Equidiagonal quadrilateral - Revision history

en>Loraof: /* Relation to other types of quadrilaterals */ name and area of midsquare quadrilateral

2015-01-10T15:46:38Z

Relation to other types of quadrilaterals: name and area of midsquare quadrilateral

← Older revision		Revision as of 17:46, 10 January 2015
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	~~'''Probalign''' is a sequence alignment tool that calculates a maximum expected accuracy alignment using partition function posterior probabilities~~.~~<ref>U~~. ~~Roshan and D. R~~. Livesay, Probalign: multiple sequence alignment using partition function posterior probabilities, Bioinformatics, 22(22):2715-21, 2006 ([http://bioinformatics.oxfordjournals.org/cgi/reprint/btl472?ijkey=GR3m5VV6yTz1jEx&keytype=ref PDF])</ref> Base pair probabilities are estimated using an estimate similar to ~~[[Boltzmann distribution]]. The partition function is calculated using a [[dynamic programming]] approach.~~		5 Hello there friend. Let me present myself. I am Collin Engelke. Among the best things on the work ([http://www.pinterest.com/judyneinstein/ www.pinterest.com]) planet for him is doing ceramics and he would never ever offer it up. My job is an administrative assistant but I've already made an application for another one. Guam is the only place she's been living in. Look into my website right here: http://www.pinterest.com/judyneinstein/

	~~== Algorithm ==~~
	~~The following describes~~ the ~~algorithm used by probalign to determine~~ the ~~base pair probabilities.<ref>~~[http://www.~~bioinf~~.~~uni-freiburg.de~~//~~Lehre/Courses/2011_WS/V_BioinfoII/probalign-partition-func~~.~~pdf Lecture "Bioinformatics II" at University of Freiburg]</ref>~~

	~~=== Alignment score ===~~
	~~To score an alignment of two sequences two things are needed:~~
	* a similarity function <math>\sigma(x,y)</math> (e.g. ~~[[PAM matrix\|PAM]], [[BLOSUM~~]~~],...~~)
	* affine gap penalty: <math> g(k) = \alpha + \beta k</math>
	~~The score <math>S(a)</math> of an alignment a~~ is ~~defined as:~~

	~~<math> S(a) = \sum_{x_i-y_j \in a} \sigma(x_i,y_j) + \text{gap cost}</math>~~

	~~Now the boltzmann weighted score of an alignment a is:~~

	~~<math> e^{\frac{S(a)}{T}} = e^{\frac{\sum_{x_i-y_j \in a} \sigma(x_i,y_j) + \text{gap cost}}{T}} =~~
	~~\left( \prod_{x_i - y_i \in a} e^{\frac{\sum_{x_i-y_j \in a} \sigma(x_i,y_j)}{T}} \right) \cdot e^{\frac{gapcost}{T}}</math>~~

	~~Where <math>T</math>~~ is ~~a scaling factor.~~

	~~The probability of~~ an ~~alignment assuming boltzmann distribution is given by~~

	~~<math>Pr[a\|x,y] = \frac{e^{\frac{S(a)}{T}}}{Z}</math>~~

	~~Where <math>Z</math> is the partition function, i.e. the sum of the boltzmann weights of all alignments.~~

	~~=== Dynamic Programming ===~~
	~~Let <math>Z_{i,j}</math> denote the partition function of the prefixes <math>x_0,x_1,...,x_i</math> and <math>y_0,y_1,...,y_j</math>. Three different cases are considered:~~
	~~# <math>Z^{M}_{i,j}:</math> the partition function of all alignments of the two prefixes that end in a match.~~
	~~# <math>Z^{~~I~~}_{i,j}:</math> the partition function of all alignments of the two prefixes that end in~~ an ~~insertion <math>(-,y_j)</math>~~.
	~~# <math>Z^{D}_{i,j}:</math>~~ the ~~partition function of all alignments of the two prefixes that end~~ in ~~a deletion <math>(x_i,-)</math>~~.
	~~Then we have: <math>Z_{i,j} = Z^{M}_{i,j} + Z^{D}_{i,j} + Z^{I}_{i,j}</math>~~

