Le présent manuscrit constitue la partie écrite du travail de thèse réalisé par Bruno Mery sous la direction de Christian Bassac et Christian Retoré entre 2006 et 2011, portant sur le sujet "Modélisation de la sémantique lexicale dans la théorie des types". Il s'agit d'une thèse d'informatique s'inscrivant dans le domaine du traitement automatique des langues, et visant à apporter un cadre formel pour la prise en compte, lors de l'analyse sémantique de la phrase, d'informations apportées par chacun des mots.Après avoir situé le sujet, cette thèse examine les nombreux travaux l'ayant précédée et s'inscrit dans la tradition du lexique génératif. Elle présente des exemples de phénomènes à traiter, et donne une proposition de système de calcul fondée sur la logique du second ordre. Elle examine ensuite la validité de cette proposition par rapport aux exemples et aux autres approches déjà formalisées, et relate une implémentation de ce système. Enfin, elle propose une brève discussion des sujets restant en suspens. / This paper is part of the thesis by Bruno Mery advised by Christian Bassac and Christian Retore in the years 2006-2011, on the topic "Modelling lexical semantics in a type-theoretic framework''. It is a doctoral thesis in computer science, in the area of natural language processing, aiming to bring forth a formal framework that takes into account, in the parsing of the semantics of a sentence, of lexical data.After a discussion of the topic, this thesis reviews the many works perceding it and adopts the tradition of the generative lexicon. It presents samples of data to account for, and gives a proposal for a calculus system based upon a second-order logic. It afterwards reviews the validity of this proposal, coming back to the data samples and the other formal approaches, and gives an implementation of that system. At last, it engages in a short discussion of the remaining questions.

Dans la première partie, on propose un système de type pour le lambda-calcul, dans le style du calcul des séquents, nomme « Soft Type Assignment » (STA) qui est inspiré par la logique linéaire « soft ». STA a la propriété de réduction du sujet et est correct et complète pour les calculs en temps polynomial. Par la suite on propose un déduction naturelle, STA_N. Ce système est simple mais il a le désavantage que les variables dans le sujet peuvent être explicitement renommées. Pour résoudre ce problème, on propose le système STA_M, où les contextes sont des multi-ensembles, donc les règles pour renommer les variables peuvent être interdit. L’inférence de type pour STA_M ne semble pas décidable. On propose un algorithme qui pour chaque lambda-terme rend l’ensemble de contraintes que doivent être satisfait pour que le terme soit type. Pi est correct et complet. Ensuite on étend le lambda-calcul par des constantes booléennes et on propose le système STA_B. La particularité de STA_B est que la règle du conditionnel utilise les contextes de façon additive. Chaque programme de STA_B peut être exécuté, par une machine abstraite, en espace polynomial. De plus le système est aussi complet pour PSPACE. Dans la deuxième partie, on propose une restriction de PCF, nommée SlPCF. Ce langage est équipé avec une sémantique opérationnelle qui mélange l’appelle par nom et l’appelle par valeur et peut être interprèté en mode standard dans les espaces cohérents linéaires. SlPCF est complet pour les fonctions récursives, mais il n’est pas complet et donc il n’est pas fully abstract pour les espaces cohérents linéaires / In the first part, we propose, inspired by Soft Linear Logic, a type assignment system for lambda-calculus in sequent calculus style, named Soft Type Assignment (STA). STA enjoys the subject reduction property. and is correct and complete for polynomial time computations. Then, we propose a natural deduction named STA_N. While simple, STA_N has the disadvantage of allowing the explicit renaming of variables in the subject. To overcome to this problem, we propose another natural deduction system, named STA_M, where contexts are multisets, hence rules renaming variables can be avoided. The type inference for STA_M seems in general undecidable. We propose an algorithm Pi returning, for every lambda-term, a set of constraints that need to be satisfied in order to type the term. Pi is correct and complete. We extend the lambda-calculus by basic boolean constants and we propose the system STA_B. The peculiarity of STA_B is that the conditional rule treats the contexts in an additive way. Every STA_B program can be executed, through an abstract machine, in polynomial space. Moreover, STA_B is also complete for PSPACE. In the second part we propose a restriction of PCF, named SlPCF. The language is naturally equipped with an operational semantics mixing call-by-name and call-by-value parameter passing and it can be interpreted in linear coherence space in a standard way. SlPCF is recursive complete, but it is not complete, and thus not fully abstract, with respect to linear coherence spaces

