Regular matroid - Revision history

en>Rjwilmsi: /* Characterizations */Added 1 doi to a journal cite using AWB (10222)

2014-06-08T13:11:47Z

Characterizations: Added 1 doi to a journal cite using AWB (10222)

← Older revision		Revision as of 15:11, 8 June 2014
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	~~In [[mathematics]] — specifically, in [[large deviations theory]] — the '''contraction principle'''~~ is ~~a [[theorem]] that states how a large deviation principle on one space "[[push forward\|pushes forward]]"~~ to ~~a large deviation principle on another space ''via~~'~~' a [[continuous function]]~~.		Alyson is what my spouse loves to contact me but I don't like when people use my full name. It's not a typical factor but what she likes performing is to perform domino but she doesn't have the time lately. He works as a bookkeeper. Her family life in Ohio but her spouse desires them to move.<br><br>My web-site :: good psychic ([http://www.aseandate.com/index.php?m=member_profile&p=profile&id=13352970 mouse click the following post])

	~~==Statement of the theorem==~~

	~~Let ''X'' and ''Y'~~' ~~be [[Hausdorff space\|Hausdorff]] [[topological space]]~~s ~~and let (''μ''<sub>''ε''</sub>)<sub>''ε''>0</sub> be~~ a ~~family of [[probability measure]]s on ''X~~'~~' that satisfies~~ the ~~large deviation principle with [[rate function]] ''I'' : ''X'' → [0, +∞]~~. ~~Let ''T'' : ''X'' → ''Y'' be~~ a continuous function, and let ''ν''<sub>''ε''</sub> = ''T''<sub>∗</sub>(''μ''<sub>''ε''</sub>) be the [[Pushforward measure\|push-forward measure]] of ''μ''<sub>''ε''</sub> by ''T'', i.e.~~, for each [[measurable set]]/event ''E'' ⊆ ''Y'', ''ν''~~<~~sub~~>~~''ε''~~<~~/sub~~>~~(''E'') = ''μ''<sub>''ε''</sub>(''T''<sup>−1</sup>(''E'')). Let~~

	:~~<math>J(y)~~ :~~= \inf \big\{ I(x) \big\| x \in X \mbox{ and } T~~(~~x) = y \big\},</math>~~

	~~with the convention that the [~~[~~infimum]] of ''I'' over the [[empty set]] ∅ is +∞. Then~~:
	* ''J'' : ''Y'' → [0, +∞] is a rate function on ''Y'',
	* ''J'' is a good rate function on ''Y'' if ''I'' is a good rate function on ''X'', and
	* (''ν''<sub>''ε''</~~sub>)<sub>''ε''>0<~~/~~sub> satisfies the large deviation principle on ''Y'' with rate function ''J''~~.

	~~==References==~~

	* {{cite book
	~~\| last= Dembo~~
	~~\| first = Amir~~
	~~\| coauthors = Zeitouni, Ofer~~
	~~\| title = Large deviations techniques and applications~~
	~~\| series = Applications of Mathematics (New York) 38~~
	~~\| edition = Second edition~~
	~~\| publisher = Springer-Verlag~~
	~~\| location = New York~~
	~~\| year = 1998~~
	~~\| pages = xvi+396~~
	~~\| isbn = 0-387-98406-2~~
	~~\| mr = 1619036~~
	~~}} (See chapter 4~~.2.1)
	* {{cite book
	~~\| last~~ = ~~den Hollander~~
	~~\| first~~ = ~~Frank~~
	~~\| title~~ = ~~Large deviations~~
	~~\| series = [[Fields Institute]] Monographs 14~~
	~~\| publisher = [[American Mathematical Society]]~~
	~~\| location = Providence, RI~~
	~~\| year = 2000~~
	~~\| pages = x+143~~
	~~\| isbn = 0-8218-1989-5~~
	~~\| mr = 1739680~~
	}}

