With the use of chiral theory of mesons [1], [2] we evaluate the decay rate of η′ → π+π−π+π−. Our theoretical study of this problem is different from the previous theo- retical study [3] and our predicted result is in a good agreement with the experiment. In this chiral theory we evaluate Feynman diagrams up to one loop and the decay rate is calculated with the use of triangle and box diagrams. The ρ0 meson includes in both type of diagrams as a resonance state. Divergent integrals in the loop calculations are regularized with the use of n-dimensional ’t Hooft-Veltman regularization technique. At the last step to obtain the decay rate, the phase space integral has been calculated.

In this thesis, the clean angular observables in the $\bar{B} \to D^{*+} \ell^- \bar{\nu}_{\ell}$ angular distribution is studied. Similar angular observables are widely studied in $B \to K^* \mu^+ \mu^-$ decays. We believed that these angular observables may have different sensitivities to different new physics structures.

La théorie de cordes unifie de façon naturelle les théories de jauge, qui décrivent les interactions entre les particules élémentaires, avec une théorie quantique de la gravitation. Ces dernières années ont apporté de grands progrès dans la compréhension des états non-perturbatifs de la théorie, ses aspects holographiques, ainsi que la construction de modèles proches du Modèle Standard. Néanmoins, il reste des défis pour la théorie de cordes, qui incluent une définition non-perturbative, une meilleure compréhension de l'holographie, et le problème de la constante cosmologique. Ma recherche s'est concentrée sur des aspects formels des théories de gravitation quantique, qui incluent les trous noirs, la dépendance du temps, et l'holographie. Gr^ace à de nouveaux résultats dans le domaine de la théorie conforme avec spectre continu, mes collaborateurs et moi-m^eme avons avancé dans la compréhension de l'holographie dans des fonds avec dilaton linéaire, ainsi que dans le plongement de théories de jauge supersymétriques dans la théorie de cordes. En particulier, on a étudié des théories conformes supersymétriques avec spectre continu que l'on utilise pour construire des fonds de théories de cordes non-compacts et courbés. Les résultats obtenus nous ont permis de décrire des exemples explicites de symétrie miroir pour des fonds non-compacts. En introduisant des bords dans les théories conformes, on a analysé des états non-perturbatifs de la théorie de cordes, les D-branes. A basse énergie, les degrés de liberté sur les D-branes interagissent par des interactions de jauge. Avec ces outils, on a réussi à plonger une dualité infrarouge de théorie de jauge supersymétrique dans la théorie de cordes, et on a montré que la dualité correspond à une monodromie pour les états de bord dans l'espace de modules de la théorie conforme.<br><br> Dans cette thèse, on discute de nombreux autres liens entre la théorie conforme, la théorie de jauge et la gravitation. La plupart des contributions décrites étaient motivées par la théorie de cordes. Des exemples sont l'analyse d'états qui préservent la supersymétrie et leur lien avec les algèbres affines, la dépendance du temps et le dictionnaire holographique, l'analyse directe de la quantification de la gravité en présence d'un trou noir, la réalisation du scenario sans-bord pour la fonction d'onde de l'univers en théorie de cordes, une formule de Verlinde pour les théories conformes non-rationnelles et la construction de solutions non-géometriques à la supergravité. Dans d'autres travaux, je me suis concentré sur des théories qui quantifient la gravité plus directement, mais qui pourraient avoir moins de succès dans le problème de l'unification des forces en quatre dimensions. Ces théories ont quand-m^eme le potentiel de nous apprendre des aspects communs à toute théorie de gravitation quantique. Par exemple, on a analysé les degrés de liberté responsables de l'entropie d'un trou noir en trois dimensions, et nous avons argumenté sur la difficulté de reconcilier l'invariance modulaire avec l'unitarité en dehors de la théorie de cordes. On a aussi discuté la diffusion de ces trous noirs. D'autres contributions à la théorie de jauge non-commutative, la théorie de jauge supersymétrique, la production de paires dans un espace courbe, et cetera, sont aussi relativement indépendantes du cadre de la théorie de cordes.<br><br> Il me semble qu'il reste intéressant d'étudier des questions difficiles sur la théorie de jauge et la gravitation quantique, dans la cadre de la théorie de cordes, et en dehors de ce cadre, et d'^etre guidé par des problèmes ouverts durs qui doivent mener à un progrès concret par incréments ou par sauts.

