Plots by Erik using matplotlib · We’ve done several combinations of the constraints of...

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Page 1: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can
Presenter
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Plots by Erik using matplotlib
Page 2: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can be locked. What about the others?

Page 3: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[Langerman 2002]

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Model and photograph by Erik Demaine
Page 4: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can
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Figure 9.7 of GFALOP
Page 5: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

The geometric (cone) model for a ribosome seems too simple. Is it actually based on some verified model from biology?

Page 6: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[Nissen, Hansen, Ban, Moore, Steitz 2000]

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Figure 11 of http://www.sciencemag.org/content/289/5481/920.abstract
Page 7: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[L21] In proving the NP-hardness of the 2D HP-model folding problem, what are the NP-hard problems used in various reductions?

Page 8: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

bin packing

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Figures 4 & 5 and clips from http://dl.acm.org/citation.cfm?id=279080
Page 9: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Hamiltonicity in max-degree-4

graphs

Trevisan code

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Figure 2 and clips from http://reference.kfupm.edu.sa/content/o/n/on_the_complexity_of_protein_folding__490.pdf
Page 10: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Any progress on any of the open problems?

Page 11: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can
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Page 3 of L20 notes
Page 12: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can
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Presentation Notes
Pages 1 & 2 of http://erikdemaine.org/papers/FixedAngle_WADS2011/ (covered under MIT Faculty Open Access Policy)
Page 13: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[Demaine & Eisenstat 2011]

Presenter
Presentation Notes
Figure 1 of http://erikdemaine.org/papers/FixedAngle_WADS2011/ (covered under MIT Faculty Open Access Policy)
Page 14: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[Demaine & Eisenstat 2011]

Presenter
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Figure 2 of http://erikdemaine.org/papers/FixedAngle_WADS2011/ (covered under MIT Faculty Open Access Policy)
Page 15: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[Demaine & Eisenstat 2011]

Presenter
Presentation Notes
Figures 2 & 3 of http://erikdemaine.org/papers/FixedAngle_WADS2011/ (covered under MIT Faculty Open Access Policy)
Page 16: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[Demaine & Eisenstat 2011]

rigid edge (unspinnable)

Presenter
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Figure 4 of http://erikdemaine.org/papers/FixedAngle_WADS2011/ (covered under MIT Faculty Open Access Policy)
Page 17: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[Demaine & Eisenstat 2011]

Presenter
Presentation Notes
Figure 7 of http://erikdemaine.org/papers/FixedAngle_WADS2011/ (covered under MIT Faculty Open Access Policy)
Page 18: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Erdős 1935

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Top: Figure 5.23 of GFALOP. Bottom: Scan from 1936 article (out of copyright), http://www.jstor.org/sici?sici=0002-9890(193512)42:10%3C625:PFS3%3E2.0.CO;2-2&
Page 19: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Erdős 1935

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Figure 5.23 of GFALOP
Page 20: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

de Sz. Nagy 1939

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Figure 5.22 of GFALOP
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Joss & Shannon 1973

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Figure 5.24 of GFALOP
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Demaine, Gassend, O’Rourke, Toussaint 2008

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Table 1 of http://erikdemaine.org/papers/Flips_DCG20/ (copyright held by authors)
Page 23: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Demaine, Gassend, O’Rourke, Toussaint 2008

Presenter
Presentation Notes
Table 1 of http://erikdemaine.org/papers/Flips_DCG20/ (copyright held by authors)
Page 24: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Demaine, Gassend, O’Rourke, Toussaint 2008

“The proof of this theorem, given by B. Sz. Nagy, is incorrect”

“Bing and Kazarinoff remark that Nagy’s proof is invalid, but there is no basis for this claim.”

Presenter
Presentation Notes
Table 1 of http://erikdemaine.org/papers/Flips_DCG20/ (copyright held by authors)
Page 25: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

de Sz. Nagy 1939

Presenter
Presentation Notes
Scan from 1939 article (out of copyright), http://www.jstor.org/sici?sici=0002-9890(193903)46:3%3C176:3%3E2.0.CO;2-S
Page 26: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

de Sz. Nagy 1939

Presenter
Presentation Notes
Scan from 1939 article (out of copyright), http://www.jstor.org/sici?sici=0002-9890(193903)46:3%3C176:3%3E2.0.CO;2-S
Page 27: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Demaine, Gassend, O’Rourke, Toussaint 2008

Presenter
Presentation Notes
Figure 5.26 of GFALOP
Page 28: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Demaine, Gassend, O’Rourke, Toussaint 2008

Presenter
Presentation Notes
Figure 3 of http://erikdemaine.org/papers/Flips_DCG20/ (copyright held by authors)
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Fevens, Hernandez,

Mesa, Morin, Soss, Toussaint

2001

Presenter
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Figure 5.27 of GFALOP
Page 30: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

Thurston 2001

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Figure 5.29 of GFALOP
Page 31: Plots by Erik using matplotlib · We’ve done several combinations of the constraints of equilateralness, equiangularity, and obtusehood for 3-D chains we want to know whether can

[Dumitrescu & Hilscher 2009]

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Figure 2 of http://arxiv.org/abs/0911.4146

ANACONDA IDLE matplotlib, numpy ...

ANACONDA IDLE matplotlib, numpy ...

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5 Introduction to Matplotlib - BYU ACMEacme.byu.edu/wp-content/uploads/2019/08/MatplotlibIntro19.pdf · 5 Introduction to Matplotlib Lab Objective: Matplotlib is the most omcmonly

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