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.

Anne McPherson family fonds, 1852-2011 [non-inclusive]

Frank C. (Case) McCordick (1873-1946) was the son of William Henry (1849-1930) and Emily D. Howell (1851-1927) McCordick. William H. McCordick was in the coal business. The McCordick family included Frank Case, Mabel Gertrude, Ethel Howell and Arthur Stanley. Frank C. McCordick was educated in St. Catharines, and worked with his father in the coal business and eventually opened up a leather tanning operation. McCordick was active in the Lincoln Regiment and in 1906 was promoted to captain and in command of Company A, 19th Regiment. He was promoted to major and at the outbreak of war he was sent overseas as a commander of the 35th Battalion of the Canadian Expeditionary Forces (CEF). Upon arrival in France he was made officer commanding the 15th Battalion, King’s Own Yorkshire Light Infantry (KOYLI). After the war and his return to Canada he continued to play an active role in the local military units in the area as well as in Hamilton. After his retirement from the military in 1927 McCordick served as alderman and then mayor of St. Catharines from 1930 to 1931. He was a member of a large number of civic clubs, including St. Catharines Chamber of Commerce, Y.M.C.A., Lion’s Club, St. Catharines Golf Club, Detroit Boat Club, the St Catharines Club, as well as a member of several Masonic lodges. He continued to operate McCordick Tannery and other local investments. In 1903 Frank C. McCordick married May Beatrice Simson, daughter of Thomas E. Simson of Thorold. They had three children, E. (Edward) Frank McCordick, Bruce McCordick and (Margaret) Doris McCordick (m. Hubert Grigaut, d. 1977). The McCordick family resided at 82 Yates Street, near Adams Street. May Simson McCordick (b. 1873) was the daughter of Thomas Edward (1836-1908) and Julia Headlam (1844-1887) Simson of Thorold. Her siblings included: Edward, Frances, John, Augusta, Georgia and Gertrude. E. (Edward) Frank McCordick (1904-1980) was born in St. Catharines, Ont., attended Lake Lodge School in Grimsby, Ridley College in St. Catharines, Beechmont Preparatory School in England, Upper Canada College in Toronto and graduated from Royal Military College in Kingston, Ont. in 1925. Upon graduation he was made a lieutenant in the 10th (St. Catharines) Field Battery. In 1929 he married Helen Stanley Smith, daughter of Stanley George and Mary Walker Smith of St. Catharines. Col. McCordick, now promoted to Major, played an active role in the 10th (St. Catharines) Field Battery, being officer commanding the battery. In late 1939 McCordick headed to England for artillery tactical training and on December 6, 1939 the battery began the long trek overseas. McCordick saw action in Italy and in Holland. Upon his return to Canada at the end of the war he was the Liberal candidate in the federal election for Lincoln County. He remained active in the local military serving as honorary lieutenant-colonel of the 56th Field Regiment (ARCA) and in 1976 as the honorary colonel of the regiment. Col. McCordick held the Efficiency Decoration, the Order of the British Empire, granted in 1945 and was made an officer in the Order of St. John in 1978. He continued to serve his community in various capacities, including the Unemployment Insurance Canada Board, Royal Trust Company and the St. John Ambulance Society. He remained an active member of the alumni of Royal Military College, editing and compiling a newsletter and organizing reunion weekends. He kept in close contact with many of his classmates. Helen Stanley Smith McCordick lived in St. Catharines, Ont., attended Robertson School, and graduated from the University of Toronto in 1926 with a Bachelor of Arts degree in Modern Languages. During the war years (1939-1945) Helen was active in the Transport division of the local branch of the Canadian Red Cross and the Women’s Auxiliary of the 10th Field Battery. In 1932 E. Frank and Helen McCordick welcomed their only child, (Catharine) Anne McCordick. Helen continued to play an active role in her community until her passing in 1997. Stanley George Smith (1865-1960) was born in St. Catharines, Ont., the only child of William Smith (d. June 16, 1876) a native of Edinburgh, Scotland and his wife Hannah Louisa Maria Bulkeley a native of Fairfield, Connecticut. Stanley George Smith married Mary Walker of Guelph, Ont.(d. 1956) Mary was the daughter of Hugh and Elizabeth (d. 1924) Walker. Her siblings included Margaret, Agnes, Jessie, Isabella, Lorne, Ada, Alice, Eva, Alexander and George. Hugh Walker was a prominent fruit and vegetable merchant in Guelph. On 1904 their only child, Helen Stanley Smith was born. He was a post office clerk, and the treasurer for the James D. Tait Co. Ltd., a clothing and dry goods retailer in St. Catharines. The family lived at 39 Church Street in St. Catharines, Ont.

