François Dubeau

Discontinuous polynomial approximations in the theory of one-step, hybrid and multistep methods for nonlinear ordinary differential equations

This paper studies the approximation of the solution of nonlinear ordinary differen- tial equations by (discontinuous) piecewise polynomials of degree K and traces at the nodes of discretization. A mesh-dependent variational framework underlying this discontinuous ap- proximation is derived. Several families of one-step, hybrid and multistep schemes are obtained. It is shown that the convergence rate in the L2-norm is K + 1. The nodal-conver- gence rate can go up to 2 K + 2, depending on the particular scheme under consideration. The mesh-dependent variational framework introduced here is of special interest in the approxi- mation of the solution of optimal control problems governed by differential equations. 1. Introduction. The object of this paper is the study of (discontinuous) piecewise polynomial approximations to the solution of systems of nonlinear ordinary dif-

The impact of daily multiphase feeding on animal performance, body composition, nitrogen and phosphorus excretions, and feed costs in growing-finishing pigs.

The effect of feeding pigs in a three-phase feeding (3PF) system or a daily-phase feeding (DPF) system on growth performance, body composition, and N and P excretions was studied on 8 pens of 10 pigs each. Feeds for the 3PF and DPF treatments were obtained by mixing two feeds, one with a high nutrient concentration and the other with a low nutrient concentration. The DPF pigs tended (P=0.08) to consume more feed (+3.7%) than the 3PF pigs, but only during the first feeding phase. The DPF pigs consumed 7.3% less protein (P<0.01) but a similar amount of total P. For the whole growing period, the DPF pigs tended (P=0.08) to gain more weight (+2.4%) than the 3PF pigs, mainly because of faster growth (P=0.02) during the first feeding period. At the end of the experiment, total body protein mass was similar in the two treatment groups, but the DPF pigs had 8% more body lipids (P=0.04) than the 3PF pigs. Daily multiphase feeding reduced N excretion by 12% (P<0.01) but did not significantly reduce P excretion. In addition, feed costs, nutrient intake and nutrient excretion under the two feeding strategies were simulated and compared after different approaches were used to formulate complete feeds for each phase of the 3PF system, as well as the two feeds used in the DPF program. Simulated feed intake and growth was similar to those observed in the animal experiment. In comparison with the simulated 3PF system, the feed cost for the DPF pigs was reduced by 1.0%, the simulated N and P intakes were reduced by 7.3% and 4.4%, respectively, and the expected N and P excretions were reduced by 12.6% and 6.6%, respectively. The concomitant adjustment of the dietary concentration of nutrients to match the evaluated requirements of pig populations can be an efficient approach to significantly reduce feeding costs and N and P excretions in pig production systems.

Weighted Pseudometric Discriminatory Power Improvement Using a Bayesian Logistic Regression Model Based on a Variational Method

In this paper, we investigate the effectiveness of a Bayesian logistic regression model to compute the weights of a pseudometric in order to improve its discriminatory capacity and thereby increase image retrieval accuracy. In the proposed Bayesian model, the prior knowledge of the observations is incorporated and the posterior distribution is approximated by a tractable Gaussian form using variational transformation and Jensens inequality, which allow a fast and straightforward computation of the weights. The pseudometric makes use of the compressed and quantized versions of wavelet decomposed feature vectors, and in our previous work, the weights were adjusted by the classical logistic regression model. A comparative evaluation of the Bayesian and classical logistic regression models is performed for content-based image retrieval, as well as for other classification tasks, in a decontextualized evaluation framework. In this same framework, we compare the Bayesian logistic regression model to some relevant state-of-the-art classification algorithms. Experimental results show that the Bayesian logistic regression model outperforms these linear classification algorithms and is a significantly better tool than the classical logistic regression model to compute the pseudometric weights and improve retrieval and classification performance. Finally, we perform a comparison with results obtained by other retrieval methods.

