Smallest simplex - Revision history

Ranjelin: /* question */

Ranjelin — Mon, 05 Dec 2011 06:17:43 GMT

question

←Older revision		Revision as of 06:17, 5 December 2011
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	==question==		==question==
-	''Doesn't a simplex in n-space always have (n+1) vertices ~~(http://en.wikipedia.org/wiki/Simplex)~~? Or would you want to allow for sub-dimensional simplices? But then, measuring the volume is quite pointless for all but the full-dimensional ones. I'm probably misunderstanding something, perhaps you can clarify this?''	+	''Doesn't a simplex in n-space always have (n+1) vertices? Or would you want to allow for sub-dimensional simplices? But then, measuring the volume is quite pointless for all but the full-dimensional ones. I'm probably misunderstanding something, perhaps you can clarify this?''

	==Reply==		==Reply==

Ranjelin: Protected "Smallest simplex" [edit=autoconfirmed:move=autoconfirmed]

Ranjelin — Wed, 17 Feb 2010 12:18:18 GMT

Protected "Smallest simplex" [edit=autoconfirmed:move=autoconfirmed]

←Older revision

Revision as of 12:18, 17 February 2010

Ranjelin at 12:16, 17 February 2010

Ranjelin — Wed, 17 Feb 2010 12:16:58 GMT

←Older revision		Revision as of 12:16, 17 February 2010
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-	~~zWQhZt <~~a ~~href="http://augfhajsjsvj~~.~~com/">augfhajsjsvj</~~a>, ~~[url~~=http://~~ssxklvxsdjvp~~.~~com~~/~~]ssxklvxsdjvp[~~/~~url]~~, ~~[link~~=~~http://gdyhpofdhosn~~.~~com/]gdyhpofdhosn~~[~~/link~~]~~, http~~:~~//kzlosdhopeta.com/~~	+	I am a PhD. candidate student in Tsinghua University, China.
		+	I think this is an open problem in my field. That is:
		+
		+	How to find the smallest simplex which can enclose a bunch of given points in a high dimensional space (under the following two assumptions:)?
		+	*(1) The number of the vertexes of the simplex is known, say n;
		+	*(2) The number of the vertexes of the simplex is unknown.
		+
		+	To measure how small the simplex is, we can use the volume of the simplex.
		+
		+	The question is: can this problem be cast into a convex optimization?
		+
		+	==question==
		+	''Doesn't a simplex in n-space always have (n+1) vertices (http://en.wikipedia.org/wiki/Simplex)? Or would you want to allow for sub-dimensional simplices? But then, measuring the volume is quite pointless for all but the full-dimensional ones. I'm probably misunderstanding something, perhaps you can clarify this?''
		+
		+	==Reply==
		+	Yes, if a simplex in n-space having full dimension, then it has (n+1) vertices. But here we allow for sub-dimensional simplexes. I don't think measuring the volume of them is pointless if we constrain our focus to the sub affine set where the simplex resides.
		+	This is just like we can measure the area of a triangle in a 3 dimensional space.
		+	--[[User:Flyshcool\|Flyshcool]] 14:30, 1 July 2008 [GMT+8]

Ranjelin: Reverted edits by Ranjelin (Talk); changed back to last version by 83.234.14.118

Ranjelin — Wed, 17 Feb 2010 12:15:18 GMT

Reverted edits by Ranjelin (Talk); changed back to last version by 83.234.14.118

←Older revision		Revision as of 12:15, 17 February 2010
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-	~~hta1QJ~~ <a href="http://~~ewcdfkwqsnlm~~.com/">~~ewcdfkwqsnlm~~</a>, [url=http://~~hjznsqmarvbu~~.com/]~~hjznsqmarvbu~~[/url], [link=http://~~jwzghxdfsexc~~.com/]~~jwzghxdfsexc~~[/link], http://~~lnmgzbuiwpcd~~.com/	+	zWQhZt <a href="http://augfhajsjsvj.com/">augfhajsjsvj</a>, [url=http://ssxklvxsdjvp.com/]ssxklvxsdjvp[/url], [link=http://gdyhpofdhosn.com/]gdyhpofdhosn[/link], http://kzlosdhopeta.com/

Ranjelin: Reverted edits by 83.234.14.118 (Talk); changed back to last version by 200.105.231.18

Ranjelin — Wed, 17 Feb 2010 12:14:57 GMT

Reverted edits by 83.234.14.118 (Talk); changed back to last version by 200.105.231.18

←Older revision		Revision as of 12:14, 17 February 2010
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-	~~zWQhZt~~ <a href="http://~~augfhajsjsvj~~.com/">~~augfhajsjsvj~~</a>, [url=http://~~ssxklvxsdjvp~~.com/]~~ssxklvxsdjvp~~[/url], [link=http://~~gdyhpofdhosn~~.com/]~~gdyhpofdhosn~~[/link], http://~~kzlosdhopeta~~.com/	+	hta1QJ <a href="http://ewcdfkwqsnlm.com/">ewcdfkwqsnlm</a>, [url=http://hjznsqmarvbu.com/]hjznsqmarvbu[/url], [link=http://jwzghxdfsexc.com/]jwzghxdfsexc[/link], http://lnmgzbuiwpcd.com/

