Clifford analysis - Revision history

en>Rjwilmsi: /* References */Added 1 dois to journal cites using AWB (10094)

2014-05-04T16:12:40Z

References: Added 1 dois to journal cites using AWB (10094)

← Older revision		Revision as of 18:12, 4 May 2014
Line 1:		Line 1:
	~~In [[applied mathematics]]~~, ~~the two-dimensional '''Spectral [[signal-~~to~~-noise ratio]]''' (SSNR) measures the normalised cross-correlation coefficient between several two-dimensional images over corresponding rings~~ in ~~Fourier space as a function of spatial frequency {{harv\|Unser\|1987}}~~. ~~It is a multi-particle extension of the Fourier ring correlation (FRC), which is related to the [[Fourier shell correlation]]~~. ~~The SSNR is a popular method~~ for ~~finding the resolution of~~ a ~~class average in~~ [~~[cryo-electron microscopy]]~~.		Nice to meet up with you, my identify is Ricky Nee. What I adore performing is to enjoy golfing and I would in no way give it up. I have generally loved dwelling in Illinois. Booking holiday seasons has been my working day occupation for a while. I am managing and [http://Search.usa.gov/search?query=maintaining maintaining] a web site below: http://www.ceeh.es/includes/src/_notes/nike-air-max-fly.cfm<br><br>Feel free to visit my webpage: [http://www.ceeh.es/includes/src/_notes/nike-air-max-fly.cfm Nike Air Max 2012]

	=~~= Calculation ==~~

	:~~<math>~~
	~~SSNR (r)~~
	=
	~~\frac{\displaystyle\sum_{r_i \in R}\left\|\sum_{k_i}{ F_{r_i,k} }\right\|^2}~~
	~~{\displaystyle \frac{K}{K-1} \sum_{r_i \in R}\sum_{k_i}{ \left\|{ F_{r_i,k} - \bar{F}_{r_i}}\right\|^2}} -1~~
	</~~math>~~
	<!--
	~~:<math>~~
	=
	~~\frac{\displaystyle\sum_{r_i \in R}\left\|\sum_{k_i}{ F_{r_i,k} }\right\|^2}~~
	~~{\displaystyle \frac{K}{K~~-~~1} \sum_{r_i \in R}~~
	~~\left\| \sum_{k_i}F^2_{r_i,k} - \frac{1}{K}\left(\sum_{k_i}F_{r_i,k}\right)^2 \right\|}~~
	<~~/math>~~
	-->

	~~where~~ <~~math~~>~~F_{r_i,k}</math> is the complex structure Factor for image k for a pixel <math>r_i</math> at radius <math>R</math>. It is possible convert the SSNR into an equivalent FRC using the following formula~~:

	:~~<math>~~
	~~FRC = \frac{SSNR}{SSNR + 1}~~
	</~~math>~~

	~~== See also ==~~
	* [[Resolution (electron density)]]
	* [[Fourier shell correlation]]

	~~== Notes ==~~
	~~{{reflist\|2}}~~

	~~== References ==~~
	~~<div class="references-small">~~
	*{{cite journal
	~~\| last = Unser~~
	~~\| first = M~~.
	~~\| coauthors = Trus, B~~.~~L.; Steven, A.C.~~
	~~\| title = A New Resolution Criterion Based on Spectral Signal-To-Noise Ratios~~
	~~\| journal = Ultramicroscopy~~
	~~\| volume = 23~~
	~~\| issue = 1~~
	~~\| pages = 39–51~~
	~~\| doi=10.1016~~/~~0304-3991(87)90225-7~~
	~~\| year = 1987~~
	~~\| pmid=3660491}}~~
	*{{cite journal
	~~\| last = Harauz~~
	~~\| first = G.~~
	~~\| coauthors = M. van Heel~~
	~~\| title = Exact filters for general geometry three dimensional reconstruction~~
	~~\| journal = Optik~~
	~~\| volume = 73~~
	~~\| pages = 146–156~~
	~~\| year = 1986}}~~
	*{{cite journal
	~~\| last = van Heel~~
	~~\| first = M.~~
	~~\| title = Detection of objects in quantum-noise limited images~~
	~~\| journal = Ultramicroscopy~~
	~~\| volume = 8~~
	~~\| pages = 331–342~~
	~~\| year = 1982}}~~
	*{{cite journal
	~~\| last = Saxton~~
	~~\| first = W.O.~~
	~~\| coauthors = W. Baumeister~~
	~~\| title = The correlation averaging of a regularly arranged bacterial cell envelope protein~~
	~~\| journal = J Microscopy~~
	~~\| volume = 127~~
	~~\| pages = 127–138~~
	~~\| year = 1982~~
	~~\| doi=10.1111~~/~~j.1365-2818.1982.tb00405.x}}~~
	*{{cite journal
	~~\| last = Böttcher~~
	~~\| first = B.~~
	~~\| coauthors = Wynne, S.A.; Crowther, R.A.~~
	~~\| title = Determination of the fold of the core protein of hepatitis B virus by electron microscopy~~
	~~\| journal = Nature~~
	~~\| volume = 386~~
	~~\| pages = 88–91~~
	~~\| doi=10.1038~~/~~386088a0~~
	~~\| year = 1997~~
	~~\| pmid = 9052786~~
	~~\| issue = 6620}}~~
	*{{cite book
	~~\| last = Frank~~
	~~\| first = Joachim~~
	~~\| authorlink = Joachim Frank~~
	~~\| title = Three-Dimnsional Electron Microscopy of Macromolecular Assemblies~~
	~~\| publisher = [[Oxford University Press]]~~
	~~\| location = New York~~
	~~\| year = 2006~~
	~~\| pages =~~
	~~\| isbn = 0~~-19-~~518218~~-~~9 }}~~
	*{{cite journal
	~~\| title=Fourier shell correlation threshold criteria~~
	~~\| journal=Journal of Structural Biology~~
	~~\| year= 2005~~
	~~\| last= van Heel~~
	~~\| first= M.~~
	~~\| coauthors = Schatz, M~~.
	~~\| volume=151~~
	~~\| pages=250–262~~
	~~\| doi=10.1016/j.jsb.2005.05.009~~
	~~\| pmid=16125414~~
	~~\| issue=3 }}~~
	~~</div>~~

