This thesis consists of three articles all relatedin some way to eigenvalues of random matrices and theirprincipal minors and also to tilings of various planar regions with dominoes or rhombuses.Consider an $N\times N$ matrix $H_N=[h_{ij}]_{i,j=1}^N$ from the Gaussian unitary ensemble (GUE). Denote its principal minors (submatrices in the upper left corner) by $H_n=[h_{ij}]_{i,j=1}^n$ for  $n=1$, \dots, $N$. We show in paper A that  all the $N(N+1)/2$ eigenvaluesof $H_1$, \dots, $H_N$ form a determinantal process on $N$ copies of the real line $\mathbb{R}$. We also show that this distribution arises as a scaling limit in tilings of an Aztec diamond with dominoes.We discuss a corresponding result for rhombus tilings of a hexagonwhich was later proved by Okounkov and Reshtikhin. We give a new proof of that statement in the introductionto this thesis.In paper B we perform a similar analysis for the Anti-symmetric Gaussian unitary ensemble (A-GUE). We show that the positive eigenvalues of an $N\times N$ A-GUE matrix andits principal minors form a determinantal processon $N$ copies of the positive real line $\mathbb{R}^+$.We also show that this distribution of all these eigenvalues appears as a scaling limit of tilings of half a hexagon with rhombuses. In paper C we study the shuffling algorithm for tilings of an Aztec diamond. This leads to the study of an interacting set of interlacedparticles that evolve in time. We conjecture that the diffusion limit of thisprocess is a process studied by Warrenand establish some results in this direction. / QC 20100804

A summary of research conducted since September 2007 at the University of Toronto in the laboratory of Professor Robert A. Batey is presented in this thesis, which is divided into four chapters. The first chapter contains a two-part introduction, where aryl- and aliphatic-Claisen rearrangements are discussed in part 1, and the nucleophilic addition of organoboron reagents to unsaturated C–N functionalities is described in part 2. Chapter 2 contains research involving synthetic and theoretical studies of aryl-Claisen rearrangements and other sigmatropic reactions. The work towards developing the lanthanide-catalyzed domino aryl-Claisen rearrangement for the synthesis of contiguous aryl–C(sp³) moieties is presented first. This is followed by computational studies involving E/Z-selectivity differences for the aryl-Claisen rearrangement, which was an issue noted for the domino aryl-Claisen reaction of a linear substrate. The mechanistic origins of E/Z-selectivity differences for the mono aryl-Claisen rearrangement, which was experimentally ambiguous for over 40 years, is resolved through computational methods. A theoretical analysis of selectivity differences for the allylic azide rearrangement is also described. The third section contains a discussion of Eu(fod)3-catalyzed aryl-Claisen rearrangements on vinyl bromide systems and preliminary studies involving application of the substrates in cross-coupling reactions, and other attempted mono- and domino sigmatropic rearrangements are presented in the fourth section. In chapter 3, the search for computational methods that can accurately predict experimental free energy of activation barriers for the aliphatic-Claisen rearrangement through benchmarking studies with a priori kinetic barrier and kinetic isotope effect data is described. Methods were found to predict new valid transition states and predict ΔG‡ values with a mean unsigned error of 0.3 kcal/mol relative to experimental values. In chapter 4, the development of new allylboration reaction is outlined, involving the double allylboration of nitriles and anhydrides, and initial studies towards the first aminoallylboration reactions of N-aluminoaldimines to form 1,2-diamines.

Internationalization of industries, international competition, and the deregulation and harmonization within the EC are some of the important factors changing the prerequisites and requirements for effective international transport systems. Thus there is a need for more articulated knowledge regarding the internationalization processes of freight transport companies. In this longitudinal study the internationalization processes of three of the largest freight transport groups in Sweden have been analyzed in terms of changes in foreign representation: agents, join ventures, sales offices, subsidiaries. In addition, the relational effects of these changes on suppliers, owners, and competitors have been analysed. The results show that internationalization patterns change over time. First there was a gradual change of single relationships and systems. As an increasing number of transport companies became internationalized, there was a shift into more leapwise changes of nets of related companies. Furthermore the patterns and effects of internationalization differed between the three cases depending on when their internationalization process started. Typical sequences of changes have been identified to occur over time. As international interconnections between transport companies has increased these sequences have induced the development of domino effects in the network of transport companies. Based on the findings in this dissertation a dynamic model of internationalization is formulated. The model synthesizes the basic driving forces derived from network, distribution and internationalization research / Diss. Handelshögsk. : Stockholm

