Nous nous intéressons, dans cette thèse, à l'étude des méthodes d'extrapolation polynômiales et à l'application de ces méthodes dans l'accélération de méthodes itératives pour la résolution de l’équation algébrique de Riccati largement utilisée dans la théorie de transport. Pour ce type d’applications, l’extrapolation polynômiales réussit à accélérer la convergence même quand la convergence devient extrêmement lente. L'avantage de ces méthodes d'extrapolation est qu'elles utilisent uniquement une suite de vecteurs qui n'est pas forcément convergente, ou qui converge très lentement pour créer une nouvelle suite pouvant admettre une convergence quadratique. De plus, le développement de méthodes redémarrées (ou cycliques) permet de limiter le coût de calculs et de stockage. Une tâche importante relative à l’analyse du cas critique a été réalisée. une technique de décalage "shift technique" afin d’éliminer le problème lié à la singularité du la matrice Jacobienne ce qui rend la convergence linéaire plutôt que quadratique. En résumé, cette technique de "shift" transforme l’équation NARE à une autre dont la matrice Jacobienne est non singulier au voisinage de la solution. L’avantage de cette transformation est que la nouvelle équation a la même solution que l’équation d’origine. L’efficacité de l’approche proposée est illustrée à travers plusieurs comparaisons et résultats numériques. / In this thesis, we are interested in the study of polynomial extrapolation methods and their application as convergence accelerators on iterative methods to solve Algebraic Riccati equations arising in transport theory . In such applications, polynomial extrapolation methods succeed to accelerate the convergence of these iterative methods, even when the convergence turns to be extremely slow.The advantage of these methods of extrapolation is that they use a sequence of vectors which is not necessarily convergent, or which converges very slowly to create a new sequence which can admit a quadratic convergence. Furthermore, the development of restarted (or cyclic) methods allows to limit the cost of computations and storage. An interpretation of the critical case where the Jacobian matrix at the required solution is singular and quadratic convergence turns to linear is made. This problem can be overcome by applying a suitable shift technique. The original equation is transformed into an equivalent Riccati equation where the singularity is removed while the matrix coefficients maintain the same structure as in the original equation. The nice feature of this transformation is that the new equation has the same solution as the original one although the new Jacobian matrix at the solution is nonsingular. Numerical experiments and comparisons which confirm the effectiveness of the new approaches are reported.

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Doctor of Philosophy / Department of Mathematics / Marianne Korten / Charles N. Moore / We start with linear single variable conservation laws and examine the conditions under which a local extrapolation method (LEM) with upwinding underlying scheme is total variation diminishing TVD. The results are then extended to non-linear conservation laws. For this later case, we restrict ourselves to convex flux functions f, whose derivatives are positive, that is, fœ A0 and fœ A0. We next show that the Goodman-LeVeque flux satisfies the conditions for the LEM to be applied to it. We make heavy use of the CFL conditions, the geometric properties of convex functions apart from the martingle type properties of functions which are increasing, continuous, and differentiable.

Participants executed right-handed reach-to-grasp movements toward horizontally translating targets. Visual feedback of the target when reaching, as well as the presence of additional cues placed close (Experiment 1) or far (Experiment 2) above and below the target’s path was manipulated. Additional cue presence appeared to impair participants’ ability to extrapolate the disappeared target’s motion, and caused grasps for occluded targets to be less accurate. Final gaze and grasp positions were more accurate when reaching for leftward moving targets, suggesting individuals use different grasp strategies when reaching for targets travelling away from the reaching hand. Comparison of average fixations at reach onset and at the time of the grasp suggested that participants accurately extrapolated the occluded target’s motion prior to reach onset, but not after, resulting in inaccurate grasps. New information is provided about the eye-hand strategies used when reaching for moving targets in unpredictable visual conditions. / October 2016

Thesis advisor: Henry Braun / The measurement of student academic growth is one of the most important statistical tasks in an educational accountability system. The current methods of measuring student growth adopted in most states have various drawbacks in terms of sensitivity, accuracy, and interpretability. In this thesis, we apply the conditional growth chart method, a well-developed diagnostic tool in pediatrics, to student longitudinal test data to produce descriptive and diagnostic statistics about students' academic growth trajectory. We also introduce an innovative simulation-extrapolation (SIMEX) method which corrects for measurement error-induced bias in the estimation of the conditional growth model. Our simulation study shows that the proposed method has an advantage in terms of mean squared error of the estimators, when compared with the growth model that ignores measurement error. Our data analysis demonstrates that the conditional growth chart method, when combined with the SIMEX method, can be a powerful tool in the educational accountability system. It produces more sensitive and accurate measures of student growth than the other currently available methods; it provides diagnostic information that is easily understandable to teachers, parents and students themselves; the individual level growth measures can also be aggregated to school level as an indicator of school growth. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement, and Evaluation.

Copies of author's previously published works inserted. Bibliography: p. 56-57.