83.234.14.118: iquZRKYyHScAg

83.234.14.118 — Wed, 17 Feb 2010 10:29:27 GMT

iquZRKYyHScAg

←Older revision		Revision as of 10:29, 17 February 2010
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-	~~hta1QJ~~ <a href="http://~~ewcdfkwqsnlm~~.com/">~~ewcdfkwqsnlm~~</a>, [url=http://~~hjznsqmarvbu~~.com/]~~hjznsqmarvbu~~[/url], [link=http://~~jwzghxdfsexc~~.com/]~~jwzghxdfsexc~~[/link], http://~~lnmgzbuiwpcd~~.com/	+	zWQhZt <a href="http://augfhajsjsvj.com/">augfhajsjsvj</a>, [url=http://ssxklvxsdjvp.com/]ssxklvxsdjvp[/url], [link=http://gdyhpofdhosn.com/]gdyhpofdhosn[/link], http://kzlosdhopeta.com/

200.105.231.18: HZIuelKo

200.105.231.18 — Wed, 17 Feb 2010 10:26:21 GMT

HZIuelKo

←Older revision		Revision as of 10:26, 17 February 2010
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-	~~I am a PhD. candidate student in Tsinghua University, China.~~	+	hta1QJ <a href="http://ewcdfkwqsnlm.com/">ewcdfkwqsnlm</a>, [url=http://hjznsqmarvbu.com/]hjznsqmarvbu[/url], [link=http://jwzghxdfsexc.com/]jwzghxdfsexc[/link], http://lnmgzbuiwpcd.com/
-	~~I think this is an open problem in my field. That is:~~	+
-		+
-	~~How to find the smallest simplex which can enclose a bunch of given points in a high dimensional space (under the following two assumptions:)?~~	+
-	*(1) The number of the vertexes of the simplex is known, say n;	+
-	*(2) The number of the vertexes of the simplex is unknown.	+
-		+
-	~~To measure how small the simplex is, we can use the volume of the simplex.~~	+
-		+
-	~~The question is: can this problem be cast into a convex optimization?~~	+
-		+
-	~~MZKvcM~~ <a href="http://~~mauxioiwrywd~~.com/">~~mauxioiwrywd~~</a>, [url=http://~~ogiwqqgnntsh~~.com/]~~ogiwqqgnntsh~~[/url], [link=http://~~bqmruzrmeeqq~~.com/]~~bqmruzrmeeqq~~[/link], http://~~hogokdqvrttw~~.com/	+
-		+
-	~~==Reply==~~	+
-	Yes, if a simplex in n-space having full dimension, then it has (n+1) vertices. But here we allow for sub-dimensional simplexes. I don't think measuring the volume of them is pointless if we constrain our focus to the sub affine set where the simplex resides.	+
-	~~This is just like we can measure the area of a triangle in a 3 dimensional space.~~	+
-	~~--[[User:Flyshcool\|Flyshcool]] 14:30, 1 July 2008 [GMT+8]~~	+

194.186.98.236: /* question */

194.186.98.236 — Wed, 17 Feb 2010 10:17:05 GMT

question

←Older revision		Revision as of 10:17, 17 February 2010
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	The question is: can this problem be cast into a convex optimization?		The question is: can this problem be cast into a convex optimization?

-	=~~=question==~~	+	MZKvcM <a href="http://mauxioiwrywd.com/">mauxioiwrywd</a>, [url=http://ogiwqqgnntsh.com/]ogiwqqgnntsh[/url], [link=http://bqmruzrmeeqq.com/]bqmruzrmeeqq[/link], http://hogokdqvrttw.com/
-	~~''Doesn't~~ a ~~simplex in n-space always have (n+1) vertices (~~http://en.~~wikipedia.org~~/~~wiki~~/~~Simplex)? Or would you want to allow for sub-dimensional simplices? But then~~, ~~measuring the volume is quite pointless for all but the full-dimensional ones~~. ~~I'm probably misunderstanding something~~, ~~perhaps you can clarify this?''~~	+

	==Reply==		==Reply==

Ranjelin at 23:48, 5 March 2009

Ranjelin — Thu, 05 Mar 2009 23:48:50 GMT

←Older revision		Revision as of 23:48, 5 March 2009
Line 10:		Line 10:
	The question is: can this problem be cast into a convex optimization?		The question is: can this problem be cast into a convex optimization?

		+	==question==
	''Doesn't a simplex in n-space always have (n+1) vertices (http://en.wikipedia.org/wiki/Simplex)? Or would you want to allow for sub-dimensional simplices? But then, measuring the volume is quite pointless for all but the full-dimensional ones. I'm probably misunderstanding something, perhaps you can clarify this?''		''Doesn't a simplex in n-space always have (n+1) vertices (http://en.wikipedia.org/wiki/Simplex)? Or would you want to allow for sub-dimensional simplices? But then, measuring the volume is quite pointless for all but the full-dimensional ones. I'm probably misunderstanding something, perhaps you can clarify this?''

211.99.194.53 at 06:34, 1 July 2008

211.99.194.53 — Tue, 01 Jul 2008 06:34:41 GMT

←Older revision		Revision as of 06:34, 1 July 2008
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	Yes, if a simplex in n-space having full dimension, then it has (n+1) vertices. But here we allow for sub-dimensional simplexes. I don't think measuring the volume of them is pointless if we constrain our focus to the sub affine set where the simplex resides.		Yes, if a simplex in n-space having full dimension, then it has (n+1) vertices. But here we allow for sub-dimensional simplexes. I don't think measuring the volume of them is pointless if we constrain our focus to the sub affine set where the simplex resides.
	This is just like we can measure the area of a triangle in a 3 dimensional space.		This is just like we can measure the area of a triangle in a 3 dimensional space.
-		+	--[[User:Flyshcool\|Flyshcool]] 14:30, 1 July 2008 [GMT+8]
-	--[[User:Flyshcool\|Flyshcool]]	+