en>Headbomb: Various citation cleanup + AWB fixes, added orphan tag using AWB

2014-08-24T04:39:31Z

Various citation cleanup + AWB fixes, added orphan tag using AWB

en>Squids and Chips: Disambiguate RF to Radio frequency using popups

2013-04-22T22:00:19Z

Disambiguate RF to Radio frequency using popups

← Older revision		Revision as of 00:00, 23 April 2013
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	~~Footwear is each~~ of ~~essential items to top off one'~~s ~~outfit~~. ~~There is absolutely nothing to say about fashion trend many~~ of ~~us leave aside shoes or boots~~. ~~Nowadays~~, ~~shoes not only protect your feet from cold or obstacle~~, ~~they play more important role~~ on ~~fashion advised. For most~~ people, both of ~~them are crucial~~. ~~If you are searching for one kind~~ of ~~shoes which can make you go~~ in the ~~fashion trend~~ and ~~also comfy to wear in winter~~, ~~Ugg shoes are the chosen choice.~~<br><br>~~These days the winds of change are blowing~~ through ~~Healthcare~~, ~~Automotive~~, ~~Banking~~, ~~and Government to name just~~ a ~~few~~. ~~How about on~~ the ~~inside field where you want to try? Are you familiar that's not~~ a ~~problem latest industry trends? Do you know how these trends are affecting the job~~-~~market~~ in ~~your soul area and also the company what your want~~ to ~~dab? You should. So onboard Infotrac~~, ~~Google~~, ~~the Wall Street Journal~~ - ~~identify the ugg news~~, ~~explore the analysis~~, ~~learn. Putting your job~~-~~application in perspective could be~~ a ~~critical strength that will put you in front of untamed dogs.~~<br><br>~~They UGG Australia ugg boots pular Po change~~ the ~~primary in two ways~~. ~~Started with traditional sour cream party love UGG boots,~~ and ~~then a wooden button~~, ~~from their best~~-~~selling book~~, as in ~~Austria Cardy~~, ~~UGG~~. ~~Bring them together~~, ~~you will unquestionably have this year, UGG style~~ - ~~Bailey tab~~. ~~cheap ugg bailey button that could be deducted Bailey~~, ~~including uggstore uding in 5 colors black~~, ~~gray~~, ~~chestnut~~, ~~chocolate and sand~~. ~~Headquarters footwear retailers receive all 5 colors to stock in their seven stores~~, ~~has been~~, and ~~positive results~~. ~~Footwear~~. ~~Massachusetts ugg boots~~, ~~uggs classic cardy cheap nager~~, ~~Andrew monarch, said~~: ~~"This is for you to sell in the event the Bailey~~, ~~but wait~~, ~~how fast~~.<~~br><br~~>~~Buying cheap snowboard boots is kind of hard to call because one way~~ links ~~will tell you never get cheap boots, having said that i say for anyone who is only intending on snowboarding several times a year then is actually also o~~.k. ~~pay for cheap snowboard boots~~. ~~cheap boots should cost around $100-$120(sometimes cheaper online)~~.~~<br><br>Here~~'s ~~neutral opinion~~ . ~~for you: two back I purchased a pair of casual mid-calf black wedge boots using a tie detail around the ankle~~. ~~I spent around my normal shoe budget generally allows, but We had arrived convinced these people would upward paying for themselves~~. ~~Turns out, I'm more than right! Here i am 24 months later with boots that meet all three of the criteria~~. ~~They're casual provides you with can wear them with a skirt your market fall look sundress using a cardigan regarding spring, they're trendy (~~and ~~age appropriate) and Allow me to into my third winter with them still being on trend hence they are age-old~~.~~<br><br>Fashion and luxury~~. ~~Women care more details on fashion~~ and ~~wonder than warmth and comfy on~~ the ~~boots, and also women's features. But UGG Boots combine all these features, which give natural disaster ? choice~~ for ~~females.<br><br>Here is more info on~~ [~~http~~://~~horizonafrica~~.com/~~img~~/ ~~ugg outlet~~] ~~look into our own web site~~.		In [[mathematical logic]] and [[computer science]], '''homotopy type theory''' ('''HoTT''') attempts to give an account of the semantics of [[intensional type theory]] using the framework of (abstract) [[homotopy theory]], in particular [[Quillen model category\|Quillen model categories]] and [[weak factorization system]]s. Conversely, intensional type theory forms a logic ([[internal language]]) for homotopy theory.

			== Development ==
			{{expand section\|date=September 2013}}

			The [[Institute for Advanced Study]] held a [http://www.math.ias.edu/sp/univalent special year] for intensive work on developing homotopy type theory in the academic year 2012-2013, jointly organised by [[Steve Awodey]], [[Thierry Coquand]] and [[Vladimir Voevodsky]], which numerous mathematicians and computer scientists attended.

			Out of this, a book, ''[http://homotopytypetheory.org/book/ Homotopy Type Theory]'', was born. Unusually for a mathematics text, it was developed collaboratively and in the open on [[GitHub]], is released under a [[Creative Commons license]] that allows people to [[fork (software development)\|fork]] their own version of the book, and is both purchasable in print and downloadable free of charge.

