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.

An Investigation of the Role of Attention in the Cross-Race Effect: An Ecological Approach

The current set of studies was conducted to examine the cross-race effect (CRE), a phenomenon commonly found in the face perception literature. The CRE is evident when participants display better own-race face recognition accuracy than other-race recognition accuracy (e.g. Ackerman et al., 2006). Typically the cross-race effect is attributed to perceptual expertise, (i.e., other-race faces are processed less holistically; Michel, Rossion, Han, Chung & Caldara, 2006), and the social cognitive model (i.e., other-race faces are processed at the categorical level by virtue of being an out-group member; Hugenberg, Young, Bernstein, & Sacco, 2010). These effects may be mediated by differential attention. I investigated whether other-race faces are disregarded and, consequently, not remembered as accurately as own-race (in-group) faces. In Experiment 1, I examined how the magnitude of the CRE differed when participants learned individual faces sequentially versus when they learned multiple faces simultaneously in arrays comprising faces and objects. I also examined how the CRE differed when participants recognized individual faces presented sequentially versus in arrays of eight faces. Participants’ recognition accuracy was better for own-race faces than other-race faces regardless of familiarization method. However, the difference between own- and other-race accuracy was larger when faces were familiarized sequentially in comparison to familiarization with arrays. Participants’ response patterns during testing differed depending on the combination of familiarization and testing method. Participants had more false alarms for other-race faces than own-race faces if they learned faces sequentially (regardless of testing strategy); if participants learned faces in arrays, they had more false alarms for other-race faces than own-races faces if ii i they were tested with sequentially presented faces. These results are consistent with the perceptual expertise model in that participants were better able to use the full two seconds in the sequential task for own-race faces, but not for other-race faces. The purpose of Experiment 2 was to examine participants’ attentional allocation in complex scenes. Participants were shown scenes comprising people in real places, but the head stimuli used in Experiment 1 were superimposed onto the bodies in each scene. Using a Tobii eyetracker, participants’ looking time for both own- and other-race faces was evaluated to determine whether participants looked longer at own-race faces and whether individual differences in looking time correlated with individual differences in recognition accuracy. The results of this experiment demonstrated that although own-race faces were preferentially attended to in comparison to other-race faces, individual differences in looking time biases towards own-race faces did not correlate with individual differences in own-race recognition advantages. These results are also consistent with perceptual expertise, as it seems that the role of attentional biases towards own-race faces is independent of the cognitive processing that occurs for own-race faces. All together, these results have implications for face perception tasks that are performed in the lab, how accurate people may be when remembering faces in the real world, and the accuracy and patterns of errors in eyewitness testimony.

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

The encounter with the real and post-Soviet trauma : fantasy construction in Russian popular cinema /

This thesis examines the impact of the Soviet Union's collapse on the Russian Symbolic as represented through popular cinema of the post-Soviet period. The disintegration of the USSR in 1991 became one of the most traumatic experiences for many Russian people. The trauma of the collapse of the Soviet Union penetrated the everyday reality of the Russian Symbolic, leaving the traces-symptoms in different cultural fonns like literature, arts, television and cinema. Because popular culture usually reacts very quickly to any social, political and economical shifts in society, it is an excellent barometer for deeper changes in society. Focusing on postSoviet popular cinema, this thesis analyzes the symptoms of cultural and individual trauma occasioned by the momentous changes of the 1990's. This study is grounded in post-analytic theory of Jacques Lacan and its interpretation by Slavoj Zizek, which emphases the traumatic encounter with the Real as a "hard core" of our reality. According to this paradigm, a new chain of signifiers is structured around the traumatic breach in the Symbolic, initiating a process of fantasy construction to deal with consequences of trauma and, thus, to support our Symbolic order. This thesis examines three major fantasy constructions - drinking, traveling to a "happy land" and family reunion and money - in popular films by Alexander Rogozhkin, Yurij Mamin, Georgij Shengelia, Dmitrij Astrakhan, Valerij Todorovskij, Alexej Balabanov, Sergej Bodrov Jr. and Petr Buslov. According to Zizek, enjoyment underlies any fantasy constructions, and that is why after the intrusion of the Real every individual and culture should go through the process of fantasizing about some substitutes which can help to minimize the traumatic effect and which can lead to a partial enjoyment. By analyzing the fantasies about drinking, "happy land", reconstruction of the family bonds and money in Russian popular cinema since 1991, this thesis demonstrates how the traumatic engagement with the Real affected the everyday lives of Russian people, and how individuals tried to fill the gap, the lack, in the post-Soviet Symbolic and "return" the lost feeling of unity and plenitude.

