Jointly multi-user detection and channel estimation with genetic algorithm

This work aims at proposing the use of the evolutionary computation methodology in order to jointly solve the multiuser channel estimation (MuChE) and detection problems at its maximum-likelihood, both related to the direct sequence code division multiple access (DS/CDMA). The effectiveness of the proposed heuristic approach is proven by comparing performance and complexity merit figures with that obtained by traditional methods found in literature. Simulation results considering genetic algorithm (GA) applied to multipath, DS/CDMA and MuChE and multi-user detection (MuD) show that the proposed genetic algorithm multi-user channel estimation (GAMuChE) yields a normalized mean square error estimation (nMSE) inferior to 11%, under slowly varying multipath fading channels, large range of Doppler frequencies and medium system load, it exhibits lower complexity when compared to both maximum likelihood multi-user channel estimation (MLMuChE) and gradient descent method (GrdDsc). A near-optimum multi-user detector (MuD) based on the genetic algorithm (GAMuD), also proposed in this work, provides a significant reduction in the computational complexity when compared to the optimum multi-user detector (OMuD). In addition, the complexity of the GAMuChE and GAMuD algorithms were (jointly) analyzed in terms of number of operations necessary to reach the convergence, and compared to other jointly MuChE and MuD strategies. The joint GAMuChE-GAMuD scheme can be regarded as a promising alternative for implementing third-generation (3G) and fourth-generation (4G) wireless systems in the near future. Copyright (C) 2010 John Wiley & Sons, Ltd.

Bayesian Estimation of Noise

In mathematical modeling the estimation of the model parameters is one of the most common problems. The goal is to seek parameters that fit to the measurements as well as possible. There is always error in the measurements which implies uncertainty to the model estimates. In Bayesian statistics all the unknown quantities are presented as probability distributions. If there is knowledge about parameters beforehand, it can be formulated as a prior distribution. The Bays’ rule combines the prior and the measurements to posterior distribution. Mathematical models are typically nonlinear, to produce statistics for them requires efficient sampling algorithms. In this thesis both Metropolis-Hastings (MH), Adaptive Metropolis (AM) algorithms and Gibbs sampling are introduced. In the thesis different ways to present prior distributions are introduced. The main issue is in the measurement error estimation and how to obtain prior knowledge for variance or covariance. Variance and covariance sampling is combined with the algorithms above. The examples of the hyperprior models are applied to estimation of model parameters and error in an outlier case.

A priori estimation of accuracy and of the number of wells to be employed in limiting dilution assays

The use of limiting dilution assay (LDA) for assessing the frequency of responders in a cell population is a method extensively used by immunologists. A series of studies addressing the statistical method of choice in an LDA have been published. However, none of these studies has addressed the point of how many wells should be employed in a given assay. The objective of this study was to demonstrate how a researcher can predict the number of wells that should be employed in order to obtain results with a given accuracy, and, therefore, to help in choosing a better experimental design to fulfill one's expectations. We present the rationale underlying the expected relative error computation based on simple binomial distributions. A series of simulated in machina experiments were performed to test the validity of the a priori computation of expected errors, thus confirming the predictions. The step-by-step procedure of the relative error estimation is given. We also discuss the constraints under which an LDA must be performed.

Approximation de la distribution a posteriori d'un modèle Gamma-Poisson hiérarchique à effets mixtes

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés.

Using error bounds to compare aggregated generalized transportation models

A comparative study of aggregation error bounds for the generalized transportation problem is presented. A priori and a posteriori error bounds were derived and a computational study was performed to (a) test the correlation between the a priori, the a posteriori, and the actual error and (b) quantify the difference of the error bounds from the actual error. Based on the results we conclude that calculating the a priori error bound can be considered as a useful strategy to select the appropriate aggregation level. The a posteriori error bound provides a good quantitative measure of the actual error.

