Photon Calculator - Revision history

imported>Projects221: Redirected page to Lin

2013-03-19T04:50:17Z

Redirected page to Lin

← Older revision		Revision as of 04:50, 19 March 2013
Line 1:		Line 1:
	~~Back to~~ [[~~Psych221-Projects-2013 \|Psych 221 Projects 2013~~]]		#REDIRECT [[Lin]]

	~~<br>~~

	~~= Background =~~

	~~You can use subsections if you like.~~
	Below is an example of a retinotopic map. Or, to be precise, below ''will'' be an example of a retinotopic map once the image is uploaded. To add an image, simply put text like this inside double brackets 'MyFile.jpg \| My figure caption'. When you save this text and click on the link, the wiki will ask you for the figure.
	~~<br>~~
	~~[[File:Example.jpg \| Figure 1]]~~

	~~Below is another example of a reinotopic map in a different subject.~~
	~~<br>~~
	~~[[File:Example2.jpg \| Figure 2]]~~

	~~Once you upload the images, they look like this. Note that you can control many features of the images, like whether to show a thumbnail, and the display resolution.~~
	~~[[File:Example3.jpg \|thumb\|300px\|center\| Figure 3]]~~
	~~<br>~~

	~~== MNI space ==~~

	~~MNI is an abbreviation for [http://en.wikipedia.org/wiki/Montreal_Neurological_Institute Montreal Neurological Institute].~~

	~~= Methods =~~
	~~== Measuring retinotopic maps ==~~
	Retinotopic maps were obtained in 5 subjects using Population Receptive Field mapping methods [http://white.stanford.edu/~brian/papers/mri/2007-Dumoulin-NI.pdf Dumoulin and Wandell (2008)]. These data were collected for another [http://www.journalofvision.org/9/8/768/ research project] in the Wandell lab. We re-analyzed the data for this project, as described below.

	~~=== Subjects ===~~
	~~Subjects were 5 healthy volunteers.~~

	~~=== MR acquisition ===~~
	~~Data were obtained on a GE scanner. Et cetera.~~

	~~=== MR Analysis ===~~
	~~The MR data was analyzed using [http://white.stanford.edu/newlm/index.php/MrVista mrVista] software tools.~~

	~~==== Pre-processing ====~~
	~~All data were slice-time corrected, motion corrected, and repeated scans were averaged together to create a single average scan for each subject. Et cetera.~~

	~~==== PRF model fits ====~~
	~~PRF models were fit with a 2-gaussian model.~~

	~~==== MNI space ====~~
	After a pRF model was solved for each subject, the model was trasnformed into MNI template space. This was done by first aligning the high resolution t1-weighted anatomical scan from each subject to an MNI template. Since the pRF model was coregistered to the t1-anatomical scan, the same alignment matrix could then be applied to the pRF model. <br>
	~~Once each pRF model was aligned to MNI space, 4 model parameters - x, y, sigma, and r^2 - were averaged across each of the 6 subjects in each voxel.~~

	~~Et cetera.~~


	~~= Results - What you found =~~

	~~== Retinotopic models in native space ==~~
	~~Some text. Some analysis. Some figures.~~

	~~== Retinotopic models in individual subjects transformed into MNI space ==~~
	~~Some text. Some analysis. Some figures.~~

	~~== Retinotopic models in group-averaged data on the MNI template brain ==~~
	~~Some text. Some analysis. Some figures. Maybe some equations.~~


	~~=== Equations===~~
	~~If you want to use equations, you can use the same formats that are use on wikipedia. <br>~~
	~~''See wikimedia help on [http://meta.wikimedia.org/wiki/Help:Displaying_a_formula formulas] for help.'' <br>~~
	~~This example of equation use is copied and pasted from [http://en.wikipedia.org/wiki/Discrete_Fourier_transform wikipedia's article on the DFT].~~