Letter to Mr. Henry H. Collier, 1837

Henry Haight Collier, was born in Howard, Steuben County, N. Y., November 28, 1818. His father, Richard Collier, was from Green County, in the same State. His grandfather, Isaac Collier, and his great-grandfather were originally from England. His mother, Mary Haight, was of Dutch origin. In 1835, Henry went to St. Catharines, where his elder brother, Richard Collier, resided. He spent two years at Grantham Academy, and then returned to Steuben County, to read law in Bath, with Edward Howell, and subsequently with Hammond and Campbell. Mr. Collier never opened a law office. He studied law for two years and in 1839 he went to Texas where he was connected with the State and Treasury Departments. In 1845 Mr. Collier returned to St. Catharines and opened a general store called St. Catharines Agricultural Works with his brother. The store remained open until May, 1877. He added the manufacturing of lumber in 1850, and manufacturing of agricultural implements in 1869. He built one of the first saw mills on the canal, on Lock No. 5, in St. Catharines. In July, 1877, he was appointed Collector of Customs. He became a Village Councilor for St. Paul’s Ward in 1859, and held that office from fifteen to twenty years. He was Deputy Reeve and member of the County Council for two terms. He was the Mayor of St. Catharines in 1872 and 1873. He was also Chairman of the Board of Water Commissioners of the city, during the time that the works were being built. He was a Justice of the Peace for twenty years or more. Mr. Collier was affiliated with the Reform Party and he was a Knight Templar in the Masonic fraternity and an Odd Fellow. He was also active in the Methodist Church. On June 1, 1858, he married Cornelia, daughter of Moses Cook, of "Westchester Place," St. Catharines, and had a daughter and son. Mary J. (married name: Mrs. Frank Camp) was a graduate of the Female Seminary at Hamilton, and Henry Herbert was a student in the University of Toronto. Henry H. Collier died on July 15, 1895 and is buried in Victoria Lawn Cemetery, St. Catharines, Ontario. Sources: www.accessgeneology.com "Historical Profiles from Victoria Lawn Cemetery" by Paul E. Lewis "Sincerely Lamented St. Catharines Obituaries 1817-1918" by Paul Hutchison

Proceedings of the Grand Lodge of the Province of Ontario, Canada (1893)

1893 Publisher: Dominion Odd Fellow Print. 1893, 39th annual session held at Niagara Falls. In pencil on front free endpaper of 1893 issue: Geneva Lodge #320

Proceedings of the Grand Lodge of the Province of Ontario, Canada (1914)

At head of title : Independent Order of Odd Fellows. 1893 Publisher: Dominion Odd Fellow Print. 1893, 39th annual session held at Niagara Falls. In pencil on front free endpaper of 1893 issue: Geneva Lodge #320.

