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Robert P. Grzeszczuk, Milana Huang, Louis H. Kauffman, "PhysicallyBased Stochastic Simplification of Mathematical Knots," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 3, pp. 262272, JulySeptember, 1997.  
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@article{ 10.1109/2945.620492, author = {Robert P. Grzeszczuk and Milana Huang and Louis H. Kauffman}, title = {PhysicallyBased Stochastic Simplification of Mathematical Knots}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {3}, number = {3}, issn = {10772626}, year = {1997}, pages = {262272}, doi = {http://doi.ieeecomputersociety.org/10.1109/2945.620492}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  PhysicallyBased Stochastic Simplification of Mathematical Knots IS  3 SN  10772626 SP262 EP272 EPD  262272 A1  Robert P. Grzeszczuk, A1  Milana Huang, A1  Louis H. Kauffman, PY  1997 KW  Mathematical visualization KW  knot theory KW  knot classification KW  polynomial invariants KW  simulated annealing. VL  3 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—The article describes a tool for simplification and analysis of tangled configurations of mathematical knots. The proposed method addresses optimization issues common in energybased approaches to knot classification. In this class of methods, an initially tangled elastic rope is "charged" with an electrostaticlike field which causes it to selfrepel, prompting it to evolve into a mechanically stable configuration. This configuration is believed to be characteristic for its knot type. We propose a physicallybased model to implicitly guard against isotopy violation during such evolution and suggest that a robust stochastic optimization procedure, simulated annealing, be used for the purpose of identifying the globally optimal solution. Because neither of these techniques depends on the properties of the energy function being optimized, our method is of general applicability, even though we applied it to a specific potential here. The method has successfully analyzed several complex tangles and is applicable to simplifying a large class of knots and links. Our work also shows that energybased techniques will not necessarily terminate in a unique configuration, thus we empirically refute a prior conjecture that one of the commonly used energy functions (Simon's) is unimodal. Based on these results we also compare techniques that rely on geometric energy optimization to conventional algebraic methods with regards to their classification power.
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