Pitzer equations - Revision history

173.25.36.249: /* The Pitzer parameters */

2014-09-16T20:45:19Z

The Pitzer parameters

← Older revision		Revision as of 22:45, 16 September 2014
Line 1:		Line 1:
	[[Image:Bivariate von Mises distribution cosine samples.svg\|thumb\|250px\|Samples from the cosine variant of the bivariate von Mises distribution. The green points are sampled from a distribution with high concentration and high correlation (<~~math~~>~~\kappa_1=\kappa_2=200~~<~~/math~~>~~, <math>\kappa_3=0</math>),~~ the ~~blue points~~ are ~~sampled from~~ a ~~distribution~~ with ~~high concentration and negative correlation (<math>\kappa_1=\kappa_2=200</math>, <math>\kappa_3=100</math>), and~~ the ~~red points are sampled~~ from ~~a distribution~~ with ~~low concentration and no correlation (~~<~~math~~>~~\kappa_1=\kappa_2=20, \kappa_3=0~~<~~/math~~>~~).]]~~		Sell My Timeshare - How To Market A Timeshare For Money Quickly<br><br>Selling a timeshare can be really simple or excruciatingly difficult relying on whom you question. 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	~~In [[probability theory]] and [[statistics]], the '''bivariate von Mises distribution''' is~~ a ~~[[probability distribution]] describing values~~ on a ~~[[torus]]~~. ~~It may be thought of as an analogue on the torus of the [[Multivariate normal distribution\|bivariate normal distribution]]~~. ~~The distribution belongs~~ to ~~the field of [[directional statistics]]. The general bivariate von Mises distribution was first proposed by [[Kanti Mardia]]~~ in ~~1975. One of its variants is today used~~ in ~~the field of [[bioinformatics]]~~ to ~~formulate a probabilistic model~~ of ~~[[protein structure]] in atomic detail~~.~~<ref name="WB08">{{doi-inline\|10~~.1073/pnas.0801715105\|Boomsma W, Mardia KV, Taylor CC, Ferkinghoff-Borg J, Krogh A, Hamelryck T (2008) A generative, probabilistic model of local protein structure. Proc Natl. Acad Sci USA 105(26): 8932–8937}}<~~/ref~~><~~ref name="Shapovalov"~~>~~{{cite journal \|author=Shapovalov MV~~, Dunbrack, RL\|title=A smoothed backbone-dependent rotamer library for proteins derived from adaptive kernel density estimates and regressions\|journal=Structure (Cell Press)\|volume=19\|issue=6\|pages=844–858\|year=2011\|doi=10.1016/j.str.2011.03.019 \|pmid=21645855\|pmc=3118414}}</ref>

	~~==Definition==~~
	~~The bivariate von Mises distribution is~~ a ~~[[probability distribution]] defined on the [[torus]]~~, ~~<math>S^1 \times S^1</math> in <math>\mathbb{R}^3</math>~~.
	~~The probability density function of~~ the ~~general bivariate von Mises distribution for~~ the ~~angles <math>\phi~~, ~~\psi \in~~ [~~0, 2\pi]<~~/~~math> is given by<ref>Mardia KV (1975) Statistics of Directional Data (with Discussion)~~. ~~J Roy Statist Soc B 37:349–393~~.</~~ref>~~

	~~:<math>~~
	~~f(\phi, \psi) \propto \exp [ \kappa_1 \cos(\phi~~ - ~~\mu) + \kappa_2 \cos(\psi~~ - ~~\nu) + (\cos(\phi~~-~~\mu), \sin(\phi~~-~~\mu)) \mathbf{A} (\cos(\psi~~ - ~~\nu), \sin(\psi~~ - ~~\nu))^T~~ ],
	</~~math>~~

	~~where <math>\mu<~~/~~math> and <math>\nu<~~/~~math> are the means for <math>\phi</math> and <math>\psi</math>, <math>\kappa_1</math> and <math>\kappa_2</math> their concentration and the matrix <math>\mathbf{A} \in \mathbb{M}~~(2,2)~~</math>~~ is ~~related~~ to ~~their correlation~~.

	~~Two commonly used variants~~ of ~~the bivariate von Mises distribution~~ are ~~the sine~~ and ~~cosine variant~~.