Investigation of the role of the nucleus accumbens in amphetamine-induced 50 kHz ultrasonic vocalizations in the rat

There is extensive evidence that the mesolimbic dopamine system underlies the production of 50 kHz ultrasonic vocalizations in rats. In particular, the shell of the nucleus accumbens is associated with generation of frequency modulated 50 kHz calls (a specific type of 50 kHz call which can be subdivided into various subtypes). There is also evidence that amphetamine administered systemically preferentially increases the proportion of trill and step calls compared to other frequency modulated 50 kHz subtypes. The purpose of this study was to investigate the effect of drug administration route and the role of the nucleus accumbens shell in amphetamine-induced 50 kHz call profile in the rat. Three experiments investigated this by using subcutaneous and intra-accumbens microinjections of amphetamine, as well as procaine (a local anesthetic) blockade of the nucleus accumbens. Ultrasonic vocalizations were recorded digitally from 24 rats and were analysed for sonographic structure based on general call parameters. The results of the three experiments were partially supportive of the hypotheses. Systemic amphetamine was found to induce greater bandwidth in 50 kHz calling compared to spontaneous calls in a vehicle condition. Systemic amphetamine was also found to preferentially increase the proportion of trill and step subtypes compared to vehicle. Moreover, there was no difference in the proportions of 50 kHz subtypes resulting from intracerebral or systemic application of amphetamine. There was, however, a significant difference for bandwidth, with systemic amphetamine inducing greater bandwidth over intraaccumbens application. Procaine blockade of the nucleus accumbens shell paired with subcutaneous amphetamine produced no difference in bandwidth of calls compared with those after a vehicle pre-treatment similarly paired. There was no reduction in the proportions of trill and step 50 kHz subtypes as well, with the procaine condition showing significantly greater proportion of step calls. The results of the study support a role for the iii nucleus accumbens shell in the amphetamine-induced changes on 50 kHz call profile. They also indicate there are more regions and pathways involved in generating 50 kHz calls than the projections from the ventral tegmental area to the nucleus accumbens. The implications of this work are that frequency modulated 50 kHz subtypes may be generated by distinct neurophysiological mechanisms and may represent a profitable avenue for investigating different circuits of 50 kHz call categories in the rat.

Using HeadSprout Early Reading with a child with Autism Spectrum Disorder: An examination of phonological awareness, participant engagement, and participant enjoyment

This study examined the effectiveness of a 9-week reading program in improving the phonological awareness (PA) skills of a seven year old boy with Autism Spectrum Disorder (ASD), Attention Deficit Hyperactivity Disorder (ADHD), and Oppositional Defiant Disorder (ODD). The study’s secondary goal was to describe how the participant engaged with and enjoyed the HeadSprout computer program. The participant attended a one hour reading program incorporating 30 minutes of HeadSprout Early Reading three days a week for 9 weeks. Results demonstrated that the participant’s PA scores increased from the 16th percentile at pre-test to the 35th percentile post program. Four of five measures of PA increased, segmenting nonwords decreased to the 2nd percentile post program. Momentary time sampling procedures revealed the participant was engaged with the computer program 94.5% of the time. Perceived ratings of enjoyment indicated the participant enjoyed using the program. Specific components of the program which may have influenced participant enjoyment and engagement are discussed. Study limitations and implications of these findings are discussed in reference to future research.

Arrow's Theorem in Spatial Environments

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Multi-Prover and parallel repetition in non-classical interactive games

Depuis l’introduction de la mécanique quantique, plusieurs mystères de la nature ont trouvé leurs explications. De plus en plus, les concepts de la mécanique quantique se sont entremêlés avec d’autres de la théorie de la complexité du calcul. De nouvelles idées et solutions ont été découvertes et élaborées dans le but de résoudre ces problèmes informatiques. En particulier, la mécanique quantique a secoué plusieurs preuves de sécurité de protocoles classiques. Dans ce m´emoire, nous faisons un étalage de résultats récents de l’implication de la mécanique quantique sur la complexité du calcul, et cela plus précisément dans le cas de classes avec interaction. Nous présentons ces travaux de recherches avec la nomenclature des jeux à information imparfaite avec coopération. Nous exposons les différences entre les théories classiques, quantiques et non-signalantes et les démontrons par l’exemple du jeu à cycle impair. Nous centralisons notre attention autour de deux grands thèmes : l’effet sur un jeu de l’ajout de joueurs et de la répétition parallèle. Nous observons que l’effet de ces modifications a des conséquences très différentes en fonction de la théorie physique considérée.