<p>This thesis describes some aspects of noncommutative geometry and conformal field theory. The motivation for the investigations made comes to a large extent from string theory. This theory is today considered to be the most promising way to find a solution to the problem of unifying the four fundamental interactions in one single theory. The thesis gives a short background presentation of string theory and points out how noncommutative geometry and conformal field theory are of relevance within the string theoretical framework. There is also given some further information on noncommutative geometry and conformal field theory. The results from the three papers on which the thesis is based are presented in the text. It is shown in Paper 1 that, for a gauge theory in a flat noncommutative background only the gauge groups <i>U(N)</i> can be used in a straightforward way. These theories can arise as low energy limits of string theory. Paper 2 concerns boundary conformal field theory, which can be used to describe open strings in various backgrounds. Here different orbifold theories which are described using simple currents of the chiral algebra are investigated. The formalism is applied to ``branes´´ in <b>Z</b>₂<b> </b>orbifolds of the <i>SU(2)</i> WZW-model and to the <i>D</i>-series of unitary minimal models. In Paper 3 two different descriptions of an invariant star-product on <i>S²</i> are compared and the characteristic class that classifies the star-product is calculated. The Fedosov-Nest-Tsygan index theorem is used to compute the characteristic class.</p>

This thesis consists of two parts, which can be read separately. In the first part we study aspects of topological field theories. We show how to topologically twist three-dimensional N=2 supersymmetric Chern-Simons theory using a contact structure on the underlying manifold. This gives us a formulation of Chern-Simons theory together with a set of auxiliary fields and an odd symmetry. For Seifert manifolds, we show how to use this odd symmetry to localize the path integral of Chern-Simons theory. The formulation of three-dimensional Chern-Simons theory using a contact structure admits natural generalizations to higher dimensions. We introduce and study these theories. The focus is on the five-dimensional theory, which can be understood as a topologically twisted version of N=1 supersymmetric Yang-Mills theory. When formulated on contact manifolds that are circle fibrations over a symplectic manifold, it localizes to contact instantons. For the theory on the five-sphere, we show that the perturbative part of the partition function is given by a matrix model. In the second part of the thesis, we study supersymmetric sigma models in the Hamiltonian formalism, both in a classical and in a quantum mechanical setup. We argue that the so called Chiral de Rham complex, which is a sheaf of vertex algebras, is a natural framework to understand quantum aspects of supersymmetric sigma models in the Hamiltonian formalism. We show how a class of currents which generate symmetry algebras for the classical sigma model can be defined within the Chiral de Rham complex framework, and for a six-dimensional Calabi-Yau manifold we calculate the equal-time commutators between the currents and show that they generate the Odake algebra.

A number of philosophical questions, all connected to modern research in quantum gravity, are discussed in this dissertation. The goal of research in quantum gravity is to find a quantum theory for gravitation; the other fundamental forces are already understood in terms of quantum physics. Quantum gravity is studied within a number of different research programmes. The most popular are string theory and loop quantum gravity; besides these a number of other approaches are pursued. Due to the lack of empirical support, it is relevant to assess the scientific status of this research. This is done from four different points of view, namely the ones held by: logical positivists, Popper, Kuhn and Lakatos. It is then argued that research in quantum gravity may be considered scientific, conditional on scientists being open with the tentative and speculative nature of their pursuits. Given the lack of empirical progress, in all approaches to quantum gravity, a pluralistic strategy is advised. In string theory there are different theoretical formulations, or dualities, which are physically equivalent. This is relevant for the problem of underdetermination of theories by data, and the debate on scientific realism. Different views on the dualities are possible. It is argued that a more empiricist view on the semantics of theories, than what has been popular lately, ought to be adopted. This is of importance for our understanding of what the theories tell us about space and time. In physics and philosophy, the idea that there are worlds or universes other than our own, has appeared in different contexts. It is discussed how we should understand these different suggestions; how they are similar and how they are different. A discussion on, how and when theoretical multiverse scenarios can be empirically testable, is also given. The reliability of thought experiments in physics in general and in quantum gravity in particular is evaluated. Thought experiments can be important for heuristic purposes, but in the case of quantum gravity, conclusions based on thoght experiments are not very reliable.

