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111	Computational and Geometric Aspects of Linear Optimization Xie, Feng 04 1900 (has links) <p>This thesis deals with combinatorial and geometric aspects of linear optimization, and consists of two parts.</p> <p>In the first part, we address a conjecture formulated in 2008 and stating that the largest possible average diameter of a bounded cell of a simple hyperplane arrangement of n hyperplanes in dimension d is not greater than the dimension d. The average diameter is the sum of the diameters of each bounded cell divided by the total number of bounded cells, and then we consider the largest possible average diameter over all simple hyperplane arrangements. This quantity can be considered as an indication of the average complexity of simplex methods for linear optimization. Previous results in dimensions 2 and 3 suggested that a specific type of extensions, namely the covering extensions, of the cyclic arrangement might achieve the largest average diameter. We introduce a method for enumerating the covering extensions of an arrangement, and show that covering extensions of the cyclic arrangement are not always among the ones achieving the largest diameter.</p> <p>The software tool we have developed for oriented matroids computation is used to exhibit a counterexample to the hypothesized minimum number of external facets of a simple arrangement of n hyperplanes in dimension d; i.e. facets belonging to exactly one bounded cell of a simple arrangement. We determine the largest possible average diameter, and verify the conjectured upper bound, in dimensions 3 and 4 for arrangements defined by no more than 8 hyperplanes via the associated uniform oriented matroids formulation. In addition, these new results substantiate the hypothesis that the largest average diameter is achieved by an arrangement minimizing the number of external facets.</p> <p>The second part focuses on the colourful simplicial depth, i.e. the number of colourful simplices in a colourful point configuration. This question is closely related to the colourful linear programming problem. We show that any point in the convex hull of each of (d+1) sets of (d+1) points in general position in R<sup>d</sup> is contained in at least (d+1)<sup>2</sup>/2 simplices with one vertex from each set. This improves the previously established lower bounds for d>=4 due to Barany in 1982, Deza et al in 2006, Barany and Matousek in 2007, and Stephen and Thomas in 2008.</p> <p>We also introduce the notion of octahedral system as a combinatorial generalization of the set of colourful simplices. Configurations of low colourful simplicial depth correspond to systems with small cardinalities. This construction is used to find lower bounds computationally for the minimum colourful simplicial depth of a configuration, and, for a relaxed version of the colourful depth, to provide a simple proof of minimality.</p> / Doctor of Philosophy (PhD) Linear optimization Hyperplane arrangement Colourful simplicial depth Oriented Matroids Octahedral systems Average diameter of arrangements Discrete Mathematics and Combinatorics Geometry and Topology Operational Research Discrete Mathematics and Combinatorics
112	Self-Assembly of DNA Graphs and Postman Tours Bakewell, Katie 01 January 2018 (has links) DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and the Windy Postman Problem. Thesis University of North Florida UNF Thickened graphs Boundary components Windy Postman Problem Reporter strands DNA computing Discrete Mathematics and Combinatorics Geometry and Topology Other Mathematics
113	The Effects of the Use of Technology In Mathematics Instruction on Student Achievement Myers, Ron Y 30 March 2009 (has links) The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics FCAT results were examined to determine if the GSP produced any effects. Students’ scores were compared based on assignment to the control or experimental group as well as gender and SES. SES measurements were based on whether students qualified for free lunch. The findings of the study revealed a significant difference in the FCAT mathematics scores of students who were taught geometry using GSP compared to those who used the traditional method. No significant differences existed between the FCAT mathematics scores of the students based on SES. Similarly, no significant differences existed between the FCAT scores based on gender. In conclusion, the use of technology (particularly GSP) is likely to boost students’ FCAT mathematics test scores. The findings also show that the use of GSP may be able to close known gender and SES related achievement gaps. The results of this study promote policy changes in the way geometry is taught to 10th grade students in Florida’s public schools. Mathematics Technology Acheivement Gender SES Geometer's Sketchpad (GSP) Geometry Manova Acheivement gap Minority Algebra Algebraic Geometry Analysis Categorical Data Analysis Curriculum and Instruction Demography, Population, and Ecology Design of Experiments and Sample Surveys Disability and Equity in Education Education Educational Psychology Gender and Sexuality Geometry and Topology Inequality and Stratification Mathematics Other Education Other Mathematics Other Physical Sciences and Mathematics Other Sociology Other Statistics and Probability Physical Sciences and Mathematics Probability Race and Ethnicity Science and Mathematics Education Science and Technology Studies Service Learning Social and Behavioral Sciences Social Psychology and Interaction Sociology Statistical Models Statistical Theory Statistics and Probability