The role of transcription factor Pitx1 and its regulation by hypoxia in Adolescent Idiopathic Scoliosis

La scoliose idiopathique de l’adolescent (SIA) est définie comme une courbure de la colonne vertébrale supérieure à 10 degrés, qui est de cause inconnue et qui affecte de façon prépondérante les adolescents. Des études précédentes sur des modèles murins ont démontré une inactivation partielle du gène Pitx1. Cette inactivation partielle provoque une déformation spinale sévère lors du développement des souris Pitx1+/-, ce qui est grandement similaire au phénotype de la SIA. En se basant sur ces observations, nous postulons que la perte de fonction de Pitx1 pourrait avoir un rôle dans la SIA et pourrait être régulée par des mécanismes moléculaires spécifiques. En effet, des études faites sur l’expression de Pitx1 révèlent une perte de son expression dans les ostéoblastes dérivés de patients SIA au niveau de l’ARNm. Nous émettons l’hypothèse que la perte de Pitx1 dans la SIA pourrait être déclenchée par des facteurs hypoxiques puisqu’il est connu que Pitx1 est réprimé par l’hypoxie et que HIF-2 alpha est surexprimés dans les ostéoblastes des patients SIA même dans des conditions normoxiques. De plus, nous avons découvert une mutation dans le domaine ODD des HIF-1 alpha chez certains patients SIA (3,1%). Une fonction connue de ce domaine est de stabiliser et d’augmenter l’activité transcriptionnelle de HIF-1 alpha dans des conditions normoxiques. Nous avons confirmé, par la technique EMSA, l’existence d’un élément de réponse fonctionnel à l’hypoxie au niveau du promoteur de Pitx1. Cependant, des co-transfections avec des vecteurs d’expression pour HIF-1 alpha et HIF-2 alpha, en présence de leur sous-unité beta ARNT, ont conduit à une activation du promoteur de Pitx1 dans la lignée cellulaire MG-63 ainsi que dans les ostéoblastes des sujets contrôles. Il est intéressant de constater qu’aucune activité du promoteur de Pitx1 dans les ostéoblastes SIA n’a été observée, même après la co-expression de HIF-2 alpha et ARNT, confirmant le fait que l’expression de Pitx1 est abrogée dans la SIA. Dans l’ensemble, nos résultats démontrent un rôle important de Pitx1 dans la SIA et une possible régulation par des facteurs hypoxiques.

Structure de la distribution de probabilités de l'état GHZ sous l'action locale de transformations du groupe U(2)

Dans ce mémoire, je démontre que la distribution de probabilités de l'état quantique Greenberger-Horne-Zeilinger (GHZ) sous l'action locale de mesures de von Neumann indépendantes sur chaque qubit suit une distribution qui est une combinaison convexe de deux distributions. Les coefficients de la combinaison sont reliés aux parties équatoriales des mesures et les distributions associées à ces coefficients sont reliées aux parties réelles des mesures. Une application possible du résultat est qu'il permet de scinder en deux la simulation de l'état GHZ. Simuler, en pire cas ou en moyenne, un état quantique comme GHZ avec des ressources aléatoires, partagées ou privées, et des ressources classiques de communication, ou même des ressources fantaisistes comme les boîtes non locales, est un problème important en complexité de la communication quantique. On peut penser à ce problème de simulation comme un problème où plusieurs personnes obtiennent chacune une mesure de von Neumann à appliquer sur le sous-système de l'état GHZ qu'il partage avec les autres personnes. Chaque personne ne connaît que les données décrivant sa mesure et d'aucune façon une personne ne connaît les données décrivant la mesure d'une autre personne. Chaque personne obtient un résultat aléatoire classique. La distribution conjointe de ces résultats aléatoires classiques suit la distribution de probabilités trouvée dans ce mémoire. Le but est de simuler classiquement la distribution de probabilités de l'état GHZ. Mon résultat indique une marche à suivre qui consiste d'abord à simuler les parties équatoriales des mesures pour pouvoir ensuite savoir laquelle des distributions associées aux parties réelles des mesures il faut simuler. D'autres chercheurs ont trouvé comment simuler les parties équatoriales des mesures de von Neumann avec de la communication classique dans le cas de 3 personnes, mais la simulation des parties réelles résiste encore et toujours.

