<p>What they mean is that as long as you rotate $C_i$ and $C_j$ by the same amount, the dot product will be the same.  This is rotational invariance because the dot product is invariant to coherent rotation of the relevant vectors.  </p>

<p>In neural terms, the correlation between the activity of two neurons (in a population representing a one dimensional circular variable) is a function of the difference in their preferred orientations and does not depend on the absolute direction of their orientations.</p>

CC BY-SA 3.0
2015-12-02T12:58:18.937Z
Got it. Thank you for your answer!
MathBgu
CC BY-SA 3.0
2015-11-22T18:16:04.690Z
2015-11-22T18:16:04.690Z
honi
<p>Is anyone familiar with <a href="ftp://ftp.cnl.salk.edu/pub/emilio/papers/cricket.pdf" rel="nofollow">this</a> article?</p>

<p>I am reading it, and it is basically very clear.
But still, some points are not clear to me.</p>

<p>For example, how is equation (7.1) in page 12:</p>

<blockquote>
  <p>$Q_{i,j}^{-1} = F(\overline C_i \overline C_j)$</p>
</blockquote>

<p>It it said there that </p>

<blockquote>
  <p>"<em>By rotational invariance, the correlation matrix element $Q_{i,j}$ and the corresponding inverse element $Q_{i,j}^{-1}$ can only depend on $\overline C_i \cdot \overline C_j$</em>".</p>
</blockquote>

<p>Does anyone here, by any chance, know what is "rotational invariance"?</p>

<p>Thank you!</p>

<theoretical-neuroscience><computational-modeling>
The article "Vector reconstruction from Firing Rates" of Abbott and Salinas
MathBgu
# The article "Vector reconstruction from Firing Rates" of Abbott and Salinas

(Asked by: username_0 on 2015-11-22)

Is anyone familiar with [this](ftp://ftp.cnl.salk.edu/pub/emilio/papers/cricket.pdf) article?

I am reading it, and it is basically very clear.
But still, some points are not clear to me.

For example, how is equation (7.1) in page 12:

> $Q\_{i,j}^{-1} = F(\overline C\_i \overline C\_j)$

It it said there that

> "*By rotational invariance, the correlation matrix element $Q\_{i,j}$ and the corresponding inverse element $Q\_{i,j}^{-1}$ can only depend on $\overline C\_i \cdot \overline C\_j$*".

Does anyone here, by any chance, know what is "rotational invariance"?

Thank you!

**Tags:** theoretical-neuroscience, computational-modeling


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## 1 answers

### Answer by username_1 on 2015-11-22. Score: 2 | Accepted answer

What they mean is that as long as you rotate $C\_i$ and $C\_j$ by the same amount, the dot product will be the same. This is rotational invariance because the dot product is invariant to coherent rotation of the relevant vectors.

In neural terms, the correlation between the activity of two neurons (in a population representing a one dimensional circular variable) is a function of the difference in their preferred orientations and does not depend on the absolute direction of their orientations.

> **Comments:**
> **username_0**: Got it. Thank you for your answer!  

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