Comparison of Mesh Adaptation Using the Adjoint Methodology and Truncation Error Estimates

Mesh adaptation based on error estimation has become a key technique to improve th eaccuracy o fcomputational-fluid-dynamics computations. The adjoint-based approach for error estimation is one of the most promising techniques for computational-fluid-dynamics applications. Nevertheless, the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method. In the present investigation, a new mesh refinement method based on estimation of truncation error is presented in the context of finite-volume discretization. The estimation method uses auxiliary coarser meshes to estimate the local truncation error, which can be used for driving an adaptation algorithm. The method is demonstrated in the context of two-dimensional NACA0012 and three-dimensional ONERA M6 wing inviscid flows, and the results are compared against the adjoint-based approach and physical sensors based on features of the flow field.

Core Reactor Calculation Using the Adaptive Remeshing with a Current Error Estimator

With the objective to improve the reactor physics calculation on a 2D and 3D nuclear reactor via the Diffusion Equation, an adaptive automatic finite element remeshing method, based on the elementary area (2D) or volume (3D) constraints, has been developed. The adaptive remeshing technique, guided by a posteriori error estimator, makes use of two external mesh generator programs: Triangle and TetGen. The use of these free external finite element mesh generators and an adaptive remeshing technique based on the current field continuity show that they are powerful tools to improve the neutron flux distribution calculation and by consequence the power solution of the reactor core even though they have a minor influence on the critical coefficient of the calculated reactor core examples. Two numerical examples are presented: the 2D IAEA reactor core numerical benchmark and the 3D model of the Argonauta research reactor, built in Brasil.

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement. The theoretical results are illustrated by a series of numerical experiments.

The impact of measurement errors in the identification of regulatory networks

Background: There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise. Results: This article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data. Conclusions: Measurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.

Therapeutic drug monitoring of imatinib: Bayesian and alternative methods to predict trough levels

Background: The imatinib trough plasma concentration (C(min)) correlates with clinical response in cancer patients. Therapeutic drug monitoring (TDM) of plasma C(min) is therefore suggested. In practice, however, blood sampling for TDM is often not performed at trough. The corresponding measurement is thus only remotely informative about C(min) exposure. Objectives: The objectives of this study were to improve the interpretation of randomly measured concentrations by using a Bayesian approach for the prediction of C(min), incorporating correlation between pharmacokinetic parameters, and to compare the predictive performance of this method with alternative approaches, by comparing predictions with actual measured trough levels, and with predictions obtained by a reference method, respectively. Methods: A Bayesian maximum a posteriori (MAP) estimation method accounting for correlation (MAP-ρ) between pharmacokinetic parameters was developed on the basis of a population pharmacokinetic model, which was validated on external data. Thirty-one paired random and trough levels, observed in gastrointestinal stromal tumour patients, were then used for the evaluation of the Bayesian MAP-ρ method: individual C(min) predictions, derived from single random observations, were compared with actual measured trough levels for assessment of predictive performance (accuracy and precision). The method was also compared with alternative approaches: classical Bayesian MAP estimation assuming uncorrelated pharmacokinetic parameters, linear extrapolation along the typical elimination constant of imatinib, and non-linear mixed-effects modelling (NONMEM) first-order conditional estimation (FOCE) with interaction. Predictions of all methods were finally compared with 'best-possible' predictions obtained by a reference method (NONMEM FOCE, using both random and trough observations for individual C(min) prediction). Results: The developed Bayesian MAP-ρ method accounting for correlation between pharmacokinetic parameters allowed non-biased prediction of imatinib C(min) with a precision of ±30.7%. This predictive performance was similar for the alternative methods that were applied. The range of relative prediction errors was, however, smallest for the Bayesian MAP-ρ method and largest for the linear extrapolation method. When compared with the reference method, predictive performance was comparable for all methods. The time interval between random and trough sampling did not influence the precision of Bayesian MAP-ρ predictions. Conclusion: Clinical interpretation of randomly measured imatinib plasma concentrations can be assisted by Bayesian TDM. Classical Bayesian MAP estimation can be applied even without consideration of the correlation between pharmacokinetic parameters. Individual C(min) predictions are expected to vary less through Bayesian TDM than linear extrapolation. Bayesian TDM could be developed in the future for other targeted anticancer drugs and for the prediction of other pharmacokinetic parameters that have been correlated with clinical outcomes.

