accurately generate independent realizations from the Bayesian posterior distribution. The corresponding results indicate that, despite its popularity, sequential resampling is rather inefficient at drawing independent posterior samples for realistic synthetic case studies, notably for the practically common and important scenario of pronounced spatial correlation between model parameters. To address this issue, I have developed a new gradual-deformation-based perturbation approach, which is flexible with regard to the number of model parameters as well as the perturbation strength. Compared to sequential resampling, this newly proposed approach was proven to be highly effective in decreasing the number of iterations required for drawing independent samples from the Bayesian posterior distribution.

An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Proposal of a parallel architecture for a motion detection algorithm

This paper proposes a parallel architecture for estimation of the motion of an underwater robot. It is well known that image processing requires a huge amount of computation, mainly at low-level processing where the algorithms are dealing with a great number of data. In a motion estimation algorithm, correspondences between two images have to be solved at the low level. In the underwater imaging, normalised correlation can be a solution in the presence of non-uniform illumination. Due to its regular processing scheme, parallel implementation of the correspondence problem can be an adequate approach to reduce the computation time. Taking into consideration the complexity of the normalised correlation criteria, a new approach using parallel organisation of every processor from the architecture is proposed

Speculative parallelization of multipath radiosity algorithm

In computer graphics, global illumination algorithms take into account not only the light that comes directly from the sources, but also the light interreflections. This kind of algorithms produce very realistic images, but at a high computational cost, especially when dealing with complex environments. Parallel computation has been successfully applied to such algorithms in order to make it possible to compute highly-realistic images in a reasonable time. We introduce here a speculation-based parallel solution for a global illumination algorithm in the context of radiosity, in which we have taken advantage of the hierarchical nature of such an algorithm

A Monte Carlo-Based Fiber Tracking Algorithm using Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging, which measures directional information of water diffusion in the brain, has emerged as a powerful tool for human brain studies. In this paper, we introduce a new Monte Carlo-based fiber tracking approach to estimate brain connectivity. One of the main characteristics of this approach is that all parameters of the algorithm are automatically determined at each point using the entropy of the eigenvalues of the diffusion tensor. Experimental results show the good performance of the proposed approach

Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,one can mimick the presymplectic constraint algorithm to obtain a constraint algorithmthat can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations offield theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.

Uncertainty Quantification Of A Semi-Supervised Support Vector Regression Reservoir Model

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. Recent advances in machine learning offer a novel approach to model spatial distribution of petrophysical properties in complex reservoirs alternative to geostatistics. The approach is based of semisupervised learning, which handles both ?labelled? observed data and ?unlabelled? data, which have no measured value but describe prior knowledge and other relevant data in forms of manifolds in the input space where the modelled property is continuous. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic geological features and describe stochastic variability and non-uniqueness of spatial properties. On the other hand, it is able to capture and preserve key spatial dependencies such as connectivity of high permeability geo-bodies, which is often difficult in contemporary petroleum reservoir studies. Semi-supervised SVR as a data driven algorithm is designed to integrate various kind of conditioning information and learn dependences from it. The semi-supervised SVR model is able to balance signal/noise levels and control the prior belief in available data. In this work, stochastic semi-supervised SVR geomodel is integrated into Bayesian framework to quantify uncertainty of reservoir production with multiple models fitted to past dynamic observations (production history). Multiple history matched models are obtained using stochastic sampling and/or MCMC-based inference algorithms, which evaluate posterior probability distribution. Uncertainty of the model is described by posterior probability of the model parameters that represent key geological properties: spatial correlation size, continuity strength, smoothness/variability of spatial property distribution. The developed approach is illustrated with a fluvial reservoir case. The resulting probabilistic production forecasts are described by uncertainty envelopes. The paper compares the performance of the models with different combinations of unknown parameters and discusses sensitivity issues.

Risk assessment of recurrence in sporadic retinoblastoma using a molecular-based algorithm

