In this thesis, we propose novel optimization and spatial queueing models that expand the currently existing methods by allowing multiple servers to be located at the same station and multiple servers to be dispatched to a single call. In particular, a mixed integer linear programming (MILP) model is introduced that determines how to locate and dispatch ambulances such that the coverage level is maximized. The model allows multiple servers to be located at the same station and balances the workload among them while maintaining contiguous first priority response districts. We also propose an extension to the approximate Hypercube queueing model by allowing multi-server dispatches. Computational results suggest that both models are effective in optimizing and analyzing the emergency systems. We also introduce the M[G]/M/s/s queueing model as an extension to the M/M/s/s model which allows for multiple servers to be assigned to a single customer.

Otoacoustic emission (OAE) data recorded for tone bursts presented separately and as a two-tone burst complex, that had been reported previously [Yoshikawa, H., Smurzynski, J., Probst R., 2000. Suppression of tone burst evoked otoacoustic emissions in relation to frequency separation. Hear. Res. 148, 95–106], were re-processed using the method of adaptive approximations by matching pursuit (MP). Two types of stimuli were applied to record tone burst OAEs (TBOAEs): (a) cosine-windowed tone bursts of 5-ms duration with center frequencies of 1, 1.5, 2 and 3kHz, (b) complex stimuli consisting of a digital addition of the 1-kHz tone burst together with either the 1.5-, 2- or 3-kHz tone burst. The MP method allowed decomposition of signals into waveforms of defined frequency, latency, time span, and amplitude. This approach provided a high time–frequency (t–f) resolution and identified patterns of resonance modes that were characteristic for TBOAEs recorded in each individual ear. Individual responses to single-tone bursts were processed off-line to form ‘sum of singles’ responses. The results confirmed linear superposition behavior for a frequency separation of two-tone bursts of 2kHz (the 1-kHz and 3-kHz condition). For the 1, 1.5-kHz condition, the MP results revealed the existence of closely positioned resonance modes associated with responses recorded individually with the stimuli differing in frequency by 500Hz. Then, the differences between t–f distributions calculated for dual (two-tone bursts) and sum-of-singles conditions exhibited mutual suppression of resonance modes common to both stimuli. The degree of attenuation depended on the individual pattern of characteristic resonance modes, i.e., suppression occurred when two resonant modes excited by both stimuli overlapped. It was postulated that the suppression observed in case of dual stimuli with closely-spaced components is due to mutual attenuation of the overlapping resonance modes.

Cette thèse traite de la résolution numérique des équations de Fredholm de seconde espèce faiblement singulières, posées dans un espace de Banach. Les méthodes décrites ici sont appliquées plus particulièrement dans le cas de l'espace des fonctions continues sur un intervalle compact et dans le cas de l'espace des fonctions intégrables, au sens de Lebesgue, sur un intervalle compact. Le premier chapitre fixe brièvement le cadre théorique de cette étude. Différents types de convergence d'une suite d'opérateurs dans un espace de Banach complexe, ainsi que leurs propriétés, y sont notamment rappelés. Le deuxième chapitre est consacré à la description et à l'analyse de deux méthodes d'approximation de rang fini sur lesquelles sont appliqués trois schémas de raffinement itératif. Des majorations des erreurs relatives associées à chaque méthode et dans chacun des espaces fonctionnels considérés y sont déduites, ainsi que les taux de convergence des schémas de raffinement correspondants. Une description détaillée de la mise en \oe uvre de ces derniers est donnée. Le troisième chapitre traite de l'application de ces méthodes à la résolution numérique de l'équation de transfert. Cette équation intervient au sein d'un problème beaucoup plus vaste (émanant de la théorie du transfert) dont une brève description est donnée dans le cadre particulier des atmosphères stellaires. Des expériences numériques, portant sur la validation des méthodes proposées et sur des cas ayant un sens astrophysique, sont présentées. La fin de ce chapitre est consacrée à la description de méthodes asymptotiques de décomposition du domaine permettant de surmonter la difficulté de résoudre cette équation lorsque le paramètre d'intégration varie dans un intervalle très large, ce qui est le cas dans certaines applications astrophysiques.