Neural conduction delay is a serious issue for organisms that need to act in real time. Perceptual phenomena such as the flash-lag effect (FLE, where the position of a moving object is perceived to be ahead of a brief flash when they are actually colocalized) suggest that the nervous system may perform extrapolation to compensate for delay. However, the precise neural mechanism for extrapolation has not been fully investigated. The main hypothesis of this dissertation is that facilitating synapses, with their dynamic sensitivity to the rate of change in the input, can serve as a neural basis for extrapolation. To test this hypothesis, computational and biologically inspired models are proposed in this dissertation. (1) The facilitatory activation model (FAM) was derived and tested in the motion FLE domain, showing that FAM with smoothing can account for human data. (2) FAM was given a neurophysiological ground by incorporating a spike-based model of facilitating synapses. The spike-based FAM was tested in the luminance FLE domain, successfully explaining extrapolation in both increasing and decreasing luminance conditions. Also, inhibitory backward masking was suggested as a potential cellular mechanism accounting for the smoothing effect. (3) The spike-based FAM was extended by combining it with spike-timing-dependent plasticity (STDP), which allows facilitation to go across multiple neurons. Through STDP, facilitation can selectively propagate to a specific direction, which enables the multi-neuron FAM to express behavior consistent with orientation FLE. (4) FAM was applied to a modified 2D pole-balancing problem to test whether the biologically inspired delay compensation model can be utilized in engineering domains. Experimental results suggest that facilitating activity greatly enhances real time control performance under various forms of input delay as well as under increasing delay and input blank-out conditions. The main contribution of this dissertation is that it shows an intimate link between the organism-level problem of delay compensation, perceptual phenomenon of FLE, computational function of extrapolation, and neurophysiological mechanisms of facilitating synapses (and STDP). The results are expected to shed new light on real-time and predictive processing in the brain, and help understand specific neural processes such as facilitating synapses.

Abstract Safety assessment relating to the presence of impurities, residual materials and contaminants in vaccines is a focus area of research at the United States Food and Drug Administration (FDA). Sponsors who submit Investigational New Drug (IND) applications for new vaccine products must report the results of safety assessments to the Division of Vaccines and Related Products Applications (DVRPA). Scientifically defining thresholds of toxicological concern (TTCs) as they apply to vaccine constituents will provide a useful aid to the sponsors and public regarding safety assessments of compounds for which there is little or no toxicity data. TTCs are mathematically modeled and extrapolated levels, below which adverse human health effects are not expected to occur (Kroes, 2004). In this project, we accessed DVRPA's submission databases and open source data to yield an initial chemical test set. Using INCHEM, RepDose, RTECS and TOXNET, we gathered LD50 and TDLo data. Using a structure-based decision tree, provided in the ToxTree software package, (3) different algorithms (The Cramer extended, the In vivo rodent micronucleus assay, and the Benigni-Bossa rule base for carcinogenicity by ISS) were applied to assign the initial test set (n= 197) of chemicals into structural families based on structural alerts (SAs). This resulted in six (6) potential methods for elucidating TTCs: In vivo rodent micronucleus assay/ LD50, Benigni-Bossa/ LD50, Cramer extended/ LD50, In vivo rodent micronucleus assay/ TDLo, Benigni-Bossa/ TDLo, and the Cramer extended/ TDLo. After each algorithm designated two structural families each, the distribution of TDLo's and LD50's for each structural family was subjected to a preliminary data analysis using JMP statistical software version 9. Based on an analysis of quantiles, skew, and kurtosis, it was concluded that the TDLo dataset was of poor quality and was dropped from further analysis, and that the In vivo rodent micronucleus assay algorithm failed to partition the initial test set in a meaningful way, so it too was culled from further consideration. This resulted in (2) remaining TTC methods for further consideration: Benigni-Bossa/ LD50 and the Cramer extended/ LD50. The remaining methods were subjected to internal validation based on Gene-Tox, CCRIS, CPDB, IARC, and EPA classaifications for genotoxic mutagenicity and carcinogenicity. Validation parameters were calculated for both methods and it was determined that the Benigni-Bossa/ LD50 method outperformed the Cramer extended/ LD50 method in terms of specificity (87.2 vs. 48.1%#37;), accuracy (65.2 vs. 52.94%#37;), positive predictivity (66.6 vs. 50%#37;), negative predictivity (64.8 vs. 56.5%#37;), ROC+ (2 vs. 1) and ROC- (1.84 vs. 1.3). These results indicated that the Benigni-Bossa/ LD50 was the most appropriate for calculating TTCs for vaccine constituents. For each class, the lower 2.5th percentile LD50 was extrapolated to a TTC value using safety estimates derived using uncertainty factors (UF) and adjusting for adult human weight. Final TTCs were designated as 18.06 μg/ person and 20.616 μg/ person for the Benigni-Bossa positive and negative structural families.

Thesis (M.Sc.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2001? / Copies of author's previously published works inserted. Bibliography: p. 56-57.

Techn. Universiẗat, Diss., 2005--Berlin.