	~~The cosine variant of~~ the ~~bivariate von Mises distribution~~<~~ref name="WB08" /~~> ~~has the probability density function~~

	:<~~math~~>
	~~f(\phi~~, ~~\psi) = Z_c(\kappa_1~~, ~~\kappa_2~~, ~~\kappa_3) \ \exp [ \kappa_1 \cos(\phi - \mu) + \kappa_2 \cos(\psi - \nu) - \kappa_3 \cos(\phi - \mu - \psi + \nu) ]~~,
	~~</math>~~

	~~where <math>\mu</math>~~ and ~~<math>\nu</math>~~ are ~~the means for <math>\phi</math>~~ and <~~math~~>~~\psi~~<~~/math~~>, ~~<math>\kappa_1</math>~~ and <~~math~~>~~\kappa_2~~<~~/math~~> ~~their concentration and <math>\kappa_3</math> is related~~ to their ~~correlation~~. <~~math~~>~~Z_c~~<~~/math~~> is the ~~normalization constant~~. This ~~distribution with <math>\kappa_3</math>=0~~ has been ~~used~~ for ~~kernel density estimates of the distribution of the protein dihedral angles~~ <~~math~~>~~\phi~~<~~/math~~> and <~~math~~>~~\psi~~<~~/math~~>.~~<ref name="Shapovalov"/>~~

	~~The sine variant has~~ the ~~probability density function<ref>{{doi-inline\|10~~.~~1093/biomet/89~~.3.~~719\|Singh H~~, ~~Hnizdo V~~, ~~Demchuk E (2002) Probabilistic model for two dependent circular variables~~. ~~Biometrika 89: 719–723}}~~<~~/ref~~>

	:<~~math~~>
	~~f(\phi, \psi) = Z_s(\kappa_1, \kappa_2, \kappa_3) \ \exp [ \kappa_1 \cos(\phi - \mu) + \kappa_2 \cos(\psi - \nu) + \kappa_3 \sin(\phi - \mu) \sin(\psi - \nu) ], </math>~~

	~~where~~ the ~~parameters have the same interpretation~~.

	~~==See also==~~
	* [[Von Mises distribution]], a similar distribution on the one-dimensional unit circle
	* [[Kent distribution]], a related distribution on the two-dimensional unit sphere
	* [[von Mises-Fisher distribution]]
	* [[Directional statistics]]

	~~==References==~~
	~~{{reflist}}~~

	~~{{ProbDistributions\|directional}}~~

	~~[[Category:Continuous distributions]]~~
	~~[[Category:Directional statistics]]~~
	~~[[Category:Multivariate continuous distributions]]~~
	~~[[Category:Probability distributions]]~~

188.26.22.131: /* Historical development */ [[]]

2014-01-27T11:12:54Z

Historical development: [[]]

← Older revision		Revision as of 13:12, 27 January 2014
Line 1:		Line 1:
	~~If youve already purchased a Trek bike or any other brand of bike and you prefer to bring your own bike on your tour, bring it along~~. ~~Macaskill is tackling the Cuillin Ridge in Scotland, not far from where this two-wheeling genius hails~~ from on the ~~Isle~~ of ~~Skye~~. ~~They both have some parts that~~ are ~~worse than another's, but it doesn't matter in general. It's really cool to ride on~~ a ~~bike that is not just efficient but also very trendy. If you beloved this article so you would like to be given more info relating to [http:~~//~~www.ofclan.de/index.php?mod~~=~~users&action~~=~~view&id~~=~~88939 Womens mountain bike sizing.] nicely visit our web-page. When shopping for different bike accessories~~, ~~parts, or whatever it is you~~ are ~~looking for, being~~ a ~~smart shopper is always in order.~~ <br><br>		[[Image:Bivariate von Mises distribution cosine samples.svg\|thumb\|250px\|Samples from the cosine variant of the bivariate von Mises distribution. The green points are sampled from a distribution with high concentration and high correlation (<math>\kappa_1=\kappa_2=200</math>, <math>\kappa_3=0</math>), the blue points are sampled from a distribution with high concentration and negative correlation (<math>\kappa_1=\kappa_2=200</math>, <math>\kappa_3=100</math>), and the red points are sampled from a distribution with low concentration and no correlation (<math>\kappa_1=\kappa_2=20, \kappa_3=0</math>).]]