	~~[[Category:Applied mathematics]~~]
	~~[[Category:Engineering ratios]]~~
	~~[[Category:Measurement]]~~
	~~[[Category:Microscopes]]~~


	~~{{mathapplied-stub}}~~

99.241.86.114: some minor things I missed in the previous edit

2013-06-18T06:01:54Z

some minor things I missed in the previous edit

← Older revision		Revision as of 08:01, 18 June 2013
Line 1:		Line 1:
	~~Zula is~~ the ~~she~~'~~s called and her husband doesn~~'~~t like it at~~ the ~~only thing~~. ~~What me and my family love usually play rock and roll but I am have~~ the ~~time lately~~. ~~Invoicing~~ is ~~his day job now but his promotion never relates~~. ~~Virginia is~~ where ~~her home~~ is. He is ~~running and maintaining a blog here~~: ~~http~~://~~Www~~.~~vimeo~~.~~com~~/~~104813619<br><br>Also visit my weblog~~ [~~http:~~/~~/Www~~.~~vimeo~~.~~com~~/~~104813619 anna kendrick nude~~]		In [[applied mathematics]], the two-dimensional '''Spectral [[signal-to-noise ratio]]''' (SSNR) measures the normalised cross-correlation coefficient between several two-dimensional images over corresponding rings in Fourier space as a function of spatial frequency {{harv\|Unser\|1987}}. It is a multi-particle extension of the Fourier ring correlation (FRC), which is related to the [[Fourier shell correlation]]. The SSNR is a popular method for finding the resolution of a class average in [[cryo-electron microscopy]].

			== Calculation ==

			:<math>
			SSNR (r)
			=
			\frac{\displaystyle\sum_{r_i \in R}\left\|\sum_{k_i}{ F_{r_i,k} }\right\|^2}
			{\displaystyle \frac{K}{K-1} \sum_{r_i \in R}\sum_{k_i}{ \left\|{ F_{r_i,k} - \bar{F}_{r_i}}\right\|^2}} -1
			</math>
			<!--
			:<math>
			=
			\frac{\displaystyle\sum_{r_i \in R}\left\|\sum_{k_i}{ F_{r_i,k} }\right\|^2}
			{\displaystyle \frac{K}{K-1} \sum_{r_i \in R}
			\left\| \sum_{k_i}F^2_{r_i,k} - \frac{1}{K}\left(\sum_{k_i}F_{r_i,k}\right)^2 \right\|}
			</math>
			-->

			where <math>F_{r_i,k}</math> is the complex structure Factor for image k for a pixel <math>r_i</math> at radius <math>R</math>. It is possible convert the SSNR into an equivalent FRC using the following formula:

			:<math>
			FRC = \frac{SSNR}{SSNR + 1}
			</math>

			== See also ==
			* [[Resolution (electron density)]]
			* [[Fourier shell correlation]]