	~~==== Initialization ====~~
	~~The matrixes are initialized as follows~~:
	* <math>Z^{M}_{0,j} = Z^{M}_{i,0} = 0</math>
	* <math>Z^{M}_{0,0} = 1</math>
	* <math>Z^{D}_{0,j} = 0</math>
	* <math>Z^{I}_{i,0} = 0</math>

	~~==== Recursion ====~~
	~~The partition function for the alignments of two sequences <math>x</math> and <math>y</math> is given by <math>Z_{\|x\|,\|y\|}</math>, which can be recursively computed:~~
	* <math>Z^{M}_{i,j} = Z_{i-1,j-1} \cdot e^{\frac{\sigma(x_i,y_j)}{T}}</math>
	* <math>Z^{D}_{i,j} = Z^{D}_{i-1,j} \cdot e^{\frac{\beta}{T}} + Z^{M}_{i-1,j} \cdot e^{\frac{g(1)}{T}} + Z^{I}_{i-1,j} \cdot e^{\frac{g(1)}{T}}</math>
	* <math>Z^{I}_{i,j}</math> analogously

	~~=== Base pair probability ===~~
	~~Finally the probability that positions <math>x_i</math> and <math>y_j</math> form a base pair is given by:~~

	~~<math>P(x_i - y_j\|x,y) = \frac{Z_{i-1,j-1} \cdot e^{\frac{\sigma(x_i,y_j)}{T}} \cdot Z'_{i',j'}}{Z_{\|x\|,\|y\|}}</math>~~

	~~<math> Z', i', j'</math> are the respective values for the recalculated <math>Z</math> with inversed base pair strings.~~

	~~== See also ==~~
	* [[ProbCons]]
	* [[Multiple Sequence Alignment]]

	~~== References ==~~
	~~{{Reflist}}~~

	~~== External links ==~~
	* [http://~~probalign~~.~~njit~~.~~edu~~/~~probalign~~/~~login Probalign Webservice]~~

	~~[[Category:Sequence alignment algorithms]]~~

en>Circlesareround: Examples -> Special cases

2013-02-24T09:53:19Z

Examples -> Special cases

← Older revision		Revision as of 11:53, 24 February 2013
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	~~Cheyenne Geib~~ is ~~what's written on my birth certification~~ and ~~I feel comfy when men and women use the total title~~. ~~To act~~ is the ~~thing I adore most of all~~. ~~For yrs I've been~~ [http://~~thesaurus~~.~~com~~/~~browse~~/~~performing performing~~] as a ~~database administrator~~. ~~I presently live in Virginia~~. ~~I have been performing on my web site for some time now~~. ~~Verify it out right here~~: ~~http~~://~~wiki~~.~~tes~~.mi.it/~~mediawiki~~/~~index~~.~~php~~/~~Discussioni_utente~~:~~GordonH02d~~<br><br>~~Feel free to surf to my blog [http~~://~~wiki~~.~~tes~~.mi.it/~~mediawiki~~/~~index~~.~~php~~/~~Discussioni_utente~~:~~GordonH02d ofertas zapatillas padel asics~~]		'''Probalign''' is a sequence alignment tool that calculates a maximum expected accuracy alignment using partition function posterior probabilities.<ref>U. Roshan and D. R. Livesay, Probalign: multiple sequence alignment using partition function posterior probabilities, Bioinformatics, 22(22):2715-21, 2006 ([http://bioinformatics.oxfordjournals.org/cgi/reprint/btl472?ijkey=GR3m5VV6yTz1jEx&keytype=ref PDF])</ref> Base pair probabilities are estimated using an estimate similar to [[Boltzmann distribution]]. The partition function is calculated using a [[dynamic programming]] approach.

			== Algorithm ==
			The following describes the algorithm used by probalign to determine the base pair probabilities.<ref>[http://www.bioinf.uni-freiburg.de//Lehre/Courses/2011_WS/V_BioinfoII/probalign-partition-func.pdf Lecture "Bioinformatics II" at University of Freiburg]</ref>

			=== Alignment score ===
			To score an alignment of two sequences two things are needed:
			* a similarity function <math>\sigma(x,y)</math> (e.g. [[PAM matrix\|PAM]], [[BLOSUM]],...)
			* affine gap penalty: <math> g(k) = \alpha + \beta k</math>
			The score <math>S(a)</math> of an alignment a is defined as:

			<math> S(a) = \sum_{x_i-y_j \in a} \sigma(x_i,y_j) + \text{gap cost}</math>

			Now the boltzmann weighted score of an alignment a is:

			<math> e^{\frac{S(a)}{T}} = e^{\frac{\sum_{x_i-y_j \in a} \sigma(x_i,y_j) + \text{gap cost}}{T}} =
			\left( \prod_{x_i - y_i \in a} e^{\frac{\sum_{x_i-y_j \in a} \sigma(x_i,y_j)}{T}} \right) \cdot e^{\frac{gapcost}{T}}</math>

			Where <math>T</math> is a scaling factor.

			The probability of an alignment assuming boltzmann distribution is given by

			<math>Pr[a\|x,y] = \frac{e^{\frac{S(a)}{T}}}{Z}</math>

			Where <math>Z</math> is the partition function, i.e. the sum of the boltzmann weights of all alignments.

			=== Dynamic Programming ===
			Let <math>Z_{i,j}</math> denote the partition function of the prefixes <math>x_0,x_1,...,x_i</math> and <math>y_0,y_1,...,y_j</math>. Three different cases are considered:
			# <math>Z^{M}_{i,j}:</math> the partition function of all alignments of the two prefixes that end in a match.
			# <math>Z^{I}_{i,j}:</math> the partition function of all alignments of the two prefixes that end in an insertion <math>(-,y_j)</math>.
			# <math>Z^{D}_{i,j}:</math> the partition function of all alignments of the two prefixes that end in a deletion <math>(x_i,-)</math>.
			Then we have: <math>Z_{i,j} = Z^{M}_{i,j} + Z^{D}_{i,j} + Z^{I}_{i,j}</math>

			==== Initialization ====
			The matrixes are initialized as follows:
			* <math>Z^{M}_{0,j} = Z^{M}_{i,0} = 0</math>
			* <math>Z^{M}_{0,0} = 1</math>
			* <math>Z^{D}_{0,j} = 0</math>
			* <math>Z^{I}_{i,0} = 0</math>

			==== Recursion ====
			The partition function for the alignments of two sequences <math>x</math> and <math>y</math> is given by <math>Z_{\|x\|,\|y\|}</math>, which can be recursively computed:
			* <math>Z^{M}_{i,j} = Z_{i-1,j-1} \cdot e^{\frac{\sigma(x_i,y_j)}{T}}</math>
			* <math>Z^{D}_{i,j} = Z^{D}_{i-1,j} \cdot e^{\frac{\beta}{T}} + Z^{M}_{i-1,j} \cdot e^{\frac{g(1)}{T}} + Z^{I}_{i-1,j} \cdot e^{\frac{g(1)}{T}}</math>
			* <math>Z^{I}_{i,j}</math> analogously

			=== Base pair probability ===
			Finally the probability that positions <math>x_i</math> and <math>y_j</math> form a base pair is given by:

			<math>P(x_i - y_j\|x,y) = \frac{Z_{i-1,j-1} \cdot e^{\frac{\sigma(x_i,y_j)}{T}} \cdot Z'_{i',j'}}{Z_{\|x\|,\|y\|}}</math>

			<math> Z', i', j'</math> are the respective values for the recalculated <math>Z</math> with inversed base pair strings.

			== See also ==
			* [[ProbCons]]
			* [[Multiple Sequence Alignment]]

			== References ==
			{{Reflist}}

			== External links ==
			* [http://probalign.njit.edu/probalign/login Probalign Webservice]

			[[Category:Sequence alignment algorithms]]

en>Circlesareround: /* Area */ formula in terms of a,b,c,d,x

2012-04-29T06:49:11Z

Area: formula in terms of a,b,c,d,x

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