Analytic approximation of matrix functions in Lp

"Vegeu el resum a l'inici del document del fitxer adjunt."

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).

Heterologous desensitization of the glucagon-like peptide-1 receptor by phorbol esters requires phosphorylation of the cytoplasmic tail at four different sites.

Glucagon-like peptide-1 stimulates glucose-induced insulin secretion by binding to a specific G protein-coupled receptor that activates the adenylyl cyclase pathway. We previously demonstrated that heterologous desensitization of the receptor by protein kinase C correlated with phosphorylation in a 33-amino acid-long segment of the receptor carboxyl-terminal cytoplasmic tail. Here, we determined that the in vivo sites of phosphorylation are four serine doublets present at positions 431/432, 441/442, 444/445, and 451/452. In vitro phosphorylation of fusion proteins containing mutant receptor C-tails, however, indicated that whereas serines at position 431/432 were good substrates for protein kinase C (PKC), serines 444/445 and 451/452 were poor substrates, and serines 441/442 were not substrates. In addition, serine 416 was phosphorylated on fusion protein but not in intact cells. This indicated that in vivo a different PKC isoform or a PKC-activated kinase may phosphorylate the receptor. The role of phosphorylation on receptor desensitization was assessed using receptor mutants expressed in COS cells or Chinese hamster lung fibroblasts. Mutation of any single serine doublet to alanines reduced the extent of phorbol 12-myristate 13-acetate-induced desensitization, whereas substitution of any combination of two serine doublets suppressed it. Our data thus show that the glucagon-like peptide-1 receptor can be phosphorylated in response to phorbol 12-myristate 13-acetate on four different sites within the cytoplasmic tail. Furthermore, phosphorylation of at least three sites was required for desensitization, although maximal desensitization was only achieved when all four sites were phosphorylated.

Disease-causing mutations improving the branch site and polypyrimidine tract: pseudoexon activation of LINE-2 and antisense Alu lacking the poly(T)-tail.

Cryptic exons or pseudoexons are typically activated by point mutations that create GT or AG dinucleotides of new 5' or 3' splice sites in introns, often in repetitive elements. Here we describe two cases of tetrahydrobiopterin deficiency caused by mutations improving the branch point sequence and polypyrimidine tracts of repeat-containing pseudoexons in the PTS gene. In the first case, we demonstrate a novel pathway of antisense Alu exonization, resulting from an intronic deletion that removed the poly(T)-tail of antisense AluSq. The deletion brought a favorable branch point sequence within proximity of the pseudoexon 3' splice site and removed an upstream AG dinucleotide required for the 3' splice site repression on normal alleles. New Alu exons can thus arise in the absence of poly(T)-tails that facilitated inclusion of most transposed elements in mRNAs by serving as polypyrimidine tracts, highlighting extraordinary flexibility of Alu repeats in shaping intron-exon structure. In the other case, a PTS pseudoexon was activated by an A>T substitution 9 nt upstream of its 3' splice site in a LINE-2 sequence, providing the first example of a disease-causing exonization of the most ancient interspersed repeat. These observations expand the spectrum of mutational mechanisms that introduce repetitive sequences in mature transcripts and illustrate the importance of intronic mutations in alternative splicing and phenotypic variability of hereditary disorders.

An approximation algorithm for #k-SAT

"Vegeu el resum a l'inici del document del fitxer adjunt"

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.

Changes in the vascular reactivity of the isolated tail arteries of spontaneous and renovascular hypertensive rats to endogenous and exogenous noradrenaline.

We have investigated the changes in the responses to noradrenaline of isolated tail arteries of spontaneously hypertensive (SHR) and renovascular hypertensive rats (Wistar-Kyoto: two-kidney, one-clip model, WKY:2K1C) compared with normotensive (Wistar-Kyoto, WKY) rats. Renovascular hypertension was induced by 4 weeks' unilateral renal artery clipping. Arteries were vasoconstricted with exogenous noradrenaline, electrical field stimulation or high potassium. The effects of the latter two stimuli were abolished by reserpine and so were presumably dependent on the presence of endogenous noradrenaline. In the SHR the maximal vasoconstriction produced by all three stimuli was greater than in WKY. Dose-response curves were steeper and there was no change in threshold. Vascular mass was greater. We interpret these results as showing an increase in vascular reactivity in the SHR caused by structural adaptation. The WKY:2K1C responses to noradrenaline could also be explained in terms of structural adaptation but there was no increase in vascular mass. Sensitivity to potassium and electrical stimulation was decreased, suggesting a defect in vascular neurotransmission. This was supported by the observations of a decreased arterial noradrenaline content and of decreased sensitivity to cocaine.

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

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