			== Notes ==
			{{reflist\|2}}

			== References ==
			<div class="references-small">
			*{{cite journal
			\| last = Unser
			\| first = M.
			\| coauthors = Trus, B.L.; Steven, A.C.
			\| title = A New Resolution Criterion Based on Spectral Signal-To-Noise Ratios
			\| journal = Ultramicroscopy
			\| volume = 23
			\| issue = 1
			\| pages = 39–51
			\| doi=10.1016/0304-3991(87)90225-7
			\| year = 1987
			\| pmid=3660491}}
			*{{cite journal
			\| last = Harauz
			\| first = G.
			\| coauthors = M. van Heel
			\| title = Exact filters for general geometry three dimensional reconstruction
			\| journal = Optik
			\| volume = 73
			\| pages = 146–156
			\| year = 1986}}
			*{{cite journal
			\| last = van Heel
			\| first = M.
			\| title = Detection of objects in quantum-noise limited images
			\| journal = Ultramicroscopy
			\| volume = 8
			\| pages = 331–342
			\| year = 1982}}
			*{{cite journal
			\| last = Saxton
			\| first = W.O.
			\| coauthors = W. Baumeister
			\| title = The correlation averaging of a regularly arranged bacterial cell envelope protein
			\| journal = J Microscopy
			\| volume = 127
			\| pages = 127–138
			\| year = 1982
			\| doi=10.1111/j.1365-2818.1982.tb00405.x}}
			*{{cite journal
			\| last = Böttcher
			\| first = B.
			\| coauthors = Wynne, S.A.; Crowther, R.A.
			\| title = Determination of the fold of the core protein of hepatitis B virus by electron microscopy
			\| journal = Nature
			\| volume = 386
			\| pages = 88–91
			\| doi=10.1038/386088a0
			\| year = 1997
			\| pmid = 9052786
			\| issue = 6620}}
			*{{cite book
			\| last = Frank
			\| first = Joachim
			\| authorlink = Joachim Frank
			\| title = Three-Dimnsional Electron Microscopy of Macromolecular Assemblies
			\| publisher = [[Oxford University Press]]
			\| location = New York
			\| year = 2006
			\| pages =
			\| isbn = 0-19-518218-9 }}
			*{{cite journal
			\| title=Fourier shell correlation threshold criteria
			\| journal=Journal of Structural Biology
			\| year= 2005
			\| last= van Heel
			\| first= M.
			\| coauthors = Schatz, M.
			\| volume=151
			\| pages=250–262
			\| doi=10.1016/j.jsb.2005.05.009
			\| pmid=16125414
			\| issue=3 }}
			</div>

			[[Category:Applied mathematics]]
			[[Category:Engineering ratios]]
			[[Category:Measurement]]
			[[Category:Microscopes]]


			{{mathapplied-stub}}

en>Typometer: /* The Atiyah-Singer-Dirac Operator */

2012-08-27T23:16:47Z

The Atiyah-Singer-Dirac Operator

New page

Zula is the she's called and her husband doesn't like it at the only thing. What me and my family love usually play rock and roll but I am have the time lately. Invoicing is his day job now but his promotion never relates. Virginia is where her home is. He is running and maintaining a blog here: http://Www.vimeo.com/104813619<br><br>Also visit my weblog [http://Www.vimeo.com/104813619 anna kendrick nude]

← Older revision		Revision as of 18:12, 4 May 2014
Line 1:		Line 1:
	~~In [[applied mathematics]]~~, ~~the two-dimensional '''Spectral [[signal-~~to~~-noise ratio]]''' (SSNR) measures the normalised cross-correlation coefficient between several two-dimensional images over corresponding rings~~ in ~~Fourier space as a function of spatial frequency {{harv\|Unser\|1987}}~~. ~~It is a multi-particle extension of the Fourier ring correlation (FRC), which is related to the [[Fourier shell correlation]]~~. ~~The SSNR is a popular method~~ for ~~finding the resolution of~~ a ~~class average in~~ [~~[cryo-electron microscopy]]~~.		Nice to meet up with you, my identify is Ricky Nee. What I adore performing is to enjoy golfing and I would in no way give it up. I have generally loved dwelling in Illinois. Booking holiday seasons has been my working day occupation for a while. I am managing and [http://Search.usa.gov/search?query=maintaining maintaining] a web site below: http://www.ceeh.es/includes/src/_notes/nike-air-max-fly.cfm<br><br>Feel free to visit my webpage: [http://www.ceeh.es/includes/src/_notes/nike-air-max-fly.cfm Nike Air Max 2012]