When a genetic factor is being studied for more than one response variable, estimates of the genetic covariances are essential, specially in breeding programs. In a genetic covariance analysis, genetic and residual mean cross-products are obtained. Stochastically, to quantify the magnitude of the joint variation of two response variables due to genetic effect with respect to the variation due to residual effect may allow one to make inferences about the significance of the associated genetic covariance. In this study it is presented tests of significance for genetic covariance upon a twofold way: tests that take into account the genetic and environmental effects and tests that only consider the genetic information. The first way refers to tests based on the mean cross-products ratio via nonparametric bootstrap resampling and Monte Carlo simulation of Wishart matrices. The second way of testing genetic covariance refers to tests based on adaptation of Wilks\' and Pillai\'s statistics for evaluating independence of two sets of variables. For the first type of tests, empirical distributions under the null hypothesis, i.e., null genetic covariance, were built and graphically analyzed. In addition, the exact distribution of mean cross-products ratio obtained from variables normally distributed with zero mean and finite variance was examined. Writing computational algorithms in R language to perform the proposed tests was also an objective of this study. Only under certain conditions does the probability density function of the product of two random Gaussian variables approximate a normal curve. Therefore, studying the distribution of a mean cross-products ratio as a quotient of two Gaussian variables is not suitable. Tests based on mean cross-products ratio are related to both the value of the genetic covariance and the magnitude of the latter relative to the residual covariance. And both approaches (bootstrap and simulation) are more sensitive than the tests based only on genetic information. The performance of the tests based on mean cross-products ratio is related to the quality of the original data set in terms of the MANOVA assumptions, and the test statistic does not depend on the estimation of the matrix of genetic covariances ΣG. The adaptation of Wilks\' and Pillai\'s statistics can be used to test the genetic covariance. Their approximations to a χ21 distribution were checked and the accuracy of their inferences is related to the quality of G. / Quando um fator genético está sendo estudado em mais de uma variável de resposta, estimativas das covariâncias genéticas são essenciais, especialmente para programas de melhoramento. Em uma análise de covariância genética, produtos cruzados médios devido ao efeito genético, a partir do qual é obtida a covariância genética, e devido ao efeito residual são obtidos. Estocasticamente, quantificar a magnitude da variação conjunta de duas variáveis resposta devido ao efeito genético em relação à variação devida ao efeito residual pode permitir realizar inferências sobre a covariância genética associada. Neste estudo são apresentados testes de significância para a covariância genética de duas formas: testes que levam em conta os efeitos genéticos e ambientais (ou residuais) e testes que consideram apenas a informação genética. A primeira forma refere-se testes baseados na razão de produtos cruzados médios via bootstrap não paramétrico e simulação de matrizes Wishart pelo método de Monte Carlo. A segunda maneira de testar a covariância genética refere-se a testes com base em uma adaptação das estatísticas de Wilks e Pillai para avaliar a independência de dois conjuntos de variáveis. Para o primeiro tipo de testes, as distribuições empíricas sob a hipótese nula, ou seja, covariância genética nula, foram construídas e analisadas graficamente. Além disso, foi feito um estudo analítico da distribuição da razão de produtos cruzados médios obtidos a partir de variáveis normalmente distribuídas com média zero e variância finita. Escrever algoritmos computacionais em linguagem R para realizar os testes propostos também foi um dos objetivos deste estudo. Apenas sob certas condições a função de densidade de probabilidade do produto de duas variáveis aleatórias gaussianas aproxima-se da curva normal. Por conseguinte, o estudo da distribuição da razão de produtos cruzados médios como um quociente de duas variáveis gaussianas não é adequado. Os testes baseados na razão de produtos cruzados médios estão relacionados tanto com o valor da covariância genética quanto com a magnitude desta em relação à covariância residual. Ambas as abordagens (bootstrap e simulação) mostraram-se mais sensíveis do que os testes baseados apenas nas informações genéticas. O desempenho dos testes baseados na razão de produtos cruzados médios está relacionado à qualidade dos dados originais em termos das pressuposições da MANOVA, e a estatística de teste não depende da estimação da matriz de covariâncias genéticas ΣG. A adaptação das estatísticas de Wilks e Pillai pode ser usada para testar a covariância genética. As aproximações à distribuição Χ21 foi verificada. A precisão de suas inferências está relacionada a qualidade da matriz G.

