I'm following this paper and came across some notation that I don't know; I've tried a number of queries such as "power to the plus", "plus exponent" etc but can't seem to find anything:

From page 4:

$\text{sign}(\beta_j)(|\beta_j| - \gamma)^+$

The "$+$" exponent is what I'm confused about.

  • $\begingroup$ Did you try looking up the paper by Donoho and Johnstone? They seem to get similar results in a different context based on what the authors suggested. Maybe what $^+$ means will be more clear there. $\endgroup$ Jul 29 '13 at 19:48
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    $\begingroup$ Great question. A good example of why authors should take steps to define all but the most standard notation... $\endgroup$
    – user7530
    Jul 29 '13 at 19:48
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    $\begingroup$ I think the definition is $a^{+}:=max\{0,a\}$. $\endgroup$
    – OR.
    Jul 29 '13 at 20:16
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    $\begingroup$ I love it. "The solutions... are easily shown to be [insert domain-specific or sparsely-defined notation here]." $\endgroup$
    – Emily
    Jul 29 '13 at 20:22

The notations $f^+$ and $f^-$ for (real valued) functions and constants denote what RGB hints at the positive and negative part, respectively.

In detail $f^+ = \max \{0, f\}$ and $f^- = - \min \{0, f \}$, so that $f = f^+ - f^-$.

See the wikipedia page Positive and negative parts.


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