Dans cette thèse on explore l'utilisation du contrôle optimal et du transport de masse pour la modélisation économique. Nous saisissons ainsi l'occasion de réunir plusieurs travaux faisant intervenir ces deux outils, parfois en interactions l'un avec l'autre. Dans un premier temps nous présentons brièvement la récente théorie des jeux à champ moyen introduite par Lasry et Lions et nous concentrons sur le point de vue du contrôle de l'équation de Fokker-Planck. Nous exploitons cet aspect à la fois pour obtenir des résultats d'existence d'équilibres et pour développer des méthodes numériques de résolution. Nous testons les algorithmes dans deux cas complémentaires à savoir le cadre convexe (aversion à la foule, dynamiques à deux populations) et le cadre concave (attraction, externalités et effets d'échelle dans un modèle stylisé de transition technologique). Dans un second temps, nous étudions un problème de matching mêlant transport optimal et contrôle optimal. Le planificateur cherche un couplage optimal, fixé pour une période donnée (engagement), étant donné que les marges évoluent (éventuellement aléatoirement) de façon contrôlée. Enfin, nous reformulons un problème de partage de risque entre d agents (pour lequel nous prouvons un résultat d'existence) en un problème de contrôle optimal avec contraintes de comonotonie; ceci nous permet d'obtenir des conditions d'optimalité à l'aide desquelles nous construisons un algorithme simple et convergent.

In high frequency computational electromagnetics, rigorous numerical methods be come unrealistic tools due to computational demand increasing with the frequency. Instead approximations to the solutions of the Maxwell equations can be employed to evaluate th electromagnetic fields. In this thesis, we present the implementations of three high frequency approximat methods. The first two, namely the Geometrical Theory of Diffraction (GTD) and th Physical Optics (PO), are commonly used approximations. The third is a new invention that will be referred to as the Surface Current Extraction-Extrapolation (SCEE). Specifically, the GTD solver is a flexible and modular software package which use Non-Uniform Rational B-spline (NURBS) surfaces to model complex geometries. The PO solver is based on a triangular description of the surfaces and includes fas shadowing by ray tracing as well as contribution from edges to the scattered fields. GTD ray tracing was combined with the PO solver by a well thought-out software architecture Both implementations are now part of the GEMS software suite, the General ElectroMag netic Solvers, which incorporates state-of-the-art numerical methods. During validations both GTD and PO techniques turned out not to be accurate enough to meet the indus trial standards, thus creating the need for a new fast approximate method providing bette control of the approximations. In the SCEE approach, we construct high frequency approximate surface currents ex trapolated from rigourous Method of Moments (MoM) models at lower frequency. T do so, the low frequency currents are projected onto special basis vectors defined on th surface relative to the direction of the incident magnetic field. In such configuration, w observe that each component displays systematic spatial patterns evolving over frequenc in close correlation with the incident magnetic field, thus allowing us to formulate a fre quency model for each component. This new approach is fast, provides good control of th error and represents a platform for future development of high frequency approximations. As an application, we have used these tools to analyse the radar detectability of a new marine distress signaling device. The device, called "Rescue-Wing", works as an inflatabl radar reflector designed to provide a strong radar echo useful for detection and positionin during rescue operations of persons missing at sea. / QC 20101004

In terms of the Bias/Variance decomposition, very flexible (i.e., complex) Supervised Machine Learning systems may lead to unbiased estimators but with high variance. A rigid model, in contrast, may lead to small variance but high bias. There is a trade-off between the bias and variance contributions to the error, where the optimal performance is achieved.In this work we present three schemes related to the control of the Bias/Variance decomposition for Feed-forward Neural Networks (FNNs) with the (sometimes modified) quadratic loss function:1. An algorithm for sequential approximation with FNNs, named Sequential Approximation with Optimal Coefficients and Interacting Frequencies (SAOCIF). Most of the sequential approximations proposed in the literature select the new frequencies (the non-linear weights) guided by the approximation of the residue of the partial approximation. We propose a sequential algorithm where the new frequency is selected taking into account its interactions with the previously selected ones. The interactions are discovered by means of their optimal coefficients (the linear weights). A number of heuristics can be used to select the new frequencies. The aim is that the same level of approximation may be achieved with less hidden units than if we only try to match the residue as best as possible. In terms of the Bias/Variance decomposition, it will be possible to obtain simpler models with the same bias. The idea behind SAOCIF can be extended to approximation in Hilbert spaces, maintaining orthogonal-like properties. In this case, the importance of the interacting frequencies lies in the expectation of increasing the rate of approximation. Experimental results show that the idea of interacting frequencies allows to construct better approximations than matching the residue.2. A study and comparison of different criteria to perform Feature Selection (FS) with Multi-Layer Perceptrons (MLPs) and the Sequential Backward Selection (SBS) procedure within the wrapper approach. FS procedures control the Bias/Variance decomposition by means of the input dimension, establishing a clear connection with the curse of dimensionality. Several critical decision points are studied and compared. First, the stopping criterion. Second, the data set where the value of the loss function is measured. Finally, we also compare two ways of computing the saliency (i.e., the relative importance) of a feature: either first train a network and then remove temporarily every feature or train a different network with every feature temporarily removed. The experiments are performed for linear and non-linear models. Experimental results suggest that the increase in the computational cost associated with retraining a different network with every feature temporarily removed previous to computing the saliency can be rewarded with a significant performance improvement, specially if non-linear models are used. Although this idea could be thought as very intuitive, it has been hardly used in practice. Regarding the data set where the value of the loss function is measured, it seems clear that the SBS procedure for MLPs takes profit from measuring the loss function in a validation set. A somewhat non-intuitive conclusion is drawn looking at the stopping criterion, where it can be seen that forcing overtraining may be as useful as early stopping.3. A modification of the quadratic loss function for classification problems, inspired in Support Vector Machines (SVMs) and the AdaBoost algorithm, named Weighted Quadratic Loss (WQL) function. The modification consists in weighting the contribution of every example to the total error. In the linearly separable case, the solution of the hard margin SVM also minimizes the proposed loss function. The hardness of the resulting solution can be controlled, as in SVMs, so that this scheme may also be used for the non-linearly separable case. The error weighting proposed in WQL forces the training procedure to pay more attention to the points with a smaller margin. Therefore, variance tries to be controlled by not attempting to overfit the points that are already well classified. The model shares several properties with the SVMs framework, with some additional advantages. On the one hand, the final solution is neither restricted to have an architecture with so many hidden units as points (or support vectors) in the data set nor to use kernel functions. The frequencies are not restricted to be a subset of the data set. On the other hand, it allows to deal with multiclass and multilabel problems in a natural way. Experimental results are shown confirming these claims.A wide experimental work has been done with the proposed schemes, including artificial data sets, well-known benchmark data sets and two real-world problems from the Natural Language Processing domain. In addition to widely used activation functions, such as the hyperbolic tangent or the Gaussian function, other activation functions have been tested. In particular, sinusoidal MLPs showed a very good behavior. The experimental results can be considered as very satisfactory. The schemes presented in this work have been found to be very competitive when compared to other existing schemes described in the literature. In addition, they can be combined among them, since they deal with complementary aspects of the whole learning process.