An adaptive finite element water column model using the Mellor-Yamada level 2.5 turbulence closure scheme

A one-dimensional water column model using the Mellor and Yamada level 2.5 parameterization of vertical turbulent fluxes is presented. The model equations are discretized with a mixed finite element scheme. Details of the finite element discrete equations are given and adaptive mesh refinement strategies are presented. The refinement criterion is an "a posteriori" error estimator based on stratification, shear and distance to surface. The model performances are assessed by studying the stress driven penetration of a turbulent layer into a stratified fluid. This example illustrates the ability of the presented model to follow some internal structures of the flow and paves the way for truly generalized vertical coordinates. (c) 2005 Elsevier Ltd. All rights reserved.

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

Satellite-supported flood forecasting in river networks: a real case study

Satellite-based (e.g., Synthetic Aperture Radar [SAR]) water level observations (WLOs) of the floodplain can be sequentially assimilated into a hydrodynamic model to decrease forecast uncertainty. This has the potential to keep the forecast on track, so providing an Earth Observation (EO) based flood forecast system. However, the operational applicability of such a system for floods developed over river networks requires further testing. One of the promising techniques for assimilation in this field is the family of ensemble Kalman (EnKF) filters. These filters use a limited-size ensemble representation of the forecast error covariance matrix. This representation tends to develop spurious correlations as the forecast-assimilation cycle proceeds, which is a further complication for dealing with floods in either urban areas or river junctions in rural environments. Here we evaluate the assimilation of WLOs obtained from a sequence of real SAR overpasses (the X-band COSMO-Skymed constellation) in a case study. We show that a direct application of a global Ensemble Transform Kalman Filter (ETKF) suffers from filter divergence caused by spurious correlations. However, a spatially-based filter localization provides a substantial moderation in the development of the forecast error covariance matrix, directly improving the forecast and also making it possible to further benefit from a simultaneous online inflow error estimation and correction. Additionally, we propose and evaluate a novel along-network metric for filter localization, which is physically-meaningful for the flood over a network problem. Using this metric, we further evaluate the simultaneous estimation of channel friction and spatially-variable channel bathymetry, for which the filter seems able to converge simultaneously to sensible values. Results also indicate that friction is a second order effect in flood inundation models applied to gradually varied flow in large rivers. The study is not conclusive regarding whether in an operational situation the simultaneous estimation of friction and bathymetry helps the current forecast. Overall, the results indicate the feasibility of stand-alone EO-based operational flood forecasting.

Generating segmented meshes from textured color images

This paper presents a new framework for generating triangular meshes from textured color images. The proposed framework combines a texture classification technique, called W-operator, with Imesh, a method originally conceived to generate simplicial meshes from gray scale images. An extension of W-operators to handle textured color images is proposed, which employs a combination of RGB and HSV channels and Sequential Floating Forward Search guided by mean conditional entropy criterion to extract features from the training data. The W-operator is built into the local error estimation used by Imesh to choose the mesh vertices. Furthermore, the W-operator also enables to assign a label to the triangles during the mesh construction, thus allowing to obtain a segmented mesh at the end of the process. The presented results show that the combination of W-operators with Imesh gives rise to a texture classification-based triangle mesh generation framework that outperforms pixel based methods. Crown Copyright (C) 2009 Published by Elsevier Inc. All rights reserved.

Tamanho de amostra para a estimativa das médias decendiais de radiação solar global no Estado do Rio Grande do Sul

Com o objetivo de verificar a variabilidade temporal e espacial do tamanho de amostra da radiação solar global média decendial, de 22 locais do Estado do Rio Grande do Sul, utilizaram-se séries de dados de radiação solar global do período de 1956 a 2003. Determinou-se o tamanho de amostra da radiação solar global média decendial em cada decêndio e local e agruparam-se os decêndios e os locais pelo método hierárquico 'vizinho mais distante'. Há variabilidade do tamanho de amostra (número de anos) para a estimativa da radiação solar global média decendial no Estado do Rio Grande do Sul no tempo e no espaço. Maior tamanho é necessário nos decêndios dos meses de junho, julho, agosto e setembro em relação aos outros meses. Para os locais e decêndios estudados, 30 anos de observações são suficientes para estimar a média (µ) de radiação solar global média decendial, para um erro de estimação igual a 12.3%, com coeficiente de confiança de 95%.