	~~[[Category:Asymptotic analysis]]~~
	~~[[Category:Large deviations theory]]~~
	~~[[Category:Mathematical principles]]~~
	~~[[Category:Probability theorems]~~]

en>David Eppstein: link oxley

2013-03-21T05:26:01Z

link oxley

← Older revision		Revision as of 07:26, 21 March 2013
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	~~Andrew Berryhill~~ is ~~what his wife loves~~ to ~~call him~~ and ~~he completely digs~~ that ~~title~~. ~~To climb is some thing I truly enjoy doing~~. I'~~ve usually cherished residing in Kentucky but now~~ I'~~m considering other options~~. ~~Distributing manufacturing~~ is ~~how he makes~~ a ~~residing.~~<br><br>~~my page [http:~~/~~/clothingcarearchworth~~.~~com/index~~.~~php?document_srl~~=~~441551&mid~~=~~customer_review real psychic~~]		In [[mathematics]] — specifically, in [[large deviations theory]] — the '''contraction principle''' is a [[theorem]] that states how a large deviation principle on one space "[[push forward\|pushes forward]]" to a large deviation principle on another space ''via'' a [[continuous function]].

			==Statement of the theorem==

			Let ''X'' and ''Y'' be [[Hausdorff space\|Hausdorff]] [[topological space]]s and let (''μ''<sub>''ε''</sub>)<sub>''ε''>0</sub> be a family of [[probability measure]]s on ''X'' that satisfies the large deviation principle with [[rate function]] ''I'' : ''X'' → [0, +∞]. Let ''T'' : ''X'' → ''Y'' be a continuous function, and let ''ν''<sub>''ε''</sub> = ''T''<sub>∗</sub>(''μ''<sub>''ε''</sub>) be the [[Pushforward measure\|push-forward measure]] of ''μ''<sub>''ε''</sub> by ''T'', i.e., for each [[measurable set]]/event ''E'' ⊆ ''Y'', ''ν''<sub>''ε''</sub>(''E'') = ''μ''<sub>''ε''</sub>(''T''<sup>−1</sup>(''E'')). Let

			:<math>J(y) := \inf \big\{ I(x) \big\| x \in X \mbox{ and } T(x) = y \big\},</math>

			with the convention that the [[infimum]] of ''I'' over the [[empty set]] ∅ is +∞. Then:
			* ''J'' : ''Y'' → [0, +∞] is a rate function on ''Y'',
			* ''J'' is a good rate function on ''Y'' if ''I'' is a good rate function on ''X'', and
			* (''ν''<sub>''ε''</sub>)<sub>''ε''>0</sub> satisfies the large deviation principle on ''Y'' with rate function ''J''.

			==References==

			* {{cite book
			\| last= Dembo
			\| first = Amir
			\| coauthors = Zeitouni, Ofer
			\| title = Large deviations techniques and applications
			\| series = Applications of Mathematics (New York) 38
			\| edition = Second edition
			\| publisher = Springer-Verlag
			\| location = New York
			\| year = 1998
			\| pages = xvi+396
			\| isbn = 0-387-98406-2
			\| mr = 1619036
			}} (See chapter 4.2.1)
			* {{cite book
			\| last = den Hollander
			\| first = Frank
			\| title = Large deviations
			\| series = [[Fields Institute]] Monographs 14
			\| publisher = [[American Mathematical Society]]
			\| location = Providence, RI
			\| year = 2000
			\| pages = x+143
			\| isbn = 0-8218-1989-5
			\| mr = 1739680
			}}

			[[Category:Asymptotic analysis]]
			[[Category:Large deviations theory]]
			[[Category:Mathematical principles]]
			[[Category:Probability theorems]]

en>David Eppstein: polynomial time recognizability

2012-08-30T23:58:38Z

polynomial time recognizability

New page

Andrew Berryhill is what his wife loves to call him and he completely digs that title. To climb is some thing I truly enjoy doing. I've usually cherished residing in Kentucky but now I'm considering other options. Distributing manufacturing is how he makes a residing.<br><br>my page [http://clothingcarearchworth.com/index.php?document_srl=441551&mid=customer_review real psychic]