Les hétérocycles azotés occupent une place importante en chimie organique et médicinale et, à ce titre, constituent des cibles de choix pour le développement de réactions toujours plus efficaces et faciles d’emploi. Les travaux antérieurs, réalisés au laboratoire URCOM sur l’accès aux γ-lactames, ont servi de base pour développer une méthodologie impliquant des conditions douces qui ont mis en évidence les propriétés spécifiques des N-alkoxy amides pour accéder aux γ- et δ-lactames hautement fonctionnalisés de manière hautement diastéréosélective selon un processus domino. Cette méthodologie a aussi pu être étendue aux hydantoïnes, 2-imino-thiazolidin-4-ones et thiazinan-4-ones qui constituent également des molécules étudiées en chimie médicinale. En parallèle, une comparaison de réactivité entre N-alkoxy amides et N-alkyl amides a montré la meilleure réactivité des composés N-alkoxylés pour l’obtention de ces différents hétérocycles azotés. Cette différence de réactivité a été attribuée à la possible chélation du contre anion alcalins des bases minérales utilisées dans notre approche par les N-alkoxy amides. Les conditions douces ont permis d’envisager des versions organocatalysées énantiosélectives ou multicomposantes des réactions précédentes conduisant à des résultats préliminaires intéressants. / Nitrogen-containing heterocycles are key compounds in organic and medicinal chemistry and continue to attract synthetic effort for the development of more efficient and convenient reaction. Previous work carried out at the URCOM laboratory for the access to γ-lactams has provided the basis for developing a highly diastereoselective methodology under mild conditions that has demonstrated the specific properties of N-alkoxy amides, allowing the access to γ- and δ-lactams following a domino process. This methodology also allowed the access to hydantoïns, 2-imino thiazolidin-4-ones and thiazinan-4-ones which are compounds of importance in medicinal chemistry. In parallel, a comparison of reactivity between N-alkoxy and N-alkyl amides was carried out in order to demonstrate the better reactivity of the N-alkoxy amide compounds. This better reactivity was attributed to a possible chelation of the alkali metal counter anion of the mineral bases used in our conditions by the N-alkoxy amides. These mild conditions allowed organocatalyzed enantioselective or multicomponents approaches providing interesting preliminary results.

Arvo Pärt, an Estonian composer, was born in 1935. Most of the works at the beginning of his career were for piano in the neo-classical style. After that, he turned his interest to serial music and continued creating works with serial techniques throughout the 1960s. After his "self-imposed silence" period (during the years 1968-1976), Pärt emerged with a new musical style, which he called tintinnabuli. Although, this technique was influenced by music from the medieval period, the texture and function of its musical style cannot be described easily in terms of any single musical technique of the past. This study explores the evolution of Arvo Pärt's tintinnabuli technique in its first decade 1976-1985, which is divided into three different types. It provides musical examples from the scores of selected works, Für Alina, Cantus in Memory of Benjamin Britten, Cantate Domino canticum novum, Missa Sillabica, Stabat Mater and Es sang vor langen Jahren, and their analyses with supporting interpretative sketches. The goal of this thesis is to provide the reader a basis for understanding and recognizing the different types of Pärt's tintinnabuli technique.

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First part is focused on finding suitable reaction conditions for organocatalytic domino Michael/Michael reaction of ethyl (E)-3-(2-thiophenyl)acrylate with α,β-unsaturated aldehydes. Second part deals with the preparation of pyrazolone derivatives from commercially available compounds and describes effects of various substituents in α-position on chemical efficiency and stereoselectivity of amination with azodicarboxylate catalyzed by quinine.

Nous avons étudié la dynamique de Glauber sur les pavages de domaines finies du plan par des losanges ou par des dominos de taille 2 × 1. Ces pavages sont naturellement associés à des surfaces de R^3, qui peuvent être vues comme des interfaces dans des modèles de physique statistique. En particulier les pavages par des losanges correspondent au modèle d'Ising tridimensionnel à température nulle. Plus précisément les pavages d'un domaine sont en bijection avec les configurations d'Ising vérifiant certaines conditions au bord (dépendant du domaine pavé). Ces conditions forcent la coexistence des phases + et - ainsi que la position du bord de l'interface. Dans la limite thermodynamique où L, la longueur caractéristique du système, tend vers l'infini, ces interfaces obéissent à une loi des grand nombre et convergent vers une forme limite déterministe ne dépendant que des conditions aux bord. Dans le cas où la forme limite est planaire et pour les losanges, Caputo, Martinelli et Toninelli [CMT12] ont montré que le temps de mélange Tmix de la dynamique est d'ordre O(L^{2+o(1)}) (scaling diffusif). Nous avons généralisé ce résultat aux pavages par des dominos, toujours dans le cas d'une forme limite planaire. Nous avons aussi prouvé une borne inférieure Tmix ≥ cL^2 qui améliore d'un facteur log le résultat de [CMT12]. Dans le cas où la forme limite n'est pas planaire, elle peut être analytique ou bien contenir des parties “gelées” où elle est en un sens dégénérée. Dans le cas où elle n'a pas de telle partie gelée, et pour les pavages par des losanges, nous avons montré que la dynamique de Glauber devient “macroscopiquement proche” de l'équilibre en un temps L^{2+o(1)} / We studied the Glauber dynamics on tilings of finite regions of the plane by lozenges or 2 × 1 dominoes. These tilings are naturally associated with surfaces of R^3, which can be seen as interfaces in statistical physics models. In particular, lozenge tilings correspond to three dimensional Ising model at zero temperature. More precisely, tilings of a finite regions are in bijection with Ising configurations with some boundary conditions (depending on the tiled domain). These boundary conditions impose the coexistence of the + and - phases, together with the position of the boundary of the interface. In the thermodynamic limit where L, the characteristic length of the system, tends toward infinity, these interface follow a law of large number and converge to a deterministic limit shape depending only on the boundary condition. When the limit shape is planar and for lozenge tilings, Caputo, Martinelli and Toninelli [CMT12] showed that the mixing time of the dynamics is of order (L^{2+o(1)}) (diffusive scaling). We generalized this result to domino tilings, always in the case of a planar limit shape. We also proved a lower bound Tmix ≥ cL^2 which improve on the result of [CMT12] by a log factor. When the limit shape is not planar, it can either be analytic or have some “frozen” domains where it is degenerated in a sense. When it does not have such frozen region, and for lozenge tilings, we showed that the Glauber dynamics becomes “macroscopically close” to equilibrium in a time L^{2+o(1)}