	=~~= Calculation ==~~

	:~~<math>~~
	~~SSNR (r)~~
	=
	~~\frac{\displaystyle\sum_{r_i \in R}\left\|\sum_{k_i}{ F_{r_i,k} }\right\|^2}~~
	~~{\displaystyle \frac{K}{K-1} \sum_{r_i \in R}\sum_{k_i}{ \left\|{ F_{r_i,k} - \bar{F}_{r_i}}\right\|^2}} -1~~
	</~~math>~~
	<!--
	~~:<math>~~
	=
	~~\frac{\displaystyle\sum_{r_i \in R}\left\|\sum_{k_i}{ F_{r_i,k} }\right\|^2}~~
	~~{\displaystyle \frac{K}{K~~-~~1} \sum_{r_i \in R}~~
	~~\left\| \sum_{k_i}F^2_{r_i,k} - \frac{1}{K}\left(\sum_{k_i}F_{r_i,k}\right)^2 \right\|}~~
	<~~/math>~~
	-->

	~~where~~ <~~math~~>~~F_{r_i,k}</math> is the complex structure Factor for image k for a pixel <math>r_i</math> at radius <math>R</math>. It is possible convert the SSNR into an equivalent FRC using the following formula~~:

	:~~<math>~~
	~~FRC = \frac{SSNR}{SSNR + 1}~~
	</~~math>~~

	~~== See also ==~~
	* [[Resolution (electron density)]]
	* [[Fourier shell correlation]]

	~~== Notes ==~~
	~~{{reflist\|2}}~~

	~~== References ==~~
	~~<div class="references-small">~~
	*{{cite journal
	~~\| last = Unser~~
	~~\| first = M~~.
	~~\| coauthors = Trus, B~~.~~L.; Steven, A.C.~~
	~~\| title = A New Resolution Criterion Based on Spectral Signal-To-Noise Ratios~~
	~~\| journal = Ultramicroscopy~~
	~~\| volume = 23~~
	~~\| issue = 1~~
	~~\| pages = 39–51~~
	~~\| doi=10.1016~~/~~0304-3991(87)90225-7~~
	~~\| year = 1987~~
	~~\| pmid=3660491}}~~
	*{{cite journal
	~~\| last = Harauz~~
	~~\| first = G.~~
	~~\| coauthors = M. van Heel~~
	~~\| title = Exact filters for general geometry three dimensional reconstruction~~
	~~\| journal = Optik~~
	~~\| volume = 73~~
	~~\| pages = 146–156~~
	~~\| year = 1986}}~~
	*{{cite journal
	~~\| last = van Heel~~
	~~\| first = M.~~
	~~\| title = Detection of objects in quantum-noise limited images~~
	~~\| journal = Ultramicroscopy~~
	~~\| volume = 8~~
	~~\| pages = 331–342~~
	~~\| year = 1982}}~~
	*{{cite journal
	~~\| last = Saxton~~
	~~\| first = W.O.~~
	~~\| coauthors = W. Baumeister~~
	~~\| title = The correlation averaging of a regularly arranged bacterial cell envelope protein~~
	~~\| journal = J Microscopy~~
	~~\| volume = 127~~
	~~\| pages = 127–138~~
	~~\| year = 1982~~
	~~\| doi=10.1111~~/~~j.1365-2818.1982.tb00405.x}}~~
	*{{cite journal
	~~\| last = Böttcher~~
	~~\| first = B.~~
	~~\| coauthors = Wynne, S.A.; Crowther, R.A.~~
	~~\| title = Determination of the fold of the core protein of hepatitis B virus by electron microscopy~~
	~~\| journal = Nature~~
	~~\| volume = 386~~
	~~\| pages = 88–91~~
	~~\| doi=10.1038~~/~~386088a0~~
	~~\| year = 1997~~
	~~\| pmid = 9052786~~
	~~\| issue = 6620}}~~
	*{{cite book
	~~\| last = Frank~~
	~~\| first = Joachim~~
	~~\| authorlink = Joachim Frank~~
	~~\| title = Three-Dimnsional Electron Microscopy of Macromolecular Assemblies~~
	~~\| publisher = [[Oxford University Press]]~~
	~~\| location = New York~~
	~~\| year = 2006~~
	~~\| pages =~~
	~~\| isbn = 0~~-19-~~518218~~-~~9 }}~~
	*{{cite journal
	~~\| title=Fourier shell correlation threshold criteria~~
	~~\| journal=Journal of Structural Biology~~
	~~\| year= 2005~~
	~~\| last= van Heel~~
	~~\| first= M.~~
	~~\| coauthors = Schatz, M~~.
	~~\| volume=151~~
	~~\| pages=250–262~~
	~~\| doi=10.1016/j.jsb.2005.05.009~~
	~~\| pmid=16125414~~
	~~\| issue=3 }}~~
	~~</div>~~

	~~[[Category:Applied mathematics]~~]
	~~[[Category:Engineering ratios]]~~
	~~[[Category:Measurement]]~~
	~~[[Category:Microscopes]]~~


	~~{{mathapplied-stub}}~~