La réalisabilité classique de Jean-Louis Krivine associe à chaque modèle de calcul et chaque modèle de la théorie des ensembles un nouveau modèle de la théorie des ensembles, appelé modèle de réalisabilité, d'une façon similaire au forcing. Chaque modèle de réalisabilité est muni d’une algèbre de Boole caractéristique $\gimel 2$ (gimel 2), dont la structure donne des informations sur les propriétés du modèle de réalisabilité. En particulier, les modèles de forcing correspondent au cas où $\gimel 2$ est l'algèbre de Boole à deux éléments.Ce travail présente de nouveaux outils pour manipuler les modèles de réalisabilité et donne de nouveaux résultats obtenus en les exploitant. L'un d'entre eux est qu'au premier ordre, la théorie des algèbres de Boole à au moins deux éléments est complète pour $\gimel 2$, au sens où $\gimel 2$ eut être rendue élémentairement équivalente à n'importe quelle algèbre de Boole. Deux autres résultats montrent que $\gimel 2$ peut être utilisée pour étudier les modèles dénotationnels de langage de programmation (chacun part d'un modèle dénotationnel et classifie ses degrés de parallélisme à l'aide de $\gimel 2$). Un autre résultat montre que la technique de Jean-Louis Krivine pour réaliser l'axiome des choix dépendants à partir de l'instruction quote peut se généraliser à des formes plus fortes de choix. Enfin, un dernier résultat, obtenu en collaboration avec Laura Fontanella, accompagne le précédent en adaptant la condition d'antichaîne dénombrable du forcing au cadre de la réalisabilité, ce qui semble semble ouvrir une piste prometteuse pour réaliser l'axiome du choix. / Jean-Louis Krivine's classical realizability defines, from any given model of computation and any given model of set theory, a new model of set theory called the realizability model, in a similar way to forcing. Each realizability model is equipped with a characteristic Boolean algebra $\gimel 2$ (gimel 2), whose structure encodes important information about the properties of the realizability model. For instance, forcing models are precisely the realizability models in which $\gimel 2$ is the Boolean algebra with to elements.This document defines new tools for studying realizability models and exploits them to derive new results. One such result is that, as far as first-order logic is concerned, the theory of Boolean algebras with at least two elements is complete for $\gimel 2$, meaning that for each Boolean algebra B (with at least two elements), there exists a realizability model in which $\gimel 2$ is elementarily equivalent to B. Next, two results show that $\gimel 2$ can be used as a tool to study denotational models of programming languages (each one of them takes a particular denotational model and classifies its degrees of parallelism using $\gimel 2$). Moving to set theory, another results generalizes Jean-Louis Krivine's technique of realizing the axiom of dependant choices using the instruction quote to higher forms of choice. Finally, a last result, which is joint work with Laura Fontanella, complements the previous one by adapting the countable antichain condition from forcing to classical realizability, which seems to open a new, promising approach to the problem of realizing the full axiom of choice.

Le $\lambda \mu^{\wedge \vee}$-calcul est une extension du $\lambda$-calcul associée à la déduction naturelle classique où sont considérés tous les connecteurs.<br>Les principaux résultats de cette thèse sont :<br>- La standardisation, la confluence et une extension de la machin de J.-L. Krivine en $\lambda \mu^{\wedge \vee}$-calcul.<br>- Une preuve sémantique de la forte normalisation du théorème d'élimination des coupures.<br>- Une sémantique de réalisabilité pour le $\lambda \mu^{\wedge \vee}$-calcul qui permet de caractériser le comportement calculatoire de certains termes typés et clos.<br>- Un théorème de complétude pour le $\lambda \mu$-calcul simplement typé.<br>- Une introduction à un $\lambda \mu^{\wedge \vee}$-calcul par valeur confluent.

L'infection par le virus de l'hépatite C implique des processus d'interaction complexe entre l'hôte et le virus. Plusieurs facteurs de l'hôte incluant des polymorphismes génétiques et les réponses immunitaires influent sur l'infection et les réponses au traitement. Aussi, il est important d'identifier en amont les facteurs pour prédire la réponse au traitement. L'objectif de la thèse est d'étudier l'influence de certains polymorphismes génétiques de l'hôte sur la réponse à la bithérapie et sur le statut immunitaire du foie dans l'infection chronique par le VHC. L'étude a porté sur les polymorphismes des gènes de l'interféron lambda 3 et 4, l'interféron gamma, l'interleukine 10, et l'interleukine 17, conjointement à la réponse au traitement avec le peg-IFNα et la RBV et aux réponses immunitaires du foie chez les patients. Nous avons établi une méthode PCR-RFLP simple et fiable pour le typage de deux polymorphismes de l'IFNL3. En utilisant les enzymes de restriction BstUI et BrsDI permet le génotypage de deux variantes de IFNL3 (rs12979860 C/T et rs8099917 T/G, respectivement). Les résultats indiquent que cette méthode PCR-RFLP donne des résultats similaires à ceux des méthodes standard et présente un intérêt pour des analyses de routine en laboratoire clinique car elle est peu coûteuse. Nous avons analysé l'association des polymorphismes avec la réponse au traitement antiviral sur une cohorte de 108 patients infectés par le VHC de génotype 1 traités par la bithérapie. Nous avons ainsi démontré que le génotype de l'IFNL4 TT/TT de ss469415590 et une réponse virologique rapide sont des facteurs prédictifs indépendants pour atteindre un taux de réponse virologique soutenue (OR = 3,93, p = 0,004 et OR = 6,74, p = 0,021). D'autre part, une charge virale initiale haute est associée à l'échec au traitement (OR = 0,34, p = 0,023). Ainsi, ces paramètres sont utiles pour la définition d'un traitement personnalisé. Pour expliquer