Dynamic Cardiac PET Imaging: Extraction of Time-Activity Curves Using ICA and a Generalized Gaussian Distribution Model

Kinetic modeling of metabolic and physiologic cardiac processes in small animals requires an input function (IF) and a tissue time-activity curves (TACs). In this paper, we present a mathematical method based on independent component analysis (ICA) to extract the IF and the myocardiums TACs directly from dynamic positron emission tomography (PET) images. The method assumes a super-Gaussian distribution model for the blood activity, and a sub-Gaussian distribution model for the tissue activity. Our appreach was applied on 22 PET measurement sets of small animals, which were obtained from the three most frequently used cardiac radiotracers, namely: desoxy-fluoro-glucose (18F-FDG), [13 N]-ammonia, and [11C]-acetate. Our study was extended to PET human measurements obtained with the Rubidium-82 (82 Rb) radiotracer. The resolved mathematical IF values compare favorably to those derived from curves extracted from regions of interest (ROI), suggesting that the procedure presents a reliable alternative to serial blood sampling for small-animal cardiac PET studies.

Extraction of time activity curves from gated FDG-PET images for small animals’ heart studies

We introduce a new approach to extract the input function and the tissue time activity curve from dynamic ECG-gated (18)F-FDG PET images. These curves are mandatory to model the myocardium metabolic rate of glucose for heart studies. The proposed method utilizes coupled active contours to track the myocardium and the blood pool deformations. Furthermore, a statistical approach is developed to model the blood and tissue activities and to correct for spillovers. The developed algorithm offers a reliable alternative to serial blood sampling for small animal cardiac PET studies. Indeed, the calculated MMRG value differs by 1.54% only from the reference value.

Non-uniform Haar wavelets

In this paper we investigate a framework for non-uniform Haar wavelet. We define the Haar scaling function, the non-uniform Haar wavelet, and the non-uniform multiresolution analysis associated to these functions. The direct and inverse non-uniform Haar wavelet transforms are given. Application for bounded interval is considered including compression and reconstruction for a single value. Examples are given.

Algorithms for n -th root approximation

Fromf(x)=xn−r and a polynomialQp(y)=∑i=0paiyi, we consider Newtons method to solveFp(x)=Qp(f(x))=0. We obtain convergent iterative methods of orderp+1 to findr1/n for arbitraryp.ZusammenfassungFürf(x)=xn−r und ein PolynomQp(y)=∑i=0paiyi betrachten wir das Newton-Verfahren fürFp(x)=Qp(f(x))=0. Wir erhalten so konvergente iterative Verfahren der Ordnungp+1 fürr1/n, mit beliebigemp.

n th root extraction: double iteration process and Newton's method

A double iteration process already used to find the nth root of a positive real number is analysed and showed to be equivalent to the Newtons method. These methods are of order two and three. Higher-order methods for finding the nth root are also mentioned.

Formulating diets for growing pigs: economic and environmental considerations

We look at the environmental impact of formulating diets for an animal production system, namely the case of growing pigs. The classic approach in animal production is to use a growth model based on the least-cost diet formulation. This optimal diet is generally established by linear programming. Such an approach can lead to adverse environmental effects in the form of nitrogen and phosphorus excretions. Multi-criteria (two and three criteria) models are proposed with the aim of addressing both economic and environmental considerations. We apply the models to two real-life contexts: Québec (Canada) and France, and make some comparisons. We show that important reductions in nitrogen and phosphorus excretions can be achieved at relatively low costs in both contexts.

IMAGE RETRIEVAL BASED ON REGION SEPARATION AND MULTIRESOLUTION ANALYSIS

In this paper, a simple and fast querying method for content-based image retrieval is represented. Using the multispectral gradient, a color image is split into two disjoint parts that are the homogeneous color regions and the edge regions. The homogeneous regions are represented by the traditional color histograms, and the edge regions are represented by the multispectral gradient module mean histograms. In order to measure the similarity degree between two color images both quickly and effectively, we use a one-dimensional pseudo-metric, which makes use of the one-dimensional Daubechies decomposition and compression of the extracted histograms. Our querying method is invariant to the query color image object translations and color intensities. The experimental results are reported on a collection of 10,000 LAB color images.