The problem of guessing a random string is studied. It arises in the analysis of the strength of secret-key cryptosystems against guessing attacks. Expected number of guesses, or more generally moments of the number of guesses needed to break the cryptosystem grow exponentially with the length of the string. This thesis studies the rate of exponential growth of these moments using the theory of large deviations. A closer elation between guessing and compression is first established. For systems with large key rates, it is shown that if the source’s sequence of so-called information spectrum random variables satisfies the large deviation property with a certain rate function, then the limiting guessing exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the rate function. This is then used to rederive several prior results. The large deviations approach brings to light the relevance of information spectrum in determining guessing exponents. For systems with key-rate constraints, bounds are derived on the limiting guessing exponents for general sources. The obtained bounds are shown to be tight for stationary memoryless, Markov, and unifilar sources, thus recovering some known results. The bounds are obtained by establishing a close relationship between error exponents and correct decoding exponents for fixed rate source compression on the one hand and exponents for guessing moments on the other.

One of the main topics in the modern String Theory are the conjectured string/gauge (AdS/CFT) dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality.The first part of this thesis is focused on the gravity side of the AdS5/CFT4 duality: we investigate the quantum integrability of the type IIB superstring on AdS5 x S5. In the pure spinor formulation we analyze the operator algebra by computing the operator product expansion of the Maurer-Cartan currents at the leading order in perturbation theory. With the same approach at one loop order, we show the path-independence of the monodromy matrix which implies the charge conservation law, strongly supporting the quantum integrability of the string sigma-model. We also verify that the Lax pair field strength remains well-defined at one-loop order being free from UV divergences. The same string sigma-model is analyzed in the Green-Schwarz formalism in the near-flat-space (NFS) limit. Such a limit remarkably simplifies the string world-sheet action but still leaving interesting physics. We use the NFS truncation to show the factorization of the world-sheet S-matrix at one-loop order. This property defines a two-dimensional field theory as integrable: it is the manifestation of the higher conserved charges. Hence, we have explicitly checked their presence at quantum level. The second part is dedicated to the AdS4/CFT3 duality: in particular the type IIA superstring on AdS4 x CP3. We compute the leading quantum corrections to the string energies for string configurations with a large but yet finite angular momentum on CP3 and show that they match the conjectured all-loop Bethe Ansatz equations.

Predicting the three-dimensional (3D) structure of proteins is a central problem in biology. These computationally predicted 3D protein structures have been successfully applied in many fields of biomedicine, e.g. family assignments and drug discovery. The accurate detection of remotely homologous templates is critical for the successful prediction of the 3D structure of proteins. Also, the prediction of one-dimensional (1D) protein structures such as secondary structures and shape strings are useful for predicting the 3D structure of proteins and important for understanding the sequence-structure relationship. In addition, the prediction of the functional sites of proteins, such as metal-binding sites, can not only reveal the important function of proteins (even in the absence of the 3D structure) but also facilitate the prediction of the 3D structure. Here, three novel methods in the field of protein structure prediction are presented: PREDZINC, a method for predicting zinc-binding sites in proteins; Frag1D, a method for predicting the 1D structure of proteins; and FragMatch, a method for detecting remotely homologous proteins. These methods compete satisfactorily with the best methods previously published and contribute to the task of protein structure prediction. / At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 3: Manuscript. / Protein structure prediction

This quantitative study explores string teachers’ perceptions of citizenship education and its use in the private lesson. Guided by Westheimer and Kahne’s (2004) model of citizenship education the study sought to identify (a) how private string teachers perceive citizenship education, and (b) the factors that influence these perceptions. Four hundred and fifteen (415) members of the American String Teachers Association (ASTA) participated in this study by completing an on-line survey that contained both closed and open-ended questions. The resulting data was coded and organized according to the survey questions and the conceptual framework. Research findings revealed that, although teachers did not explicitly consider citizenship education a part of their lessons, their intentions and their report on pedagogical practices could be described as citizenship education when viewed through the conceptual framework used in the study. Indeed, nearly all of the participant responses revealed intentions to include attributes of what Westheimer and Kahne refer to as the Personally Responsible Citizen in their music lessons with students. Educating for traits of other types of citizenship was also reported. Factors deemed influential in string teachers’ perceptions of citizenship education included the following: If the teachers had earned certification in Suzuki pedagogy; the number of years of teaching experience; if teachers self-identified as primarily educators, performers, or both; the age of the students who are taught. Additionally, the study addresses teachers’ statements about the use of competitions, dialogue in lessons, and general attitudes about the appropriateness of citizenship education in several different learning environments. The study findings add to a small but growing body of research that furthers understandings of the links between citizenship education and music education. In addition, the findings contribute to our understanding of the complexity of the relationship between private teachers and their students.