Le rétinoblastome (Rb) est une tumeur provenant des cellules rétiniennes progénitrices des photorécepteurs. C'est la tumeur pédiatrique maligne la plus fréquente avec une incidence par naissance évaluée entre 1/15Ό00 et 1/20Ό00. Les enfants atteints de Rb sont diagnostiqué dans leur grande majorité avant l'âge de 4 ans, soit le temps nécessaire à la différentiation et à la maturation des photorécepteurs et donc à la disparition de la cellule d'origine du Rb. La survie du patient, la sauvegarde oculaire et le pronostic visuel restent excellents pour autant que le traitement ne soit pas différé. Dans sa variante non héréditaire (60%) le Rb est toujours unilatéral et sporadique. Le Rb héréditaire de transmission dominante autosomique (40%), se décline sous toutes les formes, familiale (10%) ou sporadique (30%), que l'atteinte soit unilatérale ou bilatérale. La majorité des mutations causales sont uniques et distribuées de façon aléatoire sur la totalité du gène RB1 sans région prédisposante. La détection de ces mutations est couteuse et chronophage, tout en présentant un taux de détection relativement bas; surtout dans les cas de Rb sporadiques unilatéraux. Dans le but d'identifier les patients présentant un risque réel de développer un Rb, et de réduire le nombre d'examens sous narcose requis pour le dépistage de la maladie chez les sujets à risque, nous avons développé une stratégie sensible, rapide, efficace et peu couteuse basée sur une analyse de l'haplotype intragénique. Cet algorithme prend en compte a) la perte d'hétérozygotie intratumorale du gène RB1, b) l'origine paternelle préférentielle des nouvelles mutations germinales et c) un risque a priori dérivé des données empiriques de Vogel. Pendant la période allant de janvier 1994 à décembre 2006, nous avons comparé l'apparition de nouveau Rb parmi la fratrie et la descendance de patient atteints au nombre de nouveaux cas attendus calculé par notre algorithme. 134 familles ont été étudiées. L'analyse moléculaire a été effectuée chez 570 personnes dont 99 patients âgés de moins de 4 ans et donc à risque de développer un Rb. Parmi cette cohorte, nous avons observé l'apparition d'un cas de Rb, alors que les risques cumulés a posteriori calculé par notre algorithme prédisait l'apparition de 1.77 nouveau cas. Dans cette étude, nous avons pu valider notre algorithme prédisant la récurrence de Rb chez les parents de 1er degré de patients atteints. Cet outil devrait grandement faciliter le conseil génétique ainsi que le suivi des patients à risque de développer un Rb, surtout dans les cas ou le séquençage direct du gène RB1 n'est pas disponible ou est resté non informatif. - Purpose: Most RBI mutations are unique and distributed throughout the RBI gene. Their detection can be time-consuming and the yield especially low in cases of conservatively-treated sporadic unilateral retinoblas-toma (Rb) patients. In order to identify patients with true risk of developing Rb, and to reduce the number of unnecessary examinations under anesthesia in all other cases, we developed a universal sensitive, efficient and cost-effective strategy based on intragenic haplotype analysis. Methods: This algorithm allows the calculation of the a posteriori risk of developing Rb and takes into account (a) RBI loss of heterozygosity in tumors, (b) preferential paternal origin of new germline mutations, (c) a priori risk derived from empirical data by Vogel, and (d) disease penetrance of 90% in most cases. We report the occurrence of Rb in first degree relatives of patients with sporadic Rb who visited the Jules Gonin Eye Hospital, Lausanne, Switzerland, from January 1994 to December 2006 compared to expected new cases of Rb using our algorithm. Results: A total of 134 families with sporadic Rb were enrolled; testing was performed in 570 individuals and 99 patients younger than 4 years old were identified. We observed one new case of Rb. Using our algorithm, the cumulated total a posteriori risk of recurrence was 1.77. Conclusions: This is the first time that linkage analysis has been validated to monitor the risk of recurrence in sporadic Rb. This should be a useful tool in genetic counseling, especially when direct RBI screening for mutations leaves a negative result or is unavailable.

A Label space reduction algorithm for P2MP LSPs using asymmetric tunnels

The aim of traffic engineering is to optimise network resource utilization. Although several works on minimizing network resource utilization have been published, few works have focused on LSR label space. This paper proposes an algorithm that uses MPLS label stack features in order to reduce the number of labels used in LSPs forwarding. Some tunnelling methods and their MPLS implementation drawbacks are also discussed. The algorithm described sets up the NHLFE tables in each LSR, creating asymmetric tunnels when possible. Experimental results show that the algorithm achieves a large reduction factor in the label space. The work presented here applies for both types of connections: P2MP and P2P

Use of Hy's law and a new composite algorithm to predict acute liver failure in patients with drug-induced liver injury.

BACKGROUND & AIMS Hy's Law, which states that hepatocellular drug-induced liver injury (DILI) with jaundice indicates a serious reaction, is used widely to determine risk for acute liver failure (ALF). We aimed to optimize the definition of Hy's Law and to develop a model for predicting ALF in patients with DILI. METHODS We collected data from 771 patients with DILI (805 episodes) from the Spanish DILI registry, from April 1994 through August 2012. We analyzed data collected at DILI recognition and at the time of peak levels of alanine aminotransferase (ALT) and total bilirubin (TBL). RESULTS Of the 771 patients with DILI, 32 developed ALF. Hepatocellular injury, female sex, high levels of TBL, and a high ratio of aspartate aminotransferase (AST):ALT were independent risk factors for ALF. We compared 3 ways to use Hy's Law to predict which patients would develop ALF; all included TBL greater than 2-fold the upper limit of normal (×ULN) and either ALT level greater than 3 × ULN, a ratio (R) value (ALT × ULN/alkaline phosphatase × ULN) of 5 or greater, or a new ratio (nR) value (ALT or AST, whichever produced the highest ×ULN/ alkaline phosphatase × ULN value) of 5 or greater. At recognition of DILI, the R- and nR-based models identified patients who developed ALF with 67% and 63% specificity, respectively, whereas use of only ALT level identified them with 44% specificity. However, the level of ALT and the nR model each identified patients who developed ALF with 90% sensitivity, whereas the R criteria identified them with 83% sensitivity. An equal number of patients who did and did not develop ALF had alkaline phosphatase levels greater than 2 × ULN. An algorithm based on AST level greater than 17.3 × ULN, TBL greater than 6.6 × ULN, and AST:ALT greater than 1.5 identified patients who developed ALF with 82% specificity and 80% sensitivity. CONCLUSIONS When applied at DILI recognition, the nR criteria for Hy's Law provides the best balance of sensitivity and specificity whereas our new composite algorithm provides additional specificity in predicting the ultimate development of ALF.

Fast calculation of the CAC convolution algorithm using the multinomial distribution function

The authors focus on one of the methods for connection acceptance control (CAC) in an ATM network: the convolution approach. With the aim of reducing the cost in terms of calculation and storage requirements, they propose the use of the multinomial distribution function. This permits direct computation of the associated probabilities of the instantaneous bandwidth requirements. This in turn makes possible a simple deconvolution process. Moreover, under certain conditions additional improvements may be achieved