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You searched for subject:(polygon index). Showing records 1 – 2 of 2 total matches.

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Colorado State University

1. Eddy, Thomas D. Improved stick number upper bounds.

Degree: MS(M.S.), Mathematics, 2019, Colorado State University

A stick knot is a mathematical knot formed by a chain of straight line segments. For a knot K, define the stick number of K, denoted stick(K), to be the minimum number of straight edges necessary to form a stick knot which is equivalent to K. Stick number is a knot invariant whose precise value is unknown for the large majority of knots, although theoretical and observed bounds exist. There is a natural correspondence between stick knots and polygons in R3. Previous research has attempted to improve observed stick number upper bounds by computationally generating such polygons and identifying the knots that they form. This thesis presents a new variation on this method which generates equilateral polygons in tight confinement, thereby increasing the incidence of polygons forming complex knots. Our generation strategy is to sample from the space of confined polygons by leveraging the toric symplectic structure of this space. An efficient sampling algorithm based on this structure is described. This method was used to discover the precise stick number of knots 935, 939, 943, 945, and 948. In addition, the best-known stick number upper bounds were improved for 60 other knots with crossing number ten and below. Advisors/Committee Members: Shonkwiler, Clayton (advisor), Adams, Henry (committee member), Chitsaz, Hamid (committee member).

Subjects/Keywords: knot theory; stick number; toric symplectic manifold; polygon index; edge number; symplectic geometry

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APA (6th Edition):

Eddy, T. D. (2019). Improved stick number upper bounds. (Masters Thesis). Colorado State University. Retrieved from http://hdl.handle.net/10217/195411

Chicago Manual of Style (16th Edition):

Eddy, Thomas D. “Improved stick number upper bounds.” 2019. Masters Thesis, Colorado State University. Accessed July 20, 2019. http://hdl.handle.net/10217/195411.

MLA Handbook (7th Edition):

Eddy, Thomas D. “Improved stick number upper bounds.” 2019. Web. 20 Jul 2019.

Vancouver:

Eddy TD. Improved stick number upper bounds. [Internet] [Masters thesis]. Colorado State University; 2019. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/10217/195411.

Council of Science Editors:

Eddy TD. Improved stick number upper bounds. [Masters Thesis]. Colorado State University; 2019. Available from: http://hdl.handle.net/10217/195411


University of Victoria

2. Robertson, Colin John. Spatial-temporal analysis of moving polygons.

Degree: Dept. of Geography, 2010, University of Victoria

There are few methods available for the spatial-temporal analysis of polygon data. This research develops a new method for spatial-temporal analysis of moving polygons (STAMP). Using an event-based framework, polygons from neighboring time periods are related by spatial overlap and proximity. The proximity spatial relation is defined by an application specific distance threshold. STAMP is demonstrated in the spatial-temporal analysis of a wildfire burning over small spatial and temporal scales, and in the spatial-temporal analysis of mountain pine beetle (Dendroctonus ponderosae Coleoptera: Hopkins) movement patterns over large spatial and temporal scales. The mountain pine beetle analysis found that short range movement patterns of mountain pine beetles occurred at different beetle population levels. Spot proliferation occurred most when beetle presence was increasing slowly, perhaps moving into new areas for the first time. When beetle presence increased rapidly, local expansion, or spot growth, was a more common movement pattern. In the Pine Pass study area. long range dispersal markedly extended the northeast border of the mountain pine beetle range. Advisors/Committee Members: Nelson, Trisalyn (supervisor).

Subjects/Keywords: Polygon; Mountain pine beetle; Forest fires; UVic Subject Index::Sciences and Engineering::Agriculture::Forests and forestry; UVic Subject Index::Sciences and Engineering::Agriculture::Plant diseases

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Robertson, C. J. (2010). Spatial-temporal analysis of moving polygons. (Masters Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/2460

Chicago Manual of Style (16th Edition):

Robertson, Colin John. “Spatial-temporal analysis of moving polygons.” 2010. Masters Thesis, University of Victoria. Accessed July 20, 2019. http://hdl.handle.net/1828/2460.

MLA Handbook (7th Edition):

Robertson, Colin John. “Spatial-temporal analysis of moving polygons.” 2010. Web. 20 Jul 2019.

Vancouver:

Robertson CJ. Spatial-temporal analysis of moving polygons. [Internet] [Masters thesis]. University of Victoria; 2010. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/1828/2460.

Council of Science Editors:

Robertson CJ. Spatial-temporal analysis of moving polygons. [Masters Thesis]. University of Victoria; 2010. Available from: http://hdl.handle.net/1828/2460

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