Το αντικείμενο της εργασίας αυτής είναι η μελέτη των μετανευτώνειων προσεγγίσεων στο πλαίσιο της Γενικής Σχετικότητας, με έμφαση στους αστέρες νετρονίων. Λόγω του οτι, η μελέτη των αστέρων νετρονίων βασίζεται στην υδροδυναμική περιγραφή της ύλης, το κύριο ενδιαφέρον μας αφορά στον τρόπο που εισάγονται οι μετανευτώνειες προσεγγίσεις στις υδροδυναμικές εξισώσεις της Γενικής Σχετικότητας. Στο πρώτο κεφάλαιο παρουσιάζονται ορισμένα θεωρητικά στοιχεία γύρω απο φυσικά χαρακτηριστικά και τις ιδιότητες των συμπαγών αστέρων. Στο δεύτερο κεφάλαιο παρουσιάζονται τα γενικά χαρακτηριστικά των καταστατικών εξισώσεων των συμπαγών αστέρων, με έμφαση στην πολυτροπική καταστατική εξίσωση. Στο τρίτο κεφάλαιο παρουσιάζεται η θεωρία των μετανευτώνειων προσεγγίσεων, καθώς και οι μετανευτώνειες εξισώσεις πρώτης τάξης της υδροδυναμικής, στη Γενική Σχετικότητα όπως εισήχθησαν απο τον Chandrasekhar. Στο τέταρτο κεφάλαιο παρουσιάζεται η διαταρακτική μέθοδος που χρησιμοποιείται απο τους Fahlman και Anand, για την μελέτη των περιστρεφόμενων πολυτρόπων στο πλαίσιο της πρώτης μετανευτώνειας προσέγγισης στη Γενική Σχετικότητα. Στο πέμπτο κεφάλαιο παρουσιάζεται η μετανευτώνεια προσέγγιση δεύτερης τάξης όπως διατυπώθηκε απο τους Chandrasekhar και Nutku. Στο έκτο, και τελευταίο, κεφάλαιο παρουσιάζεται ένα υπολογιστικό αλγεβρικό πακέτο για μετανευτώνειους υπολογισμούς στη Γενική Σχετικότητα, το PROCRUSTES. Με την βοήθεια του πακέτου αυτού υπολογίσαμε διάφορες ποσότητες στη δεύτερη μετανευτώνεια προσέγγιση, όπως τον τανυστή ενέργειας - ορμής, 𝑇𝑖𝑗, τον τανυστή Ricci, 𝑅𝑖𝑗, τις εξισώσεις κίνησης, Τ𝑖𝑗;𝑗 = 0, και άλλες. Το PROCRUSTES είναι ένα πολύ χρήσιμο εργαλείο στη μετανευτώνεια μελέτη καθώς μπορεί κανείς να παράξει τις περίπλοκες εκφράσεις διαφόρων ποσοτήτων σε ελάχιστο χρόνο και χωρίς την πιθανότητα λάθους. Επίσης, με την βοήθεια του πακέτου αυτού, υπολογίσαμε τις αναλυτικές εκφράσεις των εξισώσεως κίνησης, Τ𝑖𝑗;𝑗 = 0, στην δεύτερη μετανευτώνεια προσέγγιση. Με κατάλληλη μετατροπή των εκφράσεων αυτών, μπορούμε να εφαρμόσουμε την μέθοδο των Fahlman και Anand, με σκοπό την μελέτη των περιστερόμενων πολυτρόπων στη μετανευτώνεια προσέγγιση δεύτερης τάξης. Στο τέλος της εργασίας παρατίθεται ένα συμπλήρωμα με τη δομή του προγράμματος και ορισμένες απο τις ποσότητες που υπολογίστηκαν στο πλαίσιο της εργασίας. / The main subject of my master thesis is the study of,the post-Newtonian approximations (PNA) in General Relativity (G-R), mainly those that concern the neutron stars. Owing to the study of neutron stars is on the hydrodynamic description of matter, our main interest lies uponthe way the PNA affects the hydrodynamic equations of G-R. In the first chapter there is presented the main theory around the physical attributes of compact stars. The second chapter reffers to the general features of the equations of state (EoS) of compact stars, giving emphasis to the polytropic EoS. In the yhird chapter, there is presented the theory of the PNA. There are also presented the the hydrodynamic equations in the PNA as the were introduced by Chandrasekhar. The fourth chapter is dedicated to the presentation of the method that was introduced by Fahlman and Anand, on the study of rotating polytropes in the PNA to G-R. The fifth chapter focuses on the second PNA as it formulated by Chandrasekhar and Nutku. During the sixth and final chapter there is presented a computer algebra package for post-Newtonian calculations in G-R, the PROCRUSTES. Whith the aid of thiw package, we calculated several quantities in the second PNA, as for example the E-M tensor 𝑇𝑖𝑗„ the Ricci tensor 𝑅𝑖𝑗 and the equations of motion (EoM) Τ𝑖𝑗 ;𝑗 = 0. PROCRUSTES is a very useful tool for the post-Newtonian study, as someone can produce the compicated equations of several quantities in no time and eliminating the possibility of making some mistake during the calculation. Moreover, using PROCRUSTES we calculated the expressions of the EoM’s in the second PNA. Under appropriate transformation of these expressions, we are able to apply the method of Fahlman and Anand onto these equations with a view to the study of rotating polytropes in the second PNA. At the end of this work there is quoted a supplement with the structure of the programm we used, along with some of the quantities that were calculated during this work.