	The [[sequence]] of ''N'' [[complex number]]s ''x''<sub>0</sub>, ..., ''x''<sub>''N''−1</sub> is transformed into the sequence of ''N'' complex numbers ''X''<sub>0</sub>, ..., ''X''<sub>''N''−1</sub> by the DFT according to the formula:

	~~:<math>X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2 \pi i}{N} k n} \quad \quad k = 0, \dots, N-1</math>~~

	where i is the imaginary unit and <math>e^{\frac{2 \pi i}{N}}</math> is a primitive N'th [[root of unity]]. (This expression can also be written in terms of a [[DFT matrix]]; when scaled appropriately it becomes a [[unitary matrix]] and the ''X''<sub>''k''</sub> can thus be viewed as coefficients of ''x'' in an [[orthonormal basis]].)

	The transform is sometimes denoted by the symbol <math>\mathcal{F}</math>, as in <math>\mathbf{X} = \mathcal{F} \left \{ \mathbf{x} \right \} </math> or <math>\mathcal{F} \left ( \mathbf{x} \right )</math> or <math>\mathcal{F} \mathbf{x}</math>.

	~~The '''inverse discrete Fourier transform (IDFT)''' is given by~~

	~~:<math>x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k e^{\frac{2\pi i}{N} k n} \quad \quad n = 0,\dots,N-1.</math>~~

	~~== Retinotopic models in group-averaged data projected back into native space ==~~
	~~Some text. Some analysis. Some figures.~~


	~~= Conclusions =~~

	~~Here is where you say what your results mean.~~

	~~= References - Resources and related work =~~

	~~References~~

	~~Software~~

	~~= Appendix I - Code and Data =~~

	~~==Code==~~
	~~[[File:CodeFile.zip]]~~

	~~==Data==~~
	~~[[File:DataFile.zip \| zip file with my data]]~~

	~~= Appendix II - Work partition (if a group project) =~~
	~~Brian and Bob gave the lectures. Jon mucked around on the wiki.~~

imported>Projects221 at 00:26, 8 March 2013

2013-03-08T00:26:54Z

← Older revision		Revision as of 00:26, 8 March 2013
Line 1:		Line 1:
	Back to [[Psych221-Projects-2013 \|Psych 221 Projects 2013]]		Back to [[Psych221-Projects-2013 \|Psych 221 Projects 2013]]



	<br>		<br>


	= Background =		= Background =

imported>Projects221: Created page with 'Back to Psych 221 Projects 2013
= Background = You can use subsections if you like. Below is an example of a retinotopic map. Or, to be p…'

2013-03-08T00:26:38Z

Created page with 'Back to Psych 221 Projects 2013 = Background = You can use subsections if you like. Below is an example of a retinotopic map. Or, to be p…'

New page

Back to [[Psych221-Projects-2013 |Psych 221 Projects 2013]]

 

= Background =

You can use subsections if you like.
Below is an example of a retinotopic map. Or, to be precise, below ''will'' be an example of a retinotopic map once the image is uploaded. To add an image, simply put text like this inside double brackets 'MyFile.jpg | My figure caption'. When you save this text and click on the link, the wiki will ask you for the figure.
 
[[File:Example.jpg | Figure 1]]

Below is another example of a reinotopic map in a different subject.
 
[[File:Example2.jpg | Figure 2]]

Once you upload the images, they look like this. Note that you can control many features of the images, like whether to show a thumbnail, and the display resolution.
[[File:Example3.jpg |thumb|300px|center| Figure 3]]
 

== MNI space ==

MNI is an abbreviation for [http://en.wikipedia.org/wiki/Montreal_Neurological_Institute Montreal Neurological Institute].

= Methods =
== Measuring retinotopic maps ==
Retinotopic maps were obtained in 5 subjects using Population Receptive Field mapping methods [http://white.stanford.edu/~brian/papers/mri/2007-Dumoulin-NI.pdf Dumoulin and Wandell (2008)]. These data were collected for another [http://www.journalofvision.org/9/8/768/ research project] in the Wandell lab. We re-analyzed the data for this project, as described below.