l'influence de ces polymorphismes dans l'infection chronique par le VHC, nous avons étudié l'association des polymorphismes IFNL3 et 4 avec la réponse immunitaire du foie chez les patients atteints d'une infection chronique par le VHC. En utilisant l'expression de CD107a comme marqueur de l'activité sécrétoires des lymphocytes, nous avons observé une activité de dégranulation des lymphocytes du foie plus importante les patients porteurs des génotypes de IFNL4 favorables en comparaison avec les patients porteurs de l'allèle défavorable. En utilisant des analyses de régression, les taux d'ALT sont en corrélation avec la fréquence des cellules NKT CD107a+ dans le foie. Enfin, chez les patients traités par la bithérapie, une forte activité de dégranulation est observée chez les patients avec les génotypes favorables IFNL3 et 4. Nous suggérons que les polymorphismes des gènes de l'interféron lambda sont associés à l'activité de la dégranulation des lymphocytes intra-hépatiques et contribuent à un mécanisme de clairance du VHC sous la bithérapie. Nous avons également étudié l'impact de plusieurs polymorphismes génétiques sur la gravité de l'hépatite C chronique. Les résultats montrent une association significative observée entre le polymorphisme de l'IFN-γ et la gravité de l'hépatite C chronique. Pour l'analyse de régression logistique, l'allèle T et la présence d'une stéatose sont des facteurs prédictifs indépendants de la sévérité de la maladie hépatique chronique associée au VHC. L'utilisation du génotypage de l'IFN-γ pourrait être utile dans la prise en charge des patients. En conclusion, nous avons montré que les polymorphismes des gènes des IFNL3 et 4 et de l'IFN-γ de l'hôte jouent un rôle important dans l'efficacité du traitement et les réponses immunitaires hépatiques. Ces résultats aident à définir un traitement personnalisé pour le contrôle de l'infection chronique par le VHC, en particulier dans les régions aux ressources limitées où les nouveaux traitements ne sont pas accessibles. / Hepatitis C virus (HCV) infection is a complex interaction process between the host and viral factors. The host immune responses and genetic polymorphisms have been shown to be associated with the outcome of HCV infections and the responses to treatments. Thus, it is very important to identify pre-treament factors to predict treatment outcomes. The overall aim of the thesis study is to investigate the role of host genetic polymorphisms on response to combination therapy and immune response in the liver in chronic HCV infection. The study has focused on polymorphisms in the interferon lambda (IFNL) genes, interferon gamma, interleukin 10, and interleukin 17 in relation to response to therapy with peg-IFNα and Ribavirin (RBV) and liver immune responses in patients with chronic HCV infection.First, we have established a simple and reliable method for genotyping of the IFNL3 polymorphisms. We designed primers and selected restriction enzymes BstUI and BrsDI for genotyping 2 variants rs12979860 C/T and rs8099917 T/G, respectively. The results indicate that this PCR-RFLP method yields to identical data than standard sequencing method and commercial kit. We suggest that PCR-RFLP method could be used routinely in conventionally clinical laboratory for genotyping of IFNL3 polymorphisms. Next, we analysed the association of these variants with response in combination therapy of peg-IFNα and RBV. Among 108 treated patients infected with HCV genotype 1, by using logistic regression model analyses, we showed that patients who had favorable IFNL4 genotype (genotype TT/TT of ss469415590) and presented a rapid virological response (RVR) were independent predictors of achieving sustained virological response rate (OR = 3.93, CI = 1.53 -10.08, p = 0.004 and OR = 6.74, CI = 1.33 - 34.06, p= 0.021), whereas patients with high baseline viral load level were associated with failure to treatment (OR = 0.34, CI = 0.13 - 0.87, p = 0.023). We suggest that patients had favorable IFNL4 genotype and achieved RVR should benefit an individualized treatment of combination therapy of peg-IFNα and RBV. To explain the influence of these polymorphisms in chronic HCV infection, we investigated the association of IFNL4 polymorphisms with immune response in the liver in patients with chronic HCV infection. By using marker CD107a, a marker expressing degranulation activity of cytotoxic lymphocytes, we indicated that degranulation process was found in liver lymphocytes in patients carrying favourable IFNL4 genotypes compared with patients with unfavourable genotypes. By using multiple regression analyses, we demonstrated that ALT levels correlate with frequency of CD107a+ NKT cells in the liver. Finally, in patients treated by peg-IFNα and RBV, high degranulation activity observed in patients with favourable genotypes of IFNL3 and IFNL4 (CC of rs12979860 and TT/TT of ss469415590). We suggest that polymorphisms in the interferon lambda genes associated with intrahepatic lymphocyte degranulation activity and contribute to clearance mechanism of HCV under combination treatment of peg-IFNα and RBV.We investigated the impact of several genetic polymorphisms on the severity of chronic hepatitis C. We showed a significant association observed between polymorphism of IFN-γ and the severity of chronic hepatitis C. By using logistic regression analysis, T allele of IFN-γ and the presence of steatosis are independent predictive factors of severity of HCV-1 - related liver disease. This suggests we can use genetic variant of IFN-γ in classification and management of chronic hepatitis C. In conclusion, we indicated that host genetic polymorphisms play critical roles both in responses to treatment and in the immunopathogenesis of chronic HCV infection. This study can help to reach a closer step to individualized medicine for the control of chronic HCV infection in resource-limited regions when new treatment regimens are not available.