While previous research shows that civil wars can spread to neighboring states, we do not know why certain neighbors are more at risk than others. To address this research gap, this dissertation proposes a contagion process approach that can identify the most likely targets of contagion effects from an ongoing conflict. Using data with global coverage, theoretical expectations about why and where civil wars would have contagion effects, are examined in a series of statistical analyses. Paper I argues and empirically supports that a country is more susceptible to contagion effects when it is characterized by ethnic polarization, where few ethnic groups form a delicate balance. Paper II argues and provides evidence that the involvement in conflict by an ethnic group in one country increases the likelihood of ethnic conflict erupting in a neighboring country that shares the same ethnic group. Paper III suggests and finds support that the arrival and long-term hosting of refugees from states in civil conflict make host states more likely to experience civil conflict. Paper IV examines the common notion that the granting of autonomy or independence to separatist groups may spur other ethnic groups to violently pursue similar demands, starting off a domino effect. Using new global data on such territorial concessions, the analysis does not support this version of the “domino theory,” which is popular among policy-makers. In sum, this dissertation contributes by demonstrating the usefulness of the contagion process approach. It offers a more comprehensive view of contagion among neighbors, and as such is able to specify arguments and intuitions in previous research.

The selective transformation of carbon-carbon and carbon-hydrogen bonds represents an attractive approach and rapidly developing frontier in synthesis. Benefits include step and atom economy, as well as the ubiquitous presence in organic molecules. Advances to this exciting realm of synthesis are described in this thesis with an emphasis on the development of catalytic, selective reactions under mild conditions. Additionally some applications of the methodologies are demonstrated. In Chapter 1, the first examples of inter-and intramolecular enantioselective conjugate alkenylations employing organostannanes are reported. A chiral, cationic Rh(I)-diene complex catalyzed the enantioselective conjugate addition of alkenylstannanes to benzylidene Meldrum’s acids in moderate enantiomeric ratios and yields. Notably, the cationic and anhydrous conditions required for the asymmetric alkenylation are complementary to existing protocols employing other alkenylmetals. In Chapter 2, a domino, one-pot formation of tetracyclic ketones from benzylidene Meldrum’s acids using Sc(OTf)3 via a [1,5]-hydride shift/cyclization/Friedel-Crafts acylation sequence is described. Respectable yields were obtained in accord with the ability to convert to the spiro-intermediate, and considering the formation of three new bonds: one C-H and two C-C bonds. An intriguing carbon-carbon bond cleavage was also serendipitously discovered as part of a competing reaction pathway. In Chapter 3, the pursuit of novel C-H bond transformations led to the development of non-carbonyl-stabilized rhodium carbenoid Csp3-H insertions. This methodology enabled the rapid synthesis of N-fused indolines and related complex heterocycles from N-aziridinylimines. By using a rhodium carboxamidate catalyst, competing processes were minimized and C-H insertions were found to proceed in moderate to high yields. Also disclosed is an expedient total synthesis of (±)-cryptaustoline, a dibenzopyrrocoline alkaloid, which highlights the methodology. In Chapter 4, the Lewis acid promoted substitution of Meldrum’s acid discovered during the course of the domino reaction was explored in detail. The protocol transforms unstrained quaternary and tertiary benzylic Csp3-Csp3 bonds into Csp3-X bonds (X = C, N, H) and has even shown to be advantageous with regards to synthetic utility over the use of alternative leaving groups for substitutions at quaternary benzylic centers. This reaction has a broad scope both in terms of suitable substrates and nucleophiles with good to excellent yields obtained (typically >90%).