Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

Repertory grid adaptations in detecting connotative trends and social behaviour problems in education

Please consult the paper edition of this thesis to read. It is available on the 5th Floor of the Library at Call Number: Z 9999 E38 K66 1983

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

Palmer's Pocket Scale with Rules for its Use in Solving Arithmetical and Geometrical Problems

The book is signed by S.D. Woodruff. A label the book indicates that it was also owned by "Band, of De Vere Gardens in Toronto".

Letter to Henry Nelles from Michael Harris regarding estate problems

Letter to Henry Nelles from Michael Harris regarding estate problems (3 pages, handwritten with writing going in 2 directions on the last page), May 30, 1821.

The question solved, an answer to Rev. Dr. Clark's Question of the hour and his other anti-catholic problems

UANL

Resource-Monotonicity for House Allocation Problems

We study a simple model of assigning indivisible objects (e.g., houses, jobs, offices, etc.) to agents. Each agent receives at most one object and monetary compensations are not possible. We completely describe all rules satisfying efficiency and resource-monotonicity. The characterized rules assign the objects in a sequence of steps such that at each step there is either a dictator or two agents who “trade” objects from their hierarchically specified “endowments.”

Von Neumann-Morgenstern Stable Sets in Matching Problems

The following properties of the core of a one well-known: (i) the core is non-empty; (ii) the core is a lattice; and (iii) the set of unmatched agents is identical for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (von Neumann-Morgenstern) stable sets in one-to-one matching problem only if it is a maximal set satisfying the following properties : (a) the core is a subset of the set; (b) the set is a lattice; (c) the set of unmatched agents is identical for any two matchings belonging to the set. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b) and (c). We also show that our main result does not extend from one-to-one matching problems to many-to-one matching problems.

Negative affect mediates the relationship between the Cortisol Awakening Response and Conduct Problems in boys

Ce mémoire débute avec deux chapitres portant sur les problèmes des conduites et la régulation du stress, notamment sur l’axe hypothalamique-pituitaire-surrénal (HPS). Ensuite, la littérature est résumée et nous voyons que les études qui cherchent à établir un lien entre les problèmes des conduites et l’axe HPS ont trouvé des résultats différents et parfois contradictoires. Le chapitre suivant illustre les problèmes méthodologiques qui pourraient expliquer ces résultats différents. Vient ensuite l’étude présentée dans ce mémoire qui cherche à établir un lien entre la réponse cortisolaire à l’éveil (RCE), considérée comme un bon indice du fonctionnent de l’axe HPS, et les problèmes de conduites chez l’enfant. De plus, les émotions négatives ont été associées avec les problèmes des conduites ainsi qu’aux dysfonctions de l’axe HPS, notamment le RCE. L’étude présentée dans ce mémoire cherche aussi à établir si les émotions négatives pourrait être une variable médiatrice dans la relation potentielle entre la RCE et les problèmes des conduites. L’étude révèle que pour les garçons mais pas pour les filles, une RCE réduite est associée avec les émotions négatives, ce qui est successivement associé avec les problèmes des conduites. Le dernier chapitre du mémoire examine les implications théoriques de cette médiatisation et propose également des pistes psychobiologiques pour expliquer les différences sexuelles observées.

The effects of Motivation-Adaptive Skills-Trauma Resolution (MASTR) : Eye Movement Desensitization and Reprocessing (EMDR) on traumatized adolescents with conduct problems

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal