Model for Z

[DSP137]

I've been trying to wrap my mind around how to create a potential model for Z and potential structure for \rho(z) and \B(z); however, I'm not sure how to do this. I understand that (if we are not assuming independence) \rho(z) and \B(z) will depend on the model for Z, but I'm not sure what kind of models would be appropriate, nor am I sure how to modify \rho(z) and \B(z) in any meaningful way. Suggestions? Thoughts?

[dlee138]

Have you found a potential model for Z yet? From last class we discussed the sample space for the Bock paper, and the directional (orientation) component was 1-8. I'm assuming a discrete model instead of a continuous one (such as 0-2pi) is the right direction, as discussed last class. I think 8 though, isn't a magic number we have to use for the model though. What do you think?

[jtmatterer]

Having \rho and B depend on Z does not give us what we want. Since \rho and B are used for the connectivity of the entire graph, irrespective of the vertices' configuration preference, such a model would not be able to distinguish a dependency between orientation and connections between two excitatory neurons and an inhibatory one. So, essentially, it's not surprising that you're having difficulty relating \rho and B to Z..

[DSP137]

@dlee138 I think that we could use other numbers. I recall that 8 were used in the Bock paper, but someone else in class mentioned potentially using 36. So I think you are right that 8 is not a magic number.

[DSP137]

Thanks @kurtosis312, that helps. I'm glad this is difficult for a good reason.

[whock]

I'm a little confused about how rho and B depending on Z affects the whole graph. I interpreted the hw as wanting to find some rationale for how the different orientations (members of Z) have different probabilities. I found a few papers basically saying not all orientations are equally preferred; there's something called the oblique effect where vertical/horizontal orientations have more machinery devoted to them than do oblique angles. So I basically built my model and probability distributions around that fact. But after @kurtosis312 's answer I'm thinking I have something a little confused. Can anyone explain this a bit more? Thanks.

Anyway here are some papers on the oblique effect and the idea of preferred angles:

1. Mach, E. 1861 Ueber das Sehen von Lagen und Winkeln durch die Bewegung des Auges. Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften, Wien 43(2), 215-224
2. Appelle S. 1972 Perception and discrimination as function of stimulus orientation. Psychological Bulletin 78,266-278.
3. Yacoub, E., & Harel, N., & Ugurbil, K. (2008). High-Field fMRI unveils orientation columns in humans. [Article]. Proc Natl Acad Sci, 105, 10607-10612.