114	BBT Acoustic Alternative Top Bracing CADD Data Set-NoRev-2022Jun28 Hemphill, Bill 22 July 2022 (has links) This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are (a) a one-piece base for the standard kit's (Martin-style) bracing, (b) 277 Ladder-style bracing, and (c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars. The CADD data set for each of the three (3) top bracing designs includes (a) a nominal 24" x 18" x 3mm (0.118") Baltic birch plywood laser layout of (1) the one-piece base with slots, (2) pre-radiused and pre-scalloped vertical braces with tabs to ensure proper orientation and alignment, and (3) various gages and jigs and (b) a nominal 15" x 20" marking template. The 'provided as is" CADD data is formatted for use on a Universal Laser Systems (ULS) laser cutter digital (CNC) device. Each CADD drawing is also provided in two (2) formats: Autodesk AutoCAD 2007 .DWG and .DXF R12. Users should modify and adapt the CADD data as required to fit their equipment. This CADD data set is released and distributed under a Creative Commons license; users are also encouraged to make changes o the data and share (with attribution) their designs with the worldwide acoustic guitar building community. BBT acoustic guitar brace bracing top CADD CAD DWG DXF R12 lutier ETSU OM orchestra model STEM STEM Guitar building project kit storefront 3mm 0.118" Baltic birch plywood sheet 24 18 3mm 0.118 laser cut engrave etch marking template layout Martin Martin-style X-brace X-bracing X-braced X tone arm tonal variant alternative alt ladder 277 fan classicial European tab slot bump out radiused 300 inch 25 foot 762 meter radius base vertical scallop glue wood go-bar go bar deck jig fixture gage gauge headstock head plate neck contour fret stack stackable align alignment position orientation vertical perpendicular T1 upper bout lower kerfing sand chisel shape weight lighten light tone tap carbon-dioxide CO2 10.6 µm Universal Laser Systems ULS workboard waxed baker sheet Acoustics, Dynamics, and Controls Adult and Continuing Education Algebraic Geometry Appalachian Studies Art Education Educational Technology Elementary Education and Teaching Engineering Education Geometry and Topology Harmonic Analysis and Representation Higher Education and Teaching Industrial and Product Design Manufacturing Music Music Education Other Engineering Science and Materials Polymer and Organic Materials Science and Mathematics Education Secondary Education and Teaching Structural Materials Vocational Education
115	BBT Acoustic Alternative Top Bracing CADD Data Set-NoRev-2022Jun28 Hemphill, Bill 22 July 2022 (has links) This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are (a) a one-piece base for the standard kit's (Martin-style) bracing, (b) 277 Ladder-style bracing, and (c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars. The CADD data set for each of the three (3) top bracing designs includes (a) a nominal 24" x 18" x 3mm (0.118") Baltic birch plywood laser layout of (1) the one-piece base with slots, (2) pre-radiused and pre-scalloped vertical braces with tabs to ensure proper orientation and alignment, and (3) various gages and jigs and (b) a nominal 15" x 20" marking template. The 'provided as is" CADD data is formatted for use on a Universal Laser Systems (ULS) laser cutter digital (CNC) device. Each CADD drawing is also provided in two (2) formats: Autodesk AutoCAD 2007 .DWG and .DXF R12. Users should modify and adapt the CADD data as required to fit their equipment. This CADD data set is released and distributed under a Creative Commons license; users are also encouraged to make changes o the data and share (with attribution) their designs with the worldwide acoustic guitar building community. BBT acoustic guitar brace bracing top CADD CAD DWG DXF R12 lutier ETSU OM orchestra model STEM STEM Guitar building project kit storefront 3mm 0.118" Baltic birch plywood sheet 24 18 3mm 0.118 laser cut engrave etch marking template layout Martin Martin-style X-brace X-bracing X-braced X tone arm tonal variant alternative alt ladder 277 fan classicial European tab slot bump out radiused 300 inch 25 foot 762 meter radius base vertical scallop glue wood go-bar go bar deck jig fixture gage gauge headstock head plate neck contour fret stack stackable align alignment position orientation vertical perpendicular T1 upper bout lower kerfing sand chisel shape weight lighten light tone tap carbon-dioxide CO2 10.6 µm Universal Laser Systems ULS workboard waxed baker sheet Acoustics, Dynamics, and Controls Adult and Continuing Education Algebra Algebraic Geometry Appalachian Studies Applied Mathematics Art Education Biology Computer-Aided Engineering and Design Educational Technology Elementary Education and Teaching Engineering Education Engineering Science and Materials Forest Sciences Geometry and Topology Harmonic Analysis and Representation Industrial and Product Design Manufacturing Music Music Education Other Engineering Other Engineering Science and Materials Physics Polymer and Organic Materials Polymer Chemistry Science and Mathematics Education Secondary Education and Teaching Structural Materials Vocational Education

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