Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

The Total fiscal cost of indirect taxation: an approximation using Catalonia's recent input-output table

In this note we quantify to what extent indirect taxation influences and distorts prices. To do so we use the networked accounting structure of the most recent input-output table of Catalonia, an autonomous region of Spain, to model price formation. The role of indirect taxation is considered both from a classical value perspective and a more neoclassical flavoured one. We show that they would yield equivalent results under some basic premises. The neoclassical perspective, however, offers a bit more flexibility to distinguish among different tax figures and hence provide a clearer disaggregate picture of how an indirect tax ends up affecting, and by how much, the cost structure.

Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Second-Order Approximation to the Rotemberg Model around a Distorted Steady State

Less is known about social welfare objectives when it is costly to change prices, as in Rotemberg (1982), compared with Calvo-type models. We derive a quadratic approximate welfare function around a distorted steady state for the costly price adjustment model. We highlight the similarities and differences to the Calvo setup. Both models imply inflation and output stabilization goals. It is explained why the degree of distortion in the economy influences inflation aversion in the Rotemberg framework in a way that differs from the Calvo setup.

Analytic approximation of matrix functions in Lp

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Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

Design and analysis of ChIP-Seq experiments for nuclear factor I DNA-binding proteins

SUMMARY : Eukaryotic DNA interacts with the nuclear proteins using non-covalent ionic interactions. Proteins can recognize specific nucleotide sequences based on the sterical interactions with the DNA and these specific protein-DNA interactions are the basis for many nuclear processes, e.g. gene transcription, chromosomal replication, and recombination. New technology termed ChIP-Seq has been recently developed for the analysis of protein-DNA interactions on a whole genome scale and it is based on immunoprecipitation of chromatin and high-throughput DNA sequencing procedure. ChIP-Seq is a novel technique with a great potential to replace older techniques for mapping of protein-DNA interactions. In this thesis, we bring some new insights into the ChIP-Seq data analysis. First, we point out to some common and so far unknown artifacts of the method. Sequence tag distribution in the genome does not follow uniform distribution and we have found extreme hot-spots of tag accumulation over specific loci in the human and mouse genomes. These artifactual sequence tags accumulations will create false peaks in every ChIP-Seq dataset and we propose different filtering methods to reduce the number of false positives. Next, we propose random sampling as a powerful analytical tool in the ChIP-Seq data analysis that could be used to infer biological knowledge from the massive ChIP-Seq datasets. We created unbiased random sampling algorithm and we used this methodology to reveal some of the important biological properties of Nuclear Factor I DNA binding proteins. Finally, by analyzing the ChIP-Seq data in detail, we revealed that Nuclear Factor I transcription factors mainly act as activators of transcription, and that they are associated with specific chromatin modifications that are markers of open chromatin. We speculate that NFI factors only interact with the DNA wrapped around the nucleosome. We also found multiple loci that indicate possible chromatin barrier activity of NFI proteins, which could suggest the use of NFI binding sequences as chromatin insulators in biotechnology applications. RESUME : L'ADN des eucaryotes interagit avec les protéines nucléaires par des interactions noncovalentes ioniques. Les protéines peuvent reconnaître les séquences nucléotidiques spécifiques basées sur l'interaction stérique avec l'ADN, et des interactions spécifiques contrôlent de nombreux processus nucléaire, p.ex. transcription du gène, la réplication chromosomique, et la recombinaison. Une nouvelle technologie appelée ChIP-Seq a été récemment développée pour l'analyse des interactions protéine-ADN à l'échelle du génome entier et cette approche est basée sur l'immuno-précipitation de la chromatine et sur la procédure de séquençage de l'ADN à haut débit. La nouvelle approche ChIP-Seq a donc un fort potentiel pour remplacer les anciennes techniques de cartographie des interactions protéine-ADN. Dans cette thèse, nous apportons de nouvelles perspectives dans l'analyse des données ChIP-Seq. Tout d'abord, nous avons identifié des artefacts très communs associés à cette méthode qui étaient jusqu'à présent insoupçonnés. La distribution des séquences dans le génome ne suit pas une distribution uniforme et nous avons constaté des positions extrêmes d'accumulation de séquence à des régions spécifiques, des génomes humains et de la souris. Ces accumulations des séquences artéfactuelles créera de faux pics dans toutes les données ChIP-Seq, et nous proposons différentes méthodes de filtrage pour réduire le nombre de faux positifs. Ensuite, nous proposons un nouvel échantillonnage aléatoire comme un outil puissant d'analyse des données ChIP-Seq, ce qui pourraient augmenter l'acquisition de connaissances biologiques à partir des données ChIP-Seq. Nous avons créé un algorithme d'échantillonnage aléatoire et nous avons utilisé cette méthode pour révéler certaines des propriétés biologiques importantes de protéines liant à l'ADN nommés Facteur Nucléaire I (NFI). Enfin, en analysant en détail les données de ChIP-Seq pour la famille de facteurs de transcription nommés Facteur Nucléaire I, nous avons révélé que ces protéines agissent principalement comme des activateurs de transcription, et qu'elles sont associées à des modifications de la chromatine spécifiques qui sont des marqueurs de la chromatine ouverte. Nous pensons que lés facteurs NFI interagir uniquement avec l'ADN enroulé autour du nucléosome. Nous avons également constaté plusieurs régions génomiques qui indiquent une éventuelle activité de barrière chromatinienne des protéines NFI, ce qui pourrait suggérer l'utilisation de séquences de liaison NFI comme séquences isolatrices dans des applications de la biotechnologie.

An approximation algorithm for #k-SAT

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Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

The robustness of the weak selection approximation for the evolution of altruism against strong selection.

The weak selection approximation of population genetics has made possible the analysis of social evolution under a considerable variety of biological scenarios. Despite its extensive usage, the accuracy of weak selection in predicting the emergence of altruism under limited dispersal when selection intensity increases remains unclear. Here, we derive the condition for the spread of an altruistic mutant in the infinite island model of dispersal under a Moran reproductive process and arbitrary strength of selection. The simplicity of the model allows us to compare weak and strong selection regimes analytically. Our results demonstrate that the weak selection approximation is robust to moderate increases in selection intensity and therefore provides a good approximation to understand the invasion of altruism in spatially structured population. In particular, we find that the weak selection approximation is excellent even if selection is very strong, when either migration is much stronger than selection or when patches are large. Importantly, we emphasize that the weak selection approximation provides the ideal condition for the invasion of altruism, and increasing selection intensity will impede the emergence of altruism. We discuss that this should also hold for more complicated life cycles and for culturally transmitted altruism. Using the weak selection approximation is therefore unlikely to miss out on any demographic scenario that lead to the evolution of altruism under limited dispersal.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

A First approximation to the realism/idealism debate about the external world

El text intenta fer una primera aproximació al debat contemporani entre realistes i anti-realistes sobre el món empíric, centrant-se en les posicions de Putnam i Nagel. El seu objectiu principal és el d'entendre les motivacions de les posicions i l'estructura actual del debat, i el d'establir les característiques que hauria de tenir qualsevol posició satisfactòria