644 research outputs found
Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs
Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis.
In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; Ī»1; Ī»2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; Ī»1, Ī»2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ā„ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; Ī»1, Ī»2)s.
Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ā„ 3.
Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices
Enumeration of inequivalent cycle decompositions
A k-cycle decomposition of order n is a partition of the edges of the complete graph on n vertices into k-cycles. In this report a backtracking algorithm is developed to count the number of inequivalent k-cycle decompositions of order n
Expression of the Aldo-Ketoreductases AKR1B1 and AKR1B10 in Human Cancers
The American Cancer Society estimates that there will be more than 1.5 million new cases of cancer in 2011, underscoring the need for identification of new therapeutic targets and development of novel cancer therapies. Previous studies have implicated the human aldo-ketoreductases AKR1B1 and AKR1B10 in cancer, and therefore we examined AKR1B1 and AKR1B10 expression across all major human cancer types using the Oncomine cancer gene expression database (Compendia Biosciences, www.oncomine.com). Using this database, we found that expression of AKR1B1 and AKR1B10 varies greatly by cancer type and tissue of origin, including agreement with previous reports that AKR1B10 is significantly over-expressed in cancers of the lungs and liver. AKR1B1 is more broadly over-expressed in human cancers than AKR1B10, albeit at a generally lower magnitude. AKR1B1 over-expression was found to be associated with shortened patient survival in acute myelogenous leukemias and multiple myelomas. High AKR1B10 expression tends to predict less aggressive clinical course generally, notably within lung cancers, where it tends to be highly over-expressed compared to normal tissue. These findings suggest that AKR1B1 inhibitors in particular hold great potential as novel cancer therapeutics
Breaking Gender Barriers Through Literature in the Elementary and Pre-School Classroom
The following research assesses how reading and discussing stories that counter gender stereotypes can increase cooperation and decrease conflict between primary- and elementary-aged students of different genders, as well as to expand studentsā conceptions of self and others beyond traditional gender expectations. The six-week study involved 50 participants total, 21 between the ages of 3 and 6 and 29 between the ages of 6 and 9 at two separate Montessori public charter schools in Minnesota. Each participant completed an activity pre- and post-intervention concerning the feminine and masculine traits that they would choose to describe themselves and those that could describe someone theyād want to be friends with. 10-minute observations were taken daily to record instances of cooperation and conflict between children of different genders. Pertinent quotes were recorded during observation periods and in discussions about the counter-stereotypical stories. Results showed an increase in the number of friendships between genders, and a greater number of traits chosen to describe selves and potential friends at the elementary school level. Further research in the area is needed to discover the long-term effects of counter-stereotypical literature, the importance of adults examining their own gender biases, and interventions beyond literature to counter patriarchal norms in classrooms
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