=== Subjects ===
Subjects were 5 healthy volunteers.

=== MR acquisition ===
Data were obtained on a GE scanner. Et cetera.

=== MR Analysis ===
The MR data was analyzed using [http://white.stanford.edu/newlm/index.php/MrVista mrVista] software tools.

==== Pre-processing ====
All data were slice-time corrected, motion corrected, and repeated scans were averaged together to create a single average scan for each subject. Et cetera.

==== PRF model fits ====
PRF models were fit with a 2-gaussian model.

==== MNI space ====
After a pRF model was solved for each subject, the model was trasnformed into MNI template space. This was done by first aligning the high resolution t1-weighted anatomical scan from each subject to an MNI template. Since the pRF model was coregistered to the t1-anatomical scan, the same alignment matrix could then be applied to the pRF model. 
Once each pRF model was aligned to MNI space, 4 model parameters - x, y, sigma, and r^2 - were averaged across each of the 6 subjects in each voxel.

Et cetera.

= Results - What you found =

== Retinotopic models in native space ==
Some text. Some analysis. Some figures.

== Retinotopic models in individual subjects transformed into MNI space ==
Some text. Some analysis. Some figures.

== Retinotopic models in group-averaged data on the MNI template brain ==
Some text. Some analysis. Some figures. Maybe some equations.

=== Equations===
If you want to use equations, you can use the same formats that are use on wikipedia. 
''See wikimedia help on [http://meta.wikimedia.org/wiki/Help:Displaying_a_formula formulas] for help.'' 
This example of equation use is copied and pasted from [http://en.wikipedia.org/wiki/Discrete_Fourier_transform wikipedia's article on the DFT].

The [[sequence]] of ''N'' [[complex number]]s ''x''0, ..., ''x''''N''−1 is transformed into the sequence of ''N'' complex numbers ''X''0, ..., ''X''''N''−1 by the DFT according to the formula:

:<math>X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2 \pi i}{N} k n} \quad \quad k = 0, \dots, N-1</math>

where i is the imaginary unit and <math>e^{\frac{2 \pi i}{N}}</math> is a primitive N'th [[root of unity]]. (This expression can also be written in terms of a [[DFT matrix]]; when scaled appropriately it becomes a [[unitary matrix]] and the ''X''''k'' can thus be viewed as coefficients of ''x'' in an [[orthonormal basis]].)

The transform is sometimes denoted by the symbol <math>\mathcal{F}</math>, as in <math>\mathbf{X} = \mathcal{F} \left \{ \mathbf{x} \right \} </math> or <math>\mathcal{F} \left ( \mathbf{x} \right )</math> or <math>\mathcal{F} \mathbf{x}</math>.

The '''inverse discrete Fourier transform (IDFT)''' is given by

:<math>x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k e^{\frac{2\pi i}{N} k n} \quad \quad n = 0,\dots,N-1.</math>

== Retinotopic models in group-averaged data projected back into native space ==
Some text. Some analysis. Some figures.

= Conclusions =

Here is where you say what your results mean.

= References - Resources and related work =

References

Software

= Appendix I - Code and Data =

==Code==
[[File:CodeFile.zip]]

==Data==
[[File:DataFile.zip | zip file with my data]]

= Appendix II - Work partition (if a group project) =
Brian and Bob gave the lectures. Jon mucked around on the wiki.

Photon Calculator - Revision history

imported>Projects221: Redirected page to Lin

imported>Projects221 at 00:26, 8 March 2013

imported>Projects221: Created page with 'Back to Psych 221 Projects 2013 = Background = You can use subsections if you like. Below is an example of a retinotopic map. Or, to be p…'

imported>Projects221: Created page with 'Back to Psych 221 Projects 2013
= Background = You can use subsections if you like. Below is an example of a retinotopic map. Or, to be p…'