A tale of two childhoods : the virtual child and the real child in Romania, 1970s and 1980s

This thesis deals with the everyday use of propaganda in Romania, between 1971 and 1989. It explores the way in which the propaganda discourse of the Romanian Communist Party was disseminated through popular culture artifacts targeting children: Pioneers' magazines, textbooks, Almanacs and moralizing stories. These artifacts configured the image of a model child, whose preoccupations complied with the requirements of the Romanian Communist Party and communicated a set of recommended practices, to be followed by Romanian children. At the same time, the thesis incorporates the response of the actual children to these desirable practices, and implicitly, their response to state propaganda.

Where's Albania? : staking out the politics of the real and reality in documentary cinema

This thesis, entitled, "Where's Albania? Staking Out the Politics of the Real and Reality in Documentary Cinema," charts the documentary tradition's path from its first incarnations, as filmed travelogue or ethnographic study, for example, right through to its development as a form acting as an objective observer, reflexive commentator, and finally, as a postmodern hybrid. This thesis begins by locating the documentary tradition's origins in realism. Foregrounding documentary cinema as a realist style is important in that it is a contention that spans this entire study. After working through the numerous modes of documentary as outlined by Bill Nichols, I suggest the documentary is often best understood as a hybrid form drawing on numerous modes and conventions. This argument permits my study to make a shift into postmodern theory, wherein I examine postmodernism's relationship to the documentary both as being influenced by it, but also as subsequently forcing documentary cinema to look back at itself and reevaluate the claims it has made in the past, and how postmodernism has drawn these claims to the surface of debate. My thesis concludes with a study of the mockumentary. This analysis confirms the link between postmodernism and documentary, but perhaps more importantly, this analysis investigates postmodemism's critique of the image and representation in general, two elements historically linked to documentary cinema's success as "truth teller."

Broadside advertising a Real Estate Auction in the Village of Niagara Falls [New York], July, 1836.

Benjamin Rathburn (1790-1873) was a builder, banker and hotel-keeper who was well-known for his work in the development and expansion of Buffalo in the 1830s. He also conducted business in the Village of Niagara Falls. He purchased large tracts of land (largely on credit) with the intent to sell the land at a profit. However, the sales did not meet his expectations and Rathburn found himself over-extended on credit, ultimately leading to his financial ruin.Jesse P. Haines (1793-1877) was an American cartographer who is credited with mapping the Villages of Lockport and Niagara Falls, New York.

Broadside advertising a Real Estate Auction in the Village of Niagara Falls [New York], July, 1836.

Benjamin Rathburn (1790-1873) was a builder, banker and hotel-keeper who was well-known for his work in the development and expansion of Buffalo in the 1830s. He also conducted business in the Village of Niagara Falls. He purchased large tracts of land (largely on credit) with the intent to sell the land at a profit. However, the sales did not meet his expectations and Rathburn found himself over-extended on credit, ultimately leading to his financial ruin. Jesse P. Haines (1793-1877) was an American cartographer who is credited with mapping the Villages of Lockport and Niagara Falls, New York.

Plan of levels of marsh land on the line of the proposed ditch from Lyons Creek Culvert on the Welland Canal to lot no. 32 in the 2nd concession of Wainfleet

Plan of levels of marsh land on the line of the proposed ditch from Lyons Creek Culvert on the Welland Canal to lot no. 32 in the 2nd concession of Wainfleet (1 page, hand drawn), n.d.