Poétiques de l'ambivalence : figures de l'ambiguïté dans la poésie de F. Pessoa, N. Parra et J.L. Borges

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

Propriétés des valeurs propres de ballotement pour contenants symétriques

Le problème d’oscillation de fluides dans un conteneur est un problème classique d’hydrodynamique qui est etudié par des mathématiciens et ingénieurs depuis plus de 150 ans. Le présent travail est lié à l’étude de l’alternance des fonctions propres paires et impaires du problème de Steklov-Neumann pour les domaines à deux dimensions ayant une forme symétrique. On obtient des résultats sur la parité de deuxième et troisième fonctions propres d’un tel problème pour les trois premiers modes, dans le cas de domaines symétriques arbitraires. On étudie aussi la simplicité de deux premières valeurs propres non nulles d’un tel problème. Il existe nombre d’hypothèses voulant que pour le cas des domaines symétriques, toutes les valeurs propres sont simples. Il y a des résultats de Kozlov, Kuznetsov et Motygin [1] sur la simplicité de la première valeur propre non nulle obtenue pour les domaines satisfaisants la condition de John. Dans ce travail, il est montré que pour les domaines symétriques, la deuxième valeur propre non-nulle du problème de Steklov-Neumann est aussi simple.

Bioethics in Health Policy Development: A Primer for Decision-Makers

Article

Pandémie H1N1 : comparaison Canada-France des enfants hospitalisés en Soins Intensifs Pédiatriques Étude épidémiologique descriptive à partir de 2 cohortes nationales

Rationnel : La pandémie de grippe A(H1N1)pdm09 a induit un grand nombre d’hospitalisation d’enfants en soins intensifs pédiatriques (SIP). L’objectif de cette étude a été de comparer l’incidence et la mortalité des enfants admis en SIP durant l’automne 2009 entre le Canada et la France, deux pays qui diffèrent essentiellement par l’immunisation de la population contre ce virus (première vague en été et taux de couverture vaccinale supérieur à 50% au Canada ; pas de vague estivale et couverture vaccinale de 18% en France). Méthodes : Nous avons comparé deux cohortes nationales qui ont inclue tous les patients avec une infection A(H1N1)pdm09 documentée, admis en SIP au Canada et en France entre le 1er Octobre 2009 et le 31 janvier 2010. Résultats : Au Canada, 160 enfants (incidence=2,63/100000 enfants) en 6 semaines ont été hospitalisés en SIP comparé aux 125 enfants (incidence=1,15/100000 enfants) en 11 semaines en France (p<0,001). Le taux de vaccination avant l’admission était inférieur à 25% parmi les enfants en situation critique dans les deux pays. La gravité à l’admission en SIP et le taux de mortalité ont été similaires au Canada et en France (4,4% en France vs 6,5% au Canada, p=0,45, respectivement). Au Canada, la vaccination contre le virus H1N1pdm09 a été associée avec une diminution du recours à la ventilation invasive (Odd Ratio 0.30, intervalle de confiance à 95% [0,11-0,83], p=0,02). Au Canada comparé à la France, les durées médianes de séjour en SIP et de ventilation invasive ont été plus courtes (2,9 vs 3 jours, p=0,03 et 4 vs 6 jours, p=0,02, respectivement). Conclusion : Les enfants canadiens et français critiquement malades ont été beaucoup moins nombreux à recevoir le vaccin contre le virus influenza A (H1N1)pdm09 en comparaison avec l’ensemble des enfants dans ces deux populations. Au Canada, où la couverture vaccinale a été élevée, le risque d’avoir une détresse respiratoire sévère était moins important parmi les enfants en situation critique ayant été vaccinés avant l’admission.