When a genetic factor is being studied for more than one response variable, estimates of the genetic covariances are essential, specially in breeding programs. In a genetic covariance analysis, genetic and residual mean cross-products are obtained. Stochastically, to quantify the magnitude of the joint variation of two response variables due to genetic effect with respect to the variation due to residual effect may allow one to make inferences about the significance of the associated genetic covariance. In this study it is presented tests of significance for genetic covariance upon a twofold way: tests that take into account the genetic and environmental effects and tests that only consider the genetic information. The first way refers to tests based on the mean cross-products ratio via nonparametric bootstrap resampling and Monte Carlo simulation of Wishart matrices. The second way of testing genetic covariance refers to tests based on adaptation of Wilks\' and Pillai\'s statistics for evaluating independence of two sets of variables. For the first type of tests, empirical distributions under the null hypothesis, i.e., null genetic covariance, were built and graphically analyzed. In addition, the exact distribution of mean cross-products ratio obtained from variables normally distributed with zero mean and finite variance was examined. Writing computational algorithms in R language to perform the proposed tests was also an objective of this study. Only under certain conditions does the probability density function of the product of two random Gaussian variables approximate a normal curve. Therefore, studying the distribution of a mean cross-products ratio as a quotient of two Gaussian variables is not suitable. Tests based on mean cross-products ratio are related to both the value of the genetic covariance and the magnitude of the latter relative to the residual covariance. And both approaches (bootstrap and simulation) are more sensitive than the tests based only on genetic information. The performance of the tests based on mean cross-products ratio is related to the quality of the original data set in terms of the MANOVA assumptions, and the test statistic does not depend on the estimation of the matrix of genetic covariances &Sigma;G. The adaptation of Wilks\' and Pillai\'s statistics can be used to test the genetic covariance. Their approximations to a &chi;21 distribution were checked and the accuracy of their inferences is related to the quality of G. / Quando um fator genético está sendo estudado em mais de uma variável de resposta, estimativas das covariâncias genéticas são essenciais, especialmente para programas de melhoramento. Em uma análise de covariância genética, produtos cruzados médios devido ao efeito genético, a partir do qual é obtida a covariância genética, e devido ao efeito residual são obtidos. Estocasticamente, quantificar a magnitude da variação conjunta de duas variáveis resposta devido ao efeito genético em relação à variação devida ao efeito residual pode permitir realizar inferências sobre a covariância genética associada. Neste estudo são apresentados testes de significância para a covariância genética de duas formas: testes que levam em conta os efeitos genéticos e ambientais (ou residuais) e testes que consideram apenas a informação genética. A primeira forma refere-se testes baseados na razão de produtos cruzados médios via bootstrap não paramétrico e simulação de matrizes Wishart pelo método de Monte Carlo. A segunda maneira de testar a covariância genética refere-se a testes com base em uma adaptação das estatísticas de Wilks e Pillai para avaliar a independência de dois conjuntos de variáveis. Para o primeiro tipo de testes, as distribuições empíricas sob a hipótese nula, ou seja, covariância genética nula, foram construídas e analisadas graficamente. Além disso, foi feito um estudo analítico da distribuição da razão de produtos cruzados médios obtidos a partir de variáveis normalmente distribuídas com média zero e variância finita. Escrever algoritmos computacionais em linguagem R para realizar os testes propostos também foi um dos objetivos deste estudo. Apenas sob certas condições a função de densidade de probabilidade do produto de duas variáveis aleatórias gaussianas aproxima-se da curva normal. Por conseguinte, o estudo da distribuição da razão de produtos cruzados médios como um quociente de duas variáveis gaussianas não é adequado. Os testes baseados na razão de produtos cruzados médios estão relacionados tanto com o valor da covariância genética quanto com a magnitude desta em relação à covariância residual. Ambas as abordagens (bootstrap e simulação) mostraram-se mais sensíveis do que os testes baseados apenas nas informações genéticas. O desempenho dos testes baseados na razão de produtos cruzados médios está relacionado à qualidade dos dados originais em termos das pressuposições da MANOVA, e a estatística de teste não depende da estimação da matriz de covariâncias genéticas &Sigma;G. A adaptação das estatísticas de Wilks e Pillai pode ser usada para testar a covariância genética. As aproximações à distribuição &Chi;21 foi verificada. A precisão de suas inferências está relacionada a qualidade da matriz G.