← Older revision		Revision as of 15:11, 8 June 2014
Line 1:		Line 1:
	~~In [[mathematics]] — specifically, in [[large deviations theory]] — the '''contraction principle'''~~ is ~~a [[theorem]] that states how a large deviation principle on one space "[[push forward\|pushes forward]]"~~ to ~~a large deviation principle on another space ''via~~'~~' a [[continuous function]]~~.		Alyson is what my spouse loves to contact me but I don't like when people use my full name. It's not a typical factor but what she likes performing is to perform domino but she doesn't have the time lately. He works as a bookkeeper. Her family life in Ohio but her spouse desires them to move.<br><br>My web-site :: good psychic ([http://www.aseandate.com/index.php?m=member_profile&p=profile&id=13352970 mouse click the following post])

	~~==Statement of the theorem==~~

	~~Let ''X'' and ''Y'~~' ~~be [[Hausdorff space\|Hausdorff]] [[topological space]]~~s ~~and let (''μ''<sub>''ε''</sub>)<sub>''ε''>0</sub> be~~ a ~~family of [[probability measure]]s on ''X~~'~~' that satisfies~~ the ~~large deviation principle with [[rate function]] ''I'' : ''X'' → [0, +∞]~~. ~~Let ''T'' : ''X'' → ''Y'' be~~ a continuous function, and let ''ν''<sub>''ε''</sub> = ''T''<sub>∗</sub>(''μ''<sub>''ε''</sub>) be the [[Pushforward measure\|push-forward measure]] of ''μ''<sub>''ε''</sub> by ''T'', i.e.~~, for each [[measurable set]]/event ''E'' ⊆ ''Y'', ''ν''~~<~~sub~~>~~''ε''~~<~~/sub~~>~~(''E'') = ''μ''<sub>''ε''</sub>(''T''<sup>−1</sup>(''E'')). Let~~

	:~~<math>J(y)~~ :~~= \inf \big\{ I(x) \big\| x \in X \mbox{ and } T~~(~~x) = y \big\},</math>~~

	~~with the convention that the [~~[~~infimum]] of ''I'' over the [[empty set]] ∅ is +∞. Then~~:
	* ''J'' : ''Y'' → [0, +∞] is a rate function on ''Y'',
	* ''J'' is a good rate function on ''Y'' if ''I'' is a good rate function on ''X'', and
	* (''ν''<sub>''ε''</~~sub>)<sub>''ε''>0<~~/~~sub> satisfies the large deviation principle on ''Y'' with rate function ''J''~~.

	~~==References==~~

	* {{cite book
	~~\| last= Dembo~~
	~~\| first = Amir~~
	~~\| coauthors = Zeitouni, Ofer~~
	~~\| title = Large deviations techniques and applications~~
	~~\| series = Applications of Mathematics (New York) 38~~
	~~\| edition = Second edition~~
	~~\| publisher = Springer-Verlag~~
	~~\| location = New York~~
	~~\| year = 1998~~
	~~\| pages = xvi+396~~
	~~\| isbn = 0-387-98406-2~~
	~~\| mr = 1619036~~
	~~}} (See chapter 4~~.2.1)
	* {{cite book
	~~\| last~~ = ~~den Hollander~~
	~~\| first~~ = ~~Frank~~
	~~\| title~~ = ~~Large deviations~~
	~~\| series = [[Fields Institute]] Monographs 14~~
	~~\| publisher = [[American Mathematical Society]]~~
	~~\| location = Providence, RI~~
	~~\| year = 2000~~
	~~\| pages = x+143~~
	~~\| isbn = 0-8218-1989-5~~
	~~\| mr = 1739680~~
	}}

	~~[[Category:Asymptotic analysis]]~~
	~~[[Category:Large deviations theory]]~~
	~~[[Category:Mathematical principles]]~~
	~~[[Category:Probability theorems]~~]