	~~The prices offered by these online stores are very competitive~~ and ~~realistic according to~~ the ~~market. in summary let me give some procuations you bshould take when ridding it , ridding~~ a ~~bike at high speed can lead to accidents just maintain~~ a ~~minimum and also follow~~ the ~~traffic lights , if it is for sport just make enough practice and enjoy~~ the ~~game~~. The ~~price you can expect~~ to ~~pay for stems~~ is ~~actually determined by~~ the ~~materials used along with its weight~~. - ~~Get a bike that is lightweight and made out~~ of ~~carbon fiber materials~~. ~~Then sense the direct route it will take to go~~ from ~~your nose to the target location~~ and ~~then back out through~~ the ~~nose.~~ <br><br>~~Mountain bikes~~ in ~~Arizona have two great rides in Sedona, Highline and the Dry Creek Loop~~. * Numbness - Impingement of ~~small nerve branches between~~ the ~~second and third or third and fourth toes can cause swelling that results~~ in ~~numbness~~, ~~tingling, or burning, or sharp shooting pains into the toes. But when it comes to mountain biking it is not enough that you own a bike. Another way to classify brakes~~ is by ~~mounting style~~. ~~These are stable forks whose weights are directly in proportion to their durability~~. <br><br>~~There are still other types of bikes that require different types of tires. There are also tires with detailed treads which are very prominent~~ and ~~these~~ are ~~very useful~~ for the ~~biker because of the grip they provide. In the purest sense of the word~~, ~~a mountain bikes sole mission~~ is to ~~travel "off-road" only~~. ~~I should have had that Bicycle repair tool with me, becuase when I got home and lowered~~ the ~~seat. To help you choose which one you to buy, here~~ are the ~~list of bikes~~ and ~~their use~~. <br><br>~~If you are just out there to like your journey or to get from position to put efficiently~~, ~~an ebike electric mountain bike~~, ~~electric mountain bike~~, ~~electric bikes for sale is the great excess boost to your experience that will permit you go farther~~, ~~more time~~ and ~~have much more electrical power above~~ the ~~course of your ride~~, ~~letting you~~ to ~~appreciate~~ the ~~journey a little extra~~. ~~There is anything from shocks to gears, special wheels, exclusive take care~~ of ~~bars that can be immediately switched to match~~ the ~~terrain you're riding on~~ and ~~so substantially much more~~. ~~One of~~ the ~~main concerns for any cyclist is safety, having the right kit is a must~~. ~~Whether it's a testament to South Dakota's commitment to recycling~~, ~~or just whimsy~~, ~~Bone Collector embodies the features of the best bike trails in the world~~: ~~Sedona~~, ~~Moab~~, ~~Flagstaff~~, ~~Whistler and Tahoe~~, ~~without~~ the ~~long drive or expensive plane ticket~~. ~~Part of Park City's distinction as~~ the ~~International Mountain Bike Association's first and only gold~~-~~level Ride Center is its abundance of beginner trails.~~		In [[probability theory]] and [[statistics]], the '''bivariate von Mises distribution''' is a [[probability distribution]] describing values on a [[torus]]. It may be thought of as an analogue on the torus of the [[Multivariate normal distribution\|bivariate normal distribution]]. The distribution belongs to the field of [[directional statistics]]. The general bivariate von Mises distribution was first proposed by [[Kanti Mardia]] in 1975. One of its variants is today used in the field of [[bioinformatics]] to formulate a probabilistic model of [[protein structure]] in atomic detail.<ref name="WB08">{{doi-inline\|10.1073/pnas.0801715105\|Boomsma W, Mardia KV, Taylor CC, Ferkinghoff-Borg J, Krogh A, Hamelryck T (2008) A generative, probabilistic model of local protein structure. Proc Natl. Acad Sci USA 105(26): 8932–8937}}</ref><ref name="Shapovalov">{{cite journal \|author=Shapovalov MV, Dunbrack, RL\|title=A smoothed backbone-dependent rotamer library for proteins derived from adaptive kernel density estimates and regressions\|journal=Structure (Cell Press)\|volume=19\|issue=6\|pages=844–858\|year=2011\|doi=10.1016/j.str.2011.03.019 \|pmid=21645855\|pmc=3118414}}</ref>

			==Definition==
			The bivariate von Mises distribution is a [[probability distribution]] defined on the [[torus]], <math>S^1 \times S^1</math> in <math>\mathbb{R}^3</math>.
			The probability density function of the general bivariate von Mises distribution for the angles <math>\phi, \psi \in [0, 2\pi]</math> is given by<ref>Mardia KV (1975) Statistics of Directional Data (with Discussion). J Roy Statist Soc B 37:349–393.</ref>

			:<math>
			f(\phi, \psi) \propto \exp [ \kappa_1 \cos(\phi - \mu) + \kappa_2 \cos(\psi - \nu) + (\cos(\phi-\mu), \sin(\phi-\mu)) \mathbf{A} (\cos(\psi - \nu), \sin(\psi - \nu))^T ],
			</math>

			where <math>\mu</math> and <math>\nu</math> are the means for <math>\phi</math> and <math>\psi</math>, <math>\kappa_1</math> and <math>\kappa_2</math> their concentration and the matrix <math>\mathbf{A} \in \mathbb{M}(2,2)</math> is related to their correlation.

			Two commonly used variants of the bivariate von Mises distribution are the sine and cosine variant.

			The cosine variant of the bivariate von Mises distribution<ref name="WB08" /> has the probability density function

			:<math>
			f(\phi, \psi) = Z_c(\kappa_1, \kappa_2, \kappa_3) \ \exp [ \kappa_1 \cos(\phi - \mu) + \kappa_2 \cos(\psi - \nu) - \kappa_3 \cos(\phi - \mu - \psi + \nu) ],
			</math>

			where <math>\mu</math> and <math>\nu</math> are the means for <math>\phi</math> and <math>\psi</math>, <math>\kappa_1</math> and <math>\kappa_2</math> their concentration and <math>\kappa_3</math> is related to their correlation. <math>Z_c</math> is the normalization constant. This distribution with <math>\kappa_3</math>=0 has been used for kernel density estimates of the distribution of the protein dihedral angles <math>\phi</math> and <math>\psi</math>.<ref name="Shapovalov"/>

			The sine variant has the probability density function<ref>{{doi-inline\|10.1093/biomet/89.3.719\|Singh H, Hnizdo V, Demchuk E (2002) Probabilistic model for two dependent circular variables. Biometrika 89: 719–723}}</ref>

			:<math>
			f(\phi, \psi) = Z_s(\kappa_1, \kappa_2, \kappa_3) \ \exp [ \kappa_1 \cos(\phi - \mu) + \kappa_2 \cos(\psi - \nu) + \kappa_3 \sin(\phi - \mu) \sin(\psi - \nu) ], </math>

			where the parameters have the same interpretation.

			==See also==
			* [[Von Mises distribution]], a similar distribution on the one-dimensional unit circle
			* [[Kent distribution]], a related distribution on the two-dimensional unit sphere
			* [[von Mises-Fisher distribution]]
			* [[Directional statistics]]

			==References==
			{{reflist}}

			{{ProbDistributions\|directional}}

			[[Category:Continuous distributions]]
			[[Category:Directional statistics]]
			[[Category:Multivariate continuous distributions]]
			[[Category:Probability distributions]]

en>Bibcode Bot: Adding 0 arxiv eprint(s), 1 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

2012-08-22T08:09:34Z

Adding 0 arxiv eprint(s), 1 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

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If youve already purchased a Trek bike or any other brand of bike and you prefer to bring your own bike on your tour, bring it along. Macaskill is tackling the Cuillin Ridge in Scotland, not far from where this two-wheeling genius hails from on the Isle of Skye. They both have some parts that are worse than another's, but it doesn't matter in general. It's really cool to ride on a bike that is not just efficient but also very trendy. If you beloved this article so you would like to be given more info relating to [http://www.ofclan.de/index.php?mod=users&action=view&id=88939 Womens mountain bike sizing.] nicely visit our web-page. When shopping for different bike accessories, parts, or whatever it is you are looking for, being a smart shopper is always in order. 

The prices offered by these online stores are very competitive and realistic according to the market. in summary let me give some procuations you bshould take when ridding it , ridding a bike at high speed can lead to accidents just maintain a minimum and also follow the traffic lights , if it is for sport just make enough practice and enjoy the game. The price you can expect to pay for stems is actually determined by the materials used along with its weight. - Get a bike that is lightweight and made out of carbon fiber materials. Then sense the direct route it will take to go from your nose to the target location and then back out through the nose. Mountain bikes in Arizona have two great rides in Sedona, Highline and the Dry Creek Loop. * Numbness - Impingement of small nerve branches between the second and third or third and fourth toes can cause swelling that results in numbness, tingling, or burning, or sharp shooting pains into the toes. But when it comes to mountain biking it is not enough that you own a bike. Another way to classify brakes is by mounting style. These are stable forks whose weights are directly in proportion to their durability. There are still other types of bikes that require different types of tires. There are also tires with detailed treads which are very prominent and these are very useful for the biker because of the grip they provide. In the purest sense of the word, a mountain bikes sole mission is to travel "off-road" only. I should have had that Bicycle repair tool with me, becuase when I got home and lowered the seat. To help you choose which one you to buy, here are the list of bikes and their use. If you are just out there to like your journey or to get from position to put efficiently, an ebike electric mountain bike, electric mountain bike, electric bikes for sale is the great excess boost to your experience that will permit you go farther, more time and have much more electrical power above the course of your ride, letting you to appreciate the journey a little extra. There is anything from shocks to gears, special wheels, exclusive take care of bars that can be immediately switched to match the terrain you're riding on and so substantially much more. One of the main concerns for any cyclist is safety, having the right kit is a must. Whether it's a testament to South Dakota's commitment to recycling, or just whimsy, Bone Collector embodies the features of the best bike trails in the world: Sedona, Moab, Flagstaff, Whistler and Tahoe, without the long drive or expensive plane ticket. Part of Park City's distinction as the International Mountain Bike Association's first and only gold-level Ride Center is its abundance of beginner trails.