Zur Erforschung des Verhaltens der Kernmaterie wurde mit dem Dielektronen-Spektrometer HADES am GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt unter anderem die Reaktion p + Nb bei 3,5 GeV kinetischer Strahlenergie untersucht. Obwohl HADES primär für den Nachweis seltener leptonischer Zerfälle der Vektormesonen ρ, ω und φ konzipiert wurde, eignet sich das Spektrometer aufgrund seiner präzisen Spurrekonstruktion auch für die Untersuchung von hadronischen Kanälen. Zum Studium der Strangeness-Signaturen in der Reaktion p + Nb wird in dieser Arbeit der im Jahr 2008 aufgezeichnete Datensatz von ca. 4,2 Milliarden Kollisionen hinsichtlich der Produktion und der dabei auftretenden Polarisation von Λ-Hyperonen untersucht. Die polarisierte Produktion von Hyperonen in Kernreaktionen mit unpolarisierten Ausgangsteilchen wurde entgegen den theoretischen Erwartungen erstmals 1976 beobachtet und fand bis heute keine allgemein akzeptierte und alle beobachteten Abhängigkeiten umfassende Erklärung auf Grundlage der starken Wechselwirkung. Es werden zunächst die theoretischen Modelle der Hyperonpolarisation diskutiert und der experimentelle Zugang erklärt. Dieser gelingt über den schwachen Zerfall des Λ-Hyperons, der als natürliches Polarimeter wirkt und somit insbesondere in Reaktionen mit unpolarisierten Nukleonen ein ideales Instrument zur Untersuchung der Polarisation darstellt. Aufgrund der großen Raumwinkelabdeckung ermöglicht HADES, Λ-Hyperonen in einem weiten Phasenraumbereich zu rekonstruieren, sodass deren Produktionsrate und Polarisation in Abhängigkeit der Observablen Transversalimpuls pt und Rapidität y analysiert werden. Aus insgesamt 1,1 Millionen rekonstruierten Λ-Hyperonen werden nach der Korrektur bezüglich der Detektorakzeptanz und -effizienz transversale Massenspektren extrahiert. Deren inverser Steigungsparameter TB (y) nimmt ein Maximum von rund 90 MeV bei y = 1, d.h. unterhalb der Schwerpunktsrapidität im Nukleon-Nukleon-Stoß (ycm = 1,12), an und fällt zu kleinen Rapiditäten deutlich schneller ab als für Teilchen im thermischen Gleichgewicht. Die Λ-Rapiditätsdichte zeigt eine asymmetrische Verteilung, die aufgrund von Mehrfachstreuung der Λ-Hyperonen hauptsächlich mit Kern-Nukleonen deutlich zur Targetrapidität verschoben ist und mit steigender Rapidität > 0,3 stark abnimmt. Auf den vollständigen Phasenraum extrapoliert, erfüllt die Produktionsrate von 0,018 ± 0,004 Λ-0 Hyperons je Ereignis, verbunden mit der Multiplizität von Ks -Mesonen und den mittels Transportmodell abgeleiteten Produktionsverhältnissen zu den übrigen Kaonen und Hyperonen, die Strangeness-Erhaltung im Mittel der gemessenen Kollisionen. Darüber hinaus zeigt das Λ-Hyperon eine signifikant negative Polarisation relativ zur Normalen seiner Produktionsebene, die über den verfügbaren Phasenraum gemittelt Px = (−10,6 ± 1,3) % beträgt und deren Betrag mit steigendem Transversalimpuls entsprechend Px (pt ) = (−0,19 ± 0,02) (GeV/c)−1 pt linear zunimmt. Die Ergebnisse bezüglich der Λ-Polarisation und Phasenraumverteilung werden mit denen anderer Experimente ähnlicher Stoßsysteme verglichen und im Rahmen von systematischen Untersuchungen mit Transportmodellen interpretiert, um Details zur Dynamik der Hyperon-Produktion in Proton-Kern-Reaktionen abzuleiten. Derzeit verfügbare Versionen der GiBUU- und UrQMD-Modelle können die experimentellen Verteilungen im Phasenraum jedoch nicht hinreichend reproduzieren. Mit der Rekonstruktion von Ξ− -Hyperonen und φ-Mesonen wird ein Ausblick auf weiterführende Studien zur Strangeness-Produktion in Nukleon-Kern-Stößen gegeben.:1 Einleitung 11 1.1 Struktur der Materie 11 1.2 Schwellennahe Erzeugung von Hadronen mit Strangeness 13 1.3 Modellbeschreibungen der Strangeness-Produktion 15 1.4 Untersuchung von Kernmaterie in Nukleon-Kern-Reaktionen 19 1.5 Zielsetzung und Gliederung der Arbeit 20 2 Hyperonpolarisation 23 2.1 Experimentelle Beobachtungen 23 2.2 Modellbeschreibungen 25 2.2.1 SU(6)-Modell 25 2.2.2 s-Quark-Streumodell 27 2.2.3 Lund-Modell (Farb-Flussröhre) 28 2.2.4 Rekombinationsmodell (Thomas-Präzession) 28 2.2.5 Quantenmechanische Modelle 29 2.3 Der selbstanalysierende Λ-Zerfall als Spin-Polarimeter 30 3 Experimentiersystem HADES und Analysewerkzeuge 33 3.1 Komponenten zur Teilchenidentifikation 35 3.2 Magnetspektrometer 37 3.3 Datenerfassung und -verarbeitung 43 3.4 Analyse- und Simulationssoftware 45 3.5 Transportmodelle 46 4 Datenanalyse zur Reaktion p + Nb 51 4.1 Charakteristika des Experiments 51 4.2 Teilchenidentifikation 55 4.2.1 Flugzeitmethode 56 4.2.2 Energieverlustmethode 58 4.3 Rekonstruktion des Λ-Hyperons 60 4.3.1 Teilchenselektion bezüglich des Energieverlustes 61 