Mod n cryptanalysis - Revision history

en>Gilo1969: fix citation with wikilinks embedded in URL

2014-12-21T17:28:40Z

fix citation with wikilinks embedded in URL

← Older revision		Revision as of 19:28, 21 December 2014
Line 1:		Line 1:
	~~'''Latin hypercube sampling''' ('''LHS''') is a [[statistics\|statistical]] method for generating a sample of plausible collections of parameter values~~ from ~~a [[multidimensional distribution]]. The [[Sampling (statistics)\|sampling method]] is often used to construct [[computer experiment]]s.~~		Panelbeater Bart Rines from Gillam, has many hobbies that include shopping, free coins fifa 14 hack and textiles. Has recently concluded a travel to La Louvière and Le Roeulx (Hainaut).<br><br>Here is my web blog; fifa 14 hack ios ([https://youtube.com/watch?v=HSoNAvTIeEc Read the Full Write-up])

	~~The LHS was described by McKay in 1979.<ref name = "C3M">{{cite journal~~
	~~\| last = McKay~~
	~~\| first = M.D.~~
	~~\| coauthors = Beckman~~, ~~R.J.; Conover, W.J.~~
	~~\|date=May 1979~~
	~~\| title = A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code~~
	~~\| journal = [[Technometrics]]~~
	~~\| volume = 21~~
	~~\| issue = 2~~
	~~\| pages = 239–245~~
	~~\| publisher = [[American Statistical Association]]~~
	~~\| issn = 0040-1706~~
	~~\| doi = 10.2307/1268522~~
	~~\| format = [[JSTOR]] Abstract~~
	~~\| laysummary =~~
	~~\| laysource =~~
	~~\| laydate =~~
	~~\| quote=~~
	~~\| osti = 5236110~~
	~~\| jstor = 1268522~~
	}}
	~~</ref> An independently equivalent technique~~ has been proposed by [[:lv:Vilnis Egl%C4%81js\|Eglājs]] in 1977.<ref>{{cite journal\|last=Eglajs\|first=V.\|coauthors=Audze P.\|title=New approach to the design of multifactor experiments\|journal=Problems of Dynamics and Strengths\|year=1977\|series=35\|pages=104–107\|publisher=Zinatne Publishing House\|location=Riga\|language=Russian}}</ref> It was further elaborated by [[Ronald L. Iman]], and ~~others<ref>{{cite journal \|last=Iman \|first=R~~.~~L. \|coauthors=Helton, J.C.; and [[James Edward Campbell\|Campbell, J.E.]] \|title=An approach~~ to ~~sensitivity analysis of computer models, Part 1. Introduction, input variable selection and preliminary variable assessment \|journal=Journal of Quality Technology \|volume=13 \|issue=3 \|pages=174–183~~ ~~\|year=1981 }}</ref> in 1981. Detailed computer codes~~ and ~~manuals were later published.<ref>{{cite book \|last=Iman \|first=R.L. \|coauthors=Davenport, J.M. ; Zeigler, D.K. \|title=Latin hypercube sampling~~ (~~program user's guide~~) ~~\|year=1980 \|osti=5571631}}</ref>~~

	In the context of statistical sampling, a square grid containing sample positions is a [[Latin square]] if (and only if) there is only one sample in each row and each column. A '''Latin [[hypercube]]''' is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned [[hyperplane]] containing it.

	~~When sampling a function of~~ <~~math~~>N<~~/math~~> ~~variables, the range of each variable~~ is ~~divided into <math>M</math> equally probable intervals. <math>M</math> sample points are then placed to satisfy the Latin hypercube requirements~~; ~~note that this forces the number of divisions, <math>M</math>, to be equal for each variable. Also note that this sampling scheme does not require more samples for more dimensions~~ (~~variables); this independence is one of the main advantages of this sampling scheme. Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far.~~

	~~The maximum number of combinations for a Latin Hypercube of <math>M</math> divisions and <math>N</math> variables (i.e., dimensions) can be computed with the following formula~~:

	~~<math>\left(\prod_{n=0}^{M-1} (M-n)\right)^{N-1} = (M!)^{N-1}<~~/~~math>~~

	~~For example, a Latin hypercube of <math>M = 4</math> divisions with <math>N = 2<~~/~~math> variables (i~~.~~e., a square) will have 24 possible combinations. A Latin hypercube of <math>M = 4<~~/~~math> divisions with <math>N~~ = ~~3</math> variables (i.e., a cube) will have 576 possible combinations.~~

	~~'''Orthogonal sampling''' adds~~ the requirement that the entire sample space must be sampled evenly. Although more efficient, orthogonal sampling strategy is more difficult to implement since all random samples must be generated simultaneously.

	~~[[Image:LHSsampling.png\|100px\|right~~]]

	~~In two dimensions the difference between random sampling, Latin Hypercube sampling and orthogonal sampling can be explained as follows:~~
	#In '''random sampling''' new sample points are generated without taking into account the previously generated sample points. One does thus not necessarily need to know beforehand how many sample points are needed.
	~~#In '''Latin Hypercube sampling''' one must first decide how many sample points to use and for each sample point remember in which row and column the sample point was taken.~~
	#In '''Orthogonal sampling''', the sample space is divided into equally probable subspaces. All sample points are then chosen simultaneously making sure that the total ensemble of sample points is a Latin Hypercube sample and that each subspace is sampled with the same density.

	Thus, orthogonal sampling ensures that the ensemble of random numbers is a very good representative of the real variability, LHS ensures that the ensemble of random numbers is representative of the real variability whereas traditional random sampling (sometimes called brute force) ~~is just an ensemble of random numbers without any guarantees.~~


	~~==References==~~
	~~<references/>~~


	~~==Further reading==~~
	*{{cite journal \|doi=10.2307/2291282 \|last=Tang \|first=B. \|title=Orthogonal Array-Based Latin Hypercubes \|journal=Journal of the American Statistical Association \|volume=88 \|issue=424 \|pages=1392–1397 \|year=1993 \|jstor=2291282 }}
	*{{cite journal \|last=Owen \|first=A.B. \|title=Orthogonal arrays for computer experiments, integration and visualization \|journal=Statistica Sinica \|volume=2 \|pages=439–452 \|year=1992 }}
	*{{cite journal \|doi=10.2307/2670057 \|last=Ye \|first=K.Q. \|title=Orthogonal column Latin hypercubes and their application in computer experiments \|journal=Journal of the American Statistical Association \|volume=93 \|issue=444 \|pages=1430–1439 \|year=1998 \|jstor=2670057 }}


	~~{{Experimental design}}~~
	~~{{Statistics}}~~
	~~[[Category:Sampling techniques]]~~
	~~[[Category:Latin squares]]~~
	~~[[Category:Design of experiments]]~~

en>BattyBot: /* References */fixed CS1 errors: dates & General fixes using AWB (9816)

2013-12-27T10:03:04Z

References: fixed CS1 errors: dates & General fixes using AWB (9816)

← Older revision		Revision as of 12:03, 27 December 2013
Line 1:		Line 1:
	Hi. The ~~author'~~s name ~~is Eusebio but rather he never really adored that name~~. ~~The hobby~~ for ~~him~~ ~~his kids is to~~ [~~http~~:~~//search~~.un.~~org/search?ie~~=~~utf8&site~~=~~un_org&output~~=~~xml_no_dtd&client~~=~~UN_Website_en&num~~=~~10&lr~~=~~lang_en&proxystylesheet~~=~~UN_Website_en&oe~~=~~utf8&q~~=~~finally+drive&Submit=Go finally drive~~] and ~~he's started doing it for several years~~. [~~http:~~/~~/www~~.~~Alexa~~.~~com/search?q~~=~~Auditing&r~~=~~topsites_index&p~~=~~bigtop Auditing~~] is ~~how he supports his own family~~. ~~Massachusetts~~ is ~~where~~ the ~~doctor and his wife live~~. ~~He's been working on his website~~ for ~~selected~~ time ~~now~~. ~~Check~~ the ~~game out here: http~~://~~prometeu~~.~~net~~<br><br>~~Here~~ is ~~my website~~: ~~[http~~://~~prometeu~~.~~net clash~~ of ~~clans hack download~~]		'''Latin hypercube sampling''' ('''LHS''') is a [[statistics\|statistical]] method for generating a sample of plausible collections of parameter values from a [[multidimensional distribution]]. The [[Sampling (statistics)\|sampling method]] is often used to construct [[computer experiment]]s.

