<p>In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked to those, fait accompli, of groups. With this, we ask if the concept of strongly simple groups has a place for consideration. We have shown that for n &gt / 5, An, the alternating group on n odd elements, is not strongly simple.</p>

In this dissertation we treat some problems about possible density of orbits for non-hypercyclic operators and we enlarge the class of known non-orbit-transitive operators. One of the questions related to hypercyclic operators that we answer is whether the density (in the set of positive real numbers) of the norms of the elements in the orbit for each nonzero vector in the Hilbert space is sufficient to imply that at least one vector has orbit dense in the Hilbert space. We show that the density of the norms is not a sufficient condition to imply hypercyclicity by constructing a weighted bilateral shift that, on one hand, satisfies the orbit-density property (in the sense defined above), but, on the other hand, fails to be hypercyclic. The second major topic that we study refers to classes of operators that are not hypertransitive (or orbit-transitive) and is related to the invariant subspace problem on Hilbert space. It was shown by Jung, Ko and Pearcy in 2005 that every compact perturbation of a normal operator is not hypertransitive. We extend this result, after introducing the related notion of weak hypertransitivity, by giving a sufficient condition for an operator to belong to the class of non-weakly-hypertransitive operators. Next, we study certain 2-normal operators and their compact perturbations. In particular, we consider operators with a slow growth rate for the essential norms of their powers. Using a new idea, of accumulation of growth for each given power on a set of different orthonormal vectors, we establish that the studied operators are not hypertransitive.

<p>In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked to those, fait accompli, of groups. With this, we ask if the concept of strongly simple groups has a place for consideration. We have shown that for n &gt / 5, An, the alternating group on n odd elements, is not strongly simple.</p>

The transitive inference (TI) problem (i.e., if A > B and B > C, then A > C) has traditionally been considered a hallmark of logical reasoning. However, considerable debate exists regarding the psychological processes involved when individuals perform TI tasks. The current thesis therefore sought to further explore this issue with adult humans as the population sample. Following a review of the literature, the first empirical chapter, Chapter 2, adopted a traditional TI task and exposed participants to training and testing with a simultaneous discrimination paradigm. In addition, the chapter sought to examine the potential facilitative effects of awareness and repeated exposure to training and test phases on the emergence of TI. Results broadly demonstrated that awareness led to more accurate responses at test, and that for a number of participants, repeated exposure to training and test phases, allowed the targeted performances to emerge over time. Chapter 3 developed and determined the utility of a novel behaviour-analytic account of TI as a form of derived comparative relational responding. For the most part, findings revealed that the model has the potential to generate arbitrarily applicable comparative responding in adults, comparable to TI. However, findings from Chapter 3 also revealed that despite the implementation of a number of interventions, response accuracy was still weak on a number of the targeted relations. Chapter 4 developed a variant of the Relational Completion Procedure (RCP) to examine derived comparative responding to 'More-than' and 'Less-than' relations, as an extension of the behavioural account of TI adopted in Chapter 3. Findings revealed that, for the most part, the protocol was effective in establishing the targeted relations, and that the linearity (e.g., A < B, B < C) of training pairs was not found to effect the emergence of this pattern of responding. Chapter 5 sought to explore the transformation of discriminative functions via a 5- member relational network of 'More-than' and 'Less-than' relations. Findings revealed that, across four experiments, approximately half of the participants displayed the predicted patterns of performance. That is, half of the participants responded 'less' to the stimuli ranked lower in the network (A and B) and 'more' to the stimuli ranked higher in the network (D and E), on the basis of training with stimulus C. The utility of the current behaviour-analytic approach to the study of TI is discussed.