4.3.2 Invariantes Massenspektrum 62 4.3.3 Zerfallsgeometrie 65 4.3.4 Vertexrekonstruktion 66 4.3.5 Determination des kombinatorischen Untergrundes 69 4.3.6 Differentielle Analyse bezüglich des Phasenraums 73 4.4 Rekonstruktion des Ξ -Hyperons 77 4.5 Effizienz- und Akzeptanzbestimmung mittels Detektorsimulation 82 4.5.1 Selbstkonsistenz der Simulation 86 4.5.2 Überprüfung der Vertexrekonstruktion 89 4.5.3 Rekonstruktion der Zerfallslänge 91 4.5.4 Normierung der Produktionsrate 93 4.5.5 Differentielle Produktionsrate der Λ-Hyperonen 95 4.6 Messung der Λ-Polarisation 97 4.6.1 Referenzkoordinatensystem 97 4.6.2 Akzeptanzkorrektur 99 4.6.3 Bestimmung der mittleren Polarisation 101 4.6.4 Differentielle Untersuchung der Polarisation 104 5 Diskussion der Ergebnisse 5.1 Λ-Phasenraumverteilung 109 5.1.1 Transversalimpulsverteilungen 110 5.1.2 Extrapolation der transversalen Impulsspektren 113 5.1.3 Systematische Unsicherheiten 114 5.1.4 Vergleich mit Vorhersagen von Transportmodellen 117 5.1.5 Λ-Produktionsmechanismen im BUU-Modell 121 5.1.6 Vergleich mit Ergebnissen anderer Experimente 124 5.2 Strangeness-Erhaltung 131 5.3 Λ-Polarisation 134 5.3.1 Phasenraumabhängigkeit der Polarisation 135 5.3.2 Einordnung der Ergebnisse in den vorhanden Weltdatensatz 139 6 Zusammenfassung und Ausblick 143 A Anhang A.1 Definition teilchenphysikalischer Variablen 149 A.2 Effizienzkorrektur für Λ-Hyperonen 153 A.3 Simulationen mit Transportmodellen 154 A.3.1 Ultrarelativistic Quantum Molecular Dynamics (UrQMD) 154 A.3.2 Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) 157 A.3.2.1 Eingangsparameter 157 A.3.2.2 Systematische Untersuchung der Λ-Produktion 159 A.3.3 Implementierung elementarer Wirkungsquerschnitte 167 Abbildungsverzeichnis 169 Tabellenverzeichnis 172 Literaturverzeichnis 173 / With the dielectron spectrometer HADES, located at the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, p + Nb reactions at a kinetic beam energy of 3.5 GeV were measured to study the behavior of nuclear matter. Although primarily designed for the detection of rare leptonic decays of the light vector mesons ρ, ω and φ, the spectrometer renders itself very well suited for the investigation of hadrons, due to its excellent tracking capability. This thesis presents results of the production and polarization of strange Λ hyperons in about 4.2 billion reactions of p + Nb recorded in 2008. In contrast to theoretical expectations, the polarized production of hyperons was observed in 1976 for the first time in nuclear reactions with unpolarized beams. Based on the fundamental properties of strong interaction, to date no single explanation exists describing all dependencies of the observed hyperon polarization. Therefore, common theoretical models of hyperon polarization are introduced. Acting as a natural polarimeter, the Λ hyperon represents an excellent tool to study the phenomenon of hyperon polarization especially in reactions with unpolarized beams and targets. Hence, the experimental technique for extracting the polarization using the weak decay of the Λ hyperon is explained. Due to a large solid angle coverage, HADES allows for the reconstruction of hadrons within a wide phase space range. Consequently, a double-differential analysis of the polarization and production probability as a function of transverse momentum pt and rapidity y is performed. In total, 1.1 million Λ hyperons are reconstructed and corrected for detector acceptance and efficiency. The inverse slope parameter TB is extracted from transverse mass spectra. Its rapidity dependence TB (y) shows a maximum of 90 MeV at y = 1, i.e. below the center-of-mass rapidity of the nucleon-nucleon collision ycm = 1.12, and a stronger decrease to lower rapidities than particles in thermal equilibrium. The Λ rapidity density shows an asymmetric distribution, shifted towards target rapidity, which is probably caused by multiple scattering on target nucleons. Extrapolated to the full phase space, the total multiplicity of 0.018 ± 0.004 Λ hyperons per event satisfies strangeness conservati- 0 on on average. For that purpose, the Ks production rate from another analysis and ratios to the other, unmeasured, strange hadrons, derived from transport simulations, are taken into account. Furthermore, the Λ hyperon shows a significant negative polarization perpendicular to its production plane, which amounts to Px = (−10.6 ± 1.3) % averaged over the phase space accessible to HADES. The measured Λ polarization increases almost linearly with increasing transverse momentum pt , according to Px (pt ) = (−0.19 ± 0.02) (GeV/c)−1 pt . In order to spot details on the dynamics of hyperon production