L'objectif de ce travail est la résolution des équations intégrales singulières à noyau Cauchy. On y traite les équations singulières de Cauchy de première espèce par la méthode des approximations successives. On s'intéresse aussi aux équations intégrales à noyau de Cauchy de seconde espèce, en utilisant les polynômes trigonométriques et les techniques de Fourier. Dans la même perspective, on utilise les polynômes de Tchebychev de quatrième degré pour résoudre une équation intégro différentielle à noyau de Cauchy. Ensuite, on s'intéresse à une autre équation intégro-différentielle à noyau de Cauchy, en utilisant les polynômes de Legendre, ce qui a donné lieu à développer deux méthodes basées sur une suite de projections qui converge simplement vers l'identité. En outre, on exploite les méthodes de projection pour les équations intégrales avec des opérateurs intégraux bornés non compacts et on a appliqué ces méthodes à l'équation intégrale singulière à noyau de Cauchy de deuxième espèce

Neste trabalho, utilizando o método espectral de Galerkin, provamos a existência de soluções fracas (quando a dimensão n é maior que 2) e existência e unicidade de soluções fracas (quando a dimensão é 2) para um sistema de equações diferenciais parciais que descrevem o movimento de um fluido quimicamente ativo em um domínio limitado em Rn, n 2≥2. / In this work, by using the spectral Galerkin method, we prove the existence of weak solutions (when the dimension n is great than 2) and existence and uniqueness of weak solutions (when the dimension is 2) for a system of partial differential equations that describes the motion of a chemical active fluid in a bounded domain in Rn, n≥2.

Neste trabalho, utilizando o método espectral de Galerkin, provamos a existência de soluções fracas (quando a dimensão n é maior que 2) e existência e unicidade de soluções fracas (quando a dimensão é 2) para um sistema de equações diferenciais parciais que descrevem o movimento de um fluido quimicamente ativo em um domínio limitado em Rn, n 2≥2. / In this work, by using the spectral Galerkin method, we prove the existence of weak solutions (when the dimension n is great than 2) and existence and uniqueness of weak solutions (when the dimension is 2) for a system of partial differential equations that describes the motion of a chemical active fluid in a bounded domain in Rn, n≥2.