			Also, unusually, key parts of the mathematics were implemented in the computer proof assistant [[Coq]]<ref>{{cite web\|url=https://github.com/HoTT/HoTT\|title=Homotopy Type Theory github repository}}</ref> and [[Agda (programming language)\|Agda]],<ref>{{cite web\|url=https://github.com/HoTT/HoTT-Agda\|title=Homotopy Type Theory Agda files}}</ref> where Agda is broadly equivalent to Coq but has a greater emphasis on functional programming than on constructing proofs through tactics. In both cases, type checking—or, viewed another way, computer proof verification—guarantees that the proofs were valid deductions, assuming that the proof assistant used was implemented correctly.

			Open questions include a computational interpretation of homotopy type theory. Work is also underway to investigate new types of computer proof assistants with the goal of better supporting homotopy type theory.

			== Interpretation ==
			{{see also\|Curry–Howard correspondence}}
			{\| class=wikitable
			! Intensional type theory !! Homotopy theory
			\|-
			\| types, <math>A</math> \|\| spaces
			\|-
			\| terms, <math>a</math> \|\| maps
			\|-
			\| <math>a:A</math> \|\| <math>a\in A</math>
			\|-
			\| [[dependent type]], <math>x:A</math> ⊢ <math> B(x)</math> \|\| [[fibration]], <math>B \to A</math>
			\|-
			\| [[identity type]], <math>\mathrm{Id}_A(a,b)</math> \|\| [[path space]]
			\|-
			\| <math>p:\mathrm{Id}_A(a,b)</math> \|\| [[Path (topology)\|path]], <math>p:a\mapsto b</math>
			\|-
			\| <math>\alpha:\mathrm{Id}_{\mathrm{Id}_A(a,b)}(p,q)</math> \|\| [[homotopy]], <math>\alpha:p\Rightarrow q</math>
			\|}

			== See also ==
			* [[weak ω-groupoid]]
			* [[Homotopy hypothesis]]
			* [[Univalence axiom]]
			* [[Vladimir Voevodsky]] – Initiator of the ''Univalent Foundations of Mathematics'' research program.
			* [[Calculus of constructions]]
			* [[Intuitionistic type theory]]
			* [[Curry–Howard isomorphism]]

			== References and further reading ==
			* [http://homotopytypetheory.org/book/ ''Homotopy Type Theory: Univalent Foundations of Mathematics'']. The Univalent Foundations Program. [[Institute for Advanced Study]].
			* [[Steve Awodey]] (2010). "[http://www.andrew.cmu.edu/user/awodey/preprints/TTH.pdf Type theory and homotopy]". To appear.
			* Martin Hofmann and [[Thomas Streicher]] (1996), [http://www.mathematik.tu-darmstadt.de/~streicher/venedig.ps.gz The groupoid interpretation of type theory], in Sambin, Giovanni (ed.) et al., Twenty-five years of constructive type theory. Proceedings of a congress, Venice, Italy, October 19–21, 1995.
			* Michael A. Warren (2008), [http://www.math.ias.edu/~mwarren/Papers/phd.pdf Homotopy theoretic aspects of constructive type theory], Ph.D. thesis, Carnegie Mellon University.
			* S. Awodey and M. A. Warren (2009), [http://www.andrew.cmu.edu/user/awodey/preprints/homotopy.pdf Homotopy theoretic models of identity types], Mathematical Proceedings of the Cambridge Philosophical Society.
			* Egbert Rijke (2012) [http://hottheory.files.wordpress.com/2012/08/hott2.pdf Homotopy Type Theory], Masters Thesis, Utrecht University.

			== References ==
			<references />

			== External links ==
			* [http://www.homotopytypetheory.org/ Homotopy Type Theory]
			* {{nlab\|id=homotopy+type+theory\|title=Homotopy type theory}}
			* [http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations.html Vladimir Voevodsky's webpage on the Univalent Foundations]
			* [http://www.andrew.cmu.edu/user/awodey/htt.html Homotopy Type Theory and the Univalent Foundations of Mathematics] by Steve Awodey
			* [http://video.ias.edu/univalent/awodey "Constructive Type Theory and Homotopy"] – Video lecture by Steve Awodey at the [[Institute for Advanced Study]]
			* [https://groups.google.com/forum/#!forum/homotopytypetheory Homotopy Type Theory Google Group]
			* [irc://irc.freenode.net/##hott Homotopy Type Theory IRC channel]

			[[Category:Type theory]]
			[[Category:Homotopy theory]]

en>Cornercase: Fixed typo in Shinnar-LeRoux

2012-04-03T20:37:34Z

Fixed typo in Shinnar-LeRoux

New page

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Shinnar-Le Roux Algorithm - Revision history

en>Headbomb: Various citation cleanup + AWB fixes, added orphan tag using AWB

en>Squids and Chips: Disambiguate RF to Radio frequency using popups

en>Cornercase: Fixed typo in Shinnar-LeRoux