in proton-nucleus reactions, the results on Λ polarization and phase space distribution are compared to those of similar reactions. Additionally, a systematic investigation with transport model simulations is performed. The experimental distributions can not be reproduced sufficiently well by the presently available GiBUU and URQMD models. Moreover, an outlook on further studies of strangeness production in nucleon-nucleus collisions by reconstruction of Ξ− hyperons and φ mesons is given.:1 Einleitung 11 1.1 Struktur der Materie 11 1.2 Schwellennahe Erzeugung von Hadronen mit Strangeness 13 1.3 Modellbeschreibungen der Strangeness-Produktion 15 1.4 Untersuchung von Kernmaterie in Nukleon-Kern-Reaktionen 19 1.5 Zielsetzung und Gliederung der Arbeit 20 2 Hyperonpolarisation 23 2.1 Experimentelle Beobachtungen 23 2.2 Modellbeschreibungen 25 2.2.1 SU(6)-Modell 25 2.2.2 s-Quark-Streumodell 27 2.2.3 Lund-Modell (Farb-Flussröhre) 28 2.2.4 Rekombinationsmodell (Thomas-Präzession) 28 2.2.5 Quantenmechanische Modelle 29 2.3 Der selbstanalysierende Λ-Zerfall als Spin-Polarimeter 30 3 Experimentiersystem HADES und Analysewerkzeuge 33 3.1 Komponenten zur Teilchenidentifikation 35 3.2 Magnetspektrometer 37 3.3 Datenerfassung und -verarbeitung 43 3.4 Analyse- und Simulationssoftware 45 3.5 Transportmodelle 46 4 Datenanalyse zur Reaktion p + Nb 51 4.1 Charakteristika des Experiments 51 4.2 Teilchenidentifikation 55 4.2.1 Flugzeitmethode 56 4.2.2 Energieverlustmethode 58 4.3 Rekonstruktion des Λ-Hyperons 60 4.3.1 Teilchenselektion bezüglich des Energieverlustes 61 4.3.2 Invariantes Massenspektrum 62 4.3.3 Zerfallsgeometrie 65 4.3.4 Vertexrekonstruktion 66 4.3.5 Determination des kombinatorischen Untergrundes 69 4.3.6 Differentielle Analyse bezüglich des Phasenraums 73 4.4 Rekonstruktion des Ξ -Hyperons 77 4.5 Effizienz- und Akzeptanzbestimmung mittels Detektorsimulation 82 4.5.1 Selbstkonsistenz der Simulation 86 4.5.2 Überprüfung der Vertexrekonstruktion 89 4.5.3 Rekonstruktion der Zerfallslänge 91 4.5.4 Normierung der Produktionsrate 93 4.5.5 Differentielle Produktionsrate der Λ-Hyperonen 95 4.6 Messung der Λ-Polarisation 97 4.6.1 Referenzkoordinatensystem 97 4.6.2 Akzeptanzkorrektur 99 4.6.3 Bestimmung der mittleren Polarisation 101 4.6.4 Differentielle Untersuchung der Polarisation 104 5 Diskussion der Ergebnisse 5.1 Λ-Phasenraumverteilung 109 5.1.1 Transversalimpulsverteilungen 110 5.1.2 Extrapolation der transversalen Impulsspektren 113 5.1.3 Systematische Unsicherheiten 114 5.1.4 Vergleich mit Vorhersagen von Transportmodellen 117 5.1.5 Λ-Produktionsmechanismen im BUU-Modell 121 5.1.6 Vergleich mit Ergebnissen anderer Experimente 124 5.2 Strangeness-Erhaltung 131 5.3 Λ-Polarisation 134 5.3.1 Phasenraumabhängigkeit der Polarisation 135 5.3.2 Einordnung der Ergebnisse in den vorhanden Weltdatensatz 139 6 Zusammenfassung und Ausblick 143 A Anhang A.1 Definition teilchenphysikalischer Variablen 149 A.2 Effizienzkorrektur für Λ-Hyperonen 153 A.3 Simulationen mit Transportmodellen 154 A.3.1 Ultrarelativistic Quantum Molecular Dynamics (UrQMD) 154 A.3.2 Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) 157 A.3.2.1 Eingangsparameter 157 A.3.2.2 Systematische Untersuchung der Λ-Produktion 159 A.3.3 Implementierung elementarer Wirkungsquerschnitte 167 Abbildungsverzeichnis 169 Tabellenverzeichnis 172 Literaturverzeichnis 173

Both dependent types and linear types have their desirable properties. Department types can express functional dependencies of inputs and outputs, while linear types offer control over the use of computational resources. Combining these two systems have been difficult because of their different interpretations of context presence of variables. Quantitative Type Theory (QTT) combines dependent types and linear types by using a semiring to track the kind of use of every resource. We extend QTT with the additive pair and additive unit types, express the complete QTT rules in bidirectional form, and then present our interpreter of a simple language based on QTT. 1

We hypothesized that the presence of monoclonal free light chains (FLC) in the serum of patients with monoclonal gammopathy of undetermined significance (MGUS) is a marker of clonal evolution and a risk factor for progression. Forty-seven patients with MGUS and documented progression to myeloma or related malignancy were compared with 50 age- and gender-matched patients with MGUS and no evidence of progression after 5 or more years of follow-up. The presence of an abnormal kappa/lambda FLC ratio in the serum was associated with a higher risk of MGUS progression (relative risk 2.5; 95% confidence interval: 1.6-4.0; P < 0.001).