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I have a simple question, but it is hard to google it. I have this equation here:

$$y(t, x) = \sum_{i=1}^{d}(|x_i| \wedge t)^{2} $$

Here $x$ is a size $d$ signal and $t$ is just a scalar. I am not sure how to read that equation in english... I understand everything except for how they use the $\wedge$ here...

If context helps, this is part of a cost function, based on a threshold $t$ that is selected, for your vector $x$.

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    $\begingroup$ It probably means the minimum of $|x_i|$ and $t$. $\endgroup$
    – user1551
    Jan 25, 2013 at 3:12
  • $\begingroup$ @user1551 Are you sure about that? If it helps, "t" is supposed to signify a threshold value, and $x(i)$ is just some sample from a d-length vector. $\endgroup$
    – Spacey
    Jan 25, 2013 at 3:15
  • $\begingroup$ Of course I am not sure, because I don't see why one would want to take the minimum of a spatial quantity ($|x_i|$) and a temporal quantity ($t$). Yet the wedge symbol usually has three meanings: logical conjunction, some sort of "wedge product" and the minimum function. As both $|x_i|$ and $t$ are scalars, we can rule out the first two possibilities. So the minimum function is the most plausible explanation I can think of. $\endgroup$
    – user1551
    Jan 25, 2013 at 3:28
  • $\begingroup$ @user1551 I didnt mean for my comment to come off as rude, far from it. I only meant to ask for further insight. The $t$ btw is not a temporal quantity, it is just a threshold. (I edited the question). Based on what you are saying, this means "take the sum of squares of whatever is minimum between x(i) and t" correct? $\endgroup$
    – Spacey
    Jan 25, 2013 at 3:31
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    $\begingroup$ Yes, I mean $(|x_i|\wedge t)\equiv\min(|x_i|,t)$. $\endgroup$
    – user1551
    Jan 25, 2013 at 3:32

1 Answer 1

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$|x_i|\wedge t$ probably means $\min(|x_i|,t)$.

There are three usual meanings of the wedge ($\wedge$) symbol: logical conjunction, some sort of "wedge product" and the minimum function. As both $|x_i|$ and $t$ are scalars, we can rule out the first two possibilities. So the minimum function is the most plausible interpretation I can think of. But certainly, you should look at the context of your equation to make sure that this is a correct interpretation.

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