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La résolution numérique de n'importe quelle discrétisation d'équations aux dérivées partielles non linéaires requiert le plus souvent un algorithme itératif. En général, la discrétisation des équations aux dérivées partielles donne lieu à des systèmes de grandes dimensions. Comme la résolution des grands systèmes est très coûteuse en terme de temps de calcul, une question importante se pose: afin d'obtenir une solution approchée de bonne qualité, quand est-ce qu'il faut arrêter l'itération afin d'éviter les itérations inutiles ? L'objectif de cette thèse est alors d'appliquer, à différentes équations, une méthode qui nous permet de diminuer le nombre d'itérations de la résolution des systèmes en gardant toujours une bonne précision de la méthode numérique. En d'autres termes, notre but est d'appliquer une nouvelle méthode qui fournira un gain remarquable en terme de temps de calcul. Tout d'abord, nous appliquons cette méthode pour un problème non linéaire modèle. Nous effectuons l'analyse a priori et a posteriori de la discrétisation par éléments finis de ce problème et nous proposons par la suite deux algorithmes de résolution itérative correspondants. Nous calculons les estimations d'erreur a posteriori de nos algorithmes itératifs proposés et nous présentons ensuite quelques résultats d'expérience numériques afin de comparer ces deux algorithmes. Nous appliquerons de même cette approche pour les équations de Navier-Stokes. Nous proposons un schéma itératif et nous étudions la convergence et l'analyse a priori et a posteriori correspondantes. Finalement, nous présentons des simulations numériques montrant l'efficacité de notre méthode.
Recent advances in digital technology and big data have allowed FinTech (financial technology) lending to emerge as a potentially promising solution to reduce the cost of credit and increase financial inclusion. However, machine learning (ML) methods that lie at the heart of FinTech credit have remained largely a black box for the nontechnical audience. This paper contributes to the literature by discussing potential strengths and weaknesses of ML-based credit assessment through (1) presenting core ideas and the most common techniques in ML for the nontechnical audience; and (2) discussing the fundamental challenges in credit risk analysis. FinTech credit has the potential to enhance financial inclusion and outperform traditional credit scoring by (1) leveraging nontraditional data sources to improve the assessment of the borrower’s track record; (2) appraising collateral value; (3) forecasting income prospects; and (4) predicting changes in general conditions. However, because of the central role of data in ML-based analysis, data relevance should be ensured, especially in situations when a deep structural change occurs, when borrowers could counterfeit certain indicators, and when agency problems arising from information asymmetry could not be resolved. To avoid digital financial exclusion and redlining, variables that trigger discrimination should not be used to assess credit rating.
Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics—including familiarity with Fourier series, matrices, probability, and statistics—this Second Edition: Contains new chapters on convolution and the vector DFT, plane-wave propagation, and the BLUE and Kalman filters Expands the material on Fourier analysis to three new chapters to provide additional background information Presents real-world examples of applications that demonstrate how mathematics is used in remote sensing Featuring problems for use in the classroom or practice, Signal Processing: A Mathematical Approach, Second Edition covers topics such as Fourier series and transforms in one and several variables; applications to acoustic and electro-magnetic propagation models, transmission and emission tomography, and image reconstruction; sampling and the limited data problem; matrix methods, singular value decomposition, and data compression; optimization techniques in signal and image reconstruction from projections; autocorrelations and power spectra; high-resolution methods; detection and optimal filtering; and eigenvector-based methods for array processing and statistical filtering, time-frequency analysis, and wavelets.
A modern look at state estimation, targeted at students and practitioners of robotics, with emphasis on three-dimensional applications.
This book is a significant contribution to the subject of mining time-changing data streams and addresses the design of learning algorithms for this purpose. It introduces new contributions on several different aspects of the problem, identifying research opportunities and increasing the scope for applications. It also includes an in-depth study of stream mining and a theoretical analysis of proposed methods and algorithms. The first section is concerned with the use of an adaptive sliding window algorithm (ADWIN). Since this has rigorous performance guarantees, using it in place of counters or accumulators, it offers the possibility of extending such guarantees to learning and mining algorithms not initially designed for drifting data. Testing with several methods, including Naïve Bayes, clustering, decision trees and ensemble methods, is discussed as well. The second part of the book describes a formal study of connected acyclic graphs, or 'trees', from the point of view of closure-based mining, presenting efficient algorithms for subtree testing and for mining ordered and unordered frequent closed trees. Lastly, a general methodology to identify closed patterns in a data stream is outlined. This is applied to develop an incremental method, a sliding-window based method, and a method that mines closed trees adaptively from data streams. These are used to introduce classification methods for tree data streams.
This book presents a compendium of methodologies for the study of membrane lipids, varying from traditional lab bench experimentation to computer simulation and theoretical models. The volume provides a comprehensive set of techniques for studying membrane lipids with a strong biophysical emphasis. It compares the various available techniques including the pros and cons as seen by the experts.
Presents state-of-the-art sparse and multiscale image and signal processing with applications in astronomy, biology, MRI, media, and forensics.
State-of-the-art algorithms and theory in a novel domain of machine learning, prediction when the output has structure.
Image Recovery: Theory and Application focuses on signal recovery and synthesis problems. This book discusses the concepts of image recovery, including regularization, the projection theorem, and the pseudoinverse operator. Comprised of 13 chapters, this volume begins with a review of the basic properties of linear vector spaces and associated operators, followed by a discussion on the Gerchberg-Papoulis algorithm. It then explores image restoration and the basic mathematical theory in image restoration problems. The reader is also introduced to the problem of obtaining artifact-free computed tomographic reconstruction. Other chapters consider the importance of Bayesian approach in the context of medical imaging. In addition, the book discusses the linear programming method, which is particularly important for images with large number of pixels with zero value. Such images are usually found in medical imaging, microscopy, electron microscopy, and astronomy. This book can be a valuable resource to materials scientists, engineers, computed tomography technologists, and astronomers.