			The LHS was described by McKay in 1979.<ref name = "C3M">{{cite journal
			\| last = McKay
			\| first = M.D.
			\| coauthors = Beckman, R.J.; Conover, W.J.
			\|date=May 1979
			\| title = A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
			\| journal = [[Technometrics]]
			\| volume = 21
			\| issue = 2
			\| pages = 239–245
			\| publisher = [[American Statistical Association]]
			\| issn = 0040-1706
			\| doi = 10.2307/1268522
			\| format = [[JSTOR]] Abstract
			\| laysummary =
			\| laysource =
			\| laydate =
			\| quote=
			\| osti = 5236110
			\| jstor = 1268522
			}}
			</ref> An independently equivalent technique has been proposed by [[:lv:Vilnis Egl%C4%81js\|Eglājs]] in 1977.<ref>{{cite journal\|last=Eglajs\|first=V.\|coauthors=Audze P.\|title=New approach to the design of multifactor experiments\|journal=Problems of Dynamics and Strengths\|year=1977\|series=35\|pages=104–107\|publisher=Zinatne Publishing House\|location=Riga\|language=Russian}}</ref> It was further elaborated by [[Ronald L. Iman]], and others<ref>{{cite journal \|last=Iman \|first=R.L. \|coauthors=Helton, J.C.; and [[James Edward Campbell\|Campbell, J.E.]] \|title=An approach to sensitivity analysis of computer models, Part 1. Introduction, input variable selection and preliminary variable assessment \|journal=Journal of Quality Technology \|volume=13 \|issue=3 \|pages=174–183 \|year=1981 }}</ref> in 1981. Detailed computer codes and manuals were later published.<ref>{{cite book \|last=Iman \|first=R.L. \|coauthors=Davenport, J.M. ; Zeigler, D.K. \|title=Latin hypercube sampling (program user's guide) \|year=1980 \|osti=5571631}}</ref>

			In the context of statistical sampling, a square grid containing sample positions is a [[Latin square]] if (and only if) there is only one sample in each row and each column. A '''Latin [[hypercube]]''' is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned [[hyperplane]] containing it.

			When sampling a function of <math>N</math> variables, the range of each variable is divided into <math>M</math> equally probable intervals. <math>M</math> sample points are then placed to satisfy the Latin hypercube requirements; note that this forces the number of divisions, <math>M</math>, to be equal for each variable. Also note that this sampling scheme does not require more samples for more dimensions (variables); this independence is one of the main advantages of this sampling scheme. Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far.

			The maximum number of combinations for a Latin Hypercube of <math>M</math> divisions and <math>N</math> variables (i.e., dimensions) can be computed with the following formula:

			<math>\left(\prod_{n=0}^{M-1} (M-n)\right)^{N-1} = (M!)^{N-1}</math>

			For example, a Latin hypercube of <math>M = 4</math> divisions with <math>N = 2</math> variables (i.e., a square) will have 24 possible combinations. A Latin hypercube of <math>M = 4</math> divisions with <math>N = 3</math> variables (i.e., a cube) will have 576 possible combinations.

			'''Orthogonal sampling''' adds the requirement that the entire sample space must be sampled evenly. Although more efficient, orthogonal sampling strategy is more difficult to implement since all random samples must be generated simultaneously.

			[[Image:LHSsampling.png\|100px\|right]]

			In two dimensions the difference between random sampling, Latin Hypercube sampling and orthogonal sampling can be explained as follows:
			#In '''random sampling''' new sample points are generated without taking into account the previously generated sample points. One does thus not necessarily need to know beforehand how many sample points are needed.
			#In '''Latin Hypercube sampling''' one must first decide how many sample points to use and for each sample point remember in which row and column the sample point was taken.
			#In '''Orthogonal sampling''', the sample space is divided into equally probable subspaces. All sample points are then chosen simultaneously making sure that the total ensemble of sample points is a Latin Hypercube sample and that each subspace is sampled with the same density.

			Thus, orthogonal sampling ensures that the ensemble of random numbers is a very good representative of the real variability, LHS ensures that the ensemble of random numbers is representative of the real variability whereas traditional random sampling (sometimes called brute force) is just an ensemble of random numbers without any guarantees.


			==References==
			<references/>


			==Further reading==
			*{{cite journal \|doi=10.2307/2291282 \|last=Tang \|first=B. \|title=Orthogonal Array-Based Latin Hypercubes \|journal=Journal of the American Statistical Association \|volume=88 \|issue=424 \|pages=1392–1397 \|year=1993 \|jstor=2291282 }}
			*{{cite journal \|last=Owen \|first=A.B. \|title=Orthogonal arrays for computer experiments, integration and visualization \|journal=Statistica Sinica \|volume=2 \|pages=439–452 \|year=1992 }}
			*{{cite journal \|doi=10.2307/2670057 \|last=Ye \|first=K.Q. \|title=Orthogonal column Latin hypercubes and their application in computer experiments \|journal=Journal of the American Statistical Association \|volume=93 \|issue=444 \|pages=1430–1439 \|year=1998 \|jstor=2670057 }}


			{{Experimental design}}
			{{Statistics}}
			[[Category:Sampling techniques]]
			[[Category:Latin squares]]
			[[Category:Design of experiments]]

en>Thehelpfulbot: r2.6.5) (Robot: Adding fr:Cryptanalyse Mod n

2012-05-20T22:33:54Z

r2.6.5) (Robot: Adding fr:Cryptanalyse Mod n

New page

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