Magister Scientiae - MSc / In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked to those, fait accompli, of groups. With this, we ask if the concept of strongly simple groups has a place for consideration. / South Africa

In language, information is omitted for brevity. Comprehension requires inferences to be made, but do we make such inferences during encoding or later? Kintsch (1988) claimed that transitive inferences are made during reading and proposed transitive inferences are extracted from a constructed mental image. Two experiments were performed to test his ideas. Participants read sentences permitting a transitive or reciprocal inference, then immediately answered an inference based question. Data included reaction time and accuracy. By comparing verification against inferential sentences, it is possible to determine if the inference is made during encoding or later. A further manipulation was to compare concrete sentences that could be easily converted to an image with abstract sentences that are hard to image. Results showed reciprocal sentences are slower to verify than transitive, suggesting additional processing is needed. In contrast, no difference was observed between concrete and abstract relations, calling into question Kintsch’s inference/image view.

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Constrained graph problems are about finding graphs respecting a given set of constraints. These problems occur in many areas. For example, security properties, biological reaction mechanisms, ecological predator/prey relationships, compiler code optimizations, and logic circuit fault diagnosis are just a few of the areas in which graph constraints play an important role. This thesis proposes a constraint programming approach for solving these problems. We present new constraints defined on top of the notions of domination and transitive closure, and their search algorithms. We have implemented these constraints in the state-of-the-art Gecode system and shown that they are competitive with or better than other approaches in realistic scenarios. / Les problèmes de graphes contraints concernent la recherche de graphes qui respectent un ensemble donné de contraintes. Ils apparaissent dans de nombreux domaines. Par exemple, la sécurité dans les logiciels, les méchanismes des réactions biologiques, les relations prédateur/proie en écologie, l'optimisation de code par les compilateurs, et le diagnostic de pannes dans des circuits logiques sont quelques-uns des domaines dans lesquels les contraintes de graphes jouent un rôle important. Cette thèse propose une approche basée sur la programmation par contraintes pour résoudre ces problèmes. Nous présentons de nouvelles contraintes définies sur les notions de domination et de clôture transitive, ainsi que leurs algorithmes de recherche. Nous avons implémenté ces contraintes dans le système de pointe Gecode, et avons montré notre approche compétitive et parfois meilleure que d'autres approches dans des cas réalistes.

Constrained graph problems are about finding graphs respecting a given set of constraints. These problems occur in many areas. For example, security properties, biological reaction mechanisms, ecological predator/prey relationships, compiler code optimizations, and logic circuit fault diagnosis are just a few of the areas in which graph constraints play an important role. This thesis proposes a constraint programming approach for solving these problems. We present new constraints defined on top of the notions of domination and transitive closure, and their search algorithms. We have implemented these constraints in the state-of-the-art Gecode system and shown that they are competitive with or better than other approaches in realistic scenarios. / Les problèmes de graphes contraints concernent la recherche de graphes qui respectent un ensemble donné de contraintes. Ils apparaissent dans de nombreux domaines. Par exemple, la sécurité dans les logiciels, les méchanismes des réactions biologiques, les relations prédateur/proie en écologie, l'optimisation de code par les compilateurs, et le diagnostic de pannes dans des circuits logiques sont quelques-uns des domaines dans lesquels les contraintes de graphes jouent un rôle important. Cette thèse propose une approche basée sur la programmation par contraintes pour résoudre ces problèmes. Nous présentons de nouvelles contraintes définies sur les notions de domination et de clôture transitive, ainsi que leurs algorithmes de recherche. Nous avons implémenté ces contraintes dans le système de pointe Gecode, et avons montré notre approche compétitive et parfois meilleure que d'autres approches dans des cas réalistes.

Are subjects produced differently based on the transitivity of the clause they are embedded in? Based on data from a narrative reading experiment, it is shown that transitive subjects are produced with a lower f0 than intransitive subjects and that this difference is statistically significant (p∠0.05). It is suggested that the purpose for such a difference originates from a propensity for English speakers to accent new referents, which are common in the object position. By lowering the f0 of the subject, speakers increase the efficacy of an accent on a new object later in the clause. Finally, the read narrative procedure is evaluated for its strict control of stimuli, while also reproducing known intonational phenomena.